LMFDB - Embedded newform 576.2.y.a.47.14

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			47.14
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.427367 + 1.67850i) q^{3} +(-0.0458174 + 0.170993i) q^{5} +(-1.17432 + 2.03397i) q^{7} +(-2.63471 + 1.43467i) q^{9} +O(q^{10})$	\(q+(0.427367 + 1.67850i) q^{3} +(-0.0458174 + 0.170993i) q^{5} +(-1.17432 + 2.03397i) q^{7} +(-2.63471 + 1.43467i) q^{9} +(0.0913188 + 0.340806i) q^{11} +(0.399362 - 1.49044i) q^{13} +(-0.306592 - 0.00382767i) q^{15} +3.58081i q^{17} +(-5.36462 + 5.36462i) q^{19} +(-3.91589 - 1.10183i) q^{21} +(-0.165085 + 0.0953117i) q^{23} +(4.30299 + 2.48433i) q^{25} +(-3.53408 - 3.80923i) q^{27} +(-2.43879 - 9.10169i) q^{29} +(-3.43903 + 1.98552i) q^{31} +(-0.533016 + 0.298928i) q^{33} +(-0.293991 - 0.293991i) q^{35} +(-3.28315 + 3.28315i) q^{37} +(2.67238 + 0.0333635i) q^{39} +(4.25538 + 7.37054i) q^{41} +(4.09402 - 1.09699i) q^{43} +(-0.124603 - 0.516251i) q^{45} +(4.93030 - 8.53953i) q^{47} +(0.741968 + 1.28513i) q^{49} +(-6.01038 + 1.53032i) q^{51} +(4.83735 + 4.83735i) q^{53} -0.0624595 q^{55} +(-11.2972 - 6.71185i) q^{57} +(2.68985 + 0.720744i) q^{59} +(-7.97394 + 2.13661i) q^{61} +(0.175902 - 7.04369i) q^{63} +(0.236557 + 0.136576i) q^{65} +(-11.4543 - 3.06917i) q^{67} +(-0.230532 - 0.236361i) q^{69} -1.13635i q^{71} +5.67961i q^{73} +(-2.33099 + 8.28428i) q^{75} +(-0.800428 - 0.214474i) q^{77} +(12.8621 + 7.42593i) q^{79} +(4.88344 - 7.55990i) q^{81} +(12.3635 - 3.31278i) q^{83} +(-0.612293 - 0.164063i) q^{85} +(14.2349 - 7.98327i) q^{87} -3.05719 q^{89} +(2.56254 + 2.56254i) q^{91} +(-4.80243 - 4.92386i) q^{93} +(-0.671520 - 1.16311i) q^{95} +(-0.996701 + 1.72634i) q^{97} +(-0.729544 - 0.766915i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

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
$3$	0.427367	+	1.67850i	0.246741	+	0.969082i
$3$	0.427367	+	1.67850i	0.246741	+	0.969082i
$4$		0			0
$5$	−0.0458174	+	0.170993i	−0.0204902	+	0.0764704i	−0.975414	−	0.220381i	$-0.929270\pi$
$5$	−0.0458174	+	0.170993i	−0.0204902	+	0.0764704i	0.954924	+	0.296851i	$0.0959366\pi$
$6$		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
$11$	0.0913188	+	0.340806i	0.0275337	+	0.102757i	0.978325	−	0.207074i	$-0.0663941\pi$
$11$	0.0913188	+	0.340806i	0.0275337	+	0.102757i	−0.950792	+	0.309831i	$0.899727\pi$
$12$		0			0
$13$	0.399362	−	1.49044i	0.110763	−	0.413374i	−0.888172	−	0.459511i	$-0.848025\pi$
$13$	0.399362	−	1.49044i	0.110763	−	0.413374i	0.998935	+	0.0461375i	$0.0146912\pi$
$14$		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	−0.267045	+	0.963684i	$0.586047\pi$
$19$	−5.36462	+	5.36462i	−1.23073	+	1.23073i	−0.963684	+	0.267045i	$0.913953\pi$
$20$		0			0
$21$	−3.91589	−	1.10183i	−0.854516	−	0.240440i
$22$		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
$27$	−3.53408	−	3.80923i	−0.680135	−	0.733087i
$28$		0			0
$29$	−2.43879	−	9.10169i	−0.452872	−	1.69014i	−0.694270	−	0.719714i	$-0.744273\pi$
$29$	−2.43879	−	9.10169i	−0.452872	−	1.69014i	0.241398	−	0.970426i	$-0.422394\pi$
$30$		0			0
$31$	−3.43903	+	1.98552i	−0.617668	+	0.356611i	−0.775960	−	0.630782i	$-0.782734\pi$
$31$	−3.43903	+	1.98552i	−0.617668	+	0.356611i	0.158293	+	0.987392i	$0.449401\pi$
