LMFDB - Embedded newform 882.3.s.f.557.1

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			557.1
Root			$-0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	882.557
Dual form			882.3.s.f.863.1

$q$-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 $\left(\mathbb{Z}/882\mathbb{Z}\right)^\times$.

$n$	$199$	$785$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$

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	−0.663103	−	0.748528i	$-0.730761\pi$
$5$	−1.73205	+	1.00000i	−0.346410	+	0.200000i	0.316693	+	0.948528i	$0.397428\pi$
$6$		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	0.384510	−	0.923121i	$-0.374370\pi$
$11$	−2.44949	−	1.41421i	−0.222681	−	0.128565i	−0.607191	+	0.794556i	$0.707704\pi$
$12$		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	−0.179149	−	0.983822i	$-0.557335\pi$
$17$	−19.0526	−	11.0000i	−1.12074	−	0.647059i	−0.941589	+	0.336763i	$0.890668\pi$
$18$		0			0
$19$	2.82843	+	4.89898i	0.148865	+	0.257841i	0.930808	−	0.365508i	$-0.119105\pi$
$19$	2.82843	+	4.89898i	0.148865	+	0.257841i	−0.781944	+	0.623349i	$0.785771\pi$
$20$			4.00000i			0.200000i
$21$		0			0
$22$	4.00000			0.181818
$23$	−2.44949	+	1.41421i	−0.106500	+	0.0614875i	−0.552304	−	0.833643i	$-0.686251\pi$
$23$	−2.44949	+	1.41421i	−0.106500	+	0.0614875i	0.445804	+	0.895131i	$0.352918\pi$
$24$		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	$0.208660\pi$
$29$			35.3553i			1.21915i	−0.792729	+	0.609575i	$0.791340\pi$
$30$		0			0
$31$	16.9706	−	29.3939i	0.547438	−	0.948190i	−0.451012	−	0.892518i	$-0.648937\pi$
$31$	16.9706	−	29.3939i	0.547438	−	0.948190i	0.998449	−	0.0556715i	$-0.0177300\pi$
$32$	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	−0.867181	−	0.497993i	$-0.834071\pi$
$37$	−32.0000	−	55.4256i	−0.864865	−	1.49799i	0.00231643	−	0.999997i	$-0.499263\pi$
$38$	−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	$-0.921572\pi$
$41$		−	20.0000i		−	0.487805i	0.969800	−	0.243902i	$-0.0784277\pi$
$42$		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	−0.971699	−	0.236223i	$-0.924090\pi$
$47$	−58.8897	+	34.0000i	−1.25297	+	0.723404i	−0.281274	+	0.959627i	$0.590757\pi$
$48$		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	0.642627	−	0.766179i	$-0.277845\pi$
$53$	15.9217	+	9.19239i	0.300409	+	0.173441i	−0.342218	+	0.939621i	$0.611178\pi$
$54$		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	−0.468488	−	0.883470i	$-0.655201\pi$
$59$	−86.6025	−	50.0000i	−1.46784	−	0.847458i	−0.999351	+	0.0360121i	$0.988535\pi$
$60$		0			0
$61$	−26.1630	−	45.3156i	−0.428901	−	0.742878i	0.567875	−	0.823115i	$-0.307766\pi$
$61$	−26.1630	−	45.3156i	−0.428901	−	0.742878i	−0.996776	+	0.0802368i	$0.974432\pi$
$62$			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	−0.0623656	+	0.998053i	$0.519864\pi$
$67$	−60.0000	+	103.923i	−0.895522	+	1.55109i	−0.833157	+	0.553037i	$0.813469\pi$
$68$	−38.1051	+	22.0000i	−0.560369	+	0.323529i
$69$		0			0
$70$		0			0
$71$		−	8.48528i		−	0.119511i	−0.998213	−	0.0597555i	$-0.980968\pi$
$71$		−	8.48528i		−	0.119511i	0.998213	−	0.0597555i	$-0.0190321\pi$
$72$		0			0
$73$	37.4767	−	64.9115i	0.513379	−	0.889198i	−0.486501	−	0.873680i	$-0.661727\pi$
