LMFDB - Embedded newform 81.5.d.b.53.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [81,5,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, 5, names="a")

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

chi := DirichletCharacter("81.26");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 81 = 3^{4} $
Weight:	$ k $	$=$	$ 5 $
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:	$8.37296700979$
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			53.2
Root			$0.866025 - 0.500000i$ of defining polynomial
Character	$\chi$	$=$	81.53
Dual form			81.5.d.b.26.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.59808 - 1.50000i) q^{2} +(-3.50000 + 6.06218i) q^{4} +(-28.5788 - 16.5000i) q^{5} +(9.50000 + 16.4545i) q^{7} +69.0000i q^{8} -99.0000 q^{10} +(-106.521 + 61.5000i) q^{11} +(-151.000 + 261.540i) q^{13} +(49.3634 + 28.5000i) q^{14} +(47.5000 + 82.2724i) q^{16} -414.000i q^{17} -304.000 q^{19} +(200.052 - 115.500i) q^{20} +(-184.500 + 319.563i) q^{22} +(259.808 + 150.000i) q^{23} +(232.000 + 401.836i) q^{25} +906.000i q^{26} -133.000 q^{28} +(587.165 - 339.000i) q^{29} +(-119.500 + 206.980i) q^{31} +(-709.275 - 409.500i) q^{32} +(-621.000 - 1075.60i) q^{34} -627.000i q^{35} +740.000 q^{37} +(-789.815 + 456.000i) q^{38} +(1138.50 - 1971.94i) q^{40} +(197.454 + 114.000i) q^{41} +(491.000 + 850.437i) q^{43} -861.000i q^{44} +900.000 q^{46} +(-1875.81 + 1083.00i) q^{47} +(1020.00 - 1766.69i) q^{49} +(1205.51 + 696.000i) q^{50} +(-1057.00 - 1830.78i) q^{52} +1593.00i q^{53} +4059.00 q^{55} +(-1135.36 + 655.500i) q^{56} +(1017.00 - 1761.50i) q^{58} +(-2530.53 - 1461.00i) q^{59} +(158.000 + 273.664i) q^{61} +717.000i q^{62} -3977.00 q^{64} +(8630.81 - 4983.00i) q^{65} +(-2311.00 + 4002.77i) q^{67} +(2509.74 + 1449.00i) q^{68} +(-940.500 - 1628.99i) q^{70} -1818.00i q^{71} -3031.00 q^{73} +(1922.58 - 1110.00i) q^{74} +(1064.00 - 1842.90i) q^{76} +(-2023.90 - 1168.50i) q^{77} +(5225.00 + 9049.97i) q^{79} -3135.00i q^{80} +684.000 q^{82} +(-10940.5 + 6316.50i) q^{83} +(-6831.00 + 11831.6i) q^{85} +(2551.31 + 1473.00i) q^{86} +(-4243.50 - 7349.96i) q^{88} +7002.00i q^{89} -5738.00 q^{91} +(-1818.65 + 1050.00i) q^{92} +(-3249.00 + 5627.43i) q^{94} +(8687.97 + 5016.00i) q^{95} +(3258.50 + 5643.89i) q^{97} -6120.00i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 14 q^{4} + 38 q^{7} - 396 q^{10} - 604 q^{13} + 190 q^{16} - 1216 q^{19} - 738 q^{22} + 928 q^{25} - 532 q^{28} - 478 q^{31} - 2484 q^{34} + 2960 q^{37} + 4554 q^{40} + 1964 q^{43} + 3600 q^{46} + 4080 q^{49}+ \cdots + 13034 q^{97}+O(q^{100}) $ 4 * q - 14 * q^4 + 38 * q^7 - 396 * q^10 - 604 * q^13 + 190 * q^16 - 1216 * q^19 - 738 * q^22 + 928 * q^25 - 532 * q^28 - 478 * q^31 - 2484 * q^34 + 2960 * q^37 + 4554 * q^40 + 1964 * q^43 + 3600 * q^46 + 4080 * q^49 - 4228 * q^52 + 16236 * q^55 + 4068 * q^58 + 632 * q^61 - 15908 * q^64 - 9244 * q^67 - 3762 * q^70 - 12124 * q^73 + 4256 * q^76 + 20900 * q^79 + 2736 * q^82 - 27324 * q^85 - 16974 * q^88 - 22952 * q^91 - 12996 * q^94 + 13034 * q^97

Character values

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

$n$	$2$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

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 $

$2$	2.59808	−	1.50000i	0.649519	−	0.375000i	−0.138753	−	0.990327i	$-0.544309\pi$
$2$	2.59808	−	1.50000i	0.649519	−	0.375000i	0.788272	+	0.615327i	$0.210976\pi$
$3$		0			0
$3$		0			0
$4$	−3.50000	+	6.06218i	−0.218750	+	0.378886i
$5$	−28.5788	−	16.5000i	−1.14315	−	0.660000i	−0.195944	−	0.980615i	$-0.562777\pi$
$5$	−28.5788	−	16.5000i	−1.14315	−	0.660000i	−0.947210	+	0.320615i	$0.896110\pi$
$6$		0			0
$7$	9.50000	+	16.4545i	0.193878	+	0.335806i	0.946532	−	0.322610i	$-0.104560\pi$
$7$	9.50000	+	16.4545i	0.193878	+	0.335806i	−0.752654	+	0.658416i	$0.771227\pi$
$8$			69.0000i			1.07812i
$9$		0			0
$10$	−99.0000			−0.990000
$11$	−106.521	+	61.5000i	−0.880340	+	0.508264i	−0.870770	−	0.491690i	$-0.836379\pi$
$11$	−106.521	+	61.5000i	−0.880340	+	0.508264i	−0.00956942	+	0.999954i	$0.503046\pi$
$12$		0			0
$13$	−151.000	+	261.540i	−0.893491	+	1.54757i	−0.0578301	+	0.998326i	$0.518418\pi$
$13$	−151.000	+	261.540i	−0.893491	+	1.54757i	−0.835661	+	0.549246i	$0.814915\pi$
$14$	49.3634	+	28.5000i	0.251854	+	0.145408i
$15$		0			0
$16$	47.5000	+	82.2724i	0.185547	+	0.321377i
$17$		−	414.000i		−	1.43253i	−0.697830	−	0.716263i	$-0.745851\pi$
$17$		−	414.000i		−	1.43253i	0.697830	−	0.716263i	$-0.254149\pi$
$18$		0			0
$19$	−304.000			−0.842105			−0.421053	−	0.907036i	$-0.638339\pi$
$19$	−304.000			−0.842105			−0.421053	+	0.907036i	$0.638339\pi$
$20$	200.052	−	115.500i	0.500130	−	0.288750i
$21$		0			0
$22$	−184.500	+	319.563i	−0.381198	+	0.660255i
$23$	259.808	+	150.000i	0.491130	+	0.283554i	0.725043	−	0.688704i	$-0.241820\pi$
$23$	259.808	+	150.000i	0.491130	+	0.283554i	−0.233913	+	0.972257i	$0.575153\pi$
$24$		0			0
$25$	232.000	+	401.836i	0.371200	+	0.642937i
$26$			906.000i			1.34024i
$27$		0			0
$28$	−133.000			−0.169643
$29$	587.165	−	339.000i	0.698175	−	0.403092i	−0.108492	−	0.994097i	$-0.534602\pi$
$29$	587.165	−	339.000i	0.698175	−	0.403092i	0.806667	+	0.591006i	$0.201269\pi$
$30$		0			0
$31$	−119.500	+	206.980i	−0.124350	+	0.215380i	−0.921479	−	0.388429i	$-0.873018\pi$
$31$	−119.500	+	206.980i	−0.124350	+	0.215380i	0.797129	+	0.603809i	$0.206351\pi$
$32$	−709.275	−	409.500i	−0.692651	−	0.399902i
$33$		0			0
$34$	−621.000	−	1075.60i	−0.537197	−	0.930453i
$35$		−	627.000i		−	0.511837i
$36$		0			0
$37$	740.000			0.540541			0.270270	−	0.962784i	$-0.412887\pi$
$37$	740.000			0.540541			0.270270	+	0.962784i	$0.412887\pi$
$38$	−789.815	+	456.000i	−0.546963	+	0.315789i
$39$		0			0
$40$	1138.50	−	1971.94i	0.711562	−	1.23246i
$41$	197.454	+	114.000i	0.117462	+	0.0678168i	0.557580	−	0.830123i	$-0.311730\pi$
$41$	197.454	+	114.000i	0.117462	+	0.0678168i	−0.440118	+	0.897940i	$0.645063\pi$
$42$		0			0
$43$	491.000	+	850.437i	0.265549	+	0.459944i	0.967707	−	0.252077i	$-0.0811135\pi$
$43$	491.000	+	850.437i	0.265549	+	0.459944i	−0.702158	+	0.712021i	$0.747780\pi$
$44$		−	861.000i		−	0.444731i
$45$		0			0
$46$	900.000			0.425331
$47$	−1875.81	+	1083.00i	−0.849168	+	0.490267i	−0.860370	−	0.509670i	$-0.829767\pi$
$47$	−1875.81	+	1083.00i	−0.849168	+	0.490267i	0.0112024	+	0.999937i	$0.496434\pi$
$48$		0			0
$49$	1020.00	−	1766.69i	0.424823	−	0.735815i
$50$	1205.51	+	696.000i	0.482203	+	0.278400i
$51$		0			0
$52$	−1057.00	−	1830.78i	−0.390902	−	0.677063i
$53$			1593.00i			0.567106i	0.958957	+	0.283553i	$0.0915131\pi$
$53$			1593.00i			0.567106i	−0.958957	+	0.283553i	$0.908487\pi$
$54$		0			0
$55$	4059.00			1.34182
$56$	−1135.36	+	655.500i	−0.362041	+	0.209024i
$57$		0			0
$58$	1017.00	−	1761.50i	0.302319	−	0.523631i
$59$	−2530.53	−	1461.00i	−0.726954	−	0.419707i	0.0903529	−	0.995910i	$-0.471200\pi$
$59$	−2530.53	−	1461.00i	−0.726954	−	0.419707i	−0.817307	+	0.576203i	$0.804534\pi$
$60$		0			0
$61$	158.000	+	273.664i	0.0424617	+	0.0735458i	0.886475	−	0.462776i	$-0.153147\pi$
$61$	158.000	+	273.664i	0.0424617	+	0.0735458i	−0.844013	+	0.536322i	$0.819813\pi$
$62$			717.000i			0.186524i
$63$		0			0
$64$	−3977.00			−0.970947
$65$	8630.81	−	4983.00i	2.04280	−	1.17941i
$66$		0			0
