LMFDB - Embedded newform 144.3.j.a.53.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [144,3,Mod(53,144)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(144, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 2]))

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

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

chi := DirichletCharacter("144.53");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 144 = 2^{4} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	144.j (of order $4$, degree $2$, 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:	$3.92371580679$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			53.3
Character	$\chi$	$=$	144.53
Dual form			144.3.j.a.125.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.76559 - 0.939508i) q^{2} +(2.23465 + 3.31758i) q^{4} +(-6.08688 + 6.08688i) q^{5} -9.40026i q^{7} +(-0.828591 - 7.95697i) q^{8} +O(q^{10})$	\(q+(-1.76559 - 0.939508i) q^{2} +(2.23465 + 3.31758i) q^{4} +(-6.08688 + 6.08688i) q^{5} -9.40026i q^{7} +(-0.828591 - 7.95697i) q^{8} +(16.4656 - 5.02829i) q^{10} +(11.9531 - 11.9531i) q^{11} +(3.47284 - 3.47284i) q^{13} +(-8.83162 + 16.5970i) q^{14} +(-6.01269 + 14.8273i) q^{16} -28.5398i q^{17} +(-3.08620 + 3.08620i) q^{19} +(-33.7958 - 6.59168i) q^{20} +(-32.3344 + 9.87430i) q^{22} +2.57437 q^{23} -49.1003i q^{25} +(-9.39439 + 2.86887i) q^{26} +(31.1861 - 21.0063i) q^{28} +(3.49628 + 3.49628i) q^{29} -21.0909 q^{31} +(24.5463 - 20.5300i) q^{32} +(-26.8134 + 50.3897i) q^{34} +(57.2183 + 57.2183i) q^{35} +(-13.2847 - 13.2847i) q^{37} +(8.34848 - 2.54947i) q^{38} +(53.4767 + 43.3896i) q^{40} -11.2365 q^{41} +(8.19150 + 8.19150i) q^{43} +(66.3664 + 12.9444i) q^{44} +(-4.54529 - 2.41864i) q^{46} -17.2381i q^{47} -39.3649 q^{49} +(-46.1301 + 86.6912i) q^{50} +(19.2820 + 3.76085i) q^{52} +(-30.5182 + 30.5182i) q^{53} +145.514i q^{55} +(-74.7976 + 7.78897i) q^{56} +(-2.88823 - 9.45780i) q^{58} +(14.7367 - 14.7367i) q^{59} +(39.3037 - 39.3037i) q^{61} +(37.2380 + 19.8151i) q^{62} +(-62.6269 + 13.1862i) q^{64} +42.2775i q^{65} +(79.6470 - 79.6470i) q^{67} +(94.6830 - 63.7764i) q^{68} +(-47.2672 - 154.781i) q^{70} +73.1921 q^{71} +1.23261i q^{73} +(10.9744 + 35.9366i) q^{74} +(-17.1353 - 3.34214i) q^{76} +(-112.362 - 112.362i) q^{77} -110.191 q^{79} +(-53.6533 - 126.850i) q^{80} +(19.8390 + 10.5568i) q^{82} +(-13.7800 - 13.7800i) q^{83} +(173.718 + 173.718i) q^{85} +(-6.76689 - 22.1589i) q^{86} +(-105.015 - 85.2063i) q^{88} -39.2555 q^{89} +(-32.6456 - 32.6456i) q^{91} +(5.75280 + 8.54067i) q^{92} +(-16.1954 + 30.4356i) q^{94} -37.5706i q^{95} -109.383 q^{97} +(69.5024 + 36.9836i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q+O(q^{10}) $ 32 * q	$ 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) $ 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/144\mathbb{Z}\right)^\times$.

$n$	$37$	$65$	$127$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$1$

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 $

$2$	−1.76559	−	0.939508i	−0.882797	−	0.469754i
$2$	−1.76559	−	0.939508i	−0.882797	−	0.469754i
$3$		0			0
$3$		0			0
$4$	2.23465	+	3.31758i	0.558662	+	0.829395i
$5$	−6.08688	+	6.08688i	−1.21738	+	1.21738i	−0.248829	+	0.968547i	$0.580046\pi$
$5$	−6.08688	+	6.08688i	−1.21738	+	1.21738i	−0.968547	+	0.248829i	$0.919954\pi$
$6$		0			0
$7$		−	9.40026i		−	1.34289i	−0.741053	−	0.671447i	$-0.765673\pi$
$7$		−	9.40026i		−	1.34289i	0.741053	−	0.671447i	$-0.234327\pi$
$8$	−0.828591	−	7.95697i	−0.103574	−	0.994622i
$9$		0			0
$10$	16.4656	−	5.02829i	1.64656	−	0.502829i
$11$	11.9531	−	11.9531i	1.08665	−	1.08665i	0.0907749	−	0.995871i	$-0.471066\pi$
$11$	11.9531	−	11.9531i	1.08665	−	1.08665i	0.995871	−	0.0907749i	$-0.0289344\pi$
$12$		0			0
$13$	3.47284	−	3.47284i	0.267142	−	0.267142i	−0.560806	−	0.827947i	$-0.689509\pi$
$13$	3.47284	−	3.47284i	0.267142	−	0.267142i	0.827947	+	0.560806i	$0.189509\pi$
$14$	−8.83162	+	16.5970i	−0.630830	+	1.18550i
$15$		0			0
$16$	−6.01269	+	14.8273i	−0.375793	+	0.926704i
$17$		−	28.5398i		−	1.67881i	−0.543506	−	0.839405i	$-0.682903\pi$
$17$		−	28.5398i		−	1.67881i	0.543506	−	0.839405i	$-0.317097\pi$
$18$		0			0
$19$	−3.08620	+	3.08620i	−0.162431	+	0.162431i	−0.783643	−	0.621212i	$-0.786641\pi$
$19$	−3.08620	+	3.08620i	−0.162431	+	0.162431i	0.621212	+	0.783643i	$0.286641\pi$
$20$	−33.7958	−	6.59168i	−1.68979	−	0.329584i
$21$		0			0
$22$	−32.3344	+	9.87430i	−1.46974	+	0.448832i
$23$	2.57437			0.111929			0.0559645	−	0.998433i	$-0.482177\pi$
$23$	2.57437			0.111929			0.0559645	+	0.998433i	$0.482177\pi$
$24$		0			0
$25$		−	49.1003i		−	1.96401i
$26$	−9.39439	+	2.86887i	−0.361323	+	0.110341i
$27$		0			0
$28$	31.1861	−	21.0063i	1.11379	−	0.750224i
$29$	3.49628	+	3.49628i	0.120561	+	0.120561i	0.764813	−	0.644252i	$-0.222831\pi$
$29$	3.49628	+	3.49628i	0.120561	+	0.120561i	−0.644252	+	0.764813i	$0.722831\pi$
$30$		0			0
$31$	−21.0909			−0.680351			−0.340176	−	0.940362i	$-0.610487\pi$
$31$	−21.0909			−0.680351			−0.340176	+	0.940362i	$0.610487\pi$
$32$	24.5463	−	20.5300i	0.767072	−	0.641561i
$33$		0			0
$34$	−26.8134	+	50.3897i	−0.788628	+	1.48205i
$35$	57.2183	+	57.2183i	1.63481	+	1.63481i
$36$		0			0
$37$	−13.2847	−	13.2847i	−0.359047	−	0.359047i	0.504414	−	0.863462i	$-0.331708\pi$
$37$	−13.2847	−	13.2847i	−0.359047	−	0.359047i	−0.863462	+	0.504414i	$0.831708\pi$
$38$	8.34848	−	2.54947i	0.219697	−	0.0670912i
$39$		0			0
$40$	53.4767	+	43.3896i	1.33692	+	1.08474i
$41$	−11.2365			−0.274060			−0.137030	−	0.990567i	$-0.543756\pi$
$41$	−11.2365			−0.274060			−0.137030	+	0.990567i	$0.543756\pi$
$42$		0			0
$43$	8.19150	+	8.19150i	0.190500	+	0.190500i	0.795912	−	0.605412i	$-0.206992\pi$
$43$	8.19150	+	8.19150i	0.190500	+	0.190500i	−0.605412	+	0.795912i	$0.706992\pi$
$44$	66.3664	+	12.9444i	1.50833	+	0.294191i
$45$		0			0
$46$	−4.54529	−	2.41864i	−0.0988106	−	0.0525791i
$47$		−	17.2381i		−	0.366769i	−0.983041	−	0.183384i	$-0.941295\pi$
$47$		−	17.2381i		−	0.366769i	0.983041	−	0.183384i	$-0.0587053\pi$
$48$		0			0
$49$	−39.3649			−0.803364
$50$	−46.1301	+	86.6912i	−0.922602	+	1.73382i
$51$		0			0
$52$	19.2820	+	3.76085i	0.370808	+	0.0723240i
$53$	−30.5182	+	30.5182i	−0.575816	+	0.575816i	−0.933748	−	0.357932i	$-0.883482\pi$
$53$	−30.5182	+	30.5182i	−0.575816	+	0.575816i	0.357932	+	0.933748i	$0.383482\pi$
$54$		0			0
$55$			145.514i			2.64572i
$56$	−74.7976	+	7.78897i	−1.33567	+	0.139089i
$57$		0			0
$58$	−2.88823	−	9.45780i	−0.0497971	−	0.163066i
$59$	14.7367	−	14.7367i	0.249774	−	0.249774i	−0.571104	−	0.820878i	$-0.693485\pi$
$59$	14.7367	−	14.7367i	0.249774	−	0.249774i	0.820878	+	0.571104i	$0.193485\pi$
$60$		0			0
$61$	39.3037	−	39.3037i	0.644323	−	0.644323i	−0.307292	−	0.951615i	$-0.599423\pi$
$61$	39.3037	−	39.3037i	0.644323	−	0.644323i	0.951615	+	0.307292i	$0.0994229\pi$
$62$	37.2380	+	19.8151i	0.600612	+	0.319598i
$63$		0			0
$64$	−62.6269	+	13.1862i	−0.978545	+	0.206034i
$65$			42.2775i			0.650424i
$66$		0			0
$67$	79.6470	−	79.6470i	1.18876	−	1.18876i	0.211351	−	0.977410i	$-0.432214\pi$
$67$	79.6470	−	79.6470i	1.18876	−	1.18876i	0.977410	−	0.211351i	$-0.0677863\pi$
$68$	94.6830	−	63.7764i	1.39240	−	0.937888i
$69$		0			0
$70$	−47.2672	−	154.781i	−0.675246	−	2.21116i
$71$	73.1921			1.03087			0.515437	−	0.856927i	$-0.327630\pi$
$71$	73.1921			1.03087			0.515437	+	0.856927i	$0.327630\pi$
