LMFDB - Embedded newform 810.2.i.g.109.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [810,2,Mod(109,810)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(810, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([2, 3])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("810.109"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.i (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [8,0,0,4,0,0,-6,0,0,-2,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.2702336256.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 $ x^8 + 9x^6 + 56x^4 + 225*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.4
Root			$-1.52274 - 1.63746i$ of defining polynomial
Character	$\chi$	$=$	810.109
Dual form			810.2.i.g.379.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.17945 - 0.500000i) q^{5} +(1.13746 - 0.656712i) q^{7} -1.00000i q^{8} +(1.63746 - 1.52274i) q^{10} +(-1.31342 - 2.27492i) q^{11} +(-1.50000 - 0.866025i) q^{13} +(0.656712 - 1.13746i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.27492i q^{17} +2.27492 q^{19} +(0.656712 - 2.13746i) q^{20} +(-2.27492 - 1.31342i) q^{22} +(5.43424 + 3.13746i) q^{23} +(4.50000 - 2.17945i) q^{25} -1.73205 q^{26} -1.31342i q^{28} +(-4.56821 - 7.91238i) q^{29} +(-4.27492 + 7.40437i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.637459 - 1.10411i) q^{34} +(2.15068 - 2.00000i) q^{35} +9.97368i q^{37} +(1.97014 - 1.13746i) q^{38} +(-0.500000 - 2.17945i) q^{40} +(-2.80739 + 4.86254i) q^{41} +(2.27492 - 1.31342i) q^{43} -2.62685 q^{44} +6.27492 q^{46} +(8.89834 - 5.13746i) q^{47} +(-2.63746 + 4.56821i) q^{49} +(2.80739 - 4.13746i) q^{50} +(-1.50000 + 0.866025i) q^{52} -8.27492i q^{53} +(-4.00000 - 4.30136i) q^{55} +(-0.656712 - 1.13746i) q^{56} +(-7.91238 - 4.56821i) q^{58} +(4.12081 - 7.13746i) q^{59} +(-3.63746 - 6.30026i) q^{61} +8.54983i q^{62} -1.00000 q^{64} +(-3.70219 - 1.13746i) q^{65} +(10.5498 + 6.09095i) q^{67} +(-1.10411 - 0.637459i) q^{68} +(0.862541 - 2.80739i) q^{70} -6.92820 q^{71} +4.83507i q^{73} +(4.98684 + 8.63746i) q^{74} +(1.13746 - 1.97014i) q^{76} +(-2.98793 - 1.72508i) q^{77} +(-1.52274 - 1.63746i) q^{80} +5.61478i q^{82} +(-3.46410 + 2.00000i) q^{83} +(-0.637459 - 2.77862i) q^{85} +(1.31342 - 2.27492i) q^{86} +(-2.27492 + 1.31342i) q^{88} +3.04547 q^{89} -2.27492 q^{91} +(5.43424 - 3.13746i) q^{92} +(5.13746 - 8.89834i) q^{94} +(4.95807 - 1.13746i) q^{95} +(-16.5498 + 9.55505i) q^{97} +5.27492i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 6 q^{7} - 2 q^{10} - 12 q^{13} - 4 q^{16} - 12 q^{19} + 12 q^{22} + 36 q^{25} - 4 q^{31} + 10 q^{34} - 4 q^{40} - 12 q^{43} + 20 q^{46} - 6 q^{49} - 12 q^{52} - 32 q^{55} - 18 q^{58} - 14 q^{61}+ \cdots - 72 q^{97}+O(q^{100}) $ 8 * q + 4 * q^4 - 6 * q^7 - 2 * q^10 - 12 * q^13 - 4 * q^16 - 12 * q^19 + 12 * q^22 + 36 * q^25 - 4 * q^31 + 10 * q^34 - 4 * q^40 - 12 * q^43 + 20 * q^46 - 6 * q^49 - 12 * q^52 - 32 * q^55 - 18 * q^58 - 14 * q^61 - 8 * q^64 + 24 * q^67 + 22 * q^70 - 6 * q^76 + 10 * q^85 + 12 * q^88 + 12 * q^91 + 26 * q^94 - 72 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	2.17945	−	0.500000i	0.974679	−	0.223607i
$5$	2.17945	−	0.500000i	0.974679	−	0.223607i
$6$		0			0
$7$	1.13746	−	0.656712i	0.429919	−	0.248214i	−0.269393	−	0.963030i	$-0.586823\pi$
$7$	1.13746	−	0.656712i	0.429919	−	0.248214i	0.699312	+	0.714816i	$0.253490\pi$
$8$		−	1.00000i		−	0.353553i
$9$		0			0
$10$	1.63746	−	1.52274i	0.517810	−	0.481532i
$11$	−1.31342	−	2.27492i	−0.396012	−	0.685913i	0.597218	−	0.802079i	$-0.296273\pi$
$11$	−1.31342	−	2.27492i	−0.396012	−	0.685913i	−0.993230	+	0.116166i	$0.962940\pi$
$12$		0			0
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	−1.50000	−	0.866025i	−0.416025	−	0.240192i	−0.693375	+	0.720577i	$0.743877\pi$
$14$	0.656712	−	1.13746i	0.175514	−	0.303999i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	1.27492i		−	0.309213i	−0.987976	−	0.154606i	$-0.950589\pi$
$17$		−	1.27492i		−	0.309213i	0.987976	−	0.154606i	$-0.0494109\pi$
$18$		0			0
$19$	2.27492			0.521902			0.260951	−	0.965352i	$-0.415964\pi$
$19$	2.27492			0.521902			0.260951	+	0.965352i	$0.415964\pi$
$20$	0.656712	−	2.13746i	0.146845	−	0.477950i
$21$		0			0
$22$	−2.27492	−	1.31342i	−0.485014	−	0.280023i
$23$	5.43424	+	3.13746i	1.13312	+	0.654205i	0.944717	−	0.327887i	$-0.106337\pi$
$23$	5.43424	+	3.13746i	1.13312	+	0.654205i	0.188400	+	0.982092i	$0.439670\pi$
$24$		0			0
$25$	4.50000	−	2.17945i	0.900000	−	0.435890i
$26$	−1.73205			−0.339683
$27$		0			0
$28$		−	1.31342i		−	0.248214i
$29$	−4.56821	−	7.91238i	−0.848296	−	1.46929i	−0.882728	−	0.469884i	$-0.844296\pi$
$29$	−4.56821	−	7.91238i	−0.848296	−	1.46929i	0.0344323	−	0.999407i	$-0.489038\pi$
$30$		0			0
$31$	−4.27492	+	7.40437i	−0.767798	+	1.32986i	0.170957	+	0.985279i	$0.445314\pi$
$31$	−4.27492	+	7.40437i	−0.767798	+	1.32986i	−0.938755	+	0.344586i	$0.888019\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−0.637459	−	1.10411i	−0.109323	−	0.189353i
$35$	2.15068	−	2.00000i	0.363531	−	0.338062i
$36$		0			0
$37$			9.97368i			1.63966i	0.572605	+	0.819831i	$0.305933\pi$
$37$			9.97368i			1.63966i	−0.572605	+	0.819831i	$0.694067\pi$
$38$	1.97014	−	1.13746i	0.319598	−	0.184520i
$39$		0			0
$40$	−0.500000	−	2.17945i	−0.0790569	−	0.344601i
$41$	−2.80739	+	4.86254i	−0.438441	+	0.759401i	−0.997569	−	0.0696794i	$-0.977802\pi$
$41$	−2.80739	+	4.86254i	−0.438441	+	0.759401i	0.559129	+	0.829081i	$0.311136\pi$
$42$		0			0
$43$	2.27492	−	1.31342i	0.346922	−	0.200295i	−0.316407	−	0.948624i	$-0.602477\pi$
$43$	2.27492	−	1.31342i	0.346922	−	0.200295i	0.663329	+	0.748328i	$0.269143\pi$
$44$	−2.62685			−0.396012
$45$		0			0
$46$	6.27492			0.925186
$47$	8.89834	−	5.13746i	1.29796	−	0.749375i	0.317905	−	0.948122i	$-0.397021\pi$
$47$	8.89834	−	5.13746i	1.29796	−	0.749375i	0.980051	+	0.198747i	$0.0636872\pi$
$48$		0			0
$49$	−2.63746	+	4.56821i	−0.376780	+	0.652602i
$50$	2.80739	−	4.13746i	0.397025	−	0.585125i
$51$		0			0
$52$	−1.50000	+	0.866025i	−0.208013	+	0.120096i
$53$		−	8.27492i		−	1.13665i	−0.822805	−	0.568324i	$-0.807592\pi$
$53$		−	8.27492i		−	1.13665i	0.822805	−	0.568324i	$-0.192408\pi$
$54$		0			0
$55$	−4.00000	−	4.30136i	−0.539360	−	0.579995i
$56$	−0.656712	−	1.13746i	−0.0877568	−	0.151999i
$57$		0			0
$58$	−7.91238	−	4.56821i	−1.03895	−	0.599836i
$59$	4.12081	−	7.13746i	0.536484	−	0.929218i	−0.462606	−	0.886564i	$-0.653085\pi$
$59$	4.12081	−	7.13746i	0.536484	−	0.929218i	0.999090	−	0.0426538i	$-0.0135813\pi$
$60$		0			0
$61$	−3.63746	−	6.30026i	−0.465729	−	0.806666i	0.533505	−	0.845797i	$-0.320874\pi$
$61$	−3.63746	−	6.30026i	−0.465729	−	0.806666i	−0.999234	+	0.0391307i	$0.987541\pi$
$62$			8.54983i			1.08583i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−3.70219	−	1.13746i	−0.459200	−	0.141084i
$66$		0			0
$67$	10.5498	+	6.09095i	1.28887	+	0.744128i	0.978452	−	0.206473i	$-0.0661986\pi$
$67$	10.5498	+	6.09095i	1.28887	+	0.744128i	0.310415	+	0.950601i	$0.399532\pi$
$68$	−1.10411	−	0.637459i	−0.133893	−	0.0773032i
$69$		0			0
$70$	0.862541	−	2.80739i	0.103093	−	0.335547i
$71$	−6.92820			−0.822226			−0.411113	−	0.911584i	$-0.634860\pi$
$71$	−6.92820			−0.822226			−0.411113	+	0.911584i	$0.634860\pi$
$72$		0			0
