LMFDB - Embedded newform 810.3.j.d.269.2

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:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 90)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			269.2
Root			$0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	810.269
Dual form			810.3.j.d.539.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(1.29410 - 4.82963i) q^{5} +(3.46410 + 2.00000i) q^{7} +2.82843 q^{8} +O(q^{10})$	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(1.29410 - 4.82963i) q^{5} +(3.46410 + 2.00000i) q^{7} +2.82843 q^{8} +(5.00000 + 5.00000i) q^{10} +(-9.79796 - 5.65685i) q^{11} +(-15.5885 + 9.00000i) q^{13} +(-4.89898 + 2.82843i) q^{14} +(-2.00000 + 3.46410i) q^{16} +1.41421 q^{17} -24.0000 q^{19} +(-9.65926 + 2.58819i) q^{20} +(13.8564 - 8.00000i) q^{22} +(19.7990 + 34.2929i) q^{23} +(-21.6506 - 12.5000i) q^{25} -25.4558i q^{26} -8.00000i q^{28} +(33.0681 + 19.0919i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(14.1421 - 14.1421i) q^{35} +56.0000i q^{37} +(16.9706 - 29.3939i) q^{38} +(3.66025 - 13.6603i) q^{40} +(20.8207 - 12.0208i) q^{41} +(69.2820 + 40.0000i) q^{43} +22.6274i q^{44} -56.0000 q^{46} +(-14.1421 + 24.4949i) q^{47} +(-16.5000 - 28.5788i) q^{49} +(30.6186 - 17.6777i) q^{50} +(31.1769 + 18.0000i) q^{52} +4.24264 q^{53} +(-40.0000 + 40.0000i) q^{55} +(9.79796 + 5.65685i) q^{56} +(-46.7654 + 27.0000i) q^{58} +(53.8888 - 31.1127i) q^{59} +(-55.0000 + 95.2628i) q^{61} +5.65685 q^{62} +8.00000 q^{64} +(23.2937 + 86.9333i) q^{65} +(-27.7128 + 16.0000i) q^{67} +(-1.41421 - 2.44949i) q^{68} +(7.32051 + 27.3205i) q^{70} +50.9117i q^{71} +46.0000i q^{73} +(-68.5857 - 39.5980i) q^{74} +(24.0000 + 41.5692i) q^{76} +(-22.6274 - 39.1918i) q^{77} +(-18.0000 + 31.1769i) q^{79} +(14.1421 + 14.1421i) q^{80} +34.0000i q^{82} +(2.82843 - 4.89898i) q^{83} +(1.83013 - 6.83013i) q^{85} +(-97.9796 + 56.5685i) q^{86} +(-27.7128 - 16.0000i) q^{88} -57.9828i q^{89} -72.0000 q^{91} +(39.5980 - 68.5857i) q^{92} +(-20.0000 - 34.6410i) q^{94} +(-31.0583 + 115.911i) q^{95} +(12.1244 + 7.00000i) q^{97} +46.6690 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 8 q^{4}+O(q^{10}) $ 8 * q - 8 * q^4	$ 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} - 192 q^{19} - 16 q^{31} - 8 q^{34} - 40 q^{40} - 448 q^{46} - 132 q^{49} - 320 q^{55} - 440 q^{61} + 64 q^{64} - 80 q^{70} + 192 q^{76} - 144 q^{79} - 20 q^{85} - 576 q^{91} - 160 q^{94}+O(q^{100}) $ 8 * q - 8 * q^4 + 40 * q^10 - 16 * q^16 - 192 * q^19 - 16 * q^31 - 8 * q^34 - 40 * q^40 - 448 * q^46 - 132 * q^49 - 320 * q^55 - 440 * q^61 + 64 * q^64 - 80 * q^70 + 192 * q^76 - 144 * q^79 - 20 * q^85 - 576 * q^91 - 160 * q^94

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	1.29410	−	4.82963i	0.258819	−	0.965926i
$5$	1.29410	−	4.82963i	0.258819	−	0.965926i
$6$		0			0
$7$	3.46410	+	2.00000i	0.494872	+	0.285714i	0.726593	−	0.687068i	$-0.241103\pi$
$7$	3.46410	+	2.00000i	0.494872	+	0.285714i	−0.231722	+	0.972782i	$0.574436\pi$
$8$	2.82843			0.353553
$9$		0			0
$10$	5.00000	+	5.00000i	0.500000	+	0.500000i
$11$	−9.79796	−	5.65685i	−0.890724	−	0.514259i	−0.0165444	−	0.999863i	$-0.505267\pi$
$11$	−9.79796	−	5.65685i	−0.890724	−	0.514259i	−0.874179	+	0.485604i	$0.838600\pi$
$12$		0			0
$13$	−15.5885	+	9.00000i	−1.19911	+	0.692308i	−0.960357	−	0.278772i	$-0.910073\pi$
$13$	−15.5885	+	9.00000i	−1.19911	+	0.692308i	−0.238755	+	0.971080i	$0.576739\pi$
$14$	−4.89898	+	2.82843i	−0.349927	+	0.202031i
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	1.41421			0.0831890			0.0415945	−	0.999135i	$-0.486756\pi$
$17$	1.41421			0.0831890			0.0415945	+	0.999135i	$0.486756\pi$
$18$		0			0
$19$	−24.0000			−1.26316			−0.631579	−	0.775312i	$-0.717593\pi$
$19$	−24.0000			−1.26316			−0.631579	+	0.775312i	$0.717593\pi$
$20$	−9.65926	+	2.58819i	−0.482963	+	0.129410i
$21$		0			0
$22$	13.8564	−	8.00000i	0.629837	−	0.363636i
$23$	19.7990	+	34.2929i	0.860826	+	1.49099i	0.871133	+	0.491047i	$0.163386\pi$
$23$	19.7990	+	34.2929i	0.860826	+	1.49099i	−0.0103075	+	0.999947i	$0.503281\pi$
$24$		0			0
$25$	−21.6506	−	12.5000i	−0.866025	−	0.500000i
$26$		−	25.4558i		−	0.979071i
$27$		0			0
$28$		−	8.00000i		−	0.285714i
$29$	33.0681	+	19.0919i	1.14028	+	0.658341i	0.946500	−	0.322704i	$-0.104592\pi$
$29$	33.0681	+	19.0919i	1.14028	+	0.658341i	0.193780	+	0.981045i	$0.437925\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.0645161	−	0.111745i	0.831963	−	0.554831i	$-0.187217\pi$
$31$	−2.00000	−	3.46410i	−0.0645161	−	0.111745i	−0.896479	+	0.443086i	$0.853884\pi$
$32$	−2.82843	−	4.89898i	−0.0883883	−	0.153093i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.0294118	+	0.0509427i
$35$	14.1421	−	14.1421i	0.404061	−	0.404061i
$36$		0			0
$37$			56.0000i			1.51351i	0.653697	+	0.756757i	$0.273217\pi$
$37$			56.0000i			1.51351i	−0.653697	+	0.756757i	$0.726783\pi$
$38$	16.9706	−	29.3939i	0.446594	−	0.773523i
$39$		0			0
$40$	3.66025	−	13.6603i	0.0915064	−	0.341506i
$41$	20.8207	−	12.0208i	0.507821	−	0.293191i	−0.224116	−	0.974562i	$-0.571950\pi$
$41$	20.8207	−	12.0208i	0.507821	−	0.293191i	0.731938	+	0.681372i	$0.238616\pi$
$42$		0			0
$43$	69.2820	+	40.0000i	1.61121	+	0.930233i	0.989090	+	0.147310i	$0.0470616\pi$
$43$	69.2820	+	40.0000i	1.61121	+	0.930233i	0.622120	+	0.782922i	$0.286272\pi$
$44$			22.6274i			0.514259i
$45$		0			0
$46$	−56.0000			−1.21739
$47$	−14.1421	+	24.4949i	−0.300897	+	0.521168i	−0.976339	−	0.216244i	$-0.930619\pi$
$47$	−14.1421	+	24.4949i	−0.300897	+	0.521168i	0.675443	+	0.737412i	$0.263953\pi$
$48$		0			0
$49$	−16.5000	−	28.5788i	−0.336735	−	0.583242i
$50$	30.6186	−	17.6777i	0.612372	−	0.353553i
$51$		0			0
$52$	31.1769	+	18.0000i	0.599556	+	0.346154i
$53$	4.24264			0.0800498			0.0400249	−	0.999199i	$-0.487256\pi$
$53$	4.24264			0.0800498			0.0400249	+	0.999199i	$0.487256\pi$
$54$		0			0
$55$	−40.0000	+	40.0000i	−0.727273	+	0.727273i
$56$	9.79796	+	5.65685i	0.174964	+	0.101015i
$57$		0			0
$58$	−46.7654	+	27.0000i	−0.806300	+	0.465517i
$59$	53.8888	−	31.1127i	0.913369	−	0.527334i	0.0318554	−	0.999492i	$-0.489858\pi$
$59$	53.8888	−	31.1127i	0.913369	−	0.527334i	0.881514	+	0.472159i	$0.156525\pi$
$60$		0			0
$61$	−55.0000	+	95.2628i	−0.901639	+	1.56169i	−0.0762735	+	0.997087i	$0.524302\pi$
$61$	−55.0000	+	95.2628i	−0.901639	+	1.56169i	−0.825366	+	0.564598i	$0.809031\pi$
$62$	5.65685			0.0912396
$63$		0			0
$64$	8.00000			0.125000
$65$	23.2937	+	86.9333i	0.358365	+	1.33744i
$66$		0			0
$67$	−27.7128	+	16.0000i	−0.413624	+	0.238806i	−0.692346	−	0.721566i	$-0.743423\pi$
$67$	−27.7128	+	16.0000i	−0.413624	+	0.238806i	0.278722	+	0.960372i	$0.410089\pi$
$68$	−1.41421	−	2.44949i	−0.0207973	−	0.0360219i
$69$		0			0
$70$	7.32051	+	27.3205i	0.104579	+	0.390293i
$71$			50.9117i			0.717066i	0.933517	+	0.358533i	$0.116723\pi$
$71$			50.9117i			0.717066i	−0.933517	+	0.358533i	$0.883277\pi$
$72$		0			0
$73$			46.0000i			0.630137i	0.949069	+	0.315068i	$0.102027\pi$
$73$			46.0000i			0.630137i	−0.949069	+	0.315068i	$0.897973\pi$
$74$	−68.5857	−	39.5980i	−0.926834	−	0.535108i
$75$		0			0
$76$	24.0000	+	41.5692i	0.315789	+	0.546963i
$77$	−22.6274	−	39.1918i	−0.293863	−	0.508985i
$78$		0			0
$79$	−18.0000	+	31.1769i	−0.227848	+	0.394644i	−0.957170	−	0.289526i	$-0.906502\pi$
$79$	−18.0000	+	31.1769i	−0.227848	+	0.394644i	0.729322	+	0.684171i	$0.239836\pi$
$80$	14.1421	+	14.1421i	0.176777	+	0.176777i