$67$	−2311.00	+	4002.77i	−0.514814	+	0.891684i	0.485038	+	0.874493i	$0.338806\pi$
$67$	−2311.00	+	4002.77i	−0.514814	+	0.891684i	−0.999852	+	0.0171910i	$0.994528\pi$
$68$	2509.74	+	1449.00i	0.542764	+	0.313365i
$69$		0			0
$70$	−940.500	−	1628.99i	−0.191939	−	0.332448i
$71$		−	1818.00i		−	0.360643i	−0.983608	−	0.180321i	$-0.942286\pi$
$71$		−	1818.00i		−	0.360643i	0.983608	−	0.180321i	$-0.0577138\pi$
$72$		0			0
$73$	−3031.00			−0.568775			−0.284387	−	0.958709i	$-0.591790\pi$
$73$	−3031.00			−0.568775			−0.284387	+	0.958709i	$0.591790\pi$
$74$	1922.58	−	1110.00i	0.351091	−	0.202703i
$75$		0			0
$76$	1064.00	−	1842.90i	0.184211	−	0.319062i
$77$	−2023.90	−	1168.50i	−0.341356	−	0.197082i
$78$		0			0
$79$	5225.00	+	9049.97i	0.837206	+	1.45008i	0.892222	+	0.451597i	$0.149146\pi$
$79$	5225.00	+	9049.97i	0.837206	+	1.45008i	−0.0550164	+	0.998485i	$0.517521\pi$
$80$		−	3135.00i		−	0.489844i
$81$		0			0
$82$	684.000			0.101725
$83$	−10940.5	+	6316.50i	−1.58811	+	0.916897i	−0.594493	+	0.804101i	$0.702647\pi$
$83$	−10940.5	+	6316.50i	−1.58811	+	0.916897i	−0.993618	+	0.112796i	$0.964019\pi$
$84$		0			0
$85$	−6831.00	+	11831.6i	−0.945467	+	1.63760i
$86$	2551.31	+	1473.00i	0.344958	+	0.199162i
$87$		0			0
$88$	−4243.50	−	7349.96i	−0.547973	−	0.949116i
$89$			7002.00i			0.883979i	0.897020	+	0.441990i	$0.145727\pi$
$89$			7002.00i			0.883979i	−0.897020	+	0.441990i	$0.854273\pi$
$90$		0			0
$91$	−5738.00			−0.692911
$92$	−1818.65	+	1050.00i	−0.214869	+	0.124055i
$93$		0			0
$94$	−3249.00	+	5627.43i	−0.367700	+	0.636876i
$95$	8687.97	+	5016.00i	0.962656	+	0.555789i
$96$		0			0
$97$	3258.50	+	5643.89i	0.346317	+	0.599839i	0.985592	−	0.169139i	$-0.0540987\pi$
$97$	3258.50	+	5643.89i	0.346317	+	0.599839i	−0.639275	+	0.768978i	$0.720765\pi$
$98$		−	6120.00i		−	0.637234i
$99$		0			0
$100$	−3248.00			−0.324800
$101$	−5126.00	+	2959.50i	−0.502500	+	0.290119i	−0.729745	−	0.683719i	$-0.760361\pi$
$101$	−5126.00	+	2959.50i	−0.502500	+	0.290119i	0.227245	+	0.973838i	$0.427028\pi$
$102$		0			0
$103$	3827.00	−	6628.56i	0.360731	−	0.624805i	−0.627350	−	0.778737i	$-0.715860\pi$
$103$	3827.00	−	6628.56i	0.360731	−	0.624805i	0.988081	+	0.153932i	$0.0491938\pi$
$104$	−18046.2	−	10419.0i	−1.66848	−	0.963295i
$105$		0			0
$106$	2389.50	+	4138.74i	0.212665	+	0.368346i
$107$			513.000i			0.0448074i	0.999749	+	0.0224037i	$0.00713192\pi$
$107$			513.000i			0.0448074i	−0.999749	+	0.0224037i	$0.992868\pi$
$108$		0			0
$109$	2324.00			0.195606			0.0978032	−	0.995206i	$-0.468818\pi$
$109$	2324.00			0.195606			0.0978032	+	0.995206i	$0.468818\pi$
$110$	10545.6	−	6088.50i	0.871536	−	0.503182i
$111$		0			0
$112$	−902.500	+	1563.18i	−0.0719467	+	0.124615i
$113$	−4260.84	−	2460.00i	−0.333687	−	0.192654i	0.323790	−	0.946129i	$-0.395043\pi$
$113$	−4260.84	−	2460.00i	−0.333687	−	0.192654i	−0.657477	+	0.753475i	$0.728376\pi$
$114$		0			0
$115$	−4950.00	−	8573.65i	−0.374291	−	0.648291i
$116$			4746.00i			0.352705i
$117$		0			0
$118$	−8766.00			−0.629560
$119$	6812.16	−	3933.00i	0.481050	−	0.277735i
$120$		0			0
$121$	244.000	−	422.620i	0.0166655	−	0.0288655i
$122$	820.992	+	474.000i	0.0551594	+	0.0318463i
$123$		0			0
$124$	−836.500	−	1448.86i	−0.0544030	−	0.0942287i
$125$			5313.00i			0.340032i
$126$		0			0
$127$	24995.0			1.54969			0.774847	−	0.632149i	$-0.217827\pi$
$127$	24995.0			1.54969			0.774847	+	0.632149i	$0.217827\pi$
$128$	1015.85	−	586.500i	0.0620024	−	0.0357971i
$129$		0			0
$130$	14949.0	−	25892.4i	0.884556	−	1.53210i
$131$	24647.9	+	14230.5i	1.43628	+	0.829235i	0.997589	−	0.0694044i	$-0.0221099\pi$
$131$	24647.9	+	14230.5i	1.43628	+	0.829235i	0.438688	+	0.898639i	$0.355443\pi$
$132$		0			0
$133$	−2888.00	−	5002.16i	−0.163265	−	0.282784i
$134$			13866.0i			0.772221i
$135$		0			0
$136$	28566.0			1.54444
$137$	−2125.23	+	1227.00i	−0.113231	+	0.0653738i	−0.555546	−	0.831486i	$-0.687491\pi$
$137$	−2125.23	+	1227.00i	−0.113231	+	0.0653738i	0.442315	+	0.896860i	$0.354157\pi$
$138$		0			0
$139$	5942.00	−	10291.8i	0.307541	−	0.532677i	−0.670283	−	0.742106i	$-0.733827\pi$
$139$	5942.00	−	10291.8i	0.307541	−	0.532677i	0.977824	+	0.209429i	$0.0671605\pi$
$140$	3800.99	+	2194.50i	0.193928	+	0.111964i
$141$		0			0
$142$	−2727.00	−	4723.30i	−0.135241	−	0.234244i
$143$		−	37146.0i		−	1.81652i
$144$		0			0
$145$	−22374.0			−1.06416
$146$	−7874.77	+	4546.50i	−0.369430	+	0.213290i
$147$		0			0
$148$	−2590.00	+	4486.01i	−0.118243	+	0.204803i
$149$	−19046.5	−	10996.5i	−0.857912	−	0.495316i	0.00540074	−	0.999985i	$-0.498281\pi$
$149$	−19046.5	−	10996.5i	−0.857912	−	0.495316i	−0.863312	+	0.504670i	$0.831614\pi$
$150$		0			0
$151$	1341.50	+	2323.55i	0.0588351	+	0.101905i	0.893943	−	0.448181i	$-0.147928\pi$
$151$	1341.50	+	2323.55i	0.0588351	+	0.101905i	−0.835108	+	0.550087i	$0.814595\pi$
$152$		−	20976.0i		−	0.907895i
$153$		0			0
$154$	−7011.00			−0.295623
$155$	6830.34	−	3943.50i	0.284301	−	0.164142i
$156$		0			0
$157$	16058.0	−	27813.3i	0.651467	−	1.12837i	−0.331301	−	0.943525i	$-0.607487\pi$
$157$	16058.0	−	27813.3i	0.651467	−	1.12837i	0.982767	−	0.184848i	$-0.0591793\pi$
$158$	27149.9	+	15675.0i	1.08756	+	0.627904i
$159$		0			0
$160$	13513.5	+	23406.1i	0.527871	+	0.914300i
$161$			5700.00i			0.219899i
$162$		0			0
$163$	22790.0			0.857767			0.428883	−	0.903360i	$-0.358907\pi$
$163$	22790.0			0.857767			0.428883	+	0.903360i	$0.358907\pi$
$164$	−1382.18	+	798.000i	−0.0513897	+	0.0296698i
$165$		0			0
$166$	−18949.5	+	32821.5i	−0.687672	+	1.19108i
$167$	−31244.5	−	18039.0i	−1.12031	−	0.646814i	−0.178834	−	0.983879i	$-0.557232\pi$
$167$	−31244.5	−	18039.0i	−1.12031	−	0.646814i	−0.941481	+	0.337065i	$0.890566\pi$
$168$		0			0
$169$	−31321.5	−	54250.4i	−1.09665	−	1.89946i
$170$			40986.0i			1.41820i
$171$		0			0
$172$	−6874.00			−0.232355
$173$	−17082.4	+	9862.50i	−0.570763	+	0.329530i	−0.757454	−	0.652889i	$-0.773557\pi$
$173$	−17082.4	+	9862.50i	−0.570763	+	0.329530i	0.186691	+	0.982419i	$0.440224\pi$
$174$		0			0
$175$	−4408.00	+	7634.88i	−0.143935	+	0.249302i
$176$	−10119.5	−	5842.50i	−0.326689	−	0.188614i
$177$		0			0
$178$	10503.0	+	18191.7i	0.331492	+	0.574161i
$179$			48915.0i			1.52664i	0.646022	+	0.763319i	$0.276431\pi$
$179$			48915.0i			1.52664i	−0.646022	+	0.763319i	$0.723569\pi$
$180$		0			0
$181$	−49552.0			−1.51253			−0.756265	−	0.654265i	$-0.772978\pi$
$181$	−49552.0			−1.51253			−0.756265	+	0.654265i	$0.772978\pi$
$182$	−14907.8	+	8607.00i	−0.450059	+	0.259842i
$183$		0			0
$184$	−10350.0	+	17926.7i	−0.305707	+	0.529499i
$185$	−21148.3	−	12210.0i	−0.617921	−	0.356757i
$186$		0			0
$187$	25461.0	+	44099.7i	0.728102	+	1.26111i
$188$		−	15162.0i		−	0.428984i
$189$		0			0
$190$	30096.0			0.833684
$191$	39308.9	−	22695.0i	1.07752	−	0.622105i	0.147291	−	0.989093i	$-0.452944\pi$
$191$	39308.9	−	22695.0i	1.07752	−	0.622105i	0.930225	+	0.366988i	$0.119611\pi$
$192$		0			0
$193$	−17723.5	+	30698.0i	−0.475811	+	0.824130i	−0.999616	−	0.0277089i	$-0.991179\pi$
$193$	−17723.5	+	30698.0i	−0.475811	+	0.824130i	0.523805	+	0.851838i	$0.324512\pi$
$194$	16931.7	+	9775.50i	0.449879	+	0.259738i
$195$		0			0
$196$	7140.00	+	12366.8i	0.185860	+	0.321919i
$197$		−	35739.0i		−	0.920895i	−0.887687	−	0.460447i	$-0.847689\pi$
$197$		−	35739.0i		−	0.920895i	0.887687	−	0.460447i	$-0.152311\pi$
$198$		0			0
