LMFDB - Embedded newform 441.4.p.d.80.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [441,4,Mod(80,441)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(441, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("441.80");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 441 = 3^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	441.p (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:	$26.0198423125$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			80.4
Character	$\chi$	$=$	441.80
Dual form			441.4.p.d.215.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-3.21193 + 1.85441i) q^{2} +(2.87764 - 4.98422i) q^{4} +(2.27338 + 3.93760i) q^{5} -8.32523i q^{8} +O(q^{10})$	\(q+(-3.21193 + 1.85441i) q^{2} +(2.87764 - 4.98422i) q^{4} +(2.27338 + 3.93760i) q^{5} -8.32523i q^{8} +(-14.6038 - 8.43153i) q^{10} +(-39.4183 - 22.7582i) q^{11} +11.6749i q^{13} +(38.4595 + 66.6138i) q^{16} +(-45.7579 + 79.2550i) q^{17} +(121.317 - 70.0425i) q^{19} +26.1679 q^{20} +168.812 q^{22} +(-38.9875 + 22.5094i) q^{23} +(52.1635 - 90.3499i) q^{25} +(-21.6500 - 37.4989i) q^{26} -47.7861i q^{29} +(-206.848 - 119.424i) q^{31} +(-189.379 - 109.338i) q^{32} -339.415i q^{34} +(74.4635 + 128.975i) q^{37} +(-259.775 + 449.943i) q^{38} +(32.7815 - 18.9264i) q^{40} +393.755 q^{41} +412.265 q^{43} +(-226.864 + 130.980i) q^{44} +(83.4833 - 144.597i) q^{46} +(-204.379 - 353.994i) q^{47} +386.929i q^{50} +(58.1903 + 33.5962i) q^{52} +(144.687 + 83.5350i) q^{53} -206.952i q^{55} +(88.6149 + 153.485i) q^{58} +(-68.7687 + 119.111i) q^{59} +(280.041 - 161.682i) q^{61} +885.842 q^{62} +195.677 q^{64} +(-45.9712 + 26.5415i) q^{65} +(-212.076 + 367.326i) q^{67} +(263.350 + 456.135i) q^{68} +727.190i q^{71} +(949.259 + 548.055i) q^{73} +(-478.343 - 276.171i) q^{74} -806.229i q^{76} +(334.630 + 579.597i) q^{79} +(-174.866 + 302.877i) q^{80} +(-1264.71 + 730.181i) q^{82} +199.014 q^{83} -416.100 q^{85} +(-1324.16 + 764.507i) q^{86} +(-189.467 + 328.167i) q^{88} +(403.674 + 699.184i) q^{89} +259.096i q^{92} +(1312.90 + 758.002i) q^{94} +(551.600 + 318.466i) q^{95} +701.053i q^{97} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 96 q^{4}+O(q^{10}) $ 48 * q + 96 * q^4	$ 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) $ 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/441\mathbb{Z}\right)^\times$.

$n$	$199$	$344$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	−3.21193	+	1.85441i	−1.13559	+	0.655631i	−0.945334	−	0.326104i	$-0.894264\pi$
$2$	−3.21193	+	1.85441i	−1.13559	+	0.655631i	−0.190253	+	0.981735i	$0.560931\pi$
$3$		0			0
$3$		0			0
$4$	2.87764	−	4.98422i	0.359705	−	0.623028i
$5$	2.27338	+	3.93760i	0.203337	+	0.352190i	0.949602	−	0.313459i	$-0.101488\pi$
$5$	2.27338	+	3.93760i	0.203337	+	0.352190i	−0.746265	+	0.665649i	$0.768155\pi$
$6$		0			0
$7$		0			0
$7$		0			0
$8$		−	8.32523i		−	0.367927i
$9$		0			0
$10$	−14.6038	−	8.43153i	−0.461814	−	0.266628i
$11$	−39.4183	−	22.7582i	−1.08046	−	0.623805i	−0.149440	−	0.988771i	$-0.547747\pi$
$11$	−39.4183	−	22.7582i	−1.08046	−	0.623805i	−0.931021	+	0.364966i	$0.881081\pi$
$12$		0			0
$13$			11.6749i			0.249080i	0.992215	+	0.124540i	$0.0397455\pi$
$13$			11.6749i			0.249080i	−0.992215	+	0.124540i	$0.960255\pi$
$14$		0			0
$15$		0			0
$16$	38.4595	+	66.6138i	0.600930	+	1.04084i
$17$	−45.7579	+	79.2550i	−0.652818	+	1.13071i	0.329618	+	0.944115i	$0.393080\pi$
$17$	−45.7579	+	79.2550i	−0.652818	+	1.13071i	−0.982436	+	0.186600i	$0.940253\pi$
$18$		0			0
$19$	121.317	−	70.0425i	1.46485	−	0.845730i	0.465617	−	0.884986i	$-0.345832\pi$
$19$	121.317	−	70.0425i	1.46485	−	0.845730i	0.999229	+	0.0392566i	$0.0124990\pi$
$20$	26.1679			0.292566
$21$		0			0
$22$	168.812			1.63594
$23$	−38.9875	+	22.5094i	−0.353455	+	0.204067i	−0.666206	−	0.745768i	$-0.732083\pi$
$23$	−38.9875	+	22.5094i	−0.353455	+	0.204067i	0.312751	+	0.949835i	$0.398749\pi$
$24$		0			0
$25$	52.1635	−	90.3499i	0.417308	−	0.722799i
$26$	−21.6500	−	37.4989i	−0.163304	−	0.282852i
$27$		0			0
$28$		0			0
$29$		−	47.7861i		−	0.305988i	−0.988227	−	0.152994i	$-0.951108\pi$
$29$		−	47.7861i		−	0.305988i	0.988227	−	0.152994i	$-0.0488916\pi$
$30$		0			0
$31$	−206.848	−	119.424i	−1.19842	−	0.691909i	−0.238218	−	0.971212i	$-0.576563\pi$
$31$	−206.848	−	119.424i	−1.19842	−	0.691909i	−0.960203	+	0.279303i	$0.909897\pi$
$32$	−189.379	−	109.338i	−1.04618	−	0.604013i
$33$		0			0
$34$		−	339.415i		−	1.71203i
$35$		0			0
$36$		0			0
$37$	74.4635	+	128.975i	0.330858	+	0.573062i	0.982680	−	0.185309i	$-0.0593287\pi$
$37$	74.4635	+	128.975i	0.330858	+	0.573062i	−0.651823	+	0.758371i	$0.725995\pi$
$38$	−259.775	+	449.943i	−1.10897	+	1.92080i
$39$		0			0
$40$	32.7815	−	18.9264i	0.129580	−	0.0748131i
$41$	393.755			1.49986			0.749929	−	0.661518i	$-0.230088\pi$
$41$	393.755			1.49986			0.749929	+	0.661518i	$0.230088\pi$
$42$		0			0
$43$	412.265			1.46209			0.731045	−	0.682329i	$-0.239033\pi$
$43$	412.265			1.46209			0.731045	+	0.682329i	$0.239033\pi$
$44$	−226.864	+	130.980i	−0.777295	+	0.448772i
$45$		0			0
$46$	83.4833	−	144.597i	0.267586	−	0.463472i
$47$	−204.379	−	353.994i	−0.634292	−	1.09863i	−0.986665	−	0.162766i	$-0.947959\pi$
$47$	−204.379	−	353.994i	−0.634292	−	1.09863i	0.352373	−	0.935860i	$-0.385375\pi$
$48$		0			0
$49$		0			0
$50$			386.929i			1.09440i
$51$		0			0
$52$	58.1903	+	33.5962i	0.155184	+	0.0895953i
$53$	144.687	+	83.5350i	0.374986	+	0.216498i	0.675635	−	0.737237i	$-0.263870\pi$
$53$	144.687	+	83.5350i	0.374986	+	0.216498i	−0.300648	+	0.953735i	$0.597203\pi$
$54$		0			0
$55$		−	206.952i		−	0.507370i
$56$		0			0
$57$		0			0
$58$	88.6149	+	153.485i	0.200616	+	0.347476i
$59$	−68.7687	+	119.111i	−0.151744	+	0.262829i	−0.931869	−	0.362795i	$-0.881822\pi$
$59$	−68.7687	+	119.111i	−0.151744	+	0.262829i	0.780124	+	0.625624i	$0.215156\pi$
$60$		0			0
$61$	280.041	−	161.682i	0.587797	−	0.339365i	−0.176429	−	0.984313i	$-0.556455\pi$
$61$	280.041	−	161.682i	0.587797	−	0.339365i	0.764226	+	0.644949i	$0.223121\pi$
$62$	885.842			1.81455
$63$		0			0
$64$	195.677			0.382181
$65$	−45.9712	+	26.5415i	−0.0877234	+	0.0506471i
$66$		0			0
$67$	−212.076	+	367.326i	−0.386705	+	0.669792i	−0.992004	−	0.126206i	$-0.959720\pi$
$67$	−212.076	+	367.326i	−0.386705	+	0.669792i	0.605299	+	0.795998i	$0.293053\pi$
$68$	263.350	+	456.135i	0.469644	+	0.813448i
$69$		0			0
$70$		0			0
$71$			727.190i			1.21551i	0.794123	+	0.607757i	$0.207931\pi$
$71$			727.190i			1.21551i	−0.794123	+	0.607757i	$0.792069\pi$
$72$		0			0
$73$	949.259	+	548.055i	1.52195	+	0.878699i	0.999664	+	0.0259286i	$0.00825425\pi$
$73$	949.259	+	548.055i	1.52195	+	0.878699i	0.522287	+	0.852770i	$0.325079\pi$
$74$	−478.343	−	276.171i	−0.751435	−	0.433841i
$75$		0			0
$76$		−	806.229i		−	1.21685i