$73$			4.83507i			0.565902i	0.959134	+	0.282951i	$0.0913134\pi$
$73$			4.83507i			0.565902i	−0.959134	+	0.282951i	$0.908687\pi$
$74$	4.98684	+	8.63746i	0.579708	+	1.00408i
$75$		0			0
$76$	1.13746	−	1.97014i	0.130475	−	0.225990i
$77$	−2.98793	−	1.72508i	−0.340506	−	0.196591i
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−1.52274	−	1.63746i	−0.170247	−	0.183073i
$81$		0			0
$82$			5.61478i			0.620049i
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	−0.677920	−	0.735135i	$-0.737119\pi$
$83$	−3.46410	+	2.00000i	−0.380235	+	0.219529i	0.297686	+	0.954664i	$0.403785\pi$
$84$		0			0
$85$	−0.637459	−	2.77862i	−0.0691421	−	0.301383i
$86$	1.31342	−	2.27492i	0.141630	−	0.245311i
$87$		0			0
$88$	−2.27492	+	1.31342i	−0.242507	+	0.140011i
$89$	3.04547			0.322820			0.161410	−	0.986887i	$-0.448396\pi$
$89$	3.04547			0.322820			0.161410	+	0.986887i	$0.448396\pi$
$90$		0			0
$91$	−2.27492			−0.238476
$92$	5.43424	−	3.13746i	0.566558	−	0.327103i
$93$		0			0
$94$	5.13746	−	8.89834i	0.529888	−	0.917794i
$95$	4.95807	−	1.13746i	0.508687	−	0.116701i
$96$		0			0
$97$	−16.5498	+	9.55505i	−1.68038	+	0.970168i	−0.718975	+	0.695036i	$0.755388\pi$
$97$	−16.5498	+	9.55505i	−1.68038	+	0.970168i	−0.961406	+	0.275132i	$0.911278\pi$
$98$			5.27492i			0.532847i
$99$		0			0
$100$	0.362541	−	4.98684i	0.0362541	−	0.498684i
$101$	4.77753	+	8.27492i	0.475382	+	0.823385i	0.999602	−	0.0281973i	$-0.00897668\pi$
$101$	4.77753	+	8.27492i	0.475382	+	0.823385i	−0.524221	+	0.851582i	$0.675643\pi$
$102$		0			0
$103$	5.68729	+	3.28356i	0.560386	+	0.323539i	0.753300	−	0.657677i	$-0.228461\pi$
$103$	5.68729	+	3.28356i	0.560386	+	0.323539i	−0.192915	+	0.981216i	$0.561794\pi$
$104$	−0.866025	+	1.50000i	−0.0849208	+	0.147087i
$105$		0			0
$106$	−4.13746	−	7.16629i	−0.401866	−	0.696051i
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		0			0
$109$	−7.82475			−0.749475			−0.374738	−	0.927131i	$-0.622267\pi$
$109$	−7.82475			−0.749475			−0.374738	+	0.927131i	$0.622267\pi$
$110$	−5.61478	−	1.72508i	−0.535348	−	0.164480i
$111$		0			0
$112$	−1.13746	−	0.656712i	−0.107480	−	0.0620535i
$113$	0.627940	+	0.362541i	0.0590716	+	0.0341050i	0.529245	−	0.848469i	$-0.322475\pi$
$113$	0.627940	+	0.362541i	0.0590716	+	0.0341050i	−0.470173	+	0.882574i	$0.655809\pi$
$114$		0			0
$115$	13.4124	+	4.12081i	1.25071	+	0.384268i
$116$	−9.13642			−0.848296
$117$		0			0
$118$		−	8.24163i		−	0.758703i
$119$	−0.837253	−	1.45017i	−0.0767509	−	0.132936i
$120$		0			0
$121$	2.04983	−	3.55042i	0.186349	−	0.322765i
$122$	−6.30026	−	3.63746i	−0.570399	−	0.329320i
$123$		0			0
$124$	4.27492	+	7.40437i	0.383899	+	0.664932i
$125$	8.71780	−	7.00000i	0.779744	−	0.626099i
$126$		0			0
$127$			22.0980i			1.96088i	0.196810	+	0.980442i	$0.436942\pi$
$127$			22.0980i			1.96088i	−0.196810	+	0.980442i	$0.563058\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	−3.77492	+	0.866025i	−0.331082	+	0.0759555i
$131$	−8.89834	+	15.4124i	−0.777452	+	1.34659i	0.155955	+	0.987764i	$0.450155\pi$
$131$	−8.89834	+	15.4124i	−0.777452	+	1.34659i	−0.933406	+	0.358821i	$0.883179\pi$
$132$		0			0
$133$	2.58762	−	1.49397i	0.224375	−	0.129543i
$134$	12.1819			1.05236
$135$		0			0
$136$	−1.27492			−0.109323
$137$	−3.31233	+	1.91238i	−0.282992	+	0.163385i	−0.634777	−	0.772695i	$-0.718908\pi$
$137$	−3.31233	+	1.91238i	−0.282992	+	0.163385i	0.351785	+	0.936081i	$0.385575\pi$
$138$		0			0
$139$	−5.13746	+	8.89834i	−0.435754	+	0.754747i	−0.997357	−	0.0726594i	$-0.976851\pi$
$139$	−5.13746	+	8.89834i	−0.435754	+	0.754747i	0.561603	+	0.827407i	$0.310185\pi$
$140$	−0.656712	−	2.86254i	−0.0555023	−	0.241929i
$141$		0			0
$142$	−6.00000	+	3.46410i	−0.503509	+	0.290701i
$143$			4.54983i			0.380476i
$144$		0			0
$145$	−13.9124	−	14.9605i	−1.15536	−	1.24240i
$146$	2.41753	+	4.18729i	0.200077	+	0.346543i
$147$		0			0
$148$	8.63746	+	4.98684i	0.709995	+	0.409916i
$149$	−0.685484	+	1.18729i	−0.0561570	+	0.0972668i	−0.892737	−	0.450578i	$-0.851218\pi$
$149$	−0.685484	+	1.18729i	−0.0561570	+	0.0972668i	0.836580	+	0.547844i	$0.184551\pi$
$150$		0			0
$151$	8.54983	+	14.8087i	0.695776	+	1.20512i	0.969919	+	0.243430i	$0.0782726\pi$
$151$	8.54983	+	14.8087i	0.695776	+	1.20512i	−0.274143	+	0.961689i	$0.588394\pi$
$152$		−	2.27492i		−	0.184520i
$153$		0			0
$154$	−3.45017			−0.278022
$155$	−5.61478	+	18.2749i	−0.450990	+	1.46788i
$156$		0			0
$157$	5.22508	+	3.01670i	0.417007	+	0.240759i	0.693796	−	0.720172i	$-0.255937\pi$
$157$	5.22508	+	3.01670i	0.417007	+	0.240759i	−0.276789	+	0.960931i	$0.589270\pi$
$158$		0			0
$159$		0			0
$160$	−2.13746	−	0.656712i	−0.168981	−	0.0519176i
$161$	8.24163			0.649531
$162$		0			0
$163$		−	24.3638i		−	1.90832i	−0.299297	−	0.954160i	$-0.596752\pi$
$163$		−	24.3638i		−	1.90832i	0.299297	−	0.954160i	$-0.403248\pi$
$164$	2.80739	+	4.86254i	0.219220	+	0.379701i
$165$		0			0
$166$	−2.00000	+	3.46410i	−0.155230	+	0.268866i
$167$	−18.2728	−	10.5498i	−1.41400	−	0.816371i	−0.418234	−	0.908339i	$-0.637351\pi$
$167$	−18.2728	−	10.5498i	−1.41400	−	0.816371i	−0.995762	+	0.0919688i	$0.970684\pi$
$168$		0			0
$169$	−5.00000	−	8.66025i	−0.384615	−	0.666173i
$170$	−1.94136	−	2.08762i	−0.148896	−	0.160113i
$171$		0			0
$172$		−	2.62685i		−	0.200295i
$173$	−17.4068	+	10.0498i	−1.32342	+	0.764075i	−0.984272	−	0.176660i	$-0.943471\pi$
$173$	−17.4068	+	10.0498i	−1.32342	+	0.764075i	−0.339144	+	0.940734i	$0.610137\pi$
$174$		0			0
$175$	3.68729	−	5.43424i	0.278733	−	0.410790i
$176$	−1.31342	+	2.27492i	−0.0990031	+	0.171478i
$177$		0			0
$178$	2.63746	−	1.52274i	0.197686	−	0.114134i
$179$	−1.31342			−0.0981699			−0.0490850	−	0.998795i	$-0.515631\pi$
$179$	−1.31342			−0.0981699			−0.0490850	+	0.998795i	$0.515631\pi$
$180$		0			0
$181$	6.54983			0.486845			0.243423	−	0.969920i	$-0.421730\pi$
$181$	6.54983			0.486845			0.243423	+	0.969920i	$0.421730\pi$
$182$	−1.97014	+	1.13746i	−0.146036	+	0.0843140i
$183$		0			0
$184$	3.13746	−	5.43424i	0.231297	−	0.400617i
$185$	4.98684	+	21.7371i	0.366640	+	1.59815i
$186$		0			0
$187$	−2.90033	+	1.67451i	−0.212093	+	0.122452i
$188$		−	10.2749i		−	0.749375i
$189$		0			0
$190$	3.72508	−	3.46410i	0.270246	−	0.251312i
$191$	7.40437	+	12.8248i	0.535762	+	0.927966i	0.999126	+	0.0417986i	$0.0133088\pi$
$191$	7.40437	+	12.8248i	0.535762	+	0.927966i	−0.463364	+	0.886168i	$0.653358\pi$
$192$		0			0
$193$	−7.18729	−	4.14959i	−0.517353	−	0.298694i	0.218498	−	0.975837i	$-0.429884\pi$
$193$	−7.18729	−	4.14959i	−0.517353	−	0.298694i	−0.735851	+	0.677144i	$0.763218\pi$
$194$	−9.55505	+	16.5498i	−0.686013	+	1.18821i
$195$		0			0
$196$	2.63746	+	4.56821i	0.188390	+	0.326301i
$197$			11.0000i			0.783718i	0.920025	+	0.391859i	$0.128168\pi$
$197$			11.0000i			0.783718i	−0.920025	+	0.391859i	$0.871832\pi$
$198$		0			0
$199$	7.45017			0.528128			0.264064	−	0.964505i	$-0.414937\pi$
$199$	7.45017			0.528128			0.264064	+	0.964505i	$0.414937\pi$
$200$	−2.17945	−	4.50000i	−0.154110	−	0.318198i
$201$		0			0
$202$	8.27492	+	4.77753i	0.582221	+	0.336146i
$203$	−10.3923	−	6.00000i	−0.729397	−	0.421117i
$204$		0			0
$205$	−3.68729	+	12.0014i	−0.257532	+	0.838211i
$206$	6.56712			0.457553
$207$		0			0
$208$			1.73205i			0.120096i
$209$	−2.98793	−	5.17525i	−0.206680	−	0.357979i
$210$		0			0
$211$	4.86254	−	8.42217i	0.334751	−	0.579806i	−0.648686	−	0.761056i	$-0.724681\pi$
