LMFDB - Embedded newform 576.2.y.a.335.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (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:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			335.2
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.67850 + 0.427367i) q^{3} +(-0.170993 - 0.0458174i) q^{5} +(-1.17432 + 2.03397i) q^{7} +(2.63471 - 1.43467i) q^{9} +O(q^{10})$	\(q+(-1.67850 + 0.427367i) q^{3} +(-0.170993 - 0.0458174i) q^{5} +(-1.17432 + 2.03397i) q^{7} +(2.63471 - 1.43467i) q^{9} +(0.340806 - 0.0913188i) q^{11} +(-1.49044 - 0.399362i) q^{13} +(0.306592 + 0.00382767i) q^{15} +3.58081i q^{17} +(-5.36462 - 5.36462i) q^{19} +(1.10183 - 3.91589i) q^{21} +(-0.165085 + 0.0953117i) q^{23} +(-4.30299 - 2.48433i) q^{25} +(-3.80923 + 3.53408i) q^{27} +(-9.10169 + 2.43879i) q^{29} +(3.43903 - 1.98552i) q^{31} +(-0.533016 + 0.298928i) q^{33} +(0.293991 - 0.293991i) q^{35} +(-3.28315 - 3.28315i) q^{37} +(2.67238 + 0.0333635i) q^{39} +(-4.25538 - 7.37054i) q^{41} +(-1.09699 - 4.09402i) q^{43} +(-0.516251 + 0.124603i) q^{45} +(-4.93030 + 8.53953i) q^{47} +(0.741968 + 1.28513i) q^{49} +(-1.53032 - 6.01038i) q^{51} +(-4.83735 + 4.83735i) q^{53} -0.0624595 q^{55} +(11.2972 + 6.71185i) q^{57} +(0.720744 - 2.68985i) q^{59} +(2.13661 + 7.97394i) q^{61} +(-0.175902 + 7.04369i) q^{63} +(0.236557 + 0.136576i) q^{65} +(3.06917 - 11.4543i) q^{67} +(0.236361 - 0.230532i) q^{69} -1.13635i q^{71} -5.67961i q^{73} +(8.28428 + 2.33099i) q^{75} +(-0.214474 + 0.800428i) q^{77} +(-12.8621 - 7.42593i) q^{79} +(4.88344 - 7.55990i) q^{81} +(3.31278 + 12.3635i) q^{83} +(0.164063 - 0.612293i) q^{85} +(14.2349 - 7.98327i) q^{87} +3.05719 q^{89} +(2.56254 - 2.56254i) q^{91} +(-4.92386 + 4.80243i) q^{93} +(0.671520 + 1.16311i) q^{95} +(-0.996701 + 1.72634i) q^{97} +(0.766915 - 0.729544i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{1}{4}\right)$

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
$3$	−1.67850	+	0.427367i	−0.969082	+	0.246741i
$3$	−1.67850	+	0.427367i	−0.969082	+	0.246741i
$4$		0			0
$5$	−0.170993	−	0.0458174i	−0.0764704	−	0.0204902i	0.220381	−	0.975414i	$-0.429270\pi$
$5$	−0.170993	−	0.0458174i	−0.0764704	−	0.0204902i	−0.296851	+	0.954924i	$0.595937\pi$
$6$		0			0
$7$	−1.17432	+	2.03397i	−0.443849	+	0.768770i	−0.997971	−	0.0636659i	$-0.979721\pi$
$7$	−1.17432	+	2.03397i	−0.443849	+	0.768770i	0.554122	+	0.832436i	$0.313054\pi$
$8$		0			0
$9$	2.63471	−	1.43467i	0.878238	−	0.478224i
$10$		0			0
$11$	0.340806	−	0.0913188i	0.102757	−	0.0275337i	−0.207074	−	0.978325i	$-0.566394\pi$
$11$	0.340806	−	0.0913188i	0.102757	−	0.0275337i	0.309831	+	0.950792i	$0.399727\pi$
$12$		0			0
$13$	−1.49044	−	0.399362i	−0.413374	−	0.110763i	0.0461375	−	0.998935i	$-0.485309\pi$
$13$	−1.49044	−	0.399362i	−0.413374	−	0.110763i	−0.459511	+	0.888172i	$0.651975\pi$
$14$		0			0
$15$	0.306592	+	0.00382767i	0.0791618	+	0.000988301i
$16$		0			0
$17$			3.58081i			0.868473i	0.900799	+	0.434236i	$0.142982\pi$
$17$			3.58081i			0.868473i	−0.900799	+	0.434236i	$0.857018\pi$
$18$		0			0
$19$	−5.36462	−	5.36462i	−1.23073	−	1.23073i	−0.963684	−	0.267045i	$-0.913953\pi$
$19$	−5.36462	−	5.36462i	−1.23073	−	1.23073i	−0.267045	−	0.963684i	$-0.586047\pi$
$20$		0			0
$21$	1.10183	−	3.91589i	0.240440	−	0.854516i
$22$		0			0
$23$	−0.165085	+	0.0953117i	−0.0344225	+	0.0198739i	−0.517113	−	0.855917i	$-0.672993\pi$
$23$	−0.165085	+	0.0953117i	−0.0344225	+	0.0198739i	0.482690	+	0.875791i	$0.339660\pi$
$24$		0			0
$25$	−4.30299	−	2.48433i	−0.860598	−	0.496866i
$26$		0			0
$27$	−3.80923	+	3.53408i	−0.733087	+	0.680135i
$28$		0			0
$29$	−9.10169	+	2.43879i	−1.69014	+	0.452872i	−0.970426	−	0.241398i	$-0.922394\pi$
$29$	−9.10169	+	2.43879i	−1.69014	+	0.452872i	−0.719714	+	0.694270i	$0.755727\pi$
$30$		0			0
$31$	3.43903	−	1.98552i	0.617668	−	0.356611i	−0.158293	−	0.987392i	$-0.550599\pi$
$31$	3.43903	−	1.98552i	0.617668	−	0.356611i	0.775960	+	0.630782i	$0.217266\pi$
$32$		0			0
$33$	−0.533016	+	0.298928i	−0.0927863	+	0.0520367i
$34$		0			0
$35$	0.293991	−	0.293991i	0.0496936	−	0.0496936i
$36$		0			0
$37$	−3.28315	−	3.28315i	−0.539746	−	0.539746i	0.383709	−	0.923454i	$-0.374647\pi$
$37$	−3.28315	−	3.28315i	−0.539746	−	0.539746i	−0.923454	+	0.383709i	$0.874647\pi$
$38$		0			0
$39$	2.67238	+	0.0333635i	0.427923	+	0.00534243i
$40$		0			0
$41$	−4.25538	−	7.37054i	−0.664579	−	1.15109i	−0.979399	−	0.201934i	$-0.935277\pi$
$41$	−4.25538	−	7.37054i	−0.664579	−	1.15109i	0.314820	−	0.949151i	$-0.398056\pi$
$42$		0			0
$43$	−1.09699	−	4.09402i	−0.167289	−	0.624332i	−0.997737	−	0.0672354i	$-0.978582\pi$
$43$	−1.09699	−	4.09402i	−0.167289	−	0.624332i	0.830448	−	0.557096i	$-0.188085\pi$
$44$		0			0
$45$	−0.516251	+	0.124603i	−0.0769581	+	0.0185747i
$46$		0			0
$47$	−4.93030	+	8.53953i	−0.719158	+	1.24562i	0.242176	+	0.970232i	$0.422139\pi$
$47$	−4.93030	+	8.53953i	−0.719158	+	1.24562i	−0.961334	+	0.275386i	$0.911194\pi$
$48$		0			0
$49$	0.741968	+	1.28513i	0.105995	+	0.183590i
$50$		0			0
$51$	−1.53032	−	6.01038i	−0.214288	−	0.841621i
$52$		0			0
$53$	−4.83735	+	4.83735i	−0.664461	+	0.664461i	−0.956428	−	0.291967i	$-0.905690\pi$
$53$	−4.83735	+	4.83735i	−0.664461	+	0.664461i	0.291967	+	0.956428i	$0.405690\pi$
$54$		0			0
$55$	−0.0624595			−0.00842204
$56$		0			0
$57$	11.2972	+	6.71185i	1.49635	+	0.889006i
$58$		0			0
$59$	0.720744	−	2.68985i	0.0938328	−	0.350189i	−0.903007	−	0.429626i	$-0.858646\pi$
$59$	0.720744	−	2.68985i	0.0938328	−	0.350189i	0.996840	+	0.0794368i	$0.0253122\pi$
$60$		0			0
$61$	2.13661	+	7.97394i	0.273565	+	1.02096i	0.956797	+	0.290757i	$0.0939071\pi$
$61$	2.13661	+	7.97394i	0.273565	+	1.02096i	−0.683232	+	0.730201i	$0.739426\pi$
$62$		0			0
$63$	−0.175902	+	7.04369i	−0.0221616	+	0.887422i
$64$		0			0
$65$	0.236557	+	0.136576i	0.0293413	+	0.0169402i
$66$		0			0
$67$	3.06917	−	11.4543i	0.374959	−	1.39936i	−0.478446	−	0.878117i	$-0.658800\pi$
$67$	3.06917	−	11.4543i	0.374959	−	1.39936i	0.853405	−	0.521248i	$-0.174533\pi$
$68$		0			0
$69$	0.236361	−	0.230532i	0.0284546	−	0.0277528i
$70$		0			0
$71$		−	1.13635i		−	0.134860i	−0.997724	−	0.0674300i	$-0.978520\pi$
$71$		−	1.13635i		−	0.134860i	0.997724	−	0.0674300i	$-0.0214799\pi$
$72$		0			0
$73$		−	5.67961i		−	0.664748i	−0.943148	−	0.332374i	$-0.892150\pi$
$73$		−	5.67961i		−	0.664748i	0.943148	−	0.332374i	$-0.107850\pi$
$74$		0			0
$75$	8.28428	+	2.33099i	0.956586	+	0.269159i
$76$		0			0
$77$	−0.214474	+	0.800428i	−0.0244416	+	0.0912173i
$78$		0			0
$79$	−12.8621	−	7.42593i	−1.44710	−	0.835482i	−0.448790	−	0.893637i	$-0.648145\pi$
$79$	−12.8621	−	7.42593i	−1.44710	−	0.835482i	−0.998308	+	0.0581546i	$0.981478\pi$
$80$		0			0
$81$	4.88344	−	7.55990i	0.542604	−	0.839988i
$82$		0			0
$83$	3.31278	+	12.3635i	0.363625	+	1.35707i	0.869275	+	0.494329i	$0.164586\pi$
