LMFDB - Embedded newform 252.3.bh.a.137.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,3,Mod(137,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1, 4]))

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

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

chi := DirichletCharacter("252.137");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	252.bh (of order $6$, 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:	$6.86650266188$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			137.14
Character	$\chi$	$=$	252.137
Dual form			252.3.bh.a.149.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.50034 - 1.65779i) q^{3} +(-6.77026 - 3.90881i) q^{5} +(-4.95821 + 4.94127i) q^{7} +(3.50345 - 8.29011i) q^{9} +O(q^{10})$	\(q+(2.50034 - 1.65779i) q^{3} +(-6.77026 - 3.90881i) q^{5} +(-4.95821 + 4.94127i) q^{7} +(3.50345 - 8.29011i) q^{9} +(-8.58135 + 4.95444i) q^{11} +(-5.60780 - 9.71299i) q^{13} +(-23.4080 + 1.45031i) q^{15} +(-12.1030 - 6.98765i) q^{17} +(7.19662 + 12.4649i) q^{19} +(-4.20562 + 20.5746i) q^{21} +(-33.0954 - 19.1077i) q^{23} +(18.0576 + 31.2767i) q^{25} +(-4.98344 - 26.5361i) q^{27} +(20.5328 + 11.8546i) q^{29} +25.1454 q^{31} +(-13.2429 + 26.6139i) q^{33} +(52.8829 - 14.0730i) q^{35} +(-19.6806 - 34.0879i) q^{37} +(-30.1235 - 14.9893i) q^{39} +(45.5225 - 26.2824i) q^{41} +(-35.6209 + 61.6972i) q^{43} +(-56.1237 + 42.4319i) q^{45} -54.2656i q^{47} +(0.167642 - 48.9997i) q^{49} +(-41.8457 + 2.59267i) q^{51} +(-47.3589 - 27.3427i) q^{53} +77.4639 q^{55} +(38.6582 + 19.2361i) q^{57} -39.0826i q^{59} -65.1147 q^{61} +(23.5928 + 58.4156i) q^{63} +87.6793i q^{65} +106.988 q^{67} +(-114.427 + 7.08962i) q^{69} -27.3419i q^{71} +(-0.465523 + 0.806310i) q^{73} +(97.0007 + 48.2668i) q^{75} +(18.0668 - 66.9679i) q^{77} +94.3233 q^{79} +(-56.4517 - 58.0879i) q^{81} +(81.5203 + 47.0658i) q^{83} +(54.6269 + 94.6165i) q^{85} +(70.9914 - 4.39848i) q^{87} +(17.9546 - 10.3661i) q^{89} +(75.7992 + 20.4494i) q^{91} +(62.8722 - 41.6859i) q^{93} -112.521i q^{95} +(77.0276 - 133.416i) q^{97} +(11.0085 + 88.4979i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - q^{7} - 14 q^{9}+O(q^{10}) $ 32 * q - q^7 - 14 * q^9	$ 32 q - q^{7} - 14 q^{9} + 18 q^{11} - 5 q^{13} - 29 q^{15} + 27 q^{17} - 14 q^{19} - 8 q^{21} - 45 q^{23} + 80 q^{25} + 45 q^{27} + 36 q^{29} + 16 q^{31} + 116 q^{33} + 45 q^{35} - 11 q^{37} + 55 q^{39} + 72 q^{41} + 16 q^{43} - 154 q^{45} - 37 q^{49} - 133 q^{51} - 180 q^{53} - 24 q^{55} + 57 q^{57} + 82 q^{61} - 99 q^{63} + 70 q^{67} - 97 q^{69} - 98 q^{73} - 149 q^{75} - 135 q^{77} + 142 q^{79} - 98 q^{81} - 30 q^{85} - 86 q^{87} + 189 q^{89} + 109 q^{91} + 109 q^{93} + 19 q^{97} - 101 q^{99}+O(q^{100}) $ 32 * q - q^7 - 14 * q^9 + 18 * q^11 - 5 * q^13 - 29 * q^15 + 27 * q^17 - 14 * q^19 - 8 * q^21 - 45 * q^23 + 80 * q^25 + 45 * q^27 + 36 * q^29 + 16 * q^31 + 116 * q^33 + 45 * q^35 - 11 * q^37 + 55 * q^39 + 72 * q^41 + 16 * q^43 - 154 * q^45 - 37 * q^49 - 133 * q^51 - 180 * q^53 - 24 * q^55 + 57 * q^57 + 82 * q^61 - 99 * q^63 + 70 * q^67 - 97 * q^69 - 98 * q^73 - 149 * q^75 - 135 * q^77 + 142 * q^79 - 98 * q^81 - 30 * q^85 - 86 * q^87 + 189 * q^89 + 109 * q^91 + 109 * q^93 + 19 * q^97 - 101 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	2.50034	−	1.65779i	0.833448	−	0.552597i
$3$	2.50034	−	1.65779i	0.833448	−	0.552597i
$4$		0			0
$5$	−6.77026	−	3.90881i	−1.35405	−	0.781763i	−0.365238	−	0.930914i	$-0.619012\pi$
$5$	−6.77026	−	3.90881i	−1.35405	−	0.781763i	−0.988814	+	0.149152i	$0.952346\pi$
$6$		0			0
$7$	−4.95821	+	4.94127i	−0.708315	+	0.705896i
$7$	−4.95821	+	4.94127i	−0.708315	+	0.705896i
$8$		0			0
$9$	3.50345	−	8.29011i	0.389272	−	0.921123i
$10$		0			0
$11$	−8.58135	+	4.95444i	−0.780122	+	0.450404i	−0.836474	−	0.548007i	$-0.815387\pi$
$11$	−8.58135	+	4.95444i	−0.780122	+	0.450404i	0.0563513	+	0.998411i	$0.482053\pi$
$12$		0			0
$13$	−5.60780	−	9.71299i	−0.431369	−	0.747153i	0.565622	−	0.824664i	$-0.308636\pi$
$13$	−5.60780	−	9.71299i	−0.431369	−	0.747153i	−0.996991	+	0.0775113i	$0.975303\pi$
$14$		0			0
$15$	−23.4080	+	1.45031i	−1.56053	+	0.0966873i
$16$		0			0
$17$	−12.1030	−	6.98765i	−0.711939	−	0.411038i	0.0998393	−	0.995004i	$-0.468167\pi$
$17$	−12.1030	−	6.98765i	−0.711939	−	0.411038i	−0.811779	+	0.583965i	$0.801500\pi$
$18$		0			0
$19$	7.19662	+	12.4649i	0.378769	+	0.656048i	0.990883	−	0.134722i	$-0.0430141\pi$
$19$	7.19662	+	12.4649i	0.378769	+	0.656048i	−0.612114	+	0.790769i	$0.709681\pi$
$20$		0			0
$21$	−4.20562	+	20.5746i	−0.200268	+	0.979741i
$22$		0			0
$23$	−33.0954	−	19.1077i	−1.43893	−	0.830768i	−0.441156	−	0.897430i	$-0.645431\pi$
$23$	−33.0954	−	19.1077i	−1.43893	−	0.830768i	−0.997776	+	0.0666629i	$0.978765\pi$
$24$		0			0
$25$	18.0576	+	31.2767i	0.722305	+	1.25107i
$26$		0			0
$27$	−4.98344	−	26.5361i	−0.184572	−	0.982819i
$28$		0			0
$29$	20.5328	+	11.8546i	0.708026	+	0.408779i	0.810330	−	0.585974i	$-0.199288\pi$
$29$	20.5328	+	11.8546i	0.708026	+	0.408779i	−0.102304	+	0.994753i	$0.532621\pi$
$30$		0			0
$31$	25.1454			0.811143			0.405571	−	0.914063i	$-0.367073\pi$
$31$	25.1454			0.811143			0.405571	+	0.914063i	$0.367073\pi$
$32$		0			0
$33$	−13.2429	+	26.6139i	−0.401300	+	0.806482i
$34$		0			0
$35$	52.8829	−	14.0730i	1.51094	−	0.402086i
$36$		0			0
$37$	−19.6806	−	34.0879i	−0.531909	−	0.921294i	−0.999306	−	0.0372462i	$-0.988141\pi$
$37$	−19.6806	−	34.0879i	−0.531909	−	0.921294i	0.467397	−	0.884048i	$-0.345192\pi$
$38$		0			0
$39$	−30.1235	−	14.9893i	−0.772399	−	0.384340i
$40$		0			0
$41$	45.5225	−	26.2824i	1.11030	−	0.641035i	0.171396	−	0.985202i	$-0.445172\pi$
$41$	45.5225	−	26.2824i	1.11030	−	0.641035i	0.938908	+	0.344168i	$0.111839\pi$
$42$		0			0
$43$	−35.6209	+	61.6972i	−0.828393	+	1.43482i	0.0709056	+	0.997483i	$0.477411\pi$
$43$	−35.6209	+	61.6972i	−0.828393	+	1.43482i	−0.899298	+	0.437335i	$0.855922\pi$
$44$		0			0
$45$	−56.1237	+	42.4319i	−1.24719	+	0.942930i
$46$		0			0
$47$		−	54.2656i		−	1.15459i	−0.816536	−	0.577294i	$-0.804109\pi$
$47$		−	54.2656i		−	1.15459i	0.816536	−	0.577294i	$-0.195891\pi$
$48$		0			0
$49$	0.167642	−	48.9997i	0.00342127	−	0.999994i
$50$		0			0
$51$	−41.8457	+	2.59267i	−0.820503	+	0.0508367i
$52$		0			0
$53$	−47.3589	−	27.3427i	−0.893565	−	0.515900i	−0.0184578	−	0.999830i	$-0.505876\pi$
$53$	−47.3589	−	27.3427i	−0.893565	−	0.515900i	−0.875107	+	0.483930i	$0.839209\pi$
$54$		0			0
$55$	77.4639			1.40844
$56$		0			0
$57$	38.6582	+	19.2361i	0.678215	+	0.337475i
$58$		0			0
$59$		−	39.0826i		−	0.662417i	−0.943558	−	0.331209i	$-0.892544\pi$
$59$		−	39.0826i		−	0.662417i	0.943558	−	0.331209i	$-0.107456\pi$
$60$		0			0
$61$	−65.1147			−1.06745			−0.533727	−	0.845657i	$-0.679209\pi$
$61$	−65.1147			−1.06745			−0.533727	+	0.845657i	$0.679209\pi$
$62$		0			0