$211$	4.86254	−	8.42217i	0.334751	−	0.579806i	0.983437	+	0.181250i	$0.0580144\pi$
$212$	−7.16629	−	4.13746i	−0.492183	−	0.284162i
$213$		0			0
$214$	6.00000	+	10.3923i	0.410152	+	0.710403i
$215$	4.30136	−	4.00000i	0.293350	−	0.272798i
$216$		0			0
$217$			11.2296i			0.762312i
$218$	−6.77643	+	3.91238i	−0.458958	+	0.264980i
$219$		0			0
$220$	−5.72508	+	1.31342i	−0.385985	+	0.0885510i
$221$	−1.10411	+	1.91238i	−0.0742705	+	0.128640i
$222$		0			0
$223$	14.2749	−	8.24163i	0.955919	−	0.551900i	0.0610045	−	0.998137i	$-0.480570\pi$
$223$	14.2749	−	8.24163i	0.955919	−	0.551900i	0.894915	+	0.446237i	$0.147236\pi$
$224$	−1.31342			−0.0877568
$225$		0			0
$226$	0.725083			0.0482318
$227$	−0.476171	+	0.274917i	−0.0316046	+	0.0182469i	−0.515719	−	0.856758i	$-0.672475\pi$
$227$	−0.476171	+	0.274917i	−0.0316046	+	0.0182469i	0.484114	+	0.875005i	$0.339142\pi$
$228$		0			0
$229$	11.1873	−	19.3770i	0.739277	−	1.28047i	−0.213544	−	0.976933i	$-0.568501\pi$
$229$	11.1873	−	19.3770i	0.739277	−	1.28047i	0.952821	−	0.303532i	$-0.0981660\pi$
$230$	13.6759	−	3.13746i	0.901760	−	0.206878i
$231$		0			0
$232$	−7.91238	+	4.56821i	−0.519473	+	0.299918i
$233$			0.175248i			0.0114809i	0.999984	+	0.00574045i	$0.00182725\pi$
$233$			0.175248i			0.0114809i	−0.999984	+	0.00574045i	$0.998173\pi$
$234$		0			0
$235$	16.8248	−	15.6460i	1.09753	−	1.02063i
$236$	−4.12081	−	7.13746i	−0.268242	−	0.464609i
$237$		0			0
$238$	−1.45017	−	0.837253i	−0.0940003	−	0.0542711i
$239$	4.77753	−	8.27492i	0.309032	−	0.535260i	−0.669119	−	0.743156i	$-0.733328\pi$
$239$	4.77753	−	8.27492i	0.309032	−	0.535260i	0.978151	+	0.207896i	$0.0666615\pi$
$240$		0			0
$241$	−6.91238	−	11.9726i	−0.445265	−	0.771222i	0.552805	−	0.833310i	$-0.313557\pi$
$241$	−6.91238	−	11.9726i	−0.445265	−	0.771222i	−0.998071	+	0.0620883i	$0.980224\pi$
$242$		−	4.09967i		−	0.263537i
$243$		0			0
$244$	−7.27492			−0.465729
$245$	−3.46410	+	11.2749i	−0.221313	+	0.720328i
$246$		0			0
$247$	−3.41238	−	1.97014i	−0.217124	−	0.125357i
$248$	7.40437	+	4.27492i	0.470178	+	0.271458i
$249$		0			0
$250$	4.04983	−	10.4211i	0.256134	−	0.659087i
$251$	−2.98793			−0.188597			−0.0942983	−	0.995544i	$-0.530061\pi$
$251$	−2.98793			−0.188597			−0.0942983	+	0.995544i	$0.530061\pi$
$252$		0			0
$253$		−	16.4833i		−	1.03629i
$254$	11.0490	+	19.1375i	0.693277	+	1.20079i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−0.627940	−	0.362541i	−0.0391698	−	0.0226147i	0.480287	−	0.877111i	$-0.340532\pi$
$257$	−0.627940	−	0.362541i	−0.0391698	−	0.0226147i	−0.519457	+	0.854497i	$0.673866\pi$
$258$		0			0
$259$	6.54983	+	11.3446i	0.406987	+	0.704922i
$260$	−2.83616	+	2.63746i	−0.175891	+	0.163568i
$261$		0			0
$262$			17.7967i			1.09948i
$263$	16.7789	−	9.68729i	1.03463	−	0.597344i	0.116323	−	0.993211i	$-0.462889\pi$
$263$	16.7789	−	9.68729i	1.03463	−	0.597344i	0.918308	+	0.395867i	$0.129556\pi$
$264$		0			0
$265$	−4.13746	−	18.0348i	−0.254162	−	1.10787i
$266$	1.49397	−	2.58762i	0.0916009	−	0.158657i
$267$		0			0
$268$	10.5498	−	6.09095i	0.644434	−	0.372064i
$269$	−11.6482			−0.710202			−0.355101	−	0.934828i	$-0.615554\pi$
$269$	−11.6482			−0.710202			−0.355101	+	0.934828i	$0.615554\pi$
$270$		0			0
$271$	−12.5498			−0.762348			−0.381174	−	0.924503i	$-0.624480\pi$
$271$	−12.5498			−0.762348			−0.381174	+	0.924503i	$0.624480\pi$
$272$	−1.10411	+	0.637459i	−0.0669465	+	0.0386516i
$273$		0			0
$274$	−1.91238	+	3.31233i	−0.115531	+	0.200105i
$275$	−10.8685	−	7.37459i	−0.655394	−	0.444704i
$276$		0			0
$277$	−17.6873	+	10.2118i	−1.06273	+	0.613565i	−0.926185	−	0.377069i	$-0.876932\pi$
$277$	−17.6873	+	10.2118i	−1.06273	+	0.613565i	−0.136541	+	0.990634i	$0.543599\pi$
$278$			10.2749i			0.616249i
$279$		0			0
$280$	−2.00000	−	2.15068i	−0.119523	−	0.128528i
$281$	−1.34220	−	2.32475i	−0.0800687	−	0.138683i	0.823211	−	0.567736i	$-0.192181\pi$
$281$	−1.34220	−	2.32475i	−0.0800687	−	0.138683i	−0.903279	+	0.429053i	$0.858847\pi$
$282$		0			0
$283$	8.27492	+	4.77753i	0.491893	+	0.283994i	0.725359	−	0.688370i	$-0.241674\pi$
$283$	8.27492	+	4.77753i	0.491893	+	0.283994i	−0.233467	+	0.972365i	$0.575007\pi$
$284$	−3.46410	+	6.00000i	−0.205557	+	0.356034i
$285$		0			0
$286$	2.27492	+	3.94027i	0.134519	+	0.232993i
$287$			7.37459i			0.435308i
$288$		0			0
$289$	15.3746			0.904387
$290$	−19.5287	−	6.00000i	−1.14677	−	0.352332i
$291$		0			0
$292$	4.18729	+	2.41753i	0.245043	+	0.141476i
$293$	12.9904	+	7.50000i	0.758906	+	0.438155i	0.828903	−	0.559393i	$-0.188966\pi$
$293$	12.9904	+	7.50000i	0.758906	+	0.438155i	−0.0699967	+	0.997547i	$0.522299\pi$
$294$		0			0
$295$	5.41238	−	17.6161i	0.315121	−	1.02565i
$296$	9.97368			0.579708
$297$		0			0
$298$			1.37097i			0.0794180i
$299$	−5.43424	−	9.41238i	−0.314270	−	0.544332i
$300$		0			0
$301$	1.72508	−	2.98793i	0.0994321	−	0.172221i
$302$	14.8087	+	8.54983i	0.852148	+	0.491988i
$303$		0			0
$304$	−1.13746	−	1.97014i	−0.0652377	−	0.112995i
$305$	−11.0778	−	11.9124i	−0.634312	−	0.682101i
$306$		0			0
$307$		−	0.952341i		−	0.0543530i	−0.999631	−	0.0271765i	$-0.991348\pi$
$307$		−	0.952341i		−	0.0543530i	0.999631	−	0.0271765i	$-0.00865161\pi$
$308$	−2.98793	+	1.72508i	−0.170253	+	0.0982957i
$309$		0			0
$310$	4.27492	+	18.6339i	0.242799	+	1.05834i
$311$	10.8685	−	18.8248i	0.616295	−	1.06745i	−0.373861	−	0.927485i	$-0.621966\pi$
$311$	10.8685	−	18.8248i	0.616295	−	1.06745i	0.990156	−	0.139969i	$-0.0447003\pi$
$312$		0			0
$313$	−15.4622	+	8.92711i	−0.873976	+	0.504590i	−0.868667	−	0.495396i	$-0.835023\pi$
$313$	−15.4622	+	8.92711i	−0.873976	+	0.504590i	−0.00530840	+	0.999986i	$0.501690\pi$
$314$	6.03341			0.340485
$315$		0			0
$316$		0			0
$317$	19.1389	−	11.0498i	1.07495	−	0.620621i	0.145418	−	0.989370i	$-0.453547\pi$
$317$	19.1389	−	11.0498i	1.07495	−	0.620621i	0.929529	+	0.368750i	$0.120214\pi$
$318$		0			0
$319$	−12.0000	+	20.7846i	−0.671871	+	1.16371i
$320$	−2.17945	+	0.500000i	−0.121835	+	0.0279508i
$321$		0			0
$322$	7.13746	−	4.12081i	0.397755	−	0.229644i
$323$		−	2.90033i		−	0.161379i
$324$		0			0
$325$	−8.63746	−	0.627940i	−0.479120	−	0.0348319i
$326$	−12.1819	−	21.0997i	−0.674693	−	1.16860i
$327$		0			0
$328$	4.86254	+	2.80739i	0.268489	+	0.155012i
$329$	6.74766	−	11.6873i	0.372011	−	0.644341i
$330$		0			0
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	0.998298	+	0.0583130i	$0.0185721\pi$
$331$	10.0000	+	17.3205i	0.549650	+	0.952021i	−0.448649	+	0.893708i	$0.648095\pi$
$332$			4.00000i			0.219529i
$333$		0			0
$334$	−21.0997			−1.15452
$335$	26.0383	+	8.00000i	1.42262	+	0.437087i
$336$		0			0
$337$	−4.54983	−	2.62685i	−0.247845	−	0.143094i	0.370932	−	0.928660i	$-0.379038\pi$
$337$	−4.54983	−	2.62685i	−0.247845	−	0.143094i	−0.618777	+	0.785567i	$0.712372\pi$
$338$	−8.66025	−	5.00000i	−0.471056	−	0.271964i
$339$		0			0
$340$	−2.72508	−	0.837253i	−0.147788	−	0.0454064i
$341$	22.4591			1.21623
$342$		0			0
$343$			16.1222i			0.870515i
$344$	−1.31342	−	2.27492i	−0.0708151	−	0.122655i
$345$		0			0
$346$	−10.0498	+	17.4068i	−0.540282	+	0.935797i
$347$	−6.45203	−	3.72508i	−0.346363	−	0.199973i	0.316719	−	0.948519i	$-0.397419\pi$
$347$	−6.45203	−	3.72508i	−0.346363	−	0.199973i	−0.663082	+	0.748546i	$0.730752\pi$
$348$		0			0
