LMFDB - Embedded newform 810.3.j.c.539.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,3,Mod(269,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("810.269");

S:= CuspForms(chi, 3);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.0709014132$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.443364212736.6
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 16x^{6} + 175x^{4} - 1296x^{2} + 6561 $ x^8 - 16x^6 + 175x^4 - 1296*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			539.2
Root			$2.87843 - 0.845366i$ of defining polynomial
Character	$\chi$	$=$	810.539
Dual form			810.3.j.c.269.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98493 - 0.387937i) q^{5} +(-5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98493 - 0.387937i) q^{5} +(-5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +(-4.00000 - 5.83095i) q^{10} +(14.2829 - 8.24621i) q^{11} +(7.14143 + 4.12311i) q^{14} +(-2.00000 - 3.46410i) q^{16} -11.3137 q^{17} +12.0000 q^{19} +(-4.31300 + 9.02209i) q^{20} +(-20.1990 - 11.6619i) q^{22} +(-12.0208 + 20.8207i) q^{23} +(24.6990 - 3.86768i) q^{25} -11.6619i q^{28} +(16.0000 - 27.7128i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.00000 + 13.8564i) q^{34} +(-24.0416 + 16.4924i) q^{35} -23.3238i q^{37} +(-8.48528 - 14.6969i) q^{38} +(14.0995 - 1.09725i) q^{40} +(49.9900 + 28.8617i) q^{41} +(35.3483 - 20.4083i) q^{43} +32.9848i q^{44} +34.0000 q^{46} +(17.6777 + 30.6186i) q^{47} +(-7.50000 + 12.9904i) q^{49} +(-22.2018 - 27.5151i) q^{50} +67.8823 q^{53} +(68.0000 - 46.6476i) q^{55} +(-14.2829 + 8.24621i) q^{56} +(-14.2829 - 8.24621i) q^{59} +(8.00000 + 13.8564i) q^{61} -45.2548 q^{62} +8.00000 q^{64} +(-5.04975 - 2.91548i) q^{67} +(11.3137 - 19.5959i) q^{68} +(37.1990 + 17.7830i) q^{70} -116.619i q^{73} +(-28.5657 + 16.4924i) q^{74} +(-12.0000 + 20.7846i) q^{76} +(-48.0833 + 83.2827i) q^{77} +(36.0000 + 62.3538i) q^{79} +(-11.3137 - 16.4924i) q^{80} -81.6333i q^{82} +(21.9203 + 37.9671i) q^{83} +(-56.3980 + 4.38901i) q^{85} +(-49.9900 - 28.8617i) q^{86} +(40.3980 - 23.3238i) q^{88} -65.9697i q^{89} +(-24.0416 - 41.6413i) q^{92} +(25.0000 - 43.3013i) q^{94} +(59.8191 - 4.65524i) q^{95} +(141.393 - 81.6333i) q^{97} +21.2132 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} - 32 q^{10} - 16 q^{16} + 96 q^{19} + 36 q^{25} + 128 q^{31} + 64 q^{34} + 32 q^{40} + 272 q^{46} - 60 q^{49} + 544 q^{55} + 64 q^{61} + 64 q^{64} + 136 q^{70} - 96 q^{76} + 288 q^{79} - 128 q^{85} + 200 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 - 32 * q^10 - 16 * q^16 + 96 * q^19 + 36 * q^25 + 128 * q^31 + 64 * q^34 + 32 * q^40 + 272 * q^46 - 60 * q^49 + 544 * q^55 + 64 * q^61 + 64 * q^64 + 136 * q^70 - 96 * q^76 + 288 * q^79 - 128 * q^85 + 200 * q^94

Display 100 coefficients 10 coefficients

Character values

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

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$2$	−0.707107	−	1.22474i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.250000	+	0.433013i
$5$	4.98493	−	0.387937i	0.996986	−	0.0775874i
$5$	4.98493	−	0.387937i	0.996986	−	0.0775874i
$6$		0			0
$7$	−5.04975	+	2.91548i	−0.721393	+	0.416497i	−0.815265	−	0.579088i	$-0.803409\pi$
$7$	−5.04975	+	2.91548i	−0.721393	+	0.416497i	0.0938720	+	0.995584i	$0.470076\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	−4.00000	−	5.83095i	−0.400000	−	0.583095i
$11$	14.2829	−	8.24621i	1.29844	−	0.749656i	0.318307	−	0.947988i	$-0.396886\pi$
$11$	14.2829	−	8.24621i	1.29844	−	0.749656i	0.980135	+	0.198332i	$0.0635525\pi$
$12$		0			0
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$	7.14143	+	4.12311i	0.510102	+	0.294508i
$15$		0			0
$16$	−2.00000	−	3.46410i	−0.125000	−	0.216506i
$17$	−11.3137			−0.665512			−0.332756	−	0.943013i	$-0.607979\pi$
$17$	−11.3137			−0.665512			−0.332756	+	0.943013i	$0.607979\pi$
$18$		0			0
$19$	12.0000			0.631579			0.315789	−	0.948829i	$-0.397731\pi$
$19$	12.0000			0.631579			0.315789	+	0.948829i	$0.397731\pi$
$20$	−4.31300	+	9.02209i	−0.215650	+	0.451104i
$21$		0			0
$22$	−20.1990	−	11.6619i	−0.918137	−	0.530087i
$23$	−12.0208	+	20.8207i	−0.522644	+	0.905246i	0.477009	+	0.878899i	$0.341721\pi$
$23$	−12.0208	+	20.8207i	−0.522644	+	0.905246i	−0.999653	+	0.0263476i	$0.991612\pi$
$24$		0			0
$25$	24.6990	−	3.86768i	0.987960	−	0.154707i
$26$		0			0
$27$		0			0
$28$		−	11.6619i		−	0.416497i
$29$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$29$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$30$		0			0
$31$	16.0000	−	27.7128i	0.516129	−	0.893962i	−0.483696	−	0.875236i	$-0.660706\pi$
$31$	16.0000	−	27.7128i	0.516129	−	0.893962i	0.999825	−	0.0187254i	$-0.00596084\pi$
$32$	−2.82843	+	4.89898i	−0.0883883	+	0.153093i
$33$		0			0
$34$	8.00000	+	13.8564i	0.235294	+	0.407541i
$35$	−24.0416	+	16.4924i	−0.686904	+	0.471212i
$36$		0			0
$37$		−	23.3238i		−	0.630373i	−0.949030	−	0.315187i	$-0.897933\pi$
$37$		−	23.3238i		−	0.630373i	0.949030	−	0.315187i	$-0.102067\pi$
$38$	−8.48528	−	14.6969i	−0.223297	−	0.386762i
$39$		0			0
$40$	14.0995	−	1.09725i	0.352488	−	0.0274313i
$41$	49.9900	+	28.8617i	1.21927	+	0.703945i	0.964761	−	0.263126i	$-0.0847535\pi$
$41$	49.9900	+	28.8617i	1.21927	+	0.703945i	0.254507	+	0.967071i	$0.418087\pi$
$42$		0			0
$43$	35.3483	−	20.4083i	0.822053	−	0.474612i	−0.0290711	−	0.999577i	$-0.509255\pi$
$43$	35.3483	−	20.4083i	0.822053	−	0.474612i	0.851124	+	0.524965i	$0.175922\pi$
$44$			32.9848i			0.749656i
$45$		0			0
$46$	34.0000			0.739130
$47$	17.6777	+	30.6186i	0.376121	+	0.651460i	0.990494	−	0.137555i	$-0.0439245\pi$
$47$	17.6777	+	30.6186i	0.376121	+	0.651460i	−0.614373	+	0.789015i	$0.710591\pi$
$48$		0			0
$49$	−7.50000	+	12.9904i	−0.153061	+	0.265110i
$50$	−22.2018	−	27.5151i	−0.444035	−	0.550303i
$51$		0			0
$52$		0			0
$53$	67.8823			1.28080			0.640399	−	0.768043i	$-0.278769\pi$
$53$	67.8823			1.28080			0.640399	+	0.768043i	$0.278769\pi$
$54$		0			0
$55$	68.0000	−	46.6476i	1.23636	−	0.848138i
$56$	−14.2829	+	8.24621i	−0.255051	+	0.147254i
$57$		0			0
$58$		0			0
$59$	−14.2829	−	8.24621i	−0.242082	−	0.139766i	0.374051	−	0.927408i	$-0.377968\pi$
$59$	−14.2829	−	8.24621i	−0.242082	−	0.139766i	−0.616133	+	0.787642i	$0.711302\pi$
$60$		0			0
$61$	8.00000	+	13.8564i	0.131148	+	0.227154i	0.924119	−	0.382104i	$-0.124801\pi$
$61$	8.00000	+	13.8564i	0.131148	+	0.227154i	−0.792972	+	0.609259i	$0.791467\pi$
$62$	−45.2548			−0.729917
$63$		0			0
$64$	8.00000			0.125000
$65$		0			0
$66$		0			0
$67$	−5.04975	−	2.91548i	−0.0753694	−	0.0435146i	0.461842	−	0.886962i	$-0.347189\pi$
$67$	−5.04975	−	2.91548i	−0.0753694	−	0.0435146i	−0.537211	+	0.843448i	$0.680522\pi$
$68$	11.3137	−	19.5959i	0.166378	−	0.288175i
$69$		0			0
$70$	37.1990	+	17.7830i	0.531414	+	0.254042i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$		0			0
$73$		−	116.619i		−	1.59752i	−0.601649	−	0.798761i	$-0.705489\pi$
$73$		−	116.619i		−	1.59752i	0.601649	−	0.798761i	$-0.294511\pi$
$74$	−28.5657	+	16.4924i	−0.386023	+	0.222871i
$75$		0			0
$76$	−12.0000	+	20.7846i	−0.157895	+	0.273482i
