LMFDB - Embedded newform 360.2.bi.b.49.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [360,2,Mod(49,360)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(360, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2, 3]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("360.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 360 = 2^{3} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	360.bi (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:	$2.87461447277$
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			49.16
Character	$\chi$	$=$	360.49
Dual form			360.2.bi.b.169.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.72704 - 0.131617i) q^{3} +(-1.06189 - 1.96784i) q^{5} +(1.19102 - 0.687633i) q^{7} +(2.96535 - 0.454616i) q^{9} +O(q^{10})$	\(q+(1.72704 - 0.131617i) q^{3} +(-1.06189 - 1.96784i) q^{5} +(1.19102 - 0.687633i) q^{7} +(2.96535 - 0.454616i) q^{9} +(-0.00579778 - 0.0100420i) q^{11} +(-0.919334 - 0.530778i) q^{13} +(-2.09292 - 3.25878i) q^{15} -1.57910i q^{17} +6.38234 q^{19} +(1.96643 - 1.34433i) q^{21} +(-6.37844 - 3.68260i) q^{23} +(-2.74480 + 4.17924i) q^{25} +(5.06146 - 1.17543i) q^{27} +(2.66231 + 4.61126i) q^{29} +(1.15651 - 2.00314i) q^{31} +(-0.0113347 - 0.0165800i) q^{33} +(-2.61787 - 1.61354i) q^{35} +10.8828i q^{37} +(-1.65759 - 0.795676i) q^{39} +(-4.09133 + 7.08638i) q^{41} +(-2.93252 + 1.69309i) q^{43} +(-4.04348 - 5.35260i) q^{45} +(4.60966 - 2.66139i) q^{47} +(-2.55432 + 4.42422i) q^{49} +(-0.207836 - 2.72717i) q^{51} -1.27370i q^{53} +(-0.0136046 + 0.0220726i) q^{55} +(11.0226 - 0.840025i) q^{57} +(3.39712 - 5.88399i) q^{59} +(-4.29148 - 7.43306i) q^{61} +(3.21917 - 2.58053i) q^{63} +(-0.0682594 + 2.37273i) q^{65} +(8.16967 + 4.71676i) q^{67} +(-11.5005 - 5.52049i) q^{69} -16.4442 q^{71} +8.32462i q^{73} +(-4.19033 + 7.57899i) q^{75} +(-0.0138105 - 0.00797348i) q^{77} +(3.86663 + 6.69719i) q^{79} +(8.58665 - 2.69620i) q^{81} +(-4.67610 + 2.69975i) q^{83} +(-3.10741 + 1.67682i) q^{85} +(5.20484 + 7.61343i) q^{87} -12.6835 q^{89} -1.45992 q^{91} +(1.73370 - 3.61172i) q^{93} +(-6.77732 - 12.5594i) q^{95} +(0.0741723 - 0.0428234i) q^{97} +(-0.0217577 - 0.0271425i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) $ 32 * q - 2 * q^5 + 4 * q^9	$ 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) $ 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/360\mathbb{Z}\right)^\times$.

$n$	$181$	$217$	$271$	$281$
$\chi(n)$	$1$	$-1$	$1$	$e\left(\frac{1}{3}\right)$

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
$3$	1.72704	−	0.131617i	0.997109	−	0.0759891i
$3$	1.72704	−	0.131617i	0.997109	−	0.0759891i
$4$		0			0
$5$	−1.06189	−	1.96784i	−0.474889	−	0.880045i
$5$	−1.06189	−	1.96784i	−0.474889	−	0.880045i
$6$		0			0
$7$	1.19102	−	0.687633i	0.450161	−	0.259901i	−0.257737	−	0.966215i	$-0.582977\pi$
$7$	1.19102	−	0.687633i	0.450161	−	0.259901i	0.707898	+	0.706314i	$0.249643\pi$
$8$		0			0
$9$	2.96535	−	0.454616i	0.988451	−	0.151539i
$10$		0			0
$11$	−0.00579778	−	0.0100420i	−0.00174810	−	0.00302779i	0.865150	−	0.501513i	$-0.167223\pi$
$11$	−0.00579778	−	0.0100420i	−0.00174810	−	0.00302779i	−0.866898	+	0.498485i	$0.833890\pi$
$12$		0			0
$13$	−0.919334	−	0.530778i	−0.254977	−	0.147211i	0.367064	−	0.930196i	$-0.380363\pi$
$13$	−0.919334	−	0.530778i	−0.254977	−	0.147211i	−0.622041	+	0.782984i	$0.713696\pi$
$14$		0			0
$15$	−2.09292	−	3.25878i	−0.540390	−	0.841415i
$16$		0			0
$17$		−	1.57910i		−	0.382987i	−0.981494	−	0.191494i	$-0.938667\pi$
$17$		−	1.57910i		−	0.382987i	0.981494	−	0.191494i	$-0.0613331\pi$
$18$		0			0
$19$	6.38234			1.46421			0.732105	−	0.681192i	$-0.238538\pi$
$19$	6.38234			1.46421			0.732105	+	0.681192i	$0.238538\pi$
$20$		0			0
$21$	1.96643	−	1.34433i	0.429110	−	0.293357i
$22$		0			0
$23$	−6.37844	−	3.68260i	−1.33000	−	0.767874i	−0.344698	−	0.938714i	$-0.612019\pi$
$23$	−6.37844	−	3.68260i	−1.33000	−	0.767874i	−0.985299	+	0.170839i	$0.945352\pi$
$24$		0			0
$25$	−2.74480	+	4.17924i	−0.548960	+	0.835849i
$26$		0			0
$27$	5.06146	−	1.17543i	0.974078	−	0.226212i
$28$		0			0
$29$	2.66231	+	4.61126i	0.494379	+	0.856289i	0.999979	−	0.00647886i	$-0.00206230\pi$
$29$	2.66231	+	4.61126i	0.494379	+	0.856289i	−0.505600	+	0.862768i	$0.668729\pi$
$30$		0			0
$31$	1.15651	−	2.00314i	0.207716	−	0.359774i	−0.743279	−	0.668982i	$-0.766730\pi$
$31$	1.15651	−	2.00314i	0.207716	−	0.359774i	0.950995	+	0.309207i	$0.100064\pi$
$32$		0			0
$33$	−0.0113347	−	0.0165800i	−0.00197312	−	0.00288620i
$34$		0			0
$35$	−2.61787	−	1.61354i	−0.442501	−	0.272738i
$36$		0			0
$37$			10.8828i			1.78912i	0.446948	+	0.894560i	$0.352511\pi$
$37$			10.8828i			1.78912i	−0.446948	+	0.894560i	$0.647489\pi$
$38$		0			0
$39$	−1.65759	−	0.795676i	−0.265427	−	0.127410i
$40$		0			0
$41$	−4.09133	+	7.08638i	−0.638958	+	1.10671i	0.346704	+	0.937975i	$0.387301\pi$
$41$	−4.09133	+	7.08638i	−0.638958	+	1.10671i	−0.985662	+	0.168733i	$0.946033\pi$
$42$		0			0
$43$	−2.93252	+	1.69309i	−0.447204	+	0.258194i	−0.706649	−	0.707564i	$-0.749794\pi$
$43$	−2.93252	+	1.69309i	−0.447204	+	0.258194i	0.259444	+	0.965758i	$0.416461\pi$
$44$		0			0
$45$	−4.04348	−	5.35260i	−0.602766	−	0.797918i
$46$		0			0
$47$	4.60966	−	2.66139i	0.672388	−	0.388203i	−0.124593	−	0.992208i	$-0.539763\pi$
$47$	4.60966	−	2.66139i	0.672388	−	0.388203i	0.796981	+	0.604005i	$0.206429\pi$
$48$		0			0
$49$	−2.55432	+	4.42422i	−0.364903	+	0.632031i
$50$		0			0
$51$	−0.207836	−	2.72717i	−0.0291028	−	0.381880i
$52$		0			0
$53$		−	1.27370i		−	0.174956i	−0.996166	−	0.0874782i	$-0.972119\pi$
$53$		−	1.27370i		−	0.174956i	0.996166	−	0.0874782i	$-0.0278808\pi$
$54$		0			0
$55$	−0.0136046	+	0.0220726i	−0.00183444	+	0.00297627i
$56$		0			0
$57$	11.0226	−	0.840025i	1.45998	−	0.111264i
$58$		0			0
$59$	3.39712	−	5.88399i	0.442268	−	0.766031i	−0.555589	−	0.831457i	$-0.687507\pi$
$59$	3.39712	−	5.88399i	0.442268	−	0.766031i	0.997857	+	0.0654262i	$0.0208407\pi$
$60$		0			0
$61$	−4.29148	−	7.43306i	−0.549468	−	0.951706i	−0.998311	−	0.0580954i	$-0.981497\pi$
$61$	−4.29148	−	7.43306i	−0.549468	−	0.951706i	0.448843	−	0.893610i	$-0.351836\pi$
$62$		0			0
$63$	3.21917	−	2.58053i	0.405578	−	0.325116i
$64$		0			0
$65$	−0.0682594	+	2.37273i	−0.00846654	+	0.294301i
$66$		0			0
$67$	8.16967	+	4.71676i	0.998084	+	0.576244i	0.907681	−	0.419661i	$-0.137851\pi$
$67$	8.16967	+	4.71676i	0.998084	+	0.576244i	0.0904031	+	0.995905i	$0.471184\pi$
$68$		0			0
$69$	−11.5005	−	5.52049i	−1.38450	−	0.664589i
$70$		0			0
$71$	−16.4442			−1.95157			−0.975786	−	0.218727i	$-0.929809\pi$
$71$	−16.4442			−1.95157			−0.975786	+	0.218727i	$0.929809\pi$
$72$		0			0
$73$			8.32462i			0.974323i	0.873312	+	0.487162i	$0.161968\pi$
$73$			8.32462i			0.974323i	−0.873312	+	0.487162i	$0.838032\pi$
$74$		0			0
$75$	−4.19033	+	7.57899i	−0.483857	+	0.875147i
$76$		0			0
$77$	−0.0138105	−	0.00797348i	−0.00157385	−	0.000908663i
