LMFDB - Embedded newform 882.3.s.g.557.4

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:	$\Q(\zeta_{24})$
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			557.4
Root			$0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	882.557
Dual form			882.3.s.g.863.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} -2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} -2.82843i q^{8} +(2.82843 - 4.89898i) q^{10} +(2.44949 + 1.41421i) q^{11} +12.7279 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-11.3137 - 19.5959i) q^{19} -8.00000i q^{20} +4.00000 q^{22} +(31.8434 - 18.3848i) q^{23} +(-4.50000 + 7.79423i) q^{25} +(15.5885 - 9.00000i) q^{26} +32.5269i q^{29} +(25.4558 - 44.0908i) q^{31} +(-4.89898 - 2.82843i) q^{32} -5.65685 q^{34} +(16.0000 + 27.7128i) q^{37} +(-27.7128 - 16.0000i) q^{38} +(-5.65685 - 9.79796i) q^{40} -38.0000i q^{41} +20.0000 q^{43} +(4.89898 - 2.82843i) q^{44} +(26.0000 - 45.0333i) q^{46} +(-17.3205 + 10.0000i) q^{47} +12.7279i q^{50} +(12.7279 - 22.0454i) q^{52} +(-82.0579 - 47.3762i) q^{53} +11.3137 q^{55} +(23.0000 + 39.8372i) q^{58} +(-3.46410 - 2.00000i) q^{59} +(-41.7193 - 72.2599i) q^{61} -72.0000i q^{62} -8.00000 q^{64} +(44.0908 - 25.4558i) q^{65} +(24.0000 - 41.5692i) q^{67} +(-6.92820 + 4.00000i) q^{68} +76.3675i q^{71} +(60.1041 - 104.103i) q^{73} +(39.1918 + 22.6274i) q^{74} -45.2548 q^{76} +(74.0000 + 128.172i) q^{79} +(-13.8564 - 8.00000i) q^{80} +(-26.8701 - 46.5403i) q^{82} +80.0000i q^{83} -16.0000 q^{85} +(24.4949 - 14.1421i) q^{86} +(4.00000 - 6.92820i) q^{88} +(-91.7987 + 53.0000i) q^{89} -73.5391i q^{92} +(-14.1421 + 24.4949i) q^{94} +(-78.3837 - 45.2548i) q^{95} +154.149 q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{4}+O(q^{10}) $ 8 * q + 8 * q^4	$ 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} - 36 q^{25} + 128 q^{37} + 160 q^{43} + 208 q^{46} + 184 q^{58} - 64 q^{64} + 192 q^{67} + 592 q^{79} - 128 q^{85} + 32 q^{88}+O(q^{100}) $ 8 * q + 8 * q^4 - 16 * q^16 + 32 * q^22 - 36 * q^25 + 128 * q^37 + 160 * q^43 + 208 * q^46 + 184 * q^58 - 64 * q^64 + 192 * q^67 + 592 * q^79 - 128 * 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
$5$	3.46410	−	2.00000i	0.692820	−	0.400000i	−0.111847	−	0.993725i	$-0.535677\pi$
$5$	3.46410	−	2.00000i	0.692820	−	0.400000i	0.804668	+	0.593725i	$0.202343\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	2.82843i		−	0.353553i
$9$		0			0
$10$	2.82843	−	4.89898i	0.282843	−	0.489898i
$11$	2.44949	+	1.41421i	0.222681	+	0.128565i	0.607191	−	0.794556i	$-0.292296\pi$
$11$	2.44949	+	1.41421i	0.222681	+	0.128565i	−0.384510	+	0.923121i	$0.625630\pi$
$12$		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
$17$	−3.46410	−	2.00000i	−0.203771	−	0.117647i	0.394642	−	0.918835i	$-0.370868\pi$
$17$	−3.46410	−	2.00000i	−0.203771	−	0.117647i	−0.598413	+	0.801188i	$0.704202\pi$
$18$		0			0
$19$	−11.3137	−	19.5959i	−0.595458	−	1.03136i	−0.993482	−	0.113989i	$-0.963637\pi$
$19$	−11.3137	−	19.5959i	−0.595458	−	1.03136i	0.398024	−	0.917375i	$-0.369696\pi$
$20$		−	8.00000i		−	0.400000i
$21$		0			0
$22$	4.00000			0.181818
$23$	31.8434	−	18.3848i	1.38449	−	0.799338i	0.391806	−	0.920048i	$-0.371850\pi$
$23$	31.8434	−	18.3848i	1.38449	−	0.799338i	0.992688	+	0.120710i	$0.0385170\pi$
$24$		0			0
$25$	−4.50000	+	7.79423i	−0.180000	+	0.311769i
$26$	15.5885	−	9.00000i	0.599556	−	0.346154i
$27$		0			0
$28$		0			0
$29$			32.5269i			1.12162i	0.827945	+	0.560809i	$0.189510\pi$
$29$			32.5269i			1.12162i	−0.827945	+	0.560809i	$0.810490\pi$
$30$		0			0
$31$	25.4558	−	44.0908i	0.821156	−	1.42228i	−0.0836655	−	0.996494i	$-0.526663\pi$
$31$	25.4558	−	44.0908i	0.821156	−	1.42228i	0.904822	−	0.425790i	$-0.140004\pi$
$32$	−4.89898	−	2.82843i	−0.153093	−	0.0883883i
$33$		0			0
$34$	−5.65685			−0.166378
$35$		0			0
$36$		0			0
$37$	16.0000	+	27.7128i	0.432432	+	0.748995i	0.997082	−	0.0763357i	$-0.0243221\pi$
$37$	16.0000	+	27.7128i	0.432432	+	0.748995i	−0.564650	+	0.825331i	$0.690989\pi$
$38$	−27.7128	−	16.0000i	−0.729285	−	0.421053i
$39$		0			0
$40$	−5.65685	−	9.79796i	−0.141421	−	0.244949i
$41$		−	38.0000i		−	0.926829i	−0.886142	−	0.463415i	$-0.846624\pi$
$41$		−	38.0000i		−	0.926829i	0.886142	−	0.463415i	$-0.153376\pi$
$42$		0			0
$43$	20.0000			0.465116			0.232558	−	0.972582i	$-0.425290\pi$
$43$	20.0000			0.465116			0.232558	+	0.972582i	$0.425290\pi$
$44$	4.89898	−	2.82843i	0.111340	−	0.0642824i
$45$		0			0
$46$	26.0000	−	45.0333i	0.565217	−	0.978985i
$47$	−17.3205	+	10.0000i	−0.368521	+	0.212766i	−0.672812	−	0.739813i	$-0.734914\pi$
$47$	−17.3205	+	10.0000i	−0.368521	+	0.212766i	0.304291	+	0.952579i	$0.401581\pi$
$48$		0			0
$49$		0			0
$50$			12.7279i			0.254558i
$51$		0			0
$52$	12.7279	−	22.0454i	0.244768	−	0.423950i
$53$	−82.0579	−	47.3762i	−1.54826	−	0.893890i	−0.998275	−	0.0587170i	$-0.981299\pi$
$53$	−82.0579	−	47.3762i	−1.54826	−	0.893890i	−0.549988	−	0.835173i	$-0.685368\pi$
$54$		0			0
$55$	11.3137			0.205704
$56$		0			0
$57$		0			0
$58$	23.0000	+	39.8372i	0.396552	+	0.686848i
$59$	−3.46410	−	2.00000i	−0.0587136	−	0.0338983i	0.470356	−	0.882477i	$-0.344126\pi$
$59$	−3.46410	−	2.00000i	−0.0587136	−	0.0338983i	−0.529069	+	0.848579i	$0.677459\pi$
$60$		0			0
$61$	−41.7193	−	72.2599i	−0.683923	−	1.18459i	−0.973774	−	0.227518i	$-0.926939\pi$
$61$	−41.7193	−	72.2599i	−0.683923	−	1.18459i	0.289851	−	0.957072i	$-0.406394\pi$
$62$		−	72.0000i		−	1.16129i
$63$		0			0
$64$	−8.00000			−0.125000
$65$	44.0908	−	25.4558i	0.678320	−	0.391628i
$66$		0			0
$67$	24.0000	−	41.5692i	0.358209	−	0.620436i	−0.629453	−	0.777039i	$-0.716721\pi$
$67$	24.0000	−	41.5692i	0.358209	−	0.620436i	0.987662	+	0.156603i	$0.0500542\pi$
$68$	−6.92820	+	4.00000i	−0.101885	+	0.0588235i
$69$		0			0
$70$		0			0
$71$			76.3675i			1.07560i	0.843073	+	0.537800i	$0.180744\pi$
$71$			76.3675i			1.07560i	−0.843073	+	0.537800i	$0.819256\pi$
$72$		0			0
$73$	60.1041	−	104.103i	0.823344	−	1.42607i	−0.0798352	−	0.996808i	$-0.525439\pi$
$73$	60.1041	−	104.103i	0.823344	−	1.42607i	0.903179	−	0.429265i	$-0.141227\pi$
$74$	39.1918	+	22.6274i	0.529619	+	0.305776i
$75$		0			0
$76$	−45.2548			−0.595458
$77$		0			0
$78$		0			0
$79$	74.0000	+	128.172i	0.936709	+	1.62243i	0.771558	+	0.636159i	$0.219478\pi$
$79$	74.0000	+	128.172i	0.936709	+	1.62243i	0.165151	+	0.986268i	$0.447189\pi$
$80$	−13.8564	−	8.00000i	−0.173205	−	0.100000i
$81$		0			0
$82$	−26.8701	−	46.5403i	−0.327684	−	0.567565i
$83$			80.0000i			0.963855i	0.876211	+	0.481928i	$0.160063\pi$
