LMFDB - Embedded newform 882.3.s.e.863.4

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:	8.0.12745506816.5
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 8x^{6} + 55x^{4} - 72x^{2} + 81 $ x^8 - 8x^6 + 55x^4 - 72*x^2 + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{25}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			863.4
Root			$1.00781 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	882.863
Dual form			882.3.s.e.557.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(5.25600 + 3.03455i) q^{5} +2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(5.25600 + 3.03455i) q^{5} +2.82843i q^{8} +(4.29150 + 7.43310i) q^{10} +(-10.5120 + 6.06910i) q^{11} -18.5830 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-9.44094 + 5.45073i) q^{17} +(-10.0000 + 17.3205i) q^{19} +12.1382i q^{20} -17.1660 q^{22} +(10.5120 + 6.06910i) q^{23} +(5.91699 + 10.2485i) q^{25} +(-22.7594 - 13.1402i) q^{26} +41.8367i q^{29} +(-12.5830 - 21.7944i) q^{31} +(-4.89898 + 2.82843i) q^{32} -15.4170 q^{34} +(-19.0000 + 32.9090i) q^{37} +(-24.4949 + 14.1421i) q^{38} +(-8.58301 + 14.8662i) q^{40} -60.6337i q^{41} +83.4980 q^{43} +(-21.0240 - 12.1382i) q^{44} +(8.58301 + 14.8662i) q^{46} +(14.6969 + 8.48528i) q^{47} +16.7358i q^{50} +(-18.5830 - 32.1867i) q^{52} +(81.4431 - 47.0212i) q^{53} -73.6680 q^{55} +(-29.5830 + 51.2393i) q^{58} +(-50.4179 + 29.1088i) q^{59} +(-7.83399 + 13.5689i) q^{61} -35.5901i q^{62} -8.00000 q^{64} +(-97.6722 - 56.3911i) q^{65} +(66.3320 + 114.890i) q^{67} +(-18.8819 - 10.9015i) q^{68} -12.1382i q^{71} +(38.4575 + 66.6104i) q^{73} +(-46.5403 + 26.8701i) q^{74} -40.0000 q^{76} +(-16.8340 + 29.1573i) q^{79} +(-21.0240 + 12.1382i) q^{80} +(42.8745 - 74.2608i) q^{82} -60.5764i q^{83} -66.1621 q^{85} +(102.264 + 59.0420i) q^{86} +(-17.1660 - 29.7324i) q^{88} +(4.13532 + 2.38753i) q^{89} +24.2764i q^{92} +(12.0000 + 20.7846i) q^{94} +(-105.120 + 60.6910i) q^{95} -188.413 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} - 8 q^{10} - 64 q^{13} - 16 q^{16} - 80 q^{19} + 32 q^{22} + 132 q^{25} - 16 q^{31} - 208 q^{34} - 152 q^{37} + 16 q^{40} + 160 q^{43} - 16 q^{46} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} + 96 q^{73} - 320 q^{76} - 304 q^{79} + 216 q^{82} + 656 q^{85} + 32 q^{88} + 96 q^{94} - 576 q^{97}+O(q^{100}) $ 8 * q + 8 * q^4 - 8 * q^10 - 64 * q^13 - 16 * q^16 - 80 * q^19 + 32 * q^22 + 132 * q^25 - 16 * q^31 - 208 * q^34 - 152 * q^37 + 16 * q^40 + 160 * q^43 - 16 * q^46 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 + 96 * q^73 - 320 * q^76 - 304 * q^79 + 216 * q^82 + 656 * q^85 + 32 * q^88 + 96 * q^94 - 576 * q^97

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
$5$	5.25600	+	3.03455i	1.05120	+	0.606910i	0.922985	−	0.384836i	$-0.125742\pi$
$5$	5.25600	+	3.03455i	1.05120	+	0.606910i	0.128214	+	0.991746i	$0.459075\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$			2.82843i			0.353553i
$9$		0			0
$10$	4.29150	+	7.43310i	0.429150	+	0.743310i
$11$	−10.5120	+	6.06910i	−0.955636	+	0.551736i	−0.894827	−	0.446413i	$-0.852701\pi$
$11$	−10.5120	+	6.06910i	−0.955636	+	0.551736i	−0.0608086	+	0.998149i	$0.519368\pi$
$12$		0			0
$13$	−18.5830			−1.42946			−0.714731	−	0.699399i	$-0.753451\pi$
$13$	−18.5830			−1.42946			−0.714731	+	0.699399i	$0.753451\pi$
$14$		0			0
$15$		0			0
$16$	−2.00000	+	3.46410i	−0.125000	+	0.216506i
$17$	−9.44094	+	5.45073i	−0.555350	+	0.320631i	−0.751277	−	0.659987i	$-0.770562\pi$
$17$	−9.44094	+	5.45073i	−0.555350	+	0.320631i	0.195927	+	0.980618i	$0.437228\pi$
$18$		0			0
$19$	−10.0000	+	17.3205i	−0.526316	+	0.911606i	0.473214	+	0.880947i	$0.343094\pi$
$19$	−10.0000	+	17.3205i	−0.526316	+	0.911606i	−0.999530	+	0.0306583i	$0.990240\pi$
$20$			12.1382i			0.606910i
$21$		0			0
$22$	−17.1660			−0.780273
$23$	10.5120	+	6.06910i	0.457043	+	0.263874i	0.710800	−	0.703394i	$-0.248333\pi$
$23$	10.5120	+	6.06910i	0.457043	+	0.263874i	−0.253757	+	0.967268i	$0.581666\pi$
$24$		0			0
$25$	5.91699	+	10.2485i	0.236680	+	0.409941i
$26$	−22.7594	−	13.1402i	−0.875363	−	0.505391i
$27$		0			0
$28$		0			0
$29$			41.8367i			1.44264i	0.692600	+	0.721322i	$0.256465\pi$
$29$			41.8367i			1.44264i	−0.692600	+	0.721322i	$0.743535\pi$
$30$		0			0
$31$	−12.5830	−	21.7944i	−0.405903	−	0.703045i	0.588523	−	0.808481i	$-0.299710\pi$
$31$	−12.5830	−	21.7944i	−0.405903	−	0.703045i	−0.994426	+	0.105435i	$0.966376\pi$
$32$	−4.89898	+	2.82843i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−15.4170			−0.453441
$35$		0			0
$36$		0			0
$37$	−19.0000	+	32.9090i	−0.513514	+	0.889431i	0.486364	+	0.873757i	$0.338323\pi$
$37$	−19.0000	+	32.9090i	−0.513514	+	0.889431i	−0.999877	+	0.0156750i	$0.995010\pi$
$38$	−24.4949	+	14.1421i	−0.644603	+	0.372161i
$39$		0			0
$40$	−8.58301	+	14.8662i	−0.214575	+	0.371655i
$41$		−	60.6337i		−	1.47887i	−0.673227	−	0.739435i	$-0.735092\pi$
$41$		−	60.6337i		−	1.47887i	0.673227	−	0.739435i	$-0.264908\pi$
$42$		0			0
$43$	83.4980			1.94181			0.970907	−	0.239455i	$-0.0769689\pi$
$43$	83.4980			1.94181			0.970907	+	0.239455i	$0.0769689\pi$
$44$	−21.0240	−	12.1382i	−0.477818	−	0.275868i
$45$		0			0
$46$	8.58301	+	14.8662i	0.186587	+	0.323178i
$47$	14.6969	+	8.48528i	0.312701	+	0.180538i	0.648134	−	0.761526i	$-0.275549\pi$
$47$	14.6969	+	8.48528i	0.312701	+	0.180538i	−0.335434	+	0.942064i	$0.608883\pi$
$48$		0			0
$49$		0			0
$50$			16.7358i			0.334716i
$51$		0			0
$52$	−18.5830	−	32.1867i	−0.357365	−	0.618975i
$53$	81.4431	−	47.0212i	1.53666	−	0.887193i	0.537632	−	0.843180i	$-0.319319\pi$
$53$	81.4431	−	47.0212i	1.53666	−	0.887193i	0.999031	−	0.0440129i	$-0.0140143\pi$
$54$		0			0
$55$	−73.6680			−1.33942
$56$		0			0
$57$		0			0
$58$	−29.5830	+	51.2393i	−0.510052	+	0.883436i
$59$	−50.4179	+	29.1088i	−0.854540	+	0.493369i	−0.862180	−	0.506602i	$-0.830901\pi$
$59$	−50.4179	+	29.1088i	−0.854540	+	0.493369i	0.00764008	+	0.999971i	$0.497568\pi$
$60$		0			0
$61$	−7.83399	+	13.5689i	−0.128426	+	0.222440i	−0.923067	−	0.384639i	$-0.874326\pi$
$61$	−7.83399	+	13.5689i	−0.128426	+	0.222440i	0.794641	+	0.607080i	$0.207659\pi$
$62$		−	35.5901i		−	0.574034i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	−97.6722	−	56.3911i	−1.50265	−	0.867555i
$66$		0			0
$67$	66.3320	+	114.890i	0.990030	+	1.71478i	0.617000	+	0.786964i	$0.288348\pi$
$67$	66.3320	+	114.890i	0.990030	+	1.71478i	0.373031	+	0.927819i	$0.378319\pi$
$68$	−18.8819	−	10.9015i	−0.277675	−	0.160316i
$69$		0			0
$70$		0			0
$71$		−	12.1382i		−	0.170961i	−0.996340	−	0.0854803i	$-0.972758\pi$
$71$		−	12.1382i		−	0.170961i	0.996340	−	0.0854803i	$-0.0272425\pi$
$72$		0			0
$73$	38.4575	+	66.6104i	0.526815	+	0.912471i	0.999512	+	0.0312455i	$0.00994736\pi$
$73$	38.4575	+	66.6104i	0.526815	+	0.912471i	−0.472696	+	0.881225i	$0.656719\pi$
$74$	−46.5403	+	26.8701i	−0.628923	+	0.363109i
$75$		0			0
$76$	−40.0000			−0.526316
$77$		0			0
$78$		0			0
