LMFDB - Embedded newform 882.3.s.f.863.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [882,3,Mod(557,882)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(882, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

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

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

chi := DirichletCharacter("882.557");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 882 = 2 \cdot 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	882.s (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:	$24.0327593166$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			863.1
Root			$-0.965926 - 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.863
Dual form			882.3.s.f.557.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.73205 - 1.00000i) q^{5} -2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.73205 - 1.00000i) q^{5} -2.82843i q^{8} +(1.41421 + 2.44949i) q^{10} +(-2.44949 + 1.41421i) q^{11} +12.7279 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-19.0526 + 11.0000i) q^{17} +(2.82843 - 4.89898i) q^{19} -4.00000i q^{20} +4.00000 q^{22} +(-2.44949 - 1.41421i) q^{23} +(-10.5000 - 18.1865i) q^{25} +(-15.5885 - 9.00000i) q^{26} -35.3553i q^{29} +(16.9706 + 29.3939i) q^{31} +(4.89898 - 2.82843i) q^{32} +31.1127 q^{34} +(-32.0000 + 55.4256i) q^{37} +(-6.92820 + 4.00000i) q^{38} +(-2.82843 + 4.89898i) q^{40} +20.0000i q^{41} +44.0000 q^{43} +(-4.89898 - 2.82843i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-58.8897 - 34.0000i) q^{47} +29.6985i q^{50} +(12.7279 + 22.0454i) q^{52} +(15.9217 - 9.19239i) q^{53} +5.65685 q^{55} +(-25.0000 + 43.3013i) q^{58} +(-86.6025 + 50.0000i) q^{59} +(-26.1630 + 45.3156i) q^{61} -48.0000i q^{62} -8.00000 q^{64} +(-22.0454 - 12.7279i) q^{65} +(-60.0000 - 103.923i) q^{67} +(-38.1051 - 22.0000i) q^{68} +8.48528i q^{71} +(37.4767 + 64.9115i) q^{73} +(78.3837 - 45.2548i) q^{74} +11.3137 q^{76} +(-46.0000 + 79.6743i) q^{79} +(6.92820 - 4.00000i) q^{80} +(14.1421 - 24.4949i) q^{82} +112.000i q^{83} +44.0000 q^{85} +(-53.8888 - 31.1127i) q^{86} +(4.00000 + 6.92820i) q^{88} +(17.3205 + 10.0000i) q^{89} -5.65685i q^{92} +(48.0833 + 83.2827i) q^{94} +(-9.79796 + 5.65685i) q^{95} -26.8701 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} - 84 q^{25} - 256 q^{37} + 352 q^{43} + 16 q^{46} - 200 q^{58} - 64 q^{64} - 480 q^{67} - 368 q^{79} + 352 q^{85} + 32 q^{88}+O(q^{100}) $ 8 * q + 8 * q^4 - 16 * q^16 + 32 * q^22 - 84 * q^25 - 256 * q^37 + 352 * q^43 + 16 * q^46 - 200 * q^58 - 64 * q^64 - 480 * q^67 - 368 * q^79 + 352 * q^85 + 32 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$-1$

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 $

$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$2$	−1.22474	−	0.707107i	−0.612372	−	0.353553i
$3$		0			0
$3$		0			0
$4$	1.00000	+	1.73205i	0.250000	+	0.433013i
$5$	−1.73205	−	1.00000i	−0.346410	−	0.200000i	0.316693	−	0.948528i	$-0.397428\pi$
$5$	−1.73205	−	1.00000i	−0.346410	−	0.200000i	−0.663103	+	0.748528i	$0.730761\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	1.41421	+	2.44949i	0.141421	+	0.244949i
$11$	−2.44949	+	1.41421i	−0.222681	+	0.128565i	−0.607191	−	0.794556i	$-0.707704\pi$
$11$	−2.44949	+	1.41421i	−0.222681	+	0.128565i	0.384510	+	0.923121i	$0.374370\pi$
$12$		0			0
$13$	12.7279			0.979071			0.489535	−	0.871983i	$-0.337166\pi$
$13$	12.7279			0.979071			0.489535	+	0.871983i	$0.337166\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−19.0526	+	11.0000i	−1.12074	+	0.647059i	−0.941589	−	0.336763i	$-0.890668\pi$
$17$	−19.0526	+	11.0000i	−1.12074	+	0.647059i	−0.179149	+	0.983822i	$0.557335\pi$
$18$		0			0
$19$	2.82843	−	4.89898i	0.148865	−	0.257841i	−0.781944	−	0.623349i	$-0.785771\pi$
$19$	2.82843	−	4.89898i	0.148865	−	0.257841i	0.930808	+	0.365508i	$0.119105\pi$
$20$		−	4.00000i		−	0.200000i
$21$		0			0
$22$	4.00000			0.181818
$23$	−2.44949	−	1.41421i	−0.106500	−	0.0614875i	0.445804	−	0.895131i	$-0.352918\pi$
$23$	−2.44949	−	1.41421i	−0.106500	−	0.0614875i	−0.552304	+	0.833643i	$0.686251\pi$
$24$		0			0
$25$	−10.5000	−	18.1865i	−0.420000	−	0.727461i
$26$	−15.5885	−	9.00000i	−0.599556	−	0.346154i
$27$		0			0
$28$		0			0
$29$		−	35.3553i		−	1.21915i	−0.792729	−	0.609575i	$-0.791340\pi$
$29$		−	35.3553i		−	1.21915i	0.792729	−	0.609575i	$-0.208660\pi$
$30$		0			0
$31$	16.9706	+	29.3939i	0.547438	+	0.948190i	0.998449	+	0.0556715i	$0.0177300\pi$
$31$	16.9706	+	29.3939i	0.547438	+	0.948190i	−0.451012	+	0.892518i	$0.648937\pi$
$32$	4.89898	−	2.82843i	0.153093	−	0.0883883i
$33$		0			0
$34$	31.1127			0.915079
$35$		0			0
$36$		0			0
$37$	−32.0000	+	55.4256i	−0.864865	+	1.49799i	0.00231643	+	0.999997i	$0.499263\pi$
$37$	−32.0000	+	55.4256i	−0.864865	+	1.49799i	−0.867181	+	0.497993i	$0.834071\pi$
$38$	−6.92820	+	4.00000i	−0.182321	+	0.105263i
$39$		0			0
$40$	−2.82843	+	4.89898i	−0.0707107	+	0.122474i
$41$			20.0000i			0.487805i	0.969800	+	0.243902i	$0.0784277\pi$
$41$			20.0000i			0.487805i	−0.969800	+	0.243902i	$0.921572\pi$
$42$		0			0
$43$	44.0000			1.02326			0.511628	−	0.859207i	$-0.329043\pi$
$43$	44.0000			1.02326			0.511628	+	0.859207i	$0.329043\pi$
$44$	−4.89898	−	2.82843i	−0.111340	−	0.0642824i
$45$		0			0
$46$	2.00000	+	3.46410i	0.0434783	+	0.0753066i
$47$	−58.8897	−	34.0000i	−1.25297	−	0.723404i	−0.281274	−	0.959627i	$-0.590757\pi$
$47$	−58.8897	−	34.0000i	−1.25297	−	0.723404i	−0.971699	+	0.236223i	$0.924090\pi$
$48$		0			0
$49$		0			0
$50$			29.6985i			0.593970i
$51$		0			0
$52$	12.7279	+	22.0454i	0.244768	+	0.423950i
$53$	15.9217	−	9.19239i	0.300409	−	0.173441i	−0.342218	−	0.939621i	$-0.611178\pi$
$53$	15.9217	−	9.19239i	0.300409	−	0.173441i	0.642627	+	0.766179i	$0.277845\pi$
$54$		0			0
$55$	5.65685			0.102852
$56$		0			0
$57$		0			0
$58$	−25.0000	+	43.3013i	−0.431034	+	0.746574i
$59$	−86.6025	+	50.0000i	−1.46784	+	0.847458i	−0.999351	−	0.0360121i	$-0.988535\pi$
$59$	−86.6025	+	50.0000i	−1.46784	+	0.847458i	−0.468488	+	0.883470i	$0.655201\pi$
$60$		0			0
$61$	−26.1630	+	45.3156i	−0.428901	+	0.742878i	−0.996776	−	0.0802368i	$-0.974432\pi$
$61$	−26.1630	+	45.3156i	−0.428901	+	0.742878i	0.567875	+	0.823115i	$0.307766\pi$
$62$		−	48.0000i		−	0.774194i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−22.0454	−	12.7279i	−0.339160	−	0.195814i
$66$		0			0
$67$	−60.0000	−	103.923i	−0.895522	−	1.55109i	−0.833157	−	0.553037i	$-0.813469\pi$
$67$	−60.0000	−	103.923i	−0.895522	−	1.55109i	−0.0623656	−	0.998053i	$-0.519864\pi$
$68$	−38.1051	−	22.0000i	−0.560369	−	0.323529i
$69$		0			0
$70$		0			0
$71$			8.48528i			0.119511i	0.998213	+	0.0597555i	$0.0190321\pi$
$71$			8.48528i			0.119511i	−0.998213	+	0.0597555i	$0.980968\pi$
$72$		0			0