$83$			80.0000i			0.963855i	−0.876211	+	0.481928i	$0.839937\pi$
$84$		0			0
$85$	−16.0000			−0.188235
$86$	24.4949	−	14.1421i	0.284824	−	0.164443i
$87$		0			0
$88$	4.00000	−	6.92820i	0.0454545	−	0.0787296i
$89$	−91.7987	+	53.0000i	−1.03145	+	0.595506i	−0.917399	−	0.397970i	$-0.869715\pi$
$89$	−91.7987	+	53.0000i	−1.03145	+	0.595506i	−0.114047	+	0.993475i	$0.536382\pi$
$90$		0			0
$91$		0			0
$92$		−	73.5391i		−	0.799338i
$93$		0			0
$94$	−14.1421	+	24.4949i	−0.150448	+	0.260584i
$95$	−78.3837	−	45.2548i	−0.825091	−	0.476367i
$96$		0			0
$97$	154.149			1.58917			0.794584	−	0.607154i	$-0.207689\pi$
$97$	154.149			1.58917			0.794584	+	0.607154i	$0.207689\pi$
$98$		0			0
$99$		0			0
$100$	9.00000	+	15.5885i	0.0900000	+	0.155885i
$101$	−109.119	−	63.0000i	−1.08039	−	0.623762i	−0.149387	−	0.988779i	$-0.547730\pi$
$101$	−109.119	−	63.0000i	−1.08039	−	0.623762i	−0.931001	+	0.365016i	$0.881063\pi$
$102$		0			0
$103$	36.7696	+	63.6867i	0.356986	+	0.618318i	0.987456	−	0.157896i	$-0.0504711\pi$
$103$	36.7696	+	63.6867i	0.356986	+	0.618318i	−0.630470	+	0.776214i	$0.717138\pi$
$104$		−	36.0000i		−	0.346154i
$105$		0			0
$106$	−134.000			−1.26415
$107$	61.2372	−	35.3553i	0.572311	−	0.330424i	−0.185761	−	0.982595i	$-0.559475\pi$
$107$	61.2372	−	35.3553i	0.572311	−	0.330424i	0.758072	+	0.652171i	$0.226142\pi$
$108$		0			0
$109$	43.0000	−	74.4782i	0.394495	−	0.683286i	−0.598541	−	0.801092i	$-0.704253\pi$
$109$	43.0000	−	74.4782i	0.394495	−	0.683286i	0.993037	+	0.117806i	$0.0375861\pi$
$110$	13.8564	−	8.00000i	0.125967	−	0.0727273i
$111$		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
$115$	73.5391	−	127.373i	0.639470	−	1.10760i
$116$	56.3383	+	32.5269i	0.485675	+	0.280404i
$117$		0			0
$118$	−5.65685			−0.0479394
$119$		0			0
$120$		0			0
$121$	−56.5000	−	97.8609i	−0.466942	−	0.808768i
$122$	−102.191	−	59.0000i	−0.837631	−	0.483607i
$123$		0			0
$124$	−50.9117	−	88.1816i	−0.410578	−	0.711142i
$125$			136.000i			1.08800i
$126$		0			0
$127$	4.00000			0.0314961			0.0157480	−	0.999876i	$-0.494987\pi$
$127$	4.00000			0.0314961			0.0157480	+	0.999876i	$0.494987\pi$
$128$	−9.79796	+	5.65685i	−0.0765466	+	0.0441942i
$129$		0			0
$130$	36.0000	−	62.3538i	0.276923	−	0.479645i
$131$	−20.7846	+	12.0000i	−0.158661	+	0.0916031i	−0.577228	−	0.816583i	$-0.695866\pi$
$131$	−20.7846	+	12.0000i	−0.158661	+	0.0916031i	0.418567	+	0.908186i	$0.362532\pi$
$132$		0			0
$133$		0			0
$134$		−	67.8823i		−	0.506584i
$135$		0			0
$136$	−5.65685	+	9.79796i	−0.0415945	+	0.0720438i
$137$	−62.4620	−	36.0624i	−0.455927	−	0.263230i	0.254403	−	0.967098i	$-0.418121\pi$
$137$	−62.4620	−	36.0624i	−0.455927	−	0.263230i	−0.710330	+	0.703869i	$0.751454\pi$
$138$		0			0
$139$	141.421			1.01742			0.508710	−	0.860938i	$-0.330123\pi$
$139$	141.421			1.01742			0.508710	+	0.860938i	$0.330123\pi$
$140$		0			0
$141$		0			0
$142$	54.0000	+	93.5307i	0.380282	+	0.658667i
$143$	31.1769	+	18.0000i	0.218020	+	0.125874i
$144$		0			0
$145$	65.0538	+	112.677i	0.448647	+	0.777080i
$146$		−	170.000i		−	1.16438i
$147$		0			0
$148$	64.0000			0.432432
$149$	23.2702	−	13.4350i	0.156176	−	0.0901680i	−0.419876	−	0.907582i	$-0.637926\pi$
$149$	23.2702	−	13.4350i	0.156176	−	0.0901680i	0.576051	+	0.817414i	$0.304593\pi$
$150$		0			0
$151$	−76.0000	+	131.636i	−0.503311	+	0.871761i	0.496681	+	0.867933i	$0.334552\pi$
$151$	−76.0000	+	131.636i	−0.503311	+	0.871761i	−0.999993	+	0.00382774i	$0.998782\pi$
$152$	−55.4256	+	32.0000i	−0.364642	+	0.210526i
$153$		0			0
$154$		0			0
$155$		−	203.647i		−	1.31385i
$156$		0			0
$157$	−47.3762	+	82.0579i	−0.301759	+	0.522662i	−0.976534	−	0.215361i	$-0.930907\pi$
$157$	−47.3762	+	82.0579i	−0.301759	+	0.522662i	0.674776	+	0.738023i	$0.264240\pi$
$158$	181.262	+	104.652i	1.14723	+	0.662353i
$159$		0			0
$160$	−22.6274			−0.141421
$161$		0			0
$162$		0			0
$163$	76.0000	+	131.636i	0.466258	+	0.807582i	0.999257	−	0.0385335i	$-0.0122686\pi$
$163$	76.0000	+	131.636i	0.466258	+	0.807582i	−0.533000	+	0.846115i	$0.678935\pi$
$164$	−65.8179	−	38.0000i	−0.401329	−	0.231707i
$165$		0			0
$166$	56.5685	+	97.9796i	0.340774	+	0.590238i
$167$			116.000i			0.694611i	0.937752	+	0.347305i	$0.112903\pi$
$167$			116.000i			0.694611i	−0.937752	+	0.347305i	$0.887097\pi$
$168$		0			0
$169$	−7.00000			−0.0414201
$170$	−19.5959	+	11.3137i	−0.115270	+	0.0665512i
$171$		0			0
$172$	20.0000	−	34.6410i	0.116279	−	0.201401i
$173$	−192.258	+	111.000i	−1.11132	+	0.641618i	−0.939170	−	0.343453i	$-0.888403\pi$
$173$	−192.258	+	111.000i	−1.11132	+	0.641618i	−0.172146	+	0.985071i	$0.555070\pi$
$174$		0			0
$175$		0			0
$176$		−	11.3137i		−	0.0642824i
$177$		0			0
$178$	−74.9533	+	129.823i	−0.421086	+	0.729342i
$179$	−51.4393	−	29.6985i	−0.287370	−	0.165913i	0.349385	−	0.936979i	$-0.386391\pi$
$179$	−51.4393	−	29.6985i	−0.287370	−	0.165913i	−0.636755	+	0.771066i	$0.719724\pi$
$180$		0			0
$181$	80.6102			0.445360			0.222680	−	0.974892i	$-0.428519\pi$
$181$	80.6102			0.445360			0.222680	+	0.974892i	$0.428519\pi$
$182$		0			0
$183$		0			0
$184$	−52.0000	−	90.0666i	−0.282609	−	0.489493i
$185$	110.851	+	64.0000i	0.599196	+	0.345946i
$186$		0			0
$187$	−5.65685	−	9.79796i	−0.0302506	−	0.0523955i
$188$			40.0000i			0.212766i
$189$		0			0
$190$	−128.000			−0.673684
$191$	−262.095	+	151.321i	−1.37223	+	0.792256i	−0.991208	−	0.132311i	$-0.957760\pi$
$191$	−262.095	+	151.321i	−1.37223	+	0.792256i	−0.381019	+	0.924567i	$0.624427\pi$
$192$		0			0
$193$	−109.000	+	188.794i	−0.564767	+	0.978205i	0.432304	+	0.901728i	$0.357701\pi$
$193$	−109.000	+	188.794i	−0.564767	+	0.978205i	−0.997071	+	0.0764772i	$0.975633\pi$
$194$	188.794	−	109.000i	0.973163	−	0.561856i
$195$		0			0
$196$		0			0
$197$			287.085i			1.45729i	0.684894	+	0.728643i	$0.259849\pi$
$197$			287.085i			1.45729i	−0.684894	+	0.728643i	$0.740151\pi$
$198$		0			0
$199$	33.9411	−	58.7878i	0.170558	−	0.295416i	−0.768057	−	0.640382i	$-0.778776\pi$
$199$	33.9411	−	58.7878i	0.170558	−	0.295416i	0.938615	+	0.344966i	$0.112110\pi$
$200$	22.0454	+	12.7279i	0.110227	+	0.0636396i
$201$		0			0
$202$	−178.191			−0.882133
$203$		0			0
$204$		0			0
$205$	−76.0000	−	131.636i	−0.370732	−	0.642126i
$206$	90.0666	+	52.0000i	0.437217	+	0.252427i
$207$		0			0
$208$	−25.4558	−	44.0908i	−0.122384	−	0.211975i
$209$		−	64.0000i		−	0.306220i
$210$		0			0
$211$	132.000			0.625592			0.312796	−	0.949820i	$-0.398734\pi$
$211$	132.000			0.625592			0.312796	+	0.949820i	$0.398734\pi$
$212$	−164.116	+	94.7523i	−0.774131	+	0.446945i
$213$		0			0