$83$	3.31278	+	12.3635i	0.363625	+	1.35707i	−0.505649	+	0.862739i	$0.668747\pi$
$84$		0			0
$85$	0.164063	−	0.612293i	0.0177952	−	0.0664125i
$86$		0			0
$87$	14.2349	−	7.98327i	1.52614	−	0.855896i
$88$		0			0
$89$	3.05719			0.324061			0.162031	−	0.986786i	$-0.448196\pi$
$89$	3.05719			0.324061			0.162031	+	0.986786i	$0.448196\pi$
$90$		0			0
$91$	2.56254	−	2.56254i	0.268627	−	0.268627i
$92$		0			0
$93$	−4.92386	+	4.80243i	−0.510580	+	0.497989i
$94$		0			0
$95$	0.671520	+	1.16311i	0.0688965	+	0.119332i
$96$		0			0
$97$	−0.996701	+	1.72634i	−0.101200	+	0.175283i	−0.912179	−	0.409792i	$-0.865601\pi$
$97$	−0.996701	+	1.72634i	−0.101200	+	0.175283i	0.810980	+	0.585075i	$0.198935\pi$
$98$		0			0
$99$	0.766915	−	0.729544i	0.0770779	−	0.0733219i
$100$		0			0
$101$	4.14419	+	15.4663i	0.412362	+	1.53896i	0.790062	+	0.613027i	$0.210048\pi$
$101$	4.14419	+	15.4663i	0.412362	+	1.53896i	−0.377700	+	0.925928i	$0.623285\pi$
$102$		0			0
$103$	8.12150	+	14.0668i	0.800235	+	1.38605i	0.919461	+	0.393181i	$0.128625\pi$
$103$	8.12150	+	14.0668i	0.800235	+	1.38605i	−0.119226	+	0.992867i	$0.538041\pi$
$104$		0			0
$105$	−0.367821	+	0.619106i	−0.0358957	+	0.0604185i
$106$		0			0
$107$	2.08262	+	2.08262i	0.201334	+	0.201334i	0.800571	−	0.599237i	$-0.204529\pi$
$107$	2.08262	+	2.08262i	0.201334	+	0.201334i	−0.599237	+	0.800571i	$0.704529\pi$
$108$		0			0
$109$	7.70191	−	7.70191i	0.737709	−	0.737709i	−0.234425	−	0.972134i	$-0.575321\pi$
$109$	7.70191	−	7.70191i	0.737709	−	0.737709i	0.972134	+	0.234425i	$0.0753207\pi$
$110$		0			0
$111$	6.91386	+	4.10765i	0.656235	+	0.389880i
$112$		0			0
$113$	10.3137	−	5.95461i	0.970230	−	0.560162i	0.0709236	−	0.997482i	$-0.477405\pi$
$113$	10.3137	−	5.95461i	0.970230	−	0.560162i	0.899306	+	0.437319i	$0.144072\pi$
$114$		0			0
$115$	0.0325953	−	0.00873387i	0.00303952	−	0.000814438i
$116$		0			0
$117$	−4.49984	+	1.08609i	−0.416010	+	0.100409i
$118$		0			0
$119$	−7.28326	−	4.20499i	−0.667656	−	0.385471i
$120$		0			0
$121$	−9.41847	+	5.43776i	−0.856225	+	0.494341i
$122$		0			0
$123$	10.2926	+	10.5528i	0.928051	+	0.951517i
$124$		0			0
$125$	1.24783	+	1.24783i	0.111610	+	0.111610i
$126$		0			0
$127$			8.43197i			0.748216i	0.927385	+	0.374108i	$0.122051\pi$
$127$			8.43197i			0.748216i	−0.927385	+	0.374108i	$0.877949\pi$
$128$		0			0
$129$	3.59094	+	6.40298i	0.316165	+	0.563751i
$130$		0			0
$131$	5.25596	+	1.40833i	0.459215	+	0.123046i	0.481008	−	0.876716i	$-0.340271\pi$
$131$	5.25596	+	1.40833i	0.459215	+	0.123046i	−0.0217928	+	0.999763i	$0.506937\pi$
$132$		0			0
$133$	17.2113	−	4.61174i	1.49241	−	0.399889i
$134$		0			0
$135$	0.813275	−	0.429774i	0.0699955	−	0.0369891i
$136$		0			0
$137$	1.62151	−	2.80854i	0.138535	−	0.239950i	−0.788407	−	0.615154i	$-0.789094\pi$
$137$	1.62151	−	2.80854i	0.138535	−	0.239950i	0.926942	+	0.375204i	$0.122427\pi$
$138$		0			0
$139$	−13.2129	−	3.54037i	−1.12070	−	0.300291i	−0.349533	−	0.936924i	$-0.613660\pi$
$139$	−13.2129	−	3.54037i	−1.12070	−	0.300291i	−0.771167	+	0.636633i	$0.780326\pi$
$140$		0			0
$141$	4.62598	−	16.4406i	0.389578	−	1.38455i
$142$		0			0
$143$	−0.544421			−0.0455268
$144$		0			0
$145$	1.66806			0.138525
$146$		0			0
$147$	−1.79461	−	1.83999i	−0.148017	−	0.151760i
$148$		0			0
$149$	12.2444	+	3.28089i	1.00310	+	0.268781i	0.722745	−	0.691115i	$-0.242880\pi$
$149$	12.2444	+	3.28089i	1.00310	+	0.268781i	0.280358	+	0.959895i	$0.409547\pi$
$150$		0			0
$151$	−0.791297	+	1.37057i	−0.0643948	+	0.111535i	−0.896425	−	0.443195i	$-0.853845\pi$
$151$	−0.791297	+	1.37057i	−0.0643948	+	0.111535i	0.832031	+	0.554730i	$0.187178\pi$
$152$		0			0
$153$	5.13728	+	9.43440i	0.415324	+	0.762726i
$154$		0			0
$155$	−0.679022	+	0.181943i	−0.0545403	+	0.0146140i
$156$		0			0
$157$	7.73231	+	2.07187i	0.617106	+	0.165353i	0.553812	−	0.832642i	$-0.313173\pi$
$157$	7.73231	+	2.07187i	0.617106	+	0.165353i	0.0632940	+	0.997995i	$0.479839\pi$
$158$		0			0
$159$	6.05216	−	10.1868i	0.479968	−	0.807867i
$160$		0			0
$161$		−	0.447704i		−	0.0352840i
$162$		0			0
$163$	10.2400	+	10.2400i	0.802055	+	0.802055i	0.983416	−	0.181362i	$-0.0580505\pi$
$163$	10.2400	+	10.2400i	0.802055	+	0.802055i	−0.181362	+	0.983416i	$0.558050\pi$
$164$		0			0
$165$	0.104838	−	0.0266932i	0.00816164	−	0.00207806i
$166$		0			0
$167$	−10.1700	+	5.87166i	−0.786979	+	0.454362i	−0.838898	−	0.544289i	$-0.816800\pi$
$167$	−10.1700	+	5.87166i	−0.786979	+	0.454362i	0.0519191	+	0.998651i	$0.483466\pi$
$168$		0			0
$169$	−9.19641	−	5.30955i	−0.707416	−	0.408427i
$170$		0			0
$171$	−21.8307	−	6.43778i	−1.66944	−	0.492309i
$172$		0			0
$173$	−14.3509	+	3.84530i	−1.09108	+	0.292353i	−0.759126	−	0.650944i	$-0.774373\pi$
$173$	−14.3509	+	3.84530i	−1.09108	+	0.292353i	−0.331950	+	0.943297i	$0.607707\pi$
$174$		0			0
$175$	10.1061	−	5.83477i	0.763951	−	0.441068i
$176$		0			0
$177$	−0.0602123	+	4.82294i	−0.00452583	+	0.362514i
$178$		0			0
$179$	−10.4051	+	10.4051i	−0.777712	+	0.777712i	−0.979441	−	0.201730i	$-0.935344\pi$
$179$	−10.4051	+	10.4051i	−0.777712	+	0.777712i	0.201730	+	0.979441i	$0.435344\pi$
$180$		0			0
$181$	−16.0569	−	16.0569i	−1.19350	−	1.19350i	−0.976077	−	0.217424i	$-0.930235\pi$
$181$	−16.0569	−	16.0569i	−1.19350	−	1.19350i	−0.217424	−	0.976077i	$-0.569765\pi$
$182$		0			0
$183$	−6.99410	−	12.4711i	−0.517019	−	0.921892i
$184$		0			0
$185$	0.410970	+	0.711820i	0.0302151	+	0.0523341i
$186$		0			0
$187$	0.326995	+	1.22036i	0.0239122	+	0.0892417i
$188$		0			0
$189$	−2.71499	−	11.8980i	−0.197487	−	0.865453i
$190$		0			0
$191$	3.45557	−	5.98522i	0.250036	−	0.433075i	−0.713499	−	0.700656i	$-0.752891\pi$
$191$	3.45557	−	5.98522i	0.250036	−	0.433075i	0.963535	+	0.267581i	$0.0862242\pi$
$192$		0			0
$193$	−7.82918	−	13.5605i	−0.563557	−	0.976109i	−0.997182	−	0.0750156i	$-0.976099\pi$
$193$	−7.82918	−	13.5605i	−0.563557	−	0.976109i	0.433626	−	0.901093i	$-0.357234\pi$
$194$		0			0
$195$	−0.455429	−	0.128146i	−0.0326139	−	0.00917675i
$196$		0			0
$197$	8.24778	−	8.24778i	0.587630	−	0.587630i	−0.349359	−	0.936989i	$-0.613601\pi$
$197$	8.24778	−	8.24778i	0.587630	−	0.587630i	0.936989	+	0.349359i	$0.113601\pi$
$198$		0			0
$199$	−5.52708			−0.391804			−0.195902	−	0.980623i	$-0.562763\pi$
$199$	−5.52708			−0.391804			−0.195902	+	0.980623i	$0.562763\pi$
$200$		0			0
$201$	−0.256404	+	20.5377i	−0.0180853	+	1.44862i
$202$		0			0
$203$	5.72781	−	21.3765i	0.402014	−	1.50034i
$204$		0			0
$205$	0.389942	+	1.45528i	0.0272347	+	0.101641i
$206$		0			0
$207$	−0.298210	+	0.487961i	−0.0207270	+	0.0339156i
$208$		0			0
$209$	−2.31819	−	1.33841i	−0.160353	−	0.0925796i
$210$		0			0
$211$	−1.09423	+	4.08372i	−0.0753299	+	0.281135i	−0.993308	−	0.115496i	$-0.963154\pi$
$211$	−1.09423	+	4.08372i	−0.0753299	+	0.281135i	0.917978	+	0.396631i	$0.129821\pi$
$212$		0			0
$213$	0.485639	+	1.90736i	0.0332754	+	0.130690i
$214$		0			0