$77$		0			0
$78$		0			0
$79$	334.630	+	579.597i	0.476568	+	0.825439i	0.999639	−	0.0268493i	$-0.00854742\pi$
$79$	334.630	+	579.597i	0.476568	+	0.825439i	−0.523072	+	0.852289i	$0.675214\pi$
$80$	−174.866	+	302.877i	−0.244382	+	0.423283i
$81$		0			0
$82$	−1264.71	+	730.181i	−1.70322	+	0.983354i
$83$	199.014			0.263189			0.131594	−	0.991304i	$-0.457990\pi$
$83$	199.014			0.263189			0.131594	+	0.991304i	$0.457990\pi$
$84$		0			0
$85$	−416.100			−0.530969
$86$	−1324.16	+	764.507i	−1.66033	+	0.958592i
$87$		0			0
$88$	−189.467	+	328.167i	−0.229514	+	0.397530i
$89$	403.674	+	699.184i	0.480779	+	0.832734i	0.999757	−	0.0220537i	$-0.00702047\pi$
$89$	403.674	+	699.184i	0.480779	+	0.832734i	−0.518977	+	0.854788i	$0.673687\pi$
$90$		0			0
$91$		0			0
$92$			259.096i			0.293616i
$93$		0			0
$94$	1312.90	+	758.002i	1.44059	+	0.831723i
$95$	551.600	+	318.466i	0.595715	+	0.343936i
$96$		0			0
$97$			701.053i			0.733827i	0.930255	+	0.366913i	$0.119585\pi$
$97$			701.053i			0.733827i	−0.930255	+	0.366913i	$0.880415\pi$
$98$		0			0
$99$		0			0
$100$	−300.216	−	519.989i	−0.300216	−	0.519989i
$101$	851.292	−	1474.48i	0.838680	−	1.45264i	−0.0523187	−	0.998630i	$-0.516661\pi$
$101$	851.292	−	1474.48i	0.838680	−	1.45264i	0.890999	−	0.454006i	$-0.150006\pi$
$102$		0			0
$103$	982.275	−	567.117i	0.939674	−	0.542521i	0.0498158	−	0.998758i	$-0.484137\pi$
$103$	982.275	−	567.117i	0.939674	−	0.542521i	0.889858	+	0.456237i	$0.150803\pi$
$104$	97.1963			0.0916431
$105$		0			0
$106$	−619.631			−0.567773
$107$	−293.345	+	169.363i	−0.265035	+	0.153018i	−0.626629	−	0.779318i	$-0.715566\pi$
$107$	−293.345	+	169.363i	−0.265035	+	0.153018i	0.361594	+	0.932336i	$0.382233\pi$
$108$		0			0
$109$	−987.768	+	1710.86i	−0.867991	+	1.50340i	−0.00394436	+	0.999992i	$0.501256\pi$
$109$	−987.768	+	1710.86i	−0.867991	+	1.50340i	−0.864046	+	0.503412i	$0.832078\pi$
$110$	383.772	+	664.713i	0.332648	+	0.576163i
$111$		0			0
$112$		0			0
$113$			1685.74i			1.40337i	0.712488	+	0.701685i	$0.247568\pi$
$113$			1685.74i			1.40337i	−0.712488	+	0.701685i	$0.752432\pi$
$114$		0			0
$115$	−177.267	−	102.345i	−0.143741	−	0.0829888i
$116$	−238.177	−	137.511i	−0.190639	−	0.110066i
$117$		0			0
$118$		−	510.100i		−	0.397954i
$119$		0			0
$120$		0			0
$121$	370.370	+	641.499i	0.278264	+	0.481968i
$122$	−599.648	+	1038.62i	−0.444996	+	0.770756i
$123$		0			0
$124$	−1190.47	+	687.319i	−0.862157	+	0.497767i
$125$	1042.69			0.746091
$126$		0			0
$127$	−1155.98			−0.807691			−0.403846	−	0.914827i	$-0.632327\pi$
$127$	−1155.98			−0.807691			−0.403846	+	0.914827i	$0.632327\pi$
$128$	886.534	−	511.840i	0.612181	−	0.353443i
$129$		0			0
$130$	98.4373	−	170.498i	0.0664117	−	0.115028i
$131$	−317.534	−	549.984i	−0.211779	−	0.366812i	0.740492	−	0.672065i	$-0.234592\pi$
$131$	−317.534	−	549.984i	−0.211779	−	0.366812i	−0.952271	+	0.305253i	$0.901259\pi$
$132$		0			0
$133$		0			0
$134$		−	1573.10i		−	1.01414i
$135$		0			0
$136$	659.816	+	380.945i	0.416020	+	0.240189i
$137$	2128.80	+	1229.06i	1.32756	+	0.766466i	0.984921	−	0.173002i	$-0.0553468\pi$
$137$	2128.80	+	1229.06i	1.32756	+	0.766466i	0.342636	+	0.939468i	$0.388680\pi$
$138$		0			0
$139$			1094.81i			0.668062i	0.942562	+	0.334031i	$0.108409\pi$
$139$			1094.81i			0.668062i	−0.942562	+	0.334031i	$0.891591\pi$
$140$		0			0
$141$		0			0
$142$	−1348.50	−	2335.68i	−0.796930	−	1.38032i
$143$	265.700	−	460.205i	0.155377	−	0.269121i
$144$		0			0
$145$	188.163	−	108.636i	0.107766	−	0.0622187i
$146$	−4065.27			−2.30441
$147$		0			0
$148$	857.117			0.476045
$149$	837.026	−	483.257i	0.460214	−	0.265704i	−0.251921	−	0.967748i	$-0.581062\pi$
$149$	837.026	−	483.257i	0.460214	−	0.265704i	0.712134	+	0.702044i	$0.247729\pi$
$150$		0			0
$151$	1164.94	−	2017.74i	0.627825	−	1.08743i	−0.360162	−	0.932890i	$-0.617279\pi$
$151$	1164.94	−	2017.74i	0.627825	−	1.08743i	0.987987	−	0.154536i	$-0.0493881\pi$
$152$	−583.120	−	1009.99i	−0.311166	−	0.538956i
$153$		0			0
$154$		0			0
$155$		−	1085.98i		−	0.562763i
$156$		0			0
$157$	−2957.39	−	1707.45i	−1.50334	−	0.867956i	−0.999992	−	0.00387483i	$-0.998767\pi$
$157$	−2957.39	−	1707.45i	−1.50334	−	0.867956i	−0.503352	−	0.864081i	$-0.667900\pi$
$158$	−2149.61	−	1241.08i	−1.08237	−	0.624905i
$159$		0			0
$160$		−	994.267i		−	0.491273i
$161$		0			0
$162$		0			0
$163$	180.834	+	313.214i	0.0868960	+	0.150508i	0.906198	−	0.422855i	$-0.138972\pi$
$163$	180.834	+	313.214i	0.0868960	+	0.150508i	−0.819302	+	0.573363i	$0.805639\pi$
$164$	1133.09	−	1962.56i	0.539507	−	0.934453i
$165$		0			0
$166$	−639.219	+	369.053i	−0.298874	+	0.172555i
$167$	1605.57			0.743969			0.371984	−	0.928239i	$-0.378678\pi$
$167$	1605.57			0.743969			0.371984	+	0.928239i	$0.378678\pi$
$168$		0			0
$169$	2060.70			0.937959
$170$	1336.48	−	771.617i	0.602961	−	0.348120i
$171$		0			0
$172$	1186.35	−	2054.82i	0.525921	−	0.910922i
$173$	−733.434	−	1270.35i	−0.322324	−	0.558281i	0.658644	−	0.752455i	$-0.271131\pi$
$173$	−733.434	−	1270.35i	−0.322324	−	0.558281i	−0.980967	+	0.194174i	$0.937797\pi$
$174$		0			0
$175$		0			0
$176$		−	3501.07i		−	1.49945i
$177$		0			0
$178$	−2593.14	−	1497.15i	−1.09193	−	0.630428i
$179$	850.303	+	490.923i	0.355054	+	0.204990i	0.666909	−	0.745139i	$-0.267617\pi$
$179$	850.303	+	490.923i	0.355054	+	0.204990i	−0.311855	+	0.950130i	$0.600950\pi$
$180$		0			0
$181$			1547.32i			0.635422i	0.948188	+	0.317711i	$0.102914\pi$
$181$			1547.32i			0.635422i	−0.948188	+	0.317711i	$0.897086\pi$
$182$		0			0
$183$		0			0
$184$	187.396	+	324.580i	0.0750817	+	0.130045i
$185$	−338.567	+	586.416i	−0.134551	+	0.233049i
$186$		0			0
$187$	3607.40	−	2082.73i	1.41069	−	0.814462i
$188$	−2352.52			−0.912632
$189$		0			0
$190$	−2362.26			−0.901982
$191$	4143.61	−	2392.32i	1.56975	−	0.906293i	0.573548	−	0.819172i	$-0.305567\pi$
$191$	4143.61	−	2392.32i	1.56975	−	0.906293i	0.996198	−	0.0871206i	$-0.0277666\pi$
$192$		0			0
$193$	638.186	−	1105.37i	0.238019	−	0.412261i	−0.722127	−	0.691761i	$-0.756835\pi$
$193$	638.186	−	1105.37i	0.238019	−	0.412261i	0.960146	+	0.279500i	$0.0901687\pi$
$194$	−1300.04	−	2251.73i	−0.481120	−	0.833324i
$195$		0			0
$196$		0			0
$197$		−	491.111i		−	0.177615i	−0.996049	−	0.0888076i	$-0.971694\pi$
$197$		−	491.111i		−	0.177615i	0.996049	−	0.0888076i	$-0.0283056\pi$
$198$		0			0
$199$	−2588.06	−	1494.22i	−0.921924	−	0.532273i	−0.0376759	−	0.999290i	$-0.511995\pi$
$199$	−2588.06	−	1494.22i	−0.921924	−	0.532273i	−0.884248	+	0.467017i	$0.845329\pi$
$200$	−752.183	−	434.273i	−0.265937	−	0.153539i
$201$		0			0
$202$			6314.56i			2.19946i
$203$		0			0
$204$		0			0
$205$	895.153	+	1550.45i	0.304977	+	0.528235i
$206$	−2103.33	+	3643.07i	−0.711388	+	1.23216i
$207$		0			0
$208$	−777.710	+	449.011i	−0.259252	+	0.149679i