$79$	−16.8340	+	29.1573i	−0.213088	+	0.369080i	−0.952680	−	0.303976i	$-0.901686\pi$
$79$	−16.8340	+	29.1573i	−0.213088	+	0.369080i	0.739591	+	0.673056i	$0.235019\pi$
$80$	−21.0240	+	12.1382i	−0.262800	+	0.151728i
$81$		0			0
$82$	42.8745	−	74.2608i	0.522860	−	0.905620i
$83$		−	60.5764i		−	0.729836i	−0.931040	−	0.364918i	$-0.881097\pi$
$83$		−	60.5764i		−	0.729836i	0.931040	−	0.364918i	$-0.118903\pi$
$84$		0			0
$85$	−66.1621			−0.778377
$86$	102.264	+	59.0420i	1.18911	+	0.686535i
$87$		0			0
$88$	−17.1660	−	29.7324i	−0.195068	−	0.337868i
$89$	4.13532	+	2.38753i	0.0464643	+	0.0268262i	0.523052	−	0.852301i	$-0.324793\pi$
$89$	4.13532	+	2.38753i	0.0464643	+	0.0268262i	−0.476588	+	0.879127i	$0.658127\pi$
$90$		0			0
$91$		0			0
$92$			24.2764i			0.263874i
$93$		0			0
$94$	12.0000	+	20.7846i	0.127660	+	0.221113i
$95$	−105.120	+	60.6910i	−1.10653	+	0.638853i
$96$		0			0
$97$	−188.413			−1.94240			−0.971201	−	0.238260i	$-0.923423\pi$
$97$	−188.413			−1.94240			−0.971201	+	0.238260i	$0.923423\pi$
$98$		0			0
$99$		0			0
$100$	−11.8340	+	20.4971i	−0.118340	+	0.204971i
$101$	92.4162	−	53.3565i	0.915012	−	0.528282i	0.0329716	−	0.999456i	$-0.489503\pi$
$101$	92.4162	−	53.3565i	0.915012	−	0.528282i	0.882040	+	0.471174i	$0.156170\pi$
$102$		0			0
$103$	−65.7490	+	113.881i	−0.638340	+	1.10564i	0.347457	+	0.937696i	$0.387045\pi$
$103$	−65.7490	+	113.881i	−0.638340	+	1.10564i	−0.985797	+	0.167941i	$0.946288\pi$
$104$		−	52.5607i		−	0.505391i
$105$		0			0
$106$	132.996			1.25468
$107$	−71.3426	−	41.1897i	−0.666753	−	0.384950i	0.128092	−	0.991762i	$-0.459115\pi$
$107$	−71.3426	−	41.1897i	−0.666753	−	0.384950i	−0.794845	+	0.606812i	$0.792448\pi$
$108$		0			0
$109$	−16.9150	−	29.2977i	−0.155184	−	0.268786i	0.777942	−	0.628336i	$-0.216264\pi$
$109$	−16.9150	−	29.2977i	−0.155184	−	0.268786i	−0.933126	+	0.359550i	$0.882930\pi$
$110$	−90.2245	−	52.0911i	−0.820223	−	0.473556i
$111$		0			0
$112$		0			0
$113$		−	28.5190i		−	0.252381i	−0.992006	−	0.126190i	$-0.959725\pi$
$113$		−	28.5190i		−	0.252381i	0.992006	−	0.126190i	$-0.0402750\pi$
$114$		0			0
$115$	36.8340	+	63.7983i	0.320296	+	0.554768i
$116$	−72.4633	+	41.8367i	−0.624683	+	0.360661i
$117$		0			0
$118$	−82.3320			−0.697729
$119$		0			0
$120$		0			0
$121$	13.1680	−	22.8076i	0.108826	−	0.188493i
$122$	−19.1893	+	11.0789i	−0.157289	+	0.0908109i
$123$		0			0
$124$	25.1660	−	43.5888i	0.202952	−	0.351523i
$125$		−	79.9059i		−	0.639247i
$126$		0			0
$127$	129.668			1.02101			0.510504	−	0.859875i	$-0.329459\pi$
$127$	129.668			1.02101			0.510504	+	0.859875i	$0.329459\pi$
$128$	−9.79796	−	5.65685i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−79.7490	−	138.129i	−0.613454	−	1.06253i
$131$	128.187	+	74.0087i	0.978525	+	0.564952i	0.901824	−	0.432103i	$-0.142228\pi$
$131$	128.187	+	74.0087i	0.978525	+	0.564952i	0.0767004	+	0.997054i	$0.475562\pi$
$132$		0			0
$133$		0			0
$134$			187.615i			1.40011i
$135$		0			0
$136$	−15.4170	−	26.7030i	−0.113360	−	0.196346i
$137$	−66.6469	+	38.4786i	−0.486474	+	0.280866i	−0.723111	−	0.690732i	$-0.757288\pi$
$137$	−66.6469	+	38.4786i	−0.486474	+	0.280866i	0.236637	+	0.971598i	$0.423955\pi$
$138$		0			0
$139$	217.328			1.56351			0.781756	−	0.623585i	$-0.214324\pi$
$139$	217.328			1.56351			0.781756	+	0.623585i	$0.214324\pi$
$140$		0			0
$141$		0			0
$142$	8.58301	−	14.8662i	0.0604437	−	0.104692i
$143$	195.344	−	112.782i	1.36604	−	0.788686i
$144$		0			0
$145$	−126.956	+	219.893i	−0.875555	+	1.51651i
$146$			108.774i			0.745029i
$147$		0			0
$148$	−76.0000			−0.513514
$149$	−140.231	−	80.9623i	−0.941147	−	0.543371i	−0.0508272	−	0.998707i	$-0.516186\pi$
$149$	−140.231	−	80.9623i	−0.941147	−	0.543371i	−0.890320	+	0.455336i	$0.849519\pi$
$150$		0			0
$151$	46.5830	+	80.6841i	0.308497	+	0.534332i	0.978034	−	0.208447i	$-0.0668408\pi$
$151$	46.5830	+	80.6841i	0.308497	+	0.534332i	−0.669537	+	0.742779i	$0.733507\pi$
$152$	−48.9898	−	28.2843i	−0.322301	−	0.186081i
$153$		0			0
$154$		0			0
$155$		−	152.735i		−	0.985388i
$156$		0			0
$157$	92.4980	+	160.211i	0.589159	+	1.02045i	0.994343	+	0.106219i	$0.0338743\pi$
$157$	92.4980	+	160.211i	0.589159	+	1.02045i	−0.405183	+	0.914235i	$0.632792\pi$
$158$	−41.2347	+	23.8069i	−0.260979	+	0.150676i
$159$		0			0
$160$	−34.3320			−0.214575
$161$		0			0
$162$		0			0
$163$	−43.4980	+	75.3408i	−0.266859	+	0.462214i	−0.968049	−	0.250761i	$-0.919319\pi$
$163$	−43.4980	+	75.3408i	−0.266859	+	0.462214i	0.701190	+	0.712975i	$0.252652\pi$
$164$	105.021	−	60.6337i	0.640370	−	0.369718i
$165$		0			0
$166$	42.8340	−	74.1906i	0.258036	−	0.446932i
$167$			60.5764i			0.362733i	0.983416	+	0.181366i	$0.0580520\pi$
$167$			60.5764i			0.362733i	−0.983416	+	0.181366i	$0.941948\pi$
$168$		0			0
$169$	176.328			1.04336
$170$	−81.0317	−	46.7837i	−0.476657	−	0.275198i
$171$		0			0
$172$	83.4980	+	144.623i	0.485454	+	0.840830i
$173$	−140.791	−	81.2858i	−0.813822	−	0.469860i	0.0344594	−	0.999406i	$-0.489029\pi$
$173$	−140.791	−	81.2858i	−0.813822	−	0.469860i	−0.848281	+	0.529546i	$0.822362\pi$
$174$		0			0
$175$		0			0
$176$		−	48.5528i		−	0.275868i
$177$		0			0
$178$	3.37648	+	5.84823i	0.0189690	+	0.0328552i
$179$	193.202	−	111.545i	1.07934	−	0.623159i	0.148623	−	0.988894i	$-0.452516\pi$
$179$	193.202	−	111.545i	1.07934	−	0.623159i	0.930719	+	0.365735i	$0.119182\pi$
$180$		0			0
$181$	188.915			1.04373			0.521865	−	0.853028i	$-0.325237\pi$
$181$	188.915			1.04373			0.521865	+	0.853028i	$0.325237\pi$
$182$		0			0
$183$		0			0
$184$	−17.1660	+	29.7324i	−0.0932935	+	0.161589i
$185$	−199.728	+	115.313i	−1.07961	+	0.623313i
$186$		0			0
$187$	66.1621	−	114.596i	0.353808	−	0.612813i
$188$			33.9411i			0.180538i
$189$		0			0
$190$	−171.660			−0.903474
$191$	197.486	+	114.019i	1.03396	+	0.596957i	0.918117	−	0.396310i	$-0.129709\pi$
$191$	197.486	+	114.019i	1.03396	+	0.596957i	0.115844	+	0.993267i	$0.463043\pi$
$192$		0			0
$193$	−67.0000	−	116.047i	−0.347150	−	0.601282i	0.638592	−	0.769546i	$-0.279517\pi$
$193$	−67.0000	−	116.047i	−0.347150	−	0.601282i	−0.985742	+	0.168264i	$0.946184\pi$
$194$	−230.758	−	133.228i	−1.18947	−	0.686743i
$195$		0			0
$196$		0			0
$197$		−	188.560i		−	0.957157i	−0.878045	−	0.478579i	$-0.841152\pi$
$197$		−	188.560i		−	0.957157i	0.878045	−	0.478579i	$-0.158848\pi$
$198$		0			0
$199$	−51.2470	−	88.7625i	−0.257523	−	0.446043i	0.708055	−	0.706157i	$-0.249573\pi$
$199$	−51.2470	−	88.7625i	−0.257523	−	0.446043i	−0.965578	+	0.260115i	$0.916240\pi$
$200$	−28.9872	+	16.7358i	−0.144936	+	0.0836789i
$201$		0			0
$202$	150.915			0.747104
$203$		0			0
$204$		0			0
$205$	183.996	−	318.691i	0.897542	−	1.55459i
$206$	−161.052	+	92.9831i	−0.781804	+	0.451375i
$207$		0			0
$208$	37.1660	−	64.3734i	0.178683	−	0.309488i
$209$		−	242.764i		−	1.16155i
$210$		0			0
$211$	−84.5020			−0.400483			−0.200242	−	0.979747i	$-0.564173\pi$
$211$	−84.5020			−0.400483			−0.200242	+	0.979747i	$0.564173\pi$
$212$	162.886	+	94.0424i	0.768331	+	0.443596i