$215$			0.750309i			0.0511707i
$216$		0			0
$217$			9.32653i			0.633126i
$218$		0			0
$219$	2.42728	+	9.53322i	0.164020	+	0.644195i
$220$		0			0
$221$	1.43004	−	5.33698i	0.0961948	−	0.359004i
$222$		0			0
$223$	6.50548	+	3.75594i	0.435639	+	0.251517i	0.701746	−	0.712427i	$-0.252404\pi$
$223$	6.50548	+	3.75594i	0.435639	+	0.251517i	−0.266107	+	0.963944i	$0.585737\pi$
$224$		0			0
$225$	−14.9013	−	0.372132i	−0.993423	−	0.0248088i
$226$		0			0
$227$	1.69150	+	6.31276i	0.112269	+	0.418993i	0.999068	−	0.0431619i	$-0.0137431\pi$
$227$	1.69150	+	6.31276i	0.112269	+	0.418993i	−0.886799	+	0.462155i	$0.847076\pi$
$228$		0			0
$229$	−0.291556	+	1.08810i	−0.0192665	+	0.0719037i	−0.974890	−	0.222688i	$-0.928517\pi$
$229$	−0.291556	+	1.08810i	−0.0192665	+	0.0719037i	0.955623	+	0.294592i	$0.0951836\pi$
$230$		0			0
$231$	0.0179176	−	1.43518i	0.00117889	−	0.0944277i
$232$		0			0
$233$	13.9406			0.913280			0.456640	−	0.889652i	$-0.349053\pi$
$233$	13.9406			0.913280			0.456640	+	0.889652i	$0.349053\pi$
$234$		0			0
$235$	1.23431	−	1.23431i	0.0805173	−	0.0805173i
$236$		0			0
$237$	24.7626	+	6.96758i	1.60850	+	0.452593i
$238$		0			0
$239$	−14.8075	−	25.6474i	−0.957820	−	1.65899i	−0.727780	−	0.685811i	$-0.759448\pi$
$239$	−14.8075	−	25.6474i	−0.957820	−	1.65899i	−0.230040	−	0.973181i	$-0.573886\pi$
$240$		0			0
$241$	−6.03200	+	10.4477i	−0.388555	+	0.672997i	−0.992255	−	0.124214i	$-0.960359\pi$
$241$	−6.03200	+	10.4477i	−0.388555	+	0.672997i	0.603700	+	0.797211i	$0.293692\pi$
$242$		0			0
$243$	−4.96599	+	14.7763i	−0.318569	+	0.947900i
$244$		0			0
$245$	−0.0679902	−	0.253743i	−0.00434373	−	0.0162110i
$246$		0			0
$247$	5.85322	+	10.1381i	0.372432	+	0.645071i
$248$		0			0
$249$	−10.8443	−	19.3363i	−0.687227	−	1.22539i
$250$		0			0
$251$	13.9356	+	13.9356i	0.879610	+	0.879610i	0.993494	−	0.113884i	$-0.0363292\pi$
$251$	13.9356	+	13.9356i	0.879610	+	0.879610i	−0.113884	+	0.993494i	$0.536329\pi$
$252$		0			0
$253$	−0.0475582	+	0.0475582i	−0.00298996	+	0.00298996i
$254$		0			0
$255$	−0.0137062	+	1.09785i	−0.000858312	+	0.0687499i
$256$		0			0
$257$	−21.0025	+	12.1258i	−1.31010	+	0.756387i	−0.982112	−	0.188295i	$-0.939704\pi$
$257$	−21.0025	+	12.1258i	−1.31010	+	0.756387i	−0.327988	+	0.944682i	$0.606370\pi$
$258$		0			0
$259$	10.5333	−	2.82238i	0.654506	−	0.175374i
$260$		0			0
$261$	−20.4815	+	19.4834i	−1.26777	+	1.20599i
$262$		0			0
$263$	−26.7072	−	15.4194i	−1.64683	−	0.950800i	−0.978319	−	0.207102i	$-0.933597\pi$
$263$	−26.7072	−	15.4194i	−1.64683	−	0.950800i	−0.668515	−	0.743699i	$-0.733070\pi$
$264$		0			0
$265$	1.04879	−	0.605518i	0.0644265	−	0.0371967i
$266$		0			0
$267$	−5.13148	+	1.30654i	−0.314042	+	0.0799590i
$268$		0			0
$269$	5.24359	+	5.24359i	0.319707	+	0.319707i	0.848655	−	0.528947i	$-0.177413\pi$
$269$	5.24359	+	5.24359i	0.319707	+	0.319707i	−0.528947	+	0.848655i	$0.677413\pi$
$270$		0			0
$271$			6.82794i			0.414768i	0.978260	+	0.207384i	$0.0664949\pi$
$271$			6.82794i			0.414768i	−0.978260	+	0.207384i	$0.933505\pi$
$272$		0			0
$273$	−3.20607	+	5.39636i	−0.194040	+	0.326603i
$274$		0			0
$275$	−1.69335	−	0.453732i	−0.102113	−	0.0273611i
$276$		0			0
$277$	6.34489	−	1.70011i	0.381228	−	0.102150i	−0.0631157	−	0.998006i	$-0.520104\pi$
$277$	6.34489	−	1.70011i	0.381228	−	0.102150i	0.444343	+	0.895857i	$0.353437\pi$
$278$		0			0
$279$	6.21229	−	10.1652i	0.371920	−	0.608573i
$280$		0			0
$281$	−2.29891	+	3.98183i	−0.137141	+	0.237536i	−0.926413	−	0.376508i	$-0.877125\pi$
$281$	−2.29891	+	3.98183i	−0.137141	+	0.237536i	0.789272	+	0.614044i	$0.210458\pi$
$282$		0			0
$283$	−8.46655	−	2.26861i	−0.503284	−	0.134855i	−0.00176039	−	0.999998i	$-0.500560\pi$
$283$	−8.46655	−	2.26861i	−0.503284	−	0.134855i	−0.501524	+	0.865144i	$0.667227\pi$
$284$		0			0
$285$	−1.62422	−	1.66529i	−0.0962104	−	0.0986431i
$286$		0			0
$287$	19.9886			1.17989
$288$		0			0
$289$	4.17783			0.245755
$290$		0			0
$291$	0.935181	−	3.32361i	0.0548213	−	0.194833i
$292$		0			0
$293$	−16.6713	−	4.46706i	−0.973948	−	0.260969i	−0.263454	−	0.964672i	$-0.584862\pi$
$293$	−16.6713	−	4.46706i	−0.973948	−	0.260969i	−0.710494	+	0.703703i	$0.751528\pi$
$294$		0			0
$295$	−0.246484	+	0.426923i	−0.0143509	+	0.0248564i
$296$		0			0
$297$	−0.975483	+	1.55229i	−0.0566032	+	0.0900732i
$298$		0			0
$299$	0.284113	−	0.0761278i	0.0164307	−	0.00440258i
$300$		0			0
$301$	9.61533	+	2.57642i	0.554218	+	0.148502i
$302$		0			0
$303$	−13.5658	−	24.1891i	−0.779335	−	1.38963i
$304$		0			0
$305$		−	1.46138i		−	0.0836785i
$306$		0			0
$307$	3.08820	+	3.08820i	0.176253	+	0.176253i	0.789720	−	0.613467i	$-0.210226\pi$
$307$	3.08820	+	3.08820i	0.176253	+	0.176253i	−0.613467	+	0.789720i	$0.710226\pi$
$308$		0			0
$309$	−19.6436	−	20.1403i	−1.11749	−	1.14574i
$310$		0			0
$311$	11.7879	−	6.80577i	0.668433	−	0.385920i	−0.127050	−	0.991896i	$-0.540551\pi$
$311$	11.7879	−	6.80577i	0.668433	−	0.385920i	0.795483	+	0.605976i	$0.207217\pi$
$312$		0			0
$313$	−9.11117	−	5.26034i	−0.514994	−	0.297332i	0.219890	−	0.975525i	$-0.429430\pi$
$313$	−9.11117	−	5.26034i	−0.514994	−	0.297332i	−0.734884	+	0.678193i	$0.762763\pi$
$314$		0			0
$315$	0.352802	−	1.19636i	0.0198781	−	0.0674074i
$316$		0			0
$317$	18.7671	−	5.02863i	1.05406	−	0.282436i	0.310134	−	0.950693i	$-0.399626\pi$
$317$	18.7671	−	5.02863i	1.05406	−	0.282436i	0.743931	+	0.668257i	$0.232959\pi$
$318$		0			0
$319$	−2.87921	+	1.66231i	−0.161205	+	0.0930715i
$320$		0			0
$321$	−4.38571	−	2.60563i	−0.244787	−	0.145432i
$322$		0			0
$323$	19.2097	−	19.2097i	1.06885	−	1.06885i
$324$		0			0
$325$	5.42120	+	5.42120i	0.300714	+	0.300714i
$326$		0			0
$327$	−9.63610	+	16.2192i	−0.532878	+	0.896923i
$328$		0			0
$329$	−11.5795	−	20.0562i	−0.638396	−	1.10573i
$330$		0			0
$331$	3.30125	+	12.3204i	0.181453	+	0.677192i	0.995362	+	0.0961997i	$0.0306688\pi$
$331$	3.30125	+	12.3204i	0.181453	+	0.677192i	−0.813909	+	0.580992i	$0.802665\pi$
$332$		0			0
$333$	−13.3604	−	3.93992i	−0.732144	−	0.215906i
$334$		0			0
$335$	−1.04961	+	1.81798i	−0.0573465	+	0.0993270i
$336$		0			0
$337$	−5.77771	−	10.0073i	−0.314732	−	0.545132i	0.664648	−	0.747156i	$-0.268581\pi$
$337$	−5.77771	−	10.0073i	−0.314732	−	0.545132i	−0.979381	+	0.202024i	$0.935248\pi$
$338$		0			0
$339$	−14.7667	+	14.4025i	−0.802017	+	0.782238i
$340$		0			0
$341$	0.990728	−	0.990728i	0.0536509	−	0.0536509i
$342$		0			0
$343$	−19.9256			−1.07588
$344$		0			0
$345$	−0.0509785	+	0.0285899i	−0.00274459	+	0.00153923i
$346$		0			0
$347$	−1.73954	+	6.49207i	−0.0933836	+	0.348512i	−0.996769	−	0.0803163i	$-0.974407\pi$
$347$	−1.73954	+	6.49207i	−0.0933836	+	0.348512i	0.903386	+	0.428829i	$0.141074\pi$
$348$		0			0
$349$	2.34830	+	8.76397i	0.125702	+	0.469125i	0.999864	−	0.0165095i	$-0.00525537\pi$
$349$	2.34830	+	8.76397i	0.125702	+	0.469125i	−0.874162	+	0.485634i	$0.838589\pi$
