LMFDB - Embedded newform 576.2.bb.e.49.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			49.11
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.460673 + 1.66966i) q^{3} +(-2.69708 + 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +(-2.57556 + 1.53834i) q^{9} +O(q^{10})$	\(q+(0.460673 + 1.66966i) q^{3} +(-2.69708 + 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +(-2.57556 + 1.53834i) q^{9} +(-1.23365 + 4.60405i) q^{11} +(0.398486 + 1.48717i) q^{13} +(-2.44910 - 4.17029i) q^{15} -6.47719 q^{17} +(-0.957336 + 0.957336i) q^{19} +(4.12172 + 4.06108i) q^{21} +(3.70277 + 2.13780i) q^{23} +(2.42183 - 1.39824i) q^{25} +(-3.75500 - 3.59165i) q^{27} +(-1.07893 - 0.289099i) q^{29} +(-1.89670 + 3.28518i) q^{31} +(-8.25552 + 0.0611777i) q^{33} +(-6.59588 + 6.59588i) q^{35} +(-6.14639 - 6.14639i) q^{37} +(-2.29950 + 1.35044i) q^{39} +(5.04156 + 2.91075i) q^{41} +(-1.69287 + 6.31788i) q^{43} +(5.83476 - 6.01032i) q^{45} +(-1.81739 - 3.14781i) q^{47} +(2.08016 - 3.60295i) q^{49} +(-2.98387 - 10.8147i) q^{51} +(0.762460 + 0.762460i) q^{53} -13.3090i q^{55} +(-2.03945 - 1.15741i) q^{57} +(8.11476 - 2.17434i) q^{59} +(6.74711 + 1.80788i) q^{61} +(-4.88188 + 8.75272i) q^{63} +(-2.14950 - 3.72304i) q^{65} +(0.487339 + 1.81878i) q^{67} +(-1.86364 + 7.16721i) q^{69} -3.98472i q^{71} +5.45461i q^{73} +(3.45027 + 3.39951i) q^{75} +(4.12126 + 15.3808i) q^{77} +(2.95225 + 5.11344i) q^{79} +(4.26702 - 7.92417i) q^{81} +(10.3428 + 2.77135i) q^{83} +(17.4695 - 4.68093i) q^{85} +(-0.0143366 - 1.93463i) q^{87} +2.24307i q^{89} +(3.63698 + 3.63698i) q^{91} +(-6.35891 - 1.65346i) q^{93} +(1.89016 - 3.27385i) q^{95} +(6.50191 + 11.2616i) q^{97} +(-3.90524 - 13.7558i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$3$	0.460673	+	1.66966i	0.265970	+	0.963981i
$3$	0.460673	+	1.66966i	0.265970	+	0.963981i
$4$		0			0
$5$	−2.69708	+	0.722679i	−1.20617	+	0.323192i	−0.805258	−	0.592925i	$-0.797973\pi$
$5$	−2.69708	+	0.722679i	−1.20617	+	0.323192i	−0.400911	+	0.916117i	$0.631306\pi$
$6$		0			0
$7$	2.89314	−	1.67035i	1.09350	−	0.631334i	0.158996	−	0.987279i	$-0.449174\pi$
$7$	2.89314	−	1.67035i	1.09350	−	0.631334i	0.934507	+	0.355945i	$0.115841\pi$
$8$		0			0
$9$	−2.57556	+	1.53834i	−0.858520	+	0.512780i
$10$		0			0
$11$	−1.23365	+	4.60405i	−0.371960	+	1.38817i	0.485777	+	0.874083i	$0.338537\pi$
$11$	−1.23365	+	4.60405i	−0.371960	+	1.38817i	−0.857737	+	0.514089i	$0.828130\pi$
$12$		0			0
$13$	0.398486	+	1.48717i	0.110520	+	0.412467i	0.998913	−	0.0466175i	$-0.0148442\pi$
$13$	0.398486	+	1.48717i	0.110520	+	0.412467i	−0.888393	+	0.459084i	$0.848178\pi$
$14$		0			0
$15$	−2.44910	−	4.17029i	−0.632356	−	1.07677i
$16$		0			0
$17$	−6.47719			−1.57095			−0.785475	−	0.618894i	$-0.787581\pi$
$17$	−6.47719			−1.57095			−0.785475	+	0.618894i	$0.787581\pi$
$18$		0			0
$19$	−0.957336	+	0.957336i	−0.219628	+	0.219628i	−0.808342	−	0.588714i	$-0.799635\pi$
$19$	−0.957336	+	0.957336i	−0.219628	+	0.219628i	0.588714	+	0.808342i	$0.299635\pi$
$20$		0			0
$21$	4.12172	+	4.06108i	0.899433	+	0.886201i
$22$		0			0
$23$	3.70277	+	2.13780i	0.772081	+	0.445761i	0.833617	−	0.552343i	$-0.186266\pi$
$23$	3.70277	+	2.13780i	0.772081	+	0.445761i	−0.0615352	+	0.998105i	$0.519600\pi$
$24$		0			0
$25$	2.42183	−	1.39824i	0.484365	−	0.279648i
$26$		0			0
$27$	−3.75500	−	3.59165i	−0.722651	−	0.691214i
$28$		0			0
$29$	−1.07893	−	0.289099i	−0.200353	−	0.0536843i	0.157247	−	0.987559i	$-0.449738\pi$
$29$	−1.07893	−	0.289099i	−0.200353	−	0.0536843i	−0.357600	+	0.933875i	$0.616405\pi$
$30$		0			0
$31$	−1.89670	+	3.28518i	−0.340657	+	0.590036i	−0.984555	−	0.175076i	$-0.943983\pi$
$31$	−1.89670	+	3.28518i	−0.340657	+	0.590036i	0.643898	+	0.765112i	$0.277316\pi$
$32$		0			0
$33$	−8.25552	+	0.0611777i	−1.43710	+	0.0106497i
$34$		0			0
$35$	−6.59588	+	6.59588i	−1.11491	+	1.11491i
$36$		0			0
$37$	−6.14639	−	6.14639i	−1.01046	−	1.01046i	−0.999945	−	0.0105160i	$-0.996653\pi$
$37$	−6.14639	−	6.14639i	−1.01046	−	1.01046i	−0.0105160	−	0.999945i	$-0.503347\pi$
$38$		0			0
$39$	−2.29950	+	1.35044i	−0.368215	+	0.216243i
$40$		0			0
$41$	5.04156	+	2.91075i	0.787359	+	0.454582i	0.839032	−	0.544082i	$-0.183122\pi$
$41$	5.04156	+	2.91075i	0.787359	+	0.454582i	−0.0516729	+	0.998664i	$0.516455\pi$
$42$		0			0
$43$	−1.69287	+	6.31788i	−0.258160	+	0.963468i	0.708144	+	0.706068i	$0.249533\pi$
$43$	−1.69287	+	6.31788i	−0.258160	+	0.963468i	−0.966305	+	0.257400i	$0.917134\pi$
$44$		0			0
$45$	5.83476	−	6.01032i	0.869794	−	0.895966i
$46$		0			0
$47$	−1.81739	−	3.14781i	−0.265093	−	0.459155i	0.702495	−	0.711689i	$-0.252069\pi$
$47$	−1.81739	−	3.14781i	−0.265093	−	0.459155i	−0.967588	+	0.252534i	$0.918736\pi$
$48$		0			0
$49$	2.08016	−	3.60295i	0.297166	−	0.514707i
$50$		0			0
$51$	−2.98387	−	10.8147i	−0.417825	−	1.51437i
$52$		0			0
$53$	0.762460	+	0.762460i	0.104732	+	0.104732i	0.757531	−	0.652799i	$-0.226405\pi$
$53$	0.762460	+	0.762460i	0.104732	+	0.104732i	−0.652799	+	0.757531i	$0.726405\pi$
$54$		0			0
$55$		−	13.3090i		−	1.79458i
$56$		0			0
$57$	−2.03945	−	1.15741i	−0.270132	−	0.153303i
$58$		0			0
$59$	8.11476	−	2.17434i	1.05645	−	0.283075i	0.311536	−	0.950234i	$-0.399156\pi$
$59$	8.11476	−	2.17434i	1.05645	−	0.283075i	0.744915	+	0.667159i	$0.232490\pi$
$60$		0			0
$61$	6.74711	+	1.80788i	0.863879	+	0.231476i	0.663439	−	0.748230i	$-0.269096\pi$
$61$	6.74711	+	1.80788i	0.863879	+	0.231476i	0.200440	+	0.979706i	$0.435763\pi$
$62$		0			0
$63$	−4.88188	+	8.75272i	−0.615059	+	1.10274i
$64$		0			0
$65$	−2.14950	−	3.72304i	−0.266612	−	0.461786i
$66$		0			0
$67$	0.487339	+	1.81878i	0.0595380	+	0.222199i	0.989284	−	0.146002i	$-0.0466406\pi$
$67$	0.487339	+	1.81878i	0.0595380	+	0.222199i	−0.929746	+	0.368201i	$0.879974\pi$
$68$		0			0
$69$	−1.86364	+	7.16721i	−0.224355	+	0.862831i
$70$		0			0
$71$		−	3.98472i		−	0.472899i	−0.971644	−	0.236450i	$-0.924016\pi$
$71$		−	3.98472i		−	0.472899i	0.971644	−	0.236450i	$-0.0759838\pi$
$72$		0			0
$73$			5.45461i			0.638414i	0.947685	+	0.319207i	$0.103417\pi$
$73$			5.45461i			0.638414i	−0.947685	+	0.319207i	$0.896583\pi$
$74$		0			0
$75$	3.45027	+	3.39951i	0.398402	+	0.392541i
$76$		0			0
$77$	4.12126	+	15.3808i	0.469662	+	1.75280i
$78$		0			0
$79$	2.95225	+	5.11344i	0.332154	+	0.575307i	0.982934	−	0.183959i	$-0.0588914\pi$
$79$	2.95225	+	5.11344i	0.332154	+	0.575307i	−0.650780	+	0.759266i	$0.725558\pi$
$80$		0			0
$81$	4.26702	−	7.92417i	0.474114	−	0.880464i
$82$		0			0
$83$	10.3428	+	2.77135i	1.13527	+	0.304195i	0.777048	−	0.629441i	$-0.216716\pi$
$83$	10.3428	+	2.77135i	1.13527	+	0.304195i	0.358223	+	0.933636i	$0.383383\pi$
$84$		0			0
$85$	17.4695	−	4.68093i	1.89483	−	0.507718i
$86$		0			0
$87$	−0.0143366	−	1.93463i	−0.00153705	−	0.207415i