$77$	−48.0833	+	83.2827i	−0.624458	+	1.08159i
$78$		0			0
$79$	36.0000	+	62.3538i	0.455696	+	0.789289i	0.998728	−	0.0504232i	$-0.0160570\pi$
$79$	36.0000	+	62.3538i	0.455696	+	0.789289i	−0.543032	+	0.839712i	$0.682724\pi$
$80$	−11.3137	−	16.4924i	−0.141421	−	0.206155i
$81$		0			0
$82$		−	81.6333i		−	0.995528i
$83$	21.9203	+	37.9671i	0.264100	+	0.457435i	0.967327	−	0.253530i	$-0.0815917\pi$
$83$	21.9203	+	37.9671i	0.264100	+	0.457435i	−0.703227	+	0.710965i	$0.748258\pi$
$84$		0			0
$85$	−56.3980	+	4.38901i	−0.663506	+	0.0516354i
$86$	−49.9900	−	28.8617i	−0.581279	−	0.335602i
$87$		0			0
$88$	40.3980	−	23.3238i	0.459068	−	0.265043i
$89$		−	65.9697i		−	0.741232i	−0.928786	−	0.370616i	$-0.879147\pi$
$89$		−	65.9697i		−	0.741232i	0.928786	−	0.370616i	$-0.120853\pi$
$90$		0			0
$91$		0			0
$92$	−24.0416	−	41.6413i	−0.261322	−	0.452623i
$93$		0			0
$94$	25.0000	−	43.3013i	0.265957	−	0.460652i
$95$	59.8191	−	4.65524i	0.629675	−	0.0490026i
$96$		0			0
$97$	141.393	−	81.6333i	1.45766	−	0.841581i	0.458765	−	0.888558i	$-0.348292\pi$
$97$	141.393	−	81.6333i	1.45766	−	0.841581i	0.998896	+	0.0469772i	$0.0149588\pi$
$98$	21.2132			0.216461
$99$		0			0
$100$	−18.0000	+	46.6476i	−0.180000	+	0.466476i
$101$	114.263	−	65.9697i	1.13132	−	0.653165i	0.187050	−	0.982350i	$-0.440107\pi$
$101$	114.263	−	65.9697i	1.13132	−	0.653165i	0.944265	+	0.329185i	$0.106774\pi$
$102$		0			0
$103$	−85.8458	−	49.5631i	−0.833454	−	0.481195i	0.0215796	−	0.999767i	$-0.493130\pi$
$103$	−85.8458	−	49.5631i	−0.833454	−	0.481195i	−0.855034	+	0.518572i	$0.826464\pi$
$104$		0			0
$105$		0			0
$106$	−48.0000	−	83.1384i	−0.452830	−	0.784325i
$107$	−55.1543			−0.515461			−0.257731	−	0.966217i	$-0.582975\pi$
$107$	−55.1543			−0.515461			−0.257731	+	0.966217i	$0.582975\pi$
$108$		0			0
$109$	80.0000			0.733945			0.366972	−	0.930232i	$-0.380394\pi$
$109$	80.0000			0.733945			0.366972	+	0.930232i	$0.380394\pi$
$110$	−105.215	−	50.2978i	−0.956497	−	0.457253i
$111$		0			0
$112$	20.1990	+	11.6619i	0.180348	+	0.104124i
$113$	76.3675	−	132.272i	0.675819	−	1.17055i	−0.300410	−	0.953810i	$-0.597123\pi$
$113$	76.3675	−	132.272i	0.675819	−	1.17055i	0.976229	−	0.216742i	$-0.0695432\pi$
$114$		0			0
$115$	−51.8458	+	108.453i	−0.450833	+	0.943068i
$116$		0			0
$117$		0			0
$118$			23.3238i			0.197659i
$119$	57.1314	−	32.9848i	0.480096	−	0.277184i
$120$		0			0
$121$	75.5000	−	130.770i	0.623967	−	1.08074i
$122$	11.3137	−	19.5959i	0.0927353	−	0.160622i
$123$		0			0
$124$	32.0000	+	55.4256i	0.258065	+	0.446981i
$125$	121.622	−	28.8617i	0.972979	−	0.230894i
$126$		0			0
$127$		−	40.8167i		−	0.321391i	−0.987004	−	0.160696i	$-0.948626\pi$
$127$		−	40.8167i		−	0.321391i	0.987004	−	0.160696i	$-0.0513737\pi$
$128$	−5.65685	−	9.79796i	−0.0441942	−	0.0765466i
$129$		0			0
$130$		0			0
$131$	−42.8486	−	24.7386i	−0.327088	−	0.188845i	0.327459	−	0.944865i	$-0.393808\pi$
$131$	−42.8486	−	24.7386i	−0.327088	−	0.188845i	−0.654548	+	0.756021i	$0.727141\pi$
$132$		0			0
$133$	−60.5970	+	34.9857i	−0.455617	+	0.263050i
$134$			8.24621i			0.0615389i
$135$		0			0
$136$	−32.0000			−0.235294
$137$	25.4558	+	44.0908i	0.185809	+	0.321831i	0.943849	−	0.330378i	$-0.107176\pi$
$137$	25.4558	+	44.0908i	0.185809	+	0.321831i	−0.758040	+	0.652208i	$0.773843\pi$
$138$		0			0
$139$	−22.0000	+	38.1051i	−0.158273	+	0.274138i	−0.934246	−	0.356629i	$-0.883926\pi$
$139$	−22.0000	+	38.1051i	−0.158273	+	0.274138i	0.775973	+	0.630766i	$0.217259\pi$
$140$	−4.52408	−	58.1337i	−0.0323149	−	0.415241i
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−142.829	+	82.4621i	−0.978278	+	0.564809i
$147$		0			0
$148$	40.3980	+	23.3238i	0.272960	+	0.157593i
$149$	7.14143	+	4.12311i	0.0479290	+	0.0276718i	0.523773	−	0.851858i	$-0.324524\pi$
$149$	7.14143	+	4.12311i	0.0479290	+	0.0276718i	−0.475844	+	0.879530i	$0.657857\pi$
$150$		0			0
$151$	−68.0000	−	117.779i	−0.450331	−	0.779996i	0.548075	−	0.836429i	$-0.315361\pi$
$151$	−68.0000	−	117.779i	−0.450331	−	0.779996i	−0.998406	+	0.0564326i	$0.982027\pi$
$152$	33.9411			0.223297
$153$		0			0
$154$	136.000			0.883117
$155$	69.0080	−	144.353i	0.445213	−	0.931312i
$156$		0			0
$157$	100.995	+	58.3095i	0.643281	+	0.371398i	0.785877	−	0.618383i	$-0.212212\pi$
$157$	100.995	+	58.3095i	0.643281	+	0.371398i	−0.142597	+	0.989781i	$0.545545\pi$
$158$	50.9117	−	88.1816i	0.322226	−	0.558112i
$159$		0			0
$160$	−12.1990	+	25.5183i	−0.0762438	+	0.159489i
$161$		−	140.186i		−	0.870718i
$162$		0			0
$163$			99.1262i			0.608136i	0.952650	+	0.304068i	$0.0983450\pi$
$163$			99.1262i			0.608136i	−0.952650	+	0.304068i	$0.901655\pi$
$164$	−99.9800	+	57.7235i	−0.609634	+	0.351972i
$165$		0			0
$166$	31.0000	−	53.6936i	0.186747	−	0.323455i
$167$	−146.371	+	253.522i	−0.876474	+	1.51810i	−0.0212891	+	0.999773i	$0.506777\pi$
$167$	−146.371	+	253.522i	−0.876474	+	1.51810i	−0.855185	+	0.518324i	$0.826556\pi$
$168$		0			0
$169$	−84.5000	−	146.358i	−0.500000	−	0.866025i
$170$	45.2548	+	65.9697i	0.266205	+	0.388057i
$171$		0			0
$172$			81.6333i			0.474612i
$173$	82.0244	+	142.070i	0.474129	+	0.821216i	0.999561	−	0.0296195i	$-0.00942955\pi$
$173$	82.0244	+	142.070i	0.474129	+	0.821216i	−0.525432	+	0.850836i	$0.676096\pi$
$174$		0			0
$175$	−113.448	+	91.5402i	−0.648273	+	0.523087i
$176$	−57.1314	−	32.9848i	−0.324610	−	0.187414i
$177$		0			0
$178$	−80.7960	+	46.6476i	−0.453910	+	0.262065i
$179$			16.4924i			0.0921364i	0.998938	+	0.0460682i	$0.0146692\pi$
$179$			16.4924i			0.0921364i	−0.998938	+	0.0460682i	$0.985331\pi$
$180$		0			0
$181$	−82.0000			−0.453039			−0.226519	−	0.974007i	$-0.572735\pi$
$181$	−82.0000			−0.453039			−0.226519	+	0.974007i	$0.572735\pi$
$182$		0			0
$183$		0			0
$184$	−34.0000	+	58.8897i	−0.184783	+	0.320053i
$185$	−9.04817	−	116.267i	−0.0489090	−	0.628473i
$186$		0			0
$187$	−161.592	+	93.2952i	−0.864129	+	0.498905i
$188$	−70.7107			−0.376121
$189$		0			0
$190$	−48.0000	−	69.9714i	−0.252632	−	0.368271i
$191$	−257.091	+	148.432i	−1.34603	+	0.777130i	−0.987684	−	0.156460i	$-0.949992\pi$
$191$	−257.091	+	148.432i	−1.34603	+	0.777130i	−0.358344	+	0.933590i	$0.616659\pi$
$192$		0			0
$193$	100.995	+	58.3095i	0.523290	+	0.302122i	0.738280	−	0.674495i	$-0.235638\pi$
$193$	100.995	+	58.3095i	0.523290	+	0.302122i	−0.214989	+	0.976616i	$0.568972\pi$
$194$	−199.960	−	115.447i	−1.03072	−	0.595087i
$195$		0			0
$196$	−15.0000	−	25.9808i	−0.0765306	−	0.132555i
$197$	−192.333			−0.976310			−0.488155	−	0.872757i	$-0.662330\pi$
$197$	−192.333			−0.976310			−0.488155	+	0.872757i	$0.662330\pi$
$198$		0			0
$199$	−312.000			−1.56784			−0.783920	−	0.620862i	$-0.786783\pi$
$199$	−312.000			−1.56784			−0.783920	+	0.620862i	$0.786783\pi$
$200$	69.8593	−	10.9394i	0.349297	−	0.0546972i
$201$		0			0
$202$	−161.592	−	93.2952i	−0.799961	−	0.461858i
$203$		0			0
$204$		0			0
$205$	260.393	+	124.481i	1.27021	+	0.607223i
$206$			140.186i			0.680513i
$207$		0			0
$208$		0			0
$209$	171.394	−	98.9545i	0.820068	−	0.473467i
$210$		0			0
$211$	6.00000	−	10.3923i	0.0284360	−	0.0492526i	−0.851457	−	0.524424i	$-0.824281\pi$
$211$	6.00000	−	10.3923i	0.0284360	−	0.0492526i	0.879893	+	0.475171i	$0.157614\pi$