$209$	−6376.16			−2.11028
$210$		0			0
$211$	978.467			0.319244			0.159622	−	0.987178i	$-0.448972\pi$
$211$	978.467			0.319244			0.159622	+	0.987178i	$0.448972\pi$
$212$	832.714	−	480.768i	0.269769	−	0.155751i
$213$		0			0
$214$	628.135	−	1087.96i	0.200647	−	0.347531i
$215$	937.234	+	1623.34i	0.297297	+	0.514933i
$216$		0			0
$217$		0			0
$218$		−	7326.89i		−	2.27633i
$219$		0			0
$220$	−1031.49	−	595.533i	−0.316106	−	0.182504i
$221$	−925.294	−	534.219i	−0.281638	−	0.162604i
$222$		0			0
$223$		−	727.150i		−	0.218357i	−0.994022	−	0.109178i	$-0.965178\pi$
$223$		−	727.150i		−	0.218357i	0.994022	−	0.109178i	$-0.0348220\pi$
$224$		0			0
$225$		0			0
$226$	−3126.04	−	5414.46i	−0.920093	−	1.59365i
$227$	3115.04	−	5395.40i	0.910803	−	1.57756i	0.0978711	−	0.995199i	$-0.468797\pi$
$227$	3115.04	−	5395.40i	0.910803	−	1.57756i	0.812932	−	0.582358i	$-0.197870\pi$
$228$		0			0
$229$	4910.42	−	2835.03i	1.41699	−	0.818097i	0.420952	−	0.907083i	$-0.361696\pi$
$229$	4910.42	−	2835.03i	1.41699	−	0.818097i	0.996033	+	0.0889858i	$0.0283626\pi$
$230$	759.156			0.217640
$231$		0			0
$232$	−397.830			−0.112581
$233$	−3424.06	+	1976.88i	−0.962737	+	0.555836i	−0.897014	−	0.442002i	$-0.854268\pi$
$233$	−3424.06	+	1976.88i	−0.962737	+	0.555836i	−0.0657224	+	0.997838i	$0.520935\pi$
$234$		0			0
$235$	929.260	−	1609.53i	0.257950	−	0.446782i
$236$	395.783	+	685.517i	0.109167	+	0.189082i
$237$		0			0
$238$		0			0
$239$			3916.55i			1.06000i	0.847997	+	0.530001i	$0.177808\pi$
$239$			3916.55i			1.06000i	−0.847997	+	0.530001i	$0.822192\pi$
$240$		0			0
$241$	−2833.37	−	1635.85i	−0.757316	−	0.437237i	0.0710150	−	0.997475i	$-0.477376\pi$
$241$	−2833.37	−	1635.85i	−0.757316	−	0.437237i	−0.828331	+	0.560238i	$0.810710\pi$
$242$	−2379.20	−	1373.63i	−0.631987	−	0.364878i
$243$		0			0
$244$		−	1861.05i		−	0.488285i
$245$		0			0
$246$		0			0
$247$	817.740	+	1416.37i	0.210654	+	0.364863i
$248$	−994.232	+	1722.06i	−0.254572	+	0.440931i
$249$		0			0
$250$	−3349.05	+	1933.58i	−0.847251	+	0.489161i
$251$	−1401.75			−0.352502			−0.176251	−	0.984345i	$-0.556397\pi$
$251$	−1401.75			−0.352502			−0.176251	+	0.984345i	$0.556397\pi$
$252$		0			0
$253$	2049.10			0.509192
$254$	3712.93	−	2143.66i	0.917204	−	0.529548i
$255$		0			0
$256$	−2681.03	+	4643.67i	−0.654548	+	1.13371i
$257$	2044.17	+	3540.61i	0.496155	+	0.859366i	0.999990	−	0.00443389i	$-0.00141136\pi$
$257$	2044.17	+	3540.61i	0.496155	+	0.859366i	−0.503835	+	0.863800i	$0.668078\pi$
$258$		0			0
$259$		0			0
$260$			305.507i			0.0728721i
$261$		0			0
$262$	2039.79	+	1177.67i	0.480987	+	0.277698i
$263$	3994.32	+	2306.12i	0.936503	+	0.540690i	0.888863	−	0.458174i	$-0.151496\pi$
$263$	3994.32	+	2306.12i	0.936503	+	0.540690i	0.0476409	+	0.998865i	$0.484830\pi$
$264$		0			0
$265$			759.626i			0.176089i
$266$		0			0
$267$		0			0
$268$	1220.56	+	2114.07i	0.278199	+	0.481855i
$269$	1839.16	−	3185.51i	0.416860	−	0.722023i	−0.578762	−	0.815497i	$-0.696464\pi$
$269$	1839.16	−	3185.51i	0.416860	−	0.722023i	0.995622	+	0.0934741i	$0.0297972\pi$
$270$		0			0
$271$	−6200.70	+	3579.98i	−1.38991	+	0.802465i	−0.993305	−	0.115524i	$-0.963145\pi$
$271$	−6200.70	+	3579.98i	−1.38991	+	0.802465i	−0.396606	+	0.917989i	$0.629812\pi$
$272$	−7039.30			−1.56919
$273$		0			0
$274$	−9116.72			−2.01008
$275$	−4112.40	+	2374.29i	−0.901770	+	0.520637i
$276$		0			0
$277$	−565.348	+	979.212i	−0.122630	+	0.212401i	−0.920804	−	0.390026i	$-0.872466\pi$
$277$	−565.348	+	979.212i	−0.122630	+	0.212401i	0.798174	+	0.602427i	$0.205799\pi$
$278$	−2030.22	−	3516.45i	−0.438003	−	0.758643i
$279$		0			0
$280$		0			0
$281$		−	3919.67i		−	0.832128i	−0.909335	−	0.416064i	$-0.863409\pi$
$281$		−	3919.67i		−	0.832128i	0.909335	−	0.416064i	$-0.136591\pi$
$282$		0			0
$283$	3902.97	+	2253.38i	0.819815	+	0.473320i	0.850353	−	0.526213i	$-0.176389\pi$
$283$	3902.97	+	2253.38i	0.819815	+	0.473320i	−0.0305379	+	0.999534i	$0.509722\pi$
$284$	3624.47	+	2092.59i	0.757299	+	0.437227i
$285$		0			0
$286$			1970.86i			0.407480i
$287$		0			0
$288$		0			0
$289$	−1731.06	−	2998.29i	−0.352344	−	0.610277i
$290$	−402.910	+	697.860i	−0.0815851	+	0.141310i
$291$		0			0
$292$	5463.26	−	3154.21i	1.09491	−	0.632145i
$293$	8956.63			1.78584			0.892922	−	0.450212i	$-0.148652\pi$
$293$	8956.63			1.78584			0.892922	+	0.450212i	$0.148652\pi$
$294$		0			0
$295$	−625.349			−0.123421
$296$	1073.74	−	619.926i	0.210845	−	0.121731i
$297$		0			0
$298$	−1792.31	+	3104.37i	−0.348408	+	0.603461i
$299$	−262.796	−	455.175i	−0.0508290	−	0.0880383i
$300$		0			0
$301$		0			0
$302$			8641.10i			1.64649i
$303$		0			0
$304$	9331.60	+	5387.60i	1.76054	+	1.01645i
$305$	1273.28	+	735.128i	0.239042	+	0.138011i
$306$		0			0
$307$		−	3522.69i		−	0.654888i	−0.944871	−	0.327444i	$-0.893813\pi$
$307$		−	3522.69i		−	0.654888i	0.944871	−	0.327444i	$-0.106187\pi$
$308$		0			0
$309$		0			0
$310$	2013.85	+	3488.10i	0.368965	+	0.639066i
$311$	1777.91	−	3079.43i	0.324168	−	0.561475i	−0.657176	−	0.753737i	$-0.728249\pi$
$311$	1777.91	−	3079.43i	0.324168	−	0.561475i	0.981344	+	0.192262i	$0.0615825\pi$
$312$		0			0
$313$	−5490.40	+	3169.88i	−0.991488	+	0.572436i	−0.905719	−	0.423879i	$-0.860668\pi$
$313$	−5490.40	+	3169.88i	−0.991488	+	0.572436i	−0.0857693	+	0.996315i	$0.527335\pi$
$314$	12665.2			2.27624
$315$		0			0
$316$	3851.78			0.685695
$317$	2203.91	−	1272.43i	0.390486	−	0.225447i	−0.291885	−	0.956454i	$-0.594282\pi$
$317$	2203.91	−	1272.43i	0.390486	−	0.225447i	0.682371	+	0.731006i	$0.260949\pi$
$318$		0			0
$319$	−1087.53	+	1883.65i	−0.190877	+	0.330608i
$320$	444.847	+	770.498i	0.0777116	+	0.134600i
$321$		0			0
$322$		0			0
$323$			12820.0i			2.20843i
$324$		0			0
$325$	1054.83	+	609.004i	0.180035	+	0.103943i
$326$	−1161.65	−	670.681i	−0.197356	−	0.113943i
$327$		0			0
$328$		−	3278.10i		−	0.551838i
$329$		0			0
$330$		0			0
$331$	−5699.21	−	9871.33i	−0.946396	−	1.63921i	−0.752931	−	0.658099i	$-0.771361\pi$
$331$	−5699.21	−	9871.33i	−0.946396	−	1.63921i	−0.193465	−	0.981107i	$-0.561973\pi$
$332$	572.692	−	991.932i	0.0946704	−	0.163974i
$333$		0			0
$334$	−5156.97	+	2977.38i	−0.844841	+	0.487769i
$335$	−1928.52			−0.314525
$336$		0			0
$337$	−551.119			−0.0890842			−0.0445421	−	0.999008i	$-0.514183\pi$
$337$	−551.119			−0.0890842			−0.0445421	+	0.999008i	$0.514183\pi$
$338$	−6618.80	+	3821.37i	−1.06513	+	0.614956i
$339$		0			0
$340$	−1197.39	+	2073.93i	−0.190992	+	0.330808i
$341$	5435.74	+	9414.99i	0.863232	+	1.49516i
$342$		0			0
$343$		0			0
$344$		−	3432.20i		−	0.537942i
$345$		0			0
$346$	4711.47	+	2720.17i	0.732053	+	0.422651i
$347$	2500.59	+	1443.72i	0.386855	+	0.223351i	0.680797	−	0.732472i	$-0.261634\pi$
$347$	2500.59	+	1443.72i	0.386855	+	0.223351i	−0.293941	+	0.955823i	$0.594967\pi$
$348$		0			0
