LMFDB - Embedded newform 81.3.d.b.26.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,3,Mod(26,81)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(81, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("81.26");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	81.d (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:	$2.20709014132$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{4}]$
Coefficient ring index:	$ 3^{2} $
Twist minimal:	no (minimal twist has level 27)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			26.1
Root			$-0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	81.26
Dual form			81.3.d.b.53.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.59808 - 1.50000i) q^{2} +(2.50000 + 4.33013i) q^{4} +(-2.59808 + 1.50000i) q^{5} +(-2.50000 + 4.33013i) q^{7} -3.00000i q^{8} +9.00000 q^{10} +(12.9904 + 7.50000i) q^{11} +(5.00000 + 8.66025i) q^{13} +(12.9904 - 7.50000i) q^{14} +(5.50000 - 9.52628i) q^{16} +18.0000i q^{17} -16.0000 q^{19} +(-12.9904 - 7.50000i) q^{20} +(-22.5000 - 38.9711i) q^{22} +(-10.3923 + 6.00000i) q^{23} +(-8.00000 + 13.8564i) q^{25} -30.0000i q^{26} -25.0000 q^{28} +(-25.9808 - 15.0000i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-38.9711 + 22.5000i) q^{32} +(27.0000 - 46.7654i) q^{34} -15.0000i q^{35} +20.0000 q^{37} +(41.5692 + 24.0000i) q^{38} +(4.50000 + 7.79423i) q^{40} +(51.9615 - 30.0000i) q^{41} +(-25.0000 + 43.3013i) q^{43} +75.0000i q^{44} +36.0000 q^{46} +(5.19615 + 3.00000i) q^{47} +(12.0000 + 20.7846i) q^{49} +(41.5692 - 24.0000i) q^{50} +(-25.0000 + 43.3013i) q^{52} -27.0000i q^{53} -45.0000 q^{55} +(12.9904 + 7.50000i) q^{56} +(45.0000 + 77.9423i) q^{58} +(-25.9808 + 15.0000i) q^{59} +(38.0000 - 65.8179i) q^{61} -3.00000i q^{62} +91.0000 q^{64} +(-25.9808 - 15.0000i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-77.9423 + 45.0000i) q^{68} +(-22.5000 + 38.9711i) q^{70} -90.0000i q^{71} +65.0000 q^{73} +(-51.9615 - 30.0000i) q^{74} +(-40.0000 - 69.2820i) q^{76} +(-64.9519 + 37.5000i) q^{77} +(-7.00000 + 12.1244i) q^{79} +33.0000i q^{80} -180.000 q^{82} +(-2.59808 - 1.50000i) q^{83} +(-27.0000 - 46.7654i) q^{85} +(129.904 - 75.0000i) q^{86} +(22.5000 - 38.9711i) q^{88} +90.0000i q^{89} -50.0000 q^{91} +(-51.9615 - 30.0000i) q^{92} +(-9.00000 - 15.5885i) q^{94} +(41.5692 - 24.0000i) q^{95} +(42.5000 - 73.6122i) q^{97} -72.0000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 10 q^{4} - 10 q^{7} + 36 q^{10} + 20 q^{13} + 22 q^{16} - 64 q^{19} - 90 q^{22} - 32 q^{25} - 100 q^{28} + 2 q^{31} + 108 q^{34} + 80 q^{37} + 18 q^{40} - 100 q^{43} + 144 q^{46} + 48 q^{49} - 100 q^{52}+ \cdots + 170 q^{97}+O(q^{100}) $ 4 * q + 10 * q^4 - 10 * q^7 + 36 * q^10 + 20 * q^13 + 22 * q^16 - 64 * q^19 - 90 * q^22 - 32 * q^25 - 100 * q^28 + 2 * q^31 + 108 * q^34 + 80 * q^37 + 18 * q^40 - 100 * q^43 + 144 * q^46 + 48 * q^49 - 100 * q^52 - 180 * q^55 + 180 * q^58 + 152 * q^61 + 364 * q^64 + 20 * q^67 - 90 * q^70 + 260 * q^73 - 160 * q^76 - 28 * q^79 - 720 * q^82 - 108 * q^85 + 90 * q^88 - 200 * q^91 - 36 * q^94 + 170 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/81\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−2.59808	−	1.50000i	−1.29904	−	0.750000i	−0.318800	−	0.947822i	$-0.603280\pi$
$2$	−2.59808	−	1.50000i	−1.29904	−	0.750000i	−0.980238	+	0.197822i	$0.936613\pi$
$3$		0			0
$3$		0			0
$4$	2.50000	+	4.33013i	0.625000	+	1.08253i
$5$	−2.59808	+	1.50000i	−0.519615	+	0.300000i	−0.736777	−	0.676136i	$-0.763653\pi$
$5$	−2.59808	+	1.50000i	−0.519615	+	0.300000i	0.217162	+	0.976136i	$0.430320\pi$
$6$		0			0
$7$	−2.50000	+	4.33013i	−0.357143	+	0.618590i	−0.987482	−	0.157730i	$-0.949582\pi$
$7$	−2.50000	+	4.33013i	−0.357143	+	0.618590i	0.630339	+	0.776320i	$0.282916\pi$
$8$		−	3.00000i		−	0.375000i
$9$		0			0
$10$	9.00000			0.900000
$11$	12.9904	+	7.50000i	1.18094	+	0.681818i	0.956233	−	0.292607i	$-0.0945229\pi$
$11$	12.9904	+	7.50000i	1.18094	+	0.681818i	0.224711	+	0.974425i	$0.427856\pi$
$12$		0			0
$13$	5.00000	+	8.66025i	0.384615	+	0.666173i	0.991716	−	0.128452i	$-0.0410008\pi$
$13$	5.00000	+	8.66025i	0.384615	+	0.666173i	−0.607100	+	0.794625i	$0.707667\pi$
$14$	12.9904	−	7.50000i	0.927884	−	0.535714i
$15$		0			0
$16$	5.50000	−	9.52628i	0.343750	−	0.595392i
$17$			18.0000i			1.05882i	0.848365	+	0.529412i	$0.177587\pi$
$17$			18.0000i			1.05882i	−0.848365	+	0.529412i	$0.822413\pi$
$18$		0			0
$19$	−16.0000			−0.842105			−0.421053	−	0.907036i	$-0.638339\pi$
$19$	−16.0000			−0.842105			−0.421053	+	0.907036i	$0.638339\pi$
$20$	−12.9904	−	7.50000i	−0.649519	−	0.375000i
$21$		0			0
$22$	−22.5000	−	38.9711i	−1.02273	−	1.77142i
$23$	−10.3923	+	6.00000i	−0.451839	+	0.260870i	−0.708607	−	0.705604i	$-0.750676\pi$
$23$	−10.3923	+	6.00000i	−0.451839	+	0.260870i	0.256767	+	0.966473i	$0.417343\pi$
$24$		0			0
$25$	−8.00000	+	13.8564i	−0.320000	+	0.554256i
$26$		−	30.0000i		−	1.15385i
$27$		0			0
$28$	−25.0000			−0.892857
$29$	−25.9808	−	15.0000i	−0.895888	−	0.517241i	−0.0200244	−	0.999799i	$-0.506374\pi$
$29$	−25.9808	−	15.0000i	−0.895888	−	0.517241i	−0.875864	+	0.482558i	$0.839708\pi$
$30$		0			0
$31$	0.500000	+	0.866025i	0.0161290	+	0.0279363i	0.873977	−	0.485967i	$-0.161532\pi$
$31$	0.500000	+	0.866025i	0.0161290	+	0.0279363i	−0.857848	+	0.513903i	$0.828199\pi$
$32$	−38.9711	+	22.5000i	−1.21785	+	0.703125i
$33$		0			0
$34$	27.0000	−	46.7654i	0.794118	−	1.37545i
$35$		−	15.0000i		−	0.428571i
$36$		0			0
$37$	20.0000			0.540541			0.270270	−	0.962784i	$-0.412887\pi$
$37$	20.0000			0.540541			0.270270	+	0.962784i	$0.412887\pi$
$38$	41.5692	+	24.0000i	1.09393	+	0.631579i
$39$		0			0
$40$	4.50000	+	7.79423i	0.112500	+	0.194856i
$41$	51.9615	−	30.0000i	1.26735	−	0.731707i	0.292868	−	0.956153i	$-0.405390\pi$
$41$	51.9615	−	30.0000i	1.26735	−	0.731707i	0.974487	+	0.224446i	$0.0720571\pi$
$42$		0			0
$43$	−25.0000	+	43.3013i	−0.581395	+	1.00701i	0.413919	+	0.910314i	$0.364160\pi$
$43$	−25.0000	+	43.3013i	−0.581395	+	1.00701i	−0.995314	+	0.0966925i	$0.969174\pi$
$44$			75.0000i			1.70455i
$45$		0			0
$46$	36.0000			0.782609
$47$	5.19615	+	3.00000i	0.110556	+	0.0638298i	0.554259	−	0.832345i	$-0.313002\pi$
$47$	5.19615	+	3.00000i	0.110556	+	0.0638298i	−0.443702	+	0.896174i	$0.646335\pi$
$48$		0			0
$49$	12.0000	+	20.7846i	0.244898	+	0.424176i
$50$	41.5692	−	24.0000i	0.831384	−	0.480000i
$51$		0			0
$52$	−25.0000	+	43.3013i	−0.480769	+	0.832717i
$53$		−	27.0000i		−	0.509434i	−0.967016	−	0.254717i	$-0.918018\pi$
$53$		−	27.0000i		−	0.509434i	0.967016	−	0.254717i	$-0.0819823\pi$
$54$		0			0
$55$	−45.0000			−0.818182
$56$	12.9904	+	7.50000i	0.231971	+	0.133929i
$57$		0			0
$58$	45.0000	+	77.9423i	0.775862	+	1.34383i
$59$	−25.9808	+	15.0000i	−0.440352	+	0.254237i	−0.703747	−	0.710451i	$-0.748491\pi$
$59$	−25.9808	+	15.0000i	−0.440352	+	0.254237i	0.263395	+	0.964688i	$0.415158\pi$
$60$		0			0
$61$	38.0000	−	65.8179i	0.622951	−	1.07898i	−0.365982	−	0.930622i	$-0.619267\pi$
$61$	38.0000	−	65.8179i	0.622951	−	1.07898i	0.988933	−	0.148361i	$-0.0473997\pi$
$62$		−	3.00000i		−	0.0483871i
$63$		0			0
$64$	91.0000			1.42188
$65$	−25.9808	−	15.0000i	−0.399704	−	0.230769i
$66$		0			0
$67$	5.00000	+	8.66025i	0.0746269	+	0.129258i	0.900924	−	0.433977i	$-0.142890\pi$