$73$	37.4767	−	64.9115i	0.513379	−	0.889198i	0.999880	−	0.0155181i	$-0.00493978\pi$
$74$	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	−0.995209	−	0.0977733i	$-0.968828\pi$
$79$	−46.0000	−	79.6743i	−0.582278	−	1.00854i	0.412930	−	0.910763i	$-0.364505\pi$
$80$	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	$-0.764274\pi$
$83$		−	112.000i		−	1.34940i	0.738093	−	0.674699i	$-0.235726\pi$
$84$		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	−0.399528	−	0.916721i	$-0.630826\pi$
$89$	17.3205	−	10.0000i	0.194612	−	0.112360i	0.594140	+	0.804362i	$0.297492\pi$
$90$		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	0.0945892	−	0.995516i	$-0.469846\pi$
$101$	−72.7461	−	42.0000i	−0.720259	−	0.415842i	−0.814848	+	0.579675i	$0.803180\pi$
$102$		0			0
$103$	−79.1960	−	137.171i	−0.768893	−	1.33176i	−0.938164	−	0.346192i	$-0.887475\pi$
$103$	−79.1960	−	137.171i	−0.768893	−	1.33176i	0.169271	−	0.985570i	$-0.445859\pi$
$104$			36.0000i			0.346154i
$105$		0			0
$106$	−26.0000			−0.245283
$107$	−120.025	+	69.2965i	−1.12173	+	0.647631i	−0.941842	−	0.336057i	$-0.890907\pi$
$107$	−120.025	+	69.2965i	−1.12173	+	0.647631i	−0.179887	+	0.983687i	$0.557573\pi$
$108$		0			0
$109$	−35.0000	+	60.6218i	−0.321101	+	0.556163i	−0.980715	−	0.195441i	$-0.937386\pi$
$109$	−35.0000	+	60.6218i	−0.321101	+	0.556163i	0.659615	+	0.751604i	$0.270720\pi$
$110$	−6.92820	+	4.00000i	−0.0629837	+	0.0363636i
$111$		0			0
$112$		0			0
$113$		−	21.2132i		−	0.187727i	−0.995585	−	0.0938637i	$-0.970078\pi$
$113$		−	21.2132i		−	0.187727i	0.995585	−	0.0938637i	$-0.0299218\pi$
$114$		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	0.0582755	−	0.998301i	$-0.481440\pi$
$131$	124.708	−	72.0000i	0.951967	−	0.549618i	0.893691	+	0.448682i	$0.148106\pi$
$132$		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	−0.287332	−	0.957831i	$-0.592768\pi$
$137$	−172.689	−	99.7021i	−1.26050	−	0.727752i	−0.973172	+	0.230079i	$0.926102\pi$
$138$		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	−0.552476	−	0.833529i	$-0.686317\pi$
$149$	−15.9217	+	9.19239i	−0.106857	+	0.0616939i	0.445619	+	0.895223i	$0.352984\pi$
$150$		0			0
$151$	32.0000	−	55.4256i	0.211921	−	0.367057i	−0.740395	−	0.672172i	$-0.765362\pi$
$151$	32.0000	−	55.4256i	0.211921	−	0.367057i	0.952316	+	0.305115i	$0.0986949\pi$
$152$	−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	−0.481838	−	0.876260i	$-0.660031\pi$
$157$	81.3173	−	140.846i	0.517944	−	0.897106i	0.999783	−	0.0208459i	$-0.00663595\pi$
$158$	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	0.972767	+	0.231787i	$0.0744572\pi$
$163$	112.000	+	193.990i	0.687117	+	1.19012i	−0.285650	+	0.958334i	$0.592209\pi$
$164$	−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	$-0.661353\pi$
$167$		−	292.000i		−	1.74850i	0.485473	−	0.874251i	$-0.338647\pi$
$168$		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	−0.0558332	−	0.998440i	$-0.517782\pi$
$173$	135.100	−	78.0000i	0.780925	−	0.450867i	0.836758	+	0.547573i	$0.184448\pi$
$174$		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	0.708498	−	0.705713i	$-0.249373\pi$
$179$	80.8332	+	46.6690i	0.451582	+	0.260721i	−0.256916	+	0.966434i	$0.582706\pi$
$180$		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	−0.167370	−	0.985894i	$-0.553528\pi$