$350$		0			0
$351$	7.08881	−	3.74608i	0.378373	−	0.199951i
$352$		0			0
$353$	−10.8100	−	6.24115i	−0.575357	−	0.332183i	0.183929	−	0.982940i	$-0.441118\pi$
$353$	−10.8100	−	6.24115i	−0.575357	−	0.332183i	−0.759286	+	0.650757i	$0.774452\pi$
$354$		0			0
$355$	−0.0520647	+	0.194308i	−0.00276331	+	0.0103128i
$356$		0			0
$357$	14.0220	+	3.94545i	0.742124	+	0.208815i
$358$		0			0
$359$			13.9088i			0.734079i	0.930205	+	0.367040i	$0.119629\pi$
$359$			13.9088i			0.734079i	−0.930205	+	0.367040i	$0.880371\pi$
$360$		0			0
$361$			38.5584i			2.02939i
$362$		0			0
$363$	13.4850	−	13.1524i	0.707777	−	0.690323i
$364$		0			0
$365$	−0.260225	+	0.971174i	−0.0136208	+	0.0508336i
$366$		0			0
$367$	−5.69950	−	3.29061i	−0.297512	−	0.171768i	0.343813	−	0.939038i	$-0.388281\pi$
$367$	−5.69950	−	3.29061i	−0.297512	−	0.171768i	−0.641325	+	0.767270i	$0.721615\pi$
$368$		0			0
$369$	−21.7860	−	13.3142i	−1.13414	−	0.693109i
$370$		0			0
$371$	−4.15847	−	15.5196i	−0.215897	−	0.805738i
$372$		0			0
$373$	−6.78631	+	25.3268i	−0.351382	+	1.31137i	0.533595	+	0.845740i	$0.320841\pi$
$373$	−6.78631	+	25.3268i	−0.351382	+	1.31137i	−0.884977	+	0.465635i	$0.845826\pi$
$374$		0			0
$375$	−2.62777	−	1.56120i	−0.135697	−	0.0806202i
$376$		0			0
$377$	14.5395			0.748821
$378$		0			0
$379$	5.68301	−	5.68301i	0.291917	−	0.291917i	−0.545920	−	0.837837i	$-0.683820\pi$
$379$	5.68301	−	5.68301i	0.291917	−	0.291917i	0.837837	+	0.545920i	$0.183820\pi$
$380$		0			0
$381$	−3.60355	−	14.1530i	−0.184615	−	0.725082i
$382$		0			0
$383$	6.91570	+	11.9783i	0.353376	+	0.612065i	0.986839	−	0.161708i	$-0.0517004\pi$
$383$	6.91570	+	11.9783i	0.353376	+	0.612065i	−0.633463	+	0.773773i	$0.718367\pi$
$384$		0			0
$385$	0.0733472	−	0.127041i	0.00373812	−	0.00647461i
$386$		0			0
$387$	−8.76382	−	9.21274i	−0.445490	−	0.468310i
$388$		0			0
$389$	−5.73529	−	21.4044i	−0.290791	−	1.08525i	−0.944503	−	0.328503i	$-0.893456\pi$
$389$	−5.73529	−	21.4044i	−0.290791	−	1.08525i	0.653712	−	0.756743i	$-0.273211\pi$
$390$		0			0
$391$	−0.341293	−	0.591136i	−0.0172599	−	0.0298950i
$392$		0			0
$393$	−9.42399	−	0.117654i	−0.475378	−	0.00593488i
$394$		0			0
$395$	1.85909	+	1.85909i	0.0935410	+	0.0935410i
$396$		0			0
$397$	−11.5684	+	11.5684i	−0.580603	+	0.580603i	−0.935069	−	0.354466i	$-0.884663\pi$
$397$	−11.5684	+	11.5684i	−0.580603	+	0.580603i	0.354466	+	0.935069i	$0.384663\pi$
$398$		0			0
$399$	−26.9182	+	15.0963i	−1.34759	+	0.755762i
$400$		0			0
$401$	19.4681	−	11.2399i	0.972191	−	0.561295i	0.0722876	−	0.997384i	$-0.476970\pi$
$401$	19.4681	−	11.2399i	0.972191	−	0.561295i	0.899904	+	0.436089i	$0.143637\pi$
$402$		0			0
$403$	−5.91861	+	1.58589i	−0.294827	+	0.0789987i
$404$		0			0
$405$	−1.18141	+	1.06894i	−0.0587047	+	0.0531162i
$406$		0			0
$407$	−1.41873	−	0.819104i	−0.0703238	−	0.0406015i
$408$		0			0
$409$	6.68684	−	3.86065i	0.330643	−	0.190897i	−0.325484	−	0.945548i	$-0.605527\pi$
$409$	6.68684	−	3.86065i	0.330643	−	0.190897i	0.656127	+	0.754651i	$0.272194\pi$
$410$		0			0
$411$	−1.52143	+	5.40712i	−0.0750465	+	0.266714i
$412$		0			0
$413$	4.62471	+	4.62471i	0.227567	+	0.227567i
$414$		0			0
$415$		−	2.26585i		−	0.111226i
$416$		0			0
$417$	23.6908	+	0.295769i	1.16014	+	0.0144839i
$418$		0			0
$419$	2.99280	+	0.801918i	0.146208	+	0.0391763i	0.331181	−	0.943567i	$-0.392553\pi$
$419$	2.99280	+	0.801918i	0.146208	+	0.0391763i	−0.184973	+	0.982744i	$0.559220\pi$
$420$		0			0
$421$	16.7110	−	4.47770i	0.814445	−	0.218230i	0.172528	−	0.985005i	$-0.444806\pi$
$421$	16.7110	−	4.47770i	0.814445	−	0.218230i	0.641916	+	0.766775i	$0.278140\pi$
$422$		0			0
$423$	−0.738517	+	29.5726i	−0.0359079	+	1.43787i
$424$		0			0
$425$	8.89591	−	15.4082i	0.431515	−	0.747406i
$426$		0			0
$427$	−18.7278	−	5.01811i	−0.906303	−	0.242843i
$428$		0			0
$429$	0.913810	−	0.232668i	0.0441191	−	0.0112333i
$430$		0			0
$431$	12.1601			0.585730			0.292865	−	0.956154i	$-0.405391\pi$
$431$	12.1601			0.585730			0.292865	+	0.956154i	$0.405391\pi$
$432$		0			0
$433$	18.6952			0.898436			0.449218	−	0.893422i	$-0.351703\pi$
$433$	18.6952			0.898436			0.449218	+	0.893422i	$0.351703\pi$
$434$		0			0
$435$	−2.79984	+	0.712876i	−0.134242	+	0.0341798i
$436$		0			0
$437$	1.39693	+	0.374306i	0.0668241	+	0.0179055i
$438$		0			0
$439$	18.2383	−	31.5896i	0.870466	−	1.50769i	0.00895100	−	0.999960i	$-0.497151\pi$
$439$	18.2383	−	31.5896i	0.870466	−	1.50769i	0.861515	−	0.507732i	$-0.169516\pi$
$440$		0			0
$441$	3.79861	+	2.32146i	0.180886	+	0.110546i
$442$		0			0
$443$	−13.2067	+	3.53871i	−0.627467	+	0.168129i	−0.558520	−	0.829491i	$-0.688631\pi$
$443$	−13.2067	+	3.53871i	−0.627467	+	0.168129i	−0.0689472	+	0.997620i	$0.521964\pi$
$444$		0			0
$445$	−0.522757	−	0.140072i	−0.0247811	−	0.00664007i
$446$		0			0
$447$	−21.9544	−	0.274091i	−1.03841	−	0.0129641i
$448$		0			0
$449$		−	8.41249i		−	0.397010i	−0.980100	−	0.198505i	$-0.936391\pi$
$449$		−	8.41249i		−	0.397010i	0.980100	−	0.198505i	$-0.0636086\pi$
$450$		0			0
$451$	−2.12333	−	2.12333i	−0.0999838	−	0.0999838i
$452$		0			0
$453$	0.742455	−	2.63867i	0.0348836	−	0.123975i
$454$		0			0
$455$	−0.555585	+	0.320767i	−0.0260462	+	0.0150378i
$456$		0			0
$457$	22.1026	+	12.7609i	1.03392	+	0.596932i	0.918104	−	0.396339i	$-0.129720\pi$
$457$	22.1026	+	12.7609i	1.03392	+	0.596932i	0.115812	+	0.993271i	$0.463053\pi$
$458$		0			0
$459$	−12.6549	−	13.6401i	−0.590679	−	0.636666i
$460$		0			0
$461$	−8.32500	+	2.23068i	−0.387734	+	0.103893i	−0.447419	−	0.894324i	$-0.647657\pi$
$461$	−8.32500	+	2.23068i	−0.387734	+	0.103893i	0.0596856	+	0.998217i	$0.480990\pi$
$462$		0			0
$463$	−13.7328	+	7.92866i	−0.638219	+	0.368476i	−0.783928	−	0.620852i	$-0.786787\pi$
$463$	−13.7328	+	7.92866i	−0.638219	+	0.368476i	0.145709	+	0.989327i	$0.453454\pi$
$464$		0			0
$465$	1.06198	−	0.595583i	0.0492482	−	0.0276195i
$466$		0			0
$467$	−3.55396	+	3.55396i	−0.164458	+	0.164458i	−0.784538	−	0.620081i	$-0.787100\pi$
$467$	−3.55396	+	3.55396i	−0.164458	+	0.164458i	0.620081	+	0.784538i	$0.287100\pi$
$468$		0			0
$469$	19.6936	+	19.6936i	0.909364	+	0.909364i
$470$		0			0
$471$	−13.8641	−	0.173088i	−0.638825	−	0.00797545i
$472$		0			0
$473$	−0.747721	−	1.29509i	−0.0343803	−	0.0595484i
$474$		0			0
$475$	9.75641	+	36.4114i	0.447655	+	1.67067i
$476$		0			0
$477$	−5.80503	+	19.6850i	−0.265794	+	0.901316i
$478$		0			0
$479$	1.39132	−	2.40984i	0.0635712	−	0.110109i	−0.832488	−	0.554043i	$-0.813084\pi$
$479$	1.39132	−	2.40984i	0.0635712	−	0.110109i	0.896059	+	0.443934i	$0.146418\pi$
$480$		0			0
$481$	3.58217	+	6.20450i	0.163333	+	0.282901i
$482$		0			0
$483$	0.191334	+	0.751470i	0.00870600	+	0.0341931i
$484$		0			0
$485$	0.249525	−	0.249525i	0.0113304	−	0.0113304i
$486$		0			0
$487$	4.42582			0.200553			0.100277	−	0.994960i	$-0.468027\pi$
$487$	4.42582			0.200553			0.100277	+	0.994960i	$0.468027\pi$