$63$	23.5928	+	58.4156i	0.374490	+	0.927231i
$64$		0			0
$65$			87.6793i			1.34891i
$66$		0			0
$67$	106.988			1.59684			0.798421	−	0.602100i	$-0.205669\pi$
$67$	106.988			1.59684			0.798421	+	0.602100i	$0.205669\pi$
$68$		0			0
$69$	−114.427	+	7.08962i	−1.65836	+	0.102748i
$70$		0			0
$71$		−	27.3419i		−	0.385097i	−0.981287	−	0.192549i	$-0.938325\pi$
$71$		−	27.3419i		−	0.385097i	0.981287	−	0.192549i	$-0.0616753\pi$
$72$		0			0
$73$	−0.465523	+	0.806310i	−0.00637703	+	0.0110453i	−0.869196	−	0.494467i	$-0.835363\pi$
$73$	−0.465523	+	0.806310i	−0.00637703	+	0.0110453i	0.862819	+	0.505513i	$0.168697\pi$
$74$		0			0
$75$	97.0007	+	48.2668i	1.29334	+	0.643558i
$76$		0			0
$77$	18.0668	−	66.9679i	0.234634	−	0.869713i
$78$		0			0
$79$	94.3233			1.19397			0.596983	−	0.802254i	$-0.296366\pi$
$79$	94.3233			1.19397			0.596983	+	0.802254i	$0.296366\pi$
$80$		0			0
$81$	−56.4517	−	58.0879i	−0.696934	−	0.717135i
$82$		0			0
$83$	81.5203	+	47.0658i	0.982172	+	0.567057i	0.902925	−	0.429798i	$-0.141415\pi$
$83$	81.5203	+	47.0658i	0.982172	+	0.567057i	0.0792470	+	0.996855i	$0.474748\pi$
$84$		0			0
$85$	54.6269	+	94.6165i	0.642669	+	1.11314i
$86$		0			0
$87$	70.9914	−	4.39848i	0.815994	−	0.0505572i
$88$		0			0
$89$	17.9546	−	10.3661i	0.201738	−	0.116473i	−0.395728	−	0.918368i	$-0.629508\pi$
$89$	17.9546	−	10.3661i	0.201738	−	0.116473i	0.597466	+	0.801894i	$0.296174\pi$
$90$		0			0
$91$	75.7992	+	20.4494i	0.832958	+	0.224718i
$92$		0			0
$93$	62.8722	−	41.6859i	0.676046	−	0.448235i
$94$		0			0
$95$		−	112.521i		−	1.18443i
$96$		0			0
$97$	77.0276	−	133.416i	0.794099	−	1.37542i	−0.129310	−	0.991604i	$-0.541276\pi$
$97$	77.0276	−	133.416i	0.794099	−	1.37542i	0.923409	−	0.383816i	$-0.125390\pi$
$98$		0			0
$99$	11.0085	+	88.4979i	0.111197	+	0.893918i
$100$		0			0
$101$	−31.8738	+	18.4023i	−0.315582	+	0.182201i	−0.649422	−	0.760428i	$-0.724989\pi$
$101$	−31.8738	+	18.4023i	−0.315582	+	0.182201i	0.333840	+	0.942630i	$0.391656\pi$
$102$		0			0
$103$	−37.7166	+	65.3271i	−0.366181	+	0.634244i	−0.988965	−	0.148150i	$-0.952668\pi$
$103$	−37.7166	+	65.3271i	−0.366181	+	0.634244i	0.622784	+	0.782394i	$0.286001\pi$
$104$		0			0
$105$	108.895	−	122.856i	1.03710	−	1.17006i
$106$		0			0
$107$	−72.7667	+	42.0119i	−0.680062	+	0.392634i	−0.799879	−	0.600162i	$-0.795103\pi$
$107$	−72.7667	+	42.0119i	−0.680062	+	0.392634i	0.119816	+	0.992796i	$0.461769\pi$
$108$		0			0
$109$	−81.0516	+	140.385i	−0.743592	+	1.28794i	0.207257	+	0.978287i	$0.433546\pi$
$109$	−81.0516	+	140.385i	−0.743592	+	1.28794i	−0.950850	+	0.309653i	$0.899787\pi$
$110$		0			0
$111$	−105.719	−	52.6050i	−0.952423	−	0.473919i
$112$		0			0
$113$	−18.5728	+	10.7230i	−0.164361	+	0.0948940i	−0.579924	−	0.814670i	$-0.696918\pi$
$113$	−18.5728	+	10.7230i	−0.164361	+	0.0948940i	0.415563	+	0.909564i	$0.363585\pi$
$114$		0			0
$115$	149.376	+	258.728i	1.29893	+	2.24981i
$116$		0			0
$117$	−100.168	+	12.4603i	−0.856140	+	0.106498i
$118$		0			0
$119$	94.5369	−	25.1578i	0.794428	−	0.211410i
$120$		0			0
$121$	−11.4070	+	19.7575i	−0.0942728	+	0.163285i
$122$		0			0
$123$	70.2511	−	141.182i	0.571147	−	1.14782i
$124$		0			0
$125$		−	86.8950i		−	0.695160i
$126$		0			0
$127$	−53.7261			−0.423040			−0.211520	−	0.977374i	$-0.567841\pi$
$127$	−53.7261			−0.423040			−0.211520	+	0.977374i	$0.567841\pi$
$128$		0			0
$129$	13.2166	+	213.316i	0.102454	+	1.65361i
$130$		0			0
$131$	−52.9098	−	30.5475i	−0.403891	−	0.233187i	0.284270	−	0.958744i	$-0.408249\pi$
$131$	−52.9098	−	30.5475i	−0.403891	−	0.233187i	−0.688162	+	0.725557i	$0.741582\pi$
$132$		0			0
$133$	−97.2748	−	26.2431i	−0.731390	−	0.197317i
$134$		0			0
$135$	−69.9855	+	199.136i	−0.518411	+	1.47508i
$136$		0			0
$137$	−106.494	+	61.4842i	−0.777327	+	0.448790i	−0.835482	−	0.549518i	$-0.814812\pi$
$137$	−106.494	+	61.4842i	−0.777327	+	0.448790i	0.0581551	+	0.998308i	$0.481478\pi$
$138$		0			0
$139$	3.77631	+	6.54076i	0.0271677	+	0.0470558i	0.879290	−	0.476288i	$-0.158018\pi$
$139$	3.77631	+	6.54076i	0.0271677	+	0.0470558i	−0.852122	+	0.523343i	$0.824685\pi$
$140$		0			0
$141$	−89.9611	−	135.683i	−0.638022	−	0.962289i
$142$		0			0
$143$	96.2449	+	55.5670i	0.673041	+	0.388580i
$144$		0			0
$145$	−92.6748	−	160.517i	−0.639136	−	1.10702i
$146$		0			0
$147$	−80.8122	−	122.794i	−0.549743	−	0.835334i
$148$		0			0
$149$	−188.632	−	108.907i	−1.26598	−	0.730917i	−0.291759	−	0.956492i	$-0.594241\pi$
$149$	−188.632	−	108.907i	−1.26598	−	0.730917i	−0.974226	+	0.225575i	$0.927574\pi$
$150$		0			0
$151$	−112.710	−	195.220i	−0.746426	−	1.29285i	−0.949526	−	0.313690i	$-0.898435\pi$
$151$	−112.710	−	195.220i	−0.746426	−	1.29285i	0.203100	−	0.979158i	$-0.434899\pi$
$152$		0			0
$153$	−100.331	+	75.8540i	−0.655755	+	0.495778i
$154$		0			0
$155$	−170.241	−	98.2888i	−1.09833	−	0.634121i
$156$		0			0
$157$	107.052			0.681858			0.340929	−	0.940089i	$-0.389258\pi$
$157$	107.052			0.681858			0.340929	+	0.940089i	$0.389258\pi$
$158$		0			0
$159$	−163.742	+	10.1451i	−1.02982	+	0.0638058i
$160$		0			0
$161$	258.510	−	68.7938i	1.60565	−	0.427291i
$162$		0			0
$163$	−121.650	−	210.704i	−0.746321	−	1.29267i	−0.949575	−	0.313539i	$-0.898485\pi$
$163$	−121.650	−	210.704i	−0.746321	−	1.29267i	0.203254	−	0.979126i	$-0.434848\pi$
$164$		0			0
$165$	193.687	−	128.419i	1.17386	−	0.778298i
$166$		0			0
$167$	−7.49683	+	4.32830i	−0.0448912	+	0.0259179i	−0.522278	−	0.852776i	$-0.674918\pi$
$167$	−7.49683	+	4.32830i	−0.0448912	+	0.0259179i	0.477386	+	0.878693i	$0.341584\pi$
$168$		0			0
$169$	21.6052	−	37.4214i	0.127842	−	0.221428i
$170$		0			0
$171$	128.548	−	15.9906i	0.751745	−	0.0935120i
$172$		0			0
$173$			173.694i			1.00401i	0.864864	+	0.502007i	$0.167405\pi$
$173$			173.694i			1.00401i	−0.864864	+	0.502007i	$0.832595\pi$
$174$		0			0
$175$	−244.080	−	65.8489i	−1.39475	−	0.376279i
$176$		0			0
$177$	−64.7909	−	97.7200i	−0.366050	−	0.552091i
$178$		0			0
$179$	143.928	+	83.0966i	0.804065	+	0.464227i	0.844890	−	0.534939i	$-0.179666\pi$
$179$	143.928	+	83.0966i	0.804065	+	0.464227i	−0.0408259	+	0.999166i	$0.512999\pi$
$180$		0			0
$181$	−46.4431			−0.256592			−0.128296	−	0.991736i	$-0.540951\pi$
$181$	−46.4431			−0.256592			−0.128296	+	0.991736i	$0.540951\pi$
$182$		0			0
$183$	−162.809	+	107.947i	−0.889668	+	0.589873i
$184$		0			0
$185$			307.712i			1.66331i
$186$		0			0
$187$	138.480			0.740533
$188$		0			0
$189$	155.831	+	106.947i	0.824503	+	0.565857i
$190$		0			0
$191$			246.423i			1.29018i	0.764109	+	0.645088i	$0.223179\pi$
$191$			246.423i			1.29018i	−0.764109	+	0.645088i	$0.776821\pi$
$192$		0			0
$193$	−61.0003			−0.316064			−0.158032	−	0.987434i	$-0.550515\pi$
$193$	−61.0003			−0.316064			−0.158032	+	0.987434i	$0.550515\pi$
$194$		0			0
$195$	145.354	+	219.229i	0.745406	+	1.12425i
$196$		0			0
$197$			63.3390i			0.321518i	0.986994	+	0.160759i	$0.0513942\pi$