$213$		0			0
$214$	−58.2510	−	100.894i	−0.272201	−	0.471466i
$215$	438.865	+	253.379i	2.04123	+	1.17851i
$216$		0			0
$217$		0			0
$218$		−	47.8429i		−	0.219463i
$219$		0			0
$220$	−73.6680	−	127.597i	−0.334854	−	0.579985i
$221$	175.441	−	101.291i	0.793851	−	0.458330i
$222$		0			0
$223$	−158.494			−0.710736			−0.355368	−	0.934727i	$-0.615644\pi$
$223$	−158.494			−0.710736			−0.355368	+	0.934727i	$0.615644\pi$
$224$		0			0
$225$		0			0
$226$	20.1660	−	34.9286i	0.0892301	−	0.154551i
$227$	88.1816	−	50.9117i	0.388465	−	0.224281i	−0.293030	−	0.956103i	$-0.594663\pi$
$227$	88.1816	−	50.9117i	0.388465	−	0.224281i	0.681495	+	0.731823i	$0.261330\pi$
$228$		0			0
$229$	134.458	−	232.887i	0.587151	−	1.01697i	−0.407453	−	0.913226i	$-0.633583\pi$
$229$	134.458	−	232.887i	0.587151	−	1.01697i	0.994604	−	0.103749i	$-0.0330837\pi$
$230$			104.182i			0.452966i
$231$		0			0
$232$	−118.332			−0.510052
$233$	22.7546	+	13.1374i	0.0976593	+	0.0563836i	0.548034	−	0.836456i	$-0.315376\pi$
$233$	22.7546	+	13.1374i	0.0976593	+	0.0563836i	−0.450375	+	0.892840i	$0.648710\pi$
$234$		0			0
$235$	51.4980	+	89.1972i	0.219141	+	0.379563i
$236$	−100.836	−	58.2175i	−0.427270	−	0.246684i
$237$		0			0
$238$		0			0
$239$			92.2733i			0.386081i	0.981191	+	0.193040i	$0.0618348\pi$
$239$			92.2733i			0.386081i	−0.981191	+	0.193040i	$0.938165\pi$
$240$		0			0
$241$	−171.624	−	297.261i	−0.712131	−	1.23345i	−0.964056	−	0.265700i	$-0.914397\pi$
$241$	−171.624	−	297.261i	−0.712131	−	1.23345i	0.251925	−	0.967747i	$-0.418936\pi$
$242$	32.2548	−	18.6223i	0.133284	−	0.0769518i
$243$		0			0
$244$	−31.3360			−0.128426
$245$		0			0
$246$		0			0
$247$	185.830	−	321.867i	0.752348	−	1.30311i
$248$	61.6439	−	35.5901i	0.248564	−	0.143509i
$249$		0			0
$250$	56.5020	−	97.8643i	0.226008	−	0.391457i
$251$			356.382i			1.41985i	0.704278	+	0.709924i	$0.251271\pi$
$251$			356.382i			1.41985i	−0.704278	+	0.709924i	$0.748729\pi$
$252$		0			0
$253$	−147.336			−0.582356
$254$	158.810	+	91.6891i	0.625237	+	0.360981i
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.0312500	−	0.0541266i
$257$	220.603	+	127.365i	0.858377	+	0.495584i	0.863469	−	0.504403i	$-0.168287\pi$
$257$	220.603	+	127.365i	0.858377	+	0.495584i	−0.00509129	+	0.999987i	$0.501621\pi$
$258$		0			0
$259$		0			0
$260$		−	225.564i		−	0.867555i
$261$		0			0
$262$	104.664	+	181.283i	0.399481	+	0.691922i
$263$	226.880	−	130.989i	0.862663	−	0.498059i	−0.00224015	−	0.999997i	$-0.500713\pi$
$263$	226.880	−	130.989i	0.862663	−	0.498059i	0.864903	+	0.501939i	$0.167380\pi$
$264$		0			0
$265$	570.753			2.15378
$266$		0			0
$267$		0			0
$268$	−132.664	+	229.781i	−0.495015	+	0.857391i
$269$	81.0813	−	46.8123i	0.301417	−	0.174023i	−0.341662	−	0.939823i	$-0.610990\pi$
$269$	81.0813	−	46.8123i	0.301417	−	0.174023i	0.643079	+	0.765799i	$0.277656\pi$
$270$		0			0
$271$	−0.583005	+	1.00979i	−0.00215131	+	0.00372618i	−0.867099	−	0.498136i	$-0.834018\pi$
$271$	−0.583005	+	1.00979i	−0.00215131	+	0.00372618i	0.864948	+	0.501862i	$0.167351\pi$
$272$		−	43.6058i		−	0.160316i
$273$		0			0
$274$	−108.834			−0.397204
$275$	−124.399	−	71.8217i	−0.452359	−	0.261170i
$276$		0			0
$277$	−16.0000	−	27.7128i	−0.0577617	−	0.100046i	0.835699	−	0.549188i	$-0.185063\pi$
$277$	−16.0000	−	27.7128i	−0.0577617	−	0.100046i	−0.893460	+	0.449142i	$0.851730\pi$
$278$	266.171	+	153.674i	0.957451	+	0.552785i
$279$		0			0
$280$		0			0
$281$			166.757i			0.593441i	0.954964	+	0.296721i	$0.0958930\pi$
$281$			166.757i			0.593441i	−0.954964	+	0.296721i	$0.904107\pi$
$282$		0			0
$283$	−8.16995	−	14.1508i	−0.0288691	−	0.0500027i	0.851230	−	0.524793i	$-0.175857\pi$
$283$	−8.16995	−	14.1508i	−0.0288691	−	0.0500027i	−0.880099	+	0.474790i	$0.842524\pi$
$284$	21.0240	−	12.1382i	0.0740281	−	0.0427401i
$285$		0			0
$286$	318.996			1.11537
$287$		0			0
$288$		0			0
$289$	−85.0791	+	147.361i	−0.294391	+	0.509901i
$290$	−310.976	+	179.542i	−1.07233	+	0.619111i
$291$		0			0
$292$	−76.9150	+	133.221i	−0.263408	+	0.456235i
$293$			368.921i			1.25912i	0.776953	+	0.629558i	$0.216764\pi$
$293$			368.921i			1.25912i	−0.776953	+	0.629558i	$0.783236\pi$
$294$		0			0
$295$	−353.328			−1.19772
$296$	−93.0806	−	53.7401i	−0.314462	−	0.181554i
$297$		0			0
$298$	−114.498	−	198.316i	−0.384222	−	0.665491i
$299$	−195.344	−	112.782i	−0.653326	−	0.377198i
$300$		0			0
$301$		0			0
$302$			131.757i			0.436280i
$303$		0			0
$304$	−40.0000	−	69.2820i	−0.131579	−	0.227901i
$305$	−82.3508	+	47.5453i	−0.270003	+	0.155886i
$306$		0			0
$307$	−192.664			−0.627570			−0.313785	−	0.949494i	$-0.601597\pi$
$307$	−192.664			−0.627570			−0.313785	+	0.949494i	$0.601597\pi$
$308$		0			0
$309$		0			0
$310$	108.000	−	187.061i	0.348387	−	0.603424i
$311$	113.688	−	65.6380i	0.365557	−	0.211055i	−0.305959	−	0.952045i	$-0.598977\pi$
$311$	113.688	−	65.6380i	0.365557	−	0.211055i	0.671516	+	0.740990i	$0.265644\pi$
$312$		0			0
$313$	−21.6640	+	37.5232i	−0.0692142	+	0.119882i	−0.898556	−	0.438860i	$-0.855383\pi$
$313$	−21.6640	+	37.5232i	−0.0692142	+	0.119882i	0.829341	+	0.558742i	$0.188716\pi$
$314$			261.624i			0.833197i
$315$		0			0
$316$	−67.3360			−0.213088
$317$	218.000	+	125.862i	0.687696	+	0.397042i	0.802748	−	0.596318i	$-0.203370\pi$
$317$	218.000	+	125.862i	0.687696	+	0.397042i	−0.115052	+	0.993359i	$0.536703\pi$
$318$		0			0
$319$	−253.911	−	439.787i	−0.795960	−	1.37864i
$320$	−42.0480	−	24.2764i	−0.131400	−	0.0758638i
$321$		0			0
$322$		0			0
$323$		−	218.029i		−	0.675013i
$324$		0			0
$325$	−109.956	−	190.449i	−0.338325	−	0.585996i
$326$	−106.548	+	61.5155i	−0.326834	+	0.188698i
$327$		0			0
$328$	171.498			0.522860
$329$		0			0
$330$		0			0
$331$	−180.745	+	313.060i	−0.546058	+	0.945800i	0.452482	+	0.891774i	$0.350539\pi$
$331$	−180.745	+	313.060i	−0.546058	+	0.945800i	−0.998540	+	0.0540260i	$0.982795\pi$
$332$	104.921	−	60.5764i	0.316028	−	0.182459i
$333$		0			0
$334$	−42.8340	+	74.1906i	−0.128245	+	0.222128i
$335$			805.151i			2.40344i
$336$		0			0
$337$	−298.834			−0.886748			−0.443374	−	0.896337i	$-0.646219\pi$
$337$	−298.834			−0.886748			−0.443374	+	0.896337i	$0.646219\pi$
$338$	215.957	+	124.683i	0.638926	+	0.368884i
$339$		0			0
$340$	−66.1621	−	114.596i	−0.194594	−	0.337047i
$341$	264.545	+	152.735i	0.775791	+	0.447903i
$342$		0			0
$343$		0			0
$344$			236.168i			0.686535i
$345$		0			0
$346$	−114.956	−	199.109i	−0.332241	−	0.575459i
$347$	178.505	−	103.060i	0.514425	−	0.297003i	−0.220226	−	0.975449i	$-0.570679\pi$
$347$	178.505	−	103.060i	0.514425	−	0.297003i	0.734651	+	0.678446i	$0.237346\pi$
$348$		0			0
$349$	434.324			1.24448			0.622241	−	0.782826i	$-0.286222\pi$
$349$	434.324			1.24448			0.622241	+	0.782826i	$0.286222\pi$
$350$		0			0
$351$		0			0
$352$	34.3320	−	59.4648i	0.0975342	−	0.168934i
$353$	−160.595	+	92.7197i	−0.454944	+	0.262662i	−0.709916	−	0.704286i	$-0.751267\pi$
$353$	−160.595	+	92.7197i	−0.454944	+	0.262662i	0.254972	+	0.966948i	$0.417934\pi$
