LMFDB - Embedded newform 216.3.p.b.19.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [216,3,Mod(19,216)]

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([3, 3, 4]))

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

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

chi := DirichletCharacter("216.19");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 216 = 2^{3} \cdot 3^{3} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	216.p (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:	$40$
Relative dimension:	$20$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 72)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			19.15
Character	$\chi$	$=$	216.19
Dual form			216.3.p.b.91.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.49437 + 1.32923i) q^{2} +(0.466308 + 3.97273i) q^{4} +(5.84790 - 3.37629i) q^{5} +(3.50808 + 2.02539i) q^{7} +(-4.58382 + 6.55657i) q^{8} +O(q^{10})$	\(q+(1.49437 + 1.32923i) q^{2} +(0.466308 + 3.97273i) q^{4} +(5.84790 - 3.37629i) q^{5} +(3.50808 + 2.02539i) q^{7} +(-4.58382 + 6.55657i) q^{8} +(13.2268 + 2.72775i) q^{10} +(4.13813 - 7.16745i) q^{11} +(-7.66384 + 4.42472i) q^{13} +(2.55018 + 7.68973i) q^{14} +(-15.5651 + 3.70503i) q^{16} +28.6444 q^{17} -7.93157 q^{19} +(16.1400 + 21.6577i) q^{20} +(15.7111 - 5.21034i) q^{22} +(-25.3249 + 14.6213i) q^{23} +(10.2986 - 17.8377i) q^{25} +(-17.3341 - 3.57480i) q^{26} +(-6.41048 + 14.8811i) q^{28} +(15.7389 + 9.08688i) q^{29} +(-40.8693 + 23.5959i) q^{31} +(-28.1849 - 15.1529i) q^{32} +(42.8054 + 38.0749i) q^{34} +27.3532 q^{35} -13.3240i q^{37} +(-11.8527 - 10.5429i) q^{38} +(-4.66886 + 53.8185i) q^{40} +(-31.0200 - 53.7281i) q^{41} +(26.5751 - 46.0295i) q^{43} +(30.4040 + 13.0974i) q^{44} +(-57.2799 - 11.8128i) q^{46} +(-12.8771 - 7.43458i) q^{47} +(-16.2956 - 28.2248i) q^{49} +(39.1004 - 12.9670i) q^{50} +(-21.1519 - 28.3831i) q^{52} -100.342i q^{53} -55.8861i q^{55} +(-29.3600 + 13.7169i) q^{56} +(11.4413 + 34.4998i) q^{58} +(11.4945 + 19.9091i) q^{59} +(51.3643 + 29.6552i) q^{61} +(-92.4384 - 19.0635i) q^{62} +(-21.9772 - 60.1083i) q^{64} +(-29.8783 + 51.7507i) q^{65} +(10.3633 + 17.9498i) q^{67} +(13.3571 + 113.796i) q^{68} +(40.8759 + 36.3586i) q^{70} +54.7853i q^{71} -27.3316 q^{73} +(17.7107 - 19.9111i) q^{74} +(-3.69856 - 31.5100i) q^{76} +(29.0338 - 16.7627i) q^{77} +(-62.9562 - 36.3478i) q^{79} +(-78.5140 + 74.2189i) q^{80} +(25.0615 - 121.523i) q^{82} +(-4.34758 + 7.53022i) q^{83} +(167.509 - 96.7116i) q^{85} +(100.897 - 33.4609i) q^{86} +(28.0255 + 59.9862i) q^{88} +28.2957 q^{89} -35.8472 q^{91} +(-69.8957 - 93.7907i) q^{92} +(-9.36091 - 28.2266i) q^{94} +(-46.3831 + 26.7793i) q^{95} +(-0.200924 + 0.348010i) q^{97} +(13.1655 - 63.8389i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	$ 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) $ 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$55$	$109$	$137$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.49437	+	1.32923i	0.747187	+	0.664614i
$2$	1.49437	+	1.32923i	0.747187	+	0.664614i
$3$		0			0
$3$		0			0
$4$	0.466308	+	3.97273i	0.116577	+	0.993182i
$5$	5.84790	−	3.37629i	1.16958	−	0.675257i	0.215999	−	0.976394i	$-0.430699\pi$
$5$	5.84790	−	3.37629i	1.16958	−	0.675257i	0.953581	+	0.301136i	$0.0973659\pi$
$6$		0			0
$7$	3.50808	+	2.02539i	0.501154	+	0.289341i	0.729190	−	0.684311i	$-0.239897\pi$
$7$	3.50808	+	2.02539i	0.501154	+	0.289341i	−0.228036	+	0.973653i	$0.573230\pi$
$8$	−4.58382	+	6.55657i	−0.572977	+	0.819571i
$9$		0			0
$10$	13.2268	+	2.72775i	1.32268	+	0.272775i
$11$	4.13813	−	7.16745i	0.376194	−	0.651587i	−0.614311	−	0.789064i	$-0.710566\pi$
$11$	4.13813	−	7.16745i	0.376194	−	0.651587i	0.990505	+	0.137477i	$0.0438994\pi$
$12$		0			0
$13$	−7.66384	+	4.42472i	−0.589527	+	0.340363i	−0.764910	−	0.644137i	$-0.777217\pi$
$13$	−7.66384	+	4.42472i	−0.589527	+	0.340363i	0.175384	+	0.984500i	$0.443883\pi$
$14$	2.55018	+	7.68973i	0.182156	+	0.549266i
$15$		0			0
$16$	−15.5651	+	3.70503i	−0.972820	+	0.231564i
$17$	28.6444			1.68496			0.842481	−	0.538725i	$-0.181094\pi$
$17$	28.6444			1.68496			0.842481	+	0.538725i	$0.181094\pi$
$18$		0			0
$19$	−7.93157			−0.417451			−0.208726	−	0.977974i	$-0.566932\pi$
$19$	−7.93157			−0.417451			−0.208726	+	0.977974i	$0.566932\pi$
$20$	16.1400	+	21.6577i	0.806999	+	1.08289i
$21$		0			0
$22$	15.7111	−	5.21034i	0.714140	−	0.236834i
$23$	−25.3249	+	14.6213i	−1.10108	+	0.635709i	−0.936505	−	0.350655i	$-0.885959\pi$
$23$	−25.3249	+	14.6213i	−1.10108	+	0.635709i	−0.164576	+	0.986364i	$0.552626\pi$
$24$		0			0
$25$	10.2986	−	17.8377i	0.411945	−	0.713510i
$26$	−17.3341	−	3.57480i	−0.666697	−	0.137492i
$27$		0			0
$28$	−6.41048	+	14.8811i	−0.228946	+	0.531468i
$29$	15.7389	+	9.08688i	0.542722	+	0.313341i	0.746181	−	0.665743i	$-0.231885\pi$
$29$	15.7389	+	9.08688i	0.542722	+	0.313341i	−0.203459	+	0.979083i	$0.565218\pi$
$30$		0			0
$31$	−40.8693	+	23.5959i	−1.31837	+	0.761159i	−0.983466	−	0.181095i	$-0.942036\pi$
$31$	−40.8693	+	23.5959i	−1.31837	+	0.761159i	−0.334900	+	0.942254i	$0.608702\pi$
$32$	−28.1849	−	15.1529i	−0.880779	−	0.473527i
$33$		0			0
$34$	42.8054	+	38.0749i	1.25898	+	1.11985i
$35$	27.3532			0.781520
$36$		0			0
$37$		−	13.3240i		−	0.360109i	−0.983657	−	0.180054i	$-0.942373\pi$
$37$		−	13.3240i		−	0.360109i	0.983657	−	0.180054i	$-0.0576274\pi$
$38$	−11.8527	−	10.5429i	−0.311914	−	0.277444i
$39$		0			0
$40$	−4.66886	+	53.8185i	−0.116721	+	1.34546i
$41$	−31.0200	−	53.7281i	−0.756584	−	1.31044i	−0.944583	−	0.328273i	$-0.893533\pi$
$41$	−31.0200	−	53.7281i	−0.756584	−	1.31044i	0.187998	−	0.982169i	$-0.439800\pi$
$42$		0			0
$43$	26.5751	−	46.0295i	0.618027	−	1.07045i	−0.371819	−	0.928305i	$-0.621266\pi$
$43$	26.5751	−	46.0295i	0.618027	−	1.07045i	0.989845	−	0.142148i	$-0.0454010\pi$
$44$	30.4040	+	13.0974i	0.690999	+	0.297669i
$45$		0			0
$46$	−57.2799	−	11.8128i	−1.24521	−	0.256800i
$47$	−12.8771	−	7.43458i	−0.273980	−	0.158183i	0.356715	−	0.934213i	$-0.383897\pi$
$47$	−12.8771	−	7.43458i	−0.273980	−	0.158183i	−0.630695	+	0.776031i	$0.717230\pi$
$48$		0			0
$49$	−16.2956	−	28.2248i	−0.332563	−	0.576016i
$50$	39.1004	−	12.9670i	0.782008	−	0.259341i
$51$		0			0
$52$	−21.1519	−	28.3831i	−0.406768	−	0.545828i
$53$		−	100.342i		−	1.89325i	−0.322339	−	0.946624i	$-0.604469\pi$
$53$		−	100.342i		−	1.89325i	0.322339	−	0.946624i	$-0.395531\pi$
$54$		0			0
$55$		−	55.8861i		−	1.01611i
$56$	−29.3600	+	13.7169i	−0.524286	+	0.244945i
$57$		0			0
$58$	11.4413	+	34.4998i	0.197264	+	0.594825i
$59$	11.4945	+	19.9091i	0.194823	+	0.337443i	0.946842	−	0.321698i	$-0.104254\pi$
$59$	11.4945	+	19.9091i	0.194823	+	0.337443i	−0.752020	+	0.659141i	$0.770920\pi$
$60$		0			0
$61$	51.3643	+	29.6552i	0.842038	+	0.486151i	0.857957	−	0.513722i	$-0.171734\pi$
$61$	51.3643	+	29.6552i	0.842038	+	0.486151i	−0.0159181	+	0.999873i	$0.505067\pi$
$62$	−92.4384	−	19.0635i	−1.49094	−	0.307476i
$63$		0			0
$64$	−21.9772	−	60.1083i	−0.343394	−	0.939191i
$65$	−29.8783	+	51.7507i	−0.459666	+	0.796164i
$66$		0			0
$67$	10.3633	+	17.9498i	0.154677	+	0.267908i	0.932941	−	0.360029i	$-0.117233\pi$
$67$	10.3633	+	17.9498i	0.154677	+	0.267908i	−0.778265	+	0.627936i	$0.783900\pi$
$68$	13.3571	+	113.796i	0.196428	+	1.67347i
$69$		0			0
$70$	40.8759	+	36.3586i	0.583942	+	0.519409i
$71$			54.7853i			0.771624i	0.922577	+	0.385812i	$0.126079\pi$
$71$			54.7853i			0.771624i	−0.922577	+	0.385812i	$0.873921\pi$
$72$		0			0
$73$	−27.3316			−0.374405			−0.187202	−	0.982321i	$-0.559942\pi$
$73$	−27.3316			−0.374405			−0.187202	+	0.982321i	$0.559942\pi$
$74$	17.7107	−	19.9111i	0.239333	−	0.269069i
$75$		0			0
$76$	−3.69856	−	31.5100i	−0.0486652	−	0.414605i