$197$			63.3390i			0.321518i	−0.986994	+	0.160759i	$0.948606\pi$
$198$		0			0
$199$	69.4520	−	120.294i	0.349005	−	0.604494i	−0.637068	−	0.770808i	$-0.719853\pi$
$199$	69.4520	−	120.294i	0.349005	−	0.604494i	0.986073	+	0.166313i	$0.0531863\pi$
$200$		0			0
$201$	267.508	−	177.365i	1.33089	−	0.882411i
$202$		0			0
$203$	−160.382	+	42.6804i	−0.790061	+	0.210248i
$204$		0			0
$205$	−410.932			−2.00455
$206$		0			0
$207$	−274.353	+	207.422i	−1.32537	+	1.00204i
$208$		0			0
$209$	−123.513	−	71.3104i	−0.590973	−	0.341198i
$210$		0			0
$211$	−113.387	−	196.391i	−0.537378	−	0.930765i	−0.999044	−	0.0437118i	$-0.986082\pi$
$211$	−113.387	−	196.391i	−0.537378	−	0.930765i	0.461667	−	0.887054i	$-0.347252\pi$
$212$		0			0
$213$	−45.3272	−	68.3642i	−0.212804	−	0.320959i
$214$		0			0
$215$	482.326	−	278.471i	2.24337	−	1.29521i
$216$		0			0
$217$	−124.676	+	124.250i	−0.574545	+	0.572583i
$218$		0			0
$219$	0.172726	+	2.78779i	0.000788702	+	0.0127296i
$220$		0			0
$221$			156.741i			0.709237i
$222$		0			0
$223$	151.921	−	263.135i	0.681261	−	1.17998i	−0.293336	−	0.956009i	$-0.594765\pi$
$223$	151.921	−	263.135i	0.681261	−	1.17998i	0.974596	−	0.223968i	$-0.0719013\pi$
$224$		0			0
$225$	322.551	−	40.1232i	1.43356	−	0.178325i
$226$		0			0
$227$	−78.5926	+	45.3754i	−0.346223	+	0.199892i	−0.663020	−	0.748601i	$-0.730726\pi$
$227$	−78.5926	+	45.3754i	−0.346223	+	0.199892i	0.316798	+	0.948493i	$0.397392\pi$
$228$		0			0
$229$	−96.9776	+	167.970i	−0.423483	+	0.733494i	−0.996277	−	0.0862051i	$-0.972526\pi$
$229$	−96.9776	+	167.970i	−0.423483	+	0.733494i	0.572795	+	0.819699i	$0.305859\pi$
$230$		0			0
$231$	−65.8456	−	197.394i	−0.285046	−	0.854519i
$232$		0			0
$233$	−342.650	+	197.829i	−1.47060	+	0.849053i	−0.999455	−	0.0330016i	$-0.989493\pi$
$233$	−342.650	+	197.829i	−1.47060	+	0.849053i	−0.471147	+	0.882054i	$0.656160\pi$
$234$		0			0
$235$	−212.114	+	367.392i	−0.902613	+	1.56337i
$236$		0			0
$237$	235.841	−	156.368i	0.995108	−	0.659782i
$238$		0			0
$239$	−121.457	+	70.1232i	−0.508188	+	0.293403i	−0.732089	−	0.681209i	$-0.761454\pi$
$239$	−121.457	+	70.1232i	−0.508188	+	0.293403i	0.223900	+	0.974612i	$0.428121\pi$
$240$		0			0
$241$	−77.6043	−	134.415i	−0.322010	−	0.557737i	0.658893	−	0.752237i	$-0.271025\pi$
$241$	−77.6043	−	134.415i	−0.322010	−	0.557737i	−0.980903	+	0.194500i	$0.937692\pi$
$242$		0			0
$243$	−237.446	−	51.6546i	−0.977146	−	0.212571i
$244$		0			0
$245$	−192.666	+	331.086i	−0.786391	+	1.35137i
$246$		0			0
$247$	80.7143	−	139.801i	0.326779	−	0.565997i
$248$		0			0
$249$	281.854	−	17.4631i	1.13194	−	0.0701329i
$250$		0			0
$251$		−	316.992i		−	1.26292i	−0.775409	−	0.631459i	$-0.782456\pi$
$251$		−	316.992i		−	1.26292i	0.775409	−	0.631459i	$-0.217544\pi$
$252$		0			0
$253$	378.671			1.49672
$254$		0			0
$255$	293.440	+	146.014i	1.15075	+	0.572603i
$256$		0			0
$257$	−262.148	−	151.351i	−1.02003	−	0.588914i	−0.105917	−	0.994375i	$-0.533778\pi$
$257$	−262.148	−	151.351i	−1.02003	−	0.588914i	−0.914113	+	0.405461i	$0.867111\pi$
$258$		0			0
$259$	266.018	+	71.7673i	1.02710	+	0.277094i
$260$		0			0
$261$	170.211	−	128.687i	0.652151	−	0.493053i
$262$		0			0
$263$	297.807	−	171.939i	1.13235	−	0.653760i	0.187822	−	0.982203i	$-0.439857\pi$
$263$	297.807	−	171.939i	1.13235	−	0.653760i	0.944524	+	0.328443i	$0.106524\pi$
$264$		0			0
$265$	213.755	+	370.234i	0.806622	+	1.39711i
$266$		0			0
$267$	27.7079	−	55.6839i	0.103775	−	0.208554i
$268$		0			0
$269$	230.930	+	133.327i	0.858474	+	0.495640i	0.863501	−	0.504347i	$-0.168267\pi$
$269$	230.930	+	133.327i	0.858474	+	0.495640i	−0.00502670	+	0.999987i	$0.501600\pi$
$270$		0			0
$271$	201.627	+	349.227i	0.744009	+	1.28866i	0.950656	+	0.310247i	$0.100412\pi$
$271$	201.627	+	349.227i	0.744009	+	1.28866i	−0.206647	+	0.978416i	$0.566255\pi$
$272$		0			0
$273$	223.425	−	74.5288i	0.818406	−	0.272999i
$274$		0			0
$275$	−309.918	−	178.931i	−1.12697	−	0.650658i
$276$		0			0
$277$	−179.217	−	310.413i	−0.646993	−	1.12062i	−0.983837	−	0.179064i	$-0.942693\pi$
$277$	−179.217	−	310.413i	−0.646993	−	1.12062i	0.336845	−	0.941560i	$-0.390640\pi$
$278$		0			0
$279$	88.0957	−	208.458i	0.315755	−	0.747162i
$280$		0			0
$281$	284.206	+	164.087i	1.01141	+	0.583938i	0.911604	−	0.411069i	$-0.134844\pi$
$281$	284.206	+	164.087i	1.01141	+	0.583938i	0.0998062	+	0.995007i	$0.468178\pi$
$282$		0			0
$283$	−378.349			−1.33692			−0.668461	−	0.743747i	$-0.733047\pi$
$283$	−378.349			−1.33692			−0.668461	+	0.743747i	$0.733047\pi$
$284$		0			0
$285$	−186.536	−	281.341i	−0.654513	−	0.987162i
$286$		0			0
$287$	−95.8413	+	355.253i	−0.333942	+	1.23781i
$288$		0			0
$289$	−46.8454	−	81.1386i	−0.162095	−	0.280757i
$290$		0			0
$291$	−28.5800	−	461.281i	−0.0982131	−	1.58516i
$292$		0			0
$293$	343.533	−	198.339i	1.17247	−	0.676924i	0.218207	−	0.975903i	$-0.429979\pi$
$293$	343.533	−	198.339i	1.17247	−	0.676924i	0.954260	+	0.298979i	$0.0966460\pi$
$294$		0			0
$295$	−152.767	+	264.600i	−0.517853	+	0.896948i
$296$		0			0
$297$	174.236	+	203.025i	0.586654	+	0.683587i
$298$		0			0
$299$			428.607i			1.43347i
$300$		0			0
$301$	−128.247	−	481.920i	−0.426069	−	1.60106i
$302$		0			0
$303$	−49.1882	+	98.8524i	−0.162337	+	0.326245i
$304$		0			0
$305$	440.844	+	254.521i	1.44539	+	0.834496i
$306$		0			0
$307$	298.494			0.972292			0.486146	−	0.873878i	$-0.338402\pi$
$307$	298.494			0.972292			0.486146	+	0.873878i	$0.338402\pi$
$308$		0			0
$309$	13.9942	+	225.867i	0.0452887	+	0.730960i
$310$		0			0
$311$		−	337.658i		−	1.08572i	−0.839824	−	0.542858i	$-0.817342\pi$
$311$		−	337.658i		−	1.08572i	0.839824	−	0.542858i	$-0.182658\pi$
$312$		0			0
$313$	269.732			0.861763			0.430881	−	0.902409i	$-0.358203\pi$
$313$	269.732			0.861763			0.430881	+	0.902409i	$0.358203\pi$
$314$		0			0
$315$	68.6057	−	487.709i	0.217796	−	1.54828i
$316$		0			0
$317$			138.157i			0.435825i	0.975968	+	0.217913i	$0.0699248\pi$
$317$			138.157i			0.435825i	−0.975968	+	0.217913i	$0.930075\pi$
$318$		0			0
$319$	−234.932			−0.736463
$320$		0			0
$321$	−112.295	+	225.676i	−0.349828	+	0.703041i
$322$		0			0
$323$		−	201.150i		−	0.622755i
$324$		0			0
$325$	202.527	−	350.787i	0.623160	−	1.07935i
$326$		0			0
$327$	30.0730	+	485.379i	0.0919665	+	1.48434i
$328$		0			0
$329$	268.141	+	269.060i	0.815019	+	0.817812i
$330$		0			0
$331$	−116.895			−0.353156			−0.176578	−	0.984287i	$-0.556503\pi$
$331$	−116.895			−0.353156			−0.176578	+	0.984287i	$0.556503\pi$
$332$		0			0
$333$	−351.542	+	43.7295i	−1.05568	+	0.131320i
$334$		0			0
$335$	−724.340	−	418.198i	−2.16221	−	1.24835i
$336$		0			0
$337$	−232.080	−	401.974i	−0.688664	−	1.19280i	−0.972270	−	0.233860i	$-0.924864\pi$
$337$	−232.080	−	401.974i	−0.688664	−	1.19280i	0.283606	−	0.958941i	$-0.408469\pi$
$338$		0			0
$339$	−28.6619	+	57.6011i	−0.0845484	+	0.169915i