$88$		0			0
$89$			2.24307i			0.237765i	0.992908	+	0.118883i	$0.0379312\pi$
$89$			2.24307i			0.237765i	−0.992908	+	0.118883i	$0.962069\pi$
$90$		0			0
$91$	3.63698	+	3.63698i	0.381259	+	0.381259i
$92$		0			0
$93$	−6.35891	−	1.65346i	−0.659388	−	0.171456i
$94$		0			0
$95$	1.89016	−	3.27385i	0.193926	−	0.335890i
$96$		0			0
$97$	6.50191	+	11.2616i	0.660169	+	1.14345i	0.980571	+	0.196165i	$0.0628488\pi$
$97$	6.50191	+	11.2616i	0.660169	+	1.14345i	−0.320402	+	0.947282i	$0.603818\pi$
$98$		0			0
$99$	−3.90524	−	13.7558i	−0.392492	−	1.38251i
$100$		0			0
$101$	−2.36072	+	8.81034i	−0.234901	+	0.876662i	0.743293	+	0.668966i	$0.233263\pi$
$101$	−2.36072	+	8.81034i	−0.234901	+	0.876662i	−0.978194	+	0.207696i	$0.933404\pi$
$102$		0			0
$103$	3.73262	+	2.15503i	0.367786	+	0.212342i	0.672491	−	0.740105i	$-0.265224\pi$
$103$	3.73262	+	2.15503i	0.367786	+	0.212342i	−0.304705	+	0.952447i	$0.598558\pi$
$104$		0			0
$105$	−14.0515	−	7.97436i	−1.37128	−	0.778218i
$106$		0			0
$107$	−0.0516852	−	0.0516852i	−0.00499659	−	0.00499659i	0.704604	−	0.709601i	$-0.251125\pi$
$107$	−0.0516852	−	0.0516852i	−0.00499659	−	0.00499659i	−0.709601	+	0.704604i	$0.751125\pi$
$108$		0			0
$109$	5.73510	−	5.73510i	0.549323	−	0.549323i	−0.376922	−	0.926245i	$-0.623018\pi$
$109$	5.73510	−	5.73510i	0.549323	−	0.549323i	0.926245	+	0.376922i	$0.123018\pi$
$110$		0			0
$111$	7.43094	−	13.0939i	0.705313	−	1.24282i
$112$		0			0
$113$	7.13575	−	12.3595i	0.671275	−	1.16268i	−0.306268	−	0.951945i	$-0.599080\pi$
$113$	7.13575	−	12.3595i	0.671275	−	1.16268i	0.977543	−	0.210737i	$-0.0675862\pi$
$114$		0			0
$115$	−11.5316	−	3.08988i	−1.07533	−	0.288133i
$116$		0			0
$117$	−3.31410	−	3.21729i	−0.306389	−	0.297439i
$118$		0			0
$119$	−18.7394	+	10.8192i	−1.71784	+	0.991794i
$120$		0			0
$121$	−10.1491	−	5.85956i	−0.922642	−	0.532688i
$122$		0			0
$123$	−2.53746	+	9.75861i	−0.228795	+	0.879905i
$124$		0			0
$125$	4.35061	−	4.35061i	0.389131	−	0.389131i
$126$		0			0
$127$	16.2634			1.44315			0.721573	−	0.692338i	$-0.243419\pi$
$127$	16.2634			1.44315			0.721573	+	0.692338i	$0.243419\pi$
$128$		0			0
$129$	−11.3286	+	0.0839508i	−0.997428	+	0.00739146i
$130$		0			0
$131$	4.58345	+	17.1057i	0.400458	+	1.49453i	0.812281	+	0.583267i	$0.198226\pi$
$131$	4.58345	+	17.1057i	0.400458	+	1.49453i	−0.411822	+	0.911264i	$0.635108\pi$
$132$		0			0
$133$	−1.17061	+	4.36879i	−0.101505	+	0.378822i
$134$		0			0
$135$	12.7231	+	6.97329i	1.09503	+	0.600166i
$136$		0			0
$137$	−9.62551	+	5.55729i	−0.822363	+	0.474791i	−0.851231	−	0.524792i	$-0.824143\pi$
$137$	−9.62551	+	5.55729i	−0.822363	+	0.474791i	0.0288677	+	0.999583i	$0.490810\pi$
$138$		0			0
$139$	−6.50347	+	1.74260i	−0.551617	+	0.147805i	−0.523852	−	0.851809i	$-0.675506\pi$
$139$	−6.50347	+	1.74260i	−0.551617	+	0.147805i	−0.0277649	+	0.999614i	$0.508839\pi$
$140$		0			0
$141$	4.41856	−	4.48454i	0.372110	−	0.377666i
$142$		0			0
$143$	−7.33859			−0.613684
$144$		0			0
$145$	3.11889			0.259009
$146$		0			0
$147$	6.97399	+	1.81339i	0.575205	+	0.149566i
$148$		0			0
$149$	−10.7583	+	2.88268i	−0.881354	+	0.236158i	−0.670991	−	0.741465i	$-0.734131\pi$
$149$	−10.7583	+	2.88268i	−0.881354	+	0.236158i	−0.210363	+	0.977623i	$0.567465\pi$
$150$		0			0
$151$	18.9045	−	10.9145i	1.53842	−	0.888210i	0.539493	−	0.841990i	$-0.318616\pi$
$151$	18.9045	−	10.9145i	1.53842	−	0.888210i	0.998931	−	0.0462196i	$-0.0147174\pi$
$152$		0			0
$153$	16.6824	−	9.96412i	1.34869	−	0.805551i
$154$		0			0
$155$	2.74141	−	10.2311i	0.220195	−	0.821780i
$156$		0			0
$157$	−2.18429	−	8.15189i	−0.174326	−	0.650592i	−0.996666	−	0.0815954i	$-0.973998\pi$
$157$	−2.18429	−	8.15189i	−0.174326	−	0.650592i	0.822340	−	0.568996i	$-0.192668\pi$
$158$		0			0
$159$	−0.921807	+	1.62430i	−0.0731041	+	0.128815i
$160$		0			0
$161$	14.2835			1.12570
$162$		0			0
$163$	6.93193	−	6.93193i	0.542950	−	0.542950i	−0.381442	−	0.924393i	$-0.624572\pi$
$163$	6.93193	−	6.93193i	0.542950	−	0.542950i	0.924393	+	0.381442i	$0.124572\pi$
$164$		0			0
$165$	22.2216	−	6.13110i	1.72995	−	0.477305i
$166$		0			0
$167$	−7.33544	−	4.23512i	−0.567633	−	0.327723i	0.188570	−	0.982060i	$-0.439615\pi$
$167$	−7.33544	−	4.23512i	−0.567633	−	0.327723i	−0.756204	+	0.654336i	$0.772948\pi$
$168$		0			0
$169$	9.20544	−	5.31477i	0.708111	−	0.408828i
$170$		0			0
$171$	0.992969	−	3.93838i	0.0759342	−	0.301176i
$172$		0			0
$173$	−5.81815	−	1.55897i	−0.442346	−	0.118526i	0.0307700	−	0.999526i	$-0.490204\pi$
$173$	−5.81815	−	1.55897i	−0.442346	−	0.118526i	−0.473116	+	0.881000i	$0.656871\pi$
$174$		0			0
$175$	4.67112	−	8.09061i	0.353103	−	0.611593i
$176$		0			0
$177$	7.36868	+	12.5473i	0.553864	+	0.943110i
$178$		0			0
$179$	8.34442	−	8.34442i	0.623692	−	0.623692i	−0.322782	−	0.946473i	$-0.604618\pi$
$179$	8.34442	−	8.34442i	0.623692	−	0.623692i	0.946473	+	0.322782i	$0.104618\pi$
$180$		0			0
$181$	−13.3444	−	13.3444i	−0.991880	−	0.991880i	0.00808779	−	0.999967i	$-0.497426\pi$
$181$	−13.3444	−	13.3444i	−0.991880	−	0.991880i	−0.999967	+	0.00808779i	$0.997426\pi$
$182$		0			0
$183$	0.0896544	+	12.0983i	0.00662744	+	0.894329i
$184$		0			0
$185$	21.0192	+	12.1354i	1.54536	+	0.892214i
$186$		0			0
$187$	7.99059	−	29.8213i	0.584330	−	2.18075i
$188$		0			0
$189$	−16.8631	−	4.11896i	−1.22661	−	0.299610i
$190$		0			0
$191$	0.892527	+	1.54590i	0.0645810	+	0.111858i	0.896508	−	0.443027i	$-0.146096\pi$
$191$	0.892527	+	1.54590i	0.0645810	+	0.111858i	−0.831927	+	0.554885i	$0.812762\pi$
$192$		0			0
$193$	−8.20588	+	14.2130i	−0.590672	+	1.02307i	0.403470	+	0.914993i	$0.367804\pi$
$193$	−8.20588	+	14.2130i	−0.590672	+	1.02307i	−0.994142	+	0.108081i	$0.965529\pi$
$194$		0			0
$195$	5.22601	−	5.30404i	0.374242	−	0.379830i
$196$		0			0
$197$	−3.44937	−	3.44937i	−0.245758	−	0.245758i	0.573469	−	0.819227i	$-0.305597\pi$
$197$	−3.44937	−	3.44937i	−0.245758	−	0.245758i	−0.819227	+	0.573469i	$0.805597\pi$
$198$		0			0
$199$			15.0093i			1.06398i	0.846751	+	0.531990i	$0.178556\pi$
$199$			15.0093i			1.06398i	−0.846751	+	0.531990i	$0.821444\pi$
$200$		0			0
$201$	−2.81224	+	1.65155i	−0.198360	+	0.116492i
$202$		0			0
$203$	−3.60439	+	0.965795i	−0.252979	+	0.0677855i
$204$		0			0
$205$	−15.7010	−	4.20707i	−1.09661	−	0.293835i
$206$		0			0
$207$	−12.8254	+	0.190096i	−0.891425	+	0.0132126i
$208$		0			0
$209$	−3.22660	−	5.58863i	−0.223189	−	0.386574i
$210$		0			0
$211$	3.18415	+	11.8834i	0.219206	+	0.818089i	0.984643	+	0.174578i	$0.0558562\pi$
$211$	3.18415	+	11.8834i	0.219206	+	0.818089i	−0.765437	+	0.643511i	$0.777477\pi$
$212$		0			0
$213$	6.65314	−	1.83565i	0.455866	−	0.125777i
$214$		0			0
$215$		−	18.2632i		−	1.24554i
$216$		0			0
$217$			12.6726i			0.860274i
$218$		0			0
