LMFDB - Embedded newform 810.3.j.d.539.4

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			539.4
Root			$0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	810.539
Dual form			810.3.j.d.269.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.82963 - 1.29410i) q^{5} +(-3.46410 + 2.00000i) q^{7} -2.82843 q^{8} +O(q^{10})$	\(q+(0.707107 + 1.22474i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(4.82963 - 1.29410i) q^{5} +(-3.46410 + 2.00000i) q^{7} -2.82843 q^{8} +(5.00000 + 5.00000i) q^{10} +(-9.79796 + 5.65685i) q^{11} +(15.5885 + 9.00000i) q^{13} +(-4.89898 - 2.82843i) q^{14} +(-2.00000 - 3.46410i) q^{16} -1.41421 q^{17} -24.0000 q^{19} +(-2.58819 + 9.65926i) q^{20} +(-13.8564 - 8.00000i) q^{22} +(-19.7990 + 34.2929i) q^{23} +(21.6506 - 12.5000i) q^{25} +25.4558i q^{26} -8.00000i q^{28} +(33.0681 - 19.0919i) q^{29} +(-2.00000 + 3.46410i) q^{31} +(2.82843 - 4.89898i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(-14.1421 + 14.1421i) q^{35} +56.0000i q^{37} +(-16.9706 - 29.3939i) q^{38} +(-13.6603 + 3.66025i) q^{40} +(20.8207 + 12.0208i) q^{41} +(-69.2820 + 40.0000i) q^{43} -22.6274i q^{44} -56.0000 q^{46} +(14.1421 + 24.4949i) q^{47} +(-16.5000 + 28.5788i) q^{49} +(30.6186 + 17.6777i) q^{50} +(-31.1769 + 18.0000i) q^{52} -4.24264 q^{53} +(-40.0000 + 40.0000i) q^{55} +(9.79796 - 5.65685i) q^{56} +(46.7654 + 27.0000i) q^{58} +(53.8888 + 31.1127i) q^{59} +(-55.0000 - 95.2628i) q^{61} -5.65685 q^{62} +8.00000 q^{64} +(86.9333 + 23.2937i) q^{65} +(27.7128 + 16.0000i) q^{67} +(1.41421 - 2.44949i) q^{68} +(-27.3205 - 7.32051i) q^{70} -50.9117i q^{71} +46.0000i q^{73} +(-68.5857 + 39.5980i) q^{74} +(24.0000 - 41.5692i) q^{76} +(22.6274 - 39.1918i) q^{77} +(-18.0000 - 31.1769i) q^{79} +(-14.1421 - 14.1421i) q^{80} +34.0000i q^{82} +(-2.82843 - 4.89898i) q^{83} +(-6.83013 + 1.83013i) q^{85} +(-97.9796 - 56.5685i) q^{86} +(27.7128 - 16.0000i) q^{88} +57.9828i q^{89} -72.0000 q^{91} +(-39.5980 - 68.5857i) q^{92} +(-20.0000 + 34.6410i) q^{94} +(-115.911 + 31.0583i) q^{95} +(-12.1244 + 7.00000i) q^{97} -46.6690 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

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

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
$5$	4.82963	−	1.29410i	0.965926	−	0.258819i
$5$	4.82963	−	1.29410i	0.965926	−	0.258819i
$6$		0			0
$7$	−3.46410	+	2.00000i	−0.494872	+	0.285714i	−0.726593	−	0.687068i	$-0.758897\pi$
$7$	−3.46410	+	2.00000i	−0.494872	+	0.285714i	0.231722	+	0.972782i	$0.425564\pi$
$8$	−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	−0.874179	−	0.485604i	$-0.838600\pi$
$11$	−9.79796	+	5.65685i	−0.890724	+	0.514259i	−0.0165444	+	0.999863i	$0.505267\pi$
$12$		0			0
$13$	15.5885	+	9.00000i	1.19911	+	0.692308i	0.960357	−	0.278772i	$-0.0899274\pi$
$13$	15.5885	+	9.00000i	1.19911	+	0.692308i	0.238755	+	0.971080i	$0.423261\pi$
$14$	−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	$-0.513244\pi$
$17$	−1.41421			−0.0831890			−0.0415945	+	0.999135i	$0.513244\pi$
$18$		0			0
$19$	−24.0000			−1.26316			−0.631579	−	0.775312i	$-0.717593\pi$
$19$	−24.0000			−1.26316			−0.631579	+	0.775312i	$0.717593\pi$
$20$	−2.58819	+	9.65926i	−0.129410	+	0.482963i
$21$		0			0
$22$	−13.8564	−	8.00000i	−0.629837	−	0.363636i
$23$	−19.7990	+	34.2929i	−0.860826	+	1.49099i	0.0103075	+	0.999947i	$0.496719\pi$
$23$	−19.7990	+	34.2929i	−0.860826	+	1.49099i	−0.871133	+	0.491047i	$0.836614\pi$
$24$		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	0.193780	−	0.981045i	$-0.437925\pi$
$29$	33.0681	−	19.0919i	1.14028	−	0.658341i	0.946500	+	0.322704i	$0.104592\pi$
$30$		0			0
$31$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i	−0.896479	−	0.443086i	$-0.853884\pi$
$31$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i	0.831963	+	0.554831i	$0.187217\pi$
$32$	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
$40$	−13.6603	+	3.66025i	−0.341506	+	0.0915064i
$41$	20.8207	+	12.0208i	0.507821	+	0.293191i	0.731938	−	0.681372i	$-0.238616\pi$
$41$	20.8207	+	12.0208i	0.507821	+	0.293191i	−0.224116	+	0.974562i	$0.571950\pi$
$42$		0			0
$43$	−69.2820	+	40.0000i	−1.61121	+	0.930233i	−0.622120	+	0.782922i	$0.713728\pi$
$43$	−69.2820	+	40.0000i	−1.61121	+	0.930233i	−0.989090	+	0.147310i	$0.952938\pi$
$44$		−	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	$-0.0693808\pi$
$47$	14.1421	+	24.4949i	0.300897	+	0.521168i	−0.675443	+	0.737412i	$0.736047\pi$
$48$		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	$-0.512744\pi$
$53$	−4.24264			−0.0800498			−0.0400249	+	0.999199i	$0.512744\pi$