$67$	5.00000	+	8.66025i	0.0746269	+	0.129258i	−0.826297	+	0.563235i	$0.809557\pi$
$68$	−77.9423	+	45.0000i	−1.14621	+	0.661765i
$69$		0			0
$70$	−22.5000	+	38.9711i	−0.321429	+	0.556731i
$71$		−	90.0000i		−	1.26761i	−0.773495	−	0.633803i	$-0.781493\pi$
$71$		−	90.0000i		−	1.26761i	0.773495	−	0.633803i	$-0.218507\pi$
$72$		0			0
$73$	65.0000			0.890411			0.445205	−	0.895428i	$-0.353131\pi$
$73$	65.0000			0.890411			0.445205	+	0.895428i	$0.353131\pi$
$74$	−51.9615	−	30.0000i	−0.702183	−	0.405405i
$75$		0			0
$76$	−40.0000	−	69.2820i	−0.526316	−	0.911606i
$77$	−64.9519	+	37.5000i	−0.843531	+	0.487013i
$78$		0			0
$79$	−7.00000	+	12.1244i	−0.0886076	+	0.153473i	−0.906923	−	0.421297i	$-0.861575\pi$
$79$	−7.00000	+	12.1244i	−0.0886076	+	0.153473i	0.818315	+	0.574770i	$0.194908\pi$
$80$			33.0000i			0.412500i
$81$		0			0
$82$	−180.000			−2.19512
$83$	−2.59808	−	1.50000i	−0.0313021	−	0.0180723i	0.484267	−	0.874920i	$-0.339086\pi$
$83$	−2.59808	−	1.50000i	−0.0313021	−	0.0180723i	−0.515569	+	0.856848i	$0.672420\pi$
$84$		0			0
$85$	−27.0000	−	46.7654i	−0.317647	−	0.550181i
$86$	129.904	−	75.0000i	1.51051	−	0.872093i
$87$		0			0
$88$	22.5000	−	38.9711i	0.255682	−	0.442854i
$89$			90.0000i			1.01124i	0.862757	+	0.505618i	$0.168735\pi$
$89$			90.0000i			1.01124i	−0.862757	+	0.505618i	$0.831265\pi$
$90$		0			0
$91$	−50.0000			−0.549451
$92$	−51.9615	−	30.0000i	−0.564799	−	0.326087i
$93$		0			0
$94$	−9.00000	−	15.5885i	−0.0957447	−	0.165835i
$95$	41.5692	−	24.0000i	0.437571	−	0.252632i
$96$		0			0
$97$	42.5000	−	73.6122i	0.438144	−	0.758888i	−0.559402	−	0.828896i	$-0.688969\pi$
$97$	42.5000	−	73.6122i	0.438144	−	0.758888i	0.997546	+	0.0700082i	$0.0223025\pi$
$98$		−	72.0000i		−	0.734694i
$99$		0			0
$100$	−80.0000			−0.800000
$101$	168.875	+	97.5000i	1.67203	+	0.965347i	0.966500	+	0.256665i	$0.0826238\pi$
$101$	168.875	+	97.5000i	1.67203	+	0.965347i	0.705529	+	0.708681i	$0.250709\pi$
$102$		0			0
$103$	−85.0000	−	147.224i	−0.825243	−	1.42936i	−0.901734	−	0.432292i	$-0.857705\pi$
$103$	−85.0000	−	147.224i	−0.825243	−	1.42936i	0.0764909	−	0.997070i	$-0.475628\pi$
$104$	25.9808	−	15.0000i	0.249815	−	0.144231i
$105$		0			0
$106$	−40.5000	+	70.1481i	−0.382075	+	0.661774i
$107$			189.000i			1.76636i	0.469039	+	0.883178i	$0.344600\pi$
$107$			189.000i			1.76636i	−0.469039	+	0.883178i	$0.655400\pi$
$108$		0			0
$109$	164.000			1.50459			0.752294	−	0.658828i	$-0.228948\pi$
$109$	164.000			1.50459			0.752294	+	0.658828i	$0.228948\pi$
$110$	116.913	+	67.5000i	1.06285	+	0.613636i
$111$		0			0
$112$	27.5000	+	47.6314i	0.245536	+	0.425280i
$113$	20.7846	−	12.0000i	0.183935	−	0.106195i	−0.405205	−	0.914226i	$-0.632800\pi$
$113$	20.7846	−	12.0000i	0.183935	−	0.106195i	0.589140	+	0.808031i	$0.299467\pi$
$114$		0			0
$115$	18.0000	−	31.1769i	0.156522	−	0.271104i
$116$		−	150.000i		−	1.29310i
$117$		0			0
$118$	90.0000			0.762712
$119$	−77.9423	−	45.0000i	−0.654977	−	0.378151i
$120$		0			0
$121$	52.0000	+	90.0666i	0.429752	+	0.744352i
$122$	−197.454	+	114.000i	−1.61847	+	0.934426i
$123$		0			0
$124$	−2.50000	+	4.33013i	−0.0201613	+	0.0349204i
$125$		−	123.000i		−	0.984000i
$126$		0			0
$127$	−205.000			−1.61417			−0.807087	−	0.590433i	$-0.798957\pi$
$127$	−205.000			−1.61417			−0.807087	+	0.590433i	$0.798957\pi$
$128$	−80.5404	−	46.5000i	−0.629222	−	0.363281i
$129$		0			0
$130$	45.0000	+	77.9423i	0.346154	+	0.599556i
$131$	12.9904	−	7.50000i	0.0991632	−	0.0572519i	−0.449598	−	0.893231i	$-0.648433\pi$
$131$	12.9904	−	7.50000i	0.0991632	−	0.0572519i	0.548761	+	0.835979i	$0.315100\pi$
$132$		0			0
$133$	40.0000	−	69.2820i	0.300752	−	0.520918i
$134$		−	30.0000i		−	0.223881i
$135$		0			0
$136$	54.0000			0.397059
$137$	−119.512	−	69.0000i	−0.872347	−	0.503650i	−0.00421937	−	0.999991i	$-0.501343\pi$
$137$	−119.512	−	69.0000i	−0.872347	−	0.503650i	−0.868127	+	0.496341i	$0.834676\pi$
$138$		0			0
$139$	14.0000	+	24.2487i	0.100719	+	0.174451i	0.911981	−	0.410232i	$-0.134552\pi$
$139$	14.0000	+	24.2487i	0.100719	+	0.174451i	−0.811262	+	0.584683i	$0.801219\pi$
$140$	64.9519	−	37.5000i	0.463942	−	0.267857i
$141$		0			0
$142$	−135.000	+	233.827i	−0.950704	+	1.64667i
$143$			150.000i			1.04895i
$144$		0			0
$145$	90.0000			0.620690
$146$	−168.875	−	97.5000i	−1.15668	−	0.667808i
$147$		0			0
$148$	50.0000	+	86.6025i	0.337838	+	0.585152i
$149$	−64.9519	+	37.5000i	−0.435919	+	0.251678i	−0.701865	−	0.712310i	$-0.747649\pi$
$149$	−64.9519	+	37.5000i	−0.435919	+	0.251678i	0.265946	+	0.963988i	$0.414316\pi$
$150$		0			0
$151$	−38.5000	+	66.6840i	−0.254967	+	0.441616i	−0.964887	−	0.262667i	$-0.915398\pi$
$151$	−38.5000	+	66.6840i	−0.254967	+	0.441616i	0.709920	+	0.704283i	$0.248731\pi$
$152$			48.0000i			0.315789i
$153$		0			0
$154$	225.000			1.46104
$155$	−2.59808	−	1.50000i	−0.0167618	−	0.00967742i
$156$		0			0
$157$	50.0000	+	86.6025i	0.318471	+	0.551609i	0.980169	−	0.198162i	$-0.0634972\pi$
$157$	50.0000	+	86.6025i	0.318471	+	0.551609i	−0.661698	+	0.749771i	$0.730164\pi$
$158$	36.3731	−	21.0000i	0.230209	−	0.132911i
$159$		0			0
$160$	67.5000	−	116.913i	0.421875	−	0.730709i
$161$		−	60.0000i		−	0.372671i
$162$		0			0
$163$	110.000			0.674847			0.337423	−	0.941353i	$-0.390445\pi$
$163$	110.000			0.674847			0.337423	+	0.941353i	$0.390445\pi$
$164$	259.808	+	150.000i	1.58419	+	0.914634i
$165$		0			0
$166$	4.50000	+	7.79423i	0.0271084	+	0.0469532i
$167$	67.5500	−	39.0000i	0.404491	−	0.233533i	−0.283929	−	0.958845i	$-0.591638\pi$
$167$	67.5500	−	39.0000i	0.404491	−	0.233533i	0.688420	+	0.725312i	$0.258305\pi$
$168$		0			0
$169$	34.5000	−	59.7558i	0.204142	−	0.353584i
$170$			162.000i			0.952941i
$171$		0			0
$172$	−250.000			−1.45349
$173$	153.286	+	88.5000i	0.886049	+	0.511561i	0.872648	−	0.488350i	$-0.162401\pi$
$173$	153.286	+	88.5000i	0.886049	+	0.511561i	0.0134010	+	0.999910i	$0.495734\pi$
$174$		0			0
$175$	−40.0000	−	69.2820i	−0.228571	−	0.395897i
$176$	142.894	−	82.5000i	0.811899	−	0.468750i
$177$		0			0
$178$	135.000	−	233.827i	0.758427	−	1.31363i
$179$		−	225.000i		−	1.25698i	−0.777816	−	0.628492i	$-0.783673\pi$
$179$		−	225.000i		−	1.25698i	0.777816	−	0.628492i	$-0.216327\pi$
$180$		0			0
$181$	−16.0000			−0.0883978			−0.0441989	−	0.999023i	$-0.514074\pi$
$181$	−16.0000			−0.0883978			−0.0441989	+	0.999023i	$0.514074\pi$
$182$	129.904	+	75.0000i	0.713757	+	0.412088i
$183$		0			0
$184$	18.0000	+	31.1769i	0.0978261	+	0.169440i
$185$	−51.9615	+	30.0000i	−0.280873	+	0.162162i
$186$		0			0
$187$	−135.000	+	233.827i	−0.721925	+	1.25041i
$188$			30.0000i			0.159574i
$189$		0			0
$190$	−144.000			−0.757895
$191$	−25.9808	−	15.0000i	−0.136025	−	0.0785340i	0.430443	−	0.902618i	$-0.358357\pi$
$191$	−25.9808	−	15.0000i	−0.136025	−	0.0785340i	−0.566468	+	0.824084i	$0.691691\pi$
$192$		0			0
$193$	−107.500	−	186.195i	−0.556995	−	0.964743i	−0.997745	−	0.0671137i	$-0.978621\pi$
$193$	−107.500	−	186.195i	−0.556995	−	0.964743i	0.440751	−	0.897630i	$-0.354712\pi$
$194$	−220.836	+	127.500i	−1.13833	+	0.657216i
$195$		0			0
$196$	−60.0000	+	103.923i	−0.306122	+	0.530220i
$197$		−	207.000i		−	1.05076i	−0.850867	−	0.525381i	$-0.823923\pi$
$197$		−	207.000i		−	1.05076i	0.850867	−	0.525381i	$-0.176077\pi$
$198$		0			0
$199$	−223.000			−1.12060			−0.560302	−	0.828289i	$-0.689315\pi$