$214$	50.0000	−	86.6025i	0.233645	−	0.404685i
$215$	69.2820	−	40.0000i	0.322242	−	0.186047i
$216$		0			0
$217$		0			0
$218$		−	121.622i		−	0.557901i
$219$		0			0
$220$	11.3137	−	19.5959i	0.0514259	−	0.0890724i
$221$	−44.0908	−	25.4558i	−0.199506	−	0.115185i
$222$		0			0
$223$	−169.706			−0.761012			−0.380506	−	0.924778i	$-0.624250\pi$
$223$	−169.706			−0.761012			−0.380506	+	0.924778i	$0.624250\pi$
$224$		0			0
$225$		0			0
$226$	−15.0000	−	25.9808i	−0.0663717	−	0.114959i
$227$	259.808	+	150.000i	1.14453	+	0.660793i	0.947548	−	0.319615i	$-0.103553\pi$
$227$	259.808	+	150.000i	1.14453	+	0.660793i	0.196979	+	0.980408i	$0.436887\pi$
$228$		0			0
$229$	125.158	+	216.780i	0.546541	+	0.946637i	0.998508	+	0.0546023i	$0.0173891\pi$
$229$	125.158	+	216.780i	0.546541	+	0.946637i	−0.451967	+	0.892035i	$0.649278\pi$
$230$		−	208.000i		−	0.904348i
$231$		0			0
$232$	92.0000			0.396552
$233$	25.7196	−	14.8492i	0.110385	−	0.0637307i	−0.443791	−	0.896130i	$-0.646367\pi$
$233$	25.7196	−	14.8492i	0.110385	−	0.0637307i	0.554176	+	0.832400i	$0.313033\pi$
$234$		0			0
$235$	−40.0000	+	69.2820i	−0.170213	+	0.294817i
$236$	−6.92820	+	4.00000i	−0.0293568	+	0.0169492i
$237$		0			0
$238$		0			0
$239$			161.220i			0.674562i	0.941404	+	0.337281i	$0.109507\pi$
$239$			161.220i			0.674562i	−0.941404	+	0.337281i	$0.890493\pi$
$240$		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
$244$	−166.877			−0.683923
$245$		0			0
$246$		0			0
$247$	−144.000	−	249.415i	−0.582996	−	1.00978i
$248$	−124.708	−	72.0000i	−0.502853	−	0.290323i
$249$		0			0
$250$	96.1665	+	166.565i	0.384666	+	0.666261i
$251$			476.000i			1.89641i	0.317653	+	0.948207i	$0.397105\pi$
$251$			476.000i			1.89641i	−0.317653	+	0.948207i	$0.602895\pi$
$252$		0			0
$253$	104.000			0.411067
$254$	4.89898	−	2.82843i	0.0192873	−	0.0111355i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.0312500	+	0.0541266i
$257$	88.3346	−	51.0000i	0.343714	−	0.198444i	−0.318199	−	0.948024i	$-0.603078\pi$
$257$	88.3346	−	51.0000i	0.343714	−	0.198444i	0.661913	+	0.749580i	$0.269745\pi$
$258$		0			0
$259$		0			0
$260$		−	101.823i		−	0.391628i
$261$		0			0
$262$	−16.9706	+	29.3939i	−0.0647731	+	0.112190i
$263$	315.984	+	182.434i	1.20146	+	0.693664i	0.960880	−	0.276965i	$-0.0893287\pi$
$263$	315.984	+	182.434i	1.20146	+	0.693664i	0.240581	+	0.970629i	$0.422662\pi$
$264$		0			0
$265$	−379.009			−1.43022
$266$		0			0
$267$		0			0
$268$	−48.0000	−	83.1384i	−0.179104	−	0.310218i
$269$	169.741	+	98.0000i	0.631007	+	0.364312i	0.781142	−	0.624353i	$-0.214637\pi$
$269$	169.741	+	98.0000i	0.631007	+	0.364312i	−0.150135	+	0.988666i	$0.547971\pi$
$270$		0			0
$271$	−87.6812	−	151.868i	−0.323547	−	0.560400i	0.657670	−	0.753306i	$-0.271542\pi$
$271$	−87.6812	−	151.868i	−0.323547	−	0.560400i	−0.981217	+	0.192906i	$0.938209\pi$
$272$			16.0000i			0.0588235i
$273$		0			0
$274$	−102.000			−0.372263
$275$	−22.0454	+	12.7279i	−0.0801651	+	0.0462834i
$276$		0			0
$277$	−128.000	+	221.703i	−0.462094	+	0.800370i	−0.999065	−	0.0432305i	$-0.986235\pi$
$277$	−128.000	+	221.703i	−0.462094	+	0.800370i	0.536971	+	0.843601i	$0.319568\pi$
$278$	173.205	−	100.000i	0.623040	−	0.359712i
$279$		0			0
$280$		0			0
$281$			26.8701i			0.0956230i	0.998856	+	0.0478115i	$0.0152247\pi$
$281$			26.8701i			0.0956230i	−0.998856	+	0.0478115i	$0.984775\pi$
$282$		0			0
$283$	−251.730	+	436.009i	−0.889505	+	1.54067i	−0.0490442	+	0.998797i	$0.515618\pi$
$283$	−251.730	+	436.009i	−0.889505	+	1.54067i	−0.840461	+	0.541872i	$0.817716\pi$
$284$	132.272	+	76.3675i	0.465748	+	0.268900i
$285$		0			0
$286$	50.9117			0.178013
$287$		0			0
$288$		0			0
$289$	−136.500	−	236.425i	−0.472318	−	0.818079i
$290$	159.349	+	92.0000i	0.549478	+	0.317241i
$291$		0			0
$292$	−120.208	−	208.207i	−0.411672	−	0.713036i
$293$		−	190.000i		−	0.648464i	−0.945978	−	0.324232i	$-0.894894\pi$
$293$		−	190.000i		−	0.648464i	0.945978	−	0.324232i	$-0.105106\pi$
$294$		0			0
$295$	−16.0000			−0.0542373
$296$	78.3837	−	45.2548i	0.264810	−	0.152888i
$297$		0			0
$298$	19.0000	−	32.9090i	0.0637584	−	0.110433i
$299$	405.300	−	234.000i	1.35552	−	0.782609i
$300$		0			0
$301$		0			0
$302$			214.960i			0.711790i
$303$		0			0
$304$	−45.2548	+	78.3837i	−0.148865	+	0.257841i
$305$	−289.040	−	166.877i	−0.947671	−	0.547138i
$306$		0			0
$307$	265.872			0.866033			0.433017	−	0.901386i	$-0.357449\pi$
$307$	265.872			0.866033			0.433017	+	0.901386i	$0.357449\pi$
$308$		0			0
$309$		0			0
$310$	−144.000	−	249.415i	−0.464516	−	0.804566i
$311$	460.726	+	266.000i	1.48143	+	0.855305i	0.999778	−	0.0210559i	$-0.00670279\pi$
$311$	460.726	+	266.000i	1.48143	+	0.855305i	0.481654	+	0.876361i	$0.340036\pi$
$312$		0			0
$313$	−74.2462	−	128.598i	−0.237208	−	0.410857i	0.722704	−	0.691158i	$-0.242899\pi$
$313$	−74.2462	−	128.598i	−0.237208	−	0.410857i	−0.959912	+	0.280301i	$0.909566\pi$
$314$			134.000i			0.426752i
$315$		0			0
$316$	296.000			0.936709
$317$	199.633	−	115.258i	0.629758	−	0.363591i	−0.150900	−	0.988549i	$-0.548217\pi$
$317$	199.633	−	115.258i	0.629758	−	0.363591i	0.780659	+	0.624958i	$0.214884\pi$
$318$		0			0
$319$	−46.0000	+	79.6743i	−0.144201	+	0.249763i
$320$	−27.7128	+	16.0000i	−0.0866025	+	0.0500000i
$321$		0			0
$322$		0			0
$323$			90.5097i			0.280216i
$324$		0			0
$325$	−57.2756	+	99.2043i	−0.176233	+	0.305244i
$326$	186.161	+	107.480i	0.571047	+	0.329694i
$327$		0			0
$328$	−107.480			−0.327684
$329$		0			0
$330$		0			0
$331$	−134.000	−	232.095i	−0.404834	−	0.701193i	0.589468	−	0.807792i	$-0.299337\pi$
$331$	−134.000	−	232.095i	−0.404834	−	0.701193i	−0.994302	+	0.106599i	$0.966004\pi$
$332$	138.564	+	80.0000i	0.417362	+	0.240964i
$333$		0			0
$334$	82.0244	+	142.070i	0.245582	+	0.425360i
$335$		−	192.000i		−	0.573134i
$336$		0			0
$337$	170.000			0.504451			0.252226	−	0.967668i	$-0.418838\pi$
$337$	170.000			0.504451			0.252226	+	0.967668i	$0.418838\pi$
$338$	−8.57321	+	4.94975i	−0.0253645	+	0.0146442i
$339$		0			0
$340$	−16.0000	+	27.7128i	−0.0470588	+	0.0815083i
$341$	124.708	−	72.0000i	0.365712	−	0.211144i
$342$		0			0
$343$		0			0
$344$		−	56.5685i		−	0.164443i
$345$		0			0
$346$	−156.978	+	271.893i	−0.453693	+	0.785819i
$347$	242.499	+	140.007i	0.698846	+	0.403479i	0.806917	−	0.590664i	$-0.201134\pi$
$347$	242.499	+	140.007i	0.698846	+	0.403479i	−0.108072	+	0.994143i	$0.534468\pi$
$348$		0			0
$349$	−241.831			−0.692924			−0.346462	−	0.938064i	$-0.612617\pi$
$349$	−241.831			−0.692924			−0.346462	+	0.938064i	$0.612617\pi$
$350$		0			0
$351$		0			0
