LMFDB - Embedded newform 819.2.s.d.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [819,2,Mod(289,819)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(819, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("819.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 819 = 3^{2} \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	819.s (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.53974792554$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} + 7x^{10} - 2x^{9} + 33x^{8} - 11x^{7} + 55x^{6} + 17x^{5} + 47x^{4} + x^{3} + 8x^{2} + x + 1 $ x^12 - x^11 + 7x^10 - 2x^9 + 33x^8 - 11x^7 + 55x^6 + 17x^5 + 47x^4 + x^3 + 8x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 91)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.6
Root			$-0.181721 + 0.314749i$ of defining polynomial
Character	$\chi$	$=$	819.289
Dual form			819.2.s.d.802.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.38804 q^{2} +3.70272 q^{4} +(0.491140 - 0.850679i) q^{5} +(-0.911766 - 2.48368i) q^{7} +4.06616 q^{8} +O(q^{10})$	\(q+2.38804 q^{2} +3.70272 q^{4} +(0.491140 - 0.850679i) q^{5} +(-0.911766 - 2.48368i) q^{7} +4.06616 q^{8} +(1.17286 - 2.03145i) q^{10} +(-0.293901 + 0.509052i) q^{11} +(2.39227 - 2.69760i) q^{13} +(-2.17733 - 5.93113i) q^{14} +2.30470 q^{16} +6.45420 q^{17} +(1.91345 + 3.31419i) q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} -8.26001 q^{23} +(2.01756 + 3.49452i) q^{25} +(5.71283 - 6.44197i) q^{26} +(-3.37601 - 9.19639i) q^{28} +(-1.98009 - 3.42962i) q^{29} +(1.49436 + 2.58831i) q^{31} -2.62861 q^{32} +15.4129 q^{34} +(-2.56062 - 0.444216i) q^{35} +1.75588 q^{37} +(4.56938 + 7.91440i) q^{38} +(1.99705 - 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(-1.08823 + 1.88488i) q^{44} -19.7252 q^{46} +(-2.17030 + 3.75906i) q^{47} +(-5.33737 + 4.52907i) q^{49} +(4.81802 + 8.34505i) q^{50} +(8.85791 - 9.98846i) q^{52} +(0.212770 + 0.368529i) q^{53} +(0.288693 + 0.500031i) q^{55} +(-3.70739 - 10.0991i) q^{56} +(-4.72853 - 8.19006i) q^{58} -6.00863 q^{59} +(-1.10337 - 1.91109i) q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(-1.11985 - 3.35995i) q^{65} +(-3.50651 + 6.07346i) q^{67} +23.8981 q^{68} +(-6.11486 - 1.06080i) q^{70} +(1.80127 - 3.11988i) q^{71} +(-2.46714 - 4.27321i) q^{73} +4.19311 q^{74} +(7.08496 + 12.2715i) q^{76} +(1.53229 + 0.265822i) q^{77} +(-1.39270 + 2.41223i) q^{79} +(1.13193 - 1.96056i) q^{80} +(4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(-7.61885 + 13.1962i) q^{86} +(-1.19505 + 2.06989i) q^{88} +2.09311 q^{89} +(-8.88117 - 3.48206i) q^{91} -30.5845 q^{92} +(-5.18275 + 8.97679i) q^{94} +3.75908 q^{95} +(-3.84852 + 6.66584i) q^{97} +(-12.7458 + 10.8156i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8	$ 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) $ 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/819\mathbb{Z}\right)^\times$.

$n$	$92$	$379$	$703$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	2.38804			1.68860			0.844299	−	0.535873i	$-0.180017\pi$
$2$	2.38804			1.68860			0.844299	+	0.535873i	$0.180017\pi$
$3$		0			0
$3$		0			0
$4$	3.70272			1.85136
$5$	0.491140	−	0.850679i	0.219644	−	0.380435i	−0.735055	−	0.678008i	$-0.762844\pi$
$5$	0.491140	−	0.850679i	0.219644	−	0.380435i	0.954699	+	0.297572i	$0.0961769\pi$
$6$		0			0
$7$	−0.911766	−	2.48368i	−0.344615	−	0.938744i
$7$	−0.911766	−	2.48368i	−0.344615	−	0.938744i
$8$	4.06616			1.43761
$9$		0			0
$10$	1.17286	−	2.03145i	0.370891	−	0.642402i
$11$	−0.293901	+	0.509052i	−0.0886146	+	0.153485i	−0.906926	−	0.421291i	$-0.861577\pi$
$11$	−0.293901	+	0.509052i	−0.0886146	+	0.153485i	0.818311	+	0.574775i	$0.194911\pi$
$12$		0			0
$13$	2.39227	−	2.69760i	0.663496	−	0.748179i
$13$	2.39227	−	2.69760i	0.663496	−	0.748179i
$14$	−2.17733	−	5.93113i	−0.581916	−	1.58516i
$15$		0			0
$16$	2.30470			0.576176
$17$	6.45420			1.56537			0.782687	−	0.622416i	$-0.213849\pi$
$17$	6.45420			1.56537			0.782687	+	0.622416i	$0.213849\pi$
$18$		0			0
$19$	1.91345	+	3.31419i	0.438975	+	0.760327i	0.997611	−	0.0690863i	$-0.0220084\pi$
$19$	1.91345	+	3.31419i	0.438975	+	0.760327i	−0.558636	+	0.829413i	$0.688675\pi$
$20$	1.81855	−	3.14983i	0.406641	−	0.704323i
$21$		0			0
$22$	−0.701847	+	1.21563i	−0.149634	+	0.259174i
$23$	−8.26001			−1.72233			−0.861166	−	0.508324i	$-0.830265\pi$
$23$	−8.26001			−1.72233			−0.861166	+	0.508324i	$0.830265\pi$
$24$		0			0
$25$	2.01756	+	3.49452i	0.403513	+	0.698904i
$26$	5.71283	−	6.44197i	1.12038	−	1.26337i
$27$		0			0
$28$	−3.37601	−	9.19639i	−0.638007	−	1.73795i
$29$	−1.98009	−	3.42962i	−0.367694	−	0.636864i	0.621511	−	0.783406i	$-0.286519\pi$
$29$	−1.98009	−	3.42962i	−0.367694	−	0.636864i	−0.989205	+	0.146541i	$0.953186\pi$
$30$		0			0
$31$	1.49436	+	2.58831i	0.268395	+	0.464874i	0.968448	−	0.249218i	$-0.0801734\pi$
$31$	1.49436	+	2.58831i	0.268395	+	0.464874i	−0.700053	+	0.714091i	$0.746840\pi$
$32$	−2.62861			−0.464676
$33$		0			0
$34$	15.4129			2.64329
$35$	−2.56062	−	0.444216i	−0.432824	−	0.0750862i
$36$		0			0
$37$	1.75588			0.288665			0.144333	−	0.989529i	$-0.453896\pi$
$37$	1.75588			0.288665			0.144333	+	0.989529i	$0.453896\pi$
$38$	4.56938	+	7.91440i	0.741252	+	1.28389i
$39$		0			0
$40$	1.99705	−	3.45900i	0.315762	−	0.546916i
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	0.973023	−	0.230710i	$-0.0741049\pi$
$41$	1.83584	+	3.17977i	0.286710	+	0.496597i	−0.686312	+	0.727307i	$0.740772\pi$
$42$		0			0
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	−0.999880	−	0.0154788i	$-0.995073\pi$
$43$	−3.19042	+	5.52598i	−0.486535	+	0.842703i	0.513345	+	0.858182i	$0.328406\pi$
$44$	−1.08823	+	1.88488i	−0.164058	+	0.284156i
$45$		0			0
$46$	−19.7252			−2.90832
$47$	−2.17030	+	3.75906i	−0.316570	+	0.548316i	−0.979770	−	0.200127i	$-0.935865\pi$
$47$	−2.17030	+	3.75906i	−0.316570	+	0.548316i	0.663200	+	0.748442i	$0.269198\pi$
$48$		0			0
$49$	−5.33737	+	4.52907i	−0.762481	+	0.647011i
$50$	4.81802	+	8.34505i	0.681370	+	1.18017i
$51$		0			0
$52$	8.85791	−	9.98846i	1.22837	−	1.38515i
$53$	0.212770	+	0.368529i	0.0292263	+	0.0506214i	0.880269	−	0.474476i	$-0.157362\pi$
$53$	0.212770	+	0.368529i	0.0292263	+	0.0506214i	−0.851042	+	0.525097i	$0.824029\pi$
$54$		0			0
$55$	0.288693	+	0.500031i	0.0389274	+	0.0674242i
$56$	−3.70739	−	10.0991i	−0.495420	−	1.34954i
$57$		0			0
$58$	−4.72853	−	8.19006i	−0.620887	−	1.07541i
$59$	−6.00863			−0.782256			−0.391128	−	0.920336i	$-0.627915\pi$
$59$	−6.00863			−0.782256			−0.391128	+	0.920336i	$0.627915\pi$
$60$		0			0
$61$	−1.10337	−	1.91109i	−0.141272	−	0.244691i	0.786704	−	0.617331i	$-0.211786\pi$
$61$	−1.10337	−	1.91109i	−0.141272	−	0.244691i	−0.927976	+	0.372640i	$0.878453\pi$
$62$	3.56859	+	6.18097i	0.453211	+	0.784985i
$63$		0			0
$64$	−10.8866			−1.36083
$65$	−1.11985	−	3.35995i	−0.138901	−	0.416751i
$66$		0			0
$67$	−3.50651	+	6.07346i	−0.428389	+	0.741991i	−0.996730	−	0.0808015i	$-0.974252\pi$
$67$	−3.50651	+	6.07346i	−0.428389	+	0.741991i	0.568341	+	0.822793i	$0.307585\pi$
$68$	23.8981			2.89807
$69$		0			0
$70$	−6.11486	−	1.06080i	−0.730866	−	0.126790i
$71$	1.80127	−	3.11988i	0.213771	−	0.370262i	−0.739121	−	0.673573i	$-0.764759\pi$
$71$	1.80127	−	3.11988i	0.213771	−	0.370262i	0.952892	+	0.303311i	$0.0980920\pi$
$72$		0			0
$73$	−2.46714	−	4.27321i	−0.288756	−	0.500141i	0.684757	−	0.728772i	$-0.259908\pi$
$73$	−2.46714	−	4.27321i	−0.288756	−	0.500141i	−0.973513	+	0.228631i	$0.926575\pi$
$74$	4.19311			0.487439
$75$		0			0
$76$	7.08496	+	12.2715i	0.812701	+	1.40764i