$54$		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	0.881514	−	0.472159i	$-0.156525\pi$
$59$	53.8888	+	31.1127i	0.913369	+	0.527334i	0.0318554	+	0.999492i	$0.489858\pi$
$60$		0			0
$61$	−55.0000	−	95.2628i	−0.901639	−	1.56169i	−0.825366	−	0.564598i	$-0.809031\pi$
$61$	−55.0000	−	95.2628i	−0.901639	−	1.56169i	−0.0762735	−	0.997087i	$-0.524302\pi$
$62$	−5.65685			−0.0912396
$63$		0			0
$64$	8.00000			0.125000
$65$	86.9333	+	23.2937i	1.33744	+	0.358365i
$66$		0			0
$67$	27.7128	+	16.0000i	0.413624	+	0.238806i	0.692346	−	0.721566i	$-0.256577\pi$
$67$	27.7128	+	16.0000i	0.413624	+	0.238806i	−0.278722	+	0.960372i	$0.589911\pi$
$68$	1.41421	−	2.44949i	0.0207973	−	0.0360219i
$69$		0			0
$70$	−27.3205	−	7.32051i	−0.390293	−	0.104579i
$71$		−	50.9117i		−	0.717066i	−0.933517	−	0.358533i	$-0.883277\pi$
$71$		−	50.9117i		−	0.717066i	0.933517	−	0.358533i	$-0.116723\pi$
$72$		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	0.729322	−	0.684171i	$-0.239836\pi$
$79$	−18.0000	−	31.1769i	−0.227848	−	0.394644i	−0.957170	+	0.289526i	$0.906502\pi$
$80$	−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	$-0.177516\pi$
$83$	−2.82843	−	4.89898i	−0.0340774	−	0.0590238i	−0.882561	+	0.470198i	$0.844183\pi$
$84$		0			0
$85$	−6.83013	+	1.83013i	−0.0803544	+	0.0215309i
$86$	−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	$0.105615\pi$
$89$			57.9828i			0.651492i	−0.945457	+	0.325746i	$0.894385\pi$
$90$		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
$95$	−115.911	+	31.0583i	−1.22012	+	0.326929i
$96$		0			0
$97$	−12.1244	+	7.00000i	−0.124993	+	0.0721649i	−0.561193	−	0.827685i	$-0.689657\pi$
$97$	−12.1244	+	7.00000i	−0.124993	+	0.0721649i	0.436200	+	0.899850i	$0.356324\pi$
$98$	−46.6690			−0.476215
$99$		0			0
$100$			50.0000i			0.500000i
$101$	−23.2702	+	13.4350i	−0.230398	+	0.133020i	−0.610755	−	0.791819i	$-0.709134\pi$
$101$	−23.2702	+	13.4350i	−0.230398	+	0.133020i	0.380358	+	0.924839i	$0.375801\pi$
$102$		0			0
$103$	−58.8897	−	34.0000i	−0.571745	−	0.330097i	0.186101	−	0.982531i	$-0.440415\pi$
$103$	−58.8897	−	34.0000i	−0.571745	−	0.330097i	−0.757846	+	0.652434i	$0.773748\pi$
$104$	−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	$-0.208509\pi$
$107$	169.706			1.58603			0.793017	+	0.609200i	$0.208509\pi$
$108$		0			0
$109$	−136.000			−1.24771			−0.623853	−	0.781542i	$-0.714434\pi$
$109$	−136.000			−1.24771			−0.623853	+	0.781542i	$0.714434\pi$
$110$	−77.2741	−	20.7055i	−0.702492	−	0.188232i
$111$		0			0
$112$	13.8564	+	8.00000i	0.123718	+	0.0714286i
$113$	−6.36396	+	11.0227i	−0.0563182	+	0.0975461i	−0.892810	−	0.450433i	$-0.851269\pi$
$113$	−6.36396	+	11.0227i	−0.0563182	+	0.0975461i	0.836492	+	0.547979i	$0.184603\pi$
$114$		0			0
$115$	−51.2436	+	191.244i	−0.445596	+	1.66299i
$116$			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
$130$	32.9423	+	122.942i	0.253402	+	0.945710i
$131$	73.4847	+	42.4264i	0.560952	+	0.323866i	0.753527	−	0.657416i	$-0.228351\pi$
$131$	73.4847	+	42.4264i	0.560952	+	0.323866i	−0.192576	+	0.981282i	$0.561684\pi$
$132$		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	$-0.181458\pi$
$137$	−6.36396	−	11.0227i	−0.0464523	−	0.0804577i	−0.888317	+	0.459231i	$0.848125\pi$
$138$		0			0
$139$	−4.00000	+	6.92820i	−0.0287770	+	0.0498432i	−0.880055	−	0.474871i	$-0.842495\pi$
$139$	−4.00000	+	6.92820i	−0.0287770	+	0.0498432i	0.851278	+	0.524715i	$0.175828\pi$
$140$	−10.3528	−	38.6370i	−0.0739483	−	0.275979i
$141$		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	0.108176	−	0.994132i	$-0.465499\pi$
$149$	−104.103	−	60.1041i	−0.698680	−	0.403383i	−0.806856	+	0.590749i	$0.798832\pi$
$150$		0			0
$151$	−86.0000	−	148.956i	−0.569536	−	0.986466i	−0.996612	−	0.0822500i	$-0.973789\pi$
$151$	−86.0000	−	148.956i	−0.569536	−	0.986466i	0.427075	−	0.904216i	$-0.359544\pi$
$152$	67.8823			0.446594
$153$		0			0
$154$	64.0000			0.415584
$155$	−5.17638	+	19.3185i	−0.0333960	+	0.124636i
$156$		0			0
$157$	131.636	+	76.0000i	0.838445	+	0.484076i	0.856735	−	0.515756i	$-0.172489\pi$
$157$	131.636	+	76.0000i	0.838445	+	0.484076i	−0.0182904	+	0.999833i	$0.505822\pi$
$158$	25.4558	−	44.0908i	0.161113	−	0.279056i
$159$		0			0
$160$	7.32051	−	27.3205i	0.0457532	−	0.170753i
$161$		−	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	−0.381565	−	0.924342i	$-0.624615\pi$
$167$	101.823	−	176.363i	0.609721	−	1.05607i	0.991286	−	0.131726i	$-0.0420518\pi$
$168$		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	0.978949	+	0.204104i	$0.0654279\pi$
$173$	115.258	+	199.633i	0.666234	+	1.15395i	−0.312716	+	0.949847i	$0.601239\pi$
$174$		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	$-0.848481\pi$