$199$	−31255.0			−0.789248			−0.394624	−	0.918843i	$-0.629125\pi$
$199$	−31255.0			−0.789248			−0.394624	+	0.918843i	$0.629125\pi$
$200$	−27726.7	+	16008.0i	−0.693167	+	0.400200i
$201$		0			0
$202$	−8878.50	+	15378.0i	−0.217589	+	0.376875i
$203$	11156.1	+	6441.00i	0.270721	+	0.156301i
$204$		0			0
$205$	−3762.00	−	6515.98i	−0.0895181	−	0.155050i
$206$		−	22962.0i		−	0.541097i
$207$		0			0
$208$	−28690.0			−0.663138
$209$	32382.4	−	18696.0i	0.741339	−	0.428012i
$210$		0			0
$211$	7526.00	−	13035.4i	0.169044	−	0.292792i	−0.769040	−	0.639201i	$-0.779265\pi$
$211$	7526.00	−	13035.4i	0.169044	−	0.292792i	0.938084	+	0.346408i	$0.112599\pi$
$212$	−9657.05	−	5575.50i	−0.214868	−	0.124054i
$213$		0			0
$214$	769.500	+	1332.81i	0.0168028	+	0.0291033i
$215$		−	32406.0i		−	0.701049i
$216$		0			0
$217$	−4541.00			−0.0964344
$218$	6037.93	−	3486.00i	0.127050	−	0.0733524i
$219$		0			0
$220$	−14206.5	+	24606.4i	−0.293523	+	0.508396i
$221$	108277.	+	62514.0i	2.21694	+	1.27995i
$222$		0			0
$223$	−25087.0	−	43452.0i	−0.504474	−	0.873775i	−0.999987	−	0.00517415i	$-0.998353\pi$
$223$	−25087.0	−	43452.0i	−0.504474	−	0.873775i	0.495512	−	0.868601i	$-0.334980\pi$
$224$		−	15561.0i		−	0.310128i
$225$		0			0
$226$	−14760.0			−0.288981
$227$	−16684.8	+	9633.00i	−0.323795	+	0.186943i	−0.653083	−	0.757286i	$-0.726525\pi$
$227$	−16684.8	+	9633.00i	−0.323795	+	0.186943i	0.329288	+	0.944230i	$0.393191\pi$
$228$		0			0
$229$	−17107.0	+	29630.2i	−0.326214	+	0.565020i	−0.981757	−	0.190138i	$-0.939106\pi$
$229$	−17107.0	+	29630.2i	−0.326214	+	0.565020i	0.655543	+	0.755158i	$0.272440\pi$
$230$	−25721.0	−	14850.0i	−0.486218	−	0.280718i
$231$		0			0
$232$	23391.0	+	40514.4i	0.434583	+	0.752720i
$233$			37386.0i			0.688648i	0.938851	+	0.344324i	$0.111892\pi$
$233$			37386.0i			0.688648i	−0.938851	+	0.344324i	$0.888108\pi$
$234$		0			0
$235$	71478.0			1.29431
$236$	17713.7	−	10227.0i	0.318042	−	0.183622i
$237$		0			0
$238$	11799.0	−	20436.5i	0.208301	−	0.360788i
$239$	−53520.4	−	30900.0i	−0.936965	−	0.540957i	−0.0479573	−	0.998849i	$-0.515271\pi$
$239$	−53520.4	−	30900.0i	−0.936965	−	0.540957i	−0.889008	+	0.457892i	$0.848604\pi$
$240$		0			0
$241$	−20695.0	−	35844.8i	−0.356313	−	0.617152i	0.631029	−	0.775759i	$-0.282633\pi$
$241$	−20695.0	−	35844.8i	−0.356313	−	0.617152i	−0.987342	+	0.158607i	$0.949300\pi$
$242$		−	1464.00i		−	0.0249983i
$243$		0			0
$244$	−2212.00			−0.0371540
$245$	−58300.8	+	33660.0i	−0.971276	+	0.560766i
$246$		0			0
$247$	45904.0	−	79508.1i	0.752414	−	1.30322i
$248$	−14281.6	−	8245.50i	−0.232206	−	0.134064i
$249$		0			0
$250$	7969.50	+	13803.6i	0.127512	+	0.220857i
$251$			82818.0i			1.31455i	0.753651	+	0.657275i	$0.228291\pi$
$251$			82818.0i			1.31455i	−0.753651	+	0.657275i	$0.771709\pi$
$252$		0			0
$253$	−36900.0			−0.576481
$254$	64938.9	−	37492.5i	1.00656	−	0.581135i
$255$		0			0
$256$	33575.5	−	58154.5i	0.512321	−	0.887367i
$257$	−16965.4	−	9795.00i	−0.256861	−	0.148299i	0.366041	−	0.930599i	$-0.380713\pi$
$257$	−16965.4	−	9795.00i	−0.256861	−	0.148299i	−0.622902	+	0.782300i	$0.714046\pi$
$258$		0			0
$259$	7030.00	+	12176.3i	0.104799	+	0.181517i
$260$			69762.0i			1.03198i
$261$		0			0
$262$	85383.0			1.24385
$263$	−14455.7	+	8346.00i	−0.208991	+	0.120661i	−0.600842	−	0.799368i	$-0.705168\pi$
$263$	−14455.7	+	8346.00i	−0.208991	+	0.120661i	0.391851	+	0.920029i	$0.371835\pi$
$264$		0			0
$265$	26284.5	−	45526.1i	0.374290	−	0.648289i
$266$	−15006.5	−	8664.00i	−0.212088	−	0.122449i
$267$		0			0
$268$	−16177.0	−	28019.4i	−0.225231	−	0.390112i
$269$		−	120906.i		−	1.67087i	−0.549587	−	0.835436i	$-0.685215\pi$
$269$		−	120906.i		−	1.67087i	0.549587	−	0.835436i	$-0.314785\pi$
$270$		0			0
$271$	73739.0			1.00406			0.502029	−	0.864851i	$-0.332587\pi$
$271$	73739.0			1.00406			0.502029	+	0.864851i	$0.332587\pi$
$272$	34060.8	−	19665.0i	0.460380	−	0.265801i
$273$		0			0
$274$	−3681.00	+	6375.68i	−0.0490303	+	0.0849230i
$275$	−49425.8	−	28536.0i	−0.653564	−	0.377336i
$276$		0			0
$277$	−5998.00	−	10388.8i	−0.0781712	−	0.135397i	0.824290	−	0.566168i	$-0.191575\pi$
$277$	−5998.00	−	10388.8i	−0.0781712	−	0.135397i	−0.902461	+	0.430772i	$0.858241\pi$
$278$		−	35652.0i		−	0.461312i
$279$		0			0
$280$	43263.0			0.551824
$281$	−44276.4	+	25563.0i	−0.560738	+	0.323742i	−0.753442	−	0.657515i	$-0.771608\pi$
$281$	−44276.4	+	25563.0i	−0.560738	+	0.323742i	0.192704	+	0.981257i	$0.438274\pi$
$282$		0			0
$283$	524.000	−	907.595i	0.00654272	−	0.0113323i	−0.862736	−	0.505655i	$-0.831251\pi$
$283$	524.000	−	907.595i	0.00654272	−	0.0113323i	0.869278	+	0.494323i	$0.164584\pi$
$284$	11021.0	+	6363.00i	0.136643	+	0.0788906i
$285$		0			0
$286$	−55719.0	−	96508.1i	−0.681195	−	1.17986i
$287$			4332.00i			0.0525926i
$288$		0			0
$289$	−87875.0			−1.05213
$290$	−58129.4	+	33561.0i	−0.691193	+	0.399061i
$291$		0			0
$292$	10608.5	−	18374.5i	0.124419	−	0.215501i
$293$	55583.2	+	32091.0i	0.647454	+	0.373807i	0.787480	−	0.616340i	$-0.211385\pi$
$293$	55583.2	+	32091.0i	0.647454	+	0.373807i	−0.140026	+	0.990148i	$0.544719\pi$
$294$		0			0
$295$	48213.0	+	83507.4i	0.554013	+	0.959579i
$296$			51060.0i			0.582770i
$297$		0			0
$298$	−65979.0			−0.742973
$299$	−78461.9	+	45300.0i	−0.877640	+	0.506706i
$300$		0			0
$301$	−9329.00	+	16158.3i	−0.102968	+	0.178346i
$302$	6970.64	+	4024.50i	0.0764291	+	0.0441264i
$303$		0			0
$304$	−14440.0	−	25010.8i	−0.156250	−	0.270633i
$305$		−	10428.0i		−	0.112099i
$306$		0			0
$307$	154154.			1.63560			0.817802	−	0.575500i	$-0.195193\pi$
$307$	154154.			1.63560			0.817802	+	0.575500i	$0.195193\pi$
$308$	14167.3	−	8179.50i	0.149343	−	0.0862234i
$309$		0			0
$310$	11830.5	−	20491.0i	0.123106	−	0.213226i
$311$	81475.7	+	47040.0i	0.842378	+	0.486347i	0.858072	−	0.513530i	$-0.171662\pi$
$311$	81475.7	+	47040.0i	0.842378	+	0.486347i	−0.0156936	+	0.999877i	$0.504996\pi$
$312$		0			0
$313$	12951.5	+	22432.7i	0.132200	+	0.228977i	0.924524	−	0.381123i	$-0.124463\pi$
$313$	12951.5	+	22432.7i	0.132200	+	0.228977i	−0.792324	+	0.610100i	$0.791129\pi$
$314$		−	96348.0i		−	0.977200i
$315$		0			0
$316$	−73150.0			−0.732555
$317$	83868.5	−	48421.5i	0.834604	−	0.481859i	−0.0208226	−	0.999783i	$-0.506629\pi$
$317$	83868.5	−	48421.5i	0.834604	−	0.481859i	0.855426	+	0.517924i	$0.173295\pi$
$318$		0			0
$319$	−41697.0	+	72221.3i	−0.409754	+	0.709715i
$320$	113658.	+	65620.5i	1.10994	+	0.640825i
$321$		0			0
$322$	8550.00	+	14809.0i	0.0824621	+	0.142829i
$323$			125856.i			1.20634i
$324$		0			0
$325$	−140128.			−1.32666
$326$	59210.2	−	34185.0i	0.557136	−	0.321662i
$327$		0			0
$328$	−7866.00	+	13624.3i	−0.0731150	+	0.126639i
$329$	−35640.4	−	20577.0i	−0.329269	−	0.190104i
$330$		0			0
$331$	82427.0	+	142768.i	0.752339	+	1.30309i	0.946686	+	0.322156i	$0.104408\pi$
$331$	82427.0	+	142768.i	0.752339	+	1.30309i	−0.194348	+	0.980933i	$0.562259\pi$
$332$		−	88431.0i		−	0.802284i
$333$		0			0
$334$	−108234.			−0.970221
$335$	132091.	−	76263.0i	1.17702	−	0.679554i
$336$		0			0
$337$	−74347.0	+	128773.i	−0.654642	+	1.13387i	0.327342	+	0.944906i	$0.393847\pi$
$337$	−74347.0	+	128773.i	−0.654642	+	1.13387i	−0.981984	+	0.188967i	$0.939486\pi$
$338$	−162751.	−	93964.5i	−1.42459	−	0.822490i
$339$		0			0
$340$	−47817.0	−	82821.5i	−0.413642	−	0.716449i