$77$	1.53229	+	0.265822i	0.174621	+	0.0302932i
$78$		0			0
$79$	−1.39270	+	2.41223i	−0.156691	+	0.271397i	−0.933674	−	0.358125i	$-0.883416\pi$
$79$	−1.39270	+	2.41223i	−0.156691	+	0.271397i	0.776982	+	0.629522i	$0.216749\pi$
$80$	1.13193	−	1.96056i	0.126554	−	0.219198i
$81$		0			0
$82$	4.38406	+	7.59342i	0.484138	+	0.838552i
$83$	2.86819			0.314825			0.157412	−	0.987533i	$-0.449685\pi$
$83$	2.86819			0.314825			0.157412	+	0.987533i	$0.449685\pi$
$84$		0			0
$85$	3.16992	−	5.49045i	0.343826	−	0.595523i
$86$	−7.61885	+	13.1962i	−0.821562	+	1.42299i
$87$		0			0
$88$	−1.19505	+	2.06989i	−0.127393	+	0.220651i
$89$	2.09311			0.221870			0.110935	−	0.993828i	$-0.464616\pi$
$89$	2.09311			0.221870			0.110935	+	0.993828i	$0.464616\pi$
$90$		0			0
$91$	−8.88117	−	3.48206i	−0.931000	−	0.365020i
$92$	−30.5845			−3.18866
$93$		0			0
$94$	−5.18275	+	8.97679i	−0.534560	+	0.925885i
$95$	3.75908			0.385674
$96$		0			0
$97$	−3.84852	+	6.66584i	−0.390758	+	0.676813i	−0.992550	−	0.121840i	$-0.961120\pi$
$97$	−3.84852	+	6.66584i	−0.390758	+	0.676813i	0.601791	+	0.798653i	$0.294454\pi$
$98$	−12.7458	+	10.8156i	−1.28752	+	1.09254i
$99$		0			0
$100$	7.47047	+	12.9392i	0.747047	+	1.29392i
$101$	−1.31866	+	2.28399i	−0.131212	+	0.227265i	−0.924144	−	0.382045i	$-0.875220\pi$
$101$	−1.31866	+	2.28399i	−0.131212	+	0.227265i	0.792932	+	0.609310i	$0.208553\pi$
$102$		0			0
$103$	5.43095	−	9.40669i	0.535128	−	0.926868i	−0.464029	−	0.885820i	$-0.653597\pi$
$103$	5.43095	−	9.40669i	0.535128	−	0.926868i	0.999157	−	0.0410486i	$-0.0130699\pi$
$104$	9.72736	−	10.9689i	0.953846	−	1.07559i
$105$		0			0
$106$	0.508103	+	0.880061i	0.0493514	+	0.0854791i
$107$	15.9805			1.54489			0.772446	−	0.635080i	$-0.219033\pi$
$107$	15.9805			1.54489			0.772446	+	0.635080i	$0.219033\pi$
$108$		0			0
$109$	−4.61738	−	7.99754i	−0.442265	−	0.766026i	0.555592	−	0.831455i	$-0.312492\pi$
$109$	−4.61738	−	7.99754i	−0.442265	−	0.766026i	−0.997857	+	0.0654294i	$0.979158\pi$
$110$	0.689410	+	1.19409i	0.0657327	+	0.113852i
$111$		0			0
$112$	−2.10135	−	5.72416i	−0.198559	−	0.540882i
$113$	5.09012	−	8.81635i	0.478838	−	0.829372i	−0.520867	−	0.853638i	$-0.674391\pi$
$113$	5.09012	−	8.81635i	0.478838	−	0.829372i	0.999706	+	0.0242655i	$0.00772470\pi$
$114$		0			0
$115$	−4.05682	+	7.02662i	−0.378301	+	0.655236i
$116$	−7.33173	−	12.6989i	−0.680734	−	1.17907i
$117$		0			0
$118$	−14.3488			−1.32092
$119$	−5.88472	−	16.0302i	−0.539451	−	1.46949i
$120$		0			0
$121$	5.32724	+	9.22706i	0.484295	+	0.838823i
$122$	−2.63489	−	4.56376i	−0.238552	−	0.413184i
$123$		0			0
$124$	5.53320	+	9.58378i	0.496896	+	0.860649i
$125$	8.87502			0.793806
$126$		0			0
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	0.756201	−	0.654340i	$-0.227053\pi$
$127$	−2.12513	−	3.68083i	−0.188575	−	0.326621i	−0.944775	+	0.327719i	$0.893720\pi$
$128$	−20.7404			−1.83321
$129$		0			0
$130$	−2.67425	−	8.02369i	−0.234547	−	0.703725i
$131$	−1.08478	+	1.87890i	−0.0947779	+	0.164160i	−0.909516	−	0.415669i	$-0.863547\pi$
$131$	−1.08478	+	1.87890i	−0.0947779	+	0.164160i	0.814738	+	0.579829i	$0.196881\pi$
$132$		0			0
$133$	6.48678	−	7.77416i	0.562475	−	0.674105i
$134$	−8.37369	+	14.5037i	−0.723376	+	1.25292i
$135$		0			0
$136$	26.2438			2.25039
$137$	−8.36316			−0.714513			−0.357257	−	0.934006i	$-0.616288\pi$
$137$	−8.36316			−0.714513			−0.357257	+	0.934006i	$0.616288\pi$
$138$		0			0
$139$	0.288457	−	0.499622i	0.0244666	−	0.0423774i	−0.853533	−	0.521039i	$-0.825545\pi$
$139$	0.288457	−	0.499622i	0.0244666	−	0.0423774i	0.877999	+	0.478662i	$0.158878\pi$
$140$	−9.48127	−	1.64481i	−0.801314	−	0.139012i
$141$		0			0
$142$	4.30149	−	7.45040i	0.360973	−	0.625224i
$143$	0.670127	+	2.01062i	0.0560388	+	0.168136i
$144$		0			0
$145$	−3.89001			−0.323048
$146$	−5.89161	−	10.2046i	−0.487593	−	0.844537i
$147$		0			0
$148$	6.50154			0.534423
$149$	1.40331	+	2.43061i	0.114964	+	0.199123i	0.917765	−	0.397123i	$-0.129991\pi$
$149$	1.40331	+	2.43061i	0.114964	+	0.199123i	−0.802801	+	0.596246i	$0.796658\pi$
$150$		0			0
$151$	11.5054	+	19.9280i	0.936300	+	1.62172i	0.772300	+	0.635258i	$0.219106\pi$
$151$	11.5054	+	19.9280i	0.936300	+	1.62172i	0.164000	+	0.986460i	$0.447560\pi$
$152$	7.78039	+	13.4760i	0.631073	+	1.09305i
$153$		0			0
$154$	3.65917	+	0.634792i	0.294864	+	0.0511530i
$155$	2.93576			0.235806
$156$		0			0
$157$	−11.2880	−	19.5513i	−0.900879	−	1.56037i	−0.826356	−	0.563148i	$-0.809590\pi$
$157$	−11.2880	−	19.5513i	−0.900879	−	1.56037i	−0.0745227	−	0.997219i	$-0.523743\pi$
$158$	−3.32583	+	5.76050i	−0.264588	+	0.458281i
$159$		0			0
$160$	−1.29101	+	2.23610i	−0.102064	+	0.176779i
$161$	7.53119	+	20.5153i	0.593541	+	1.61683i
$162$		0			0
$163$	−4.08857	−	7.08161i	−0.320242	−	0.554675i	0.660296	−	0.751005i	$-0.270431\pi$
$163$	−4.08857	−	7.08161i	−0.320242	−	0.554675i	−0.980538	+	0.196331i	$0.937097\pi$
$164$	6.79761	+	11.7738i	0.530804	+	0.919380i
$165$		0			0
$166$	6.84934			0.531612
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	0.817475	−	0.575964i	$-0.195373\pi$
$167$	−1.16386	−	2.01586i	−0.0900619	−	0.155992i	−0.907537	+	0.419972i	$0.862040\pi$
$168$		0			0
$169$	−1.55408	−	12.9068i	−0.119545	−	0.992829i
$170$	7.56988	−	13.1114i	0.580583	−	1.00560i
$171$		0			0
$172$	−11.8133	+	20.4611i	−0.900752	+	1.56015i
$173$	−4.06686	−	7.04401i	−0.309198	−	0.535546i	0.668989	−	0.743272i	$-0.266727\pi$
$173$	−4.06686	−	7.04401i	−0.309198	−	0.535546i	−0.978187	+	0.207726i	$0.933394\pi$
$174$		0			0
$175$	6.83974	−	8.19717i	0.517036	−	0.619648i
$176$	−0.677355	+	1.17321i	−0.0510576	+	0.0884343i
$177$		0			0
$178$	4.99843			0.374648
$179$	−10.4963	+	18.1801i	−0.784528	+	1.35884i	0.144752	+	0.989468i	$0.453761\pi$
$179$	−10.4963	+	18.1801i	−0.784528	+	1.35884i	−0.929281	+	0.369375i	$0.879572\pi$
$180$		0			0
$181$	−1.60807			−0.119527			−0.0597635	−	0.998213i	$-0.519035\pi$
$181$	−1.60807			−0.119527			−0.0597635	+	0.998213i	$0.519035\pi$
$182$	−21.2086	−	8.31530i	−1.57208	−	0.616371i
$183$		0			0
$184$	−33.5865			−2.47603
$185$	0.862384	−	1.49369i	0.0634037	−	0.109818i
$186$		0			0
$187$	−1.89690	+	3.28552i	−0.138715	+	0.240261i
$188$	−8.03601	+	13.9188i	−0.586086	+	1.01513i
$189$		0			0
$190$	8.97683			0.651247
$191$	−5.78111	−	10.0132i	−0.418307	−	0.724529i	0.577463	−	0.816417i	$-0.304043\pi$
$191$	−5.78111	−	10.0132i	−0.418307	−	0.724529i	−0.995769	+	0.0918886i	$0.970710\pi$
$192$		0			0
$193$	−11.7894	+	20.4199i	−0.848621	+	1.46985i	0.0338178	+	0.999428i	$0.489233\pi$
$193$	−11.7894	+	20.4199i	−0.848621	+	1.46985i	−0.882439	+	0.470427i	$0.844100\pi$
$194$	−9.19041	+	15.9183i	−0.659833	+	1.14286i
$195$		0			0
$196$	−19.7628	+	16.7699i	−1.41163	+	1.19785i
$197$	−0.735472	−	1.27387i	−0.0524002	−	0.0907598i	0.838636	−	0.544693i	$-0.183354\pi$
$197$	−0.735472	−	1.27387i	−0.0524002	−	0.0907598i	−0.891036	+	0.453933i	$0.850020\pi$
$198$		0			0
$199$	9.39399			0.665922			0.332961	−	0.942941i	$-0.391952\pi$
$199$	9.39399			0.665922			0.332961	+	0.942941i	$0.391952\pi$
$200$	8.20374	+	14.2093i	0.580092	+	1.00475i
$201$		0			0
$202$	−3.14901	+	5.45425i	−0.221564	+	0.383760i
$203$	−6.71271	+	8.04493i	−0.471140	+	0.564643i
$204$		0			0
$205$	3.60662			0.251897
$206$	12.9693	−	22.4635i	0.903615	−	1.56511i
$207$		0			0
$208$	5.51348	−	6.21717i	0.382291	−	0.431083i
$209$	−2.24946			−0.155598
$210$		0			0
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	0.977881	−	0.209160i	$-0.0670730\pi$
$211$	4.47109	+	7.74416i	0.307803	+	0.533130i	−0.670079	+	0.742290i	$0.733740\pi$