$179$		−	164.049i		−	0.916474i	0.888830	−	0.458237i	$-0.151519\pi$
$180$		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
$185$	72.4693	+	270.459i	0.391726	+	1.46194i
$186$		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	0.392299	−	0.919838i	$-0.371680\pi$
$191$	264.545	−	152.735i	1.38505	−	0.799660i	0.992752	+	0.120178i	$0.0383464\pi$
$192$		0			0
$193$	−55.4256	−	32.0000i	−0.287179	−	0.165803i	0.349490	−	0.936940i	$-0.386355\pi$
$193$	−55.4256	−	32.0000i	−0.287179	−	0.165803i	−0.636669	+	0.771137i	$0.719688\pi$
$194$	−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	$-0.301068\pi$
$197$	230.517			1.17014			0.585068	+	0.810984i	$0.301068\pi$
$198$		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
$205$	116.112	+	31.1122i	0.566401	+	0.151767i
$206$		−	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	−0.362834	−	0.931854i	$-0.618191\pi$
$211$	132.000	−	228.631i	0.625592	−	1.08356i	0.988426	−	0.151704i	$-0.0484760\pi$
$212$	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
$220$	−29.2820	−	109.282i	−0.133100	−	0.496737i
$221$	−22.0454	−	12.7279i	−0.0997530	−	0.0575924i
$222$		0			0
$223$	273.664	−	158.000i	1.22719	−	0.708520i	0.260751	−	0.965406i	$-0.416030\pi$
$223$	273.664	−	158.000i	1.22719	−	0.708520i	0.966442	+	0.256886i	$0.0826964\pi$
$224$			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	$-0.234606\pi$
$227$	−48.0833	−	83.2827i	−0.211821	−	0.366884i	−0.952284	+	0.305212i	$0.901273\pi$
$228$		0			0
$229$	4.00000	−	6.92820i	0.0174672	−	0.0302542i	−0.857160	−	0.515051i	$-0.827773\pi$
$229$	4.00000	−	6.92820i	0.0174672	−	0.0302542i	0.874627	+	0.484797i	$0.161106\pi$
$230$	−270.459	+	72.4693i	−1.17591	+	0.315084i
$231$		0			0
$232$	−93.5307	+	54.0000i	−0.403150	+	0.232759i
$233$	227.688			0.977203			0.488602	−	0.872507i	$-0.337507\pi$
$233$	227.688			0.977203			0.488602	+	0.872507i	$0.337507\pi$
$234$		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	0.806201	−	0.591641i	$-0.201520\pi$
$239$	166.565	+	96.1665i	0.696926	+	0.402370i	−0.109276	+	0.994012i	$0.534853\pi$
$240$		0			0
$241$	64.0000	+	110.851i	0.265560	+	0.459964i	0.967710	−	0.252065i	$-0.0811098\pi$
$241$	64.0000	+	110.851i	0.265560	+	0.459964i	−0.702150	+	0.712029i	$0.747776\pi$
$242$	9.89949			0.0409070
$243$		0			0
$244$	220.000			0.901639
$245$	−42.7051	+	159.378i	−0.174307	+	0.650521i
$246$		0			0
$247$	−374.123	−	216.000i	−1.51467	−	0.874494i
$248$	5.65685	−	9.79796i	0.0228099	−	0.0395079i
$249$		0			0
$250$	170.753	+	45.7532i	0.683013	+	0.183013i
$251$			475.176i			1.89313i	0.322512	+	0.946565i	$0.395473\pi$
$251$			475.176i			1.89313i	−0.322512	+	0.946565i	$0.604527\pi$
$252$		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	−0.350823	−	0.936442i	$-0.614098\pi$
$257$	163.342	−	282.916i	0.635571	−	1.10084i	0.986394	−	0.164399i	$-0.0525685\pi$
$258$		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	$-0.118558\pi$
$263$	39.5980	+	68.5857i	0.150563	+	0.260782i	−0.780872	+	0.624691i	$0.785225\pi$
$264$		0			0
$265$	−20.4904	+	5.49038i	−0.0773222	+	0.0207184i
$266$	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	$-0.900490\pi$
$269$		−	165.463i		−	0.615104i	0.951531	−	0.307552i	$-0.0995098\pi$
$270$		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	$-0.665518\pi$
$277$	1.73205	−	1.00000i	0.00625289	−	0.00361011i	0.503123	+	0.864215i	$0.332184\pi$
$278$	−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	−0.519485	−	0.854480i	$-0.673876\pi$
$281$	−11.0227	+	6.36396i	−0.0392267	+	0.0226475i	0.480258	+	0.877127i	$0.340543\pi$
$282$		0			0
$283$	408.764	+	236.000i	1.44440	+	0.833922i	0.998139	−	0.0609826i	$-0.0194234\pi$
$283$	408.764	+	236.000i	1.44440	+	0.833922i	0.446257	+	0.894905i	$0.352757\pi$
$284$	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
$290$	260.800	+	69.8811i	0.899310	+	0.240969i
$291$		0			0
$292$	−79.6743	−	46.0000i	−0.272857	−	0.157534i
$293$	−205.768	+	356.401i	−0.702280	+	1.21638i	0.265384	+	0.964143i	$0.414501\pi$
$293$	−205.768	+	356.401i	−0.702280	+	1.21638i	−0.967664	+	0.252242i	$0.918832\pi$
$294$		0			0
$295$	300.526	+	80.5256i	1.01873	+	0.272968i
$296$		−	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
$310$	−27.3205	+	7.32051i	−0.0881307	+	0.0236145i
$311$	29.3939	+	16.9706i	0.0945141	+	0.0545677i	0.546512	−	0.837451i	$-0.315955\pi$
$311$	29.3939	+	16.9706i	0.0945141	+	0.0545677i	−0.451998	+	0.892019i	$0.649289\pi$
$312$		0			0
$313$	−360.267	+	208.000i	−1.15101	+	0.664537i	−0.949133	−	0.314874i	$-0.898038\pi$
$313$	−360.267	+	208.000i	−1.15101	+	0.664537i	−0.201878	+	0.979411i	$0.564704\pi$