$72$		0			0
$73$			1.23261i			0.0168851i	0.999964	+	0.00844256i	$0.00268738\pi$
$73$			1.23261i			0.0168851i	−0.999964	+	0.00844256i	$0.997313\pi$
$74$	10.9744	+	35.9366i	0.148302	+	0.485630i
$75$		0			0
$76$	−17.1353	−	3.34214i	−0.225464	−	0.0439755i
$77$	−112.362	−	112.362i	−1.45925	−	1.45925i
$78$		0			0
$79$	−110.191			−1.39482			−0.697411	−	0.716672i	$-0.745665\pi$
$79$	−110.191			−1.39482			−0.697411	+	0.716672i	$0.745665\pi$
$80$	−53.6533	−	126.850i	−0.670666	−	1.58563i
$81$		0			0
$82$	19.8390	+	10.5568i	0.241940	+	0.128741i
$83$	−13.7800	−	13.7800i	−0.166025	−	0.166025i	0.619205	−	0.785229i	$-0.287455\pi$
$83$	−13.7800	−	13.7800i	−0.166025	−	0.166025i	−0.785229	+	0.619205i	$0.787455\pi$
$84$		0			0
$85$	173.718	+	173.718i	2.04374	+	2.04374i
$86$	−6.76689	−	22.1589i	−0.0786848	−	0.257661i
$87$		0			0
$88$	−105.015	−	85.2063i	−1.19335	−	0.968254i
$89$	−39.2555			−0.441073			−0.220537	−	0.975379i	$-0.570781\pi$
$89$	−39.2555			−0.441073			−0.220537	+	0.975379i	$0.570781\pi$
$90$		0			0
$91$	−32.6456	−	32.6456i	−0.358743	−	0.358743i
$92$	5.75280	+	8.54067i	0.0625305	+	0.0928333i
$93$		0			0
$94$	−16.1954	+	30.4356i	−0.172291	+	0.323783i
$95$		−	37.5706i		−	0.395480i
$96$		0			0
$97$	−109.383			−1.12766			−0.563830	−	0.825891i	$-0.690673\pi$
$97$	−109.383			−1.12766			−0.563830	+	0.825891i	$0.690673\pi$
$98$	69.5024	+	36.9836i	0.709208	+	0.377384i
$99$		0			0
$100$	162.894	−	109.722i	1.62894	−	1.09722i
$101$	−102.843	+	102.843i	−1.01824	+	1.01824i	−0.0184123	+	0.999830i	$0.505861\pi$
$101$	−102.843	+	102.843i	−1.01824	+	1.01824i	−0.999830	+	0.0184123i	$0.994139\pi$
$102$		0			0
$103$			66.0152i			0.640924i	0.947261	+	0.320462i	$0.103838\pi$
$103$			66.0152i			0.640924i	−0.947261	+	0.320462i	$0.896162\pi$
$104$	−30.5109	−	24.7557i	−0.293374	−	0.238036i
$105$		0			0
$106$	82.5549	−	25.2107i	0.778820	−	0.237837i
$107$	−87.3982	+	87.3982i	−0.816805	+	0.816805i	−0.985644	−	0.168838i	$-0.945998\pi$
$107$	−87.3982	+	87.3982i	−0.816805	+	0.816805i	0.168838	+	0.985644i	$0.445998\pi$
$108$		0			0
$109$	0.493298	−	0.493298i	0.00452567	−	0.00452567i	−0.704840	−	0.709366i	$-0.748981\pi$
$109$	0.493298	−	0.493298i	0.00452567	−	0.00452567i	0.709366	+	0.704840i	$0.248981\pi$
$110$	136.712	−	256.919i	1.24284	−	2.33563i
$111$		0			0
$112$	139.380	+	56.5208i	1.24446	+	0.504650i
$113$		−	181.667i		−	1.60768i	−0.594848	−	0.803838i	$-0.702788\pi$
$113$		−	181.667i		−	1.60768i	0.594848	−	0.803838i	$-0.297212\pi$
$114$		0			0
$115$	−15.6699	+	15.6699i	−0.136260	+	0.136260i
$116$	−3.78623	+	19.4122i	−0.0326400	+	0.167346i
$117$		0			0
$118$	−39.8642	+	12.1738i	−0.337832	+	0.103168i
$119$	−268.281			−2.25447
$120$		0			0
$121$		−	164.754i		−	1.36160i
$122$	−106.321	+	32.4683i	−0.871480	+	0.266133i
$123$		0			0
$124$	−47.1307	−	69.9707i	−0.380087	−	0.564280i
$125$	146.696	+	146.696i	1.17356	+	1.17356i
$126$		0			0
$127$	188.223			1.48207			0.741035	−	0.671466i	$-0.234335\pi$
$127$	188.223			1.48207			0.741035	+	0.671466i	$0.234335\pi$
$128$	122.962	+	35.5570i	0.960642	+	0.277789i
$129$		0			0
$130$	39.7201	−	74.6450i	0.305539	−	0.574192i
$131$	79.5518	+	79.5518i	0.607266	+	0.607266i	0.942231	−	0.334965i	$-0.108725\pi$
$131$	79.5518	+	79.5518i	0.607266	+	0.607266i	−0.334965	+	0.942231i	$0.608725\pi$
$132$		0			0
$133$	29.0110	+	29.0110i	0.218128	+	0.218128i
$134$	−215.453	+	65.7953i	−1.60786	+	0.491010i
$135$		0			0
$136$	−227.090	+	23.6478i	−1.66978	+	0.173881i
$137$	204.894			1.49557			0.747787	−	0.663939i	$-0.231117\pi$
$137$	204.894			1.49557			0.747787	+	0.663939i	$0.231117\pi$
$138$		0			0
$139$	153.586	+	153.586i	1.10494	+	1.10494i	0.993806	+	0.111133i	$0.0354478\pi$
$139$	153.586	+	153.586i	1.10494	+	1.10494i	0.111133	+	0.993806i	$0.464552\pi$
$140$	−61.9635	+	317.689i	−0.442596	+	2.26921i
$141$		0			0
$142$	−129.228	−	68.7645i	−0.910053	−	0.484257i
$143$		−	83.0225i		−	0.580577i
$144$		0			0
$145$	−42.5629			−0.293537
$146$	1.15805	−	2.17630i	0.00793186	−	0.0149061i
$147$		0			0
$148$	14.3865	−	73.7600i	0.0972059	−	0.498378i
$149$	24.6527	−	24.6527i	0.165455	−	0.165455i	−0.619523	−	0.784978i	$-0.712674\pi$
$149$	24.6527	−	24.6527i	0.165455	−	0.165455i	0.784978	+	0.619523i	$0.212674\pi$
$150$		0			0
$151$		−	56.2047i		−	0.372216i	−0.982529	−	0.186108i	$-0.940412\pi$
$151$		−	56.2047i		−	0.372216i	0.982529	−	0.186108i	$-0.0595875\pi$
$152$	27.1140	+	21.9996i	0.178381	+	0.144734i
$153$		0			0
$154$	92.8210	+	303.952i	0.602734	+	1.97371i
$155$	128.378	−	128.378i	0.828244	−	0.828244i
$156$		0			0
$157$	−152.225	+	152.225i	−0.969589	+	0.969589i	−0.999551	−	0.0299624i	$-0.990461\pi$
$157$	−152.225	+	152.225i	−0.969589	+	0.969589i	0.0299624	+	0.999551i	$0.490461\pi$
$158$	194.552	+	103.525i	1.23134	+	0.655223i
$159$		0			0
$160$	−24.4469	+	274.374i	−0.152793	+	1.71484i
$161$		−	24.1997i		−	0.150309i
$162$		0			0
$163$	147.071	−	147.071i	0.902276	−	0.902276i	−0.0933563	−	0.995633i	$-0.529760\pi$
$163$	147.071	−	147.071i	0.902276	−	0.902276i	0.995633	+	0.0933563i	$0.0297596\pi$
$164$	−25.1096	−	37.2779i	−0.153107	−	0.227304i
$165$		0			0
$166$	11.3835	+	37.2764i	0.0685753	+	0.224557i
$167$	−100.239			−0.600232			−0.300116	−	0.953903i	$-0.597025\pi$
$167$	−100.239			−0.600232			−0.300116	+	0.953903i	$0.597025\pi$
$168$		0			0
$169$			144.879i			0.857271i
$170$	−143.506	−	469.926i	−0.844155	−	2.76427i
$171$		0			0
$172$	−8.87084	+	45.4811i	−0.0515746	+	0.264425i
$173$	179.056	+	179.056i	1.03501	+	1.03501i	0.999365	+	0.0356433i	$0.0113480\pi$
$173$	179.056	+	179.056i	1.03501	+	1.03501i	0.0356433	+	0.999365i	$0.488652\pi$
$174$		0			0
$175$	−461.555			−2.63746
$176$	105.362	+	249.102i	0.598645	+	1.41535i
$177$		0			0
$178$	69.3094	+	36.8809i	0.389378	+	0.207196i
$179$	−8.84637	−	8.84637i	−0.0494211	−	0.0494211i	0.681964	−	0.731385i	$-0.261126\pi$
$179$	−8.84637	−	8.84637i	−0.0494211	−	0.0494211i	−0.731385	+	0.681964i	$0.761126\pi$
$180$		0			0
$181$	−135.353	−	135.353i	−0.747807	−	0.747807i	0.226260	−	0.974067i	$-0.427350\pi$
$181$	−135.353	−	135.353i	−0.747807	−	0.747807i	−0.974067	+	0.226260i	$0.927350\pi$
$182$	26.9681	+	88.3097i	0.148176	+	0.485218i
$183$		0			0
$184$	−2.13310	−	20.4842i	−0.0115929	−	0.111327i
$185$	161.725			0.874191
$186$		0			0
$187$	−341.139	−	341.139i	−1.82427	−	1.82427i
$188$	57.1889	−	38.5212i	0.304196	−	0.204900i
$189$		0			0
$190$	−35.2979	+	66.3345i	−0.185779	+	0.349129i
$191$			117.914i			0.617351i	0.951167	+	0.308675i	$0.0998856\pi$
$191$			117.914i			0.617351i	−0.951167	+	0.308675i	$0.900114\pi$
$192$		0			0
$193$	65.1940			0.337793			0.168896	−	0.985634i	$-0.445980\pi$
$193$	65.1940			0.337793			0.168896	+	0.985634i	$0.445980\pi$
$194$	193.126	+	102.766i	0.995496	+	0.529723i
$195$		0			0
$196$	−87.9666	−	130.596i	−0.448809	−	0.666307i
$197$	26.9481	−	26.9481i	0.136793	−	0.136793i	−0.635395	−	0.772187i	$-0.719163\pi$
$197$	26.9481	−	26.9481i	0.136793	−	0.136793i	0.772187	+	0.635395i	$0.219163\pi$
$198$		0			0
$199$		−	290.806i		−	1.46133i	−0.682734	−	0.730667i	$-0.739209\pi$
$199$		−	290.806i		−	1.46133i	0.682734	−	0.730667i	$-0.260791\pi$
$200$	−390.690	+	40.6841i	−1.95345	+	0.203420i
$201$		0			0
$202$	278.200	−	84.9568i	1.37723	−	0.420578i
$203$	32.8660	−	32.8660i	0.161901	−	0.161901i
$204$		0			0
$205$	68.3951	−	68.3951i	0.333634	−	0.333634i