$340$		0			0
$341$	−215.782	+	124.582i	−0.632791	+	0.365342i
$342$		0			0
$343$	241.290	+	243.779i	0.703469	+	0.710726i
$344$		0			0
$345$	802.409	+	399.273i	2.32582	+	1.15731i
$346$		0			0
$347$			544.658i			1.56962i	0.619737	+	0.784809i	$0.287239\pi$
$347$			544.658i			1.56962i	−0.619737	+	0.784809i	$0.712761\pi$
$348$		0			0
$349$	−209.129	+	362.222i	−0.599224	+	1.03789i	0.393712	+	0.919234i	$0.371191\pi$
$349$	−209.129	+	362.222i	−0.599224	+	1.03789i	−0.992936	+	0.118653i	$0.962142\pi$
$350$		0			0
$351$	−229.799	+	197.213i	−0.654698	+	0.561861i
$352$		0			0
$353$	−287.230	+	165.833i	−0.813684	+	0.469781i	−0.848234	−	0.529622i	$-0.822334\pi$
$353$	−287.230	+	165.833i	−0.813684	+	0.469781i	0.0345497	+	0.999403i	$0.489000\pi$
$354$		0			0
$355$	−106.874	+	185.112i	−0.301055	+	0.521442i
$356$		0			0
$357$	194.668	−	219.626i	0.545290	−	0.615199i
$358$		0			0
$359$	364.336	−	210.349i	1.01486	−	0.585932i	0.102251	−	0.994759i	$-0.467395\pi$
$359$	364.336	−	210.349i	1.01486	−	0.585932i	0.912612	+	0.408827i	$0.134062\pi$
$360$		0			0
$361$	76.9174	−	133.225i	0.213068	−	0.369044i
$362$		0			0
$363$	4.23241	+	68.3110i	0.0116595	+	0.188185i
$364$		0			0
$365$	6.30343	−	3.63928i	0.0172697	−	0.00997064i
$366$		0			0
$367$	−24.3578	−	42.1890i	−0.0663701	−	0.114956i	0.830931	−	0.556376i	$-0.187808\pi$
$367$	−24.3578	−	42.1890i	−0.0663701	−	0.114956i	−0.897301	+	0.441419i	$0.854475\pi$
$368$		0			0
$369$	−58.3983	−	469.465i	−0.158261	−	1.27226i
$370$		0			0
$371$	369.923	−	98.4426i	0.997097	−	0.265344i
$372$		0			0
$373$	176.402	−	305.537i	0.472927	−	0.819133i	−0.526593	−	0.850118i	$-0.676531\pi$
$373$	176.402	−	305.537i	0.472927	−	0.819133i	0.999520	+	0.0309841i	$0.00986414\pi$
$374$		0			0
$375$	−144.054	−	217.268i	−0.384144	−	0.579380i
$376$		0			0
$377$		−	265.913i		−	0.705339i
$378$		0			0
$379$	132.331			0.349158			0.174579	−	0.984643i	$-0.444144\pi$
$379$	132.331			0.349158			0.174579	+	0.984643i	$0.444144\pi$
$380$		0			0
$381$	−134.334	+	89.0668i	−0.352582	+	0.233771i
$382$		0			0
$383$	63.9136	+	36.9005i	0.166876	+	0.0963461i	0.581112	−	0.813824i	$-0.302618\pi$
$383$	63.9136	+	36.9005i	0.166876	+	0.0963461i	−0.414236	+	0.910170i	$0.635951\pi$
$384$		0			0
$385$	−384.082	+	382.771i	−0.997616	+	0.994209i
$386$		0			0
$387$	386.680	+	511.454i	0.999174	+	1.32159i
$388$		0			0
$389$	317.315	−	183.202i	0.815719	−	0.470956i	−0.0332189	−	0.999448i	$-0.510576\pi$
$389$	317.315	−	183.202i	0.815719	−	0.470956i	0.848938	+	0.528492i	$0.177243\pi$
$390$		0			0
$391$	267.035	+	462.519i	0.682955	+	1.18291i
$392$		0			0
$393$	−182.934	+	11.3342i	−0.465481	+	0.0288402i
$394$		0			0
$395$	−638.593	−	368.692i	−1.61669	−	0.933397i
$396$		0			0
$397$	−266.425	−	461.462i	−0.671097	−	1.16237i	−0.977593	−	0.210502i	$-0.932490\pi$
$397$	−266.425	−	461.462i	−0.671097	−	1.16237i	0.306497	−	0.951872i	$-0.400843\pi$
$398$		0			0
$399$	−286.726	+	95.6446i	−0.718612	+	0.239711i
$400$		0			0
$401$	526.244	+	303.827i	1.31233	+	0.757673i	0.982481	−	0.186361i	$-0.0596695\pi$
$401$	526.244	+	303.827i	1.31233	+	0.757673i	0.329847	+	0.944034i	$0.393003\pi$
$402$		0			0
$403$	−141.010	−	244.237i	−0.349902	−	0.606048i
$404$		0			0
$405$	155.138	+	613.930i	0.383057	+	1.51588i
$406$		0			0
$407$	337.773	+	195.013i	0.829909	+	0.479148i
$408$		0			0
$409$	390.924			0.955803			0.477902	−	0.878413i	$-0.341397\pi$
$409$	390.924			0.955803			0.477902	+	0.878413i	$0.341397\pi$
$410$		0			0
$411$	−164.343	+	330.276i	−0.399862	+	0.803592i
$412$		0			0
$413$	193.118	+	193.780i	0.467598	+	0.469200i
$414$		0			0
$415$	−367.943	−	637.295i	−0.886609	−	1.53565i
$416$		0			0
$417$	20.2853	+	10.0938i	0.0486458	+	0.0242058i
$418$		0			0
$419$	−361.229	+	208.556i	−0.862122	+	0.497746i	−0.864722	−	0.502250i	$-0.832506\pi$
$419$	−361.229	+	208.556i	−0.862122	+	0.497746i	0.00260040	+	0.999997i	$0.499172\pi$
$420$		0			0
$421$	35.2932	−	61.1296i	0.0838318	−	0.145201i	−0.821061	−	0.570840i	$-0.806617\pi$
$421$	35.2932	−	61.1296i	0.0838318	−	0.145201i	0.904893	+	0.425639i	$0.139951\pi$
$422$		0			0
$423$	−449.868	−	190.117i	−1.06352	−	0.449449i
$424$		0			0
$425$		−	504.722i		−	1.18758i
$426$		0			0
$427$	322.852	−	321.750i	0.756094	−	0.753512i
$428$		0			0
$429$	332.764	−	20.6174i	0.775674	−	0.0480591i
$430$		0			0
$431$	−20.3061	−	11.7237i	−0.0471139	−	0.0272012i	0.476258	−	0.879306i	$-0.341993\pi$
$431$	−20.3061	−	11.7237i	−0.0471139	−	0.0272012i	−0.523372	+	0.852104i	$0.675326\pi$
$432$		0			0
$433$	−354.517			−0.818746			−0.409373	−	0.912367i	$-0.634253\pi$
$433$	−354.517			−0.818746			−0.409373	+	0.912367i	$0.634253\pi$
$434$		0			0
$435$	−497.823	−	247.713i	−1.14442	−	0.569456i
$436$		0			0
$437$		−	550.042i		−	1.25868i
$438$		0			0
$439$	509.996			1.16172			0.580861	−	0.814003i	$-0.302716\pi$
$439$	509.996			1.16172			0.580861	+	0.814003i	$0.302716\pi$
$440$		0			0
$441$	−405.625	−	173.058i	−0.919786	−	0.392421i
$442$		0			0
$443$		−	301.489i		−	0.680561i	−0.940324	−	0.340281i	$-0.889478\pi$
$443$		−	301.489i		−	0.680561i	0.940324	−	0.340281i	$-0.110522\pi$
$444$		0			0
$445$	−162.077			−0.364218
$446$		0			0
$447$	−652.189	+	40.4082i	−1.45904	+	0.0903988i
$448$		0			0
$449$			73.5476i			0.163803i	0.996640	+	0.0819015i	$0.0260993\pi$
$449$			73.5476i			0.163803i	−0.996640	+	0.0819015i	$0.973901\pi$
$450$		0			0
$451$	−260.429	+	451.077i	−0.577449	+	1.00017i
$452$		0			0
$453$	−605.449	−	301.267i	−1.33653	−	0.665049i
$454$		0			0
$455$	−433.247	−	434.732i	−0.952192	−	0.955455i
$456$		0			0
$457$	710.494			1.55469			0.777346	−	0.629074i	$-0.216566\pi$
$457$	710.494			1.55469			0.777346	+	0.629074i	$0.216566\pi$
$458$		0			0
$459$	−125.111	+	355.988i	−0.272572	+	0.775574i
$460$		0			0
$461$	−472.697	−	272.912i	−1.02537	−	0.591999i	−0.109717	−	0.993963i	$-0.534995\pi$
$461$	−472.697	−	272.912i	−1.02537	−	0.591999i	−0.915656	+	0.401964i	$0.868328\pi$
$462$		0			0
$463$	337.645	+	584.819i	0.729255	+	1.26311i	0.957198	+	0.289433i	$0.0934667\pi$
$463$	337.645	+	584.819i	0.729255	+	1.26311i	−0.227943	+	0.973675i	$0.573200\pi$
$464$		0			0
$465$	−588.604	+	36.4687i	−1.26581	+	0.0784272i
$466$		0			0
$467$	−95.1678	+	54.9452i	−0.203785	+	0.117656i	−0.598420	−	0.801183i	$-0.704205\pi$
$467$	−95.1678	+	54.9452i	−0.203785	+	0.117656i	0.394635	+	0.918838i	$0.370871\pi$
$468$		0			0
$469$	−530.471	+	528.659i	−1.13107	+	1.12720i
$470$		0			0
$471$	267.666	−	177.469i	0.568293	−	0.376793i
$472$		0			0
$473$		−	705.927i		−	1.49245i
$474$		0			0
$475$	−259.908	+	450.173i	−0.547174	+	0.947734i
$476$		0			0
$477$	−392.593	+	296.817i	−0.823047	+	0.622257i
$478$		0			0
$479$	62.0215	−	35.8081i	0.129481	−	0.0747560i	−0.433860	−	0.900980i	$-0.642849\pi$
$479$	62.0215	−	35.8081i	0.129481	−	0.0747560i	0.563342	+	0.826224i	$0.309516\pi$