$199$	−223.000			−1.12060			−0.560302	+	0.828289i	$0.689315\pi$
$200$	41.5692	+	24.0000i	0.207846	+	0.120000i
$201$		0			0
$202$	−292.500	−	506.625i	−1.44802	−	2.50804i
$203$	129.904	−	75.0000i	0.639920	−	0.369458i
$204$		0			0
$205$	−90.0000	+	155.885i	−0.439024	+	0.760413i
$206$			510.000i			2.47573i
$207$		0			0
$208$	110.000			0.528846
$209$	−207.846	−	120.000i	−0.994479	−	0.574163i
$210$		0			0
$211$	158.000	+	273.664i	0.748815	+	1.29699i	0.948391	+	0.317104i	$0.102710\pi$
$211$	158.000	+	273.664i	0.748815	+	1.29699i	−0.199576	+	0.979882i	$0.563956\pi$
$212$	116.913	−	67.5000i	0.551478	−	0.318396i
$213$		0			0
$214$	283.500	−	491.036i	1.32477	−	2.29456i
$215$		−	150.000i		−	0.697674i
$216$		0			0
$217$	−5.00000			−0.0230415
$218$	−426.084	−	246.000i	−1.95452	−	1.12844i
$219$		0			0
$220$	−112.500	−	194.856i	−0.511364	−	0.885708i
$221$	−155.885	+	90.0000i	−0.705360	+	0.407240i
$222$		0			0
$223$	65.0000	−	112.583i	0.291480	−	0.504858i	−0.682680	−	0.730717i	$-0.739186\pi$
$223$	65.0000	−	112.583i	0.291480	−	0.504858i	0.974160	+	0.225860i	$0.0725190\pi$
$224$		−	225.000i		−	1.00446i
$225$		0			0
$226$	−72.0000			−0.318584
$227$	36.3731	+	21.0000i	0.160234	+	0.0925110i	0.577973	−	0.816056i	$-0.303844\pi$
$227$	36.3731	+	21.0000i	0.160234	+	0.0925110i	−0.417739	+	0.908567i	$0.637177\pi$
$228$		0			0
$229$	113.000	+	195.722i	0.493450	+	0.854680i	0.999972	−	0.00754710i	$-0.00240234\pi$
$229$	113.000	+	195.722i	0.493450	+	0.854680i	−0.506522	+	0.862227i	$0.669069\pi$
$230$	−93.5307	+	54.0000i	−0.406655	+	0.234783i
$231$		0			0
$232$	−45.0000	+	77.9423i	−0.193966	+	0.335958i
$233$			234.000i			1.00429i	0.864783	+	0.502146i	$0.167456\pi$
$233$			234.000i			1.00429i	−0.864783	+	0.502146i	$0.832544\pi$
$234$		0			0
$235$	−18.0000			−0.0765957
$236$	−129.904	−	75.0000i	−0.550440	−	0.317797i
$237$		0			0
$238$	135.000	+	233.827i	0.567227	+	0.982466i
$239$	−103.923	+	60.0000i	−0.434824	+	0.251046i	−0.701400	−	0.712768i	$-0.747441\pi$
$239$	−103.923	+	60.0000i	−0.434824	+	0.251046i	0.266575	+	0.963814i	$0.414108\pi$
$240$		0			0
$241$	−7.00000	+	12.1244i	−0.0290456	+	0.0503085i	−0.880183	−	0.474635i	$-0.842580\pi$
$241$	−7.00000	+	12.1244i	−0.0290456	+	0.0503085i	0.851137	+	0.524943i	$0.175913\pi$
$242$		−	312.000i		−	1.28926i
$243$		0			0
$244$	380.000			1.55738
$245$	−62.3538	−	36.0000i	−0.254505	−	0.146939i
$246$		0			0
$247$	−80.0000	−	138.564i	−0.323887	−	0.560988i
$248$	2.59808	−	1.50000i	0.0104761	−	0.00604839i
$249$		0			0
$250$	−184.500	+	319.563i	−0.738000	+	1.27825i
$251$			90.0000i			0.358566i	0.983798	+	0.179283i	$0.0573777\pi$
$251$			90.0000i			0.358566i	−0.983798	+	0.179283i	$0.942622\pi$
$252$		0			0
$253$	−180.000			−0.711462
$254$	532.606	+	307.500i	2.09687	+	1.21063i
$255$		0			0
$256$	−42.5000	−	73.6122i	−0.166016	−	0.287547i
$257$	379.319	−	219.000i	1.47595	−	0.852140i	0.476318	−	0.879273i	$-0.341971\pi$
$257$	379.319	−	219.000i	1.47595	−	0.852140i	0.999632	+	0.0271330i	$0.00863775\pi$
$258$		0			0
$259$	−50.0000	+	86.6025i	−0.193050	+	0.334373i
$260$		−	150.000i		−	0.576923i
$261$		0			0
$262$	−45.0000			−0.171756
$263$	239.023	+	138.000i	0.908833	+	0.524715i	0.880055	−	0.474871i	$-0.157505\pi$
$263$	239.023	+	138.000i	0.908833	+	0.524715i	0.0287773	+	0.999586i	$0.490839\pi$
$264$		0			0
$265$	40.5000	+	70.1481i	0.152830	+	0.264710i
$266$	−207.846	+	120.000i	−0.781376	+	0.451128i
$267$		0			0
$268$	−25.0000	+	43.3013i	−0.0932836	+	0.161572i
$269$			270.000i			1.00372i	0.864950	+	0.501859i	$0.167350\pi$
$269$			270.000i			1.00372i	−0.864950	+	0.501859i	$0.832650\pi$
$270$		0			0
$271$	299.000			1.10332			0.551661	−	0.834069i	$-0.313994\pi$
$271$	299.000			1.10332			0.551661	+	0.834069i	$0.313994\pi$
$272$	171.473	+	99.0000i	0.630416	+	0.363971i
$273$		0			0
$274$	207.000	+	358.535i	0.755474	+	1.30852i
$275$	−207.846	+	120.000i	−0.755804	+	0.436364i
$276$		0			0
$277$	−70.0000	+	121.244i	−0.252708	+	0.437702i	−0.964270	−	0.264920i	$-0.914654\pi$
$277$	−70.0000	+	121.244i	−0.252708	+	0.437702i	0.711563	+	0.702623i	$0.247988\pi$
$278$		−	84.0000i		−	0.302158i
$279$		0			0
$280$	−45.0000			−0.160714
$281$	129.904	+	75.0000i	0.462291	+	0.266904i	0.713007	−	0.701157i	$-0.247333\pi$
$281$	129.904	+	75.0000i	0.462291	+	0.266904i	−0.250716	+	0.968061i	$0.580666\pi$
$282$		0			0
$283$	140.000	+	242.487i	0.494700	+	0.856845i	0.999981	−	0.00610955i	$-0.00194474\pi$
$283$	140.000	+	242.487i	0.494700	+	0.856845i	−0.505282	+	0.862954i	$0.668611\pi$
$284$	389.711	−	225.000i	1.37222	−	0.792254i
$285$		0			0
$286$	225.000	−	389.711i	0.786713	−	1.36263i
$287$			300.000i			1.04530i
$288$		0			0
$289$	−35.0000			−0.121107
$290$	−233.827	−	135.000i	−0.806300	−	0.465517i
$291$		0			0
$292$	162.500	+	281.458i	0.556507	+	0.963898i
$293$	223.435	−	129.000i	0.762575	−	0.440273i	−0.0676443	−	0.997709i	$-0.521548\pi$
$293$	223.435	−	129.000i	0.762575	−	0.440273i	0.830220	+	0.557436i	$0.188215\pi$
$294$		0			0
$295$	45.0000	−	77.9423i	0.152542	−	0.264211i
$296$		−	60.0000i		−	0.202703i
$297$		0			0
$298$	225.000			0.755034
$299$	−103.923	−	60.0000i	−0.347569	−	0.200669i
$300$		0			0
$301$	−125.000	−	216.506i	−0.415282	−	0.719290i
$302$	200.052	−	115.500i	0.662423	−	0.382450i
$303$		0			0
$304$	−88.0000	+	152.420i	−0.289474	+	0.501383i
$305$			228.000i			0.747541i
$306$		0			0
$307$	290.000			0.944625			0.472313	−	0.881431i	$-0.343419\pi$
$307$	290.000			0.944625			0.472313	+	0.881431i	$0.343419\pi$
$308$	−324.760	−	187.500i	−1.05441	−	0.608766i
$309$		0			0
$310$	4.50000	+	7.79423i	0.0145161	+	0.0251427i
$311$	−415.692	+	240.000i	−1.33663	+	0.771704i	−0.986306	−	0.164924i	$-0.947262\pi$
$311$	−415.692	+	240.000i	−1.33663	+	0.771704i	−0.350325	+	0.936628i	$0.613929\pi$
$312$		0			0
$313$	−92.5000	+	160.215i	−0.295527	+	0.511868i	−0.975107	−	0.221733i	$-0.928829\pi$
$313$	−92.5000	+	160.215i	−0.295527	+	0.511868i	0.679580	+	0.733601i	$0.262162\pi$
$314$		−	300.000i		−	0.955414i
$315$		0			0
$316$	−70.0000			−0.221519
$317$	−158.483	−	91.5000i	−0.499945	−	0.288644i	0.228746	−	0.973486i	$-0.426538\pi$
$317$	−158.483	−	91.5000i	−0.499945	−	0.288644i	−0.728691	+	0.684843i	$0.759871\pi$
$318$		0			0
$319$	−225.000	−	389.711i	−0.705329	−	1.22167i
$320$	−236.425	+	136.500i	−0.738828	+	0.426563i
$321$		0			0
$322$	−90.0000	+	155.885i	−0.279503	+	0.484114i
$323$		−	288.000i		−	0.891641i
$324$		0			0
$325$	−160.000			−0.492308
$326$	−285.788	−	165.000i	−0.876651	−	0.506135i
$327$		0			0
$328$	−90.0000	−	155.885i	−0.274390	−	0.475258i
$329$	−25.9808	+	15.0000i	−0.0789689	+	0.0455927i
$330$		0			0
$331$	119.000	−	206.114i	0.359517	−	0.622701i	−0.628363	−	0.777920i	$-0.716275\pi$
$331$	119.000	−	206.114i	0.359517	−	0.622701i	0.987880	+	0.155219i	$0.0496083\pi$
$332$		−	15.0000i		−	0.0451807i
$333$		0			0
$334$	−234.000			−0.700599
$335$	−25.9808	−	15.0000i	−0.0775545	−	0.0447761i
$336$		0			0
$337$	5.00000	+	8.66025i	0.0148368	+	0.0256981i	0.873348	−	0.487096i	$-0.161944\pi$
$337$	5.00000	+	8.66025i	0.0148368	+	0.0256981i	−0.858512	+	0.512794i	$0.828610\pi$
$338$	−179.267	+	103.500i	−0.530377	+	0.306213i
$339$		0			0
$340$	135.000	−	233.827i	0.397059	−	0.687726i
$341$			15.0000i			0.0439883i
$342$		0			0
$343$	−365.000			−1.06414
$344$	129.904	+	75.0000i	0.377627	+	0.218023i