$212$	−67.8823	+	117.576i	−0.320199	+	0.554601i
$213$		0			0
$214$	39.0000	+	67.5500i	0.182243	+	0.315654i
$215$	168.291	−	115.447i	0.782751	−	0.536963i
$216$		0			0
$217$			186.590i			0.859864i
$218$	−56.5685	−	97.9796i	−0.259489	−	0.449448i
$219$		0			0
$220$	12.7960	+	164.427i	0.0581638	+	0.747396i
$221$		0			0
$222$		0			0
$223$	35.3483	−	20.4083i	0.158512	−	0.0915172i	−0.418646	−	0.908150i	$-0.637495\pi$
$223$	35.3483	−	20.4083i	0.158512	−	0.0915172i	0.577158	+	0.816633i	$0.304162\pi$
$224$		−	32.9848i		−	0.147254i
$225$		0			0
$226$	−216.000			−0.955752
$227$	79.9031	+	138.396i	0.351996	+	0.609675i	0.986599	−	0.163163i	$-0.0521698\pi$
$227$	79.9031	+	138.396i	0.351996	+	0.609675i	−0.634603	+	0.772838i	$0.718836\pi$
$228$		0			0
$229$	−41.0000	+	71.0141i	−0.179039	+	0.310105i	−0.941552	−	0.336868i	$-0.890632\pi$
$229$	−41.0000	+	71.0141i	−0.179039	+	0.310105i	0.762512	+	0.646974i	$0.223966\pi$
$230$	169.488	−	13.1899i	0.736902	−	0.0573472i
$231$		0			0
$232$		0			0
$233$	192.333			0.825464			0.412732	−	0.910853i	$-0.364575\pi$
$233$	192.333			0.825464			0.412732	+	0.910853i	$0.364575\pi$
$234$		0			0
$235$	100.000	+	145.774i	0.425532	+	0.620314i
$236$	28.5657	−	16.4924i	0.121041	−	0.0698831i
$237$		0			0
$238$	−80.7960	−	46.6476i	−0.339479	−	0.195998i
$239$	399.920	+	230.894i	1.67331	+	0.966083i	0.965768	+	0.259407i	$0.0835273\pi$
$239$	399.920	+	230.894i	1.67331	+	0.966083i	0.707537	+	0.706676i	$0.249806\pi$
$240$		0			0
$241$	−152.000	−	263.272i	−0.630705	−	1.09241i	−0.987408	−	0.158196i	$-0.949432\pi$
$241$	−152.000	−	263.272i	−0.630705	−	1.09241i	0.356702	−	0.934218i	$-0.383901\pi$
$242$	−213.546			−0.882423
$243$		0			0
$244$	−32.0000			−0.131148
$245$	−32.3475	+	67.6656i	−0.132031	+	0.276186i
$246$		0			0
$247$		0			0
$248$	45.2548	−	78.3837i	0.182479	−	0.316063i
$249$		0			0
$250$	−121.348	−	128.548i	−0.485393	−	0.514192i
$251$			346.341i			1.37984i	0.723884	+	0.689922i	$0.242355\pi$
$251$			346.341i			1.37984i	−0.723884	+	0.689922i	$0.757645\pi$
$252$		0			0
$253$			396.505i			1.56721i
$254$	−49.9900	+	28.8617i	−0.196811	+	0.113629i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	−195.161	+	338.030i	−0.759383	+	1.31529i	0.183782	+	0.982967i	$0.441166\pi$
$257$	−195.161	+	338.030i	−0.759383	+	1.31529i	−0.943166	+	0.332323i	$0.892168\pi$
$258$		0			0
$259$	68.0000	+	117.779i	0.262548	+	0.454747i
$260$		0			0
$261$		0			0
$262$			69.9714i			0.267066i
$263$	−147.785	−	255.972i	−0.561921	−	0.973276i	−0.997329	−	0.0730428i	$-0.976729\pi$
$263$	−147.785	−	255.972i	−0.561921	−	0.973276i	0.435407	−	0.900234i	$-0.356604\pi$
$264$		0			0
$265$	338.388	−	26.3340i	1.27694	−	0.0993737i
$266$	85.6971	+	49.4773i	0.322170	+	0.186005i
$267$		0			0
$268$	10.0995	−	5.83095i	0.0376847	−	0.0217573i
$269$			74.2159i			0.275896i	0.990440	+	0.137948i	$0.0440506\pi$
$269$			74.2159i			0.275896i	−0.990440	+	0.137948i	$0.955949\pi$
$270$		0			0
$271$	40.0000			0.147601			0.0738007	−	0.997273i	$-0.476487\pi$
$271$	40.0000			0.147601			0.0738007	+	0.997273i	$0.476487\pi$
$272$	22.6274	+	39.1918i	0.0831890	+	0.144088i
$273$		0			0
$274$	36.0000	−	62.3538i	0.131387	−	0.227569i
$275$	320.879	−	258.915i	1.16683	−	0.941508i
$276$		0			0
$277$	−383.781	+	221.576i	−1.38549	+	0.799914i	−0.992803	−	0.119758i	$-0.961788\pi$
$277$	−383.781	+	221.576i	−1.38549	+	0.799914i	−0.392688	+	0.919672i	$0.628455\pi$
$278$	62.2254			0.223832
$279$		0			0
$280$	−68.0000	+	46.6476i	−0.242857	+	0.166599i
$281$	449.910	−	259.756i	1.60110	−	0.924397i	0.609836	−	0.792528i	$-0.291235\pi$
$281$	449.910	−	259.756i	1.60110	−	0.924397i	0.991267	−	0.131870i	$-0.0420981\pi$
$282$		0			0
$283$	277.736	+	160.351i	0.981401	+	0.566612i	0.902693	−	0.430286i	$-0.141587\pi$
$283$	277.736	+	160.351i	0.981401	+	0.566612i	0.0787079	+	0.996898i	$0.474921\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$	−336.583			−1.17276
$288$		0			0
$289$	−161.000			−0.557093
$290$		0			0
$291$		0			0
$292$	201.990	+	116.619i	0.691747	+	0.399380i
$293$	−42.4264	+	73.4847i	−0.144800	+	0.250801i	−0.929298	−	0.369330i	$-0.879587\pi$
$293$	−42.4264	+	73.4847i	−0.144800	+	0.250801i	0.784498	+	0.620131i	$0.212921\pi$
$294$		0			0
$295$	−74.3980	−	35.5659i	−0.252197	−	0.120562i
$296$		−	65.9697i		−	0.222871i
$297$		0			0
$298$		−	11.6619i		−	0.0391339i
$299$		0			0
$300$		0			0
$301$	−119.000	+	206.114i	−0.395349	+	0.684764i
$302$	−96.1665	+	166.565i	−0.318432	+	0.551541i
$303$		0			0
$304$	−24.0000	−	41.5692i	−0.0789474	−	0.136741i
$305$	45.2548	+	65.9697i	0.148377	+	0.216294i
$306$		0			0
$307$			367.350i			1.19658i	0.801280	+	0.598290i	$0.204153\pi$
$307$			367.350i			1.19658i	−0.801280	+	0.598290i	$0.795847\pi$
$308$	−96.1665	−	166.565i	−0.312229	−	0.540796i
$309$		0			0
$310$	−225.592	+	17.5560i	−0.727716	+	0.0566323i
$311$	85.6971	+	49.4773i	0.275554	+	0.159091i	0.631409	−	0.775450i	$-0.282477\pi$
$311$	85.6971	+	49.4773i	0.275554	+	0.159091i	−0.355855	+	0.934541i	$0.615810\pi$
$312$		0			0
$313$	−161.592	+	93.2952i	−0.516269	+	0.298068i	−0.735407	−	0.677626i	$-0.763009\pi$
$313$	−161.592	+	93.2952i	−0.516269	+	0.298068i	0.219138	+	0.975694i	$0.429675\pi$
$314$		−	164.924i		−	0.525236i
$315$		0			0
$316$	−144.000			−0.455696
$317$	260.215	+	450.706i	0.820868	+	1.42179i	0.905036	+	0.425334i	$0.139843\pi$
$317$	260.215	+	450.706i	0.820868	+	1.42179i	−0.0841679	+	0.996452i	$0.526823\pi$
$318$		0			0
$319$		0			0
$320$	39.8794	−	3.10350i	0.124623	−	0.00969842i
$321$		0			0
$322$	−171.692	+	99.1262i	−0.533204	+	0.307845i
$323$	−135.765			−0.420324
$324$		0			0
$325$		0			0
$326$	121.404	−	70.0928i	0.372406	−	0.215009i
$327$		0			0
$328$	141.393	+	81.6333i	0.431076	+	0.248882i
$329$	−178.536	−	103.078i	−0.542662	−	0.313306i
$330$		0			0
$331$	−146.000	−	252.879i	−0.441088	−	0.763986i	0.556683	−	0.830725i	$-0.312074\pi$
$331$	−146.000	−	252.879i	−0.441088	−	0.763986i	−0.997770	+	0.0667389i	$0.978741\pi$
$332$	−87.6812			−0.264100
$333$		0			0
$334$	414.000			1.23952
$335$	−26.3037	−	12.5745i	−0.0785184	−	0.0375357i
$336$		0			0
$337$	−282.786	−	163.267i	−0.839128	−	0.484471i	0.0178397	−	0.999841i	$-0.494321\pi$
$337$	−282.786	−	163.267i	−0.839128	−	0.484471i	−0.856968	+	0.515370i	$0.827654\pi$
$338$	−119.501	+	206.982i	−0.353553	+	0.612372i
$339$		0			0
$340$	48.7960	−	102.073i	0.143518	−	0.300215i
$341$		−	527.758i		−	1.54768i
$342$		0			0
$343$		−	373.181i		−	1.08799i
$344$	99.9800	−	57.7235i	0.290640	−	0.167801i
$345$		0			0
$346$	116.000	−	200.918i	0.335260	−	0.580688i
$347$	−197.283	+	341.704i	−0.568538	+	0.984737i	0.428173	+	0.903697i	$0.359158\pi$
$347$	−197.283	+	341.704i	−0.568538	+	0.984737i	−0.996711	+	0.0810402i	$0.974176\pi$
$348$		0			0
$349$	−127.000	−	219.970i	−0.363897	−	0.630288i	0.624702	−	0.780864i	$-0.285221\pi$
$349$	−127.000	−	219.970i	−0.363897	−	0.630288i	−0.988598	+	0.150576i	$0.951887\pi$
$350$	192.333	+	74.2159i	0.549523	+	0.212045i
$351$		0			0
$352$			93.2952i			0.265043i
$353$	−172.534	−	298.838i	−0.488765	−	0.846566i	0.511151	−	0.859491i	$-0.329219\pi$