$488$		0			0
$489$	−21.5640	−	12.8115i	−0.975156	−	0.579357i
$490$		0			0
$491$	0.423288	−	1.57973i	0.0191027	−	0.0712923i	−0.955717	−	0.294289i	$-0.904917\pi$
$491$	0.423288	−	1.57973i	0.0191027	−	0.0712923i	0.974819	+	0.222997i	$0.0715839\pi$
$492$		0			0
$493$	−8.73283	−	32.5914i	−0.393307	−	1.46784i
$494$		0			0
$495$	−0.164563	+	0.0896089i	−0.00739656	+	0.00402762i
$496$		0			0
$497$	2.31131	+	1.33443i	0.103676	+	0.0598575i
$498$		0			0
$499$	1.20957	−	4.51417i	0.0541478	−	0.202082i	−0.933553	−	0.358440i	$-0.883309\pi$
$499$	1.20957	−	4.51417i	0.0541478	−	0.202082i	0.987700	+	0.156358i	$0.0499754\pi$
$500$		0			0
$501$	14.5610	−	14.2019i	0.650537	−	0.634494i
$502$		0			0
$503$		−	18.8954i		−	0.842506i	−0.906943	−	0.421253i	$-0.861590\pi$
$503$		−	18.8954i		−	0.842506i	0.906943	−	0.421253i	$-0.138410\pi$
$504$		0			0
$505$		−	2.83451i		−	0.126134i
$506$		0			0
$507$	17.7053	+	4.98183i	0.786319	+	0.221251i
$508$		0			0
$509$	7.56644	−	28.2383i	0.335377	−	1.25164i	−0.568084	−	0.822971i	$-0.692315\pi$
$509$	7.56644	−	28.2383i	0.335377	−	1.25164i	0.903460	−	0.428672i	$-0.141018\pi$
$510$		0			0
$511$	11.5522	+	6.66965i	0.511038	+	0.295048i
$512$		0			0
$513$	39.3941	+	1.47607i	1.73929	+	0.0651701i
$514$		0			0
$515$	−0.744213	−	2.77744i	−0.0327939	−	0.122389i
$516$		0			0
$517$	−0.900458	+	3.36056i	−0.0396021	+	0.147797i
$518$		0			0
$519$	22.4445	−	12.5874i	0.985206	−	0.552526i
$520$		0			0
$521$	−18.9291			−0.829299			−0.414649	−	0.909981i	$-0.636096\pi$
$521$	−18.9291			−0.829299			−0.414649	+	0.909981i	$0.636096\pi$
$522$		0			0
$523$	22.0490	−	22.0490i	0.964137	−	0.964137i	−0.0352421	−	0.999379i	$-0.511220\pi$
$523$	22.0490	−	22.0490i	0.964137	−	0.964137i	0.999379	+	0.0352421i	$0.0112202\pi$
$524$		0			0
$525$	−14.4695	+	14.1127i	−0.631502	+	0.615928i
$526$		0			0
$527$	7.10978	+	12.3145i	0.309707	+	0.536428i
$528$		0			0
$529$	−11.4818	+	19.8871i	−0.499210	+	0.864657i
$530$		0			0
$531$	−1.96010	−	8.12102i	−0.0850610	−	0.352422i
$532$		0			0
$533$	3.39888	+	12.6848i	0.147222	+	0.549439i
$534$		0			0
$535$	−0.260693	−	0.451533i	−0.0112707	−	0.0195215i
$536$		0			0
$537$	13.0181	−	21.9117i	0.561773	−	0.945559i
$538$		0			0
$539$	0.370224	+	0.370224i	0.0159467	+	0.0159467i
$540$		0			0
$541$	−16.0780	+	16.0780i	−0.691246	+	0.691246i	−0.962506	−	0.271260i	$-0.912560\pi$
$541$	−16.0780	+	16.0780i	−0.691246	+	0.691246i	0.271260	+	0.962506i	$0.412560\pi$
$542$		0			0
$543$	33.8137	+	20.0893i	1.45108	+	0.862115i
$544$		0			0
$545$	−1.66986	+	0.964091i	−0.0715287	+	0.0412971i
$546$		0			0
$547$	9.74859	−	2.61213i	0.416819	−	0.111686i	−0.0443131	−	0.999018i	$-0.514110\pi$
$547$	9.74859	−	2.61213i	0.416819	−	0.111686i	0.461133	+	0.887331i	$0.347443\pi$
$548$		0			0
$549$	17.0693	+	17.9437i	0.728502	+	0.765819i
$550$		0			0
$551$	61.9103	+	35.7439i	2.63747	+	1.52274i
$552$		0			0
$553$	30.2083	−	17.4408i	1.28459	−	0.741657i
$554$		0			0
$555$	−0.994020	−	1.01915i	−0.0421938	−	0.0432607i
$556$		0			0
$557$	9.47553	+	9.47553i	0.401491	+	0.401491i	0.878758	−	0.477267i	$-0.158373\pi$
$557$	9.47553	+	9.47553i	0.401491	+	0.401491i	−0.477267	+	0.878758i	$0.658373\pi$
$558$		0			0
$559$			6.53998i			0.276612i
$560$		0			0
$561$	−1.07040	−	1.90863i	−0.0451925	−	0.0805823i
$562$		0			0
$563$	−5.63595	−	1.51015i	−0.237527	−	0.0636451i	0.138092	−	0.990419i	$-0.455903\pi$
$563$	−5.63595	−	1.51015i	−0.237527	−	0.0636451i	−0.375619	+	0.926774i	$0.622570\pi$
$564$		0			0
$565$	−2.03639	+	0.545650i	−0.0856717	+	0.0229557i
$566$		0			0
$567$	9.64193	+	18.8105i	0.404923	+	0.789966i
$568$		0			0
$569$	−13.1217	+	22.7275i	−0.550090	+	0.952784i	0.448177	+	0.893945i	$0.352073\pi$
$569$	−13.1217	+	22.7275i	−0.550090	+	0.952784i	−0.998267	+	0.0588397i	$0.981260\pi$
$570$		0			0
$571$	1.55718	+	0.417246i	0.0651661	+	0.0174612i	0.291255	−	0.956646i	$-0.405927\pi$
$571$	1.55718	+	0.417246i	0.0651661	+	0.0174612i	−0.226089	+	0.974107i	$0.572594\pi$
$572$		0			0
$573$	−3.24228	+	11.5230i	−0.135448	+	0.481379i
$574$		0			0
$575$	0.947143			0.0394986
$576$		0			0
$577$	29.9562			1.24709			0.623546	−	0.781787i	$-0.285691\pi$
$577$	29.9562			1.24709			0.623546	+	0.781787i	$0.285691\pi$
$578$		0			0
$579$	18.9366	+	19.4154i	0.786978	+	0.806877i
$580$		0			0
$581$	−29.0372	−	7.78051i	−1.20467	−	0.322790i
$582$		0			0
$583$	−1.20686	+	2.09034i	−0.0499830	+	0.0865731i
$584$		0			0
$585$	0.819202	+	0.0204580i	0.0338699	+	0.000845833i
$586$		0			0
$587$	−3.76680	+	1.00931i	−0.155473	+	0.0416587i	−0.335716	−	0.941963i	$-0.608978\pi$
$587$	−3.76680	+	1.00931i	−0.155473	+	0.0416587i	0.180243	+	0.983622i	$0.442312\pi$
$588$		0			0
$589$	−29.1007	−	7.79751i	−1.19907	−	0.321291i
$590$		0			0
$591$	−10.3191	+	17.3687i	−0.424469	+	0.714453i
$592$		0			0
$593$			33.7168i			1.38459i	0.721617	+	0.692293i	$0.243399\pi$
$593$			33.7168i			1.38459i	−0.721617	+	0.692293i	$0.756601\pi$
$594$		0			0
$595$	1.05272	+	1.05272i	0.0431575	+	0.0431575i
$596$		0			0
$597$	9.27719	−	2.36209i	0.379690	−	0.0966740i
$598$		0			0
$599$	23.4461	−	13.5366i	0.957981	−	0.553091i	0.0624300	−	0.998049i	$-0.480115\pi$
$599$	23.4461	−	13.5366i	0.957981	−	0.553091i	0.895551	+	0.444959i	$0.146782\pi$
$600$		0			0
$601$	−25.7087	−	14.8429i	−1.04868	−	0.605455i	−0.126400	−	0.991979i	$-0.540342\pi$
$601$	−25.7087	−	14.8429i	−1.04868	−	0.605455i	−0.922279	+	0.386524i	$0.873676\pi$
$602$		0			0
$603$	−8.34676	−	34.5820i	−0.339906	−	1.40829i
$604$		0			0
$605$	1.85964	−	0.498288i	0.0756050	−	0.0202583i
$606$		0			0
$607$	28.8436	−	16.6529i	1.17073	−	0.675918i	0.216874	−	0.976200i	$-0.430414\pi$
$607$	28.8436	−	16.6529i	1.17073	−	0.675918i	0.953851	+	0.300281i	$0.0970805\pi$
$608$		0			0
$609$	−0.478512	+	38.3283i	−0.0193903	+	1.55314i
$610$		0			0
$611$	10.7587	−	10.7587i	0.435250	−	0.435250i
$612$		0			0
$613$	−16.1448	−	16.1448i	−0.652082	−	0.652082i	0.301412	−	0.953494i	$-0.402542\pi$
$613$	−16.1448	−	16.1448i	−0.652082	−	0.652082i	−0.953494	+	0.301412i	$0.902542\pi$
$614$		0			0
$615$	−1.27646	−	2.27604i	−0.0514717	−	0.0917788i
$616$		0			0
$617$	18.3244	+	31.7389i	0.737714	+	1.27776i	0.953522	+	0.301323i	$0.0974282\pi$
$617$	18.3244	+	31.7389i	0.737714	+	1.27776i	−0.215808	+	0.976436i	$0.569238\pi$
$618$		0			0
$619$	0.913019	+	3.40743i	0.0366973	+	0.136956i	0.981844	−	0.189690i	$-0.0607482\pi$
$619$	0.913019	+	3.40743i	0.0366973	+	0.136956i	−0.945147	+	0.326646i	$0.894082\pi$
$620$		0			0
$621$	0.292006	−	0.946487i	0.0117178	−	0.0379812i
$622$		0			0
$623$	−3.59010	+	6.21824i	−0.143834	+	0.249128i
$624$		0			0
$625$	12.2655	+	21.2444i	0.490618	+	0.849776i
$626$		0			0
$627$	4.46307	+	1.25580i	0.178238	+	0.0501517i
$628$		0			0
$629$	11.7563	−	11.7563i	0.468754	−	0.468754i
$630$		0			0
$631$	10.2367			0.407515			0.203758	−	0.979021i	$-0.434685\pi$