$73$	37.4767	+	64.9115i	0.513379	+	0.889198i	0.999880	+	0.0155181i	$0.00493978\pi$
$73$	37.4767	+	64.9115i	0.513379	+	0.889198i	−0.486501	+	0.873680i	$0.661727\pi$
$74$	78.3837	−	45.2548i	1.05924	−	0.611552i
$75$		0			0
$76$	11.3137			0.148865
$77$		0			0
$78$		0			0
$79$	−46.0000	+	79.6743i	−0.582278	+	1.00854i	0.412930	+	0.910763i	$0.364505\pi$
$79$	−46.0000	+	79.6743i	−0.582278	+	1.00854i	−0.995209	+	0.0977733i	$0.968828\pi$
$80$	6.92820	−	4.00000i	0.0866025	−	0.0500000i
$81$		0			0
$82$	14.1421	−	24.4949i	0.172465	−	0.298718i
$83$			112.000i			1.34940i	0.738093	+	0.674699i	$0.235726\pi$
$83$			112.000i			1.34940i	−0.738093	+	0.674699i	$0.764274\pi$
$84$		0			0
$85$	44.0000			0.517647
$86$	−53.8888	−	31.1127i	−0.626614	−	0.361776i
$87$		0			0
$88$	4.00000	+	6.92820i	0.0454545	+	0.0787296i
$89$	17.3205	+	10.0000i	0.194612	+	0.112360i	0.594140	−	0.804362i	$-0.297492\pi$
$89$	17.3205	+	10.0000i	0.194612	+	0.112360i	−0.399528	+	0.916721i	$0.630826\pi$
$90$		0			0
$91$		0			0
$92$		−	5.65685i		−	0.0614875i
$93$		0			0
$94$	48.0833	+	83.2827i	0.511524	+	0.885986i
$95$	−9.79796	+	5.65685i	−0.103136	+	0.0595458i
$96$		0			0
$97$	−26.8701			−0.277011			−0.138505	−	0.990362i	$-0.544230\pi$
$97$	−26.8701			−0.277011			−0.138505	+	0.990362i	$0.544230\pi$
$98$		0			0
$99$		0			0
$100$	21.0000	−	36.3731i	0.210000	−	0.363731i
$101$	−72.7461	+	42.0000i	−0.720259	+	0.415842i	−0.814848	−	0.579675i	$-0.803180\pi$
$101$	−72.7461	+	42.0000i	−0.720259	+	0.415842i	0.0945892	+	0.995516i	$0.469846\pi$
$102$		0			0
$103$	−79.1960	+	137.171i	−0.768893	+	1.33176i	0.169271	+	0.985570i	$0.445859\pi$
$103$	−79.1960	+	137.171i	−0.768893	+	1.33176i	−0.938164	+	0.346192i	$0.887475\pi$
$104$		−	36.0000i		−	0.346154i
$105$		0			0
$106$	−26.0000			−0.245283
$107$	−120.025	−	69.2965i	−1.12173	−	0.647631i	−0.179887	−	0.983687i	$-0.557573\pi$
$107$	−120.025	−	69.2965i	−1.12173	−	0.647631i	−0.941842	+	0.336057i	$0.890907\pi$
$108$		0			0
$109$	−35.0000	−	60.6218i	−0.321101	−	0.556163i	0.659615	−	0.751604i	$-0.270720\pi$
$109$	−35.0000	−	60.6218i	−0.321101	−	0.556163i	−0.980715	+	0.195441i	$0.937386\pi$
$110$	−6.92820	−	4.00000i	−0.0629837	−	0.0363636i
$111$		0			0
$112$		0			0
$113$			21.2132i			0.187727i	0.995585	+	0.0938637i	$0.0299218\pi$
$113$			21.2132i			0.187727i	−0.995585	+	0.0938637i	$0.970078\pi$
$114$		0			0
$115$	2.82843	+	4.89898i	0.0245950	+	0.0425998i
$116$	61.2372	−	35.3553i	0.527907	−	0.304787i
$117$		0			0
$118$	141.421			1.19849
$119$		0			0
$120$		0			0
$121$	−56.5000	+	97.8609i	−0.466942	+	0.808768i
$122$	64.0859	−	37.0000i	0.525294	−	0.303279i
$123$		0			0
$124$	−33.9411	+	58.7878i	−0.273719	+	0.474095i
$125$			92.0000i			0.736000i
$126$		0			0
$127$	−20.0000			−0.157480			−0.0787402	−	0.996895i	$-0.525090\pi$
$127$	−20.0000			−0.157480			−0.0787402	+	0.996895i	$0.525090\pi$
$128$	9.79796	+	5.65685i	0.0765466	+	0.0441942i
$129$		0			0
$130$	18.0000	+	31.1769i	0.138462	+	0.239822i
$131$	124.708	+	72.0000i	0.951967	+	0.549618i	0.893691	−	0.448682i	$-0.148106\pi$
$131$	124.708	+	72.0000i	0.951967	+	0.549618i	0.0582755	+	0.998301i	$0.481440\pi$
$132$		0			0
$133$		0			0
$134$			169.706i			1.26646i
$135$		0			0
$136$	31.1127	+	53.8888i	0.228770	+	0.396241i
$137$	−172.689	+	99.7021i	−1.26050	+	0.727752i	−0.973172	−	0.230079i	$-0.926102\pi$
$137$	−172.689	+	99.7021i	−1.26050	+	0.727752i	−0.287332	+	0.957831i	$0.592768\pi$
$138$		0			0
$139$	−5.65685			−0.0406968			−0.0203484	−	0.999793i	$-0.506478\pi$
$139$	−5.65685			−0.0406968			−0.0203484	+	0.999793i	$0.506478\pi$
$140$		0			0
$141$		0			0
$142$	6.00000	−	10.3923i	0.0422535	−	0.0731852i
$143$	−31.1769	+	18.0000i	−0.218020	+	0.125874i
$144$		0			0
$145$	−35.3553	+	61.2372i	−0.243830	+	0.422326i
$146$		−	106.000i		−	0.726027i
$147$		0			0
$148$	−128.000			−0.864865
$149$	−15.9217	−	9.19239i	−0.106857	−	0.0616939i	0.445619	−	0.895223i	$-0.352984\pi$
$149$	−15.9217	−	9.19239i	−0.106857	−	0.0616939i	−0.552476	+	0.833529i	$0.686317\pi$
$150$		0			0
$151$	32.0000	+	55.4256i	0.211921	+	0.367057i	0.952316	−	0.305115i	$-0.0986949\pi$
$151$	32.0000	+	55.4256i	0.211921	+	0.367057i	−0.740395	+	0.672172i	$0.765362\pi$
$152$	−13.8564	−	8.00000i	−0.0911606	−	0.0526316i
$153$		0			0
$154$		0			0
$155$		−	67.8823i		−	0.437950i
$156$		0			0
$157$	81.3173	+	140.846i	0.517944	+	0.897106i	0.999783	+	0.0208459i	$0.00663595\pi$
$157$	81.3173	+	140.846i	0.517944	+	0.897106i	−0.481838	+	0.876260i	$0.660031\pi$
$158$	112.677	−	65.0538i	0.713143	−	0.411733i
$159$		0			0
$160$	−11.3137			−0.0707107
$161$		0			0
$162$		0			0
$163$	112.000	−	193.990i	0.687117	−	1.19012i	−0.285650	−	0.958334i	$-0.592209\pi$
$163$	112.000	−	193.990i	0.687117	−	1.19012i	0.972767	−	0.231787i	$-0.0744572\pi$
$164$	−34.6410	+	20.0000i	−0.211226	+	0.121951i
$165$		0			0
$166$	79.1960	−	137.171i	0.477084	−	0.826334i
$167$			292.000i			1.74850i	0.485473	+	0.874251i	$0.338647\pi$
$167$			292.000i			1.74850i	−0.485473	+	0.874251i	$0.661353\pi$
$168$		0			0
$169$	−7.00000			−0.0414201
$170$	−53.8888	−	31.1127i	−0.316993	−	0.183016i
$171$		0			0
$172$	44.0000	+	76.2102i	0.255814	+	0.443083i
$173$	135.100	+	78.0000i	0.780925	+	0.450867i	0.836758	−	0.547573i	$-0.184448\pi$
$173$	135.100	+	78.0000i	0.780925	+	0.450867i	−0.0558332	+	0.998440i	$0.517782\pi$
$174$		0			0
$175$		0			0
$176$		−	11.3137i		−	0.0642824i
$177$		0			0
$178$	−14.1421	−	24.4949i	−0.0794502	−	0.137612i
$179$	80.8332	−	46.6690i	0.451582	−	0.260721i	−0.256916	−	0.966434i	$-0.582706\pi$
$179$	80.8332	−	46.6690i	0.451582	−	0.260721i	0.708498	+	0.705713i	$0.249373\pi$
$180$		0			0
$181$	−190.919			−1.05480			−0.527400	−	0.849617i	$-0.676833\pi$
$181$	−190.919			−1.05480			−0.527400	+	0.849617i	$0.676833\pi$
$182$		0			0
$183$		0			0
$184$	−4.00000	+	6.92820i	−0.0217391	+	0.0376533i
$185$	110.851	−	64.0000i	0.599196	−	0.345946i
$186$		0			0
$187$	31.1127	−	53.8888i	0.166378	−	0.288175i
$188$		−	136.000i		−	0.723404i
$189$		0			0
$190$	16.0000			0.0842105
$191$	115.126	+	66.4680i	0.602754	+	0.348000i	0.770124	−	0.637894i	$-0.220194\pi$
$191$	115.126	+	66.4680i	0.602754	+	0.348000i	−0.167370	+	0.985894i	$0.553528\pi$
$192$		0			0
$193$	−61.0000	−	105.655i	−0.316062	−	0.547436i	0.663601	−	0.748087i	$-0.269027\pi$
$193$	−61.0000	−	105.655i	−0.316062	−	0.547436i	−0.979663	+	0.200651i	$0.935694\pi$
$194$	32.9090	+	19.0000i	0.169634	+	0.0979381i
$195$		0			0
$196$		0			0
$197$			7.07107i			0.0358937i	0.999839	+	0.0179469i	$0.00571297\pi$
$197$			7.07107i			0.0358937i	−0.999839	+	0.0179469i	$0.994287\pi$
$198$		0			0
$199$	−186.676	−	323.333i	−0.938071	−	1.62479i	−0.769063	−	0.639172i	$-0.779277\pi$
$199$	−186.676	−	323.333i	−0.938071	−	1.62479i	−0.169008	−	0.985615i	$-0.554056\pi$
$200$	−51.4393	+	29.6985i	−0.257196	+	0.148492i