$314$			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	$-0.204386\pi$
$317$	−37.4767	−	64.9115i	−0.118223	−	0.204768i	−0.919063	+	0.394110i	$0.871053\pi$
$318$		0			0
$319$	−216.000	+	374.123i	−0.677116	+	1.17280i
$320$	38.6370	−	10.3528i	0.120741	−	0.0323524i
$321$		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	0.968149	+	0.250376i	$0.0805543\pi$
$331$	232.000	+	401.836i	0.700906	+	1.21401i	−0.267242	+	0.963629i	$0.586112\pi$
$332$	11.3137			0.0340774
$333$		0			0
$334$	288.000			0.862275
$335$	154.548	+	41.4110i	0.461338	+	0.123615i
$336$		0			0
$337$	−53.6936	−	31.0000i	−0.159328	−	0.0919881i	0.418216	−	0.908348i	$-0.362656\pi$
$337$	−53.6936	−	31.0000i	−0.159328	−	0.0919881i	−0.577544	+	0.816359i	$0.695989\pi$
$338$	−109.602	+	189.835i	−0.324265	+	0.561643i
$339$		0			0
$340$	3.66025	−	13.6603i	0.0107655	−	0.0401772i
$341$		−	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	−0.320315	−	0.947311i	$-0.603789\pi$
$347$	229.103	−	396.817i	0.660238	−	1.14357i	0.980553	−	0.196255i	$-0.0628779\pi$
$348$		0			0
$349$	71.0000	+	122.976i	0.203438	+	0.352366i	0.949634	−	0.313361i	$-0.101455\pi$
$349$	71.0000	+	122.976i	0.203438	+	0.352366i	−0.746196	+	0.665727i	$0.768122\pi$
$350$	−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	$-0.212092\pi$
$353$	−50.2046	−	86.9569i	−0.142223	−	0.246337i	−0.928333	+	0.371749i	$0.878758\pi$
$354$		0			0
$355$	−65.8846	−	245.885i	−0.185590	−	0.692633i
$356$	−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	$0.182949\pi$
$359$			390.323i			1.08725i	−0.839328	+	0.543625i	$0.817051\pi$
$360$		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
$365$	59.5284	+	222.163i	0.163091	+	0.608666i
$366$		0			0
$367$	245.951	−	142.000i	0.670167	−	0.386921i	−0.125973	−	0.992034i	$-0.540205\pi$
$367$	245.951	−	142.000i	0.670167	−	0.386921i	0.796140	+	0.605113i	$0.206872\pi$
$368$	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	$-0.493631\pi$
$373$	−311.769	−	180.000i	−0.835842	−	0.482574i	−0.855849	+	0.517226i	$0.826965\pi$
$374$	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	$0.638729\pi$
$380$	62.1166	−	231.822i	0.163465	−	0.610058i
$381$		0			0
$382$	374.123	+	216.000i	0.979380	+	0.565445i
$383$	−90.5097	+	156.767i	−0.236318	+	0.409314i	−0.959655	−	0.281181i	$-0.909274\pi$
$383$	−90.5097	+	156.767i	−0.236318	+	0.409314i	0.723337	+	0.690495i	$0.242607\pi$
$384$		0			0
$385$	58.5641	−	218.564i	0.152114	−	0.567699i
$386$		−	90.5097i		−	0.234481i
$387$		0			0
$388$		−	28.0000i		−	0.0721649i
$389$	594.001	−	342.947i	1.52700	−	0.881611i	0.527510	−	0.849549i	$-0.323126\pi$
$389$	594.001	−	342.947i	1.52700	−	0.881611i	0.999486	−	0.0320622i	$-0.0102075\pi$
$390$		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	−0.0568256	−	0.998384i	$-0.518098\pi$
$401$	−380.896	−	219.910i	−0.949864	−	0.548405i	−0.893039	+	0.449980i	$0.851431\pi$
$402$		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	−0.548500	−	0.836151i	$-0.684801\pi$
$409$	184.000	−	318.697i	0.449878	−	0.779211i	0.998378	+	0.0569395i	$0.0181342\pi$
$410$	43.9992	+	164.207i	0.107315	+	0.400506i
$411$		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	0.685418	−	0.728150i	$-0.259620\pi$
$419$	166.565	+	96.1665i	0.397531	+	0.229514i	−0.287887	+	0.957664i	$0.592953\pi$
$420$		0			0
$421$	−140.000	−	242.487i	−0.332542	−	0.575979i	0.650468	−	0.759534i	$-0.274573\pi$
$421$	−140.000	−	242.487i	−0.332542	−	0.575979i	−0.983009	+	0.183555i	$0.941240\pi$
$422$	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
$430$	−546.410	−	146.410i	−1.27072	−	0.340489i
$431$		−	96.1665i		−	0.223124i	−0.993757	−	0.111562i	$-0.964415\pi$
$431$		−	96.1665i		−	0.223124i	0.993757	−	0.111562i	$-0.0355854\pi$
$432$		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	0.620392	−	0.784292i	$-0.286973\pi$
$439$	−162.000	−	280.592i	−0.369021	−	0.639162i	−0.989413	+	0.145129i	$0.953640\pi$
$440$	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	$-0.285231\pi$
$443$	−161.220	−	279.242i	−0.363929	−	0.630343i	−0.988604	+	0.150542i	$0.951898\pi$
$444$		0			0
$445$	75.0352	+	280.035i	0.168618	+	0.629293i
$446$	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	$0.0437498\pi$
$449$			123.037i			0.274024i	−0.990569	+	0.137012i	$0.956250\pi$
$450$		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
$455$	−347.733	+	93.1749i	−0.764249	+	0.204780i
$456$		0			0
$457$	−112.583	+	65.0000i	−0.246353	+	0.142232i	−0.618093	−	0.786105i	$-0.712095\pi$
$457$	−112.583	+	65.0000i	−0.246353	+	0.142232i	0.371740	+	0.928337i	$0.378761\pi$