$32$		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	−0.923454	−	0.383709i	$-0.874647\pi$
$37$	−3.28315	+	3.28315i	−0.539746	+	0.539746i	0.383709	+	0.923454i	$0.374647\pi$
$38$		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	$0.0647226\pi$
$41$	4.25538	+	7.37054i	0.664579	+	1.15109i	−0.314820	+	0.949151i	$0.601944\pi$
$42$		0			0
$43$	4.09402	−	1.09699i	0.624332	−	0.167289i	0.0672354	−	0.997737i	$-0.478582\pi$
$43$	4.09402	−	1.09699i	0.624332	−	0.167289i	0.557096	+	0.830448i	$0.311915\pi$
$44$		0			0
$45$	−0.124603	−	0.516251i	−0.0185747	−	0.0769581i
$46$		0			0
$47$	4.93030	−	8.53953i	0.719158	−	1.24562i	−0.242176	−	0.970232i	$-0.577861\pi$
$47$	4.93030	−	8.53953i	0.719158	−	1.24562i	0.961334	−	0.275386i	$-0.0888057\pi$
$48$		0			0
$49$	0.741968	+	1.28513i	0.105995	+	0.183590i
$50$		0			0
$51$	−6.01038	+	1.53032i	−0.841621	+	0.214288i
$52$		0			0
$53$	4.83735	+	4.83735i	0.664461	+	0.664461i	0.956428	−	0.291967i	$-0.0943098\pi$
$53$	4.83735	+	4.83735i	0.664461	+	0.664461i	−0.291967	+	0.956428i	$0.594310\pi$
$54$		0			0
$55$	−0.0624595			−0.00842204
$56$		0			0
$57$	−11.2972	−	6.71185i	−1.49635	−	0.889006i
$58$		0			0
$59$	2.68985	+	0.720744i	0.350189	+	0.0938328i	0.429626	−	0.903007i	$-0.358646\pi$
$59$	2.68985	+	0.720744i	0.350189	+	0.0938328i	−0.0794368	+	0.996840i	$0.525312\pi$
$60$		0			0
$61$	−7.97394	+	2.13661i	−1.02096	+	0.273565i	−0.730201	−	0.683232i	$-0.760574\pi$
$61$	−7.97394	+	2.13661i	−1.02096	+	0.273565i	−0.290757	+	0.956797i	$0.593907\pi$
$62$		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
$67$	−11.4543	−	3.06917i	−1.39936	−	0.374959i	−0.521248	−	0.853405i	$-0.674533\pi$
$67$	−11.4543	−	3.06917i	−1.39936	−	0.374959i	−0.878117	+	0.478446i	$0.841200\pi$
$68$		0			0
$69$	−0.230532	−	0.236361i	−0.0277528	−	0.0284546i
$70$		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	$0.107850\pi$
$73$			5.67961i			0.664748i	−0.943148	+	0.332374i	$0.892150\pi$
$74$		0			0
$75$	−2.33099	+	8.28428i	−0.269159	+	0.956586i
$76$		0			0
$77$	−0.800428	−	0.214474i	−0.0912173	−	0.0244416i
$78$		0			0
$79$	12.8621	+	7.42593i	1.44710	+	0.835482i	0.998308	−	0.0581546i	$-0.0185216\pi$
$79$	12.8621	+	7.42593i	1.44710	+	0.835482i	0.448790	+	0.893637i	$0.351855\pi$
$80$		0			0
$81$	4.88344	−	7.55990i	0.542604	−	0.839988i
$82$		0			0
$83$	12.3635	−	3.31278i	1.35707	−	0.363625i	0.494329	−	0.869275i	$-0.335414\pi$
$83$	12.3635	−	3.31278i	1.35707	−	0.363625i	0.862739	+	0.505649i	$0.168747\pi$
$84$		0			0
$85$	−0.612293	−	0.164063i	−0.0664125	−	0.0177952i
$86$		0			0
$87$	14.2349	−	7.98327i	1.52614	−	0.855896i
$88$		0			0
$89$	−3.05719			−0.324061			−0.162031	−	0.986786i	$-0.551804\pi$
$89$	−3.05719			−0.324061			−0.162031	+	0.986786i	$0.551804\pi$
$90$		0			0
$91$	2.56254	+	2.56254i	0.268627	+	0.268627i
$92$		0			0
$93$	−4.80243	−	4.92386i	−0.497989	−	0.510580i
$94$		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
$99$	−0.729544	−	0.766915i	−0.0733219	−	0.0770779i
$100$		0			0
$101$	15.4663	−	4.14419i	1.53896	−	0.412362i	0.613027	−	0.790062i	$-0.289952\pi$
$101$	15.4663	−	4.14419i	1.53896	−	0.412362i	0.925928	+	0.377700i	$0.123285\pi$
$102$		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	$-0.795471\pi$
$107$	−2.08262	+	2.08262i	−0.201334	+	0.201334i	0.599237	+	0.800571i	$0.295471\pi$