$78$		0			0
$79$	3.86663	+	6.69719i	0.435030	+	0.753493i	0.997298	−	0.0734615i	$-0.0234046\pi$
$79$	3.86663	+	6.69719i	0.435030	+	0.753493i	−0.562269	+	0.826955i	$0.690071\pi$
$80$		0			0
$81$	8.58665	−	2.69620i	0.954072	−	0.299577i
$82$		0			0
$83$	−4.67610	+	2.69975i	−0.513269	+	0.296336i	−0.734176	−	0.678959i	$-0.762431\pi$
$83$	−4.67610	+	2.69975i	−0.513269	+	0.296336i	0.220907	+	0.975295i	$0.429098\pi$
$84$		0			0
$85$	−3.10741	+	1.67682i	−0.337046	+	0.181877i
$86$		0			0
$87$	5.20484	+	7.61343i	0.558018	+	0.816246i
$88$		0			0
$89$	−12.6835			−1.34445			−0.672223	−	0.740349i	$-0.734660\pi$
$89$	−12.6835			−1.34445			−0.672223	+	0.740349i	$0.734660\pi$
$90$		0			0
$91$	−1.45992			−0.153041
$92$		0			0
$93$	1.73370	−	3.61172i	0.179776	−	0.374518i
$94$		0			0
$95$	−6.77732	−	12.5594i	−0.695338	−	1.28857i
$96$		0			0
$97$	0.0741723	−	0.0428234i	0.00753106	−	0.00434806i	−0.496230	−	0.868191i	$-0.665283\pi$
$97$	0.0741723	−	0.0428234i	0.00753106	−	0.00434806i	0.503761	+	0.863843i	$0.331949\pi$
$98$		0			0
$99$	−0.0217577	−	0.0271425i	−0.00218673	−	0.00272792i
$100$		0			0
$101$	7.22526	+	12.5145i	0.718940	+	1.24524i	0.961420	+	0.275085i	$0.0887058\pi$
$101$	7.22526	+	12.5145i	0.718940	+	1.24524i	−0.242480	+	0.970156i	$0.577961\pi$
$102$		0			0
$103$	−4.27682	−	2.46922i	−0.421407	−	0.243300i	0.274272	−	0.961652i	$-0.411563\pi$
$103$	−4.27682	−	2.46922i	−0.421407	−	0.243300i	−0.695679	+	0.718353i	$0.744897\pi$
$104$		0			0
$105$	−4.73355	−	2.44210i	−0.461947	−	0.238325i
$106$		0			0
$107$			13.5968i			1.31445i	0.753693	+	0.657227i	$0.228271\pi$
$107$			13.5968i			1.31445i	−0.753693	+	0.657227i	$0.771729\pi$
$108$		0			0
$109$	−9.92265			−0.950417			−0.475209	−	0.879873i	$-0.657627\pi$
$109$	−9.92265			−0.950417			−0.475209	+	0.879873i	$0.657627\pi$
$110$		0			0
$111$	1.43236	+	18.7951i	0.135954	+	1.78395i
$112$		0			0
$113$	−2.19397	−	1.26669i	−0.206391	−	0.119160i	0.393242	−	0.919435i	$-0.371354\pi$
$113$	−2.19397	−	1.26669i	−0.206391	−	0.119160i	−0.599633	+	0.800275i	$0.704687\pi$
$114$		0			0
$115$	−0.473592	+	16.4623i	−0.0441626	+	1.53511i
$116$		0			0
$117$	−2.96745	−	1.15600i	−0.274341	−	0.106872i
$118$		0			0
$119$	−1.08584	−	1.88073i	−0.0995387	−	0.172406i
$120$		0			0
$121$	5.49993	−	9.52616i	0.499994	−	0.866015i
$122$		0			0
$123$	−6.13321	+	12.7770i	−0.553013	+	1.15206i
$124$		0			0
$125$	11.1388	+	0.963456i	0.996280	+	0.0861742i
$126$		0			0
$127$		−	18.2790i		−	1.62200i	−0.585046	−	0.811000i	$-0.698924\pi$
$127$		−	18.2790i		−	1.62200i	0.585046	−	0.811000i	$-0.301076\pi$
$128$		0			0
$129$	−4.84174	+	3.31000i	−0.426291	+	0.291430i
$130$		0			0
$131$	1.64613	−	2.85119i	0.143823	−	0.249109i	−0.785110	−	0.619356i	$-0.787394\pi$
$131$	1.64613	−	2.85119i	0.143823	−	0.249109i	0.928933	+	0.370247i	$0.120727\pi$
$132$		0			0
$133$	7.60147	−	4.38871i	0.659131	−	0.380549i
$134$		0			0
$135$	−7.68775	−	8.71197i	−0.661656	−	0.749807i
$136$		0			0
$137$	7.56464	−	4.36744i	0.646290	−	0.373136i	−0.140743	−	0.990046i	$-0.544949\pi$
$137$	7.56464	−	4.36744i	0.646290	−	0.373136i	0.787034	+	0.616910i	$0.211616\pi$
$138$		0			0
$139$	3.30750	−	5.72876i	0.280539	−	0.485908i	−0.690979	−	0.722875i	$-0.742820\pi$
$139$	3.30750	−	5.72876i	0.280539	−	0.485908i	0.971518	+	0.236968i	$0.0761535\pi$
$140$		0			0
$141$	7.61079	−	5.20304i	0.640944	−	0.438175i
$142$		0			0
$143$			0.0123093i			0.00102936i
$144$		0			0
$145$	6.24716	−	10.1356i	0.518798	−	0.841718i
$146$		0			0
$147$	−3.82912	+	7.97700i	−0.315821	+	0.657932i
$148$		0			0
$149$	3.11139	−	5.38909i	0.254895	−	0.441491i	−0.709972	−	0.704230i	$-0.751292\pi$
$149$	3.11139	−	5.38909i	0.254895	−	0.441491i	0.964867	+	0.262739i	$0.0846257\pi$
$150$		0			0
$151$	−2.46299	−	4.26602i	−0.200435	−	0.347164i	0.748233	−	0.663436i	$-0.230902\pi$
$151$	−2.46299	−	4.26602i	−0.200435	−	0.347164i	−0.948669	+	0.316271i	$0.897569\pi$
$152$		0			0
$153$	−0.717883	−	4.68258i	−0.0580374	−	0.378564i
$154$		0			0
$155$	−5.16994	−	0.148731i	−0.415260	−	0.0119463i
$156$		0			0
$157$	8.14939	+	4.70505i	0.650392	+	0.375504i	0.788606	−	0.614898i	$-0.210803\pi$
$157$	8.14939	+	4.70505i	0.650392	+	0.375504i	−0.138214	+	0.990402i	$0.544136\pi$
$158$		0			0
$159$	−0.167641	−	2.19974i	−0.0132948	−	0.174450i
$160$		0			0
$161$	−10.1291			−0.798285
$162$		0			0
$163$			0.333348i			0.0261098i	0.999915	+	0.0130549i	$0.00415562\pi$
$163$			0.333348i			0.0261098i	−0.999915	+	0.0130549i	$0.995844\pi$
$164$		0			0
$165$	−0.0205906	+	0.0399109i	−0.00160297	+	0.00310706i
$166$		0			0
$167$	5.75260	+	3.32126i	0.445150	+	0.257007i	0.705780	−	0.708432i	$-0.250597\pi$
$167$	5.75260	+	3.32126i	0.445150	+	0.257007i	−0.260630	+	0.965439i	$0.583930\pi$
$168$		0			0
$169$	−5.93655	−	10.2824i	−0.456658	−	0.790954i
$170$		0			0
$171$	18.9259	−	2.90152i	1.44730	−	0.221885i
$172$		0			0
$173$	17.7457	−	10.2455i	1.34918	−	0.778952i	0.361050	−	0.932546i	$-0.382418\pi$
$173$	17.7457	−	10.2455i	1.34918	−	0.778952i	0.988134	+	0.153595i	$0.0490850\pi$
$174$		0			0
$175$	−0.395314	+	6.86496i	−0.0298829	+	0.518942i
$176$		0			0
$177$	5.09255	−	10.6090i	0.382779	−	0.797423i
$178$		0			0
$179$	16.0795			1.20184			0.600919	−	0.799310i	$-0.294802\pi$
$179$	16.0795			1.20184			0.600919	+	0.799310i	$0.294802\pi$
$180$		0			0
$181$	−10.6942			−0.794891			−0.397445	−	0.917626i	$-0.630103\pi$
$181$	−10.6942			−0.794891			−0.397445	+	0.917626i	$0.630103\pi$
$182$		0			0
$183$	−8.38989	−	12.2724i	−0.620198	−	0.907201i
$184$		0			0
$185$	21.4156	−	11.5563i	1.57451	−	0.849634i
$186$		0			0
$187$	−0.0158574	+	0.00915525i	−0.00115960	+	0.000669498i
$188$		0			0
$189$	5.22001	−	4.88038i	0.379700	−	0.354996i
$190$		0			0
$191$	8.16174	+	14.1366i	0.590563	+	1.02289i	0.994157	+	0.107947i	$0.0344277\pi$
$191$	8.16174	+	14.1366i	0.590563	+	1.02289i	−0.403594	+	0.914938i	$0.632239\pi$
$192$		0			0
$193$	−18.0526	−	10.4227i	−1.29945	−	0.750240i	−0.319144	−	0.947706i	$-0.603395\pi$
$193$	−18.0526	−	10.4227i	−1.29945	−	0.750240i	−0.980310	+	0.197466i	$0.936729\pi$
$194$		0			0
$195$	0.194404	+	4.10679i	0.0139216	+	0.294093i
$196$		0			0
$197$		−	4.80666i		−	0.342460i	−0.985231	−	0.171230i	$-0.945226\pi$
$197$		−	4.80666i		−	0.342460i	0.985231	−	0.171230i	$-0.0547742\pi$
$198$		0			0
$199$	7.79500			0.552573			0.276286	−	0.961075i	$-0.410896\pi$
$199$	7.79500			0.552573			0.276286	+	0.961075i	$0.410896\pi$
$200$		0			0
$201$	14.7302	+	7.07078i	1.03899	+	0.498734i
$202$		0			0
$203$	6.34170	+	3.66138i	0.445100	+	0.256979i
$204$		0			0
$205$	18.2894	+	0.526155i	1.27739	+	0.0367483i
$206$		0			0
$207$	−20.5885	−	8.02046i	−1.43100	−	0.557460i
$208$		0			0
$209$	−0.0370034	−	0.0640918i	−0.00255958	−	0.00443332i
$210$		0			0
$211$	10.8034	−	18.7121i	0.743740	−	1.28820i	−0.207041	−	0.978332i	$-0.566383\pi$
$211$	10.8034	−	18.7121i	0.743740	−	1.28820i	0.950781	−	0.309863i	$-0.100283\pi$