$201$		0			0
$202$	118.794			0.588089
$203$		0			0
$204$		0			0
$205$	20.0000	−	34.6410i	0.0975610	−	0.168981i
$206$	193.990	−	112.000i	0.941698	−	0.543689i
$207$		0			0
$208$	−25.4558	+	44.0908i	−0.122384	+	0.211975i
$209$			16.0000i			0.0765550i
$210$		0			0
$211$	−12.0000			−0.0568720			−0.0284360	−	0.999596i	$-0.509053\pi$
$211$	−12.0000			−0.0568720			−0.0284360	+	0.999596i	$0.509053\pi$
$212$	31.8434	+	18.3848i	0.150205	+	0.0867206i
$213$		0			0
$214$	98.0000	+	169.741i	0.457944	+	0.793182i
$215$	−76.2102	−	44.0000i	−0.354466	−	0.204651i
$216$		0			0
$217$		0			0
$218$			98.9949i			0.454105i
$219$		0			0
$220$	5.65685	+	9.79796i	0.0257130	+	0.0445362i
$221$	−242.499	+	140.007i	−1.09728	+	0.633516i
$222$		0			0
$223$	−203.647			−0.913214			−0.456607	−	0.889668i	$-0.650935\pi$
$223$	−203.647			−0.913214			−0.456607	+	0.889668i	$0.650935\pi$
$224$		0			0
$225$		0			0
$226$	15.0000	−	25.9808i	0.0663717	−	0.114959i
$227$	−176.669	+	102.000i	−0.778278	+	0.449339i	−0.835820	−	0.549004i	$-0.815007\pi$
$227$	−176.669	+	102.000i	−0.778278	+	0.449339i	0.0575414	+	0.998343i	$0.481674\pi$
$228$		0			0
$229$	23.3345	−	40.4166i	0.101897	−	0.176492i	−0.810569	−	0.585643i	$-0.800842\pi$
$229$	23.3345	−	40.4166i	0.101897	−	0.176492i	0.912466	+	0.409152i	$0.134175\pi$
$230$		−	8.00000i		−	0.0347826i
$231$		0			0
$232$	−100.000			−0.431034
$233$	268.219	+	154.856i	1.15116	+	0.664620i	0.949168	−	0.314769i	$-0.101927\pi$
$233$	268.219	+	154.856i	1.15116	+	0.664620i	0.201987	+	0.979388i	$0.435260\pi$
$234$		0			0
$235$	68.0000	+	117.779i	0.289362	+	0.501189i
$236$	−173.205	−	100.000i	−0.733920	−	0.423729i
$237$		0			0
$238$		0			0
$239$		−	42.4264i		−	0.177516i	−0.996053	−	0.0887582i	$-0.971710\pi$
$239$		−	42.4264i		−	0.177516i	0.996053	−	0.0887582i	$-0.0282898\pi$
$240$		0			0
$241$	−188.798	−	327.007i	−0.783392	−	1.35688i	−0.929955	−	0.367674i	$-0.880154\pi$
$241$	−188.798	−	327.007i	−0.783392	−	1.35688i	0.146563	−	0.989201i	$-0.453179\pi$
$242$	138.396	−	79.9031i	0.571885	−	0.330178i
$243$		0			0
$244$	−104.652			−0.428901
$245$		0			0
$246$		0			0
$247$	36.0000	−	62.3538i	0.145749	−	0.252445i
$248$	83.1384	−	48.0000i	0.335236	−	0.193548i
$249$		0			0
$250$	65.0538	−	112.677i	0.260215	−	0.450706i
$251$		−	332.000i		−	1.32271i	−0.750073	−	0.661355i	$-0.769982\pi$
$251$		−	332.000i		−	1.32271i	0.750073	−	0.661355i	$-0.230018\pi$
$252$		0			0
$253$	8.00000			0.0316206
$254$	24.4949	+	14.1421i	0.0964366	+	0.0556777i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	155.885	+	90.0000i	0.606555	+	0.350195i	0.771616	−	0.636089i	$-0.219449\pi$
$257$	155.885	+	90.0000i	0.606555	+	0.350195i	−0.165061	+	0.986283i	$0.552782\pi$
$258$		0			0
$259$		0			0
$260$		−	50.9117i		−	0.195814i
$261$		0			0
$262$	−101.823	−	176.363i	−0.388639	−	0.673142i
$263$	−139.621	+	80.6102i	−0.530878	+	0.306503i	−0.741374	−	0.671092i	$-0.765825\pi$
$263$	−139.621	+	80.6102i	−0.530878	+	0.306503i	0.210496	+	0.977595i	$0.432492\pi$
$264$		0			0
$265$	−36.7696			−0.138753
$266$		0			0
$267$		0			0
$268$	120.000	−	207.846i	0.447761	−	0.775545i
$269$	455.529	−	263.000i	1.69342	−	0.977695i	0.741694	−	0.670738i	$-0.234022\pi$
$269$	455.529	−	263.000i	1.69342	−	0.977695i	0.951723	−	0.306957i	$-0.0993108\pi$
$270$		0			0
$271$	214.960	−	372.322i	0.793212	−	1.37388i	−0.130756	−	0.991415i	$-0.541741\pi$
$271$	214.960	−	372.322i	0.793212	−	1.37388i	0.923968	−	0.382469i	$-0.124926\pi$
$272$		−	88.0000i		−	0.323529i
$273$		0			0
$274$	282.000			1.02920
$275$	51.4393	+	29.6985i	0.187052	+	0.107994i
$276$		0			0
$277$	−32.0000	−	55.4256i	−0.115523	−	0.200093i	0.802465	−	0.596699i	$-0.203521\pi$
$277$	−32.0000	−	55.4256i	−0.115523	−	0.200093i	−0.917989	+	0.396606i	$0.870188\pi$
$278$	6.92820	+	4.00000i	0.0249216	+	0.0143885i
$279$		0			0
$280$		0			0
$281$		−	448.306i		−	1.59539i	−0.603058	−	0.797697i	$-0.706051\pi$
$281$		−	448.306i		−	1.59539i	0.603058	−	0.797697i	$-0.293949\pi$
$282$		0			0
$283$	−62.2254	−	107.778i	−0.219878	−	0.380839i	0.734893	−	0.678183i	$-0.237233\pi$
$283$	−62.2254	−	107.778i	−0.219878	−	0.380839i	−0.954770	+	0.297344i	$0.903899\pi$
$284$	−14.6969	+	8.48528i	−0.0517498	+	0.0298778i
$285$		0			0
$286$	50.9117			0.178013
$287$		0			0
$288$		0			0
$289$	97.5000	−	168.875i	0.337370	−	0.584342i
$290$	86.6025	−	50.0000i	0.298629	−	0.172414i
$291$		0			0
$292$	−74.9533	+	129.823i	−0.256689	+	0.444599i
$293$		−	284.000i		−	0.969283i	−0.874713	−	0.484642i	$-0.838950\pi$
$293$		−	284.000i		−	0.969283i	0.874713	−	0.484642i	$-0.161050\pi$
$294$		0			0
$295$	200.000			0.677966
$296$	156.767	+	90.5097i	0.529619	+	0.305776i
$297$		0			0
$298$	13.0000	+	22.5167i	0.0436242	+	0.0755593i
$299$	−31.1769	−	18.0000i	−0.104271	−	0.0602007i
$300$		0			0
$301$		0			0
$302$		−	90.5097i		−	0.299701i
$303$		0			0
$304$	11.3137	+	19.5959i	0.0372161	+	0.0644603i
$305$	90.6311	−	52.3259i	0.297151	−	0.171560i
$306$		0			0
$307$	−282.843			−0.921312			−0.460656	−	0.887579i	$-0.652386\pi$
$307$	−282.843			−0.921312			−0.460656	+	0.887579i	$0.652386\pi$
$308$		0			0
$309$		0			0
$310$	−48.0000	+	83.1384i	−0.154839	+	0.268189i
$311$	−162.813	+	94.0000i	−0.523514	+	0.302251i	−0.738371	−	0.674395i	$-0.764405\pi$
$311$	−162.813	+	94.0000i	−0.523514	+	0.302251i	0.214857	+	0.976645i	$0.431071\pi$
$312$		0			0
$313$	108.187	−	187.386i	0.345646	−	0.598677i	−0.639825	−	0.768521i	$-0.720993\pi$
$313$	108.187	−	187.386i	0.345646	−	0.598677i	0.985471	+	0.169844i	$0.0543263\pi$
$314$		−	230.000i		−	0.732484i
$315$		0			0
$316$	−184.000			−0.582278
$317$	395.593	+	228.395i	1.24793	+	0.720491i	0.970695	−	0.240313i	$-0.0772500\pi$
$317$	395.593	+	228.395i	1.24793	+	0.720491i	0.277231	+	0.960803i	$0.410583\pi$
$318$		0			0
$319$	50.0000	+	86.6025i	0.156740	+	0.271481i
$320$	13.8564	+	8.00000i	0.0433013	+	0.0250000i
$321$		0			0
$322$		0			0
$323$			124.451i			0.385297i
$324$		0			0
$325$	−133.643	−	231.477i	−0.411210	−	0.712236i
$326$	−274.343	+	158.392i	−0.841542	+	0.485865i
$327$		0			0
$328$	56.5685			0.172465
$329$		0			0
$330$		0			0
$331$	250.000	−	433.013i	0.755287	−	1.30820i	−0.189945	−	0.981795i	$-0.560831\pi$
$331$	250.000	−	433.013i	0.755287	−	1.30820i	0.945232	−	0.326401i	$-0.105836\pi$
$332$	−193.990	+	112.000i	−0.584306	+	0.337349i
$333$		0			0
$334$	206.475	−	357.626i	0.618189	−	1.07074i
$335$			240.000i			0.716418i
$336$		0			0
$337$	86.0000			0.255193			0.127596	−	0.991826i	$-0.459274\pi$
$337$	86.0000			0.255193			0.127596	+	0.991826i	$0.459274\pi$
$338$	8.57321	+	4.94975i	0.0253645	+	0.0146442i
$339$		0			0
$340$	44.0000	+	76.2102i	0.129412	+	0.224148i
$341$	−83.1384	−	48.0000i	−0.243808	−	0.140762i
$342$		0			0
$343$		0			0
$344$		−	124.451i		−	0.361776i
$345$		0			0