$354$		0			0
$355$	36.8340	−	63.7983i	0.103758	−	0.179714i
$356$			9.55012i			0.0268262i
$357$		0			0
$358$	315.498			0.881279
$359$	447.533	+	258.383i	1.24661	+	0.719731i	0.970432	−	0.241376i	$-0.0775987\pi$
$359$	447.533	+	258.383i	1.24661	+	0.719731i	0.276178	+	0.961106i	$0.410932\pi$
$360$		0			0
$361$	−19.5000	−	33.7750i	−0.0540166	−	0.0935595i
$362$	231.373	+	133.583i	0.639151	+	0.369014i
$363$		0			0
$364$		0			0
$365$			466.805i			1.27892i
$366$		0			0
$367$	58.7451	+	101.749i	0.160068	+	0.277246i	0.934893	−	0.354930i	$-0.115495\pi$
$367$	58.7451	+	101.749i	0.160068	+	0.277246i	−0.774825	+	0.632176i	$0.782162\pi$
$368$	−42.0480	+	24.2764i	−0.114261	+	0.0659685i
$369$		0			0
$370$	−326.154			−0.881498
$371$		0			0
$372$		0			0
$373$	201.332	−	348.717i	0.539764	−	0.934899i	−0.459152	−	0.888358i	$-0.651847\pi$
$373$	201.332	−	348.717i	0.539764	−	0.934899i	0.998916	−	0.0465413i	$-0.0148199\pi$
$374$	162.063	−	93.5673i	0.433324	−	0.250180i
$375$		0			0
$376$	−24.0000	+	41.5692i	−0.0638298	+	0.110556i
$377$		−	777.451i		−	2.06221i
$378$		0			0
$379$	398.834			1.05233			0.526166	−	0.850382i	$-0.323629\pi$
$379$	398.834			1.05233			0.526166	+	0.850382i	$0.323629\pi$
$380$	−210.240	−	121.382i	−0.553263	−	0.319426i
$381$		0			0
$382$	161.247	+	279.288i	0.422113	+	0.731121i
$383$	−645.019	−	372.402i	−1.68412	−	0.972329i	−0.958869	−	0.283849i	$-0.908389\pi$
$383$	−645.019	−	372.402i	−1.68412	−	0.972329i	−0.725255	−	0.688481i	$-0.758278\pi$
$384$		0			0
$385$		0			0
$386$		−	189.505i		−	0.490945i
$387$		0			0
$388$	−188.413	−	326.341i	−0.485601	−	0.841085i
$389$	−463.464	+	267.581i	−1.19142	+	0.687869i	−0.958630	−	0.284656i	$-0.908121\pi$
$389$	−463.464	+	267.581i	−1.19142	+	0.687869i	−0.232795	+	0.972526i	$0.574787\pi$
$390$		0			0
$391$	−132.324			−0.338425
$392$		0			0
$393$		0			0
$394$	133.332	−	230.938i	0.338406	−	0.586137i
$395$	−176.959	+	102.167i	−0.447997	+	0.258651i
$396$		0			0
$397$	47.1621	−	81.6871i	0.118796	−	0.205761i	−0.800495	−	0.599340i	$-0.795430\pi$
$397$	47.1621	−	81.6871i	0.118796	−	0.205761i	0.919291	+	0.393579i	$0.128763\pi$
$398$		−	144.949i		−	0.364192i
$399$		0			0
$400$	−47.3360			−0.118340
$401$	89.7138	+	51.7963i	0.223725	+	0.129168i	0.607674	−	0.794187i	$-0.292103\pi$
$401$	89.7138	+	51.7963i	0.223725	+	0.129168i	−0.383949	+	0.923354i	$0.625436\pi$
$402$		0			0
$403$	233.830	+	405.006i	0.580223	+	1.00498i
$404$	184.832	+	106.713i	0.457506	+	0.264141i
$405$		0			0
$406$		0			0
$407$		−	461.252i		−	1.13330i
$408$		0			0
$409$	4.87844	+	8.44971i	0.0119277	+	0.0206594i	0.871928	−	0.489635i	$-0.162870\pi$
$409$	4.87844	+	8.44971i	0.0119277	+	0.0206594i	−0.860000	+	0.510294i	$0.829537\pi$
$410$	450.696	−	260.210i	1.09926	−	0.634658i
$411$		0			0
$412$	−262.996			−0.638340
$413$		0			0
$414$		0			0
$415$	183.822	−	318.389i	0.442945	−	0.767203i
$416$	91.0378	−	52.5607i	0.218841	−	0.126348i
$417$		0			0
$418$	171.660	−	297.324i	0.410670	−	0.711301i
$419$			339.411i			0.810051i	0.914305	+	0.405025i	$0.132737\pi$
$419$			339.411i			0.810051i	−0.914305	+	0.405025i	$0.867263\pi$
$420$		0			0
$421$	−599.320			−1.42356			−0.711782	−	0.702401i	$-0.752111\pi$
$421$	−599.320			−1.42356			−0.711782	+	0.702401i	$0.752111\pi$
$422$	−103.493	−	59.7519i	−0.245245	−	0.141592i
$423$		0			0
$424$	132.996	+	230.356i	0.313670	+	0.543292i
$425$	−111.724	−	64.5039i	−0.262880	−	0.151774i
$426$		0			0
$427$		0			0
$428$		−	164.759i		−	0.384950i
$429$		0			0
$430$	358.332	+	620.649i	0.833330	+	1.44337i
$431$	615.725	−	355.489i	1.42860	−	0.824800i	0.431586	−	0.902072i	$-0.357954\pi$
$431$	615.725	−	355.489i	1.42860	−	0.824800i	0.997010	+	0.0772717i	$0.0246209\pi$
$432$		0			0
$433$	377.984			0.872943			0.436471	−	0.899718i	$-0.356228\pi$
$433$	377.984			0.872943			0.436471	+	0.899718i	$0.356228\pi$
$434$		0			0
$435$		0			0
$436$	33.8301	−	58.5954i	0.0775919	−	0.134393i
$437$	−210.240	+	121.382i	−0.481098	+	0.277762i
$438$		0			0
$439$	−264.073	+	457.388i	−0.601533	+	1.04189i	0.391056	+	0.920367i	$0.372110\pi$
$439$	−264.073	+	457.388i	−0.601533	+	1.04189i	−0.992589	+	0.121519i	$0.961223\pi$
$440$		−	208.365i		−	0.473556i
$441$		0			0
$442$	286.494			0.648177
$443$	−31.7345	−	18.3219i	−0.0716354	−	0.0413587i	0.463754	−	0.885964i	$-0.346502\pi$
$443$	−31.7345	−	18.3219i	−0.0716354	−	0.0413587i	−0.535390	+	0.844605i	$0.679835\pi$
$444$		0			0
$445$	14.4902	+	25.0977i	0.0325622	+	0.0563993i
$446$	−194.115	−	112.072i	−0.435235	−	0.251283i
$447$		0			0
$448$		0			0
$449$		−	397.612i		−	0.885550i	−0.896633	−	0.442775i	$-0.853994\pi$
$449$		−	397.612i		−	0.885550i	0.896633	−	0.442775i	$-0.146006\pi$
$450$		0			0
$451$	367.992	+	637.381i	0.815947	+	1.41326i
$452$	49.3964	−	28.5190i	0.109284	−	0.0630952i
$453$		0			0
$454$	144.000			0.317181
$455$		0			0
$456$		0			0
$457$	−172.162	+	298.193i	−0.376722	+	0.652502i	−0.990583	−	0.136912i	$-0.956282\pi$
$457$	−172.162	+	298.193i	−0.376722	+	0.652502i	0.613861	+	0.789414i	$0.289616\pi$
$458$	329.352	−	190.152i	0.719110	−	0.415178i
$459$		0			0
$460$	−73.6680	+	127.597i	−0.160148	+	0.277384i
$461$		−	370.936i		−	0.804634i	−0.915500	−	0.402317i	$-0.868205\pi$
$461$		−	370.936i		−	0.804634i	0.915500	−	0.402317i	$-0.131795\pi$
$462$		0			0
$463$	78.3320			0.169184			0.0845918	−	0.996416i	$-0.473041\pi$
$463$	78.3320			0.169184			0.0845918	+	0.996416i	$0.473041\pi$
$464$	−144.927	−	83.6734i	−0.312342	−	0.180331i
$465$		0			0
$466$	18.5791	+	32.1799i	0.0398692	+	0.0690556i
$467$	346.201	+	199.879i	0.741330	+	0.428007i	0.822553	−	0.568689i	$-0.192549\pi$
$467$	346.201	+	199.879i	0.741330	+	0.428007i	−0.0812229	+	0.996696i	$0.525883\pi$
$468$		0			0
$469$		0			0
$470$			145.658i			0.309912i
$471$		0			0
$472$	−82.3320	−	142.603i	−0.174432	−	0.302126i
$473$	−877.731	+	506.758i	−1.85567	+	1.07137i
$474$		0			0
$475$	−236.680			−0.498273
$476$		0			0
$477$		0			0
$478$	−65.2470	+	113.011i	−0.136500	+	0.236425i
$479$	−609.100	+	351.664i	−1.27161	+	0.734163i	−0.975290	−	0.220927i	$-0.929092\pi$
$479$	−609.100	+	351.664i	−1.27161	+	0.734163i	−0.296317	+	0.955090i	$0.595759\pi$
$480$		0			0
$481$	353.077	−	611.547i	0.734048	−	1.27141i
$482$		−	485.425i		−	1.00711i
$483$		0			0
$484$	52.6719			0.108826
$485$	−990.298	−	571.749i	−2.04185	−	1.17886i
$486$		0			0
$487$	41.2549	+	71.4556i	0.0847124	+	0.146726i	0.905269	−	0.424840i	$-0.139670\pi$
$487$	41.2549	+	71.4556i	0.0847124	+	0.146726i	−0.820556	+	0.571566i	$0.806336\pi$
$488$	−38.3786	−	22.1579i	−0.0786446	−	0.0454055i
$489$		0			0
$490$		0			0
$491$		−	184.203i		−	0.375158i	−0.982249	−	0.187579i	$-0.939936\pi$
$491$		−	184.203i		−	0.375158i	0.982249	−	0.187579i	$-0.0600641\pi$
$492$		0			0
$493$	−228.041	−	394.978i	−0.462557	−	0.801172i
$494$	455.189	−	262.803i	0.921435	−	0.531991i
$495$		0			0
$496$	100.664			0.202952
$497$		0			0
$498$		0			0
$499$	−376.405	+	651.953i	−0.754319	+	1.30652i	0.191393	+	0.981513i	$0.438699\pi$