$191$	115.126	−	66.4680i	0.602754	−	0.348000i	0.770124	+	0.637894i	$0.220194\pi$
$192$		0			0
$193$	−61.0000	+	105.655i	−0.316062	+	0.547436i	−0.979663	−	0.200651i	$-0.935694\pi$
$193$	−61.0000	+	105.655i	−0.316062	+	0.547436i	0.663601	+	0.748087i	$0.269027\pi$
$194$	32.9090	−	19.0000i	0.169634	−	0.0979381i
$195$		0			0
$196$		0			0
$197$		−	7.07107i		−	0.0358937i	−0.999839	−	0.0179469i	$-0.994287\pi$
$197$		−	7.07107i		−	0.0358937i	0.999839	−	0.0179469i	$-0.00571297\pi$
$198$		0			0
$199$	−186.676	+	323.333i	−0.938071	+	1.62479i	−0.169008	+	0.985615i	$0.554056\pi$
$199$	−186.676	+	323.333i	−0.938071	+	1.62479i	−0.769063	+	0.639172i	$0.779277\pi$
$200$	−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	0.0575414	−	0.998343i	$-0.481674\pi$
$227$	−176.669	−	102.000i	−0.778278	−	0.449339i	−0.835820	+	0.549004i	$0.815007\pi$
$228$		0			0
$229$	23.3345	+	40.4166i	0.101897	+	0.176492i	0.912466	−	0.409152i	$-0.134175\pi$
$229$	23.3345	+	40.4166i	0.101897	+	0.176492i	−0.810569	+	0.585643i	$0.800842\pi$
$230$			8.00000i			0.0347826i
$231$		0			0
$232$	−100.000			−0.431034
$233$	268.219	−	154.856i	1.15116	−	0.664620i	0.201987	−	0.979388i	$-0.435260\pi$
$233$	268.219	−	154.856i	1.15116	−	0.664620i	0.949168	+	0.314769i	$0.101927\pi$
$234$		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	$0.0282898\pi$
$239$			42.4264i			0.177516i	−0.996053	+	0.0887582i	$0.971710\pi$
$240$		0			0
$241$	−188.798	+	327.007i	−0.783392	+	1.35688i	0.146563	+	0.989201i	$0.453179\pi$
$241$	−188.798	+	327.007i	−0.783392	+	1.35688i	−0.929955	+	0.367674i	$0.880154\pi$
$242$	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	$0.230018\pi$
$251$			332.000i			1.32271i	−0.750073	+	0.661355i	$0.769982\pi$
$252$		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	−0.165061	−	0.986283i	$-0.552782\pi$
$257$	155.885	−	90.0000i	0.606555	−	0.350195i	0.771616	+	0.636089i	$0.219449\pi$
$258$		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	0.210496	−	0.977595i	$-0.432492\pi$
$263$	−139.621	−	80.6102i	−0.530878	−	0.306503i	−0.741374	+	0.671092i	$0.765825\pi$
$264$		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	0.951723	+	0.306957i	$0.0993108\pi$
$269$	455.529	+	263.000i	1.69342	+	0.977695i	0.741694	+	0.670738i	$0.234022\pi$
$270$		0			0
$271$	214.960	+	372.322i	0.793212	+	1.37388i	0.923968	+	0.382469i	$0.124926\pi$
$271$	214.960	+	372.322i	0.793212	+	1.37388i	−0.130756	+	0.991415i	$0.541741\pi$
$272$			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	−0.917989	−	0.396606i	$-0.870188\pi$
$277$	−32.0000	+	55.4256i	−0.115523	+	0.200093i	0.802465	+	0.596699i	$0.203521\pi$
$278$	6.92820	−	4.00000i	0.0249216	−	0.0143885i
$279$		0			0
$280$		0			0
$281$			448.306i			1.59539i	0.603058	+	0.797697i	$0.293949\pi$
$281$			448.306i			1.59539i	−0.603058	+	0.797697i	$0.706051\pi$
$282$		0			0
$283$	−62.2254	+	107.778i	−0.219878	+	0.380839i	−0.954770	−	0.297344i	$-0.903899\pi$
$283$	−62.2254	+	107.778i	−0.219878	+	0.380839i	0.734893	+	0.678183i	$0.237233\pi$
$284$	−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	$0.161050\pi$
$293$			284.000i			0.969283i	−0.874713	+	0.484642i	$0.838950\pi$