$458$	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	−0.872200	−	0.489149i	$-0.837308\pi$
$461$	−407.840	+	235.467i	−0.884686	+	0.510773i	−0.0124851	+	0.999922i	$0.503974\pi$
$462$		0			0
$463$	−384.515	−	222.000i	−0.830487	−	0.479482i	0.0235327	−	0.999723i	$-0.492509\pi$
$463$	−384.515	−	222.000i	−0.830487	−	0.479482i	−0.854019	+	0.520241i	$0.825842\pi$
$464$	−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	$-0.564051\pi$
$467$	−186.676			−0.399735			−0.199867	+	0.979823i	$0.564051\pi$
$468$		0			0
$469$	−128.000			−0.272921
$470$	−51.7638	+	193.185i	−0.110136	+	0.411032i
$471$		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	−0.923609	−	0.383336i	$-0.874775\pi$
$479$	−504.595	+	291.328i	−1.05343	+	0.608200i	−0.129825	+	0.991537i	$0.541442\pi$
$480$		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
$490$	−225.394	+	60.3942i	−0.459988	+	0.123253i
$491$	−279.242	−	161.220i	−0.568721	−	0.328351i	0.187918	−	0.982185i	$-0.439826\pi$
$491$	−279.242	−	161.220i	−0.568721	−	0.328351i	−0.756638	+	0.653834i	$0.773160\pi$
$492$		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	−0.998796	−	0.0490565i	$-0.984379\pi$
$499$	−228.000	+	394.908i	−0.456914	+	0.791398i	0.541882	+	0.840454i	$0.317712\pi$
$500$	64.7048	+	241.481i	0.129410	+	0.482963i
$501$		0			0
$502$	−581.969	+	336.000i	−1.15930	+	0.669323i
$503$	−492.146			−0.978422			−0.489211	−	0.872165i	$-0.662715\pi$
$503$	−492.146			−0.978422			−0.489211	+	0.872165i	$0.662715\pi$
$504$		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	−0.0839823	−	0.996467i	$-0.526764\pi$
$509$	−503.370	−	290.621i	−0.988939	−	0.570964i	−0.904957	+	0.425503i	$0.860097\pi$
$510$		0			0
$511$	−92.0000	−	159.349i	−0.180039	−	0.311837i
$512$	−22.6274			−0.0441942
$513$		0			0
$514$	462.000			0.898833
$515$	−328.415	−	87.9985i	−0.637699	−	0.170871i
$516$		0			0
$517$	−277.128	−	160.000i	−0.536031	−	0.309478i
$518$	158.392	−	274.343i	0.305776	−	0.529619i
$519$		0			0
$520$	−245.885	−	65.8846i	−0.472855	−	0.126701i
$521$		−	408.708i		−	0.784468i	−0.919866	−	0.392234i	$-0.871702\pi$
$521$		−	408.708i		−	0.784468i	0.919866	−	0.392234i	$-0.128298\pi$
$522$		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
$535$	819.615	−	219.615i	1.53199	−	0.410496i
$536$	−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
$545$	−656.830	+	175.997i	−1.20519	+	0.322930i
$546$		0			0
$547$	−263.272	+	152.000i	−0.481301	+	0.277879i	−0.720959	−	0.692978i	$-0.756298\pi$
$547$	−263.272	+	152.000i	−0.481301	+	0.277879i	0.239657	+	0.970858i	$0.422965\pi$
$548$	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	$-0.206961\pi$
$557$	886.712			1.59194			0.795971	+	0.605335i	$0.206961\pi$
$558$		0			0
$559$	−1440.00			−2.57603
$560$	77.2741	+	20.7055i	0.137989	+	0.0369741i
$561$		0			0
$562$	−15.5885	−	9.00000i	−0.0277375	−	0.0160142i
$563$	19.7990	−	34.2929i	0.0351669	−	0.0609109i	−0.847906	−	0.530146i	$-0.822137\pi$
$563$	19.7990	−	34.2929i	0.0351669	−	0.0609109i	0.883073	+	0.469235i	$0.155470\pi$
$564$		0			0
$565$	−16.4711	+	61.4711i	−0.0291525	+	0.108798i
$566$			667.509i			1.17934i
$567$		0			0
$568$			144.000i			0.253521i
$569$	−37.9671	+	21.9203i	−0.0667260	+	0.0385243i	−0.532992	−	0.846120i	$-0.678932\pi$
$569$	−37.9671	+	21.9203i	−0.0667260	+	0.0385243i	0.466266	+	0.884645i	$0.345599\pi$
$570$		0			0
$571$	196.000	−	339.482i	0.343257	−	0.594539i	−0.641778	−	0.766890i	$-0.721803\pi$
$571$	196.000	−	339.482i	0.343257	−	0.594539i	0.985036	+	0.172351i	$0.0551363\pi$
$572$	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
$580$	98.8269	+	368.827i	0.170391	+	0.635908i
$581$	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	−0.650661	−	0.759368i	$-0.725508\pi$
$587$	−576.999	−	999.392i	−0.982963	−	1.70254i	−0.332302	−	0.943173i	$-0.607825\pi$
$588$		0			0
$589$	48.0000	−	83.1384i	0.0814941	−	0.141152i
$590$	113.880	+	425.007i	0.193018	+	0.720351i
$591$		0			0
$592$	193.990	−	112.000i	0.327685	−	0.189189i
$593$	258.801			0.436427			0.218213	−	0.975901i	$-0.429977\pi$
$593$	258.801			0.436427			0.218213	+	0.975901i	$0.429977\pi$
$594$		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	0.693839	−	0.720130i	$-0.255918\pi$
$599$	249.848	+	144.250i	0.417108	+	0.240818i	−0.276731	+	0.960947i	$0.589251\pi$
$600$		0			0
$601$	431.000	+	746.514i	0.717138	+	1.24212i	0.962129	+	0.272594i	$0.0878817\pi$
$601$	431.000	+	746.514i	0.717138	+	1.24212i	−0.244991	+	0.969525i	$0.578785\pi$
$602$	452.548			0.751741
$603$		0			0
$604$	344.000			0.569536
$605$	9.05867	−	33.8074i	0.0149730	−	0.0558800i
$606$		0			0