$349$	−16.0997	−	27.8854i	−0.861796	−	1.49267i	−0.870194	−	0.492709i	$-0.836007\pi$
$349$	−16.0997	−	27.8854i	−0.861796	−	1.49267i	0.00839869	−	0.999965i	$-0.497327\pi$
$350$	0.476171	−	6.54983i	0.0254524	−	0.350103i
$351$		0			0
$352$			2.62685i			0.140011i
$353$	12.6005	−	7.27492i	0.670658	−	0.387205i	−0.125668	−	0.992072i	$-0.540107\pi$
$353$	12.6005	−	7.27492i	0.670658	−	0.387205i	0.796326	+	0.604868i	$0.206774\pi$
$354$		0			0
$355$	−15.0997	+	3.46410i	−0.801407	+	0.183855i
$356$	1.52274	−	2.63746i	0.0807049	−	0.139785i
$357$		0			0
$358$	−1.13746	+	0.656712i	−0.0601166	+	0.0347083i
$359$	−21.7370			−1.14723			−0.573616	−	0.819124i	$-0.694460\pi$
$359$	−21.7370			−1.14723			−0.573616	+	0.819124i	$0.694460\pi$
$360$		0			0
$361$	−13.8248			−0.727619
$362$	5.67232	−	3.27492i	0.298131	−	0.172126i
$363$		0			0
$364$	−1.13746	+	1.97014i	−0.0596190	+	0.103263i
$365$	2.41753	+	10.5378i	0.126540	+	0.551573i
$366$		0			0
$367$	−2.27492	+	1.31342i	−0.118750	+	0.0685602i	−0.558198	−	0.829708i	$-0.688507\pi$
$367$	−2.27492	+	1.31342i	−0.118750	+	0.0685602i	0.439449	+	0.898268i	$0.355174\pi$
$368$		−	6.27492i		−	0.327103i
$369$		0			0
$370$	15.1873	+	16.3315i	0.789550	+	0.849033i
$371$	−5.43424	−	9.41238i	−0.282132	−	0.488666i
$372$		0			0
$373$	−19.6495	−	11.3446i	−1.01741	−	0.587404i	−0.104059	−	0.994571i	$-0.533183\pi$
$373$	−19.6495	−	11.3446i	−1.01741	−	0.587404i	−0.913353	+	0.407168i	$0.866516\pi$
$374$	−1.67451	+	2.90033i	−0.0865867	+	0.149973i
$375$		0			0
$376$	−5.13746	−	8.89834i	−0.264944	−	0.458897i
$377$			15.8248i			0.815016i
$378$		0			0
$379$	27.3746			1.40614			0.703069	−	0.711122i	$-0.251812\pi$
$379$	27.3746			1.40614			0.703069	+	0.711122i	$0.251812\pi$
$380$	1.49397	−	4.86254i	0.0766388	−	0.249443i
$381$		0			0
$382$	12.8248	+	7.40437i	0.656171	+	0.378841i
$383$	−2.92248	−	1.68729i	−0.149332	−	0.0862166i	0.423472	−	0.905909i	$-0.360811\pi$
$383$	−2.92248	−	1.68729i	−0.149332	−	0.0862166i	−0.572804	+	0.819692i	$0.694144\pi$
$384$		0			0
$385$	−7.37459	−	2.26577i	−0.375844	−	0.115474i
$386$	−8.29917			−0.422417
$387$		0			0
$388$			19.1101i			0.970168i
$389$	−16.9594	−	29.3746i	−0.859877	−	1.48935i	−0.872046	−	0.489425i	$-0.837207\pi$
$389$	−16.9594	−	29.3746i	−0.859877	−	1.48935i	0.0121686	−	0.999926i	$-0.496127\pi$
$390$		0			0
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$	4.56821	+	2.63746i	0.230730	+	0.133212i
$393$		0			0
$394$	5.50000	+	9.52628i	0.277086	+	0.479927i
$395$		0			0
$396$		0			0
$397$			14.3901i			0.722219i	0.932523	+	0.361110i	$0.117602\pi$
$397$			14.3901i			0.722219i	−0.932523	+	0.361110i	$0.882398\pi$
$398$	6.45203	−	3.72508i	0.323411	−	0.186722i
$399$		0			0
$400$	−4.13746	−	2.80739i	−0.206873	−	0.140369i
$401$	10.8397	−	18.7749i	0.541309	−	0.937575i	−0.457520	−	0.889199i	$-0.651262\pi$
$401$	10.8397	−	18.7749i	0.541309	−	0.937575i	0.998829	−	0.0483754i	$-0.0154044\pi$
$402$		0			0
$403$	12.8248	−	7.40437i	0.638846	−	0.368838i
$404$	9.55505			0.475382
$405$		0			0
$406$	−12.0000			−0.595550
$407$	22.6893	−	13.0997i	1.12467	−	0.649326i
$408$		0			0
$409$	−8.04983	+	13.9427i	−0.398039	+	0.689423i	−0.993484	−	0.113973i	$-0.963642\pi$
$409$	−8.04983	+	13.9427i	−0.398039	+	0.689423i	0.595445	+	0.803396i	$0.296976\pi$
$410$	2.80739	+	12.2371i	0.138647	+	0.604349i
$411$		0			0
$412$	5.68729	−	3.28356i	0.280193	−	0.161769i
$413$		−	10.8248i		−	0.532651i
$414$		0			0
$415$	−6.54983	+	6.09095i	−0.321519	+	0.298993i
$416$	0.866025	+	1.50000i	0.0424604	+	0.0735436i
$417$		0			0
$418$	−5.17525	−	2.98793i	−0.253130	−	0.146144i
$419$	8.24163	−	14.2749i	0.402630	−	0.697375i	−0.591413	−	0.806369i	$-0.701430\pi$
$419$	8.24163	−	14.2749i	0.402630	−	0.697375i	0.994042	+	0.108994i	$0.0347629\pi$
$420$		0			0
$421$	−4.63746	−	8.03231i	−0.226016	−	0.391471i	0.730608	−	0.682797i	$-0.239237\pi$
$421$	−4.63746	−	8.03231i	−0.226016	−	0.391471i	−0.956624	+	0.291326i	$0.905903\pi$
$422$		−	9.72508i		−	0.473410i
$423$		0			0
$424$	−8.27492			−0.401866
$425$	−2.77862	−	5.73713i	−0.134783	−	0.278292i
$426$		0			0
$427$	−8.27492	−	4.77753i	−0.400451	−	0.231201i
$428$	10.3923	+	6.00000i	0.502331	+	0.290021i
$429$		0			0
$430$	1.72508	−	5.61478i	0.0831909	−	0.270769i
$431$	−33.9189			−1.63381			−0.816907	−	0.576770i	$-0.804313\pi$
$431$	−33.9189			−1.63381			−0.816907	+	0.576770i	$0.804313\pi$
$432$		0			0
$433$			10.8109i			0.519540i	0.965670	+	0.259770i	$0.0836468\pi$
$433$			10.8109i			0.519540i	−0.965670	+	0.259770i	$0.916353\pi$
$434$	5.61478	+	9.72508i	0.269518	+	0.466819i
$435$		0			0
$436$	−3.91238	+	6.77643i	−0.187369	+	0.324532i
$437$	12.3624	+	7.13746i	0.591376	+	0.341431i
$438$		0			0
$439$	−18.0000	−	31.1769i	−0.859093	−	1.48799i	−0.872795	−	0.488087i	$-0.837695\pi$
$439$	−18.0000	−	31.1769i	−0.859093	−	1.48799i	0.0137020	−	0.999906i	$-0.495638\pi$
$440$	−4.30136	+	4.00000i	−0.205059	+	0.190693i
$441$		0			0
$442$			2.20822i			0.105034i
$443$	−6.45203	+	3.72508i	−0.306545	+	0.176984i	−0.645380	−	0.763862i	$-0.723301\pi$
$443$	−6.45203	+	3.72508i	−0.306545	+	0.176984i	0.338834	+	0.940846i	$0.389967\pi$
$444$		0			0
$445$	6.63746	−	1.52274i	0.314646	−	0.0721847i
$446$	8.24163	−	14.2749i	0.390252	−	0.675937i
$447$		0			0
$448$	−1.13746	+	0.656712i	−0.0537399	+	0.0310267i
$449$	−10.8685			−0.512915			−0.256458	−	0.966555i	$-0.582555\pi$
$449$	−10.8685			−0.512915			−0.256458	+	0.966555i	$0.582555\pi$
$450$		0			0
$451$	14.7492			0.694511
$452$	0.627940	−	0.362541i	0.0295358	−	0.0170525i
$453$		0			0
$454$	−0.274917	+	0.476171i	−0.0129025	+	0.0223478i
$455$	−4.95807	+	1.13746i	−0.232438	+	0.0533249i
$456$		0			0
$457$	13.8127	−	7.97477i	0.646131	−	0.373044i	−0.140841	−	0.990032i	$-0.544981\pi$
$457$	13.8127	−	7.97477i	0.646131	−	0.373044i	0.786972	+	0.616988i	$0.211647\pi$
$458$		−	22.3746i		−	1.04550i
$459$		0			0
$460$	10.2749	−	9.55505i	0.479070	−	0.445507i
$461$	3.46410	+	6.00000i	0.161339	+	0.279448i	0.935349	−	0.353726i	$-0.115085\pi$
$461$	3.46410	+	6.00000i	0.161339	+	0.279448i	−0.774010	+	0.633173i	$0.781752\pi$
$462$		0			0
$463$	−14.5876	−	8.42217i	−0.677944	−	0.391411i	0.121136	−	0.992636i	$-0.461346\pi$
$463$	−14.5876	−	8.42217i	−0.677944	−	0.391411i	−0.799080	+	0.601225i	$0.794680\pi$
$464$	−4.56821	+	7.91238i	−0.212074	+	0.367323i
$465$		0			0
$466$	0.0876242	+	0.151770i	0.00405911	+	0.00703059i
$467$		−	13.6495i		−	0.631624i	−0.948822	−	0.315812i	$-0.897723\pi$
$467$		−	13.6495i		−	0.631624i	0.948822	−	0.315812i	$-0.102277\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$	6.74766	−	21.9622i	0.311246	−	1.01304i
$471$		0			0
$472$	−7.13746	−	4.12081i	−0.328528	−	0.189676i
$473$	−5.97586	−	3.45017i	−0.274770	−	0.158639i
$474$		0			0
$475$	10.2371	−	4.95807i	0.469712	−	0.227492i
$476$	−1.67451			−0.0767509
$477$		0			0
$478$		−	9.55505i		−	0.437038i
$479$	0.837253	+	1.45017i	0.0382551	+	0.0662598i	0.884519	−	0.466504i	$-0.154487\pi$
$479$	0.837253	+	1.45017i	0.0382551	+	0.0662598i	−0.846264	+	0.532764i	$0.821153\pi$
$480$		0			0
$481$	8.63746	−	14.9605i	0.393834	−	0.682141i
$482$	−11.9726	−	6.91238i	−0.545336	−	0.314850i
$483$		0			0
$484$	−2.04983	−	3.55042i	−0.0931743	−	0.161383i
$485$	−31.2920	+	29.0997i	−1.42090	+	1.32135i
$486$		0			0
$487$		−	9.91613i		−	0.449343i	−0.974435	−	0.224671i	$-0.927869\pi$