$206$	62.0218	−	116.556i	0.301077	−	0.565806i
$207$		0			0
$208$	30.6116	+	72.3738i	0.147171	+	0.347951i
$209$			73.7793i			0.353011i
$210$		0			0
$211$	143.972	−	143.972i	0.682334	−	0.682334i	−0.278192	−	0.960526i	$-0.589735\pi$
$211$	143.972	−	143.972i	0.682334	−	0.682334i	0.960526	+	0.278192i	$0.0897351\pi$
$212$	−169.444	−	33.0492i	−0.799265	−	0.155892i
$213$		0			0
$214$	236.421	−	72.1985i	1.10477	−	0.337376i
$215$	−99.7214			−0.463821
$216$		0			0
$217$			198.260i			0.913640i
$218$	−1.33442	+	0.407507i	−0.00612120	+	0.00186930i
$219$		0			0
$220$	−482.756	+	325.174i	−2.19434	+	1.47806i
$221$	−99.1141	−	99.1141i	−0.448480	−	0.448480i
$222$		0			0
$223$	200.870			0.900761			0.450381	−	0.892837i	$-0.351288\pi$
$223$	200.870			0.900761			0.450381	+	0.892837i	$0.351288\pi$
$224$	−192.987	−	230.742i	−0.861549	−	1.03010i
$225$		0			0
$226$	−170.678	+	320.751i	−0.755212	+	1.41925i
$227$	37.3792	+	37.3792i	0.164666	+	0.164666i	0.784630	−	0.619964i	$-0.212853\pi$
$227$	37.3792	+	37.3792i	0.164666	+	0.164666i	−0.619964	+	0.784630i	$0.712853\pi$
$228$		0			0
$229$	101.806	+	101.806i	0.444569	+	0.444569i	0.893544	−	0.448975i	$-0.148211\pi$
$229$	101.806	+	101.806i	0.444569	+	0.444569i	−0.448975	+	0.893544i	$0.648211\pi$
$230$	42.3886	−	12.9447i	0.184298	−	0.0562811i
$231$		0			0
$232$	24.9228	−	30.7168i	0.107426	−	0.132400i
$233$	80.6982			0.346344			0.173172	−	0.984892i	$-0.444598\pi$
$233$	80.6982			0.346344			0.173172	+	0.984892i	$0.444598\pi$
$234$		0			0
$235$	104.927	+	104.927i	0.446496	+	0.446496i
$236$	81.8214	+	15.9588i	0.346701	+	0.0676221i
$237$		0			0
$238$	473.676	+	252.052i	1.99024	+	1.05904i
$239$		−	301.011i		−	1.25946i	−0.776814	−	0.629730i	$-0.783166\pi$
$239$		−	301.011i		−	1.25946i	0.776814	−	0.629730i	$-0.216834\pi$
$240$		0			0
$241$	159.477			0.661732			0.330866	−	0.943678i	$-0.392659\pi$
$241$	159.477			0.661732			0.330866	+	0.943678i	$0.392659\pi$
$242$	−154.787	+	290.888i	−0.639617	+	1.20202i
$243$		0			0
$244$	218.223	+	42.5632i	0.894357	+	0.174439i
$245$	239.609	−	239.609i	0.977997	−	0.977997i
$246$		0			0
$247$			21.4357i			0.0867844i
$248$	17.4757	+	167.820i	0.0704666	+	0.676692i
$249$		0			0
$250$	−121.183	−	396.827i	−0.484733	−	1.58731i
$251$	−291.951	+	291.951i	−1.16315	+	1.16315i	−0.179368	+	0.983782i	$0.557405\pi$
$251$	−291.951	+	291.951i	−1.16315	+	1.16315i	−0.983782	+	0.179368i	$0.942595\pi$
$252$		0			0
$253$	30.7717	−	30.7717i	0.121627	−	0.121627i
$254$	−332.325	−	176.837i	−1.30837	−	0.696208i
$255$		0			0
$256$	−183.695	−	178.303i	−0.717559	−	0.696497i
$257$			136.807i			0.532323i	0.963929	+	0.266161i	$0.0857554\pi$
$257$			136.807i			0.532323i	−0.963929	+	0.266161i	$0.914245\pi$
$258$		0			0
$259$	−124.880	+	124.880i	−0.482162	+	0.482162i
$260$	−140.259	+	94.4755i	−0.539458	+	0.363367i
$261$		0			0
$262$	−65.7167	−	215.196i	−0.250827	−	0.821358i
$263$	449.794			1.71024			0.855121	−	0.518429i	$-0.173483\pi$
$263$	449.794			1.71024			0.855121	+	0.518429i	$0.173483\pi$
$264$		0			0
$265$		−	371.522i		−	1.40197i
$266$	−23.9656	−	78.4779i	−0.0900964	−	0.295030i
$267$		0			0
$268$	442.218	+	86.2523i	1.65007	+	0.321837i
$269$	−77.2032	−	77.2032i	−0.287001	−	0.287001i	0.548892	−	0.835893i	$-0.315050\pi$
$269$	−77.2032	−	77.2032i	−0.287001	−	0.287001i	−0.835893	+	0.548892i	$0.815050\pi$
$270$		0			0
$271$	496.378			1.83165			0.915827	−	0.401574i	$-0.131537\pi$
$271$	496.378			1.83165			0.915827	+	0.401574i	$0.131537\pi$
$272$	423.167	+	171.601i	1.55576	+	0.630885i
$273$		0			0
$274$	−361.759	−	192.499i	−1.32029	−	0.702552i
$275$	−586.901	−	586.901i	−2.13419	−	2.13419i
$276$		0			0
$277$	−25.7238	−	25.7238i	−0.0928658	−	0.0928658i	0.659148	−	0.752014i	$-0.270917\pi$
$277$	−25.7238	−	25.7238i	−0.0928658	−	0.0928658i	−0.752014	+	0.659148i	$0.770917\pi$
$278$	−126.876	−	415.467i	−0.456387	−	1.49449i
$279$		0			0
$280$	407.874	−	502.695i	1.45669	−	1.79534i
$281$	−380.796			−1.35515			−0.677573	−	0.735456i	$-0.736968\pi$
$281$	−380.796			−1.35515			−0.677573	+	0.735456i	$0.736968\pi$
$282$		0			0
$283$	−36.5558	−	36.5558i	−0.129172	−	0.129172i	0.639565	−	0.768737i	$-0.279115\pi$
$283$	−36.5558	−	36.5558i	−0.129172	−	0.129172i	−0.768737	+	0.639565i	$0.779115\pi$
$284$	163.559	+	242.821i	0.575911	+	0.855002i
$285$		0			0
$286$	−78.0003	+	146.584i	−0.272728	+	0.512532i
$287$			105.626i			0.368034i
$288$		0			0
$289$	−525.519			−1.81841
$290$	75.1489	+	39.9882i	0.259134	+	0.137890i
$291$		0			0
$292$	−4.08930	+	2.75446i	−0.0140044	+	0.00943308i
$293$	119.828	−	119.828i	0.408970	−	0.408970i	−0.472409	−	0.881379i	$-0.656615\pi$
$293$	119.828	−	119.828i	0.408970	−	0.408970i	0.881379	+	0.472409i	$0.156615\pi$
$294$		0			0
$295$			179.401i			0.608138i
$296$	−94.6988	+	116.714i	−0.319928	+	0.394304i
$297$		0			0
$298$	−66.6882	+	20.3653i	−0.223786	+	0.0683400i
$299$	8.94036	−	8.94036i	0.0299009	−	0.0299009i
$300$		0			0
$301$	77.0023	−	77.0023i	0.255821	−	0.255821i
$302$	−52.8048	+	99.2347i	−0.174850	+	0.328592i
$303$		0			0
$304$	−27.2035	−	64.3162i	−0.0894852	−	0.211566i
$305$			478.474i			1.56877i
$306$		0			0
$307$	−368.177	+	368.177i	−1.19927	+	1.19927i	−0.224889	+	0.974384i	$0.572202\pi$
$307$	−368.177	+	368.177i	−1.19927	+	1.19927i	−0.974384	+	0.224889i	$0.927798\pi$
$308$	121.681	−	623.861i	0.395067	−	2.02552i
$309$		0			0
$310$	−347.275	+	106.051i	−1.12024	+	0.342101i
$311$	82.3959			0.264939			0.132469	−	0.991187i	$-0.457709\pi$
$311$	82.3959			0.264939			0.132469	+	0.991187i	$0.457709\pi$
$312$		0			0
$313$			368.385i			1.17695i	0.808516	+	0.588474i	$0.200271\pi$
$313$			368.385i			1.17695i	−0.808516	+	0.588474i	$0.799729\pi$
$314$	411.785	−	125.751i	1.31142	−	0.400482i
$315$		0			0
$316$	−246.238	−	365.567i	−0.779234	−	1.15686i
$317$	−185.382	−	185.382i	−0.584800	−	0.584800i	0.351419	−	0.936218i	$-0.385699\pi$
$317$	−185.382	−	185.382i	−0.584800	−	0.584800i	−0.936218	+	0.351419i	$0.885699\pi$
$318$		0			0
$319$	83.5829			0.262015
$320$	300.940	−	461.465i	0.940437	−	1.44208i
$321$		0			0
$322$	−22.7358	+	42.7269i	−0.0706081	+	0.132692i
$323$	88.0794	+	88.0794i	0.272692	+	0.272692i
$324$		0			0
$325$	−170.517	−	170.517i	−0.524669	−	0.524669i
$326$	−397.842	+	121.493i	−1.22038	+	0.372679i
$327$		0			0
$328$	9.31043	+	89.4083i	0.0283855	+	0.272586i
$329$	−162.043			−0.492532
$330$		0			0
$331$	209.678	+	209.678i	0.633467	+	0.633467i	0.948936	−	0.315469i	$-0.102162\pi$
$331$	209.678	+	209.678i	0.633467	+	0.633467i	−0.315469	+	0.948936i	$0.602162\pi$
$332$	14.9228	−	76.5099i	0.0449483	−	0.230452i
$333$		0			0
$334$	176.981	+	94.1750i	0.529883	+	0.281961i
$335$			969.604i			2.89434i
$336$		0			0
$337$	417.353			1.23844			0.619218	−	0.785219i	$-0.287450\pi$
$337$	417.353			1.23844			0.619218	+	0.785219i	$0.287450\pi$
$338$	136.115	−	255.797i	0.402706	−	0.756796i
$339$		0			0
$340$	−188.125	+	964.524i	−0.553309	+	2.83684i
$341$	−252.102	+	252.102i	−0.739301	+	0.739301i
$342$		0			0
$343$		−	90.5729i		−	0.264061i
$344$	58.3922	−	71.9670i	0.169745	−	0.209206i
$345$		0			0
$346$	−147.916	−	484.366i	−0.427503	−	1.39990i
$347$	−99.3706	+	99.3706i	−0.286371	+	0.286371i	−0.835643	−	0.549273i	$-0.814905\pi$
$347$	−99.3706	+	99.3706i	−0.286371	+	0.286371i	0.549273	+	0.835643i	$0.314905\pi$
$348$		0			0
$349$	−9.95933	+	9.95933i	−0.0285368	+	0.0285368i	−0.721231	−	0.692694i	$-0.756423\pi$