$353$	−172.534	−	298.838i	−0.488765	−	0.846566i	−0.999916	+	0.0129248i	$0.995886\pi$
$354$		0			0
$355$		0			0
$356$	114.263	+	65.9697i	0.320963	+	0.185308i
$357$		0			0
$358$	20.1990	−	11.6619i	0.0564218	−	0.0325752i
$359$			395.818i			1.10256i	0.834321	+	0.551279i	$0.185860\pi$
$359$			395.818i			1.10256i	−0.834321	+	0.551279i	$0.814140\pi$
$360$		0			0
$361$	−217.000			−0.601108
$362$	57.9828	+	100.429i	0.160173	+	0.277428i
$363$		0			0
$364$		0			0
$365$	−45.2408	−	581.337i	−0.123947	−	1.59271i
$366$		0			0
$367$	358.532	−	206.999i	0.976928	−	0.564029i	0.0755864	−	0.997139i	$-0.475917\pi$
$367$	358.532	−	206.999i	0.976928	−	0.564029i	0.901341	+	0.433110i	$0.142584\pi$
$368$	96.1665			0.261322
$369$		0			0
$370$	−136.000	+	93.2952i	−0.367568	+	0.252149i
$371$	−342.789	+	197.909i	−0.923958	+	0.533448i
$372$		0			0
$373$	−545.373	−	314.871i	−1.46213	−	0.844159i	−0.463017	−	0.886349i	$-0.653233\pi$
$373$	−545.373	−	314.871i	−1.46213	−	0.844159i	−0.999110	+	0.0421901i	$0.986566\pi$
$374$	228.526	+	131.939i	0.611031	+	0.352779i
$375$		0			0
$376$	50.0000	+	86.6025i	0.132979	+	0.230326i
$377$		0			0
$378$		0			0
$379$	−572.000			−1.50923			−0.754617	−	0.656165i	$-0.772178\pi$
$379$	−572.000			−1.50923			−0.754617	+	0.656165i	$0.772178\pi$
$380$	−51.7560	+	108.265i	−0.136200	+	0.284908i
$381$		0			0
$382$	363.582	+	209.914i	0.951786	+	0.549514i
$383$	96.8736	−	167.790i	0.252934	−	0.438094i	−0.711398	−	0.702789i	$-0.751938\pi$
$383$	96.8736	−	167.790i	0.252934	−	0.438094i	0.964332	+	0.264695i	$0.0852712\pi$
$384$		0			0
$385$	−207.383	+	433.811i	−0.538658	+	1.12678i
$386$		−	164.924i		−	0.427265i
$387$		0			0
$388$			326.533i			0.841581i
$389$	−335.647	+	193.786i	−0.862846	+	0.498164i	−0.864964	−	0.501833i	$-0.832659\pi$
$389$	−335.647	+	193.786i	−0.862846	+	0.498164i	0.00211824	+	0.999998i	$0.499326\pi$
$390$		0			0
$391$	136.000	−	235.559i	0.347826	−	0.602452i
$392$	−21.2132	+	36.7423i	−0.0541153	+	0.0937305i
$393$		0			0
$394$	136.000	+	235.559i	0.345178	+	0.597865i
$395$	203.647	+	296.864i	0.515561	+	0.751553i
$396$		0			0
$397$		−	513.124i		−	1.29250i	−0.763124	−	0.646252i	$-0.776336\pi$
$397$		−	513.124i		−	1.29250i	0.763124	−	0.646252i	$-0.223664\pi$
$398$	220.617	+	382.120i	0.554315	+	0.960102i
$399$		0			0
$400$	−62.7960	−	77.8245i	−0.156990	−	0.194561i
$401$	57.1314	+	32.9848i	0.142472	+	0.0822565i	0.569542	−	0.821962i	$-0.307121\pi$
$401$	57.1314	+	32.9848i	0.142472	+	0.0822565i	−0.427069	+	0.904219i	$0.640454\pi$
$402$		0			0
$403$		0			0
$404$			263.879i			0.653165i
$405$		0			0
$406$		0			0
$407$	−192.333	−	333.131i	−0.472563	−	0.818503i
$408$		0			0
$409$	−320.000	+	554.256i	−0.782396	+	1.35515i	0.148146	+	0.988965i	$0.452669\pi$
$409$	−320.000	+	554.256i	−0.782396	+	1.35515i	−0.930542	+	0.366184i	$0.880664\pi$
$410$	−31.6686	−	406.936i	−0.0772404	−	0.992527i
$411$		0			0
$412$	171.692	−	99.1262i	0.416727	−	0.240598i
$413$	96.1665			0.232849
$414$		0			0
$415$	124.000	+	180.760i	0.298795	+	0.435565i
$416$		0			0
$417$		0			0
$418$	−242.388	−	139.943i	−0.579876	−	0.334791i
$419$	−499.900	−	288.617i	−1.19308	−	0.688824i	−0.234075	−	0.972218i	$-0.575206\pi$
$419$	−499.900	−	288.617i	−1.19308	−	0.688824i	−0.959004	+	0.283394i	$0.908540\pi$
$420$		0			0
$421$	328.000	+	568.113i	0.779097	+	1.34944i	0.932463	+	0.361267i	$0.117656\pi$
$421$	328.000	+	568.113i	0.779097	+	1.34944i	−0.153365	+	0.988170i	$0.549011\pi$
$422$	−16.9706			−0.0402146
$423$		0			0
$424$	192.000			0.452830
$425$	−279.437	+	43.7577i	−0.657500	+	0.102959i
$426$		0			0
$427$	−80.7960	−	46.6476i	−0.189218	−	0.109245i
$428$	55.1543	−	95.5301i	0.128865	−	0.223201i
$429$		0			0
$430$	−260.393	−	124.481i	−0.605565	−	0.289490i
$431$			362.833i			0.841841i	0.907098	+	0.420920i	$0.138293\pi$
$431$			362.833i			0.841841i	−0.907098	+	0.420920i	$0.861707\pi$
$432$		0			0
$433$			163.267i			0.377059i	0.982068	+	0.188530i	$0.0603722\pi$
$433$			163.267i			0.377059i	−0.982068	+	0.188530i	$0.939628\pi$
$434$	228.526	−	131.939i	0.526557	−	0.304008i
$435$		0			0
$436$	−80.0000	+	138.564i	−0.183486	+	0.317807i
$437$	−144.250	+	249.848i	−0.330091	+	0.571734i
$438$		0			0
$439$	−216.000	−	374.123i	−0.492027	−	0.852216i	0.507931	−	0.861398i	$-0.330411\pi$
$439$	−216.000	−	374.123i	−0.492027	−	0.852216i	−0.999958	+	0.00918170i	$0.997077\pi$
$440$	192.333	−	131.939i	0.437121	−	0.299862i
$441$		0			0
$442$		0			0
$443$	−61.5183	−	106.553i	−0.138867	−	0.240526i	0.788201	−	0.615418i	$-0.211013\pi$
$443$	−61.5183	−	106.553i	−0.138867	−	0.240526i	−0.927068	+	0.374893i	$0.877680\pi$
$444$		0			0
$445$	−25.5921	−	328.854i	−0.0575103	−	0.738998i
$446$	−49.9900	−	28.8617i	−0.112085	−	0.0647124i
$447$		0			0
$448$	−40.3980	+	23.3238i	−0.0901742	+	0.0520621i
$449$		−	865.852i		−	1.92840i	−0.265174	−	0.964201i	$-0.585429\pi$
$449$		−	865.852i		−	1.92840i	0.265174	−	0.964201i	$-0.414571\pi$
$450$		0			0
$451$	952.000			2.11086
$452$	152.735	+	264.545i	0.337909	+	0.585276i
$453$		0			0
$454$	113.000	−	195.722i	0.248899	−	0.431105i
$455$		0			0
$456$		0			0
$457$	403.980	−	233.238i	0.883983	−	0.510368i	0.0120133	−	0.999928i	$-0.496176\pi$
$457$	403.980	−	233.238i	0.883983	−	0.510368i	0.871970	+	0.489560i	$0.162843\pi$
$458$	115.966			0.253200
$459$		0			0
$460$	−136.000	−	198.252i	−0.295652	−	0.430983i
$461$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$461$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$462$		0			0
$463$	530.224	+	306.125i	1.14519	+	0.661177i	0.947711	−	0.319130i	$-0.103391\pi$
$463$	530.224	+	306.125i	1.14519	+	0.661177i	0.197481	+	0.980307i	$0.436724\pi$
$464$		0			0
$465$		0			0
$466$	−136.000	−	235.559i	−0.291845	−	0.505491i
$467$	−767.918			−1.64436			−0.822182	−	0.569225i	$-0.807243\pi$
$467$	−767.918			−1.64436			−0.822182	+	0.569225i	$0.807243\pi$
$468$		0			0
$469$	34.0000			0.0724947
$470$	107.825	−	225.552i	0.229415	−	0.479898i
$471$		0			0
$472$	−40.3980	−	23.3238i	−0.0855890	−	0.0494148i
$473$	336.583	−	582.979i	0.711592	−	1.23251i
$474$		0			0
$475$	296.388	−	46.4121i	0.623975	−	0.0977097i
$476$			131.939i			0.277184i
$477$		0			0
$478$		−	653.067i		−	1.36625i
$479$	−485.617	+	280.371i	−1.01381	+	0.585326i	−0.912306	−	0.409509i	$-0.865700\pi$
$479$	−485.617	+	280.371i	−1.01381	+	0.585326i	−0.101508	+	0.994835i	$0.532367\pi$
$480$		0			0
$481$		0			0
$482$	−214.960	+	372.322i	−0.445976	+	0.772453i
$483$		0			0
$484$	151.000	+	261.540i	0.311983	+	0.540371i
$485$	673.166	−	461.788i	1.38797	−	0.952140i
$486$		0			0
$487$		−	647.236i		−	1.32903i	−0.747277	−	0.664513i	$-0.768639\pi$
$487$		−	647.236i		−	1.32903i	0.747277	−	0.664513i	$-0.231361\pi$
$488$	22.6274	+	39.1918i	0.0463677	+	0.0803111i
$489$		0			0
$490$	105.746	−	8.22939i	0.215809	−	0.0167947i
$491$	−299.940	−	173.170i	−0.610876	−	0.352689i	0.162432	−	0.986720i	$-0.448066\pi$
$491$	−299.940	−	173.170i	−0.610876	−	0.352689i	−0.773308	+	0.634030i	$0.781399\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−128.000			−0.258065
$497$		0			0
$498$		0			0
$499$	330.000	−	571.577i	0.661323	−	1.14544i	−0.318946	−	0.947773i	$-0.603329\pi$