$77$	29.0338	−	16.7627i	0.377062	−	0.217697i
$78$		0			0
$79$	−62.9562	−	36.3478i	−0.796914	−	0.460098i	0.0454770	−	0.998965i	$-0.485519\pi$
$79$	−62.9562	−	36.3478i	−0.796914	−	0.460098i	−0.842391	+	0.538867i	$0.818853\pi$
$80$	−78.5140	+	74.2189i	−0.981425	+	0.927737i
$81$		0			0
$82$	25.0615	−	121.523i	0.305628	−	1.48198i
$83$	−4.34758	+	7.53022i	−0.0523804	+	0.0907256i	−0.891027	−	0.453951i	$-0.850014\pi$
$83$	−4.34758	+	7.53022i	−0.0523804	+	0.0907256i	0.838646	+	0.544676i	$0.183348\pi$
$84$		0			0
$85$	167.509	−	96.7116i	1.97070	−	1.13778i
$86$	100.897	−	33.4609i	1.17322	−	0.389080i
$87$		0			0
$88$	28.0255	+	59.9862i	0.318471	+	0.681662i
$89$	28.2957			0.317929			0.158965	−	0.987284i	$-0.449184\pi$
$89$	28.2957			0.317929			0.158965	+	0.987284i	$0.449184\pi$
$90$		0			0
$91$	−35.8472			−0.393925
$92$	−69.8957	−	93.7907i	−0.759736	−	1.01946i
$93$		0			0
$94$	−9.36091	−	28.2266i	−0.0995842	−	0.300283i
$95$	−46.3831	+	26.7793i	−0.488243	+	0.281887i
$96$		0			0
$97$	−0.200924	+	0.348010i	−0.00207138	+	0.00358773i	−0.867059	−	0.498205i	$-0.833993\pi$
$97$	−0.200924	+	0.348010i	−0.00207138	+	0.00358773i	0.864988	+	0.501793i	$0.167326\pi$
$98$	13.1655	−	63.8389i	0.134341	−	0.651418i
$99$		0			0
$100$	75.6668	+	32.5957i	0.756668	+	0.325957i
$101$	−59.1823	−	34.1689i	−0.585964	−	0.338306i	0.177536	−	0.984114i	$-0.443187\pi$
$101$	−59.1823	−	34.1689i	−0.585964	−	0.338306i	−0.763500	+	0.645808i	$0.776521\pi$
$102$		0			0
$103$	−155.860	+	89.9857i	−1.51320	+	0.873647i	−0.513321	+	0.858197i	$0.671585\pi$
$103$	−155.860	+	89.9857i	−1.51320	+	0.873647i	−0.999881	+	0.0154503i	$0.995082\pi$
$104$	6.11867	−	70.5307i	0.0588334	−	0.678179i
$105$		0			0
$106$	133.378	−	149.949i	1.25828	−	1.41461i
$107$	11.3024			0.105630			0.0528149	−	0.998604i	$-0.483181\pi$
$107$	11.3024			0.105630			0.0528149	+	0.998604i	$0.483181\pi$
$108$		0			0
$109$			129.193i			1.18525i	0.805477	+	0.592627i	$0.201909\pi$
$109$			129.193i			1.18525i	−0.805477	+	0.592627i	$0.798091\pi$
$110$	74.2853	−	83.5147i	0.675321	−	0.759224i
$111$		0			0
$112$	−62.1078	−	18.5279i	−0.554534	−	0.165428i
$113$	10.9016	+	18.8820i	0.0964740	+	0.167098i	0.910223	−	0.414119i	$-0.135910\pi$
$113$	10.9016	+	18.8820i	0.0964740	+	0.167098i	−0.813749	+	0.581217i	$0.802577\pi$
$114$		0			0
$115$	−98.7315	+	171.008i	−0.858535	+	1.48703i
$116$	−28.7605	+	66.7638i	−0.247935	+	0.575550i
$117$		0			0
$118$	−9.28661	+	45.0305i	−0.0787001	+	0.381615i
$119$	100.487	+	58.0160i	0.844426	+	0.487530i
$120$		0			0
$121$	26.2518	+	45.4694i	0.216957	+	0.375780i
$122$	37.3390	+	112.591i	0.306058	+	0.922876i
$123$		0			0
$124$	−112.798	−	151.360i	−0.909660	−	1.22064i
$125$			29.7299i			0.237839i
$126$		0			0
$127$		−	28.2062i		−	0.222096i	−0.993815	−	0.111048i	$-0.964579\pi$
$127$		−	28.2062i		−	0.222096i	0.993815	−	0.111048i	$-0.0354207\pi$
$128$	47.0554	−	119.037i	0.367620	−	0.929976i
$129$		0			0
$130$	−113.438	+	37.6199i	−0.872598	+	0.289383i
$131$	−97.1108	−	168.201i	−0.741304	−	1.28398i	−0.951902	−	0.306403i	$-0.900874\pi$
$131$	−97.1108	−	168.201i	−0.741304	−	1.28398i	0.210598	−	0.977573i	$-0.432459\pi$
$132$		0			0
$133$	−27.8246	−	16.0645i	−0.209207	−	0.120786i
$134$	−8.37270	+	40.5990i	−0.0624828	+	0.302978i
$135$		0			0
$136$	−131.301	+	187.809i	−0.965446	+	1.38095i
$137$	−13.0689	+	22.6361i	−0.0953937	+	0.165227i	−0.909773	−	0.415106i	$-0.863744\pi$
$137$	−13.0689	+	22.6361i	−0.0953937	+	0.165227i	0.814379	+	0.580333i	$0.197078\pi$
$138$		0			0
$139$	33.2939	+	57.6667i	0.239524	+	0.414868i	0.960578	−	0.278011i	$-0.0896752\pi$
$139$	33.2939	+	57.6667i	0.239524	+	0.414868i	−0.721054	+	0.692879i	$0.756342\pi$
$140$	12.7550	+	108.667i	0.0911073	+	0.776191i
$141$		0			0
$142$	−72.8222	+	81.8698i	−0.512832	+	0.576548i
$143$			73.2403i			0.512170i
$144$		0			0
$145$	122.720			0.846343
$146$	−40.8436	−	36.3299i	−0.279751	−	0.248835i
$147$		0			0
$148$	52.9327	−	6.21310i	0.357653	−	0.0419804i
$149$	47.6221	−	27.4947i	0.319612	−	0.184528i	−0.331608	−	0.943417i	$-0.607591\pi$
$149$	47.6221	−	27.4947i	0.319612	−	0.184528i	0.651220	+	0.758889i	$0.274258\pi$
$150$		0			0
$151$	195.247	+	112.726i	1.29302	+	0.746528i	0.979189	−	0.202949i	$-0.0650526\pi$
$151$	195.247	+	112.726i	1.29302	+	0.746528i	0.313836	+	0.949477i	$0.398386\pi$
$152$	36.3569	−	52.0039i	0.239190	−	0.342131i
$153$		0			0
$154$	65.6687	+	13.5428i	0.426420	+	0.0879403i
$155$	−159.333	+	275.973i	−1.02796	+	1.78047i
$156$		0			0
$157$	7.15183	−	4.12911i	0.0455530	−	0.0263001i	−0.477051	−	0.878876i	$-0.658294\pi$
$157$	7.15183	−	4.12911i	0.0455530	−	0.0263001i	0.522604	+	0.852576i	$0.324961\pi$
$158$	−45.7656	−	138.000i	−0.289656	−	0.873420i
$159$		0			0
$160$	−215.983	+	6.54789i	−1.34989	+	0.0409243i
$161$	−118.455			−0.735748
$162$		0			0
$163$	96.9898			0.595029			0.297515	−	0.954717i	$-0.403842\pi$
$163$	96.9898			0.595029			0.297515	+	0.954717i	$0.403842\pi$
$164$	198.982	−	148.288i	1.21331	−	0.904193i
$165$		0			0
$166$	−16.5063	+	5.47405i	−0.0994355	+	0.0329762i
$167$	−70.6764	+	40.8050i	−0.423212	+	0.244342i	−0.696451	−	0.717605i	$-0.745238\pi$
$167$	−70.6764	+	40.8050i	−0.423212	+	0.244342i	0.273239	+	0.961946i	$0.411905\pi$
$168$		0			0
$169$	−45.3437	+	78.5375i	−0.268306	+	0.464719i
$170$	378.873	+	78.1348i	2.22867	+	0.459617i
$171$		0			0
$172$	195.255	+	84.1119i	1.13520	+	0.489022i
$173$	243.592	+	140.638i	1.40805	+	0.812937i	0.995200	−	0.0978632i	$-0.0312008\pi$
$173$	243.592	+	140.638i	1.40805	+	0.812937i	0.412848	+	0.910800i	$0.364534\pi$
$174$		0			0
$175$	72.2568	−	41.7175i	0.412896	−	0.238386i
$176$	−37.8548	+	126.894i	−0.215084	+	0.720989i
$177$		0			0
$178$	42.2844	+	37.6114i	0.237553	+	0.211300i
$179$	152.063			0.849516			0.424758	−	0.905307i	$-0.360359\pi$
$179$	152.063			0.849516			0.424758	+	0.905307i	$0.360359\pi$
$180$		0			0
$181$			64.8364i			0.358212i	0.983830	+	0.179106i	$0.0573206\pi$
$181$			64.8364i			0.358212i	−0.983830	+	0.179106i	$0.942679\pi$
$182$	−53.5691	−	47.6490i	−0.294336	−	0.261808i
$183$		0			0
$184$	20.2189	−	233.066i	0.109885	−	1.26666i
$185$	−44.9857	−	77.9176i	−0.243166	−	0.421176i
$186$		0			0
$187$	118.534	−	205.307i	0.633872	−	1.09790i
$188$	23.5309	−	54.6239i	0.125164	−	0.290553i
$189$		0			0
$190$	−104.909	−	21.6354i	−0.552155	−	0.113870i
$191$	−27.8403	−	16.0736i	−0.145761	−	0.0841551i	0.425346	−	0.905031i	$-0.360152\pi$
$191$	−27.8403	−	16.0736i	−0.145761	−	0.0841551i	−0.571107	+	0.820876i	$0.693486\pi$
$192$		0			0
$193$	59.1882	+	102.517i	0.306675	+	0.531176i	0.977633	−	0.210319i	$-0.0674503\pi$
$193$	59.1882	+	102.517i	0.306675	+	0.531176i	−0.670958	+	0.741495i	$0.734117\pi$
$194$	−0.762840	+	0.252984i	−0.00393216	+	0.00130404i
$195$		0			0
$196$	104.531	−	77.8994i	0.533319	−	0.397446i
$197$			122.474i			0.621693i	0.950460	+	0.310847i	$0.100613\pi$
$197$			122.474i			0.621693i	−0.950460	+	0.310847i	$0.899387\pi$
$198$		0			0
$199$		−	194.746i		−	0.978625i	−0.872109	−	0.489312i	$-0.837248\pi$
$199$		−	194.746i		−	0.978625i	0.872109	−	0.489312i	$-0.162752\pi$
$200$	69.7474	+	149.289i	0.348737	+	0.746443i
$201$		0			0
$202$	−43.0223	−	129.728i	−0.212982	−	0.642218i
$203$	36.8090	+	63.7550i	0.181325	+	0.314064i
$204$		0			0
$205$	−362.803	−	209.465i	−1.76977	−	1.02178i
$206$	−352.524	−	72.7008i	−1.71128	−	0.352917i
$207$		0			0
$208$	102.895	−	97.2661i	0.494687	−	0.467625i
$209$	−32.8219	+	56.8492i	−0.157043	+	0.272006i
$210$		0			0
$211$	31.3850	+	54.3604i	0.148744	+	0.257632i	0.930764	−	0.365622i	$-0.119144\pi$
$211$	31.3850	+	54.3604i	0.148744	+	0.257632i	−0.782019	+	0.623254i	$0.785810\pi$
$212$	398.632	−	46.7904i	1.88034	−	0.220709i
$213$		0			0
$214$	16.8900	+	15.0234i	0.0789252	+	0.0702030i