$341$		−	29397.0i		−	0.252810i
$342$		0			0
$343$	84379.0			0.717210
$344$	−58680.1	+	33879.0i	−0.495877	+	0.286295i
$345$		0			0
$346$	−29587.5	+	51247.1i	−0.247147	+	0.428072i
$347$	−93247.6	−	53836.5i	−0.774423	−	0.447114i	0.0600269	−	0.998197i	$-0.480881\pi$
$347$	−93247.6	−	53836.5i	−0.774423	−	0.447114i	−0.834450	+	0.551083i	$0.814215\pi$
$348$		0			0
$349$	−63760.0	−	110436.i	−0.523477	−	0.906688i	−0.999627	−	0.0273243i	$-0.991301\pi$
$349$	−63760.0	−	110436.i	−0.523477	−	0.906688i	0.476150	−	0.879364i	$-0.342032\pi$
$350$			26448.0i			0.215902i
$351$		0			0
$352$	100737.			0.813025
$353$	123066.	−	71052.0i	0.987615	−	0.570200i	0.0830542	−	0.996545i	$-0.473533\pi$
$353$	123066.	−	71052.0i	0.987615	−	0.570200i	0.904560	+	0.426345i	$0.140199\pi$
$354$		0			0
$355$	−29997.0	+	51956.3i	−0.238024	+	0.412270i
$356$	−42447.4	−	24507.0i	−0.334927	−	0.193370i
$357$		0			0
$358$	73372.5	+	127085.i	0.572489	+	0.991580i
$359$			19422.0i			0.150697i	0.997157	+	0.0753486i	$0.0240069\pi$
$359$			19422.0i			0.150697i	−0.997157	+	0.0753486i	$0.975993\pi$
$360$		0			0
$361$	−37905.0			−0.290859
$362$	−128740.	+	74328.0i	−0.982417	+	0.567199i
$363$		0			0
$364$	20083.0	−	34784.8i	0.151574	−	0.262535i
$365$	86622.5	+	50011.5i	0.650197	+	0.375391i
$366$		0			0
$367$	75672.5	+	131069.i	0.561831	+	0.973120i	0.997337	+	0.0729343i	$0.0232363\pi$
$367$	75672.5	+	131069.i	0.561831	+	0.973120i	−0.435505	+	0.900186i	$0.643430\pi$
$368$			28500.0i			0.210450i
$369$		0			0
$370$	−73260.0			−0.535135
$371$	−26212.0	+	15133.5i	−0.190437	+	0.109949i
$372$		0			0
$373$	−118753.	+	205686.i	−0.853546	+	1.47839i	0.0244414	+	0.999701i	$0.492219\pi$
$373$	−118753.	+	205686.i	−0.853546	+	1.47839i	−0.877987	+	0.478684i	$0.841114\pi$
$374$	132299.	+	76383.0i	0.945832	+	0.546077i
$375$		0			0
$376$	−74727.0	−	129431.i	−0.528569	−	0.915509i
$377$			204756.i			1.44063i
$378$		0			0
$379$	−261952.			−1.82366			−0.911829	−	0.410571i	$-0.865330\pi$
$379$	−261952.			−1.82366			−0.911829	+	0.410571i	$0.865330\pi$
$380$	−60815.8	+	35112.0i	−0.421162	+	0.243158i
$381$		0			0
$382$	68085.0	−	117927.i	0.466578	−	0.808138i
$383$	−75484.5	−	43581.0i	−0.514589	−	0.297098i	0.220129	−	0.975471i	$-0.429352\pi$
$383$	−75484.5	−	43581.0i	−0.514589	−	0.297098i	−0.734718	+	0.678373i	$0.762685\pi$
$384$		0			0
$385$	38560.5	+	66788.7i	0.260148	+	0.450590i
$386$			106341.i			0.713717i
$387$		0			0
$388$	−45619.0			−0.303028
$389$	−207277.	+	119672.i	−1.36978	+	0.790845i	−0.990900	−	0.134599i	$-0.957025\pi$
$389$	−207277.	+	119672.i	−1.36978	+	0.790845i	−0.378884	+	0.925444i	$0.623692\pi$
$390$		0			0
$391$	62100.0	−	107560.i	0.406198	−	0.703556i
$392$	121902.	+	70380.0i	0.793301	+	0.458012i
$393$		0			0
$394$	−53608.5	−	92852.6i	−0.345335	−	0.598139i
$395$		−	344850.i		−	2.21022i
$396$		0			0
$397$	217154.			1.37780			0.688901	−	0.724855i	$-0.258093\pi$
$397$	217154.			1.37780			0.688901	+	0.724855i	$0.258093\pi$
$398$	−81202.9	+	46882.5i	−0.512631	+	0.295968i
$399$		0			0
$400$	−22040.0	+	38174.4i	−0.137750	+	0.238590i
$401$	−221876.	−	128100.i	−1.37982	−	0.796637i	−0.387679	−	0.921795i	$-0.626723\pi$
$401$	−221876.	−	128100.i	−1.37982	−	0.796637i	−0.992137	+	0.125158i	$0.960056\pi$
$402$		0			0
$403$	−36089.0	−	62508.0i	−0.222211	−	0.384880i
$404$		−	41433.0i		−	0.253854i
$405$		0			0
$406$	38646.0			0.234451
$407$	−78825.6	+	45510.0i	−0.475859	+	0.274738i
$408$		0			0
$409$	99645.5	−	172591.i	0.595677	−	1.03174i	−0.397774	−	0.917484i	$-0.630217\pi$
$409$	99645.5	−	172591.i	0.595677	−	1.03174i	0.993451	−	0.114260i	$-0.0364496\pi$
$410$	−19547.9	−	11286.0i	−0.116287	−	0.0671386i
$411$		0			0
$412$	26789.0	+	46399.9i	0.157820	+	0.273352i
$413$		−	55518.0i		−	0.325487i
$414$		0			0
$415$	416889.			2.42061
$416$	214201.	−	123669.i	1.23776	−	0.714618i
$417$		0			0
$418$	56088.0	−	97147.3i	0.321009	−	0.556004i
$419$	217610.	+	125637.i	1.23951	+	0.715632i	0.968994	−	0.247084i	$-0.0794723\pi$
$419$	217610.	+	125637.i	1.23951	+	0.715632i	0.270516	+	0.962715i	$0.412806\pi$
$420$		0			0
$421$	15206.0	+	26337.6i	0.0857928	+	0.148597i	0.905729	−	0.423858i	$-0.139324\pi$
$421$	15206.0	+	26337.6i	0.0857928	+	0.148597i	−0.819936	+	0.572455i	$0.805991\pi$
$422$		−	45156.0i		−	0.253566i
$423$		0			0
$424$	−109917.			−0.611411
$425$	166360.	−	96048.0i	0.921024	−	0.531754i
$426$		0			0
$427$	−3002.00	+	5199.62i	−0.0164647	+	0.0285178i
$428$	−3109.90	−	1795.50i	−0.0169769	−	0.00980162i
$429$		0			0
$430$	−48609.0	−	84193.3i	−0.262893	−	0.455345i
$431$		−	161730.i		−	0.870635i	−0.900277	−	0.435317i	$-0.856636\pi$
$431$		−	161730.i		−	0.870635i	0.900277	−	0.435317i	$-0.143364\pi$
$432$		0			0
$433$	−213541.			−1.13895			−0.569476	−	0.822008i	$-0.692854\pi$
$433$	−213541.			−1.13895			−0.569476	+	0.822008i	$0.692854\pi$
$434$	−11797.9	+	6811.50i	−0.0626360	+	0.0361629i
$435$		0			0
$436$	−8134.00	+	14088.5i	−0.0427889	+	0.0741126i
$437$	−78981.5	−	45600.0i	−0.413583	−	0.238782i
$438$		0			0
$439$	−33362.5	−	57785.5i	−0.173113	−	0.299840i	0.766394	−	0.642371i	$-0.222049\pi$
$439$	−33362.5	−	57785.5i	−0.173113	−	0.299840i	−0.939507	+	0.342531i	$0.888716\pi$
$440$			280071.i			1.44665i
$441$		0			0
$442$	375084.			1.91992
$443$	237438.	−	137085.i	1.20988	−	0.698526i	0.247149	−	0.968978i	$-0.420506\pi$
$443$	237438.	−	137085.i	1.20988	−	0.698526i	0.962734	+	0.270452i	$0.0871730\pi$
$444$		0			0
$445$	115533.	−	200109.i	0.583426	−	1.01052i
$446$	−130356.	−	75261.0i	−0.655331	−	0.378356i
$447$		0			0
$448$	−37781.5	−	65439.5i	−0.188245	−	0.326050i
$449$			233784.i			1.15964i	0.814746	+	0.579819i	$0.196877\pi$
$449$			233784.i			1.15964i	−0.814746	+	0.579819i	$0.803123\pi$
$450$		0			0
$451$	−28044.0			−0.137875
$452$	29825.9	−	17220.0i	0.145988	−	0.0842862i
$453$		0			0
$454$	−28899.0	+	50054.5i	−0.140207	+	0.242846i
$455$	163985.	+	94677.0i	0.792104	+	0.457322i
$456$		0			0
$457$	45333.5	+	78519.9i	0.217064	+	0.375965i	0.953909	−	0.300096i	$-0.0970188\pi$
$457$	45333.5	+	78519.9i	0.217064	+	0.375965i	−0.736845	+	0.676061i	$0.763685\pi$
$458$			102642.i			0.489321i
$459$		0			0
$460$	69300.0			0.327505
$461$	−174900.	+	100978.i	−0.822977	+	0.475146i	−0.851442	−	0.524449i	$-0.824271\pi$
$461$	−174900.	+	100978.i	−0.822977	+	0.475146i	0.0284650	+	0.999595i	$0.490938\pi$
$462$		0			0
$463$	161988.	−	280572.i	0.755653	−	1.30883i	−0.189397	−	0.981901i	$-0.560653\pi$
$463$	161988.	−	280572.i	0.755653	−	1.30883i	0.945049	−	0.326928i	$-0.106013\pi$
$464$	55780.7	+	32205.0i	0.259088	+	0.149585i
$465$		0			0
$466$	56079.0	+	97131.7i	0.258243	+	0.447290i
$467$		−	76941.0i		−	0.352796i	−0.984319	−	0.176398i	$-0.943555\pi$
$467$		−	76941.0i		−	0.352796i	0.984319	−	0.176398i	$-0.0564446\pi$
$468$		0			0
$469$	−87818.0			−0.399244
$470$	185705.	−	107217.i	0.840676	−	0.485364i
$471$		0			0
$472$	100809.	−	174606.i	0.452497	−	0.783747i
$473$	−104604.	−	60393.0i	−0.467547	−	0.269938i
$474$		0			0
$475$	−70528.0	−	122158.i	−0.312589	−	0.541421i
$476$			55062.0i			0.243018i
$477$		0			0
$478$	−185400.			−0.811435
$479$	−167332.	+	96609.0i	−0.729302	+	0.421062i	−0.818167	−	0.574981i	$-0.805009\pi$
$479$	−167332.	+	96609.0i	−0.729302	+	0.421062i	0.0888650	+	0.996044i	$0.471676\pi$
$480$		0			0
$481$	−111740.	+	193539.i	−0.482968	+	0.836525i