$607$	682.428	+	394.000i	1.12426	+	0.649094i	0.942486	−	0.334246i	$-0.108482\pi$
$607$	682.428	+	394.000i	1.12426	+	0.649094i	0.181778	+	0.983340i	$0.441815\pi$
$608$	−67.8823	+	117.576i	−0.111648	+	0.193381i
$609$		0			0
$610$	201.314	−	751.314i	0.330023	−	1.23166i
$611$			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	$-0.732811\pi$
$617$	191.626	−	331.906i	0.310577	−	0.537935i	0.978487	+	0.206307i	$0.0661444\pi$
$618$		0			0
$619$	−152.000	−	263.272i	−0.245557	−	0.425318i	0.716731	−	0.697350i	$-0.245638\pi$
$619$	−152.000	−	263.272i	−0.245557	−	0.425318i	−0.962288	+	0.272032i	$0.912304\pi$
$620$	−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
$635$	−36.2347	−	135.230i	−0.0570625	−	0.212960i
$636$		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	−0.170229	−	0.985405i	$-0.554451\pi$
$641$	383.345	−	221.324i	0.598042	−	0.345280i	0.768271	+	0.640125i	$0.221117\pi$
$642$		0			0
$643$	561.184	+	324.000i	0.872760	+	0.503888i	0.868264	−	0.496102i	$-0.165236\pi$
$643$	561.184	+	324.000i	0.872760	+	0.503888i	0.00449534	+	0.999990i	$0.498569\pi$
$644$	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	$-0.597534\pi$
$647$	−390.323			−0.603281			−0.301641	+	0.953422i	$0.597534\pi$
$648$		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	0.273470	+	0.961881i	$0.411829\pi$
$653$	−454.670	+	787.511i	−0.696278	+	1.20599i	−0.969748	+	0.244109i	$0.921505\pi$
$654$		0			0
$655$	409.808	+	109.808i	0.625660	+	0.167645i
$656$		−	96.1665i		−	0.146595i
$657$		0			0
$658$		−	160.000i		−	0.243161i
$659$	298.838	−	172.534i	0.453472	−	0.261812i	−0.255824	−	0.966723i	$-0.582347\pi$
$659$	298.838	−	172.534i	0.453472	−	0.261812i	0.709295	+	0.704912i	$0.249013\pi$
$660$		0			0
$661$	−481.000	+	833.116i	−0.727685	+	1.26039i	0.230174	+	0.973150i	$0.426071\pi$
$661$	−481.000	+	833.116i	−0.727685	+	1.26039i	−0.957859	+	0.287238i	$0.907263\pi$
$662$	−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
$670$	58.5641	+	218.564i	0.0874091	+	0.326215i
$671$	1077.78	+	622.254i	1.60622	+	0.927353i
$672$		0			0
$673$	207.846	−	120.000i	0.308835	−	0.178306i	−0.337570	−	0.941300i	$-0.609605\pi$
$673$	207.846	−	120.000i	0.308835	−	0.178306i	0.646405	+	0.762994i	$0.276272\pi$
$674$		−	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	$-0.0877307\pi$
$677$	166.170	+	287.815i	0.245451	+	0.425133i	−0.716808	+	0.697271i	$0.754397\pi$
$678$		0			0
$679$	28.0000	−	48.4974i	0.0412371	−	0.0714248i
$680$	19.3185	−	5.17638i	0.0284096	−	0.00761232i
$681$		0			0
$682$	55.4256	−	32.0000i	0.0812692	−	0.0469208i
$683$	−1012.58			−1.48254			−0.741272	−	0.671205i	$-0.765777\pi$
$683$	−1012.58			−1.48254			−0.741272	+	0.671205i	$0.765777\pi$
$684$		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	0.893517	−	0.449030i	$-0.148230\pi$
$691$	40.0000	+	69.2820i	0.0578871	+	0.100263i	−0.835630	+	0.549293i	$0.814897\pi$
$692$	−461.034			−0.666234
$693$		0			0
$694$	648.000			0.933718
$695$	−10.3528	+	38.6370i	−0.0148961	+	0.0555929i
$696$		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	$-0.869551\pi$
$701$		−	558.614i		−	0.796882i	0.917194	−	0.398441i	$-0.130449\pi$
$702$		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	0.734788	−	0.678297i	$-0.237282\pi$
$709$	−156.000	−	270.200i	−0.220028	−	0.381100i	−0.954816	+	0.297197i	$0.903948\pi$
$710$	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
$715$	−983.538	+	263.538i	−1.37558	+	0.368585i
$716$	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	$0.294409\pi$
$719$			1148.34i			1.59714i	−0.601904	+	0.798568i	$0.705591\pi$
$720$		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	$-0.770978\pi$
$727$	−405.300	+	234.000i	−0.557496	+	0.321871i	0.194644	+	0.980874i	$0.437645\pi$
$728$	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	$-0.216520\pi$
$733$	455.529	+	263.000i	0.621459	+	0.358799i	−0.155978	+	0.987761i	$0.549853\pi$
$734$	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	$0.425229\pi$
$740$	−540.918	−	144.939i	−0.730971	−	0.195863i
$741$		0			0
$742$	20.7846	+	12.0000i	0.0280116	+	0.0161725i
$743$	−339.411	+	587.878i	−0.456812	+	0.791221i	−0.998790	−	0.0491709i	$-0.984342\pi$
$743$	−339.411	+	587.878i	−0.456812	+	0.791221i	0.541978	+	0.840392i	$0.317675\pi$
$744$		0			0
$745$	−580.561	−	155.561i	−0.779276	−	0.208806i
$746$		−	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	−0.950152	−	0.311788i	$-0.899072\pi$
$751$	−154.000	+	266.736i	−0.205060	+	0.355174i	0.745092	+	0.666962i	$0.232406\pi$
$752$	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
$760$	327.846	−	87.8461i	0.431376	−	0.115587i