$215$		−	358.901i		−	1.66931i
$216$		0			0
$217$	−191.164			−0.880939
$218$	−171.726	+	193.062i	−0.787736	+	0.885606i
$219$		0			0
$220$	222.020	−	26.0601i	1.00918	−	0.118455i
$221$	−219.526	+	126.743i	−0.993330	+	0.573500i
$222$		0			0
$223$	200.170	+	115.568i	0.897622	+	0.518242i	0.876428	−	0.481533i	$-0.159920\pi$
$223$	200.170	+	115.568i	0.897622	+	0.518242i	0.0211942	+	0.999775i	$0.493253\pi$
$224$	−68.1845	−	110.243i	−0.304395	−	0.492156i
$225$		0			0
$226$	−8.80754	+	42.7075i	−0.0389714	+	0.188971i
$227$	79.2191	−	137.211i	0.348983	−	0.604456i	−0.637086	−	0.770792i	$-0.719861\pi$
$227$	79.2191	−	137.211i	0.348983	−	0.604456i	0.986069	+	0.166337i	$0.0531939\pi$
$228$		0			0
$229$	3.51151	−	2.02737i	0.0153341	−	0.00885316i	−0.492313	−	0.870418i	$-0.663849\pi$
$229$	3.51151	−	2.02737i	0.0153341	−	0.00885316i	0.507647	+	0.861565i	$0.330515\pi$
$230$	−374.850	+	124.313i	−1.62978	+	0.540493i
$231$		0			0
$232$	−131.723	+	61.5409i	−0.567773	+	0.265262i
$233$	70.3318			0.301853			0.150927	−	0.988545i	$-0.451774\pi$
$233$	70.3318			0.301853			0.150927	+	0.988545i	$0.451774\pi$
$234$		0			0
$235$	−100.405			−0.427256
$236$	−73.7335	+	54.9484i	−0.312430	+	0.232832i
$237$		0			0
$238$	73.0482	+	220.267i	0.306925	+	0.925493i
$239$	140.113	−	80.8941i	0.586246	−	0.338469i	−0.177366	−	0.984145i	$-0.556758\pi$
$239$	140.113	−	80.8941i	0.586246	−	0.338469i	0.763612	+	0.645676i	$0.223424\pi$
$240$		0			0
$241$	−135.139	+	234.068i	−0.560744	+	0.971237i	0.436688	+	0.899613i	$0.356151\pi$
$241$	−135.139	+	234.068i	−0.560744	+	0.971237i	−0.997432	+	0.0716235i	$0.977182\pi$
$242$	−21.2092	+	102.843i	−0.0876413	+	0.424970i
$243$		0			0
$244$	−93.8605	+	217.885i	−0.384674	+	0.892971i
$245$	−190.590	−	110.037i	−0.777918	−	0.449131i
$246$		0			0
$247$	60.7864	−	35.0950i	0.246099	−	0.142085i
$248$	32.6293	−	376.122i	0.131570	−	1.51662i
$249$		0			0
$250$	−39.5178	+	44.4276i	−0.158071	+	0.177710i
$251$	−23.8313			−0.0949452			−0.0474726	−	0.998873i	$-0.515117\pi$
$251$	−23.8313			−0.0949452			−0.0474726	+	0.998873i	$0.515117\pi$
$252$		0			0
$253$			242.020i			0.956600i
$254$	37.4924	−	42.1506i	0.147608	−	0.165947i
$255$		0			0
$256$	228.546	−	115.338i	0.892756	−	0.450541i
$257$	93.2969	+	161.595i	0.363023	+	0.628774i	0.988457	−	0.151503i	$-0.0484113\pi$
$257$	93.2969	+	161.595i	0.363023	+	0.628774i	−0.625434	+	0.780277i	$0.715078\pi$
$258$		0			0
$259$	26.9864	−	46.7417i	0.104194	−	0.180470i
$260$	−219.524	−	94.5664i	−0.844322	−	0.363717i
$261$		0			0
$262$	78.4573	−	380.437i	0.299455	−	1.45205i
$263$	−149.060	−	86.0600i	−0.566769	−	0.327224i	0.189089	−	0.981960i	$-0.439447\pi$
$263$	−149.060	−	86.0600i	−0.566769	−	0.327224i	−0.755858	+	0.654736i	$0.772780\pi$
$264$		0			0
$265$	−338.784	−	586.791i	−1.27843	−	2.21431i
$266$	−20.2269	−	60.9916i	−0.0760411	−	0.229292i
$267$		0			0
$268$	−66.4772	+	49.5409i	−0.248049	+	0.184854i
$269$		−	89.9147i		−	0.334256i	−0.985935	−	0.167128i	$-0.946551\pi$
$269$		−	89.9147i		−	0.334256i	0.985935	−	0.167128i	$-0.0534492\pi$
$270$		0			0
$271$			112.456i			0.414965i	0.978239	+	0.207483i	$0.0665270\pi$
$271$			112.456i			0.414965i	−0.978239	+	0.207483i	$0.933473\pi$
$272$	−445.853	+	106.128i	−1.63916	+	0.390177i
$273$		0			0
$274$	−49.6184	+	16.4552i	−0.181089	+	0.0600553i
$275$	−85.2341	−	147.630i	−0.309942	−	0.536836i
$276$		0			0
$277$	−370.881	−	214.128i	−1.33892	−	0.773026i	−0.352274	−	0.935897i	$-0.614591\pi$
$277$	−370.881	−	214.128i	−1.33892	−	0.773026i	−0.986647	+	0.162871i	$0.947925\pi$
$278$	−26.8986	+	130.431i	−0.0967577	+	0.469175i
$279$		0			0
$280$	−125.382	+	179.343i	−0.447793	+	0.640511i
$281$	192.963	−	334.221i	0.686700	−	1.18940i	−0.286200	−	0.958170i	$-0.592392\pi$
$281$	192.963	−	334.221i	0.686700	−	1.18940i	0.972899	−	0.231229i	$-0.0742746\pi$
$282$		0			0
$283$	−257.657	−	446.275i	−0.910448	−	1.57694i	−0.813433	−	0.581659i	$-0.802404\pi$
$283$	−257.657	−	446.275i	−0.910448	−	1.57694i	−0.0970153	−	0.995283i	$-0.530930\pi$
$284$	−217.647	+	25.5468i	−0.766363	+	0.0899537i
$285$		0			0
$286$	−97.3531	+	109.448i	−0.340395	+	0.382687i
$287$		−	251.310i		−	0.875645i
$288$		0			0
$289$	531.500			1.83910
$290$	183.389	+	163.122i	0.632376	+	0.562491i
$291$		0			0
$292$	−12.7449	−	108.581i	−0.0436470	−	0.371852i
$293$	−88.1771	+	50.9091i	−0.300946	+	0.173751i	−0.642868	−	0.765977i	$-0.722255\pi$
$293$	−88.1771	+	50.9091i	−0.300946	+	0.173751i	0.341922	+	0.939728i	$0.388922\pi$
$294$		0			0
$295$	134.438	+	77.6177i	0.455721	+	0.263111i
$296$	87.3599	+	61.0749i	0.295135	+	0.206334i
$297$		0			0
$298$	107.712	+	22.2134i	0.361450	+	0.0745415i
$299$	129.391	−	224.111i	0.432744	−	0.749535i
$300$		0			0
$301$	186.455	−	107.650i	0.619453	−	0.357641i
$302$	141.934	+	427.982i	0.469979	+	1.41716i
$303$		0			0
$304$	123.456	−	29.3867i	0.406105	−	0.0966668i
$305$	400.498			1.31311
$306$		0			0
$307$	−265.132			−0.863623			−0.431812	−	0.901964i	$-0.642125\pi$
$307$	−265.132			−0.863623			−0.431812	+	0.901964i	$0.642125\pi$
$308$	80.1321	+	107.527i	0.260169	+	0.349113i
$309$		0			0
$310$	−604.935	+	200.617i	−1.95140	+	0.647152i
$311$	313.799	−	181.172i	1.00900	−	0.582546i	0.0981006	−	0.995177i	$-0.468723\pi$
$311$	313.799	−	181.172i	1.00900	−	0.582546i	0.910898	+	0.412631i	$0.135390\pi$
$312$		0			0
$313$	195.154	−	338.017i	0.623496	−	1.07993i	−0.365334	−	0.930877i	$-0.619045\pi$
$313$	195.154	−	338.017i	0.623496	−	1.07993i	0.988830	−	0.149050i	$-0.0476215\pi$
$314$	16.1760	+	3.33597i	0.0515160	+	0.0106241i
$315$		0			0
$316$	115.043	−	267.057i	0.364059	−	0.845117i
$317$	−259.589	−	149.874i	−0.818894	−	0.472788i	0.0311412	−	0.999515i	$-0.490086\pi$
$317$	−259.589	−	149.874i	−0.818894	−	0.472788i	−0.850035	+	0.526727i	$0.823419\pi$
$318$		0			0
$319$	130.260	−	75.2054i	0.408337	−	0.235754i
$320$	−331.463	−	277.306i	−1.03582	−	0.866580i
$321$		0			0
$322$	−177.017	−	157.454i	−0.549742	−	0.488989i
$323$	−227.195			−0.703390
$324$		0			0
$325$			182.274i			0.560844i
$326$	144.939	+	128.921i	0.444598	+	0.395465i
$327$		0			0
$328$	494.462	+	42.8956i	1.50751	+	0.130779i
$329$	−30.1159	−	52.1622i	−0.0915376	−	0.158548i
$330$		0			0
$331$	−47.4581	+	82.1998i	−0.143378	+	0.248338i	−0.928767	−	0.370665i	$-0.879130\pi$
$331$	−47.4581	+	82.1998i	−0.143378	+	0.248338i	0.785389	+	0.619003i	$0.212463\pi$
$332$	−31.9428	−	13.7603i	−0.0962133	−	0.0414468i
$333$		0			0
$334$	−159.856	−	32.9670i	−0.478611	−	0.0987037i
$335$	121.208	+	69.9792i	0.361813	+	0.208893i
$336$		0			0
$337$	207.466	+	359.342i	0.615626	+	1.06630i	0.990274	+	0.139129i	$0.0444302\pi$
$337$	207.466	+	359.342i	0.615626	+	1.06630i	−0.374648	+	0.927167i	$0.622236\pi$
$338$	−172.155	+	57.0924i	−0.509333	+	0.168912i
$339$		0			0
$340$	462.320	+	620.372i	1.35976	+	1.82462i
$341$			390.572i			1.14537i
$342$		0			0
$343$		−	330.508i		−	0.963580i
$344$	179.980	+	385.233i	0.523198	+	1.11986i
$345$		0			0
$346$	177.078	+	533.955i	0.511786	+	1.54322i
$347$	198.531	+	343.865i	0.572134	+	0.990965i	0.996347	+	0.0854026i	$0.0272177\pi$
$347$	198.531	+	343.865i	0.572134	+	0.990965i	−0.424212	+	0.905563i	$0.639449\pi$
$348$		0			0
$349$	−51.1143	−	29.5109i	−0.146459	−	0.0845584i	0.424980	−	0.905203i	$-0.360281\pi$
$349$	−51.1143	−	29.5109i	−0.146459	−	0.0845584i	−0.571439	+	0.820645i	$0.693615\pi$
$350$	163.431	+	33.7042i	0.466945	+	0.0962977i
$351$		0			0
$352$	−225.240	+	139.310i	−0.639888	+	0.395766i
$353$	−206.522	+	357.707i	−0.585048	+	1.01333i	0.409821	+	0.912166i	$0.365591\pi$
$353$	−206.522	+	357.707i	−0.585048	+	1.01333i	−0.994869	+	0.101167i	$0.967742\pi$
$354$		0			0
$355$	184.971	+	320.379i	0.521045	+	0.902476i
$356$	13.1945	+	112.411i	0.0370632	+	0.315761i