$345$		0			0
$346$	−265.500	−	459.859i	−0.767341	−	1.32907i
$347$	59.7558	−	34.5000i	0.172207	−	0.0994236i	−0.411419	−	0.911446i	$-0.634967\pi$
$347$	59.7558	−	34.5000i	0.172207	−	0.0994236i	0.583626	+	0.812023i	$0.301633\pi$
$348$		0			0
$349$	128.000	−	221.703i	0.366762	−	0.635251i	−0.622295	−	0.782783i	$-0.713800\pi$
$349$	128.000	−	221.703i	0.366762	−	0.635251i	0.989057	+	0.147532i	$0.0471329\pi$
$350$			240.000i			0.685714i
$351$		0			0
$352$	−675.000			−1.91761
$353$	394.908	+	228.000i	1.11872	+	0.645892i	0.941073	−	0.338202i	$-0.109819\pi$
$353$	394.908	+	228.000i	1.11872	+	0.645892i	0.177645	+	0.984095i	$0.443152\pi$
$354$		0			0
$355$	135.000	+	233.827i	0.380282	+	0.658667i
$356$	−389.711	+	225.000i	−1.09470	+	0.632022i
$357$		0			0
$358$	−337.500	+	584.567i	−0.942737	+	1.63287i
$359$		−	450.000i		−	1.25348i	−0.779228	−	0.626741i	$-0.784388\pi$
$359$		−	450.000i		−	1.25348i	0.779228	−	0.626741i	$-0.215612\pi$
$360$		0			0
$361$	−105.000			−0.290859
$362$	41.5692	+	24.0000i	0.114832	+	0.0662983i
$363$		0			0
$364$	−125.000	−	216.506i	−0.343407	−	0.594798i
$365$	−168.875	+	97.5000i	−0.462671	+	0.267123i
$366$		0			0
$367$	312.500	−	541.266i	0.851499	−	1.47484i	−0.0283570	−	0.999598i	$-0.509028\pi$
$367$	312.500	−	541.266i	0.851499	−	1.47484i	0.879856	−	0.475241i	$-0.157639\pi$
$368$			132.000i			0.358696i
$369$		0			0
$370$	180.000			0.486486
$371$	116.913	+	67.5000i	0.315131	+	0.181941i
$372$		0			0
$373$	−85.0000	−	147.224i	−0.227882	−	0.394703i	0.729298	−	0.684196i	$-0.239847\pi$
$373$	−85.0000	−	147.224i	−0.227882	−	0.394703i	−0.957180	+	0.289493i	$0.906513\pi$
$374$	701.481	−	405.000i	1.87562	−	1.08289i
$375$		0			0
$376$	9.00000	−	15.5885i	0.0239362	−	0.0414587i
$377$		−	300.000i		−	0.795756i
$378$		0			0
$379$	704.000			1.85752			0.928760	−	0.370682i	$-0.120876\pi$
$379$	704.000			1.85752			0.928760	+	0.370682i	$0.120876\pi$
$380$	207.846	+	120.000i	0.546963	+	0.315789i
$381$		0			0
$382$	45.0000	+	77.9423i	0.117801	+	0.204037i
$383$	535.204	−	309.000i	1.39740	−	0.806789i	0.403279	−	0.915077i	$-0.367870\pi$
$383$	535.204	−	309.000i	1.39740	−	0.806789i	0.994120	+	0.108288i	$0.0345370\pi$
$384$		0			0
$385$	112.500	−	194.856i	0.292208	−	0.506119i
$386$			645.000i			1.67098i
$387$		0			0
$388$	425.000			1.09536
$389$	−454.663	−	262.500i	−1.16880	−	0.674807i	−0.215403	−	0.976525i	$-0.569107\pi$
$389$	−454.663	−	262.500i	−1.16880	−	0.674807i	−0.953397	+	0.301718i	$0.902440\pi$
$390$		0			0
$391$	−108.000	−	187.061i	−0.276215	−	0.478418i
$392$	62.3538	−	36.0000i	0.159066	−	0.0918367i
$393$		0			0
$394$	−310.500	+	537.802i	−0.788071	+	1.36498i
$395$		−	42.0000i		−	0.106329i
$396$		0			0
$397$	−70.0000			−0.176322			−0.0881612	−	0.996106i	$-0.528099\pi$
$397$	−70.0000			−0.176322			−0.0881612	+	0.996106i	$0.528099\pi$
$398$	579.371	+	334.500i	1.45571	+	0.840452i
$399$		0			0
$400$	88.0000	+	152.420i	0.220000	+	0.381051i
$401$	−103.923	+	60.0000i	−0.259160	+	0.149626i	−0.623951	−	0.781463i	$-0.714474\pi$
$401$	−103.923	+	60.0000i	−0.259160	+	0.149626i	0.364791	+	0.931089i	$0.381140\pi$
$402$		0			0
$403$	−5.00000	+	8.66025i	−0.0124069	+	0.0214895i
$404$			975.000i			2.41337i
$405$		0			0
$406$	−450.000			−1.10837
$407$	259.808	+	150.000i	0.638348	+	0.368550i
$408$		0			0
$409$	−134.500	−	232.961i	−0.328851	−	0.569586i	0.653433	−	0.756984i	$-0.273328\pi$
$409$	−134.500	−	232.961i	−0.328851	−	0.569586i	−0.982284	+	0.187398i	$0.939995\pi$
$410$	467.654	−	270.000i	1.14062	−	0.658537i
$411$		0			0
$412$	425.000	−	736.122i	1.03155	−	1.78670i
$413$		−	150.000i		−	0.363196i
$414$		0			0
$415$	9.00000			0.0216867
$416$	−389.711	−	225.000i	−0.936806	−	0.540865i
$417$		0			0
$418$	360.000	+	623.538i	0.861244	+	1.49172i
$419$	−181.865	+	105.000i	−0.434046	+	0.250597i	−0.701069	−	0.713094i	$-0.747293\pi$
$419$	−181.865	+	105.000i	−0.434046	+	0.250597i	0.267023	+	0.963690i	$0.413960\pi$
$420$		0			0
$421$	−322.000	+	557.720i	−0.764846	+	1.32475i	0.175483	+	0.984483i	$0.443851\pi$
$421$	−322.000	+	557.720i	−0.764846	+	1.32475i	−0.940328	+	0.340269i	$0.889482\pi$
$422$		−	948.000i		−	2.24645i
$423$		0			0
$424$	−81.0000			−0.191038
$425$	−249.415	−	144.000i	−0.586860	−	0.338824i
$426$		0			0
$427$	190.000	+	329.090i	0.444965	+	0.770702i
$428$	−818.394	+	472.500i	−1.91214	+	1.10397i
$429$		0			0
$430$	−225.000	+	389.711i	−0.523256	+	0.906306i
$431$			270.000i			0.626450i	0.949679	+	0.313225i	$0.101409\pi$
$431$			270.000i			0.626450i	−0.949679	+	0.313225i	$0.898591\pi$
$432$		0			0
$433$	−565.000			−1.30485			−0.652425	−	0.757853i	$-0.726248\pi$
$433$	−565.000			−1.30485			−0.652425	+	0.757853i	$0.726248\pi$
$434$	12.9904	+	7.50000i	0.0299318	+	0.0172811i
$435$		0			0
$436$	410.000	+	710.141i	0.940367	+	1.62876i
$437$	166.277	−	96.0000i	0.380496	−	0.219680i
$438$		0			0
$439$	105.500	−	182.731i	0.240319	−	0.416245i	−0.720486	−	0.693469i	$-0.756081\pi$
$439$	105.500	−	182.731i	0.240319	−	0.416245i	0.960805	+	0.277225i	$0.0894146\pi$
$440$			135.000i			0.306818i
$441$		0			0
$442$	540.000			1.22172
$443$	−431.281	−	249.000i	−0.973545	−	0.562077i	−0.0732302	−	0.997315i	$-0.523331\pi$
$443$	−431.281	−	249.000i	−0.973545	−	0.562077i	−0.900315	+	0.435238i	$0.856664\pi$
$444$		0			0
$445$	−135.000	−	233.827i	−0.303371	−	0.525454i
$446$	−337.750	+	195.000i	−0.757287	+	0.437220i
$447$		0			0
$448$	−227.500	+	394.042i	−0.507812	+	0.879557i
$449$		−	360.000i		−	0.801782i	−0.916126	−	0.400891i	$-0.868701\pi$
$449$		−	360.000i		−	0.801782i	0.916126	−	0.400891i	$-0.131299\pi$
$450$		0			0
$451$	900.000			1.99557
$452$	103.923	+	60.0000i	0.229918	+	0.132743i
$453$		0			0
$454$	−63.0000	−	109.119i	−0.138767	−	0.240351i
$455$	129.904	−	75.0000i	0.285503	−	0.164835i
$456$		0			0
$457$	−182.500	+	316.099i	−0.399344	+	0.691683i	−0.993645	−	0.112559i	$-0.964095\pi$
$457$	−182.500	+	316.099i	−0.399344	+	0.691683i	0.594301	+	0.804242i	$0.297429\pi$
$458$		−	678.000i		−	1.48035i
$459$		0			0
$460$	180.000			0.391304
$461$	90.9327	+	52.5000i	0.197251	+	0.113883i	0.595373	−	0.803450i	$-0.297004\pi$
$461$	90.9327	+	52.5000i	0.197251	+	0.113883i	−0.398122	+	0.917333i	$0.630338\pi$
$462$		0			0
$463$	−107.500	−	186.195i	−0.232181	−	0.402150i	0.726268	−	0.687411i	$-0.241253\pi$
$463$	−107.500	−	186.195i	−0.232181	−	0.402150i	−0.958450	+	0.285261i	$0.907920\pi$
$464$	−285.788	+	165.000i	−0.615923	+	0.355603i
$465$		0			0
$466$	351.000	−	607.950i	0.753219	−	1.30461i
$467$			63.0000i			0.134904i	0.997723	+	0.0674518i	$0.0214869\pi$
$467$			63.0000i			0.134904i	−0.997723	+	0.0674518i	$0.978513\pi$
$468$		0			0
$469$	−50.0000			−0.106610
$470$	46.7654	+	27.0000i	0.0995008	+	0.0574468i
$471$		0			0
$472$	45.0000	+	77.9423i	0.0953390	+	0.165132i
$473$	−649.519	+	375.000i	−1.37319	+	0.792812i
$474$		0			0
$475$	128.000	−	221.703i	0.269474	−	0.466742i
$476$		−	450.000i		−	0.945378i
$477$		0			0
$478$	360.000			0.753138
$479$	−649.519	−	375.000i	−1.35599	−	0.782881i	−0.366909	−	0.930257i	$-0.619584\pi$
$479$	−649.519	−	375.000i	−1.35599	−	0.782881i	−0.989081	+	0.147376i	$0.952917\pi$
$480$		0			0
$481$	100.000	+	173.205i	0.207900	+	0.360094i
$482$	36.3731	−	21.0000i	0.0754628	−	0.0435685i
$483$		0			0
$484$	−260.000	+	450.333i	−0.537190	+	0.930441i
$485$			255.000i			0.525773i