$108$		0			0
$109$	7.70191	+	7.70191i	0.737709	+	0.737709i	0.972134	−	0.234425i	$-0.0753207\pi$
$109$	7.70191	+	7.70191i	0.737709	+	0.737709i	−0.234425	+	0.972134i	$0.575321\pi$
$110$		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
$115$	−0.00873387	−	0.0325953i	−0.000814438	−	0.00303952i
$116$		0			0
$117$	1.08609	+	4.49984i	0.100409	+	0.416010i
$118$		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
$123$	−10.5528	+	10.2926i	−0.951517	+	0.928051i
$124$		0			0
$125$	−1.24783	+	1.24783i	−0.111610	+	0.111610i
$126$		0			0
$127$		−	8.43197i		−	0.748216i	−0.927385	−	0.374108i	$-0.877949\pi$
$127$		−	8.43197i		−	0.748216i	0.927385	−	0.374108i	$-0.122051\pi$
$128$		0			0
$129$	3.59094	+	6.40298i	0.316165	+	0.563751i
$130$		0			0
$131$	1.40833	−	5.25596i	0.123046	−	0.459215i	−0.876716	−	0.481008i	$-0.840271\pi$
$131$	1.40833	−	5.25596i	0.123046	−	0.459215i	0.999763	+	0.0217928i	$0.00693742\pi$
$132$		0			0
$133$	−4.61174	−	17.2113i	−0.399889	−	1.49241i
$134$		0			0
$135$	0.813275	−	0.429774i	0.0699955	−	0.0369891i
$136$		0			0
$137$	−1.62151	+	2.80854i	−0.138535	+	0.239950i	−0.926942	−	0.375204i	$-0.877573\pi$
$137$	−1.62151	+	2.80854i	−0.138535	+	0.239950i	0.788407	+	0.615154i	$0.210906\pi$
$138$		0			0
$139$	3.54037	−	13.2129i	0.300291	−	1.12070i	−0.636633	−	0.771167i	$-0.719674\pi$
$139$	3.54037	−	13.2129i	0.300291	−	1.12070i	0.936924	−	0.349533i	$-0.113660\pi$
$140$		0			0
$141$	16.4406	+	4.62598i	1.38455	+	0.389578i
$142$		0			0
$143$	0.544421			0.0455268
$144$		0			0
$145$	1.66806			0.138525
$146$		0			0
$147$	−1.83999	+	1.79461i	−0.151760	+	0.148017i
$148$		0			0
$149$	3.28089	−	12.2444i	0.268781	−	1.00310i	−0.691115	−	0.722745i	$-0.742880\pi$
$149$	3.28089	−	12.2444i	0.268781	−	1.00310i	0.959895	−	0.280358i	$-0.0904533\pi$
$150$		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
$155$	−0.181943	−	0.679022i	−0.0146140	−	0.0545403i
$156$		0			0
$157$	−2.07187	+	7.73231i	−0.165353	+	0.617106i	0.832642	+	0.553812i	$0.186827\pi$
$157$	−2.07187	+	7.73231i	−0.165353	+	0.617106i	−0.997995	+	0.0632940i	$0.979839\pi$
$158$		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	−0.181362	−	0.983416i	$-0.558050\pi$
$163$	10.2400	−	10.2400i	0.802055	−	0.802055i	0.983416	+	0.181362i	$0.0580505\pi$
$164$		0			0
$165$	−0.0266932	−	0.104838i	−0.00207806	−	0.00816164i
$166$		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
$171$	6.43778	−	21.8307i	0.492309	−	1.66944i
$172$		0			0
$173$	−3.84530	−	14.3509i	−0.292353	−	1.09108i	−0.943297	−	0.331950i	$-0.892293\pi$
$173$	−3.84530	−	14.3509i	−0.292353	−	1.09108i	0.650944	−	0.759126i	$-0.274373\pi$
$174$		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	$-0.0646563\pi$
$179$	10.4051	+	10.4051i	0.777712	+	0.777712i	−0.201730	+	0.979441i	$0.564656\pi$
$180$		0			0
$181$	−16.0569	+	16.0569i	−1.19350	+	1.19350i	−0.217424	+	0.976077i	$0.569765\pi$
$181$	−16.0569	+	16.0569i	−1.19350	+	1.19350i	−0.976077	+	0.217424i	$0.930235\pi$
$182$		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
$187$	−1.22036	+	0.326995i	−0.0892417	+	0.0239122i
$188$		0			0
$189$	11.8980	−	2.71499i	0.865453	−	0.197487i
$190$		0			0
$191$	−3.45557	+	5.98522i	−0.250036	+	0.433075i	−0.963535	−	0.267581i	$-0.913776\pi$