$346$	−110.309	−	191.060i	−0.318811	−	0.552197i
$347$	−213.106	+	123.037i	−0.614137	+	0.354572i	−0.774583	−	0.632472i	$-0.782040\pi$
$347$	−213.106	+	123.037i	−0.614137	+	0.354572i	0.160446	+	0.987045i	$0.448707\pi$
$348$		0			0
$349$	445.477			1.27644			0.638220	−	0.769854i	$-0.279671\pi$
$349$	445.477			1.27644			0.638220	+	0.769854i	$0.279671\pi$
$350$		0			0
$351$		0			0
$352$	−8.00000	+	13.8564i	−0.0227273	+	0.0393648i
$353$	188.794	−	109.000i	0.534826	−	0.308782i	−0.208153	−	0.978096i	$-0.566745\pi$
$353$	188.794	−	109.000i	0.534826	−	0.308782i	0.742979	+	0.669314i	$0.233412\pi$
$354$		0			0
$355$	8.48528	−	14.6969i	0.0239022	−	0.0413998i
$356$			40.0000i			0.112360i
$357$		0			0
$358$	−132.000			−0.368715
$359$	−320.883	−	185.262i	−0.893825	−	0.516050i	−0.0186333	−	0.999826i	$-0.505931\pi$
$359$	−320.883	−	185.262i	−0.893825	−	0.516050i	−0.875192	+	0.483776i	$0.839265\pi$
$360$		0			0
$361$	164.500	+	284.922i	0.455679	+	0.789259i
$362$	233.827	+	135.000i	0.645931	+	0.372928i
$363$		0			0
$364$		0			0
$365$		−	149.907i		−	0.410703i
$366$		0			0
$367$	−223.446	−	387.019i	−0.608844	−	1.05455i	−0.991431	−	0.130629i	$-0.958300\pi$
$367$	−223.446	−	387.019i	−0.608844	−	1.05455i	0.382587	−	0.923919i	$-0.375033\pi$
$368$	9.79796	−	5.65685i	0.0266249	−	0.0153719i
$369$		0			0
$370$	−181.019			−0.489241
$371$		0			0
$372$		0			0
$373$	−143.000	+	247.683i	−0.383378	+	0.664030i	−0.991543	−	0.129781i	$-0.958573\pi$
$373$	−143.000	+	247.683i	−0.383378	+	0.664030i	0.608165	+	0.793811i	$0.291906\pi$
$374$	−76.2102	+	44.0000i	−0.203771	+	0.117647i
$375$		0			0
$376$	−96.1665	+	166.565i	−0.255762	+	0.442993i
$377$		−	450.000i		−	1.19363i
$378$		0			0
$379$	−188.000			−0.496042			−0.248021	−	0.968755i	$-0.579780\pi$
$379$	−188.000			−0.496042			−0.248021	+	0.968755i	$0.579780\pi$
$380$	−19.5959	−	11.3137i	−0.0515682	−	0.0297729i
$381$		0			0
$382$	−94.0000	−	162.813i	−0.246073	−	0.426211i
$383$	−304.841	−	176.000i	−0.795929	−	0.459530i	0.0461164	−	0.998936i	$-0.485315\pi$
$383$	−304.841	−	176.000i	−0.795929	−	0.459530i	−0.842046	+	0.539406i	$0.818649\pi$
$384$		0			0
$385$		0			0
$386$			172.534i			0.446979i
$387$		0			0
$388$	−26.8701	−	46.5403i	−0.0692527	−	0.119949i
$389$	−177.588	+	102.530i	−0.456524	+	0.263575i	−0.710582	−	0.703615i	$-0.751568\pi$
$389$	−177.588	+	102.530i	−0.456524	+	0.263575i	0.254057	+	0.967189i	$0.418235\pi$
$390$		0			0
$391$	62.2254			0.159144
$392$		0			0
$393$		0			0
$394$	5.00000	−	8.66025i	0.0126904	−	0.0219803i
$395$	159.349	−	92.0000i	0.403414	−	0.232911i
$396$		0			0
$397$	−122.329	+	211.881i	−0.308135	+	0.533705i	−0.977954	−	0.208819i	$-0.933038\pi$
$397$	−122.329	+	211.881i	−0.308135	+	0.533705i	0.669820	+	0.742524i	$0.266371\pi$
$398$			528.000i			1.32663i
$399$		0			0
$400$	84.0000			0.210000
$401$	385.795	+	222.739i	0.962081	+	0.555458i	0.896813	−	0.442410i	$-0.145876\pi$
$401$	385.795	+	222.739i	0.962081	+	0.555458i	0.0652684	+	0.997868i	$0.479210\pi$
$402$		0			0
$403$	216.000	+	374.123i	0.535980	+	0.928345i
$404$	−145.492	−	84.0000i	−0.360129	−	0.207921i
$405$		0			0
$406$		0			0
$407$		−	181.019i		−	0.444765i
$408$		0			0
$409$	375.474	+	650.340i	0.918029	+	1.59007i	0.802406	+	0.596779i	$0.203553\pi$
$409$	375.474	+	650.340i	0.918029	+	1.59007i	0.115623	+	0.993293i	$0.463114\pi$
$410$	−48.9898	+	28.2843i	−0.119487	+	0.0689860i
$411$		0			0
$412$	−316.784			−0.768893
$413$		0			0
$414$		0			0
$415$	112.000	−	193.990i	0.269880	−	0.467445i
$416$	62.3538	−	36.0000i	0.149889	−	0.0865385i
$417$		0			0
$418$	11.3137	−	19.5959i	0.0270663	−	0.0468802i
$419$			236.000i			0.563246i	0.959525	+	0.281623i	$0.0908727\pi$
$419$			236.000i			0.563246i	−0.959525	+	0.281623i	$0.909127\pi$
$420$		0			0
$421$	−96.0000			−0.228029			−0.114014	−	0.993479i	$-0.536371\pi$
$421$	−96.0000			−0.228029			−0.114014	+	0.993479i	$0.536371\pi$
$422$	14.6969	+	8.48528i	0.0348269	+	0.0201073i
$423$		0			0
$424$	−26.0000	−	45.0333i	−0.0613208	−	0.106211i
$425$	400.104	+	231.000i	0.941421	+	0.543529i
$426$		0			0
$427$		0			0
$428$		−	277.186i		−	0.647631i
$429$		0			0
$430$	62.2254	+	107.778i	0.144710	+	0.250645i
$431$	742.195	−	428.507i	1.72203	−	0.994215i	0.807312	−	0.590125i	$-0.200922\pi$
$431$	742.195	−	428.507i	1.72203	−	0.994215i	0.914719	−	0.404090i	$-0.132412\pi$
$432$		0			0
$433$	156.978			0.362535			0.181268	−	0.983434i	$-0.441980\pi$
$433$	156.978			0.362535			0.181268	+	0.983434i	$0.441980\pi$
$434$		0			0
$435$		0			0
$436$	70.0000	−	121.244i	0.160550	−	0.278082i
$437$	−13.8564	+	8.00000i	−0.0317080	+	0.0183066i
$438$		0			0
$439$	322.441	−	558.484i	0.734489	−	1.27217i	−0.220458	−	0.975396i	$-0.570755\pi$
$439$	322.441	−	558.484i	0.734489	−	1.27217i	0.954947	−	0.296776i	$-0.0959114\pi$
$440$		−	16.0000i		−	0.0363636i
$441$		0			0
$442$	396.000			0.895928
$443$	−502.145	−	289.914i	−1.13351	−	0.654433i	−0.188695	−	0.982036i	$-0.560426\pi$
$443$	−502.145	−	289.914i	−1.13351	−	0.654433i	−0.944816	+	0.327603i	$0.893759\pi$
$444$		0			0
$445$	−20.0000	−	34.6410i	−0.0449438	−	0.0778450i
$446$	249.415	+	144.000i	0.559227	+	0.322870i
$447$		0			0
$448$		0			0
$449$			869.741i			1.93706i	0.248891	+	0.968532i	$0.419934\pi$
$449$			869.741i			1.93706i	−0.248891	+	0.968532i	$0.580066\pi$
$450$		0			0
$451$	−28.2843	−	48.9898i	−0.0627146	−	0.108625i
$452$	−36.7423	+	21.2132i	−0.0812884	+	0.0469319i
$453$		0			0
$454$	288.500			0.635462
$455$		0			0
$456$		0			0
$457$	−192.000	+	332.554i	−0.420131	+	0.727689i	−0.995952	−	0.0898873i	$-0.971349\pi$
$457$	−192.000	+	332.554i	−0.420131	+	0.727689i	0.575821	+	0.817576i	$0.304683\pi$
$458$	−57.1577	+	33.0000i	−0.124798	+	0.0720524i
$459$		0			0
$460$	−5.65685	+	9.79796i	−0.0122975	+	0.0212999i
$461$			268.000i			0.581345i	0.956823	+	0.290672i	$0.0938790\pi$
$461$			268.000i			0.581345i	−0.956823	+	0.290672i	$0.906121\pi$
$462$		0			0
$463$	−716.000			−1.54644			−0.773218	−	0.634140i	$-0.781354\pi$
$463$	−716.000			−1.54644			−0.773218	+	0.634140i	$0.781354\pi$
$464$	122.474	+	70.7107i	0.263954	+	0.152394i
$465$		0			0
$466$	−219.000	−	379.319i	−0.469957	−	0.813990i
$467$	−266.736	−	154.000i	−0.571169	−	0.329764i	0.186447	−	0.982465i	$-0.440303\pi$
$467$	−266.736	−	154.000i	−0.571169	−	0.329764i	−0.757616	+	0.652701i	$0.773636\pi$
$468$		0			0
$469$		0			0
$470$		−	192.333i		−	0.409219i
$471$		0			0
$472$	141.421	+	244.949i	0.299622	+	0.518960i
$473$	−107.778	+	62.2254i	−0.227860	+	0.131555i
$474$		0			0
$475$	−118.794			−0.250093
$476$		0			0
$477$		0			0
$478$	−30.0000	+	51.9615i	−0.0627615	+	0.108706i
$479$	−336.018	+	194.000i	−0.701499	+	0.405010i	−0.807905	−	0.589312i	$-0.799399\pi$
$479$	−336.018	+	194.000i	−0.701499	+	0.405010i	0.106407	+	0.994323i	$0.466065\pi$