$486$		0			0
$487$	110.000			0.225873			0.112936	−	0.993602i	$-0.463974\pi$
$487$	110.000			0.225873			0.112936	+	0.993602i	$0.463974\pi$
$488$	−197.454	−	114.000i	−0.404618	−	0.233607i
$489$		0			0
$490$	108.000	+	187.061i	0.220408	+	0.381758i
$491$	558.586	−	322.500i	1.13765	−	0.656823i	0.191803	−	0.981433i	$-0.438567\pi$
$491$	558.586	−	322.500i	1.13765	−	0.656823i	0.945848	+	0.324611i	$0.105233\pi$
$492$		0			0
$493$	270.000	−	467.654i	0.547667	−	0.948588i
$494$			480.000i			0.971660i
$495$		0			0
$496$	11.0000			0.0221774
$497$	389.711	+	225.000i	0.784128	+	0.452716i
$498$		0			0
$499$	383.000	+	663.375i	0.767535	+	1.32941i	0.938896	+	0.344201i	$0.111850\pi$
$499$	383.000	+	663.375i	0.767535	+	1.32941i	−0.171361	+	0.985208i	$0.554816\pi$
$500$	532.606	−	307.500i	1.06521	−	0.615000i
$501$		0			0
$502$	135.000	−	233.827i	0.268924	−	0.465791i
$503$			828.000i			1.64612i	0.567952	+	0.823062i	$0.307736\pi$
$503$			828.000i			1.64612i	−0.567952	+	0.823062i	$0.692264\pi$
$504$		0			0
$505$	−585.000			−1.15842
$506$	467.654	+	270.000i	0.924217	+	0.533597i
$507$		0			0
$508$	−512.500	−	887.676i	−1.00886	−	1.74739i
$509$	480.644	−	277.500i	0.944291	−	0.545187i	0.0529881	−	0.998595i	$-0.483125\pi$
$509$	480.644	−	277.500i	0.944291	−	0.545187i	0.891303	+	0.453409i	$0.149792\pi$
$510$		0			0
$511$	−162.500	+	281.458i	−0.318004	+	0.550799i
$512$			627.000i			1.22461i
$513$		0			0
$514$	−1314.00			−2.55642
$515$	441.673	+	255.000i	0.857617	+	0.495146i
$516$		0			0
$517$	45.0000	+	77.9423i	0.0870406	+	0.150759i
$518$	259.808	−	150.000i	0.501559	−	0.289575i
$519$		0			0
$520$	−45.0000	+	77.9423i	−0.0865385	+	0.149889i
$521$		−	450.000i		−	0.863724i	−0.901940	−	0.431862i	$-0.857857\pi$
$521$		−	450.000i		−	0.863724i	0.901940	−	0.431862i	$-0.142143\pi$
$522$		0			0
$523$	−250.000			−0.478011			−0.239006	−	0.971018i	$-0.576821\pi$
$523$	−250.000			−0.478011			−0.239006	+	0.971018i	$0.576821\pi$
$524$	64.9519	+	37.5000i	0.123954	+	0.0715649i
$525$		0			0
$526$	−414.000	−	717.069i	−0.787072	−	1.36325i
$527$	−15.5885	+	9.00000i	−0.0295796	+	0.0170778i
$528$		0			0
$529$	−192.500	+	333.420i	−0.363894	+	0.630283i
$530$		−	243.000i		−	0.458491i
$531$		0			0
$532$	400.000			0.751880
$533$	519.615	+	300.000i	0.974888	+	0.562852i
$534$		0			0
$535$	−283.500	−	491.036i	−0.529907	−	0.917825i
$536$	25.9808	−	15.0000i	0.0484716	−	0.0279851i
$537$		0			0
$538$	405.000	−	701.481i	0.752788	−	1.30387i
$539$			360.000i			0.667904i
$540$		0			0
$541$	−268.000			−0.495379			−0.247689	−	0.968839i	$-0.579671\pi$
$541$	−268.000			−0.495379			−0.247689	+	0.968839i	$0.579671\pi$
$542$	−776.825	−	448.500i	−1.43326	−	0.827491i
$543$		0			0
$544$	−405.000	−	701.481i	−0.744485	−	1.28949i
$545$	−426.084	+	246.000i	−0.781806	+	0.451376i
$546$		0			0
$547$	−205.000	+	355.070i	−0.374771	+	0.649123i	−0.990293	−	0.138997i	$-0.955612\pi$
$547$	−205.000	+	355.070i	−0.374771	+	0.649123i	0.615521	+	0.788120i	$0.288945\pi$
$548$		−	690.000i		−	1.25912i
$549$		0			0
$550$	720.000			1.30909
$551$	415.692	+	240.000i	0.754432	+	0.435572i
$552$		0			0
$553$	−35.0000	−	60.6218i	−0.0632911	−	0.109623i
$554$	363.731	−	210.000i	0.656554	−	0.379061i
$555$		0			0
$556$	−70.0000	+	121.244i	−0.125899	+	0.218064i
$557$			639.000i			1.14722i	0.819130	+	0.573609i	$0.194457\pi$
$557$			639.000i			1.14722i	−0.819130	+	0.573609i	$0.805543\pi$
$558$		0			0
$559$	−500.000			−0.894454
$560$	−142.894	−	82.5000i	−0.255168	−	0.147321i
$561$		0			0
$562$	−225.000	−	389.711i	−0.400356	−	0.693437i
$563$	−174.071	+	100.500i	−0.309185	+	0.178508i	−0.646562	−	0.762862i	$-0.723794\pi$
$563$	−174.071	+	100.500i	−0.309185	+	0.178508i	0.337377	+	0.941370i	$0.390460\pi$
$564$		0			0
$565$	−36.0000	+	62.3538i	−0.0637168	+	0.110361i
$566$		−	840.000i		−	1.48410i
$567$		0			0
$568$	−270.000			−0.475352
$569$	207.846	+	120.000i	0.365283	+	0.210896i	0.671396	−	0.741099i	$-0.265695\pi$
$569$	207.846	+	120.000i	0.365283	+	0.210896i	−0.306113	+	0.951995i	$0.599028\pi$
$570$		0			0
$571$	473.000	+	819.260i	0.828371	+	1.43478i	0.899315	+	0.437301i	$0.144066\pi$
$571$	473.000	+	819.260i	0.828371	+	1.43478i	−0.0709440	+	0.997480i	$0.522601\pi$
$572$	−649.519	+	375.000i	−1.13552	+	0.655594i
$573$		0			0
$574$	450.000	−	779.423i	0.783972	−	1.35788i
$575$		−	192.000i		−	0.333913i
$576$		0			0
$577$	830.000			1.43847			0.719237	−	0.694764i	$-0.244491\pi$
$577$	830.000			1.43847			0.719237	+	0.694764i	$0.244491\pi$
$578$	90.9327	+	52.5000i	0.157323	+	0.0908304i
$579$		0			0
$580$	225.000	+	389.711i	0.387931	+	0.671916i
$581$	12.9904	−	7.50000i	0.0223587	−	0.0129088i
$582$		0			0
$583$	202.500	−	350.740i	0.347341	−	0.601613i
$584$		−	195.000i		−	0.333904i
$585$		0			0
$586$	−774.000			−1.32082
$587$	−392.310	−	226.500i	−0.668330	−	0.385860i	0.127114	−	0.991888i	$-0.459429\pi$
$587$	−392.310	−	226.500i	−0.668330	−	0.385860i	−0.795443	+	0.606028i	$0.792762\pi$
$588$		0			0
$589$	−8.00000	−	13.8564i	−0.0135823	−	0.0235253i
$590$	−233.827	+	135.000i	−0.396317	+	0.228814i
$591$		0			0
$592$	110.000	−	190.526i	0.185811	−	0.321834i
$593$		−	702.000i		−	1.18381i	−0.806007	−	0.591906i	$-0.798376\pi$
$593$		−	702.000i		−	1.18381i	0.806007	−	0.591906i	$-0.201624\pi$
$594$		0			0
$595$	270.000			0.453782
$596$	−324.760	−	187.500i	−0.544899	−	0.314597i
$597$		0			0
$598$	180.000	+	311.769i	0.301003	+	0.521353i
$599$	−961.288	+	555.000i	−1.60482	+	0.926544i	−0.614318	+	0.789059i	$0.710569\pi$
$599$	−961.288	+	555.000i	−1.60482	+	0.926544i	−0.990504	+	0.137486i	$0.956098\pi$
$600$		0			0
$601$	−434.500	+	752.576i	−0.722962	+	1.25221i	0.236846	+	0.971547i	$0.423886\pi$
$601$	−434.500	+	752.576i	−0.722962	+	1.25221i	−0.959807	+	0.280659i	$0.909447\pi$
$602$			750.000i			1.24585i
$603$		0			0
$604$	−385.000			−0.637417
$605$	−270.200	−	156.000i	−0.446611	−	0.257851i
$606$		0			0
$607$	−265.000	−	458.993i	−0.436573	−	0.756167i	0.560849	−	0.827918i	$-0.310475\pi$
$607$	−265.000	−	458.993i	−0.436573	−	0.756167i	−0.997423	+	0.0717508i	$0.977141\pi$
$608$	623.538	−	360.000i	1.02556	−	0.592105i
$609$		0			0
$610$	342.000	−	592.361i	0.560656	−	0.971084i
$611$			60.0000i			0.0981997i
$612$		0			0
$613$	−70.0000			−0.114192			−0.0570962	−	0.998369i	$-0.518184\pi$
$613$	−70.0000			−0.114192			−0.0570962	+	0.998369i	$0.518184\pi$
$614$	−753.442	−	435.000i	−1.22710	−	0.708469i
$615$		0			0
$616$	112.500	+	194.856i	0.182630	+	0.316324i
$617$	−478.046	+	276.000i	−0.774791	+	0.447326i	−0.834581	−	0.550885i	$-0.814290\pi$
$617$	−478.046	+	276.000i	−0.774791	+	0.447326i	0.0597901	+	0.998211i	$0.480957\pi$
$618$		0			0
$619$	−331.000	+	573.309i	−0.534733	+	0.926185i	0.464443	+	0.885603i	$0.346255\pi$
$619$	−331.000	+	573.309i	−0.534733	+	0.926185i	−0.999176	+	0.0405823i	$0.987079\pi$
$620$		−	15.0000i		−	0.0241935i
$621$		0			0
$622$	1440.00			2.31511
$623$	−389.711	−	225.000i	−0.625540	−	0.361156i
$624$		0			0
$625$	−15.5000	−	26.8468i	−0.0248000	−	0.0429549i
$626$	480.644	−	277.500i	0.767802	−	0.443291i
$627$		0			0
$628$	−250.000	+	433.013i	−0.398089	+	0.689511i
$629$			360.000i			0.572337i
$630$		0			0
$631$	−331.000			−0.524564			−0.262282	−	0.964991i	$-0.584475\pi$
$631$	−331.000			−0.524564			−0.262282	+	0.964991i	$0.584475\pi$
$632$	36.3731	+	21.0000i	0.0575523	+	0.0332278i