$191$	−3.45557	+	5.98522i	−0.250036	+	0.433075i	0.713499	+	0.700656i	$0.247109\pi$
$192$		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
$195$	−0.128146	+	0.455429i	−0.00917675	+	0.0326139i
$196$		0			0
$197$	−8.24778	−	8.24778i	−0.587630	−	0.587630i	0.349359	−	0.936989i	$-0.386399\pi$
$197$	−8.24778	−	8.24778i	−0.587630	−	0.587630i	−0.936989	+	0.349359i	$0.886399\pi$
$198$		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
$203$	21.3765	+	5.72781i	1.50034	+	0.402014i
$204$		0			0
$205$	−1.45528	+	0.389942i	−0.101641	+	0.0272347i
$206$		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
$211$	4.08372	+	1.09423i	0.281135	+	0.0753299i	0.396631	−	0.917978i	$-0.370179\pi$
$211$	4.08372	+	1.09423i	0.281135	+	0.0753299i	−0.115496	+	0.993308i	$0.536846\pi$
$212$		0			0
$213$	1.90736	−	0.485639i	0.130690	−	0.0332754i
$214$		0			0
$215$			0.750309i			0.0511707i
$216$		0			0
$217$		−	9.32653i		−	0.633126i
$218$		0			0
$219$	−9.53322	+	2.42728i	−0.644195	+	0.164020i
$220$		0			0
$221$	5.33698	+	1.43004i	0.359004	+	0.0961948i
$222$		0			0
$223$	−6.50548	−	3.75594i	−0.435639	−	0.251517i	0.266107	−	0.963944i	$-0.414263\pi$
$223$	−6.50548	−	3.75594i	−0.435639	−	0.251517i	−0.701746	+	0.712427i	$0.747596\pi$
$224$		0			0
$225$	−14.9013	−	0.372132i	−0.993423	−	0.0248088i
$226$		0			0
$227$	6.31276	−	1.69150i	0.418993	−	0.112269i	−0.0431619	−	0.999068i	$-0.513743\pi$
$227$	6.31276	−	1.69150i	0.418993	−	0.112269i	0.462155	+	0.886799i	$0.347076\pi$
$228$		0			0
$229$	1.08810	+	0.291556i	0.0719037	+	0.0192665i	0.294592	−	0.955623i	$-0.404816\pi$
$229$	1.08810	+	0.291556i	0.0719037	+	0.0192665i	−0.222688	+	0.974890i	$0.571483\pi$
$230$		0			0
$231$	0.0179176	−	1.43518i	0.00117889	−	0.0944277i
$232$		0			0
$233$	−13.9406			−0.913280			−0.456640	−	0.889652i	$-0.650947\pi$
$233$	−13.9406			−0.913280			−0.456640	+	0.889652i	$0.650947\pi$
$234$		0			0
$235$	1.23431	+	1.23431i	0.0805173	+	0.0805173i
$236$		0			0
$237$	−6.96758	+	24.7626i	−0.452593	+	1.60850i
$238$		0			0
$239$	14.8075	+	25.6474i	0.957820	+	1.65899i	0.727780	+	0.685811i	$0.240552\pi$
$239$	14.8075	+	25.6474i	0.957820	+	1.65899i	0.230040	+	0.973181i	$0.426114\pi$
$240$		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
$243$	14.7763	+	4.96599i	0.947900	+	0.318569i
$244$		0			0
$245$	−0.253743	+	0.0679902i	−0.0162110	+	0.00434373i
$246$		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	$-0.963671\pi$
$251$	−13.9356	+	13.9356i	−0.879610	+	0.879610i	0.113884	+	0.993494i	$0.463671\pi$
$252$		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
$259$	−2.82238	−	10.5333i	−0.175374	−	0.654506i
$260$		0			0
$261$	19.4834	+	20.4815i	1.20599	+	1.26777i
$262$		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
$267$	−1.30654	−	5.13148i	−0.0799590	−	0.314042i
$268$		0			0
$269$	−5.24359	+	5.24359i	−0.319707	+	0.319707i	−0.848655	−	0.528947i	$-0.822587\pi$
$269$	−5.24359	+	5.24359i	−0.319707	+	0.319707i	0.528947	+	0.848655i	$0.322587\pi$
$270$		0			0
$271$		−	6.82794i		−	0.414768i	−0.978260	−	0.207384i	$-0.933505\pi$
$271$		−	6.82794i		−	0.414768i	0.978260	−	0.207384i	$-0.0664949\pi$
$272$		0			0
$273$	−3.20607	+	5.39636i	−0.194040	+	0.326603i
$274$		0			0
$275$	−0.453732	+	1.69335i	−0.0273611	+	0.102113i