$499$	−376.405	+	651.953i	−0.754319	+	1.30652i	−0.945712	+	0.325005i	$0.894634\pi$
$500$	138.401	−	79.9059i	0.276802	−	0.159812i
$501$		0			0
$502$	−252.000	+	436.477i	−0.501992	+	0.869476i
$503$		−	662.540i		−	1.31718i	−0.752504	−	0.658588i	$-0.771154\pi$
$503$		−	662.540i		−	1.31718i	0.752504	−	0.658588i	$-0.228846\pi$
$504$		0			0
$505$	647.652			1.28248
$506$	−180.449	−	104.182i	−0.356618	−	0.205894i
$507$		0			0
$508$	129.668	+	224.592i	0.255252	+	0.442109i
$509$	−821.958	−	474.557i	−1.61485	−	0.932333i	−0.988225	−	0.153010i	$-0.951103\pi$
$509$	−821.958	−	474.557i	−1.61485	−	0.932333i	−0.626623	−	0.779322i	$-0.715563\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	0.0441942i
$513$		0			0
$514$	180.122	+	311.980i	0.350431	+	0.606964i
$515$	−691.153	+	399.037i	−1.34204	+	0.774830i
$516$		0			0
$517$	−205.992			−0.398437
$518$		0			0
$519$		0			0
$520$	159.498	−	276.259i	0.306727	−	0.531267i
$521$	618.640	−	357.172i	1.18741	−	0.685551i	0.229692	−	0.973263i	$-0.426228\pi$
$521$	618.640	−	357.172i	1.18741	−	0.685551i	0.957717	+	0.287712i	$0.0928947\pi$
$522$		0			0
$523$	116.000	−	200.918i	0.221797	−	0.384164i	−0.733556	−	0.679629i	$-0.762141\pi$
$523$	116.000	−	200.918i	0.221797	−	0.384164i	0.955354	+	0.295464i	$0.0954743\pi$
$524$			296.035i			0.564952i
$525$		0			0
$526$	370.494			0.704361
$527$	237.591	+	137.173i	0.450837	+	0.260291i
$528$		0			0
$529$	−190.832	−	330.531i	−0.360741	−	0.624822i
$530$	699.027	+	403.583i	1.31892	+	0.761478i
$531$		0			0
$532$		0			0
$533$			1126.76i			2.11399i
$534$		0			0
$535$	−249.984	−	432.985i	−0.467260	−	0.809319i
$536$	−324.959	+	187.615i	−0.606267	+	0.350029i
$537$		0			0
$538$	132.405			0.246106
$539$		0			0
$540$		0			0
$541$	−82.8340	+	143.473i	−0.153113	+	0.265199i	−0.932370	−	0.361505i	$-0.882263\pi$
$541$	−82.8340	+	143.473i	−0.153113	+	0.265199i	0.779257	+	0.626704i	$0.215596\pi$
$542$	−1.42807	+	0.824494i	−0.00263481	+	0.00152121i
$543$		0			0
$544$	30.8340	−	53.4060i	0.0566801	−	0.0981729i
$545$		−	205.318i		−	0.376730i
$546$		0			0
$547$	295.676			0.540541			0.270270	−	0.962784i	$-0.412887\pi$
$547$	295.676			0.540541			0.270270	+	0.962784i	$0.412887\pi$
$548$	−133.294	−	76.9573i	−0.243237	−	0.140433i
$549$		0			0
$550$	−101.571	−	175.926i	−0.184675	−	0.319866i
$551$	−724.633	−	418.367i	−1.31512	−	0.759287i
$552$		0			0
$553$		0			0
$554$		−	45.2548i		−	0.0816874i
$555$		0			0
$556$	217.328	+	376.423i	0.390878	+	0.677020i
$557$	66.5477	−	38.4213i	0.119475	−	0.0689790i	−0.439071	−	0.898452i	$-0.644693\pi$
$557$	66.5477	−	38.4213i	0.119475	−	0.0689790i	0.558547	+	0.829473i	$0.311359\pi$
$558$		0			0
$559$	−1551.64			−2.77575
$560$		0			0
$561$		0			0
$562$	−117.915	+	204.235i	−0.209813	+	0.363407i
$563$	880.170	−	508.167i	1.56336	−	0.902605i	0.566444	−	0.824100i	$-0.308319\pi$
$563$	880.170	−	508.167i	1.56336	−	0.902605i	0.996914	−	0.0785049i	$-0.0250146\pi$
$564$		0			0
$565$	86.5425	−	149.896i	0.153173	−	0.265303i
$566$		−	23.1081i		−	0.0408270i
$567$		0			0
$568$	34.3320			0.0604437
$569$	507.952	+	293.266i	0.892710	+	0.515406i	0.874828	−	0.484434i	$-0.160974\pi$
$569$	507.952	+	293.266i	0.892710	+	0.515406i	0.0178822	+	0.999840i	$0.494308\pi$
$570$		0			0
$571$	−475.822	−	824.148i	−0.833314	−	1.44334i	−0.895396	−	0.445271i	$-0.853107\pi$
$571$	−475.822	−	824.148i	−0.833314	−	1.44334i	0.0620822	−	0.998071i	$-0.480226\pi$
$572$	390.689	+	225.564i	0.683022	+	0.394343i
$573$		0			0
$574$		0			0
$575$			143.643i			0.249815i
$576$		0			0
$577$	74.3360	+	128.754i	0.128832	+	0.223143i	0.923224	−	0.384262i	$-0.125544\pi$
$577$	74.3360	+	128.754i	0.128832	+	0.223143i	−0.794392	+	0.607405i	$0.792211\pi$
$578$	−208.400	+	120.320i	−0.360554	+	0.208166i
$579$		0			0
$580$	−507.822			−0.875555
$581$		0			0
$582$		0			0
$583$	−570.753	+	988.573i	−0.978993	+	1.69567i
$584$	−188.403	+	108.774i	−0.322607	+	0.186257i
$585$		0			0
$586$	−260.867	+	451.834i	−0.445165	+	0.771048i
$587$			332.564i			0.566548i	0.959039	+	0.283274i	$0.0914206\pi$
$587$			332.564i			0.566548i	−0.959039	+	0.283274i	$0.908579\pi$
$588$		0			0
$589$	503.320			0.854533
$590$	−432.737	−	249.841i	−0.733452	−	0.423459i
$591$		0			0
$592$	−76.0000	−	131.636i	−0.128378	−	0.222358i
$593$	−188.145	−	108.625i	−0.317276	−	0.183180i	0.332902	−	0.942962i	$-0.391972\pi$
$593$	−188.145	−	108.625i	−0.317276	−	0.183180i	−0.650178	+	0.759782i	$0.725306\pi$
$594$		0			0
$595$		0			0
$596$		−	323.849i		−	0.543371i
$597$		0			0
$598$	−159.498	−	276.259i	−0.266719	−	0.461971i
$599$	−149.111	+	86.0896i	−0.248934	+	0.143722i	−0.619276	−	0.785173i	$-0.712574\pi$
$599$	−149.111	+	86.0896i	−0.248934	+	0.143722i	0.370342	+	0.928895i	$0.379240\pi$
$600$		0			0
$601$	−418.000			−0.695507			−0.347754	−	0.937586i	$-0.613055\pi$
$601$	−418.000			−0.695507			−0.347754	+	0.937586i	$0.613055\pi$
$602$		0			0
$603$		0			0
$604$	−93.1660	+	161.368i	−0.154248	+	0.267166i
$605$	138.422	−	79.9178i	0.228796	−	0.132096i
$606$		0			0
$607$	−313.579	+	543.135i	−0.516605	+	0.894786i	0.483209	+	0.875505i	$0.339471\pi$
$607$	−313.579	+	543.135i	−0.516605	+	0.894786i	−0.999814	+	0.0192808i	$0.993862\pi$
$608$		−	113.137i		−	0.186081i
$609$		0			0
$610$	−134.478			−0.220456
$611$	−273.113	−	157.682i	−0.446994	−	0.258072i
$612$		0			0
$613$	139.664	+	241.905i	0.227837	+	0.394625i	0.957167	−	0.289537i	$-0.0935014\pi$
$613$	139.664	+	241.905i	0.227837	+	0.394625i	−0.729330	+	0.684162i	$0.760168\pi$
$614$	−235.964	−	136.234i	−0.384307	−	0.221880i
$615$		0			0
$616$		0			0
$617$			358.380i			0.580843i	0.956899	+	0.290422i	$0.0937955\pi$
$617$			358.380i			0.580843i	−0.956899	+	0.290422i	$0.906204\pi$
$618$		0			0
$619$	491.822	+	851.861i	0.794543	+	1.37619i	0.923129	+	0.384491i	$0.125623\pi$
$619$	491.822	+	851.861i	0.794543	+	1.37619i	−0.128586	+	0.991698i	$0.541044\pi$
$620$	264.545	−	152.735i	0.426685	−	0.246347i
$621$		0			0
$622$	185.652			0.298476
$623$		0			0
$624$		0			0
$625$	390.403	−	676.198i	0.624645	−	1.08192i
$626$	−53.0658	+	30.6376i	−0.0847697	+	0.0489418i
$627$		0			0
$628$	−184.996	+	320.423i	−0.294580	+	0.510227i
$629$		−	414.256i		−	0.658594i
$630$		0			0
$631$	−298.996			−0.473845			−0.236922	−	0.971529i	$-0.576139\pi$
$631$	−298.996			−0.473845			−0.236922	+	0.971529i	$0.576139\pi$
$632$	−82.4694	−	47.6137i	−0.130490	−	0.0753382i
$633$		0			0
$634$	177.996	+	308.298i	0.280751	+	0.486275i
$635$	681.534	+	393.484i	1.07328	+	0.619660i
$636$		0			0
$637$		0			0
$638$		−	718.169i		−	1.12566i
$639$		0			0
$640$	−34.3320	−	59.4648i	−0.0536438	−	0.0929138i
$641$	−270.163	+	155.979i	−0.421471	+	0.243336i	−0.695706	−	0.718326i	$-0.744909\pi$
$641$	−270.163	+	155.979i	−0.421471	+	0.243336i	0.274236	+	0.961663i	$0.411575\pi$
$642$		0			0
$643$	−604.000			−0.939347			−0.469673	−	0.882840i	$-0.655628\pi$
$643$	−604.000			−0.939347			−0.469673	+	0.882840i	$0.655628\pi$