$219$	−9.10738	+	2.51279i	−0.615419	+	0.169799i
$220$		0			0
$221$	−2.58107	−	9.63269i	−0.173622	−	0.647965i
$222$		0			0
$223$	−0.258294	−	0.447379i	−0.0172967	−	0.0299587i	0.857248	−	0.514905i	$-0.172173\pi$
$223$	−0.258294	−	0.447379i	−0.0172967	−	0.0299587i	−0.874544	+	0.484946i	$0.838839\pi$
$224$		0			0
$225$	−4.08659	+	7.32685i	−0.272439	+	0.488457i
$226$		0			0
$227$	−9.84745	−	2.63862i	−0.653598	−	0.175131i	−0.0832432	−	0.996529i	$-0.526528\pi$
$227$	−9.84745	−	2.63862i	−0.653598	−	0.175131i	−0.570355	+	0.821398i	$0.693194\pi$
$228$		0			0
$229$	−20.6838	+	5.54222i	−1.36683	+	0.366240i	−0.866319	−	0.499491i	$-0.833520\pi$
$229$	−20.6838	+	5.54222i	−1.36683	+	0.366240i	−0.500508	+	0.865732i	$0.666854\pi$
$230$		0			0
$231$	−23.7822	+	13.9666i	−1.56475	+	0.918937i
$232$		0			0
$233$		−	23.2468i		−	1.52295i	−0.648194	−	0.761476i	$-0.724475\pi$
$233$		−	23.2468i		−	1.52295i	0.648194	−	0.761476i	$-0.275525\pi$
$234$		0			0
$235$	7.17649	+	7.17649i	0.468142	+	0.468142i
$236$		0			0
$237$	−7.17771	+	7.28488i	−0.466242	+	0.473204i
$238$		0			0
$239$	−0.219358	+	0.379939i	−0.0141891	+	0.0245762i	−0.873033	−	0.487662i	$-0.837850\pi$
$239$	−0.219358	+	0.379939i	−0.0141891	+	0.0245762i	0.858844	+	0.512238i	$0.171183\pi$
$240$		0			0
$241$	7.67406	+	13.2919i	0.494330	+	0.856204i	0.999979	−	0.00653501i	$-0.00208017\pi$
$241$	7.67406	+	13.2919i	0.494330	+	0.856204i	−0.505649	+	0.862739i	$0.668747\pi$
$242$		0			0
$243$	15.1964	+	3.47405i	0.974850	+	0.222860i
$244$		0			0
$245$	−3.00658	+	11.2207i	−0.192083	+	0.716865i
$246$		0			0
$247$	−1.80521	−	1.04224i	−0.114863	−	0.0663159i
$248$		0			0
$249$	0.137433	+	18.5457i	0.00870948	+	1.17529i
$250$		0			0
$251$	−8.02147	−	8.02147i	−0.506310	−	0.506310i	0.407081	−	0.913392i	$-0.366547\pi$
$251$	−8.02147	−	8.02147i	−0.506310	−	0.506310i	−0.913392	+	0.407081i	$0.866547\pi$
$252$		0			0
$253$	−14.4104	+	14.4104i	−0.905977	+	0.905977i
$254$		0			0
$255$	15.8633	+	27.0118i	0.993399	+	1.69154i
$256$		0			0
$257$	4.72936	−	8.19149i	0.295009	−	0.510971i	−0.679978	−	0.733233i	$-0.738011\pi$
$257$	4.72936	−	8.19149i	0.295009	−	0.510971i	0.974987	+	0.222262i	$0.0713439\pi$
$258$		0			0
$259$	−28.0490	−	7.51571i	−1.74288	−	0.467003i
$260$		0			0
$261$	3.22359	−	0.915171i	0.199535	−	0.0566477i
$262$		0			0
$263$	−16.2413	+	9.37694i	−1.00148	+	0.578207i	−0.908687	−	0.417478i	$-0.862914\pi$
$263$	−16.2413	+	9.37694i	−1.00148	+	0.578207i	−0.0927966	+	0.995685i	$0.529581\pi$
$264$		0			0
$265$	−2.60743	−	1.50540i	−0.160173	−	0.0924759i
$266$		0			0
$267$	−3.74518	+	1.03332i	−0.229201	+	0.0632384i
$268$		0			0
$269$	−13.5606	+	13.5606i	−0.826805	+	0.826805i	−0.987073	−	0.160269i	$-0.948764\pi$
$269$	−13.5606	+	13.5606i	−0.826805	+	0.826805i	0.160269	+	0.987073i	$0.448764\pi$
$270$		0			0
$271$	−30.6233			−1.86023			−0.930115	−	0.367268i	$-0.880293\pi$
$271$	−30.6233			−1.86023			−0.930115	+	0.367268i	$0.880293\pi$
$272$		0			0
$273$	−4.39707	+	7.74799i	−0.266123	+	0.468930i
$274$		0			0
$275$	3.44988	+	12.8751i	0.208036	+	0.776400i
$276$		0			0
$277$	5.40521	−	20.1725i	0.324767	−	1.21205i	−0.589778	−	0.807565i	$-0.700785\pi$
$277$	5.40521	−	20.1725i	0.324767	−	1.21205i	0.914545	−	0.404483i	$-0.132549\pi$
$278$		0			0
$279$	−0.168657	−	11.3789i	−0.0100972	−	0.681240i
$280$		0			0
$281$	10.6538	−	6.15097i	0.635552	−	0.366936i	−0.147347	−	0.989085i	$-0.547073\pi$
$281$	10.6538	−	6.15097i	0.635552	−	0.366936i	0.782899	+	0.622149i	$0.213740\pi$
$282$		0			0
$283$	−12.8013	+	3.43009i	−0.760957	+	0.203898i	−0.618373	−	0.785885i	$-0.712208\pi$
$283$	−12.8013	+	3.43009i	−0.760957	+	0.203898i	−0.142584	+	0.989783i	$0.545541\pi$
$284$		0			0
$285$	6.33698	+	1.64776i	0.375371	+	0.0976047i
$286$		0			0
$287$	19.4479			1.14797
$288$		0			0
$289$	24.9540			1.46788
$290$		0			0
$291$	−15.8079	+	16.0440i	−0.926676	+	0.940513i
$292$		0			0
$293$	21.3351	−	5.71672i	1.24641	−	0.333974i	0.425460	−	0.904977i	$-0.360112\pi$
$293$	21.3351	−	5.71672i	1.24641	−	0.333974i	0.820948	+	0.571003i	$0.193446\pi$
$294$		0			0
$295$	−20.3148	+	11.7287i	−1.18277	+	0.682874i
$296$		0			0
$297$	21.1685	−	12.8574i	1.22832	−	0.746060i
$298$		0			0
$299$	−1.70377	+	6.35854i	−0.0985313	+	0.367724i
$300$		0			0
$301$	5.65539	+	21.1062i	0.325971	+	1.21654i
$302$		0			0
$303$	−15.7978	+	0.117070i	−0.907562	+	0.00672551i
$304$		0			0
$305$	−19.5040			−1.11680
$306$		0			0
$307$	3.59225	−	3.59225i	0.205021	−	0.205021i	−0.597126	−	0.802147i	$-0.703691\pi$
$307$	3.59225	−	3.59225i	0.205021	−	0.205021i	0.802147	+	0.597126i	$0.203691\pi$
$308$		0			0
$309$	−1.87866	+	7.22499i	−0.106873	+	0.411016i
$310$		0			0
$311$	8.62665	+	4.98060i	0.489173	+	0.282424i	0.724231	−	0.689557i	$-0.242195\pi$
$311$	8.62665	+	4.98060i	0.489173	+	0.282424i	−0.235058	+	0.971981i	$0.575528\pi$
$312$		0			0
$313$	−22.1588	+	12.7934i	−1.25249	+	0.723124i	−0.971603	−	0.236617i	$-0.923961\pi$
$313$	−22.1588	+	12.7934i	−1.25249	+	0.723124i	−0.280885	+	0.959741i	$0.590628\pi$
$314$		0			0
$315$	6.84139	−	27.1348i	0.385469	−	1.52887i
$316$		0			0
$317$	17.8781	+	4.79041i	1.00413	+	0.269056i	0.723176	−	0.690664i	$-0.242682\pi$
$317$	17.8781	+	4.79041i	1.00413	+	0.269056i	0.280957	+	0.959720i	$0.409348\pi$
$318$		0			0
$319$	2.66205	−	4.61080i	0.149046	−	0.258155i
$320$		0			0
$321$	0.0624869	−	0.110107i	0.00348768	−	0.00614557i
$322$		0			0
$323$	6.20084	−	6.20084i	0.345024	−	0.345024i
$324$		0			0
$325$	3.04449	+	3.04449i	0.168878	+	0.168878i
$326$		0			0
$327$	12.2177	+	6.93369i	0.675641	+	0.383434i
$328$		0			0
$329$	−10.5159	−	6.07136i	−0.579760	−	0.334725i
$330$		0			0
$331$	−5.10146	+	19.0389i	−0.280402	+	1.04647i	0.671733	+	0.740794i	$0.265550\pi$
$331$	−5.10146	+	19.0389i	−0.280402	+	1.04647i	−0.952134	+	0.305680i	$0.901116\pi$
$332$		0			0
$333$	25.2856	+	6.37517i	1.38564	+	0.349357i
$334$		0			0
$335$	−2.62878	−	4.55319i	−0.143626	−	0.248767i
$336$		0			0
$337$	3.29609	−	5.70899i	0.179549	−	0.310988i	−0.762177	−	0.647369i	$-0.775869\pi$
$337$	3.29609	−	5.70899i	0.179549	−	0.310988i	0.941726	+	0.336380i	$0.109203\pi$
$338$		0			0
$339$	23.9234	+	6.22063i	1.29934	+	0.337858i
$340$		0			0
$341$	−12.7852	−	12.7852i	−0.692360	−	0.692360i
$342$		0			0
$343$			9.48653i			0.512224i
$344$		0			0
$345$	−0.153230	−	20.6773i	−0.00824961	−	1.11323i
$346$		0			0
$347$	3.20074	−	0.857635i	0.171825	−	0.0460403i	−0.171881	−	0.985118i	$-0.554984\pi$
$347$	3.20074	−	0.857635i	0.171825	−	0.0460403i	0.343706	+	0.939077i	$0.388318\pi$
$348$		0			0
$349$	−22.0000	−	5.89488i	−1.17763	−	0.315546i	−0.383645	−	0.923480i	$-0.625331\pi$
$349$	−22.0000	−	5.89488i	−1.17763	−	0.315546i	−0.793987	+	0.607935i	$0.791998\pi$
$350$		0			0
$351$	3.84508	−	7.01555i	0.205235	−	0.374463i