$633$		0			0
$634$	274.500	+	475.448i	0.432965	+	0.749918i
$635$	532.606	−	307.500i	0.838749	−	0.484252i
$636$		0			0
$637$	−120.000	+	207.846i	−0.188383	+	0.326289i
$638$			1350.00i			2.11599i
$639$		0			0
$640$	279.000			0.435937
$641$	51.9615	+	30.0000i	0.0810632	+	0.0468019i	0.539984	−	0.841675i	$-0.318430\pi$
$641$	51.9615	+	30.0000i	0.0810632	+	0.0468019i	−0.458920	+	0.888477i	$0.651764\pi$
$642$		0			0
$643$	−220.000	−	381.051i	−0.342146	−	0.592615i	0.642685	−	0.766131i	$-0.277820\pi$
$643$	−220.000	−	381.051i	−0.342146	−	0.592615i	−0.984831	+	0.173516i	$0.944487\pi$
$644$	259.808	−	150.000i	0.403428	−	0.232919i
$645$		0			0
$646$	−432.000	+	748.246i	−0.668731	+	1.15828i
$647$		−	972.000i		−	1.50232i	−0.660121	−	0.751159i	$-0.729495\pi$
$647$		−	972.000i		−	1.50232i	0.660121	−	0.751159i	$-0.270505\pi$
$648$		0			0
$649$	−450.000			−0.693374
$650$	415.692	+	240.000i	0.639526	+	0.369231i
$651$		0			0
$652$	275.000	+	476.314i	0.421779	+	0.730543i
$653$	418.290	−	241.500i	0.640567	−	0.369832i	−0.144266	−	0.989539i	$-0.546082\pi$
$653$	418.290	−	241.500i	0.640567	−	0.369832i	0.784833	+	0.619707i	$0.212749\pi$
$654$		0			0
$655$	−22.5000	+	38.9711i	−0.0343511	+	0.0594979i
$656$		−	660.000i		−	1.00610i
$657$		0			0
$658$	90.0000			0.136778
$659$	714.471	+	412.500i	1.08417	+	0.625948i	0.932019	−	0.362408i	$-0.118045\pi$
$659$	714.471	+	412.500i	1.08417	+	0.625948i	0.152155	+	0.988357i	$0.451379\pi$
$660$		0			0
$661$	464.000	+	803.672i	0.701967	+	1.21584i	0.967775	+	0.251816i	$0.0810278\pi$
$661$	464.000	+	803.672i	0.701967	+	1.21584i	−0.265808	+	0.964026i	$0.585639\pi$
$662$	−618.342	+	357.000i	−0.934052	+	0.539275i
$663$		0			0
$664$	−4.50000	+	7.79423i	−0.00677711	+	0.0117383i
$665$			240.000i			0.360902i
$666$		0			0
$667$	360.000			0.539730
$668$	337.750	+	195.000i	0.505614	+	0.291916i
$669$		0			0
$670$	45.0000	+	77.9423i	0.0671642	+	0.116332i
$671$	987.269	−	570.000i	1.47134	−	0.849478i
$672$		0			0
$673$	492.500	−	853.035i	0.731798	−	1.26751i	−0.224316	−	0.974516i	$-0.572015\pi$
$673$	492.500	−	853.035i	0.731798	−	1.26751i	0.956114	−	0.292995i	$-0.0946518\pi$
$674$		−	30.0000i		−	0.0445104i
$675$		0			0
$676$	345.000			0.510355
$677$	−306.573	−	177.000i	−0.452840	−	0.261448i	0.256189	−	0.966627i	$-0.417533\pi$
$677$	−306.573	−	177.000i	−0.452840	−	0.261448i	−0.709029	+	0.705179i	$0.750867\pi$
$678$		0			0
$679$	212.500	+	368.061i	0.312960	+	0.542063i
$680$	−140.296	+	81.0000i	−0.206318	+	0.119118i
$681$		0			0
$682$	22.5000	−	38.9711i	0.0329912	−	0.0571424i
$683$			198.000i			0.289898i	0.989439	+	0.144949i	$0.0463017\pi$
$683$			198.000i			0.289898i	−0.989439	+	0.144949i	$0.953698\pi$
$684$		0			0
$685$	414.000			0.604380
$686$	948.298	+	547.500i	1.38236	+	0.798105i
$687$		0			0
$688$	275.000	+	476.314i	0.399709	+	0.692317i
$689$	233.827	−	135.000i	0.339371	−	0.195936i
$690$		0			0
$691$	218.000	−	377.587i	0.315485	−	0.546436i	−0.664056	−	0.747683i	$-0.731166\pi$
$691$	218.000	−	377.587i	0.315485	−	0.546436i	0.979540	+	0.201247i	$0.0644995\pi$
$692$			885.000i			1.27890i
$693$		0			0
$694$	−207.000			−0.298271
$695$	−72.7461	−	42.0000i	−0.104671	−	0.0604317i
$696$		0			0
$697$	540.000	+	935.307i	0.774749	+	1.34190i
$698$	−665.108	+	384.000i	−0.952876	+	0.550143i
$699$		0			0
$700$	200.000	−	346.410i	0.285714	−	0.494872i
$701$			135.000i			0.192582i	0.995353	+	0.0962910i	$0.0306979\pi$
$701$			135.000i			0.192582i	−0.995353	+	0.0962910i	$0.969302\pi$
$702$		0			0
$703$	−320.000			−0.455192
$704$	1182.12	+	682.500i	1.67915	+	0.969460i
$705$		0			0
$706$	−684.000	−	1184.72i	−0.968839	−	1.67808i
$707$	−844.375	+	487.500i	−1.19431	+	0.689533i
$708$		0			0
$709$	−16.0000	+	27.7128i	−0.0225670	+	0.0390872i	−0.877088	−	0.480329i	$-0.840517\pi$
$709$	−16.0000	+	27.7128i	−0.0225670	+	0.0390872i	0.854521	+	0.519416i	$0.173851\pi$
$710$		−	810.000i		−	1.14085i
$711$		0			0
$712$	270.000			0.379213
$713$	−10.3923	−	6.00000i	−0.0145755	−	0.00841515i
$714$		0			0
$715$	−225.000	−	389.711i	−0.314685	−	0.545051i
$716$	974.279	−	562.500i	1.36072	−	0.785615i
$717$		0			0
$718$	−675.000	+	1169.13i	−0.940111	+	1.62832i
$719$		−	900.000i		−	1.25174i	−0.779928	−	0.625869i	$-0.784744\pi$
$719$		−	900.000i		−	1.25174i	0.779928	−	0.625869i	$-0.215256\pi$
$720$		0			0
$721$	850.000			1.17892
$722$	272.798	+	157.500i	0.377837	+	0.218144i
$723$		0			0
$724$	−40.0000	−	69.2820i	−0.0552486	−	0.0956934i
$725$	415.692	−	240.000i	0.573369	−	0.331034i
$726$		0			0
$727$	87.5000	−	151.554i	0.120358	−	0.208466i	−0.799551	−	0.600598i	$-0.794929\pi$
$727$	87.5000	−	151.554i	0.120358	−	0.208466i	0.919909	+	0.392133i	$0.128263\pi$
$728$			150.000i			0.206044i
$729$		0			0
$730$	585.000			0.801370
$731$	−779.423	−	450.000i	−1.06624	−	0.615595i
$732$		0			0
$733$	−580.000	−	1004.59i	−0.791269	−	1.37052i	−0.925182	−	0.379525i	$-0.876088\pi$
$733$	−580.000	−	1004.59i	−0.791269	−	1.37052i	0.133913	−	0.990993i	$-0.457246\pi$
$734$	−1623.80	+	937.500i	−2.21226	+	1.27725i
$735$		0			0
$736$	270.000	−	467.654i	0.366848	−	0.635399i
$737$			150.000i			0.203528i
$738$		0			0
$739$	−1006.00			−1.36130			−0.680650	−	0.732609i	$-0.738302\pi$
$739$	−1006.00			−1.36130			−0.680650	+	0.732609i	$0.738302\pi$
$740$	−259.808	−	150.000i	−0.351091	−	0.202703i
$741$		0			0
$742$	−202.500	−	350.740i	−0.272911	−	0.472696i
$743$	98.7269	−	57.0000i	0.132876	−	0.0767160i	−0.432088	−	0.901831i	$-0.642223\pi$
$743$	98.7269	−	57.0000i	0.132876	−	0.0767160i	0.564965	+	0.825115i	$0.308890\pi$
$744$		0			0
$745$	112.500	−	194.856i	0.151007	−	0.261551i
$746$			510.000i			0.683646i
$747$		0			0
$748$	−1350.00			−1.80481
$749$	−818.394	−	472.500i	−1.09265	−	0.630841i
$750$		0			0
$751$	−179.500	−	310.903i	−0.239015	−	0.413986i	0.721417	−	0.692501i	$-0.243491\pi$
$751$	−179.500	−	310.903i	−0.239015	−	0.413986i	−0.960432	+	0.278515i	$0.910158\pi$
$752$	57.1577	−	33.0000i	0.0760075	−	0.0438830i
$753$		0			0
$754$	−450.000	+	779.423i	−0.596817	+	1.03372i
$755$		−	231.000i		−	0.305960i
$756$		0			0
$757$	−430.000			−0.568032			−0.284016	−	0.958820i	$-0.591667\pi$
$757$	−430.000			−0.568032			−0.284016	+	0.958820i	$0.591667\pi$
$758$	−1829.05	−	1056.00i	−2.41299	−	1.39314i
$759$		0			0
$760$	−72.0000	−	124.708i	−0.0947368	−	0.164089i
$761$	1143.15	−	660.000i	1.50217	−	0.867280i	0.502176	−	0.864765i	$-0.332533\pi$
$761$	1143.15	−	660.000i	1.50217	−	0.867280i	0.999997	−	0.00251446i	$-0.000800378\pi$
$762$		0			0
$763$	−410.000	+	710.141i	−0.537353	+	0.930722i
$764$		−	150.000i		−	0.196335i
$765$		0			0
$766$	−1854.00			−2.42037
$767$	−259.808	−	150.000i	−0.338732	−	0.195567i
$768$		0			0
$769$	−629.500	−	1090.33i	−0.818596	−	1.41785i	−0.906717	−	0.421739i	$-0.861420\pi$
$769$	−629.500	−	1090.33i	−0.818596	−	1.41785i	0.0881215	−	0.996110i	$-0.471914\pi$
$770$	−584.567	+	337.500i	−0.759178	+	0.438312i
$771$		0			0
$772$	537.500	−	930.977i	0.696244	−	1.20593i
$773$		−	522.000i		−	0.675291i	−0.941273	−	0.337646i	$-0.890369\pi$
$773$		−	522.000i		−	0.675291i	0.941273	−	0.337646i	$-0.109631\pi$
$774$		0			0
$775$	−16.0000			−0.0206452
$776$	−220.836	−	127.500i	−0.284583	−	0.164304i
$777$		0			0
$778$	787.500	+	1363.99i	1.01221	+	1.75320i
$779$	−831.384	+	480.000i	−1.06725	+	0.616175i