$644$		0			0
$645$		0			0
$646$	154.170	−	267.030i	0.238653	−	0.413359i
$647$	155.538	−	89.7998i	0.240398	−	0.138794i	−0.374961	−	0.927040i	$-0.622344\pi$
$647$	155.538	−	89.7998i	0.240398	−	0.138794i	0.615360	+	0.788246i	$0.289011\pi$
$648$		0			0
$649$	353.328	−	611.982i	0.544419	−	0.942962i
$650$		−	311.001i		−	0.478463i
$651$		0			0
$652$	−173.992			−0.266859
$653$	−417.331	−	240.946i	−0.639097	−	0.368983i	0.145169	−	0.989407i	$-0.453627\pi$
$653$	−417.331	−	240.946i	−0.639097	−	0.368983i	−0.784267	+	0.620424i	$0.786961\pi$
$654$		0			0
$655$	449.166	+	777.978i	0.685750	+	1.18775i
$656$	210.041	+	121.267i	0.320185	+	0.184859i
$657$		0			0
$658$		0			0
$659$			877.408i			1.33142i	0.746209	+	0.665711i	$0.231872\pi$
$659$			877.408i			1.33142i	−0.746209	+	0.665711i	$0.768128\pi$
$660$		0			0
$661$	260.822	+	451.757i	0.394587	+	0.683445i	0.993048	−	0.117707i	$-0.0375543\pi$
$661$	260.822	+	451.757i	0.394587	+	0.683445i	−0.598461	+	0.801152i	$0.704221\pi$
$662$	−442.733	+	255.612i	−0.668781	+	0.386121i
$663$		0			0
$664$	171.336			0.258036
$665$		0			0
$666$		0			0
$667$	−253.911	+	439.787i	−0.380676	+	0.659351i
$668$	−104.921	+	60.5764i	−0.157068	+	0.0906832i
$669$		0			0
$670$	−569.328	+	986.105i	−0.849743	+	1.47180i
$671$		−	190.181i		−	0.283429i
$672$		0			0
$673$	−659.992			−0.980672			−0.490336	−	0.871534i	$-0.663126\pi$
$673$	−659.992			−0.980672			−0.490336	+	0.871534i	$0.663126\pi$
$674$	−365.995	−	211.308i	−0.543020	−	0.313513i
$675$		0			0
$676$	176.328	+	305.409i	0.260840	+	0.451789i
$677$	−880.121	−	508.138i	−1.30003	−	0.750573i	−0.319622	−	0.947545i	$-0.603556\pi$
$677$	−880.121	−	508.138i	−1.30003	−	0.750573i	−0.980409	+	0.196972i	$0.936889\pi$
$678$		0			0
$679$		0			0
$680$		−	187.135i		−	0.275198i
$681$		0			0
$682$	216.000	+	374.123i	0.316716	+	0.548567i
$683$	−203.615	+	117.557i	−0.298119	+	0.172119i	−0.641597	−	0.767042i	$-0.721728\pi$
$683$	−203.615	+	117.557i	−0.298119	+	0.172119i	0.343479	+	0.939160i	$0.388395\pi$
$684$		0			0
$685$	−467.061			−0.681841
$686$		0			0
$687$		0			0
$688$	−166.996	+	289.246i	−0.242727	+	0.420415i
$689$	−1513.46	+	873.795i	−2.19660	+	1.26821i
$690$		0			0
$691$	25.4902	−	44.1502i	0.0368888	−	0.0638933i	−0.846992	−	0.531606i	$-0.821589\pi$
$691$	25.4902	−	44.1502i	0.0368888	−	0.0638933i	0.883880	+	0.467713i	$0.154922\pi$
$692$		−	325.143i		−	0.469860i
$693$		0			0
$694$	291.498			0.420026
$695$	1142.28	+	659.493i	1.64356	+	0.948911i
$696$		0			0
$697$	330.498	+	572.439i	0.474172	+	0.821290i
$698$	531.936	+	307.114i	0.762086	+	0.439991i
$699$		0			0
$700$		0			0
$701$			141.530i			0.201898i	0.994892	+	0.100949i	$0.0321879\pi$
$701$			141.530i			0.201898i	−0.994892	+	0.100949i	$0.967812\pi$
$702$		0			0
$703$	−380.000	−	658.179i	−0.540541	−	0.936244i
$704$	84.0959	−	48.5528i	0.119454	−	0.0689671i
$705$		0			0
$706$	−262.251			−0.371460
$707$		0			0
$708$		0			0
$709$	27.7490	−	48.0627i	0.0391382	−	0.0677894i	−0.845793	−	0.533512i	$-0.820872\pi$
$709$	27.7490	−	48.0627i	0.0391382	−	0.0677894i	0.884931	+	0.465722i	$0.154205\pi$
$710$	90.2245	−	52.0911i	0.127077	−	0.0733678i
$711$		0			0
$712$	−6.75295	+	11.6965i	−0.00948448	+	0.0164276i
$713$		−	305.470i		−	0.428429i
$714$		0			0
$715$	1368.97			1.91465
$716$	386.405	+	223.091i	0.539671	+	0.311579i
$717$		0			0
$718$	365.409	+	632.907i	0.508926	+	0.881486i
$719$	873.843	+	504.514i	1.21536	+	0.701688i	0.963922	−	0.266185i	$-0.0857634\pi$
$719$	873.843	+	504.514i	1.21536	+	0.701688i	0.251438	+	0.967874i	$0.419097\pi$
$720$		0			0
$721$		0			0
$722$		−	55.1543i		−	0.0763910i
$723$		0			0
$724$	188.915	+	327.210i	0.260932	+	0.451948i
$725$	−428.765	+	247.547i	−0.591400	+	0.341445i
$726$		0			0
$727$	−365.182			−0.502313			−0.251157	−	0.967946i	$-0.580811\pi$
$727$	−365.182			−0.502313			−0.251157	+	0.967946i	$0.580811\pi$
$728$		0			0
$729$		0			0
$730$	−330.081	+	571.717i	−0.452166	+	0.783174i
$731$	−788.300	+	455.125i	−1.07839	+	0.622606i
$732$		0			0
$733$	176.539	−	305.774i	0.240844	−	0.417154i	−0.720111	−	0.693859i	$-0.755909\pi$
$733$	176.539	−	305.774i	0.240844	−	0.417154i	0.960955	+	0.276705i	$0.0892425\pi$
$734$			166.156i			0.226371i
$735$		0			0
$736$	−68.6640			−0.0932935
$737$	−1394.56	−	805.151i	−1.89222	−	1.09247i
$738$		0			0
$739$	−164.842	−	285.514i	−0.223061	−	0.386352i	0.732675	−	0.680579i	$-0.238271\pi$
$739$	−164.842	−	285.514i	−0.223061	−	0.386352i	−0.955736	+	0.294226i	$0.904938\pi$
$740$	−399.456	−	230.626i	−0.539805	−	0.311657i
$741$		0			0
$742$		0			0
$743$		−	112.061i		−	0.150822i	−0.997153	−	0.0754112i	$-0.975973\pi$
$743$		−	112.061i		−	0.150822i	0.997153	−	0.0754112i	$-0.0240270\pi$
$744$		0			0
$745$	−491.369	−	851.075i	−0.659555	−	1.14238i
$746$	493.161	−	284.726i	0.661073	−	0.381671i
$747$		0			0
$748$	264.648			0.353808
$749$		0			0
$750$		0			0
$751$	72.4131	−	125.423i	0.0964222	−	0.167008i	−0.813779	−	0.581174i	$-0.802593\pi$
$751$	72.4131	−	125.423i	0.0964222	−	0.167008i	0.910201	+	0.414166i	$0.135927\pi$
$752$	−58.7878	+	33.9411i	−0.0781752	+	0.0451345i
$753$		0			0
$754$	549.741	−	952.180i	0.729100	−	1.26284i
$755$			565.434i			0.748919i
$756$		0			0
$757$	78.1699			0.103263			0.0516314	−	0.998666i	$-0.483558\pi$
$757$	78.1699			0.103263			0.0516314	+	0.998666i	$0.483558\pi$
$758$	488.470	+	282.018i	0.644419	+	0.372056i
$759$		0			0
$760$	−171.660	−	297.324i	−0.225869	−	0.391216i
$761$	−1269.16	−	732.752i	−1.66776	−	0.962880i	−0.968843	−	0.247676i	$-0.920333\pi$
$761$	−1269.16	−	732.752i	−1.66776	−	0.962880i	−0.698915	−	0.715205i	$-0.746333\pi$
$762$		0			0
$763$		0			0
$764$			456.076i			0.596957i
$765$		0			0
$766$	−526.656	−	912.195i	−0.687541	−	1.19086i
$767$	936.915	−	540.928i	1.22153	−	0.705252i
$768$		0			0
$769$	729.320			0.948401			0.474200	−	0.880417i	$-0.342737\pi$
$769$	729.320			0.948401			0.474200	+	0.880417i	$0.342737\pi$
$770$		0			0
$771$		0			0
$772$	134.000	−	232.095i	0.173575	−	0.300641i
$773$	−376.339	+	217.280i	−0.486855	+	0.281086i	−0.723269	−	0.690566i	$-0.757361\pi$
$773$	−376.339	+	217.280i	−0.486855	+	0.281086i	0.236414	+	0.971653i	$0.424028\pi$
$774$		0			0
$775$	148.907	−	257.915i	0.192138	−	0.332793i
$776$		−	532.913i		−	0.686743i
$777$		0			0
$778$	−756.834			−0.972794
$779$	1050.21	+	606.337i	1.34815	+	0.778353i
$780$		0			0
$781$	73.6680	+	127.597i	0.0943252	+	0.163376i
$782$	−162.063	−	93.5673i	−0.207242	−	0.119651i
$783$		0			0
$784$		0			0
$785$			1122.76i			1.43027i
$786$		0			0
$787$	7.67585	+	13.2950i	0.00975331	+	0.0168932i	0.870861	−	0.491530i	$-0.163562\pi$
$787$	7.67585	+	13.2950i	0.00975331	+	0.0168932i	−0.861108	+	0.508423i	$0.830229\pi$
$788$	326.595	−	188.560i	0.414461	−	0.239289i
$789$		0			0
$790$	−288.972			−0.365788
$791$		0			0
$792$		0			0
$793$	145.579	−	252.150i	0.183580	−	0.317970i
$794$	115.523	−	66.6972i	0.145495	−	0.0840016i
$795$		0			0
$796$	102.494	−	177.525i	0.128761	−	0.223021i