$480$		0			0
$481$	−220.730	+	382.316i	−0.458898	+	0.794835i
$482$		0			0
$483$	532.319	−	600.564i	1.10211	−	1.24340i
$484$		0			0
$485$	−1042.99	+	602.173i	−2.15050	+	1.24159i
$486$		0			0
$487$	−294.873	+	510.736i	−0.605490	+	1.04874i	0.386484	+	0.922296i	$0.373689\pi$
$487$	−294.873	+	510.736i	−0.605490	+	1.04874i	−0.991974	+	0.126443i	$0.959644\pi$
$488$		0			0
$489$	−653.472	−	325.163i	−1.33634	−	0.664955i
$490$		0			0
$491$	−154.271	+	89.0686i	−0.314198	+	0.181403i	−0.648804	−	0.760956i	$-0.724730\pi$
$491$	−154.271	+	89.0686i	−0.314198	+	0.181403i	0.334605	+	0.942358i	$0.391397\pi$
$492$		0			0
$493$	−165.672	−	286.952i	−0.336048	−	0.582052i
$494$		0			0
$495$	271.391	−	642.184i	0.548265	−	1.29734i
$496$		0			0
$497$	135.104	+	135.567i	0.271839	+	0.272770i
$498$		0			0
$499$	298.362	−	516.779i	0.597920	−	1.03563i	−0.395207	−	0.918592i	$-0.629327\pi$
$499$	298.362	−	516.779i	0.597920	−	1.03563i	0.993128	−	0.117036i	$-0.0373394\pi$
$500$		0			0
$501$	−11.5692	+	23.2504i	−0.0230923	+	0.0464080i
$502$		0			0
$503$		−	135.851i		−	0.270081i	−0.990840	−	0.135041i	$-0.956884\pi$
$503$		−	135.851i		−	0.270081i	0.990840	−	0.135041i	$-0.0431165\pi$
$504$		0			0
$505$	287.725			0.569753
$506$		0			0
$507$	−8.01631	−	129.383i	−0.0158113	−	0.255194i
$508$		0			0
$509$	266.491	+	153.859i	0.523558	+	0.302276i	0.738389	−	0.674375i	$-0.235587\pi$
$509$	266.491	+	153.859i	0.523558	+	0.302276i	−0.214831	+	0.976651i	$0.568920\pi$
$510$		0			0
$511$	−1.67604	−	6.29813i	−0.00327991	−	0.0123251i
$512$		0			0
$513$	294.906	−	253.088i	0.574866	−	0.493350i
$514$		0			0
$515$	510.703	−	294.854i	0.991656	−	0.572533i
$516$		0			0
$517$	268.856	+	465.672i	0.520031	+	0.900720i
$518$		0			0
$519$	287.949	+	434.296i	0.554815	+	0.836794i
$520$		0			0
$521$	−359.480	−	207.546i	−0.689981	−	0.398361i	0.113624	−	0.993524i	$-0.463754\pi$
$521$	−359.480	−	207.546i	−0.689981	−	0.398361i	−0.803605	+	0.595163i	$0.797087\pi$
$522$		0			0
$523$	−32.5093	−	56.3077i	−0.0621592	−	0.107663i	0.833271	−	0.552865i	$-0.186465\pi$
$523$	−32.5093	−	56.3077i	−0.0621592	−	0.107663i	−0.895430	+	0.445202i	$0.853132\pi$
$524$		0			0
$525$	−719.449	+	239.990i	−1.37038	+	0.457123i
$526$		0			0
$527$	−304.334	−	175.708i	−0.577485	−	0.333411i
$528$		0			0
$529$	465.705	+	806.624i	0.880349	+	1.52481i
$530$		0			0
$531$	−323.999	−	136.924i	−0.610168	−	0.257861i
$532$		0			0
$533$	−510.562	−	294.773i	−0.957902	−	0.553045i
$534$		0			0
$535$	656.866			1.22779
$536$		0			0
$537$	497.625	−	30.8318i	0.926677	−	0.0574149i
$538$		0			0
$539$	241.328	+	421.314i	0.447732	+	0.781659i
$540$		0			0
$541$	44.9103	+	77.7869i	0.0830135	+	0.143784i	0.904543	−	0.426382i	$-0.140212\pi$
$541$	44.9103	+	77.7869i	0.0830135	+	0.143784i	−0.821530	+	0.570166i	$0.806879\pi$
$542$		0			0
$543$	−116.124	+	76.9930i	−0.213856	+	0.141792i
$544$		0			0
$545$	1097.48	−	633.631i	2.01373	−	1.16263i
$546$		0			0
$547$	14.9248	−	25.8506i	0.0272849	−	0.0472588i	−0.852061	−	0.523443i	$-0.824647\pi$
$547$	14.9248	−	25.8506i	0.0272849	−	0.0472588i	0.879345	+	0.476184i	$0.157981\pi$
$548$		0			0
$549$	−228.126	+	539.808i	−0.415530	+	0.983257i
$550$		0			0
$551$			341.252i			0.619332i
$552$		0			0
$553$	−467.674	+	466.077i	−0.845704	+	0.842816i
$554$		0			0
$555$	510.122	+	769.386i	0.919139	+	1.38628i
$556$		0			0
$557$	−314.117	−	181.355i	−0.563944	−	0.325593i	0.190783	−	0.981632i	$-0.438897\pi$
$557$	−314.117	−	181.355i	−0.563944	−	0.325593i	−0.754727	+	0.656039i	$0.772231\pi$
$558$		0			0
$559$	799.019			1.42937
$560$		0			0
$561$	346.247	−	229.571i	0.617196	−	0.409217i
$562$		0			0
$563$		−	545.681i		−	0.969238i	−0.874725	−	0.484619i	$-0.838958\pi$
$563$		−	545.681i		−	0.969238i	0.874725	−	0.484619i	$-0.161042\pi$
$564$		0			0
$565$	167.657			0.296738
$566$		0			0
$567$	566.927	+	9.06872i	0.999872	+	0.0159942i
$568$		0			0
$569$			260.614i			0.458020i	0.973424	+	0.229010i	$0.0735489\pi$
$569$			260.614i			0.458020i	−0.973424	+	0.229010i	$0.926451\pi$
$570$		0			0
$571$	650.559			1.13933			0.569666	−	0.821876i	$-0.307072\pi$
$571$	650.559			1.13933			0.569666	+	0.821876i	$0.307072\pi$
$572$		0			0
$573$	408.519	+	616.144i	0.712948	+	1.07529i
$574$		0			0
$575$		−	1380.16i		−	2.40027i
$576$		0			0
$577$	515.854	−	893.485i	0.894027	−	1.54850i	0.0590234	−	0.998257i	$-0.481201\pi$
$577$	515.854	−	893.485i	0.894027	−	1.54850i	0.835004	−	0.550244i	$-0.185465\pi$
$578$		0			0
$579$	−152.522	+	101.126i	−0.263423	+	0.174656i
$580$		0			0
$581$	−636.759	+	169.452i	−1.09597	+	0.291656i
$582$		0			0
$583$	541.871			0.929453
$584$		0			0
$585$	726.871	+	307.180i	1.24251	+	0.525094i
$586$		0			0
$587$	715.056	+	412.838i	1.21815	+	0.703302i	0.964523	−	0.263999i	$-0.0850417\pi$
$587$	715.056	+	412.838i	1.21815	+	0.703302i	0.253631	+	0.967301i	$0.418375\pi$
$588$		0			0
$589$	180.962	+	313.435i	0.307236	+	0.532148i
$590$		0			0
$591$	105.003	+	158.369i	0.177670	+	0.267968i
$592$		0			0
$593$	620.271	−	358.114i	1.04599	−	0.603902i	0.124465	−	0.992224i	$-0.460279\pi$
$593$	620.271	−	358.114i	1.04599	−	0.603902i	0.921524	+	0.388322i	$0.126945\pi$
$594$		0			0
$595$	−738.377	−	199.202i	−1.24097	−	0.334793i
$596$		0			0
$597$	−25.7692	−	415.914i	−0.0431644	−	0.696674i
$598$		0			0
$599$			982.529i			1.64028i	0.572162	+	0.820141i	$0.306105\pi$
$599$			982.529i			1.64028i	−0.572162	+	0.820141i	$0.693895\pi$
$600$		0			0
$601$	280.080	−	485.113i	0.466024	−	0.807177i	−0.533223	−	0.845975i	$-0.679019\pi$
$601$	280.080	−	485.113i	0.466024	−	0.807177i	0.999247	+	0.0387975i	$0.0123527\pi$
$602$		0			0
$603$	374.828	−	886.945i	0.621606	−	1.47089i
$604$		0			0
$605$	154.457	−	89.1757i	0.255301	−	0.147398i
$606$		0			0
$607$	−77.5868	+	134.384i	−0.127820	+	0.221391i	−0.922832	−	0.385203i	$-0.874131\pi$
$607$	−77.5868	+	134.384i	−0.127820	+	0.221391i	0.795012	+	0.606594i	$0.207465\pi$
$608$		0			0
$609$	−330.256	+	372.597i	−0.542293	+	0.611817i
$610$		0			0
$611$	−527.081	+	304.311i	−0.862654	+	0.498053i
$612$		0			0
$613$	−197.990	+	342.929i	−0.322986	+	0.559428i	−0.981103	−	0.193488i	$-0.938020\pi$
$613$	−197.990	+	342.929i	−0.322986	+	0.559428i	0.658117	+	0.752916i	$0.271353\pi$
$614$		0			0
$615$	−1027.47	+	681.240i	−1.67069	+	1.10771i
$616$		0			0
$617$	346.378	−	199.982i	0.561391	−	0.324119i	−0.192313	−	0.981334i	$-0.561599\pi$
$617$	346.378	−	199.982i	0.561391	−	0.324119i	0.753704	+	0.657215i	$0.228265\pi$
$618$		0			0
$619$	−453.781	−	785.971i	−0.733087	−	1.26974i	−0.955558	−	0.294804i	$-0.904746\pi$
$619$	−453.781	−	785.971i	−0.733087	−	1.26974i	0.222471	−	0.974939i	$-0.428588\pi$
$620$		0			0
$621$	−342.114	+	973.446i	−0.550908	+	1.56755i
$622$		0			0
$623$	−37.8010	+	140.116i	−0.0606758	+	0.224906i
$624$		0			0
$625$	111.785	−	193.616i	0.178855	−	0.309786i
$626$		0			0