$480$		0			0
$481$	−407.294	+	705.453i	−0.846764	+	1.46664i
$482$			534.000i			1.10788i
$483$		0			0
$484$	−226.000			−0.466942
$485$	46.5403	+	26.8701i	0.0959594	+	0.0554022i
$486$		0			0
$487$	−60.0000	−	103.923i	−0.123203	−	0.213394i	0.797826	−	0.602888i	$-0.205983\pi$
$487$	−60.0000	−	103.923i	−0.123203	−	0.213394i	−0.921029	+	0.389494i	$0.872650\pi$
$488$	128.172	+	74.0000i	0.262647	+	0.151639i
$489$		0			0
$490$		0			0
$491$			619.426i			1.26156i	0.775962	+	0.630780i	$0.217265\pi$
$491$			619.426i			1.26156i	−0.775962	+	0.630780i	$0.782735\pi$
$492$		0			0
$493$	388.909	+	673.610i	0.788862	+	1.36635i
$494$	−88.1816	+	50.9117i	−0.178505	+	0.103060i
$495$		0			0
$496$	−135.765			−0.273719
$497$		0			0
$498$		0			0
$499$	−238.000	+	412.228i	−0.476954	+	0.826108i	−0.999651	−	0.0264100i	$-0.991592\pi$
$499$	−238.000	+	412.228i	−0.476954	+	0.826108i	0.522697	+	0.852518i	$0.324926\pi$
$500$	−159.349	+	92.0000i	−0.318697	+	0.184000i
$501$		0			0
$502$	−234.759	+	406.615i	−0.467648	+	0.809991i
$503$		−	968.000i		−	1.92445i	−0.272250	−	0.962227i	$-0.587768\pi$
$503$		−	968.000i		−	1.92445i	0.272250	−	0.962227i	$-0.412232\pi$
$504$		0			0
$505$	168.000			0.332673
$506$	−9.79796	−	5.65685i	−0.0193636	−	0.0111796i
$507$		0			0
$508$	−20.0000	−	34.6410i	−0.0393701	−	0.0681910i
$509$	219.970	+	127.000i	0.432162	+	0.249509i	0.700267	−	0.713881i	$-0.253064\pi$
$509$	219.970	+	127.000i	0.432162	+	0.249509i	−0.268105	+	0.963390i	$0.586398\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	−127.279	−	220.454i	−0.247625	−	0.428899i
$515$	274.343	−	158.392i	0.532705	−	0.307557i
$516$		0			0
$517$	192.333			0.372017
$518$		0			0
$519$		0			0
$520$	−36.0000	+	62.3538i	−0.0692308	+	0.119911i
$521$	698.016	−	403.000i	1.33976	−	0.773512i	0.352991	−	0.935627i	$-0.385165\pi$
$521$	698.016	−	403.000i	1.33976	−	0.773512i	0.986772	+	0.162114i	$0.0518313\pi$
$522$		0			0
$523$	−305.470	+	529.090i	−0.584073	+	1.01164i	0.410917	+	0.911673i	$0.365208\pi$
$523$	−305.470	+	529.090i	−0.584073	+	1.01164i	−0.994990	+	0.0999714i	$0.968125\pi$
$524$			288.000i			0.549618i
$525$		0			0
$526$	228.000			0.433460
$527$	−646.665	−	373.352i	−1.22707	−	0.708449i
$528$		0			0
$529$	−260.500	−	451.199i	−0.492439	−	0.852929i
$530$	45.0333	+	26.0000i	0.0849685	+	0.0490566i
$531$		0			0
$532$		0			0
$533$			254.558i			0.477596i
$534$		0			0
$535$	138.593	+	240.050i	0.259052	+	0.448692i
$536$	−293.939	+	169.706i	−0.548393	+	0.316615i
$537$		0			0
$538$	−743.876			−1.38267
$539$		0			0
$540$		0			0
$541$	40.0000	−	69.2820i	0.0739372	−	0.128063i	−0.826686	−	0.562663i	$-0.809777\pi$
$541$	40.0000	−	69.2820i	0.0739372	−	0.128063i	0.900624	+	0.434600i	$0.143110\pi$
$542$	−526.543	+	304.000i	−0.971482	+	0.560886i
$543$		0			0
$544$	−62.2254	+	107.778i	−0.114385	+	0.198120i
$545$			140.000i			0.256881i
$546$		0			0
$547$	256.000			0.468007			0.234004	−	0.972236i	$-0.424817\pi$
$547$	256.000			0.468007			0.234004	+	0.972236i	$0.424817\pi$
$548$	−345.378	−	199.404i	−0.630252	−	0.363876i
$549$		0			0
$550$	−42.0000	−	72.7461i	−0.0763636	−	0.132266i
$551$	−173.205	−	100.000i	−0.314347	−	0.181488i
$552$		0			0
$553$		0			0
$554$			90.5097i			0.163375i
$555$		0			0
$556$	−5.65685	−	9.79796i	−0.0101742	−	0.0176222i
$557$	679.733	−	392.444i	1.22035	−	0.704568i	0.255355	−	0.966847i	$-0.417808\pi$
$557$	679.733	−	392.444i	1.22035	−	0.704568i	0.964992	+	0.262279i	$0.0844742\pi$
$558$		0			0
$559$	560.029			1.00184
$560$		0			0
$561$		0			0
$562$	−317.000	+	549.060i	−0.564057	+	0.976975i
$563$	−523.079	+	302.000i	−0.929093	+	0.536412i	−0.886525	−	0.462681i	$-0.846887\pi$
$563$	−523.079	+	302.000i	−0.929093	+	0.536412i	−0.0425684	+	0.999094i	$0.513554\pi$
$564$		0			0
$565$	21.2132	−	36.7423i	0.0375455	−	0.0650307i
$566$			176.000i			0.310954i
$567$		0			0
$568$	24.0000			0.0422535
$569$	−375.997	−	217.082i	−0.660803	−	0.381515i	0.131780	−	0.991279i	$-0.457931\pi$
$569$	−375.997	−	217.082i	−0.660803	−	0.381515i	−0.792583	+	0.609764i	$0.791264\pi$
$570$		0			0
$571$	124.000	+	214.774i	0.217163	+	0.376137i	0.953939	−	0.299999i	$-0.0969864\pi$
$571$	124.000	+	214.774i	0.217163	+	0.376137i	−0.736777	+	0.676136i	$0.763653\pi$
$572$	−62.3538	−	36.0000i	−0.109010	−	0.0629371i
$573$		0			0
$574$		0			0
$575$			59.3970i			0.103299i
$576$		0			0
$577$	383.959	+	665.036i	0.665440	+	1.15258i	0.979166	+	0.203063i	$0.0650895\pi$
$577$	383.959	+	665.036i	0.665440	+	1.15258i	−0.313726	+	0.949514i	$0.601577\pi$
$578$	−238.825	+	137.886i	−0.413192	+	0.238557i
$579$		0			0
$580$	−141.421			−0.243830
$581$		0			0
$582$		0			0
$583$	−26.0000	+	45.0333i	−0.0445969	+	0.0772441i
$584$	183.597	−	106.000i	0.314379	−	0.181507i
$585$		0			0
$586$	−200.818	+	347.828i	−0.342693	+	0.593562i
$587$			1140.00i			1.94208i	0.238920	+	0.971039i	$0.423207\pi$
$587$			1140.00i			1.94208i	−0.238920	+	0.971039i	$0.576793\pi$
$588$		0			0
$589$	192.000			0.325976
$590$	−244.949	−	141.421i	−0.415168	−	0.239697i
$591$		0			0
$592$	−128.000	−	221.703i	−0.216216	−	0.374497i
$593$	−590.629	−	341.000i	−0.996002	−	0.575042i	−0.0889392	−	0.996037i	$-0.528348\pi$
$593$	−590.629	−	341.000i	−0.996002	−	0.575042i	−0.907063	+	0.420995i	$0.861681\pi$
$594$		0			0
$595$		0			0
$596$		−	36.7696i		−	0.0616939i
$597$		0			0
$598$	25.4558	+	44.0908i	0.0425683	+	0.0737305i
$599$	913.660	−	527.502i	1.52531	−	0.880637i	0.525759	−	0.850634i	$-0.323782\pi$
$599$	913.660	−	527.502i	1.52531	−	0.880637i	0.999550	−	0.0300033i	$-0.00955177\pi$
$600$		0			0
$601$	555.786			0.924769			0.462384	−	0.886680i	$-0.346994\pi$
$601$	555.786			0.924769			0.462384	+	0.886680i	$0.346994\pi$
$602$		0			0
$603$		0			0
$604$	−64.0000	+	110.851i	−0.105960	+	0.183529i
$605$	195.722	−	113.000i	0.323507	−	0.186777i
$606$		0			0
$607$	−212.132	+	367.423i	−0.349476	+	0.605310i	−0.986156	−	0.165817i	$-0.946974\pi$
$607$	−212.132	+	367.423i	−0.349476	+	0.605310i	0.636680	+	0.771128i	$0.280307\pi$
$608$		−	32.0000i		−	0.0526316i
$609$		0			0
$610$	−148.000			−0.242623
$611$	−749.544	−	432.749i	−1.22675	−	0.708264i
$612$		0			0
$613$	−156.000	−	270.200i	−0.254486	−	0.440783i	0.710270	−	0.703930i	$-0.248573\pi$
$613$	−156.000	−	270.200i	−0.254486	−	0.440783i	−0.964756	+	0.263147i	$0.915240\pi$
$614$	346.410	+	200.000i	0.564186	+	0.325733i
$615$		0			0
$616$		0			0
$617$		−	490.732i		−	0.795352i	−0.917526	−	0.397676i	$-0.869817\pi$
$617$		−	490.732i		−	0.795352i	0.917526	−	0.397676i	$-0.130183\pi$
$618$		0			0
$619$	138.593	+	240.050i	0.223898	+	0.387803i	0.955988	−	0.293405i	$-0.0947884\pi$
$619$	138.593	+	240.050i	0.223898	+	0.387803i	−0.732090	+	0.681208i	$0.761455\pi$
$620$	117.576	−	67.8823i	0.189638	−	0.109488i
$621$		0			0
$622$	265.872			0.427447
$623$		0			0