$780$		0			0
$781$	675.000	−	1169.13i	0.864277	−	1.49697i
$782$			648.000i			0.828645i
$783$		0			0
$784$	264.000			0.336735
$785$	−259.808	−	150.000i	−0.330965	−	0.191083i
$786$		0			0
$787$	230.000	+	398.372i	0.292249	+	0.506190i	0.974341	−	0.225076i	$-0.0722630\pi$
$787$	230.000	+	398.372i	0.292249	+	0.506190i	−0.682092	+	0.731266i	$0.738930\pi$
$788$	896.336	−	517.500i	1.13748	−	0.656726i
$789$		0			0
$790$	−63.0000	+	109.119i	−0.0797468	+	0.138126i
$791$			120.000i			0.151707i
$792$		0			0
$793$	760.000			0.958386
$794$	181.865	+	105.000i	0.229050	+	0.132242i
$795$		0			0
$796$	−557.500	−	965.618i	−0.700377	−	1.21309i
$797$	−205.248	+	118.500i	−0.257526	+	0.148683i	−0.623205	−	0.782058i	$-0.714170\pi$
$797$	−205.248	+	118.500i	−0.257526	+	0.148683i	0.365680	+	0.930741i	$0.380837\pi$
$798$		0			0
$799$	−54.0000	+	93.5307i	−0.0675845	+	0.117060i
$800$		−	720.000i		−	0.900000i
$801$		0			0
$802$	360.000			0.448878
$803$	844.375	+	487.500i	1.05153	+	0.607098i
$804$		0			0
$805$	90.0000	+	155.885i	0.111801	+	0.193645i
$806$	25.9808	−	15.0000i	0.0322342	−	0.0186104i
$807$		0			0
$808$	292.500	−	506.625i	0.362005	−	0.627011i
$809$			810.000i			1.00124i	0.865668	+	0.500618i	$0.166894\pi$
$809$			810.000i			1.00124i	−0.865668	+	0.500618i	$0.833106\pi$
$810$		0			0
$811$	272.000			0.335388			0.167694	−	0.985839i	$-0.446368\pi$
$811$	272.000			0.335388			0.167694	+	0.985839i	$0.446368\pi$
$812$	649.519	+	375.000i	0.799900	+	0.461823i
$813$		0			0
$814$	−450.000	−	779.423i	−0.552826	−	0.957522i
$815$	−285.788	+	165.000i	−0.350661	+	0.202454i
$816$		0			0
$817$	400.000	−	692.820i	0.489596	−	0.848005i
$818$			807.000i			0.986553i
$819$		0			0
$820$	−900.000			−1.09756
$821$	−337.750	−	195.000i	−0.411388	−	0.237515i	0.279998	−	0.960001i	$-0.409666\pi$
$821$	−337.750	−	195.000i	−0.411388	−	0.237515i	−0.691386	+	0.722485i	$0.743000\pi$
$822$		0			0
$823$	−602.500	−	1043.56i	−0.732078	−	1.26800i	−0.955994	−	0.293387i	$-0.905217\pi$
$823$	−602.500	−	1043.56i	−0.732078	−	1.26800i	0.223916	−	0.974608i	$-0.428116\pi$
$824$	−441.673	+	255.000i	−0.536011	+	0.309466i
$825$		0			0
$826$	−225.000	+	389.711i	−0.272397	+	0.471806i
$827$			18.0000i			0.0217654i	0.999941	+	0.0108827i	$0.00346414\pi$
$827$			18.0000i			0.0217654i	−0.999941	+	0.0108827i	$0.996536\pi$
$828$		0			0
$829$	1442.00			1.73945			0.869723	−	0.493541i	$-0.164298\pi$
$829$	1442.00			1.73945			0.869723	+	0.493541i	$0.164298\pi$
$830$	−23.3827	−	13.5000i	−0.0281719	−	0.0162651i
$831$		0			0
$832$	455.000	+	788.083i	0.546875	+	0.947215i
$833$	−374.123	+	216.000i	−0.449127	+	0.259304i
$834$		0			0
$835$	−117.000	+	202.650i	−0.140120	+	0.242695i
$836$		−	1200.00i		−	1.43541i
$837$		0			0
$838$	630.000			0.751790
$839$	1376.98	+	795.000i	1.64122	+	0.947557i	0.980402	+	0.197007i	$0.0631222\pi$
$839$	1376.98	+	795.000i	1.64122	+	0.947557i	0.660814	+	0.750550i	$0.270211\pi$
$840$		0			0
$841$	29.5000	+	51.0955i	0.0350773	+	0.0607556i
$842$	1673.16	−	966.000i	1.98713	−	1.14727i
$843$		0			0
$844$	−790.000	+	1368.32i	−0.936019	+	1.62123i
$845$			207.000i			0.244970i
$846$		0			0
$847$	−520.000			−0.613932
$848$	−257.210	−	148.500i	−0.303313	−	0.175118i
$849$		0			0
$850$	432.000	+	748.246i	0.508235	+	0.880289i
$851$	−207.846	+	120.000i	−0.244237	+	0.141011i
$852$		0			0
$853$	−295.000	+	510.955i	−0.345838	+	0.599009i	−0.985506	−	0.169642i	$-0.945739\pi$
$853$	−295.000	+	510.955i	−0.345838	+	0.599009i	0.639667	+	0.768652i	$0.279072\pi$
$854$		−	1140.00i		−	1.33489i
$855$		0			0
$856$	567.000			0.662383
$857$	1127.57	+	651.000i	1.31571	+	0.759627i	0.983036	−	0.183415i	$-0.0587150\pi$
$857$	1127.57	+	651.000i	1.31571	+	0.759627i	0.332676	+	0.943041i	$0.392048\pi$
$858$		0			0
$859$	158.000	+	273.664i	0.183935	+	0.318584i	0.943217	−	0.332177i	$-0.107783\pi$
$859$	158.000	+	273.664i	0.183935	+	0.318584i	−0.759282	+	0.650761i	$0.774450\pi$
$860$	649.519	−	375.000i	0.755255	−	0.436047i
$861$		0			0
$862$	405.000	−	701.481i	0.469838	−	0.813783i
$863$			1188.00i			1.37659i	0.725429	+	0.688297i	$0.241641\pi$
$863$			1188.00i			1.37659i	−0.725429	+	0.688297i	$0.758359\pi$
$864$		0			0
$865$	−531.000			−0.613873
$866$	1467.91	+	847.500i	1.69505	+	0.978637i
$867$		0			0
$868$	−12.5000	−	21.6506i	−0.0144009	−	0.0249431i
$869$	−181.865	+	105.000i	−0.209281	+	0.120829i
$870$		0			0
$871$	−50.0000	+	86.6025i	−0.0574053	+	0.0994289i
$872$		−	492.000i		−	0.564220i
$873$		0			0
$874$	−576.000			−0.659039
$875$	532.606	+	307.500i	0.608692	+	0.351429i
$876$		0			0
$877$	275.000	+	476.314i	0.313569	+	0.543117i	0.979132	−	0.203224i	$-0.0651420\pi$
$877$	275.000	+	476.314i	0.313569	+	0.543117i	−0.665563	+	0.746341i	$0.731809\pi$
$878$	−548.194	+	316.500i	−0.624367	+	0.360478i
$879$		0			0
$880$	−247.500	+	428.683i	−0.281250	+	0.487139i
$881$		−	90.0000i		−	0.102157i	−0.998695	−	0.0510783i	$-0.983734\pi$
$881$		−	90.0000i		−	0.102157i	0.998695	−	0.0510783i	$-0.0162658\pi$
$882$		0			0
$883$	−880.000			−0.996602			−0.498301	−	0.867004i	$-0.666043\pi$
$883$	−880.000			−0.996602			−0.498301	+	0.867004i	$0.666043\pi$
$884$	−779.423	−	450.000i	−0.881700	−	0.509050i
$885$		0			0
$886$	747.000	+	1293.84i	0.843115	+	1.46032i
$887$	−244.219	+	141.000i	−0.275332	+	0.158963i	−0.631308	−	0.775532i	$-0.717482\pi$
$887$	−244.219	+	141.000i	−0.275332	+	0.158963i	0.355976	+	0.934495i	$0.384148\pi$
$888$		0			0
$889$	512.500	−	887.676i	0.576490	−	0.998511i
$890$			810.000i			0.910112i
$891$		0			0
$892$	650.000			0.728700
$893$	−83.1384	−	48.0000i	−0.0931002	−	0.0537514i
$894$		0			0
$895$	337.500	+	584.567i	0.377095	+	0.653148i
$896$	402.702	−	232.500i	0.449444	−	0.259487i
$897$		0			0
$898$	−540.000	+	935.307i	−0.601336	+	1.04155i
$899$		−	30.0000i		−	0.0333704i
$900$		0			0
$901$	486.000			0.539401
$902$	−2338.27	−	1350.00i	−2.59232	−	1.49667i
$903$		0			0
$904$	−36.0000	−	62.3538i	−0.0398230	−	0.0689755i
$905$	41.5692	−	24.0000i	0.0459328	−	0.0265193i
$906$		0			0
$907$	650.000	−	1125.83i	0.716648	−	1.24127i	−0.245672	−	0.969353i	$-0.579009\pi$
$907$	650.000	−	1125.83i	0.716648	−	1.24127i	0.962320	−	0.271918i	$-0.0876580\pi$
$908$			210.000i			0.231278i
$909$		0			0
$910$	−450.000			−0.494505
$911$	−181.865	−	105.000i	−0.199633	−	0.115258i	0.396851	−	0.917883i	$-0.370103\pi$
$911$	−181.865	−	105.000i	−0.199633	−	0.115258i	−0.596484	+	0.802625i	$0.703436\pi$
$912$		0			0
$913$	−22.5000	−	38.9711i	−0.0246440	−	0.0426847i
$914$	948.298	−	547.500i	1.03752	−	0.599015i
$915$		0			0
$916$	−565.000	+	978.609i	−0.616812	+	1.06835i
$917$			75.0000i			0.0817884i
$918$		0			0
$919$	137.000			0.149075			0.0745375	−	0.997218i	$-0.476252\pi$
$919$	137.000			0.149075			0.0745375	+	0.997218i	$0.476252\pi$
$920$	−93.5307	−	54.0000i	−0.101664	−	0.0586957i
$921$		0			0
$922$	−157.500	−	272.798i	−0.170824	−	0.295876i
$923$	779.423	−	450.000i	0.844445	−	0.487541i
$924$		0			0
$925$	−160.000	+	277.128i	−0.172973	+	0.299598i
$926$			645.000i			0.696544i
$927$		0			0
$928$	1350.00			1.45474
$929$	−571.577	−	330.000i	−0.615260	−	0.355221i	0.159761	−	0.987156i	$-0.448928\pi$
$929$	−571.577	−	330.000i	−0.615260	−	0.355221i	−0.775021	+	0.631935i	$0.782261\pi$
$930$		0			0
$931$	−192.000	−	332.554i	−0.206230	−	0.357201i
$932$	−1013.25	+	585.000i	−1.08718	+	0.627682i