$81$		0			0
$82$			34.0000i			0.414634i
$83$	2.82843	−	4.89898i	0.0340774	−	0.0590238i	−0.848484	−	0.529222i	$-0.822484\pi$
$83$	2.82843	−	4.89898i	0.0340774	−	0.0590238i	0.882561	+	0.470198i	$0.155817\pi$
$84$		0			0
$85$	1.83013	−	6.83013i	0.0215309	−	0.0803544i
$86$	−97.9796	+	56.5685i	−1.13930	+	0.657774i
$87$		0			0
$88$	−27.7128	−	16.0000i	−0.314918	−	0.181818i
$89$		−	57.9828i		−	0.651492i	−0.945457	−	0.325746i	$-0.894385\pi$
$89$		−	57.9828i		−	0.651492i	0.945457	−	0.325746i	$-0.105615\pi$
$90$		0			0
$91$	−72.0000			−0.791209
$92$	39.5980	−	68.5857i	0.430413	−	0.745497i
$93$		0			0
$94$	−20.0000	−	34.6410i	−0.212766	−	0.368521i
$95$	−31.0583	+	115.911i	−0.326929	+	1.22012i
$96$		0			0
$97$	12.1244	+	7.00000i	0.124993	+	0.0721649i	0.561193	−	0.827685i	$-0.310343\pi$
$97$	12.1244	+	7.00000i	0.124993	+	0.0721649i	−0.436200	+	0.899850i	$0.643676\pi$
$98$	46.6690			0.476215
$99$		0			0
$100$			50.0000i			0.500000i
$101$	−23.2702	−	13.4350i	−0.230398	−	0.133020i	0.380358	−	0.924839i	$-0.375801\pi$
$101$	−23.2702	−	13.4350i	−0.230398	−	0.133020i	−0.610755	+	0.791819i	$0.709134\pi$
$102$		0			0
$103$	58.8897	−	34.0000i	0.571745	−	0.330097i	−0.186101	−	0.982531i	$-0.559585\pi$
$103$	58.8897	−	34.0000i	0.571745	−	0.330097i	0.757846	+	0.652434i	$0.226252\pi$
$104$	−44.0908	+	25.4558i	−0.423950	+	0.244768i
$105$		0			0
$106$	−3.00000	+	5.19615i	−0.0283019	+	0.0490203i
$107$	−169.706			−1.58603			−0.793017	−	0.609200i	$-0.791491\pi$
$107$	−169.706			−1.58603			−0.793017	+	0.609200i	$0.791491\pi$
$108$		0			0
$109$	−136.000			−1.24771			−0.623853	−	0.781542i	$-0.714434\pi$
$109$	−136.000			−1.24771			−0.623853	+	0.781542i	$0.714434\pi$
$110$	−20.7055	−	77.2741i	−0.188232	−	0.702492i
$111$		0			0
$112$	−13.8564	+	8.00000i	−0.123718	+	0.0714286i
$113$	6.36396	+	11.0227i	0.0563182	+	0.0975461i	0.892810	−	0.450433i	$-0.148731\pi$
$113$	6.36396	+	11.0227i	0.0563182	+	0.0975461i	−0.836492	+	0.547979i	$0.815397\pi$
$114$		0			0
$115$	191.244	−	51.2436i	1.66299	−	0.445596i
$116$		−	76.3675i		−	0.658341i
$117$		0			0
$118$			88.0000i			0.745763i
$119$	4.89898	+	2.82843i	0.0411679	+	0.0237683i
$120$		0			0
$121$	3.50000	+	6.06218i	0.0289256	+	0.0501006i
$122$	−77.7817	−	134.722i	−0.637555	−	1.10428i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.0322581	+	0.0558726i
$125$	−88.3883	+	88.3883i	−0.707107	+	0.707107i
$126$		0			0
$127$		−	28.0000i		−	0.220472i	−0.993905	−	0.110236i	$-0.964839\pi$
$127$		−	28.0000i		−	0.220472i	0.993905	−	0.110236i	$-0.0351607\pi$
$128$	−5.65685	+	9.79796i	−0.0441942	+	0.0765466i
$129$		0			0
$130$	−122.942	−	32.9423i	−0.945710	−	0.253402i
$131$	73.4847	−	42.4264i	0.560952	−	0.323866i	−0.192576	−	0.981282i	$-0.561684\pi$
$131$	73.4847	−	42.4264i	0.560952	−	0.323866i	0.753527	+	0.657416i	$0.228351\pi$
$132$		0			0
$133$	−83.1384	−	48.0000i	−0.625101	−	0.360902i
$134$		−	45.2548i		−	0.337723i
$135$		0			0
$136$	4.00000			0.0294118
$137$	6.36396	−	11.0227i	0.0464523	−	0.0804577i	−0.841864	−	0.539689i	$-0.818542\pi$
$137$	6.36396	−	11.0227i	0.0464523	−	0.0804577i	0.888317	+	0.459231i	$0.151875\pi$
$138$		0			0
$139$	−4.00000	−	6.92820i	−0.0287770	−	0.0498432i	0.851278	−	0.524715i	$-0.175828\pi$
$139$	−4.00000	−	6.92820i	−0.0287770	−	0.0498432i	−0.880055	+	0.474871i	$0.842495\pi$
$140$	−38.6370	−	10.3528i	−0.275979	−	0.0739483i
$141$		0			0
$142$	−62.3538	−	36.0000i	−0.439111	−	0.253521i
$143$	203.647			1.42410
$144$		0			0
$145$	135.000	−	135.000i	0.931034	−	0.931034i
$146$	−56.3383	−	32.5269i	−0.385879	−	0.222787i
$147$		0			0
$148$	96.9948	−	56.0000i	0.655371	−	0.378378i
$149$	−104.103	+	60.1041i	−0.698680	+	0.403383i	−0.806856	−	0.590749i	$-0.798832\pi$
$149$	−104.103	+	60.1041i	−0.698680	+	0.403383i	0.108176	+	0.994132i	$0.465499\pi$
$150$		0			0
$151$	−86.0000	+	148.956i	−0.569536	+	0.986466i	0.427075	+	0.904216i	$0.359544\pi$
$151$	−86.0000	+	148.956i	−0.569536	+	0.986466i	−0.996612	+	0.0822500i	$0.973789\pi$
$152$	−67.8823			−0.446594
$153$		0			0
$154$	64.0000			0.415584
$155$	−19.3185	+	5.17638i	−0.124636	+	0.0333960i
$156$		0			0
$157$	−131.636	+	76.0000i	−0.838445	+	0.484076i	−0.856735	−	0.515756i	$-0.827511\pi$
$157$	−131.636	+	76.0000i	−0.838445	+	0.484076i	0.0182904	+	0.999833i	$0.494178\pi$
$158$	−25.4558	−	44.0908i	−0.161113	−	0.279056i
$159$		0			0
$160$	−27.3205	+	7.32051i	−0.170753	+	0.0457532i
$161$			158.392i			0.983801i
$162$		0			0
$163$			104.000i			0.638037i	0.947749	+	0.319018i	$0.103353\pi$
$163$			104.000i			0.638037i	−0.947749	+	0.319018i	$0.896647\pi$
$164$	−41.6413	−	24.0416i	−0.253911	−	0.146595i
$165$		0			0
$166$	4.00000	+	6.92820i	0.0240964	+	0.0417362i
$167$	−101.823	−	176.363i	−0.609721	−	1.05607i	−0.991286	−	0.131726i	$-0.957948\pi$
$167$	−101.823	−	176.363i	−0.609721	−	1.05607i	0.381565	−	0.924342i	$-0.375385\pi$
$168$		0			0
$169$	77.5000	−	134.234i	0.458580	−	0.794284i
$170$	7.07107	+	7.07107i	0.0415945	+	0.0415945i
$171$		0			0
$172$		−	160.000i		−	0.930233i
$173$	−115.258	+	199.633i	−0.666234	+	1.15395i	0.312716	+	0.949847i	$0.398761\pi$
$173$	−115.258	+	199.633i	−0.666234	+	1.15395i	−0.978949	+	0.204104i	$0.934572\pi$
$174$		0			0
$175$	−50.0000	−	86.6025i	−0.285714	−	0.494872i
$176$	39.1918	−	22.6274i	0.222681	−	0.128565i
$177$		0			0
$178$	71.0141	+	41.0000i	0.398956	+	0.230337i
$179$			164.049i			0.916474i	0.888830	+	0.458237i	$0.151519\pi$
$179$			164.049i			0.916474i	−0.888830	+	0.458237i	$0.848481\pi$
$180$		0			0
$181$	8.00000			0.0441989			0.0220994	−	0.999756i	$-0.492965\pi$
$181$	8.00000			0.0441989			0.0220994	+	0.999756i	$0.492965\pi$
$182$	50.9117	−	88.1816i	0.279735	−	0.484514i
$183$		0			0
$184$	56.0000	+	96.9948i	0.304348	+	0.527146i
$185$	270.459	+	72.4693i	1.46194	+	0.391726i
$186$		0			0
$187$	−13.8564	−	8.00000i	−0.0740984	−	0.0427807i
$188$	56.5685			0.300897
$189$		0			0
$190$	−120.000	−	120.000i	−0.631579	−	0.631579i
$191$	264.545	+	152.735i	1.38505	+	0.799660i	0.992752	−	0.120178i	$-0.0383464\pi$
$191$	264.545	+	152.735i	1.38505	+	0.799660i	0.392299	+	0.919838i	$0.371680\pi$
$192$		0			0
$193$	55.4256	−	32.0000i	0.287179	−	0.165803i	−0.349490	−	0.936940i	$-0.613645\pi$
$193$	55.4256	−	32.0000i	0.287179	−	0.165803i	0.636669	+	0.771137i	$0.280312\pi$
$194$	−17.1464	+	9.89949i	−0.0883837	+	0.0510283i
$195$		0			0
$196$	−33.0000	+	57.1577i	−0.168367	+	0.291621i
$197$	−230.517			−1.17014			−0.585068	−	0.810984i	$-0.698932\pi$
$197$	−230.517			−1.17014			−0.585068	+	0.810984i	$0.698932\pi$
$198$		0			0
$199$	300.000			1.50754			0.753769	−	0.657140i	$-0.228234\pi$
$199$	300.000			1.50754			0.753769	+	0.657140i	$0.228234\pi$
$200$	−61.2372	−	35.3553i	−0.306186	−	0.176777i
$201$		0			0
$202$	32.9090	−	19.0000i	0.162916	−	0.0940594i
$203$	76.3675	+	132.272i	0.376195	+	0.651588i
$204$		0			0
$205$	−31.1122	−	116.112i	−0.151767	−	0.566401i
$206$			96.1665i			0.466828i
$207$		0			0
$208$		−	72.0000i		−	0.346154i
$209$	235.151	+	135.765i	1.12512	+	0.649591i
$210$		0			0
$211$	132.000	+	228.631i	0.625592	+	1.08356i	0.988426	+	0.151704i	$0.0484760\pi$
$211$	132.000	+	228.631i	0.625592	+	1.08356i	−0.362834	+	0.931854i	$0.618191\pi$
$212$	−4.24264	−	7.34847i	−0.0200125	−	0.0346626i
$213$		0			0
$214$	120.000	−	207.846i	0.560748	−	0.971243i
$215$	282.843	−	282.843i	1.31555	−	1.31555i
$216$		0			0
$217$		−	16.0000i		−	0.0737327i
$218$	96.1665	−	166.565i	0.441131	−	0.764061i