$349$	−9.95933	+	9.95933i	−0.0285368	+	0.0285368i	0.692694	+	0.721231i	$0.256423\pi$
$350$	814.920	+	433.635i	2.32834	+	1.23896i
$351$		0			0
$352$	48.0076	−	538.801i	0.136385	−	1.53069i
$353$		−	509.355i		−	1.44293i	−0.692451	−	0.721465i	$-0.743469\pi$
$353$		−	509.355i		−	1.44293i	0.692451	−	0.721465i	$-0.256531\pi$
$354$		0			0
$355$	−445.511	+	445.511i	−1.25496	+	1.25496i
$356$	−87.7223	−	130.233i	−0.246411	−	0.365824i
$357$		0			0
$358$	7.30787	+	23.9304i	0.0204131	+	0.0668446i
$359$	401.516			1.11843			0.559214	−	0.829023i	$-0.311103\pi$
$359$	401.516			1.11843			0.559214	+	0.829023i	$0.311103\pi$
$360$		0			0
$361$			341.951i			0.947232i
$362$	111.813	+	366.144i	0.308877	+	1.01145i
$363$		0			0
$364$	35.3529	−	181.256i	0.0971235	−	0.497956i
$365$	−7.50278	−	7.50278i	−0.0205556	−	0.0205556i
$366$		0			0
$367$	−338.335			−0.921894			−0.460947	−	0.887428i	$-0.652490\pi$
$367$	−338.335			−0.921894			−0.460947	+	0.887428i	$0.652490\pi$
$368$	−15.4789	+	38.1708i	−0.0420621	+	0.103725i
$369$		0			0
$370$	−285.541	−	151.942i	−0.771734	−	0.410655i
$371$	286.879	+	286.879i	0.773259	+	0.773259i
$372$		0			0
$373$	−342.158	−	342.158i	−0.917314	−	0.917314i	0.0795197	−	0.996833i	$-0.474661\pi$
$373$	−342.158	−	342.158i	−0.917314	−	0.917314i	−0.996833	+	0.0795197i	$0.974661\pi$
$374$	281.811	+	922.816i	0.753504	+	2.46742i
$375$		0			0
$376$	−137.163	+	14.2834i	−0.364796	+	0.0379877i
$377$	24.2841			0.0644140
$378$		0			0
$379$	400.188	+	400.188i	1.05591	+	1.05591i	0.998342	+	0.0575645i	$0.0183335\pi$
$379$	400.188	+	400.188i	1.05591	+	1.05591i	0.0575645	+	0.998342i	$0.481667\pi$
$380$	124.644	−	83.9572i	0.328010	−	0.220940i
$381$		0			0
$382$	110.781	−	208.188i	0.290003	−	0.544995i
$383$		−	595.773i		−	1.55554i	−0.628548	−	0.777771i	$-0.716350\pi$
$383$		−	595.773i		−	1.55554i	0.628548	−	0.777771i	$-0.283650\pi$
$384$		0			0
$385$	1367.87			3.55292
$386$	−115.106	−	61.2503i	−0.298203	−	0.158680i
$387$		0			0
$388$	−244.433	−	362.887i	−0.629982	−	0.935276i
$389$	−83.6879	+	83.6879i	−0.215136	+	0.215136i	−0.806445	−	0.591309i	$-0.798611\pi$
$389$	−83.6879	+	83.6879i	−0.215136	+	0.215136i	0.591309	+	0.806445i	$0.298611\pi$
$390$		0			0
$391$		−	73.4718i		−	0.187908i
$392$	32.6174	+	313.225i	0.0832076	+	0.799044i
$393$		0			0
$394$	−72.8975	+	22.2615i	−0.185019	+	0.0565013i
$395$	670.719	−	670.719i	1.69802	−	1.69802i
$396$		0			0
$397$	−311.065	+	311.065i	−0.783539	+	0.783539i	−0.980426	−	0.196887i	$-0.936917\pi$
$397$	−311.065	+	311.065i	−0.783539	+	0.783539i	0.196887	+	0.980426i	$0.436917\pi$
$398$	−273.214	+	513.445i	−0.686468	+	1.29006i
$399$		0			0
$400$	728.023	+	295.225i	1.82006	+	0.738061i
$401$			279.299i			0.696505i	0.937401	+	0.348253i	$0.113225\pi$
$401$			279.299i			0.696505i	−0.937401	+	0.348253i	$0.886775\pi$
$402$		0			0
$403$	−73.2453	+	73.2453i	−0.181750	+	0.181750i
$404$	−571.005	−	111.371i	−1.41338	−	0.275672i
$405$		0			0
$406$	−88.9058	+	27.1501i	−0.218980	+	0.0668722i
$407$	−317.588			−0.780315
$408$		0			0
$409$			446.244i			1.09106i	0.838091	+	0.545530i	$0.183672\pi$
$409$			446.244i			1.09106i	−0.838091	+	0.545530i	$0.816328\pi$
$410$	−185.016	+	56.5002i	−0.451258	+	0.137805i
$411$		0			0
$412$	−219.011	+	147.521i	−0.531579	+	0.358060i
$413$	−138.529	−	138.529i	−0.335420	−	0.335420i
$414$		0			0
$415$	167.755			0.404229
$416$	13.9481	−	156.543i	0.0335290	−	0.376304i
$417$		0			0
$418$	69.3162	−	130.264i	0.165828	−	0.311637i
$419$	331.372	+	331.372i	0.790864	+	0.790864i	0.981635	−	0.190770i	$-0.0610986\pi$
$419$	331.372	+	331.372i	0.790864	+	0.790864i	−0.190770	+	0.981635i	$0.561099\pi$
$420$		0			0
$421$	−74.8932	−	74.8932i	−0.177893	−	0.177893i	0.612543	−	0.790437i	$-0.290146\pi$
$421$	−74.8932	−	74.8932i	−0.177893	−	0.177893i	−0.790437	+	0.612543i	$0.790146\pi$
$422$	−389.460	+	118.934i	−0.922891	+	0.281833i
$423$		0			0
$424$	268.120	+	217.546i	0.632358	+	0.513079i
$425$	−1401.31			−3.29720
$426$		0			0
$427$	−369.465	−	369.465i	−0.865258	−	0.865258i
$428$	−485.255	−	94.6462i	−1.13377	−	0.221136i
$429$		0			0
$430$	176.068	+	93.6891i	0.409460	+	0.217882i
$431$			433.486i			1.00577i	0.864354	+	0.502884i	$0.167728\pi$
$431$			433.486i			1.00577i	−0.864354	+	0.502884i	$0.832272\pi$
$432$		0			0
$433$	−279.207			−0.644820			−0.322410	−	0.946600i	$-0.604493\pi$
$433$	−279.207			−0.644820			−0.322410	+	0.946600i	$0.604493\pi$
$434$	186.267	−	350.046i	0.429186	−	0.806559i
$435$		0			0
$436$	2.73890	+	0.534208i	0.00628189	+	0.00122525i
$437$	−7.94500	+	7.94500i	−0.0181808	+	0.0181808i
$438$		0			0
$439$		−	564.253i		−	1.28531i	−0.766154	−	0.642657i	$-0.777832\pi$
$439$		−	564.253i		−	1.28531i	0.766154	−	0.642657i	$-0.222168\pi$
$440$	1157.85	−	120.572i	2.63149	−	0.274027i
$441$		0			0
$442$	81.8768	+	268.114i	0.185242	+	0.606592i
$443$	39.2113	−	39.2113i	0.0885131	−	0.0885131i	−0.661464	−	0.749977i	$-0.730065\pi$
$443$	39.2113	−	39.2113i	0.0885131	−	0.0885131i	0.749977	+	0.661464i	$0.230065\pi$
$444$		0			0
$445$	238.944	−	238.944i	0.536952	−	0.536952i
$446$	−354.655	−	188.719i	−0.795190	−	0.423136i
$447$		0			0
$448$	123.953	+	588.709i	0.276681	+	1.31408i
$449$			277.135i			0.617228i	0.951187	+	0.308614i	$0.0998651\pi$
$449$			277.135i			0.617228i	−0.951187	+	0.308614i	$0.900135\pi$
$450$		0			0
$451$	−134.311	+	134.311i	−0.297806	+	0.297806i
$452$	602.696	−	405.963i	1.33340	−	0.898148i
$453$		0			0
$454$	−30.8785	−	101.115i	−0.0680143	−	0.222720i
$455$	397.420			0.873450
$456$		0			0
$457$		−	631.173i		−	1.38112i	−0.723274	−	0.690561i	$-0.757364\pi$
$457$		−	631.173i		−	1.38112i	0.723274	−	0.690561i	$-0.242636\pi$
$458$	−84.1008	−	275.396i	−0.183626	−	0.601302i
$459$		0			0
$460$	−87.0027	−	16.9694i	−0.189136	−	0.0368900i
$461$	494.475	+	494.475i	1.07261	+	1.07261i	0.997149	+	0.0754643i	$0.0240439\pi$
$461$	494.475	+	494.475i	1.07261	+	1.07261i	0.0754643	+	0.997149i	$0.475956\pi$
$462$		0			0
$463$	394.376			0.851784			0.425892	−	0.904774i	$-0.359960\pi$
$463$	394.376			0.851784			0.425892	+	0.904774i	$0.359960\pi$
$464$	−72.8623	+	30.8182i	−0.157031	+	0.0664186i
$465$		0			0
$466$	−142.480	−	75.8166i	−0.305752	−	0.162697i
$467$	−214.554	−	214.554i	−0.459430	−	0.459430i	0.439039	−	0.898468i	$-0.355319\pi$
$467$	−214.554	−	214.554i	−0.459430	−	0.459430i	−0.898468	+	0.439039i	$0.855319\pi$
$468$		0			0
$469$	−748.702	−	748.702i	−1.59638	−	1.59638i
$470$	−86.6784	−	283.837i	−0.184422	−	0.603909i
$471$		0			0
$472$	−129.470	−	105.049i	−0.274301	−	0.222561i
$473$	195.828			0.414012
$474$		0			0
$475$	151.533	+	151.533i	0.319017	+	0.319017i
$476$	−599.515	−	890.045i	−1.25948	−	1.86984i
$477$		0			0
$478$	−282.802	+	531.463i	−0.591636	+	1.11185i
$479$		−	636.488i		−	1.32879i	−0.747383	−	0.664393i	$-0.768690\pi$
$479$		−	636.488i		−	1.32879i	0.747383	−	0.664393i	$-0.231310\pi$
$480$		0			0
$481$	−92.2716			−0.191833
$482$	−281.573	−	149.830i	−0.584175	−	0.310851i
$483$		0			0
$484$	546.584	−	368.167i	1.12930	−	0.760675i
$485$	665.802	−	665.802i	1.37279	−	1.37279i
$486$		0			0
$487$			550.556i			1.13051i	0.824918	+	0.565253i	$0.191221\pi$
$487$			550.556i			1.13051i	−0.824918	+	0.565253i	$0.808779\pi$
$488$	−345.305	−	280.172i	−0.707593	−	0.574123i
$489$		0			0
$490$	−648.168	+	197.938i	−1.32279	+	0.403955i