$212$		0			0
$213$	−28.3999	+	2.16434i	−1.94593	+	0.148298i
$214$		0			0
$215$	6.44572	+	3.97286i	0.439595	+	0.270947i
$216$		0			0
$217$		−	3.18102i		−	0.215942i
$218$		0			0
$219$	1.09566	+	14.3770i	0.0740379	+	0.971506i
$220$		0			0
$221$	−0.838149	+	1.45172i	−0.0563800	+	0.0976531i
$222$		0			0
$223$	8.59672	−	4.96332i	0.575679	−	0.332368i	−0.183735	−	0.982976i	$-0.558819\pi$
$223$	8.59672	−	4.96332i	0.575679	−	0.332368i	0.759414	+	0.650607i	$0.225486\pi$
$224$		0			0
$225$	−6.23935	+	13.6408i	−0.415957	+	0.909384i
$226$		0			0
$227$	1.23057	−	0.710467i	0.0816755	−	0.0471554i	−0.458606	−	0.888640i	$-0.651651\pi$
$227$	1.23057	−	0.710467i	0.0816755	−	0.0471554i	0.540282	+	0.841484i	$0.318318\pi$
$228$		0			0
$229$	−13.7536	+	23.8220i	−0.908866	+	1.57420i	−0.0932237	+	0.995645i	$0.529717\pi$
$229$	−13.7536	+	23.8220i	−0.908866	+	1.57420i	−0.815642	+	0.578557i	$0.803616\pi$
$230$		0			0
$231$	−0.0249007	−	0.0119529i	−0.00163835	−	0.000786440i
$232$		0			0
$233$			27.1509i			1.77871i	0.457213	+	0.889357i	$0.348848\pi$
$233$			27.1509i			1.77871i	−0.457213	+	0.889357i	$0.651152\pi$
$234$		0			0
$235$	−10.1321	−	6.24499i	−0.660946	−	0.407378i
$236$		0			0
$237$	7.55929	+	11.0574i	0.491029	+	0.718257i
$238$		0			0
$239$	11.9142	−	20.6361i	0.770668	−	1.33484i	−0.166530	−	0.986036i	$-0.553256\pi$
$239$	11.9142	−	20.6361i	0.770668	−	1.33484i	0.937197	−	0.348799i	$-0.113411\pi$
$240$		0			0
$241$	−12.1551	−	21.0533i	−0.782979	−	1.35616i	−0.930199	−	0.367056i	$-0.880366\pi$
$241$	−12.1551	−	21.0533i	−0.782979	−	1.35616i	0.147220	−	0.989104i	$-0.452968\pi$
$242$		0			0
$243$	14.4746	−	5.78659i	0.928549	−	0.371210i
$244$		0			0
$245$	11.4186	+	0.328493i	0.729504	+	0.0209866i
$246$		0			0
$247$	−5.86751	−	3.38761i	−0.373341	−	0.215548i
$248$		0			0
$249$	−7.72050	+	5.27804i	−0.489267	+	0.334482i
$250$		0			0
$251$	−16.1181			−1.01737			−0.508683	−	0.860954i	$-0.669868\pi$
$251$	−16.1181			−1.01737			−0.508683	+	0.860954i	$0.669868\pi$
$252$		0			0
$253$			0.0854035i			0.00536927i
$254$		0			0
$255$	−5.14593	+	3.30493i	−0.322251	+	0.206962i
$256$		0			0
$257$	−12.3751	−	7.14475i	−0.771936	−	0.445678i	0.0616287	−	0.998099i	$-0.480371\pi$
$257$	−12.3751	−	7.14475i	−0.771936	−	0.445678i	−0.833565	+	0.552422i	$0.813704\pi$
$258$		0			0
$259$	7.48337	+	12.9616i	0.464994	+	0.805393i
$260$		0			0
$261$	9.99104	+	12.4637i	0.618430	+	0.771482i
$262$		0			0
$263$	5.56810	−	3.21475i	0.343344	−	0.198230i	−0.318406	−	0.947955i	$-0.603147\pi$
$263$	5.56810	−	3.21475i	0.343344	−	0.198230i	0.661750	+	0.749725i	$0.269814\pi$
$264$		0			0
$265$	−2.50644	+	1.35252i	−0.153970	+	0.0830849i
$266$		0			0
$267$	−21.9049	+	1.66936i	−1.34056	+	0.102163i
$268$		0			0
$269$	8.18395			0.498984			0.249492	−	0.968377i	$-0.419736\pi$
$269$	8.18395			0.498984			0.249492	+	0.968377i	$0.419736\pi$
$270$		0			0
$271$	−21.8758			−1.32886			−0.664430	−	0.747350i	$-0.731326\pi$
$271$	−21.8758			−1.32886			−0.664430	+	0.747350i	$0.731326\pi$
$272$		0			0
$273$	−2.52135	+	0.192150i	−0.152599	+	0.0116295i
$274$		0			0
$275$	0.0578819	+	0.00333309i	0.00349041	+	0.000200993i
$276$		0			0
$277$	−10.6432	+	6.14485i	−0.639487	+	0.369208i	−0.784417	−	0.620234i	$-0.787038\pi$
$277$	−10.6432	+	6.14485i	−0.639487	+	0.369208i	0.144930	+	0.989442i	$0.453704\pi$
$278$		0			0
$279$	2.51881	−	6.46578i	0.150797	−	0.387096i
$280$		0			0
$281$	−7.29349	−	12.6327i	−0.435093	−	0.753603i	0.562210	−	0.826994i	$-0.309951\pi$
$281$	−7.29349	−	12.6327i	−0.435093	−	0.753603i	−0.997303	+	0.0733910i	$0.976618\pi$
$282$		0			0
$283$	10.0885	+	5.82460i	0.599699	+	0.346236i	0.768923	−	0.639341i	$-0.220793\pi$
$283$	10.0885	+	5.82460i	0.599699	+	0.346236i	−0.169224	+	0.985578i	$0.554126\pi$
$284$		0			0
$285$	−13.3578	−	20.7987i	−0.791245	−	1.23201i
$286$		0			0
$287$			11.2533i			0.664262i
$288$		0			0
$289$	14.5065			0.853321
$290$		0			0
$291$	0.122462	−	0.0837202i	0.00717888	−	0.00490776i
$292$		0			0
$293$	4.50023	+	2.59821i	0.262906	+	0.151789i	0.625659	−	0.780096i	$-0.284830\pi$
$293$	4.50023	+	2.59821i	0.262906	+	0.151789i	−0.362753	+	0.931885i	$0.618163\pi$
$294$		0			0
$295$	−15.1861	−	0.436879i	−0.884170	−	0.0254361i
$296$		0			0
$297$	−0.0411489	−	0.0440125i	−0.00238770	−	0.00255386i
$298$		0			0
$299$	3.90928	+	6.77107i	0.226080	+	0.391581i
$300$		0			0
$301$	−2.32845	+	4.03299i	−0.134209	+	0.232458i
$302$		0			0
$303$	14.1255	+	20.6621i	0.811486	+	1.18701i
$304$		0			0
$305$	−10.0700	+	16.3380i	−0.576608	+	0.935512i
$306$		0			0
$307$		−	31.2676i		−	1.78453i	−0.451509	−	0.892267i	$-0.649114\pi$
$307$		−	31.2676i		−	1.78453i	0.451509	−	0.892267i	$-0.350886\pi$
$308$		0			0
$309$	−7.71124	−	3.70155i	−0.438677	−	0.210574i
$310$		0			0
$311$	−13.5500	+	23.4692i	−0.768348	+	1.33082i	0.170110	+	0.985425i	$0.445588\pi$
$311$	−13.5500	+	23.4692i	−0.768348	+	1.33082i	−0.938458	+	0.345393i	$0.887746\pi$
$312$		0			0
$313$	30.3115	−	17.5004i	1.71331	−	0.989179i	0.783297	−	0.621647i	$-0.213536\pi$
$313$	30.3115	−	17.5004i	1.71331	−	0.989179i	0.930011	−	0.367532i	$-0.119797\pi$
$314$		0			0
$315$	−8.49646	−	3.59460i	−0.478722	−	0.202533i
$316$		0			0
$317$	−15.1212	+	8.73025i	−0.849293	+	0.490339i	−0.860412	−	0.509599i	$-0.829794\pi$
$317$	−15.1212	+	8.73025i	−0.849293	+	0.490339i	0.0111193	+	0.999938i	$0.496461\pi$
$318$		0			0
$319$	0.0308710	−	0.0534701i	0.00172844	−	0.00299375i
$320$		0			0
$321$	1.78957	+	23.4823i	0.0998841	+	1.31065i
$322$		0			0
$323$		−	10.0783i		−	0.560774i
$324$		0			0
$325$	4.74164	−	2.38524i	0.263019	−	0.132309i
$326$		0			0
$327$	−17.1368	+	1.30599i	−0.947669	+	0.0722213i
$328$		0			0
$329$	3.66011	−	6.33950i	0.201789	−	0.349508i
$330$		0			0
$331$	−14.5945	−	25.2785i	−0.802189	−	1.38943i	−0.918173	−	0.396181i	$-0.870335\pi$
$331$	−14.5945	−	25.2785i	−0.802189	−	1.38943i	0.115984	−	0.993251i	$-0.462998\pi$
$332$		0			0
$333$	4.94749	+	32.2713i	0.271121	+	1.76846i
$334$		0			0
$335$	0.606588	−	21.0853i	0.0331414	−	1.15201i
$336$		0			0
$337$	−14.5048	−	8.37436i	−0.790128	−	0.456181i	0.0498797	−	0.998755i	$-0.484116\pi$
$337$	−14.5048	−	8.37436i	−0.790128	−	0.456181i	−0.840008	+	0.542575i	$0.817450\pi$
$338$		0			0
$339$	−3.95580	−	1.89886i	−0.214850	−	0.103132i
$340$		0			0
$341$	−0.0268208			−0.00145243
$342$		0			0
$343$			16.6526i			0.899156i
$344$		0			0
$345$	1.34880	+	28.4934i	0.0726169	+	1.53403i
$346$		0			0
$347$	18.1261	+	10.4651i	0.973062	+	0.561798i	0.900169	−	0.435542i	$-0.143443\pi$
$347$	18.1261	+	10.4651i	0.973062	+	0.561798i	0.0728940	+	0.997340i	$0.476777\pi$
$348$		0			0
$349$	6.05625	+	10.4897i	0.324184	+	0.561503i	0.981347	−	0.192246i	$-0.0615771\pi$
$349$	6.05625	+	10.4897i	0.324184	+	0.561503i	−0.657163	+	0.753748i	$0.728244\pi$
$350$		0			0
$351$	−5.27707	−	1.60589i	−0.281669	−	0.0857163i
$352$		0			0