$352$	−8.00000	−	13.8564i	−0.0227273	−	0.0393648i
$353$	−460.726	−	266.000i	−1.30517	−	0.753541i	−0.323885	−	0.946096i	$-0.604989\pi$
$353$	−460.726	−	266.000i	−1.30517	−	0.753541i	−0.981286	+	0.192555i	$0.938323\pi$
$354$		0			0
$355$	152.735	+	264.545i	0.430240	+	0.745197i
$356$			212.000i			0.595506i
$357$		0			0
$358$	−84.0000			−0.234637
$359$	−296.388	+	171.120i	−0.825594	+	0.476657i	−0.852342	−	0.522985i	$-0.824818\pi$
$359$	−296.388	+	171.120i	−0.825594	+	0.476657i	0.0267477	+	0.999642i	$0.491485\pi$
$360$		0			0
$361$	−75.5000	+	130.770i	−0.209141	+	0.362243i
$362$	98.7269	−	57.0000i	0.272726	−	0.157459i
$363$		0			0
$364$		0			0
$365$		−	480.833i		−	1.31735i
$366$		0			0
$367$	342.240	−	592.777i	0.932533	−	1.61519i	0.153558	−	0.988140i	$-0.450927\pi$
$367$	342.240	−	592.777i	0.932533	−	1.61519i	0.778975	−	0.627055i	$-0.215740\pi$
$368$	−127.373	−	73.5391i	−0.346124	−	0.199835i
$369$		0			0
$370$	181.019			0.489241
$371$		0			0
$372$		0			0
$373$	−191.000	−	330.822i	−0.512064	−	0.886921i	−0.999902	−	0.0139872i	$-0.995548\pi$
$373$	−191.000	−	330.822i	−0.512064	−	0.886921i	0.487838	−	0.872934i	$-0.337786\pi$
$374$	−13.8564	−	8.00000i	−0.0370492	−	0.0213904i
$375$		0			0
$376$	28.2843	+	48.9898i	0.0752241	+	0.130292i
$377$			414.000i			1.09814i
$378$		0			0
$379$	−140.000			−0.369393			−0.184697	−	0.982796i	$-0.559130\pi$
$379$	−140.000			−0.369393			−0.184697	+	0.982796i	$0.559130\pi$
$380$	−156.767	+	90.5097i	−0.412546	+	0.238183i
$381$		0			0
$382$	−214.000	+	370.659i	−0.560209	+	0.970311i
$383$	214.774	−	124.000i	0.560768	−	0.323760i	−0.192685	−	0.981261i	$-0.561720\pi$
$383$	214.774	−	124.000i	0.560768	−	0.323760i	0.753454	+	0.657501i	$0.228386\pi$
$384$		0			0
$385$		0			0
$386$			308.299i			0.798701i
$387$		0			0
$388$	154.149	−	266.994i	0.397292	−	0.688130i
$389$	295.164	+	170.413i	0.758775	+	0.438079i	0.828856	−	0.559462i	$-0.188992\pi$
$389$	295.164	+	170.413i	0.758775	+	0.438079i	−0.0700807	+	0.997541i	$0.522326\pi$
$390$		0			0
$391$	−147.078			−0.376159
$392$		0			0
$393$		0			0
$394$	203.000	+	351.606i	0.515228	+	0.892402i
$395$	512.687	+	296.000i	1.29794	+	0.749367i
$396$		0			0
$397$	122.329	+	211.881i	0.308135	+	0.533705i	0.977954	−	0.208819i	$-0.0669619\pi$
$397$	122.329	+	211.881i	0.308135	+	0.533705i	−0.669820	+	0.742524i	$0.733629\pi$
$398$		−	96.0000i		−	0.241206i
$399$		0			0
$400$	36.0000			0.0900000
$401$	25.7196	−	14.8492i	0.0641388	−	0.0370305i	−0.467588	−	0.883947i	$-0.654877\pi$
$401$	25.7196	−	14.8492i	0.0641388	−	0.0370305i	0.531726	+	0.846916i	$0.321543\pi$
$402$		0			0
$403$	324.000	−	561.184i	0.803970	−	1.39252i
$404$	−218.238	+	126.000i	−0.540194	+	0.311881i
$405$		0			0
$406$		0			0
$407$			90.5097i			0.222382i
$408$		0			0
$409$	−303.349	+	525.416i	−0.741684	+	1.28463i	0.210044	+	0.977692i	$0.432639\pi$
$409$	−303.349	+	525.416i	−0.741684	+	1.28463i	−0.951728	+	0.306943i	$0.900694\pi$
$410$	−186.161	−	107.480i	−0.454052	−	0.262147i
$411$		0			0
$412$	147.078			0.356986
$413$		0			0
$414$		0			0
$415$	160.000	+	277.128i	0.385542	+	0.667779i
$416$	−62.3538	−	36.0000i	−0.149889	−	0.0865385i
$417$		0			0
$418$	−45.2548	−	78.3837i	−0.108265	−	0.187521i
$419$		−	692.000i		−	1.65155i	−0.563999	−	0.825776i	$-0.690738\pi$
$419$		−	692.000i		−	1.65155i	0.563999	−	0.825776i	$-0.309262\pi$
$420$		0			0
$421$	384.000			0.912114			0.456057	−	0.889951i	$-0.349261\pi$
$421$	384.000			0.912114			0.456057	+	0.889951i	$0.349261\pi$
$422$	161.666	−	93.3381i	0.383096	−	0.221180i
$423$		0			0
$424$	−134.000	+	232.095i	−0.316038	+	0.547393i
$425$	31.1769	−	18.0000i	0.0733574	−	0.0423529i
$426$		0			0
$427$		0			0
$428$		−	141.421i		−	0.330424i
$429$		0			0
$430$	56.5685	−	97.9796i	0.131555	−	0.227860i
$431$	−95.5301	−	55.1543i	−0.221648	−	0.127968i	0.385065	−	0.922889i	$-0.374179\pi$
$431$	−95.5301	−	55.1543i	−0.221648	−	0.127968i	−0.606713	+	0.794921i	$0.707512\pi$
$432$		0			0
$433$	−156.978			−0.362535			−0.181268	−	0.983434i	$-0.558020\pi$
$433$	−156.978			−0.362535			−0.181268	+	0.983434i	$0.558020\pi$
$434$		0			0
$435$		0			0
$436$	−86.0000	−	148.956i	−0.197248	−	0.341643i
$437$	−720.533	−	416.000i	−1.64882	−	0.951945i
$438$		0			0
$439$	−101.823	−	176.363i	−0.231944	−	0.401739i	0.726436	−	0.687234i	$-0.241175\pi$
$439$	−101.823	−	176.363i	−0.231944	−	0.401739i	−0.958380	+	0.285495i	$0.907842\pi$
$440$		−	32.0000i		−	0.0727273i
$441$		0			0
$442$	−72.0000			−0.162896
$443$	−703.004	+	405.879i	−1.58692	+	0.916206i	−0.593104	+	0.805126i	$0.702098\pi$
$443$	−703.004	+	405.879i	−1.58692	+	0.916206i	−0.993811	+	0.111080i	$0.964569\pi$
$444$		0			0
$445$	−212.000	+	367.195i	−0.476404	+	0.825157i
$446$	−207.846	+	120.000i	−0.466023	+	0.269058i
$447$		0			0
$448$		0			0
$449$			284.257i			0.633089i	0.948578	+	0.316544i	$0.102523\pi$
$449$			284.257i			0.633089i	−0.948578	+	0.316544i	$0.897477\pi$
$450$		0			0
$451$	53.7401	−	93.0806i	0.119158	−	0.206387i
$452$	−36.7423	−	21.2132i	−0.0812884	−	0.0469319i
$453$		0			0
$454$	424.264			0.934502
$455$		0			0
$456$		0			0
$457$	144.000	+	249.415i	0.315098	+	0.545767i	0.979458	−	0.201646i	$-0.0646291\pi$
$457$	144.000	+	249.415i	0.315098	+	0.545767i	−0.664360	+	0.747413i	$0.731296\pi$
$458$	306.573	+	177.000i	0.669373	+	0.386463i
$459$		0			0
$460$	−147.078	−	254.747i	−0.319735	−	0.553798i
$461$		−	706.000i		−	1.53145i	−0.643166	−	0.765727i	$-0.722380\pi$
$461$		−	706.000i		−	1.53145i	0.643166	−	0.765727i	$-0.277620\pi$
$462$		0			0
$463$	−356.000			−0.768898			−0.384449	−	0.923146i	$-0.625609\pi$
$463$	−356.000			−0.768898			−0.384449	+	0.923146i	$0.625609\pi$
$464$	112.677	−	65.0538i	0.242837	−	0.140202i
$465$		0			0
$466$	21.0000	−	36.3731i	0.0450644	−	0.0780538i
$467$	−765.566	+	442.000i	−1.63933	+	0.946467i	−0.658264	+	0.752787i	$0.728709\pi$
$467$	−765.566	+	442.000i	−1.63933	+	0.946467i	−0.981065	+	0.193679i	$0.937958\pi$
$468$		0			0
$469$		0			0
$470$			113.137i			0.240717i
$471$		0			0
$472$	−5.65685	+	9.79796i	−0.0119849	+	0.0207584i
$473$	48.9898	+	28.2843i	0.103573	+	0.0597976i
$474$		0			0
$475$	203.647			0.428730
$476$		0			0
$477$		0			0
$478$	114.000	+	197.454i	0.238494	+	0.413083i
$479$	−439.941	−	254.000i	−0.918457	−	0.530271i	−0.0353145	−	0.999376i	$-0.511243\pi$
$479$	−439.941	−	254.000i	−0.918457	−	0.530271i	−0.883142	+	0.469105i	$0.844577\pi$
$480$		0			0
$481$	203.647	+	352.727i	0.423382	+	0.733319i
$482$			534.000i			1.10788i
$483$		0			0
$484$	−226.000			−0.466942