$294$		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	0.214857	−	0.976645i	$-0.431071\pi$
$311$	−162.813	−	94.0000i	−0.523514	−	0.302251i	−0.738371	+	0.674395i	$0.764405\pi$
$312$		0			0
$313$	108.187	+	187.386i	0.345646	+	0.598677i	0.985471	−	0.169844i	$-0.0543263\pi$
$313$	108.187	+	187.386i	0.345646	+	0.598677i	−0.639825	+	0.768521i	$0.720993\pi$
$314$			230.000i			0.732484i
$315$		0			0
$316$	−184.000			−0.582278
$317$	395.593	−	228.395i	1.24793	−	0.720491i	0.277231	−	0.960803i	$-0.410583\pi$
$317$	395.593	−	228.395i	1.24793	−	0.720491i	0.970695	+	0.240313i	$0.0772500\pi$
$318$		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	0.945232	+	0.326401i	$0.105836\pi$
$331$	250.000	+	433.013i	0.755287	+	1.30820i	−0.189945	+	0.981795i	$0.560831\pi$
$332$	−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	0.160446	−	0.987045i	$-0.448707\pi$
$347$	−213.106	−	123.037i	−0.614137	−	0.354572i	−0.774583	+	0.632472i	$0.782040\pi$
$348$		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	0.742979	−	0.669314i	$-0.233412\pi$
$353$	188.794	+	109.000i	0.534826	+	0.308782i	−0.208153	+	0.978096i	$0.566745\pi$
$354$		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	−0.875192	−	0.483776i	$-0.839265\pi$
$359$	−320.883	+	185.262i	−0.893825	+	0.516050i	−0.0186333	+	0.999826i	$0.505931\pi$
$360$		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	0.382587	+	0.923919i	$0.375033\pi$
$367$	−223.446	+	387.019i	−0.608844	+	1.05455i	−0.991431	+	0.130629i	$0.958300\pi$
$368$	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	0.608165	−	0.793811i	$-0.291906\pi$
$373$	−143.000	−	247.683i	−0.383378	−	0.664030i	−0.991543	+	0.129781i	$0.958573\pi$
$374$	−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	−0.842046	−	0.539406i	$-0.818649\pi$
$383$	−304.841	+	176.000i	−0.795929	+	0.459530i	0.0461164	+	0.998936i	$0.485315\pi$
$384$		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	0.254057	−	0.967189i	$-0.418235\pi$
$389$	−177.588	−	102.530i	−0.456524	−	0.263575i	−0.710582	+	0.703615i	$0.751568\pi$
$390$		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	0.669820	−	0.742524i	$-0.266371\pi$
$397$	−122.329	−	211.881i	−0.308135	−	0.533705i	−0.977954	+	0.208819i	$0.933038\pi$
$398$		−	528.000i		−	1.32663i
$399$		0			0
$400$	84.0000			0.210000
$401$	385.795	−	222.739i	0.962081	−	0.555458i	0.0652684	−	0.997868i	$-0.479210\pi$
$401$	385.795	−	222.739i	0.962081	−	0.555458i	0.896813	+	0.442410i	$0.145876\pi$
$402$		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	0.115623	−	0.993293i	$-0.463114\pi$
$409$	375.474	−	650.340i	0.918029	−	1.59007i	0.802406	−	0.596779i	$-0.203553\pi$
$410$	−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	$-0.909127\pi$
$419$		−	236.000i		−	0.563246i	0.959525	−	0.281623i	$-0.0908727\pi$
$420$		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	0.914719	+	0.404090i	$0.132412\pi$
$431$	742.195	+	428.507i	1.72203	+	0.994215i	0.807312	+	0.590125i	$0.200922\pi$
$432$		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	0.954947	+	0.296776i	$0.0959114\pi$
$439$	322.441	+	558.484i	0.734489	+	1.27217i	−0.220458	+	0.975396i	$0.570755\pi$
$440$			16.0000i			0.0363636i
$441$		0			0
$442$	396.000			0.895928