$349$		−	2290.34i		−	0.351286i	−0.984454	−	0.175643i	$-0.943800\pi$
$349$		−	2290.34i		−	0.351286i	0.984454	−	0.175643i	$-0.0562005\pi$
$350$		0			0
$351$		0			0
$352$	4976.67	+	8619.85i	0.753572	+	1.30523i
$353$	704.760	−	1220.68i	0.106262	−	0.184052i	−0.807991	−	0.589195i	$-0.799445\pi$
$353$	704.760	−	1220.68i	0.106262	−	0.184052i	0.914253	+	0.405143i	$0.132778\pi$
$354$		0			0
$355$	−2863.38	+	1653.18i	−0.428092	+	0.247159i
$356$	4646.52			0.691755
$357$		0			0
$358$	−3641.48			−0.537593
$359$	−6021.18	+	3476.33i	−0.885196	+	0.511068i	−0.872368	−	0.488849i	$-0.837417\pi$
$359$	−6021.18	+	3476.33i	−0.885196	+	0.511068i	−0.0128282	+	0.999918i	$0.504083\pi$
$360$		0			0
$361$	6382.42	−	11054.7i	0.930517	−	1.61170i
$362$	−2869.36	−	4969.88i	−0.416603	−	0.721577i
$363$		0			0
$364$		0			0
$365$			4983.74i			0.714688i
$366$		0			0
$367$	1300.86	+	751.049i	0.185025	+	0.106824i	0.589651	−	0.807658i	$-0.299265\pi$
$367$	1300.86	+	751.049i	0.185025	+	0.106824i	−0.404627	+	0.914482i	$0.632598\pi$
$368$	−2998.88	−	1731.40i	−0.424802	−	0.245260i
$369$		0			0
$370$		−	2511.37i		−	0.352864i
$371$		0			0
$372$		0			0
$373$	3527.52	+	6109.84i	0.489673	+	0.848138i	0.999929	−	0.0118844i	$-0.00378300\pi$
$373$	3527.52	+	6109.84i	0.489673	+	0.848138i	−0.510257	+	0.860022i	$0.670450\pi$
$374$	−7724.46	+	13379.2i	−1.06797	+	1.84979i
$375$		0			0
$376$	−2947.08	+	1701.50i	−0.404214	+	0.233373i
$377$	557.898			0.0762155
$378$		0			0
$379$	5163.51			0.699820			0.349910	−	0.936783i	$-0.386212\pi$
$379$	5163.51			0.699820			0.349910	+	0.936783i	$0.386212\pi$
$380$	3174.61	−	1832.86i	0.428564	−	0.247431i
$381$		0			0
$382$	−8872.65	+	15367.9i	−1.18839	+	2.05835i
$383$	1258.96	+	2180.58i	0.167963	+	0.290921i	0.937704	−	0.347436i	$-0.112948\pi$
$383$	1258.96	+	2180.58i	0.167963	+	0.290921i	−0.769740	+	0.638357i	$0.779614\pi$
$384$		0			0
$385$		0			0
$386$			4733.82i			0.624210i
$387$		0			0
$388$	3494.21	+	2017.38i	0.457194	+	0.263961i
$389$	−4145.43	−	2393.37i	−0.540313	−	0.311950i	0.204893	−	0.978784i	$-0.434315\pi$
$389$	−4145.43	−	2393.37i	−0.540313	−	0.311950i	−0.745206	+	0.666834i	$0.767649\pi$
$390$		0			0
$391$		−	4119.94i		−	0.532875i
$392$		0			0
$393$		0			0
$394$	910.718	+	1577.41i	0.116450	+	0.201697i
$395$	−1521.48	+	2635.28i	−0.193808	+	0.335685i
$396$		0			0
$397$	8309.07	−	4797.25i	1.05043	−	0.606466i	0.127660	−	0.991818i	$-0.459253\pi$
$397$	8309.07	−	4797.25i	1.05043	−	0.606466i	0.922770	+	0.385352i	$0.125920\pi$
$398$	11083.6			1.39590
$399$		0			0
$400$	8024.73			1.00309
$401$	−11732.4	+	6773.68i	−1.46106	+	0.843544i	−0.999061	−	0.0433348i	$-0.986202\pi$
$401$	−11732.4	+	6773.68i	−1.46106	+	0.843544i	−0.462001	+	0.886879i	$0.652868\pi$
$402$		0			0
$403$	1394.26	−	2414.93i	0.172340	−	0.298502i
$404$	−4899.42	−	8486.05i	−0.603355	−	1.04504i
$405$		0			0
$406$		0			0
$407$		−	6778.62i		−	0.825562i
$408$		0			0
$409$	−1872.55	−	1081.12i	−0.226386	−	0.130704i	0.382518	−	0.923948i	$-0.375057\pi$
$409$	−1872.55	−	1081.12i	−0.226386	−	0.130704i	−0.608904	+	0.793244i	$0.708390\pi$
$410$	−5750.33	−	3319.95i	−0.692655	−	0.399905i
$411$		0			0
$412$		−	6527.83i		−	0.780590i
$413$		0			0
$414$		0			0
$415$	452.435	+	783.640i	0.0535160	+	0.0926925i
$416$	1276.51	−	2210.98i	0.150447	−	0.260583i
$417$		0			0
$418$	20479.8	−	11824.0i	2.39641	−	1.38357i
$419$	4907.59			0.572199			0.286099	−	0.958200i	$-0.407641\pi$
$419$	4907.59			0.572199			0.286099	+	0.958200i	$0.407641\pi$
$420$		0			0
$421$	5719.49			0.662116			0.331058	−	0.943610i	$-0.392594\pi$
$421$	5719.49			0.662116			0.331058	+	0.943610i	$0.392594\pi$
$422$	−3142.76	+	1814.48i	−0.362529	+	0.209306i
$423$		0			0
$424$	695.448	−	1204.55i	0.0796555	−	0.137967i
$425$	4773.78	+	8268.43i	0.544853	+	0.943713i
$426$		0			0
$427$		0			0
$428$			1949.46i			0.220166i
$429$		0			0
$430$	−6020.65	−	3476.03i	−0.675213	−	0.389834i
$431$	−3314.11	−	1913.41i	−0.370384	−	0.213841i	0.303242	−	0.952913i	$-0.401931\pi$
$431$	−3314.11	−	1913.41i	−0.370384	−	0.213841i	−0.673626	+	0.739072i	$0.735264\pi$
$432$		0			0
$433$		−	9120.21i		−	1.01222i	−0.862470	−	0.506108i	$-0.831084\pi$
$433$		−	9120.21i		−	1.01222i	0.862470	−	0.506108i	$-0.168916\pi$
$434$		0			0
$435$		0			0
$436$	5684.88	+	9846.51i	0.624442	+	1.08156i
$437$	−3153.24	+	5461.57i	−0.345171	+	0.597854i
$438$		0			0
$439$	−2550.00	+	1472.24i	−0.277232	+	0.160060i	−0.632170	−	0.774830i	$-0.717835\pi$
$439$	−2550.00	+	1472.24i	−0.277232	+	0.160060i	0.354938	+	0.934890i	$0.384502\pi$
$440$	−1722.92			−0.186675
$441$		0			0
$442$	3962.63			0.426433
$443$	3692.44	−	2131.83i	0.396011	−	0.228637i	−0.288750	−	0.957404i	$-0.593240\pi$
$443$	3692.44	−	2131.83i	0.396011	−	0.228637i	0.684762	+	0.728767i	$0.259906\pi$
$444$		0			0
$445$	−1835.41	+	3179.02i	−0.195520	+	0.338651i
$446$	1348.43	+	2335.55i	0.143162	+	0.247963i
$447$		0			0
$448$		0			0
$449$		−	1608.94i		−	0.169110i	−0.996419	−	0.0845550i	$-0.973053\pi$
$449$		−	1608.94i		−	0.169110i	0.996419	−	0.0845550i	$-0.0269469\pi$
$450$		0			0
$451$	−15521.2	−	8961.14i	−1.62054	−	0.935618i
$452$	8402.08	+	4850.94i	0.874338	+	0.504799i
$453$		0			0
$454$			23106.2i			2.38861i
$455$		0			0
$456$		0			0
$457$	2626.91	+	4549.94i	0.268887	+	0.465727i	0.968575	−	0.248723i	$-0.0800107\pi$
$457$	2626.91	+	4549.94i	0.268887	+	0.465727i	−0.699687	+	0.714449i	$0.746677\pi$
$458$	−10514.6	+	18211.8i	−1.07274	+	1.85804i
$459$		0			0
$460$	−1020.22	+	589.024i	−0.103409	+	0.0597030i
$461$	−19229.1			−1.94271			−0.971356	−	0.237627i	$-0.923630\pi$
$461$	−19229.1			−1.94271			−0.971356	+	0.237627i	$0.923630\pi$
$462$		0			0
$463$	6539.63			0.656420			0.328210	−	0.944605i	$-0.393555\pi$
$463$	6539.63			0.656420			0.328210	+	0.944605i	$0.393555\pi$
$464$	3183.21	−	1837.83i	0.318485	−	0.183877i
$465$		0			0
$466$	7331.88	−	12699.2i	0.728847	−	1.26240i
$467$	−4508.88	−	7809.61i	−0.446780	−	0.773845i	0.551395	−	0.834245i	$-0.314096\pi$
$467$	−4508.88	−	7809.61i	−0.446780	−	0.773845i	−0.998174	+	0.0603995i	$0.980763\pi$
$468$		0			0
$469$		0			0
$470$			6892.90i			0.676480i
$471$		0			0
$472$	991.626	+	572.515i	0.0967018	+	0.0558308i
$473$	−16250.8	−	9382.41i	−1.57973	−	0.912058i
$474$		0			0
$475$		−	14614.7i		−	1.41172i
$476$		0			0
$477$		0			0
$478$	−7262.87	−	12579.7i	−0.694971	−	1.20372i
$479$	−4112.88	+	7123.71i	−0.392322	+	0.679521i	−0.992755	−	0.120153i	$-0.961661\pi$
$479$	−4112.88	+	7123.71i	−0.392322	+	0.679521i	0.600434	+	0.799675i	$0.294995\pi$
$480$		0			0
$481$	−1505.77	+	869.355i	−0.142738	+	0.0824099i
$482$	12134.1			1.14666
$483$		0			0
$484$	4263.17			0.400372
$485$	−2760.47	+	1593.76i	−0.258446	+	0.149214i
$486$		0			0
$487$	9017.38	−	15618.6i	0.839048	−	1.45327i	−0.0516439	−	0.998666i	$-0.516446\pi$