$499$	330.000	−	571.577i	0.661323	−	1.14544i	0.980268	−	0.197671i	$-0.0633379\pi$
$500$	−71.6324	+	239.518i	−0.143265	+	0.479036i
$501$		0			0
$502$	424.179	−	244.900i	0.844979	−	0.487849i
$503$	−182.434			−0.362691			−0.181345	−	0.983419i	$-0.558045\pi$
$503$	−182.434			−0.362691			−0.181345	+	0.983419i	$0.558045\pi$
$504$		0			0
$505$	544.000	−	373.181i	1.07723	−	0.738972i
$506$	485.617	−	280.371i	0.959718	−	0.554093i
$507$		0			0
$508$	70.6965	+	40.8167i	0.139166	+	0.0803478i
$509$	−342.789	−	197.909i	−0.673455	−	0.388819i	0.123930	−	0.992291i	$-0.460450\pi$
$509$	−342.789	−	197.909i	−0.673455	−	0.388819i	−0.797384	+	0.603472i	$0.793784\pi$
$510$		0			0
$511$	340.000	+	588.897i	0.665362	+	1.15244i
$512$	22.6274			0.0441942
$513$		0			0
$514$	552.000			1.07393
$515$	−447.162	−	213.766i	−0.868277	−	0.415079i
$516$		0			0
$517$	504.975	+	291.548i	0.976741	+	0.563922i
$518$	96.1665	−	166.565i	0.185650	−	0.321555i
$519$		0			0
$520$		0			0
$521$			131.939i			0.253243i	0.991951	+	0.126621i	$0.0404133\pi$
$521$			131.939i			0.253243i	−0.991951	+	0.126621i	$0.959587\pi$
$522$		0			0
$523$		−	145.774i		−	0.278726i	−0.990241	−	0.139363i	$-0.955494\pi$
$523$		−	145.774i		−	0.278726i	0.990241	−	0.139363i	$-0.0445055\pi$
$524$	85.6971	−	49.4773i	0.163544	−	0.0944223i
$525$		0			0
$526$	−209.000	+	361.999i	−0.397338	+	0.688210i
$527$	−181.019	+	313.535i	−0.343490	+	0.594942i
$528$		0			0
$529$	−24.5000	−	42.4352i	−0.0463138	−	0.0802179i
$530$	−271.529	−	395.818i	−0.512319	−	0.746827i
$531$		0			0
$532$		−	139.943i		−	0.263050i
$533$		0			0
$534$		0			0
$535$	−274.940	+	21.3964i	−0.513907	+	0.0399933i
$536$	−14.2829	−	8.24621i	−0.0266471	−	0.0153847i
$537$		0			0
$538$	90.8955	−	52.4786i	0.168951	−	0.0975438i
$539$			247.386i			0.458973i
$540$		0			0
$541$	418.000			0.772643			0.386322	−	0.922364i	$-0.373745\pi$
$541$	418.000			0.772643			0.386322	+	0.922364i	$0.373745\pi$
$542$	−28.2843	−	48.9898i	−0.0521850	−	0.0903871i
$543$		0			0
$544$	32.0000	−	55.4256i	0.0588235	−	0.101885i
$545$	398.794	−	31.0350i	0.731733	−	0.0569449i
$546$		0			0
$547$	−247.438	+	142.858i	−0.452354	+	0.261167i	−0.708824	−	0.705385i	$-0.750774\pi$
$547$	−247.438	+	142.858i	−0.452354	+	0.261167i	0.256470	+	0.966552i	$0.417441\pi$
$548$	−101.823			−0.185809
$549$		0			0
$550$	−544.000	−	209.914i	−0.989091	−	0.381662i
$551$		0			0
$552$		0			0
$553$	−363.582	−	209.914i	−0.657472	−	0.379592i
$554$	542.749	+	313.356i	0.979691	+	0.565625i
$555$		0			0
$556$	−44.0000	−	76.2102i	−0.0791367	−	0.137069i
$557$	424.264			0.761695			0.380847	−	0.924638i	$-0.375632\pi$
$557$	424.264			0.761695			0.380847	+	0.924638i	$0.375632\pi$
$558$		0			0
$559$		0			0
$560$	105.215	+	50.2978i	0.187883	+	0.0898175i
$561$		0			0
$562$	−636.269	−	367.350i	−1.13215	−	0.653648i
$563$	406.586	−	704.228i	0.722178	−	1.25085i	−0.237947	−	0.971278i	$-0.576474\pi$
$563$	406.586	−	704.228i	0.722178	−	1.25085i	0.960125	−	0.279571i	$-0.0901923\pi$
$564$		0			0
$565$	329.373	−	688.994i	0.582962	−	1.21946i
$566$		−	453.542i		−	0.801310i
$567$		0			0
$568$		0			0
$569$	392.779	−	226.771i	0.690296	−	0.398543i	−0.113427	−	0.993546i	$-0.536183\pi$
$569$	392.779	−	226.771i	0.690296	−	0.398543i	0.803723	+	0.595004i	$0.202849\pi$
$570$		0			0
$571$	−110.000	+	190.526i	−0.192644	+	0.333670i	−0.946126	−	0.323799i	$-0.895040\pi$
$571$	−110.000	+	190.526i	−0.192644	+	0.333670i	0.753481	+	0.657469i	$0.228373\pi$
$572$		0			0
$573$		0			0
$574$	238.000	+	412.228i	0.414634	+	0.718167i
$575$	−216.375	+	560.742i	−0.376304	+	0.975204i
$576$		0			0
$577$			46.6476i			0.0808451i	0.999183	+	0.0404225i	$0.0128704\pi$
$577$			46.6476i			0.0808451i	−0.999183	+	0.0404225i	$0.987130\pi$
$578$	113.844	+	197.184i	0.196962	+	0.341149i
$579$		0			0
$580$		0			0
$581$	−221.384	−	127.816i	−0.381040	−	0.219994i
$582$		0			0
$583$	969.552	−	559.771i	1.66304	−	0.960157i
$584$		−	329.848i		−	0.564809i
$585$		0			0
$586$	120.000			0.204778
$587$	−27.5772	−	47.7650i	−0.0469798	−	0.0813715i	0.841579	−	0.540134i	$-0.181626\pi$
$587$	−27.5772	−	47.7650i	−0.0469798	−	0.0813715i	−0.888559	+	0.458762i	$0.848293\pi$
$588$		0			0
$589$	192.000	−	332.554i	0.325976	−	0.564607i
$590$	9.04817	+	116.267i	0.0153359	+	0.197064i
$591$		0			0
$592$	−80.7960	+	46.6476i	−0.136480	+	0.0787966i
$593$	390.323			0.658217			0.329109	−	0.944292i	$-0.393252\pi$
$593$	390.323			0.658217			0.329109	+	0.944292i	$0.393252\pi$
$594$		0			0
$595$	272.000	−	186.590i	0.457143	−	0.313597i
$596$	−14.2829	+	8.24621i	−0.0239645	+	0.0138359i
$597$		0			0
$598$		0			0
$599$	85.6971	+	49.4773i	0.143067	+	0.0825998i	0.569825	−	0.821766i	$-0.307011\pi$
$599$	85.6971	+	49.4773i	0.143067	+	0.0825998i	−0.426758	+	0.904366i	$0.640344\pi$
$600$		0			0
$601$	440.000	+	762.102i	0.732113	+	1.26806i	0.955978	+	0.293437i	$0.0947991\pi$
$601$	440.000	+	762.102i	0.732113	+	1.26806i	−0.223865	+	0.974620i	$0.571868\pi$
$602$	336.583			0.559108
$603$		0			0
$604$	272.000			0.450331
$605$	325.632	−	681.167i	0.538234	−	1.12590i
$606$		0			0
$607$	−368.632	−	212.830i	−0.607301	−	0.350626i	0.164607	−	0.986359i	$-0.447364\pi$
$607$	−368.632	−	212.830i	−0.607301	−	0.350626i	−0.771909	+	0.635734i	$0.780698\pi$
$608$	−33.9411	+	58.7878i	−0.0558242	+	0.0966904i
$609$		0			0
$610$	48.7960	−	102.073i	0.0799935	−	0.167333i
$611$		0			0
$612$		0			0
$613$		−	606.419i		−	0.989264i	−0.869102	−	0.494632i	$-0.835303\pi$
$613$		−	606.419i		−	0.989264i	0.869102	−	0.494632i	$-0.164697\pi$
$614$	449.910	−	259.756i	0.732752	−	0.423055i
$615$		0			0
$616$	−136.000	+	235.559i	−0.220779	+	0.382401i
$617$	56.5685	−	97.9796i	0.0916832	−	0.158800i	−0.816536	−	0.577294i	$-0.804109\pi$
$617$	56.5685	−	97.9796i	0.0916832	−	0.158800i	0.908220	+	0.418494i	$0.137442\pi$
$618$		0			0
$619$	−26.0000	−	45.0333i	−0.0420032	−	0.0727517i	0.844259	−	0.535935i	$-0.180041\pi$
$619$	−26.0000	−	45.0333i	−0.0420032	−	0.0727517i	−0.886263	+	0.463183i	$0.846707\pi$
$620$	181.019	+	263.879i	0.291967	+	0.425611i
$621$		0			0
$622$		−	139.943i		−	0.224988i
$623$	192.333	+	333.131i	0.308721	+	0.534720i
$624$		0			0
$625$	595.082	−	191.055i	0.952131	−	0.305689i
$626$	228.526	+	131.939i	0.365057	+	0.210766i
$627$		0			0
$628$	−201.990	+	116.619i	−0.321640	+	0.185699i
$629$			263.879i			0.419521i
$630$		0			0
$631$	−544.000			−0.862124			−0.431062	−	0.902322i	$-0.641861\pi$
$631$	−544.000			−0.862124			−0.431062	+	0.902322i	$0.641861\pi$
$632$	101.823	+	176.363i	0.161113	+	0.279056i
$633$		0			0
$634$	368.000	−	637.395i	0.580442	−	1.00535i
$635$	−15.8343	−	203.468i	−0.0249359	−	0.320422i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−32.0000	−	46.6476i	−0.0500000	−	0.0728869i
$641$	−735.567	+	424.680i	−1.14753	+	0.662527i	−0.948284	−	0.317422i	$-0.897183\pi$
$641$	−735.567	+	424.680i	−1.14753	+	0.662527i	−0.199246	+	0.979949i	$0.563849\pi$
$642$		0			0
$643$	−318.134	−	183.675i	−0.494766	−	0.285653i	0.231784	−	0.972767i	$-0.425544\pi$
$643$	−318.134	−	183.675i	−0.494766	−	0.285653i	−0.726549	+	0.687114i	$0.758877\pi$
$644$	242.809	+	140.186i	0.377032	+	0.217679i