$219$		0			0
$220$	109.282	+	29.2820i	0.496737	+	0.133100i
$221$	−22.0454	+	12.7279i	−0.0997530	+	0.0575924i
$222$		0			0
$223$	−273.664	−	158.000i	−1.22719	−	0.708520i	−0.260751	−	0.965406i	$-0.583970\pi$
$223$	−273.664	−	158.000i	−1.22719	−	0.708520i	−0.966442	+	0.256886i	$0.917304\pi$
$224$		−	22.6274i		−	0.101015i
$225$		0			0
$226$	−18.0000			−0.0796460
$227$	48.0833	−	83.2827i	0.211821	−	0.366884i	−0.740464	−	0.672096i	$-0.765394\pi$
$227$	48.0833	−	83.2827i	0.211821	−	0.366884i	0.952284	+	0.305212i	$0.0987274\pi$
$228$		0			0
$229$	4.00000	+	6.92820i	0.0174672	+	0.0302542i	0.874627	−	0.484797i	$-0.161106\pi$
$229$	4.00000	+	6.92820i	0.0174672	+	0.0302542i	−0.857160	+	0.515051i	$0.827773\pi$
$230$	−72.4693	+	270.459i	−0.315084	+	1.17591i
$231$		0			0
$232$	93.5307	+	54.0000i	0.403150	+	0.232759i
$233$	−227.688			−0.977203			−0.488602	−	0.872507i	$-0.662493\pi$
$233$	−227.688			−0.977203			−0.488602	+	0.872507i	$0.662493\pi$
$234$		0			0
$235$	100.000	+	100.000i	0.425532	+	0.425532i
$236$	−107.778	−	62.2254i	−0.456685	−	0.263667i
$237$		0			0
$238$	−6.92820	+	4.00000i	−0.0291101	+	0.0168067i
$239$	166.565	−	96.1665i	0.696926	−	0.402370i	−0.109276	−	0.994012i	$-0.534853\pi$
$239$	166.565	−	96.1665i	0.696926	−	0.402370i	0.806201	+	0.591641i	$0.201520\pi$
$240$		0			0
$241$	64.0000	−	110.851i	0.265560	−	0.459964i	−0.702150	−	0.712029i	$-0.747776\pi$
$241$	64.0000	−	110.851i	0.265560	−	0.459964i	0.967710	+	0.252065i	$0.0811098\pi$
$242$	−9.89949			−0.0409070
$243$		0			0
$244$	220.000			0.901639
$245$	−159.378	+	42.7051i	−0.650521	+	0.174307i
$246$		0			0
$247$	374.123	−	216.000i	1.51467	−	0.874494i
$248$	−5.65685	−	9.79796i	−0.0228099	−	0.0395079i
$249$		0			0
$250$	−45.7532	−	170.753i	−0.183013	−	0.683013i
$251$		−	475.176i		−	1.89313i	−0.322512	−	0.946565i	$-0.604527\pi$
$251$		−	475.176i		−	1.89313i	0.322512	−	0.946565i	$-0.395473\pi$
$252$		0			0
$253$		−	448.000i		−	1.77075i
$254$	34.2929	+	19.7990i	0.135011	+	0.0779488i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	−163.342	−	282.916i	−0.635571	−	1.10084i	−0.986394	−	0.164399i	$-0.947432\pi$
$257$	−163.342	−	282.916i	−0.635571	−	1.10084i	0.350823	−	0.936442i	$-0.385902\pi$
$258$		0			0
$259$	−112.000	+	193.990i	−0.432432	+	0.748995i
$260$	127.279	−	127.279i	0.489535	−	0.489535i
$261$		0			0
$262$			120.000i			0.458015i
$263$	−39.5980	+	68.5857i	−0.150563	+	0.260782i	−0.931434	−	0.363909i	$-0.881442\pi$
$263$	−39.5980	+	68.5857i	−0.150563	+	0.260782i	0.780872	+	0.624691i	$0.214775\pi$
$264$		0			0
$265$	5.49038	−	20.4904i	0.0207184	−	0.0773222i
$266$	117.576	−	67.8823i	0.442013	−	0.255196i
$267$		0			0
$268$	55.4256	+	32.0000i	0.206812	+	0.119403i
$269$			165.463i			0.615104i	0.951531	+	0.307552i	$0.0995098\pi$
$269$			165.463i			0.615104i	−0.951531	+	0.307552i	$0.900490\pi$
$270$		0			0
$271$	220.000			0.811808			0.405904	−	0.913916i	$-0.366957\pi$
$271$	220.000			0.811808			0.405904	+	0.913916i	$0.366957\pi$
$272$	−2.82843	+	4.89898i	−0.0103986	+	0.0180110i
$273$		0			0
$274$	9.00000	+	15.5885i	0.0328467	+	0.0568922i
$275$	141.421	+	244.949i	0.514259	+	0.890724i
$276$		0			0
$277$	−1.73205	−	1.00000i	−0.00625289	−	0.00361011i	0.496870	−	0.867825i	$-0.334482\pi$
$277$	−1.73205	−	1.00000i	−0.00625289	−	0.00361011i	−0.503123	+	0.864215i	$0.667816\pi$
$278$	11.3137			0.0406968
$279$		0			0
$280$	40.0000	−	40.0000i	0.142857	−	0.142857i
$281$	−11.0227	−	6.36396i	−0.0392267	−	0.0226475i	0.480258	−	0.877127i	$-0.340543\pi$
$281$	−11.0227	−	6.36396i	−0.0392267	−	0.0226475i	−0.519485	+	0.854480i	$0.673876\pi$
$282$		0			0
$283$	−408.764	+	236.000i	−1.44440	+	0.833922i	−0.998139	−	0.0609826i	$-0.980577\pi$
$283$	−408.764	+	236.000i	−1.44440	+	0.833922i	−0.446257	+	0.894905i	$0.647243\pi$
$284$	88.1816	−	50.9117i	0.310499	−	0.179267i
$285$		0			0
$286$	−144.000	+	249.415i	−0.503497	+	0.872082i
$287$	96.1665			0.335075
$288$		0			0
$289$	−287.000			−0.993080
$290$	69.8811	+	260.800i	0.240969	+	0.899310i
$291$		0			0
$292$	79.6743	−	46.0000i	0.272857	−	0.157534i
$293$	205.768	+	356.401i	0.702280	+	1.21638i	0.967664	+	0.252242i	$0.0811679\pi$
$293$	205.768	+	356.401i	0.702280	+	1.21638i	−0.265384	+	0.964143i	$0.585499\pi$
$294$		0			0
$295$	−80.5256	−	300.526i	−0.272968	−	1.01873i
$296$			158.392i			0.535108i
$297$		0			0
$298$		−	170.000i		−	0.570470i
$299$	−617.271	−	356.382i	−2.06445	−	1.19191i
$300$		0			0
$301$	160.000	+	277.128i	0.531561	+	0.920691i
$302$	−121.622	−	210.656i	−0.402723	−	0.697537i
$303$		0			0
$304$	48.0000	−	83.1384i	0.157895	−	0.273482i
$305$	388.909	+	388.909i	1.27511	+	1.27511i
$306$		0			0
$307$		−	360.000i		−	1.17264i	−0.810080	−	0.586319i	$-0.800576\pi$
$307$		−	360.000i		−	1.17264i	0.810080	−	0.586319i	$-0.199424\pi$
$308$	−45.2548	+	78.3837i	−0.146931	+	0.254492i
$309$		0			0
$310$	7.32051	−	27.3205i	0.0236145	−	0.0881307i
$311$	29.3939	−	16.9706i	0.0945141	−	0.0545677i	−0.451998	−	0.892019i	$-0.649289\pi$
$311$	29.3939	−	16.9706i	0.0945141	−	0.0545677i	0.546512	+	0.837451i	$0.315955\pi$
$312$		0			0
$313$	360.267	+	208.000i	1.15101	+	0.664537i	0.949133	−	0.314874i	$-0.101962\pi$
$313$	360.267	+	208.000i	1.15101	+	0.664537i	0.201878	+	0.979411i	$0.435296\pi$
$314$		−	214.960i		−	0.684587i
$315$		0			0
$316$	72.0000			0.227848
$317$	37.4767	−	64.9115i	0.118223	−	0.204768i	−0.800841	−	0.598878i	$-0.795614\pi$
$317$	37.4767	−	64.9115i	0.118223	−	0.204768i	0.919063	+	0.394110i	$0.128947\pi$
$318$		0			0
$319$	−216.000	−	374.123i	−0.677116	−	1.17280i
$320$	10.3528	−	38.6370i	0.0323524	−	0.120741i
$321$		0			0
$322$	−193.990	−	112.000i	−0.602452	−	0.347826i
$323$	−33.9411			−0.105081
$324$		0			0
$325$	450.000			1.38462
$326$	−127.373	−	73.5391i	−0.390716	−	0.225580i
$327$		0			0
$328$	58.8897	−	34.0000i	0.179542	−	0.103659i
$329$	−97.9796	+	56.5685i	−0.297810	+	0.171941i
$330$		0			0
$331$	232.000	−	401.836i	0.700906	−	1.21401i	−0.267242	−	0.963629i	$-0.586112\pi$
$331$	232.000	−	401.836i	0.700906	−	1.21401i	0.968149	−	0.250376i	$-0.0805543\pi$
$332$	−11.3137			−0.0340774
$333$		0			0
$334$	288.000			0.862275
$335$	41.4110	+	154.548i	0.123615	+	0.461338i
$336$		0			0
$337$	53.6936	−	31.0000i	0.159328	−	0.0919881i	−0.418216	−	0.908348i	$-0.637344\pi$
$337$	53.6936	−	31.0000i	0.159328	−	0.0919881i	0.577544	+	0.816359i	$0.304011\pi$
$338$	109.602	+	189.835i	0.324265	+	0.561643i
$339$		0			0
$340$	−13.6603	+	3.66025i	−0.0401772	+	0.0107655i
$341$			45.2548i			0.132712i
$342$		0			0
$343$		−	328.000i		−	0.956268i
$344$	195.959	+	113.137i	0.569649	+	0.328887i
$345$		0			0
$346$	−163.000	−	282.324i	−0.471098	−	0.815966i
$347$	−229.103	−	396.817i	−0.660238	−	1.14357i	−0.980553	−	0.196255i	$-0.937122\pi$
$347$	−229.103	−	396.817i	−0.660238	−	1.14357i	0.320315	−	0.947311i	$-0.396211\pi$
$348$		0			0
$349$	71.0000	−	122.976i	0.203438	−	0.352366i	−0.746196	−	0.665727i	$-0.768122\pi$
$349$	71.0000	−	122.976i	0.203438	−	0.352366i	0.949634	+	0.313361i	$0.101455\pi$
$350$	141.421			0.404061
$351$		0			0
$352$			64.0000i			0.181818i
$353$	50.2046	−	86.9569i	0.142223	−	0.246337i	−0.786111	−	0.618086i	$-0.787908\pi$
$353$	50.2046	−	86.9569i	0.142223	−	0.246337i	0.928333	+	0.371749i	$0.121242\pi$
$354$		0			0
$355$	245.885	+	65.8846i	0.692633	+	0.185590i
$356$	−100.429	+	57.9828i	−0.282104	+	0.162873i
$357$		0			0
$358$	−200.918	−	116.000i	−0.561223	−	0.324022i