$212$	0.787829	+	1.36456i	0.0541083	+	0.0937184i
$213$		0			0
$214$	38.1620			2.60870
$215$	3.13389	+	5.42805i	0.213729	+	0.370190i
$216$		0			0
$217$	5.06603	−	6.07145i	0.343905	−	0.412157i
$218$	−11.0265	−	19.0984i	−0.746808	−	1.29351i
$219$		0			0
$220$	1.06895	+	1.85148i	0.0720686	+	0.124827i
$221$	15.4402	−	17.4108i	1.03862	−	1.17118i
$222$		0			0
$223$	−10.9098	−	18.8963i	−0.730574	−	1.26539i	−0.956638	−	0.291279i	$-0.905919\pi$
$223$	−10.9098	−	18.8963i	−0.730574	−	1.26539i	0.226064	−	0.974112i	$-0.427414\pi$
$224$	2.39667	+	6.52862i	0.160134	+	0.436212i
$225$		0			0
$226$	12.1554	−	21.0538i	0.808565	−	1.40048i
$227$	18.5525			1.23137			0.615687	−	0.787990i	$-0.288878\pi$
$227$	18.5525			1.23137			0.615687	+	0.787990i	$0.288878\pi$
$228$		0			0
$229$	−9.67525	+	16.7580i	−0.639359	+	1.10740i	0.346215	+	0.938155i	$0.387467\pi$
$229$	−9.67525	+	16.7580i	−0.639359	+	1.10740i	−0.985574	+	0.169247i	$0.945867\pi$
$230$	−9.68784	+	16.7798i	−0.638797	+	1.10643i
$231$		0			0
$232$	−8.05137	−	13.9454i	−0.528599	−	0.915560i
$233$	8.08170	−	13.9979i	0.529450	−	0.917034i	−0.469960	−	0.882688i	$-0.655732\pi$
$233$	8.08170	−	13.9979i	0.529450	−	0.917034i	0.999410	−	0.0343462i	$-0.0109349\pi$
$234$		0			0
$235$	2.13184	+	3.69245i	0.139066	+	0.240869i
$236$	−22.2483			−1.44824
$237$		0			0
$238$	−14.0529	−	38.2807i	−0.910916	−	2.48137i
$239$	−16.1037			−1.04166			−0.520831	−	0.853660i	$-0.674378\pi$
$239$	−16.1037			−1.04166			−0.520831	+	0.853660i	$0.674378\pi$
$240$		0			0
$241$	−4.00600			−0.258049			−0.129025	−	0.991641i	$-0.541185\pi$
$241$	−4.00600			−0.258049			−0.129025	+	0.991641i	$0.541185\pi$
$242$	12.7217	+	22.0346i	0.817779	+	1.41643i
$243$		0			0
$244$	−4.08548	−	7.07625i	−0.261546	−	0.453011i
$245$	1.23140	+	6.76480i	0.0786710	+	0.432187i
$246$		0			0
$247$	13.5178	+	2.76672i	0.860119	+	0.176042i
$248$	6.07631	+	10.5245i	0.385846	+	0.668305i
$249$		0			0
$250$	21.1939			1.34042
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	−0.810231	−	0.586110i	$-0.800659\pi$
$251$	1.62344	−	2.81188i	0.102471	−	0.177484i	0.912702	+	0.408626i	$0.133992\pi$
$252$		0			0
$253$	2.42763	−	4.20477i	0.152624	−	0.264352i
$254$	−5.07489	−	8.78996i	−0.318427	−	0.551531i
$255$		0			0
$256$	−27.7557			−1.73473
$257$	26.8924			1.67750			0.838751	−	0.544516i	$-0.183287\pi$
$257$	26.8924			1.67750			0.838751	+	0.544516i	$0.183287\pi$
$258$		0			0
$259$	−1.60095	−	4.36106i	−0.0994784	−	0.270983i
$260$	−4.14650	−	12.4410i	−0.257155	−	0.771556i
$261$		0			0
$262$	−2.59050	+	4.48688i	−0.160042	+	0.277200i
$263$	−1.90353	+	3.29701i	−0.117377	+	0.203302i	−0.918727	−	0.394893i	$-0.870782\pi$
$263$	−1.90353	+	3.29701i	−0.117377	+	0.203302i	0.801351	+	0.598195i	$0.204115\pi$
$264$		0			0
$265$	0.418000			0.0256775
$266$	15.4907	−	18.5650i	0.949794	−	1.13829i
$267$		0			0
$268$	−12.9836	+	22.4883i	−0.793102	+	1.37369i
$269$	23.8381			1.45343			0.726716	−	0.686938i	$-0.241046\pi$
$269$	23.8381			1.45343			0.726716	+	0.686938i	$0.241046\pi$
$270$		0			0
$271$	9.90135			0.601464			0.300732	−	0.953709i	$-0.402769\pi$
$271$	9.90135			0.601464			0.300732	+	0.953709i	$0.402769\pi$
$272$	14.8750			0.901931
$273$		0			0
$274$	−19.9715			−1.20653
$275$	−2.37186			−0.143028
$276$		0			0
$277$	11.7858			0.708139			0.354069	−	0.935219i	$-0.384798\pi$
$277$	11.7858			0.708139			0.354069	+	0.935219i	$0.384798\pi$
$278$	0.688846	−	1.19312i	0.0413142	−	0.0715584i
$279$		0			0
$280$	−10.4119	−	1.80625i	−0.622231	−	0.107944i
$281$	−12.9976			−0.775372			−0.387686	−	0.921791i	$-0.626726\pi$
$281$	−12.9976			−0.775372			−0.387686	+	0.921791i	$0.626726\pi$
$282$		0			0
$283$	8.40249	−	14.5535i	0.499476	−	0.865118i	−0.500524	−	0.865723i	$-0.666859\pi$
$283$	8.40249	−	14.5535i	0.499476	−	0.865118i	1.00000		0.000604910i	$0.000192549\pi$
$284$	6.66959	−	11.5521i	0.395767	−	0.685489i
$285$		0			0
$286$	1.60029	+	4.80143i	0.0946270	+	0.283914i
$287$	6.22369	−	7.45886i	0.367373	−	0.440283i
$288$		0			0
$289$	24.6567			1.45039
$290$	−9.28948			−0.545497
$291$		0			0
$292$	−9.13512	−	15.8225i	−0.534592	−	0.925941i
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	−0.995080	−	0.0990757i	$-0.968411\pi$
$293$	−7.04782	+	12.2072i	−0.411738	+	0.713151i	0.583342	+	0.812227i	$0.301745\pi$
$294$		0			0
$295$	−2.95108	+	5.11141i	−0.171818	+	0.297598i
$296$	7.13970			0.414987
$297$		0			0
$298$	3.35116	+	5.80438i	0.194128	+	0.336239i
$299$	−19.7602	+	22.2822i	−1.14276	+	1.28861i
$300$		0			0
$301$	16.6337	+	2.88561i	0.958750	+	0.166324i
$302$	27.4754	+	47.5888i	1.58103	+	2.73843i
$303$		0			0
$304$	4.40993	+	7.63822i	0.252927	+	0.438082i
$305$	−2.16764			−0.124119
$306$		0			0
$307$	15.8786			0.906240			0.453120	−	0.891450i	$-0.350311\pi$
$307$	15.8786			0.906240			0.453120	+	0.891450i	$0.350311\pi$
$308$	5.67365	+	0.984264i	0.323286	+	0.0560836i
$309$		0			0
$310$	7.01070			0.398181
$311$	−14.3017	−	24.7713i	−0.810975	−	1.40465i	−0.912183	−	0.409784i	$-0.865604\pi$
$311$	−14.3017	−	24.7713i	−0.810975	−	1.40465i	0.101208	−	0.994865i	$-0.467729\pi$
$312$		0			0
$313$	9.28962	−	16.0901i	0.525080	−	0.909465i	−0.474493	−	0.880259i	$-0.657369\pi$
$313$	9.28962	−	16.0901i	0.525080	−	0.909465i	0.999573	−	0.0292063i	$-0.00929798\pi$
$314$	−26.9561	−	46.6893i	−1.52122	−	2.63483i
$315$		0			0
$316$	−5.15679	+	8.93182i	−0.290092	+	0.502454i
$317$	15.3223	−	26.5389i	0.860584	−	1.49057i	−0.0107826	−	0.999942i	$-0.503432\pi$
$317$	15.3223	−	26.5389i	0.860584	−	1.49057i	0.871366	−	0.490633i	$-0.163234\pi$
$318$		0			0
$319$	2.32781			0.130332
$320$	−5.34685	+	9.26102i	−0.298898	+	0.517707i
$321$		0			0
$322$	17.9848	+	48.9912i	1.00225	+	2.73017i
$323$	12.3498	+	21.3904i	0.687160	+	1.19020i
$324$		0			0
$325$	14.2534	+	2.91727i	0.790635	+	0.161821i
$326$	−9.76366	−	16.9112i	−0.540759	−	0.936622i
$327$		0			0
$328$	7.46483	+	12.9295i	0.412177	+	0.713911i
$329$	11.3151	+	1.96295i	0.623823	+	0.108221i
$330$		0			0
$331$	−13.6138	−	23.5799i	−0.748284	−	1.29607i	−0.948644	−	0.316344i	$-0.897545\pi$
$331$	−13.6138	−	23.5799i	−0.748284	−	1.29607i	0.200360	−	0.979722i	$-0.435789\pi$
$332$	10.6201			0.582854
$333$		0			0
$334$	−2.77933	−	4.81395i	−0.152078	−	0.263407i
$335$	3.44438	+	5.96584i	0.188187	+	0.325949i
$336$		0			0
$337$	−12.3160			−0.670898			−0.335449	−	0.942058i	$-0.608888\pi$
$337$	−12.3160			−0.670898			−0.335449	+	0.942058i	$0.608888\pi$
$338$	−3.71121	−	30.8219i	−0.201863	−	1.67649i
$339$		0			0
$340$	11.7373	−	20.3296i	0.636545	−	1.10253i
$341$	−1.75678			−0.0951348
$342$		0			0
$343$	16.1152	+	9.12688i	0.870140	+	0.492805i
$344$	−12.9728	+	22.4695i	−0.699445	+	1.21148i
$345$		0			0
$346$	−9.71182	−	16.8214i	−0.522111	−	0.904322i
$347$	−6.14506			−0.329884			−0.164942	−	0.986303i	$-0.552744\pi$
$347$	−6.14506			−0.329884			−0.164942	+	0.986303i	$0.552744\pi$
$348$		0			0
$349$	−6.51563	−	11.2854i	−0.348774	−	0.604094i	0.637258	−	0.770650i	$-0.280068\pi$
$349$	−6.51563	−	11.2854i	−0.348774	−	0.604094i	−0.986032	+	0.166557i	$0.946735\pi$
$350$	16.3336	−	19.5752i	0.873065	−	1.04634i
$351$		0			0
$352$	0.772550	−	1.33810i	0.0411771	−	0.0713208i
$353$	15.8332	−	27.4240i	0.842718	−	1.45963i	−0.0448710	−	0.998993i	$-0.514288\pi$
$353$	15.8332	−	27.4240i	0.842718	−	1.45963i	0.887589	−	0.460637i	$-0.152379\pi$
$354$		0			0
$355$	−1.76935	−	3.06460i	−0.0939072	−	0.162652i
$356$	7.75021			0.410761
$357$		0			0
$358$	−25.0655	+	43.4147i	−1.32475	+	2.29454i
$359$	9.96610	−	17.2618i	0.525991	−	0.911043i	−0.473551	−	0.880767i	$-0.657028\pi$