$797$		−	1043.48i		−	1.30927i	−0.755947	−	0.654633i	$-0.772823\pi$
$797$		−	1043.48i		−	1.30927i	0.755947	−	0.654633i	$-0.227177\pi$
$798$		0			0
$799$	−185.004			−0.231544
$800$	−57.9745	−	33.4716i	−0.0724681	−	0.0418395i
$801$		0			0
$802$	73.2510	+	126.874i	0.0913354	+	0.158198i
$803$	−808.530	−	466.805i	−1.00689	−	0.581326i
$804$		0			0
$805$		0			0
$806$			661.371i			0.820560i
$807$		0			0
$808$	150.915	+	261.392i	0.186776	+	0.323506i
$809$	901.804	−	520.657i	1.11471	−	0.643581i	0.174668	−	0.984627i	$-0.444115\pi$
$809$	901.804	−	520.657i	1.11471	−	0.643581i	0.940046	+	0.341046i	$0.110781\pi$
$810$		0			0
$811$	502.316			0.619379			0.309689	−	0.950838i	$-0.399775\pi$
$811$	502.316			0.619379			0.309689	+	0.950838i	$0.399775\pi$
$812$		0			0
$813$		0			0
$814$	326.154	−	564.916i	0.400681	−	0.694000i
$815$	−457.251	+	263.994i	−0.561044	+	0.323919i
$816$		0			0
$817$	−834.980	+	1446.23i	−1.02201	+	1.77017i
$818$			13.7983i			0.0168684i
$819$		0			0
$820$	735.984			0.897542
$821$	20.0170	+	11.5568i	0.0243813	+	0.0140765i	0.512141	−	0.858901i	$-0.328852\pi$
$821$	20.0170	+	11.5568i	0.0243813	+	0.0140765i	−0.487760	+	0.872978i	$0.662186\pi$
$822$		0			0
$823$	300.332	+	520.190i	0.364923	+	0.632066i	0.988764	−	0.149486i	$-0.0477618\pi$
$823$	300.332	+	520.190i	0.364923	+	0.632066i	−0.623840	+	0.781552i	$0.714428\pi$
$824$	−322.103	−	185.966i	−0.390902	−	0.225687i
$825$		0			0
$826$		0			0
$827$		−	1309.21i		−	1.58308i	−0.611118	−	0.791540i	$-0.709280\pi$
$827$		−	1309.21i		−	1.58308i	0.611118	−	0.791540i	$-0.290720\pi$
$828$		0			0
$829$	310.959	+	538.598i	0.375102	+	0.649696i	0.990342	−	0.138644i	$-0.0442744\pi$
$829$	310.959	+	538.598i	0.375102	+	0.649696i	−0.615240	+	0.788340i	$0.710941\pi$
$830$	450.271	−	259.964i	0.542495	−	0.313209i
$831$		0			0
$832$	148.664			0.178683
$833$		0			0
$834$		0			0
$835$	−183.822	+	318.389i	−0.220146	+	0.381305i
$836$	420.480	−	242.764i	0.502966	−	0.290388i
$837$		0			0
$838$	−240.000	+	415.692i	−0.286396	+	0.496053i
$839$			1190.30i			1.41871i	0.704851	+	0.709355i	$0.251014\pi$
$839$			1190.30i			1.41871i	−0.704851	+	0.709355i	$0.748986\pi$
$840$		0			0
$841$	−909.308			−1.08122
$842$	−734.014	−	423.783i	−0.871751	−	0.503306i
$843$		0			0
$844$	−84.5020	−	146.362i	−0.100121	−	0.173414i
$845$	926.780	+	535.076i	1.09678	+	0.633227i
$846$		0			0
$847$		0			0
$848$			376.170i			0.443596i
$849$		0			0
$850$	−91.2223	−	158.002i	−0.107320	−	0.185884i
$851$	−399.456	+	230.626i	−0.469396	+	0.271006i
$852$		0			0
$853$	137.012			0.160623			0.0803117	−	0.996770i	$-0.474408\pi$
$853$	137.012			0.160623			0.0803117	+	0.996770i	$0.474408\pi$
$854$		0			0
$855$		0			0
$856$	116.502	−	201.787i	0.136100	−	0.235733i
$857$	403.690	−	233.071i	0.471050	−	0.271961i	−0.245629	−	0.969364i	$-0.578994\pi$
$857$	403.690	−	233.071i	0.471050	−	0.271961i	0.716679	+	0.697403i	$0.245661\pi$
$858$		0			0
$859$	−11.9921	+	20.7710i	−0.0139606	+	0.0241804i	−0.872921	−	0.487861i	$-0.837777\pi$
$859$	−11.9921	+	20.7710i	−0.0139606	+	0.0241804i	0.858961	+	0.512041i	$0.171111\pi$
$860$			1013.52i			1.17851i
$861$		0			0
$862$	1005.47			1.16644
$863$	−0.0992493	−	0.0573016i	−0.000115005	−	6.63982e-5i	0.499942	−	0.866059i	$-0.333354\pi$
$863$	−0.0992493	−	0.0573016i	−0.000115005	−	6.63982e-5i	−0.500058	+	0.865992i	$0.666688\pi$
$864$		0			0
$865$	−493.332	−	854.476i	−0.570326	−	0.987834i
$866$	462.934	+	267.275i	0.534566	+	0.308632i
$867$		0			0
$868$		0			0
$869$		−	408.669i		−	0.470275i
$870$		0			0
$871$	−1232.65	−	2135.01i	−1.41521	−	2.45122i
$872$	82.8664	−	47.8429i	0.0950302	−	0.0548657i
$873$		0			0
$874$	−343.320			−0.392815
$875$		0			0
$876$		0			0
$877$	−498.652	+	863.691i	−0.568589	+	0.984824i	0.428117	+	0.903723i	$0.359177\pi$
$877$	−498.652	+	863.691i	−0.568589	+	0.984824i	−0.996706	+	0.0811012i	$0.974156\pi$
$878$	−646.845	+	373.456i	−0.736725	+	0.425348i
$879$		0			0
$880$	147.336	−	255.193i	0.167427	−	0.289992i
$881$			935.649i			1.06203i	0.847362	+	0.531015i	$0.178189\pi$
$881$			935.649i			1.06203i	−0.847362	+	0.531015i	$0.821811\pi$
$882$		0			0
$883$	−1549.47			−1.75478			−0.877392	−	0.479774i	$-0.840719\pi$
$883$	−1549.47			−1.75478			−0.877392	+	0.479774i	$0.840719\pi$
$884$	350.882	+	202.582i	0.396926	+	0.229165i
$885$		0			0
$886$	−25.9111	−	44.8793i	−0.0292450	−	0.0506539i
$887$	774.654	+	447.246i	0.873341	+	0.504224i	0.868457	−	0.495764i	$-0.165112\pi$
$887$	774.654	+	447.246i	0.873341	+	0.504224i	0.00488401	+	0.999988i	$0.498445\pi$
$888$		0			0
$889$		0			0
$890$			40.9844i			0.0460498i
$891$		0			0
$892$	−158.494	−	274.520i	−0.177684	−	0.307758i
$893$	−293.939	+	169.706i	−0.329159	+	0.190040i
$894$		0			0
$895$	1353.96			1.51281
$896$		0			0
$897$		0			0
$898$	281.154	−	486.973i	0.313089	−	0.542287i
$899$	911.806	−	526.431i	1.01424	−	0.585574i
$900$		0			0
$901$	−512.600	+	887.849i	−0.568923	+	0.985404i
$902$			1040.84i			1.15392i
$903$		0			0
$904$	80.6640			0.0892301
$905$	992.937	+	573.272i	1.09717	+	0.633450i
$906$		0			0
$907$	67.9190	+	117.639i	0.0748831	+	0.129701i	0.901035	−	0.433746i	$-0.142808\pi$
$907$	67.9190	+	117.639i	0.0748831	+	0.129701i	−0.826152	+	0.563447i	$0.809475\pi$
$908$	176.363	+	101.823i	0.194233	+	0.112140i
$909$		0			0
$910$		0			0
$911$		−	1242.01i		−	1.36335i	−0.731655	−	0.681675i	$-0.761252\pi$
$911$		−	1242.01i		−	1.36335i	0.731655	−	0.681675i	$-0.238748\pi$
$912$		0			0
$913$	367.644	+	636.779i	0.402677	+	0.697458i
$914$	−421.709	+	243.474i	−0.461389	+	0.266383i
$915$		0			0
$916$	537.830			0.587151
$917$		0			0
$918$		0			0
$919$	194.081	−	336.158i	0.211187	−	0.365787i	−0.740899	−	0.671616i	$-0.765600\pi$
$919$	194.081	−	336.158i	0.211187	−	0.365787i	0.952086	+	0.305829i	$0.0989337\pi$
$920$	−180.449	+	104.182i	−0.196140	+	0.113242i
$921$		0			0
$922$	262.292	−	454.302i	0.284481	−	0.492736i
$923$			225.564i			0.244382i
$924$		0			0
$925$	−449.692			−0.486153
$926$	95.9367	+	55.3891i	0.103603	+	0.0598154i
$927$		0			0
$928$	−118.332	−	204.957i	−0.127513	−	0.220859i
$929$	538.403	+	310.847i	0.579551	+	0.334604i	0.760955	−	0.648805i	$-0.224731\pi$
$929$	538.403	+	310.847i	0.579551	+	0.334604i	−0.181404	+	0.983409i	$0.558064\pi$
$930$		0			0
$931$		0			0
$932$			52.5495i			0.0563836i
$933$		0			0
$934$	282.672	+	489.602i	0.302647	+	0.524199i
$935$	695.495	−	401.544i	0.743845	−	0.429459i
$936$		0			0
$937$	1262.00			1.34685			0.673426	−	0.739255i	$-0.264822\pi$
$937$	1262.00			1.34685			0.673426	+	0.739255i	$0.264822\pi$
$938$		0			0
$939$		0			0
$940$	−102.996	+	178.394i	−0.109570	+	0.189781i
$941$	582.324	−	336.205i	0.618835	−	0.357285i	−0.157580	−	0.987506i	$-0.550369\pi$
$941$	582.324	−	336.205i	0.618835	−	0.357285i	0.776415	+	0.630222i	$0.217036\pi$
$942$		0			0
$943$	367.992	−	637.381i	0.390236	−	0.675908i
$944$		−	232.870i		−	0.246684i
$945$		0			0
$946$	−1433.33			−1.51515