$624$		0			0
$625$	−170.500	+	295.315i	−0.272800	+	0.472503i
$626$	−265.004	+	153.000i	−0.423329	+	0.244409i
$627$		0			0
$628$	−162.635	+	281.691i	−0.258972	+	0.448553i
$629$		−	1408.00i		−	2.23847i
$630$		0			0
$631$	−316.000			−0.500792			−0.250396	−	0.968143i	$-0.580561\pi$
$631$	−316.000			−0.500792			−0.250396	+	0.968143i	$0.580561\pi$
$632$	225.353	+	130.108i	0.356571	+	0.205867i
$633$		0			0
$634$	−323.000	−	559.452i	−0.509464	−	0.882417i
$635$	34.6410	+	20.0000i	0.0545528	+	0.0314961i
$636$		0			0
$637$		0			0
$638$		−	141.421i		−	0.221664i
$639$		0			0
$640$	−11.3137	−	19.5959i	−0.0176777	−	0.0306186i
$641$	−375.997	+	217.082i	−0.586578	+	0.338661i	−0.763743	−	0.645520i	$-0.776641\pi$
$641$	−375.997	+	217.082i	−0.586578	+	0.338661i	0.177165	+	0.984181i	$0.443307\pi$
$642$		0			0
$643$	−158.392			−0.246333			−0.123166	−	0.992386i	$-0.539305\pi$
$643$	−158.392			−0.246333			−0.123166	+	0.992386i	$0.539305\pi$
$644$		0			0
$645$		0			0
$646$	88.0000	−	152.420i	0.136223	−	0.235945i
$647$	−758.638	+	438.000i	−1.17255	+	0.676971i	−0.954279	−	0.298918i	$-0.903374\pi$
$647$	−758.638	+	438.000i	−1.17255	+	0.676971i	−0.218269	+	0.975889i	$0.570041\pi$
$648$		0			0
$649$	141.421	−	244.949i	0.217907	−	0.377425i
$650$			378.000i			0.581538i
$651$		0			0
$652$	448.000			0.687117
$653$	253.522	+	146.371i	0.388242	+	0.224152i	0.681398	−	0.731913i	$-0.261372\pi$
$653$	253.522	+	146.371i	0.388242	+	0.224152i	−0.293156	+	0.956065i	$0.594706\pi$
$654$		0			0
$655$	−144.000	−	249.415i	−0.219847	−	0.380787i
$656$	−69.2820	−	40.0000i	−0.105613	−	0.0609756i
$657$		0			0
$658$		0			0
$659$			907.925i			1.37773i	0.724889	+	0.688866i	$0.241891\pi$
$659$			907.925i			1.37773i	−0.724889	+	0.688866i	$0.758109\pi$
$660$		0			0
$661$	392.444	+	679.733i	0.593713	+	1.02834i	0.993727	+	0.111832i	$0.0356719\pi$
$661$	392.444	+	679.733i	0.593713	+	1.02834i	−0.400014	+	0.916509i	$0.630995\pi$
$662$	−612.372	+	353.553i	−0.925034	+	0.534069i
$663$		0			0
$664$	316.784			0.477084
$665$		0			0
$666$		0			0
$667$	−50.0000	+	86.6025i	−0.0749625	+	0.129839i
$668$	−505.759	+	292.000i	−0.757124	+	0.437126i
$669$		0			0
$670$	169.706	−	293.939i	0.253292	−	0.438715i
$671$		−	148.000i		−	0.220566i
$672$		0			0
$673$	−264.000			−0.392273			−0.196137	−	0.980577i	$-0.562840\pi$
$673$	−264.000			−0.392273			−0.196137	+	0.980577i	$0.562840\pi$
$674$	−105.328	−	60.8112i	−0.156273	−	0.0902243i
$675$		0			0
$676$	−7.00000	−	12.1244i	−0.0103550	−	0.0179354i
$677$	259.808	+	150.000i	0.383763	+	0.221566i	0.679454	−	0.733718i	$-0.262217\pi$
$677$	259.808	+	150.000i	0.383763	+	0.221566i	−0.295691	+	0.955284i	$0.595550\pi$
$678$		0			0
$679$		0			0
$680$		−	124.451i		−	0.183016i
$681$		0			0
$682$	67.8823	+	117.576i	0.0995341	+	0.172398i
$683$	1006.74	−	581.242i	1.47400	−	0.851013i	0.474426	−	0.880295i	$-0.342656\pi$
$683$	1006.74	−	581.242i	1.47400	−	0.851013i	0.999571	+	0.0292824i	$0.00932220\pi$
$684$		0			0
$685$	398.808			0.582202
$686$		0			0
$687$		0			0
$688$	−88.0000	+	152.420i	−0.127907	+	0.221541i
$689$	202.650	−	117.000i	0.294122	−	0.169811i
$690$		0			0
$691$	254.558	−	440.908i	0.368391	−	0.638073i	−0.620923	−	0.783872i	$-0.713242\pi$
$691$	254.558	−	440.908i	0.368391	−	0.638073i	0.989314	+	0.145799i	$0.0465753\pi$
$692$			312.000i			0.450867i
$693$		0			0
$694$	348.000			0.501441
$695$	9.79796	+	5.65685i	0.0140978	+	0.00813936i
$696$		0			0
$697$	−220.000	−	381.051i	−0.315638	−	0.546702i
$698$	−545.596	−	315.000i	−0.781656	−	0.451289i
$699$		0			0
$700$		0			0
$701$			182.434i			0.260248i	0.991498	+	0.130124i	$0.0415375\pi$
$701$			182.434i			0.260248i	−0.991498	+	0.130124i	$0.958463\pi$
$702$		0			0
$703$	181.019	+	313.535i	0.257495	+	0.445995i
$704$	19.5959	−	11.3137i	0.0278351	−	0.0160706i
$705$		0			0
$706$	−308.299			−0.436684
$707$		0			0
$708$		0			0
$709$	−659.000	+	1141.42i	−0.929478	+	1.60990i	−0.145282	+	0.989390i	$0.546409\pi$
$709$	−659.000	+	1141.42i	−0.929478	+	1.60990i	−0.784196	+	0.620513i	$0.786924\pi$
$710$	−20.7846	+	12.0000i	−0.0292741	+	0.0169014i
$711$		0			0
$712$	28.2843	−	48.9898i	0.0397251	−	0.0688059i
$713$		−	96.0000i		−	0.134642i
$714$		0			0
$715$	72.0000			0.100699
$716$	161.666	+	93.3381i	0.225791	+	0.130360i
$717$		0			0
$718$	262.000	+	453.797i	0.364903	+	0.632030i
$719$	−879.882	−	508.000i	−1.22376	−	0.706537i	−0.258041	−	0.966134i	$-0.583077\pi$
$719$	−879.882	−	508.000i	−1.22376	−	0.706537i	−0.965717	+	0.259597i	$0.916410\pi$
$720$		0			0
$721$		0			0
$722$		−	465.276i		−	0.644427i
$723$		0			0
$724$	−190.919	−	330.681i	−0.263700	−	0.456742i
$725$	−642.991	+	371.231i	−0.886884	+	0.512043i
$726$		0			0
$727$	384.666			0.529114			0.264557	−	0.964370i	$-0.414774\pi$
$727$	384.666			0.529114			0.264557	+	0.964370i	$0.414774\pi$
$728$		0			0
$729$		0			0
$730$	−106.000	+	183.597i	−0.145205	+	0.251503i
$731$	−838.313	+	484.000i	−1.14680	+	0.662107i
$732$		0			0
$733$	−277.893	+	481.325i	−0.379117	+	0.656650i	−0.990934	−	0.134349i	$-0.957106\pi$
$733$	−277.893	+	481.325i	−0.379117	+	0.656650i	0.611817	+	0.791000i	$0.290439\pi$
$734$			632.000i			0.861035i
$735$		0			0
$736$	−16.0000			−0.0217391
$737$	293.939	+	169.706i	0.398831	+	0.230265i
$738$		0			0
$739$	600.000	+	1039.23i	0.811908	+	1.40627i	0.911527	+	0.411240i	$0.134904\pi$
$739$	600.000	+	1039.23i	0.811908	+	1.40627i	−0.0996190	+	0.995026i	$0.531762\pi$
$740$	221.703	+	128.000i	0.299598	+	0.172973i
$741$		0			0
$742$		0			0
$743$		−	1309.56i		−	1.76253i	−0.472620	−	0.881266i	$-0.656692\pi$
$743$		−	1309.56i		−	1.76253i	0.472620	−	0.881266i	$-0.343308\pi$
$744$		0			0
$745$	18.3848	+	31.8434i	0.0246776	+	0.0427428i
$746$	350.277	−	202.233i	0.469540	−	0.271089i
$747$		0			0
$748$	124.451			0.166378
$749$		0			0
$750$		0			0
$751$	284.000	−	491.902i	0.378162	−	0.654997i	−0.612632	−	0.790368i	$-0.709889\pi$
$751$	284.000	−	491.902i	0.378162	−	0.654997i	0.990795	+	0.135371i	$0.0432227\pi$
$752$	235.559	−	136.000i	0.313243	−	0.180851i
$753$		0			0
$754$	−318.198	+	551.135i	−0.422013	+	0.730949i
$755$		−	128.000i		−	0.169536i
$756$		0			0
$757$	−358.000			−0.472919			−0.236460	−	0.971641i	$-0.575987\pi$
$757$	−358.000			−0.472919			−0.236460	+	0.971641i	$0.575987\pi$
$758$	230.252	+	132.936i	0.303763	+	0.175377i
$759$		0			0
$760$	16.0000	+	27.7128i	0.0210526	+	0.0364642i
$761$	−439.941	−	254.000i	−0.578109	−	0.333771i	0.182273	−	0.983248i	$-0.441655\pi$
$761$	−439.941	−	254.000i	−0.578109	−	0.333771i	−0.760382	+	0.649477i	$0.774988\pi$
$762$		0			0
$763$		0			0
$764$			265.872i			0.348000i
$765$		0			0
$766$	248.902	+	431.110i	0.324937	+	0.562807i
$767$	−1102.27	+	636.396i	−1.43712	+	0.829721i
$768$		0			0
$769$	861.256			1.11997			0.559984	−	0.828503i	$-0.310807\pi$