$645$		0			0
$646$	96.0000	+	166.277i	0.148607	+	0.257395i
$647$	−971.565			−1.50165			−0.750823	−	0.660504i	$-0.770343\pi$
$647$	−971.565			−1.50165			−0.750823	+	0.660504i	$0.770343\pi$
$648$		0			0
$649$	−272.000			−0.419106
$650$		0			0
$651$		0			0
$652$	−171.692	−	99.1262i	−0.263331	−	0.152034i
$653$	−175.362	+	303.737i	−0.268549	+	0.465140i	−0.968487	−	0.249063i	$-0.919877\pi$
$653$	−175.362	+	303.737i	−0.268549	+	0.465140i	0.699938	+	0.714203i	$0.253211\pi$
$654$		0			0
$655$	−223.194	−	106.698i	−0.340754	−	0.162897i
$656$		−	230.894i		−	0.351972i
$657$		0			0
$658$			291.548i			0.443081i
$659$	−499.900	+	288.617i	−0.758574	+	0.437963i	−0.828783	−	0.559570i	$-0.810966\pi$
$659$	−499.900	+	288.617i	−0.758574	+	0.437963i	0.0702098	+	0.997532i	$0.477633\pi$
$660$		0			0
$661$	−40.0000	+	69.2820i	−0.0605144	+	0.104814i	−0.894695	−	0.446677i	$-0.852607\pi$
$661$	−40.0000	+	69.2820i	−0.0605144	+	0.104814i	0.834181	+	0.551491i	$0.185941\pi$
$662$	−206.475	+	357.626i	−0.311896	+	0.540220i
$663$		0			0
$664$	62.0000	+	107.387i	0.0933735	+	0.161728i
$665$	−288.500	+	197.909i	−0.433834	+	0.297608i
$666$		0			0
$667$		0			0
$668$	−292.742	−	507.044i	−0.438237	−	0.759048i
$669$		0			0
$670$	3.19901	+	41.1068i	0.00477464	+	0.0613534i
$671$	228.526	+	131.939i	0.340575	+	0.196631i
$672$		0			0
$673$	−424.179	+	244.900i	−0.630281	+	0.363893i	−0.780861	−	0.624705i	$-0.785219\pi$
$673$	−424.179	+	244.900i	−0.630281	+	0.363893i	0.150580	+	0.988598i	$0.451886\pi$
$674$			461.788i			0.685145i
$675$		0			0
$676$	338.000			0.500000
$677$	−96.1665	−	166.565i	−0.142048	−	0.246034i	0.786220	−	0.617947i	$-0.212035\pi$
$677$	−96.1665	−	166.565i	−0.142048	−	0.246034i	−0.928268	+	0.371913i	$0.878702\pi$
$678$		0			0
$679$	−476.000	+	824.456i	−0.701031	+	1.21422i
$680$	−159.518	+	12.4140i	−0.234585	+	0.0182559i
$681$		0			0
$682$	−646.368	+	373.181i	−0.947754	+	0.547186i
$683$	236.174			0.345789			0.172894	−	0.984940i	$-0.444688\pi$
$683$	236.174			0.345789			0.172894	+	0.984940i	$0.444688\pi$
$684$		0			0
$685$	144.000	+	209.914i	0.210219	+	0.306444i
$686$	−457.051	+	263.879i	−0.666256	+	0.384663i
$687$		0			0
$688$	−141.393	−	81.6333i	−0.205513	−	0.118653i
$689$		0			0
$690$		0			0
$691$	274.000	+	474.582i	0.396527	+	0.686805i	0.993295	−	0.115609i	$-0.0368821\pi$
$691$	274.000	+	474.582i	0.396527	+	0.686805i	−0.596768	+	0.802414i	$0.703549\pi$
$692$	−328.098			−0.474129
$693$		0			0
$694$	558.000			0.804035
$695$	−94.8860	+	198.486i	−0.136527	+	0.285591i
$696$		0			0
$697$	−565.572	−	326.533i	−0.811438	−	0.468484i
$698$	−179.605	+	311.085i	−0.257314	+	0.445681i
$699$		0			0
$700$	−45.1045	−	288.037i	−0.0644349	−	0.411482i
$701$		−	57.7235i		−	0.0823445i	−0.999152	−	0.0411722i	$-0.986891\pi$
$701$		−	57.7235i		−	0.0823445i	0.999152	−	0.0411722i	$-0.0131092\pi$
$702$		0			0
$703$		−	279.886i		−	0.398130i
$704$	114.263	−	65.9697i	0.162305	−	0.0937069i
$705$		0			0
$706$	−244.000	+	422.620i	−0.345609	+	0.598612i
$707$	−384.666	+	666.261i	−0.544082	+	0.942378i
$708$		0			0
$709$	−615.000	−	1065.21i	−0.867419	−	1.50241i	−0.864625	−	0.502418i	$-0.832444\pi$
$709$	−615.000	−	1065.21i	−0.867419	−	1.50241i	−0.00279375	−	0.999996i	$-0.500889\pi$
$710$		0			0
$711$		0			0
$712$		−	186.590i		−	0.262065i
$713$	384.666	+	666.261i	0.539504	+	0.934448i
$714$		0			0
$715$		0			0
$716$	−28.5657	−	16.4924i	−0.0398962	−	0.0230341i
$717$		0			0
$718$	484.776	−	279.886i	0.675176	−	0.389813i
$719$			626.712i			0.871644i	0.900033	+	0.435822i	$0.143542\pi$
$719$			626.712i			0.871644i	−0.900033	+	0.435822i	$0.856458\pi$
$720$		0			0
$721$	578.000			0.801664
$722$	153.442	+	265.770i	0.212524	+	0.368102i
$723$		0			0
$724$	82.0000	−	142.028i	0.113260	−	0.196172i
$725$		0			0
$726$		0			0
$727$	−318.134	+	183.675i	−0.437599	+	0.252648i	−0.702579	−	0.711606i	$-0.747968\pi$
$727$	−318.134	+	183.675i	−0.437599	+	0.252648i	0.264980	+	0.964254i	$0.414635\pi$
$728$		0			0
$729$		0			0
$730$	−680.000	+	466.476i	−0.931507	+	0.639008i
$731$	−399.920	+	230.894i	−0.547086	+	0.315860i
$732$		0			0
$733$	868.557	+	501.462i	1.18494	+	0.684123i	0.957151	−	0.289589i	$-0.0935186\pi$
$733$	868.557	+	501.462i	1.18494	+	0.684123i	0.227784	+	0.973712i	$0.426852\pi$
$734$	−507.041	−	292.740i	−0.690792	−	0.398829i
$735$		0			0
$736$	−68.0000	−	117.779i	−0.0923913	−	0.160026i
$737$	−96.1665			−0.130484
$738$		0			0
$739$	−340.000			−0.460081			−0.230041	−	0.973181i	$-0.573886\pi$
$739$	−340.000			−0.460081			−0.230041	+	0.973181i	$0.573886\pi$
$740$	210.429	+	100.596i	0.284364	+	0.135940i
$741$		0			0
$742$	484.776	+	279.886i	0.653337	+	0.377204i
$743$	−621.547	+	1076.55i	−0.836537	+	1.44892i	0.0562362	+	0.998417i	$0.482090\pi$
$743$	−621.547	+	1076.55i	−0.836537	+	1.44892i	−0.892773	+	0.450507i	$0.851243\pi$
$744$		0			0
$745$	37.1990	+	17.7830i	0.0499316	+	0.0238697i
$746$			890.591i			1.19382i
$747$		0			0
$748$		−	373.181i		−	0.498905i
$749$	278.516	−	160.801i	0.371850	−	0.214688i
$750$		0			0
$751$	260.000	−	450.333i	0.346205	−	0.599645i	−0.639367	−	0.768902i	$-0.720803\pi$
$751$	260.000	−	450.333i	0.346205	−	0.599645i	0.985572	+	0.169257i	$0.0541368\pi$
$752$	70.7107	−	122.474i	0.0940302	−	0.162865i
$753$		0			0
$754$		0			0
$755$	−384.666	−	560.742i	−0.509492	−	0.742705i
$756$		0			0
$757$			816.333i			1.07838i	0.842184	+	0.539190i	$0.181269\pi$
$757$			816.333i			1.07838i	−0.842184	+	0.539190i	$0.818731\pi$
$758$	404.465	+	700.554i	0.533595	+	0.924214i
$759$		0			0
$760$	169.194	−	13.1670i	0.222624	−	0.0173250i
$761$	−342.789	−	197.909i	−0.450445	−	0.260064i	0.257573	−	0.966259i	$-0.417077\pi$
$761$	−342.789	−	197.909i	−0.450445	−	0.260064i	−0.708018	+	0.706194i	$0.750410\pi$
$762$		0			0
$763$	−403.980	+	233.238i	−0.529463	+	0.305686i
$764$		−	593.727i		−	0.777130i
$765$		0			0
$766$	−274.000			−0.357702
$767$		0			0
$768$		0			0
$769$	153.000	−	265.004i	0.198960	−	0.344608i	−0.749232	−	0.662308i	$-0.769577\pi$
$769$	153.000	−	265.004i	0.198960	−	0.344608i	0.948191	+	0.317700i	$0.102910\pi$
$770$	677.950	−	52.7594i	0.880455	−	0.0685187i
$771$		0			0
$772$	−201.990	+	116.619i	−0.261645	+	0.151061i
$773$	305.470			0.395175			0.197587	−	0.980285i	$-0.436689\pi$
$773$	305.470			0.395175			0.197587	+	0.980285i	$0.436689\pi$
$774$		0			0
$775$	288.000	−	746.362i	0.371613	−	0.963048i
$776$	399.920	−	230.894i	0.515361	−	0.297544i
$777$		0			0
$778$	474.677	+	274.055i	0.610124	+	0.352255i
$779$	599.880	+	346.341i	0.770064	+	0.444597i
$780$		0			0
$781$		0			0
$782$	−384.666			−0.491900
$783$		0			0
$784$	60.0000			0.0765306
$785$	526.073	+	251.489i	0.670157	+	0.320368i
$786$		0			0
$787$	489.826	+	282.801i	0.622396	+	0.359341i	0.777801	−	0.628510i	$-0.216335\pi$
$787$	489.826	+	282.801i	0.622396	+	0.359341i	−0.155405	+	0.987851i	$0.549668\pi$
$788$	192.333	−	333.131i	0.244077	−	0.422755i
$789$		0			0
$790$	219.582	−	459.330i	0.277952	−	0.581430i
$791$			890.591i			1.12590i
$792$		0			0
$793$		0			0
$794$	−628.446	+	362.833i	−0.791493	+	0.456969i
$795$		0			0
$796$	312.000	−	540.400i	0.391960	−	0.678894i