$352$		0			0
$353$	14.2071	+	24.6074i	0.756167	+	1.30972i	0.944792	+	0.327670i	$0.106263\pi$
$353$	14.2071	+	24.6074i	0.756167	+	1.30972i	−0.188626	+	0.982049i	$0.560403\pi$
$354$		0			0
$355$	2.87967	+	10.7471i	0.152837	+	0.570396i
$356$		0			0
$357$	−26.6972	−	26.3044i	−1.41296	−	1.39218i
$358$		0			0
$359$			7.35521i			0.388193i	0.980982	+	0.194097i	$0.0621775\pi$
$359$			7.35521i			0.388193i	−0.980982	+	0.194097i	$0.937823\pi$
$360$		0			0
$361$			17.1670i			0.903527i
$362$		0			0
$363$	5.10811	−	19.6449i	0.268106	−	1.03109i
$364$		0			0
$365$	−3.94194	−	14.7115i	−0.206330	−	0.770035i
$366$		0			0
$367$	17.0496	+	29.5308i	0.889984	+	1.54150i	0.839893	+	0.542752i	$0.182618\pi$
$367$	17.0496	+	29.5308i	0.889984	+	1.54150i	0.0500906	+	0.998745i	$0.484049\pi$
$368$		0			0
$369$	−17.4626	+	0.258827i	−0.909064	+	0.0134740i
$370$		0			0
$371$	3.47948	+	0.932323i	0.180646	+	0.0484038i
$372$		0			0
$373$	23.8179	−	6.38198i	1.23324	−	0.330447i	0.417402	−	0.908722i	$-0.362941\pi$
$373$	23.8179	−	6.38198i	1.23324	−	0.330447i	0.815842	+	0.578275i	$0.196274\pi$
$374$		0			0
$375$	9.26828	+	5.25986i	0.478612	+	0.271618i
$376$		0			0
$377$		−	1.71976i		−	0.0885720i
$378$		0			0
$379$	2.66916	+	2.66916i	0.137106	+	0.137106i	0.772329	−	0.635223i	$-0.219092\pi$
$379$	2.66916	+	2.66916i	0.137106	+	0.137106i	−0.635223	+	0.772329i	$0.719092\pi$
$380$		0			0
$381$	7.49212	+	27.1545i	0.383833	+	1.39117i
$382$		0			0
$383$	3.14570	−	5.44851i	0.160738	−	0.278406i	−0.774396	−	0.632701i	$-0.781946\pi$
$383$	3.14570	−	5.44851i	0.160738	−	0.278406i	0.935133	+	0.354296i	$0.115279\pi$
$384$		0			0
$385$	−22.2307	−	38.5047i	−1.13298	−	1.96238i
$386$		0			0
$387$	−5.35895	−	18.8763i	−0.272411	−	0.959536i
$388$		0			0
$389$	−0.724164	+	2.70262i	−0.0367166	+	0.137028i	−0.981851	−	0.189653i	$-0.939264\pi$
$389$	−0.724164	+	2.70262i	−0.0367166	+	0.137028i	0.945135	+	0.326681i	$0.105930\pi$
$390$		0			0
$391$	−23.9836	−	13.8469i	−1.21290	−	0.700269i
$392$		0			0
$393$	−26.4493	+	15.5330i	−1.33419	+	0.783534i
$394$		0			0
$395$	−11.6578	−	11.6578i	−0.586568	−	0.586568i
$396$		0			0
$397$	−4.29700	+	4.29700i	−0.215660	+	0.215660i	−0.806667	−	0.591007i	$-0.798731\pi$
$397$	−4.29700	+	4.29700i	−0.215660	+	0.215660i	0.591007	+	0.806667i	$0.298731\pi$
$398$		0			0
$399$	−7.83369	+	0.0580517i	−0.392175	+	0.00290622i
$400$		0			0
$401$	−6.63116	+	11.4855i	−0.331145	+	0.573559i	−0.982737	−	0.185010i	$-0.940768\pi$
$401$	−6.63116	+	11.4855i	−0.331145	+	0.573559i	0.651592	+	0.758570i	$0.274101\pi$
$402$		0			0
$403$	−5.64143	−	1.51162i	−0.281020	−	0.0752990i
$404$		0			0
$405$	−5.78185	+	24.4558i	−0.287303	+	1.21522i
$406$		0			0
$407$	35.8808	−	20.7158i	1.77854	−	1.02684i
$408$		0			0
$409$	−10.6538	−	6.15100i	−0.526799	−	0.304147i	0.212913	−	0.977071i	$-0.431705\pi$
$409$	−10.6538	−	6.15100i	−0.526799	−	0.304147i	−0.739712	+	0.672924i	$0.765038\pi$
$410$		0			0
$411$	−13.7130	−	13.5113i	−0.676414	−	0.666462i
$412$		0			0
$413$	19.8452	−	19.8452i	0.976518	−	0.976518i
$414$		0			0
$415$	−29.8981			−1.46764
$416$		0			0
$417$	−5.90553	−	10.0558i	−0.289195	−	0.492437i
$418$		0			0
$419$	−7.82317	−	29.1965i	−0.382187	−	1.42634i	−0.842554	−	0.538612i	$-0.818949\pi$
$419$	−7.82317	−	29.1965i	−0.382187	−	1.42634i	0.460367	−	0.887729i	$-0.347718\pi$
$420$		0			0
$421$	−5.75964	+	21.4953i	−0.280708	+	1.04762i	0.671211	+	0.741266i	$0.265774\pi$
$421$	−5.75964	+	21.4953i	−0.280708	+	1.04762i	−0.951919	+	0.306350i	$0.900892\pi$
$422$		0			0
$423$	9.52319	+	5.31161i	0.463033	+	0.258259i
$424$		0			0
$425$	−15.6866	+	9.05668i	−0.760913	+	0.439314i
$426$		0			0
$427$	22.5401	−	6.03961i	1.09079	−	0.292277i
$428$		0			0
$429$	−3.38069	−	12.2530i	−0.163221	−	0.591580i
$430$		0			0
$431$	−15.3940			−0.741505			−0.370752	−	0.928732i	$-0.620900\pi$
$431$	−15.3940			−0.741505			−0.370752	+	0.928732i	$0.620900\pi$
$432$		0			0
$433$	−17.2454			−0.828763			−0.414382	−	0.910103i	$-0.636002\pi$
$433$	−17.2454			−0.828763			−0.414382	+	0.910103i	$0.636002\pi$
$434$		0			0
$435$	1.43679	+	5.20749i	0.0688887	+	0.249680i
$436$		0			0
$437$	−5.59138	+	1.49821i	−0.267472	+	0.0716690i
$438$		0			0
$439$	4.55070	−	2.62735i	0.217193	−	0.125397i	−0.387457	−	0.921888i	$-0.626646\pi$
$439$	4.55070	−	2.62735i	0.217193	−	0.125397i	0.604650	+	0.796491i	$0.293313\pi$
$440$		0			0
$441$	0.184971	+	12.4796i	0.00880813	+	0.594267i
$442$		0			0
$443$	−3.35032	+	12.5036i	−0.159179	+	0.594062i	0.839533	+	0.543309i	$0.182829\pi$
$443$	−3.35032	+	12.5036i	−0.159179	+	0.594062i	−0.998711	+	0.0507532i	$0.983838\pi$
$444$		0			0
$445$	−1.62102	−	6.04974i	−0.0768438	−	0.286785i
$446$		0			0
$447$	−9.76916	−	16.6348i	−0.462066	−	0.786798i
$448$		0			0
$449$	27.9740			1.32018			0.660088	−	0.751189i	$-0.270519\pi$
$449$	27.9740			1.32018			0.660088	+	0.751189i	$0.270519\pi$
$450$		0			0
$451$	−19.6207	+	19.6207i	−0.923904	+	0.923904i
$452$		0			0
$453$	26.9323	+	26.5361i	1.26539	+	1.24678i
$454$		0			0
$455$	−12.4376	−	7.18083i	−0.583082	−	0.336643i
$456$		0			0
$457$	35.2732	−	20.3650i	1.65001	−	0.952635i	0.672947	−	0.739690i	$-0.265028\pi$
$457$	35.2732	−	20.3650i	1.65001	−	0.952635i	0.977064	−	0.212944i	$-0.0683053\pi$
$458$		0			0
$459$	24.3219	+	23.2638i	1.13525	+	1.08586i
$460$		0			0
$461$	−36.8721	−	9.87984i	−1.71730	−	0.460150i	−0.740107	−	0.672489i	$-0.765225\pi$
$461$	−36.8721	−	9.87984i	−1.71730	−	0.460150i	−0.977196	+	0.212339i	$0.931892\pi$
$462$		0			0
$463$	17.7637	−	30.7676i	0.825549	−	1.42989i	−0.0759497	−	0.997112i	$-0.524199\pi$
$463$	17.7637	−	30.7676i	0.825549	−	1.42989i	0.901499	−	0.432781i	$-0.142468\pi$
$464$		0			0
$465$	18.3454	−	0.135949i	0.850746	−	0.00630447i
$466$		0			0
$467$	17.1010	−	17.1010i	0.791341	−	0.791341i	−0.190371	−	0.981712i	$-0.560969\pi$
$467$	17.1010	−	17.1010i	0.791341	−	0.791341i	0.981712	+	0.190371i	$0.0609692\pi$
$468$		0			0
$469$	4.44794	+	4.44794i	0.205387	+	0.205387i
$470$		0			0
$471$	12.6047	−	7.40239i	0.580793	−	0.341084i
$472$		0			0
$473$	−26.9994	−	15.5881i	−1.24143	−	0.716742i
$474$		0			0
$475$	−0.979914	+	3.65709i	−0.0449615	+	0.167799i
$476$		0			0
$477$	−3.13668	−	0.790839i	−0.143619	−	0.0362101i
$478$		0			0
$479$	6.76619	+	11.7194i	0.309155	+	0.535473i	0.978178	−	0.207769i	$-0.0666204\pi$
$479$	6.76619	+	11.7194i	0.309155	+	0.535473i	−0.669023	+	0.743242i	$0.733287\pi$
$480$		0			0
$481$	6.69148	−	11.5900i	0.305105	−	0.528458i
$482$		0			0
$483$	6.58003	+	23.8487i	0.299402	+	1.08515i
$484$		0			0
$485$	−25.6747	−	25.6747i	−1.16583	−	1.16583i
$486$		0			0
$487$		−	16.1436i		−	0.731536i	−0.930706	−	0.365768i	$-0.880806\pi$
$487$		−	16.1436i		−	0.731536i	0.930706	−	0.365768i	$-0.119194\pi$