$487$		−	9.91613i		−	0.449343i	0.974435	−	0.224671i	$-0.0721309\pi$
$488$	−6.30026	+	3.63746i	−0.285200	+	0.164660i
$489$		0			0
$490$	2.63746	+	11.4964i	0.119148	+	0.519355i
$491$	9.37451	−	16.2371i	0.423066	−	0.732771i	−0.573172	−	0.819435i	$-0.694287\pi$
$491$	9.37451	−	16.2371i	0.423066	−	0.732771i	0.996238	+	0.0866638i	$0.0276206\pi$
$492$		0			0
$493$	−10.0876	+	5.82409i	−0.454324	+	0.262304i
$494$	−3.94027			−0.177281
$495$		0			0
$496$	8.54983			0.383899
$497$	−7.88054	+	4.54983i	−0.353491	+	0.204088i
$498$		0			0
$499$	7.13746	−	12.3624i	0.319517	−	0.553419i	−0.660871	−	0.750500i	$-0.729813\pi$
$499$	7.13746	−	12.3624i	0.319517	−	0.553419i	0.980387	+	0.197081i	$0.0631462\pi$
$500$	−1.70328	−	11.0498i	−0.0761729	−	0.494164i
$501$		0			0
$502$	−2.58762	+	1.49397i	−0.115491	+	0.0666789i
$503$			33.0997i			1.47584i	0.674887	+	0.737921i	$0.264192\pi$
$503$			33.0997i			1.47584i	−0.674887	+	0.737921i	$0.735808\pi$
$504$		0			0
$505$	14.5498	+	15.6460i	0.647459	+	0.696238i
$506$	−8.24163	−	14.2749i	−0.366385	−	0.634597i
$507$		0			0
$508$	19.1375	+	11.0490i	0.849087	+	0.490221i
$509$	−3.46410	+	6.00000i	−0.153544	+	0.265945i	−0.932528	−	0.361098i	$-0.882402\pi$
$509$	−3.46410	+	6.00000i	−0.153544	+	0.265945i	0.778984	+	0.627044i	$0.215735\pi$
$510$		0			0
$511$	3.17525	+	5.49969i	0.140465	+	0.243292i
$512$			1.00000i			0.0441942i
$513$		0			0
$514$	−0.725083			−0.0319820
$515$	14.0369	+	4.31271i	0.618542	+	0.190041i
$516$		0			0
$517$	−23.3746	−	13.4953i	−1.02801	−	0.593524i
$518$	11.3446	+	6.54983i	0.498455	+	0.287783i
$519$		0			0
$520$	−1.13746	+	3.70219i	−0.0498809	+	0.162352i
$521$	43.8350			1.92045			0.960223	−	0.279235i	$-0.0900809\pi$
$521$	43.8350			1.92045			0.960223	+	0.279235i	$0.0900809\pi$
$522$		0			0
$523$		−	10.5074i		−	0.459456i	−0.973255	−	0.229728i	$-0.926216\pi$
$523$		−	10.5074i		−	0.459456i	0.973255	−	0.229728i	$-0.0737837\pi$
$524$	8.89834	+	15.4124i	0.388726	+	0.673293i
$525$		0			0
$526$	9.68729	−	16.7789i	0.422386	−	0.731594i
$527$	9.43996	+	5.45017i	0.411211	+	0.237413i
$528$		0			0
$529$	8.18729	+	14.1808i	0.355969	+	0.616557i
$530$	−12.6005	−	13.5498i	−0.547332	−	0.588567i
$531$		0			0
$532$		−	2.98793i		−	0.129543i
$533$	8.42217	−	4.86254i	0.364805	−	0.210620i
$534$		0			0
$535$	6.00000	+	26.1534i	0.259403	+	1.13071i
$536$	6.09095	−	10.5498i	0.263089	−	0.455683i
$537$		0			0
$538$	−10.0876	+	5.82409i	−0.434908	+	0.251094i
$539$	13.8564			0.596838
$540$		0			0
$541$	10.7251			0.461107			0.230554	−	0.973060i	$-0.425946\pi$
$541$	10.7251			0.461107			0.230554	+	0.973060i	$0.425946\pi$
$542$	−10.8685	+	6.27492i	−0.466841	+	0.269531i
$543$		0			0
$544$	−0.637459	+	1.10411i	−0.0273308	+	0.0473384i
$545$	−17.0537	+	3.91238i	−0.730498	+	0.167588i
$546$		0			0
$547$	29.3746	−	16.9594i	1.25597	−	0.725133i	0.283679	−	0.958919i	$-0.408445\pi$
$547$	29.3746	−	16.9594i	1.25597	−	0.725133i	0.972288	+	0.233787i	$0.0751118\pi$
$548$			3.82475i			0.163385i
$549$		0			0
$550$	−13.0997	−	0.952341i	−0.558572	−	0.0406080i
$551$	−10.3923	−	18.0000i	−0.442727	−	0.766826i
$552$		0			0
$553$		0			0
$554$	−10.2118	+	17.6873i	−0.433856	+	0.751461i
$555$		0			0
$556$	5.13746	+	8.89834i	0.217877	+	0.377374i
$557$		−	45.1993i		−	1.91516i	−0.288172	−	0.957579i	$-0.593047\pi$
$557$		−	45.1993i		−	1.91516i	0.288172	−	0.957579i	$-0.406953\pi$
$558$		0			0
$559$	−4.54983			−0.192437
$560$	−2.80739	−	0.862541i	−0.118634	−	0.0364490i
$561$		0			0
$562$	−2.32475	−	1.34220i	−0.0980637	−	0.0566171i
$563$	25.2011	+	14.5498i	1.06210	+	0.613202i	0.926012	−	0.377495i	$-0.123214\pi$
$563$	25.2011	+	14.5498i	1.06210	+	0.613202i	0.136086	+	0.990697i	$0.456548\pi$
$564$		0			0
$565$	1.54983	+	0.476171i	0.0652020	+	0.0200326i
$566$	9.55505			0.401629
$567$		0			0
$568$			6.92820i			0.290701i
$569$	−6.48080	−	11.2251i	−0.271689	−	0.470580i	0.697605	−	0.716482i	$-0.254249\pi$
$569$	−6.48080	−	11.2251i	−0.271689	−	0.470580i	−0.969295	+	0.245903i	$0.920916\pi$
$570$		0			0
$571$	8.54983	−	14.8087i	0.357799	−	0.619727i	−0.629793	−	0.776763i	$-0.716860\pi$
$571$	8.54983	−	14.8087i	0.357799	−	0.619727i	0.987593	+	0.157036i	$0.0501938\pi$
$572$	3.94027	+	2.27492i	0.164751	+	0.0951191i
$573$		0			0
$574$	3.68729	+	6.38658i	0.153905	+	0.266571i
$575$	31.2920	+	2.27492i	1.30497	+	0.0948706i
$576$		0			0
$577$		−	29.0838i		−	1.21077i	−0.795931	−	0.605387i	$-0.793018\pi$
$577$		−	29.0838i		−	1.21077i	0.795931	−	0.605387i	$-0.206982\pi$
$578$	13.3148	−	7.68729i	0.553822	−	0.319749i
$579$		0			0
$580$	−19.9124	+	4.56821i	−0.826816	+	0.189685i
$581$	−2.62685	+	4.54983i	−0.108980	+	0.188759i
$582$		0			0
$583$	−18.8248	+	10.8685i	−0.779642	+	0.450126i
$584$	4.83507			0.200077
$585$		0			0
$586$	15.0000			0.619644
$587$	−28.6652	+	16.5498i	−1.18314	+	0.683085i	−0.956738	−	0.290950i	$-0.906029\pi$
$587$	−28.6652	+	16.5498i	−1.18314	+	0.683085i	−0.226399	+	0.974035i	$0.572695\pi$
$588$		0			0
$589$	−9.72508	+	16.8443i	−0.400715	+	0.694059i
$590$	−4.12081	−	17.9622i	−0.169651	−	0.739492i
$591$		0			0
$592$	8.63746	−	4.98684i	0.354997	−	0.204958i
$593$		−	20.1752i		−	0.828498i	−0.910164	−	0.414249i	$-0.864044\pi$
$593$		−	20.1752i		−	0.828498i	0.910164	−	0.414249i	$-0.135956\pi$
$594$		0			0
$595$	−2.54983	−	2.74194i	−0.104533	−	0.112408i
$596$	0.685484	+	1.18729i	0.0280785	+	0.0486334i
$597$		0			0
$598$	−9.41238	−	5.43424i	−0.384901	−	0.222223i
$599$	3.46410	−	6.00000i	0.141539	−	0.245153i	−0.786537	−	0.617543i	$-0.788128\pi$
$599$	3.46410	−	6.00000i	0.141539	−	0.245153i	0.928076	+	0.372390i	$0.121461\pi$
$600$		0			0
$601$	−0.225083	−	0.389855i	−0.00918132	−	0.0159025i	0.861398	−	0.507930i	$-0.169589\pi$
$601$	−0.225083	−	0.389855i	−0.00918132	−	0.0159025i	−0.870580	+	0.492028i	$0.836256\pi$
$602$		−	3.45017i		−	0.140618i
$603$		0			0
$604$	17.0997			0.695776
$605$	2.69230	−	8.76287i	0.109458	−	0.356261i
$606$		0			0
$607$	29.3746	+	16.9594i	1.19228	+	0.688362i	0.958823	−	0.284006i	$-0.0916635\pi$
$607$	29.3746	+	16.9594i	1.19228	+	0.688362i	0.233455	+	0.972368i	$0.424997\pi$
$608$	−1.97014	−	1.13746i	−0.0798996	−	0.0461300i
$609$		0			0
$610$	−15.5498	−	4.77753i	−0.629594	−	0.193436i
$611$	−17.7967			−0.719977
$612$		0			0
$613$			12.5430i			0.506606i	0.967387	+	0.253303i	$0.0815170\pi$
$613$			12.5430i			0.506606i	−0.967387	+	0.253303i	$0.918483\pi$
$614$	−0.476171	−	0.824752i	−0.0192167	−	0.0332843i
$615$		0			0
$616$	−1.72508	+	2.98793i	−0.0695056	+	0.120387i
$617$	−6.77643	−	3.91238i	−0.272809	−	0.157506i	0.357355	−	0.933969i	$-0.383679\pi$
$617$	−6.77643	−	3.91238i	−0.272809	−	0.157506i	−0.630163	+	0.776462i	$0.717012\pi$
$618$		0			0
$619$	11.1375	+	19.2906i	0.447652	+	0.775356i	0.998233	−	0.0594256i	$-0.0189269\pi$
$619$	11.1375	+	19.2906i	0.447652	+	0.775356i	−0.550580	+	0.834782i	$0.685594\pi$
$620$	13.0192	+	14.0000i	0.522862	+	0.562254i
$621$		0			0
$622$		−	21.7370i		−	0.871572i
$623$	3.46410	−	2.00000i	0.138786	−	0.0801283i
$624$		0			0
$625$	15.5000	−	19.6150i	0.620000	−	0.784602i
$626$	−8.92711	+	15.4622i	−0.356799	+	0.617994i
$627$		0			0
$628$	5.22508	−	3.01670i	0.208504	−	0.120380i
$629$	12.7156			0.507005
$630$		0			0
$631$	−40.0000			−1.59237			−0.796187	−	0.605050i	$-0.793153\pi$