$359$	9.96610	−	17.2618i	0.525991	−	0.911043i	0.999542	−	0.0302764i	$-0.00963874\pi$
$360$		0			0
$361$	2.17744	−	3.77144i	0.114602	−	0.198497i
$362$	−3.84014			−0.201833
$363$		0			0
$364$	−32.8845	−	12.8931i	−1.72362	−	0.675783i
$365$	−4.84684			−0.253695
$366$		0			0
$367$	−9.85950	+	17.0772i	−0.514662	+	0.891420i	0.485194	+	0.874407i	$0.338749\pi$
$367$	−9.85950	+	17.0772i	−0.514662	+	0.891420i	−0.999855	+	0.0170133i	$0.994584\pi$
$368$	−19.0369			−0.992366
$369$		0			0
$370$	2.05940	−	3.56699i	0.107063	−	0.185439i
$371$	0.721313	−	0.864466i	0.0374487	−	0.0448808i
$372$		0			0
$373$	−8.77345	−	15.1961i	−0.454272	−	0.786823i	0.544374	−	0.838843i	$-0.316767\pi$
$373$	−8.77345	−	15.1961i	−0.454272	−	0.786823i	−0.998646	+	0.0520202i	$0.983434\pi$
$374$	−4.52986	+	7.84595i	−0.234234	+	0.405704i
$375$		0			0
$376$	−8.82478	+	15.2850i	−0.455103	+	0.788262i
$377$	−13.9887	−	2.86308i	−0.720452	−	0.147456i
$378$		0			0
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	0.976256	−	0.216620i	$-0.0695034\pi$
$379$	5.85068	+	10.1337i	0.300529	+	0.520532i	−0.675727	+	0.737152i	$0.736170\pi$
$380$	13.9188			0.714021
$381$		0			0
$382$	−13.8055	−	23.9119i	−0.706352	−	1.22344i
$383$	−10.7644	−	18.6445i	−0.550036	−	0.952690i	−0.998271	−	0.0587748i	$-0.981281\pi$
$383$	−10.7644	−	18.6445i	−0.550036	−	0.952690i	0.448235	−	0.893916i	$-0.352053\pi$
$384$		0			0
$385$	0.978699	−	1.17293i	0.0498791	−	0.0597783i
$386$	−28.1536	+	48.7634i	−1.43298	+	2.48199i
$387$		0			0
$388$	−14.2500	+	24.6817i	−0.723435	+	1.25303i
$389$	13.2455	+	22.9419i	0.671574	+	1.16320i	0.977458	+	0.211131i	$0.0677147\pi$
$389$	13.2455	+	22.9419i	0.671574	+	1.16320i	−0.305884	+	0.952069i	$0.598952\pi$
$390$		0			0
$391$	−53.3118			−2.69609
$392$	−21.7026	+	18.4160i	−1.09615	+	0.930146i
$393$		0			0
$394$	−1.75633	−	3.04206i	−0.0884828	−	0.153257i
$395$	1.36802	+	2.36949i	0.0688327	+	0.119222i
$396$		0			0
$397$	16.8995	+	29.2707i	0.848160	+	1.46906i	0.882849	+	0.469658i	$0.155623\pi$
$397$	16.8995	+	29.2707i	0.848160	+	1.46906i	−0.0346887	+	0.999398i	$0.511044\pi$
$398$	22.4332			1.12447
$399$		0			0
$400$	4.64989	+	8.05384i	0.232494	+	0.402692i
$401$	−21.6119			−1.07925			−0.539623	−	0.841907i	$-0.681433\pi$
$401$	−21.6119			−1.07925			−0.539623	+	0.841907i	$0.681433\pi$
$402$		0			0
$403$	10.5571	+	2.16075i	0.525888	+	0.107635i
$404$	−4.88264	+	8.45697i	−0.242920	+	0.420750i
$405$		0			0
$406$	−16.0302	+	19.2116i	−0.795565	+	0.953455i
$407$	−0.516056	+	0.893835i	−0.0255799	+	0.0443058i
$408$		0			0
$409$	7.74217			0.382826			0.191413	−	0.981510i	$-0.438693\pi$
$409$	7.74217			0.382826			0.191413	+	0.981510i	$0.438693\pi$
$410$	8.61275			0.425353
$411$		0			0
$412$	20.1093	−	34.8303i	0.990714	−	1.71597i
$413$	5.47846	+	14.9235i	0.269577	+	0.734339i
$414$		0			0
$415$	1.40868	−	2.43991i	0.0691495	−	0.119770i
$416$	−6.28834	+	7.09092i	−0.308311	+	0.347661i
$417$		0			0
$418$	−5.37179			−0.262743
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	0.749945	−	0.661500i	$-0.230080\pi$
$419$	−4.05097	−	7.01649i	−0.197903	−	0.342778i	−0.947848	+	0.318722i	$0.896746\pi$
$420$		0			0
$421$	−32.1124			−1.56506			−0.782530	−	0.622612i	$-0.786071\pi$
$421$	−32.1124			−1.56506			−0.782530	+	0.622612i	$0.786071\pi$
$422$	10.6771	+	18.4933i	0.519755	+	0.900242i
$423$		0			0
$424$	0.865159	+	1.49850i	0.0420158	+	0.0727735i
$425$	13.0218	+	22.5543i	0.631648	+	1.09405i
$426$		0			0
$427$	−3.74054	+	4.48289i	−0.181017	+	0.216942i
$428$	59.1713			2.86015
$429$		0			0
$430$	7.48384	+	12.9624i	0.360903	+	0.625102i
$431$	−14.7640	+	25.5721i	−0.711159	+	1.23176i	0.253263	+	0.967397i	$0.418496\pi$
$431$	−14.7640	+	25.5721i	−0.711159	+	1.23176i	−0.964422	+	0.264366i	$0.914837\pi$
$432$		0			0
$433$	−11.0455	+	19.1314i	−0.530813	+	0.919395i	0.468540	+	0.883442i	$0.344780\pi$
$433$	−11.0455	+	19.1314i	−0.530813	+	0.919395i	−0.999353	+	0.0359531i	$0.988553\pi$
$434$	12.0979	−	14.4988i	0.580716	−	0.695967i
$435$		0			0
$436$	−17.0969	−	29.6127i	−0.818792	−	1.41819i
$437$	−15.8051	−	27.3752i	−0.756060	−	1.30953i
$438$		0			0
$439$	−6.35580			−0.303346			−0.151673	−	0.988431i	$-0.548466\pi$
$439$	−6.35580			−0.303346			−0.151673	+	0.988431i	$0.548466\pi$
$440$	1.17387	+	2.03321i	0.0559622	+	0.0969294i
$441$		0			0
$442$	36.8718	−	41.5777i	1.75381	−	1.97765i
$443$	−6.78135	+	11.7456i	−0.322192	+	0.558052i	−0.980940	−	0.194311i	$-0.937753\pi$
$443$	−6.78135	+	11.7456i	−0.322192	+	0.558052i	0.658748	+	0.752363i	$0.271086\pi$
$444$		0			0
$445$	1.02801	−	1.78057i	0.0487324	−	0.0844070i
$446$	−26.0530	−	45.1251i	−1.23365	−	2.13674i
$447$		0			0
$448$	9.92604	+	27.0389i	0.468961	+	1.27747i
$449$	10.9559	−	18.9762i	0.517041	−	0.895541i	−0.482763	−	0.875751i	$-0.660367\pi$
$449$	10.9559	−	18.9762i	0.517041	−	0.895541i	0.999804	−	0.0197900i	$-0.00629977\pi$
$450$		0			0
$451$	−2.15823			−0.101627
$452$	18.8473	−	32.6445i	0.886502	−	1.53547i
$453$		0			0
$454$	44.3041			2.07930
$455$	−7.32402	+	5.84485i	−0.343355	+	0.274011i
$456$		0			0
$457$	15.2146			0.711710			0.355855	−	0.934541i	$-0.384190\pi$
$457$	15.2146			0.711710			0.355855	+	0.934541i	$0.384190\pi$
$458$	−23.1049	+	40.0188i	−1.07962	+	1.86996i
$459$		0			0
$460$	−15.0213	+	26.0176i	−0.700371	+	1.21308i
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	−0.990717	−	0.135937i	$-0.956595\pi$
$461$	−8.10813	+	14.0437i	−0.377633	+	0.654080i	0.613084	+	0.790018i	$0.289929\pi$
$462$		0			0
$463$	−1.44769			−0.0672799			−0.0336400	−	0.999434i	$-0.510710\pi$
$463$	−1.44769			−0.0672799			−0.0336400	+	0.999434i	$0.510710\pi$
$464$	−4.56353	−	7.90426i	−0.211856	−	0.366946i
$465$		0			0
$466$	19.2994	−	33.4275i	0.894027	−	1.54850i
$467$	7.00337	−	12.1302i	0.324078	−	0.561319i	−0.657248	−	0.753675i	$-0.728279\pi$
$467$	7.00337	−	12.1302i	0.324078	−	0.561319i	0.981325	+	0.192356i	$0.0616128\pi$
$468$		0			0
$469$	18.2817	+	3.17150i	0.844169	+	0.146446i
$470$	5.09091	+	8.81772i	0.234826	+	0.406731i
$471$		0			0
$472$	−24.4320			−1.12458
$473$	−1.87534	−	3.24818i	−0.0862282	−	0.149352i
$474$		0			0
$475$	−7.72100	+	13.3732i	−0.354264	+	0.613603i
$476$	−21.7895	−	59.3553i	−0.998719	−	2.72055i
$477$		0			0
$478$	−38.4562			−1.75895
$479$	−15.0122	+	26.0018i	−0.685923	+	1.18805i	0.287223	+	0.957864i	$0.407268\pi$
$479$	−15.0122	+	26.0018i	−0.685923	+	1.18805i	−0.973146	+	0.230189i	$0.926065\pi$
$480$		0			0
$481$	4.20055	−	4.73667i	0.191528	−	0.215973i
$482$	−9.56649			−0.435742
$483$		0			0
$484$	19.7253	+	34.1652i	0.896605	+	1.55296i
$485$	3.78033	+	6.54772i	0.171656	+	0.297317i
$486$		0			0
$487$	−28.4903			−1.29102			−0.645510	−	0.763752i	$-0.723355\pi$
$487$	−28.4903			−1.29102			−0.645510	+	0.763752i	$0.723355\pi$
$488$	−4.48649	−	7.77082i	−0.203094	−	0.351769i
$489$		0			0
$490$	2.94062	+	16.1546i	0.132844	+	0.729790i
$491$	−14.2339	−	24.6538i	−0.642365	−	1.11261i	−0.984903	−	0.173105i	$-0.944620\pi$
$491$	−14.2339	−	24.6538i	−0.642365	−	1.11261i	0.342539	−	0.939504i	$-0.388713\pi$
$492$		0			0
$493$	−12.7799	−	22.1354i	−0.575578	−	0.996930i
$494$	32.2811	+	6.60703i	1.45239	+	0.297264i
$495$		0			0
$496$	3.44406	+	5.96528i	0.154643	+	0.267849i
$497$	−9.39114	−	1.62917i	−0.421250	−	0.0730783i
$498$		0			0
$499$	13.1164	−	22.7183i	0.587172	−	1.01701i	−0.407429	−	0.913237i	$-0.633575\pi$
$499$	13.1164	−	22.7183i	0.587172	−	1.01701i	0.994601	−	0.103775i	$-0.0330921\pi$
$500$	32.8617			1.46962
$501$		0			0
$502$	3.87684	−	6.71488i	0.173032	−	0.299700i