$933$		0			0
$934$	94.5000	−	163.679i	0.101178	−	0.175245i
$935$		−	810.000i		−	0.866310i
$936$		0			0
$937$	605.000			0.645678			0.322839	−	0.946454i	$-0.395363\pi$
$937$	605.000			0.645678			0.322839	+	0.946454i	$0.395363\pi$
$938$	129.904	+	75.0000i	0.138490	+	0.0799574i
$939$		0			0
$940$	−45.0000	−	77.9423i	−0.0478723	−	0.0829173i
$941$	−1389.97	+	802.500i	−1.47712	+	0.852816i	−0.999666	−	0.0258401i	$-0.991774\pi$
$941$	−1389.97	+	802.500i	−1.47712	+	0.852816i	−0.477455	+	0.878656i	$0.658441\pi$
$942$		0			0
$943$	−360.000	+	623.538i	−0.381760	+	0.661228i
$944$			330.000i			0.349576i
$945$		0			0
$946$	2250.00			2.37844
$947$	−470.252	−	271.500i	−0.496570	−	0.286695i	0.230726	−	0.973019i	$-0.425890\pi$
$947$	−470.252	−	271.500i	−0.496570	−	0.286695i	−0.727296	+	0.686324i	$0.759223\pi$
$948$		0			0
$949$	325.000	+	562.917i	0.342466	+	0.593168i
$950$	−665.108	+	384.000i	−0.700113	+	0.404211i
$951$		0			0
$952$	−135.000	+	233.827i	−0.141807	+	0.245616i
$953$			144.000i			0.151102i	0.997142	+	0.0755509i	$0.0240715\pi$
$953$			144.000i			0.151102i	−0.997142	+	0.0755509i	$0.975928\pi$
$954$		0			0
$955$	90.0000			0.0942408
$956$	−519.615	−	300.000i	−0.543531	−	0.313808i
$957$		0			0
$958$	1125.00	+	1948.56i	1.17432	+	2.03398i
$959$	597.558	−	345.000i	0.623105	−	0.359750i
$960$		0			0
$961$	480.000	−	831.384i	0.499480	−	0.865124i
$962$		−	600.000i		−	0.623701i
$963$		0			0
$964$	−70.0000			−0.0726141
$965$	558.586	+	322.500i	0.578846	+	0.334197i
$966$		0			0
$967$	−422.500	−	731.791i	−0.436918	−	0.756765i	0.560532	−	0.828133i	$-0.310597\pi$
$967$	−422.500	−	731.791i	−0.436918	−	0.756765i	−0.997450	+	0.0713682i	$0.977263\pi$
$968$	270.200	−	156.000i	0.279132	−	0.161157i
$969$		0			0
$970$	382.500	−	662.509i	0.394330	−	0.682999i
$971$			405.000i			0.417096i	0.978012	+	0.208548i	$0.0668737\pi$
$971$			405.000i			0.417096i	−0.978012	+	0.208548i	$0.933126\pi$
$972$		0			0
$973$	−140.000			−0.143885
$974$	−285.788	−	165.000i	−0.293417	−	0.169405i
$975$		0			0
$976$	−418.000	−	723.997i	−0.428279	−	0.741800i
$977$	−213.042	+	123.000i	−0.218058	+	0.125896i	−0.605051	−	0.796187i	$-0.706847\pi$
$977$	−213.042	+	123.000i	−0.218058	+	0.125896i	0.386993	+	0.922083i	$0.373514\pi$
$978$		0			0
$979$	−675.000	+	1169.13i	−0.689479	+	1.19421i
$980$		−	360.000i		−	0.367347i
$981$		0			0
$982$	−1935.00			−1.97047
$983$	−898.934	−	519.000i	−0.914481	−	0.527976i	−0.0326105	−	0.999468i	$-0.510382\pi$
$983$	−898.934	−	519.000i	−0.914481	−	0.527976i	−0.881870	+	0.471493i	$0.843715\pi$
$984$		0			0
$985$	310.500	+	537.802i	0.315228	+	0.545992i
$986$	−1402.96	+	810.000i	−1.42288	+	0.821501i
$987$		0			0
$988$	400.000	−	692.820i	0.404858	−	0.701235i
$989$		−	600.000i		−	0.606673i
$990$		0			0
$991$	−1501.00			−1.51463			−0.757316	−	0.653049i	$-0.773490\pi$
$991$	−1501.00			−1.51463			−0.757316	+	0.653049i	$0.773490\pi$
$992$	−38.9711	−	22.5000i	−0.0392854	−	0.0226815i
$993$		0			0
$994$	−675.000	−	1169.13i	−0.679074	−	1.17619i
$995$	579.371	−	334.500i	0.582282	−	0.336181i
$996$		0			0
$997$	−385.000	+	666.840i	−0.386158	+	0.668846i	−0.991929	−	0.126793i	$-0.959532\pi$
$997$	−385.000	+	666.840i	−0.386158	+	0.668846i	0.605771	+	0.795639i	$0.292865\pi$
$998$		−	2298.00i		−	2.30261i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.3.d.b.26.1		4
3.2	odd	2	inner	81.3.d.b.26.2		4
4.3	odd	2		1296.3.q.j.593.1		4
9.2	odd	6		27.3.b.b.26.1	✓	2
9.4	even	3	inner	81.3.d.b.53.2		4
9.5	odd	6	inner	81.3.d.b.53.1		4
9.7	even	3		27.3.b.b.26.2	yes	2
12.11	even	2		1296.3.q.j.593.2		4
36.7	odd	6		432.3.e.c.161.1		2
36.11	even	6		432.3.e.c.161.2		2
36.23	even	6		1296.3.q.j.1025.1		4
36.31	odd	6		1296.3.q.j.1025.2		4
45.2	even	12		675.3.d.d.674.2		2
45.7	odd	12		675.3.d.a.674.2		2
45.29	odd	6		675.3.c.h.26.2		2
45.34	even	6		675.3.c.h.26.1		2
45.38	even	12		675.3.d.a.674.1		2
45.43	odd	12		675.3.d.d.674.1		2
72.11	even	6		1728.3.e.g.1025.1		2
72.29	odd	6		1728.3.e.m.1025.1		2
72.43	odd	6		1728.3.e.g.1025.2		2
72.61	even	6		1728.3.e.m.1025.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.3.b.b.26.1	✓	2	9.2	odd	6
27.3.b.b.26.2	yes	2	9.7	even	3
81.3.d.b.26.1		4	1.1	even	1	trivial
81.3.d.b.26.2		4	3.2	odd	2	inner
81.3.d.b.53.1		4	9.5	odd	6	inner
81.3.d.b.53.2		4	9.4	even	3	inner
432.3.e.c.161.1		2	36.7	odd	6
432.3.e.c.161.2		2	36.11	even	6
675.3.c.h.26.1		2	45.34	even	6
675.3.c.h.26.2		2	45.29	odd	6
675.3.d.a.674.1		2	45.38	even	12
675.3.d.a.674.2		2	45.7	odd	12
675.3.d.d.674.1		2	45.43	odd	12
675.3.d.d.674.2		2	45.2	even	12
1296.3.q.j.593.1		4	4.3	odd	2
1296.3.q.j.593.2		4	12.11	even	2
1296.3.q.j.1025.1		4	36.23	even	6
1296.3.q.j.1025.2		4	36.31	odd	6
1728.3.e.g.1025.1		2	72.11	even	6
1728.3.e.g.1025.2		2	72.43	odd	6
1728.3.e.m.1025.1		2	72.29	odd	6
1728.3.e.m.1025.2		2	72.61	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.59808 - 1.50000i) q^{2} +(2.50000 + 4.33013i) q^{4} +(-2.59808 + 1.50000i) q^{5} +(-2.50000 + 4.33013i) q^{7} -3.00000i q^{8} +9.00000 q^{10} +(12.9904 + 7.50000i) q^{11} +(5.00000 + 8.66025i) q^{13} +(12.9904 - 7.50000i) q^{14} +(5.50000 - 9.52628i) q^{16} +18.0000i q^{17} -16.0000 q^{19} +(-12.9904 - 7.50000i) q^{20} +(-22.5000 - 38.9711i) q^{22} +(-10.3923 + 6.00000i) q^{23} +(-8.00000 + 13.8564i) q^{25} -30.0000i q^{26} -25.0000 q^{28} +(-25.9808 - 15.0000i) q^{29} +(0.500000 + 0.866025i) q^{31} +(-38.9711 + 22.5000i) q^{32} +(27.0000 - 46.7654i) q^{34} -15.0000i q^{35} +20.0000 q^{37} +(41.5692 + 24.0000i) q^{38} +(4.50000 + 7.79423i) q^{40} +(51.9615 - 30.0000i) q^{41} +(-25.0000 + 43.3013i) q^{43} +75.0000i q^{44} +36.0000 q^{46} +(5.19615 + 3.00000i) q^{47} +(12.0000 + 20.7846i) q^{49} +(41.5692 - 24.0000i) q^{50} +(-25.0000 + 43.3013i) q^{52} -27.0000i q^{53} -45.0000 q^{55} +(12.9904 + 7.50000i) q^{56} +(45.0000 + 77.9423i) q^{58} +(-25.9808 + 15.0000i) q^{59} +(38.0000 - 65.8179i) q^{61} -3.00000i q^{62} +91.0000 q^{64} +(-25.9808 - 15.0000i) q^{65} +(5.00000 + 8.66025i) q^{67} +(-77.9423 + 45.0000i) q^{68} +(-22.5000 + 38.9711i) q^{70} -90.0000i q^{71} +65.0000 q^{73} +(-51.9615 - 30.0000i) q^{74} +(-40.0000 - 69.2820i) q^{76} +(-64.9519 + 37.5000i) q^{77} +(-7.00000 + 12.1244i) q^{79} +33.0000i q^{80} -180.000 q^{82} +(-2.59808 - 1.50000i) q^{83} +(-27.0000 - 46.7654i) q^{85} +(129.904 - 75.0000i) q^{86} +(22.5000 - 38.9711i) q^{88} +90.0000i q^{89} -50.0000 q^{91} +(-51.9615 - 30.0000i) q^{92} +(-9.00000 - 15.5885i) q^{94} +(41.5692 - 24.0000i) q^{95} +(42.5000 - 73.6122i) q^{97} -72.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 10 q^{4} - 10 q^{7} + 36 q^{10} + 20 q^{13} + 22 q^{16} - 64 q^{19} - 90 q^{22} - 32 q^{25} - 100 q^{28} + 2 q^{31} + 108 q^{34} + 80 q^{37} + 18 q^{40} - 100 q^{43} + 144 q^{46} + 48 q^{49} - 100 q^{52}+ \cdots + 170 q^{97}+O(q^{100}) \) 4 * q + 10 * q^4 - 10 * q^7 + 36 * q^10 + 20 * q^13 + 22 * q^16 - 64 * q^19 - 90 * q^22 - 32 * q^25 - 100 * q^28 + 2 * q^31 + 108 * q^34 + 80 * q^37 + 18 * q^40 - 100 * q^43 + 144 * q^46 + 48 * q^49 - 100 * q^52 - 180 * q^55 + 180 * q^58 + 152 * q^61 + 364 * q^64 + 20 * q^67 - 90 * q^70 + 260 * q^73 - 160 * q^76 - 28 * q^79 - 720 * q^82 - 108 * q^85 + 90 * q^88 - 200 * q^91 - 36 * q^94 + 170 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more