$491$	−192.006	+	192.006i	−0.391051	+	0.391051i	−0.875062	−	0.484011i	$-0.839179\pi$
$491$	−192.006	+	192.006i	−0.391051	+	0.391051i	0.484011	+	0.875062i	$0.339179\pi$
$492$		0			0
$493$	99.7832	−	99.7832i	0.202400	−	0.202400i
$494$	20.1390	−	37.8468i	0.0407673	−	0.0766130i
$495$		0			0
$496$	126.813	−	312.720i	0.255671	−	0.630484i
$497$		−	688.024i		−	1.38435i
$498$		0			0
$499$	156.794	−	156.794i	0.314215	−	0.314215i	−0.532325	−	0.846540i	$-0.678681\pi$
$499$	156.794	−	156.794i	0.314215	−	0.314215i	0.846540	+	0.532325i	$0.178681\pi$
$500$	−158.861	+	814.488i	−0.317723	+	1.62898i
$501$		0			0
$502$	789.757	−	241.177i	1.57322	−	0.480431i
$503$	88.5520			0.176048			0.0880239	−	0.996118i	$-0.471945\pi$
$503$	88.5520			0.176048			0.0880239	+	0.996118i	$0.471945\pi$
$504$		0			0
$505$		−	1251.98i		−	2.47917i
$506$	−83.2405	+	25.4201i	−0.164507	+	0.0502373i
$507$		0			0
$508$	420.612	+	624.445i	0.827977	+	1.22922i
$509$	−430.228	−	430.228i	−0.845242	−	0.845242i	0.144293	−	0.989535i	$-0.453909\pi$
$509$	−430.228	−	430.228i	−0.845242	−	0.845242i	−0.989535	+	0.144293i	$0.953909\pi$
$510$		0			0
$511$	11.5869			0.0226749
$512$	156.814	+	487.394i	0.306277	+	0.951942i
$513$		0			0
$514$	128.531	−	241.546i	0.250061	−	0.469933i
$515$	−401.827	−	401.827i	−0.780246	−	0.780246i
$516$		0			0
$517$	−206.049	−	206.049i	−0.398548	−	0.398548i
$518$	337.813	−	103.162i	0.652149	−	0.199154i
$519$		0			0
$520$	336.401	−	35.0308i	0.646926	−	0.0673669i
$521$	889.748			1.70777			0.853885	−	0.520462i	$-0.174240\pi$
$521$	889.748			1.70777			0.853885	+	0.520462i	$0.174240\pi$
$522$		0			0
$523$	134.417	+	134.417i	0.257012	+	0.257012i	0.823838	−	0.566826i	$-0.191829\pi$
$523$	134.417	+	134.417i	0.257012	+	0.257012i	−0.566826	+	0.823838i	$0.691829\pi$
$524$	−86.1491	+	441.690i	−0.164407	+	0.842919i
$525$		0			0
$526$	−794.153	−	422.585i	−1.50980	−	0.803393i
$527$			601.929i			1.14218i
$528$		0			0
$529$	−522.373			−0.987472
$530$	−349.048	+	655.957i	−0.658581	+	1.23765i
$531$		0			0
$532$	−31.4170	+	161.076i	−0.0590545	+	0.302774i
$533$	−39.0225	+	39.0225i	−0.0732129	+	0.0732129i
$534$		0			0
$535$		−	1063.96i		−	1.98872i
$536$	−699.744	−	567.754i	−1.30549	−	1.05924i
$537$		0			0
$538$	63.7766	+	208.843i	0.118544	+	0.388183i
$539$	−470.532	+	470.532i	−0.872973	+	0.872973i
$540$		0			0
$541$	309.758	−	309.758i	0.572565	−	0.572565i	−0.360279	−	0.932844i	$-0.617319\pi$
$541$	309.758	−	309.758i	0.572565	−	0.572565i	0.932844	+	0.360279i	$0.117319\pi$
$542$	−876.402	−	466.351i	−1.61698	−	0.860426i
$543$		0			0
$544$	−585.921	−	700.546i	−1.07706	−	1.28777i
$545$			6.00529i			0.0110189i
$546$		0			0
$547$	−609.425	+	609.425i	−1.11412	+	1.11412i	−0.121535	+	0.992587i	$0.538782\pi$
$547$	−609.425	+	609.425i	−1.11412	+	1.11412i	−0.992587	+	0.121535i	$0.961218\pi$
$548$	457.865	+	679.751i	0.835520	+	1.24042i
$549$		0			0
$550$	484.831	+	1587.63i	0.881511	+	2.88660i
$551$	−21.5804			−0.0391659
$552$		0			0
$553$			1035.82i			1.87310i
$554$	21.2501	+	69.5856i	0.0383576	+	0.125606i
$555$		0			0
$556$	−166.324	+	852.747i	−0.299143	+	1.53372i
$557$	−605.408	−	605.408i	−1.08691	−	1.08691i	−0.995845	−	0.0910624i	$-0.970974\pi$
$557$	−605.408	−	605.408i	−1.08691	−	1.08691i	−0.0910624	−	0.995845i	$-0.529026\pi$
$558$		0			0
$559$	56.8956			0.101781
$560$	−1192.43	+	504.355i	−2.12933	+	0.900633i
$561$		0			0
$562$	672.331	+	357.761i	1.19632	+	0.636585i
$563$	−68.2515	−	68.2515i	−0.121228	−	0.121228i	0.643890	−	0.765118i	$-0.277319\pi$
$563$	−68.2515	−	68.2515i	−0.121228	−	0.121228i	−0.765118	+	0.643890i	$0.777319\pi$
$564$		0			0
$565$	1105.79	+	1105.79i	1.95715	+	1.95715i
$566$	30.1983	+	98.8872i	0.0533538	+	0.174712i
$567$		0			0
$568$	−60.6463	−	582.387i	−0.106772	−	1.02533i
$569$	758.298			1.33269			0.666343	−	0.745646i	$-0.267859\pi$
$569$	758.298			1.33269			0.666343	+	0.745646i	$0.267859\pi$
$570$		0			0
$571$	−663.635	−	663.635i	−1.16223	−	1.16223i	−0.983986	−	0.178248i	$-0.942957\pi$
$571$	−663.635	−	663.635i	−1.16223	−	1.16223i	−0.178248	−	0.983986i	$-0.557043\pi$
$572$	275.434	−	185.526i	0.481528	−	0.324346i
$573$		0			0
$574$	99.2362	−	186.492i	0.172885	−	0.324899i
$575$		−	126.402i		−	0.219830i
$576$		0			0
$577$	−68.8744			−0.119366			−0.0596832	−	0.998217i	$-0.519009\pi$
$577$	−68.8744			−0.119366			−0.0596832	+	0.998217i	$0.519009\pi$
$578$	927.854	+	493.730i	1.60528	+	0.854203i
$579$		0			0
$580$	−95.1132	−	141.206i	−0.163988	−	0.243459i
$581$	−129.536	+	129.536i	−0.222953	+	0.222953i
$582$		0			0
$583$			729.575i			1.25142i
$584$	9.80788	−	1.02133i	0.0167943	−	0.00174886i
$585$		0			0
$586$	−324.148	+	98.9886i	−0.553154	+	0.168923i
$587$	720.353	−	720.353i	1.22718	−	1.22718i	0.262151	−	0.965027i	$-0.415568\pi$
$587$	720.353	−	720.353i	1.22718	−	1.22718i	0.965027	−	0.262151i	$-0.0844317\pi$
$588$		0			0
$589$	65.0906	−	65.0906i	0.110510	−	0.110510i
$590$	168.548	−	316.749i	0.285675	−	0.536863i
$591$		0			0
$592$	276.853	−	117.099i	0.467658	−	0.197803i
$593$			585.630i			0.987572i	0.869583	+	0.493786i	$0.164387\pi$
$593$			585.630i			0.987572i	−0.869583	+	0.493786i	$0.835613\pi$
$594$		0			0
$595$	1633.00	−	1633.00i	2.74453	−	2.74453i
$596$	136.878	+	26.6972i	0.229661	+	0.0447940i
$597$		0			0
$598$	−24.1846	+	7.38551i	−0.0404425	+	0.0123504i
$599$	1006.31			1.67999			0.839995	−	0.542594i	$-0.182558\pi$
$599$	1006.31			1.67999			0.839995	+	0.542594i	$0.182558\pi$
$600$		0			0
$601$			534.875i			0.889976i	0.895537	+	0.444988i	$0.146792\pi$
$601$			534.875i			0.889976i	−0.895537	+	0.444988i	$0.853208\pi$
$602$	−208.299	+	63.6105i	−0.346012	+	0.105665i
$603$		0			0
$604$	186.464	−	125.598i	0.308715	−	0.207943i
$605$	1002.84	+	1002.84i	1.65758	+	1.65758i
$606$		0			0
$607$	−219.896			−0.362267			−0.181133	−	0.983459i	$-0.557977\pi$
$607$	−219.896			−0.362267			−0.181133	+	0.983459i	$0.557977\pi$
$608$	−12.3952	+	139.114i	−0.0203868	+	0.228806i
$609$		0			0
$610$	449.530	−	844.791i	0.736935	−	1.38490i
$611$	−59.8653	−	59.8653i	−0.0979792	−	0.0979792i
$612$		0			0
$613$	389.389	+	389.389i	0.635219	+	0.635219i	0.949372	−	0.314153i	$-0.101721\pi$
$613$	389.389	+	389.389i	0.635219	+	0.635219i	−0.314153	+	0.949372i	$0.601721\pi$
$614$	995.957	−	304.146i	1.62208	−	0.495352i
$615$		0			0
$616$	−800.962	+	987.166i	−1.30026	+	1.60254i
$617$	261.466			0.423771			0.211885	−	0.977295i	$-0.432040\pi$
$617$	261.466			0.423771			0.211885	+	0.977295i	$0.432040\pi$
$618$		0			0
$619$	−275.915	−	275.915i	−0.445743	−	0.445743i	0.448193	−	0.893937i	$-0.352068\pi$
$619$	−275.915	−	275.915i	−0.445743	−	0.445743i	−0.893937	+	0.448193i	$0.852068\pi$
$620$	712.783	+	139.024i	1.14965	+	0.224233i
$621$		0			0
$622$	−145.478	−	77.4116i	−0.233887	−	0.124456i
$623$			369.012i			0.592315i
$624$		0			0
$625$	−558.331			−0.893329
$626$	346.101	−	650.418i	0.552876	−	1.03901i
$627$		0			0
$628$	−845.191	−	164.850i	−1.34584	−	0.262500i
$629$	−379.144	+	379.144i	−0.602772	+	0.602772i
$630$		0			0
$631$		−	237.889i		−	0.377003i	−0.982073	−	0.188501i	$-0.939637\pi$
$631$		−	237.889i		−	0.377003i	0.982073	−	0.188501i	$-0.0603630\pi$
$632$	91.3032	+	876.786i	0.144467	+	1.38732i
$633$		0			0
$634$	153.141	+	501.476i	0.241548	+	0.790972i
$635$	−1145.69	+	1145.69i	−1.80424	+	1.80424i
$636$		0			0
$637$	−136.708	+	136.708i	−0.214612	+	0.214612i
$638$	−147.574	−	78.5268i	−0.231306	−	0.123083i