$276$		0			0
$277$	−1.70011	−	6.34489i	−0.102150	−	0.381228i	0.895857	−	0.444343i	$-0.146563\pi$
$277$	−1.70011	−	6.34489i	−0.102150	−	0.381228i	−0.998006	+	0.0631157i	$0.979896\pi$
$278$		0			0
$279$	6.21229	−	10.1652i	0.371920	−	0.608573i
$280$		0			0
$281$	2.29891	−	3.98183i	0.137141	−	0.237536i	−0.789272	−	0.614044i	$-0.789542\pi$
$281$	2.29891	−	3.98183i	0.137141	−	0.237536i	0.926413	+	0.376508i	$0.122875\pi$
$282$		0			0
$283$	2.26861	−	8.46655i	0.134855	−	0.503284i	−0.865144	−	0.501524i	$-0.832773\pi$
$283$	2.26861	−	8.46655i	0.134855	−	0.503284i	0.999998	−	0.00176039i	$-0.000560351\pi$
$284$		0			0
$285$	1.66529	−	1.62422i	0.0986431	−	0.0962104i
$286$		0			0
$287$	−19.9886			−1.17989
$288$		0			0
$289$	4.17783			0.245755
$290$		0			0
$291$	−3.32361	−	0.935181i	−0.194833	−	0.0548213i
$292$		0			0
$293$	−4.46706	+	16.6713i	−0.260969	+	0.973948i	0.703703	+	0.710494i	$0.251528\pi$
$293$	−4.46706	+	16.6713i	−0.260969	+	0.973948i	−0.964672	+	0.263454i	$0.915138\pi$
$294$		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
$299$	0.0761278	+	0.284113i	0.00440258	+	0.0164307i
$300$		0			0
$301$	−2.57642	+	9.61533i	−0.148502	+	0.554218i
$302$		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	−0.613467	−	0.789720i	$-0.710226\pi$
$307$	3.08820	−	3.08820i	0.176253	−	0.176253i	0.789720	+	0.613467i	$0.210226\pi$
$308$		0			0
$309$	−20.1403	+	19.6436i	−1.14574	+	1.11749i
$310$		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	0.734884	−	0.678193i	$-0.237237\pi$
$313$	9.11117	+	5.26034i	0.514994	+	0.297332i	−0.219890	+	0.975525i	$0.570570\pi$
$314$		0			0
$315$	1.19636	+	0.352802i	0.0674074	+	0.0198781i
$316$		0			0
$317$	5.02863	+	18.7671i	0.282436	+	1.05406i	0.950693	+	0.310134i	$0.100374\pi$
$317$	5.02863	+	18.7671i	0.282436	+	1.05406i	−0.668257	+	0.743931i	$0.732959\pi$
$318$		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
$331$	−12.3204	+	3.30125i	−0.677192	+	0.181453i	−0.580992	−	0.813909i	$-0.697335\pi$
$331$	−12.3204	+	3.30125i	−0.677192	+	0.181453i	−0.0961997	+	0.995362i	$0.530669\pi$
$332$		0			0
$333$	3.93992	−	13.3604i	0.215906	−	0.732144i
$334$		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
$339$	14.4025	+	14.7667i	0.782238	+	0.802017i
$340$		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
$347$	−6.49207	−	1.73954i	−0.348512	−	0.0933836i	0.0803163	−	0.996769i	$-0.474407\pi$
$347$	−6.49207	−	1.73954i	−0.348512	−	0.0933836i	−0.428829	+	0.903386i	$0.641074\pi$
$348$		0			0
$349$	−8.76397	+	2.34830i	−0.469125	+	0.125702i	−0.485634	−	0.874162i	$-0.661411\pi$
$349$	−8.76397	+	2.34830i	−0.469125	+	0.125702i	0.0165095	+	0.999864i	$0.494745\pi$
$350$		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
$355$	0.194308	+	0.0520647i	0.0103128	+	0.00276331i
$356$		0			0
$357$	3.94545	−	14.0220i	0.208815	−	0.742124i
$358$		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
$363$	13.1524	+	13.4850i	0.690323	+	0.707777i
$364$		0			0
$365$	−0.971174	−	0.260225i	−0.0508336	−	0.0136208i
$366$		0			0
$367$	5.69950	+	3.29061i	0.297512	+	0.171768i	0.641325	−	0.767270i	$-0.278385\pi$
$367$	5.69950	+	3.29061i	0.297512	+	0.171768i	−0.343813	+	0.939038i	$0.611719\pi$
$368$		0			0
$369$	−21.7860	−	13.3142i	−1.13414	−	0.693109i
$370$		0			0