$482$	−107534.	−	62085.0i	−0.462864	−	0.267235i
$483$		0			0
$484$	1708.00	+	2958.34i	0.00729117	+	0.0126287i
$485$		−	215061.i		−	0.914278i
$486$		0			0
$487$	−34882.0			−0.147077			−0.0735383	−	0.997292i	$-0.523429\pi$
$487$	−34882.0			−0.147077			−0.0735383	+	0.997292i	$0.523429\pi$
$488$	−18882.8	+	10902.0i	−0.0792916	+	0.0457790i
$489$		0			0
$490$	−100980.	+	174902.i	−0.420575	+	0.728457i
$491$	187968.	+	108524.i	0.779689	+	0.450154i	0.836320	−	0.548241i	$-0.184703\pi$
$491$	187968.	+	108524.i	0.779689	+	0.450154i	−0.0566310	+	0.998395i	$0.518036\pi$
$492$		0			0
$493$	−140346.	−	243086.i	−0.577439	−	1.00015i
$494$		−	275424.i		−	1.12862i
$495$		0			0
$496$	−22705.0			−0.0922907
$497$	29914.2	−	17271.0i	0.121106	−	0.0699205i
$498$		0			0
$499$	−232405.	+	402537.i	−0.933350	+	1.61661i	−0.155799	+	0.987789i	$0.549795\pi$
$499$	−232405.	+	402537.i	−0.933350	+	1.61661i	−0.777551	+	0.628820i	$0.783538\pi$
$500$	−32208.4	−	18595.5i	−0.128833	−	0.0743820i
$501$		0			0
$502$	124227.	+	215167.i	0.492956	+	0.853826i
$503$			167580.i			0.662348i	0.943570	+	0.331174i	$0.107445\pi$
$503$			167580.i			0.662348i	−0.943570	+	0.331174i	$0.892555\pi$
$504$		0			0
$505$	195327.			0.765913
$506$	−95869.0	+	55350.0i	−0.374436	+	0.216181i
$507$		0			0
$508$	−87482.5	+	151524.i	−0.338995	+	0.587157i
$509$	30914.5	+	17848.5i	0.119324	+	0.0688916i	0.558474	−	0.829522i	$-0.311387\pi$
$509$	30914.5	+	17848.5i	0.119324	+	0.0688916i	−0.439150	+	0.898414i	$0.644720\pi$
$510$		0			0
$511$	−28794.5	−	49873.5i	−0.110273	−	0.190998i
$512$		−	182685.i		−	0.696888i
$513$		0			0
$514$	−58770.0			−0.222448
$515$	−218742.	+	126291.i	−0.824743	+	0.476166i
$516$		0			0
$517$	133209.	−	230725.i	0.498371	−	0.863203i
$518$	36529.0	+	21090.0i	0.136137	+	0.0785990i
$519$		0			0
$520$	343827.	+	595526.i	1.27155	+	2.20239i
$521$			42750.0i			0.157493i	0.996895	+	0.0787464i	$0.0250917\pi$
$521$			42750.0i			0.157493i	−0.996895	+	0.0787464i	$0.974908\pi$
$522$		0			0
$523$	−176434.			−0.645028			−0.322514	−	0.946565i	$-0.604528\pi$
$523$	−176434.			−0.645028			−0.322514	+	0.946565i	$0.604528\pi$
$524$	−172536.	+	99613.5i	−0.628371	+	0.362790i
$525$		0			0
$526$	−25038.0	+	43367.1i	−0.0904957	+	0.156743i
$527$	85689.7	+	49473.0i	0.308537	+	0.178134i
$528$		0			0
$529$	−94920.5	−	164407.i	−0.339194	−	0.587502i
$530$		−	157707.i		−	0.561435i
$531$		0			0
$532$	40432.0			0.142857
$533$	−59631.0	+	34428.0i	−0.209903	+	0.121187i
$534$		0			0
$535$	8464.50	−	14660.9i	0.0295729	−	0.0512217i
$536$	−276191.	−	159459.i	−0.961347	−	0.555034i
$537$		0			0
$538$	−181359.	−	314123.i	−0.626577	−	1.08526i
$539$			250920.i			0.863690i
$540$		0			0
$541$	−323836.			−1.10645			−0.553223	−	0.833033i	$-0.686602\pi$
$541$	−323836.			−1.10645			−0.553223	+	0.833033i	$0.686602\pi$
$542$	191580.	−	110609.i	0.652155	−	0.376522i
$543$		0			0
$544$	−169533.	+	293640.i	−0.572870	+	0.992241i
$545$	−66417.2	−	38346.0i	−0.223608	−	0.129100i
$546$		0			0
$547$	111695.	+	193461.i	0.373301	+	0.646576i	0.990071	−	0.140567i	$-0.0448926\pi$
$547$	111695.	+	193461.i	0.373301	+	0.646576i	−0.616770	+	0.787143i	$0.711559\pi$
$548$		−	17178.0i		−	0.0572020i
$549$		0			0
$550$	−171216.			−0.566003
$551$	−178498.	+	103056.i	−0.587937	+	0.339446i
$552$		0			0
$553$	−99275.0	+	171949.i	−0.324631	+	0.562277i
$554$	−31166.5	−	17994.0i	−0.101547	−	0.0586284i
$555$		0			0
$556$	41594.0	+	72042.9i	0.134549	+	0.233046i
$557$			585027.i			1.88567i	0.333261	+	0.942835i	$0.391851\pi$
$557$			585027.i			1.88567i	−0.333261	+	0.942835i	$0.608149\pi$
$558$		0			0
$559$	−296564.			−0.949063
$560$	51584.8	−	29782.5i	0.164492	−	0.0949697i
$561$		0			0
$562$	−76689.0	+	132829.i	−0.242807	+	0.420553i
$563$	−72811.1	−	42037.5i	−0.229710	−	0.132623i	0.380728	−	0.924687i	$-0.375673\pi$
$563$	−72811.1	−	42037.5i	−0.229710	−	0.132623i	−0.610438	+	0.792064i	$0.709007\pi$
$564$		0			0
$565$	81180.0	+	140608.i	0.254303	+	0.440466i
$566$		−	3144.00i		−	0.00981408i
$567$		0			0
$568$	125442.			0.388818
$569$	551998.	−	318696.i	1.70495	−	0.984356i	0.764381	−	0.644765i	$-0.223045\pi$
$569$	551998.	−	318696.i	1.70495	−	0.984356i	0.940573	−	0.339591i	$-0.110289\pi$
$570$		0			0
$571$	−40363.0	+	69910.8i	−0.123797	+	0.214423i	−0.921262	−	0.388942i	$-0.872841\pi$
$571$	−40363.0	+	69910.8i	−0.123797	+	0.214423i	0.797465	+	0.603365i	$0.206174\pi$
$572$	225186.	+	130011.i	0.688254	+	0.397364i
$573$		0			0
$574$	6498.00	+	11254.9i	0.0197222	+	0.0341599i
$575$			139200.i			0.421021i
$576$		0			0
$577$	261182.			0.784498			0.392249	−	0.919859i	$-0.371697\pi$
$577$	261182.			0.784498			0.392249	+	0.919859i	$0.371697\pi$
$578$	−228306.	+	131812.i	−0.683379	+	0.394549i
$579$		0			0
$580$	78309.0	−	135635.i	0.232785	−	0.403196i
$581$	−207869.	−	120013.i	−0.615798	−	0.355531i
$582$		0			0
$583$	−97969.5	−	169688.i	−0.288240	−	0.499246i
$584$		−	209139.i		−	0.613210i
$585$		0			0
$586$	192546.			0.560711
$587$	338880.	−	195652.i	0.983490	−	0.567818i	0.0801678	−	0.996781i	$-0.474454\pi$
$587$	338880.	−	195652.i	0.983490	−	0.567818i	0.903322	+	0.428963i	$0.141121\pi$
$588$		0			0
$589$	36328.0	−	62921.9i	0.104715	−	0.181373i
$590$	250522.	+	144639.i	0.719684	+	0.415510i
$591$		0			0
$592$	35150.0	+	60881.6i	0.100296	+	0.173717i
$593$		−	302670.i		−	0.860716i	−0.902658	−	0.430358i	$-0.858387\pi$
$593$		−	302670.i		−	0.860716i	0.902658	−	0.430358i	$-0.141613\pi$
$594$		0			0
$595$	−259578.			−0.733219
$596$	133325.	−	76975.5i	0.375336	−	0.216701i
$597$		0			0
$598$	−135900.	+	235386.i	−0.380029	+	0.658230i
$599$	−252445.	−	145749.i	−0.703579	−	0.406211i	0.105100	−	0.994462i	$-0.466484\pi$
$599$	−252445.	−	145749.i	−0.703579	−	0.406211i	−0.808679	+	0.588250i	$0.799817\pi$
$600$		0			0
$601$	−201087.	−	348292.i	−0.556716	−	0.964261i	−0.997768	−	0.0667792i	$-0.978728\pi$
$601$	−201087.	−	348292.i	−0.556716	−	0.964261i	0.441051	−	0.897482i	$-0.354606\pi$
$602$			55974.0i			0.154452i
$603$		0			0
$604$	−18781.0			−0.0514807
$605$	−13946.5	+	8052.00i	−0.0381025	+	0.0219985i
$606$		0			0
$607$	189335.	−	327938.i	0.513870	−	0.890049i	−0.486000	−	0.873959i	$-0.661545\pi$
$607$	189335.	−	327938.i	0.513870	−	0.890049i	0.999871	−	0.0160908i	$-0.00512208\pi$
$608$	215620.	+	124488.i	0.583285	+	0.336760i
$609$		0			0
$610$	−15642.0	−	27092.7i	−0.0420371	−	0.0728104i
$611$		−	654132.i		−	1.75220i
$612$		0			0
$613$	287570.			0.765284			0.382642	−	0.923897i	$-0.375014\pi$
$613$	287570.			0.765284			0.382642	+	0.923897i	$0.375014\pi$
$614$	400504.	−	231231.i	1.06236	−	0.613351i
$615$		0			0
$616$	80626.5	−	139649.i	0.212479	−	0.368025i
$617$	499059.	+	288132.i	1.31094	+	0.756870i	0.982251	−	0.187570i	$-0.0600610\pi$
$617$	499059.	+	288132.i	1.31094	+	0.756870i	0.328686	+	0.944439i	$0.393394\pi$
$618$		0			0
$619$	−111631.	−	193351.i	−0.291342	−	0.504620i	0.682785	−	0.730619i	$-0.260769\pi$
$619$	−111631.	−	193351.i	−0.291342	−	0.504620i	−0.974127	+	0.226000i	$0.927435\pi$
$620$			55209.0i			0.143624i
$621$		0			0
$622$	282240.			0.729521
$623$	−115214.	+	66519.0i	−0.296845	+	0.171384i
$624$		0			0
$625$	232664.	−	402987.i	0.595621	−	1.03165i
$626$	67298.0	+	38854.5i	0.171733	+	0.0991500i
$627$		0			0
$628$	112406.	+	194693.i	0.285017	+	0.493663i