$488$		0			0
$489$	14.7673	+	8.38064i	0.667802	+	0.378986i
$490$		0			0
$491$	34.9555	−	9.36630i	1.57752	−	0.422695i	0.639363	−	0.768905i	$-0.279198\pi$
$491$	34.9555	−	9.36630i	1.57752	−	0.422695i	0.938157	+	0.346209i	$0.112531\pi$
$492$		0			0
$493$	6.98844	+	1.87255i	0.314744	+	0.0843353i
$494$		0			0
$495$	20.4737	+	34.2781i	0.920227	+	1.54069i
$496$		0			0
$497$	−6.65589	−	11.5283i	−0.298557	−	0.517117i
$498$		0			0
$499$	1.70347	+	6.35742i	0.0762576	+	0.284597i	0.993516	−	0.113696i	$-0.0362691\pi$
$499$	1.70347	+	6.35742i	0.0762576	+	0.284597i	−0.917258	+	0.398294i	$0.869602\pi$
$500$		0			0
$501$	3.69199	−	14.1987i	0.164946	−	0.634352i
$502$		0			0
$503$			8.67964i			0.387006i	0.981100	+	0.193503i	$0.0619849\pi$
$503$			8.67964i			0.387006i	−0.981100	+	0.193503i	$0.938015\pi$
$504$		0			0
$505$		−	25.4682i		−	1.13332i
$506$		0			0
$507$	13.1146	+	12.9216i	0.582439	+	0.573870i
$508$		0			0
$509$	0.894794	+	3.33942i	0.0396611	+	0.148017i	0.982917	−	0.184050i	$-0.0589207\pi$
$509$	0.894794	+	3.33942i	0.0396611	+	0.148017i	−0.943256	+	0.332067i	$0.892254\pi$
$510$		0			0
$511$	9.11113	+	15.7809i	0.403053	+	0.698108i
$512$		0			0
$513$	7.03321	−	0.156382i	0.310524	−	0.00690444i
$514$		0			0
$515$	−11.6246	−	3.11479i	−0.512240	−	0.137254i
$516$		0			0
$517$	16.7347	−	4.48404i	0.735990	−	0.197208i
$518$		0			0
$519$	−0.0773105	−	10.4325i	−0.00339355	−	0.457937i
$520$		0			0
$521$			15.7843i			0.691524i	0.938322	+	0.345762i	$0.112380\pi$
$521$			15.7843i			0.691524i	−0.938322	+	0.345762i	$0.887620\pi$
$522$		0			0
$523$	−6.62449	−	6.62449i	−0.289669	−	0.289669i	0.547280	−	0.836949i	$-0.315663\pi$
$523$	−6.62449	−	6.62449i	−0.289669	−	0.289669i	−0.836949	+	0.547280i	$0.815663\pi$
$524$		0			0
$525$	15.6605	+	4.07207i	0.683479	+	0.177720i
$526$		0			0
$527$	12.2853	−	21.2787i	0.535155	−	0.926916i
$528$		0			0
$529$	−2.35965	−	4.08703i	−0.102593	−	0.177697i
$530$		0			0
$531$	−17.5552	+	18.0834i	−0.761830	+	0.784753i
$532$		0			0
$533$	−2.31978	+	8.65755i	−0.100481	+	0.375000i
$534$		0			0
$535$	0.176751	+	0.102047i	0.00764160	+	0.00441188i
$536$		0			0
$537$	17.7764	+	10.0883i	0.767110	+	0.435344i
$538$		0			0
$539$	14.0219	+	14.0219i	0.603967	+	0.603967i
$540$		0			0
$541$	32.2832	−	32.2832i	1.38796	−	1.38796i	0.558377	−	0.829587i	$-0.311424\pi$
$541$	32.2832	−	32.2832i	1.38796	−	1.38796i	0.829587	−	0.558377i	$-0.188576\pi$
$542$		0			0
$543$	16.1332	−	28.4280i	0.692343	−	1.21996i
$544$		0			0
$545$	−11.3234	+	19.6126i	−0.485040	+	0.840113i
$546$		0			0
$547$	7.43060	+	1.99102i	0.317710	+	0.0851300i	0.414150	−	0.910209i	$-0.364079\pi$
$547$	7.43060	+	1.99102i	0.317710	+	0.0851300i	−0.0964402	+	0.995339i	$0.530746\pi$
$548$		0			0
$549$	−20.1587	+	5.72304i	−0.860354	+	0.244253i
$550$		0			0
$551$	1.30966	−	0.756135i	0.0557936	−	0.0322124i
$552$		0			0
$553$	17.0825	+	9.86259i	0.726422	+	0.419400i
$554$		0			0
$555$	−10.5791	+	40.6854i	−0.449058	+	1.72700i
$556$		0			0
$557$	24.4143	−	24.4143i	1.03447	−	1.03447i	0.0350828	−	0.999384i	$-0.488830\pi$
$557$	24.4143	−	24.4143i	1.03447	−	1.03447i	0.999384	−	0.0350828i	$-0.0111695\pi$
$558$		0			0
$559$	−10.0704			−0.425931
$560$		0			0
$561$	53.4726	−	0.396260i	2.25761	−	0.0167301i
$562$		0			0
$563$	−3.30278	−	12.3261i	−0.139196	−	0.519485i	−0.999945	−	0.0104567i	$-0.996671\pi$
$563$	−3.30278	−	12.3261i	−0.139196	−	0.519485i	0.860750	−	0.509028i	$-0.169995\pi$
$564$		0			0
$565$	−10.3137	+	38.4913i	−0.433901	+	1.61934i
$566$		0			0
$567$	−0.891083	−	30.0532i	−0.0374220	−	1.26211i
$568$		0			0
$569$	22.2747	−	12.8603i	0.933803	−	0.539132i	0.0457910	−	0.998951i	$-0.485419\pi$
$569$	22.2747	−	12.8603i	0.933803	−	0.539132i	0.888012	+	0.459819i	$0.152086\pi$
$570$		0			0
$571$	−33.6207	+	9.00865i	−1.40698	+	0.377000i	−0.880848	−	0.473400i	$-0.843027\pi$
$571$	−33.6207	+	9.00865i	−1.40698	+	0.377000i	−0.526136	+	0.850400i	$0.676360\pi$
$572$		0			0
$573$	−2.16997	+	2.20238i	−0.0906520	+	0.0920056i
$574$		0			0
$575$	11.9566			0.498626
$576$		0			0
$577$	−26.7695			−1.11443			−0.557215	−	0.830369i	$-0.688130\pi$
$577$	−26.7695			−1.11443			−0.557215	+	0.830369i	$0.688130\pi$
$578$		0			0
$579$	−27.5112	−	7.15352i	−1.14333	−	0.297290i
$580$		0			0
$581$	34.5523	−	9.25826i	1.43347	−	0.384097i
$582$		0			0
$583$	−4.45101	+	2.56979i	−0.184342	+	0.106430i
$584$		0			0
$585$	11.2634	+	6.28225i	0.465686	+	0.259739i
$586$		0			0
$587$	−9.79668	+	36.5617i	−0.404352	+	1.50906i	0.400895	+	0.916124i	$0.368699\pi$
$587$	−9.79668	+	36.5617i	−0.404352	+	1.50906i	−0.805247	+	0.592939i	$0.797967\pi$
$588$		0			0
$589$	−1.32924	−	4.96080i	−0.0547704	−	0.204406i
$590$		0			0
$591$	4.17026	−	7.34833i	0.171542	−	0.302270i
$592$		0			0
$593$	−7.98596			−0.327944			−0.163972	−	0.986465i	$-0.552431\pi$
$593$	−7.98596			−0.327944			−0.163972	+	0.986465i	$0.552431\pi$
$594$		0			0
$595$	42.7228	−	42.7228i	1.75146	−	1.75146i
$596$		0			0
$597$	−25.0605	+	6.91437i	−1.02566	+	0.282986i
$598$		0			0
$599$	−1.64879	−	0.951932i	−0.0673679	−	0.0388949i	0.465938	−	0.884818i	$-0.345717\pi$
$599$	−1.64879	−	0.951932i	−0.0673679	−	0.0388949i	−0.533306	+	0.845923i	$0.679050\pi$
$600$		0			0
$601$	−11.7530	+	6.78561i	−0.479416	+	0.276791i	−0.720173	−	0.693794i	$-0.755938\pi$
$601$	−11.7530	+	6.78561i	−0.479416	+	0.276791i	0.240757	+	0.970585i	$0.422604\pi$
$602$		0			0
$603$	−4.05307	−	3.93467i	−0.165054	−	0.160232i
$604$		0			0
$605$	31.6074	+	8.46917i	1.28502	+	0.344321i
$606$		0			0
$607$	3.16527	−	5.48241i	0.128474	−	0.222524i	−0.794611	−	0.607119i	$-0.792325\pi$
$607$	3.16527	−	5.48241i	0.128474	−	0.222524i	0.923086	+	0.384594i	$0.125659\pi$
$608$		0			0
$609$	−3.27300	−	5.57321i	−0.132629	−	0.225838i
$610$		0			0
$611$	3.95712	−	3.95712i	0.160088	−	0.160088i
$612$		0			0
$613$	−1.83081	−	1.83081i	−0.0739458	−	0.0739458i	0.669167	−	0.743112i	$-0.266651\pi$
$613$	−1.83081	−	1.83081i	−0.0739458	−	0.0739458i	−0.743112	+	0.669167i	$0.766651\pi$
$614$		0			0
$615$	−0.208632	−	28.1535i	−0.00841285	−	1.13526i
$616$		0			0
$617$	3.82758	+	2.20985i	0.154092	+	0.0889653i	0.575064	−	0.818109i	$-0.304977\pi$
$617$	3.82758	+	2.20985i	0.154092	+	0.0889653i	−0.420971	+	0.907074i	$0.638311\pi$
$618$		0			0
$619$	−3.75899	+	14.0287i	−0.151087	+	0.563863i	0.848322	+	0.529480i	$0.177613\pi$
$619$	−3.75899	+	14.0287i	−0.151087	+	0.563863i	−0.999409	+	0.0343824i	$0.989054\pi$
$620$		0			0
$621$	−6.22570	−	21.3265i	−0.249829	−	0.855803i
$622$		0			0
$623$	3.74672	+	6.48952i	0.150109	+	0.259997i
$624$		0			0
$625$	−15.5810	+	26.9872i	−0.623242	+	1.07949i
$626$		0			0
$627$	7.84474	−	7.96187i	0.313289	−	0.317967i
$628$		0			0
$629$	39.8114	+	39.8114i	1.58738	+	1.58738i
$630$		0			0