$631$	10.2367			0.407515			0.203758	+	0.979021i	$0.434685\pi$
$632$		0			0
$633$	0.0914139	−	7.32216i	0.00363338	−	0.291030i
$634$		0			0
$635$	0.386331	−	1.44181i	0.0153311	−	0.0572164i
$636$		0			0
$637$	−0.592628	−	2.21172i	−0.0234808	−	0.0876315i
$638$		0			0
$639$	−1.63029	−	2.99396i	−0.0644932	−	0.118439i
$640$		0			0
$641$	13.3541	+	7.70998i	0.527454	+	0.304526i	0.739979	−	0.672630i	$-0.234835\pi$
$641$	13.3541	+	7.70998i	0.527454	+	0.304526i	−0.212525	+	0.977156i	$0.568169\pi$
$642$		0			0
$643$	−4.94396	+	18.4511i	−0.194971	+	0.727641i	0.797303	+	0.603579i	$0.206259\pi$
$643$	−4.94396	+	18.4511i	−0.194971	+	0.727641i	−0.992274	+	0.124063i	$0.960408\pi$
$644$		0			0
$645$	−0.320658	−	1.25939i	−0.0126259	−	0.0495885i
$646$		0			0
$647$		−	0.502526i		−	0.0197563i	−0.999951	−	0.00987817i	$-0.996856\pi$
$647$		−	0.502526i		−	0.0197563i	0.999951	−	0.00987817i	$-0.00314437\pi$
$648$		0			0
$649$		−	0.982536i		−	0.0385679i
$650$		0			0
$651$	−3.98585	−	15.6546i	−0.156218	−	0.613551i
$652$		0			0
$653$	−8.02087	+	29.9343i	−0.313881	+	1.17142i	0.611146	+	0.791518i	$0.290709\pi$
$653$	−8.02087	+	29.9343i	−0.313881	+	1.17142i	−0.925027	+	0.379902i	$0.875958\pi$
$654$		0			0
$655$	−0.834206	−	0.481629i	−0.0325951	−	0.0188188i
$656$		0			0
$657$	−8.14837	−	14.9642i	−0.317898	−	0.583807i
$658$		0			0
$659$	−7.61220	−	28.4091i	−0.296529	−	1.10666i	−0.939995	−	0.341188i	$-0.889171\pi$
$659$	−7.61220	−	28.4091i	−0.296529	−	1.10666i	0.643466	−	0.765475i	$-0.277496\pi$
$660$		0			0
$661$	−5.99448	+	22.3717i	−0.233158	+	0.870159i	0.745812	+	0.666156i	$0.232062\pi$
$661$	−5.99448	+	22.3717i	−0.233158	+	0.870159i	−0.978970	+	0.204002i	$0.934605\pi$
$662$		0			0
$663$	−0.119468	+	9.56926i	−0.00463975	+	0.371639i
$664$		0			0
$665$	−3.15430			−0.122319
$666$		0			0
$667$	1.27010	−	1.27010i	0.0491786	−	0.0491786i
$668$		0			0
$669$	−12.5246	−	3.52411i	−0.484230	−	0.136250i
$670$		0			0
$671$	1.45634	+	2.52246i	0.0562214	+	0.0973784i
$672$		0			0
$673$	20.8639	−	36.1374i	0.804246	−	1.39300i	−0.112553	−	0.993646i	$-0.535903\pi$
$673$	20.8639	−	36.1374i	0.804246	−	1.39300i	0.916799	−	0.399349i	$-0.130764\pi$
$674$		0			0
$675$	25.1709	−	5.74372i	0.968829	−	0.221076i
$676$		0			0
$677$	−7.20552	−	26.8914i	−0.276931	−	1.03352i	−0.954537	−	0.298094i	$-0.903649\pi$
$677$	−7.20552	−	26.8914i	−0.276931	−	1.03352i	0.677606	−	0.735425i	$-0.263017\pi$
$678$		0			0
$679$	−2.34088	−	4.05452i	−0.0898348	−	0.155598i
$680$		0			0
$681$	−5.53705	−	9.87307i	−0.212180	−	0.378337i
$682$		0			0
$683$	−31.1964	−	31.1964i	−1.19370	−	1.19370i	−0.976022	−	0.217674i	$-0.930153\pi$
$683$	−31.1964	−	31.1964i	−1.19370	−	1.19370i	−0.217674	−	0.976022i	$-0.569847\pi$
$684$		0			0
$685$	−0.405948	+	0.405948i	−0.0155105	+	0.0155105i
$686$		0			0
$687$	0.0243571	−	1.95098i	0.000929281	−	0.0744344i
$688$		0			0
$689$	9.14164	−	5.27793i	0.348269	−	0.201073i
$690$		0			0
$691$	−31.9525	+	8.56164i	−1.21553	+	0.325700i	−0.808929	−	0.587906i	$-0.799953\pi$
$691$	−31.9525	+	8.56164i	−1.21553	+	0.325700i	−0.406600	+	0.913606i	$0.633286\pi$
$692$		0			0
$693$	0.583273	+	2.41660i	0.0221567	+	0.0917990i
$694$		0			0
$695$	2.09710	+	1.21076i	0.0795474	+	0.0459267i
$696$		0			0
$697$	26.3925	−	15.2377i	0.999686	−	0.577169i
$698$		0			0
$699$	−23.3993	+	5.95776i	−0.885043	+	0.225343i
$700$		0			0
$701$	−22.9365	−	22.9365i	−0.866299	−	0.866299i	0.125761	−	0.992061i	$-0.459863\pi$
$701$	−22.9365	−	22.9365i	−0.866299	−	0.866299i	−0.992061	+	0.125761i	$0.959863\pi$
$702$		0			0
$703$			35.2257i			1.32856i
$704$		0			0
$705$	−1.54428	+	2.59928i	−0.0581609	+	0.0978947i
$706$		0			0
$707$	−36.3246	−	9.73316i	−1.36613	−	0.366053i
$708$		0			0
$709$	−10.8123	+	2.89716i	−0.406066	+	0.108805i	−0.456070	−	0.889944i	$-0.650743\pi$
$709$	−10.8123	+	2.89716i	−0.406066	+	0.108805i	0.0500039	+	0.998749i	$0.484077\pi$
$710$		0			0
$711$	−44.5417	−	1.11234i	−1.67044	−	0.0417160i
$712$		0			0
$713$	−0.378487	+	0.655559i	−0.0141745	+	0.0245509i
$714$		0			0
$715$	0.0930922	+	0.0249440i	0.00348145	+	0.000932852i
$716$		0			0
$717$	35.8153	+	36.7209i	1.33755	+	1.37137i
$718$		0			0
$719$	−45.6552			−1.70265			−0.851325	−	0.524639i	$-0.824200\pi$
$719$	−45.6552			−1.70265			−0.851325	+	0.524639i	$0.824200\pi$
$720$		0			0
$721$	−38.1488			−1.42074
$722$		0			0
$723$	5.65968	−	20.1144i	0.210486	−	0.748061i
$724$		0			0
$725$	45.2232	+	12.1175i	1.67955	+	0.450033i
$726$		0			0
$727$	14.6537	−	25.3810i	0.543477	−	0.941331i	−0.455224	−	0.890377i	$-0.650441\pi$
$727$	14.6537	−	25.3810i	0.543477	−	0.941331i	0.998701	−	0.0509534i	$-0.0162260\pi$
$728$		0			0
$729$	2.02050	−	26.9243i	0.0748335	−	0.997196i
$730$		0			0
$731$	14.6599	−	3.92810i	0.542215	−	0.145286i
$732$		0			0
$733$	−5.18294	−	1.38877i	−0.191436	−	0.0512952i	0.161827	−	0.986819i	$-0.448261\pi$
$733$	−5.18294	−	1.38877i	−0.191436	−	0.0512952i	−0.353263	+	0.935524i	$0.614928\pi$
$734$		0			0
$735$	0.222563	+	0.396850i	0.00820935	+	0.0146380i
$736$		0			0
$737$		−	4.18397i		−	0.154119i
$738$		0			0
$739$	−25.3597	−	25.3597i	−0.932873	−	0.932873i	0.0650119	−	0.997884i	$-0.479291\pi$
$739$	−25.3597	−	25.3597i	−0.932873	−	0.932873i	−0.997884	+	0.0650119i	$0.979291\pi$
$740$		0			0
$741$	−14.1573	−	14.5153i	−0.520082	−	0.533232i
$742$		0			0
$743$	−2.86105	+	1.65183i	−0.104962	+	0.0605998i	−0.551562	−	0.834134i	$-0.685968\pi$
$743$	−2.86105	+	1.65183i	−0.104962	+	0.0605998i	0.446600	+	0.894734i	$0.352635\pi$
$744$		0			0
$745$	−1.94339	−	1.12202i	−0.0712004	−	0.0411075i
$746$		0			0
$747$	26.4658	+	27.8215i	0.968332	+	1.01793i
$748$		0			0
$749$	−6.68164	+	1.79034i	−0.244142	+	0.0654176i
$750$		0			0
$751$	−15.0045	+	8.66287i	−0.547523	+	0.316112i	−0.748122	−	0.663561i	$-0.769044\pi$
$751$	−15.0045	+	8.66287i	−0.547523	+	0.316112i	0.200599	+	0.979673i	$0.435711\pi$
$752$		0			0
$753$	−29.3466	−	17.4353i	−1.06945	−	0.635378i
$754$		0			0
$755$	0.198102	−	0.198102i	0.00720967	−	0.00720967i
$756$		0			0
$757$	−29.0206	−	29.0206i	−1.05477	−	1.05477i	−0.998410	−	0.0563619i	$-0.982050\pi$
$757$	−29.0206	−	29.0206i	−1.05477	−	1.05477i	−0.0563619	−	0.998410i	$-0.517950\pi$
$758$		0			0
$759$	0.0595015	−	0.100151i	0.00215977	−	0.00363526i
$760$		0			0
$761$	9.85285	+	17.0656i	0.357166	+	0.618629i	0.987486	−	0.157706i	$-0.0504098\pi$
$761$	9.85285	+	17.0656i	0.357166	+	0.618629i	−0.630320	+	0.776335i	$0.717076\pi$
$762$		0			0
$763$	6.62101	+	24.7100i	0.239697	+	0.894560i
$764$		0			0
$765$	−0.446178	−	1.84859i	−0.0161316	−	0.0668360i
$766$		0			0
$767$	−2.14845	+	3.72123i	−0.0775761	+	0.134366i
$768$		0			0
$769$	−20.5479	−	35.5899i	−0.740974	−	1.28341i	−0.952052	−	0.305936i	$-0.901031\pi$
$769$	−20.5479	−	35.5899i	−0.740974	−	1.28341i	0.211078	−	0.977469i	$-0.432303\pi$
$770$		0			0