$353$	−22.1118	+	12.7663i	−1.17689	+	0.679480i	−0.955294	−	0.295658i	$-0.904461\pi$
$353$	−22.1118	+	12.7663i	−1.17689	+	0.679480i	−0.221600	+	0.975138i	$0.571128\pi$
$354$		0			0
$355$	17.4619	+	32.3597i	0.926781	+	1.71747i
$356$		0			0
$357$	−2.12283	−	3.10518i	−0.112352	−	0.164344i
$358$		0			0
$359$	−6.41790			−0.338724			−0.169362	−	0.985554i	$-0.554171\pi$
$359$	−6.41790			−0.338724			−0.169362	+	0.985554i	$0.554171\pi$
$360$		0			0
$361$	21.7343			1.14391
$362$		0			0
$363$	8.24482	−	17.1760i	0.432741	−	0.901505i
$364$		0			0
$365$	16.3815	−	8.83979i	0.857449	−	0.462696i
$366$		0			0
$367$	4.01929	−	2.32054i	0.209805	−	0.121131i	−0.391416	−	0.920214i	$-0.628014\pi$
$367$	4.01929	−	2.32054i	0.209805	−	0.121131i	0.601221	+	0.799083i	$0.294681\pi$
$368$		0			0
$369$	−8.91064	+	22.8736i	−0.463870	+	1.19075i
$370$		0			0
$371$	−0.875839	−	1.51700i	−0.0454713	−	0.0787586i
$372$		0			0
$373$	−18.9009	−	10.9124i	−0.978652	−	0.565025i	−0.0767888	−	0.997047i	$-0.524467\pi$
$373$	−18.9009	−	10.9124i	−0.978652	−	0.565025i	−0.901863	+	0.432023i	$0.857800\pi$
$374$		0			0
$375$	19.3639	+	0.197883i	0.999948	+	0.0102186i
$376$		0			0
$377$		−	5.65238i		−	0.291112i
$378$		0			0
$379$	−29.1095			−1.49526			−0.747628	−	0.664117i	$-0.768808\pi$
$379$	−29.1095			−1.49526			−0.747628	+	0.664117i	$0.768808\pi$
$380$		0			0
$381$	−2.40583	−	31.5686i	−0.123254	−	1.61731i
$382$		0			0
$383$	7.20924	+	4.16226i	0.368375	+	0.212681i	0.672748	−	0.739871i	$-0.265114\pi$
$383$	7.20924	+	4.16226i	0.368375	+	0.212681i	−0.304373	+	0.952553i	$0.598447\pi$
$384$		0			0
$385$	−0.00102541	+	0.0356438i	−5.22598e−5	+	0.00181657i
$386$		0			0
$387$	−7.92624	+	6.35377i	−0.402913	+	0.322981i
$388$		0			0
$389$	−1.42579	−	2.46953i	−0.0722902	−	0.125210i	0.827614	−	0.561297i	$-0.189697\pi$
$389$	−1.42579	−	2.46953i	−0.0722902	−	0.125210i	−0.899905	+	0.436087i	$0.856364\pi$
$390$		0			0
$391$	−5.81517	+	10.0722i	−0.294086	+	0.509372i
$392$		0			0
$393$	2.46768	−	5.14078i	0.124478	−	0.259318i
$394$		0			0
$395$	9.07310	−	14.7206i	0.456517	−	0.740672i
$396$		0			0
$397$			29.4781i			1.47946i	0.672903	+	0.739731i	$0.265047\pi$
$397$			29.4781i			1.47946i	−0.672903	+	0.739731i	$0.734953\pi$
$398$		0			0
$399$	12.5504	−	8.57997i	0.628308	−	0.429536i
$400$		0			0
$401$	−12.9053	+	22.3526i	−0.644460	+	1.11624i	0.339966	+	0.940438i	$0.389584\pi$
$401$	−12.9053	+	22.3526i	−0.644460	+	1.11624i	−0.984426	+	0.175799i	$0.943749\pi$
$402$		0			0
$403$	−2.12644	+	1.22770i	−0.105926	+	0.0611562i
$404$		0			0
$405$	−14.4237	−	14.0341i	−0.716720	−	0.697361i
$406$		0			0
$407$	0.109285	−	0.0630960i	0.00541708	−	0.00312755i
$408$		0			0
$409$	13.5371	−	23.4470i	0.669367	−	1.15938i	−0.308714	−	0.951155i	$-0.599899\pi$
$409$	13.5371	−	23.4470i	0.669367	−	1.15938i	0.978081	−	0.208223i	$-0.0667679\pi$
$410$		0			0
$411$	12.4896	−	8.53840i	0.616068	−	0.421168i
$412$		0			0
$413$		−	9.34390i		−	0.459783i
$414$		0			0
$415$	10.2782	+	6.33501i	0.504535	+	0.310973i
$416$		0			0
$417$	4.95820	−	10.3291i	0.242804	−	0.505820i
$418$		0			0
$419$	−12.0092	+	20.8005i	−0.586688	+	1.01617i	0.407975	+	0.912993i	$0.366235\pi$
$419$	−12.0092	+	20.8005i	−0.586688	+	1.01617i	−0.994663	+	0.103180i	$0.967098\pi$
$420$		0			0
$421$	4.09439	+	7.09168i	0.199548	+	0.345628i	0.948382	−	0.317130i	$-0.102719\pi$
$421$	4.09439	+	7.09168i	0.199548	+	0.345628i	−0.748834	+	0.662758i	$0.769386\pi$
$422$		0			0
$423$	12.4594	−	9.98758i	0.605795	−	0.485613i
$424$		0			0
$425$	6.59943	+	4.33430i	0.320119	+	0.210245i
$426$		0			0
$427$	−10.2224	−	5.90193i	−0.494698	−	0.285614i
$428$		0			0
$429$	0.00162012	+	0.0212587i	7.82199e−5	+	0.00102638i
$430$		0			0
$431$	5.20494			0.250713			0.125357	−	0.992112i	$-0.459992\pi$
$431$	5.20494			0.250713			0.125357	+	0.992112i	$0.459992\pi$
$432$		0			0
$433$			22.2500i			1.06927i	0.845084	+	0.534633i	$0.179550\pi$
$433$			22.2500i			1.06927i	−0.845084	+	0.534633i	$0.820450\pi$
$434$		0			0
$435$	9.45508	−	18.3269i	0.453337	−	0.878708i
$436$		0			0
$437$	−40.7094	−	23.5036i	−1.94740	−	1.12433i
$438$		0			0
$439$	−6.98693	−	12.1017i	−0.333468	−	0.577583i	0.649721	−	0.760172i	$-0.274886\pi$
$439$	−6.98693	−	12.1017i	−0.333468	−	0.577583i	−0.983189	+	0.182589i	$0.941552\pi$
$440$		0			0
$441$	−5.56315	+	14.2806i	−0.264912	+	0.680029i
$442$		0			0
$443$	4.57467	−	2.64119i	0.217349	−	0.125487i	−0.387373	−	0.921923i	$-0.626617\pi$
$443$	4.57467	−	2.64119i	0.217349	−	0.125487i	0.604722	+	0.796436i	$0.293284\pi$
$444$		0			0
$445$	13.4684	+	24.9591i	0.638463	+	1.18317i
$446$		0			0
$447$	4.66421	−	9.71670i	0.220610	−	0.459584i
$448$		0			0
$449$	−1.87417			−0.0884474			−0.0442237	−	0.999022i	$-0.514081\pi$
$449$	−1.87417			−0.0884474			−0.0442237	+	0.999022i	$0.514081\pi$
$450$		0			0
$451$	0.0948824			0.00446784
$452$		0			0
$453$	−4.81517	−	7.04343i	−0.226236	−	0.330929i
$454$		0			0
$455$	1.55027	+	2.87289i	0.0726777	+	0.134683i
$456$		0			0
$457$	−19.3262	+	11.1580i	−0.904040	+	0.521948i	−0.878509	−	0.477726i	$-0.841461\pi$
$457$	−19.3262	+	11.1580i	−0.904040	+	0.521948i	−0.0255315	+	0.999674i	$0.508128\pi$
$458$		0			0
$459$	−1.85612	−	7.99253i	−0.0866363	−	0.373059i
$460$		0			0
$461$	−5.87818	−	10.1813i	−0.273774	−	0.474191i	0.696051	−	0.717992i	$-0.254939\pi$
$461$	−5.87818	−	10.1813i	−0.273774	−	0.474191i	−0.969825	+	0.243802i	$0.921605\pi$
$462$		0			0
$463$	−10.2152	−	5.89776i	−0.474741	−	0.274092i	0.243481	−	0.969906i	$-0.421711\pi$
$463$	−10.2152	−	5.89776i	−0.474741	−	0.274092i	−0.718222	+	0.695814i	$0.755044\pi$
$464$		0			0
$465$	−8.94829	+	0.423588i	−0.414967	+	0.0196434i
$466$		0			0
$467$		−	21.4898i		−	0.994431i	−0.867627	−	0.497215i	$-0.834356\pi$
$467$		−	21.4898i		−	0.994431i	0.867627	−	0.497215i	$-0.165644\pi$
$468$		0			0
$469$	12.9736			0.599065
$470$		0			0
$471$	14.6936	+	7.05323i	0.677046	+	0.324996i
$472$		0			0
$473$	0.0340041	+	0.0196323i	0.00156351	+	0.000902694i
$474$		0			0
$475$	−17.5183	+	26.6734i	−0.803793	+	1.22386i
$476$		0			0
$477$	−0.579045	−	3.77697i	−0.0265127	−	0.172936i
$478$		0			0
$479$	1.98546	+	3.43891i	0.0907178	+	0.157128i	0.907813	−	0.419374i	$-0.137751\pi$
$479$	1.98546	+	3.43891i	0.0907178	+	0.157128i	−0.817096	+	0.576502i	$0.804417\pi$
$480$		0			0
$481$	5.77635	−	10.0049i	0.263379	−	0.456185i
$482$		0			0
$483$	−17.4934	+	1.33316i	−0.795976	+	0.0606609i
$484$		0			0
$485$	−0.163032	−	0.100486i	−0.00740291	−	0.00456283i
$486$		0			0
$487$			12.7847i			0.579329i	0.957128	+	0.289664i	$0.0935437\pi$
$487$			12.7847i			0.579329i	−0.957128	+	0.289664i	$0.906456\pi$
$488$		0			0
$489$	0.0438742	+	0.575705i	0.00198406	+	0.0260343i
$490$		0			0
$491$	3.50061	−	6.06323i	0.157980	−	0.273630i	−0.776160	−	0.630536i	$-0.782835\pi$
$491$	3.50061	−	6.06323i	0.157980	−	0.273630i	0.934140	+	0.356906i	$0.116168\pi$
$492$		0			0
$493$	7.28162	−	4.20404i	0.327948	−	0.189341i