$443$	−502.145	+	289.914i	−1.13351	+	0.654433i	−0.944816	−	0.327603i	$-0.893759\pi$
$443$	−502.145	+	289.914i	−1.13351	+	0.654433i	−0.188695	+	0.982036i	$0.560426\pi$
$444$		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	$-0.580066\pi$
$449$		−	869.741i		−	1.93706i	0.248891	−	0.968532i	$-0.419934\pi$
$450$		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	0.575821	−	0.817576i	$-0.304683\pi$
$457$	−192.000	−	332.554i	−0.420131	−	0.727689i	−0.995952	+	0.0898873i	$0.971349\pi$
$458$	−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	$-0.906121\pi$
$461$		−	268.000i		−	0.581345i	0.956823	−	0.290672i	$-0.0938790\pi$
$462$		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	−0.757616	−	0.652701i	$-0.773636\pi$
$467$	−266.736	+	154.000i	−0.571169	+	0.329764i	0.186447	+	0.982465i	$0.440303\pi$
$468$		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	0.106407	−	0.994323i	$-0.466065\pi$
$479$	−336.018	−	194.000i	−0.701499	−	0.405010i	−0.807905	+	0.589312i	$0.799399\pi$
$480$		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	−0.921029	−	0.389494i	$-0.872650\pi$
$487$	−60.0000	+	103.923i	−0.123203	+	0.213394i	0.797826	+	0.602888i	$0.205983\pi$
$488$	128.172	−	74.0000i	0.262647	−	0.151639i
$489$		0			0
$490$		0			0
$491$		−	619.426i		−	1.26156i	−0.775962	−	0.630780i	$-0.782735\pi$
$491$		−	619.426i		−	1.26156i	0.775962	−	0.630780i	$-0.217265\pi$
$492$		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	0.522697	−	0.852518i	$-0.324926\pi$
$499$	−238.000	−	412.228i	−0.476954	−	0.826108i	−0.999651	+	0.0264100i	$0.991592\pi$
$500$	−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	$0.412232\pi$
$503$			968.000i			1.92445i	−0.272250	+	0.962227i	$0.587768\pi$
$504$		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	−0.268105	−	0.963390i	$-0.586398\pi$
$509$	219.970	−	127.000i	0.432162	−	0.249509i	0.700267	+	0.713881i	$0.253064\pi$
$510$		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	0.986772	−	0.162114i	$-0.0518313\pi$
$521$	698.016	+	403.000i	1.33976	+	0.773512i	0.352991	+	0.935627i	$0.385165\pi$
$522$		0			0
$523$	−305.470	−	529.090i	−0.584073	−	1.01164i	−0.994990	−	0.0999714i	$-0.968125\pi$
$523$	−305.470	−	529.090i	−0.584073	−	1.01164i	0.410917	−	0.911673i	$-0.365208\pi$
$524$		−	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	0.900624	−	0.434600i	$-0.143110\pi$
$541$	40.0000	+	69.2820i	0.0739372	+	0.128063i	−0.826686	+	0.562663i	$0.809777\pi$
$542$	−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	0.964992	−	0.262279i	$-0.0844742\pi$
$557$	679.733	+	392.444i	1.22035	+	0.704568i	0.255355	+	0.966847i	$0.417808\pi$
$558$		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	−0.0425684	−	0.999094i	$-0.513554\pi$
$563$	−523.079	−	302.000i	−0.929093	−	0.536412i	−0.886525	+	0.462681i	$0.846887\pi$
$564$		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	−0.792583	−	0.609764i	$-0.791264\pi$
$569$	−375.997	+	217.082i	−0.660803	+	0.381515i	0.131780	+	0.991279i	$0.457931\pi$
$570$		0			0
$571$	124.000	−	214.774i	0.217163	−	0.376137i	−0.736777	−	0.676136i	$-0.763653\pi$
$571$	124.000	−	214.774i	0.217163	−	0.376137i	0.953939	+	0.299999i	$0.0969864\pi$