$629$		−	306360.i		−	0.774338i
$630$		0			0
$631$	43373.0			0.108933			0.0544667	−	0.998516i	$-0.482654\pi$
$631$	43373.0			0.108933			0.0544667	+	0.998516i	$0.482654\pi$
$632$	−624448.	+	360525.i	−1.56337	+	0.902612i
$633$		0			0
$634$	145264.	−	251605.i	0.361394	−	0.625953i
$635$	−714328.	−	412418.i	−1.77154	−	1.02280i
$636$		0			0
$637$	308040.	+	533541.i	0.759151	+	1.31489i
$638$			250182.i			0.614631i
$639$		0			0
$640$	−38709.0			−0.0945044
$641$	−366692.	+	211710.i	−0.892454	+	0.515259i	−0.874744	−	0.484584i	$-0.838971\pi$
$641$	−366692.	+	211710.i	−0.892454	+	0.515259i	−0.0177097	+	0.999843i	$0.505637\pi$
$642$		0			0
$643$	273044.	−	472926.i	0.660406	−	1.14386i	−0.320104	−	0.947383i	$-0.603718\pi$
$643$	273044.	−	472926.i	0.660406	−	1.14386i	0.980509	−	0.196473i	$-0.0629489\pi$
$644$	−34554.4	−	19950.0i	−0.0833166	−	0.0481029i
$645$		0			0
$646$	188784.	+	326983.i	0.452377	+	0.783539i
$647$			418932.i			1.00077i	0.865803	+	0.500386i	$0.166808\pi$
$647$			418932.i			1.00077i	−0.865803	+	0.500386i	$0.833192\pi$
$648$		0			0
$649$	359406.			0.853289
$650$	−364063.	+	210192.i	−0.861688	+	0.497496i
$651$		0			0
$652$	−79765.0	+	138157.i	−0.187636	+	0.324996i
$653$	608997.	+	351604.i	1.42820	+	0.824571i	0.996979	−	0.0776757i	$-0.0247499\pi$
$653$	608997.	+	351604.i	1.42820	+	0.824571i	0.431220	+	0.902247i	$0.358083\pi$
$654$		0			0
$655$	−469606.	−	813382.i	−1.09459	−	1.89589i
$656$			21660.0i			0.0503328i
$657$		0			0
$658$	−123462.			−0.285155
$659$	−88352.8	+	51010.5i	−0.203446	+	0.117460i	−0.598262	−	0.801301i	$-0.704142\pi$
$659$	−88352.8	+	51010.5i	−0.203446	+	0.117460i	0.394816	+	0.918760i	$0.370808\pi$
$660$		0			0
$661$	−115360.	+	199809.i	−0.264029	+	0.457312i	−0.967309	−	0.253601i	$-0.918385\pi$
$661$	−115360.	+	199809.i	−0.264029	+	0.457312i	0.703279	+	0.710914i	$0.251718\pi$
$662$	428303.	+	247281.i	0.977317	+	0.564254i
$663$		0			0
$664$	−435838.	−	754894.i	−0.988529	−	1.71218i
$665$			190608.i			0.431020i
$666$		0			0
$667$	203400.			0.457193
$668$	218711.	−	126273.i	0.490138	−	0.282981i
$669$		0			0
$670$	228789.	−	396274.i	0.509666	−	0.882767i
$671$	−33660.7	−	19434.0i	−0.0747615	−	0.0431636i
$672$		0			0
$673$	234684.	+	406485.i	0.518149	+	0.897460i	0.999778	+	0.0210845i	$0.00671189\pi$
$673$	234684.	+	406485.i	0.518149	+	0.897460i	−0.481629	+	0.876375i	$0.659955\pi$
$674$			446082.i			0.981963i
$675$		0			0
$676$	438501.			0.959571
$677$	297173.	−	171573.i	0.648384	−	0.374345i	−0.139453	−	0.990229i	$-0.544534\pi$
$677$	297173.	−	171573.i	0.648384	−	0.374345i	0.787837	+	0.615884i	$0.211201\pi$
$678$		0			0
$679$	−61911.5	+	107234.i	−0.134286	+	0.232591i
$680$	−816383.	−	471339.i	−1.76553	−	1.01933i
$681$		0			0
$682$	−44095.5	−	76375.6i	−0.0948038	−	0.164205i
$683$		−	24642.0i		−	0.0528244i	−0.999651	−	0.0264122i	$-0.991592\pi$
$683$		−	24642.0i		−	0.0528244i	0.999651	−	0.0264122i	$-0.00840824\pi$
$684$		0			0
$685$	80982.0			0.172587
$686$	219223.	−	126568.i	0.465841	−	0.268954i
$687$		0			0
$688$	−46645.0	+	80791.5i	−0.0985436	+	0.170682i
$689$	−416633.	−	240543.i	−0.877637	−	0.506704i
$690$		0			0
$691$	133250.	+	230796.i	0.279069	+	0.483361i	0.971154	−	0.238455i	$-0.0766409\pi$
$691$	133250.	+	230796.i	0.279069	+	0.483361i	−0.692085	+	0.721816i	$0.743308\pi$
$692$		−	138075.i		−	0.288339i
$693$		0			0
$694$	−323019.			−0.670670
$695$	−339631.	+	196086.i	−0.703133	+	0.405954i
$696$		0			0
$697$	47196.0	−	81745.9i	0.0971493	−	0.168268i
$698$	−331307.	−	191280.i	−0.680016	−	0.392608i
$699$		0			0
$700$	−30856.0	−	53444.2i	−0.0629714	−	0.109070i
$701$		−	690309.i		−	1.40478i	−0.711794	−	0.702389i	$-0.752117\pi$
$701$		−	690309.i		−	1.40478i	0.711794	−	0.702389i	$-0.247883\pi$
$702$		0			0
$703$	−224960.			−0.455192
$704$	423635.	−	244586.i	0.854764	−	0.493498i
$705$		0			0
$706$	213156.	−	369197.i	0.427650	−	0.740711i
$707$	−97394.1	−	56230.5i	−0.194847	−	0.112495i
$708$		0			0
$709$	52592.0	+	91092.0i	0.104623	+	0.181212i	0.913584	−	0.406650i	$-0.133303\pi$
$709$	52592.0	+	91092.0i	0.104623	+	0.181212i	−0.808961	+	0.587862i	$0.799970\pi$
$710$			179982.i			0.357036i
$711$		0			0
$712$	−483138.			−0.953040
$713$	−62094.0	+	35850.0i	−0.122144	+	0.0705196i
$714$		0			0
$715$	−612909.	+	1.06159e6i	−1.19890	+	2.07656i
$716$	−296531.	−	171202.i	−0.578422	−	0.333952i
$717$		0			0
$718$	29133.0	+	50459.8i	0.0565114	+	0.0978807i
$719$			704988.i			1.36372i	0.731485	+	0.681858i	$0.238828\pi$
$719$			704988.i			1.36372i	−0.731485	+	0.681858i	$0.761172\pi$
$720$		0			0
$721$	145426.			0.279751
$722$	−98480.1	+	56857.5i	−0.188918	+	0.109072i
$723$		0			0
$724$	173432.	−	300393.i	0.330866	−	0.573077i
$725$	272445.	+	157296.i	0.518325	+	0.299255i
$726$		0			0
$727$	−63044.5	−	109196.i	−0.119283	−	0.206604i	0.800201	−	0.599732i	$-0.204726\pi$
$727$	−63044.5	−	109196.i	−0.119283	−	0.206604i	−0.919484	+	0.393128i	$0.871393\pi$
$728$		−	395922.i		−	0.747045i
$729$		0			0
$730$	300069.			0.563087
$731$	352081.	−	203274.i	0.658882	−	0.380406i
$732$		0			0
$733$	−48868.0	+	84641.9i	−0.0909529	+	0.157535i	−0.907912	−	0.419160i	$-0.862325\pi$
$733$	−48868.0	+	84641.9i	−0.0909529	+	0.157535i	0.816959	+	0.576695i	$0.195658\pi$
$734$	393206.	+	227018.i	0.729840	+	0.421373i
$735$		0			0
$736$	−122850.	−	212782.i	−0.226788	−	0.392808i
$737$		−	568506.i		−	1.04665i
$738$		0			0
$739$	−857158.			−1.56954			−0.784769	−	0.619788i	$-0.787219\pi$
$739$	−857158.			−1.56954			−0.784769	+	0.619788i	$0.787219\pi$
$740$	148038.	−	85470.0i	0.270340	−	0.156081i
$741$		0			0
$742$	−45400.5	+	78636.0i	−0.0824618	+	0.142828i
$743$	788054.	+	454983.i	1.42751	+	0.824171i	0.996924	−	0.0783795i	$-0.0249746\pi$
$743$	788054.	+	454983.i	1.42751	+	0.824171i	0.430583	+	0.902551i	$0.358308\pi$
$744$		0			0
$745$	362884.	+	628534.i	0.653816	+	1.13244i
$746$			712518.i			1.28032i
$747$		0			0
$748$	−356454.			−0.637089
$749$	−8441.15	+	4873.50i	−0.0150466	+	0.00868715i
$750$		0			0
$751$	−30611.5	+	53020.7i	−0.0542756	+	0.0940081i	−0.891887	−	0.452259i	$-0.850618\pi$
$751$	−30611.5	+	53020.7i	−0.0542756	+	0.0940081i	0.837611	+	0.546267i	$0.183952\pi$
$752$	−178202.	−	102885.i	−0.315121	−	0.181935i
$753$		0			0
$754$	307134.	+	531972.i	0.540238	+	0.935720i
$755$		−	88539.0i		−	0.155325i
$756$		0			0
$757$	782570.			1.36562			0.682812	−	0.730594i	$-0.260757\pi$
$757$	782570.			1.36562			0.682812	+	0.730594i	$0.260757\pi$
$758$	−680571.	+	392928.i	−1.18450	+	0.683872i
$759$		0			0
$760$	−346104.	+	599470.i	−0.599211	+	1.03786i
$761$	607430.	+	350700.i	1.04888	+	0.605573i	0.922336	−	0.386388i	$-0.126277\pi$
$761$	607430.	+	350700.i	1.04888	+	0.605573i	0.126547	+	0.991961i	$0.459611\pi$
$762$		0			0
$763$	22078.0	+	38240.2i	0.0379237	+	0.0656858i
$764$			317730.i			0.544342i
$765$		0			0
$766$	−261486.			−0.445647
$767$	764219.	−	441222.i	1.29905	−	0.750009i
$768$		0			0
$769$	42522.5	−	73651.1i	0.0719062	−	0.124545i	−0.827831	−	0.560978i	$-0.810425\pi$
$769$	42522.5	−	73651.1i	0.0719062	−	0.124545i	0.899737	+	0.436433i	$0.143758\pi$
$770$	200366.	+	115682.i	0.337943	+	0.195111i
$771$		0			0
$772$	−124065.	−	214886.i	−0.208168	−	0.360557i
$773$		−	643122.i		−	1.07630i	−0.842848	−	0.538151i	$-0.819123\pi$
$773$		−	643122.i		−	1.07630i	0.842848	−	0.538151i	$-0.180877\pi$