$371$	−15.5196	+	4.15847i	−0.805738	+	0.215897i
$372$		0			0
$373$	25.3268	+	6.78631i	1.31137	+	0.351382i	0.845740	−	0.533595i	$-0.179159\pi$
$373$	25.3268	+	6.78631i	1.31137	+	0.351382i	0.465635	+	0.884977i	$0.345826\pi$
$374$		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	0.837837	−	0.545920i	$-0.183820\pi$
$379$	5.68301	+	5.68301i	0.291917	+	0.291917i	−0.545920	+	0.837837i	$0.683820\pi$
$380$		0			0
$381$	14.1530	−	3.60355i	0.725082	−	0.184615i
$382$		0			0
$383$	−6.91570	−	11.9783i	−0.353376	−	0.612065i	0.633463	−	0.773773i	$-0.281633\pi$
$383$	−6.91570	−	11.9783i	−0.353376	−	0.612065i	−0.986839	+	0.161708i	$0.948300\pi$
$384$		0			0
$385$	0.0733472	−	0.127041i	0.00373812	−	0.00647461i
$386$		0			0
$387$	−9.21274	+	8.76382i	−0.468310	+	0.445490i
$388$		0			0
$389$	−21.4044	+	5.73529i	−1.08525	+	0.290791i	−0.756743	−	0.653712i	$-0.773211\pi$
$389$	−21.4044	+	5.73529i	−1.08525	+	0.290791i	−0.328503	+	0.944503i	$0.606544\pi$
$390$		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	0.354466	−	0.935069i	$-0.384663\pi$
$397$	−11.5684	−	11.5684i	−0.580603	−	0.580603i	−0.935069	+	0.354466i	$0.884663\pi$
$398$		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
$403$	1.58589	+	5.91861i	0.0789987	+	0.294827i
$404$		0			0
$405$	1.06894	+	1.18141i	0.0531162	+	0.0587047i
$406$		0			0
$407$	−1.41873	−	0.819104i	−0.0703238	−	0.0406015i
$408$		0			0
$409$	−6.68684	+	3.86065i	−0.330643	+	0.190897i	−0.656127	−	0.754651i	$-0.727806\pi$
$409$	−6.68684	+	3.86065i	−0.330643	+	0.190897i	0.325484	+	0.945548i	$0.394473\pi$
$410$		0			0
$411$	−5.40712	−	1.52143i	−0.266714	−	0.0750465i
$412$		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
$419$	0.801918	−	2.99280i	0.0391763	−	0.146208i	−0.943567	−	0.331181i	$-0.892553\pi$
$419$	0.801918	−	2.99280i	0.0391763	−	0.146208i	0.982744	+	0.184973i	$0.0592197\pi$
$420$		0			0
$421$	−4.47770	−	16.7110i	−0.218230	−	0.814445i	−0.985005	−	0.172528i	$-0.944806\pi$
$421$	−4.47770	−	16.7110i	−0.218230	−	0.814445i	0.766775	−	0.641916i	$-0.221860\pi$
$422$		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
$427$	5.01811	−	18.7278i	0.242843	−	0.906303i
$428$		0			0
$429$	0.232668	+	0.913810i	0.0112333	+	0.0441191i
$430$		0			0
$431$	−12.1601			−0.585730			−0.292865	−	0.956154i	$-0.594609\pi$
$431$	−12.1601			−0.585730			−0.292865	+	0.956154i	$0.594609\pi$
$432$		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
$435$	0.712876	+	2.79984i	0.0341798	+	0.134242i
$436$		0			0
$437$	0.374306	−	1.39693i	0.0179055	−	0.0668241i
$438$		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
$443$	−3.53871	−	13.2067i	−0.168129	−	0.627467i	−0.997620	−	0.0689472i	$-0.978036\pi$
$443$	−3.53871	−	13.2067i	−0.168129	−	0.627467i	0.829491	−	0.558520i	$-0.188631\pi$
$444$		0			0
$445$	0.140072	−	0.522757i	0.00664007	−	0.0247811i
$446$		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
$453$	−2.63867	−	0.742455i	−0.123975	−	0.0348836i
$454$		0			0
$455$	−0.555585	+	0.320767i	−0.0260462	+	0.0150378i
$456$		0			0
$457$	−22.1026	−	12.7609i	−1.03392	−	0.596932i	−0.115812	−	0.993271i	$-0.536947\pi$
$457$	−22.1026	−	12.7609i	−1.03392	−	0.596932i	−0.918104	+	0.396339i	$0.870280\pi$
$458$		0			0
$459$	13.6401	−	12.6549i	0.636666	−	0.590679i
$460$		0			0