$769$	861.256			1.11997			0.559984	+	0.828503i	$0.310807\pi$
$770$		0			0
$771$		0			0
$772$	122.000	−	211.310i	0.158031	−	0.273718i
$773$	772.495	−	446.000i	0.999346	−	0.576973i	0.0912915	−	0.995824i	$-0.470901\pi$
$773$	772.495	−	446.000i	0.999346	−	0.576973i	0.908055	+	0.418851i	$0.137567\pi$
$774$		0			0
$775$	356.382	−	617.271i	0.459848	−	0.796479i
$776$			76.0000i			0.0979381i
$777$		0			0
$778$	290.000			0.372751
$779$	97.9796	+	56.5685i	0.125776	+	0.0726169i
$780$		0			0
$781$	−12.0000	−	20.7846i	−0.0153649	−	0.0266128i
$782$	−76.2102	−	44.0000i	−0.0974555	−	0.0562660i
$783$		0			0
$784$		0			0
$785$		−	325.269i		−	0.414356i
$786$		0			0
$787$	−214.960	−	372.322i	−0.273139	−	0.473091i	0.696525	−	0.717533i	$-0.254729\pi$
$787$	−214.960	−	372.322i	−0.273139	−	0.473091i	−0.969664	+	0.244442i	$0.921395\pi$
$788$	−12.2474	+	7.07107i	−0.0155424	+	0.00897344i
$789$		0			0
$790$	−260.215			−0.329386
$791$		0			0
$792$		0			0
$793$	−333.000	+	576.773i	−0.419924	+	0.727330i
$794$	299.645	−	173.000i	0.377386	−	0.217884i
$795$		0			0
$796$	373.352	−	646.665i	0.469036	−	0.812394i
$797$			540.000i			0.677541i	0.940869	+	0.338770i	$0.110011\pi$
$797$			540.000i			0.677541i	−0.940869	+	0.338770i	$0.889989\pi$
$798$		0			0
$799$	1496.00			1.87234
$800$	−102.879	−	59.3970i	−0.128598	−	0.0742462i
$801$		0			0
$802$	−315.000	−	545.596i	−0.392768	−	0.680294i
$803$	−183.597	−	106.000i	−0.228639	−	0.132005i
$804$		0			0
$805$		0			0
$806$		−	610.940i		−	0.757990i
$807$		0			0
$808$	118.794	+	205.757i	0.147022	+	0.254650i
$809$	755.668	−	436.285i	0.934076	−	0.539289i	0.0459777	−	0.998942i	$-0.485360\pi$
$809$	755.668	−	436.285i	0.934076	−	0.539289i	0.888098	+	0.459653i	$0.152026\pi$
$810$		0			0
$811$	−492.146			−0.606839			−0.303419	−	0.952857i	$-0.598128\pi$
$811$	−492.146			−0.606839			−0.303419	+	0.952857i	$0.598128\pi$
$812$		0			0
$813$		0			0
$814$	−128.000	+	221.703i	−0.157248	+	0.272362i
$815$	−387.979	+	224.000i	−0.476048	+	0.274847i
$816$		0			0
$817$	124.451	−	215.555i	0.152327	−	0.263837i
$818$		−	1062.00i		−	1.29829i
$819$		0			0
$820$	80.0000			0.0975610
$821$	650.340	+	375.474i	0.792131	+	0.457337i	0.840712	−	0.541482i	$-0.182137\pi$
$821$	650.340	+	375.474i	0.792131	+	0.457337i	−0.0485812	+	0.998819i	$0.515470\pi$
$822$		0			0
$823$	58.0000	+	100.459i	0.0704739	+	0.122064i	0.899109	−	0.437725i	$-0.144216\pi$
$823$	58.0000	+	100.459i	0.0704739	+	0.122064i	−0.828635	+	0.559789i	$0.810882\pi$
$824$	387.979	+	224.000i	0.470849	+	0.271845i
$825$		0			0
$826$		0			0
$827$			873.984i			1.05681i	0.848992	+	0.528406i	$0.177210\pi$
$827$			873.984i			1.05681i	−0.848992	+	0.528406i	$0.822790\pi$
$828$		0			0
$829$	−136.472	−	236.376i	−0.164622	−	0.285134i	0.771899	−	0.635745i	$-0.219307\pi$
$829$	−136.472	−	236.376i	−0.164622	−	0.285134i	−0.936521	+	0.350612i	$0.885974\pi$
$830$	−274.343	+	158.392i	−0.330534	+	0.190834i
$831$		0			0
$832$	−101.823			−0.122384
$833$		0			0
$834$		0			0
$835$	292.000	−	505.759i	0.349701	−	0.605699i
$836$	−27.7128	+	16.0000i	−0.0331493	+	0.0191388i
$837$		0			0
$838$	166.877	−	289.040i	0.199137	−	0.344916i
$839$			188.000i			0.224076i	0.993704	+	0.112038i	$0.0357379\pi$
$839$			188.000i			0.224076i	−0.993704	+	0.112038i	$0.964262\pi$
$840$		0			0
$841$	−409.000			−0.486326
$842$	117.576	+	67.8823i	0.139638	+	0.0806203i
$843$		0			0
$844$	−12.0000	−	20.7846i	−0.0142180	−	0.0246263i
$845$	12.1244	+	7.00000i	0.0143483	+	0.00828402i
$846$		0			0
$847$		0			0
$848$			73.5391i			0.0867206i
$849$		0			0
$850$	−326.683	−	565.832i	−0.384333	−	0.665685i
$851$	156.767	−	90.5097i	0.184215	−	0.106357i
$852$		0			0
$853$	63.6396			0.0746068			0.0373034	−	0.999304i	$-0.488123\pi$
$853$	63.6396			0.0746068			0.0373034	+	0.999304i	$0.488123\pi$
$854$		0			0
$855$		0			0
$856$	−196.000	+	339.482i	−0.228972	+	0.396591i
$857$	−225.167	+	130.000i	−0.262738	+	0.151692i	−0.625583	−	0.780158i	$-0.715139\pi$
$857$	−225.167	+	130.000i	−0.262738	+	0.151692i	0.362845	+	0.931850i	$0.381806\pi$
$858$		0			0
$859$	395.980	−	685.857i	0.460978	−	0.798437i	−0.538032	−	0.842924i	$-0.680832\pi$
$859$	395.980	−	685.857i	0.460978	−	0.798437i	0.999010	+	0.0444875i	$0.0141655\pi$
$860$		−	176.000i		−	0.204651i
$861$		0			0
$862$	−1212.00			−1.40603
$863$	364.974	+	210.718i	0.422913	+	0.244169i	0.696323	−	0.717729i	$-0.254818\pi$
$863$	364.974	+	210.718i	0.422913	+	0.244169i	−0.273410	+	0.961898i	$0.588152\pi$
$864$		0			0
$865$	−156.000	−	270.200i	−0.180347	−	0.312370i
$866$	−192.258	−	111.000i	−0.222007	−	0.128176i
$867$		0			0
$868$		0			0
$869$		−	260.215i		−	0.299442i
$870$		0			0
$871$	−763.675	−	1322.72i	−0.876780	−	1.51863i
$872$	−171.464	+	98.9949i	−0.196633	+	0.113526i
$873$		0			0
$874$	22.6274			0.0258895
$875$		0			0
$876$		0			0
$877$	476.000	−	824.456i	0.542759	−	0.940087i	−0.455985	−	0.889988i	$-0.650713\pi$
$877$	476.000	−	824.456i	0.542759	−	0.940087i	0.998744	−	0.0500993i	$-0.0159538\pi$
$878$	−789.815	+	456.000i	−0.899562	+	0.519362i
$879$		0			0
$880$	−11.3137	+	19.5959i	−0.0128565	+	0.0222681i
$881$		−	1158.00i		−	1.31442i	−0.753710	−	0.657208i	$-0.771737\pi$
$881$		−	1158.00i		−	1.31442i	0.753710	−	0.657208i	$-0.228263\pi$
$882$		0			0
$883$	−1036.00			−1.17327			−0.586636	−	0.809850i	$-0.699548\pi$
$883$	−1036.00			−1.17327			−0.586636	+	0.809850i	$0.699548\pi$
$884$	−484.999	−	280.014i	−0.548641	−	0.316758i
$885$		0			0
$886$	410.000	+	710.141i	0.462754	+	0.801513i
$887$	−398.372	−	230.000i	−0.449123	−	0.259301i	0.258337	−	0.966055i	$-0.416826\pi$
$887$	−398.372	−	230.000i	−0.449123	−	0.259301i	−0.707460	+	0.706754i	$0.750159\pi$
$888$		0			0
$889$		0			0
$890$			56.5685i			0.0635602i
$891$		0			0
$892$	−203.647	−	352.727i	−0.228304	−	0.395433i
$893$	−333.131	+	192.333i	−0.373047	+	0.215379i
$894$		0			0
$895$	−186.676			−0.208577
$896$		0			0
$897$		0			0
$898$	615.000	−	1065.21i	0.684855	−	1.18620i
$899$	1039.23	−	600.000i	1.15598	−	0.667408i
$900$		0			0
$901$	−202.233	+	350.277i	−0.224453	+	0.388765i
$902$			80.0000i			0.0886918i
$903$		0			0
$904$	60.0000			0.0663717
$905$	330.681	+	190.919i	0.365393	+	0.210960i
$906$		0			0
$907$	−110.000	−	190.526i	−0.121279	−	0.210061i	0.798993	−	0.601340i	$-0.205366\pi$
$907$	−110.000	−	190.526i	−0.121279	−	0.210061i	−0.920272	+	0.391279i	$0.872033\pi$
$908$	−353.338	−	204.000i	−0.389139	−	0.224670i
$909$		0			0
$910$		0			0
$911$		−	1049.35i		−	1.15186i	−0.817498	−	0.575931i	$-0.804640\pi$
$911$		−	1049.35i		−	1.15186i	0.817498	−	0.575931i	$-0.195360\pi$
$912$		0			0
$913$	−158.392	−	274.343i	−0.173485	−	0.300485i
$914$	470.302	−	271.529i	0.514554	−	0.297078i
$915$		0			0
$916$	93.3381			0.101897
$917$		0			0
$918$		0			0
$919$	160.000	−	277.128i	0.174102	−	0.301554i	−0.765748	−	0.643141i	$-0.777631\pi$