$359$		−	390.323i		−	1.08725i	−0.839328	−	0.543625i	$-0.817051\pi$
$359$		−	390.323i		−	1.08725i	0.839328	−	0.543625i	$-0.182949\pi$
$360$		0			0
$361$	215.000			0.595568
$362$	−5.65685	+	9.79796i	−0.0156267	+	0.0270662i
$363$		0			0
$364$	72.0000	+	124.708i	0.197802	+	0.342603i
$365$	222.163	+	59.5284i	0.608666	+	0.163091i
$366$		0			0
$367$	−245.951	−	142.000i	−0.670167	−	0.386921i	0.125973	−	0.992034i	$-0.459795\pi$
$367$	−245.951	−	142.000i	−0.670167	−	0.386921i	−0.796140	+	0.605113i	$0.793128\pi$
$368$	−158.392			−0.430413
$369$		0			0
$370$	−280.000	+	280.000i	−0.756757	+	0.756757i
$371$	14.6969	+	8.48528i	0.0396144	+	0.0228714i
$372$		0			0
$373$	311.769	−	180.000i	0.835842	−	0.482574i	−0.0200066	−	0.999800i	$-0.506369\pi$
$373$	311.769	−	180.000i	0.835842	−	0.482574i	0.855849	+	0.517226i	$0.173035\pi$
$374$	19.5959	−	11.3137i	0.0523955	−	0.0302506i
$375$		0			0
$376$	−40.0000	+	69.2820i	−0.106383	+	0.184261i
$377$	−687.308			−1.82310
$378$		0			0
$379$	−320.000			−0.844327			−0.422164	−	0.906520i	$-0.638729\pi$
$379$	−320.000			−0.844327			−0.422164	+	0.906520i	$0.638729\pi$
$380$	231.822	−	62.1166i	0.610058	−	0.163465i
$381$		0			0
$382$	−374.123	+	216.000i	−0.979380	+	0.565445i
$383$	90.5097	+	156.767i	0.236318	+	0.409314i	0.959655	−	0.281181i	$-0.0907261\pi$
$383$	90.5097	+	156.767i	0.236318	+	0.409314i	−0.723337	+	0.690495i	$0.757393\pi$
$384$		0			0
$385$	−218.564	+	58.5641i	−0.567699	+	0.152114i
$386$			90.5097i			0.234481i
$387$		0			0
$388$		−	28.0000i		−	0.0721649i
$389$	594.001	+	342.947i	1.52700	+	0.881611i	0.999486	+	0.0320622i	$0.0102075\pi$
$389$	594.001	+	342.947i	1.52700	+	0.881611i	0.527510	+	0.849549i	$0.323126\pi$
$390$		0			0
$391$	28.0000	+	48.4974i	0.0716113	+	0.124034i
$392$	−46.6690	−	80.8332i	−0.119054	−	0.206207i
$393$		0			0
$394$	163.000	−	282.324i	0.413706	−	0.716559i
$395$	127.279	+	127.279i	0.322226	+	0.322226i
$396$		0			0
$397$			296.000i			0.745592i	0.927913	+	0.372796i	$0.121601\pi$
$397$			296.000i			0.745592i	−0.927913	+	0.372796i	$0.878399\pi$
$398$	−212.132	+	367.423i	−0.532995	+	0.923175i
$399$		0			0
$400$	86.6025	−	50.0000i	0.216506	−	0.125000i
$401$	−380.896	+	219.910i	−0.949864	+	0.548405i	−0.893039	−	0.449980i	$-0.851431\pi$
$401$	−380.896	+	219.910i	−0.949864	+	0.548405i	−0.0568256	+	0.998384i	$0.518098\pi$
$402$		0			0
$403$	62.3538	+	36.0000i	0.154724	+	0.0893300i
$404$			53.7401i			0.133020i
$405$		0			0
$406$	−216.000			−0.532020
$407$	316.784	−	548.686i	0.778339	−	1.34812i
$408$		0			0
$409$	184.000	+	318.697i	0.449878	+	0.779211i	0.998378	−	0.0569395i	$-0.0181342\pi$
$409$	184.000	+	318.697i	0.449878	+	0.779211i	−0.548500	+	0.836151i	$0.684801\pi$
$410$	164.207	+	43.9992i	0.400506	+	0.107315i
$411$		0			0
$412$	−117.779	−	68.0000i	−0.285872	−	0.165049i
$413$	248.902			0.602667
$414$		0			0
$415$	−20.0000	−	20.0000i	−0.0481928	−	0.0481928i
$416$	88.1816	+	50.9117i	0.211975	+	0.122384i
$417$		0			0
$418$	−332.554	+	192.000i	−0.795583	+	0.459330i
$419$	166.565	−	96.1665i	0.397531	−	0.229514i	−0.287887	−	0.957664i	$-0.592953\pi$
$419$	166.565	−	96.1665i	0.397531	−	0.229514i	0.685418	+	0.728150i	$0.259620\pi$
$420$		0			0
$421$	−140.000	+	242.487i	−0.332542	+	0.575979i	−0.983009	−	0.183555i	$-0.941240\pi$
$421$	−140.000	+	242.487i	−0.332542	+	0.575979i	0.650468	+	0.759534i	$0.274573\pi$
$422$	−373.352			−0.884721
$423$		0			0
$424$	12.0000			0.0283019
$425$	−30.6186	−	17.6777i	−0.0720438	−	0.0415945i
$426$		0			0
$427$	−381.051	+	220.000i	−0.892392	+	0.515222i
$428$	169.706	+	293.939i	0.396508	+	0.686773i
$429$		0			0
$430$	146.410	+	546.410i	0.340489	+	1.27072i
$431$			96.1665i			0.223124i	0.993757	+	0.111562i	$0.0355854\pi$
$431$			96.1665i			0.223124i	−0.993757	+	0.111562i	$0.964415\pi$
$432$		0			0
$433$			688.000i			1.58891i	0.607320	+	0.794457i	$0.292245\pi$
$433$			688.000i			1.58891i	−0.607320	+	0.794457i	$0.707755\pi$
$434$	19.5959	+	11.3137i	0.0451519	+	0.0260685i
$435$		0			0
$436$	136.000	+	235.559i	0.311927	+	0.540273i
$437$	−475.176	−	823.029i	−1.08736	−	1.88336i
$438$		0			0
$439$	−162.000	+	280.592i	−0.369021	+	0.639162i	−0.989413	−	0.145129i	$-0.953640\pi$
$439$	−162.000	+	280.592i	−0.369021	+	0.639162i	0.620392	+	0.784292i	$0.286973\pi$
$440$	−113.137	+	113.137i	−0.257130	+	0.257130i
$441$		0			0
$442$		−	36.0000i		−	0.0814480i
$443$	161.220	−	279.242i	0.363929	−	0.630343i	−0.624675	−	0.780885i	$-0.714769\pi$
$443$	161.220	−	279.242i	0.363929	−	0.630343i	0.988604	+	0.150542i	$0.0481019\pi$
$444$		0			0
$445$	−280.035	−	75.0352i	−0.629293	−	0.168618i
$446$	387.019	−	223.446i	0.867756	−	0.500999i
$447$		0			0
$448$	27.7128	+	16.0000i	0.0618590	+	0.0357143i
$449$		−	123.037i		−	0.274024i	−0.990569	−	0.137012i	$-0.956250\pi$
$449$		−	123.037i		−	0.274024i	0.990569	−	0.137012i	$-0.0437498\pi$
$450$		0			0
$451$	−272.000			−0.603104
$452$	12.7279	−	22.0454i	0.0281591	−	0.0487730i
$453$		0			0
$454$	68.0000	+	117.779i	0.149780	+	0.259426i
$455$	−93.1749	+	347.733i	−0.204780	+	0.764249i
$456$		0			0
$457$	112.583	+	65.0000i	0.246353	+	0.142232i	0.618093	−	0.786105i	$-0.287905\pi$
$457$	112.583	+	65.0000i	0.246353	+	0.142232i	−0.371740	+	0.928337i	$0.621239\pi$
$458$	−11.3137			−0.0247024
$459$		0			0
$460$	−280.000	−	280.000i	−0.608696	−	0.608696i
$461$	−407.840	−	235.467i	−0.884686	−	0.510773i	−0.0124851	−	0.999922i	$-0.503974\pi$
$461$	−407.840	−	235.467i	−0.884686	−	0.510773i	−0.872200	+	0.489149i	$0.837308\pi$
$462$		0			0
$463$	384.515	−	222.000i	0.830487	−	0.479482i	−0.0235327	−	0.999723i	$-0.507491\pi$
$463$	384.515	−	222.000i	0.830487	−	0.479482i	0.854019	+	0.520241i	$0.174158\pi$
$464$	−132.272	+	76.3675i	−0.285070	+	0.164585i
$465$		0			0
$466$	161.000	−	278.860i	0.345494	−	0.598412i
$467$	186.676			0.399735			0.199867	−	0.979823i	$-0.435949\pi$
$467$	186.676			0.399735			0.199867	+	0.979823i	$0.435949\pi$
$468$		0			0
$469$	−128.000			−0.272921
$470$	−193.185	+	51.7638i	−0.411032	+	0.110136i
$471$		0			0
$472$	152.420	−	88.0000i	0.322925	−	0.186441i
$473$	−452.548	−	783.837i	−0.956762	−	1.65716i
$474$		0			0
$475$	519.615	+	300.000i	1.09393	+	0.631579i
$476$		−	11.3137i		−	0.0237683i
$477$		0			0
$478$			272.000i			0.569038i
$479$	−504.595	−	291.328i	−1.05343	−	0.608200i	−0.129825	−	0.991537i	$-0.541442\pi$
$479$	−504.595	−	291.328i	−1.05343	−	0.608200i	−0.923609	+	0.383336i	$0.874775\pi$
$480$		0			0
$481$	−504.000	−	872.954i	−1.04782	−	1.81487i
$482$	90.5097	+	156.767i	0.187779	+	0.325243i
$483$		0			0
$484$	7.00000	−	12.1244i	0.0144628	−	0.0250503i
$485$	49.4975	−	49.4975i	0.102057	−	0.102057i
$486$		0			0
$487$		−	84.0000i		−	0.172485i	−0.996274	−	0.0862423i	$-0.972514\pi$
$487$		−	84.0000i		−	0.172485i	0.996274	−	0.0862423i	$-0.0274859\pi$
$488$	−155.563	+	269.444i	−0.318778	+	0.552139i
$489$		0			0
$490$	60.3942	−	225.394i	0.123253	−	0.459988i
$491$	−279.242	+	161.220i	−0.568721	+	0.328351i	−0.756638	−	0.653834i	$-0.773160\pi$
$491$	−279.242	+	161.220i	−0.568721	+	0.328351i	0.187918	+	0.982185i	$0.439826\pi$
$492$		0			0
$493$	46.7654	+	27.0000i	0.0948588	+	0.0547667i
$494$			610.940i			1.23672i
$495$		0			0
$496$	16.0000			0.0322581
$497$	−101.823	+	176.363i	−0.204876	+	0.354856i
$498$		0			0
$499$	−228.000	−	394.908i	−0.456914	−	0.791398i	0.541882	−	0.840454i	$-0.317712\pi$
$499$	−228.000	−	394.908i	−0.456914	−	0.791398i	−0.998796	+	0.0490565i	$0.984379\pi$