$487$	9017.38	−	15618.6i	0.839048	−	1.45327i	0.890692	−	0.454608i	$-0.150221\pi$
$488$	−1346.04	−	2331.41i	−0.124861	−	0.216266i
$489$		0			0
$490$		0			0
$491$		−	12148.2i		−	1.11658i	−0.829646	−	0.558290i	$-0.811458\pi$
$491$		−	12148.2i		−	1.11658i	0.829646	−	0.558290i	$-0.188542\pi$
$492$		0			0
$493$	3787.29	+	2186.59i	0.345985	+	0.199755i
$494$	−5253.04	−	3032.84i	−0.478432	−	0.276223i
$495$		0			0
$496$		−	18371.9i		−	1.66315i
$497$		0			0
$498$		0			0
$499$	1473.28	+	2551.79i	0.132170	+	0.228925i	0.924513	−	0.381151i	$-0.124472\pi$
$499$	1473.28	+	2551.79i	0.132170	+	0.228925i	−0.792343	+	0.610076i	$0.791139\pi$
$500$	3000.50	−	5197.02i	0.268373	−	0.464835i
$501$		0			0
$502$	4502.33	−	2599.42i	0.400296	−	0.231111i
$503$	11290.2			1.00080			0.500402	−	0.865793i	$-0.333186\pi$
$503$	11290.2			1.00080			0.500402	+	0.865793i	$0.333186\pi$
$504$		0			0
$505$	7741.23			0.682139
$506$	−6581.54	+	3799.85i	−0.578232	+	0.333842i
$507$		0			0
$508$	−3326.50	+	5761.67i	−0.290531	+	0.503214i
$509$	−3214.41	−	5567.52i	−0.279914	−	0.484825i	0.691449	−	0.722425i	$-0.256973\pi$
$509$	−3214.41	−	5567.52i	−0.279914	−	0.484825i	−0.971363	+	0.237600i	$0.923639\pi$
$510$		0			0
$511$		0			0
$512$		−	11697.4i		−	1.00968i
$513$		0			0
$514$	−13131.4	−	7581.45i	−1.12685	−	0.650590i
$515$	4466.16	+	2578.54i	0.382141	+	0.220629i
$516$		0			0
$517$			18605.2i			1.58270i
$518$		0			0
$519$		0			0
$520$	220.964	+	382.720i	0.0186344	+	0.0322758i
$521$	3150.38	−	5456.62i	0.264915	−	0.458846i	−0.702626	−	0.711559i	$-0.747989\pi$
$521$	3150.38	−	5456.62i	0.264915	−	0.458846i	0.967541	+	0.252713i	$0.0813228\pi$
$522$		0			0
$523$	−11423.1	+	6595.13i	−0.955061	+	0.551405i	−0.894650	−	0.446769i	$-0.852575\pi$
$523$	−11423.1	+	6595.13i	−0.955061	+	0.551405i	−0.0604118	+	0.998174i	$0.519241\pi$
$524$	−3654.99			−0.304712
$525$		0			0
$526$	−17105.9			−1.41797
$527$	18929.9	−	10929.2i	1.56470	−	0.903382i
$528$		0			0
$529$	−5070.15	+	8781.76i	−0.416713	+	0.721769i
$530$	−1408.66	−	2439.86i	−0.115449	−	0.199964i
$531$		0			0
$532$		0			0
$533$			4597.05i			0.373584i
$534$		0			0
$535$	−1333.77	−	770.051i	−0.107783	−	0.0622285i
$536$	3058.08	+	1765.58i	0.246434	+	0.142279i
$537$		0			0
$538$			13642.2i			1.09323i
$539$		0			0
$540$		0			0
$541$	−5946.49	−	10299.6i	−0.472568	−	0.818513i	0.526939	−	0.849903i	$-0.323340\pi$
$541$	−5946.49	−	10299.6i	−0.472568	−	0.818513i	−0.999507	+	0.0313907i	$0.990006\pi$
$542$	13277.5	−	22997.2i	1.05224	−	1.82254i
$543$		0			0
$544$	17331.2	−	10006.2i	1.36593	−	0.788622i
$545$	−8982.27			−0.705979
$546$		0			0
$547$	1348.19			0.105383			0.0526915	−	0.998611i	$-0.483220\pi$
$547$	1348.19			0.105383			0.0526915	+	0.998611i	$0.483220\pi$
$548$	12251.8	−	7073.60i	0.955059	−	0.551404i
$549$		0			0
$550$	8805.81	−	15252.1i	0.682693	−	1.18246i
$551$	−3347.06	−	5797.28i	−0.258783	−	0.448226i
$552$		0			0
$553$		0			0
$554$		−	4193.54i		−	0.321600i
$555$		0			0
$556$	5456.78	+	3150.47i	0.416221	+	0.240305i
$557$	16461.7	+	9504.16i	1.25225	+	0.722988i	0.971556	−	0.236809i	$-0.0761016\pi$
$557$	16461.7	+	9504.16i	1.25225	+	0.722988i	0.280695	+	0.959797i	$0.409435\pi$
$558$		0			0
$559$			4813.16i			0.364177i
$560$		0			0
$561$		0			0
$562$	7268.66	+	12589.7i	0.545569	+	0.944953i
$563$	−1365.26	+	2364.70i	−0.102201	+	0.177017i	−0.912591	−	0.408874i	$-0.865922\pi$
$563$	−1365.26	+	2364.70i	−0.102201	+	0.177017i	0.810390	+	0.585890i	$0.199255\pi$
$564$		0			0
$565$	−6637.76	+	3832.31i	−0.494253	+	0.285357i
$566$	−16714.7			−1.24129
$567$		0			0
$568$	6054.02			0.447220
$569$	1334.77	−	770.632i	0.0983421	−	0.0567778i	−0.450022	−	0.893017i	$-0.648584\pi$
$569$	1334.77	−	770.632i	0.0983421	−	0.0567778i	0.548364	+	0.836239i	$0.315251\pi$
$570$		0			0
$571$	1735.00	−	3005.11i	0.127158	−	0.220245i	−0.795416	−	0.606064i	$-0.792748\pi$
$571$	1735.00	−	3005.11i	0.127158	−	0.220245i	0.922575	+	0.385819i	$0.126081\pi$
$572$	−1529.18	−	2648.61i	−0.111780	−	0.193608i
$573$		0			0
$574$		0			0
$575$			4696.69i			0.340635i
$576$		0			0
$577$	4030.32	+	2326.91i	0.290788	+	0.167886i	0.638297	−	0.769790i	$-0.279639\pi$
$577$	4030.32	+	2326.91i	0.290788	+	0.167886i	−0.347509	+	0.937676i	$0.612973\pi$
$578$	11120.1	+	6420.19i	0.800234	+	0.462015i
$579$		0			0
$580$		−	1250.46i		−	0.0895216i
$581$		0			0
$582$		0			0
$583$	−3802.21	−	6585.62i	−0.270105	−	0.467836i
$584$	4562.68	−	7902.80i	0.323297	−	0.559966i
$585$		0			0
$586$	−28768.0	+	16609.2i	−2.02798	+	1.17086i
$587$	12056.1			0.847717			0.423858	−	0.905728i	$-0.360675\pi$
$587$	12056.1			0.847717			0.423858	+	0.905728i	$0.360675\pi$
$588$		0			0
$589$	−33459.0			−2.34067
$590$	2008.57	−	1159.65i	0.140155	−	0.0809187i
$591$		0			0
$592$	−5727.66	+	9920.60i	−0.397644	+	0.688740i
$593$	6450.02	+	11171.8i	0.446662	+	0.773641i	0.998166	−	0.0605310i	$-0.0192794\pi$
$593$	6450.02	+	11171.8i	0.446662	+	0.773641i	−0.551505	+	0.834172i	$0.685946\pi$
$594$		0			0
$595$		0			0
$596$		−	5562.56i		−	0.382301i
$597$		0			0
$598$	1688.16	+	974.659i	0.115441	+	0.0666501i
$599$	3037.85	+	1753.90i	0.207217	+	0.119637i	0.600017	−	0.799987i	$-0.295160\pi$
$599$	3037.85	+	1753.90i	0.207217	+	0.119637i	−0.392800	+	0.919624i	$0.628494\pi$
$600$		0			0
$601$		−	1767.94i		−	0.119993i	−0.998199	−	0.0599966i	$-0.980891\pi$
$601$		−	1767.94i		−	0.119993i	0.998199	−	0.0599966i	$-0.0191090\pi$
$602$		0			0
$603$		0			0
$604$	−6704.57	−	11612.7i	−0.451664	−	0.782305i
$605$	−1683.98	+	2916.74i	−0.113163	+	0.196004i
$606$		0			0
$607$	12027.1	−	6943.85i	0.804225	−	0.464320i	−0.0407213	−	0.999171i	$-0.512966\pi$
$607$	12027.1	−	6943.85i	0.804225	−	0.464320i	0.844946	+	0.534851i	$0.179632\pi$
$608$	−30633.3			−2.04333
$609$		0			0
$610$	−5452.90			−0.361937
$611$	4132.85	−	2386.10i	0.273645	−	0.157989i
$612$		0			0
$613$	−11254.9	+	19494.1i	−0.741569	+	1.28443i	0.210212	+	0.977656i	$0.432584\pi$
$613$	−11254.9	+	19494.1i	−0.741569	+	1.28443i	−0.951781	+	0.306779i	$0.900749\pi$
$614$	6532.50	+	11314.6i	0.429365	+	0.743682i
$615$		0			0
$616$		0			0
$617$			1591.00i			0.103811i	0.998652	+	0.0519053i	$0.0165294\pi$
$617$			1591.00i			0.103811i	−0.998652	+	0.0519053i	$0.983471\pi$
$618$		0			0
$619$	11495.2	+	6636.75i	0.746415	+	0.430943i	0.824397	−	0.566012i	$-0.191514\pi$
$619$	11495.2	+	6636.75i	0.746415	+	0.430943i	−0.0779820	+	0.996955i	$0.524848\pi$
$620$	−5412.78	−	3125.07i	−0.350617	−	0.202429i
$621$		0			0
$622$			13187.9i			0.850138i
$623$		0			0
$624$		0			0
$625$	−4150.00	−	7188.02i	−0.265600	−	0.460033i
$626$	11756.5	−	20362.9i	0.750614	−	1.30010i
$627$		0			0
$628$	−17020.6	+	9826.84i	−1.08152	+	0.624417i
$629$	−13629.2			−0.863960
$630$		0			0
$631$	−11933.2			−0.752860			−0.376430	−	0.926445i	$-0.622848\pi$