$774$		0			0
$775$	−110896.			−0.184634
$776$	−389428.	+	224836.i	−0.646702	+	0.373373i
$777$		0			0
$778$	−359014.	+	621831.i	−0.593134	+	1.02734i
$779$	−60026.0	−	34656.0i	−0.0989155	−	0.0571089i
$780$		0			0
$781$	111807.	+	193655.i	0.183302	+	0.317488i
$782$		−	372600.i		−	0.609297i
$783$		0			0
$784$	193800.			0.315298
$785$	−917838.	+	529914.i	−1.48945	+	0.859936i
$786$		0			0
$787$	−534274.	+	925390.i	−0.862610	+	1.49408i	0.00679053	+	0.999977i	$0.497838\pi$
$787$	−534274.	+	925390.i	−0.862610	+	1.49408i	−0.869401	+	0.494108i	$0.835495\pi$
$788$	216656.	+	125086.i	0.348914	+	0.201446i
$789$		0			0
$790$	−517275.	−	895947.i	−0.828834	−	1.43558i
$791$		−	93480.0i		−	0.149405i
$792$		0			0
$793$	−95432.0			−0.151757
$794$	564183.	−	325731.i	0.894909	−	0.516676i
$795$		0			0
$796$	109392.	−	189473.i	0.172648	−	0.299035i
$797$	−466731.	−	269468.i	−0.734768	−	0.424219i	0.0853958	−	0.996347i	$-0.472785\pi$
$797$	−466731.	−	269468.i	−0.734768	−	0.424219i	−0.820164	+	0.572128i	$0.806118\pi$
$798$		0			0
$799$	448362.	+	776586.i	0.702320	+	1.21645i
$800$		−	380016.i		−	0.593775i
$801$		0			0
$802$	−768600.			−1.19496
$803$	322866.	−	186406.i	0.500715	−	0.289088i
$804$		0			0
$805$	94050.0	−	162899.i	0.145133	−	0.251378i
$806$	−187524.	−	108267.i	−0.288660	−	0.166658i
$807$		0			0
$808$	−204205.	−	353694.i	−0.312784	−	0.541758i
$809$			459594.i			0.702227i	0.936333	+	0.351113i	$0.114197\pi$
$809$			459594.i			0.702227i	−0.936333	+	0.351113i	$0.885803\pi$
$810$		0			0
$811$	−961360.			−1.46165			−0.730827	−	0.682563i	$-0.760865\pi$
$811$	−961360.			−1.46165			−0.730827	+	0.682563i	$0.760865\pi$
$812$	−78093.0	+	45087.0i	−0.118440	+	0.0683816i
$813$		0			0
$814$	−136530.	+	236477.i	−0.206053	+	0.356895i
$815$	−651312.	−	376035.i	−0.980559	−	0.566126i
$816$		0			0
$817$	−149264.	−	258533.i	−0.223620	−	0.387321i
$818$		−	597873.i		−	0.893516i
$819$		0			0
$820$	52668.0			0.0783284
$821$	−91509.4	+	52833.0i	−0.135762	+	0.0783825i	−0.566343	−	0.824170i	$-0.691642\pi$
$821$	−91509.4	+	52833.0i	−0.135762	+	0.0783825i	0.430580	+	0.902552i	$0.358309\pi$
$822$		0			0
$823$	246778.	−	427431.i	0.364339	−	0.631054i	−0.624331	−	0.781160i	$-0.714628\pi$
$823$	246778.	−	427431.i	0.364339	−	0.631054i	0.988670	+	0.150106i	$0.0479615\pi$
$824$	457371.	+	264063.i	0.673618	+	0.388914i
$825$		0			0
$826$	−83277.0	−	144240.i	−0.122058	−	0.211410i
$827$		−	192870.i		−	0.282003i	−0.990009	−	0.141001i	$-0.954968\pi$
$827$		−	192870.i		−	0.282003i	0.990009	−	0.141001i	$-0.0450322\pi$
$828$		0			0
$829$	577226.			0.839918			0.419959	−	0.907543i	$-0.362044\pi$
$829$	577226.			0.839918			0.419959	+	0.907543i	$0.362044\pi$
$830$	1.08311e6	−	625334.i	1.57223	−	0.907728i
$831$		0			0
$832$	600527.	−	1.04014e6i	0.867533	−	1.50261i
$833$	−731410.	−	422280.i	−1.05407	−	0.608570i
$834$		0			0
$835$	595287.	+	1.03107e6i	0.853795	+	1.47882i
$836$			261744.i			0.374511i
$837$		0			0
$838$	753822.			1.07345
$839$	61475.7	−	35493.0i	0.0873332	−	0.0504219i	−0.455697	−	0.890135i	$-0.650610\pi$
$839$	61475.7	−	35493.0i	0.0873332	−	0.0504219i	0.543031	+	0.839713i	$0.317277\pi$
$840$		0			0
$841$	−123798.	+	214425.i	−0.175034	+	0.303168i
$842$	79012.7	+	45618.0i	0.111448	+	0.0643446i
$843$		0			0
$844$	52682.0	+	91247.9i	0.0739567	+	0.128097i
$845$			2.06722e6i			2.89516i
$846$		0			0
$847$	9272.00			0.0129243
$848$	−131060.	+	75667.5i	−0.182255	+	0.105225i
$849$		0			0
$850$	288144.	−	499080.i	0.398815	−	0.690768i
$851$	192258.	+	111000.i	0.265476	+	0.153272i
$852$		0			0
$853$	−40603.0	−	70326.5i	−0.0558033	−	0.0966542i	0.836774	−	0.547548i	$-0.184439\pi$
$853$	−40603.0	−	70326.5i	−0.0558033	−	0.0966542i	−0.892578	+	0.450894i	$0.851105\pi$
$854$			18012.0i			0.0246971i
$855$		0			0
$856$	−35397.0			−0.0483080
$857$	−935687.	+	540219.i	−1.27400	+	0.735543i	−0.975738	−	0.218941i	$-0.929740\pi$
$857$	−935687.	+	540219.i	−1.27400	+	0.735543i	−0.298260	+	0.954485i	$0.596406\pi$
$858$		0			0
$859$	−251674.	+	435912.i	−0.341077	+	0.590762i	−0.984633	−	0.174637i	$-0.944125\pi$
$859$	−251674.	+	435912.i	−0.341077	+	0.590762i	0.643556	+	0.765399i	$0.277458\pi$
$860$	196451.	+	113421.i	0.265618	+	0.153355i
$861$		0			0
$862$	−242595.	−	420187.i	−0.326488	−	0.565494i
$863$			548100.i			0.735933i	0.929839	+	0.367966i	$0.119946\pi$
$863$			548100.i			0.735933i	−0.929839	+	0.367966i	$0.880054\pi$
$864$		0			0
$865$	650925.			0.869959
$866$	−554796.	+	320312.i	−0.739771	+	0.427107i
$867$		0			0
$868$	15893.5	−	27528.3i	0.0210950	−	0.0365377i
$869$	−1.11315e6	−	642675.i	−1.47405	−	0.851044i
$870$		0			0
$871$	−697922.	−	1.20884e6i	−0.919963	−	1.59342i
$872$			160356.i			0.210888i
$873$		0			0
$874$	−273600.			−0.358173
$875$	−87422.7	+	50473.5i	−0.114185	+	0.0659246i
$876$		0			0
$877$	−350017.	+	606247.i	−0.455082	+	0.788226i	−0.998693	−	0.0511118i	$-0.983724\pi$
$877$	−350017.	+	606247.i	−0.455082	+	0.788226i	0.543611	+	0.839338i	$0.317057\pi$
$878$	−173357.	−	100088.i	−0.224880	−	0.129835i
$879$		0			0
$880$	192802.	+	333944.i	0.248970	+	0.431229i
$881$		−	806634.i		−	1.03926i	−0.854391	−	0.519631i	$-0.826070\pi$
$881$		−	806634.i		−	1.03926i	0.854391	−	0.519631i	$-0.173930\pi$
$882$		0			0
$883$	342704.			0.439539			0.219770	−	0.975552i	$-0.429469\pi$
$883$	342704.			0.439539			0.219770	+	0.975552i	$0.429469\pi$
$884$	−757942.	+	437598.i	−0.969910	+	0.559978i
$885$		0			0
$886$	411255.	−	712315.i	0.523894	−	0.907412i
$887$	13962.1	+	8061.00i	0.0177461	+	0.0102457i	0.508847	−	0.860857i	$-0.330072\pi$
$887$	13962.1	+	8061.00i	0.0177461	+	0.0102457i	−0.491101	+	0.871103i	$0.663405\pi$
$888$		0			0
$889$	237452.	+	411280.i	0.300451	+	0.520396i
$890$		−	693198.i		−	0.875140i
$891$		0			0
$892$	351218.			0.441415
$893$	570247.	−	329232.i	0.715088	−	0.412856i
$894$		0			0
$895$	807098.	−	1.39793e6i	1.00758	−	1.74518i
$896$	19301.1	+	11143.5i	0.0240418	+	0.0138805i
$897$		0			0
$898$	350676.	+	607389.i	0.434864	+	0.753206i
$899$			162042.i			0.200497i
$900$		0			0
$901$	659502.			0.812394
$902$	−72860.4	+	42066.0i	−0.0895527	+	0.0517033i
$903$		0			0
$904$	169740.	−	293998.i	0.207705	−	0.359756i
$905$	1.41614e6	+	817608.i	1.72905	+	0.998270i
$906$		0			0
$907$	−784750.	−	1.35923e6i	−0.953931	−	1.65226i	−0.736797	−	0.676114i	$-0.763663\pi$
$907$	−784750.	−	1.35923e6i	−0.953931	−	1.65226i	−0.217134	−	0.976142i	$-0.569671\pi$
$908$		−	134862.i		−	0.163575i
$909$		0			0
$910$	568062.			0.685982
$911$	433790.	−	250449.i	0.522689	−	0.301775i	−0.215345	−	0.976538i	$-0.569088\pi$
$911$	433790.	−	250449.i	0.522689	−	0.301775i	0.738034	+	0.674763i	$0.235754\pi$
$912$		0			0
$913$	776930.	−	1.34568e6i	0.932052	−	1.61436i
$914$	235560.	+	136000.i	0.281974	+	0.162798i
$915$		0			0
$916$	−119749.	−	207411.i	−0.142719	−	0.247196i
$917$			540759.i			0.643080i
$918$		0			0
$919$	1.03715e6			1.22804			0.614019	−	0.789291i	$-0.289552\pi$
$919$	1.03715e6			1.22804			0.614019	+	0.789291i	$0.289552\pi$
$920$	591582.	−	341550.i	0.698939	−	0.403533i
$921$		0			0
$922$	−302936.	+	524700.i	−0.356359	+	0.617233i
$923$	475479.	+	274518.i	0.558121	+	0.322231i
$924$		0			0
$925$	171680.	+	297358.i	0.200649	+	0.347534i
$926$		−	971931.i		−	1.13348i
$927$		0			0
$928$	−555282.			−0.644789