$631$			33.6255i			1.33861i	0.742987	+	0.669305i	$0.233408\pi$
$631$			33.6255i			1.33861i	−0.742987	+	0.669305i	$0.766592\pi$
$632$		0			0
$633$	−18.3745	+	10.7908i	−0.730320	+	0.428898i
$634$		0			0
$635$	−43.8637	+	11.7532i	−1.74068	+	0.466413i
$636$		0			0
$637$	6.18711	+	1.65783i	0.245142	+	0.0656857i
$638$		0			0
$639$	6.12985	+	10.2629i	0.242493	+	0.405993i
$640$		0			0
$641$	−22.9601	−	39.7681i	−0.906871	−	1.57075i	−0.818386	−	0.574668i	$-0.805131\pi$
$641$	−22.9601	−	39.7681i	−0.906871	−	1.57075i	−0.0884843	−	0.996078i	$-0.528202\pi$
$642$		0			0
$643$	−6.92565	−	25.8469i	−0.273121	−	1.01930i	−0.957090	−	0.289790i	$-0.906415\pi$
$643$	−6.92565	−	25.8469i	−0.273121	−	1.01930i	0.683969	−	0.729511i	$-0.260252\pi$
$644$		0			0
$645$	30.4934	−	8.41337i	1.20068	−	0.331276i
$646$		0			0
$647$			11.4351i			0.449559i	0.974410	+	0.224780i	$0.0721662\pi$
$647$			11.4351i			0.449559i	−0.974410	+	0.224780i	$0.927834\pi$
$648$		0			0
$649$			40.0431i			1.57183i
$650$		0			0
$651$	−21.1590	+	5.83794i	−0.829288	+	0.228807i
$652$		0			0
$653$	5.73613	+	21.4075i	0.224472	+	0.837741i	0.982615	+	0.185653i	$0.0594401\pi$
$653$	5.73613	+	21.4075i	0.224472	+	0.837741i	−0.758143	+	0.652088i	$0.773893\pi$
$654$		0			0
$655$	−24.7239	−	42.8230i	−0.966041	−	1.67323i
$656$		0			0
$657$	−8.39105	−	14.0487i	−0.327366	−	0.548091i
$658$		0			0
$659$	−26.7345	−	7.16348i	−1.04143	−	0.279050i	−0.302723	−	0.953079i	$-0.597896\pi$
$659$	−26.7345	−	7.16348i	−1.04143	−	0.279050i	−0.738705	+	0.674029i	$0.764562\pi$
$660$		0			0
$661$	9.68293	−	2.59453i	0.376622	−	0.100916i	−0.0655417	−	0.997850i	$-0.520878\pi$
$661$	9.68293	−	2.59453i	0.376622	−	0.100916i	0.442164	+	0.896934i	$0.354211\pi$
$662$		0			0
$663$	14.8943	−	8.74704i	0.578448	−	0.339707i
$664$		0			0
$665$		−	12.6289i		−	0.489729i
$666$		0			0
$667$	−3.37700	−	3.37700i	−0.130758	−	0.130758i
$668$		0			0
$669$	0.627984	−	0.637360i	0.0242792	−	0.0246418i
$670$		0			0
$671$	−16.6472	+	28.8337i	−0.642656	+	1.11311i
$672$		0			0
$673$	−16.7789	−	29.0620i	−0.646781	−	1.12026i	−0.983887	−	0.178791i	$-0.942782\pi$
$673$	−16.7789	−	29.0620i	−0.646781	−	1.12026i	0.337106	−	0.941467i	$-0.390552\pi$
$674$		0			0
$675$	−14.1160	−	3.44795i	−0.543324	−	0.132712i
$676$		0			0
$677$	6.92612	−	25.8486i	0.266192	−	0.993443i	−0.695324	−	0.718696i	$-0.744739\pi$
$677$	6.92612	−	25.8486i	0.266192	−	0.993443i	0.961517	−	0.274747i	$-0.0885941\pi$
$678$		0			0
$679$	37.6218	+	21.7210i	1.44379	+	0.833575i
$680$		0			0
$681$	−0.130851	−	17.6575i	−0.00501423	−	0.676636i
$682$		0			0
$683$	9.62993	+	9.62993i	0.368479	+	0.368479i	0.866922	−	0.498443i	$-0.166095\pi$
$683$	9.62993	+	9.62993i	0.368479	+	0.368479i	−0.498443	+	0.866922i	$0.666095\pi$
$684$		0			0
$685$	21.9446	−	21.9446i	0.838460	−	0.838460i
$686$		0			0
$687$	−18.7821	−	31.9819i	−0.716583	−	1.22019i
$688$		0			0
$689$	−0.830078	+	1.43774i	−0.0316235	+	0.0547734i
$690$		0			0
$691$	36.8896	+	9.88454i	1.40335	+	0.376025i	0.879545	−	0.475815i	$-0.157847\pi$
$691$	36.8896	+	9.88454i	1.40335	+	0.376025i	0.523801	+	0.851841i	$0.324514\pi$
$692$		0			0
$693$	−34.2754	−	33.2742i	−1.30201	−	1.26398i
$694$		0			0
$695$	16.2810	−	9.39985i	0.617574	−	0.356557i
$696$		0			0
$697$	−32.6551	−	18.8534i	−1.23690	−	0.714125i
$698$		0			0
$699$	38.8144	−	10.7092i	1.46810	−	0.405059i
$700$		0			0
$701$	−24.7308	+	24.7308i	−0.934070	+	0.934070i	−0.997957	−	0.0638873i	$-0.979650\pi$
$701$	−24.7308	+	24.7308i	−0.934070	+	0.934070i	0.0638873	+	0.997957i	$0.479650\pi$
$702$		0			0
$703$	11.7683			0.443851
$704$		0			0
$705$	−8.67631	+	15.2883i	−0.326769	+	0.575792i
$706$		0			0
$707$	7.88649	+	29.4328i	0.296602	+	1.10693i
$708$		0			0
$709$	−7.27509	+	27.1510i	−0.273222	+	1.01968i	0.683802	+	0.729668i	$0.260325\pi$
$709$	−7.27509	+	27.1510i	−0.273222	+	1.01968i	−0.957024	+	0.290010i	$0.906341\pi$
$710$		0			0
$711$	−15.4699	−	8.62842i	−0.580166	−	0.323591i
$712$		0			0
$713$	−14.0461	+	8.10951i	−0.526030	+	0.303704i
$714$		0			0
$715$	19.7927	−	5.30345i	0.740207	−	0.198338i
$716$		0			0
$717$	−0.735423	−	0.191226i	−0.0274649	−	0.00714148i
$718$		0			0
$719$	−12.7928			−0.477091			−0.238546	−	0.971131i	$-0.576671\pi$
$719$	−12.7928			−0.477091			−0.238546	+	0.971131i	$0.576671\pi$
$720$		0			0
$721$	14.3987			0.536234
$722$		0			0
$723$	−18.6577	+	18.9363i	−0.693888	+	0.704249i
$724$		0			0
$725$	−3.01722	+	0.808460i	−0.112057	+	0.0300255i
$726$		0			0
$727$	−3.44828	+	1.99086i	−0.127890	+	0.0738371i	−0.562580	−	0.826743i	$-0.690191\pi$
$727$	−3.44828	+	1.99086i	−0.127890	+	0.0738371i	0.434690	+	0.900580i	$0.356858\pi$
$728$		0			0
$729$	1.20009	+	26.9733i	0.0444477	+	0.999012i
$730$		0			0
$731$	10.9650	−	40.9221i	0.405557	−	1.51356i
$732$		0			0
$733$	9.71206	+	36.2459i	0.358723	+	1.33877i	0.875734	+	0.482794i	$0.160378\pi$
$733$	9.71206	+	36.2459i	0.358723	+	1.33877i	−0.517011	+	0.855979i	$0.672955\pi$
$734$		0			0
$735$	−20.1199	+	0.149099i	−0.742133	+	0.00549959i
$736$		0			0
$737$	−8.97493			−0.330596
$738$		0			0
$739$	−3.06425	+	3.06425i	−0.112720	+	0.112720i	−0.761217	−	0.648497i	$-0.775398\pi$
$739$	−3.06425	+	3.06425i	−0.112720	+	0.112720i	0.648497	+	0.761217i	$0.275398\pi$
$740$		0			0
$741$	0.908575	−	3.49422i	0.0333774	−	0.128363i
$742$		0			0
$743$	30.1059	+	17.3817i	1.10448	+	0.637671i	0.937394	−	0.348272i	$-0.113231\pi$
$743$	30.1059	+	17.3817i	1.10448	+	0.637671i	0.167085	+	0.985943i	$0.446565\pi$
$744$		0			0
$745$	26.9327	−	15.5496i	0.986738	−	0.569693i
$746$		0			0
$747$	−30.9018	+	8.77298i	−1.13064	+	0.320986i
$748$		0			0
$749$	−0.235865	−	0.0631998i	−0.00861831	−	0.00230927i
$750$		0			0
$751$	7.10890	−	12.3130i	0.259407	−	0.449307i	−0.706676	−	0.707537i	$-0.749806\pi$
$751$	7.10890	−	12.3130i	0.259407	−	0.449307i	0.966083	+	0.258231i	$0.0831394\pi$
$752$		0			0
$753$	9.69789	−	17.0884i	0.353411	−	0.622737i
$754$		0			0
$755$	−43.0991	+	43.0991i	−1.56854	+	1.56854i
$756$		0			0
$757$	2.11199	+	2.11199i	0.0767615	+	0.0767615i	0.744445	−	0.667684i	$-0.232714\pi$
$757$	2.11199	+	2.11199i	0.0767615	+	0.0767615i	−0.667684	+	0.744445i	$0.732714\pi$
$758$		0			0
$759$	−30.6991	−	17.4221i	−1.11431	−	0.632382i
$760$		0			0
$761$	−16.3519	−	9.44076i	−0.592755	−	0.342227i	0.173431	−	0.984846i	$-0.444515\pi$
$761$	−16.3519	−	9.44076i	−0.592755	−	0.342227i	−0.766186	+	0.642619i	$0.777848\pi$
$762$		0			0
$763$	7.01279	−	26.1721i	0.253880	−	0.947493i
$764$		0			0
$765$	−37.7928	+	38.9300i	−1.36640	+	1.40752i
$766$		0			0
$767$	6.46724	+	11.2016i	0.233519	+	0.404466i
$768$		0			0
$769$	3.50579	−	6.07221i	0.126422	−	0.218970i	−0.795866	−	0.605473i	$-0.792984\pi$
$769$	3.50579	−	6.07221i	0.126422	−	0.218970i	0.922288	+	0.386503i	$0.126317\pi$