$485$	533.989	−	308.299i	1.10101	−	0.635667i
$486$		0			0
$487$	312.000	−	540.400i	0.640657	−	1.10965i	−0.344629	−	0.938739i	$-0.611995\pi$
$487$	312.000	−	540.400i	0.640657	−	1.10965i	0.985286	−	0.170912i	$-0.0546713\pi$
$488$	−204.382	+	118.000i	−0.418816	+	0.241803i
$489$		0			0
$490$		0			0
$491$		−	840.043i		−	1.71088i	−0.517901	−	0.855441i	$-0.673286\pi$
$491$		−	840.043i		−	1.71088i	0.517901	−	0.855441i	$-0.326714\pi$
$492$		0			0
$493$	65.0538	−	112.677i	0.131955	−	0.228553i
$494$	−352.727	−	203.647i	−0.714021	−	0.412240i
$495$		0			0
$496$	−203.647			−0.410578
$497$		0			0
$498$		0			0
$499$	470.000	+	814.064i	0.941884	+	1.63139i	0.761874	+	0.647726i	$0.224280\pi$
$499$	470.000	+	814.064i	0.941884	+	1.63139i	0.180010	+	0.983665i	$0.442387\pi$
$500$	235.559	+	136.000i	0.471118	+	0.272000i
$501$		0			0
$502$	336.583	+	582.979i	0.670484	+	1.16131i
$503$			632.000i			1.25646i	0.778027	+	0.628231i	$0.216221\pi$
$503$			632.000i			1.25646i	−0.778027	+	0.628231i	$0.783779\pi$
$504$		0			0
$505$	−504.000			−0.998020
$506$	127.373	−	73.5391i	0.251726	−	0.145334i
$507$		0			0
$508$	4.00000	−	6.92820i	0.00787402	−	0.0136382i
$509$	−190.526	+	110.000i	−0.374314	+	0.216110i	−0.675341	−	0.737505i	$-0.736004\pi$
$509$	−190.526	+	110.000i	−0.374314	+	0.216110i	0.301028	+	0.953615i	$0.402670\pi$
$510$		0			0
$511$		0			0
$512$			22.6274i			0.0441942i
$513$		0			0
$514$	72.1249	−	124.924i	0.140321	−	0.243043i
$515$	254.747	+	147.078i	0.494654	+	0.285589i
$516$		0			0
$517$	−56.5685			−0.109417
$518$		0			0
$519$		0			0
$520$	−72.0000	−	124.708i	−0.138462	−	0.239822i
$521$	−439.941	−	254.000i	−0.844416	−	0.487524i	0.0143466	−	0.999897i	$-0.495433\pi$
$521$	−439.941	−	254.000i	−0.844416	−	0.487524i	−0.858763	+	0.512373i	$0.828767\pi$
$522$		0			0
$523$	−407.294	−	705.453i	−0.778764	−	1.34886i	−0.932655	−	0.360771i	$-0.882514\pi$
$523$	−407.294	−	705.453i	−0.778764	−	1.34886i	0.153891	−	0.988088i	$-0.450820\pi$
$524$			48.0000i			0.0916031i
$525$		0			0
$526$	516.000			0.980989
$527$	−176.363	+	101.823i	−0.334655	+	0.193213i
$528$		0			0
$529$	411.500	−	712.739i	0.777883	−	1.34733i
$530$	−464.190	+	268.000i	−0.875829	+	0.505660i
$531$		0			0
$532$		0			0
$533$		−	483.661i		−	0.907432i
$534$		0			0
$535$	141.421	−	244.949i	0.264339	−	0.457849i
$536$	−117.576	−	67.8823i	−0.219357	−	0.126646i
$537$		0			0
$538$	277.186			0.515215
$539$		0			0
$540$		0			0
$541$	232.000	+	401.836i	0.428835	+	0.742765i	0.996770	−	0.0803089i	$-0.0255907\pi$
$541$	232.000	+	401.836i	0.428835	+	0.742765i	−0.567935	+	0.823074i	$0.692257\pi$
$542$	−214.774	−	124.000i	−0.396263	−	0.228782i
$543$		0			0
$544$	11.3137	+	19.5959i	0.0207973	+	0.0360219i
$545$		−	344.000i		−	0.631193i
$546$		0			0
$547$	−80.0000			−0.146252			−0.0731261	−	0.997323i	$-0.523298\pi$
$547$	−80.0000			−0.146252			−0.0731261	+	0.997323i	$0.523298\pi$
$548$	−124.924	+	72.1249i	−0.227963	+	0.131615i
$549$		0			0
$550$	−18.0000	+	31.1769i	−0.0327273	+	0.0566853i
$551$	637.395	−	368.000i	1.15680	−	0.667877i
$552$		0			0
$553$		0			0
$554$			362.039i			0.653499i
$555$		0			0
$556$	141.421	−	244.949i	0.254355	−	0.440556i
$557$	−789.960	−	456.084i	−1.41824	−	0.818822i	−0.422097	−	0.906551i	$-0.638706\pi$
$557$	−789.960	−	456.084i	−1.41824	−	0.818822i	−0.996144	+	0.0877287i	$0.972039\pi$
$558$		0			0
$559$	254.558			0.455382
$560$		0			0
$561$		0			0
$562$	19.0000	+	32.9090i	0.0338078	+	0.0585569i
$563$	−273.664	−	158.000i	−0.486082	−	0.280639i	0.236866	−	0.971542i	$-0.423880\pi$
$563$	−273.664	−	158.000i	−0.486082	−	0.280639i	−0.722948	+	0.690903i	$0.757213\pi$
$564$		0			0
$565$	−42.4264	−	73.4847i	−0.0750910	−	0.130061i
$566$			712.000i			1.25795i
$567$		0			0
$568$	216.000			0.380282
$569$	963.874	−	556.493i	1.69398	−	0.978019i	0.742733	−	0.669588i	$-0.233529\pi$
$569$	963.874	−	556.493i	1.69398	−	0.978019i	0.951247	−	0.308431i	$-0.0998040\pi$
$570$		0			0
$571$	220.000	−	381.051i	0.385289	−	0.667340i	−0.606520	−	0.795068i	$-0.707435\pi$
$571$	220.000	−	381.051i	0.385289	−	0.667340i	0.991809	+	0.127728i	$0.0407684\pi$
$572$	62.3538	−	36.0000i	0.109010	−	0.0629371i
$573$		0			0
$574$		0			0
$575$			330.926i			0.575523i
$576$		0			0
$577$	159.099	−	275.568i	0.275735	−	0.477587i	−0.694585	−	0.719410i	$-0.744412\pi$
$577$	159.099	−	275.568i	0.275735	−	0.477587i	0.970320	+	0.241823i	$0.0777455\pi$
$578$	−334.355	−	193.040i	−0.578469	−	0.333980i
$579$		0			0
$580$	260.215			0.448647
$581$		0			0
$582$		0			0
$583$	−134.000	−	232.095i	−0.229846	−	0.398104i
$584$	−294.449	−	170.000i	−0.504193	−	0.291096i
$585$		0			0
$586$	−134.350	−	232.702i	−0.229267	−	0.397102i
$587$		−	300.000i		−	0.511073i	−0.966799	−	0.255537i	$-0.917748\pi$
$587$		−	300.000i		−	0.511073i	0.966799	−	0.255537i	$-0.0822521\pi$
$588$		0			0
$589$	−1152.00			−1.95586
$590$	−19.5959	+	11.3137i	−0.0332134	+	0.0191758i
$591$		0			0
$592$	64.0000	−	110.851i	0.108108	−	0.187249i
$593$	−897.202	+	518.000i	−1.51299	+	0.873524i	−0.513104	+	0.858326i	$0.671505\pi$
$593$	−897.202	+	518.000i	−1.51299	+	0.873524i	−0.999885	+	0.0151981i	$0.995162\pi$
$594$		0			0
$595$		0			0
$596$		−	53.7401i		−	0.0901680i
$597$		0			0
$598$	330.926	−	573.181i	0.553388	−	0.958496i
$599$	849.973	+	490.732i	1.41899	+	0.819252i	0.996210	−	0.0869817i	$-0.0277222\pi$
$599$	849.973	+	490.732i	1.41899	+	0.819252i	0.422777	+	0.906234i	$0.361055\pi$
$600$		0			0
$601$	−352.139			−0.585922			−0.292961	−	0.956124i	$-0.594641\pi$
$601$	−352.139			−0.585922			−0.292961	+	0.956124i	$0.594641\pi$
$602$		0			0
$603$		0			0
$604$	152.000	+	263.272i	0.251656	+	0.435880i
$605$	−391.443	−	226.000i	−0.647014	−	0.373554i
$606$		0			0
$607$	−432.749	−	749.544i	−0.712931	−	1.23483i	−0.963752	−	0.266800i	$-0.914034\pi$
$607$	−432.749	−	749.544i	−0.712931	−	1.23483i	0.250821	−	0.968034i	$-0.419300\pi$
$608$			128.000i			0.210526i
$609$		0			0
$610$	−472.000			−0.773770
$611$	−220.454	+	127.279i	−0.360809	+	0.208313i
$612$		0			0
$613$	132.000	−	228.631i	0.215334	−	0.372970i	−0.738042	−	0.674755i	$-0.764249\pi$
$613$	132.000	−	228.631i	0.215334	−	0.372970i	0.953376	+	0.301785i	$0.0975825\pi$
$614$	325.626	−	188.000i	0.530335	−	0.306189i
$615$		0			0
$616$		0			0
$617$		−	15.5563i		−	0.0252129i	−0.999921	−	0.0126064i	$-0.995987\pi$
$617$		−	15.5563i		−	0.0252129i	0.999921	−	0.0126064i	$-0.00401286\pi$
$618$		0			0
$619$	200.818	−	347.828i	0.324424	−	0.561918i	−0.656972	−	0.753915i	$-0.728163\pi$
$619$	200.818	−	347.828i	0.324424	−	0.561918i	0.981396	+	0.191997i	$0.0614963\pi$