$639$		0			0
$640$	−964.888	+	532.025i	−1.50764	+	0.831289i
$641$			858.416i			1.33918i	0.742730	+	0.669591i	$0.233531\pi$
$641$			858.416i			1.33918i	−0.742730	+	0.669591i	$0.766469\pi$
$642$		0			0
$643$	−643.410	+	643.410i	−1.00064	+	1.00064i	−0.000638349		1.00000i	$0.500203\pi$
$643$	−643.410	+	643.410i	−1.00064	+	1.00064i	−1.00000		0.000638349i	$0.999797\pi$
$644$	80.2845	−	54.0778i	0.124665	−	0.0839718i
$645$		0			0
$646$	−72.7612	−	238.264i	−0.112633	−	0.368829i
$647$	−597.840			−0.924019			−0.462009	−	0.886875i	$-0.652871\pi$
$647$	−597.840			−0.924019			−0.462009	+	0.886875i	$0.652871\pi$
$648$		0			0
$649$		−	352.298i		−	0.542832i
$650$	140.862	+	461.267i	0.216711	+	0.709642i
$651$		0			0
$652$	816.572	+	159.268i	1.25241	+	0.244276i
$653$	−91.3671	−	91.3671i	−0.139919	−	0.139919i	0.633678	−	0.773597i	$-0.281544\pi$
$653$	−91.3671	−	91.3671i	−0.139919	−	0.139919i	−0.773597	+	0.633678i	$0.781544\pi$
$654$		0			0
$655$	−968.445			−1.47854
$656$	67.5613	−	166.606i	0.102990	−	0.253973i
$657$		0			0
$658$	286.102	+	152.241i	0.434806	+	0.231369i
$659$	−445.487	−	445.487i	−0.676004	−	0.676004i	0.283089	−	0.959094i	$-0.408641\pi$
$659$	−445.487	−	445.487i	−0.676004	−	0.676004i	−0.959094	+	0.283089i	$0.908641\pi$
$660$		0			0
$661$	387.304	+	387.304i	0.585937	+	0.585937i	0.936528	−	0.350592i	$-0.114019\pi$
$661$	387.304	+	387.304i	0.585937	+	0.585937i	−0.350592	+	0.936528i	$0.614019\pi$
$662$	−173.212	−	567.199i	−0.261649	−	0.856797i
$663$		0			0
$664$	−98.2294	+	121.065i	−0.147936	+	0.182327i
$665$	−353.174			−0.531088
$666$		0			0
$667$	9.00071	+	9.00071i	0.0134943	+	0.0134943i
$668$	−223.998	−	332.550i	−0.335327	−	0.497829i
$669$		0			0
$670$	910.951	−	1711.93i	1.35963	−	2.55512i
$671$		−	939.603i		−	1.40030i
$672$		0			0
$673$	−845.703			−1.25662			−0.628309	−	0.777964i	$-0.716252\pi$
$673$	−845.703			−1.25662			−0.628309	+	0.777964i	$0.716252\pi$
$674$	−736.877	−	392.107i	−1.09329	−	0.581761i
$675$		0			0
$676$	−480.647	+	323.753i	−0.711016	+	0.478925i
$677$	311.755	−	311.755i	0.460495	−	0.460495i	−0.438323	−	0.898818i	$-0.644427\pi$
$677$	311.755	−	311.755i	0.460495	−	0.460495i	0.898818	+	0.438323i	$0.144427\pi$
$678$		0			0
$679$			1028.23i			1.51433i
$680$	1238.33	−	1526.21i	1.82107	−	2.24443i
$681$		0			0
$682$	681.961	−	208.258i	0.999943	−	0.305363i
$683$	214.466	−	214.466i	0.314005	−	0.314005i	−0.532454	−	0.846459i	$-0.678730\pi$
$683$	214.466	−	214.466i	0.314005	−	0.314005i	0.846459	+	0.532454i	$0.178730\pi$
$684$		0			0
$685$	−1247.16	+	1247.16i	−1.82068	+	1.82068i
$686$	−85.0939	+	159.915i	−0.124044	+	0.233112i
$687$		0			0
$688$	−170.710	+	72.2046i	−0.248126	+	0.104949i
$689$			211.970i			0.307649i
$690$		0			0
$691$	812.184	−	812.184i	1.17537	−	1.17537i	0.194465	−	0.980909i	$-0.437703\pi$
$691$	812.184	−	812.184i	1.17537	−	1.17537i	0.980909	−	0.194465i	$-0.0622972\pi$
$692$	−193.906	+	994.162i	−0.280211	+	1.43665i
$693$		0			0
$694$	268.808	−	82.0887i	0.387331	−	0.118283i
$695$	−1869.72			−2.69025
$696$		0			0
$697$			320.686i			0.460095i
$698$	26.9410	−	8.22727i	0.0385974	−	0.0117869i
$699$		0			0
$700$	−1031.41	−	1531.25i	−1.47345	−	2.18750i
$701$	105.563	+	105.563i	0.150589	+	0.150589i	0.778381	−	0.627792i	$-0.216041\pi$
$701$	105.563	+	105.563i	0.150589	+	0.150589i	−0.627792	+	0.778381i	$0.716041\pi$
$702$		0			0
$703$	81.9987			0.116641
$704$	−590.970	+	906.201i	−0.839447	+	1.28722i
$705$		0			0
$706$	−478.543	+	899.314i	−0.677822	+	1.27382i
$707$	966.746	+	966.746i	1.36739	+	1.36739i
$708$		0			0
$709$	−106.375	−	106.375i	−0.150035	−	0.150035i	0.628099	−	0.778134i	$-0.283833\pi$
$709$	−106.375	−	106.375i	−0.150035	−	0.150035i	−0.778134	+	0.628099i	$0.783833\pi$
$710$	1205.15	−	368.031i	1.69740	−	0.518354i
$711$		0			0
$712$	32.5268	+	312.355i	0.0456837	+	0.438701i
$713$	−54.2957			−0.0761510
$714$		0			0
$715$	505.348	+	505.348i	0.706781	+	0.706781i
$716$	9.58002	−	49.1171i	0.0133799	−	0.0685993i
$717$		0			0
$718$	−708.914	−	377.227i	−0.987346	−	0.525386i
$719$		−	1119.16i		−	1.55656i	−0.627919	−	0.778278i	$-0.716093\pi$
$719$		−	1119.16i		−	1.55656i	0.627919	−	0.778278i	$-0.283907\pi$
$720$		0			0
$721$	620.560			0.860693
$722$	321.266	−	603.746i	0.444966	−	0.836214i
$723$		0			0
$724$	146.578	−	751.511i	0.202456	−	1.03800i
$725$	171.668	−	171.668i	0.236784	−	0.236784i
$726$		0			0
$727$		−	334.759i		−	0.460466i	−0.973136	−	0.230233i	$-0.926051\pi$
$727$		−	334.759i		−	0.460466i	0.973136	−	0.230233i	$-0.0739489\pi$
$728$	−232.710	+	286.810i	−0.319657	+	0.393970i
$729$		0			0
$730$	6.19795	+	20.2958i	0.00849034	+	0.0278024i
$731$	233.784	−	233.784i	0.319814	−	0.319814i
$732$		0			0
$733$	97.8371	−	97.8371i	0.133475	−	0.133475i	−0.637213	−	0.770688i	$-0.719913\pi$
$733$	97.8371	−	97.8371i	0.133475	−	0.133475i	0.770688	+	0.637213i	$0.219913\pi$
$734$	597.363	+	317.869i	0.813846	+	0.433064i
$735$		0			0
$736$	63.1911	−	52.8516i	0.0858575	−	0.0718093i
$737$		−	1904.06i		−	2.58353i
$738$		0			0
$739$	249.678	−	249.678i	0.337860	−	0.337860i	−0.517702	−	0.855561i	$-0.673212\pi$
$739$	249.678	−	249.678i	0.337860	−	0.337860i	0.855561	+	0.517702i	$0.173212\pi$
$740$	361.400	+	536.537i	0.488378	+	0.725050i
$741$		0			0
$742$	−236.987	−	776.038i	−0.319390	−	1.04587i
$743$	−1176.88			−1.58396			−0.791981	−	0.610545i	$-0.790950\pi$
$743$	−1176.88			−1.58396			−0.791981	+	0.610545i	$0.790950\pi$
$744$		0			0
$745$			300.117i			0.402841i
$746$	282.652	+	925.572i	0.378890	+	1.24071i
$747$		0			0
$748$	369.430	−	1894.08i	0.493891	−	2.53220i
$749$	821.565	+	821.565i	1.09688	+	1.09688i
$750$		0			0
$751$	909.942			1.21164			0.605821	−	0.795601i	$-0.292845\pi$
$751$	909.942			1.21164			0.605821	+	0.795601i	$0.292845\pi$
$752$	255.594	+	103.648i	0.339886	+	0.137829i
$753$		0			0
$754$	−42.8758	−	22.8151i	−0.0568645	−	0.0302587i
$755$	342.111	+	342.111i	0.453128	+	0.453128i
$756$		0			0
$757$	418.277	+	418.277i	0.552545	+	0.552545i	0.927175	−	0.374629i	$-0.122230\pi$
$757$	418.277	+	418.277i	0.552545	+	0.552545i	−0.374629	+	0.927175i	$0.622230\pi$
$758$	−330.590	−	1082.55i	−0.436135	−	1.42817i
$759$		0			0
$760$	−298.949	+	31.1307i	−0.393353	+	0.0409614i
$761$	670.931			0.881644			0.440822	−	0.897594i	$-0.354687\pi$
$761$	670.931			0.881644			0.440822	+	0.897594i	$0.354687\pi$
$762$		0			0
$763$	−4.63713	−	4.63713i	−0.00607750	−	0.00607750i
$764$	−391.189	+	263.496i	−0.512028	+	0.344890i
$765$		0			0
$766$	−559.733	+	1051.89i	−0.730722	+	1.37323i
$767$		−	102.356i		−	0.133450i
$768$		0			0
$769$	1054.59			1.37138			0.685689	−	0.727895i	$-0.259501\pi$
$769$	1054.59			1.37138			0.685689	+	0.727895i	$0.259501\pi$
$770$	−2415.11	−	1285.13i	−3.13650	−	1.66900i
$771$		0			0
$772$	145.686	+	216.286i	0.188712	+	0.280164i
$773$	−877.952	+	877.952i	−1.13577	+	1.13577i	−0.146573	+	0.989200i	$0.546824\pi$
$773$	−877.952	+	877.952i	−1.13577	+	1.13577i	−0.989200	+	0.146573i	$0.953176\pi$
$774$		0			0
$775$			1035.57i			1.33622i
$776$	90.6338	+	870.358i	0.116796	+	1.12160i
$777$		0			0
$778$	226.384	−	69.1335i	0.290983	−	0.0888605i
$779$	34.6780	−	34.6780i	0.0445160	−	0.0445160i
$780$		0			0
$781$	874.873	−	874.873i	1.12020	−	1.12020i
$782$	−69.0274	+	129.721i	−0.0882703	+	0.165884i
$783$		0			0
$784$	236.688	−	583.673i	0.301899	−	0.744481i
$785$		−	1853.16i		−	2.36071i