$770$		0			0
$771$	15.8557	+	4.12284i	0.571030	+	0.148481i
$772$		0			0
$773$	8.54407	+	8.54407i	0.307309	+	0.307309i	0.843865	−	0.536556i	$-0.180275\pi$
$773$	8.54407	+	8.54407i	0.307309	+	0.307309i	−0.536556	+	0.843865i	$0.680275\pi$
$774$		0			0
$775$			10.6082i			0.381057i
$776$		0			0
$777$	−0.372710	−	50.2947i	−0.0133709	−	1.80431i
$778$		0			0
$779$	−7.61302	+	2.03990i	−0.272765	+	0.0730871i
$780$		0			0
$781$	18.3458	+	4.91575i	0.656465	+	0.175899i
$782$		0			0
$783$	3.01305	+	4.96071i	0.107678	+	0.177281i
$784$		0			0
$785$	11.7824	+	20.4077i	0.420532	+	0.728383i
$786$		0			0
$787$	6.16205	+	22.9971i	0.219653	+	0.819758i	0.984476	+	0.175517i	$0.0561598\pi$
$787$	6.16205	+	22.9971i	0.219653	+	0.819758i	−0.764823	+	0.644241i	$0.777174\pi$
$788$		0			0
$789$	−23.1383	−	22.7979i	−0.823745	−	0.811626i
$790$		0			0
$791$		−	47.6769i		−	1.69519i
$792$		0			0
$793$			10.7545i			0.381904i
$794$		0			0
$795$	1.31234	−	5.04702i	0.0465439	−	0.178999i
$796$		0			0
$797$	1.78931	+	6.67778i	0.0633804	+	0.236539i	0.990348	−	0.138602i	$-0.0442609\pi$
$797$	1.78931	+	6.67778i	0.0633804	+	0.236539i	−0.926968	+	0.375141i	$0.877594\pi$
$798$		0			0
$799$	11.7716	+	20.3889i	0.416448	+	0.721309i
$800$		0			0
$801$	−3.45061	−	5.77717i	−0.121921	−	0.204126i
$802$		0			0
$803$	−25.1133	−	6.72909i	−0.886229	−	0.237464i
$804$		0			0
$805$	−38.5237	+	10.3224i	−1.35778	+	0.363817i
$806$		0			0
$807$	−28.8887	−	16.3947i	−1.01693	−	0.577119i
$808$		0			0
$809$			39.0505i			1.37294i	0.727157	+	0.686471i	$0.240841\pi$
$809$			39.0505i			1.37294i	−0.727157	+	0.686471i	$0.759159\pi$
$810$		0			0
$811$	2.40853	+	2.40853i	0.0845748	+	0.0845748i	0.748129	−	0.663554i	$-0.230953\pi$
$811$	2.40853	+	2.40853i	0.0845748	+	0.0845748i	−0.663554	+	0.748129i	$0.730953\pi$
$812$		0			0
$813$	−14.1073	−	51.1306i	−0.494765	−	1.79323i
$814$		0			0
$815$	−13.6864	+	23.7055i	−0.479413	+	0.830367i
$816$		0			0
$817$	−4.42769	−	7.66898i	−0.154905	−	0.268304i
$818$		0			0
$819$	−14.9622	−	3.77235i	−0.522820	−	0.131817i
$820$		0			0
$821$	7.66611	−	28.6103i	0.267549	−	0.998506i	−0.693123	−	0.720820i	$-0.743766\pi$
$821$	7.66611	−	28.6103i	0.267549	−	0.998506i	0.960672	−	0.277687i	$-0.0895677\pi$
$822$		0			0
$823$	−22.1086	−	12.7644i	−0.770659	−	0.444940i	0.0624509	−	0.998048i	$-0.480108\pi$
$823$	−22.1086	−	12.7644i	−0.770659	−	0.444940i	−0.833110	+	0.553108i	$0.813442\pi$
$824$		0			0
$825$	−19.9079	+	11.6914i	−0.693104	+	0.407042i
$826$		0			0
$827$	−5.10050	−	5.10050i	−0.177362	−	0.177362i	0.612843	−	0.790205i	$-0.290026\pi$
$827$	−5.10050	−	5.10050i	−0.177362	−	0.177362i	−0.790205	+	0.612843i	$0.790026\pi$
$828$		0			0
$829$	1.30033	−	1.30033i	0.0451624	−	0.0451624i	−0.684165	−	0.729327i	$-0.739833\pi$
$829$	1.30033	−	1.30033i	0.0451624	−	0.0451624i	0.729327	+	0.684165i	$0.239833\pi$
$830$		0			0
$831$	36.1714	−	0.268049i	1.25477	−	0.00929850i
$832$		0			0
$833$	−13.4736	+	23.3370i	−0.466833	+	0.808578i
$834$		0			0
$835$	22.8449	+	6.12126i	0.790579	+	0.211835i
$836$		0			0
$837$	18.9213	−	5.52357i	0.654017	−	0.190923i
$838$		0			0
$839$	28.6072	−	16.5164i	0.987631	−	0.570209i	0.0830657	−	0.996544i	$-0.473529\pi$
$839$	28.6072	−	16.5164i	0.987631	−	0.570209i	0.904565	+	0.426335i	$0.140196\pi$
$840$		0			0
$841$	−24.0342	−	13.8762i	−0.828766	−	0.478488i
$842$		0			0
$843$	15.1780	+	14.9547i	0.522757	+	0.515067i
$844$		0			0
$845$	−20.9869	+	20.9869i	−0.721972	+	0.721972i
$846$		0			0
$847$	−39.1502			−1.34522
$848$		0			0
$849$	−11.6243	−	19.7937i	−0.398945	−	0.679317i
$850$		0			0
$851$	−9.61896	−	35.8984i	−0.329734	−	1.23058i
$852$		0			0
$853$	−4.12451	+	15.3929i	−0.141221	+	0.527043i	0.858674	+	0.512522i	$0.171289\pi$
$853$	−4.12451	+	15.3929i	−0.141221	+	0.527043i	−0.999895	+	0.0145204i	$0.995378\pi$
$854$		0			0
$855$	0.168076	+	11.3397i	0.00574806	+	0.387810i
$856$		0			0
$857$	−13.6603	+	7.88675i	−0.466625	+	0.269406i	−0.714826	−	0.699302i	$-0.753494\pi$
$857$	−13.6603	+	7.88675i	−0.466625	+	0.269406i	0.248201	+	0.968709i	$0.420161\pi$
$858$		0			0
$859$	31.9956	−	8.57320i	1.09168	−	0.292514i	0.332306	−	0.943172i	$-0.392173\pi$
$859$	31.9956	−	8.57320i	1.09168	−	0.292514i	0.759371	+	0.650658i	$0.225507\pi$
$860$		0			0
$861$	8.95912	+	32.4715i	0.305326	+	1.10662i
$862$		0			0
$863$	−37.4407			−1.27449			−0.637247	−	0.770659i	$-0.719927\pi$
$863$	−37.4407			−1.27449			−0.637247	+	0.770659i	$0.719927\pi$
$864$		0			0
$865$	16.8186			0.571850
$866$		0			0
$867$	11.4956	+	41.6648i	0.390412	+	1.41501i
$868$		0			0
$869$	−27.1845	+	7.28408i	−0.922173	+	0.247095i
$870$		0			0
$871$	−2.51063	+	1.44951i	−0.0850695	+	0.0491149i
$872$		0			0
$873$	−34.0703	−	19.0029i	−1.15310	−	0.643151i
$874$		0			0
$875$	5.31986	−	19.8540i	0.179844	−	0.671187i
$876$		0			0
$877$	7.55790	+	28.2065i	0.255212	+	0.952465i	0.967972	+	0.251057i	$0.0807781\pi$
$877$	7.55790	+	28.2065i	0.255212	+	0.952465i	−0.712760	+	0.701408i	$0.752555\pi$
$878$		0			0
$879$	19.3735	+	32.9889i	0.653452	+	1.11269i
$880$		0			0
$881$	−11.5567			−0.389355			−0.194678	−	0.980867i	$-0.562366\pi$
$881$	−11.5567			−0.389355			−0.194678	+	0.980867i	$0.562366\pi$
$882$		0			0
$883$	19.2632	−	19.2632i	0.648260	−	0.648260i	−0.304313	−	0.952572i	$-0.598427\pi$
$883$	19.2632	−	19.2632i	0.648260	−	0.648260i	0.952572	+	0.304313i	$0.0984267\pi$
$884$		0			0
$885$	−28.9415	−	28.5157i	−0.972859	−	0.958546i
$886$		0			0
$887$	19.8424	+	11.4560i	0.666243	+	0.384656i	0.794652	−	0.607066i	$-0.207653\pi$
$887$	19.8424	+	11.4560i	0.666243	+	0.384656i	−0.128408	+	0.991721i	$0.540987\pi$
$888$		0			0
$889$	47.0523	−	27.1657i	1.57808	−	0.911107i
$890$		0			0
$891$	31.2192	+	29.4212i	1.04588	+	0.985648i
$892$		0			0
$893$	4.75336	+	1.27366i	0.159065	+	0.0426214i
$894$		0			0
$895$	−16.4752	+	28.5359i	−0.550705	+	0.953850i
$896$		0			0
$897$	−11.4015	+	0.0844911i	−0.380685	+	0.00282107i
$898$		0			0
$899$	2.99615	−	2.99615i	0.0999272	−	0.0999272i
$900$		0			0
$901$	−4.93860	−	4.93860i	−0.164529	−	0.164529i
$902$		0			0
$903$	−32.6350	+	19.1657i	−1.08602	+	0.637793i
$904$		0			0
$905$	45.6345	+	26.3471i	1.51694	+	0.875807i
$906$		0			0
$907$	12.7169	−	47.4603i	0.422259	−	1.57589i	−0.347577	−	0.937651i	$-0.612995\pi$
$907$	12.7169	−	47.4603i	0.422259	−	1.57589i	0.769836	−	0.638242i	$-0.220338\pi$
$908$		0			0
$909$	−7.47311	−	26.3232i	−0.247867	−	0.873084i
$910$		0			0
$911$	−6.47683	−	11.2182i	−0.214587	−	0.371675i	0.738558	−	0.674190i	$-0.235507\pi$
$911$	−6.47683	−	11.2182i	−0.214587	−	0.371675i	−0.953145	+	0.302515i	$0.902174\pi$
$912$		0			0
$913$	−25.5188	+	44.1999i	−0.844550	+	1.46280i
$914$		0			0
$915$	−8.98497	−	32.5651i	−0.297034	−	1.07657i
$916$		0			0
$917$	41.8331	+	41.8331i	1.38145	+	1.38145i