$631$	−11933.2			−0.752860			−0.376430	+	0.926445i	$0.622848\pi$
$632$	4825.27	−	2785.87i	0.303701	−	0.175342i
$633$		0			0
$634$	−4719.21	+	8173.90i	−0.295621	+	0.512030i
$635$	−2627.98	−	4551.80i	−0.164234	−	0.284461i
$636$		0			0
$637$		0			0
$638$		−	8066.85i		−	0.500580i
$639$		0			0
$640$	4030.85	+	2327.21i	0.248958	+	0.143736i
$641$	−23852.5	−	13771.2i	−1.46976	−	0.848566i	−0.470335	−	0.882488i	$-0.655867\pi$
$641$	−23852.5	−	13771.2i	−1.46976	−	0.848566i	−0.999424	+	0.0339218i	$0.989200\pi$
$642$		0			0
$643$			19003.1i			1.16549i	0.812655	+	0.582746i	$0.198022\pi$
$643$			19003.1i			1.16549i	−0.812655	+	0.582746i	$0.801978\pi$
$644$		0			0
$645$		0			0
$646$	−23773.5	−	41176.8i	−1.44792	−	2.50787i
$647$	12524.2	−	21692.6i	0.761016	−	1.31812i	−0.181312	−	0.983426i	$-0.558034\pi$
$647$	12524.2	−	21692.6i	0.761016	−	1.31812i	0.942327	−	0.334692i	$-0.108632\pi$
$648$		0			0
$649$	5421.49	−	3130.10i	0.327908	−	0.189318i
$650$	−4517.36			−0.272593
$651$		0			0
$652$	2081.51			0.125028
$653$	−11903.6	+	6872.56i	−0.713361	+	0.411859i	−0.812304	−	0.583234i	$-0.801787\pi$
$653$	−11903.6	+	6872.56i	−0.713361	+	0.411859i	0.0989433	+	0.995093i	$0.468454\pi$
$654$		0			0
$655$	1443.75	−	2500.64i	0.0861250	−	0.149173i
$656$	15143.6	+	26229.5i	0.901309	+	1.56111i
$657$		0			0
$658$		0			0
$659$		−	6965.25i		−	0.411726i	−0.978581	−	0.205863i	$-0.934000\pi$
$659$		−	6965.25i		−	0.411726i	0.978581	−	0.205863i	$-0.0660002\pi$
$660$		0			0
$661$	10265.5	+	5926.78i	0.604056	+	0.348752i	0.770636	−	0.637276i	$-0.219939\pi$
$661$	10265.5	+	5926.78i	0.604056	+	0.348752i	−0.166579	+	0.986028i	$0.553272\pi$
$662$	36610.9	+	21137.3i	2.14943	+	1.24097i
$663$		0			0
$664$		−	1656.84i		−	0.0968342i
$665$		0			0
$666$		0			0
$667$	1075.64	+	1863.06i	0.0624421	+	0.108153i
$668$	4620.26	−	8002.52i	0.267609	−	0.463513i
$669$		0			0
$670$	6194.25	−	3576.25i	0.357171	−	0.206213i
$671$	−14718.3			−0.846789
$672$		0			0
$673$	−30769.5			−1.76238			−0.881188	−	0.472766i	$-0.843255\pi$
$673$	−30769.5			−1.76238			−0.881188	+	0.472766i	$0.843255\pi$
$674$	1770.15	−	1022.00i	0.101163	−	0.0584064i
$675$		0			0
$676$	5929.95	−	10271.0i	0.337389	−	0.584375i
$677$	−654.744	−	1134.05i	−0.0371696	−	0.0643797i	0.846842	−	0.531844i	$-0.178501\pi$
$677$	−654.744	−	1134.05i	−0.0371696	−	0.0643797i	−0.884012	+	0.467465i	$0.845168\pi$
$678$		0			0
$679$		0			0
$680$			3464.12i			0.195358i
$681$		0			0
$682$	−34918.4	−	20160.2i	−1.96055	−	1.13192i
$683$	20035.2	+	11567.3i	1.12244	+	0.648041i	0.942023	−	0.335549i	$-0.108922\pi$
$683$	20035.2	+	11567.3i	1.12244	+	0.648041i	0.180417	+	0.983590i	$0.442255\pi$
$684$		0			0
$685$			11176.5i			0.623403i
$686$		0			0
$687$		0			0
$688$	15855.5	+	27462.5i	0.878613	+	1.52180i
$689$	−975.263	+	1689.21i	−0.0539254	+	0.0934015i
$690$		0			0
$691$	−21031.0	+	12142.3i	−1.15782	+	0.668471i	−0.950782	−	0.309861i	$-0.899717\pi$
$691$	−21031.0	+	12142.3i	−1.15782	+	0.668471i	−0.207043	+	0.978332i	$0.566384\pi$
$692$	−8442.24			−0.463766
$693$		0			0
$694$	−10708.9			−0.585744
$695$	−4310.93	+	2488.92i	−0.235285	+	0.135842i
$696$		0			0
$697$	−18017.4	+	31207.0i	−0.979135	+	1.69591i
$698$	4247.21	+	7356.39i	0.230314	+	0.398916i
$699$		0			0
$700$		0			0
$701$		−	20398.8i		−	1.09907i	−0.835469	−	0.549537i	$-0.814804\pi$
$701$		−	20398.8i		−	1.09907i	0.835469	−	0.549537i	$-0.185196\pi$
$702$		0			0
$703$	18067.4	+	10431.2i	0.969311	+	0.559632i
$704$	−7713.25	−	4453.25i	−0.412932	−	0.238406i
$705$		0			0
$706$			5227.65i			0.278676i
$707$		0			0
$708$		0			0
$709$	15428.5	+	26723.0i	0.817250	+	1.41552i	0.907701	+	0.419617i	$0.137836\pi$
$709$	15428.5	+	26723.0i	0.817250	+	1.41552i	−0.0904511	+	0.995901i	$0.528831\pi$
$710$	6131.32	−	10619.8i	0.324091	−	0.561341i
$711$		0			0
$712$	5820.87	−	3360.68i	0.306385	−	0.176892i
$713$	10752.7			0.564783
$714$		0			0
$715$	2416.14			0.126376
$716$	4893.74	−	2825.40i	0.255430	−	0.147472i
$717$		0			0
$718$	12893.0	−	22331.4i	0.670145	−	1.16073i
$719$	−17203.6	−	29797.5i	−0.892332	−	1.54556i	−0.837072	−	0.547092i	$-0.815735\pi$
$719$	−17203.6	−	29797.5i	−0.892332	−	1.54556i	−0.0552599	−	0.998472i	$-0.517599\pi$
$720$		0			0
$721$		0			0
$722$			47342.4i			2.44030i
$723$		0			0
$724$	7712.18	+	4452.63i	0.395885	+	0.228565i
$725$	−4317.47	−	2492.69i	−0.221168	−	0.127691i
$726$		0			0
$727$			11996.1i			0.611983i	0.952034	+	0.305992i	$0.0989880\pi$
$727$			11996.1i			0.611983i	−0.952034	+	0.305992i	$0.901012\pi$
$728$		0			0
$729$		0			0
$730$	−9241.88	−	16007.4i	−0.468572	−	0.811590i
$731$	−18864.4	+	32674.1i	−0.954479	+	1.65321i
$732$		0			0
$733$	27819.5	−	16061.6i	1.40182	−	0.809342i	0.407242	−	0.913320i	$-0.366490\pi$
$733$	27819.5	−	16061.6i	1.40182	−	0.809342i	0.994580	+	0.103978i	$0.0331571\pi$
$734$	−5571.00			−0.280149
$735$		0			0
$736$	9844.55			0.493037
$737$	16719.4	−	9652.93i	0.835639	−	0.482456i
$738$		0			0
$739$	−11436.0	+	19807.7i	−0.569254	+	0.985977i	0.427386	+	0.904069i	$0.359435\pi$
$739$	−11436.0	+	19807.7i	−0.569254	+	0.985977i	−0.996640	+	0.0819076i	$0.973899\pi$
$740$	1948.55	+	3374.99i	0.0967975	+	0.167658i
$741$		0			0
$742$		0			0
$743$		−	20982.3i		−	1.03602i	−0.855373	−	0.518012i	$-0.826672\pi$
$743$		−	20982.3i		−	1.03602i	0.855373	−	0.518012i	$-0.173328\pi$
$744$		0			0
$745$	3805.75	+	2197.25i	0.187157	+	0.108055i
$746$	−22660.2	−	13082.9i	−1.11213	−	0.642089i
$747$		0			0
$748$		−	23973.4i		−	1.17187i
$749$		0			0
$750$		0			0
$751$	−9321.27	−	16144.9i	−0.452914	−	0.784469i	0.545652	−	0.838012i	$-0.316282\pi$
$751$	−9321.27	−	16144.9i	−0.452914	−	0.784469i	−0.998566	+	0.0535425i	$0.982949\pi$
$752$	15720.6	−	27228.9i	0.762329	−	1.32039i
$753$		0			0
$754$	−1791.93	+	1034.57i	−0.0865493	+	0.0499692i
$755$	10593.4			0.510641
$756$		0			0
$757$	4135.46			0.198555			0.0992774	−	0.995060i	$-0.468347\pi$
$757$	4135.46			0.198555			0.0992774	+	0.995060i	$0.468347\pi$
$758$	−16584.8	+	9575.25i	−0.794707	+	0.458824i
$759$		0			0
$760$	2651.30	−	4592.19i	0.126543	−	0.219179i
$761$	1790.84	+	3101.83i	0.0853062	+	0.147755i	0.905522	−	0.424300i	$-0.139480\pi$
$761$	1790.84	+	3101.83i	0.0853062	+	0.147755i	−0.820215	+	0.572055i	$0.806146\pi$
$762$		0			0
$763$		0			0
$764$		−	27536.9i		−	1.30399i
$765$		0			0
$766$	−8087.37	−	4669.25i	−0.381474	−	0.220244i
$767$	−1390.61	−	802.868i	−0.0654654	−	0.0377965i
$768$		0			0
$769$			11427.1i			0.535852i	0.963439	+	0.267926i	$0.0863383\pi$
$769$			11427.1i			0.535852i	−0.963439	+	0.267926i	$0.913662\pi$
$770$		0			0
$771$		0			0
$772$	−3672.94	−	6361.72i	−0.171233	−	0.296585i
$773$	−741.803	+	1284.84i	−0.0345159	+	0.0597833i	−0.882767	−	0.469810i	$-0.844322\pi$