$929$	−110917.	+	64038.0i	−0.128519	+	0.0742004i	−0.562881	−	0.826538i	$-0.690307\pi$
$929$	−110917.	+	64038.0i	−0.128519	+	0.0742004i	0.434362	+	0.900738i	$0.356974\pi$
$930$		0			0
$931$	−310080.	+	537074.i	−0.357746	+	0.619634i
$932$	−226641.	−	130851.i	−0.260919	−	0.150642i
$933$		0			0
$934$	−115412.	−	199899.i	−0.132299	−	0.229148i
$935$		−	1.68043e6i		−	1.92219i
$936$		0			0
$937$	−879451.			−1.00169			−0.500844	−	0.865538i	$-0.666977\pi$
$937$	−879451.			−1.00169			−0.500844	+	0.865538i	$0.666977\pi$
$938$	−228158.	+	131727.i	−0.259316	+	0.149716i
$939$		0			0
$940$	−250173.	+	433312.i	−0.283129	+	0.490394i
$941$	622029.	+	359128.i	0.702476	+	0.405574i	0.808269	−	0.588814i	$-0.200405\pi$
$941$	622029.	+	359128.i	0.702476	+	0.405574i	−0.105793	+	0.994388i	$0.533738\pi$
$942$		0			0
$943$	34200.0	+	59236.1i	0.0384594	+	0.0666137i
$944$		−	277590.i		−	0.311501i
$945$		0			0
$946$	−362358.			−0.404907
$947$	−63224.2	+	36502.5i	−0.0704991	+	0.0407026i	−0.534835	−	0.844956i	$-0.679626\pi$
$947$	−63224.2	+	36502.5i	−0.0704991	+	0.0407026i	0.464336	+	0.885659i	$0.346293\pi$
$948$		0			0
$949$	457681.	−	792727.i	0.508195	−	0.880220i
$950$	−366474.	−	211584.i	−0.406066	−	0.234442i
$951$		0			0
$952$	271377.	+	470039.i	0.299433	+	0.518633i
$953$		−	309168.i		−	0.340415i	−0.985408	−	0.170208i	$-0.945556\pi$
$953$		−	309168.i		−	0.340415i	0.985408	−	0.170208i	$-0.0544438\pi$
$954$		0			0
$955$	−1.49787e6			−1.64236
$956$	374643.	−	216300.i	0.409922	−	0.236669i
$957$		0			0
$958$	−289827.	+	501995.i	−0.315797	+	0.546976i
$959$	−40379.3	−	23313.0i	−0.0439058	−	0.0253490i
$960$		0			0
$961$	433200.	+	750324.i	0.469074	+	0.812461i
$962$			670440.i			0.724452i
$963$		0			0
$964$	289730.			0.311774
$965$	1.01303e6	−	584876.i	1.08785	−	0.628071i
$966$		0			0
$967$	183094.	−	317127.i	0.195803	−	0.339141i	−0.751360	−	0.659892i	$-0.770602\pi$
$967$	183094.	−	317127.i	0.195803	−	0.339141i	0.947164	+	0.320751i	$0.103935\pi$
$968$	29160.8	+	16836.0i	0.0311207	+	0.0179675i
$969$		0			0
$970$	−322592.	−	558745.i	−0.342854	−	0.593841i
$971$			1.43410e6i			1.52105i	0.649311	+	0.760523i	$0.275057\pi$
$971$			1.43410e6i			1.52105i	−0.649311	+	0.760523i	$0.724943\pi$
$972$		0			0
$973$	225796.			0.238501
$974$	−90626.1	+	52323.0i	−0.0955290	+	0.0551537i
$975$		0			0
$976$	−15010.0	+	25998.1i	−0.0157573	+	0.0272924i
$977$	−270028.	−	155901.i	−0.282892	−	0.163328i	0.351840	−	0.936060i	$-0.385556\pi$
$977$	−270028.	−	155901.i	−0.282892	−	0.163328i	−0.634732	+	0.772732i	$0.718889\pi$
$978$		0			0
$979$	−430623.	−	745861.i	−0.449295	−	0.778202i
$980$		−	471240.i		−	0.490671i
$981$		0			0
$982$	651141.			0.675231
$983$	−597698.	+	345081.i	−0.618550	+	0.357120i	−0.776304	−	0.630359i	$-0.782908\pi$
$983$	−597698.	+	345081.i	−0.618550	+	0.357120i	0.157754	+	0.987478i	$0.449575\pi$
$984$		0			0
$985$	−589694.	+	1.02138e6i	−0.607790	+	1.05272i
$986$	−729259.	−	421038.i	−0.750115	−	0.433079i
$987$		0			0
$988$	321328.	+	556556.i	0.329181	+	0.570158i
$989$			294600.i			0.301190i
$990$		0			0
$991$	981875.			0.999790			0.499895	−	0.866086i	$-0.333372\pi$
$991$	981875.			0.999790			0.499895	+	0.866086i	$0.333372\pi$
$992$	169517.	−	97870.5i	0.172262	−	0.0994554i
$993$		0			0
$994$	51813.0	−	89742.7i	0.0524404	−	0.0908294i
$995$	893232.	+	515708.i	0.902231	+	0.520904i
$996$		0			0
$997$	−120973.	−	209531.i	−0.121702	−	0.210794i	0.798737	−	0.601680i	$-0.205502\pi$
$997$	−120973.	−	209531.i	−0.121702	−	0.210794i	−0.920439	+	0.390886i	$0.872169\pi$
$998$			1.39443e6i			1.40002i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	81.5.d.b.53.2		4
3.2	odd	2	inner	81.5.d.b.53.1		4
9.2	odd	6	inner	81.5.d.b.26.2		4
9.4	even	3		27.5.b.c.26.2	yes	2
9.5	odd	6		27.5.b.c.26.1	✓	2
9.7	even	3	inner	81.5.d.b.26.1		4
36.23	even	6		432.5.e.e.161.1		2
36.31	odd	6		432.5.e.e.161.2		2
45.4	even	6		675.5.c.h.26.1		2
45.13	odd	12		675.5.d.d.674.2		2
45.14	odd	6		675.5.c.h.26.2		2
45.22	odd	12		675.5.d.a.674.1		2
45.23	even	12		675.5.d.a.674.2		2
45.32	even	12		675.5.d.d.674.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
27.5.b.c.26.1	✓	2	9.5	odd	6
27.5.b.c.26.2	yes	2	9.4	even	3
81.5.d.b.26.1		4	9.7	even	3	inner
81.5.d.b.26.2		4	9.2	odd	6	inner
81.5.d.b.53.1		4	3.2	odd	2	inner
81.5.d.b.53.2		4	1.1	even	1	trivial
432.5.e.e.161.1		2	36.23	even	6
432.5.e.e.161.2		2	36.31	odd	6
675.5.c.h.26.1		2	45.4	even	6
675.5.c.h.26.2		2	45.14	odd	6
675.5.d.a.674.1		2	45.22	odd	12
675.5.d.a.674.2		2	45.23	even	12
675.5.d.d.674.1		2	45.32	even	12
675.5.d.d.674.2		2	45.13	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 81 = 3^{4} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	81.d (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(2.59808 - 1.50000i) q^{2} +(-3.50000 + 6.06218i) q^{4} +(-28.5788 - 16.5000i) q^{5} +(9.50000 + 16.4545i) q^{7} +69.0000i q^{8} -99.0000 q^{10} +(-106.521 + 61.5000i) q^{11} +(-151.000 + 261.540i) q^{13} +(49.3634 + 28.5000i) q^{14} +(47.5000 + 82.2724i) q^{16} -414.000i q^{17} -304.000 q^{19} +(200.052 - 115.500i) q^{20} +(-184.500 + 319.563i) q^{22} +(259.808 + 150.000i) q^{23} +(232.000 + 401.836i) q^{25} +906.000i q^{26} -133.000 q^{28} +(587.165 - 339.000i) q^{29} +(-119.500 + 206.980i) q^{31} +(-709.275 - 409.500i) q^{32} +(-621.000 - 1075.60i) q^{34} -627.000i q^{35} +740.000 q^{37} +(-789.815 + 456.000i) q^{38} +(1138.50 - 1971.94i) q^{40} +(197.454 + 114.000i) q^{41} +(491.000 + 850.437i) q^{43} -861.000i q^{44} +900.000 q^{46} +(-1875.81 + 1083.00i) q^{47} +(1020.00 - 1766.69i) q^{49} +(1205.51 + 696.000i) q^{50} +(-1057.00 - 1830.78i) q^{52} +1593.00i q^{53} +4059.00 q^{55} +(-1135.36 + 655.500i) q^{56} +(1017.00 - 1761.50i) q^{58} +(-2530.53 - 1461.00i) q^{59} +(158.000 + 273.664i) q^{61} +717.000i q^{62} -3977.00 q^{64} +(8630.81 - 4983.00i) q^{65} +(-2311.00 + 4002.77i) q^{67} +(2509.74 + 1449.00i) q^{68} +(-940.500 - 1628.99i) q^{70} -1818.00i q^{71} -3031.00 q^{73} +(1922.58 - 1110.00i) q^{74} +(1064.00 - 1842.90i) q^{76} +(-2023.90 - 1168.50i) q^{77} +(5225.00 + 9049.97i) q^{79} -3135.00i q^{80} +684.000 q^{82} +(-10940.5 + 6316.50i) q^{83} +(-6831.00 + 11831.6i) q^{85} +(2551.31 + 1473.00i) q^{86} +(-4243.50 - 7349.96i) q^{88} +7002.00i q^{89} -5738.00 q^{91} +(-1818.65 + 1050.00i) q^{92} +(-3249.00 + 5627.43i) q^{94} +(8687.97 + 5016.00i) q^{95} +(3258.50 + 5643.89i) q^{97} -6120.00i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 14 q^{4} + 38 q^{7} - 396 q^{10} - 604 q^{13} + 190 q^{16} - 1216 q^{19} - 738 q^{22} + 928 q^{25} - 532 q^{28} - 478 q^{31} - 2484 q^{34} + 2960 q^{37} + 4554 q^{40} + 1964 q^{43} + 3600 q^{46} + 4080 q^{49}+ \cdots + 13034 q^{97}+O(q^{100}) \) 4 * q - 14 * q^4 + 38 * q^7 - 396 * q^10 - 604 * q^13 + 190 * q^16 - 1216 * q^19 - 738 * q^22 + 928 * q^25 - 532 * q^28 - 478 * q^31 - 2484 * q^34 + 2960 * q^37 + 4554 * q^40 + 1964 * q^43 + 3600 * q^46 + 4080 * q^49 - 4228 * q^52 + 16236 * q^55 + 4068 * q^58 + 632 * q^61 - 15908 * q^64 - 9244 * q^67 - 3762 * q^70 - 12124 * q^73 + 4256 * q^76 + 20900 * q^79 + 2736 * q^82 - 27324 * q^85 - 16974 * q^88 - 22952 * q^91 - 12996 * q^94 + 13034 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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