$631$	−40.0000			−1.59237			−0.796187	+	0.605050i	$0.793153\pi$
$632$		0			0
$633$		0			0
$634$	11.0498	−	19.1389i	0.438845	−	0.760102i
$635$	11.0490	+	48.1615i	0.438467	+	1.91123i
$636$		0			0
$637$	7.91238	−	4.56821i	0.313500	−	0.180999i
$638$			24.0000i			0.950169i
$639$		0			0
$640$	−1.63746	+	1.52274i	−0.0647262	+	0.0601915i
$641$	15.3791	+	26.6375i	0.607440	+	1.05212i	0.991661	+	0.128875i	$0.0411367\pi$
$641$	15.3791	+	26.6375i	0.607440	+	1.05212i	−0.384221	+	0.923241i	$0.625530\pi$
$642$		0			0
$643$	−0.824752	−	0.476171i	−0.0325250	−	0.0187783i	0.483649	−	0.875262i	$-0.339311\pi$
$643$	−0.824752	−	0.476171i	−0.0325250	−	0.0187783i	−0.516174	+	0.856484i	$0.672644\pi$
$644$	4.12081	−	7.13746i	0.162383	−	0.281255i
$645$		0			0
$646$	−1.45017	−	2.51176i	−0.0570560	−	0.0988239i
$647$			21.0997i			0.829514i	0.909932	+	0.414757i	$0.136133\pi$
$647$			21.0997i			0.829514i	−0.909932	+	0.414757i	$0.863867\pi$
$648$		0			0
$649$	−21.6495			−0.849817
$650$	−7.79423	+	3.77492i	−0.305715	+	0.148064i
$651$		0			0
$652$	−21.0997	−	12.1819i	−0.826327	−	0.477080i
$653$	−12.1244	−	7.00000i	−0.474463	−	0.273931i	0.243643	−	0.969865i	$-0.421657\pi$
$653$	−12.1244	−	7.00000i	−0.474463	−	0.273931i	−0.718106	+	0.695934i	$0.754991\pi$
$654$		0			0
$655$	−11.6873	+	38.0397i	−0.456660	+	1.48633i
$656$	5.61478			0.219220
$657$		0			0
$658$		−	13.4953i		−	0.526102i
$659$	−2.33122	−	4.03779i	−0.0908114	−	0.157290i	0.817041	−	0.576579i	$-0.195613\pi$
$659$	−2.33122	−	4.03779i	−0.0908114	−	0.157290i	−0.907853	+	0.419289i	$0.862279\pi$
$660$		0			0
$661$	−15.6375	+	27.0849i	−0.608227	+	1.05348i	0.383306	+	0.923621i	$0.374785\pi$
$661$	−15.6375	+	27.0849i	−0.608227	+	1.05348i	−0.991533	+	0.129858i	$0.958548\pi$
$662$	17.3205	+	10.0000i	0.673181	+	0.388661i
$663$		0			0
$664$	2.00000	+	3.46410i	0.0776151	+	0.134433i
$665$	4.89261	−	4.54983i	0.189727	−	0.176435i
$666$		0			0
$667$		−	57.3303i		−	2.21984i
$668$	−18.2728	+	10.5498i	−0.706998	+	0.408185i
$669$		0			0
$670$	26.5498	−	6.09095i	1.02571	−	0.235314i
$671$	−9.55505	+	16.5498i	−0.368869	+	0.638899i
$672$		0			0
$673$	4.91238	−	2.83616i	0.189358	−	0.109326i	−0.402324	−	0.915497i	$-0.631797\pi$
$673$	4.91238	−	2.83616i	0.189358	−	0.109326i	0.591682	+	0.806171i	$0.298464\pi$
$674$	−5.25370			−0.202365
$675$		0			0
$676$	−10.0000			−0.384615
$677$	−20.5465	+	11.8625i	−0.789667	+	0.455915i	−0.839845	−	0.542826i	$-0.817354\pi$
$677$	−20.5465	+	11.8625i	−0.789667	+	0.455915i	0.0501782	+	0.998740i	$0.484021\pi$
$678$		0			0
$679$	−12.5498	+	21.7370i	−0.481618	+	0.834188i
$680$	−2.77862	+	0.637459i	−0.106555	+	0.0244454i
$681$		0			0
$682$	19.4502	−	11.2296i	0.744785	−	0.430002i
$683$		−	26.7492i		−	1.02353i	−0.859126	−	0.511764i	$-0.828992\pi$
$683$		−	26.7492i		−	1.02353i	0.859126	−	0.511764i	$-0.171008\pi$
$684$		0			0
$685$	−6.26287	+	5.82409i	−0.239292	+	0.222527i
$686$	8.06109	+	13.9622i	0.307774	+	0.533080i
$687$		0			0
$688$	−2.27492	−	1.31342i	−0.0867304	−	0.0500738i
$689$	−7.16629	+	12.4124i	−0.273014	+	0.472874i
$690$		0			0
$691$	11.9622	+	20.7192i	0.455064	+	0.788194i	0.998692	−	0.0511325i	$-0.0162831\pi$
$691$	11.9622	+	20.7192i	0.455064	+	0.788194i	−0.543628	+	0.839326i	$0.682950\pi$
$692$			20.0997i			0.764075i
$693$		0			0
$694$	−7.45017			−0.282804
$695$	−6.74766	+	21.9622i	−0.255953	+	0.833074i
$696$		0			0
$697$	6.19934	+	3.57919i	0.234817	+	0.135571i
$698$	−27.8854	−	16.0997i	−1.05548	−	0.609381i
$699$		0			0
$700$	−2.86254	−	5.91041i	−0.108194	−	0.223392i
$701$	18.6915			0.705967			0.352984	−	0.935629i	$-0.385167\pi$
$701$	18.6915			0.705967			0.352984	+	0.935629i	$0.385167\pi$
$702$		0			0
$703$			22.6893i			0.855743i
$704$	1.31342	+	2.27492i	0.0495015	+	0.0857392i
$705$		0			0
$706$	7.27492	−	12.6005i	0.273795	−	0.474227i
$707$	10.8685	+	6.27492i	0.408751	+	0.235993i
$708$		0			0
$709$	−1.91238	−	3.31233i	−0.0718208	−	0.124397i	0.827879	−	0.560907i	$-0.189548\pi$
$709$	−1.91238	−	3.31233i	−0.0718208	−	0.124397i	−0.899699	+	0.436510i	$0.856214\pi$
$710$	−11.3446	+	10.5498i	−0.425757	+	0.395928i
$711$		0			0
$712$		−	3.04547i		−	0.114134i
$713$	−46.4618	+	26.8248i	−1.74001	+	1.00459i
$714$		0			0
$715$	2.27492	+	9.91613i	0.0850771	+	0.370842i
$716$	−0.656712	+	1.13746i	−0.0245425	+	0.0425088i
$717$		0			0
$718$	−18.8248	+	10.8685i	−0.702533	+	0.405608i
$719$	−8.60271			−0.320827			−0.160413	−	0.987050i	$-0.551283\pi$
$719$	−8.60271			−0.320827			−0.160413	+	0.987050i	$0.551283\pi$
$720$		0			0
$721$	8.62541			0.321227
$722$	−11.9726	+	6.91238i	−0.445574	+	0.257252i
$723$		0			0
$724$	3.27492	−	5.67232i	0.121711	−	0.210810i
$725$	−37.8016	−	25.6495i	−1.40392	−	0.952599i
$726$		0			0
$727$	−10.2371	+	5.91041i	−0.379674	+	0.219205i	−0.677676	−	0.735360i	$-0.737013\pi$
$727$	−10.2371	+	5.91041i	−0.379674	+	0.219205i	0.298002	+	0.954565i	$0.403680\pi$
$728$			2.27492i			0.0843140i
$729$		0			0
$730$	7.36254	+	7.91723i	0.272500	+	0.293030i
$731$	−1.67451	−	2.90033i	−0.0619339	−	0.107273i
$732$		0			0
$733$	40.7492	+	23.5265i	1.50511	+	0.868973i	0.999982	+	0.00592517i	$0.00188605\pi$
$733$	40.7492	+	23.5265i	1.50511	+	0.868973i	0.505123	+	0.863048i	$0.331447\pi$
$734$	−1.31342	+	2.27492i	−0.0484794	+	0.0839687i
$735$		0			0
$736$	−3.13746	−	5.43424i	−0.115648	−	0.200309i
$737$		−	32.0000i		−	1.17874i
$738$		0			0
$739$	10.9003			0.400975			0.200488	−	0.979696i	$-0.435747\pi$
$739$	10.9003			0.400975			0.200488	+	0.979696i	$0.435747\pi$
$740$	21.3183	+	6.54983i	0.783677	+	0.240777i
$741$		0			0
$742$	−9.41238	−	5.43424i	−0.345539	−	0.199497i
$743$	−39.0575	−	22.5498i	−1.43288	−	0.827273i	−0.435540	−	0.900170i	$-0.643442\pi$
$743$	−39.0575	−	22.5498i	−1.43288	−	0.827273i	−0.997340	+	0.0728963i	$0.976776\pi$
$744$		0			0
$745$	−0.900331	+	2.93039i	−0.0329856	+	0.107361i
$746$	−22.6893			−0.830714
$747$		0			0
$748$			3.34901i			0.122452i
$749$	7.88054	+	13.6495i	0.287949	+	0.498742i
$750$		0			0
$751$	16.2749	−	28.1890i	0.593880	−	1.02863i	−0.399824	−	0.916592i	$-0.630929\pi$
$751$	16.2749	−	28.1890i	0.593880	−	1.02863i	0.993704	−	0.112039i	$-0.0357380\pi$
$752$	−8.89834	−	5.13746i	−0.324489	−	0.187344i
$753$		0			0
$754$	7.91238	+	13.7046i	0.288152	+	0.499093i
$755$	26.0383	+	28.0000i	0.947631	+	1.01902i
$756$		0			0
$757$		−	26.3994i		−	0.959502i	−0.877405	−	0.479751i	$-0.840727\pi$
$757$		−	26.3994i		−	0.959502i	0.877405	−	0.479751i	$-0.159273\pi$
$758$	23.7071	−	13.6873i	0.861080	−	0.497145i
$759$		0			0
$760$	−1.13746	−	4.95807i	−0.0412600	−	0.179848i
$761$	−8.74657	+	15.1495i	−0.317063	+	0.549169i	−0.979874	−	0.199618i	$-0.936030\pi$
$761$	−8.74657	+	15.1495i	−0.317063	+	0.549169i	0.662811	+	0.748787i	$0.269363\pi$
$762$		0			0
$763$	−8.90033	+	5.13861i	−0.322214	+	0.186030i
$764$	14.8087			0.535762
$765$		0			0
$766$	−3.37459			−0.121929
$767$	−12.3624	+	7.13746i	−0.446382	+	0.257719i
$768$		0			0
$769$	17.6375	−	30.5490i	0.636023	−	1.10162i	−0.350274	−	0.936647i	$-0.613912\pi$
$769$	17.6375	−	30.5490i	0.636023	−	1.10162i	0.986297	−	0.164977i	$-0.0527550\pi$
$770$	−7.51946	+	1.72508i	−0.270983	+	0.0621677i
$771$		0			0
$772$	−7.18729	+	4.14959i	−0.258676	+	0.149347i
$773$			45.8248i			1.64820i	0.566443	+	0.824101i	$0.308319\pi$
$773$			45.8248i			1.64820i	−0.566443	+	0.824101i	$0.691681\pi$