$500$	241.481	+	64.7048i	0.482963	+	0.129410i
$501$		0			0
$502$	581.969	+	336.000i	1.15930	+	0.669323i
$503$	492.146			0.978422			0.489211	−	0.872165i	$-0.337285\pi$
$503$	492.146			0.978422			0.489211	+	0.872165i	$0.337285\pi$
$504$		0			0
$505$	−95.0000	+	95.0000i	−0.188119	+	0.188119i
$506$	548.686	+	316.784i	1.08436	+	0.626055i
$507$		0			0
$508$	−48.4974	+	28.0000i	−0.0954674	+	0.0551181i
$509$	−503.370	+	290.621i	−0.988939	+	0.570964i	−0.904957	−	0.425503i	$-0.860097\pi$
$509$	−503.370	+	290.621i	−0.988939	+	0.570964i	−0.0839823	+	0.996467i	$0.526764\pi$
$510$		0			0
$511$	−92.0000	+	159.349i	−0.180039	+	0.311837i
$512$	22.6274			0.0441942
$513$		0			0
$514$	462.000			0.898833
$515$	−87.9985	−	328.415i	−0.170871	−	0.637699i
$516$		0			0
$517$	277.128	−	160.000i	0.536031	−	0.309478i
$518$	−158.392	−	274.343i	−0.305776	−	0.529619i
$519$		0			0
$520$	65.8846	+	245.885i	0.126701	+	0.472855i
$521$			408.708i			0.784468i	0.919866	+	0.392234i	$0.128298\pi$
$521$			408.708i			0.784468i	−0.919866	+	0.392234i	$0.871702\pi$
$522$		0			0
$523$			656.000i			1.25430i	0.778898	+	0.627151i	$0.215779\pi$
$523$			656.000i			1.25430i	−0.778898	+	0.627151i	$0.784221\pi$
$524$	−146.969	−	84.8528i	−0.280476	−	0.161933i
$525$		0			0
$526$	−56.0000	−	96.9948i	−0.106464	−	0.184401i
$527$	−2.82843	−	4.89898i	−0.00536703	−	0.00929598i
$528$		0			0
$529$	−519.500	+	899.800i	−0.982042	+	1.70095i
$530$	21.2132	+	21.2132i	0.0400249	+	0.0400249i
$531$		0			0
$532$			192.000i			0.360902i
$533$	−216.375	+	374.772i	−0.405956	+	0.703137i
$534$		0			0
$535$	−219.615	+	819.615i	−0.410496	+	1.53199i
$536$	−78.3837	+	45.2548i	−0.146238	+	0.0844307i
$537$		0			0
$538$	−202.650	−	117.000i	−0.376673	−	0.217472i
$539$			373.352i			0.692676i
$540$		0			0
$541$	−248.000			−0.458410			−0.229205	−	0.973378i	$-0.573613\pi$
$541$	−248.000			−0.458410			−0.229205	+	0.973378i	$0.573613\pi$
$542$	−155.563	+	269.444i	−0.287018	+	0.497129i
$543$		0			0
$544$	−4.00000	−	6.92820i	−0.00735294	−	0.0127357i
$545$	−175.997	+	656.830i	−0.322930	+	1.20519i
$546$		0			0
$547$	263.272	+	152.000i	0.481301	+	0.277879i	0.720959	−	0.692978i	$-0.243702\pi$
$547$	263.272	+	152.000i	0.481301	+	0.277879i	−0.239657	+	0.970858i	$0.577035\pi$
$548$	−25.4558			−0.0464523
$549$		0			0
$550$	−400.000			−0.727273
$551$	−793.635	−	458.205i	−1.44035	−	0.831588i
$552$		0			0
$553$	−124.708	+	72.0000i	−0.225511	+	0.130199i
$554$	2.44949	−	1.41421i	0.00442146	−	0.00255273i
$555$		0			0
$556$	−8.00000	+	13.8564i	−0.0143885	+	0.0249216i
$557$	−886.712			−1.59194			−0.795971	−	0.605335i	$-0.793039\pi$
$557$	−886.712			−1.59194			−0.795971	+	0.605335i	$0.793039\pi$
$558$		0			0
$559$	−1440.00			−2.57603
$560$	20.7055	+	77.2741i	0.0369741	+	0.137989i
$561$		0			0
$562$	15.5885	−	9.00000i	0.0277375	−	0.0160142i
$563$	−19.7990	−	34.2929i	−0.0351669	−	0.0609109i	0.847906	−	0.530146i	$-0.177863\pi$
$563$	−19.7990	−	34.2929i	−0.0351669	−	0.0609109i	−0.883073	+	0.469235i	$0.844530\pi$
$564$		0			0
$565$	61.4711	−	16.4711i	0.108798	−	0.0291525i
$566$		−	667.509i		−	1.17934i
$567$		0			0
$568$			144.000i			0.253521i
$569$	−37.9671	−	21.9203i	−0.0667260	−	0.0385243i	0.466266	−	0.884645i	$-0.345599\pi$
$569$	−37.9671	−	21.9203i	−0.0667260	−	0.0385243i	−0.532992	+	0.846120i	$0.678932\pi$
$570$		0			0
$571$	196.000	+	339.482i	0.343257	+	0.594539i	0.985036	−	0.172351i	$-0.0551363\pi$
$571$	196.000	+	339.482i	0.343257	+	0.594539i	−0.641778	+	0.766890i	$0.721803\pi$
$572$	−203.647	−	352.727i	−0.356026	−	0.616655i
$573$		0			0
$574$	−68.0000	+	117.779i	−0.118467	+	0.205191i
$575$		−	989.949i		−	1.72165i
$576$		0			0
$577$		−	112.000i		−	0.194107i	−0.995279	−	0.0970537i	$-0.969058\pi$
$577$		−	112.000i		−	0.194107i	0.995279	−	0.0970537i	$-0.0309419\pi$
$578$	202.940	−	351.502i	0.351107	−	0.608135i
$579$		0			0
$580$	−368.827	−	98.8269i	−0.635908	−	0.170391i
$581$	19.5959	−	11.3137i	0.0337279	−	0.0194728i
$582$		0			0
$583$	−41.5692	−	24.0000i	−0.0713023	−	0.0411664i
$584$			130.108i			0.222787i
$585$		0			0
$586$	−582.000			−0.993174
$587$	576.999	−	999.392i	0.982963	−	1.70254i	0.332302	−	0.943173i	$-0.392175\pi$
$587$	576.999	−	999.392i	0.982963	−	1.70254i	0.650661	−	0.759368i	$-0.274492\pi$
$588$		0			0
$589$	48.0000	+	83.1384i	0.0814941	+	0.141152i
$590$	425.007	+	113.880i	0.720351	+	0.193018i
$591$		0			0
$592$	−193.990	−	112.000i	−0.327685	−	0.189189i
$593$	−258.801			−0.436427			−0.218213	−	0.975901i	$-0.570023\pi$
$593$	−258.801			−0.436427			−0.218213	+	0.975901i	$0.570023\pi$
$594$		0			0
$595$	20.0000	−	20.0000i	0.0336134	−	0.0336134i
$596$	208.207	+	120.208i	0.349340	+	0.201692i
$597$		0			0
$598$	872.954	−	504.000i	1.45979	−	0.842809i
$599$	249.848	−	144.250i	0.417108	−	0.240818i	−0.276731	−	0.960947i	$-0.589251\pi$
$599$	249.848	−	144.250i	0.417108	−	0.240818i	0.693839	+	0.720130i	$0.255918\pi$
$600$		0			0
$601$	431.000	−	746.514i	0.717138	−	1.24212i	−0.244991	−	0.969525i	$-0.578785\pi$
$601$	431.000	−	746.514i	0.717138	−	1.24212i	0.962129	−	0.272594i	$-0.0878817\pi$
$602$	−452.548			−0.751741
$603$		0			0
$604$	344.000			0.569536
$605$	33.8074	−	9.05867i	0.0558800	−	0.0149730i
$606$		0			0
$607$	−682.428	+	394.000i	−1.12426	+	0.649094i	−0.942486	−	0.334246i	$-0.891518\pi$
$607$	−682.428	+	394.000i	−1.12426	+	0.649094i	−0.181778	+	0.983340i	$0.558185\pi$
$608$	67.8823	+	117.576i	0.111648	+	0.193381i
$609$		0			0
$610$	−751.314	+	201.314i	−1.23166	+	0.330023i
$611$		−	509.117i		−	0.833252i
$612$		0			0
$613$			952.000i			1.55302i	0.630106	+	0.776509i	$0.283011\pi$
$613$			952.000i			1.55302i	−0.630106	+	0.776509i	$0.716989\pi$
$614$	440.908	+	254.558i	0.718091	+	0.414590i
$615$		0			0
$616$	−64.0000	−	110.851i	−0.103896	−	0.179953i
$617$	−191.626	−	331.906i	−0.310577	−	0.537935i	0.667911	−	0.744242i	$-0.267189\pi$
$617$	−191.626	−	331.906i	−0.310577	−	0.537935i	−0.978487	+	0.206307i	$0.933856\pi$
$618$		0			0
$619$	−152.000	+	263.272i	−0.245557	+	0.425318i	−0.962288	−	0.272032i	$-0.912304\pi$
$619$	−152.000	+	263.272i	−0.245557	+	0.425318i	0.716731	+	0.697350i	$0.245638\pi$
$620$	28.2843	+	28.2843i	0.0456198	+	0.0456198i
$621$		0			0
$622$			48.0000i			0.0771704i
$623$	115.966	−	200.858i	0.186140	−	0.322405i
$624$		0			0
$625$	312.500	+	541.266i	0.500000	+	0.866025i
$626$	−509.494	+	294.156i	−0.813888	+	0.469898i
$627$		0			0
$628$	263.272	+	152.000i	0.419222	+	0.242038i
$629$			79.1960i			0.125908i
$630$		0			0
$631$	860.000			1.36292			0.681458	−	0.731857i	$-0.261346\pi$
$631$	860.000			1.36292			0.681458	+	0.731857i	$0.261346\pi$
$632$	−50.9117	+	88.1816i	−0.0805565	+	0.139528i
$633$		0			0
$634$	53.0000	+	91.7987i	0.0835962	+	0.144793i
$635$	−135.230	−	36.2347i	−0.212960	−	0.0570625i
$636$		0			0
$637$	514.419	+	297.000i	0.807565	+	0.466248i
$638$	610.940			0.957587
$639$		0			0
$640$	40.0000	+	40.0000i	0.0625000	+	0.0625000i
$641$	383.345	+	221.324i	0.598042	+	0.345280i	0.768271	−	0.640125i	$-0.221117\pi$
$641$	383.345	+	221.324i	0.598042	+	0.345280i	−0.170229	+	0.985405i	$0.554451\pi$
$642$		0			0
$643$	−561.184	+	324.000i	−0.872760	+	0.503888i	−0.868264	−	0.496102i	$-0.834764\pi$
$643$	−561.184	+	324.000i	−0.872760	+	0.503888i	−0.00449534	+	0.999990i	$0.501431\pi$
$644$	274.343	−	158.392i	0.425998	−	0.245950i
$645$		0			0
$646$	24.0000	−	41.5692i	0.0371517	−	0.0643486i