$797$	531.744	−	921.008i	0.667182	−	1.15559i	−0.311506	−	0.950244i	$-0.600834\pi$
$797$	531.744	−	921.008i	0.667182	−	1.15559i	0.978689	−	0.205350i	$-0.0658331\pi$
$798$		0			0
$799$	−200.000	−	346.410i	−0.250313	−	0.433555i
$800$	−50.9117	+	131.939i	−0.0636396	+	0.164924i
$801$		0			0
$802$		−	93.2952i		−	0.116328i
$803$	−961.665	−	1665.65i	−1.19759	−	2.07429i
$804$		0			0
$805$	−54.3832	−	698.815i	−0.0675567	−	0.868093i
$806$		0			0
$807$		0			0
$808$	323.184	−	186.590i	0.399980	−	0.230929i
$809$		−	791.636i		−	0.978537i	−0.872133	−	0.489268i	$-0.837264\pi$
$809$		−	791.636i		−	0.978537i	0.872133	−	0.489268i	$-0.162736\pi$
$810$		0			0
$811$	436.000			0.537608			0.268804	−	0.963195i	$-0.413372\pi$
$811$	436.000			0.537608			0.268804	+	0.963195i	$0.413372\pi$
$812$		0			0
$813$		0			0
$814$	−272.000	+	471.118i	−0.334152	+	0.578769i
$815$	38.4547	+	494.137i	0.0471837	+	0.606303i
$816$		0			0
$817$	424.179	−	244.900i	0.519191	−	0.299755i
$818$	905.097			1.10648
$819$		0			0
$820$	−476.000	+	326.533i	−0.580488	+	0.398211i
$821$	692.719	−	399.941i	0.843750	−	0.487139i	−0.0147873	−	0.999891i	$-0.504707\pi$
$821$	692.719	−	399.941i	0.843750	−	0.487139i	0.858537	+	0.512752i	$0.171374\pi$
$822$		0			0
$823$	−1136.19	−	655.982i	−1.38055	−	0.797062i	−0.388327	−	0.921522i	$-0.626947\pi$
$823$	−1136.19	−	655.982i	−1.38055	−	0.797062i	−0.992225	+	0.124459i	$0.960280\pi$
$824$	−242.809	−	140.186i	−0.294671	−	0.170128i
$825$		0			0
$826$	−68.0000	−	117.779i	−0.0823245	−	0.142590i
$827$	985.707			1.19191			0.595953	−	0.803019i	$-0.296774\pi$
$827$	985.707			1.19191			0.595953	+	0.803019i	$0.296774\pi$
$828$		0			0
$829$	−1488.00			−1.79493			−0.897467	−	0.441082i	$-0.854595\pi$
$829$	−1488.00			−1.79493			−0.897467	+	0.441082i	$0.854595\pi$
$830$	133.703	−	279.685i	0.161088	−	0.336969i
$831$		0			0
$832$		0			0
$833$	84.8528	−	146.969i	0.101864	−	0.176434i
$834$		0			0
$835$	−631.299	+	1320.57i	−0.756046	+	1.58152i
$836$			395.818i			0.473467i
$837$		0			0
$838$			816.333i			0.974145i
$839$	399.920	−	230.894i	0.476663	−	0.275201i	−0.242362	−	0.970186i	$-0.577922\pi$
$839$	399.920	−	230.894i	0.476663	−	0.275201i	0.719025	+	0.694985i	$0.244589\pi$
$840$		0			0
$841$	−420.500	+	728.327i	−0.500000	+	0.866025i
$842$	463.862	−	803.433i	0.550905	−	0.954196i
$843$		0			0
$844$	12.0000	+	20.7846i	0.0142180	+	0.0246263i
$845$	−478.004	−	696.805i	−0.565685	−	0.824621i
$846$		0			0
$847$			880.474i			1.03952i
$848$	−135.765	−	235.151i	−0.160100	−	0.277301i
$849$		0			0
$850$	251.184	+	311.298i	0.295511	+	0.366233i
$851$	485.617	+	280.371i	0.570643	+	0.329461i
$852$		0			0
$853$	282.786	−	163.267i	0.331520	−	0.191403i	−0.324996	−	0.945715i	$-0.605363\pi$
$853$	282.786	−	163.267i	0.331520	−	0.191403i	0.656516	+	0.754313i	$0.272030\pi$
$854$			131.939i			0.154496i
$855$		0			0
$856$	−156.000			−0.182243
$857$	144.250	+	249.848i	0.168319	+	0.291538i	0.937829	−	0.347097i	$-0.112833\pi$
$857$	144.250	+	249.848i	0.168319	+	0.291538i	−0.769510	+	0.638635i	$0.779499\pi$
$858$		0			0
$859$	−398.000	+	689.356i	−0.463329	+	0.802510i	−0.999124	−	0.0418380i	$-0.986679\pi$
$859$	−398.000	+	689.356i	−0.463329	+	0.802510i	0.535795	+	0.844348i	$0.320012\pi$
$860$	31.6686	+	406.936i	0.0368239	+	0.473182i
$861$		0			0
$862$	444.378	−	256.562i	0.515520	−	0.297636i
$863$	−352.139			−0.408041			−0.204020	−	0.978967i	$-0.565401\pi$
$863$	−352.139			−0.408041			−0.204020	+	0.978967i	$0.565401\pi$
$864$		0			0
$865$	464.000	+	676.390i	0.536416	+	0.781954i
$866$	199.960	−	115.447i	0.230901	−	0.133311i
$867$		0			0
$868$	−323.184	−	186.590i	−0.372332	−	0.214966i
$869$	1028.37	+	593.727i	1.18339	+	0.683230i
$870$		0			0
$871$		0			0
$872$	226.274			0.259489
$873$		0			0
$874$	408.000			0.466819
$875$	−530.017	+	500.332i	−0.605734	+	0.571808i
$876$		0			0
$877$	585.771	+	338.195i	0.667926	+	0.385627i	0.795290	−	0.606229i	$-0.207318\pi$
$877$	585.771	+	338.195i	0.667926	+	0.385627i	−0.127364	+	0.991856i	$0.540652\pi$
$878$	−305.470	+	529.090i	−0.347916	+	0.602608i
$879$		0			0
$880$	−297.592	−	142.264i	−0.338173	−	0.161663i
$881$		−	519.511i		−	0.589684i	−0.955546	−	0.294842i	$-0.904733\pi$
$881$		−	519.511i		−	0.589684i	0.955546	−	0.294842i	$-0.0952670\pi$
$882$		0			0
$883$			1591.85i			1.80277i	0.433014	+	0.901387i	$0.357450\pi$
$883$			1591.85i			1.80277i	−0.433014	+	0.901387i	$0.642550\pi$
$884$		0			0
$885$		0			0
$886$	−87.0000	+	150.688i	−0.0981941	+	0.170077i
$887$	383.959	−	665.036i	0.432874	−	0.749759i	−0.564246	−	0.825607i	$-0.690833\pi$
$887$	383.959	−	665.036i	0.432874	−	0.749759i	0.997119	+	0.0758477i	$0.0241663\pi$
$888$		0			0
$889$	119.000	+	206.114i	0.133858	+	0.231849i
$890$	−384.666	+	263.879i	−0.432209	+	0.296493i
$891$		0			0
$892$			81.6333i			0.0915172i
$893$	212.132	+	367.423i	0.237550	+	0.411448i
$894$		0			0
$895$	6.39802	+	82.2135i	0.00714863	+	0.0918587i
$896$	57.1314	+	32.9848i	0.0637628	+	0.0368134i
$897$		0			0
$898$	−1060.45	+	612.250i	−1.18090	+	0.681793i
$899$		0			0
$900$		0			0
$901$	−768.000			−0.852386
$902$	−673.166	−	1165.96i	−0.746303	−	1.29264i
$903$		0			0
$904$	216.000	−	374.123i	0.238938	−	0.413853i
$905$	−408.764	+	31.8108i	−0.451673	+	0.0351501i
$906$		0			0
$907$	287.836	−	166.182i	0.317349	−	0.183222i	−0.332861	−	0.942976i	$-0.608014\pi$
$907$	287.836	−	166.182i	0.317349	−	0.183222i	0.650210	+	0.759754i	$0.274681\pi$
$908$	−319.612			−0.351996
$909$		0			0
$910$		0			0
$911$	599.880	−	346.341i	0.658485	−	0.380177i	−0.133214	−	0.991087i	$-0.542530\pi$
$911$	599.880	−	346.341i	0.658485	−	0.380177i	0.791700	+	0.610911i	$0.209197\pi$
$912$		0			0
$913$	626.169	+	361.519i	0.685837	+	0.395968i
$914$	−571.314	−	329.848i	−0.625070	−	0.360885i
$915$		0			0
$916$	−82.0000	−	142.028i	−0.0895197	−	0.155053i
$917$	288.500			0.314612
$918$		0			0
$919$	−912.000			−0.992383			−0.496192	−	0.868213i	$-0.665269\pi$
$919$	−912.000			−0.992383			−0.496192	+	0.868213i	$0.665269\pi$
$920$	−146.642	+	306.751i	−0.159394	+	0.333425i
$921$		0			0
$922$		0			0
$923$		0			0
$924$		0			0
$925$	−90.2089	−	576.075i	−0.0975231	−	0.622784i
$926$		−	865.852i		−	0.935046i
$927$		0			0
$928$		0			0
$929$	1092.64	−	630.835i	1.17614	−	0.679048i	0.221025	−	0.975268i	$-0.429060\pi$
$929$	1092.64	−	630.835i	1.17614	−	0.679048i	0.955120	+	0.296221i	$0.0957263\pi$
$930$		0			0
$931$	−90.0000	+	155.885i	−0.0966702	+	0.167438i
$932$	−192.333	+	333.131i	−0.206366	+	0.357436i
$933$		0			0
$934$	543.000	+	940.504i	0.581370	+	1.00696i
$935$	−769.332	+	527.758i	−0.822815	+	0.564447i
$936$		0			0
$937$		−	816.333i		−	0.871220i	−0.900135	−	0.435610i	$-0.856533\pi$
$937$		−	816.333i		−	0.871220i	0.900135	−	0.435610i	$-0.143467\pi$
$938$	−24.0416	−	41.6413i	−0.0256307	−	0.0443937i
$939$		0			0
$940$	−352.488	+	27.4313i	−0.374987	+	0.0291822i
$941$	−914.103	−	527.758i	−0.971416	−	0.560848i	−0.0717486	−	0.997423i	$-0.522858\pi$
$941$	−914.103	−	527.758i	−0.971416	−	0.560848i	−0.899668	+	0.436575i	$0.856191\pi$
$942$		0			0
$943$	−1201.84	+	693.883i	−1.27449	+	0.735825i
$944$			65.9697i			0.0698831i