$786$		0			0
$787$	18.3967	−	18.3967i	0.0233758	−	0.0233758i	−0.695322	−	0.718698i	$-0.744738\pi$
$787$	18.3967	−	18.3967i	0.0233758	−	0.0233758i	0.718698	+	0.695322i	$0.244738\pi$
$788$	149.622	+	29.1830i	0.189876	+	0.0370343i
$789$		0			0
$790$	−1814.36	+	554.072i	−2.29666	+	0.701357i
$791$	−1707.72			−2.15894
$792$		0			0
$793$		−	272.991i		−	0.344251i
$794$	841.463	−	256.967i	1.05978	−	0.323636i
$795$		0			0
$796$	964.771	−	649.848i	1.21202	−	0.816393i
$797$	−27.8374	−	27.8374i	−0.0349278	−	0.0349278i	0.689427	−	0.724355i	$-0.257862\pi$
$797$	−27.8374	−	27.8374i	−0.0349278	−	0.0349278i	−0.724355	+	0.689427i	$0.757862\pi$
$798$		0			0
$799$	−491.973			−0.615736
$800$	−1008.03	−	1205.23i	−1.26003	−	1.50654i
$801$		0			0
$802$	262.403	−	493.128i	0.327186	−	0.614873i
$803$	14.7336	+	14.7336i	0.0183482	+	0.0183482i
$804$		0			0
$805$	147.301	+	147.301i	0.182982	+	0.182982i
$806$	198.136	−	60.5070i	0.245826	−	0.0750707i
$807$		0			0
$808$	903.530	+	733.101i	1.11823	+	0.907303i
$809$	416.938			0.515374			0.257687	−	0.966228i	$-0.417040\pi$
$809$	416.938			0.515374			0.257687	+	0.966228i	$0.417040\pi$
$810$		0			0
$811$	699.525	+	699.525i	0.862546	+	0.862546i	0.991633	−	0.129087i	$-0.0412047\pi$
$811$	699.525	+	699.525i	0.862546	+	0.862546i	−0.129087	+	0.991633i	$0.541205\pi$
$812$	182.479	+	35.5916i	0.224728	+	0.0438320i
$813$		0			0
$814$	560.732	+	298.377i	0.688860	+	0.366556i
$815$			1790.41i			2.19682i
$816$		0			0
$817$	−50.5612			−0.0618864
$818$	419.250	−	787.886i	0.512530	−	0.963186i
$819$		0			0
$820$	379.745	+	74.0672i	0.463104	+	0.0903258i
$821$	−200.751	+	200.751i	−0.244520	+	0.244520i	−0.818717	−	0.574197i	$-0.805314\pi$
$821$	−200.751	+	200.751i	−0.244520	+	0.244520i	0.574197	+	0.818717i	$0.305314\pi$
$822$		0			0
$823$		−	159.123i		−	0.193345i	−0.995316	−	0.0966724i	$-0.969180\pi$
$823$		−	159.123i		−	0.193345i	0.995316	−	0.0966724i	$-0.0308199\pi$
$824$	525.281	−	54.6996i	0.637477	−	0.0663830i
$825$		0			0
$826$	114.437	+	374.734i	0.138543	+	0.453673i
$827$	−790.803	+	790.803i	−0.956231	+	0.956231i	−0.999081	−	0.0428505i	$-0.986356\pi$
$827$	−790.803	+	790.803i	−0.956231	+	0.956231i	0.0428505	+	0.999081i	$0.486356\pi$
$828$		0			0
$829$	−827.815	+	827.815i	−0.998570	+	0.998570i	−0.999999	−	0.00142868i	$-0.999545\pi$
$829$	−827.815	+	827.815i	−0.998570	+	0.998570i	0.00142868	+	0.999999i	$0.499545\pi$
$830$	−296.187	−	157.607i	−0.356852	−	0.189888i
$831$		0			0
$832$	−171.700	+	263.287i	−0.206370	+	0.316450i
$833$			1123.46i			1.34870i
$834$		0			0
$835$	610.141	−	610.141i	0.730708	−	0.730708i
$836$	−244.769	+	164.871i	−0.292786	+	0.197214i
$837$		0			0
$838$	−273.742	−	896.396i	−0.326661	−	1.06968i
$839$	65.9441			0.0785985			0.0392992	−	0.999227i	$-0.487487\pi$
$839$	65.9441			0.0785985			0.0392992	+	0.999227i	$0.487487\pi$
$840$		0			0
$841$		−	816.552i		−	0.970930i
$842$	61.8682	+	202.594i	0.0734777	+	0.240610i
$843$		0			0
$844$	799.368	+	155.912i	0.947118	+	0.184730i
$845$	−881.860	−	881.860i	−1.04362	−	1.04362i
$846$		0			0
$847$	−1548.73			−1.82849
$848$	−269.005	−	635.998i	−0.317223	−	0.749998i
$849$		0			0
$850$	2474.15	+	1316.54i	2.91076	+	1.54887i
$851$	−34.1998	−	34.1998i	−0.0401878	−	0.0401878i
$852$		0			0
$853$	−22.8417	−	22.8417i	−0.0267780	−	0.0267780i	0.693591	−	0.720369i	$-0.256028\pi$
$853$	−22.8417	−	22.8417i	−0.0267780	−	0.0267780i	−0.720369	+	0.693591i	$0.756028\pi$
$854$	305.210	+	999.441i	0.357389	+	1.17031i
$855$		0			0
$856$	767.842	+	623.008i	0.897012	+	0.727813i
$857$	−630.654			−0.735886			−0.367943	−	0.929848i	$-0.619938\pi$
$857$	−630.654			−0.735886			−0.367943	+	0.929848i	$0.619938\pi$
$858$		0			0
$859$	161.861	+	161.861i	0.188430	+	0.188430i	0.795017	−	0.606587i	$-0.207462\pi$
$859$	161.861	+	161.861i	0.188430	+	0.188430i	−0.606587	+	0.795017i	$0.707462\pi$
$860$	−222.842	−	330.834i	−0.259119	−	0.384691i
$861$		0			0
$862$	407.264	−	765.361i	0.472464	−	0.887890i
$863$		−	1070.23i		−	1.24013i	−0.784549	−	0.620066i	$-0.787106\pi$
$863$		−	1070.23i		−	1.24013i	0.784549	−	0.620066i	$-0.212894\pi$
$864$		0			0
$865$	−2179.79			−2.51999
$866$	492.967	+	262.317i	0.569246	+	0.302907i
$867$		0			0
$868$	−657.743	+	443.041i	−0.757768	+	0.510416i
$869$	−1317.12	+	1317.12i	−1.51568	+	1.51568i
$870$		0			0
$871$		−	553.203i		−	0.635135i
$872$	−4.33390	−	3.51642i	−0.00497007	−	0.00403259i
$873$		0			0
$874$	21.4920	−	6.56326i	0.0245904	−	0.00750945i
$875$	1378.98	−	1378.98i	1.57597	−	1.57597i
$876$		0			0
$877$	773.573	−	773.573i	0.882067	−	0.882067i	−0.111677	−	0.993745i	$-0.535622\pi$
$877$	773.573	−	773.573i	0.882067	−	0.882067i	0.993745	+	0.111677i	$0.0356223\pi$
$878$	−530.120	+	996.241i	−0.603781	+	1.13467i
$879$		0			0
$880$	−2157.58	−	874.932i	−2.45179	−	0.994241i
$881$		−	495.482i		−	0.562408i	−0.959648	−	0.281204i	$-0.909266\pi$
$881$		−	495.482i		−	0.562408i	0.959648	−	0.281204i	$-0.0907338\pi$
$882$		0			0
$883$	−119.779	+	119.779i	−0.135650	+	0.135650i	−0.771671	−	0.636021i	$-0.780579\pi$
$883$	−119.779	+	119.779i	−0.135650	+	0.135650i	0.636021	+	0.771671i	$0.280579\pi$
$884$	107.334	−	550.304i	0.121418	−	0.622516i
$885$		0			0
$886$	−106.071	+	32.3919i	−0.119719	+	0.0365598i
$887$	895.932			1.01007			0.505035	−	0.863099i	$-0.331480\pi$
$887$	895.932			1.01007			0.505035	+	0.863099i	$0.331480\pi$
$888$		0			0
$889$		−	1769.34i		−	1.99026i
$890$	−646.368	+	197.388i	−0.726256	+	0.221785i
$891$		0			0
$892$	448.874	+	666.402i	0.503221	+	0.747087i
$893$	53.2003	+	53.2003i	0.0595748	+	0.0595748i
$894$		0			0
$895$	107.694			0.120328
$896$	334.245	−	1155.88i	0.373042	−	1.29004i
$897$		0			0
$898$	260.371	−	489.309i	0.289945	−	0.544887i
$899$	−73.7397	−	73.7397i	−0.0820242	−	0.0820242i
$900$		0			0
$901$	870.984	+	870.984i	0.966686	+	0.966686i
$902$	363.324	−	110.952i	0.402799	−	0.123007i
$903$		0			0
$904$	−1445.52	+	150.528i	−1.59903	+	0.166513i
$905$	1647.76			1.82073
$906$		0			0
$907$	−852.347	−	852.347i	−0.939743	−	0.939743i	0.0585418	−	0.998285i	$-0.481355\pi$
$907$	−852.347	−	852.347i	−0.939743	−	0.939743i	−0.998285	+	0.0585418i	$0.981355\pi$
$908$	−40.4792	+	207.538i	−0.0445806	+	0.228566i
$909$		0			0
$910$	−701.682	−	373.379i	−0.771079	−	0.410307i
$911$			748.289i			0.821393i	0.911772	+	0.410697i	$0.134714\pi$
$911$			748.289i			0.821393i	−0.911772	+	0.410697i	$0.865286\pi$
$912$		0			0
$913$	−329.429			−0.360820
$914$	−592.992	+	1114.40i	−0.648788	+	1.21925i
$915$		0			0
$916$	−110.249	+	565.252i	−0.120359	+	0.617087i
$917$	747.807	−	747.807i	0.815493	−	0.815493i
$918$		0			0
$919$			85.7074i			0.0932616i	0.998912	+	0.0466308i	$0.0148484\pi$
$919$			85.7074i			0.0932616i	−0.998912	+	0.0466308i	$0.985152\pi$
$920$	137.669	+	111.701i	0.149640	+	0.121414i
$921$		0			0
$922$	−408.479	−	1337.60i	−0.443036	−	1.45076i
$923$	254.184	−	254.184i	0.275389	−	0.275389i
$924$		0			0
$925$	−652.285	+	652.285i	−0.705173	+	0.705173i
$926$	−696.309	−	370.520i	−0.751953	−	0.400129i
$927$		0			0
$928$	157.599	+	14.0422i	0.169827	+	0.0151317i
$929$			119.970i			0.129139i	0.997913	+	0.0645696i	$0.0205675\pi$
$929$			119.970i			0.129139i	−0.997913	+	0.0645696i	$0.979433\pi$
$930$		0			0
$931$	121.488	−	121.488i	0.130492	−	0.130492i
$932$	180.332	+	267.723i	0.193489	+	0.287256i
$933$		0			0
$934$	177.240	+	580.389i	0.189764	+	0.621402i