$494$		0			0
$495$	−0.0303078	+	0.0716379i	−0.00136224	+	0.00321989i
$496$		0			0
$497$	−19.5853	+	11.3076i	−0.878522	+	0.507215i
$498$		0			0
$499$	−5.76235	+	9.98068i	−0.257958	+	0.446796i	−0.965695	−	0.259680i	$-0.916383\pi$
$499$	−5.76235	+	9.98068i	−0.257958	+	0.446796i	0.707737	+	0.706476i	$0.249716\pi$
$500$		0			0
$501$	10.3721	+	4.97883i	0.463392	+	0.222438i
$502$		0			0
$503$		−	7.38880i		−	0.329450i	−0.986340	−	0.164725i	$-0.947326\pi$
$503$		−	7.38880i		−	0.329450i	0.986340	−	0.164725i	$-0.0526737\pi$
$504$		0			0
$505$	16.9542	−	27.5071i	0.754452	−	1.22405i
$506$		0			0
$507$	−11.6060	−	16.9768i	−0.515441	−	0.753966i
$508$		0			0
$509$	1.11067	−	1.92373i	0.0492294	−	0.0852678i	−0.840361	−	0.542028i	$-0.817657\pi$
$509$	1.11067	−	1.92373i	0.0492294	−	0.0852678i	0.889590	+	0.456760i	$0.150990\pi$
$510$		0			0
$511$	5.72428	+	9.91475i	0.253227	+	0.438603i
$512$		0			0
$513$	32.3040	−	7.50201i	1.42626	−	0.331222i
$514$		0			0
$515$	−0.317549	+	11.0381i	−0.0139929	+	0.486398i
$516$		0			0
$517$	−0.0534515	−	0.0308603i	−0.00235080	−	0.00135723i
$518$		0			0
$519$	29.2992	−	20.0301i	1.28609	−	0.879223i
$520$		0			0
$521$	8.09160			0.354499			0.177250	−	0.984166i	$-0.443280\pi$
$521$	8.09160			0.354499			0.177250	+	0.984166i	$0.443280\pi$
$522$		0			0
$523$			14.4193i			0.630512i	0.949007	+	0.315256i	$0.102090\pi$
$523$			14.4193i			0.630512i	−0.949007	+	0.315256i	$0.897910\pi$
$524$		0			0
$525$	0.220821	+	11.9081i	0.00963740	+	0.519712i
$526$		0			0
$527$	−3.16315	−	1.82625i	−0.137789	−	0.0795525i
$528$		0			0
$529$	15.6230	+	27.0599i	0.679262	+	1.17652i
$530$		0			0
$531$	7.39872	−	18.9925i	0.321077	−	0.824205i
$532$		0			0
$533$	7.52259	−	4.34317i	0.325840	−	0.188124i
$534$		0			0
$535$	26.7564	−	14.4383i	1.15678	−	0.624220i
$536$		0			0
$537$	27.7700	−	2.11633i	1.19836	−	0.0913265i
$538$		0			0
$539$	0.0592376			0.00255154
$540$		0			0
$541$	5.37804			0.231220			0.115610	−	0.993295i	$-0.463118\pi$
$541$	5.37804			0.231220			0.115610	+	0.993295i	$0.463118\pi$
$542$		0			0
$543$	−18.4693	+	1.40753i	−0.792593	+	0.0604030i
$544$		0			0
$545$	10.5367	+	19.5262i	0.451343	+	0.836410i
$546$		0			0
$547$	−22.1488	+	12.7876i	−0.947016	+	0.546760i	−0.892153	−	0.451734i	$-0.850806\pi$
$547$	−22.1488	+	12.7876i	−0.947016	+	0.546760i	−0.0548630	+	0.998494i	$0.517472\pi$
$548$		0			0
$549$	−16.1049	−	20.0907i	−0.687342	−	0.857449i
$550$		0			0
$551$	16.9918	+	29.4306i	0.723874	+	1.25379i
$552$		0			0
$553$	9.21042	+	5.31764i	0.391667	+	0.226129i
$554$		0			0
$555$	35.4647	−	22.7768i	1.50539	−	0.966823i
$556$		0			0
$557$		−	36.1519i		−	1.53181i	−0.642956	−	0.765903i	$-0.722292\pi$
$557$		−	36.1519i		−	1.53181i	0.642956	−	0.765903i	$-0.277708\pi$
$558$		0			0
$559$	3.59462			0.152036
$560$		0			0
$561$	−0.0261813	+	0.0178986i	−0.00110538	+	0.000755680i
$562$		0			0
$563$	−29.3594	−	16.9507i	−1.23735	−	0.714385i	−0.268800	−	0.963196i	$-0.586627\pi$
$563$	−29.3594	−	16.9507i	−1.23735	−	0.714385i	−0.968552	+	0.248811i	$0.919960\pi$
$564$		0			0
$565$	−0.162900	+	5.66247i	−0.00685324	+	0.238222i
$566$		0			0
$567$	8.37284	−	9.11567i	0.351626	−	0.382822i
$568$		0			0
$569$	−14.0057	−	24.2586i	−0.587149	−	1.01697i	−0.994604	−	0.103747i	$-0.966917\pi$
$569$	−14.0057	−	24.2586i	−0.587149	−	1.01697i	0.407454	−	0.913226i	$-0.366417\pi$
$570$		0			0
$571$	17.3040	−	29.9714i	0.724150	−	1.25427i	−0.235173	−	0.971954i	$-0.575566\pi$
$571$	17.3040	−	29.9714i	0.724150	−	1.25427i	0.959323	−	0.282311i	$-0.0911011\pi$
$572$		0			0
$573$	15.9563	+	23.3402i	0.666584	+	0.975051i
$574$		0			0
$575$	32.8980	−	16.5491i	1.37194	−	0.690144i
$576$		0			0
$577$		−	1.88098i		−	0.0783062i	−0.999233	−	0.0391531i	$-0.987534\pi$
$577$		−	1.88098i		−	0.0783062i	0.999233	−	0.0391531i	$-0.0124660\pi$
$578$		0			0
$579$	−32.5494	−	15.6244i	−1.35271	−	0.649326i
$580$		0			0
$581$	−3.71287	+	6.43089i	−0.154036	+	0.266798i
$582$		0			0
$583$	−0.0127906	+	0.00738463i	−0.000529731	+	0.000305840i
$584$		0			0
$585$	0.876267	+	7.06701i	0.0362292	+	0.292185i
$586$		0			0
$587$	4.92665	−	2.84440i	0.203345	−	0.117401i	−0.394870	−	0.918737i	$-0.629210\pi$
$587$	4.92665	−	2.84440i	0.203345	−	0.117401i	0.598215	+	0.801336i	$0.295877\pi$
$588$		0			0
$589$	7.38126	−	12.7847i	0.304140	−	0.526785i
$590$		0			0
$591$	−0.632638	−	8.30131i	−0.0260232	−	0.341470i
$592$		0			0
$593$		−	23.6302i		−	0.970378i	−0.874409	−	0.485189i	$-0.838751\pi$
$593$		−	23.6302i		−	0.970378i	0.874409	−	0.485189i	$-0.161249\pi$
$594$		0			0
$595$	−2.54794	+	4.13388i	−0.104455	+	0.169472i
$596$		0			0
$597$	13.4623	−	1.02595i	0.550975	−	0.0419895i
$598$		0			0
$599$	−11.8923	+	20.5981i	−0.485908	+	0.841617i	−0.999869	−	0.0161965i	$-0.994844\pi$
$599$	−11.8923	+	20.5981i	−0.485908	+	0.841617i	0.513961	+	0.857814i	$0.328178\pi$
$600$		0			0
$601$	4.30901	+	7.46343i	0.175768	+	0.304440i	0.940427	−	0.339996i	$-0.110426\pi$
$601$	4.30901	+	7.46343i	0.175768	+	0.304440i	−0.764659	+	0.644436i	$0.777092\pi$
$602$		0			0
$603$	26.3703	+	10.2728i	1.07388	+	0.418341i
$604$		0			0
$605$	−24.5863	−	0.707306i	−0.999574	−	0.0287561i
$606$		0			0
$607$	23.7172	+	13.6931i	0.962652	+	0.555787i	0.896988	−	0.442054i	$-0.145750\pi$
$607$	23.7172	+	13.6931i	0.962652	+	0.555787i	0.0656637	+	0.997842i	$0.479084\pi$
$608$		0			0
$609$	11.4343	+	5.48869i	0.463341	+	0.222413i
$610$		0			0
$611$	−5.65042			−0.228592
$612$		0			0
$613$		−	1.61637i		−	0.0652845i	−0.999467	−	0.0326422i	$-0.989608\pi$
$613$		−	1.61637i		−	0.0652845i	0.999467	−	0.0326422i	$-0.0103922\pi$
$614$		0			0
$615$	31.6558	−	1.49850i	1.27649	−	0.0604254i
$616$		0			0
$617$	−8.14521	−	4.70264i	−0.327914	−	0.189321i	0.327001	−	0.945024i	$-0.393962\pi$
$617$	−8.14521	−	4.70264i	−0.327914	−	0.189321i	−0.654915	+	0.755703i	$0.727295\pi$
$618$		0			0
$619$	1.62429	+	2.81336i	0.0652858	+	0.113078i	0.896821	−	0.442394i	$-0.145871\pi$
$619$	1.62429	+	2.81336i	0.0652858	+	0.113078i	−0.831535	+	0.555472i	$0.812537\pi$
$620$		0			0
$621$	−36.6129	−	11.1419i	−1.46922	−	0.447108i
$622$		0			0
$623$	−15.1062	+	8.72158i	−0.605218	+	0.349423i
$624$		0			0
$625$	−9.93214	−	22.9424i	−0.397286	−	0.917695i
$626$		0			0
$627$	−0.0723420	−	0.105819i	−0.00288906	−	0.00422600i
$628$		0			0
$629$	17.1850			0.685210
$630$		0			0
$631$	22.0746			0.878777			0.439389	−	0.898297i	$-0.355195\pi$
$631$	22.0746			0.878777			0.439389	+	0.898297i	$0.355195\pi$
$632$		0			0
$633$	16.1952	−	33.7386i	0.643701	−	1.34099i
$634$		0			0
$635$	−35.9702	+	19.4102i	−1.42743	+	0.770271i
$636$		0			0
$637$	4.69655	−	2.71155i	0.186084	−	0.107436i
$638$		0			0
$639$	−48.7630	+	7.47582i	−1.92903	+	0.295739i
$640$		0			0
$641$	−21.6150	−	37.4382i	−0.853739	−	1.47872i	−0.877809	−	0.479010i	$-0.840996\pi$
$641$	−21.6150	−	37.4382i	−0.853739	−	1.47872i	0.0240700	−	0.999710i	$-0.492338\pi$
$642$		0			0