$918$		0			0
$919$			5.55214i			0.183148i	0.995798	+	0.0915740i	$0.0291898\pi$
$919$			5.55214i			0.183148i	−0.995798	+	0.0915740i	$0.970810\pi$
$920$		0			0
$921$	7.65271	+	4.34300i	0.252166	+	0.143107i
$922$		0			0
$923$	5.92596	−	1.58786i	0.195055	−	0.0522649i
$924$		0			0
$925$	−23.4796	−	6.29135i	−0.772006	−	0.206858i
$926$		0			0
$927$	−12.9288	+	0.191628i	−0.424636	+	0.00629390i
$928$		0			0
$929$	28.8356	+	49.9447i	0.946066	+	1.63863i	0.753603	+	0.657330i	$0.228314\pi$
$929$	28.8356	+	49.9447i	0.946066	+	1.63863i	0.192462	+	0.981304i	$0.438353\pi$
$930$		0			0
$931$	1.45782	+	5.44064i	0.0477780	+	0.178310i
$932$		0			0
$933$	−4.34187	+	16.6981i	−0.142146	+	0.546670i
$934$		0			0
$935$			86.2049i			2.81920i
$936$		0			0
$937$		−	44.7899i		−	1.46322i	−0.681722	−	0.731612i	$-0.738768\pi$
$937$		−	44.7899i		−	1.46322i	0.681722	−	0.731612i	$-0.261232\pi$
$938$		0			0
$939$	−31.5686	−	31.1042i	−1.03020	−	1.01505i
$940$		0			0
$941$	−9.72682	−	36.3010i	−0.317085	−	1.18338i	−0.922032	−	0.387113i	$-0.873472\pi$
$941$	−9.72682	−	36.3010i	−0.317085	−	1.18338i	0.604947	−	0.796266i	$-0.293194\pi$
$942$		0			0
$943$	12.4452	+	21.5557i	0.405270	+	0.701949i
$944$		0			0
$945$	48.4577	−	1.07745i	1.57633	−	0.0350493i
$946$		0			0
$947$	54.8652	+	14.7011i	1.78288	+	0.477721i	0.991104	−	0.133093i	$-0.0424908\pi$
$947$	54.8652	+	14.7011i	1.78288	+	0.477721i	0.791775	+	0.610813i	$0.209157\pi$
$948$		0			0
$949$	−8.11194	+	2.17359i	−0.263325	+	0.0705577i
$950$		0			0
$951$	0.237560	+	32.0572i	0.00770343	+	1.03953i
$952$		0			0
$953$			7.26359i			0.235291i	0.993056	+	0.117645i	$0.0375346\pi$
$953$			7.26359i			0.235291i	−0.993056	+	0.117645i	$0.962465\pi$
$954$		0			0
$955$	−3.52440	−	3.52440i	−0.114047	−	0.114047i
$956$		0			0
$957$	8.92483	+	2.32066i	0.288499	+	0.0750161i
$958$		0			0
$959$	−18.5653	+	32.1560i	−0.599504	+	1.03837i
$960$		0			0
$961$	8.30507	+	14.3848i	0.267905	+	0.464026i
$962$		0			0
$963$	0.212628	+	0.0536090i	0.00685183	+	0.00172752i
$964$		0			0
$965$	11.8604	−	44.2638i	0.381801	−	1.42490i
$966$		0			0
$967$	−4.17378	−	2.40973i	−0.134220	−	0.0774917i	0.431387	−	0.902167i	$-0.358024\pi$
$967$	−4.17378	−	2.40973i	−0.134220	−	0.0774917i	−0.565606	+	0.824675i	$0.691358\pi$
$968$		0			0
$969$	13.2099	+	7.49677i	0.424363	+	0.240831i
$970$		0			0
$971$	−2.69916	−	2.69916i	−0.0866202	−	0.0866202i	0.662469	−	0.749089i	$-0.269509\pi$
$971$	−2.69916	−	2.69916i	−0.0866202	−	0.0866202i	−0.749089	+	0.662469i	$0.769509\pi$
$972$		0			0
$973$	−15.9047	+	15.9047i	−0.509881	+	0.509881i
$974$		0			0
$975$	−3.68076	+	6.48579i	−0.117879	+	0.207712i
$976$		0			0
$977$	−6.16168	+	10.6724i	−0.197130	+	0.341439i	−0.947597	−	0.319469i	$-0.896495\pi$
$977$	−6.16168	+	10.6724i	−0.197130	+	0.341439i	0.750467	+	0.660908i	$0.229829\pi$
$978$		0			0
$979$	−10.3272	−	2.76717i	−0.330059	−	0.0884390i
$980$		0			0
$981$	−5.94857	+	23.5936i	−0.189923	+	0.753287i
$982$		0			0
$983$	−42.5445	+	24.5631i	−1.35696	+	0.783441i	−0.989213	−	0.146485i	$-0.953204\pi$
$983$	−42.5445	+	24.5631i	−1.35696	+	0.783441i	−0.367747	+	0.929926i	$0.619871\pi$
$984$		0			0
$985$	11.7960	+	6.81043i	0.375852	+	0.216998i
$986$		0			0
$987$	5.29274	−	20.3549i	0.168470	−	0.647905i
$988$		0			0
$989$	−19.7747	+	19.7747i	−0.628798	+	0.628798i
$990$		0			0
$991$	40.4968			1.28642			0.643212	−	0.765688i	$-0.277601\pi$
$991$	40.4968			1.28642			0.643212	+	0.765688i	$0.277601\pi$
$992$		0			0
$993$	−34.1387	+	0.252986i	−1.08336	+	0.00802825i
$994$		0			0
$995$	−10.8469	−	40.4812i	−0.343870	−	1.28334i
$996$		0			0
$997$	6.26425	−	23.3785i	0.198391	−	0.740404i	−0.792972	−	0.609258i	$-0.791467\pi$
$997$	6.26425	−	23.3785i	0.198391	−	0.740404i	0.991363	−	0.131147i	$-0.0418659\pi$
$998$		0			0
$999$	1.00402	+	45.1554i	0.0317659	+	1.42865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.49.11		72
3.2	odd	2		1728.2.bc.e.1009.17		72
4.3	odd	2		144.2.x.e.85.6	yes	72
9.2	odd	6		1728.2.bc.e.1585.2		72
9.7	even	3	inner	576.2.bb.e.241.3		72
12.11	even	2		432.2.y.e.37.13		72
16.3	odd	4		144.2.x.e.13.6	✓	72
16.13	even	4	inner	576.2.bb.e.337.3		72
36.7	odd	6		144.2.x.e.133.6	yes	72
36.11	even	6		432.2.y.e.181.13		72
48.29	odd	4		1728.2.bc.e.145.2		72
48.35	even	4		432.2.y.e.253.13		72
144.29	odd	12		1728.2.bc.e.721.17		72
144.61	even	12	inner	576.2.bb.e.529.11		72
144.83	even	12		432.2.y.e.397.13		72
144.115	odd	12		144.2.x.e.61.6	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.6	✓	72	16.3	odd	4
144.2.x.e.61.6	yes	72	144.115	odd	12
144.2.x.e.85.6	yes	72	4.3	odd	2
144.2.x.e.133.6	yes	72	36.7	odd	6
432.2.y.e.37.13		72	12.11	even	2
432.2.y.e.181.13		72	36.11	even	6
432.2.y.e.253.13		72	48.35	even	4
432.2.y.e.397.13		72	144.83	even	12
576.2.bb.e.49.11		72	1.1	even	1	trivial
576.2.bb.e.241.3		72	9.7	even	3	inner
576.2.bb.e.337.3		72	16.13	even	4	inner
576.2.bb.e.529.11		72	144.61	even	12	inner
1728.2.bc.e.145.2		72	48.29	odd	4
1728.2.bc.e.721.17		72	144.29	odd	12
1728.2.bc.e.1009.17		72	3.2	odd	2
1728.2.bc.e.1585.2		72	9.2	odd	6

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.460673 + 1.66966i) q^{3} +(-2.69708 + 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +(-2.57556 + 1.53834i) q^{9} +O(q^{10})\)	\(q+(0.460673 + 1.66966i) q^{3} +(-2.69708 + 0.722679i) q^{5} +(2.89314 - 1.67035i) q^{7} +(-2.57556 + 1.53834i) q^{9} +(-1.23365 + 4.60405i) q^{11} +(0.398486 + 1.48717i) q^{13} +(-2.44910 - 4.17029i) q^{15} -6.47719 q^{17} +(-0.957336 + 0.957336i) q^{19} +(4.12172 + 4.06108i) q^{21} +(3.70277 + 2.13780i) q^{23} +(2.42183 - 1.39824i) q^{25} +(-3.75500 - 3.59165i) q^{27} +(-1.07893 - 0.289099i) q^{29} +(-1.89670 + 3.28518i) q^{31} +(-8.25552 + 0.0611777i) q^{33} +(-6.59588 + 6.59588i) q^{35} +(-6.14639 - 6.14639i) q^{37} +(-2.29950 + 1.35044i) q^{39} +(5.04156 + 2.91075i) q^{41} +(-1.69287 + 6.31788i) q^{43} +(5.83476 - 6.01032i) q^{45} +(-1.81739 - 3.14781i) q^{47} +(2.08016 - 3.60295i) q^{49} +(-2.98387 - 10.8147i) q^{51} +(0.762460 + 0.762460i) q^{53} -13.3090i q^{55} +(-2.03945 - 1.15741i) q^{57} +(8.11476 - 2.17434i) q^{59} +(6.74711 + 1.80788i) q^{61} +(-4.88188 + 8.75272i) q^{63} +(-2.14950 - 3.72304i) q^{65} +(0.487339 + 1.81878i) q^{67} +(-1.86364 + 7.16721i) q^{69} -3.98472i q^{71} +5.45461i q^{73} +(3.45027 + 3.39951i) q^{75} +(4.12126 + 15.3808i) q^{77} +(2.95225 + 5.11344i) q^{79} +(4.26702 - 7.92417i) q^{81} +(10.3428 + 2.77135i) q^{83} +(17.4695 - 4.68093i) q^{85} +(-0.0143366 - 1.93463i) q^{87} +2.24307i q^{89} +(3.63698 + 3.63698i) q^{91} +(-6.35891 - 1.65346i) q^{93} +(1.89016 - 3.27385i) q^{95} +(6.50191 + 11.2616i) q^{97} +(-3.90524 - 13.7558i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more