$357$		0			0
$358$	227.239	+	202.127i	0.634747	+	0.564600i
$359$			497.633i			1.38616i	0.720858	+	0.693082i	$0.243748\pi$
$359$			497.633i			1.38616i	−0.720858	+	0.693082i	$0.756252\pi$
$360$		0			0
$361$	−298.090			−0.825734
$362$	−86.1824	+	96.8899i	−0.238073	+	0.267652i
$363$		0			0
$364$	−16.7158	−	142.411i	−0.0459226	−	0.391239i
$365$	−159.832	+	92.2792i	−0.437897	+	0.252820i
$366$		0			0
$367$	−191.739	−	110.700i	−0.522449	−	0.301636i	0.215487	−	0.976507i	$-0.430866\pi$
$367$	−191.739	−	110.700i	−0.522449	−	0.301636i	−0.737936	+	0.674871i	$0.764199\pi$
$368$	340.012	−	321.412i	0.923946	−	0.873402i
$369$		0			0
$370$	36.3447	−	176.234i	0.0982288	−	0.476309i
$371$	203.232	−	352.008i	0.547795	−	0.948809i
$372$		0			0
$373$	−346.015	+	199.772i	−0.927654	+	0.535582i	−0.886069	−	0.463553i	$-0.846574\pi$
$373$	−346.015	+	199.772i	−0.927654	+	0.535582i	−0.0415855	+	0.999135i	$0.513241\pi$
$374$	450.034	−	149.247i	1.20330	−	0.399056i
$375$		0			0
$376$	107.772	−	50.3506i	0.286626	−	0.133911i
$377$	−160.828			−0.426599
$378$		0			0
$379$	639.278			1.68675			0.843375	−	0.537325i	$-0.180565\pi$
$379$	639.278			1.68675			0.843375	+	0.537325i	$0.180565\pi$
$380$	−128.016	−	171.780i	−0.336883	−	0.452052i
$381$		0			0
$382$	−20.2384	−	61.0261i	−0.0529800	−	0.159754i
$383$	338.887	−	195.656i	0.884822	−	0.510852i	0.0125769	−	0.999921i	$-0.495997\pi$
$383$	338.887	−	195.656i	0.884822	−	0.510852i	0.872245	+	0.489069i	$0.162663\pi$
$384$		0			0
$385$	113.191	−	196.053i	0.294003	−	0.509228i
$386$	−47.8191	+	231.873i	−0.123884	+	0.600708i
$387$		0			0
$388$	−1.47624	−	0.635935i	−0.00380474	−	0.00163901i
$389$	321.509	+	185.623i	0.826500	+	0.477180i	0.852653	−	0.522478i	$-0.174992\pi$
$389$	321.509	+	185.623i	0.826500	+	0.477180i	−0.0261526	+	0.999658i	$0.508326\pi$
$390$		0			0
$391$	−725.415	+	418.818i	−1.85528	+	1.07115i
$392$	259.754	+	22.5342i	0.662637	+	0.0574851i
$393$		0			0
$394$	−162.795	+	183.021i	−0.413186	+	0.464521i
$395$	−490.882			−1.24274
$396$		0			0
$397$		−	193.410i		−	0.487179i	−0.969878	−	0.243590i	$-0.921675\pi$
$397$		−	193.410i		−	0.487179i	0.969878	−	0.243590i	$-0.0783250\pi$
$398$	258.862	−	291.024i	0.650407	−	0.731216i
$399$		0			0
$400$	−94.2099	+	315.803i	−0.235525	+	0.789508i
$401$	159.611	+	276.454i	0.398032	+	0.689411i	0.993483	−	0.113980i	$-0.0363601\pi$
$401$	159.611	+	276.454i	0.398032	+	0.689411i	−0.595451	+	0.803391i	$0.703027\pi$
$402$		0			0
$403$	208.811	−	361.671i	0.518141	−	0.897446i
$404$	108.147	−	251.049i	0.267690	−	0.621407i
$405$		0			0
$406$	−29.7385	+	144.201i	−0.0732476	+	0.355176i
$407$	−95.4993	−	55.1366i	−0.234642	−	0.135471i
$408$		0			0
$409$	147.422	+	255.343i	0.360445	+	0.624310i	0.988034	−	0.154235i	$-0.0492914\pi$
$409$	147.422	+	255.343i	0.360445	+	0.624310i	−0.627589	+	0.778545i	$0.715958\pi$
$410$	−263.738	−	795.267i	−0.643263	−	1.93967i
$411$		0			0
$412$	−430.167	−	577.227i	−1.04409	−	1.40104i
$413$			93.1237i			0.225481i
$414$		0			0
$415$			58.7147i			0.141481i
$416$	283.052	−	8.58120i	0.680414	−	0.0206279i
$417$		0			0
$418$	−124.614	+	41.3262i	−0.298119	+	0.0988665i
$419$	265.487	+	459.837i	0.633621	+	1.09746i	0.986805	+	0.161910i	$0.0517655\pi$
$419$	265.487	+	459.837i	0.633621	+	1.09746i	−0.353184	+	0.935554i	$0.614901\pi$
$420$		0			0
$421$	320.122	+	184.822i	0.760384	+	0.439008i	0.829434	−	0.558605i	$-0.188663\pi$
$421$	320.122	+	184.822i	0.760384	+	0.439008i	−0.0690497	+	0.997613i	$0.521997\pi$
$422$	−25.3564	+	122.953i	−0.0600863	+	0.291357i
$423$		0			0
$424$	657.900	+	459.950i	1.55165	+	1.08479i
$425$	294.998	−	510.951i	0.694112	−	1.20224i
$426$		0			0
$427$	120.127	+	208.066i	0.281327	+	0.487273i
$428$	5.27039	+	44.9013i	0.0123140	+	0.104910i
$429$		0			0
$430$	477.061	−	536.333i	1.10945	−	1.24729i
$431$			177.085i			0.410871i	0.978671	+	0.205435i	$0.0658610\pi$
$431$			177.085i			0.410871i	−0.978671	+	0.205435i	$0.934139\pi$
$432$		0			0
$433$	−281.684			−0.650541			−0.325270	−	0.945621i	$-0.605455\pi$
$433$	−281.684			−0.650541			−0.325270	+	0.945621i	$0.605455\pi$
$434$	−285.670	−	254.100i	−0.658226	−	0.585484i
$435$		0			0
$436$	−513.247	+	60.2436i	−1.17717	+	0.138173i
$437$	200.866	−	115.970i	0.459648	−	0.265378i
$438$		0			0
$439$	689.028	+	397.810i	1.56954	+	0.906174i	0.996222	+	0.0868401i	$0.0276769\pi$
$439$	689.028	+	397.810i	1.56954	+	0.906174i	0.573317	+	0.819334i	$0.305656\pi$
$440$	366.421	+	256.172i	0.832775	+	0.582208i
$441$		0			0
$442$	−496.525	−	102.398i	−1.12336	−	0.231670i
$443$	240.252	−	416.128i	0.542329	−	0.939342i	−0.456441	−	0.889754i	$-0.650876\pi$
$443$	240.252	−	416.128i	0.542329	−	0.939342i	0.998770	−	0.0495877i	$-0.0157907\pi$
$444$		0			0
$445$	165.470	−	95.5344i	0.371844	−	0.214684i
$446$	145.512	+	438.773i	0.326261	+	0.983796i
$447$		0			0
$448$	44.6449	−	255.377i	0.0996538	−	0.570038i
$449$	−723.097			−1.61046			−0.805230	−	0.592962i	$-0.797958\pi$
$449$	−723.097			−1.61046			−0.805230	+	0.592962i	$0.797958\pi$
$450$		0			0
$451$	−513.459			−1.13849
$452$	−69.9297	+	52.1138i	−0.154712	+	0.115296i
$453$		0			0
$454$	300.768	−	99.7451i	0.662485	−	0.219703i
$455$	−209.631	+	121.030i	−0.460727	+	0.266001i
$456$		0			0
$457$	−357.116	+	618.543i	−0.781436	+	1.35349i	0.149669	+	0.988736i	$0.452179\pi$
$457$	−357.116	+	618.543i	−0.781436	+	1.35349i	−0.931105	+	0.364751i	$0.881154\pi$
$458$	7.94235	+	1.63795i	0.0173414	+	0.00357630i
$459$		0			0
$460$	−725.407	−	312.491i	−1.57697	−	0.679328i
$461$	−436.324	−	251.912i	−0.946473	−	0.546447i	−0.0544896	−	0.998514i	$-0.517353\pi$
$461$	−436.324	−	251.912i	−0.946473	−	0.546447i	−0.891984	+	0.452068i	$0.850687\pi$
$462$		0			0
$463$	195.198	−	112.698i	0.421595	−	0.243408i	−0.274165	−	0.961683i	$-0.588401\pi$
$463$	195.198	−	112.698i	0.421595	−	0.243408i	0.695759	+	0.718275i	$0.255068\pi$
$464$	−278.646	−	83.1251i	−0.600529	−	0.179149i
$465$		0			0
$466$	105.102	+	93.4870i	0.225541	+	0.200616i
$467$	172.272			0.368891			0.184445	−	0.982843i	$-0.440951\pi$
$467$	172.272			0.368891			0.184445	+	0.982843i	$0.440951\pi$
$468$		0			0
$469$			83.9592i			0.179017i
$470$	−150.043	−	133.461i	−0.319240	−	0.283960i
$471$		0			0
$472$	−183.224	−	15.8951i	−0.388187	−	0.0336760i
$473$	−219.943	−	380.952i	−0.464995	−	0.805396i
$474$		0			0
$475$	−81.6843	+	141.481i	−0.171967	+	0.297856i
$476$	−183.624	+	426.260i	−0.385765	+	0.895503i
$477$		0			0
$478$	316.908	+	65.3556i	0.662986	+	0.136727i
$479$	−84.5244	−	48.8002i	−0.176460	−	0.101879i	0.409168	−	0.912459i	$-0.365819\pi$
$479$	−84.5244	−	48.8002i	−0.176460	−	0.101879i	−0.585628	+	0.810580i	$0.699152\pi$
$480$		0			0
$481$	58.9551	+	102.113i	0.122568	+	0.212294i
$482$	−513.078	+	170.154i	−1.06448	+	0.353017i
$483$		0			0
$484$	−168.396	+	125.494i	−0.347926	+	0.259285i
$485$			2.71350i			0.00559485i
$486$		0			0
$487$		−	523.901i		−	1.07577i	−0.843017	−	0.537886i	$-0.819223\pi$
$487$		−	523.901i		−	1.07577i	0.843017	−	0.537886i	$-0.180777\pi$
$488$	−429.881	+	200.840i	−0.880904	+	0.411557i
$489$		0			0
$490$	−138.548	−	417.774i	−0.282752	−	0.852600i
$491$	8.95449	+	15.5096i	0.0182373	+	0.0315879i	0.875000	−	0.484123i	$-0.160861\pi$
$491$	8.95449	+	15.5096i	0.0182373	+	0.0315879i	−0.856763	+	0.515711i	$0.827528\pi$
$492$		0			0
$493$	450.832	+	260.288i	0.914467	+	0.527968i
$494$	137.487	+	28.3538i	0.278313	+	0.0573964i
$495$		0			0
$496$	548.712	−	518.695i	1.10627	−	1.04576i
$497$	−110.962	+	192.191i	−0.223263	+	0.386703i
$498$		0			0
$499$	−2.74589	−	4.75602i	−0.00550278	−	0.00953110i	0.863261	−	0.504758i	$-0.168418\pi$
$499$	−2.74589	−	4.75602i	−0.00550278	−	0.00953110i	−0.868764	+	0.495227i	$0.835085\pi$