$643$	−13.6233	−	7.86544i	−0.537252	−	0.310183i	0.206712	−	0.978402i	$-0.433724\pi$
$643$	−13.6233	−	7.86544i	−0.537252	−	0.310183i	−0.743965	+	0.668219i	$0.767057\pi$
$644$		0			0
$645$	11.6549	+	6.01293i	0.458913	+	0.236759i
$646$		0			0
$647$			25.8513i			1.01632i	0.861263	+	0.508159i	$0.169674\pi$
$647$			25.8513i			1.01632i	−0.861263	+	0.508159i	$0.830326\pi$
$648$		0			0
$649$	−0.0787831			−0.00309251
$650$		0			0
$651$	−0.418677	−	5.49377i	−0.0164092	−	0.215318i
$652$		0			0
$653$	21.9197	+	12.6553i	0.857784	+	0.495242i	0.863269	−	0.504743i	$-0.168413\pi$
$653$	21.9197	+	12.6553i	0.857784	+	0.495242i	−0.00548578	+	0.999985i	$0.501746\pi$
$654$		0			0
$655$	−7.35869	−	0.211697i	−0.287528	−	0.00827169i
$656$		0			0
$657$	3.78451	+	24.6854i	0.147648	+	0.963071i
$658$		0			0
$659$	−13.6426	−	23.6297i	−0.531442	−	0.920484i	−0.999327	−	0.0366946i	$-0.988317\pi$
$659$	−13.6426	−	23.6297i	−0.531442	−	0.920484i	0.467885	−	0.883789i	$-0.345016\pi$
$660$		0			0
$661$	−11.1277	+	19.2737i	−0.432817	+	0.749661i	−0.997115	−	0.0759103i	$-0.975814\pi$
$661$	−11.1277	+	19.2737i	−0.432817	+	0.749661i	0.564298	+	0.825571i	$0.309147\pi$
$662$		0			0
$663$	−1.25645	+	2.61749i	−0.0487964	+	0.101655i
$664$		0			0
$665$	−16.7082	−	10.2982i	−0.647915	−	0.399346i
$666$		0			0
$667$		−	39.2169i		−	1.51848i
$668$		0			0
$669$	14.1936	−	9.70333i	0.548758	−	0.375153i
$670$		0			0
$671$	−0.0497621	+	0.0861905i	−0.00192104	+	0.00332735i
$672$		0			0
$673$	14.9334	−	8.62183i	0.575642	−	0.332347i	−0.183758	−	0.982972i	$-0.558826\pi$
$673$	14.9334	−	8.62183i	0.575642	−	0.332347i	0.759400	+	0.650625i	$0.225493\pi$
$674$		0			0
$675$	−8.98028	+	24.3794i	−0.345651	+	0.938363i
$676$		0			0
$677$	−0.940266	+	0.542863i	−0.0361373	+	0.0208639i	−0.517960	−	0.855405i	$-0.673308\pi$
$677$	−0.940266	+	0.542863i	−0.0361373	+	0.0208639i	0.481822	+	0.876269i	$0.339975\pi$
$678$		0			0
$679$	0.0588936	−	0.102007i	0.00226013	−	0.00391466i
$680$		0			0
$681$	2.03173	−	1.38897i	0.0778560	−	0.0532255i
$682$		0			0
$683$			3.62926i			0.138870i	0.997586	+	0.0694349i	$0.0221196\pi$
$683$			3.62926i			0.138870i	−0.997586	+	0.0694349i	$0.977880\pi$
$684$		0			0
$685$	−16.6272	−	10.2483i	−0.635293	−	0.391567i
$686$		0			0
$687$	−20.6177	+	42.9518i	−0.786616	+	1.63871i
$688$		0			0
$689$	−0.676052	+	1.17096i	−0.0257555	+	0.0446099i
$690$		0			0
$691$	14.4867	+	25.0916i	0.551099	+	0.954531i	0.998196	+	0.0600453i	$0.0191245\pi$
$691$	14.4867	+	25.0916i	0.551099	+	0.954531i	−0.447097	+	0.894485i	$0.647542\pi$
$692$		0			0
$693$	−0.0445778	−	0.0173657i	−0.00169337	−	0.000659670i
$694$		0			0
$695$	−14.7855	−	0.425354i	−0.560846	−	0.0161346i
$696$		0			0
$697$	11.1901	+	6.46060i	0.423855	+	0.244713i
$698$		0			0
$699$	3.57352	+	46.8908i	0.135163	+	1.77357i
$700$		0			0
$701$	28.4520			1.07462			0.537309	−	0.843385i	$-0.319441\pi$
$701$	28.4520			1.07462			0.537309	+	0.843385i	$0.319441\pi$
$702$		0			0
$703$			69.4577i			2.61965i
$704$		0			0
$705$	−18.3205	−	9.45180i	−0.689992	−	0.355976i
$706$		0			0
$707$	17.2108	+	9.93665i	0.647278	+	0.373706i
$708$		0			0
$709$	−9.40582	−	16.2914i	−0.353243	−	0.611835i	0.633573	−	0.773683i	$-0.281588\pi$
$709$	−9.40582	−	16.2914i	−0.353243	−	0.611835i	−0.986816	+	0.161848i	$0.948254\pi$
$710$		0			0
$711$	14.5106	+	18.1017i	0.544189	+	0.678868i
$712$		0			0
$713$	−14.7535	+	8.51794i	−0.552523	+	0.318999i
$714$		0			0
$715$	0.0242228	−	0.0130711i	0.000905881	−	0.000488831i
$716$		0			0
$717$	17.8603	−	37.2075i	0.667007	−	1.38954i
$718$		0			0
$719$	4.22562			0.157589			0.0787946	−	0.996891i	$-0.474893\pi$
$719$	4.22562			0.157589			0.0787946	+	0.996891i	$0.474893\pi$
$720$		0			0
$721$	−6.79167			−0.252935
$722$		0			0
$723$	−23.7634	−	34.7601i	−0.883769	−	1.29274i
$724$		0			0
$725$	−26.5791	−	1.53054i	−0.987122	−	0.0568427i
$726$		0			0
$727$	4.03048	−	2.32700i	0.149482	−	0.0863036i	−0.423393	−	0.905946i	$-0.639161\pi$
$727$	4.03048	−	2.32700i	0.149482	−	0.0863036i	0.572876	+	0.819642i	$0.305828\pi$
$728$		0			0
$729$	24.2367	−	11.8988i	0.897656	−	0.440696i
$730$		0			0
$731$	2.67355	+	4.63072i	0.0988848	+	0.171274i
$732$		0			0
$733$	−21.6506	−	12.5000i	−0.799683	−	0.461697i	0.0436770	−	0.999046i	$-0.486093\pi$
$733$	−21.6506	−	12.5000i	−0.799683	−	0.461697i	−0.843360	+	0.537348i	$0.819426\pi$
$734$		0			0
$735$	19.7636	−	0.935554i	0.728990	−	0.0345084i
$736$		0			0
$737$		−	0.109387i		−	0.00402932i
$738$		0			0
$739$	−18.4824			−0.679887			−0.339944	−	0.940446i	$-0.610408\pi$
$739$	−18.4824			−0.679887			−0.339944	+	0.940446i	$0.610408\pi$
$740$		0			0
$741$	−10.5793	−	5.07828i	−0.388640	−	0.186555i
$742$		0			0
$743$	−2.86448	−	1.65381i	−0.105088	−	0.0606723i	0.446535	−	0.894766i	$-0.352658\pi$
$743$	−2.86448	−	1.65381i	−0.105088	−	0.0606723i	−0.551623	+	0.834094i	$0.685991\pi$
$744$		0			0
$745$	−13.9088	−	0.400133i	−0.509579	−	0.0146597i
$746$		0			0
$747$	−12.6390	+	10.1315i	−0.462435	+	0.370694i
$748$		0			0
$749$	9.34962	+	16.1940i	0.341628	+	0.591716i
$750$		0			0
$751$	−22.9233	+	39.7043i	−0.836483	+	1.44883i	0.0563335	+	0.998412i	$0.482059\pi$
$751$	−22.9233	+	39.7043i	−0.836483	+	1.44883i	−0.892817	+	0.450420i	$0.851274\pi$
$752$		0			0
$753$	−27.8367	+	2.12142i	−1.01443	+	0.0773088i
$754$		0			0
$755$	−5.77945	+	9.37680i	−0.210336	+	0.341257i
$756$		0			0
$757$			12.2649i			0.445775i	0.974844	+	0.222888i	$0.0715483\pi$
$757$			12.2649i			0.445775i	−0.974844	+	0.222888i	$0.928452\pi$
$758$		0			0
$759$	0.0112405	+	0.147495i	0.000408006	+	0.00535375i
$760$		0			0
$761$	−9.54420	+	16.5310i	−0.345977	+	0.599250i	−0.985531	−	0.169497i	$-0.945786\pi$
$761$	−9.54420	+	16.5310i	−0.345977	+	0.599250i	0.639554	+	0.768746i	$0.279119\pi$
$762$		0			0
$763$	−11.8180	+	6.82314i	−0.427841	+	0.247014i
$764$		0			0
$765$	−8.45227	+	6.38504i	−0.305592	+	0.230852i
$766$		0			0
$767$	−6.24619	+	3.60624i	−0.225537	+	0.130214i
$768$		0			0
$769$	−3.60033	+	6.23595i	−0.129831	+	0.224874i	−0.923611	−	0.383331i	$-0.874777\pi$
$769$	−3.60033	+	6.23595i	−0.129831	+	0.224874i	0.793780	+	0.608205i	$0.208110\pi$
$770$		0			0
$771$	−22.3127	−	10.7105i	−0.803571	−	0.385730i
$772$		0			0
$773$		−	1.69028i		−	0.0607950i	−0.999538	−	0.0303975i	$-0.990323\pi$
$773$		−	1.69028i		−	0.0607950i	0.999538	−	0.0303975i	$-0.00967732\pi$
$774$		0			0
$775$	5.19721	+	10.3316i	0.186689	+	0.371121i
$776$		0			0
$777$	14.6301	+	21.4003i	0.524850	+	0.767730i
$778$		0			0
$779$	−26.1122	+	45.2277i	−0.935568	+	1.62045i
$780$		0			0
$781$	0.0953400	+	0.165134i	0.00341153	+	0.00590895i
$782$		0			0
$783$	18.8954	+	20.2103i	0.675266	+	0.722258i
$784$		0			0
$785$	0.605082	−	21.0329i	0.0215963	−	0.750697i
$786$		0			0
$787$	28.7876	+	16.6205i	1.02617	+	0.592457i	0.915884	−	0.401443i	$-0.131491\pi$
$787$	28.7876	+	16.6205i	1.02617	+	0.592457i	0.110282	+	0.993900i	$0.464825\pi$
$788$		0			0