$627$	−427.044	+	26.4587i	−0.681091	+	0.0421989i
$628$		0			0
$629$			550.086i			0.874541i
$630$		0			0
$631$	−105.596			−0.167347			−0.0836736	−	0.996493i	$-0.526665\pi$
$631$	−105.596			−0.167347			−0.0836736	+	0.996493i	$0.526665\pi$
$632$		0			0
$633$	−609.082	−	303.075i	−0.962215	−	0.478791i
$634$		0			0
$635$	363.740	+	210.005i	0.572819	+	0.330717i
$636$		0			0
$637$	−476.874	+	273.152i	−0.748624	+	0.428810i
$638$		0			0
$639$	−226.667	−	95.7910i	−0.354722	−	0.149908i
$640$		0			0
$641$	331.536	−	191.412i	0.517217	−	0.298615i	−0.218578	−	0.975819i	$-0.570142\pi$
$641$	331.536	−	191.412i	0.517217	−	0.298615i	0.735795	+	0.677204i	$0.236809\pi$
$642$		0			0
$643$	−245.677	−	425.525i	−0.382080	−	0.661781i	0.609280	−	0.792955i	$-0.291459\pi$
$643$	−245.677	−	425.525i	−0.382080	−	0.661781i	−0.991359	+	0.131174i	$0.958125\pi$
$644$		0			0
$645$	744.333	−	1495.87i	1.15401	−	2.31918i
$646$		0			0
$647$	−741.786	−	428.270i	−1.14650	−	0.661933i	−0.198469	−	0.980107i	$-0.563597\pi$
$647$	−741.786	−	428.270i	−1.14650	−	0.661933i	−0.948032	+	0.318175i	$0.896930\pi$
$648$		0			0
$649$	193.633	+	335.381i	0.298355	+	0.516767i
$650$		0			0
$651$	−105.752	+	517.356i	−0.162446	+	0.794710i
$652$		0			0
$653$	649.815	+	375.171i	0.995122	+	0.574534i	0.906801	−	0.421558i	$-0.138517\pi$
$653$	649.815	+	375.171i	0.995122	+	0.574534i	0.0883208	+	0.996092i	$0.471850\pi$
$654$		0			0
$655$	238.809	+	413.629i	0.364593	+	0.631494i
$656$		0			0
$657$	5.05346	+	6.68410i	0.00769171	+	0.0101737i
$658$		0			0
$659$	390.298	+	225.339i	0.592258	+	0.341940i	0.765990	−	0.642853i	$-0.222249\pi$
$659$	390.298	+	225.339i	0.592258	+	0.341940i	−0.173732	+	0.984793i	$0.555583\pi$
$660$		0			0
$661$	28.3884			0.0429476			0.0214738	−	0.999769i	$-0.493164\pi$
$661$	28.3884			0.0429476			0.0214738	+	0.999769i	$0.493164\pi$
$662$		0			0
$663$	259.845	+	391.907i	0.391923	+	0.591112i
$664$		0			0
$665$	555.997	+	557.902i	0.836085	+	0.838950i
$666$		0			0
$667$	−453.027	−	784.666i	−0.679201	−	1.17641i
$668$		0			0
$669$	−56.3682	−	909.782i	−0.0842574	−	1.35991i
$670$		0			0
$671$	558.772	−	322.607i	0.832745	−	0.480786i
$672$		0			0
$673$	211.002	−	365.466i	0.313524	−	0.543040i	−0.665599	−	0.746310i	$-0.731824\pi$
$673$	211.002	−	365.466i	0.313524	−	0.543040i	0.979123	+	0.203270i	$0.0651570\pi$
$674$		0			0
$675$	739.974	−	635.045i	1.09626	−	0.940808i
$676$		0			0
$677$		−	884.109i		−	1.30592i	−0.757391	−	0.652961i	$-0.773527\pi$
$677$		−	884.109i		−	1.30592i	0.757391	−	0.652961i	$-0.226473\pi$
$678$		0			0
$679$	277.325	+	1042.12i	0.408431	+	1.53478i
$680$		0			0
$681$	−121.285	+	243.744i	−0.178099	+	0.357921i
$682$		0			0
$683$	99.1010	+	57.2160i	0.145097	+	0.0837716i	0.570791	−	0.821096i	$-0.306637\pi$
$683$	99.1010	+	57.2160i	0.145097	+	0.0837716i	−0.425694	+	0.904867i	$0.639970\pi$
$684$		0			0
$685$	961.321			1.40339
$686$		0			0
$687$	35.9822	+	580.752i	0.0523758	+	0.845345i
$688$		0			0
$689$			613.329i			0.890173i
$690$		0			0
$691$	−488.558			−0.707031			−0.353515	−	0.935429i	$-0.615014\pi$
$691$	−488.558			−0.707031			−0.353515	+	0.935429i	$0.615014\pi$
$692$		0			0
$693$	−491.875	−	384.395i	−0.709776	−	0.554682i
$694$		0			0
$695$		−	59.0435i		−	0.0849547i
$696$		0			0
$697$	−734.610			−1.05396
$698$		0			0
$699$	−528.784	+	1062.68i	−0.756487	+	1.52029i
$700$		0			0
$701$			57.6991i			0.0823098i	0.999153	+	0.0411549i	$0.0131037\pi$
$701$			57.6991i			0.0823098i	−0.999153	+	0.0411549i	$0.986896\pi$
$702$		0			0
$703$	283.268	−	490.635i	0.402942	−	0.697916i
$704$		0			0
$705$	78.7019	+	1270.25i	0.111634	+	1.80177i
$706$		0			0
$707$	67.1059	−	248.740i	0.0949164	−	0.351824i
$708$		0			0
$709$	−624.591			−0.880946			−0.440473	−	0.897766i	$-0.645189\pi$
$709$	−624.591			−0.880946			−0.440473	+	0.897766i	$0.645189\pi$
$710$		0			0
$711$	330.457	−	781.950i	0.464777	−	1.09979i
$712$		0			0
$713$	−832.199	−	480.470i	−1.16718	−	0.673871i
$714$		0			0
$715$	−434.402	−	752.406i	−0.607555	−	1.05232i
$716$		0			0
$717$	−187.435	+	376.683i	−0.261415	+	0.525359i
$718$		0			0
$719$	785.622	−	453.579i	1.09266	−	0.630847i	0.158376	−	0.987379i	$-0.449374\pi$
$719$	785.622	−	453.579i	1.09266	−	0.630847i	0.934283	+	0.356531i	$0.116041\pi$
$720$		0			0
$721$	−135.792	−	510.273i	−0.188339	−	0.707730i
$722$		0			0
$723$	−416.869	−	207.431i	−0.576582	−	0.286903i
$724$		0			0
$725$			856.264i			1.18105i
$726$		0			0
$727$	−43.9060	+	76.0475i	−0.0603934	+	0.104605i	−0.894641	−	0.446785i	$-0.852569\pi$
$727$	−43.9060	+	76.0475i	−0.0603934	+	0.104605i	0.834248	+	0.551390i	$0.185902\pi$
$728$		0			0
$729$	−679.331	+	264.482i	−0.931866	+	0.362802i
$730$		0			0
$731$	862.237	−	497.813i	1.17953	−	0.681003i
$732$		0			0
$733$	570.670	−	988.429i	0.778540	−	1.34847i	−0.154243	−	0.988033i	$-0.549294\pi$
$733$	570.670	−	988.429i	0.778540	−	1.34847i	0.932783	−	0.360438i	$-0.117373\pi$
$734$		0			0
$735$	67.1406	+	1147.23i	0.0913477	+	1.56085i
$736$		0			0
$737$	−918.105	+	530.068i	−1.24573	+	0.719224i
$738$		0			0
$739$	−403.086	+	698.166i	−0.545448	+	0.944744i	0.453130	+	0.891444i	$0.350307\pi$
$739$	−403.086	+	698.166i	−0.545448	+	0.944744i	−0.998579	+	0.0532999i	$0.983026\pi$
$740$		0			0
$741$	−29.9479	−	483.359i	−0.0404155	−	0.652306i
$742$		0			0
$743$	858.109	−	495.429i	1.15492	−	0.666796i	0.204842	−	0.978795i	$-0.434332\pi$
$743$	858.109	−	495.429i	1.15492	−	0.666796i	0.950082	+	0.311999i	$0.100999\pi$
$744$		0			0
$745$	851.391	+	1474.65i	1.14281	+	1.97940i
$746$		0			0
$747$	675.782	−	510.919i	0.904662	−	0.683962i
$748$		0			0
$749$	153.200	−	567.863i	0.204540	−	0.758162i
$750$		0			0
$751$	202.222	−	350.259i	0.269270	−	0.466390i	−0.699403	−	0.714727i	$-0.746551\pi$
$751$	202.222	−	350.259i	0.269270	−	0.466390i	0.968674	+	0.248338i	$0.0798842\pi$
$752$		0			0
$753$	−525.508	−	792.590i	−0.697885	−	1.05258i
$754$		0			0
$755$			1762.25i			2.33411i
$756$		0			0
$757$	322.682			0.426264			0.213132	−	0.977023i	$-0.431634\pi$
$757$	322.682			0.426264			0.213132	+	0.977023i	$0.431634\pi$
$758$		0			0
$759$	946.808	−	627.758i	1.24744	−	0.827086i
$760$		0			0
$761$	−808.228	−	466.630i	−1.06206	−	0.613181i	−0.136059	−	0.990701i	$-0.543444\pi$
$761$	−808.228	−	466.630i	−1.06206	−	0.613181i	−0.926001	+	0.377520i	$0.876777\pi$
$762$		0			0
$763$	−291.812	−	1096.56i	−0.382454	−	1.43717i
$764$		0			0
$765$	975.763	−	121.378i	1.27551	−	0.158665i
$766$		0			0
$767$	−379.609	+	219.167i	−0.494927	+	0.285746i
$768$		0			0
$769$	109.357	+	189.411i	0.142206	+	0.246309i	0.928327	−	0.371764i	$-0.121247\pi$
$769$	109.357	+	189.411i	0.142206	+	0.246309i	−0.786121	+	0.618073i	$0.787914\pi$
$770$		0			0
$771$	−906.368	+	56.1566i	−1.17557	+	0.0728361i
$772$		0			0
$773$	−1184.55	−	683.901i	−1.53241	−	0.884736i	−0.999250	−	0.0387193i	$-0.987672\pi$