$935$	4152.95			4.44166
$936$		0			0
$937$			631.867i			0.674351i	0.941442	+	0.337176i	$0.109472\pi$
$937$			631.867i			0.674351i	−0.941442	+	0.337176i	$0.890528\pi$
$938$	618.493	+	2025.32i	0.659374	+	2.15919i
$939$		0			0
$940$	−113.628	+	582.576i	−0.120881	+	0.619762i
$941$	370.590	+	370.590i	0.393825	+	0.393825i	0.876048	−	0.482223i	$-0.160171\pi$
$941$	370.590	+	370.590i	0.393825	+	0.393825i	−0.482223	+	0.876048i	$0.660171\pi$
$942$		0			0
$943$	−28.9268			−0.0306753
$944$	129.897	+	307.111i	0.137603	+	0.325330i
$945$		0			0
$946$	−345.753	−	183.982i	−0.365489	−	0.194484i
$947$	−16.2368	−	16.2368i	−0.0171455	−	0.0171455i	0.698482	−	0.715628i	$-0.253859\pi$
$947$	−16.2368	−	16.2368i	−0.0171455	−	0.0171455i	−0.715628	+	0.698482i	$0.753859\pi$
$948$		0			0
$949$	4.28067	+	4.28067i	0.00451072	+	0.00451072i
$950$	−125.180	−	409.913i	−0.131768	−	0.431487i
$951$		0			0
$952$	222.295	+	2134.71i	0.233504	+	2.24234i
$953$	−1216.35			−1.27634			−0.638168	−	0.769897i	$-0.720307\pi$
$953$	−1216.35			−1.27634			−0.638168	+	0.769897i	$0.720307\pi$
$954$		0			0
$955$	−717.728	−	717.728i	−0.751548	−	0.751548i
$956$	998.628	−	672.654i	1.04459	−	0.703613i
$957$		0			0
$958$	−597.986	+	1123.78i	−0.624202	+	1.17305i
$959$		−	1926.05i		−	2.00840i
$960$		0			0
$961$	−516.174			−0.537122
$962$	162.914	+	86.6899i	0.169350	+	0.0901143i
$963$		0			0
$964$	356.376	+	529.079i	0.369685	+	0.548838i
$965$	−396.828	+	396.828i	−0.411221	+	0.411221i
$966$		0			0
$967$			781.540i			0.808211i	0.914712	+	0.404105i	$0.132417\pi$
$967$			781.540i			0.808211i	−0.914712	+	0.404105i	$0.867583\pi$
$968$	−1310.94	+	136.513i	−1.35428	+	0.141026i
$969$		0			0
$970$	−1801.06	+	550.010i	−1.85677	+	0.567021i
$971$	15.3700	−	15.3700i	0.0158290	−	0.0158290i	−0.699148	−	0.714977i	$-0.746437\pi$
$971$	15.3700	−	15.3700i	0.0158290	−	0.0158290i	0.714977	+	0.699148i	$0.246437\pi$
$972$		0			0
$973$	1443.75	−	1443.75i	1.48381	−	1.48381i
$974$	517.252	−	972.059i	0.531060	−	0.998008i
$975$		0			0
$976$	346.445	+	819.087i	0.354965	+	0.839229i
$977$			806.751i			0.825743i	0.910789	+	0.412871i	$0.135474\pi$
$977$			806.751i			0.825743i	−0.910789	+	0.412871i	$0.864526\pi$
$978$		0			0
$979$	−469.226	+	469.226i	−0.479291	+	0.479291i
$980$	1330.37	+	259.480i	1.35752	+	0.264776i
$981$		0			0
$982$	519.396	−	158.614i	0.528917	−	0.161521i
$983$	−1060.81			−1.07916			−0.539579	−	0.841935i	$-0.681417\pi$
$983$	−1060.81			−1.07916			−0.539579	+	0.841935i	$0.681417\pi$
$984$		0			0
$985$			328.060i			0.333056i
$986$	−269.924	+	82.4295i	−0.273756	+	0.0835999i
$987$		0			0
$988$	−71.1148	+	47.9014i	−0.0719785	+	0.0484832i
$989$	21.0879	+	21.0879i	0.0213225	+	0.0213225i
$990$		0			0
$991$	1036.12			1.04553			0.522766	−	0.852476i	$-0.324900\pi$
$991$	1036.12			1.04553			0.522766	+	0.852476i	$0.324900\pi$
$992$	−517.703	+	432.995i	−0.521878	+	0.436487i
$993$		0			0
$994$	−646.404	+	1214.77i	−0.650306	+	1.22210i
$995$	1770.10	+	1770.10i	1.77899	+	1.77899i
$996$		0			0
$997$	44.6898	+	44.6898i	0.0448242	+	0.0448242i	0.729164	−	0.684339i	$-0.239909\pi$
$997$	44.6898	+	44.6898i	0.0448242	+	0.0448242i	−0.684339	+	0.729164i	$0.739909\pi$
$998$	−424.143	+	129.525i	−0.424993	+	0.129785i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	144.3.j.a.53.3	✓	32
3.2	odd	2	inner	144.3.j.a.53.14	yes	32
4.3	odd	2		576.3.j.a.305.1		32
8.3	odd	2		1152.3.j.b.737.16		32
8.5	even	2		1152.3.j.a.737.16		32
12.11	even	2		576.3.j.a.305.16		32
16.3	odd	4		576.3.j.a.17.16		32
16.5	even	4		1152.3.j.a.161.1		32
16.11	odd	4		1152.3.j.b.161.1		32
16.13	even	4	inner	144.3.j.a.125.14	yes	32
24.5	odd	2		1152.3.j.a.737.1		32
24.11	even	2		1152.3.j.b.737.1		32
48.5	odd	4		1152.3.j.a.161.16		32
48.11	even	4		1152.3.j.b.161.16		32
48.29	odd	4	inner	144.3.j.a.125.3	yes	32
48.35	even	4		576.3.j.a.17.1		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.3.j.a.53.3	✓	32	1.1	even	1	trivial
144.3.j.a.53.14	yes	32	3.2	odd	2	inner
144.3.j.a.125.3	yes	32	48.29	odd	4	inner
144.3.j.a.125.14	yes	32	16.13	even	4	inner
576.3.j.a.17.1		32	48.35	even	4
576.3.j.a.17.16		32	16.3	odd	4
576.3.j.a.305.1		32	4.3	odd	2
576.3.j.a.305.16		32	12.11	even	2
1152.3.j.a.161.1		32	16.5	even	4
1152.3.j.a.161.16		32	48.5	odd	4
1152.3.j.a.737.1		32	24.5	odd	2
1152.3.j.a.737.16		32	8.5	even	2
1152.3.j.b.161.1		32	16.11	odd	4
1152.3.j.b.161.16		32	48.11	even	4
1152.3.j.b.737.1		32	24.11	even	2
1152.3.j.b.737.16		32	8.3	odd	2

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:	\( N \)	\(=\)	\( 144 = 2^{4} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	144.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.76559 - 0.939508i) q^{2} +(2.23465 + 3.31758i) q^{4} +(-6.08688 + 6.08688i) q^{5} -9.40026i q^{7} +(-0.828591 - 7.95697i) q^{8} +O(q^{10})\)	\(q+(-1.76559 - 0.939508i) q^{2} +(2.23465 + 3.31758i) q^{4} +(-6.08688 + 6.08688i) q^{5} -9.40026i q^{7} +(-0.828591 - 7.95697i) q^{8} +(16.4656 - 5.02829i) q^{10} +(11.9531 - 11.9531i) q^{11} +(3.47284 - 3.47284i) q^{13} +(-8.83162 + 16.5970i) q^{14} +(-6.01269 + 14.8273i) q^{16} -28.5398i q^{17} +(-3.08620 + 3.08620i) q^{19} +(-33.7958 - 6.59168i) q^{20} +(-32.3344 + 9.87430i) q^{22} +2.57437 q^{23} -49.1003i q^{25} +(-9.39439 + 2.86887i) q^{26} +(31.1861 - 21.0063i) q^{28} +(3.49628 + 3.49628i) q^{29} -21.0909 q^{31} +(24.5463 - 20.5300i) q^{32} +(-26.8134 + 50.3897i) q^{34} +(57.2183 + 57.2183i) q^{35} +(-13.2847 - 13.2847i) q^{37} +(8.34848 - 2.54947i) q^{38} +(53.4767 + 43.3896i) q^{40} -11.2365 q^{41} +(8.19150 + 8.19150i) q^{43} +(66.3664 + 12.9444i) q^{44} +(-4.54529 - 2.41864i) q^{46} -17.2381i q^{47} -39.3649 q^{49} +(-46.1301 + 86.6912i) q^{50} +(19.2820 + 3.76085i) q^{52} +(-30.5182 + 30.5182i) q^{53} +145.514i q^{55} +(-74.7976 + 7.78897i) q^{56} +(-2.88823 - 9.45780i) q^{58} +(14.7367 - 14.7367i) q^{59} +(39.3037 - 39.3037i) q^{61} +(37.2380 + 19.8151i) q^{62} +(-62.6269 + 13.1862i) q^{64} +42.2775i q^{65} +(79.6470 - 79.6470i) q^{67} +(94.6830 - 63.7764i) q^{68} +(-47.2672 - 154.781i) q^{70} +73.1921 q^{71} +1.23261i q^{73} +(10.9744 + 35.9366i) q^{74} +(-17.1353 - 3.34214i) q^{76} +(-112.362 - 112.362i) q^{77} -110.191 q^{79} +(-53.6533 - 126.850i) q^{80} +(19.8390 + 10.5568i) q^{82} +(-13.7800 - 13.7800i) q^{83} +(173.718 + 173.718i) q^{85} +(-6.76689 - 22.1589i) q^{86} +(-105.015 - 85.2063i) q^{88} -39.2555 q^{89} +(-32.6456 - 32.6456i) q^{91} +(5.75280 + 8.54067i) q^{92} +(-16.1954 + 30.4356i) q^{94} -37.5706i q^{95} -109.383 q^{97} +(69.5024 + 36.9836i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q+O(q^{10}) \) 32 * q	\( 32 q + 40 q^{10} + 48 q^{16} + 64 q^{19} - 88 q^{22} - 120 q^{28} - 248 q^{34} - 184 q^{40} + 128 q^{43} + 24 q^{46} - 224 q^{49} + 632 q^{52} + 456 q^{58} + 64 q^{61} - 48 q^{64} - 64 q^{67} - 312 q^{70} - 576 q^{76} - 512 q^{79} - 720 q^{82} + 320 q^{85} - 400 q^{88} - 192 q^{91} + 696 q^{94}+O(q^{100}) \) 32 * q + 40 * q^10 + 48 * q^16 + 64 * q^19 - 88 * q^22 - 120 * q^28 - 248 * q^34 - 184 * q^40 + 128 * q^43 + 24 * q^46 - 224 * q^49 + 632 * q^52 + 456 * q^58 + 64 * q^61 - 48 * q^64 - 64 * q^67 - 312 * q^70 - 576 * q^76 - 512 * q^79 - 720 * q^82 + 320 * q^85 - 400 * q^88 - 192 * q^91 + 696 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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