$947$	−1004.37	−	579.874i	−1.06058	−	0.612327i	−0.134989	−	0.990847i	$-0.543100\pi$
$947$	−1004.37	−	579.874i	−1.06058	−	0.612327i	−0.925593	+	0.378520i	$0.876433\pi$
$948$		0			0
$949$	−714.656	−	1237.82i	−0.753062	−	1.30434i
$950$	−289.872	−	167.358i	−0.305129	−	0.176166i
$951$		0			0
$952$		0			0
$953$		−	163.104i		−	0.171148i	−0.996332	−	0.0855740i	$-0.972728\pi$
$953$		−	163.104i		−	0.171148i	0.996332	−	0.0855740i	$-0.0272724\pi$
$954$		0			0
$955$	691.992	+	1198.57i	0.724599	+	1.25504i
$956$	−159.822	+	92.2733i	−0.167178	+	0.0965201i
$957$		0			0
$958$	−994.656			−1.03826
$959$		0			0
$960$		0			0
$961$	163.836	−	283.772i	0.170485	−	0.295288i
$962$	864.859	−	499.326i	0.899022	−	0.519050i
$963$		0			0
$964$	343.247	−	594.521i	0.356065	−	0.616723i
$965$		−	813.260i		−	0.842756i
$966$		0			0
$967$	887.012			0.917282			0.458641	−	0.888622i	$-0.348336\pi$
$967$	887.012			0.917282			0.458641	+	0.888622i	$0.348336\pi$
$968$	64.5097	+	37.2447i	0.0666422	+	0.0384759i
$969$		0			0
$970$	−808.575	−	1400.49i	−0.833583	−	1.44381i
$971$	1226.57	+	708.160i	1.26320	+	0.729310i	0.973693	−	0.227865i	$-0.0731743\pi$
$971$	1226.57	+	708.160i	1.26320	+	0.729310i	0.289510	+	0.957175i	$0.406508\pi$
$972$		0			0
$973$		0			0
$974$			116.687i			0.119801i
$975$		0			0
$976$	−31.3360	−	54.2755i	−0.0321065	−	0.0556101i
$977$	293.627	−	169.525i	0.300539	−	0.173516i	−0.342146	−	0.939647i	$-0.611154\pi$
$977$	293.627	−	169.525i	0.300539	−	0.173516i	0.642685	+	0.766131i	$0.277820\pi$
$978$		0			0
$979$	−57.9606			−0.0592039
$980$		0			0
$981$		0			0
$982$	130.251	−	225.601i	0.132638	−	0.229737i
$983$	−422.523	+	243.943i	−0.429830	+	0.248162i	−0.699274	−	0.714854i	$-0.746493\pi$
$983$	−422.523	+	243.943i	−0.429830	+	0.248162i	0.269444	+	0.963016i	$0.413160\pi$
$984$		0			0
$985$	572.195	−	991.070i	0.580908	−	1.00616i
$986$		−	644.996i		−	0.654154i
$987$		0			0
$988$	743.320			0.752348
$989$	877.731	+	506.758i	0.887493	+	0.512394i
$990$		0			0
$991$	468.737	+	811.877i	0.472994	+	0.819250i	0.999522	−	0.0309078i	$-0.00983984\pi$
$991$	468.737	+	811.877i	0.472994	+	0.819250i	−0.526528	+	0.850158i	$0.676507\pi$
$992$	123.288	+	71.1802i	0.124282	+	0.0717543i
$993$		0			0
$994$		0			0
$995$		−	622.047i		−	0.625173i
$996$		0			0
$997$	−230.506	−	399.248i	−0.231200	−	0.400449i	0.726962	−	0.686678i	$-0.240932\pi$
$997$	−230.506	−	399.248i	−0.231200	−	0.400449i	−0.958161	+	0.286229i	$0.907598\pi$
$998$	−922.001	+	532.317i	−0.923848	+	0.533384i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	882.3.s.e.863.4		8
3.2	odd	2	inner	882.3.s.e.863.1		8
7.2	even	3		126.3.b.a.71.1	✓	4
7.3	odd	6		882.3.s.i.557.2		8
7.4	even	3	inner	882.3.s.e.557.1		8
7.5	odd	6		882.3.b.f.197.2		4
7.6	odd	2		882.3.s.i.863.3		8
21.2	odd	6		126.3.b.a.71.4	yes	4
21.5	even	6		882.3.b.f.197.3		4
21.11	odd	6	inner	882.3.s.e.557.4		8
21.17	even	6		882.3.s.i.557.3		8
21.20	even	2		882.3.s.i.863.2		8
28.23	odd	6		1008.3.d.a.449.2		4
35.2	odd	12		3150.3.c.b.449.6		8
35.9	even	6		3150.3.e.e.701.4		4
35.23	odd	12		3150.3.c.b.449.4		8
56.37	even	6		4032.3.d.i.449.3		4
56.51	odd	6		4032.3.d.j.449.3		4
63.2	odd	6		1134.3.q.c.701.3		8
63.16	even	3		1134.3.q.c.701.2		8
63.23	odd	6		1134.3.q.c.1079.2		8
63.58	even	3		1134.3.q.c.1079.3		8
84.23	even	6		1008.3.d.a.449.3		4
105.2	even	12		3150.3.c.b.449.1		8
105.23	even	12		3150.3.c.b.449.7		8
105.44	odd	6		3150.3.e.e.701.2		4
168.107	even	6		4032.3.d.j.449.2		4
168.149	odd	6		4032.3.d.i.449.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.3.b.a.71.1	✓	4	7.2	even	3
126.3.b.a.71.4	yes	4	21.2	odd	6
882.3.b.f.197.2		4	7.5	odd	6
882.3.b.f.197.3		4	21.5	even	6
882.3.s.e.557.1		8	7.4	even	3	inner
882.3.s.e.557.4		8	21.11	odd	6	inner
882.3.s.e.863.1		8	3.2	odd	2	inner
882.3.s.e.863.4		8	1.1	even	1	trivial
882.3.s.i.557.2		8	7.3	odd	6
882.3.s.i.557.3		8	21.17	even	6
882.3.s.i.863.2		8	21.20	even	2
882.3.s.i.863.3		8	7.6	odd	2
1008.3.d.a.449.2		4	28.23	odd	6
1008.3.d.a.449.3		4	84.23	even	6
1134.3.q.c.701.2		8	63.16	even	3
1134.3.q.c.701.3		8	63.2	odd	6
1134.3.q.c.1079.2		8	63.23	odd	6
1134.3.q.c.1079.3		8	63.58	even	3
3150.3.c.b.449.1		8	105.2	even	12
3150.3.c.b.449.4		8	35.23	odd	12
3150.3.c.b.449.6		8	35.2	odd	12
3150.3.c.b.449.7		8	105.23	even	12
3150.3.e.e.701.2		4	105.44	odd	6
3150.3.e.e.701.4		4	35.9	even	6
4032.3.d.i.449.2		4	168.149	odd	6
4032.3.d.i.449.3		4	56.37	even	6
4032.3.d.j.449.2		4	168.107	even	6
4032.3.d.j.449.3		4	56.51	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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)

\(f(q)\)	\(=\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(5.25600 + 3.03455i) q^{5} +2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 + 0.707107i) q^{2} +(1.00000 + 1.73205i) q^{4} +(5.25600 + 3.03455i) q^{5} +2.82843i q^{8} +(4.29150 + 7.43310i) q^{10} +(-10.5120 + 6.06910i) q^{11} -18.5830 q^{13} +(-2.00000 + 3.46410i) q^{16} +(-9.44094 + 5.45073i) q^{17} +(-10.0000 + 17.3205i) q^{19} +12.1382i q^{20} -17.1660 q^{22} +(10.5120 + 6.06910i) q^{23} +(5.91699 + 10.2485i) q^{25} +(-22.7594 - 13.1402i) q^{26} +41.8367i q^{29} +(-12.5830 - 21.7944i) q^{31} +(-4.89898 + 2.82843i) q^{32} -15.4170 q^{34} +(-19.0000 + 32.9090i) q^{37} +(-24.4949 + 14.1421i) q^{38} +(-8.58301 + 14.8662i) q^{40} -60.6337i q^{41} +83.4980 q^{43} +(-21.0240 - 12.1382i) q^{44} +(8.58301 + 14.8662i) q^{46} +(14.6969 + 8.48528i) q^{47} +16.7358i q^{50} +(-18.5830 - 32.1867i) q^{52} +(81.4431 - 47.0212i) q^{53} -73.6680 q^{55} +(-29.5830 + 51.2393i) q^{58} +(-50.4179 + 29.1088i) q^{59} +(-7.83399 + 13.5689i) q^{61} -35.5901i q^{62} -8.00000 q^{64} +(-97.6722 - 56.3911i) q^{65} +(66.3320 + 114.890i) q^{67} +(-18.8819 - 10.9015i) q^{68} -12.1382i q^{71} +(38.4575 + 66.6104i) q^{73} +(-46.5403 + 26.8701i) q^{74} -40.0000 q^{76} +(-16.8340 + 29.1573i) q^{79} +(-21.0240 + 12.1382i) q^{80} +(42.8745 - 74.2608i) q^{82} -60.5764i q^{83} -66.1621 q^{85} +(102.264 + 59.0420i) q^{86} +(-17.1660 - 29.7324i) q^{88} +(4.13532 + 2.38753i) q^{89} +24.2764i q^{92} +(12.0000 + 20.7846i) q^{94} +(-105.120 + 60.6910i) q^{95} -188.413 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} - 8 q^{10} - 64 q^{13} - 16 q^{16} - 80 q^{19} + 32 q^{22} + 132 q^{25} - 16 q^{31} - 208 q^{34} - 152 q^{37} + 16 q^{40} + 160 q^{43} - 16 q^{46} - 64 q^{52} - 928 q^{55} - 152 q^{58} - 232 q^{61} - 64 q^{64} + 192 q^{67} + 96 q^{73} - 320 q^{76} - 304 q^{79} + 216 q^{82} + 656 q^{85} + 32 q^{88} + 96 q^{94} - 576 q^{97}+O(q^{100}) \) 8 * q + 8 * q^4 - 8 * q^10 - 64 * q^13 - 16 * q^16 - 80 * q^19 + 32 * q^22 + 132 * q^25 - 16 * q^31 - 208 * q^34 - 152 * q^37 + 16 * q^40 + 160 * q^43 - 16 * q^46 - 64 * q^52 - 928 * q^55 - 152 * q^58 - 232 * q^61 - 64 * q^64 + 192 * q^67 + 96 * q^73 - 320 * q^76 - 304 * q^79 + 216 * q^82 + 656 * q^85 + 32 * q^88 + 96 * q^94 - 576 * q^97

Introduction

L-functions

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