$774$		0			0
$775$	−3.09967	+	42.6366i	−0.111343	+	1.53155i
$776$	9.55505	+	16.5498i	0.343006	+	0.594104i
$777$		0			0
$778$	−29.3746	−	16.9594i	−1.05313	−	0.608025i
$779$	−6.38658	+	11.0619i	−0.228823	+	0.396333i
$780$		0			0
$781$	9.09967	+	15.7611i	0.325612	+	0.563976i
$782$		−	8.00000i		−	0.286079i
$783$		0			0
$784$	5.27492			0.188390
$785$	12.8962	+	3.96221i	0.460284	+	0.141417i
$786$		0			0
$787$	−2.90033	−	1.67451i	−0.103386	−	0.0596897i	0.447416	−	0.894326i	$-0.352344\pi$
$787$	−2.90033	−	1.67451i	−0.103386	−	0.0596897i	−0.550801	+	0.834636i	$0.685678\pi$
$788$	9.52628	+	5.50000i	0.339360	+	0.195929i
$789$		0			0
$790$		0			0
$791$	0.952341			0.0338614
$792$		0			0
$793$			12.6005i			0.447458i
$794$	7.19506	+	12.4622i	0.255343	+	0.442267i
$795$		0			0
$796$	3.72508	−	6.45203i	0.132032	−	0.228686i
$797$	24.5731	+	14.1873i	0.870424	+	0.502540i	0.867489	−	0.497456i	$-0.165732\pi$
$797$	24.5731	+	14.1873i	0.870424	+	0.502540i	0.00293508	+	0.999996i	$0.499066\pi$
$798$		0			0
$799$	−6.54983	−	11.3446i	−0.231716	−	0.401345i
$800$	−4.98684	−	0.362541i	−0.176311	−	0.0128178i
$801$		0			0
$802$		−	21.6794i		−	0.765526i
$803$	10.9994	−	6.35050i	0.388160	−	0.224104i
$804$		0			0
$805$	17.9622	−	4.12081i	0.633085	−	0.145240i
$806$	7.40437	−	12.8248i	0.260808	−	0.451733i
$807$		0			0
$808$	8.27492	−	4.77753i	0.291111	−	0.168073i
$809$	−49.6224			−1.74463			−0.872315	−	0.488944i	$-0.837382\pi$
$809$	−49.6224			−1.74463			−0.872315	+	0.488944i	$0.837382\pi$
$810$		0			0
$811$	6.90033			0.242303			0.121152	−	0.992634i	$-0.461341\pi$
$811$	6.90033			0.242303			0.121152	+	0.992634i	$0.461341\pi$
$812$	−10.3923	+	6.00000i	−0.364698	+	0.210559i
$813$		0			0
$814$	13.0997	−	22.6893i	0.459143	−	0.795259i
$815$	−12.1819	−	53.0997i	−0.426713	−	1.86000i
$816$		0			0
$817$	5.17525	−	2.98793i	0.181059	−	0.104534i
$818$			16.0997i			0.562912i
$819$		0			0
$820$	8.54983	+	9.19397i	0.298573	+	0.321067i
$821$	10.6016	+	18.3625i	0.369999	+	0.640857i	0.989565	−	0.144088i	$-0.0460247\pi$
$821$	10.6016	+	18.3625i	0.369999	+	0.640857i	−0.619566	+	0.784945i	$0.712691\pi$
$822$		0			0
$823$	36.8248	+	21.2608i	1.28363	+	0.741104i	0.977510	−	0.210889i	$-0.0676358\pi$
$823$	36.8248	+	21.2608i	1.28363	+	0.741104i	0.306120	+	0.951993i	$0.400969\pi$
$824$	3.28356	−	5.68729i	0.114388	−	0.198126i
$825$		0			0
$826$	−5.41238	−	9.37451i	−0.188321	−	0.326181i
$827$		−	27.4502i		−	0.954536i	−0.878758	−	0.477268i	$-0.841627\pi$
$827$		−	27.4502i		−	0.954536i	0.878758	−	0.477268i	$-0.158373\pi$
$828$		0			0
$829$	−46.5498			−1.61674			−0.808371	−	0.588673i	$-0.799651\pi$
$829$	−46.5498			−1.61674			−0.808371	+	0.588673i	$0.799651\pi$
$830$	−2.62685	+	8.54983i	−0.0911792	+	0.296769i
$831$		0			0
$832$	1.50000	+	0.866025i	0.0520031	+	0.0300240i
$833$	5.82409	+	3.36254i	0.201793	+	0.116505i
$834$		0			0
$835$	−45.0997	−	13.8564i	−1.56074	−	0.479521i
$836$	−5.97586			−0.206680
$837$		0			0
$838$		−	16.4833i		−	0.569405i
$839$	24.3638	+	42.1993i	0.841132	+	1.45688i	0.888939	+	0.458026i	$0.151443\pi$
$839$	24.3638	+	42.1993i	0.841132	+	1.45688i	−0.0478069	+	0.998857i	$0.515223\pi$
$840$		0			0
$841$	−27.2371	+	47.1761i	−0.939211	+	1.62676i
$842$	−8.03231	−	4.63746i	−0.276812	−	0.159817i
$843$		0			0
$844$	−4.86254	−	8.42217i	−0.167376	−	0.289903i
$845$	−15.2274	−	16.3746i	−0.523838	−	0.563303i
$846$		0			0
$847$		−	5.38460i		−	0.185017i
$848$	−7.16629	+	4.13746i	−0.246091	+	0.142081i
$849$		0			0
$850$	−5.27492	−	3.57919i	−0.180928	−	0.122765i
$851$	−31.2920	+	54.1993i	−1.07268	+	1.85793i
$852$		0			0
$853$	8.90033	−	5.13861i	0.304742	−	0.175943i	−0.339829	−	0.940487i	$-0.610369\pi$
$853$	8.90033	−	5.13861i	0.304742	−	0.175943i	0.644571	+	0.764544i	$0.277036\pi$
$854$	−9.55505			−0.326967
$855$		0			0
$856$	12.0000			0.410152
$857$	−29.2931	+	16.9124i	−1.00063	+	0.577716i	−0.908436	−	0.418025i	$-0.862722\pi$
$857$	−29.2931	+	16.9124i	−1.00063	+	0.577716i	−0.0921975	+	0.995741i	$0.529389\pi$
$858$		0			0
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	−0.898126	−	0.439738i	$-0.855071\pi$
$859$	−2.00000	+	3.46410i	−0.0682391	+	0.118194i	0.829887	+	0.557931i	$0.188405\pi$
$860$	−1.31342	−	5.72508i	−0.0447874	−	0.195224i
$861$		0			0
$862$	−29.3746	+	16.9594i	−1.00050	+	0.577640i
$863$		−	9.72508i		−	0.331046i	−0.986206	−	0.165523i	$-0.947069\pi$
$863$		−	9.72508i		−	0.331046i	0.986206	−	0.165523i	$-0.0529312\pi$
$864$		0			0
$865$	−32.9124	+	30.6065i	−1.11905	+	1.04065i
$866$	5.40547	+	9.36254i	0.183685	+	0.318152i
$867$		0			0
$868$	9.72508	+	5.61478i	0.330091	+	0.190578i
$869$		0			0
$870$		0			0
$871$	−10.5498	−	18.2728i	−0.357468	−	0.619152i
$872$			7.82475i			0.264980i
$873$		0			0
$874$	14.2749			0.482856
$875$	5.31915	−	13.6873i	0.179820	−	0.462715i
$876$		0			0
$877$	−8.95017	−	5.16738i	−0.302226	−	0.174490i	0.341217	−	0.939985i	$-0.389161\pi$
$877$	−8.95017	−	5.16738i	−0.302226	−	0.174490i	−0.643442	+	0.765495i	$0.722494\pi$
$878$	−31.1769	−	18.0000i	−1.05217	−	0.607471i
$879$		0			0
$880$	−1.72508	+	5.61478i	−0.0581525	+	0.189274i
$881$	15.7611			0.531005			0.265502	−	0.964110i	$-0.414462\pi$
$881$	15.7611			0.531005			0.265502	+	0.964110i	$0.414462\pi$
$882$		0			0
$883$		−	0.952341i		−	0.0320488i	−0.999872	−	0.0160244i	$-0.994899\pi$
$883$		−	0.952341i		−	0.0320488i	0.999872	−	0.0160244i	$-0.00510095\pi$
$884$	1.10411	+	1.91238i	0.0371353	+	0.0643202i
$885$		0			0
$886$	−3.72508	+	6.45203i	−0.125147	+	0.216760i
$887$	16.3027	+	9.41238i	0.547392	+	0.316037i	0.748069	−	0.663621i	$-0.230981\pi$
$887$	16.3027	+	9.41238i	0.547392	+	0.316037i	−0.200678	+	0.979657i	$0.564314\pi$
$888$		0			0
$889$	14.5120	+	25.1356i	0.486718	+	0.843021i
$890$	4.98684	−	4.63746i	0.167159	−	0.155448i
$891$		0			0
$892$		−	16.4833i		−	0.551900i
$893$	20.2430	−	11.6873i	0.677406	−	0.391100i
$894$		0			0
$895$	−2.86254	+	0.656712i	−0.0956842	+	0.0219515i
$896$	−0.656712	+	1.13746i	−0.0219392	+	0.0379998i
$897$		0			0
$898$	−9.41238	+	5.43424i	−0.314095	+	0.181343i
$899$	78.1149			2.60528
$900$		0			0
$901$	−10.5498			−0.351466
$902$	12.7732	−	7.37459i	0.425300	−	0.245547i
$903$		0			0
$904$	0.362541	−	0.627940i	0.0120579	−	0.0208850i
$905$	14.2750	−	3.27492i	0.474518	−	0.108862i
$906$		0			0
$907$	36.0000	−	20.7846i	1.19536	−	0.690142i	0.235843	−	0.971791i	$-0.424215\pi$
$907$	36.0000	−	20.7846i	1.19536	−	0.690142i	0.959517	+	0.281650i	$0.0908815\pi$
$908$			0.549834i			0.0182469i
$909$		0			0
$910$	−3.72508	+	3.46410i	−0.123485	+	0.114834i
$911$	−2.98793	−	5.17525i	−0.0989946	−	0.171464i	0.812274	−	0.583276i	$-0.198229\pi$
$911$	−2.98793	−	5.17525i	−0.0989946	−	0.171464i	−0.911269	+	0.411812i	$0.864896\pi$
$912$		0			0
$913$	9.09967	+	5.25370i	0.301155	+	0.173872i
$914$	7.97477	−	13.8127i	0.263782	−	0.456884i
$915$		0			0
$916$	−11.1873	−	19.3770i	−0.369639	−	0.640233i
$917$			23.3746i			0.771897i
$918$		0			0
$919$	−33.0997			−1.09186			−0.545929	−	0.837832i	$-0.683823\pi$
$919$	−33.0997			−1.09186			−0.545929	+	0.837832i	$0.683823\pi$
$920$	4.12081	−	13.4124i	0.135859	−	0.442193i
$921$		0			0
$922$	6.00000	+	3.46410i	0.197599	+	0.114084i
$923$	10.3923	+	6.00000i	0.342067	+	0.197492i
$924$		0			0
$925$	21.7371	+	44.8816i	0.714712	+	1.47570i