$647$	390.323			0.603281			0.301641	−	0.953422i	$-0.402466\pi$
$647$	390.323			0.603281			0.301641	+	0.953422i	$0.402466\pi$
$648$		0			0
$649$	−704.000			−1.08475
$650$	−318.198	+	551.135i	−0.489535	+	0.847900i
$651$		0			0
$652$	180.133	−	104.000i	0.276278	−	0.159509i
$653$	454.670	+	787.511i	0.696278	+	1.20599i	0.969748	+	0.244109i	$0.0784953\pi$
$653$	454.670	+	787.511i	0.696278	+	1.20599i	−0.273470	+	0.961881i	$0.588171\pi$
$654$		0			0
$655$	−109.808	−	409.808i	−0.167645	−	0.625660i
$656$			96.1665i			0.146595i
$657$		0			0
$658$		−	160.000i		−	0.243161i
$659$	298.838	+	172.534i	0.453472	+	0.261812i	0.709295	−	0.704912i	$-0.249013\pi$
$659$	298.838	+	172.534i	0.453472	+	0.261812i	−0.255824	+	0.966723i	$0.582347\pi$
$660$		0			0
$661$	−481.000	−	833.116i	−0.727685	−	1.26039i	−0.957859	−	0.287238i	$-0.907263\pi$
$661$	−481.000	−	833.116i	−0.727685	−	1.26039i	0.230174	−	0.973150i	$-0.426071\pi$
$662$	328.098	+	568.282i	0.495616	+	0.858431i
$663$		0			0
$664$	8.00000	−	13.8564i	0.0120482	−	0.0208681i
$665$	−339.411	+	339.411i	−0.510393	+	0.510393i
$666$		0			0
$667$			1512.00i			2.26687i
$668$	−203.647	+	352.727i	−0.304860	+	0.528034i
$669$		0			0
$670$	−218.564	−	58.5641i	−0.326215	−	0.0874091i
$671$	1077.78	−	622.254i	1.60622	−	0.927353i
$672$		0			0
$673$	−207.846	−	120.000i	−0.308835	−	0.178306i	0.337570	−	0.941300i	$-0.390395\pi$
$673$	−207.846	−	120.000i	−0.308835	−	0.178306i	−0.646405	+	0.762994i	$0.723728\pi$
$674$			87.6812i			0.130091i
$675$		0			0
$676$	−310.000			−0.458580
$677$	−166.170	+	287.815i	−0.245451	+	0.425133i	−0.962258	−	0.272138i	$-0.912269\pi$
$677$	−166.170	+	287.815i	−0.245451	+	0.425133i	0.716808	+	0.697271i	$0.245603\pi$
$678$		0			0
$679$	28.0000	+	48.4974i	0.0412371	+	0.0714248i
$680$	5.17638	−	19.3185i	0.00761232	−	0.0284096i
$681$		0			0
$682$	−55.4256	−	32.0000i	−0.0812692	−	0.0469208i
$683$	1012.58			1.48254			0.741272	−	0.671205i	$-0.234223\pi$
$683$	1012.58			1.48254			0.741272	+	0.671205i	$0.234223\pi$
$684$		0			0
$685$	−45.0000	−	45.0000i	−0.0656934	−	0.0656934i
$686$	401.716	+	231.931i	0.585592	+	0.338092i
$687$		0			0
$688$	−277.128	+	160.000i	−0.402803	+	0.232558i
$689$	−66.1362	+	38.1838i	−0.0959887	+	0.0554191i
$690$		0			0
$691$	40.0000	−	69.2820i	0.0578871	−	0.100263i	−0.835630	−	0.549293i	$-0.814897\pi$
$691$	40.0000	−	69.2820i	0.0578871	−	0.100263i	0.893517	+	0.449030i	$0.148230\pi$
$692$	461.034			0.666234
$693$		0			0
$694$	648.000			0.933718
$695$	−38.6370	+	10.3528i	−0.0555929	+	0.0148961i
$696$		0			0
$697$	29.4449	−	17.0000i	0.0422451	−	0.0243902i
$698$	100.409	+	173.914i	0.143853	+	0.249160i
$699$		0			0
$700$	−100.000	+	173.205i	−0.142857	+	0.247436i
$701$			558.614i			0.796882i	0.917194	+	0.398441i	$0.130449\pi$
$701$			558.614i			0.796882i	−0.917194	+	0.398441i	$0.869551\pi$
$702$		0			0
$703$		−	1344.00i		−	1.91181i
$704$	−78.3837	−	45.2548i	−0.111340	−	0.0642824i
$705$		0			0
$706$	71.0000	+	122.976i	0.100567	+	0.174186i
$707$	−53.7401	−	93.0806i	−0.0760115	−	0.131656i
$708$		0			0
$709$	−156.000	+	270.200i	−0.220028	+	0.381100i	−0.954816	−	0.297197i	$-0.903948\pi$
$709$	−156.000	+	270.200i	−0.220028	+	0.381100i	0.734788	+	0.678297i	$0.237282\pi$
$710$	−254.558	+	254.558i	−0.358533	+	0.358533i
$711$		0			0
$712$		−	164.000i		−	0.230337i
$713$	79.1960	−	137.171i	0.111074	−	0.192386i
$714$		0			0
$715$	263.538	−	983.538i	0.368585	−	1.37558i
$716$	284.141	−	164.049i	0.396845	−	0.229118i
$717$		0			0
$718$	478.046	+	276.000i	0.665802	+	0.384401i
$719$		−	1148.34i		−	1.59714i	−0.601904	−	0.798568i	$-0.705591\pi$
$719$		−	1148.34i		−	1.59714i	0.601904	−	0.798568i	$-0.294409\pi$
$720$		0			0
$721$	272.000			0.377254
$722$	−152.028	+	263.320i	−0.210565	+	0.364709i
$723$		0			0
$724$	−8.00000	−	13.8564i	−0.0110497	−	0.0191387i
$725$	−477.297	−	826.703i	−0.658341	−	1.14028i
$726$		0			0
$727$	405.300	+	234.000i	0.557496	+	0.321871i	0.752140	−	0.659003i	$-0.229022\pi$
$727$	405.300	+	234.000i	0.557496	+	0.321871i	−0.194644	+	0.980874i	$0.562355\pi$
$728$	−203.647			−0.279735
$729$		0			0
$730$	−230.000	+	230.000i	−0.315068	+	0.315068i
$731$	97.9796	+	56.5685i	0.134035	+	0.0773851i
$732$		0			0
$733$	−455.529	+	263.000i	−0.621459	+	0.358799i	−0.777437	−	0.628961i	$-0.783480\pi$
$733$	−455.529	+	263.000i	−0.621459	+	0.358799i	0.155978	+	0.987761i	$0.450147\pi$
$734$	347.828	−	200.818i	0.473879	−	0.273594i
$735$		0			0
$736$	112.000	−	193.990i	0.152174	−	0.263573i
$737$	362.039			0.491233
$738$		0			0
$739$	344.000			0.465494			0.232747	−	0.972537i	$-0.425229\pi$
$739$	344.000			0.465494			0.232747	+	0.972537i	$0.425229\pi$
$740$	−144.939	−	540.918i	−0.195863	−	0.730971i
$741$		0			0
$742$	−20.7846	+	12.0000i	−0.0280116	+	0.0161725i
$743$	339.411	+	587.878i	0.456812	+	0.791221i	0.998790	−	0.0491709i	$-0.0156579\pi$
$743$	339.411	+	587.878i	0.456812	+	0.791221i	−0.541978	+	0.840392i	$0.682325\pi$
$744$		0			0
$745$	155.561	+	580.561i	0.208806	+	0.779276i
$746$			509.117i			0.682462i
$747$		0			0
$748$			32.0000i			0.0427807i
$749$	−587.878	−	339.411i	−0.784883	−	0.453153i
$750$		0			0
$751$	−154.000	−	266.736i	−0.205060	−	0.355174i	0.745092	−	0.666962i	$-0.232406\pi$
$751$	−154.000	−	266.736i	−0.205060	−	0.355174i	−0.950152	+	0.311788i	$0.899072\pi$
$752$	−56.5685	−	97.9796i	−0.0752241	−	0.130292i
$753$		0			0
$754$	486.000	−	841.777i	0.644562	−	1.11641i
$755$	608.112	+	608.112i	0.805446	+	0.805446i
$756$		0			0
$757$		−	610.000i		−	0.805812i	−0.915241	−	0.402906i	$-0.868000\pi$
$757$		−	610.000i		−	0.805812i	0.915241	−	0.402906i	$-0.132000\pi$
$758$	226.274	−	391.918i	0.298515	−	0.517043i
$759$		0			0
$760$	−87.8461	+	327.846i	−0.115587	+	0.431376i
$761$	1017.76	−	587.606i	1.33740	−	0.772149i	0.350981	−	0.936383i	$-0.385848\pi$
$761$	1017.76	−	587.606i	1.33740	−	0.772149i	0.986422	+	0.164233i	$0.0525150\pi$
$762$		0			0
$763$	−471.118	−	272.000i	−0.617455	−	0.356488i
$764$		−	610.940i		−	0.799660i
$765$		0			0
$766$	−256.000			−0.334204
$767$	−560.029	+	969.998i	−0.730155	+	1.26466i
$768$		0			0
$769$	135.000	+	233.827i	0.175553	+	0.304066i	0.940352	−	0.340202i	$-0.110495\pi$
$769$	135.000	+	233.827i	0.175553	+	0.304066i	−0.764800	+	0.644268i	$0.777162\pi$
$770$	82.8221	−	309.096i	0.107561	−	0.401424i
$771$		0			0
$772$	−110.851	−	64.0000i	−0.143590	−	0.0829016i
$773$	−267.286			−0.345778			−0.172889	−	0.984941i	$-0.555310\pi$
$773$	−267.286			−0.345778			−0.172889	+	0.984941i	$0.555310\pi$
$774$		0			0
$775$			100.000i			0.129032i
$776$	34.2929	+	19.7990i	0.0441918	+	0.0255142i
$777$		0			0
$778$	−840.045	+	485.000i	−1.07975	+	0.623393i
$779$	−499.696	+	288.500i	−0.641458	+	0.370346i
$780$		0			0
$781$	288.000	−	498.831i	0.368758	−	0.638708i
$782$	−79.1960			−0.101274
$783$		0			0
$784$	132.000			0.168367
$785$	196.702	+	734.104i	0.250576	+	0.935164i
$786$		0			0
$787$	1316.36	−	760.000i	1.67263	−	0.965693i	0.706470	−	0.707743i	$-0.250286\pi$
$787$	1316.36	−	760.000i	1.67263	−	0.965693i	0.966158	−	0.257950i	$-0.0830469\pi$
$788$	230.517	+	399.267i	0.292534	+	0.506684i
$789$		0			0
$790$	−245.885	+	65.8846i	−0.311246	+	0.0833982i
$791$			50.9117i			0.0643637i
$792$		0			0
$793$		−	1980.00i		−	2.49685i
$794$	−362.524	−	209.304i	−0.456580	−	0.263607i
$795$		0			0
$796$	−300.000	−	519.615i	−0.376884	−	0.652783i
$797$	194.454	+	336.805i	0.243983	+	0.422591i	0.961845	−	0.273594i	$-0.0882126\pi$