$500$	−118.109	+	13.8633i	−0.236217	+	0.0277266i
$501$		0			0
$502$	−35.6128	−	31.6772i	−0.0709419	−	0.0631019i
$503$		−	374.616i		−	0.744764i	−0.928080	−	0.372382i	$-0.878541\pi$
$503$		−	374.616i		−	0.744764i	0.928080	−	0.372382i	$-0.121459\pi$
$504$		0			0
$505$	−461.457			−0.913775
$506$	−321.699	+	361.668i	−0.635769	+	0.714759i
$507$		0			0
$508$	112.055	−	13.1528i	0.220581	−	0.0258913i
$509$	854.052	−	493.087i	1.67790	−	0.968738i	0.714907	−	0.699219i	$-0.246469\pi$
$509$	854.052	−	493.087i	1.67790	−	0.968738i	0.962995	−	0.269518i	$-0.0868645\pi$
$510$		0			0
$511$	−95.8813	−	55.3571i	−0.187635	−	0.108331i
$512$	494.843	+	131.430i	0.966491	+	0.256700i
$513$		0			0
$514$	−75.3760	+	365.496i	−0.146646	+	0.711082i
$515$	−607.635	+	1052.45i	−1.17987	+	2.04360i
$516$		0			0
$517$	−106.574	+	61.5305i	−0.206139	+	0.119015i
$518$	102.458	−	33.9786i	0.197796	−	0.0655958i
$519$		0			0
$520$	−202.350	−	433.115i	−0.389135	−	0.832913i
$521$	−243.318			−0.467021			−0.233510	−	0.972354i	$-0.575021\pi$
$521$	−243.318			−0.467021			−0.233510	+	0.972354i	$0.575021\pi$
$522$		0			0
$523$	−443.977			−0.848904			−0.424452	−	0.905451i	$-0.639533\pi$
$523$	−443.977			−0.848904			−0.424452	+	0.905451i	$0.639533\pi$
$524$	622.933	−	464.228i	1.18880	−	0.885932i
$525$		0			0
$526$	−108.359	−	326.741i	−0.206005	−	0.621180i
$527$	−1170.68	+	675.890i	−2.22140	+	1.28252i
$528$		0			0
$529$	163.066	−	282.438i	0.308253	−	0.533910i
$530$	273.709	−	1327.21i	0.516432	−	2.50416i
$531$		0			0
$532$	50.8452	−	118.031i	0.0955736	−	0.221862i
$533$	475.464	+	274.509i	0.892053	+	0.515027i
$534$		0			0
$535$	66.0952	−	38.1601i	0.123542	−	0.0713273i
$536$	−165.193	−	14.3308i	−0.308196	−	0.0267366i
$537$		0			0
$538$	119.517	−	134.366i	0.222151	−	0.249751i
$539$	−269.733			−0.500432
$540$		0			0
$541$		−	889.636i		−	1.64443i	−0.569178	−	0.822214i	$-0.692739\pi$
$541$		−	889.636i		−	1.64443i	0.569178	−	0.822214i	$-0.307261\pi$
$542$	−149.479	+	168.051i	−0.275792	+	0.310057i
$543$		0			0
$544$	−807.340	−	434.045i	−1.48408	−	0.797876i
$545$	436.191	+	755.506i	0.800351	+	1.38625i
$546$		0			0
$547$	−364.877	+	631.985i	−0.667050	+	1.15537i	0.311675	+	0.950189i	$0.399110\pi$
$547$	−364.877	+	631.985i	−0.667050	+	1.15537i	−0.978725	+	0.205176i	$0.934223\pi$
$548$	−96.0210	−	41.3639i	−0.175221	−	0.0754816i
$549$		0			0
$550$	68.8620	−	333.910i	0.125204	−	0.607109i
$551$	−124.835	−	72.0733i	−0.226560	−	0.130805i
$552$		0			0
$553$	−147.237	−	255.022i	−0.266251	−	0.461160i
$554$	−269.610	−	812.973i	−0.486660	−	1.46746i
$555$		0			0
$556$	−213.569	+	159.158i	−0.384116	+	0.286255i
$557$		−	727.272i		−	1.30569i	−0.757490	−	0.652847i	$-0.773574\pi$
$557$		−	727.272i		−	1.30569i	0.757490	−	0.652847i	$-0.226426\pi$
$558$		0			0
$559$			470.351i			0.841414i
$560$	−425.756	+	101.344i	−0.760278	+	0.180972i
$561$		0			0
$562$	732.614	−	242.960i	1.30358	−	0.432313i
$563$	−299.076	−	518.015i	−0.531219	−	0.920098i	−0.999336	−	0.0364314i	$-0.988401\pi$
$563$	−299.076	−	518.015i	−0.531219	−	0.920098i	0.468118	−	0.883666i	$-0.344932\pi$
$564$		0			0
$565$	127.502	+	73.6136i	0.225668	+	0.130289i
$566$	208.165	−	1009.39i	0.367783	−	1.78337i
$567$		0			0
$568$	−359.204	−	251.126i	−0.632401	−	0.442123i
$569$	12.9590	−	22.4457i	0.0227751	−	0.0394475i	−0.854413	−	0.519594i	$-0.826083\pi$
$569$	12.9590	−	22.4457i	0.0227751	−	0.0394475i	0.877188	+	0.480147i	$0.159417\pi$
$570$		0			0
$571$	192.052	+	332.644i	0.336344	+	0.582564i	0.983742	−	0.179587i	$-0.0574763\pi$
$571$	192.052	+	332.644i	0.336344	+	0.582564i	−0.647398	+	0.762152i	$0.724143\pi$
$572$	−290.964	+	34.1526i	−0.508678	+	0.0597073i
$573$		0			0
$574$	334.048	−	375.551i	0.581966	−	0.654271i
$575$			602.318i			1.04751i
$576$		0			0
$577$	942.619			1.63366			0.816828	−	0.576882i	$-0.195731\pi$
$577$	942.619			1.63366			0.816828	+	0.576882i	$0.195731\pi$
$578$	794.260	+	706.484i	1.37415	+	1.22229i
$579$		0			0
$580$	57.2252	+	487.532i	0.0986641	+	0.840572i
$581$	−30.5033	+	17.6111i	−0.0525013	+	0.0303117i
$582$		0			0
$583$	−719.198	−	415.229i	−1.23362	−	0.712228i
$584$	125.283	−	179.201i	0.214526	−	0.306852i
$585$		0			0
$586$	−199.439	−	41.1302i	−0.340340	−	0.0701881i
$587$	−43.1113	+	74.6710i	−0.0734435	+	0.127208i	−0.900408	−	0.435046i	$-0.856732\pi$
$587$	−43.1113	+	74.6710i	−0.0734435	+	0.127208i	0.826965	+	0.562254i	$0.190066\pi$
$588$		0			0
$589$	324.158	−	187.153i	0.550353	−	0.317747i
$590$	97.7288	+	294.688i	0.165642	+	0.499472i
$591$		0			0
$592$	49.3659	+	207.390i	0.0833884	+	0.350321i
$593$	96.9609			0.163509			0.0817546	−	0.996652i	$-0.473948\pi$
$593$	96.9609			0.163509			0.0817546	+	0.996652i	$0.473948\pi$
$594$		0			0
$595$	783.515			1.31683
$596$	131.435	+	176.369i	0.220529	+	0.295921i
$597$		0			0
$598$	491.252	−	162.916i	0.821492	−	0.272435i
$599$	264.452	−	152.682i	0.441490	−	0.254894i	−0.262740	−	0.964867i	$-0.584626\pi$
$599$	264.452	−	152.682i	0.441490	−	0.254894i	0.704229	+	0.709973i	$0.251293\pi$
$600$		0			0
$601$	89.4789	−	154.982i	0.148883	−	0.257874i	−0.781932	−	0.623364i	$-0.785765\pi$
$601$	89.4789	−	154.982i	0.148883	−	0.257874i	0.930815	+	0.365491i	$0.119099\pi$
$602$	421.726	+	86.9722i	0.700541	+	0.144472i
$603$		0			0
$604$	−356.784	+	828.227i	−0.590701	+	1.37124i
$605$	307.035	+	177.267i	0.507496	+	0.293003i
$606$		0			0
$607$	241.505	−	139.433i	0.397867	−	0.229709i	−0.287696	−	0.957722i	$-0.592889\pi$
$607$	241.505	−	139.433i	0.397867	−	0.229709i	0.685563	+	0.728013i	$0.259556\pi$
$608$	223.551	+	120.186i	0.367682	+	0.197675i
$609$		0			0
$610$	598.494	+	532.353i	0.981138	+	0.872710i
$611$	131.584			0.215358
$612$		0			0
$613$			253.084i			0.412862i	0.978461	+	0.206431i	$0.0661849\pi$
$613$			253.084i			0.412862i	−0.978461	+	0.206431i	$0.933815\pi$
$614$	−396.207	−	352.421i	−0.645288	−	0.573976i
$615$		0			0
$616$	−23.1800	+	267.199i	−0.0376299	+	0.433765i
$617$	−354.895	−	614.696i	−0.575194	−	0.996266i	−0.996021	−	0.0891244i	$-0.971593\pi$
$617$	−354.895	−	614.696i	−0.575194	−	0.996266i	0.420826	−	0.907141i	$-0.361740\pi$
$618$		0			0
$619$	−192.304	+	333.080i	−0.310668	+	0.538093i	−0.978507	−	0.206212i	$-0.933886\pi$
$619$	−192.304	+	333.080i	−0.310668	+	0.538093i	0.667839	+	0.744306i	$0.267220\pi$
$620$	−1170.66	−	504.299i	−1.88817	−	0.813385i
$621$		0			0
$622$	709.751	+	146.371i	1.14108	+	0.235324i
$623$	99.2635	+	57.3098i	0.159332	+	0.0919901i
$624$		0			0
$625$	357.842	+	619.801i	0.572548	+	0.991682i
$626$	740.935	−	245.719i	1.18360	−	0.392523i
$627$		0			0
$628$	19.7388	+	26.4868i	0.0314312	+	0.0421765i
$629$		−	381.658i		−	0.606770i
$630$		0			0
$631$			691.507i			1.09589i	0.836514	+	0.547946i	$0.184590\pi$
$631$			691.507i			1.09589i	−0.836514	+	0.547946i	$0.815410\pi$
$632$	526.897	−	246.165i	0.833697	−	0.389502i
$633$		0			0
$634$	−188.707	−	569.021i	−0.297645	−	0.897509i
$635$	−95.2321	−	164.947i	−0.149972	−	0.259759i
$636$		0			0
$637$	249.774	+	144.207i	0.392109	+	0.226384i
$638$	294.622	+	60.7596i	0.461790	+	0.0952345i
$639$		0			0
$640$	−126.728	−	854.989i	−0.198012	−	1.33592i
$641$	−282.648	+	489.560i	−0.440948	+	0.763744i	−0.997760	−	0.0668943i	$-0.978691\pi$
$641$	−282.648	+	489.560i	−0.440948	+	0.763744i	0.556812	+	0.830638i	$0.312024\pi$
$642$		0			0
$643$	−317.606	−	550.110i	−0.493944	−	0.855536i	0.506032	−	0.862515i	$-0.331112\pi$
$643$	−317.606	−	550.110i	−0.493944	−	0.855536i	−0.999976	+	0.00697878i	$0.997779\pi$
$644$	−55.2368	−	470.591i	−0.0857714	−	0.730732i
$645$		0			0
$646$	−339.514	−	301.994i	−0.525564	−	0.467483i
$647$			962.388i			1.48746i	0.668479	+	0.743731i	$0.266946\pi$
$647$			962.388i			1.48746i	−0.668479	+	0.743731i	$0.733054\pi$
$648$		0			0
$649$	190.264			0.293164