$919$	160.000	−	277.128i	0.174102	−	0.301554i	0.939850	+	0.341587i	$0.110964\pi$
$920$	13.8564	−	8.00000i	0.0150613	−	0.00869565i
$921$		0			0
$922$	189.505	−	328.232i	0.205536	−	0.356000i
$923$			108.000i			0.117010i
$924$		0			0
$925$	1344.00			1.45297
$926$	876.917	+	506.288i	0.946995	+	0.546748i
$927$		0			0
$928$	−100.000	−	173.205i	−0.107759	−	0.186643i
$929$	1520.74	+	878.000i	1.63697	+	0.945102i	0.981870	+	0.189556i	$0.0607048\pi$
$929$	1520.74	+	878.000i	1.63697	+	0.945102i	0.655095	+	0.755546i	$0.272629\pi$
$930$		0			0
$931$		0			0
$932$			619.426i			0.664620i
$933$		0			0
$934$	217.789	+	377.221i	0.233179	+	0.403877i
$935$	−107.778	+	62.2254i	−0.115270	+	0.0665512i
$936$		0			0
$937$	−1740.90			−1.85795			−0.928974	−	0.370145i	$-0.879308\pi$
$937$	−1740.90			−1.85795			−0.928974	+	0.370145i	$0.879308\pi$
$938$		0			0
$939$		0			0
$940$	−136.000	+	235.559i	−0.144681	+	0.250595i
$941$	542.132	−	313.000i	0.576123	−	0.332625i	−0.183468	−	0.983026i	$-0.558732\pi$
$941$	542.132	−	313.000i	0.576123	−	0.332625i	0.759591	+	0.650401i	$0.225399\pi$
$942$		0			0
$943$	28.2843	−	48.9898i	0.0299939	−	0.0519510i
$944$		−	400.000i		−	0.423729i
$945$		0			0
$946$	176.000			0.186047
$947$	−683.408	−	394.566i	−0.721655	−	0.416648i	0.0937063	−	0.995600i	$-0.470129\pi$
$947$	−683.408	−	394.566i	−0.721655	−	0.416648i	−0.815362	+	0.578952i	$0.803462\pi$
$948$		0			0
$949$	477.000	+	826.188i	0.502634	+	0.870588i
$950$	145.492	+	84.0000i	0.153150	+	0.0884211i
$951$		0			0
$952$		0			0
$953$		−	193.747i		−	0.203302i	−0.994820	−	0.101651i	$-0.967587\pi$
$953$		−	193.747i		−	0.203302i	0.994820	−	0.101651i	$-0.0324126\pi$
$954$		0			0
$955$	−132.936	−	230.252i	−0.139200	−	0.241102i
$956$	73.4847	−	42.4264i	0.0768668	−	0.0443791i
$957$		0			0
$958$	548.715			0.572771
$959$		0			0
$960$		0			0
$961$	−95.5000	+	165.411i	−0.0993757	+	0.172124i
$962$	997.661	−	576.000i	1.03707	−	0.598753i
$963$		0			0
$964$	377.595	−	654.014i	0.391696	−	0.678438i
$965$			244.000i			0.252850i
$966$		0			0
$967$	132.000			0.136505			0.0682523	−	0.997668i	$-0.478258\pi$
$967$	132.000			0.136505			0.0682523	+	0.997668i	$0.478258\pi$
$968$	276.792	+	159.806i	0.285943	+	0.165089i
$969$		0			0
$970$	−38.0000	−	65.8179i	−0.0391753	−	0.0678535i
$971$	138.564	+	80.0000i	0.142702	+	0.0823893i	0.569651	−	0.821886i	$-0.307078\pi$
$971$	138.564	+	80.0000i	0.142702	+	0.0823893i	−0.426949	+	0.904276i	$0.640412\pi$
$972$		0			0
$973$		0			0
$974$			169.706i			0.174236i
$975$		0			0
$976$	−104.652	−	181.262i	−0.107225	−	0.185720i
$977$	−1297.00	+	748.826i	−1.32754	+	0.766455i	−0.984918	−	0.173020i	$-0.944648\pi$
$977$	−1297.00	+	748.826i	−1.32754	+	0.766455i	−0.342620	+	0.939474i	$0.611314\pi$
$978$		0			0
$979$	−56.5685			−0.0577820
$980$		0			0
$981$		0			0
$982$	438.000	−	758.638i	0.446029	−	0.772544i
$983$	284.056	−	164.000i	0.288969	−	0.166836i	−0.348508	−	0.937306i	$-0.613312\pi$
$983$	284.056	−	164.000i	0.288969	−	0.166836i	0.637477	+	0.770470i	$0.279978\pi$
$984$		0			0
$985$	7.07107	−	12.2474i	0.00717875	−	0.0124340i
$986$		−	1100.00i		−	1.11562i
$987$		0			0
$988$	144.000			0.145749
$989$	−107.778	−	62.2254i	−0.108976	−	0.0629175i
$990$		0			0
$991$	8.00000	+	13.8564i	0.00807265	+	0.0139822i	0.870034	−	0.492993i	$-0.164097\pi$
$991$	8.00000	+	13.8564i	0.00807265	+	0.0139822i	−0.861961	+	0.506975i	$0.830764\pi$
$992$	166.277	+	96.0000i	0.167618	+	0.0967742i
$993$		0			0
$994$		0			0
$995$			746.705i			0.750457i
$996$		0			0
$997$	−437.699	−	758.117i	−0.439016	−	0.760398i	0.558598	−	0.829439i	$-0.311340\pi$
$997$	−437.699	−	758.117i	−0.439016	−	0.760398i	−0.997614	+	0.0690405i	$0.978006\pi$
$998$	582.979	−	336.583i	0.584147	−	0.337257i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.s.f.863.1		8
3.2	odd	2	inner	882.3.s.f.863.4		8
7.2	even	3		882.3.b.i.197.4	yes	4
7.3	odd	6	inner	882.3.s.f.557.3		8
7.4	even	3	inner	882.3.s.f.557.4		8
7.5	odd	6		882.3.b.i.197.3	yes	4
7.6	odd	2	inner	882.3.s.f.863.2		8
21.2	odd	6		882.3.b.i.197.1	✓	4
21.5	even	6		882.3.b.i.197.2	yes	4
21.11	odd	6	inner	882.3.s.f.557.1		8
21.17	even	6	inner	882.3.s.f.557.2		8
21.20	even	2	inner	882.3.s.f.863.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
882.3.b.i.197.1	✓	4	21.2	odd	6
882.3.b.i.197.2	yes	4	21.5	even	6
882.3.b.i.197.3	yes	4	7.5	odd	6
882.3.b.i.197.4	yes	4	7.2	even	3
882.3.s.f.557.1		8	21.11	odd	6	inner
882.3.s.f.557.2		8	21.17	even	6	inner
882.3.s.f.557.3		8	7.3	odd	6	inner
882.3.s.f.557.4		8	7.4	even	3	inner
882.3.s.f.863.1		8	1.1	even	1	trivial
882.3.s.f.863.2		8	7.6	odd	2	inner
882.3.s.f.863.3		8	21.20	even	2	inner
882.3.s.f.863.4		8	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	882.s (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.73205 - 1.00000i) q^{5} -2.82843i q^{8} +O(q^{10})\)	\(q+(-1.22474 - 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(-1.73205 - 1.00000i) q^{5} -2.82843i q^{8} +(1.41421 + 2.44949i) q^{10} +(-2.44949 + 1.41421i) q^{11} +12.7279 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-19.0526 + 11.0000i) q^{17} +(2.82843 - 4.89898i) q^{19} -4.00000i q^{20} +4.00000 q^{22} +(-2.44949 - 1.41421i) q^{23} +(-10.5000 - 18.1865i) q^{25} +(-15.5885 - 9.00000i) q^{26} -35.3553i q^{29} +(16.9706 + 29.3939i) q^{31} +(4.89898 - 2.82843i) q^{32} +31.1127 q^{34} +(-32.0000 + 55.4256i) q^{37} +(-6.92820 + 4.00000i) q^{38} +(-2.82843 + 4.89898i) q^{40} +20.0000i q^{41} +44.0000 q^{43} +(-4.89898 - 2.82843i) q^{44} +(2.00000 + 3.46410i) q^{46} +(-58.8897 - 34.0000i) q^{47} +29.6985i q^{50} +(12.7279 + 22.0454i) q^{52} +(15.9217 - 9.19239i) q^{53} +5.65685 q^{55} +(-25.0000 + 43.3013i) q^{58} +(-86.6025 + 50.0000i) q^{59} +(-26.1630 + 45.3156i) q^{61} -48.0000i q^{62} -8.00000 q^{64} +(-22.0454 - 12.7279i) q^{65} +(-60.0000 - 103.923i) q^{67} +(-38.1051 - 22.0000i) q^{68} +8.48528i q^{71} +(37.4767 + 64.9115i) q^{73} +(78.3837 - 45.2548i) q^{74} +11.3137 q^{76} +(-46.0000 + 79.6743i) q^{79} +(6.92820 - 4.00000i) q^{80} +(14.1421 - 24.4949i) q^{82} +112.000i q^{83} +44.0000 q^{85} +(-53.8888 - 31.1127i) q^{86} +(4.00000 + 6.92820i) q^{88} +(17.3205 + 10.0000i) q^{89} -5.65685i q^{92} +(48.0833 + 83.2827i) q^{94} +(-9.79796 + 5.65685i) q^{95} -26.8701 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} - 84 q^{25} - 256 q^{37} + 352 q^{43} + 16 q^{46} - 200 q^{58} - 64 q^{64} - 480 q^{67} - 368 q^{79} + 352 q^{85} + 32 q^{88}+O(q^{100}) \) 8 * q + 8 * q^4 - 16 * q^16 + 32 * q^22 - 84 * q^25 - 256 * q^37 + 352 * q^43 + 16 * q^46 - 200 * q^58 - 64 * q^64 - 480 * q^67 - 368 * q^79 + 352 * q^85 + 32 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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