$797$	194.454	+	336.805i	0.243983	+	0.422591i	−0.717862	+	0.696185i	$0.754879\pi$
$798$		0			0
$799$	−20.0000	+	34.6410i	−0.0250313	+	0.0433555i
$800$			141.421i			0.176777i
$801$		0			0
$802$		−	622.000i		−	0.775561i
$803$	260.215	−	450.706i	0.324054	−	0.561278i
$804$		0			0
$805$	764.974	+	204.974i	0.950279	+	0.254626i
$806$	−88.1816	+	50.9117i	−0.109406	+	0.0631659i
$807$		0			0
$808$	−65.8179	−	38.0000i	−0.0814578	−	0.0470297i
$809$		−	46.6690i		−	0.0576873i	−0.999584	−	0.0288437i	$-0.990818\pi$
$809$		−	46.6690i		−	0.0576873i	0.999584	−	0.0288437i	$-0.00918250\pi$
$810$		0			0
$811$	1120.00			1.38101			0.690506	−	0.723327i	$-0.257388\pi$
$811$	1120.00			1.38101			0.690506	+	0.723327i	$0.257388\pi$
$812$	152.735	−	264.545i	0.188097	−	0.325794i
$813$		0			0
$814$	448.000	+	775.959i	0.550369	+	0.953266i
$815$	502.281	+	134.586i	0.616296	+	0.165136i
$816$		0			0
$817$	−1662.77	−	960.000i	−2.03521	−	1.17503i
$818$	−520.431			−0.636223
$819$		0			0
$820$	−170.000	+	170.000i	−0.207317	+	0.207317i
$821$	1101.05	+	635.689i	1.34110	+	0.774286i	0.986969	−	0.160909i	$-0.0514424\pi$
$821$	1101.05	+	635.689i	1.34110	+	0.774286i	0.354134	+	0.935195i	$0.384776\pi$
$822$		0			0
$823$	717.069	−	414.000i	0.871287	−	0.503038i	0.00351115	−	0.999994i	$-0.498882\pi$
$823$	717.069	−	414.000i	0.871287	−	0.503038i	0.867776	+	0.496956i	$0.165549\pi$
$824$	166.565	−	96.1665i	0.202142	−	0.116707i
$825$		0			0
$826$	−176.000	+	304.841i	−0.213075	+	0.369057i
$827$	158.392			0.191526			0.0957629	−	0.995404i	$-0.469471\pi$
$827$	158.392			0.191526			0.0957629	+	0.995404i	$0.469471\pi$
$828$		0			0
$829$	−552.000			−0.665862			−0.332931	−	0.942951i	$-0.608038\pi$
$829$	−552.000			−0.665862			−0.332931	+	0.942951i	$0.608038\pi$
$830$	38.6370	−	10.3528i	0.0465506	−	0.0124732i
$831$		0			0
$832$	−124.708	+	72.0000i	−0.149889	+	0.0865385i
$833$	−23.3345	−	40.4166i	−0.0280126	−	0.0485193i
$834$		0			0
$835$	−983.538	+	263.538i	−1.17789	+	0.315615i
$836$		−	543.058i		−	0.649591i
$837$		0			0
$838$			272.000i			0.324582i
$839$	739.746	+	427.092i	0.881700	+	0.509049i	0.871218	−	0.490896i	$-0.163330\pi$
$839$	739.746	+	427.092i	0.881700	+	0.509049i	0.0104811	+	0.999945i	$0.496664\pi$
$840$		0			0
$841$	308.500	+	534.338i	0.366825	+	0.635360i
$842$	−197.990	−	342.929i	−0.235142	−	0.407279i
$843$		0			0
$844$	264.000	−	457.261i	0.312796	−	0.541779i
$845$	−548.008	−	548.008i	−0.648530	−	0.648530i
$846$		0			0
$847$			28.0000i			0.0330579i
$848$	−8.48528	+	14.6969i	−0.0100062	+	0.0173313i
$849$		0			0
$850$	43.3013	−	25.0000i	0.0509427	−	0.0294118i
$851$	−1920.40	+	1108.74i	−2.25664	+	1.30287i
$852$		0			0
$853$	741.318	+	428.000i	0.869071	+	0.501758i	0.867039	−	0.498239i	$-0.166020\pi$
$853$	741.318	+	428.000i	0.869071	+	0.501758i	0.00203173	+	0.999998i	$0.499353\pi$
$854$		−	622.254i		−	0.728635i
$855$		0			0
$856$	−480.000			−0.560748
$857$	277.893	−	481.325i	0.324263	−	0.561639i	−0.657100	−	0.753803i	$-0.728217\pi$
$857$	277.893	−	481.325i	0.324263	−	0.561639i	0.981363	+	0.192164i	$0.0615506\pi$
$858$		0			0
$859$	−236.000	−	408.764i	−0.274738	−	0.475860i	0.695331	−	0.718690i	$-0.255258\pi$
$859$	−236.000	−	408.764i	−0.274738	−	0.475860i	−0.970069	+	0.242829i	$0.921924\pi$
$860$	−772.741	−	207.055i	−0.898536	−	0.240762i
$861$		0			0
$862$	−117.779	−	68.0000i	−0.136635	−	0.0788863i
$863$	−441.235			−0.511280			−0.255640	−	0.966772i	$-0.582286\pi$
$863$	−441.235			−0.511280			−0.255640	+	0.966772i	$0.582286\pi$
$864$		0			0
$865$	815.000	+	815.000i	0.942197	+	0.942197i
$866$	−842.624	−	486.489i	−0.973007	−	0.561766i
$867$		0			0
$868$	−27.7128	+	16.0000i	−0.0319272	+	0.0184332i
$869$	352.727	−	203.647i	0.405899	−	0.234346i
$870$		0			0
$871$	288.000	−	498.831i	0.330654	−	0.572710i
$872$	−384.666			−0.441131
$873$		0			0
$874$	1344.00			1.53776
$875$	−482.963	+	129.410i	−0.551958	+	0.147897i
$876$		0			0
$877$	−588.897	+	340.000i	−0.671491	+	0.387685i	−0.796641	−	0.604452i	$-0.793392\pi$
$877$	−588.897	+	340.000i	−0.671491	+	0.387685i	0.125151	+	0.992138i	$0.460059\pi$
$878$	−229.103	−	396.817i	−0.260937	−	0.451956i
$879$		0			0
$880$	−58.5641	−	218.564i	−0.0665501	−	0.248368i
$881$			292.742i			0.332284i	0.986102	+	0.166142i	$0.0531310\pi$
$881$			292.742i			0.332284i	−0.986102	+	0.166142i	$0.946869\pi$
$882$		0			0
$883$			696.000i			0.788222i	0.919063	+	0.394111i	$0.128947\pi$
$883$			696.000i			0.788222i	−0.919063	+	0.394111i	$0.871053\pi$
$884$	44.0908	+	25.4558i	0.0498765	+	0.0287962i
$885$		0			0
$886$	228.000	+	394.908i	0.257336	+	0.445720i
$887$	441.235	+	764.241i	0.497446	+	0.861602i	0.999996	−	0.00294656i	$-0.000937921\pi$
$887$	441.235	+	764.241i	0.497446	+	0.861602i	−0.502550	+	0.864548i	$0.667605\pi$
$888$		0			0
$889$	56.0000	−	96.9948i	0.0629921	−	0.109106i
$890$	289.914	−	289.914i	0.325746	−	0.325746i
$891$		0			0
$892$			632.000i			0.708520i
$893$	339.411	−	587.878i	0.380080	−	0.658318i
$894$		0			0
$895$	792.295	+	212.295i	0.885246	+	0.237201i
$896$	−39.1918	+	22.6274i	−0.0437409	+	0.0252538i
$897$		0			0
$898$	150.688	+	87.0000i	0.167804	+	0.0968820i
$899$		−	152.735i		−	0.169894i
$900$		0			0
$901$	6.00000			0.00665927
$902$	192.333	−	333.131i	0.213230	−	0.369324i
$903$		0			0
$904$	18.0000	+	31.1769i	0.0199115	+	0.0344877i
$905$	10.3528	−	38.6370i	0.0114395	−	0.0426929i
$906$		0			0
$907$	457.261	+	264.000i	0.504147	+	0.291069i	0.730425	−	0.682993i	$-0.239322\pi$
$907$	457.261	+	264.000i	0.504147	+	0.291069i	−0.226277	+	0.974063i	$0.572656\pi$
$908$	−192.333			−0.211821
$909$		0			0
$910$	−360.000	−	360.000i	−0.395604	−	0.395604i
$911$	−1381.51	−	797.616i	−1.51648	−	0.875539i	−0.999813	−	0.0193525i	$-0.993840\pi$
$911$	−1381.51	−	797.616i	−1.51648	−	0.875539i	−0.516666	−	0.856187i	$-0.672827\pi$
$912$		0			0
$913$	−55.4256	+	32.0000i	−0.0607071	+	0.0350493i
$914$	−159.217	+	91.9239i	−0.174198	+	0.100573i
$915$		0			0
$916$	8.00000	−	13.8564i	0.00873362	−	0.0151271i
$917$	339.411			0.370132
$918$		0			0
$919$	−660.000			−0.718172			−0.359086	−	0.933304i	$-0.616912\pi$
$919$	−660.000			−0.718172			−0.359086	+	0.933304i	$0.616912\pi$
$920$	540.918	−	144.939i	0.587955	−	0.157542i
$921$		0			0
$922$	576.773	−	333.000i	0.625567	−	0.361171i
$923$	−458.205	−	793.635i	−0.496430	−	0.859843i
$924$		0			0
$925$	700.000	−	1212.44i	0.756757	−	1.31074i
$926$			627.911i			0.678089i
$927$		0			0
$928$		−	216.000i		−	0.232759i
$929$	−870.794	−	502.753i	−0.937345	−	0.541176i	−0.0482180	−	0.998837i	$-0.515354\pi$
$929$	−870.794	−	502.753i	−0.937345	−	0.541176i	−0.889127	+	0.457660i	$0.848688\pi$
$930$		0			0
$931$	396.000	+	685.892i	0.425349	+	0.736726i
$932$	227.688	+	394.368i	0.244301	+	0.423141i
$933$		0			0
$934$	−132.000	+	228.631i	−0.141328	+	0.244787i
$935$	−56.5685	+	56.5685i	−0.0605011	+	0.0605011i
$936$		0			0
$937$		−	1568.00i		−	1.67343i	−0.547642	−	0.836713i	$-0.684474\pi$
$937$		−	1568.00i		−	1.67343i	0.547642	−	0.836713i	$-0.315526\pi$
$938$	90.5097	−	156.767i	0.0964922	−	0.167129i
$939$		0			0
$940$	73.2051	−	273.205i	0.0778777	−	0.290644i
$941$	−552.360	+	318.905i	−0.586992	+	0.338900i	−0.763907	−	0.645326i	$-0.776722\pi$
$941$	−552.360	+	318.905i	−0.586992	+	0.338900i	0.176915	+	0.984226i	$0.443388\pi$
$942$		0			0
$943$	824.456	+	476.000i	0.874291	+	0.504772i
$944$			248.902i			0.263667i
$945$		0			0
$946$	1280.00			1.35307
$947$	−814.587	+	1410.91i	−0.860176	+	1.48987i	0.0115819	+	0.999933i	$0.496313\pi$