$620$	−352.727	−	203.647i	−0.568914	−	0.328463i
$621$		0			0
$622$	752.362			1.20958
$623$		0			0
$624$		0			0
$625$	159.500	+	276.262i	0.255200	+	0.442019i
$626$	−181.865	−	105.000i	−0.290520	−	0.167732i
$627$		0			0
$628$	94.7523	+	164.116i	0.150879	+	0.261331i
$629$		−	128.000i		−	0.203498i
$630$		0			0
$631$	−676.000			−1.07132			−0.535658	−	0.844435i	$-0.679936\pi$
$631$	−676.000			−1.07132			−0.535658	+	0.844435i	$0.679936\pi$
$632$	362.524	−	209.304i	0.573615	−	0.331177i
$633$		0			0
$634$	163.000	−	282.324i	0.257098	−	0.445306i
$635$	13.8564	−	8.00000i	0.0218211	−	0.0125984i
$636$		0			0
$637$		0			0
$638$			130.108i			0.203930i
$639$		0			0
$640$	−22.6274	+	39.1918i	−0.0353553	+	0.0612372i
$641$	787.511	+	454.670i	1.22857	+	0.709313i	0.966730	−	0.255799i	$-0.0823386\pi$
$641$	787.511	+	454.670i	1.22857	+	0.709313i	0.261836	+	0.965112i	$0.415672\pi$
$642$		0			0
$643$	480.833			0.747796			0.373898	−	0.927470i	$-0.378021\pi$
$643$	480.833			0.747796			0.373898	+	0.927470i	$0.378021\pi$
$644$		0			0
$645$		0			0
$646$	64.0000	+	110.851i	0.0990712	+	0.171596i
$647$	509.223	+	294.000i	0.787052	+	0.454405i	0.838924	−	0.544249i	$-0.183185\pi$
$647$	509.223	+	294.000i	0.787052	+	0.454405i	−0.0518714	+	0.998654i	$0.516519\pi$
$648$		0			0
$649$	−5.65685	−	9.79796i	−0.00871626	−	0.0150970i
$650$			162.000i			0.249231i
$651$		0			0
$652$	304.000			0.466258
$653$	393.143	−	226.981i	0.602057	−	0.347598i	−0.167793	−	0.985822i	$-0.553664\pi$
$653$	393.143	−	226.981i	0.602057	−	0.347598i	0.769850	+	0.638225i	$0.220331\pi$
$654$		0			0
$655$	−48.0000	+	83.1384i	−0.0732824	+	0.126929i
$656$	−131.636	+	76.0000i	−0.200664	+	0.115854i
$657$		0			0
$658$		0			0
$659$		−	755.190i		−	1.14596i	−0.819568	−	0.572982i	$-0.805787\pi$
$659$		−	755.190i		−	1.14596i	0.819568	−	0.572982i	$-0.194213\pi$
$660$		0			0
$661$	−120.915	+	209.431i	−0.182928	+	0.316840i	−0.942876	−	0.333143i	$-0.891891\pi$
$661$	−120.915	+	209.431i	−0.182928	+	0.316840i	0.759949	+	0.649983i	$0.225224\pi$
$662$	−328.232	−	189.505i	−0.495818	−	0.286261i
$663$		0			0
$664$	226.274			0.340774
$665$		0			0
$666$		0			0
$667$	598.000	+	1035.77i	0.896552	+	1.55287i
$668$	200.918	+	116.000i	0.300775	+	0.173653i
$669$		0			0
$670$	−135.765	−	235.151i	−0.202634	−	0.350972i
$671$		−	236.000i		−	0.351714i
$672$		0			0
$673$	1176.00			1.74740			0.873700	−	0.486465i	$-0.161714\pi$
$673$	1176.00			1.74740			0.873700	+	0.486465i	$0.161714\pi$
$674$	208.207	−	120.208i	0.308912	−	0.178350i
$675$		0			0
$676$	−7.00000	+	12.1244i	−0.0103550	+	0.0179354i
$677$	−192.258	+	111.000i	−0.283985	+	0.163959i	−0.635226	−	0.772326i	$-0.719093\pi$
$677$	−192.258	+	111.000i	−0.283985	+	0.163959i	0.351241	+	0.936285i	$0.385760\pi$
$678$		0			0
$679$		0			0
$680$			45.2548i			0.0665512i
$681$		0			0
$682$	101.823	−	176.363i	0.149301	−	0.258597i
$683$	−448.257	−	258.801i	−0.656305	−	0.378918i	0.134562	−	0.990905i	$-0.457037\pi$
$683$	−448.257	−	258.801i	−0.656305	−	0.378918i	−0.790868	+	0.611987i	$0.790370\pi$
$684$		0			0
$685$	−288.500			−0.421167
$686$		0			0
$687$		0			0
$688$	−40.0000	−	69.2820i	−0.0581395	−	0.100701i
$689$	−1044.43	−	603.000i	−1.51586	−	0.875181i
$690$		0			0
$691$	−322.441	−	558.484i	−0.466629	−	0.808225i	0.532644	−	0.846339i	$-0.321198\pi$
$691$	−322.441	−	558.484i	−0.466629	−	0.808225i	−0.999273	+	0.0381139i	$0.987865\pi$
$692$			444.000i			0.641618i
$693$		0			0
$694$	396.000			0.570605
$695$	489.898	−	282.843i	0.704889	−	0.406968i
$696$		0			0
$697$	−76.0000	+	131.636i	−0.109039	+	0.188861i
$698$	−296.181	+	171.000i	−0.424328	+	0.244986i
$699$		0			0
$700$		0			0
$701$			657.609i			0.938102i	0.883171	+	0.469051i	$0.155404\pi$
$701$			657.609i			0.938102i	−0.883171	+	0.469051i	$0.844596\pi$
$702$		0			0
$703$	362.039	−	627.069i	0.514991	−	0.891991i
$704$	−19.5959	−	11.3137i	−0.0278351	−	0.0160706i
$705$		0			0
$706$	−752.362			−1.06567
$707$		0			0
$708$		0			0
$709$	−53.0000	−	91.7987i	−0.0747532	−	0.129476i	0.826226	−	0.563339i	$-0.190484\pi$
$709$	−53.0000	−	91.7987i	−0.0747532	−	0.129476i	−0.900979	+	0.433863i	$0.857150\pi$
$710$	374.123	+	216.000i	0.526934	+	0.304225i
$711$		0			0
$712$	149.907	+	259.646i	0.210543	+	0.364671i
$713$		−	1872.00i		−	2.62553i
$714$		0			0
$715$	144.000			0.201399
$716$	−102.879	+	59.3970i	−0.143685	+	0.0829567i
$717$		0			0
$718$	−242.000	+	419.156i	−0.337047	+	0.583783i
$719$	1053.09	−	608.000i	1.46465	−	0.845619i	0.465434	−	0.885083i	$-0.345898\pi$
$719$	1053.09	−	608.000i	1.46465	−	0.845619i	0.999221	+	0.0394637i	$0.0125650\pi$
$720$		0			0
$721$		0			0
$722$			213.546i			0.295770i
$723$		0			0
$724$	80.6102	−	139.621i	0.111340	−	0.192847i
$725$	−253.522	−	146.371i	−0.349686	−	0.201891i
$726$		0			0
$727$	73.5391			0.101154			0.0505771	−	0.998720i	$-0.483894\pi$
$727$	73.5391			0.101154			0.0505771	+	0.998720i	$0.483894\pi$
$728$		0			0
$729$		0			0
$730$	−340.000	−	588.897i	−0.465753	−	0.806709i
$731$	−69.2820	−	40.0000i	−0.0947771	−	0.0547196i
$732$		0			0
$733$	−210.011	−	363.749i	−0.286508	−	0.496247i	0.686465	−	0.727162i	$-0.259161\pi$
$733$	−210.011	−	363.749i	−0.286508	−	0.496247i	−0.972974	+	0.230915i	$0.925828\pi$
$734$		−	968.000i		−	1.31880i
$735$		0			0
$736$	−208.000			−0.282609
$737$	117.576	−	67.8823i	0.159533	−	0.0921062i
$738$		0			0
$739$	204.000	−	353.338i	0.276049	−	0.478130i	−0.694350	−	0.719637i	$-0.744308\pi$
$739$	204.000	−	353.338i	0.276049	−	0.478130i	0.970399	+	0.241507i	$0.0776416\pi$
$740$	221.703	−	128.000i	0.299598	−	0.172973i
$741$		0			0
$742$		0			0
$743$			489.318i			0.658571i	0.944230	+	0.329285i	$0.106808\pi$
$743$			489.318i			0.658571i	−0.944230	+	0.329285i	$0.893192\pi$
$744$		0			0
$745$	53.7401	−	93.0806i	0.0721344	−	0.124940i
$746$	−467.853	−	270.115i	−0.627148	−	0.362084i
$747$		0			0
$748$	−22.6274			−0.0302506
$749$		0			0
$750$		0			0
$751$	68.0000	+	117.779i	0.0905459	+	0.156830i	0.907741	−	0.419531i	$-0.137805\pi$
$751$	68.0000	+	117.779i	0.0905459	+	0.156830i	−0.817195	+	0.576361i	$0.804472\pi$
$752$	69.2820	+	40.0000i	0.0921304	+	0.0531915i
$753$		0			0
$754$	292.742	+	507.044i	0.388252	+	0.672473i
$755$			608.000i			0.805298i
$756$		0			0
$757$	758.000			1.00132			0.500661	−	0.865644i	$-0.333091\pi$
$757$	758.000			1.00132			0.500661	+	0.865644i	$0.333091\pi$
$758$	−171.464	+	98.9949i	−0.226206	+	0.130600i
$759$		0			0
$760$	−128.000	+	221.703i	−0.168421	+	0.291714i
$761$	−50.2295	+	29.0000i	−0.0660046	+	0.0381078i	−0.532639	−	0.846342i	$-0.678800\pi$