$572$	−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	−0.313726	−	0.949514i	$-0.601577\pi$
$577$	383.959	−	665.036i	0.665440	−	1.15258i	0.979166	−	0.203063i	$-0.0650895\pi$
$578$	−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	$-0.576793\pi$
$587$		−	1140.00i		−	1.94208i	0.238920	−	0.971039i	$-0.423207\pi$
$588$		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	−0.907063	−	0.420995i	$-0.861681\pi$
$593$	−590.629	+	341.000i	−0.996002	+	0.575042i	−0.0889392	+	0.996037i	$0.528348\pi$
$594$		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	0.999550	+	0.0300033i	$0.00955177\pi$
$599$	913.660	+	527.502i	1.52531	+	0.880637i	0.525759	+	0.850634i	$0.323782\pi$
$600$		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	0.636680	−	0.771128i	$-0.280307\pi$
$607$	−212.132	−	367.423i	−0.349476	−	0.605310i	−0.986156	+	0.165817i	$0.946974\pi$
$608$			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	−0.964756	−	0.263147i	$-0.915240\pi$
$613$	−156.000	+	270.200i	−0.254486	+	0.440783i	0.710270	+	0.703930i	$0.248573\pi$
$614$	346.410	−	200.000i	0.564186	−	0.325733i
$615$		0			0
$616$		0			0
$617$			490.732i			0.795352i	0.917526	+	0.397676i	$0.130183\pi$
$617$			490.732i			0.795352i	−0.917526	+	0.397676i	$0.869817\pi$
$618$		0			0
$619$	138.593	−	240.050i	0.223898	−	0.387803i	−0.732090	−	0.681208i	$-0.761455\pi$
$619$	138.593	−	240.050i	0.223898	−	0.387803i	0.955988	+	0.293405i	$0.0947884\pi$
$620$	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	0.177165	−	0.984181i	$-0.443307\pi$
$641$	−375.997	−	217.082i	−0.586578	−	0.338661i	−0.763743	+	0.645520i	$0.776641\pi$
$642$		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	−0.218269	−	0.975889i	$-0.570041\pi$
$647$	−758.638	−	438.000i	−1.17255	−	0.676971i	−0.954279	+	0.298918i	$0.903374\pi$
$648$		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	−0.293156	−	0.956065i	$-0.594706\pi$
$653$	253.522	−	146.371i	0.388242	−	0.224152i	0.681398	+	0.731913i	$0.261372\pi$
$654$		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	$-0.758109\pi$
$659$		−	907.925i		−	1.37773i	0.724889	−	0.688866i	$-0.241891\pi$
$660$		0			0
$661$	392.444	−	679.733i	0.593713	−	1.02834i	−0.400014	−	0.916509i	$-0.630995\pi$
$661$	392.444	−	679.733i	0.593713	−	1.02834i	0.993727	−	0.111832i	$-0.0356719\pi$
$662$	−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	−0.295691	−	0.955284i	$-0.595550\pi$
$677$	259.808	−	150.000i	0.383763	−	0.221566i	0.679454	+	0.733718i	$0.262217\pi$
$678$		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	0.999571	−	0.0292824i	$-0.00932220\pi$
$683$	1006.74	+	581.242i	1.47400	+	0.851013i	0.474426	+	0.880295i	$0.342656\pi$
$684$		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	0.989314	−	0.145799i	$-0.0465753\pi$
$691$	254.558	+	440.908i	0.368391	+	0.638073i	−0.620923	+	0.783872i	$0.713242\pi$
$692$		−	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	$-0.958463\pi$
$701$		−	182.434i		−	0.260248i	0.991498	−	0.130124i	$-0.0415375\pi$
$702$		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	−0.784196	−	0.620513i	$-0.786924\pi$
$709$	−659.000	−	1141.42i	−0.929478	−	1.60990i	−0.145282	−	0.989390i	$-0.546409\pi$
$710$	−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	−0.965717	−	0.259597i	$-0.916410\pi$