$773$	−741.803	+	1284.84i	−0.0345159	+	0.0597833i	0.848251	+	0.529594i	$0.177656\pi$
$774$		0			0
$775$	−21579.9	+	12459.1i	−1.00022	+	0.577478i
$776$	5836.43			0.269994
$777$		0			0
$778$	17753.1			0.818097
$779$	47769.2	−	27579.6i	2.19706	−	1.26847i
$780$		0			0
$781$	16549.5	−	28664.6i	0.758243	−	1.31332i
$782$	7640.03	+	13232.9i	0.349370	+	0.605126i
$783$		0			0
$784$		0			0
$785$		−	15526.7i		−	0.705951i
$786$		0			0
$787$	−15173.0	−	8760.12i	−0.687240	−	0.396778i	0.115337	−	0.993326i	$-0.463205\pi$
$787$	−15173.0	−	8760.12i	−0.687240	−	0.396778i	−0.802577	+	0.596548i	$0.796538\pi$
$788$	−2447.80	−	1413.24i	−0.110659	−	0.0638891i
$789$		0			0
$790$		−	11285.8i		−	0.508266i
$791$		0			0
$792$		0			0
$793$	1887.62	+	3269.46i	0.0845289	+	0.146408i
$794$	−17792.1	+	30816.8i	−0.795236	+	1.37739i
$795$		0			0
$796$	−14895.0	+	8599.65i	−0.663242	+	0.382923i
$797$	−2687.85			−0.119459			−0.0597293	−	0.998215i	$-0.519024\pi$
$797$	−2687.85			−0.119459			−0.0597293	+	0.998215i	$0.519024\pi$
$798$		0			0
$799$	37407.7			1.65631
$800$	−19757.4	+	11406.9i	−0.873160	+	0.504119i
$801$		0			0
$802$	25122.3	−	43513.1i	1.10611	−	1.91584i
$803$	−24945.5	−	43206.8i	−1.09627	−	1.89880i
$804$		0			0
$805$		0			0
$806$			10342.1i			0.451967i
$807$		0			0
$808$	−12275.4	−	7087.20i	−0.534464	−	0.308573i
$809$	728.881	+	420.819i	0.0316762	+	0.0182883i	0.515754	−	0.856736i	$-0.327512\pi$
$809$	728.881	+	420.819i	0.0316762	+	0.0182883i	−0.484078	+	0.875025i	$0.660845\pi$
$810$		0			0
$811$		−	37115.6i		−	1.60704i	−0.595281	−	0.803518i	$-0.702959\pi$
$811$		−	37115.6i		−	1.60704i	0.595281	−	0.803518i	$-0.297041\pi$
$812$		0			0
$813$		0			0
$814$	12570.3	+	21772.4i	0.541264	+	0.937497i
$815$	−822.209	+	1424.11i	−0.0353383	+	0.0612078i
$816$		0			0
$817$	50014.9	−	28876.1i	2.14174	−	1.23653i
$818$	8019.33			0.342774
$819$		0			0
$820$	10303.7			0.438807
$821$	−23903.7	+	13800.8i	−1.01613	+	0.586664i	−0.912981	−	0.408002i	$-0.866226\pi$
$821$	−23903.7	+	13800.8i	−1.01613	+	0.586664i	−0.103151	+	0.994666i	$0.532892\pi$
$822$		0			0
$823$	−3682.60	+	6378.45i	−0.155975	+	0.270156i	−0.933414	−	0.358802i	$-0.883185\pi$
$823$	−3682.60	+	6378.45i	−0.155975	+	0.270156i	0.777439	+	0.628959i	$0.216519\pi$
$824$	−4721.38	−	8177.66i	−0.199608	−	0.345731i
$825$		0			0
$826$		0			0
$827$			46801.3i			1.96789i	0.178485	+	0.983943i	$0.442880\pi$
$827$			46801.3i			1.96789i	−0.178485	+	0.983943i	$0.557120\pi$
$828$		0			0
$829$	8806.68	+	5084.54i	0.368961	+	0.213020i	0.673004	−	0.739638i	$-0.265003\pi$
$829$	8806.68	+	5084.54i	0.368961	+	0.213020i	−0.304044	+	0.952658i	$0.598337\pi$
$830$	−2906.37	−	1678.00i	−0.121544	−	0.0701736i
$831$		0			0
$832$			2284.51i			0.0951936i
$833$		0			0
$834$		0			0
$835$	3650.07	+	6322.10i	0.151276	+	0.262018i
$836$	−18348.3	+	31780.2i	−0.759079	+	1.31476i
$837$		0			0
$838$	−15762.8	+	9100.66i	−0.649782	+	0.375152i
$839$	45477.6			1.87135			0.935674	−	0.352864i	$-0.114792\pi$
$839$	45477.6			1.87135			0.935674	+	0.352864i	$0.114792\pi$
$840$		0			0
$841$	22105.5			0.906371
$842$	−18370.6	+	10606.3i	−0.751891	+	0.434104i
$843$		0			0
$844$	2815.68	−	4876.90i	0.114834	−	0.198898i
$845$	4684.74	+	8114.21i	0.190722	+	0.330340i
$846$		0			0
$847$		0			0
$848$			12850.9i			0.520401i
$849$		0			0
$850$	−30666.1	−	17705.1i	−1.23746	−	0.714445i
$851$	−5806.29	−	3352.26i	−0.233886	−	0.135034i
$852$		0			0
$853$		−	3005.89i		−	0.120656i	−0.998179	−	0.0603281i	$-0.980785\pi$
$853$		−	3005.89i		−	0.120656i	0.998179	−	0.0603281i	$-0.0192147\pi$
$854$		0			0
$855$		0			0
$856$	1409.99	+	2442.17i	0.0562994	+	0.0975135i
$857$	−22426.6	+	38844.0i	−0.893907	+	1.54829i	−0.0587561	+	0.998272i	$0.518713\pi$
$857$	−22426.6	+	38844.0i	−0.893907	+	1.54829i	−0.835151	+	0.550020i	$0.814620\pi$
$858$		0			0
$859$	11337.0	−	6545.40i	0.450305	−	0.259984i	−0.257654	−	0.966237i	$-0.582949\pi$
$859$	11337.0	−	6545.40i	0.450305	−	0.259984i	0.707959	+	0.706253i	$0.249616\pi$
$860$	10788.1			0.427757
$861$		0			0
$862$	14192.9			0.560804
$863$	18376.4	−	10609.6i	0.724843	−	0.418488i	−0.0916894	−	0.995788i	$-0.529227\pi$
$863$	18376.4	−	10609.6i	0.724843	−	0.418488i	0.816533	+	0.577299i	$0.195893\pi$
$864$		0			0
$865$	3334.74	−	5775.95i	0.131081	−	0.227038i
$866$	16912.6	+	29293.4i	0.663641	+	1.14946i
$867$		0			0
$868$		0			0
$869$		−	30462.3i		−	1.18914i
$870$		0			0
$871$	−4288.50	−	2475.97i	−0.166832	−	0.0963203i
$872$	14243.3	+	8223.40i	0.553143	+	0.319357i
$873$		0			0
$874$		−	23389.5i		−	0.905220i
$875$		0			0
$876$		0			0
$877$	20938.2	+	36266.1i	0.806195	+	1.39637i	0.915481	+	0.402361i	$0.131810\pi$
$877$	20938.2	+	36266.1i	0.806195	+	1.39637i	−0.109286	+	0.994010i	$0.534856\pi$
$878$	5460.27	−	9457.47i	0.209881	−	0.363524i
$879$		0			0
$880$	13785.8	−	7959.26i	0.528091	−	0.304894i
$881$	−16277.8			−0.622490			−0.311245	−	0.950330i	$-0.600746\pi$
$881$	−16277.8			−0.622490			−0.311245	+	0.950330i	$0.600746\pi$
$882$		0			0
$883$	−32041.9			−1.22117			−0.610586	−	0.791950i	$-0.709066\pi$
$883$	−32041.9			−1.22117			−0.610586	+	0.791950i	$0.709066\pi$
$884$	−5325.33	+	3074.58i	−0.202613	+	0.116979i
$885$		0			0
$886$	−7906.56	+	13694.6i	−0.299804	+	0.519275i
$887$	−23076.8	−	39970.2i	−0.873555	−	1.51304i	−0.858294	−	0.513158i	$-0.828476\pi$
$887$	−23076.8	−	39970.2i	−0.873555	−	1.51304i	−0.0152603	−	0.999884i	$-0.504858\pi$
$888$		0			0
$889$		0			0
$890$		−	13614.4i		−	0.512758i
$891$		0			0
$892$	−3624.28	−	2092.48i	−0.136042	−	0.0785441i
$893$	−49589.3	−	28630.4i	−1.85828	−	1.07288i
$894$		0			0
$895$			4464.21i			0.166729i
$896$		0			0
$897$		0			0
$898$	2983.62	+	5167.78i	0.110874	+	0.192039i
$899$	−5706.81	+	9884.48i	−0.211716	+	0.366703i
$900$		0			0
$901$	−13241.1	+	7644.77i	−0.489596	+	0.282668i
$902$	66470.4			2.45368
$903$		0			0
$904$	14034.1			0.516337
$905$	−6092.73	+	3517.64i	−0.223789	+	0.129205i
$906$		0			0
$907$	−13614.8	+	23581.6i	−0.498427	+	0.863301i	−0.999998	−	0.00181559i	$-0.999422\pi$
$907$	−13614.8	+	23581.6i	−0.498427	+	0.863301i	0.501572	+	0.865116i	$0.332755\pi$
$908$	−17927.9	−	31052.1i	−0.655241	−	1.13491i
$909$		0			0
$910$		0			0
$911$			11012.2i			0.400494i	0.979745	+	0.200247i	$0.0641745\pi$
$911$			11012.2i			0.400494i	−0.979745	+	0.200247i	$0.935826\pi$
$912$		0			0
$913$	−7844.82	−	4529.21i	−0.284365	−	0.164178i
$914$	−16874.9	−	9742.70i	−0.610690	−	0.352582i
$915$		0			0
$916$		−	32632.8i		−	1.17709i
$917$		0			0
$918$		0			0
$919$	−10888.8	−	18859.9i	−0.390846	−	0.676965i	0.601715	−	0.798711i	$-0.294484\pi$
$919$	−10888.8	−	18859.9i	−0.390846	−	0.676965i	−0.992561	+	0.121745i	$0.961151\pi$
$920$	−852.045	+	1475.78i	−0.0305338	+	0.0528861i
$921$		0			0
$922$	61762.6	−	35658.6i	2.20612	−	1.27370i
$923$	−8489.87			−0.302760
$924$		0			0