$761$	−50.2295	+	29.0000i	−0.0660046	+	0.0381078i	0.466635	+	0.884450i	$0.345466\pi$
$762$		0			0
$763$		0			0
$764$			605.283i			0.792256i
$765$		0			0
$766$	175.362	−	303.737i	0.228933	−	0.396523i
$767$	−44.0908	−	25.4558i	−0.0574848	−	0.0331888i
$768$		0			0
$769$	292.742			0.380679			0.190340	−	0.981718i	$-0.439041\pi$
$769$	292.742			0.380679			0.190340	+	0.981718i	$0.439041\pi$
$770$		0			0
$771$		0			0
$772$	218.000	+	377.587i	0.282383	+	0.489102i
$773$	−261.540	−	151.000i	−0.338344	−	0.195343i	0.321196	−	0.947013i	$-0.395915\pi$
$773$	−261.540	−	151.000i	−0.338344	−	0.195343i	−0.659539	+	0.751670i	$0.729249\pi$
$774$		0			0
$775$	229.103	+	396.817i	0.295616	+	0.512022i
$776$		−	436.000i		−	0.561856i
$777$		0			0
$778$	482.000			0.619537
$779$	−744.645	+	429.921i	−0.955898	+	0.551888i
$780$		0			0
$781$	−108.000	+	187.061i	−0.138284	+	0.239515i
$782$	−180.133	+	104.000i	−0.230349	+	0.132992i
$783$		0			0
$784$		0			0
$785$			379.009i			0.482814i
$786$		0			0
$787$	248.902	−	431.110i	0.316266	−	0.547789i	−0.663440	−	0.748230i	$-0.730904\pi$
$787$	248.902	−	431.110i	0.316266	−	0.547789i	0.979706	+	0.200441i	$0.0642374\pi$
$788$	497.246	+	287.085i	0.631023	+	0.364322i
$789$		0			0
$790$	837.214			1.05977
$791$		0			0
$792$		0			0
$793$	−531.000	−	919.719i	−0.669609	−	1.15980i
$794$	299.645	+	173.000i	0.377386	+	0.217884i
$795$		0			0
$796$	−67.8823	−	117.576i	−0.0852792	−	0.147708i
$797$			30.0000i			0.0376412i	0.999823	+	0.0188206i	$0.00599113\pi$
$797$			30.0000i			0.0376412i	−0.999823	+	0.0188206i	$0.994009\pi$
$798$		0			0
$799$	80.0000			0.100125
$800$	44.0908	−	25.4558i	0.0551135	−	0.0318198i
$801$		0			0
$802$	21.0000	−	36.3731i	0.0261845	−	0.0453530i
$803$	294.449	−	170.000i	0.366686	−	0.211706i
$804$		0			0
$805$		0			0
$806$		−	916.410i		−	1.13699i
$807$		0			0
$808$	−178.191	+	308.636i	−0.220533	+	0.381975i
$809$	−851.198	−	491.439i	−1.05216	−	0.607465i	−0.128907	−	0.991657i	$-0.541147\pi$
$809$	−851.198	−	491.439i	−1.05216	−	0.607465i	−0.923253	+	0.384192i	$0.874480\pi$
$810$		0			0
$811$	−458.205			−0.564988			−0.282494	−	0.959269i	$-0.591162\pi$
$811$	−458.205			−0.564988			−0.282494	+	0.959269i	$0.591162\pi$
$812$		0			0
$813$		0			0
$814$	64.0000	+	110.851i	0.0786241	+	0.136181i
$815$	526.543	+	304.000i	0.646066	+	0.373006i
$816$		0			0
$817$	−226.274	−	391.918i	−0.276957	−	0.479704i
$818$			858.000i			1.04890i
$819$		0			0
$820$	−304.000			−0.370732
$821$	−525.416	+	303.349i	−0.639970	+	0.369487i	−0.784603	−	0.619998i	$-0.787133\pi$
$821$	−525.416	+	303.349i	−0.639970	+	0.369487i	0.144633	+	0.989485i	$0.453800\pi$
$822$		0			0
$823$	34.0000	−	58.8897i	0.0413123	−	0.0715550i	−0.844630	−	0.535351i	$-0.820179\pi$
$823$	34.0000	−	58.8897i	0.0413123	−	0.0715550i	0.885942	+	0.463796i	$0.153513\pi$
$824$	180.133	−	104.000i	0.218608	−	0.126214i
$825$		0			0
$826$		0			0
$827$			195.161i			0.235987i	0.993014	+	0.117994i	$0.0376462\pi$
$827$			195.161i			0.235987i	−0.993014	+	0.117994i	$0.962354\pi$
$828$		0			0
$829$	−622.961	+	1079.00i	−0.751461	+	1.30157i	0.195654	+	0.980673i	$0.437317\pi$
$829$	−622.961	+	1079.00i	−0.751461	+	1.30157i	−0.947115	+	0.320895i	$0.896016\pi$
$830$	391.918	+	226.274i	0.472191	+	0.272619i
$831$		0			0
$832$	−101.823			−0.122384
$833$		0			0
$834$		0			0
$835$	232.000	+	401.836i	0.277844	+	0.481240i
$836$	−110.851	−	64.0000i	−0.132597	−	0.0765550i
$837$		0			0
$838$	−489.318	−	847.523i	−0.583912	−	1.01136i
$839$		−	1196.00i		−	1.42551i	−0.701415	−	0.712753i	$-0.747448\pi$
$839$		−	1196.00i		−	1.42551i	0.701415	−	0.712753i	$-0.252552\pi$
$840$		0			0
$841$	−217.000			−0.258026
$842$	470.302	−	271.529i	0.558553	−	0.322481i
$843$		0			0
$844$	132.000	−	228.631i	0.156398	−	0.270889i
$845$	−24.2487	+	14.0000i	−0.0286967	+	0.0165680i
$846$		0			0
$847$		0			0
$848$			379.009i			0.446945i
$849$		0			0
$850$	25.4558	−	44.0908i	0.0299481	−	0.0518715i
$851$	1018.99	+	588.313i	1.19740	+	0.691319i
$852$		0			0
$853$	−1217.64			−1.42748			−0.713738	−	0.700412i	$-0.752999\pi$
$853$	−1217.64			−1.42748			−0.713738	+	0.700412i	$0.752999\pi$
$854$		0			0
$855$		0			0
$856$	−100.000	−	173.205i	−0.116822	−	0.202342i
$857$	549.060	+	317.000i	0.640677	+	0.369895i	0.784875	−	0.619654i	$-0.212727\pi$
$857$	549.060	+	317.000i	0.640677	+	0.369895i	−0.144198	+	0.989549i	$0.546060\pi$
$858$		0			0
$859$	800.445	+	1386.41i	0.931833	+	1.61398i	0.780186	+	0.625548i	$0.215125\pi$
$859$	800.445	+	1386.41i	0.931833	+	1.61398i	0.151648	+	0.988435i	$0.451542\pi$
$860$		−	160.000i		−	0.186047i
$861$		0			0
$862$	−156.000			−0.180974
$863$	399.267	−	230.517i	0.462650	−	0.267111i	−0.250508	−	0.968115i	$-0.580598\pi$
$863$	399.267	−	230.517i	0.462650	−	0.267111i	0.713158	+	0.701004i	$0.247264\pi$
$864$		0			0
$865$	−444.000	+	769.031i	−0.513295	+	0.889053i
$866$	−192.258	+	111.000i	−0.222007	+	0.128176i
$867$		0			0
$868$		0			0
$869$			418.607i			0.481711i
$870$		0			0
$871$	305.470	−	529.090i	0.350712	−	0.607451i
$872$	−210.656	−	121.622i	−0.241578	−	0.139475i
$873$		0			0
$874$	−1176.63			−1.34625
$875$		0			0
$876$		0			0
$877$	−628.000	−	1087.73i	−0.716078	−	1.24028i	−0.962542	−	0.271131i	$-0.912602\pi$
$877$	−628.000	−	1087.73i	−0.716078	−	1.24028i	0.246465	−	0.969152i	$-0.420731\pi$
$878$	−249.415	−	144.000i	−0.284072	−	0.164009i
$879$		0			0
$880$	−22.6274	−	39.1918i	−0.0257130	−	0.0445362i
$881$			1092.00i			1.23950i	0.784799	+	0.619750i	$0.212766\pi$
$881$			1092.00i			1.23950i	−0.784799	+	0.619750i	$0.787234\pi$
$882$		0			0
$883$	284.000			0.321631			0.160815	−	0.986985i	$-0.448588\pi$
$883$	284.000			0.321631			0.160815	+	0.986985i	$0.448588\pi$
$884$	−88.1816	+	50.9117i	−0.0997530	+	0.0575924i
$885$		0			0
$886$	−574.000	+	994.197i	−0.647856	+	1.12212i
$887$	620.074	−	358.000i	0.699069	−	0.403608i	−0.107932	−	0.994158i	$-0.534423\pi$
$887$	620.074	−	358.000i	0.699069	−	0.403608i	0.807001	+	0.590551i	$0.201089\pi$
$888$		0			0
$889$		0			0
$890$			599.627i			0.673738i
$891$		0			0
$892$	−169.706	+	293.939i	−0.190253	+	0.329528i
$893$	391.918	+	226.274i	0.438878	+	0.253387i
$894$		0			0
$895$	−237.588			−0.265461
$896$		0			0
$897$		0			0
$898$	201.000	+	348.142i	0.223831	+	0.387686i
$899$	1434.14	+	828.000i	1.59526	+	0.921023i
$900$		0			0
$901$	189.505	+	328.232i	0.210327	+	0.364297i
$902$		−	152.000i		−	0.168514i
$903$		0			0
$904$	−60.0000			−0.0663717
$905$	279.242	−	161.220i	0.308555	−	0.178144i
$906$		0			0