$789$	9.19324	−	6.28486i	0.327288	−	0.223747i
$790$		0			0
$791$	−3.48407			−0.123879
$792$		0			0
$793$			9.11129i			0.323551i
$794$		0			0
$795$	−4.15072	+	2.66576i	−0.147211	+	0.0945447i
$796$		0			0
$797$	37.4748	+	21.6361i	1.32743	+	0.766390i	0.984901	−	0.173119i	$-0.0553845\pi$
$797$	37.4748	+	21.6361i	1.32743	+	0.766390i	0.342525	+	0.939509i	$0.388718\pi$
$798$		0			0
$799$	−4.20259	−	7.27909i	−0.148677	−	0.257516i
$800$		0			0
$801$	−37.6110	+	5.76611i	−1.32892	+	0.203736i
$802$		0			0
$803$	0.0835962	−	0.0482643i	0.00295005	−	0.00170321i
$804$		0			0
$805$	10.7559	+	19.9325i	0.379097	+	0.702527i
$806$		0			0
$807$	14.1340	−	1.07715i	0.497541	−	0.0379173i
$808$		0			0
$809$	−10.4664			−0.367981			−0.183990	−	0.982928i	$-0.558902\pi$
$809$	−10.4664			−0.367981			−0.183990	+	0.982928i	$0.558902\pi$
$810$		0			0
$811$	−21.4200			−0.752158			−0.376079	−	0.926588i	$-0.622728\pi$
$811$	−21.4200			−0.752158			−0.376079	+	0.926588i	$0.622728\pi$
$812$		0			0
$813$	−37.7805	+	2.87923i	−1.32502	+	0.100979i
$814$		0			0
$815$	0.655975	−	0.353977i	0.0229778	−	0.0123993i
$816$		0			0
$817$	−18.7163	+	10.8059i	−0.654801	+	0.378050i
$818$		0			0
$819$	−4.32918	+	0.663704i	−0.151274	+	0.0231917i
$820$		0			0
$821$	−4.02464	−	6.97089i	−0.140461	−	0.243286i	0.787209	−	0.616686i	$-0.211525\pi$
$821$	−4.02464	−	6.97089i	−0.140461	−	0.243286i	−0.927670	+	0.373400i	$0.878192\pi$
$822$		0			0
$823$	−31.6630	−	18.2806i	−1.10370	−	0.637223i	−0.166512	−	0.986039i	$-0.553250\pi$
$823$	−31.6630	−	18.2806i	−1.10370	−	0.637223i	−0.937191	+	0.348816i	$0.886584\pi$
$824$		0			0
$825$	0.100403	−	0.00186185i	0.00349559	−	6.48213e-5i
$826$		0			0
$827$			7.52915i			0.261814i	0.991395	+	0.130907i	$0.0417890\pi$
$827$			7.52915i			0.261814i	−0.991395	+	0.130907i	$0.958211\pi$
$828$		0			0
$829$	−0.188646			−0.00655195			−0.00327597	−	0.999995i	$-0.501043\pi$
$829$	−0.188646			−0.00655195			−0.00327597	+	0.999995i	$0.501043\pi$
$830$		0			0
$831$	−17.5725	+	12.0132i	−0.609582	+	0.416735i
$832$		0			0
$833$	6.98626	+	4.03352i	0.242060	+	0.139753i
$834$		0			0
$835$	0.427123	−	14.8470i	0.0147812	−	0.513802i
$836$		0			0
$837$	3.49909	−	11.4982i	0.120946	−	0.397436i
$838$		0			0
$839$	−8.22498	−	14.2461i	−0.283958	−	0.491830i	0.688398	−	0.725333i	$-0.258314\pi$
$839$	−8.22498	−	14.2461i	−0.283958	−	0.491830i	−0.972356	+	0.233504i	$0.924981\pi$
$840$		0			0
$841$	0.324206	−	0.561541i	0.0111795	−	0.0193635i
$842$		0			0
$843$	−14.2588	−	20.8573i	−0.491101	−	0.718362i
$844$		0			0
$845$	−13.9302	+	22.6009i	−0.479214	+	0.777495i
$846$		0			0
$847$		−	15.1277i		−	0.519795i
$848$		0			0
$849$	18.1899	+	8.73151i	0.624275	+	0.299665i
$850$		0			0
$851$	40.0769	−	69.4153i	1.37382	−	2.37953i
$852$		0			0
$853$	20.3132	−	11.7278i	0.695509	−	0.401552i	−0.110163	−	0.993913i	$-0.535137\pi$
$853$	20.3132	−	11.7278i	0.695509	−	0.401552i	0.805673	+	0.592361i	$0.201804\pi$
$854$		0			0
$855$	−25.8069	−	34.1621i	−0.882576	−	1.16832i
$856$		0			0
$857$	16.4722	−	9.51024i	0.562680	−	0.324864i	−0.191540	−	0.981485i	$-0.561348\pi$
$857$	16.4722	−	9.51024i	0.562680	−	0.324864i	0.754221	+	0.656621i	$0.228015\pi$
$858$		0			0
$859$	7.90912	−	13.6990i	0.269856	−	0.467404i	−0.698969	−	0.715152i	$-0.746357\pi$
$859$	7.90912	−	13.6990i	0.269856	−	0.467404i	0.968824	+	0.247749i	$0.0796907\pi$
$860$		0			0
$861$	1.48113	+	19.4350i	0.0504767	+	0.662342i
$862$		0			0
$863$		−	7.81226i		−	0.265933i	−0.991121	−	0.132966i	$-0.957550\pi$
$863$		−	7.81226i		−	0.265933i	0.991121	−	0.132966i	$-0.0424502\pi$
$864$		0			0
$865$	−39.0055	−	24.0413i	−1.32623	−	0.817427i
$866$		0			0
$867$	25.0533	−	1.90929i	0.850854	−	0.0648431i
$868$		0			0
$869$	0.0448357	−	0.0776577i	0.00152095	−	0.00263436i
$870$		0			0
$871$	−5.00710	−	8.67256i	−0.169659	−	0.293858i
$872$		0			0
$873$	0.200479	−	0.160706i	0.00678518	−	0.00543909i
$874$		0			0
$875$	13.9289	−	6.51188i	0.470884	−	0.220142i
$876$		0			0
$877$	47.5193	+	27.4353i	1.60461	+	0.926424i	0.990548	+	0.137168i	$0.0438001\pi$
$877$	47.5193	+	27.4353i	1.60461	+	0.926424i	0.614065	+	0.789255i	$0.289533\pi$
$878$		0			0
$879$	8.11405	+	3.89491i	0.273680	+	0.131372i
$880$		0			0
$881$	31.1017			1.04784			0.523922	−	0.851766i	$-0.324468\pi$
$881$	31.1017			1.04784			0.523922	+	0.851766i	$0.324468\pi$
$882$		0			0
$883$		−	20.5411i		−	0.691264i	−0.938370	−	0.345632i	$-0.887665\pi$
$883$		−	20.5411i		−	0.691264i	0.938370	−	0.345632i	$-0.112335\pi$
$884$		0			0
$885$	−26.2846	+	1.24424i	−0.883546	+	0.0418247i
$886$		0			0
$887$	45.1925	+	26.0919i	1.51742	+	0.876081i	0.999790	+	0.0204736i	$0.00651740\pi$
$887$	45.1925	+	26.0919i	1.51742	+	0.876081i	0.517626	+	0.855607i	$0.326816\pi$
$888$		0			0
$889$	−12.5693	−	21.7706i	−0.421559	−	0.730162i
$890$		0			0
$891$	−0.0768588	−	0.0705956i	−0.00257487	−	0.00236504i
$892$		0			0
$893$	29.4204	−	16.9859i	0.984517	−	0.568411i
$894$		0			0
$895$	−17.0746	−	31.6419i	−0.570740	−	1.05767i
$896$		0			0
$897$	7.64268	+	11.1794i	0.255182	+	0.373269i
$898$		0			0
$899$	12.3160			0.410761
$900$		0			0
$901$	−2.01130			−0.0670060
$902$		0			0
$903$	−3.49052	+	7.27161i	−0.116157	+	0.241984i
$904$		0			0
$905$	11.3560	+	21.0444i	0.377485	+	0.699540i
$906$		0			0
$907$	22.1672	−	12.7983i	0.736051	−	0.424959i	−0.0845808	−	0.996417i	$-0.526955\pi$
$907$	22.1672	−	12.7983i	0.736051	−	0.424959i	0.820632	+	0.571457i	$0.193622\pi$
$908$		0			0
$909$	27.1148	+	33.8253i	0.899340	+	1.12191i
$910$		0			0
$911$	−20.5975	−	35.6760i	−0.682426	−	1.18200i	−0.974238	−	0.225521i	$-0.927591\pi$
$911$	−20.5975	−	35.6760i	−0.682426	−	1.18200i	0.291812	−	0.956476i	$-0.405742\pi$
$912$		0			0
$913$	0.0542220	+	0.0313051i	0.00179449	+	0.00103605i
$914$		0			0
$915$	−15.2410	+	29.5418i	−0.503852	+	0.976623i
$916$		0			0
$917$		−	4.52774i		−	0.149519i
$918$		0			0
$919$	−4.84011			−0.159661			−0.0798303	−	0.996808i	$-0.525438\pi$
$919$	−4.84011			−0.159661			−0.0798303	+	0.996808i	$0.525438\pi$
$920$		0			0
$921$	−4.11534	−	54.0004i	−0.135605	−	1.77937i
$922$		0			0
$923$	15.1178	+	8.72824i	0.497607	+	0.287293i
$924$		0			0
$925$	−45.4818	−	29.8711i	−1.49543	−	0.982156i
$926$		0			0
$927$	−13.8048	−	5.37781i	−0.453410	−	0.176630i
$928$		0			0
$929$	19.9319	+	34.5231i	0.653945	+	1.13267i	0.982157	+	0.188063i	$0.0602208\pi$
$929$	19.9319	+	34.5231i	0.653945	+	1.13267i	−0.328212	+	0.944604i	$0.606446\pi$
$930$		0			0
$931$	−16.3026	+	28.2369i	−0.534295	+	0.925426i
$932$		0			0
$933$	−20.3124	+	42.3158i	−0.664999	+	1.38536i
$934$		0			0
$935$	0.0348548	+	0.0214829i	0.00113987	+	0.000702567i
$936$		0			0
$937$			5.03028i			0.164332i	0.996619	+	0.0821661i	$0.0261838\pi$
$937$			5.03028i			0.164332i	−0.996619	+	0.0821661i	$0.973816\pi$
$938$		0			0
$939$	50.0459	−	34.2134i	1.63319	−	1.11651i
$940$		0			0
$941$	−10.4374	+	18.0781i	−0.340250	+	0.589330i	−0.984479	−	0.175503i	$-0.943845\pi$