$650$	−242.284	+	272.386i	−0.372745	+	0.419055i
$651$		0			0
$652$	45.2271	+	385.314i	0.0693667	+	0.590972i
$653$	−314.254	+	181.434i	−0.481246	+	0.277847i	−0.720936	−	0.693002i	$-0.756288\pi$
$653$	−314.254	+	181.434i	−0.481246	+	0.277847i	0.239690	+	0.970850i	$0.422954\pi$
$654$		0			0
$655$	−1135.79	−	655.748i	−1.73403	−	1.00114i
$656$	681.894	+	721.355i	1.03947	+	1.09963i
$657$		0			0
$658$	24.3311	−	117.981i	0.0369773	−	0.179302i
$659$	−255.781	+	443.026i	−0.388136	+	0.672270i	−0.992199	−	0.124666i	$-0.960214\pi$
$659$	−255.781	+	443.026i	−0.388136	+	0.672270i	0.604063	+	0.796936i	$0.293547\pi$
$660$		0			0
$661$	763.384	−	440.740i	1.15489	−	0.666778i	0.204818	−	0.978800i	$-0.434340\pi$
$661$	763.384	−	440.740i	1.15489	−	0.666778i	0.950075	+	0.312022i	$0.101006\pi$
$662$	−180.182	+	59.7547i	−0.272179	+	0.0902638i
$663$		0			0
$664$	−29.4439	−	63.0224i	−0.0443433	−	0.0949132i
$665$	−216.954			−0.326246
$666$		0			0
$667$	−531.449			−0.796775
$668$	−195.064	−	261.750i	−0.292012	−	0.391842i
$669$		0			0
$670$	88.1111	+	265.687i	0.131509	+	0.396548i
$671$	425.105	−	245.434i	0.633539	−	0.365774i
$672$		0			0
$673$	−14.8867	+	25.7846i	−0.0221200	+	0.0383129i	−0.876873	−	0.480721i	$-0.840375\pi$
$673$	−14.8867	+	25.7846i	−0.0221200	+	0.0383129i	0.854754	+	0.519034i	$0.173708\pi$
$674$	−167.615	+	812.761i	−0.248687	+	1.20588i
$675$		0			0
$676$	−333.152	−	143.515i	−0.492829	−	0.212301i
$677$	−652.352	−	376.635i	−0.963592	−	0.556330i	−0.0663150	−	0.997799i	$-0.521124\pi$
$677$	−652.352	−	376.635i	−0.963592	−	0.556330i	−0.897277	+	0.441469i	$0.854458\pi$
$678$		0			0
$679$	−1.40971	+	0.813898i	−0.00207616	+	0.00119867i
$680$	−133.736	+	1541.60i	−0.196671	+	2.26705i
$681$		0			0
$682$	−519.159	+	583.661i	−0.761230	+	0.855807i
$683$	597.240			0.874437			0.437218	−	0.899355i	$-0.355964\pi$
$683$	597.240			0.874437			0.437218	+	0.899355i	$0.355964\pi$
$684$		0			0
$685$			176.498i			0.257661i
$686$	439.320	−	493.903i	0.640409	−	0.719975i
$687$		0			0
$688$	−243.104	+	814.916i	−0.353350	+	1.18447i
$689$	443.986	+	769.007i	0.644392	+	1.11612i
$690$		0			0
$691$	675.806	−	1170.53i	0.978012	−	1.69397i	0.308397	−	0.951258i	$-0.400207\pi$
$691$	675.806	−	1170.53i	0.978012	−	1.69397i	0.669615	−	0.742709i	$-0.266459\pi$
$692$	−445.128	+	1033.31i	−0.643248	+	1.49322i
$693$		0			0
$694$	−160.396	+	777.755i	−0.231118	+	1.12068i
$695$	389.398	+	224.819i	0.560286	+	0.323481i
$696$		0			0
$697$	−888.547	−	1539.01i	−1.27482	−	2.20805i
$698$	−37.1573	−	112.043i	−0.0532339	−	0.160520i
$699$		0			0
$700$	199.426	+	267.603i	0.284894	+	0.382290i
$701$		−	42.1057i		−	0.0600652i	−0.999549	−	0.0300326i	$-0.990439\pi$
$701$		−	42.1057i		−	0.0600652i	0.999549	−	0.0300326i	$-0.00956111\pi$
$702$		0			0
$703$			105.680i			0.150328i
$704$	−521.768	−	91.2152i	−0.741147	−	0.129567i
$705$		0			0
$706$	−784.095	+	260.033i	−1.11062	+	0.368318i
$707$	−138.411	−	239.735i	−0.195772	−	0.339087i
$708$		0			0
$709$	565.804	+	326.667i	0.798031	+	0.460743i	0.842782	−	0.538255i	$-0.180916\pi$
$709$	565.804	+	326.667i	0.798031	+	0.460743i	−0.0447514	+	0.998998i	$0.514250\pi$
$710$	−149.441	+	724.635i	−0.210480	+	1.02061i
$711$		0			0
$712$	−129.702	+	185.523i	−0.182166	+	0.260566i
$713$	690.007	−	1195.13i	0.967752	−	1.67619i
$714$		0			0
$715$	247.280	+	428.302i	0.345847	+	0.599024i
$716$	70.9084	+	604.106i	0.0990340	+	0.843723i
$717$		0			0
$718$	−661.468	+	743.650i	−0.921264	+	1.03572i
$719$		−	879.739i		−	1.22356i	−0.791028	−	0.611779i	$-0.790454\pi$
$719$		−	879.739i		−	1.22356i	0.791028	−	0.611779i	$-0.209546\pi$
$720$		0			0
$721$	−729.024			−1.01113
$722$	−445.458	−	396.230i	−0.616978	−	0.548794i
$723$		0			0
$724$	−257.577	+	30.2338i	−0.355770	+	0.0417593i
$725$	324.179	−	187.165i	0.447143	−	0.258158i
$726$		0			0
$727$	−515.386	−	297.558i	−0.708922	−	0.409296i	0.101740	−	0.994811i	$-0.467559\pi$
$727$	−515.386	−	297.558i	−0.708922	−	0.409296i	−0.810662	+	0.585515i	$0.800892\pi$
$728$	164.317	−	235.034i	0.225710	−	0.322849i
$729$		0			0
$730$	−361.509	−	74.5538i	−0.495218	−	0.102128i
$731$	761.228	−	1318.49i	1.04135	−	1.80367i
$732$		0			0
$733$	−753.208	+	434.865i	−1.02757	+	0.593267i	−0.916287	−	0.400522i	$-0.868829\pi$
$733$	−753.208	+	434.865i	−1.02757	+	0.593267i	−0.111282	+	0.993789i	$0.535496\pi$
$734$	−139.383	−	420.293i	−0.189896	−	0.572606i
$735$		0			0
$736$	935.335	−	28.3562i	1.27084	−	0.0385275i
$737$	171.539			0.232754
$738$		0			0
$739$	927.052			1.25447			0.627234	−	0.778831i	$-0.284187\pi$
$739$	927.052			1.25447			0.627234	+	0.778831i	$0.284187\pi$
$740$	288.568	−	215.050i	0.389957	−	0.290608i
$741$		0			0
$742$	771.604	−	255.890i	1.03990	−	0.344866i
$743$	−792.270	+	457.417i	−1.06631	+	0.615636i	−0.927172	−	0.374637i	$-0.877767\pi$
$743$	−792.270	+	457.417i	−1.06631	+	0.615636i	−0.139141	+	0.990273i	$0.544434\pi$
$744$		0			0
$745$	185.660	−	321.572i	0.249208	−	0.431640i
$746$	−782.618	−	161.399i	−1.04909	−	0.216352i
$747$		0			0
$748$	870.903	+	375.167i	1.16431	+	0.501561i
$749$	39.6497	+	22.8917i	0.0529368	+	0.0305631i
$750$		0			0
$751$	−782.191	+	451.598i	−1.04153	+	0.601329i	−0.920267	−	0.391291i	$-0.872029\pi$
$751$	−782.191	+	451.598i	−1.04153	+	0.601329i	−0.121266	+	0.992620i	$0.538695\pi$
$752$	227.978	+	68.0102i	0.303163	+	0.0904390i
$753$		0			0
$754$	−240.337	−	213.777i	−0.318749	−	0.283523i
$755$	1522.38			2.01639
$756$		0			0
$757$			146.988i			0.194171i	0.995276	+	0.0970857i	$0.0309521\pi$
$757$			146.988i			0.194171i	−0.995276	+	0.0970857i	$0.969048\pi$
$758$	955.321	+	849.746i	1.26032	+	1.12104i
$759$		0			0
$760$	37.0314	−	426.865i	0.0487255	−	0.561665i
$761$	−461.253	−	798.913i	−0.606114	−	1.04982i	−0.991874	−	0.127221i	$-0.959394\pi$
$761$	−461.253	−	798.913i	−0.606114	−	1.04982i	0.385760	−	0.922599i	$-0.373939\pi$
$762$		0			0
$763$	−261.665	+	453.218i	−0.342943	+	0.593995i
$764$	50.8739	−	118.097i	0.0665889	−	0.154578i
$765$		0			0
$766$	766.496	+	158.074i	1.00065	+	0.206363i
$767$	−176.185	−	101.720i	−0.229706	−	0.132621i
$768$		0			0
$769$	468.680	+	811.777i	0.609467	+	1.05563i	0.991328	+	0.131408i	$0.0419497\pi$
$769$	468.680	+	811.777i	0.609467	+	1.05563i	−0.381862	+	0.924219i	$0.624717\pi$
$770$	429.749	−	142.519i	0.558115	−	0.185090i
$771$		0			0
$772$	−379.672	+	282.943i	−0.491803	+	0.366506i
$773$			111.162i			0.143806i	0.997412	+	0.0719031i	$0.0229073\pi$
$773$			111.162i			0.143806i	−0.997412	+	0.0719031i	$0.977093\pi$
$774$		0			0
$775$			972.022i			1.25422i
$776$	−1.36075	−	2.91258i	−0.00175355	−	0.00375333i
$777$		0			0
$778$	233.719	+	704.748i	0.300410	+	0.905846i
$779$	246.037	+	426.149i	0.315837	+	0.547046i
$780$		0			0
$781$	392.671	+	226.709i	0.502780	+	0.290280i
$782$	−1640.75	−	338.370i	−2.09814	−	0.432698i
$783$		0			0
$784$	358.216	+	378.946i	0.456909	+	0.483350i
$785$	27.8821	−	48.2932i	0.0355186	−	0.0615201i
$786$		0			0
$787$	−567.281	−	982.559i	−0.720814	−	1.24849i	−0.960674	−	0.277679i	$-0.910435\pi$
$787$	−567.281	−	982.559i	−0.720814	−	1.24849i	0.239860	−	0.970808i	$-0.422899\pi$
$788$	−486.554	+	57.1104i	−0.617454	+	0.0724752i
$789$		0			0
$790$	−733.561	−	652.494i	−0.928559	−	0.825942i
$791$			88.3196i			0.111656i
$792$		0			0
$793$	−524.864			−0.661872
$794$	257.086	−	289.027i	0.323786	−	0.364014i
$795$		0			0
$796$	773.674	−	90.8118i	0.971952	−	0.114085i
$797$	−218.512	+	126.158i	−0.274168	+	0.158291i	−0.630780	−	0.775962i	$-0.717265\pi$
$797$	−218.512	+	126.158i	−0.274168	+	0.158291i	0.356612	+	0.934252i	$0.383932\pi$
$798$		0			0
$799$	−368.856	−	212.959i	−0.461647	−	0.266532i
$800$	−560.559	+	346.702i	−0.700699	+	0.433377i
$801$		0			0
$802$	−128.952	+	625.284i	−0.160788	+	0.779656i