$771$	30.0705	−	29.3289i	1.08296	−	1.05626i
$772$		0			0
$773$	−18.7350	+	18.7350i	−0.673853	+	0.673853i	−0.958602	−	0.284749i	$-0.908090\pi$
$773$	−18.7350	+	18.7350i	−0.673853	+	0.673853i	0.284749	+	0.958602i	$0.408090\pi$
$774$		0			0
$775$	−19.7308			−0.708751
$776$		0			0
$777$	−16.4739	+	9.23894i	−0.590998	+	0.331445i
$778$		0			0
$779$	−16.7116	+	62.3687i	−0.598757	+	2.23459i
$780$		0			0
$781$	−0.103770	−	0.387276i	−0.00371319	−	0.0138578i
$782$		0			0
$783$	26.0516	−	41.4560i	0.931006	−	1.48152i
$784$		0			0
$785$	−1.22724	−	0.708550i	−0.0438022	−	0.0252892i
$786$		0			0
$787$	−9.12803	+	34.0663i	−0.325379	+	1.21433i	0.588551	+	0.808460i	$0.299699\pi$
$787$	−9.12803	+	34.0663i	−0.325379	+	1.21433i	−0.913930	+	0.405872i	$0.866968\pi$
$788$		0			0
$789$	51.4177	+	14.4677i	1.83052	+	0.515062i
$790$		0			0
$791$			27.9703i			0.994511i
$792$		0			0
$793$		−	12.7380i		−	0.452338i
$794$		0			0
$795$	−1.50161	+	1.46458i	−0.0532566	+	0.0519433i
$796$		0			0
$797$	−2.97502	+	11.1029i	−0.105381	+	0.393286i	−0.998388	−	0.0567557i	$-0.981924\pi$
$797$	−2.97502	+	11.1029i	−0.105381	+	0.393286i	0.893007	+	0.450042i	$0.148591\pi$
$798$		0			0
$799$	−30.5784	−	17.6544i	−1.08179	−	0.624569i
$800$		0			0
$801$	8.05481	−	4.38606i	0.284603	−	0.154974i
$802$		0			0
$803$	−0.518655	−	1.93565i	−0.0183030	−	0.0683076i
$804$		0			0
$805$	−0.0205126	+	0.0765542i	−0.000722976	+	0.00269818i
$806$		0			0
$807$	−11.0423	−	6.56042i	−0.388707	−	0.230938i
$808$		0			0
$809$	−25.8320			−0.908205			−0.454102	−	0.890950i	$-0.650040\pi$
$809$	−25.8320			−0.908205			−0.454102	+	0.890950i	$0.650040\pi$
$810$		0			0
$811$	16.1463	−	16.1463i	0.566973	−	0.566973i	−0.364306	−	0.931279i	$-0.618694\pi$
$811$	16.1463	−	16.1463i	0.566973	−	0.566973i	0.931279	+	0.364306i	$0.118694\pi$
$812$		0			0
$813$	−2.91804	−	11.4607i	−0.102340	−	0.401944i
$814$		0			0
$815$	−1.28179	−	2.22013i	−0.0448992	−	0.0777677i
$816$		0			0
$817$	−16.0779	+	27.8478i	−0.562495	+	0.974271i
$818$		0			0
$819$	3.07516	−	10.4280i	0.107455	−	0.364382i
$820$		0			0
$821$	−1.87921	−	7.01329i	−0.0655848	−	0.244766i	0.925349	−	0.379116i	$-0.123772\pi$
$821$	−1.87921	−	7.01329i	−0.0655848	−	0.244766i	−0.990934	+	0.134350i	$0.957105\pi$
$822$		0			0
$823$	−16.1543	−	27.9801i	−0.563103	−	0.975324i	−0.997223	−	0.0744686i	$-0.976274\pi$
$823$	−16.1543	−	27.9801i	−0.563103	−	0.975324i	0.434120	−	0.900855i	$-0.357059\pi$
$824$		0			0
$825$	3.03620	+	0.0379056i	0.105707	+	0.00131970i
$826$		0			0
$827$	12.0458	+	12.0458i	0.418875	+	0.418875i	0.884816	−	0.465941i	$-0.154284\pi$
$827$	12.0458	+	12.0458i	0.418875	+	0.418875i	−0.465941	+	0.884816i	$0.654284\pi$
$828$		0			0
$829$	22.8912	−	22.8912i	0.795046	−	0.795046i	−0.187264	−	0.982310i	$-0.559962\pi$
$829$	22.8912	−	22.8912i	0.795046	−	0.795046i	0.982310	+	0.187264i	$0.0599619\pi$
$830$		0			0
$831$	−9.92332	+	5.56523i	−0.344236	+	0.193056i
$832$		0			0
$833$	−4.60179	+	2.65684i	−0.159443	+	0.0920542i
$834$		0			0
$835$	2.00802	−	0.538048i	0.0694905	−	0.0186199i
$836$		0			0
$837$	−6.08305	+	19.7171i	−0.210261	+	0.681524i
$838$		0			0
$839$	4.97011	+	2.86949i	0.171587	+	0.0990659i	0.583334	−	0.812232i	$-0.301748\pi$
$839$	4.97011	+	2.86949i	0.171587	+	0.0990659i	−0.411747	+	0.911298i	$0.635081\pi$
$840$		0			0
$841$	51.7783	−	29.8942i	1.78546	−	1.03083i
$842$		0			0
$843$	2.15701	−	7.66597i	0.0742914	−	0.264030i
$844$		0			0
$845$	1.32925	+	1.32925i	0.0457276	+	0.0457276i
$846$		0			0
$847$		−	25.5426i		−	0.877653i
$848$		0			0
$849$	15.1806	+	0.189523i	0.520998	+	0.00650443i
$850$		0			0
$851$	0.854919	+	0.229075i	0.0293062	+	0.00785258i
$852$		0			0
$853$	−45.5977	+	12.2179i	−1.56123	+	0.418331i	−0.933054	−	0.359737i	$-0.882867\pi$
$853$	−45.5977	+	12.2179i	−1.56123	+	0.418331i	−0.628180	+	0.778068i	$0.716200\pi$
$854$		0			0
$855$	3.43794	+	2.10104i	0.117575	+	0.0718542i
$856$		0			0
$857$	−23.4789	+	40.6666i	−0.802023	+	1.38914i	0.116260	+	0.993219i	$0.462910\pi$
$857$	−23.4789	+	40.6666i	−0.802023	+	1.38914i	−0.918283	+	0.395926i	$0.870424\pi$
$858$		0			0
$859$	15.7229	+	4.21294i	0.536459	+	0.143744i	0.516869	−	0.856064i	$-0.327097\pi$
$859$	15.7229	+	4.21294i	0.536459	+	0.143744i	0.0195896	+	0.999808i	$0.493764\pi$
$860$		0			0
$861$	−33.5509	+	8.54249i	−1.14341	+	0.291127i
$862$		0			0
$863$	−51.2010			−1.74290			−0.871451	−	0.490482i	$-0.836821\pi$
$863$	−51.2010			−1.74290			−0.871451	+	0.490482i	$0.836821\pi$
$864$		0			0
$865$	2.63008			0.0894253
$866$		0			0
$867$	−7.01249	+	1.78547i	−0.238157	+	0.0606377i
$868$		0			0
$869$	−5.06161	−	1.35625i	−0.171703	−	0.0460078i
$870$		0			0
$871$	−9.14883	+	15.8462i	−0.309996	+	0.536929i
$872$		0			0
$873$	−0.149297	+	5.97834i	−0.00505295	+	0.202336i
$874$		0			0
$875$	−4.00341	+	1.07271i	−0.135340	+	0.0362642i
$876$		0			0
$877$	−32.7562	−	8.77699i	−1.10610	−	0.296378i	−0.340852	−	0.940117i	$-0.610716\pi$
$877$	−32.7562	−	8.77699i	−1.10610	−	0.296378i	−0.765245	+	0.643739i	$0.777382\pi$
$878$		0			0
$879$	29.8918	+	0.373187i	1.00823	+	0.0125873i
$880$		0			0
$881$		−	54.6465i		−	1.84109i	−0.390639	−	0.920544i	$-0.627746\pi$
$881$		−	54.6465i		−	1.84109i	0.390639	−	0.920544i	$-0.372254\pi$
$882$		0			0
$883$	−6.31259	−	6.31259i	−0.212436	−	0.212436i	0.592866	−	0.805301i	$-0.297996\pi$
$883$	−6.31259	−	6.31259i	−0.212436	−	0.212436i	−0.805301	+	0.592866i	$0.797996\pi$
$884$		0			0
$885$	0.231270	−	0.821929i	0.00777407	−	0.0276289i
$886$		0			0
$887$	−33.1288	+	19.1269i	−1.11236	+	0.642219i	−0.939438	−	0.342718i	$-0.888652\pi$
$887$	−33.1288	+	19.1269i	−1.11236	+	0.642219i	−0.172917	+	0.984936i	$0.555319\pi$
$888$		0			0
$889$	−17.1504	−	9.90179i	−0.575206	−	0.332095i
$890$		0			0
$891$	0.973947	−	3.02241i	0.0326284	−	0.101255i
$892$		0			0
$893$	72.2606	−	19.3622i	2.41811	−	0.647930i
$894$		0			0
$895$	2.25593	−	1.30246i	0.0754074	−	0.0435365i
$896$		0			0
$897$	−0.444348	+	0.249201i	−0.0148364	+	0.00832057i
$898$		0			0
$899$	−26.4587	+	26.4587i	−0.882447	+	0.882447i
$900$		0			0
$901$	−17.3216	−	17.3216i	−0.577066	−	0.577066i
$902$		0			0
$903$	−17.2404	−	0.215239i	−0.573724	−	0.00716270i
$904$		0			0
$905$	2.00993	+	3.48131i	0.0668124	+	0.115723i
$906$		0			0
$907$	−2.82954	−	10.5600i	−0.0939534	−	0.350639i	0.902905	−	0.429840i	$-0.141430\pi$
$907$	−2.82954	−	10.5600i	−0.0939534	−	0.350639i	−0.996859	+	0.0792006i	$0.974763\pi$
$908$		0			0
$909$	33.1078	+	34.8038i	1.09812	+	1.15437i
$910$		0			0
$911$	4.41606	−	7.64884i	0.146311	−	0.253417i	−0.783551	−	0.621328i	$-0.786593\pi$
$911$	4.41606	−	7.64884i	0.146311	−	0.253417i	0.929861	+	0.367911i	$0.119927\pi$
$912$		0			0
$913$	2.25804	+	3.91103i	0.0747301	+	0.129436i
$914$		0			0
$915$	0.624547	+	2.45293i	0.0206469	+	0.0810913i
$916$		0			0
$917$	−9.03666	+	9.03666i	−0.298417	+	0.298417i
$918$		0			0