$761$	1017.76	+	587.606i	1.33740	+	0.772149i	0.986422	−	0.164233i	$-0.0525150\pi$
$761$	1017.76	+	587.606i	1.33740	+	0.772149i	0.350981	+	0.936383i	$0.385848\pi$
$762$		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	−0.764800	−	0.644268i	$-0.777162\pi$
$769$	135.000	−	233.827i	0.175553	−	0.304066i	0.940352	+	0.340202i	$0.110495\pi$
$770$	309.096	−	82.8221i	0.401424	−	0.107561i
$771$		0			0
$772$	110.851	−	64.0000i	0.143590	−	0.0829016i
$773$	267.286			0.345778			0.172889	−	0.984941i	$-0.444690\pi$
$773$	267.286			0.345778			0.172889	+	0.984941i	$0.444690\pi$
$774$		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
$785$	734.104	+	196.702i	0.935164	+	0.250576i
$786$		0			0
$787$	−1316.36	−	760.000i	−1.67263	−	0.965693i	−0.966158	−	0.257950i	$-0.916953\pi$
$787$	−1316.36	−	760.000i	−1.67263	−	0.965693i	−0.706470	−	0.707743i	$-0.749714\pi$
$788$	−230.517	+	399.267i	−0.292534	+	0.506684i
$789$		0			0
$790$	65.8846	−	245.885i	0.0833982	−	0.311246i
$791$		−	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	$-0.911787\pi$
$797$	−194.454	+	336.805i	−0.243983	+	0.422591i	0.717862	+	0.696185i	$0.245121\pi$
$798$		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
$805$	−204.974	−	764.974i	−0.254626	−	0.950279i
$806$	−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	$0.00918250\pi$
$809$			46.6690i			0.0576873i	−0.999584	+	0.0288437i	$0.990818\pi$
$810$		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
$815$	134.586	+	502.281i	0.165136	+	0.616296i
$816$		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	0.354134	−	0.935195i	$-0.384776\pi$
$821$	1101.05	−	635.689i	1.34110	−	0.774286i	0.986969	+	0.160909i	$0.0514424\pi$
$822$		0			0
$823$	−717.069	−	414.000i	−0.871287	−	0.503038i	−0.00351115	−	0.999994i	$-0.501118\pi$
$823$	−717.069	−	414.000i	−0.871287	−	0.503038i	−0.867776	+	0.496956i	$0.834451\pi$
$824$	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	$-0.530529\pi$
$827$	−158.392			−0.191526			−0.0957629	+	0.995404i	$0.530529\pi$
$828$		0			0
$829$	−552.000			−0.665862			−0.332931	−	0.942951i	$-0.608038\pi$
$829$	−552.000			−0.665862			−0.332931	+	0.942951i	$0.608038\pi$
$830$	10.3528	−	38.6370i	0.0124732	−	0.0465506i
$831$		0			0
$832$	124.708	+	72.0000i	0.149889	+	0.0865385i
$833$	23.3345	−	40.4166i	0.0280126	−	0.0485193i
$834$		0			0
$835$	263.538	−	983.538i	0.315615	−	1.17789i
$836$			543.058i			0.649591i
$837$		0			0
$838$			272.000i			0.324582i
$839$	739.746	−	427.092i	0.881700	−	0.509049i	0.0104811	−	0.999945i	$-0.496664\pi$
$839$	739.746	−	427.092i	0.881700	−	0.509049i	0.871218	+	0.490896i	$0.163330\pi$
$840$		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	$-0.833980\pi$
$853$	−741.318	+	428.000i	−0.869071	+	0.501758i	−0.00203173	+	0.999998i	$0.500647\pi$
$854$			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	$-0.271783\pi$
$857$	−277.893	−	481.325i	−0.324263	−	0.561639i	−0.981363	+	0.192164i	$0.938449\pi$
$858$		0			0
$859$	−236.000	+	408.764i	−0.274738	+	0.475860i	−0.970069	−	0.242829i	$-0.921924\pi$
$859$	−236.000	+	408.764i	−0.274738	+	0.475860i	0.695331	+	0.718690i	$0.255258\pi$
$860$	−207.055	−	772.741i	−0.240762	−	0.898536i
$861$		0			0
$862$	117.779	−	68.0000i	0.136635	−	0.0788863i
$863$	441.235			0.511280			0.255640	−	0.966772i	$-0.417714\pi$
$863$	441.235			0.511280			0.255640	+	0.966772i	$0.417714\pi$
$864$		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
$875$	−129.410	+	482.963i	−0.147897	+	0.551958i
$876$		0			0
$877$	588.897	+	340.000i	0.671491	+	0.387685i	0.796641	−	0.604452i	$-0.206608\pi$
$877$	588.897	+	340.000i	0.671491	+	0.387685i	−0.125151	+	0.992138i	$0.539941\pi$
$878$	229.103	−	396.817i	0.260937	−	0.451956i
$879$		0			0
$880$	218.564	+	58.5641i	0.248368	+	0.0665501i
$881$		−	292.742i		−	0.332284i	−0.986102	−	0.166142i	$-0.946869\pi$
$881$		−	292.742i		−	0.332284i	0.986102	−	0.166142i	$-0.0531310\pi$
$882$		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	$-0.999062\pi$
$887$	−441.235	+	764.241i	−0.497446	+	0.861602i	0.502550	+	0.864548i	$0.332395\pi$
$888$		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
$895$	−212.295	−	792.295i	−0.237201	−	0.885246i
$896$	−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
$905$	38.6370	−	10.3528i	0.0426929	−	0.0114395i
$906$		0			0
$907$	−457.261	+	264.000i	−0.504147	+	0.291069i	−0.730425	−	0.682993i	$-0.760678\pi$
$907$	−457.261	+	264.000i	−0.504147	+	0.291069i	0.226277	+	0.974063i	$0.427344\pi$
$908$	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	−0.516666	+	0.856187i	$0.672827\pi$
$911$	−1381.51	+	797.616i	−1.51648	+	0.875539i	−0.999813	+	0.0193525i	$0.993840\pi$