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	−0.755112	−	0.655595i	$-0.772418\pi$
$503$	4.26588	−	7.38872i	0.190206	−	0.329447i	0.945318	+	0.326149i	$0.105751\pi$
$504$		0			0
$505$	1.29529	+	2.24352i	0.0576398	+	0.0998351i
$506$	5.79726	−	10.0412i	0.257720	−	0.446384i
$507$		0			0
$508$	−7.86876	−	13.6291i	−0.349120	−	0.604693i
$509$	13.0260			0.577366			0.288683	−	0.957425i	$-0.406783\pi$
$509$	13.0260			0.577366			0.288683	+	0.957425i	$0.406783\pi$
$510$		0			0
$511$	−8.36384	+	10.0237i	−0.369995	+	0.443425i
$512$	−24.8008			−1.09605
$513$		0			0
$514$	64.2200			2.83262
$515$	−5.33472	−	9.24000i	−0.235076	−	0.407163i
$516$		0			0
$517$	−1.27571	−	2.20959i	−0.0561055	−	0.0971775i
$518$	−3.82313	−	10.4144i	−0.167979	−	0.457581i
$519$		0			0
$520$	−4.55350	−	13.6621i	−0.199684	−	0.599124i
$521$	2.23285	+	3.86741i	0.0978230	+	0.169434i	0.910783	−	0.412885i	$-0.135479\pi$
$521$	2.23285	+	3.86741i	0.0978230	+	0.169434i	−0.812960	+	0.582319i	$0.802145\pi$
$522$		0			0
$523$	−2.90811			−0.127163			−0.0635815	−	0.997977i	$-0.520252\pi$
$523$	−2.90811			−0.127163			−0.0635815	+	0.997977i	$0.520252\pi$
$524$	−4.01665	+	6.95704i	−0.175468	+	0.303920i
$525$		0			0
$526$	−4.54570	+	7.87339i	−0.198202	+	0.343296i
$527$	9.64490	+	16.7055i	0.420138	+	0.727701i
$528$		0			0
$529$	45.2278			1.96643
$530$	0.998200			0.0433590
$531$		0			0
$532$	24.0187	−	28.7855i	1.04134	−	1.24801i
$533$	12.9696	+	2.65451i	0.561775	+	0.114980i
$534$		0			0
$535$	7.84866	−	13.5943i	0.339327	−	0.587732i
$536$	−14.2581	+	24.6957i	−0.615854	+	1.06669i
$537$		0			0
$538$	56.9262			2.45426
$539$	−0.736875	−	4.04810i	−0.0317394	−	0.174364i
$540$		0			0
$541$	9.23193	−	15.9902i	0.396912	−	0.687471i	−0.596431	−	0.802664i	$-0.703415\pi$
$541$	9.23193	−	15.9902i	0.396912	−	0.687471i	0.993343	+	0.115193i	$0.0367486\pi$
$542$	23.6448			1.01563
$543$		0			0
$544$	−16.9655			−0.727392
$545$	−9.07112			−0.388564
$546$		0			0
$547$	34.9817			1.49571			0.747856	−	0.663861i	$-0.231083\pi$
$547$	34.9817			1.49571			0.747856	+	0.663861i	$0.231083\pi$
$548$	−30.9665			−1.32282
$549$		0			0
$550$	−5.66408			−0.241517
$551$	7.57760	−	13.1248i	0.322817	−	0.559135i
$552$		0			0
$553$	7.26104	+	1.25964i	0.308771	+	0.0535655i
$554$	28.1449			1.19576
$555$		0			0
$556$	1.06808	−	1.84996i	0.0452965	−	0.0784559i
$557$	0.0265706	−	0.0460217i	0.00112583	−	0.00195000i	−0.865462	−	0.500975i	$-0.832975\pi$
$557$	0.0265706	−	0.0460217i	0.00112583	−	0.00195000i	0.866588	+	0.499025i	$0.166308\pi$
$558$		0			0
$559$	7.27451	+	21.8261i	0.307679	+	0.923146i
$560$	−5.90148	−	1.02379i	−0.249383	−	0.0432629i
$561$		0			0
$562$	−31.0388			−1.30929
$563$	−7.98506			−0.336530			−0.168265	−	0.985742i	$-0.553816\pi$
$563$	−7.98506			−0.336530			−0.168265	+	0.985742i	$0.553816\pi$
$564$		0			0
$565$	−4.99992	−	8.66012i	−0.210348	−	0.364334i
$566$	20.0655	−	34.7544i	0.843414	−	1.46084i
$567$		0			0
$568$	7.32424	−	12.6860i	0.307318	−	0.532291i
$569$	26.7241			1.12033			0.560167	−	0.828380i	$-0.310737\pi$
$569$	26.7241			1.12033			0.560167	+	0.828380i	$0.310737\pi$
$570$		0			0
$571$	−6.74647	−	11.6852i	−0.282331	−	0.489012i	0.689627	−	0.724164i	$-0.257774\pi$
$571$	−6.74647	−	11.6852i	−0.282331	−	0.489012i	−0.971958	+	0.235153i	$0.924441\pi$
$572$	2.48129	+	7.44476i	0.103748	+	0.311281i
$573$		0			0
$574$	14.8624	−	17.8120i	0.620345	−	0.743460i
$575$	−16.6651	−	28.8648i	−0.694982	−	1.20374i
$576$		0			0
$577$	−6.00662	−	10.4038i	−0.250059	−	0.433115i	0.713483	−	0.700673i	$-0.247117\pi$
$577$	−6.00662	−	10.4038i	−0.250059	−	0.433115i	−0.963542	+	0.267558i	$0.913783\pi$
$578$	58.8811			2.44913
$579$		0			0
$580$	−14.4036			−0.598078
$581$	−2.61512	−	7.12367i	−0.108493	−	0.295540i
$582$		0			0
$583$	−0.250134			−0.0103595
$584$	−10.0318	−	17.3756i	−0.415118	−	0.719005i
$585$		0			0
$586$	−16.8305	+	29.1512i	−0.695260	+	1.20422i
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	0.953307	−	0.302002i	$-0.0976548\pi$
$587$	5.21177	+	9.02705i	0.215113	+	0.372586i	−0.738195	+	0.674588i	$0.764321\pi$
$588$		0			0
$589$	−5.71876	+	9.90518i	−0.235637	+	0.408136i
$590$	−7.04728	+	12.2062i	−0.290132	+	0.502523i
$591$		0			0
$592$	4.04679			0.166322
$593$	−11.1751	+	19.3558i	−0.458905	+	0.794847i	−0.998903	−	0.0468194i	$-0.985091\pi$
$593$	−11.1751	+	19.3558i	−0.458905	+	0.794847i	0.539998	+	0.841666i	$0.318425\pi$
$594$		0			0
$595$	−16.5268	−	2.86706i	−0.677532	−	0.117538i
$596$	5.19607	+	8.99986i	0.212839	+	0.368649i
$597$		0			0
$598$	−47.1880	+	53.2107i	−1.92966	+	2.17595i
$599$	0.579463	+	1.00366i	0.0236762	+	0.0410084i	0.877621	−	0.479356i	$-0.159130\pi$
$599$	0.579463	+	1.00366i	0.0236762	+	0.0410084i	−0.853945	+	0.520364i	$0.825796\pi$
$600$		0			0
$601$	−21.0907	−	36.5301i	−0.860306	−	1.49009i	−0.871633	−	0.490158i	$-0.836939\pi$
$601$	−21.0907	−	36.5301i	−0.860306	−	1.49009i	0.0113271	−	0.999936i	$-0.496394\pi$
$602$	39.7219	+	6.89094i	1.61894	+	0.280854i
$603$		0			0
$604$	42.6014	+	73.7879i	1.73343	+	3.00239i
$605$	10.4657			0.425491
$606$		0			0
$607$	9.07844	+	15.7243i	0.368482	+	0.638230i	0.989328	−	0.145702i	$-0.0465441\pi$
$607$	9.07844	+	15.7243i	0.368482	+	0.638230i	−0.620846	+	0.783932i	$0.713211\pi$
$608$	−5.02970	−	8.71169i	−0.203981	−	0.353306i
$609$		0			0
$610$	−5.17640			−0.209586
$611$	4.94851	+	14.8473i	0.200195	+	0.600657i
$612$		0			0
$613$	0.451323	−	0.781714i	0.0182288	−	0.0315731i	−0.856767	−	0.515703i	$-0.827531\pi$
$613$	0.451323	−	0.781714i	0.0182288	−	0.0315731i	0.874996	+	0.484130i	$0.160864\pi$
$614$	37.9187			1.53027
$615$		0			0
$616$	6.23055	+	1.08087i	0.251036	+	0.0435497i
$617$	−13.0218	+	22.5544i	−0.524238	+	0.908008i	0.475363	+	0.879790i	$0.342317\pi$
$617$	−13.0218	+	22.5544i	−0.524238	+	0.908008i	−0.999602	+	0.0282180i	$0.991017\pi$
$618$		0			0
$619$	−13.4171	−	23.2390i	−0.539277	−	0.934056i	−0.998943	−	0.0459638i	$-0.985364\pi$
$619$	−13.4171	−	23.2390i	−0.539277	−	0.934056i	0.459666	−	0.888092i	$-0.347969\pi$
$620$	10.8703			0.436562
$621$		0			0
$622$	−34.1530	−	59.1547i	−1.36941	−	2.37189i
$623$	−1.90843	−	5.19863i	−0.0764596	−	0.208279i
$624$		0			0
$625$	−5.72894	+	9.92281i	−0.229158	+	0.396912i
$626$	22.1839	−	38.4237i	0.886649	−	1.53572i
$627$		0			0
$628$	−41.7962	−	72.3932i	−1.66785	−	2.88880i
$629$	11.3328			0.451869
$630$		0			0
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	−0.309135	−	0.951018i	$-0.600039\pi$
$631$	16.8061	−	29.1089i	0.669039	−	1.15881i	0.978173	−	0.207791i	$-0.0666273\pi$
$632$	−5.66296	+	9.80853i	−0.225260	+	0.390162i
$633$		0			0
$634$	36.5901	−	63.3760i	1.45318	−	2.51698i
$635$	−4.17494			−0.165678
$636$		0			0
$637$	−0.550800	+	25.2328i	−0.0218235	+	0.999762i
$638$	5.55889			0.220078
$639$		0			0
$640$	−10.1865	+	17.6435i	−0.402655	+	0.697419i
$641$	−21.1841			−0.836722			−0.418361	−	0.908281i	$-0.637395\pi$
$641$	−21.1841			−0.836722			−0.418361	+	0.908281i	$0.637395\pi$
$642$		0			0
$643$	−0.330770	+	0.572910i	−0.0130443	+	0.0225933i	−0.872474	−	0.488661i	$-0.837486\pi$
$643$	−0.330770	+	0.572910i	−0.0130443	+	0.0225933i	0.859430	+	0.511254i	$0.170819\pi$
$644$	27.8859	+	75.9623i	1.09886	+	2.99333i
$645$		0			0
$646$	29.4917	+	51.0811i	1.16034	+	2.00976i
$647$	−20.0162	+	34.6690i	−0.786916	+	1.36298i	0.140931	+	0.990019i	$0.454990\pi$
$647$	−20.0162	+	34.6690i	−0.786916	+	1.36298i	−0.927848	+	0.372960i	$0.878343\pi$
$648$		0			0
$649$	1.76594	−	3.05870i	0.0693193	−	0.120065i
$650$	34.0376	+	6.96654i	1.33506	+	0.273250i