$803$	−113.102	+	195.898i	−0.140849	+	0.243957i
$804$		0			0
$805$	−692.716	+	399.940i	−0.860517	+	0.496820i
$806$	792.784	−	262.915i	0.983603	−	0.326197i
$807$		0			0
$808$	495.312	−	231.409i	0.613010	−	0.286397i
$809$	1046.97			1.29416			0.647078	−	0.762424i	$-0.275991\pi$
$809$	1046.97			1.29416			0.647078	+	0.762424i	$0.275991\pi$
$810$		0			0
$811$	364.334			0.449240			0.224620	−	0.974446i	$-0.427886\pi$
$811$	364.334			0.449240			0.224620	+	0.974446i	$0.427886\pi$
$812$	−236.117	+	175.961i	−0.290784	+	0.216701i
$813$		0			0
$814$	−69.4227	−	209.335i	−0.0852858	−	0.257168i
$815$	567.186	−	327.465i	0.695934	−	0.401798i
$816$		0			0
$817$	−210.783	+	365.086i	−0.257996	+	0.446862i
$818$	−119.105	+	577.535i	−0.145605	+	0.706033i
$819$		0			0
$820$	662.967	−	1538.99i	0.808497	−	1.87682i
$821$	−371.524	−	214.499i	−0.452526	−	0.261266i	0.256371	−	0.966579i	$-0.417473\pi$
$821$	−371.524	−	214.499i	−0.452526	−	0.261266i	−0.708896	+	0.705313i	$0.750807\pi$
$822$		0			0
$823$	1244.52	−	718.522i	1.51217	−	0.873053i	0.512273	−	0.858823i	$-0.328804\pi$
$823$	1244.52	−	718.522i	1.51217	−	0.873053i	0.999899	−	0.0142299i	$-0.00452968\pi$
$824$	124.436	−	1434.38i	0.151014	−	1.74076i
$825$		0			0
$826$	−123.783	+	139.162i	−0.149858	+	0.168477i
$827$	−266.734			−0.322532			−0.161266	−	0.986911i	$-0.551558\pi$
$827$	−266.734			−0.322532			−0.161266	+	0.986911i	$0.551558\pi$
$828$		0			0
$829$			311.848i			0.376174i	0.982152	+	0.188087i	$0.0602287\pi$
$829$			311.848i			0.376174i	−0.982152	+	0.188087i	$0.939771\pi$
$830$	−78.0451	+	87.7417i	−0.0940303	+	0.105713i
$831$		0			0
$832$	434.392	+	363.417i	0.522106	+	0.436800i
$833$	−466.777	−	808.481i	−0.560356	−	0.970566i
$834$		0			0
$835$	−275.539	+	477.248i	−0.329987	+	0.571554i
$836$	−241.151	−	103.883i	−0.288459	−	0.124262i
$837$		0			0
$838$	−214.491	+	1040.06i	−0.255956	+	1.24112i
$839$	595.826	+	344.000i	0.710162	+	0.410013i	0.811121	−	0.584878i	$-0.198858\pi$
$839$	595.826	+	344.000i	0.710162	+	0.410013i	−0.100959	+	0.994891i	$0.532191\pi$
$840$		0			0
$841$	−255.357	−	442.291i	−0.303635	−	0.525911i
$842$	232.711	+	701.708i	0.276378	+	0.833383i
$843$		0			0
$844$	−201.324	+	150.033i	−0.238536	+	0.177764i
$845$			612.373i			0.724702i
$846$		0			0
$847$			212.680i			0.251098i
$848$	371.771	+	1561.84i	0.438409	+	1.84179i
$849$		0			0
$850$	1120.01	−	371.433i	1.31766	−	0.436980i
$851$	194.815	+	337.429i	0.228925	+	0.396509i
$852$		0			0
$853$	−672.772	−	388.425i	−0.788713	−	0.455364i	0.0507961	−	0.998709i	$-0.483824\pi$
$853$	−672.772	−	388.425i	−0.788713	−	0.455364i	−0.839509	+	0.543345i	$0.817157\pi$
$854$	−97.0523	+	470.604i	−0.113644	+	0.551058i
$855$		0			0
$856$	−51.8081	+	74.1049i	−0.0605235	+	0.0865711i
$857$	−449.233	+	778.095i	−0.524193	+	0.907929i	0.475411	+	0.879764i	$0.342300\pi$
$857$	−449.233	+	778.095i	−0.524193	+	0.907929i	−0.999603	+	0.0281645i	$0.991034\pi$
$858$		0			0
$859$	−229.707	−	397.865i	−0.267413	−	0.463172i	0.700780	−	0.713377i	$-0.252835\pi$
$859$	−229.707	−	397.865i	−0.267413	−	0.463172i	−0.968193	+	0.250205i	$0.919502\pi$
$860$	1425.82	−	167.359i	1.65793	−	0.194603i
$861$		0			0
$862$	−235.387	+	264.632i	−0.273070	+	0.306997i
$863$		−	610.959i		−	0.707948i	−0.935255	−	0.353974i	$-0.884830\pi$
$863$		−	610.959i		−	0.707948i	0.935255	−	0.353974i	$-0.115170\pi$
$864$		0			0
$865$	1899.34			2.19577
$866$	−420.942	−	374.422i	−0.486076	−	0.432358i
$867$		0			0
$868$	−89.1412	−	759.441i	−0.102697	−	0.874933i
$869$	−521.042	+	300.824i	−0.599588	+	0.346172i
$870$		0			0
$871$	−158.846	−	91.7098i	−0.182372	−	0.105293i
$872$	−847.060	−	592.196i	−0.971400	−	0.679123i
$873$		0			0
$874$	454.320	+	93.6940i	0.519817	+	0.107201i
$875$	−60.2146	+	104.295i	−0.0688167	+	0.119194i
$876$		0			0
$877$	−873.219	+	504.153i	−0.995689	+	0.574861i	−0.906970	−	0.421196i	$-0.861611\pi$
$877$	−873.219	+	504.153i	−0.995689	+	0.574861i	−0.0887188	+	0.996057i	$0.528277\pi$
$878$	500.885	+	1510.35i	0.570484	+	1.72022i
$879$		0			0
$880$	207.060	+	869.873i	0.235295	+	0.988492i
$881$	1241.88			1.40963			0.704814	−	0.709392i	$-0.251030\pi$
$881$	1241.88			1.40963			0.704814	+	0.709392i	$0.251030\pi$
$882$		0			0
$883$	−810.284			−0.917649			−0.458825	−	0.888527i	$-0.651729\pi$
$883$	−810.284			−0.917649			−0.458825	+	0.888527i	$0.651729\pi$
$884$	−605.884	−	813.015i	−0.685389	−	0.919701i
$885$		0			0
$886$	912.155	−	302.502i	1.02952	−	0.341424i
$887$	139.166	−	80.3478i	0.156896	−	0.0905838i	−0.419497	−	0.907757i	$-0.637793\pi$
$887$	139.166	−	80.3478i	0.156896	−	0.0905838i	0.576392	+	0.817173i	$0.304460\pi$
$888$		0			0
$889$	57.1285	−	98.9494i	0.0642615	−	0.111304i
$890$	374.262	+	77.1837i	0.420519	+	0.0867233i
$891$		0			0
$892$	−365.780	+	849.110i	−0.410067	+	0.951917i
$893$	102.135	+	58.9679i	0.114373	+	0.0660335i
$894$		0			0
$895$	889.251	−	513.409i	0.993577	−	0.573642i
$896$	406.170	−	322.285i	0.453315	−	0.359694i
$897$		0			0
$898$	−1080.58	−	961.160i	−1.20332	−	1.07033i
$899$	−857.654			−0.954008
$900$		0			0
$901$		−	2874.24i		−	3.19005i
$902$	−767.299	−	682.503i	−0.850664	−	0.756656i
$903$		0			0
$904$	−173.772	−	15.0751i	−0.192226	−	0.0166760i
$905$	218.906	+	379.157i	0.241886	+	0.418958i
$906$		0			0
$907$	259.064	−	448.712i	0.285627	−	0.494721i	−0.687134	−	0.726531i	$-0.741131\pi$
$907$	259.064	−	448.712i	0.285627	−	0.494721i	0.972761	+	0.231810i	$0.0744648\pi$
$908$	582.044	+	250.733i	0.641018	+	0.276138i
$909$		0			0
$910$	−474.143	−	97.7823i	−0.521037	−	0.107453i
$911$	−153.559	−	88.6573i	−0.168561	−	0.0973187i	0.413346	−	0.910574i	$-0.364360\pi$
$911$	−153.559	−	88.6573i	−0.168561	−	0.0973187i	−0.581907	+	0.813255i	$0.697693\pi$
$912$		0			0
$913$	35.9817	+	62.3221i	0.0394104	+	0.0682608i
$914$	−1355.85	+	449.647i	−1.48342	+	0.491955i
$915$		0			0
$916$	9.69164	+	13.0049i	0.0105804	+	0.0141975i
$917$		−	786.749i		−	0.857960i
$918$		0			0
$919$		−	535.325i		−	0.582508i	−0.956646	−	0.291254i	$-0.905928\pi$
$919$		−	535.325i		−	0.582508i	0.956646	−	0.291254i	$-0.0940725\pi$
$920$	−668.659	−	1431.21i	−0.726803	−	1.55566i
$921$		0			0
$922$	−317.183	−	956.425i	−0.344017	−	1.03734i
$923$	−242.410	−	419.866i	−0.262633	−	0.454893i
$924$		0			0
$925$	−237.671	−	137.219i	−0.256941	−	0.148345i
$926$	441.500	+	91.0503i	0.476782	+	0.0983264i
$927$		0			0
$928$	−305.909	−	494.604i	−0.329643	−	0.532978i
$929$	−849.962	+	1472.18i	−0.914922	+	1.58469i	−0.107905	+	0.994161i	$0.534414\pi$
$929$	−849.962	+	1472.18i	−0.914922	+	1.58469i	−0.807016	+	0.590529i	$0.798919\pi$
$930$		0			0
$931$	129.250	+	223.867i	0.138829	+	0.240459i
$932$	32.7963	+	279.409i	0.0351891	+	0.299795i
$933$		0			0
$934$	257.439	+	228.989i	0.275630	+	0.245170i
$935$		−	1600.82i		−	1.71211i
$936$		0			0
$937$	−1524.40			−1.62690			−0.813448	−	0.581638i	$-0.802412\pi$
$937$	−1524.40			−1.62690			−0.813448	+	0.581638i	$0.802412\pi$
$938$	−111.601	+	125.466i	−0.118977	+	0.133760i
$939$		0			0
$940$	−46.8197	−	398.882i	−0.0498082	−	0.424343i
$941$	33.6063	−	19.4026i	0.0357134	−	0.0206191i	−0.482037	−	0.876151i	$-0.660103\pi$
$941$	33.6063	−	19.4026i	0.0357134	−	0.0206191i	0.517750	+	0.855532i	$0.326770\pi$
$942$		0			0
$943$	1571.15	+	907.105i	1.66612	+	0.961936i
$944$	−252.678	−	267.300i	−0.267667	−	0.283157i
$945$		0			0
$946$	177.695	−	861.639i	0.187839	−	0.910824i
$947$	−360.984	+	625.242i	−0.381187	+	0.660234i	−0.991232	−	0.132132i	$-0.957818\pi$
$947$	−360.984	+	625.242i	−0.381187	+	0.660234i	0.610046	+	0.792366i	$0.291151\pi$
$948$		0			0
$949$	209.465	−	120.935i	0.220722	−	0.127434i
$950$	−310.128	+	102.849i	−0.326450	+	0.108262i
$951$		0			0
$952$	−840.999	+	392.913i	−0.883402	+	0.412724i