$773$	−1184.55	−	683.901i	−1.53241	−	0.884736i	−0.533157	−	0.846016i	$-0.678994\pi$
$774$		0			0
$775$	454.067	+	786.467i	0.585893	+	1.01480i
$776$		0			0
$777$	784.113	−	261.560i	1.00915	−	0.336628i
$778$		0			0
$779$	655.216	+	378.289i	0.841099	+	0.485608i
$780$		0			0
$781$	135.464	+	234.630i	0.173449	+	0.300423i
$782$		0			0
$783$	212.251	−	603.936i	0.271074	−	0.771311i
$784$		0			0
$785$	−724.768	−	418.445i	−0.923271	−	0.533051i
$786$		0			0
$787$	−581.440			−0.738805			−0.369403	−	0.929269i	$-0.620438\pi$
$787$	−581.440			−0.738805			−0.369403	+	0.929269i	$0.620438\pi$
$788$		0			0
$789$	459.581	−	923.609i	0.582486	−	1.17061i
$790$		0			0
$791$	39.1025	−	144.940i	0.0494343	−	0.183237i
$792$		0			0
$793$	365.150	+	632.459i	0.460467	+	0.797552i
$794$		0			0
$795$	1148.23	+	571.352i	1.44432	+	0.718682i
$796$		0			0
$797$	−209.389	+	120.891i	−0.262721	+	0.151682i	−0.625575	−	0.780164i	$-0.715136\pi$
$797$	−209.389	+	120.891i	−0.262721	+	0.151682i	0.362854	+	0.931846i	$0.381802\pi$
$798$		0			0
$799$	−379.189	+	656.775i	−0.474580	+	0.821996i
$800$		0			0
$801$	−23.0330	−	185.163i	−0.0287554	−	0.231165i
$802$		0			0
$803$		−	9.22563i		−	0.0114890i
$804$		0			0
$805$	−2019.08	−	544.715i	−2.50818	−	0.676665i
$806$		0			0
$807$	798.433	−	49.4692i	0.989384	−	0.0613001i
$808$		0			0
$809$	−609.778	−	352.056i	−0.753743	−	0.435174i	0.0733017	−	0.997310i	$-0.476646\pi$
$809$	−609.778	−	352.056i	−0.753743	−	0.435174i	−0.827045	+	0.562136i	$0.809980\pi$
$810$		0			0
$811$	421.013			0.519128			0.259564	−	0.965726i	$-0.416421\pi$
$811$	421.013			0.519128			0.259564	+	0.965726i	$0.416421\pi$
$812$		0			0
$813$	1083.08	+	538.934i	1.33220	+	0.662896i
$814$		0			0
$815$			1902.03i			2.33378i
$816$		0			0
$817$	−1025.40			−1.25508
$818$		0			0
$819$	435.086	−	556.740i	0.531240	−	0.679780i
$820$		0			0
$821$		−	696.026i		−	0.847778i	−0.905714	−	0.423889i	$-0.860665\pi$
$821$		−	696.026i		−	0.847778i	0.905714	−	0.423889i	$-0.139335\pi$
$822$		0			0
$823$	−161.792			−0.196588			−0.0982938	−	0.995157i	$-0.531338\pi$
$823$	−161.792			−0.196588			−0.0982938	+	0.995157i	$0.531338\pi$
$824$		0			0
$825$	−1071.53	+	66.3898i	−1.29883	+	0.0804725i
$826$		0			0
$827$			785.578i			0.949913i	0.880009	+	0.474957i	$0.157536\pi$
$827$			785.578i			0.949913i	−0.880009	+	0.474957i	$0.842464\pi$
$828$		0			0
$829$	−814.931	+	1411.50i	−0.983029	+	1.70266i	−0.332644	+	0.943052i	$0.607941\pi$
$829$	−814.931	+	1411.50i	−0.983029	+	1.70266i	−0.650385	+	0.759604i	$0.725393\pi$
$830$		0			0
$831$	−962.704	−	479.035i	−1.15849	−	0.576456i
$832$		0			0
$833$	−344.422	+	591.871i	−0.413472	+	0.710529i
$834$		0			0
$835$	67.6740			0.0810467
$836$		0			0
$837$	−125.311	−	667.262i	−0.149714	−	0.797207i
$838$		0			0
$839$	−1013.79	−	585.314i	−1.20834	−	0.697633i	−0.245940	−	0.969285i	$-0.579097\pi$
$839$	−1013.79	−	585.314i	−1.20834	−	0.697633i	−0.962396	+	0.271652i	$0.912430\pi$
$840$		0			0
$841$	−139.437	−	241.512i	−0.165799	−	0.287173i
$842$		0			0
$843$	982.635	−	60.8820i	1.16564	−	0.0722207i
$844$		0			0
$845$	−292.546	+	168.902i	−0.346208	+	0.199884i
$846$		0			0
$847$	−41.0690	−	154.327i	−0.0484876	−	0.182204i
$848$		0			0
$849$	−946.003	+	627.224i	−1.11426	+	0.738780i
$850$		0			0
$851$			1504.20i			1.76757i
$852$		0			0
$853$	247.678	−	428.991i	0.290361	−	0.502920i	−0.683534	−	0.729919i	$-0.739558\pi$
$853$	247.678	−	428.991i	0.290361	−	0.502920i	0.973895	+	0.226999i	$0.0728913\pi$
$854$		0			0
$855$	−932.810	−	394.211i	−1.09101	−	0.461066i
$856$		0			0
$857$	−639.972	+	369.488i	−0.746759	+	0.431141i	−0.824522	−	0.565831i	$-0.808556\pi$
$857$	−639.972	+	369.488i	−0.746759	+	0.431141i	0.0777629	+	0.996972i	$0.475222\pi$
$858$		0			0
$859$	−360.760	+	624.855i	−0.419977	+	0.727421i	−0.995937	−	0.0900568i	$-0.971295\pi$
$859$	−360.760	+	624.855i	−0.419977	+	0.727421i	0.575960	+	0.817478i	$0.304628\pi$
$860$		0			0
$861$	349.299	+	1047.14i	0.405690	+	1.21619i
$862$		0			0
$863$	−756.958	+	437.030i	−0.877124	+	0.506408i	−0.869709	−	0.493565i	$-0.835694\pi$
$863$	−756.958	+	437.030i	−0.877124	+	0.506408i	−0.00741492	+	0.999973i	$0.502360\pi$
$864$		0			0
$865$	678.939	−	1175.96i	0.784900	−	1.35949i
$866$		0			0
$867$	−251.641	−	125.215i	−0.290243	−	0.144423i
$868$		0			0
$869$	−809.421	+	467.319i	−0.931439	+	0.537767i
$870$		0			0
$871$	−599.969	−	1039.18i	−0.688828	−	1.19309i
$872$		0			0
$873$	−836.169	−	1105.98i	−0.957810	−	1.26688i
$874$		0			0
$875$	429.372	+	430.844i	0.490711	+	0.492393i
$876$		0			0
$877$	276.070	−	478.167i	0.314789	−	0.545230i	−0.664604	−	0.747196i	$-0.731400\pi$
$877$	276.070	−	478.167i	0.314789	−	0.545230i	0.979393	+	0.201966i	$0.0647331\pi$
$878$		0			0
$879$	530.146	−	1065.42i	0.603124	−	1.21208i
$880$		0			0
$881$			665.872i			0.755813i	0.925844	+	0.377907i	$0.123356\pi$
$881$			665.872i			0.755813i	−0.925844	+	0.377907i	$0.876644\pi$
$882$		0			0
$883$	−1122.90			−1.27169			−0.635843	−	0.771819i	$-0.719347\pi$
$883$	−1122.90			−1.27169			−0.635843	+	0.771819i	$0.719347\pi$
$884$		0			0
$885$	56.6819	+	914.846i	0.0640473	+	1.03372i
$886$		0			0
$887$	8.18965	+	4.72830i	0.00923298	+	0.00533066i	0.504609	−	0.863348i	$-0.331637\pi$
$887$	8.18965	+	4.72830i	0.00923298	+	0.00533066i	−0.495376	+	0.868678i	$0.664970\pi$
$888$		0			0
$889$	266.385	−	265.475i	0.299646	−	0.298623i
$890$		0			0
$891$	772.225	+	218.786i	0.866694	+	0.245551i
$892$		0			0
$893$	676.416	−	390.529i	0.757465	−	0.437322i
$894$		0			0
$895$	−649.618	−	1125.17i	−0.725830	−	1.25718i
$896$		0			0
$897$	710.542	+	1071.67i	0.792132	+	1.19472i
$898$		0			0
$899$	516.305	+	298.089i	0.574310	+	0.331578i
$900$		0			0
$901$	382.122	+	661.855i	0.424109	+	0.734579i
$902$		0			0
$903$	−1119.58	−	992.360i	−1.23985	−	1.09896i
$904$		0			0
$905$	314.432	+	181.537i	0.347438	+	0.200594i
$906$		0			0
$907$	127.953	+	221.621i	0.141073	+	0.244345i	0.927901	−	0.372827i	$-0.121611\pi$
$907$	127.953	+	221.621i	0.141073	+	0.244345i	−0.786828	+	0.617172i	$0.788278\pi$
$908$		0			0
$909$	40.8892	+	328.709i	0.0449826	+	0.361616i
$910$		0			0
$911$	−762.662	−	440.323i	−0.837170	−	0.483340i	0.0191314	−	0.999817i	$-0.493910\pi$
$911$	−762.662	−	440.323i	−0.837170	−	0.483340i	−0.856301	+	0.516477i	$0.827243\pi$
$912$		0			0
$913$	−932.738			−1.02162
$914$		0			0
$915$	1524.20	−	94.4365i	1.66580	−	0.103209i
$916$		0			0
$917$	413.281	−	109.981i	0.450688	−	0.119936i
$918$		0			0
$919$	156.040	+	270.269i	0.169793	+	0.294090i	0.938347	−	0.345695i	$-0.112357\pi$
$919$	156.040	+	270.269i	0.169793	+	0.294090i	−0.768554	+	0.639785i	$0.779023\pi$
$920$		0			0
$921$	746.337	−	494.840i	0.810355	−	0.537286i
$922$		0			0
$923$	−265.572	+	153.328i	−0.287727	+	0.166119i
$924$		0			0
$925$	710.772	−	1231.09i	0.768402	−	1.33091i
$926$		0			0
$927$	409.430	+	541.545i	0.441672	+	0.584191i