$651$		0			0
$652$	−15.1388	−	26.2212i	−0.592883	−	1.02690i
$653$	−12.7120			−0.497460			−0.248730	−	0.968573i	$-0.580013\pi$
$653$	−12.7120			−0.497460			−0.248730	+	0.968573i	$0.580013\pi$
$654$		0			0
$655$	1.06556	+	1.84560i	0.0416349	+	0.0721138i
$656$	4.23107	+	7.32844i	0.165196	+	0.286127i
$657$		0			0
$658$	27.0209	+	4.68759i	1.05339	+	0.182741i
$659$	−7.09522	+	12.2893i	−0.276391	+	0.478723i	−0.970485	−	0.241161i	$-0.922472\pi$
$659$	−7.09522	+	12.2893i	−0.276391	+	0.478723i	0.694094	+	0.719884i	$0.255805\pi$
$660$		0			0
$661$	−25.0890	+	43.4554i	−0.975848	+	1.69022i	−0.298742	+	0.954334i	$0.596567\pi$
$661$	−25.0890	+	43.4554i	−0.975848	+	1.69022i	−0.677106	+	0.735885i	$0.736766\pi$
$662$	−32.5104	−	56.3096i	−1.26355	−	2.18853i
$663$		0			0
$664$	11.6625			0.452594
$665$	−3.42740	−	9.33637i	−0.132909	−	0.362049i
$666$		0			0
$667$	16.3556	+	28.3287i	0.633290	+	1.09689i
$668$	−4.30944	−	7.46417i	−0.166737	−	0.288797i
$669$		0			0
$670$	8.22530	+	14.2466i	0.317771	+	0.550396i
$671$	1.29713			0.0500751
$672$		0			0
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	0.883522	−	0.468389i	$-0.155166\pi$
$673$	0.937137	+	1.62317i	0.0361240	+	0.0625685i	−0.847398	+	0.530958i	$0.821832\pi$
$674$	−29.4112			−1.13288
$675$		0			0
$676$	−5.75433	−	47.7902i	−0.221321	−	1.83808i
$677$	−1.00439	+	1.73966i	−0.0386020	+	0.0668607i	−0.884681	−	0.466197i	$-0.845624\pi$
$677$	−1.00439	+	1.73966i	−0.0386020	+	0.0668607i	0.846079	+	0.533058i	$0.178957\pi$
$678$		0			0
$679$	20.0648	+	3.48083i	0.770015	+	0.133582i
$680$	12.8894	−	22.3251i	0.494286	−	0.856128i
$681$		0			0
$682$	−4.19525			−0.160644
$683$	14.1012			0.539568			0.269784	−	0.962921i	$-0.413048\pi$
$683$	14.1012			0.539568			0.269784	+	0.962921i	$0.413048\pi$
$684$		0			0
$685$	−4.10748	+	7.11437i	−0.156939	+	0.271826i
$686$	38.4837	+	21.7953i	1.46932	+	0.832149i
$687$		0			0
$688$	−7.35298	+	12.7357i	−0.280330	+	0.485546i
$689$	1.50315	+	0.307652i	0.0572654	+	0.0117206i
$690$		0			0
$691$	−35.6920			−1.35779			−0.678895	−	0.734236i	$-0.737541\pi$
$691$	−35.6920			−1.35779			−0.678895	+	0.734236i	$0.737541\pi$
$692$	−15.0585	−	26.0820i	−0.572437	−	0.991489i
$693$		0			0
$694$	−14.6746			−0.557041
$695$	−0.283346	−	0.490769i	−0.0107479	−	0.0186159i
$696$		0			0
$697$	11.8489	+	20.5229i	0.448809	+	0.777360i
$698$	−15.5596	−	26.9500i	−0.588938	−	1.02007i
$699$		0			0
$700$	25.3257	−	30.3518i	0.957220	−	1.14719i
$701$	6.15865			0.232609			0.116305	−	0.993214i	$-0.462895\pi$
$701$	6.15865			0.232609			0.116305	+	0.993214i	$0.462895\pi$
$702$		0			0
$703$	3.35979	+	5.81932i	0.126717	+	0.219480i
$704$	3.19959	−	5.54185i	0.120589	−	0.208866i
$705$		0			0
$706$	37.8103	−	65.4894i	1.42301	−	2.46473i
$707$	6.87501	+	1.19268i	0.258561	+	0.0448552i
$708$		0			0
$709$	−17.0185	−	29.4770i	−0.639144	−	1.10703i	−0.985621	−	0.168972i	$-0.945955\pi$
$709$	−17.0185	−	29.4770i	−0.639144	−	1.10703i	0.346477	−	0.938059i	$-0.387378\pi$
$710$	−4.22527	−	7.31838i	−0.158571	−	0.274654i
$711$		0			0
$712$	8.51094			0.318961
$713$	−12.3434	−	21.3794i	−0.462265	−	0.800667i
$714$		0			0
$715$	2.03952	+	0.417432i	0.0762736	+	0.0156111i
$716$	−38.8648	+	67.3158i	−1.45244	+	2.51571i
$717$		0			0
$718$	23.7994	−	41.2218i	0.888187	−	1.53838i
$719$	−11.4824	−	19.8881i	−0.428222	−	0.741702i	0.568493	−	0.822688i	$-0.307526\pi$
$719$	−11.4824	−	19.8881i	−0.428222	−	0.741702i	−0.996715	+	0.0809859i	$0.974193\pi$
$720$		0			0
$721$	−28.3150	−	4.91208i	−1.05451	−	0.182935i
$722$	5.19981	−	9.00633i	0.193517	−	0.335181i
$723$		0			0
$724$	−5.95424			−0.221288
$725$	7.98992	−	13.8389i	0.296738	−	0.513966i
$726$		0			0
$727$	1.06558			0.0395203			0.0197601	−	0.999805i	$-0.493710\pi$
$727$	1.06558			0.0395203			0.0197601	+	0.999805i	$0.493710\pi$
$728$	−36.1123	−	14.1586i	−1.33841	−	0.524754i
$729$		0			0
$730$	−11.5744			−0.428389
$731$	−20.5916	+	35.6658i	−0.761609	+	1.31915i
$732$		0			0
$733$	13.1689	−	22.8092i	0.486404	−	0.842476i	−0.513474	−	0.858105i	$-0.671642\pi$
$733$	13.1689	−	22.8092i	0.486404	−	0.842476i	0.999878	+	0.0156289i	$0.00497504\pi$
$734$	−23.5448	+	40.7809i	−0.869056	+	1.50525i
$735$		0			0
$736$	21.7123			0.800326
$737$	−2.06114	−	3.57000i	−0.0759230	−	0.131502i
$738$		0			0
$739$	−17.1075	+	29.6310i	−0.629308	+	1.08999i	0.358383	+	0.933575i	$0.383328\pi$
$739$	−17.1075	+	29.6310i	−0.629308	+	1.08999i	−0.987691	+	0.156419i	$0.950005\pi$
$740$	3.19317	−	5.53073i	0.117383	−	0.203314i
$741$		0			0
$742$	1.72252	−	2.06438i	0.0632358	−	0.0757857i
$743$	11.2391	+	19.4667i	0.412322	+	0.714163i	0.995143	−	0.0984379i	$-0.0313846\pi$
$743$	11.2391	+	19.4667i	0.412322	+	0.714163i	−0.582821	+	0.812600i	$0.698051\pi$
$744$		0			0
$745$	2.75689			0.101005
$746$	−20.9513	−	36.2888i	−0.767083	−	1.32863i
$747$		0			0
$748$	−7.02368	+	12.1654i	−0.256811	+	0.444810i
$749$	−14.5705	−	39.6905i	−0.532393	−	1.45026i
$750$		0			0
$751$	−42.5424			−1.55239			−0.776197	−	0.630491i	$-0.782854\pi$
$751$	−42.5424			−1.55239			−0.776197	+	0.630491i	$0.782854\pi$
$752$	−5.00189	+	8.66353i	−0.182400	+	0.315927i
$753$		0			0
$754$	−33.4054	−	6.83715i	−1.21655	−	0.248994i
$755$	22.6031			0.822612
$756$		0			0
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	0.949886	−	0.312596i	$-0.101199\pi$
$757$	5.61902	+	9.73243i	0.204227	+	0.353731i	−0.745659	+	0.666327i	$0.767865\pi$
$758$	13.9716	+	24.1996i	0.507473	+	0.878969i
$759$		0			0
$760$	15.2850			0.554447
$761$	6.40422	+	11.0924i	0.232153	+	0.402101i	0.958441	−	0.285289i	$-0.0920897\pi$
$761$	6.40422	+	11.0924i	0.232153	+	0.402101i	−0.726289	+	0.687390i	$0.758756\pi$
$762$		0			0
$763$	−15.6534	+	18.7600i	−0.566691	+	0.679158i
$764$	−21.4059	−	37.0760i	−0.774437	−	1.34136i
$765$		0			0
$766$	−25.7058	−	44.5238i	−0.928789	−	1.60871i
$767$	−14.3743	+	16.2089i	−0.519024	+	0.585268i
$768$		0			0
$769$	25.6759	+	44.4719i	0.925895	+	1.60370i	0.790115	+	0.612958i	$0.210021\pi$
$769$	25.6759	+	44.4719i	0.925895	+	1.60370i	0.135780	+	0.990739i	$0.456646\pi$
$770$	2.33717	−	2.80101i	0.0842258	−	0.100941i
$771$		0			0
$772$	−43.6529	+	75.6091i	−1.57110	+	2.72123i
$773$	−20.0046			−0.719517			−0.359759	−	0.933045i	$-0.617141\pi$
$773$	−20.0046			−0.719517			−0.359759	+	0.933045i	$0.617141\pi$
$774$		0			0
$775$	−6.02993	+	10.4441i	−0.216602	+	0.375165i
$776$	−15.6487	+	27.1044i	−0.561756	+	0.972990i
$777$		0			0
$778$	31.6308	+	54.7861i	1.13402	+	1.96418i
$779$	−7.02558	+	12.1687i	−0.251717	+	0.435987i
$780$		0			0
$781$	1.05879	+	1.83388i	0.0378864	+	0.0656212i
$782$	−127.310			−4.55261
$783$		0			0
$784$	−12.3011	+	10.4382i	−0.439323	+	0.372792i
$785$	−22.1759			−0.791492
$786$		0			0
$787$	29.3192			1.04512			0.522558	−	0.852604i	$-0.324978\pi$
$787$	29.3192			1.04512			0.522558	+	0.852604i	$0.324978\pi$
$788$	−2.72325	−	4.71680i	−0.0970117	−	0.168029i
$789$		0			0
$790$	3.26689	+	5.65842i	0.116231	+	0.201318i
$791$	−26.5380	−	4.60381i	−0.943583	−	0.163693i
$792$		0			0
$793$	−7.79493	−	1.59540i	−0.276806	−	0.0566544i
$794$	40.3566	+	69.8996i	1.43220	+	2.48064i
$795$		0			0
$796$	34.7833			1.23286
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	−0.837258	−	0.546809i	$-0.815842\pi$
$797$	1.55050	−	2.68554i	0.0549215	−	0.0951269i	0.892179	+	0.451682i	$0.149176\pi$
$798$		0			0
$799$	−14.0075	+	24.2618i	−0.495551	+	0.858319i
$800$	−5.30338	−	9.18572i	−0.187503	−	0.324764i
$801$		0			0
$802$	−51.6100			−1.82241
$803$	2.90038			0.102352
$804$		0			0
$805$	21.1508	+	3.66923i	0.745467	+	0.129323i