$953$	288.128			0.302338			0.151169	−	0.988508i	$-0.451696\pi$
$953$	288.128			0.302338			0.151169	+	0.988508i	$0.451696\pi$
$954$		0			0
$955$	−217.077			−0.227305
$956$	386.706	+	518.908i	0.404504	+	0.542791i
$957$		0			0
$958$	−61.4446	−	185.278i	−0.0641384	−	0.193401i
$959$	−91.6937	+	52.9394i	−0.0956139	+	0.0552027i
$960$		0			0
$961$	633.035	−	1096.45i	0.658725	−	1.14095i
$962$	−47.6308	+	230.960i	−0.0495122	+	0.240083i
$963$		0			0
$964$	−992.905	−	427.723i	−1.02998	−	0.443696i
$965$	692.253	+	399.673i	0.717361	+	0.414169i
$966$		0			0
$967$	1101.67	−	636.052i	1.13927	−	0.657758i	0.193021	−	0.981195i	$-0.438172\pi$
$967$	1101.67	−	636.052i	1.13927	−	0.657758i	0.946250	+	0.323437i	$0.104838\pi$
$968$	−418.456	−	36.3019i	−0.432290	−	0.0375020i
$969$		0			0
$970$	−3.60686	+	4.05499i	−0.00371842	+	0.00418040i
$971$	−1678.61			−1.72874			−0.864372	−	0.502852i	$-0.832284\pi$
$971$	−1678.61			−1.72874			−0.864372	+	0.502852i	$0.832284\pi$
$972$		0			0
$973$			269.732i			0.277217i
$974$	696.384	−	782.905i	0.714974	−	0.803804i
$975$		0			0
$976$	−909.365	−	271.280i	−0.931727	−	0.277951i
$977$	−206.778	−	358.151i	−0.211646	−	0.366582i	0.740584	−	0.671964i	$-0.234549\pi$
$977$	−206.778	−	358.151i	−0.211646	−	0.366582i	−0.952230	+	0.305382i	$0.901216\pi$
$978$		0			0
$979$	117.091	−	202.808i	0.119603	−	0.207158i
$980$	348.274	−	808.473i	0.355382	−	0.824972i
$981$		0			0
$982$	−7.23447	+	35.0798i	−0.00736708	+	0.0357228i
$983$	−1640.88	−	947.361i	−1.66925	−	0.963744i	−0.968041	−	0.250793i	$-0.919309\pi$
$983$	−1640.88	−	947.361i	−1.66925	−	0.963744i	−0.701213	−	0.712952i	$-0.747358\pi$
$984$		0			0
$985$	413.506	+	716.213i	0.419803	+	0.727120i
$986$	327.730	+	988.226i	0.332383	+	1.00226i
$987$		0			0
$988$	167.768	+	225.122i	0.169806	+	0.227857i
$989$			1554.25i			1.57154i
$990$		0			0
$991$			515.586i			0.520268i	0.965572	+	0.260134i	$0.0837668\pi$
$991$			515.586i			0.520268i	−0.965572	+	0.260134i	$0.916233\pi$
$992$	1509.45	−	45.7614i	1.52162	−	0.0461304i
$993$		0			0
$994$	−421.284	+	139.712i	−0.423827	+	0.140556i
$995$	−657.519	−	1138.86i	−0.660824	−	1.14458i
$996$		0			0
$997$	315.896	+	182.383i	0.316846	+	0.182931i	0.649986	−	0.759946i	$-0.274775\pi$
$997$	315.896	+	182.383i	0.316846	+	0.182931i	−0.333140	+	0.942877i	$0.608108\pi$
$998$	2.21845	−	10.7572i	0.00222289	−	0.0107787i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	216.3.p.b.19.15		40
3.2	odd	2		72.3.p.b.43.6	✓	40
4.3	odd	2		864.3.t.b.559.18		40
8.3	odd	2	inner	216.3.p.b.19.3		40
8.5	even	2		864.3.t.b.559.3		40
9.2	odd	6		648.3.b.f.163.8		20
9.4	even	3	inner	216.3.p.b.91.3		40
9.5	odd	6		72.3.p.b.67.18	yes	40
9.7	even	3		648.3.b.e.163.13		20
12.11	even	2		288.3.t.b.79.13		40
24.5	odd	2		288.3.t.b.79.14		40
24.11	even	2		72.3.p.b.43.18	yes	40
36.7	odd	6		2592.3.b.f.1135.18		20
36.11	even	6		2592.3.b.e.1135.3		20
36.23	even	6		288.3.t.b.175.14		40
36.31	odd	6		864.3.t.b.847.3		40
72.5	odd	6		288.3.t.b.175.13		40
72.11	even	6		648.3.b.f.163.7		20
72.13	even	6		864.3.t.b.847.18		40
72.29	odd	6		2592.3.b.e.1135.18		20
72.43	odd	6		648.3.b.e.163.14		20
72.59	even	6		72.3.p.b.67.6	yes	40
72.61	even	6		2592.3.b.f.1135.3		20
72.67	odd	6	inner	216.3.p.b.91.15		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
72.3.p.b.43.6	✓	40	3.2	odd	2
72.3.p.b.43.18	yes	40	24.11	even	2
72.3.p.b.67.6	yes	40	72.59	even	6
72.3.p.b.67.18	yes	40	9.5	odd	6
216.3.p.b.19.3		40	8.3	odd	2	inner
216.3.p.b.19.15		40	1.1	even	1	trivial
216.3.p.b.91.3		40	9.4	even	3	inner
216.3.p.b.91.15		40	72.67	odd	6	inner
288.3.t.b.79.13		40	12.11	even	2
288.3.t.b.79.14		40	24.5	odd	2
288.3.t.b.175.13		40	72.5	odd	6
288.3.t.b.175.14		40	36.23	even	6
648.3.b.e.163.13		20	9.7	even	3
648.3.b.e.163.14		20	72.43	odd	6
648.3.b.f.163.7		20	72.11	even	6
648.3.b.f.163.8		20	9.2	odd	6
864.3.t.b.559.3		40	8.5	even	2
864.3.t.b.559.18		40	4.3	odd	2
864.3.t.b.847.3		40	36.31	odd	6
864.3.t.b.847.18		40	72.13	even	6
2592.3.b.e.1135.3		20	36.11	even	6
2592.3.b.e.1135.18		20	72.29	odd	6
2592.3.b.f.1135.3		20	72.61	even	6
2592.3.b.f.1135.18		20	36.7	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:	\( N \)	\(=\)	\( 216 = 2^{3} \cdot 3^{3} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	216.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.49437 + 1.32923i) q^{2} +(0.466308 + 3.97273i) q^{4} +(5.84790 - 3.37629i) q^{5} +(3.50808 + 2.02539i) q^{7} +(-4.58382 + 6.55657i) q^{8} +O(q^{10})\)	\(q+(1.49437 + 1.32923i) q^{2} +(0.466308 + 3.97273i) q^{4} +(5.84790 - 3.37629i) q^{5} +(3.50808 + 2.02539i) q^{7} +(-4.58382 + 6.55657i) q^{8} +(13.2268 + 2.72775i) q^{10} +(4.13813 - 7.16745i) q^{11} +(-7.66384 + 4.42472i) q^{13} +(2.55018 + 7.68973i) q^{14} +(-15.5651 + 3.70503i) q^{16} +28.6444 q^{17} -7.93157 q^{19} +(16.1400 + 21.6577i) q^{20} +(15.7111 - 5.21034i) q^{22} +(-25.3249 + 14.6213i) q^{23} +(10.2986 - 17.8377i) q^{25} +(-17.3341 - 3.57480i) q^{26} +(-6.41048 + 14.8811i) q^{28} +(15.7389 + 9.08688i) q^{29} +(-40.8693 + 23.5959i) q^{31} +(-28.1849 - 15.1529i) q^{32} +(42.8054 + 38.0749i) q^{34} +27.3532 q^{35} -13.3240i q^{37} +(-11.8527 - 10.5429i) q^{38} +(-4.66886 + 53.8185i) q^{40} +(-31.0200 - 53.7281i) q^{41} +(26.5751 - 46.0295i) q^{43} +(30.4040 + 13.0974i) q^{44} +(-57.2799 - 11.8128i) q^{46} +(-12.8771 - 7.43458i) q^{47} +(-16.2956 - 28.2248i) q^{49} +(39.1004 - 12.9670i) q^{50} +(-21.1519 - 28.3831i) q^{52} -100.342i q^{53} -55.8861i q^{55} +(-29.3600 + 13.7169i) q^{56} +(11.4413 + 34.4998i) q^{58} +(11.4945 + 19.9091i) q^{59} +(51.3643 + 29.6552i) q^{61} +(-92.4384 - 19.0635i) q^{62} +(-21.9772 - 60.1083i) q^{64} +(-29.8783 + 51.7507i) q^{65} +(10.3633 + 17.9498i) q^{67} +(13.3571 + 113.796i) q^{68} +(40.8759 + 36.3586i) q^{70} +54.7853i q^{71} -27.3316 q^{73} +(17.7107 - 19.9111i) q^{74} +(-3.69856 - 31.5100i) q^{76} +(29.0338 - 16.7627i) q^{77} +(-62.9562 - 36.3478i) q^{79} +(-78.5140 + 74.2189i) q^{80} +(25.0615 - 121.523i) q^{82} +(-4.34758 + 7.53022i) q^{83} +(167.509 - 96.7116i) q^{85} +(100.897 - 33.4609i) q^{86} +(28.0255 + 59.9862i) q^{88} +28.2957 q^{89} -35.8472 q^{91} +(-69.8957 - 93.7907i) q^{92} +(-9.36091 - 28.2266i) q^{94} +(-46.3831 + 26.7793i) q^{95} +(-0.200924 + 0.348010i) q^{97} +(13.1655 - 63.8389i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8}+O(q^{10}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8	\( 40 q + 5 q^{2} + 7 q^{4} - 46 q^{8} - 12 q^{10} + 16 q^{11} - 6 q^{14} + 31 q^{16} + 4 q^{17} - 76 q^{19} + 12 q^{20} + 35 q^{22} + 118 q^{25} + 72 q^{26} - 36 q^{28} + 5 q^{32} + 5 q^{34} + 108 q^{35} + 169 q^{38} - 6 q^{40} - 20 q^{41} - 16 q^{43} - 362 q^{44} - 96 q^{46} + 166 q^{49} - 73 q^{50} - 24 q^{52} - 186 q^{56} + 36 q^{58} + 64 q^{59} - 384 q^{62} - 518 q^{64} + 102 q^{65} - 64 q^{67} + 295 q^{68} - 6 q^{70} - 292 q^{73} - 318 q^{74} + 197 q^{76} + 720 q^{80} + 386 q^{82} - 554 q^{83} + 295 q^{86} + 59 q^{88} + 688 q^{89} - 204 q^{91} + 378 q^{92} - 66 q^{94} + 92 q^{97} + 614 q^{98}+O(q^{100}) \) 40 * q + 5 * q^2 + 7 * q^4 - 46 * q^8 - 12 * q^10 + 16 * q^11 - 6 * q^14 + 31 * q^16 + 4 * q^17 - 76 * q^19 + 12 * q^20 + 35 * q^22 + 118 * q^25 + 72 * q^26 - 36 * q^28 + 5 * q^32 + 5 * q^34 + 108 * q^35 + 169 * q^38 - 6 * q^40 - 20 * q^41 - 16 * q^43 - 362 * q^44 - 96 * q^46 + 166 * q^49 - 73 * q^50 - 24 * q^52 - 186 * q^56 + 36 * q^58 + 64 * q^59 - 384 * q^62 - 518 * q^64 + 102 * q^65 - 64 * q^67 + 295 * q^68 - 6 * q^70 - 292 * q^73 - 318 * q^74 + 197 * q^76 + 720 * q^80 + 386 * q^82 - 554 * q^83 + 295 * q^86 + 59 * q^88 + 688 * q^89 - 204 * q^91 + 378 * q^92 - 66 * q^94 + 92 * q^97 + 614 * q^98

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