$919$	5.12206			0.168961			0.0844806	−	0.996425i	$-0.473077\pi$
$919$	5.12206			0.168961			0.0844806	+	0.996425i	$0.473077\pi$
$920$		0			0
$921$	−6.50333	−	3.86374i	−0.214292	−	0.127315i
$922$		0			0
$923$	−0.453816	+	1.69366i	−0.0149375	+	0.0557476i
$924$		0			0
$925$	5.97091	+	22.2838i	0.196322	+	0.732685i
$926$		0			0
$927$	41.5791	+	25.4104i	1.36564	+	0.834589i
$928$		0			0
$929$	−7.86161	−	4.53890i	−0.257931	−	0.148916i	0.365459	−	0.930827i	$-0.380912\pi$
$929$	−7.86161	−	4.53890i	−0.257931	−	0.148916i	−0.623390	+	0.781911i	$0.714245\pi$
$930$		0			0
$931$	2.91384	−	10.8746i	0.0954973	−	0.356401i
$932$		0			0
$933$	−16.8775	+	16.4613i	−0.552544	+	0.538918i
$934$		0			0
$935$		−	0.223655i		−	0.00731431i
$936$		0			0
$937$		−	8.98159i		−	0.293416i	−0.989180	−	0.146708i	$-0.953132\pi$
$937$		−	8.98159i		−	0.293416i	0.989180	−	0.146708i	$-0.0468677\pi$
$938$		0			0
$939$	17.5412	+	4.93565i	0.572435	+	0.161069i
$940$		0			0
$941$	10.3372	−	38.5789i	0.336982	−	1.25764i	−0.564721	−	0.825282i	$-0.691016\pi$
$941$	10.3372	−	38.5789i	0.336982	−	1.25764i	0.901704	−	0.432354i	$-0.142317\pi$
$942$		0			0
$943$	1.40500	+	0.811176i	0.0457530	+	0.0264155i
$944$		0			0
$945$	−0.0808913	+	2.15887i	−0.00263139	+	0.0702280i
$946$		0			0
$947$	1.97321	+	7.36412i	0.0641207	+	0.239302i	0.990547	−	0.137175i	$-0.0438022\pi$
$947$	1.97321	+	7.36412i	0.0641207	+	0.239302i	−0.926426	+	0.376476i	$0.877136\pi$
$948$		0			0
$949$	−2.26822	+	8.46512i	−0.0736296	+	0.274789i
$950$		0			0
$951$	−29.3515	+	16.4610i	−0.951786	+	0.533784i
$952$		0			0
$953$	−9.35277			−0.302966			−0.151483	−	0.988460i	$-0.548405\pi$
$953$	−9.35277			−0.302966			−0.151483	+	0.988460i	$0.548405\pi$
$954$		0			0
$955$	−0.865105	+	0.865105i	−0.0279941	+	0.0279941i
$956$		0			0
$957$	4.12233	−	4.02066i	0.133256	−	0.129970i
$958$		0			0
$959$	3.80834	+	6.59623i	0.122978	+	0.213003i
$960$		0			0
$961$	−7.61538	+	13.1902i	−0.245658	+	0.425491i
$962$		0			0
$963$	8.47497	+	2.49923i	0.273102	+	0.0805366i
$964$		0			0
$965$	0.717426	+	2.67747i	0.0230948	+	0.0861908i
$966$		0			0
$967$	−5.00369	−	8.66664i	−0.160908	−	0.278700i	0.774287	−	0.632835i	$-0.218109\pi$
$967$	−5.00369	−	8.66664i	−0.160908	−	0.278700i	−0.935194	+	0.354135i	$0.884775\pi$
$968$		0			0
$969$	−24.0338	+	40.4530i	−0.772078	+	1.29954i
$970$		0			0
$971$	−35.7927	−	35.7927i	−1.14864	−	1.14864i	−0.986820	−	0.161822i	$-0.948263\pi$
$971$	−35.7927	−	35.7927i	−1.14864	−	1.14864i	−0.161822	−	0.986820i	$-0.551737\pi$
$972$		0			0
$973$	22.7171	−	22.7171i	0.728276	−	0.728276i
$974$		0			0
$975$	−11.4163	−	6.78263i	−0.365615	−	0.217218i
$976$		0			0
$977$	−18.9576	+	10.9452i	−0.606506	+	0.350167i	−0.771597	−	0.636112i	$-0.780542\pi$
$977$	−18.9576	+	10.9452i	−0.606506	+	0.350167i	0.165091	+	0.986278i	$0.447208\pi$
$978$		0			0
$979$	1.04191	−	0.279179i	0.0332996	−	0.00892259i
$980$		0			0
$981$	9.24263	−	31.3420i	0.295094	−	1.00067i
$982$		0			0
$983$	11.0681	+	6.39017i	0.353018	+	0.203815i	0.666014	−	0.745940i	$-0.267999\pi$
$983$	11.0681	+	6.39017i	0.353018	+	0.203815i	−0.312996	+	0.949754i	$0.601333\pi$
$984$		0			0
$985$	−1.78820	+	1.03242i	−0.0569769	+	0.0328956i
$986$		0			0
$987$	28.0075	+	28.7156i	0.891487	+	0.914028i
$988$		0			0
$989$	0.571303	+	0.571303i	0.0181664	+	0.0181664i
$990$		0			0
$991$		−	51.8246i		−	1.64626i	−0.567852	−	0.823131i	$-0.692225\pi$
$991$		−	51.8246i		−	1.64626i	0.567852	−	0.823131i	$-0.307775\pi$
$992$		0			0
$993$	−10.8065	−	19.2690i	−0.342934	−	0.611483i
$994$		0			0
$995$	0.945091	+	0.253236i	0.0299614	+	0.00802813i
$996$		0			0
$997$	45.6984	−	12.2448i	1.44728	−	0.387798i	0.552204	−	0.833709i	$-0.313787\pi$
$997$	45.6984	−	12.2448i	1.44728	−	0.387798i	0.895077	+	0.445911i	$0.147120\pi$
$998$		0			0
$999$	24.1092	+	0.903353i	0.762780	+	0.0285808i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.335.2		88
3.2	odd	2		1728.2.z.a.143.12		88
4.3	odd	2		144.2.u.a.11.6	✓	88
9.4	even	3		1728.2.z.a.719.12		88
9.5	odd	6	inner	576.2.y.a.527.14		88
12.11	even	2		432.2.v.a.251.17		88
16.3	odd	4	inner	576.2.y.a.47.14		88
16.13	even	4		144.2.u.a.83.13	yes	88
36.23	even	6		144.2.u.a.59.13	yes	88
36.31	odd	6		432.2.v.a.395.10		88
48.29	odd	4		432.2.v.a.35.10		88
48.35	even	4		1728.2.z.a.1007.12		88
144.13	even	12		432.2.v.a.179.17		88
144.67	odd	12		1728.2.z.a.1583.12		88
144.77	odd	12		144.2.u.a.131.6	yes	88
144.131	even	12	inner	576.2.y.a.239.2		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.6	✓	88	4.3	odd	2
144.2.u.a.59.13	yes	88	36.23	even	6
144.2.u.a.83.13	yes	88	16.13	even	4
144.2.u.a.131.6	yes	88	144.77	odd	12
432.2.v.a.35.10		88	48.29	odd	4
432.2.v.a.179.17		88	144.13	even	12
432.2.v.a.251.17		88	12.11	even	2
432.2.v.a.395.10		88	36.31	odd	6
576.2.y.a.47.14		88	16.3	odd	4	inner
576.2.y.a.239.2		88	144.131	even	12	inner
576.2.y.a.335.2		88	1.1	even	1	trivial
576.2.y.a.527.14		88	9.5	odd	6	inner
1728.2.z.a.143.12		88	3.2	odd	2
1728.2.z.a.719.12		88	9.4	even	3
1728.2.z.a.1007.12		88	48.35	even	4
1728.2.z.a.1583.12		88	144.67	odd	12

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.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.67850 + 0.427367i) q^{3} +(-0.170993 - 0.0458174i) q^{5} +(-1.17432 + 2.03397i) q^{7} +(2.63471 - 1.43467i) q^{9} +O(q^{10})\)	\(q+(-1.67850 + 0.427367i) q^{3} +(-0.170993 - 0.0458174i) q^{5} +(-1.17432 + 2.03397i) q^{7} +(2.63471 - 1.43467i) q^{9} +(0.340806 - 0.0913188i) q^{11} +(-1.49044 - 0.399362i) q^{13} +(0.306592 + 0.00382767i) q^{15} +3.58081i q^{17} +(-5.36462 - 5.36462i) q^{19} +(1.10183 - 3.91589i) q^{21} +(-0.165085 + 0.0953117i) q^{23} +(-4.30299 - 2.48433i) q^{25} +(-3.80923 + 3.53408i) q^{27} +(-9.10169 + 2.43879i) q^{29} +(3.43903 - 1.98552i) q^{31} +(-0.533016 + 0.298928i) q^{33} +(0.293991 - 0.293991i) q^{35} +(-3.28315 - 3.28315i) q^{37} +(2.67238 + 0.0333635i) q^{39} +(-4.25538 - 7.37054i) q^{41} +(-1.09699 - 4.09402i) q^{43} +(-0.516251 + 0.124603i) q^{45} +(-4.93030 + 8.53953i) q^{47} +(0.741968 + 1.28513i) q^{49} +(-1.53032 - 6.01038i) q^{51} +(-4.83735 + 4.83735i) q^{53} -0.0624595 q^{55} +(11.2972 + 6.71185i) q^{57} +(0.720744 - 2.68985i) q^{59} +(2.13661 + 7.97394i) q^{61} +(-0.175902 + 7.04369i) q^{63} +(0.236557 + 0.136576i) q^{65} +(3.06917 - 11.4543i) q^{67} +(0.236361 - 0.230532i) q^{69} -1.13635i q^{71} -5.67961i q^{73} +(8.28428 + 2.33099i) q^{75} +(-0.214474 + 0.800428i) q^{77} +(-12.8621 - 7.42593i) q^{79} +(4.88344 - 7.55990i) q^{81} +(3.31278 + 12.3635i) q^{83} +(0.164063 - 0.612293i) q^{85} +(14.2349 - 7.98327i) q^{87} +3.05719 q^{89} +(2.56254 - 2.56254i) q^{91} +(-4.92386 + 4.80243i) q^{93} +(0.671520 + 1.16311i) q^{95} +(-0.996701 + 1.72634i) q^{97} +(0.766915 - 0.729544i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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