$461$	−2.23068	−	8.32500i	−0.103893	−	0.387734i	0.894324	−	0.447419i	$-0.147657\pi$
$461$	−2.23068	−	8.32500i	−0.103893	−	0.387734i	−0.998217	+	0.0596856i	$0.980990\pi$
$462$		0			0
$463$	13.7328	−	7.92866i	0.638219	−	0.368476i	−0.145709	−	0.989327i	$-0.546546\pi$
$463$	13.7328	−	7.92866i	0.638219	−	0.368476i	0.783928	+	0.620852i	$0.213213\pi$
$464$		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	$-0.212900\pi$
$467$	3.55396	+	3.55396i	0.164458	+	0.164458i	−0.620081	+	0.784538i	$0.712900\pi$
$468$		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
$475$	−36.4114	+	9.75641i	−1.67067	+	0.447655i
$476$		0			0
$477$	−19.6850	−	5.80503i	−0.901316	−	0.265794i
$478$		0			0
$479$	−1.39132	+	2.40984i	−0.0635712	+	0.110109i	−0.896059	−	0.443934i	$-0.853582\pi$
$479$	−1.39132	+	2.40984i	−0.0635712	+	0.110109i	0.832488	+	0.554043i	$0.186916\pi$
$480$		0			0
$481$	3.58217	+	6.20450i	0.163333	+	0.282901i
$482$		0			0
$483$	0.751470	−	0.191334i	0.0341931	−	0.00870600i
$484$		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
$491$	1.57973	+	0.423288i	0.0712923	+	0.0191027i	0.294289	−	0.955717i	$-0.404917\pi$
$491$	1.57973	+	0.423288i	0.0712923	+	0.0191027i	−0.222997	+	0.974819i	$0.571584\pi$
$492$		0			0
$493$	32.5914	−	8.73283i	1.46784	−	0.393307i
$494$		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
$499$	−4.51417	−	1.20957i	−0.202082	−	0.0541478i	0.156358	−	0.987700i	$-0.450025\pi$
$499$	−4.51417	−	1.20957i	−0.202082	−	0.0541478i	−0.358440	+	0.933553i	$0.616691\pi$
$500$		0			0
$501$	−14.2019	−	14.5610i	−0.634494	−	0.650537i
$502$		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
$507$	−4.98183	+	17.7053i	−0.221251	+	0.786319i
$508$		0			0
$509$	28.2383	+	7.56644i	1.25164	+	0.335377i	0.822971	−	0.568084i	$-0.192315\pi$
$509$	28.2383	+	7.56644i	1.25164	+	0.335377i	0.428672	+	0.903460i	$0.358982\pi$
$510$		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
$515$	−2.77744	+	0.744213i	−0.122389	+	0.0327939i
$516$		0			0
$517$	3.36056	+	0.900458i	0.147797	+	0.0396021i
$518$		0			0
$519$	22.4445	−	12.5874i	0.985206	−	0.552526i
$520$		0			0
$521$	18.9291			0.829299			0.414649	−	0.909981i	$-0.363904\pi$
$521$	18.9291			0.829299			0.414649	+	0.909981i	$0.363904\pi$
$522$		0			0
$523$	22.0490	+	22.0490i	0.964137	+	0.964137i	0.999379	−	0.0352421i	$-0.0112202\pi$
$523$	22.0490	+	22.0490i	0.964137	+	0.964137i	−0.0352421	+	0.999379i	$0.511220\pi$
$524$		0			0
$525$	−14.1127	−	14.4695i	−0.615928	−	0.631502i
$526$		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
$531$	−8.12102	+	1.96010i	−0.352422	+	0.0850610i
$532$		0			0
$533$	12.6848	−	3.39888i	0.549439	−	0.147222i
$534$		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	0.271260	−	0.962506i	$-0.412560\pi$
$541$	−16.0780	−	16.0780i	−0.691246	−	0.691246i	−0.962506	+	0.271260i	$0.912560\pi$
$542$		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
$547$	−2.61213	−	9.74859i	−0.111686	−	0.416819i	0.887331	−	0.461133i	$-0.152557\pi$
$547$	−2.61213	−	9.74859i	−0.111686	−	0.416819i	−0.999018	+	0.0443131i	$0.985890\pi$
$548$		0			0
$549$	17.9437	−	17.0693i	0.765819	−	0.728502i
$550$		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
$555$	1.01915	−	0.994020i	0.0432607	−	0.0421938i
$556$		0			0