$925$	15537.1			0.552278
$926$	−21004.8	+	12127.1i	−0.745422	+	0.430370i
$927$		0			0
$928$	−5224.84	+	9049.69i	−0.184821	+	0.320119i
$929$	−6186.14	−	10714.7i	−0.218472	−	0.378405i	0.735869	−	0.677124i	$-0.236774\pi$
$929$	−6186.14	−	10714.7i	−0.218472	−	0.378405i	−0.954341	+	0.298719i	$0.903441\pi$
$930$		0			0
$931$		0			0
$932$			22755.0i			0.799749i
$933$		0			0
$934$	28964.4	+	16722.6i	1.01471	+	0.585846i
$935$	16401.9	+	9469.67i	0.573691	+	0.331221i
$936$		0			0
$937$			41577.7i			1.44961i	0.688954	+	0.724806i	$0.258070\pi$
$937$			41577.7i			1.44961i	−0.688954	+	0.724806i	$0.741930\pi$
$938$		0			0
$939$		0			0
$940$	−5348.15	−	9263.27i	−0.185572	−	0.321420i
$941$	−16245.4	+	28137.8i	−0.562789	+	0.974779i	0.434463	+	0.900690i	$0.356938\pi$
$941$	−16245.4	+	28137.8i	−0.562789	+	0.974779i	−0.997252	+	0.0740893i	$0.976395\pi$
$942$		0			0
$943$	−15351.5	+	8863.20i	−0.530131	+	0.306072i
$944$	−10579.2			−0.364751
$945$		0			0
$946$	69595.2			2.39190
$947$	−44020.7	+	25415.4i	−1.51054	+	0.872110i	−0.510615	+	0.859809i	$0.670582\pi$
$947$	−44020.7	+	25415.4i	−1.51054	+	0.872110i	−0.999924	+	0.0123009i	$0.996084\pi$
$948$		0			0
$949$	−6398.49	+	11082.5i	−0.218866	+	0.379087i
$950$	27101.5	+	46941.2i	0.925568	+	1.60313i
$951$		0			0
$952$		0			0
$953$		−	4892.40i		−	0.166296i	−0.996537	−	0.0831482i	$-0.973503\pi$
$953$		−	4892.40i		−	0.166296i	0.996537	−	0.0831482i	$-0.0264975\pi$
$954$		0			0
$955$	18840.0	+	10877.3i	0.638375	+	0.368566i
$956$	19521.0	+	11270.4i	0.660411	+	0.381288i
$957$		0			0
$958$		−	30507.8i		−	1.02887i
$959$		0			0
$960$		0			0
$961$	13628.7	+	23605.5i	0.457476	+	0.792372i
$962$	3224.27	−	5584.60i	0.108061	−	0.187167i
$963$		0			0
$964$	−16306.8	+	9414.76i	−0.544821	+	0.314553i
$965$	5803.35			0.193592
$966$		0			0
$967$	−41170.9			−1.36915			−0.684575	−	0.728943i	$-0.740012\pi$
$967$	−41170.9			−1.36915			−0.684575	+	0.728943i	$0.740012\pi$
$968$	5340.63	−	3083.41i	0.177329	−	0.102381i
$969$		0			0
$970$	5910.95	−	10238.1i	0.195659	−	0.338891i
$971$	21643.8	+	37488.1i	0.715327	+	1.23898i	0.962833	+	0.270096i	$0.0870554\pi$
$971$	21643.8	+	37488.1i	0.715327	+	1.23898i	−0.247507	+	0.968886i	$0.579611\pi$
$972$		0			0
$973$		0			0
$974$			66887.5i			2.20042i
$975$		0			0
$976$	21540.5	+	12436.4i	0.706449	+	0.407869i
$977$	−15651.8	−	9036.54i	−0.512532	−	0.295911i	0.221342	−	0.975196i	$-0.428956\pi$
$977$	−15651.8	−	9036.54i	−0.512532	−	0.295911i	−0.733874	+	0.679286i	$0.762290\pi$
$978$		0			0
$979$		−	36747.5i		−	1.19965i
$980$		0			0
$981$		0			0
$982$	22527.7	+	39019.1i	0.732065	+	1.26797i
$983$	−9865.31	+	17087.2i	−0.320096	+	0.554423i	−0.980508	−	0.196481i	$-0.937049\pi$
$983$	−9865.31	+	17087.2i	−0.320096	+	0.554423i	0.660411	+	0.750904i	$0.270382\pi$
$984$		0			0
$985$	1933.80	−	1116.48i	0.0625543	−	0.0361157i
$986$	−16219.3			−0.523862
$987$		0			0
$988$	9412.65			0.303093
$989$	−16073.2	+	9279.86i	−0.516782	+	0.298364i
$990$		0			0
$991$	6846.14	−	11857.9i	0.219450	−	0.380098i	−0.735190	−	0.677861i	$-0.762907\pi$
$991$	6846.14	−	11857.9i	0.219450	−	0.380098i	0.954640	+	0.297763i	$0.0962405\pi$
$992$	26115.2	+	45232.8i	0.835844	+	1.44772i
$993$		0			0
$994$		0			0
$995$		−	13587.7i		−	0.432923i
$996$		0			0
$997$	−2672.18	−	1542.78i	−0.0848833	−	0.0490074i	0.456958	−	0.889489i	$-0.348939\pi$
$997$	−2672.18	−	1542.78i	−0.0848833	−	0.0490074i	−0.541841	+	0.840481i	$0.682272\pi$
$998$	−9464.11	−	5464.10i	−0.300181	−	0.173310i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	441.4.p.d.80.4		48
3.2	odd	2	inner	441.4.p.d.80.21		48
7.2	even	3	inner	441.4.p.d.215.22		48
7.3	odd	6		441.4.c.b.440.17	yes	24
7.4	even	3		441.4.c.b.440.7	✓	24
7.5	odd	6	inner	441.4.p.d.215.21		48
7.6	odd	2	inner	441.4.p.d.80.3		48
21.2	odd	6	inner	441.4.p.d.215.3		48
21.5	even	6	inner	441.4.p.d.215.4		48
21.11	odd	6		441.4.c.b.440.18	yes	24
21.17	even	6		441.4.c.b.440.8	yes	24
21.20	even	2	inner	441.4.p.d.80.22		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
441.4.c.b.440.7	✓	24	7.4	even	3
441.4.c.b.440.8	yes	24	21.17	even	6
441.4.c.b.440.17	yes	24	7.3	odd	6
441.4.c.b.440.18	yes	24	21.11	odd	6
441.4.p.d.80.3		48	7.6	odd	2	inner
441.4.p.d.80.4		48	1.1	even	1	trivial
441.4.p.d.80.21		48	3.2	odd	2	inner
441.4.p.d.80.22		48	21.20	even	2	inner
441.4.p.d.215.3		48	21.2	odd	6	inner
441.4.p.d.215.4		48	21.5	even	6	inner
441.4.p.d.215.21		48	7.5	odd	6	inner
441.4.p.d.215.22		48	7.2	even	3	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 441 = 3^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	441.p (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-3.21193 + 1.85441i) q^{2} +(2.87764 - 4.98422i) q^{4} +(2.27338 + 3.93760i) q^{5} -8.32523i q^{8} +O(q^{10})\)	\(q+(-3.21193 + 1.85441i) q^{2} +(2.87764 - 4.98422i) q^{4} +(2.27338 + 3.93760i) q^{5} -8.32523i q^{8} +(-14.6038 - 8.43153i) q^{10} +(-39.4183 - 22.7582i) q^{11} +11.6749i q^{13} +(38.4595 + 66.6138i) q^{16} +(-45.7579 + 79.2550i) q^{17} +(121.317 - 70.0425i) q^{19} +26.1679 q^{20} +168.812 q^{22} +(-38.9875 + 22.5094i) q^{23} +(52.1635 - 90.3499i) q^{25} +(-21.6500 - 37.4989i) q^{26} -47.7861i q^{29} +(-206.848 - 119.424i) q^{31} +(-189.379 - 109.338i) q^{32} -339.415i q^{34} +(74.4635 + 128.975i) q^{37} +(-259.775 + 449.943i) q^{38} +(32.7815 - 18.9264i) q^{40} +393.755 q^{41} +412.265 q^{43} +(-226.864 + 130.980i) q^{44} +(83.4833 - 144.597i) q^{46} +(-204.379 - 353.994i) q^{47} +386.929i q^{50} +(58.1903 + 33.5962i) q^{52} +(144.687 + 83.5350i) q^{53} -206.952i q^{55} +(88.6149 + 153.485i) q^{58} +(-68.7687 + 119.111i) q^{59} +(280.041 - 161.682i) q^{61} +885.842 q^{62} +195.677 q^{64} +(-45.9712 + 26.5415i) q^{65} +(-212.076 + 367.326i) q^{67} +(263.350 + 456.135i) q^{68} +727.190i q^{71} +(949.259 + 548.055i) q^{73} +(-478.343 - 276.171i) q^{74} -806.229i q^{76} +(334.630 + 579.597i) q^{79} +(-174.866 + 302.877i) q^{80} +(-1264.71 + 730.181i) q^{82} +199.014 q^{83} -416.100 q^{85} +(-1324.16 + 764.507i) q^{86} +(-189.467 + 328.167i) q^{88} +(403.674 + 699.184i) q^{89} +259.096i q^{92} +(1312.90 + 758.002i) q^{94} +(551.600 + 318.466i) q^{95} +701.053i q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 96 q^{4}+O(q^{10}) \) 48 * q + 96 * q^4	\( 48 q + 96 q^{4} - 144 q^{16} + 1248 q^{22} - 312 q^{25} + 864 q^{37} + 2496 q^{43} + 3888 q^{46} + 7440 q^{58} - 6720 q^{64} + 2688 q^{67} - 480 q^{79} + 26496 q^{85} + 7248 q^{88}+O(q^{100}) \) 48 * q + 96 * q^4 - 144 * q^16 + 1248 * q^22 - 312 * q^25 + 864 * q^37 + 2496 * q^43 + 3888 * q^46 + 7440 * q^58 - 6720 * q^64 + 2688 * q^67 - 480 * q^79 + 26496 * q^85 + 7248 * q^88

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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