$941$	−10.4374	+	18.0781i	−0.340250	+	0.589330i	0.644229	+	0.764832i	$0.277178\pi$
$942$		0			0
$943$	52.1926	−	30.1334i	1.69962	−	0.981278i
$944$		0			0
$945$	−15.1469	−	5.08974i	−0.492728	−	0.165569i
$946$		0			0
$947$	0.0653614	−	0.0377364i	0.00212396	−	0.00122627i	−0.498938	−	0.866638i	$-0.666276\pi$
$947$	0.0653614	−	0.0377364i	0.00212396	−	0.00122627i	0.501062	+	0.865412i	$0.332943\pi$
$948$		0			0
$949$	4.41852	−	7.65311i	0.143431	−	0.248430i
$950$		0			0
$951$	−24.9660	+	17.0677i	−0.809577	+	0.553459i
$952$		0			0
$953$			23.6892i			0.767370i	0.923464	+	0.383685i	$0.125345\pi$
$953$			23.6892i			0.767370i	−0.923464	+	0.383685i	$0.874655\pi$
$954$		0			0
$955$	19.1517	−	31.0724i	0.619733	−	1.00548i
$956$		0			0
$957$	0.0462779	−	0.0964083i	0.00149595	−	0.00311644i
$958$		0			0
$959$	6.00640	−	10.4034i	0.193957	−	0.335943i
$960$		0			0
$961$	12.8250	+	22.2135i	0.413708	+	0.716564i
$962$		0			0
$963$	6.18133	+	40.3194i	0.199191	+	1.29927i
$964$		0			0
$965$	−1.34038	+	46.5923i	−0.0431484	+	1.49986i
$966$		0			0
$967$	−39.2206	−	22.6440i	−1.26125	−	0.728183i	−0.287934	−	0.957650i	$-0.592968\pi$
$967$	−39.2206	−	22.6440i	−1.26125	−	0.728183i	−0.973316	+	0.229467i	$0.926302\pi$
$968$		0			0
$969$	−1.32648	−	17.4057i	−0.0426127	−	0.559152i
$970$		0			0
$971$	25.4586			0.817004			0.408502	−	0.912757i	$-0.366051\pi$
$971$	25.4586			0.817004			0.408502	+	0.912757i	$0.366051\pi$
$972$		0			0
$973$		−	9.09739i		−	0.291649i
$974$		0			0
$975$	7.87507	−	4.74349i	0.252204	−	0.151913i
$976$		0			0
$977$	7.09127	+	4.09415i	0.226870	+	0.130983i	0.609127	−	0.793073i	$-0.291520\pi$
$977$	7.09127	+	4.09415i	0.226870	+	0.130983i	−0.382257	+	0.924056i	$0.624853\pi$
$978$		0			0
$979$	0.0735360	+	0.127368i	0.00235022	+	0.00407070i
$980$		0			0
$981$	−29.4242	+	4.51100i	−0.939441	+	0.144025i
$982$		0			0
$983$	−10.6001	+	6.11998i	−0.338091	+	0.195197i	−0.659428	−	0.751768i	$-0.729201\pi$
$983$	−10.6001	+	6.11998i	−0.338091	+	0.195197i	0.321336	+	0.946965i	$0.395868\pi$
$984$		0			0
$985$	−9.45875	+	5.10412i	−0.301381	+	0.162631i
$986$		0			0
$987$	5.48679	−	11.4303i	0.174646	−	0.363831i
$988$		0			0
$989$	24.9398			0.793041
$990$		0			0
$991$	48.0040			1.52490			0.762448	−	0.647049i	$-0.223997\pi$
$991$	48.0040			1.52490			0.762448	+	0.647049i	$0.223997\pi$
$992$		0			0
$993$	−28.5325	−	41.7362i	−0.905451	−	1.32446i
$994$		0			0
$995$	−8.27739	−	15.3393i	−0.262411	−	0.486289i
$996$		0			0
$997$	5.36574	−	3.09791i	0.169935	−	0.0981118i	−0.412620	−	0.910903i	$-0.635386\pi$
$997$	5.36574	−	3.09791i	0.169935	−	0.0981118i	0.582555	+	0.812791i	$0.302053\pi$
$998$		0			0
$999$	12.7920	+	55.0828i	0.404721	+	1.74274i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	360.2.bi.b.49.16	yes	32
3.2	odd	2		1080.2.bi.b.1009.11		32
4.3	odd	2		720.2.by.f.49.1		32
5.4	even	2	inner	360.2.bi.b.49.1	✓	32
9.2	odd	6		1080.2.bi.b.289.1		32
9.4	even	3		3240.2.f.k.649.6		16
9.5	odd	6		3240.2.f.i.649.11		16
9.7	even	3	inner	360.2.bi.b.169.1	yes	32
12.11	even	2		2160.2.by.f.1009.11		32
15.14	odd	2		1080.2.bi.b.1009.1		32
20.19	odd	2		720.2.by.f.49.16		32
36.7	odd	6		720.2.by.f.529.16		32
36.11	even	6		2160.2.by.f.289.1		32
45.4	even	6		3240.2.f.k.649.5		16
45.14	odd	6		3240.2.f.i.649.12		16
45.29	odd	6		1080.2.bi.b.289.11		32
45.34	even	6	inner	360.2.bi.b.169.16	yes	32
60.59	even	2		2160.2.by.f.1009.1		32
180.79	odd	6		720.2.by.f.529.1		32
180.119	even	6		2160.2.by.f.289.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
360.2.bi.b.49.1	✓	32	5.4	even	2	inner
360.2.bi.b.49.16	yes	32	1.1	even	1	trivial
360.2.bi.b.169.1	yes	32	9.7	even	3	inner
360.2.bi.b.169.16	yes	32	45.34	even	6	inner
720.2.by.f.49.1		32	4.3	odd	2
720.2.by.f.49.16		32	20.19	odd	2
720.2.by.f.529.1		32	180.79	odd	6
720.2.by.f.529.16		32	36.7	odd	6
1080.2.bi.b.289.1		32	9.2	odd	6
1080.2.bi.b.289.11		32	45.29	odd	6
1080.2.bi.b.1009.1		32	15.14	odd	2
1080.2.bi.b.1009.11		32	3.2	odd	2
2160.2.by.f.289.1		32	36.11	even	6
2160.2.by.f.289.11		32	180.119	even	6
2160.2.by.f.1009.1		32	60.59	even	2
2160.2.by.f.1009.11		32	12.11	even	2
3240.2.f.i.649.11		16	9.5	odd	6
3240.2.f.i.649.12		16	45.14	odd	6
3240.2.f.k.649.5		16	45.4	even	6
3240.2.f.k.649.6		16	9.4	even	3

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:	\( N \)	\(=\)	\( 360 = 2^{3} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	360.bi (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.72704 - 0.131617i) q^{3} +(-1.06189 - 1.96784i) q^{5} +(1.19102 - 0.687633i) q^{7} +(2.96535 - 0.454616i) q^{9} +O(q^{10})\)	\(q+(1.72704 - 0.131617i) q^{3} +(-1.06189 - 1.96784i) q^{5} +(1.19102 - 0.687633i) q^{7} +(2.96535 - 0.454616i) q^{9} +(-0.00579778 - 0.0100420i) q^{11} +(-0.919334 - 0.530778i) q^{13} +(-2.09292 - 3.25878i) q^{15} -1.57910i q^{17} +6.38234 q^{19} +(1.96643 - 1.34433i) q^{21} +(-6.37844 - 3.68260i) q^{23} +(-2.74480 + 4.17924i) q^{25} +(5.06146 - 1.17543i) q^{27} +(2.66231 + 4.61126i) q^{29} +(1.15651 - 2.00314i) q^{31} +(-0.0113347 - 0.0165800i) q^{33} +(-2.61787 - 1.61354i) q^{35} +10.8828i q^{37} +(-1.65759 - 0.795676i) q^{39} +(-4.09133 + 7.08638i) q^{41} +(-2.93252 + 1.69309i) q^{43} +(-4.04348 - 5.35260i) q^{45} +(4.60966 - 2.66139i) q^{47} +(-2.55432 + 4.42422i) q^{49} +(-0.207836 - 2.72717i) q^{51} -1.27370i q^{53} +(-0.0136046 + 0.0220726i) q^{55} +(11.0226 - 0.840025i) q^{57} +(3.39712 - 5.88399i) q^{59} +(-4.29148 - 7.43306i) q^{61} +(3.21917 - 2.58053i) q^{63} +(-0.0682594 + 2.37273i) q^{65} +(8.16967 + 4.71676i) q^{67} +(-11.5005 - 5.52049i) q^{69} -16.4442 q^{71} +8.32462i q^{73} +(-4.19033 + 7.57899i) q^{75} +(-0.0138105 - 0.00797348i) q^{77} +(3.86663 + 6.69719i) q^{79} +(8.58665 - 2.69620i) q^{81} +(-4.67610 + 2.69975i) q^{83} +(-3.10741 + 1.67682i) q^{85} +(5.20484 + 7.61343i) q^{87} -12.6835 q^{89} -1.45992 q^{91} +(1.73370 - 3.61172i) q^{93} +(-6.77732 - 12.5594i) q^{95} +(0.0741723 - 0.0428234i) q^{97} +(-0.0217577 - 0.0271425i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{5} + 4 q^{9}+O(q^{10}) \) 32 * q - 2 * q^5 + 4 * q^9	\( 32 q - 2 q^{5} + 4 q^{9} + 16 q^{11} - 10 q^{15} + 8 q^{19} - 4 q^{21} - 6 q^{25} + 20 q^{29} - 12 q^{31} + 4 q^{35} - 28 q^{39} - 8 q^{41} + 38 q^{45} + 36 q^{49} - 84 q^{51} + 20 q^{55} - 20 q^{61} + 10 q^{65} - 4 q^{69} + 16 q^{71} - 10 q^{75} + 4 q^{79} - 52 q^{81} + 36 q^{85} - 96 q^{89} - 8 q^{91} - 32 q^{95} - 28 q^{99}+O(q^{100}) \) 32 * q - 2 * q^5 + 4 * q^9 + 16 * q^11 - 10 * q^15 + 8 * q^19 - 4 * q^21 - 6 * q^25 + 20 * q^29 - 12 * q^31 + 4 * q^35 - 28 * q^39 - 8 * q^41 + 38 * q^45 + 36 * q^49 - 84 * q^51 + 20 * q^55 - 20 * q^61 + 10 * q^65 - 4 * q^69 + 16 * q^71 - 10 * q^75 + 4 * q^79 - 52 * q^81 + 36 * q^85 - 96 * q^89 - 8 * q^91 - 32 * q^95 - 28 * q^99

Introduction

L-functions

Modular forms

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