$907$	−362.000	+	627.002i	−0.399118	+	0.691293i	−0.993617	−	0.112803i	$-0.964017\pi$
$907$	−362.000	+	627.002i	−0.399118	+	0.691293i	0.594499	+	0.804096i	$0.297350\pi$
$908$	519.615	−	300.000i	0.572263	−	0.330396i
$909$		0			0
$910$		0			0
$911$		−	302.642i		−	0.332208i	−0.986108	−	0.166104i	$-0.946881\pi$
$911$		−	302.642i		−	0.332208i	0.986108	−	0.166104i	$-0.0531188\pi$
$912$		0			0
$913$	−113.137	+	195.959i	−0.123918	+	0.214632i
$914$	352.727	+	203.647i	0.385915	+	0.222808i
$915$		0			0
$916$	500.632			0.546541
$917$		0			0
$918$		0			0
$919$	−188.000	−	325.626i	−0.204570	−	0.354326i	0.745426	−	0.666589i	$-0.232246\pi$
$919$	−188.000	−	325.626i	−0.204570	−	0.354326i	−0.949996	+	0.312263i	$0.898913\pi$
$920$	−360.267	−	208.000i	−0.391594	−	0.226087i
$921$		0			0
$922$	−499.217	−	864.670i	−0.541451	−	0.937820i
$923$			972.000i			1.05309i
$924$		0			0
$925$	−288.000			−0.311351
$926$	−436.009	+	251.730i	−0.470852	+	0.271847i
$927$		0			0
$928$	92.0000	−	159.349i	0.0991379	−	0.171712i
$929$	1047.89	−	605.000i	1.12798	−	0.651238i	0.184552	−	0.982823i	$-0.440917\pi$
$929$	1047.89	−	605.000i	1.12798	−	0.651238i	0.943425	+	0.331585i	$0.107583\pi$
$930$		0			0
$931$		0			0
$932$		−	59.3970i		−	0.0637307i
$933$		0			0
$934$	−625.082	+	1082.67i	−0.669253	+	1.15918i
$935$	−39.1918	−	22.6274i	−0.0419164	−	0.0242004i
$936$		0			0
$937$	994.192			1.06104			0.530519	−	0.847673i	$-0.321997\pi$
$937$	994.192			1.06104			0.530519	+	0.847673i	$0.321997\pi$
$938$		0			0
$939$		0			0
$940$	80.0000	+	138.564i	0.0851064	+	0.147409i
$941$	38.1051	+	22.0000i	0.0404943	+	0.0233794i	0.520110	−	0.854099i	$-0.325891\pi$
$941$	38.1051	+	22.0000i	0.0404943	+	0.0233794i	−0.479616	+	0.877478i	$0.659224\pi$
$942$		0			0
$943$	−698.621	−	1210.05i	−0.740850	−	1.28319i
$944$			16.0000i			0.0169492i
$945$		0			0
$946$	80.0000			0.0845666
$947$	−874.468	+	504.874i	−0.923408	+	0.533130i	−0.884721	−	0.466121i	$-0.845651\pi$
$947$	−874.468	+	504.874i	−0.923408	+	0.533130i	−0.0386876	+	0.999251i	$0.512318\pi$
$948$		0			0
$949$	765.000	−	1325.02i	0.806112	−	1.39623i
$950$	249.415	−	144.000i	0.262542	−	0.151579i
$951$		0			0
$952$		0			0
$953$		−	1322.29i		−	1.38750i	−0.720215	−	0.693751i	$-0.755957\pi$
$953$		−	1322.29i		−	1.38750i	0.720215	−	0.693751i	$-0.244043\pi$
$954$		0			0
$955$	−605.283	+	1048.38i	−0.633805	+	1.09778i
$956$	279.242	+	161.220i	0.292094	+	0.168641i
$957$		0			0
$958$	−718.420			−0.749917
$959$		0			0
$960$		0			0
$961$	−815.500	−	1412.49i	−0.848595	−	1.46981i
$962$	498.831	+	288.000i	0.518535	+	0.299376i
$963$		0			0
$964$	377.595	+	654.014i	0.391696	+	0.678438i
$965$			872.000i			0.903627i
$966$		0			0
$967$	876.000			0.905895			0.452947	−	0.891537i	$-0.350373\pi$
$967$	876.000			0.905895			0.452947	+	0.891537i	$0.350373\pi$
$968$	−276.792	+	159.806i	−0.285943	+	0.165089i
$969$		0			0
$970$	436.000	−	755.174i	0.449485	−	0.778530i
$971$	−1254.00	+	724.000i	−1.29146	+	0.745623i	−0.978912	−	0.204280i	$-0.934515\pi$
$971$	−1254.00	+	724.000i	−1.29146	+	0.745623i	−0.312545	+	0.949903i	$0.601181\pi$
$972$		0			0
$973$		0			0
$974$		−	882.469i		−	0.906026i
$975$		0			0
$976$	−166.877	+	289.040i	−0.170981	+	0.296147i
$977$	−1289.66	−	744.583i	−1.32002	−	0.762112i	−0.336286	−	0.941760i	$-0.609171\pi$
$977$	−1289.66	−	744.583i	−1.32002	−	0.762112i	−0.983731	+	0.179648i	$0.942504\pi$
$978$		0			0
$979$	−299.813			−0.306244
$980$		0			0
$981$		0			0
$982$	−594.000	−	1028.84i	−0.604888	−	1.04770i
$983$	−27.7128	−	16.0000i	−0.0281921	−	0.0162767i	0.485838	−	0.874049i	$-0.338515\pi$
$983$	−27.7128	−	16.0000i	−0.0281921	−	0.0162767i	−0.514030	+	0.857772i	$0.671848\pi$
$984$		0			0
$985$	574.171	+	994.493i	0.582914	+	1.00964i
$986$		−	184.000i		−	0.186613i
$987$		0			0
$988$	−576.000			−0.582996
$989$	636.867	−	367.696i	0.643951	−	0.371785i
$990$		0			0
$991$	140.000	−	242.487i	0.141271	−	0.244689i	−0.786704	−	0.617330i	$-0.788214\pi$
$991$	140.000	−	242.487i	0.141271	−	0.244689i	0.927976	+	0.372641i	$0.121548\pi$
$992$	−249.415	+	144.000i	−0.251427	+	0.145161i
$993$		0			0
$994$		0			0
$995$		−	271.529i		−	0.272893i
$996$		0			0
$997$	−546.594	+	946.728i	−0.548238	+	0.949577i	0.450157	+	0.892949i	$0.351368\pi$
$997$	−546.594	+	946.728i	−0.548238	+	0.949577i	−0.998395	+	0.0566272i	$0.981965\pi$
$998$	1151.26	+	664.680i	1.15357	+	0.666012i
$999$		0			0

Twists

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

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

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} -2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(1.00000 - 1.73205i) q^{4} +(3.46410 - 2.00000i) q^{5} -2.82843i q^{8} +(2.82843 - 4.89898i) q^{10} +(2.44949 + 1.41421i) q^{11} +12.7279 q^{13} +(-2.00000 - 3.46410i) q^{16} +(-3.46410 - 2.00000i) q^{17} +(-11.3137 - 19.5959i) q^{19} -8.00000i q^{20} +4.00000 q^{22} +(31.8434 - 18.3848i) q^{23} +(-4.50000 + 7.79423i) q^{25} +(15.5885 - 9.00000i) q^{26} +32.5269i q^{29} +(25.4558 - 44.0908i) q^{31} +(-4.89898 - 2.82843i) q^{32} -5.65685 q^{34} +(16.0000 + 27.7128i) q^{37} +(-27.7128 - 16.0000i) q^{38} +(-5.65685 - 9.79796i) q^{40} -38.0000i q^{41} +20.0000 q^{43} +(4.89898 - 2.82843i) q^{44} +(26.0000 - 45.0333i) q^{46} +(-17.3205 + 10.0000i) q^{47} +12.7279i q^{50} +(12.7279 - 22.0454i) q^{52} +(-82.0579 - 47.3762i) q^{53} +11.3137 q^{55} +(23.0000 + 39.8372i) q^{58} +(-3.46410 - 2.00000i) q^{59} +(-41.7193 - 72.2599i) q^{61} -72.0000i q^{62} -8.00000 q^{64} +(44.0908 - 25.4558i) q^{65} +(24.0000 - 41.5692i) q^{67} +(-6.92820 + 4.00000i) q^{68} +76.3675i q^{71} +(60.1041 - 104.103i) q^{73} +(39.1918 + 22.6274i) q^{74} -45.2548 q^{76} +(74.0000 + 128.172i) q^{79} +(-13.8564 - 8.00000i) q^{80} +(-26.8701 - 46.5403i) q^{82} +80.0000i q^{83} -16.0000 q^{85} +(24.4949 - 14.1421i) q^{86} +(4.00000 - 6.92820i) q^{88} +(-91.7987 + 53.0000i) q^{89} -73.5391i q^{92} +(-14.1421 + 24.4949i) q^{94} +(-78.3837 - 45.2548i) q^{95} +154.149 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{4}+O(q^{10}) \) 8 * q + 8 * q^4	\( 8 q + 8 q^{4} - 16 q^{16} + 32 q^{22} - 36 q^{25} + 128 q^{37} + 160 q^{43} + 208 q^{46} + 184 q^{58} - 64 q^{64} + 192 q^{67} + 592 q^{79} - 128 q^{85} + 32 q^{88}+O(q^{100}) \) 8 * q + 8 * q^4 - 16 * q^16 + 32 * q^22 - 36 * q^25 + 128 * q^37 + 160 * q^43 + 208 * q^46 + 184 * q^58 - 64 * q^64 + 192 * q^67 + 592 * q^79 - 128 * q^85 + 32 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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