$719$	−879.882	+	508.000i	−1.22376	+	0.706537i	−0.258041	+	0.966134i	$0.583077\pi$
$720$		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	0.611817	−	0.791000i	$-0.290439\pi$
$733$	−277.893	−	481.325i	−0.379117	−	0.656650i	−0.990934	+	0.134349i	$0.957106\pi$
$734$		−	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	−0.0996190	−	0.995026i	$-0.531762\pi$
$739$	600.000	−	1039.23i	0.811908	−	1.40627i	0.911527	−	0.411240i	$-0.134904\pi$
$740$	221.703	−	128.000i	0.299598	−	0.172973i
$741$		0			0
$742$		0			0
$743$			1309.56i			1.76253i	0.472620	+	0.881266i	$0.343308\pi$
$743$			1309.56i			1.76253i	−0.472620	+	0.881266i	$0.656692\pi$
$744$		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	0.990795	−	0.135371i	$-0.0432227\pi$
$751$	284.000	+	491.902i	0.378162	+	0.654997i	−0.612632	+	0.790368i	$0.709889\pi$
$752$	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	−0.760382	−	0.649477i	$-0.774988\pi$
$761$	−439.941	+	254.000i	−0.578109	+	0.333771i	0.182273	+	0.983248i	$0.441655\pi$
$762$		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	0.908055	−	0.418851i	$-0.137567\pi$
$773$	772.495	+	446.000i	0.999346	+	0.576973i	0.0912915	+	0.995824i	$0.470901\pi$
$774$		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	−0.969664	−	0.244442i	$-0.921395\pi$
$787$	−214.960	+	372.322i	−0.273139	+	0.473091i	0.696525	+	0.717533i	$0.254729\pi$
$788$	−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	$-0.889989\pi$
$797$		−	540.000i		−	0.677541i	0.940869	−	0.338770i	$-0.110011\pi$
$798$		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	0.888098	−	0.459653i	$-0.152026\pi$
$809$	755.668	+	436.285i	0.934076	+	0.539289i	0.0459777	+	0.998942i	$0.485360\pi$
$810$		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	−0.0485812	−	0.998819i	$-0.515470\pi$
$821$	650.340	−	375.474i	0.792131	−	0.457337i	0.840712	+	0.541482i	$0.182137\pi$
$822$		0			0
$823$	58.0000	−	100.459i	0.0704739	−	0.122064i	−0.828635	−	0.559789i	$-0.810882\pi$
$823$	58.0000	−	100.459i	0.0704739	−	0.122064i	0.899109	+	0.437725i	$0.144216\pi$
$824$	387.979	−	224.000i	0.470849	−	0.271845i
$825$		0			0
$826$		0			0
$827$		−	873.984i		−	1.05681i	−0.848992	−	0.528406i	$-0.822790\pi$
$827$		−	873.984i		−	1.05681i	0.848992	−	0.528406i	$-0.177210\pi$
$828$		0			0
$829$	−136.472	+	236.376i	−0.164622	+	0.285134i	−0.936521	−	0.350612i	$-0.885974\pi$
$829$	−136.472	+	236.376i	−0.164622	+	0.285134i	0.771899	+	0.635745i	$0.219307\pi$
$830$	−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	$-0.964262\pi$
$839$		−	188.000i		−	0.224076i	0.993704	−	0.112038i	$-0.0357379\pi$
$840$		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	0.362845	−	0.931850i	$-0.381806\pi$
$857$	−225.167	−	130.000i	−0.262738	−	0.151692i	−0.625583	+	0.780158i	$0.715139\pi$
$858$		0			0
$859$	395.980	+	685.857i	0.460978	+	0.798437i	0.999010	−	0.0444875i	$-0.0141655\pi$
$859$	395.980	+	685.857i	0.460978	+	0.798437i	−0.538032	+	0.842924i	$0.680832\pi$
$860$			176.000i			0.204651i
$861$		0			0
$862$	−1212.00			−1.40603
$863$	364.974	−	210.718i	0.422913	−	0.244169i	−0.273410	−	0.961898i	$-0.588152\pi$
$863$	364.974	−	210.718i	0.422913	−	0.244169i	0.696323	+	0.717729i	$0.254818\pi$