$806$	25.2108	+	5.15995i	0.888013	+	0.181751i
$807$		0			0
$808$	−5.36189	+	9.28707i	−0.188631	+	0.326718i
$809$	3.99501	−	6.91957i	0.140457	−	0.243279i	−0.787212	−	0.616683i	$-0.788476\pi$
$809$	3.99501	−	6.91957i	0.140457	−	0.243279i	0.927669	+	0.373404i	$0.121809\pi$
$810$		0			0
$811$	−48.2554			−1.69448			−0.847239	−	0.531213i	$-0.821737\pi$
$811$	−48.2554			−1.69448			−0.847239	+	0.531213i	$0.821737\pi$
$812$	−24.8553	+	29.7881i	−0.872250	+	1.04536i
$813$		0			0
$814$	−1.23236	+	2.13451i	−0.0431942	+	0.0748146i
$815$	−8.03224			−0.281357
$816$		0			0
$817$	−24.4188			−0.854307
$818$	18.4886			0.646439
$819$		0			0
$820$	13.3543			0.466353
$821$	27.5519			0.961569			0.480785	−	0.876839i	$-0.340352\pi$
$821$	27.5519			0.961569			0.480785	+	0.876839i	$0.340352\pi$
$822$		0			0
$823$	20.4274			0.712056			0.356028	−	0.934475i	$-0.384131\pi$
$823$	20.4274			0.712056			0.356028	+	0.934475i	$0.384131\pi$
$824$	22.0831	−	38.2491i	0.769303	−	1.33247i
$825$		0			0
$826$	13.0828	+	35.6379i	0.455207	+	1.24000i
$827$	27.7142			0.963719			0.481859	−	0.876249i	$-0.339962\pi$
$827$	27.7142			0.963719			0.481859	+	0.876249i	$0.339962\pi$
$828$		0			0
$829$	−4.62832	+	8.01648i	−0.160748	+	0.278424i	−0.935137	−	0.354286i	$-0.884724\pi$
$829$	−4.62832	+	8.01648i	−0.160748	+	0.278424i	0.774389	+	0.632710i	$0.218057\pi$
$830$	3.36398	−	5.82659i	0.116766	−	0.202244i
$831$		0			0
$832$	−26.0437	+	29.3677i	−0.902904	+	1.01814i
$833$	−34.4484	+	29.2315i	−1.19357	+	1.01281i
$834$		0			0
$835$	−2.28647			−0.0791264
$836$	−8.32912			−0.288069
$837$		0			0
$838$	−9.67387	−	16.7556i	−0.334178	−	0.578814i
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	0.475287	+	0.879831i	$0.342344\pi$
$839$	−15.1870	+	26.3046i	−0.524312	+	0.908135i	−0.999599	+	0.0283045i	$0.990989\pi$
$840$		0			0
$841$	6.65848	−	11.5328i	0.229603	−	0.397683i
$842$	−76.6855			−2.64276
$843$		0			0
$844$	16.5552	+	28.6745i	0.569854	+	0.987016i
$845$	−11.7428	−	5.01701i	−0.403965	−	0.172590i
$846$		0			0
$847$	18.0599	−	21.6441i	0.620545	−	0.743700i
$848$	0.490373	+	0.849350i	0.0168395	+	0.0291668i
$849$		0			0
$850$	31.0964	+	53.8606i	1.06660	+	1.84740i
$851$	−14.5036			−0.497177
$852$		0			0
$853$	−5.30773			−0.181733			−0.0908666	−	0.995863i	$-0.528964\pi$
$853$	−5.30773			−0.181733			−0.0908666	+	0.995863i	$0.528964\pi$
$854$	−8.93254	+	10.7053i	−0.305665	+	0.366328i
$855$		0			0
$856$	64.9793			2.22095
$857$	−8.31857	−	14.4082i	−0.284157	−	0.492175i	0.688247	−	0.725476i	$-0.258380\pi$
$857$	−8.31857	−	14.4082i	−0.284157	−	0.492175i	−0.972404	+	0.233302i	$0.925047\pi$
$858$		0			0
$859$	5.29426	−	9.16993i	0.180638	−	0.312874i	−0.761460	−	0.648212i	$-0.775517\pi$
$859$	5.29426	−	9.16993i	0.180638	−	0.312874i	0.942098	+	0.335338i	$0.108850\pi$
$860$	11.6039	+	20.0986i	0.395690	+	0.685356i
$861$		0			0
$862$	−35.2571	+	61.0671i	−1.20086	+	2.07995i
$863$	−28.0316	+	48.5522i	−0.954207	+	1.65273i	−0.218033	+	0.975941i	$0.569964\pi$
$863$	−28.0316	+	48.5522i	−0.954207	+	1.65273i	−0.736173	+	0.676793i	$0.763369\pi$
$864$		0			0
$865$	−7.98959			−0.271654
$866$	−26.3771	+	45.6864i	−0.896329	+	1.55249i
$867$		0			0
$868$	18.7581	−	22.4809i	0.636691	−	0.763051i
$869$	−0.818634	−	1.41792i	−0.0277703	−	0.0480995i
$870$		0			0
$871$	7.99523	+	23.9885i	0.270908	+	0.812820i
$872$	−18.7750	−	32.5193i	−0.635803	−	1.10124i
$873$		0			0
$874$	−37.7432	−	65.3731i	−1.27668	−	2.21128i
$875$	−8.09194	−	22.0427i	−0.273558	−	0.745181i
$876$		0			0
$877$	1.83026	+	3.17010i	0.0618033	+	0.107047i	0.895272	−	0.445521i	$-0.146982\pi$
$877$	1.83026	+	3.17010i	0.0618033	+	0.107047i	−0.833468	+	0.552567i	$0.813648\pi$
$878$	−15.1779			−0.512229
$879$		0			0
$880$	0.665353	+	1.15242i	0.0224290	+	0.0388482i
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	0.939233	−	0.343281i	$-0.111538\pi$
$881$	5.11493	+	8.85932i	0.172326	+	0.298478i	−0.766906	+	0.641759i	$0.778205\pi$
$882$		0			0
$883$	−3.98979			−0.134267			−0.0671335	−	0.997744i	$-0.521385\pi$
$883$	−3.98979			−0.134267			−0.0671335	+	0.997744i	$0.521385\pi$
$884$	57.1707	−	64.4675i	1.92286	−	2.16828i
$885$		0			0
$886$	−16.1941	+	28.0490i	−0.544052	+	0.942325i
$887$	14.2208			0.477487			0.238743	−	0.971083i	$-0.423265\pi$
$887$	14.2208			0.477487			0.238743	+	0.971083i	$0.423265\pi$
$888$		0			0
$889$	−7.20440	+	8.63420i	−0.241628	+	0.289582i
$890$	2.45493	−	4.25206i	0.0822894	−	0.142529i
$891$		0			0
$892$	−40.3960	−	69.9678i	−1.35256	−	2.34270i
$893$	−16.6110			−0.555866
$894$		0			0
$895$	10.3103	+	17.8579i	0.344635	+	0.596924i
$896$	18.9104	+	51.5127i	0.631753	+	1.72092i
$897$		0			0
$898$	26.1631	−	45.3158i	0.873074	−	1.51221i
$899$	5.91794	−	10.2502i	0.197374	−	0.341862i
$900$		0			0
$901$	1.37326	+	2.37856i	0.0457500	+	0.0792413i
$902$	−5.15392			−0.171607
$903$		0			0
$904$	20.6973	−	35.8487i	0.688381	−	1.19231i
$905$	−0.789789	+	1.36795i	−0.0262535	+	0.0454723i
$906$		0			0
$907$	−21.7126	+	37.6074i	−0.720956	+	1.24873i	0.239661	+	0.970857i	$0.422964\pi$
$907$	−21.7126	+	37.6074i	−0.720956	+	1.24873i	−0.960617	+	0.277876i	$0.910370\pi$
$908$	68.6949			2.27972
$909$		0			0
$910$	−17.4900	+	13.9577i	−0.579789	+	0.462694i
$911$	−24.8617			−0.823706			−0.411853	−	0.911250i	$-0.635118\pi$
$911$	−24.8617			−0.823706			−0.411853	+	0.911250i	$0.635118\pi$
$912$		0			0
$913$	−0.842964	+	1.46006i	−0.0278980	+	0.0483208i
$914$	36.3331			1.20179
$915$		0			0
$916$	−35.8248	+	62.0503i	−1.18368	+	2.05020i
$917$	5.65566	+	0.981142i	0.186766	+	0.0324002i
$918$		0			0
$919$	0.831637	+	1.44044i	0.0274332	+	0.0475157i	0.879416	−	0.476054i	$-0.157933\pi$
$919$	0.831637	+	1.44044i	0.0274332	+	0.0475157i	−0.851983	+	0.523570i	$0.824600\pi$
$920$	−16.4957	+	28.5714i	−0.543847	+	0.941971i
$921$		0			0
$922$	−19.3625	+	33.5369i	−0.637671	+	1.10448i
$923$	−4.10708	−	12.3227i	−0.135186	−	0.405607i
$924$		0			0
$925$	3.54260	+	6.13597i	0.116480	+	0.201749i
$926$	−3.45714			−0.113609
$927$		0			0
$928$	5.20488	+	9.01512i	0.170859	+	0.295936i
$929$	4.74761	+	8.22310i	0.155764	+	0.269791i	0.933337	−	0.359002i	$-0.116883\pi$
$929$	4.74761	+	8.22310i	0.155764	+	0.269791i	−0.777573	+	0.628793i	$0.783549\pi$
$930$		0			0
$931$	−25.2230	−	9.02289i	−0.826649	−	0.295713i
$932$	29.9243	−	51.8304i	0.980202	−	1.69776i
$933$		0			0
$934$	16.7243	−	28.9674i	0.547236	−	0.947841i
$935$	1.86328	+	3.22730i	0.0609359	+	0.105544i
$936$		0			0
$937$	−6.41678			−0.209627			−0.104813	−	0.994492i	$-0.533425\pi$
$937$	−6.41678			−0.209627			−0.104813	+	0.994492i	$0.533425\pi$
$938$	43.6573	+	7.57366i	1.42546	+	0.247289i
$939$		0			0
$940$	7.89361	+	13.6721i	0.257461	+	0.445936i
$941$	−25.7593	−	44.6164i	−0.839730	−	1.45445i	−0.890121	−	0.455725i	$-0.849380\pi$
$941$	−25.7593	−	44.6164i	−0.839730	−	1.45445i	0.0503911	−	0.998730i	$-0.483953\pi$
$942$		0			0
$943$	−15.1641	−	26.2650i	−0.493810	−	0.855305i
$944$	−13.8481			−0.450717
$945$		0			0
$946$	−4.47838	−	7.75678i	−0.145605	−	0.252195i
$947$	8.40219			0.273034			0.136517	−	0.990638i	$-0.456409\pi$
$947$	8.40219			0.273034			0.136517	+	0.990638i	$0.456409\pi$
$948$		0			0
$949$	−17.4295	−	3.56732i	−0.565784	−	0.115800i
$950$	−18.4380	+	31.9356i	−0.598209	+	1.03613i
$951$		0			0
$952$	−23.9282	−	65.1814i	−0.775518	−	2.11254i
$953$	−18.0455	+	31.2558i	−0.584552	+	1.01247i	0.410379	+	0.911915i	$0.365396\pi$
$953$	−18.0455	+	31.2558i	−0.584552	+	1.01247i	−0.994931	+	0.100559i	$0.967937\pi$
$954$		0			0
$955$	−11.3573			−0.367515
$956$	−59.6275			−1.92849
$957$		0			0