$928$		0			0
$929$		−	823.181i		−	0.886094i	−0.896499	−	0.443047i	$-0.853898\pi$
$929$		−	823.181i		−	0.886094i	0.896499	−	0.443047i	$-0.146102\pi$
$930$		0			0
$931$	611.983	−	350.543i	0.657340	−	0.376523i
$932$		0			0
$933$	−559.766	−	844.261i	−0.599964	−	0.904888i
$934$		0			0
$935$	−937.544	−	541.291i	−1.00272	−	0.578921i
$936$		0			0
$937$	−1596.78			−1.70414			−0.852070	−	0.523428i	$-0.824653\pi$
$937$	−1596.78			−1.70414			−0.852070	+	0.523428i	$0.824653\pi$
$938$		0			0
$939$	674.422	−	447.159i	0.718234	−	0.476208i
$940$		0			0
$941$		−	643.859i		−	0.684229i	−0.939658	−	0.342114i	$-0.888857\pi$
$941$		−	643.859i		−	0.684229i	0.939658	−	0.342114i	$-0.111143\pi$
$942$		0			0
$943$	−2008.78			−2.13020
$944$		0			0
$945$	−636.982	−	1333.17i	−0.674055	−	1.41077i
$946$		0			0
$947$			983.962i			1.03903i	0.854461	+	0.519515i	$0.173887\pi$
$947$			983.962i			1.03903i	−0.854461	+	0.519515i	$0.826113\pi$
$948$		0			0
$949$	10.4422			0.0110034
$950$		0			0
$951$	229.035	+	345.439i	0.240836	+	0.363238i
$952$		0			0
$953$			950.170i			0.997030i	0.866881	+	0.498515i	$0.166121\pi$
$953$			950.170i			0.997030i	−0.866881	+	0.498515i	$0.833879\pi$
$954$		0			0
$955$	963.223	−	1668.35i	1.00861	−	1.74697i
$956$		0			0
$957$	−587.410	+	389.468i	−0.613804	+	0.406967i
$958$		0			0
$959$	224.208	−	831.066i	0.233794	−	0.866597i
$960$		0			0
$961$	−328.707			−0.342047
$962$		0			0
$963$	93.3484	+	750.430i	0.0969350	+	0.779262i
$964$		0			0
$965$	412.988	+	238.439i	0.427967	+	0.247087i
$966$		0			0
$967$	567.995	+	983.796i	0.587378	+	1.01737i	0.994574	+	0.104028i	$0.0331733\pi$
$967$	567.995	+	983.796i	0.587378	+	1.01737i	−0.407196	+	0.913341i	$0.633493\pi$
$968$		0			0
$969$	−333.465	−	502.944i	−0.344133	−	0.519034i
$970$		0			0
$971$	46.3049	−	26.7342i	0.0476879	−	0.0275326i	−0.475967	−	0.879463i	$-0.657902\pi$
$971$	46.3049	−	26.7342i	0.0476879	−	0.0275326i	0.523654	+	0.851931i	$0.324568\pi$
$972$		0			0
$973$	−51.0434	−	13.7707i	−0.0524598	−	0.0141528i
$974$		0			0
$975$	−75.1448	−	1212.84i	−0.0770716	−	1.24394i
$976$		0			0
$977$			57.2767i			0.0586251i	0.999570	+	0.0293125i	$0.00933180\pi$
$977$			57.2767i			0.0586251i	−0.999570	+	0.0293125i	$0.990668\pi$
$978$		0			0
$979$	−102.717	+	177.910i	−0.104920	+	0.181727i
$980$		0			0
$981$	879.850	+	1163.76i	0.896891	+	1.18630i
$982$		0			0
$983$	−182.596	+	105.422i	−0.185754	+	0.107245i	−0.589993	−	0.807408i	$-0.700870\pi$
$983$	−182.596	+	105.422i	−0.185754	+	0.107245i	0.404239	+	0.914653i	$0.367536\pi$
$984$		0			0
$985$	247.580	−	428.822i	0.251351	−	0.435352i
$986$		0			0
$987$	1116.49	+	228.221i	1.13120	+	0.231227i
$988$		0			0
$989$	2357.78	−	1361.26i	2.38400	−	1.37640i
$990$		0			0
$991$	472.405	−	818.229i	0.476695	−	0.825660i	−0.522948	−	0.852364i	$-0.675168\pi$
$991$	472.405	−	818.229i	0.476695	−	0.825660i	0.999643	+	0.0267044i	$0.00850128\pi$
$992$		0			0
$993$	−292.277	+	193.787i	−0.294337	+	0.195153i
$994$		0			0
$995$	−940.416	+	542.949i	−0.945142	+	0.545678i
$996$		0			0
$997$	−107.050	−	185.416i	−0.107372	−	0.185974i	0.807333	−	0.590096i	$-0.200910\pi$
$997$	−107.050	−	185.416i	−0.107372	−	0.185974i	−0.914705	+	0.404123i	$0.867577\pi$
$998$		0			0
$999$	−806.482	+	692.123i	−0.807290	+	0.692816i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.3.bh.a.137.14	yes	32
3.2	odd	2		756.3.bh.a.305.16		32
7.2	even	3		252.3.m.a.65.9	✓	32
9.4	even	3		756.3.m.a.557.16		32
9.5	odd	6		252.3.m.a.221.9	yes	32
21.2	odd	6		756.3.m.a.737.1		32
63.23	odd	6	inner	252.3.bh.a.149.14	yes	32
63.58	even	3		756.3.bh.a.233.16		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.3.m.a.65.9	✓	32	7.2	even	3
252.3.m.a.221.9	yes	32	9.5	odd	6
252.3.bh.a.137.14	yes	32	1.1	even	1	trivial
252.3.bh.a.149.14	yes	32	63.23	odd	6	inner
756.3.m.a.557.16		32	9.4	even	3
756.3.m.a.737.1		32	21.2	odd	6
756.3.bh.a.233.16		32	63.58	even	3
756.3.bh.a.305.16		32	3.2	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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	252.bh (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.50034 - 1.65779i) q^{3} +(-6.77026 - 3.90881i) q^{5} +(-4.95821 + 4.94127i) q^{7} +(3.50345 - 8.29011i) q^{9} +O(q^{10})\)	\(q+(2.50034 - 1.65779i) q^{3} +(-6.77026 - 3.90881i) q^{5} +(-4.95821 + 4.94127i) q^{7} +(3.50345 - 8.29011i) q^{9} +(-8.58135 + 4.95444i) q^{11} +(-5.60780 - 9.71299i) q^{13} +(-23.4080 + 1.45031i) q^{15} +(-12.1030 - 6.98765i) q^{17} +(7.19662 + 12.4649i) q^{19} +(-4.20562 + 20.5746i) q^{21} +(-33.0954 - 19.1077i) q^{23} +(18.0576 + 31.2767i) q^{25} +(-4.98344 - 26.5361i) q^{27} +(20.5328 + 11.8546i) q^{29} +25.1454 q^{31} +(-13.2429 + 26.6139i) q^{33} +(52.8829 - 14.0730i) q^{35} +(-19.6806 - 34.0879i) q^{37} +(-30.1235 - 14.9893i) q^{39} +(45.5225 - 26.2824i) q^{41} +(-35.6209 + 61.6972i) q^{43} +(-56.1237 + 42.4319i) q^{45} -54.2656i q^{47} +(0.167642 - 48.9997i) q^{49} +(-41.8457 + 2.59267i) q^{51} +(-47.3589 - 27.3427i) q^{53} +77.4639 q^{55} +(38.6582 + 19.2361i) q^{57} -39.0826i q^{59} -65.1147 q^{61} +(23.5928 + 58.4156i) q^{63} +87.6793i q^{65} +106.988 q^{67} +(-114.427 + 7.08962i) q^{69} -27.3419i q^{71} +(-0.465523 + 0.806310i) q^{73} +(97.0007 + 48.2668i) q^{75} +(18.0668 - 66.9679i) q^{77} +94.3233 q^{79} +(-56.4517 - 58.0879i) q^{81} +(81.5203 + 47.0658i) q^{83} +(54.6269 + 94.6165i) q^{85} +(70.9914 - 4.39848i) q^{87} +(17.9546 - 10.3661i) q^{89} +(75.7992 + 20.4494i) q^{91} +(62.8722 - 41.6859i) q^{93} -112.521i q^{95} +(77.0276 - 133.416i) q^{97} +(11.0085 + 88.4979i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - q^{7} - 14 q^{9}+O(q^{10}) \) 32 * q - q^7 - 14 * q^9	\( 32 q - q^{7} - 14 q^{9} + 18 q^{11} - 5 q^{13} - 29 q^{15} + 27 q^{17} - 14 q^{19} - 8 q^{21} - 45 q^{23} + 80 q^{25} + 45 q^{27} + 36 q^{29} + 16 q^{31} + 116 q^{33} + 45 q^{35} - 11 q^{37} + 55 q^{39} + 72 q^{41} + 16 q^{43} - 154 q^{45} - 37 q^{49} - 133 q^{51} - 180 q^{53} - 24 q^{55} + 57 q^{57} + 82 q^{61} - 99 q^{63} + 70 q^{67} - 97 q^{69} - 98 q^{73} - 149 q^{75} - 135 q^{77} + 142 q^{79} - 98 q^{81} - 30 q^{85} - 86 q^{87} + 189 q^{89} + 109 q^{91} + 109 q^{93} + 19 q^{97} - 101 q^{99}+O(q^{100}) \) 32 * q - q^7 - 14 * q^9 + 18 * q^11 - 5 * q^13 - 29 * q^15 + 27 * q^17 - 14 * q^19 - 8 * q^21 - 45 * q^23 + 80 * q^25 + 45 * q^27 + 36 * q^29 + 16 * q^31 + 116 * q^33 + 45 * q^35 - 11 * q^37 + 55 * q^39 + 72 * q^41 + 16 * q^43 - 154 * q^45 - 37 * q^49 - 133 * q^51 - 180 * q^53 - 24 * q^55 + 57 * q^57 + 82 * q^61 - 99 * q^63 + 70 * q^67 - 97 * q^69 - 98 * q^73 - 149 * q^75 - 135 * q^77 + 142 * q^79 - 98 * q^81 - 30 * q^85 - 86 * q^87 + 189 * q^89 + 109 * q^91 + 109 * q^93 + 19 * q^97 - 101 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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