$945$		0			0
$946$	−952.000			−1.00634
$947$	57.2756	+	99.2043i	0.0604812	+	0.104756i	0.894681	−	0.446706i	$-0.147403\pi$
$947$	57.2756	+	99.2043i	0.0604812	+	0.104756i	−0.834199	+	0.551463i	$0.814070\pi$
$948$		0			0
$949$		0			0
$950$	−266.421	−	330.182i	−0.280443	−	0.347559i
$951$		0			0
$952$	161.592	−	93.2952i	0.169740	−	0.0979992i
$953$	243.245			0.255241			0.127621	−	0.991823i	$-0.459266\pi$
$953$	243.245			0.255241			0.127621	+	0.991823i	$0.459266\pi$
$954$		0			0
$955$	−1224.00	+	839.657i	−1.28168	+	0.879222i
$956$	−799.840	+	461.788i	−0.836653	+	0.483042i
$957$		0			0
$958$	686.766	+	396.505i	0.716875	+	0.413888i
$959$	−257.091	−	148.432i	−0.268083	−	0.154778i
$960$		0			0
$961$	−31.5000	−	54.5596i	−0.0327784	−	0.0567738i
$962$		0			0
$963$		0			0
$964$	608.000			0.630705
$965$	526.073	+	251.489i	0.545154	+	0.260610i
$966$		0			0
$967$	813.010	+	469.392i	0.840755	+	0.485410i	0.857521	−	0.514449i	$-0.172004\pi$
$967$	813.010	+	469.392i	0.840755	+	0.485410i	−0.0167657	+	0.999859i	$0.505337\pi$
$968$	213.546	−	369.873i	0.220606	−	0.382100i
$969$		0			0
$970$	−1041.57	−	497.923i	−1.07379	−	0.513323i
$971$		−	1335.89i		−	1.37578i	−0.725813	−	0.687892i	$-0.758536\pi$
$971$		−	1335.89i		−	1.37578i	0.725813	−	0.687892i	$-0.241464\pi$
$972$		0			0
$973$		−	256.562i		−	0.263681i
$974$	−792.699	+	457.665i	−0.813859	+	0.469882i
$975$		0			0
$976$	32.0000	−	55.4256i	0.0327869	−	0.0567886i
$977$	−152.735	+	264.545i	−0.156331	+	0.270773i	−0.933543	−	0.358466i	$-0.883300\pi$
$977$	−152.735	+	264.545i	−0.156331	+	0.270773i	0.777212	+	0.629239i	$0.216633\pi$
$978$		0			0
$979$	−544.000	−	942.236i	−0.555669	−	0.962447i
$980$	−84.8528	−	123.693i	−0.0865845	−	0.126218i
$981$		0			0
$982$			489.800i			0.498778i
$983$	555.079	+	961.425i	0.564678	+	0.978052i	0.997080	+	0.0763703i	$0.0243331\pi$
$983$	555.079	+	961.425i	0.564678	+	0.978052i	−0.432401	+	0.901681i	$0.642334\pi$
$984$		0			0
$985$	−958.766	+	74.6131i	−0.973367	+	0.0757493i
$986$		0			0
$987$		0			0
$988$		0			0
$989$			981.299i			0.992213i
$990$		0			0
$991$	640.000			0.645812			0.322906	−	0.946431i	$-0.395340\pi$
$991$	640.000			0.645812			0.322906	+	0.946431i	$0.395340\pi$
$992$	90.5097	+	156.767i	0.0912396	+	0.158032i
$993$		0			0
$994$		0			0
$995$	−1555.30	+	121.036i	−1.56311	+	0.121645i
$996$		0			0
$997$	−242.388	+	139.943i	−0.243117	+	0.140364i	−0.616609	−	0.787270i	$-0.711494\pi$
$997$	−242.388	+	139.943i	−0.243117	+	0.140364i	0.373491	+	0.927634i	$0.378161\pi$
$998$	−933.381			−0.935251
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.c.539.2		8
3.2	odd	2	inner	810.3.j.c.539.3		8
5.4	even	2	inner	810.3.j.c.539.4		8
9.2	odd	6	inner	810.3.j.c.269.4		8
9.4	even	3		30.3.b.a.29.4	yes	4
9.5	odd	6		30.3.b.a.29.2	yes	4
9.7	even	3	inner	810.3.j.c.269.1		8
15.14	odd	2	inner	810.3.j.c.539.1		8
36.23	even	6		240.3.c.c.209.1		4
36.31	odd	6		240.3.c.c.209.3		4
45.4	even	6		30.3.b.a.29.1	✓	4
45.13	odd	12		150.3.d.d.101.1		4
45.14	odd	6		30.3.b.a.29.3	yes	4
45.22	odd	12		150.3.d.d.101.4		4
45.23	even	12		150.3.d.d.101.3		4
45.29	odd	6	inner	810.3.j.c.269.2		8
45.32	even	12		150.3.d.d.101.2		4
45.34	even	6	inner	810.3.j.c.269.3		8
72.5	odd	6		960.3.c.f.449.1		4
72.13	even	6		960.3.c.f.449.3		4
72.59	even	6		960.3.c.e.449.4		4
72.67	odd	6		960.3.c.e.449.2		4
180.23	odd	12		1200.3.l.t.401.3		4
180.59	even	6		240.3.c.c.209.4		4
180.67	even	12		1200.3.l.t.401.1		4
180.103	even	12		1200.3.l.t.401.4		4
180.139	odd	6		240.3.c.c.209.2		4
180.167	odd	12		1200.3.l.t.401.2		4
360.59	even	6		960.3.c.e.449.1		4
360.139	odd	6		960.3.c.e.449.3		4
360.149	odd	6		960.3.c.f.449.4		4
360.229	even	6		960.3.c.f.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.3.b.a.29.1	✓	4	45.4	even	6
30.3.b.a.29.2	yes	4	9.5	odd	6
30.3.b.a.29.3	yes	4	45.14	odd	6
30.3.b.a.29.4	yes	4	9.4	even	3
150.3.d.d.101.1		4	45.13	odd	12
150.3.d.d.101.2		4	45.32	even	12
150.3.d.d.101.3		4	45.23	even	12
150.3.d.d.101.4		4	45.22	odd	12
240.3.c.c.209.1		4	36.23	even	6
240.3.c.c.209.2		4	180.139	odd	6
240.3.c.c.209.3		4	36.31	odd	6
240.3.c.c.209.4		4	180.59	even	6
810.3.j.c.269.1		8	9.7	even	3	inner
810.3.j.c.269.2		8	45.29	odd	6	inner
810.3.j.c.269.3		8	45.34	even	6	inner
810.3.j.c.269.4		8	9.2	odd	6	inner
810.3.j.c.539.1		8	15.14	odd	2	inner
810.3.j.c.539.2		8	1.1	even	1	trivial
810.3.j.c.539.3		8	3.2	odd	2	inner
810.3.j.c.539.4		8	5.4	even	2	inner
960.3.c.e.449.1		4	360.59	even	6
960.3.c.e.449.2		4	72.67	odd	6
960.3.c.e.449.3		4	360.139	odd	6
960.3.c.e.449.4		4	72.59	even	6
960.3.c.f.449.1		4	72.5	odd	6
960.3.c.f.449.2		4	360.229	even	6
960.3.c.f.449.3		4	72.13	even	6
960.3.c.f.449.4		4	360.149	odd	6
1200.3.l.t.401.1		4	180.67	even	12
1200.3.l.t.401.2		4	180.167	odd	12
1200.3.l.t.401.3		4	180.23	odd	12
1200.3.l.t.401.4		4	180.103	even	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98493 - 0.387937i) q^{5} +(-5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 - 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.98493 - 0.387937i) q^{5} +(-5.04975 + 2.91548i) q^{7} +2.82843 q^{8} +(-4.00000 - 5.83095i) q^{10} +(14.2829 - 8.24621i) q^{11} +(7.14143 + 4.12311i) q^{14} +(-2.00000 - 3.46410i) q^{16} -11.3137 q^{17} +12.0000 q^{19} +(-4.31300 + 9.02209i) q^{20} +(-20.1990 - 11.6619i) q^{22} +(-12.0208 + 20.8207i) q^{23} +(24.6990 - 3.86768i) q^{25} -11.6619i q^{28} +(16.0000 - 27.7128i) q^{31} +(-2.82843 + 4.89898i) q^{32} +(8.00000 + 13.8564i) q^{34} +(-24.0416 + 16.4924i) q^{35} -23.3238i q^{37} +(-8.48528 - 14.6969i) q^{38} +(14.0995 - 1.09725i) q^{40} +(49.9900 + 28.8617i) q^{41} +(35.3483 - 20.4083i) q^{43} +32.9848i q^{44} +34.0000 q^{46} +(17.6777 + 30.6186i) q^{47} +(-7.50000 + 12.9904i) q^{49} +(-22.2018 - 27.5151i) q^{50} +67.8823 q^{53} +(68.0000 - 46.6476i) q^{55} +(-14.2829 + 8.24621i) q^{56} +(-14.2829 - 8.24621i) q^{59} +(8.00000 + 13.8564i) q^{61} -45.2548 q^{62} +8.00000 q^{64} +(-5.04975 - 2.91548i) q^{67} +(11.3137 - 19.5959i) q^{68} +(37.1990 + 17.7830i) q^{70} -116.619i q^{73} +(-28.5657 + 16.4924i) q^{74} +(-12.0000 + 20.7846i) q^{76} +(-48.0833 + 83.2827i) q^{77} +(36.0000 + 62.3538i) q^{79} +(-11.3137 - 16.4924i) q^{80} -81.6333i q^{82} +(21.9203 + 37.9671i) q^{83} +(-56.3980 + 4.38901i) q^{85} +(-49.9900 - 28.8617i) q^{86} +(40.3980 - 23.3238i) q^{88} -65.9697i q^{89} +(-24.0416 - 41.6413i) q^{92} +(25.0000 - 43.3013i) q^{94} +(59.8191 - 4.65524i) q^{95} +(141.393 - 81.6333i) q^{97} +21.2132 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} - 32 q^{10} - 16 q^{16} + 96 q^{19} + 36 q^{25} + 128 q^{31} + 64 q^{34} + 32 q^{40} + 272 q^{46} - 60 q^{49} + 544 q^{55} + 64 q^{61} + 64 q^{64} + 136 q^{70} - 96 q^{76} + 288 q^{79} - 128 q^{85} + 200 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 - 32 * q^10 - 16 * q^16 + 96 * q^19 + 36 * q^25 + 128 * q^31 + 64 * q^34 + 32 * q^40 + 272 * q^46 - 60 * q^49 + 544 * q^55 + 64 * q^61 + 64 * q^64 + 136 * q^70 - 96 * q^76 + 288 * q^79 - 128 * q^85 + 200 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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