$864$		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	0.998744	+	0.0500993i	$0.0159538\pi$
$877$	476.000	+	824.456i	0.542759	+	0.940087i	−0.455985	+	0.889988i	$0.650713\pi$
$878$	−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	$0.228263\pi$
$881$			1158.00i			1.31442i	−0.753710	+	0.657208i	$0.771737\pi$
$882$		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	−0.707460	−	0.706754i	$-0.750159\pi$
$887$	−398.372	+	230.000i	−0.449123	+	0.259301i	0.258337	+	0.966055i	$0.416826\pi$
$888$		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	−0.920272	−	0.391279i	$-0.872033\pi$
$907$	−110.000	+	190.526i	−0.121279	+	0.210061i	0.798993	+	0.601340i	$0.205366\pi$
$908$	−353.338	+	204.000i	−0.389139	+	0.224670i
$909$		0			0
$910$		0			0
$911$			1049.35i			1.15186i	0.817498	+	0.575931i	$0.195360\pi$
$911$			1049.35i			1.15186i	−0.817498	+	0.575931i	$0.804640\pi$
$912$		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	0.939850	−	0.341587i	$-0.110964\pi$
$919$	160.000	+	277.128i	0.174102	+	0.301554i	−0.765748	+	0.643141i	$0.777631\pi$
$920$	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	0.655095	−	0.755546i	$-0.272629\pi$
$929$	1520.74	−	878.000i	1.63697	−	0.945102i	0.981870	−	0.189556i	$-0.0607048\pi$
$930$		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	0.759591	−	0.650401i	$-0.225399\pi$
$941$	542.132	+	313.000i	0.576123	+	0.332625i	−0.183468	+	0.983026i	$0.558732\pi$
$942$		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	−0.815362	−	0.578952i	$-0.803462\pi$
$947$	−683.408	+	394.566i	−0.721655	+	0.416648i	0.0937063	+	0.995600i	$0.470129\pi$
$948$		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	$0.0324126\pi$
$953$			193.747i			0.203302i	−0.994820	+	0.101651i	$0.967587\pi$
$954$		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	−0.426949	−	0.904276i	$-0.640412\pi$
$971$	138.564	−	80.0000i	0.142702	−	0.0823893i	0.569651	+	0.821886i	$0.307078\pi$
$972$		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	−0.342620	−	0.939474i	$-0.611314\pi$
$977$	−1297.00	−	748.826i	−1.32754	−	0.766455i	−0.984918	+	0.173020i	$0.944648\pi$
$978$		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	0.637477	−	0.770470i	$-0.279978\pi$
$983$	284.056	+	164.000i	0.288969	+	0.166836i	−0.348508	+	0.937306i	$0.613312\pi$
$984$		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	−0.861961	−	0.506975i	$-0.830764\pi$
$991$	8.00000	−	13.8564i	0.00807265	−	0.0139822i	0.870034	+	0.492993i	$0.164097\pi$
$992$	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	−0.997614	−	0.0690405i	$-0.978006\pi$
$997$	−437.699	+	758.117i	−0.439016	+	0.760398i	0.558598	+	0.829439i	$0.311340\pi$
$998$	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.557.1		8
3.2	odd	2	inner	882.3.s.f.557.4		8
7.2	even	3	inner	882.3.s.f.863.4		8
7.3	odd	6		882.3.b.i.197.2	yes	4
7.4	even	3		882.3.b.i.197.1	✓	4
7.5	odd	6	inner	882.3.s.f.863.3		8
7.6	odd	2	inner	882.3.s.f.557.2		8
21.2	odd	6	inner	882.3.s.f.863.1		8
21.5	even	6	inner	882.3.s.f.863.2		8
21.11	odd	6		882.3.b.i.197.4	yes	4
21.17	even	6		882.3.b.i.197.3	yes	4
21.20	even	2	inner	882.3.s.f.557.3		8

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