$926$	−16.8443			−0.553539
$927$		0			0
$928$			9.13642i			0.299918i
$929$	−6.77643	−	11.7371i	−0.222328	−	0.385083i	0.733187	−	0.680027i	$-0.238032\pi$
$929$	−6.77643	−	11.7371i	−0.222328	−	0.385083i	−0.955514	+	0.294945i	$0.904699\pi$
$930$		0			0
$931$	−6.00000	+	10.3923i	−0.196642	+	0.340594i
$932$	0.151770	+	0.0876242i	0.00497138	+	0.00287023i
$933$		0			0
$934$	−6.82475	−	11.8208i	−0.223313	−	0.386789i
$935$	−5.48387	+	5.09967i	−0.179342	+	0.166777i
$936$		0			0
$937$		−	5.55724i		−	0.181547i	−0.995872	−	0.0907735i	$-0.971066\pi$
$937$		−	5.55724i		−	0.181547i	0.995872	−	0.0907735i	$-0.0289339\pi$
$938$	13.8564	−	8.00000i	0.452428	−	0.261209i
$939$		0			0
$940$	−5.13746	−	22.3937i	−0.167565	−	0.730401i
$941$	5.46301	−	9.46221i	0.178089	−	0.308459i	−0.763137	−	0.646237i	$-0.776342\pi$
$941$	5.46301	−	9.46221i	0.178089	−	0.308459i	0.941226	+	0.337778i	$0.109675\pi$
$942$		0			0
$943$	−30.5120	+	17.6161i	−0.993609	+	0.573660i
$944$	−8.24163			−0.268242
$945$		0			0
$946$	−6.90033			−0.224349
$947$	−14.3326	+	8.27492i	−0.465746	+	0.268899i	−0.714457	−	0.699679i	$-0.753326\pi$
$947$	−14.3326	+	8.27492i	−0.465746	+	0.268899i	0.248711	+	0.968578i	$0.419993\pi$
$948$		0			0
$949$	4.18729	−	7.25260i	0.135925	−	0.235429i
$950$	6.38658	−	9.41238i	0.207208	−	0.305378i
$951$		0			0
$952$	−1.45017	+	0.837253i	−0.0470001	+	0.0271355i
$953$			39.2749i			1.27224i	0.771590	+	0.636120i	$0.219462\pi$
$953$			39.2749i			1.27224i	−0.771590	+	0.636120i	$0.780538\pi$
$954$		0			0
$955$	22.5498	+	24.2487i	0.729696	+	0.784670i
$956$	−4.77753	−	8.27492i	−0.154516	−	0.267630i
$957$		0			0
$958$	1.45017	+	0.837253i	0.0468527	+	0.0270504i
$959$	−2.51176	+	4.35050i	−0.0811090	+	0.140485i
$960$		0			0
$961$	−21.0498	−	36.4594i	−0.679027	−	1.17611i
$962$		−	17.2749i		−	0.556966i
$963$		0			0
$964$	−13.8248			−0.445265
$965$	−17.7391	−	5.45017i	−0.571043	−	0.175447i
$966$		0			0
$967$	−8.27492	−	4.77753i	−0.266103	−	0.153635i	0.361012	−	0.932561i	$-0.382431\pi$
$967$	−8.27492	−	4.77753i	−0.266103	−	0.153635i	−0.627116	+	0.778926i	$0.715765\pi$
$968$	−3.55042	−	2.04983i	−0.114115	−	0.0658842i
$969$		0			0
$970$	−12.5498	+	40.8471i	−0.402951	+	1.31152i
$971$	−37.6289			−1.20757			−0.603785	−	0.797147i	$-0.706342\pi$
$971$	−37.6289			−1.20757			−0.603785	+	0.797147i	$0.706342\pi$
$972$		0			0
$973$			13.4953i			0.432640i
$974$	−4.95807	−	8.58762i	−0.158867	−	0.275165i
$975$		0			0
$976$	−3.63746	+	6.30026i	−0.116432	+	0.201667i
$977$	−0.172632	−	0.0996689i	−0.00552297	−	0.00318869i	0.497236	−	0.867615i	$-0.334348\pi$
$977$	−0.172632	−	0.0996689i	−0.00552297	−	0.00318869i	−0.502759	+	0.864427i	$0.667682\pi$
$978$		0			0
$979$	−4.00000	−	6.92820i	−0.127841	−	0.221426i
$980$	8.03231	+	8.63746i	0.256583	+	0.275913i
$981$		0			0
$982$		−	18.7490i		−	0.598305i
$983$	−27.7128	+	16.0000i	−0.883901	+	0.510321i	−0.871943	−	0.489608i	$-0.837140\pi$
$983$	−27.7128	+	16.0000i	−0.883901	+	0.510321i	−0.0119587	+	0.999928i	$0.503807\pi$
$984$		0			0
$985$	5.50000	+	23.9739i	0.175245	+	0.763873i
$986$	−5.82409	+	10.0876i	−0.185477	+	0.321255i
$987$		0			0
$988$	−3.41238	+	1.97014i	−0.108562	+	0.0626784i
$989$	16.4833			0.524137
$990$		0			0
$991$	−47.2990			−1.50250			−0.751251	−	0.660016i	$-0.770549\pi$
$991$	−47.2990			−1.50250			−0.751251	+	0.660016i	$0.770549\pi$
$992$	7.40437	−	4.27492i	0.235089	−	0.135729i
$993$		0			0
$994$	−4.54983	+	7.88054i	−0.144312	+	0.249956i
$995$	16.2373	−	3.72508i	0.514756	−	0.118093i
$996$		0			0
$997$	39.9743	−	23.0791i	1.26600	−	0.730924i	0.291769	−	0.956489i	$-0.405756\pi$
$997$	39.9743	−	23.0791i	1.26600	−	0.730924i	0.974228	+	0.225565i	$0.0724227\pi$
$998$		−	14.2749i		−	0.451865i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.i.g.109.4		8
3.2	odd	2	inner	810.2.i.g.109.1		8
5.4	even	2		810.2.i.i.109.1		8
9.2	odd	6		810.2.i.i.379.4		8
9.4	even	3		810.2.c.g.649.5	yes	8
9.5	odd	6		810.2.c.g.649.4	yes	8
9.7	even	3		810.2.i.i.379.1		8
15.14	odd	2		810.2.i.i.109.4		8
45.4	even	6		810.2.c.g.649.1	✓	8
45.13	odd	12		4050.2.a.cb.1.3		4
45.14	odd	6		810.2.c.g.649.8	yes	8
45.22	odd	12		4050.2.a.ca.1.2		4
45.23	even	12		4050.2.a.ca.1.3		4
45.29	odd	6	inner	810.2.i.g.379.1		8
45.32	even	12		4050.2.a.cb.1.2		4
45.34	even	6	inner	810.2.i.g.379.4		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
810.2.c.g.649.1	✓	8	45.4	even	6
810.2.c.g.649.4	yes	8	9.5	odd	6
810.2.c.g.649.5	yes	8	9.4	even	3
810.2.c.g.649.8	yes	8	45.14	odd	6
810.2.i.g.109.1		8	3.2	odd	2	inner
810.2.i.g.109.4		8	1.1	even	1	trivial
810.2.i.g.379.1		8	45.29	odd	6	inner
810.2.i.g.379.4		8	45.34	even	6	inner
810.2.i.i.109.1		8	5.4	even	2
810.2.i.i.109.4		8	15.14	odd	2
810.2.i.i.379.1		8	9.7	even	3
810.2.i.i.379.4		8	9.2	odd	6
4050.2.a.ca.1.2		4	45.22	odd	12
4050.2.a.ca.1.3		4	45.23	even	12
4050.2.a.cb.1.2		4	45.32	even	12
4050.2.a.cb.1.3		4	45.13	odd	12

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(2.17945 - 0.500000i) q^{5} +(1.13746 - 0.656712i) q^{7} -1.00000i q^{8} +(1.63746 - 1.52274i) q^{10} +(-1.31342 - 2.27492i) q^{11} +(-1.50000 - 0.866025i) q^{13} +(0.656712 - 1.13746i) q^{14} +(-0.500000 - 0.866025i) q^{16} -1.27492i q^{17} +2.27492 q^{19} +(0.656712 - 2.13746i) q^{20} +(-2.27492 - 1.31342i) q^{22} +(5.43424 + 3.13746i) q^{23} +(4.50000 - 2.17945i) q^{25} -1.73205 q^{26} -1.31342i q^{28} +(-4.56821 - 7.91238i) q^{29} +(-4.27492 + 7.40437i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(-0.637459 - 1.10411i) q^{34} +(2.15068 - 2.00000i) q^{35} +9.97368i q^{37} +(1.97014 - 1.13746i) q^{38} +(-0.500000 - 2.17945i) q^{40} +(-2.80739 + 4.86254i) q^{41} +(2.27492 - 1.31342i) q^{43} -2.62685 q^{44} +6.27492 q^{46} +(8.89834 - 5.13746i) q^{47} +(-2.63746 + 4.56821i) q^{49} +(2.80739 - 4.13746i) q^{50} +(-1.50000 + 0.866025i) q^{52} -8.27492i q^{53} +(-4.00000 - 4.30136i) q^{55} +(-0.656712 - 1.13746i) q^{56} +(-7.91238 - 4.56821i) q^{58} +(4.12081 - 7.13746i) q^{59} +(-3.63746 - 6.30026i) q^{61} +8.54983i q^{62} -1.00000 q^{64} +(-3.70219 - 1.13746i) q^{65} +(10.5498 + 6.09095i) q^{67} +(-1.10411 - 0.637459i) q^{68} +(0.862541 - 2.80739i) q^{70} -6.92820 q^{71} +4.83507i q^{73} +(4.98684 + 8.63746i) q^{74} +(1.13746 - 1.97014i) q^{76} +(-2.98793 - 1.72508i) q^{77} +(-1.52274 - 1.63746i) q^{80} +5.61478i q^{82} +(-3.46410 + 2.00000i) q^{83} +(-0.637459 - 2.77862i) q^{85} +(1.31342 - 2.27492i) q^{86} +(-2.27492 + 1.31342i) q^{88} +3.04547 q^{89} -2.27492 q^{91} +(5.43424 - 3.13746i) q^{92} +(5.13746 - 8.89834i) q^{94} +(4.95807 - 1.13746i) q^{95} +(-16.5498 + 9.55505i) q^{97} +5.27492i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 6 q^{7} - 2 q^{10} - 12 q^{13} - 4 q^{16} - 12 q^{19} + 12 q^{22} + 36 q^{25} - 4 q^{31} + 10 q^{34} - 4 q^{40} - 12 q^{43} + 20 q^{46} - 6 q^{49} - 12 q^{52} - 32 q^{55} - 18 q^{58} - 14 q^{61}+ \cdots - 72 q^{97}+O(q^{100}) \) 8 * q + 4 * q^4 - 6 * q^7 - 2 * q^10 - 12 * q^13 - 4 * q^16 - 12 * q^19 + 12 * q^22 + 36 * q^25 - 4 * q^31 + 10 * q^34 - 4 * q^40 - 12 * q^43 + 20 * q^46 - 6 * q^49 - 12 * q^52 - 32 * q^55 - 18 * q^58 - 14 * q^61 - 8 * q^64 + 24 * q^67 + 22 * q^70 - 6 * q^76 + 10 * q^85 + 12 * q^88 + 12 * q^91 + 26 * q^94 - 72 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more