$958$	−35.8496	+	62.0933i	−1.15825	+	2.00614i
$959$	7.62524	+	20.7715i	0.246232	+	0.670745i
$960$		0			0
$961$	11.0338	−	19.1111i	0.355928	−	0.616486i
$962$	10.0311	−	11.3113i	0.323414	−	0.364692i
$963$		0			0
$964$	−14.8331			−0.477743
$965$	11.5805	+	20.0580i	0.372790	+	0.645691i
$966$		0			0
$967$	3.18338			0.102371			0.0511853	−	0.998689i	$-0.483700\pi$
$967$	3.18338			0.102371			0.0511853	+	0.998689i	$0.483700\pi$
$968$	21.6614	+	37.5187i	0.696225	+	1.20590i
$969$		0			0
$970$	9.02756	+	15.6362i	0.289857	+	0.502048i
$971$	18.8738	+	32.6904i	0.605690	+	1.04909i	0.991942	+	0.126692i	$0.0404360\pi$
$971$	18.8738	+	32.6904i	0.605690	+	1.04909i	−0.386253	+	0.922393i	$0.626231\pi$
$972$		0			0
$973$	−1.50391	−	0.260898i	−0.0482131	−	0.00836399i
$974$	−68.0359			−2.18001
$975$		0			0
$976$	−2.54294	−	4.40451i	−0.0813977	−	0.140985i
$977$	−10.6538	+	18.4530i	−0.340846	+	0.590363i	−0.984590	−	0.174878i	$-0.944047\pi$
$977$	−10.6538	+	18.4530i	−0.340846	+	0.590363i	0.643744	+	0.765241i	$0.277380\pi$
$978$		0			0
$979$	−0.615168	+	1.06550i	−0.0196609	+	0.0340536i
$980$	4.55951	+	25.0482i	0.145648	+	0.800134i
$981$		0			0
$982$	−33.9910	−	58.8741i	−1.08470	−	1.87875i
$983$	−11.0158	−	19.0799i	−0.351350	−	0.608556i	0.635136	−	0.772400i	$-0.280944\pi$
$983$	−11.0158	−	19.0799i	−0.351350	−	0.608556i	−0.986486	+	0.163844i	$0.947611\pi$
$984$		0			0
$985$	−1.44488			−0.0460377
$986$	−30.5189	−	52.8603i	−0.971919	−	1.68341i
$987$		0			0
$988$	50.0528	+	10.2444i	1.59239	+	0.325918i
$989$	26.3529	−	45.6446i	0.837975	−	1.45141i
$990$		0			0
$991$	11.0129	−	19.0750i	0.349838	−	0.605937i	−0.636383	−	0.771374i	$-0.719570\pi$
$991$	11.0129	−	19.0750i	0.349838	−	0.605937i	0.986220	+	0.165437i	$0.0529033\pi$
$992$	−3.92808	−	6.80364i	−0.124717	−	0.216016i
$993$		0			0
$994$	−22.4264	−	3.89052i	−0.711322	−	0.123400i
$995$	4.61376	−	7.99127i	0.146266	−	0.253340i
$996$		0			0
$997$	10.0820			0.319301			0.159651	−	0.987174i	$-0.448963\pi$
$997$	10.0820			0.319301			0.159651	+	0.987174i	$0.448963\pi$
$998$	31.3225	−	54.2522i	0.991497	−	1.71732i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	819.2.s.d.289.6		12
3.2	odd	2		91.2.h.b.16.1	yes	12
7.4	even	3		819.2.n.d.172.1		12
13.9	even	3		819.2.n.d.100.1		12
21.2	odd	6		637.2.f.k.393.6		12
21.5	even	6		637.2.f.j.393.6		12
21.11	odd	6		91.2.g.b.81.6	yes	12
21.17	even	6		637.2.g.l.263.6		12
21.20	even	2		637.2.h.l.471.1		12
39.23	odd	6		1183.2.e.g.170.1		12
39.29	odd	6		1183.2.e.h.170.6		12
39.35	odd	6		91.2.g.b.9.6	✓	12
91.74	even	3	inner	819.2.s.d.802.6		12
273.23	odd	6		8281.2.a.ce.1.6		6
273.68	even	6		8281.2.a.ca.1.1		6
273.74	odd	6		91.2.h.b.74.1	yes	12
273.107	odd	6		8281.2.a.bz.1.1		6
273.152	even	6		637.2.f.j.295.6		12
273.179	odd	6		1183.2.e.g.508.1		12
273.191	odd	6		637.2.f.k.295.6		12
273.230	even	6		637.2.g.l.373.6		12
273.257	even	6		8281.2.a.cf.1.6		6
273.263	odd	6		1183.2.e.h.508.6		12
273.269	even	6		637.2.h.l.165.1		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
91.2.g.b.9.6	✓	12	39.35	odd	6
91.2.g.b.81.6	yes	12	21.11	odd	6
91.2.h.b.16.1	yes	12	3.2	odd	2
91.2.h.b.74.1	yes	12	273.74	odd	6
637.2.f.j.295.6		12	273.152	even	6
637.2.f.j.393.6		12	21.5	even	6
637.2.f.k.295.6		12	273.191	odd	6
637.2.f.k.393.6		12	21.2	odd	6
637.2.g.l.263.6		12	21.17	even	6
637.2.g.l.373.6		12	273.230	even	6
637.2.h.l.165.1		12	273.269	even	6
637.2.h.l.471.1		12	21.20	even	2
819.2.n.d.100.1		12	13.9	even	3
819.2.n.d.172.1		12	7.4	even	3
819.2.s.d.289.6		12	1.1	even	1	trivial
819.2.s.d.802.6		12	91.74	even	3	inner
1183.2.e.g.170.1		12	39.23	odd	6
1183.2.e.g.508.1		12	273.179	odd	6
1183.2.e.h.170.6		12	39.29	odd	6
1183.2.e.h.508.6		12	273.263	odd	6
8281.2.a.bz.1.1		6	273.107	odd	6
8281.2.a.ca.1.1		6	273.68	even	6
8281.2.a.ce.1.6		6	273.23	odd	6
8281.2.a.cf.1.6		6	273.257	even	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:	\( N \)	\(=\)	\( 819 = 3^{2} \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	819.s (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.38804 q^{2} +3.70272 q^{4} +(0.491140 - 0.850679i) q^{5} +(-0.911766 - 2.48368i) q^{7} +4.06616 q^{8} +O(q^{10})\)	\(q+2.38804 q^{2} +3.70272 q^{4} +(0.491140 - 0.850679i) q^{5} +(-0.911766 - 2.48368i) q^{7} +4.06616 q^{8} +(1.17286 - 2.03145i) q^{10} +(-0.293901 + 0.509052i) q^{11} +(2.39227 - 2.69760i) q^{13} +(-2.17733 - 5.93113i) q^{14} +2.30470 q^{16} +6.45420 q^{17} +(1.91345 + 3.31419i) q^{19} +(1.81855 - 3.14983i) q^{20} +(-0.701847 + 1.21563i) q^{22} -8.26001 q^{23} +(2.01756 + 3.49452i) q^{25} +(5.71283 - 6.44197i) q^{26} +(-3.37601 - 9.19639i) q^{28} +(-1.98009 - 3.42962i) q^{29} +(1.49436 + 2.58831i) q^{31} -2.62861 q^{32} +15.4129 q^{34} +(-2.56062 - 0.444216i) q^{35} +1.75588 q^{37} +(4.56938 + 7.91440i) q^{38} +(1.99705 - 3.45900i) q^{40} +(1.83584 + 3.17977i) q^{41} +(-3.19042 + 5.52598i) q^{43} +(-1.08823 + 1.88488i) q^{44} -19.7252 q^{46} +(-2.17030 + 3.75906i) q^{47} +(-5.33737 + 4.52907i) q^{49} +(4.81802 + 8.34505i) q^{50} +(8.85791 - 9.98846i) q^{52} +(0.212770 + 0.368529i) q^{53} +(0.288693 + 0.500031i) q^{55} +(-3.70739 - 10.0991i) q^{56} +(-4.72853 - 8.19006i) q^{58} -6.00863 q^{59} +(-1.10337 - 1.91109i) q^{61} +(3.56859 + 6.18097i) q^{62} -10.8866 q^{64} +(-1.11985 - 3.35995i) q^{65} +(-3.50651 + 6.07346i) q^{67} +23.8981 q^{68} +(-6.11486 - 1.06080i) q^{70} +(1.80127 - 3.11988i) q^{71} +(-2.46714 - 4.27321i) q^{73} +4.19311 q^{74} +(7.08496 + 12.2715i) q^{76} +(1.53229 + 0.265822i) q^{77} +(-1.39270 + 2.41223i) q^{79} +(1.13193 - 1.96056i) q^{80} +(4.38406 + 7.59342i) q^{82} +2.86819 q^{83} +(3.16992 - 5.49045i) q^{85} +(-7.61885 + 13.1962i) q^{86} +(-1.19505 + 2.06989i) q^{88} +2.09311 q^{89} +(-8.88117 - 3.48206i) q^{91} -30.5845 q^{92} +(-5.18275 + 8.97679i) q^{94} +3.75908 q^{95} +(-3.84852 + 6.66584i) q^{97} +(-12.7458 + 10.8156i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8}+O(q^{10}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8	\( 12 q + 4 q^{2} + 8 q^{4} - q^{5} - 3 q^{7} + 6 q^{8} + 4 q^{10} - 4 q^{11} - 2 q^{13} + 2 q^{14} - 16 q^{16} + 10 q^{17} - q^{19} + q^{20} - 5 q^{22} - 2 q^{23} + 7 q^{25} + 16 q^{26} - q^{28} - 3 q^{29} + 16 q^{31} + 16 q^{32} + 32 q^{34} - 20 q^{35} + 26 q^{37} + 17 q^{38} - 5 q^{40} + 8 q^{41} - 11 q^{43} - 21 q^{44} - 32 q^{46} + q^{47} - 3 q^{49} - 6 q^{50} + 41 q^{52} + 2 q^{53} + 9 q^{55} - 9 q^{56} - 8 q^{58} + 26 q^{59} - 5 q^{61} - 5 q^{62} - 30 q^{64} + 5 q^{65} - 11 q^{67} + 58 q^{68} - 39 q^{70} - 6 q^{71} - 30 q^{73} - 6 q^{74} - 9 q^{76} - 11 q^{77} + 7 q^{79} + 7 q^{80} + q^{82} + 54 q^{83} - q^{85} + 7 q^{86} + 8 q^{89} - 23 q^{91} - 54 q^{92} + 45 q^{94} - 12 q^{95} - 35 q^{97} - 20 q^{98}+O(q^{100}) \) 12 * q + 4 * q^2 + 8 * q^4 - q^5 - 3 * q^7 + 6 * q^8 + 4 * q^10 - 4 * q^11 - 2 * q^13 + 2 * q^14 - 16 * q^16 + 10 * q^17 - q^19 + q^20 - 5 * q^22 - 2 * q^23 + 7 * q^25 + 16 * q^26 - q^28 - 3 * q^29 + 16 * q^31 + 16 * q^32 + 32 * q^34 - 20 * q^35 + 26 * q^37 + 17 * q^38 - 5 * q^40 + 8 * q^41 - 11 * q^43 - 21 * q^44 - 32 * q^46 + q^47 - 3 * q^49 - 6 * q^50 + 41 * q^52 + 2 * q^53 + 9 * q^55 - 9 * q^56 - 8 * q^58 + 26 * q^59 - 5 * q^61 - 5 * q^62 - 30 * q^64 + 5 * q^65 - 11 * q^67 + 58 * q^68 - 39 * q^70 - 6 * q^71 - 30 * q^73 - 6 * q^74 - 9 * q^76 - 11 * q^77 + 7 * q^79 + 7 * q^80 + q^82 + 54 * q^83 - q^85 + 7 * q^86 + 8 * q^89 - 23 * q^91 - 54 * q^92 + 45 * q^94 - 12 * q^95 - 35 * q^97 - 20 * q^98

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