$912$		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	$0.616912\pi$
$920$	144.939	−	540.918i	0.157542	−	0.587955i
$921$		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	−0.889127	−	0.457660i	$-0.848688\pi$
$929$	−870.794	+	502.753i	−0.937345	+	0.541176i	−0.0482180	+	0.998837i	$0.515354\pi$
$930$		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
$940$	−273.205	+	73.2051i	−0.290644	+	0.0778777i
$941$	−552.360	−	318.905i	−0.586992	−	0.338900i	0.176915	−	0.984226i	$-0.443388\pi$
$941$	−552.360	−	318.905i	−0.586992	−	0.338900i	−0.763907	+	0.645326i	$0.776722\pi$
$942$		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	0.871758	+	0.489936i	$0.162980\pi$
$947$	814.587	+	1410.91i	0.860176	+	1.48987i	−0.0115819	+	0.999933i	$0.503687\pi$
$948$		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	$-0.340615\pi$
$953$	914.996			0.960122			0.480061	+	0.877235i	$0.340615\pi$
$954$		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
$965$	−309.096	−	82.8221i	−0.320307	−	0.0858260i
$966$		0			0
$967$	433.013	+	250.000i	0.447790	+	0.258532i	0.706896	−	0.707317i	$-0.250095\pi$
$967$	433.013	+	250.000i	0.447790	+	0.258532i	−0.259107	+	0.965849i	$0.583428\pi$
$968$	−9.89949	+	17.1464i	−0.0102268	+	0.0177133i
$969$		0			0
$970$	−95.6218	−	25.6218i	−0.0985792	−	0.0264142i
$971$			1221.88i			1.25837i	0.777254	+	0.629187i	$0.216612\pi$
$971$			1221.88i			1.25837i	−0.777254	+	0.629187i	$0.783388\pi$
$972$		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	−0.0553827	+	0.998465i	$0.517638\pi$
$977$	−871.863	+	1510.11i	−0.892388	+	1.54566i	−0.837005	+	0.547195i	$0.815695\pi$
$978$		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	$-0.179493\pi$
$983$	−39.5980	−	68.5857i	−0.0402828	−	0.0697718i	−0.885464	+	0.464708i	$0.846159\pi$
$984$		0			0
$985$	1113.31	−	298.311i	1.13026	−	0.302854i
$986$	−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
$995$	1448.89	−	388.229i	1.45617	−	0.390179i
$996$		0			0
$997$	1267.86	−	732.000i	1.27168	−	0.734203i	0.296373	−	0.955072i	$-0.404223\pi$
$997$	1267.86	−	732.000i	1.27168	−	0.734203i	0.975303	+	0.220870i	$0.0708896\pi$
$998$	−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.539.4		8
3.2	odd	2	inner	810.3.j.d.539.1		8
5.4	even	2	inner	810.3.j.d.539.2		8
9.2	odd	6	inner	810.3.j.d.269.2		8
9.4	even	3		90.3.b.a.89.1	✓	4
9.5	odd	6		90.3.b.a.89.4	yes	4
9.7	even	3	inner	810.3.j.d.269.3		8
15.14	odd	2	inner	810.3.j.d.539.3		8
36.23	even	6		720.3.c.c.449.4		4
36.31	odd	6		720.3.c.c.449.1		4
45.4	even	6		90.3.b.a.89.3	yes	4
45.13	odd	12		450.3.d.b.251.2		2
45.14	odd	6		90.3.b.a.89.2	yes	4
45.22	odd	12		450.3.d.e.251.1		2
45.23	even	12		450.3.d.b.251.1		2
45.29	odd	6	inner	810.3.j.d.269.4		8
45.32	even	12		450.3.d.e.251.2		2
45.34	even	6	inner	810.3.j.d.269.1		8
72.5	odd	6		2880.3.c.h.449.1		4
72.13	even	6		2880.3.c.h.449.4		4
72.59	even	6		2880.3.c.a.449.1		4
72.67	odd	6		2880.3.c.a.449.4		4
180.23	odd	12		3600.3.l.i.1601.1		2
180.59	even	6		720.3.c.c.449.2		4
180.67	even	12		3600.3.l.c.1601.2		2
180.103	even	12		3600.3.l.i.1601.2		2
180.139	odd	6		720.3.c.c.449.3		4
180.167	odd	12		3600.3.l.c.1601.1		2
360.59	even	6		2880.3.c.a.449.3		4
360.139	odd	6		2880.3.c.a.449.2		4
360.149	odd	6		2880.3.c.h.449.3		4
360.229	even	6		2880.3.c.h.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
90.3.b.a.89.1	✓	4	9.4	even	3
90.3.b.a.89.2	yes	4	45.14	odd	6
90.3.b.a.89.3	yes	4	45.4	even	6
90.3.b.a.89.4	yes	4	9.5	odd	6
450.3.d.b.251.1		2	45.23	even	12
450.3.d.b.251.2		2	45.13	odd	12
450.3.d.e.251.1		2	45.22	odd	12
450.3.d.e.251.2		2	45.32	even	12
720.3.c.c.449.1		4	36.31	odd	6
720.3.c.c.449.2		4	180.59	even	6
720.3.c.c.449.3		4	180.139	odd	6
720.3.c.c.449.4		4	36.23	even	6
810.3.j.d.269.1		8	45.34	even	6	inner
810.3.j.d.269.2		8	9.2	odd	6	inner
810.3.j.d.269.3		8	9.7	even	3	inner
810.3.j.d.269.4		8	45.29	odd	6	inner
810.3.j.d.539.1		8	3.2	odd	2	inner
810.3.j.d.539.2		8	5.4	even	2	inner
810.3.j.d.539.3		8	15.14	odd	2	inner
810.3.j.d.539.4		8	1.1	even	1	trivial
2880.3.c.a.449.1		4	72.59	even	6
2880.3.c.a.449.2		4	360.139	odd	6
2880.3.c.a.449.3		4	360.59	even	6
2880.3.c.a.449.4		4	72.67	odd	6
2880.3.c.h.449.1		4	72.5	odd	6
2880.3.c.h.449.2		4	360.229	even	6
2880.3.c.h.449.3		4	360.149	odd	6
2880.3.c.h.449.4		4	72.13	even	6
3600.3.l.c.1601.1		2	180.167	odd	12
3600.3.l.c.1601.2		2	180.67	even	12
3600.3.l.i.1601.1		2	180.23	odd	12
3600.3.l.i.1601.2		2	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)

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

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