$947$	−814.587	+	1410.91i	−0.860176	+	1.48987i	−0.871758	+	0.489936i	$0.837020\pi$
$948$		0			0
$949$	−414.000	−	717.069i	−0.436249	−	0.755605i
$950$	−734.847	+	424.264i	−0.773523	+	0.446594i
$951$		0			0
$952$	13.8564	+	8.00000i	0.0145550	+	0.00840336i
$953$	−914.996			−0.960122			−0.480061	−	0.877235i	$-0.659385\pi$
$953$	−914.996			−0.960122			−0.480061	+	0.877235i	$0.659385\pi$
$954$		0			0
$955$	1080.00	−	1080.00i	1.13089	−	1.13089i
$956$	−333.131	−	192.333i	−0.348463	−	0.201185i
$957$		0			0
$958$	713.605	−	412.000i	0.744890	−	0.430063i
$959$	44.0908	−	25.4558i	0.0459758	−	0.0265442i
$960$		0			0
$961$	472.500	−	818.394i	0.491675	−	0.851607i
$962$	1425.53			1.48184
$963$		0			0
$964$	−256.000			−0.265560
$965$	−82.8221	−	309.096i	−0.0858260	−	0.320307i
$966$		0			0
$967$	−433.013	+	250.000i	−0.447790	+	0.258532i	−0.706896	−	0.707317i	$-0.749905\pi$
$967$	−433.013	+	250.000i	−0.447790	+	0.258532i	0.259107	+	0.965849i	$0.416572\pi$
$968$	9.89949	+	17.1464i	0.0102268	+	0.0177133i
$969$		0			0
$970$	25.6218	+	95.6218i	0.0264142	+	0.0985792i
$971$		−	1221.88i		−	1.25837i	−0.777254	−	0.629187i	$-0.783388\pi$
$971$		−	1221.88i		−	1.25837i	0.777254	−	0.629187i	$-0.216612\pi$
$972$		0			0
$973$		−	32.0000i		−	0.0328880i
$974$	102.879	+	59.3970i	0.105625	+	0.0609825i
$975$		0			0
$976$	−220.000	−	381.051i	−0.225410	−	0.390421i
$977$	871.863	+	1510.11i	0.892388	+	1.54566i	0.837005	+	0.547195i	$0.184305\pi$
$977$	871.863	+	1510.11i	0.892388	+	1.54566i	0.0553827	+	0.998465i	$0.482362\pi$
$978$		0			0
$979$	−328.000	+	568.113i	−0.335036	+	0.580299i
$980$	233.345	+	233.345i	0.238107	+	0.238107i
$981$		0			0
$982$		−	456.000i		−	0.464358i
$983$	39.5980	−	68.5857i	0.0402828	−	0.0697718i	−0.845181	−	0.534480i	$-0.820507\pi$
$983$	39.5980	−	68.5857i	0.0402828	−	0.0697718i	0.885464	+	0.464708i	$0.153841\pi$
$984$		0			0
$985$	−298.311	+	1113.31i	−0.302854	+	1.13026i
$986$	−66.1362	+	38.1838i	−0.0670753	+	0.0387259i
$987$		0			0
$988$	−748.246	−	432.000i	−0.757334	−	0.437247i
$989$			3167.84i			3.20307i
$990$		0			0
$991$	748.000			0.754793			0.377397	−	0.926052i	$-0.376819\pi$
$991$	748.000			0.754793			0.377397	+	0.926052i	$0.376819\pi$
$992$	−11.3137	+	19.5959i	−0.0114049	+	0.0197539i
$993$		0			0
$994$	−144.000	−	249.415i	−0.144869	−	0.250921i
$995$	388.229	−	1448.89i	0.390179	−	1.45617i
$996$		0			0
$997$	−1267.86	−	732.000i	−1.27168	−	0.734203i	−0.296373	−	0.955072i	$-0.595777\pi$
$997$	−1267.86	−	732.000i	−1.27168	−	0.734203i	−0.975303	+	0.220870i	$0.929110\pi$
$998$	644.881			0.646174
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.3.j.d.269.2		8
3.2	odd	2	inner	810.3.j.d.269.3		8
5.4	even	2	inner	810.3.j.d.269.4		8
9.2	odd	6		90.3.b.a.89.1	✓	4
9.4	even	3	inner	810.3.j.d.539.1		8
9.5	odd	6	inner	810.3.j.d.539.4		8
9.7	even	3		90.3.b.a.89.4	yes	4
15.14	odd	2	inner	810.3.j.d.269.1		8
36.7	odd	6		720.3.c.c.449.4		4
36.11	even	6		720.3.c.c.449.1		4
45.2	even	12		450.3.d.e.251.1		2
45.4	even	6	inner	810.3.j.d.539.3		8
45.7	odd	12		450.3.d.e.251.2		2
45.14	odd	6	inner	810.3.j.d.539.2		8
45.29	odd	6		90.3.b.a.89.3	yes	4
45.34	even	6		90.3.b.a.89.2	yes	4
45.38	even	12		450.3.d.b.251.2		2
45.43	odd	12		450.3.d.b.251.1		2
72.11	even	6		2880.3.c.a.449.4		4
72.29	odd	6		2880.3.c.h.449.4		4
72.43	odd	6		2880.3.c.a.449.1		4
72.61	even	6		2880.3.c.h.449.1		4
180.7	even	12		3600.3.l.c.1601.1		2
180.43	even	12		3600.3.l.i.1601.1		2
180.47	odd	12		3600.3.l.c.1601.2		2
180.79	odd	6		720.3.c.c.449.2		4
180.83	odd	12		3600.3.l.i.1601.2		2
180.119	even	6		720.3.c.c.449.3		4
360.29	odd	6		2880.3.c.h.449.2		4
360.259	odd	6		2880.3.c.a.449.3		4
360.299	even	6		2880.3.c.a.449.2		4
360.349	even	6		2880.3.c.h.449.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.b.a.89.1	✓	4	9.2	odd	6
90.3.b.a.89.2	yes	4	45.34	even	6
90.3.b.a.89.3	yes	4	45.29	odd	6
90.3.b.a.89.4	yes	4	9.7	even	3
450.3.d.b.251.1		2	45.43	odd	12
450.3.d.b.251.2		2	45.38	even	12
450.3.d.e.251.1		2	45.2	even	12
450.3.d.e.251.2		2	45.7	odd	12
720.3.c.c.449.1		4	36.11	even	6
720.3.c.c.449.2		4	180.79	odd	6
720.3.c.c.449.3		4	180.119	even	6
720.3.c.c.449.4		4	36.7	odd	6
810.3.j.d.269.1		8	15.14	odd	2	inner
810.3.j.d.269.2		8	1.1	even	1	trivial
810.3.j.d.269.3		8	3.2	odd	2	inner
810.3.j.d.269.4		8	5.4	even	2	inner
810.3.j.d.539.1		8	9.4	even	3	inner
810.3.j.d.539.2		8	45.14	odd	6	inner
810.3.j.d.539.3		8	45.4	even	6	inner
810.3.j.d.539.4		8	9.5	odd	6	inner
2880.3.c.a.449.1		4	72.43	odd	6
2880.3.c.a.449.2		4	360.299	even	6
2880.3.c.a.449.3		4	360.259	odd	6
2880.3.c.a.449.4		4	72.11	even	6
2880.3.c.h.449.1		4	72.61	even	6
2880.3.c.h.449.2		4	360.29	odd	6
2880.3.c.h.449.3		4	360.349	even	6
2880.3.c.h.449.4		4	72.29	odd	6
3600.3.l.c.1601.1		2	180.7	even	12
3600.3.l.c.1601.2		2	180.47	odd	12
3600.3.l.i.1601.1		2	180.43	even	12
3600.3.l.i.1601.2		2	180.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(1.29410 - 4.82963i) q^{5} +(3.46410 + 2.00000i) q^{7} +2.82843 q^{8} +O(q^{10})\)	\(q+(-0.707107 + 1.22474i) q^{2} +(-1.00000 - 1.73205i) q^{4} +(1.29410 - 4.82963i) q^{5} +(3.46410 + 2.00000i) q^{7} +2.82843 q^{8} +(5.00000 + 5.00000i) q^{10} +(-9.79796 - 5.65685i) q^{11} +(-15.5885 + 9.00000i) q^{13} +(-4.89898 + 2.82843i) q^{14} +(-2.00000 + 3.46410i) q^{16} +1.41421 q^{17} -24.0000 q^{19} +(-9.65926 + 2.58819i) q^{20} +(13.8564 - 8.00000i) q^{22} +(19.7990 + 34.2929i) q^{23} +(-21.6506 - 12.5000i) q^{25} -25.4558i q^{26} -8.00000i q^{28} +(33.0681 + 19.0919i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-2.82843 - 4.89898i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(14.1421 - 14.1421i) q^{35} +56.0000i q^{37} +(16.9706 - 29.3939i) q^{38} +(3.66025 - 13.6603i) q^{40} +(20.8207 - 12.0208i) q^{41} +(69.2820 + 40.0000i) q^{43} +22.6274i q^{44} -56.0000 q^{46} +(-14.1421 + 24.4949i) q^{47} +(-16.5000 - 28.5788i) q^{49} +(30.6186 - 17.6777i) q^{50} +(31.1769 + 18.0000i) q^{52} +4.24264 q^{53} +(-40.0000 + 40.0000i) q^{55} +(9.79796 + 5.65685i) q^{56} +(-46.7654 + 27.0000i) q^{58} +(53.8888 - 31.1127i) q^{59} +(-55.0000 + 95.2628i) q^{61} +5.65685 q^{62} +8.00000 q^{64} +(23.2937 + 86.9333i) q^{65} +(-27.7128 + 16.0000i) q^{67} +(-1.41421 - 2.44949i) q^{68} +(7.32051 + 27.3205i) q^{70} +50.9117i q^{71} +46.0000i q^{73} +(-68.5857 - 39.5980i) q^{74} +(24.0000 + 41.5692i) q^{76} +(-22.6274 - 39.1918i) q^{77} +(-18.0000 + 31.1769i) q^{79} +(14.1421 + 14.1421i) q^{80} +34.0000i q^{82} +(2.82843 - 4.89898i) q^{83} +(1.83013 - 6.83013i) q^{85} +(-97.9796 + 56.5685i) q^{86} +(-27.7128 - 16.0000i) q^{88} -57.9828i q^{89} -72.0000 q^{91} +(39.5980 - 68.5857i) q^{92} +(-20.0000 - 34.6410i) q^{94} +(-31.0583 + 115.911i) q^{95} +(12.1244 + 7.00000i) q^{97} +46.6690 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 8 q^{4}+O(q^{10}) \) 8 * q - 8 * q^4	\( 8 q - 8 q^{4} + 40 q^{10} - 16 q^{16} - 192 q^{19} - 16 q^{31} - 8 q^{34} - 40 q^{40} - 448 q^{46} - 132 q^{49} - 320 q^{55} - 440 q^{61} + 64 q^{64} - 80 q^{70} + 192 q^{76} - 144 q^{79} - 20 q^{85} - 576 q^{91} - 160 q^{94}+O(q^{100}) \) 8 * q - 8 * q^4 + 40 * q^10 - 16 * q^16 - 192 * q^19 - 16 * q^31 - 8 * q^34 - 40 * q^40 - 448 * q^46 - 132 * q^49 - 320 * q^55 - 440 * q^61 + 64 * q^64 - 80 * q^70 + 192 * q^76 - 144 * q^79 - 20 * q^85 - 576 * q^91 - 160 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more