$557$	−9.47553	+	9.47553i	−0.401491	+	0.401491i	−0.878758	−	0.477267i	$-0.841627\pi$
$557$	−9.47553	+	9.47553i	−0.401491	+	0.401491i	0.477267	+	0.878758i	$0.341627\pi$
$558$		0			0
$559$		−	6.53998i		−	0.276612i
$560$		0			0
$561$	−1.07040	−	1.90863i	−0.0451925	−	0.0805823i
$562$		0			0
$563$	−1.51015	+	5.63595i	−0.0636451	+	0.237527i	−0.990419	−	0.138092i	$-0.955903\pi$
$563$	−1.51015	+	5.63595i	−0.0636451	+	0.237527i	0.926774	+	0.375619i	$0.122570\pi$
$564$		0			0
$565$	0.545650	+	2.03639i	0.0229557	+	0.0856717i
$566$		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	$-0.647927\pi$
$569$	13.1217	−	22.7275i	0.550090	−	0.952784i	0.998267	−	0.0588397i	$-0.0187401\pi$
$570$		0			0
$571$	−0.417246	+	1.55718i	−0.0174612	+	0.0651661i	−0.974107	−	0.226089i	$-0.927406\pi$
$571$	−0.417246	+	1.55718i	−0.0174612	+	0.0651661i	0.956646	+	0.291255i	$0.0940727\pi$
$572$		0			0
$573$	−11.5230	−	3.24228i	−0.481379	−	0.135448i
$574$		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
$579$	19.4154	−	18.9366i	0.806877	−	0.786978i
$580$		0			0
$581$	−7.78051	+	29.0372i	−0.322790	+	1.20467i
$582$		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
$587$	−1.00931	−	3.76680i	−0.0416587	−	0.155473i	0.941963	−	0.335716i	$-0.108978\pi$
$587$	−1.00931	−	3.76680i	−0.0416587	−	0.155473i	−0.983622	+	0.180243i	$0.942312\pi$
$588$		0			0
$589$	7.79751	−	29.1007i	0.321291	−	1.19907i
$590$		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
$597$	−2.36209	−	9.27719i	−0.0966740	−	0.379690i
$598$		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	0.922279	−	0.386524i	$-0.126324\pi$
$601$	25.7087	+	14.8429i	1.04868	+	0.605455i	0.126400	+	0.991979i	$0.459658\pi$
$602$		0			0
$603$	34.5820	−	8.34676i	1.40829	−	0.339906i
$604$		0			0
$605$	0.498288	+	1.85964i	0.0202583	+	0.0756050i
$606$		0			0
$607$	−28.8436	+	16.6529i	−1.17073	+	0.675918i	−0.953851	−	0.300281i	$-0.902920\pi$
$607$	−28.8436	+	16.6529i	−1.17073	+	0.675918i	−0.216874	+	0.976200i	$0.569586\pi$
$608$		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	−0.953494	−	0.301412i	$-0.902542\pi$
$613$	−16.1448	+	16.1448i	−0.652082	+	0.652082i	0.301412	+	0.953494i	$0.402542\pi$
$614$		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	$-0.902572\pi$
$617$	−18.3244	−	31.7389i	−0.737714	−	1.27776i	0.215808	−	0.976436i	$-0.430762\pi$
$618$		0			0
$619$	−3.40743	+	0.913019i	−0.136956	+	0.0366973i	−0.326646	−	0.945147i	$-0.605918\pi$
$619$	−3.40743	+	0.913019i	−0.136956	+	0.0366973i	0.189690	+	0.981844i	$0.439252\pi$
$620$		0			0
$621$	0.946487	+	0.292006i	0.0379812	+	0.0117178i
$622$		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
$627$	1.25580	−	4.46307i	0.0501517	−	0.178238i
$628$		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
$635$	1.44181	+	0.386331i	0.0572164	+	0.0153311i
$636$		0			0
$637$	2.21172	−	0.592628i	0.0876315	−	0.0234808i
$638$		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
$643$	18.4511	+	4.94396i	0.727641	+	0.194971i	0.603579	−	0.797303i	$-0.293741\pi$
$643$	18.4511	+	4.94396i	0.727641	+	0.194971i	0.124063	+	0.992274i	$0.460408\pi$
$644$		0			0
$645$	−1.25939	+	0.320658i	−0.0495885	+	0.0126259i
$646$		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
$651$	15.6546	−	3.98585i	0.613551	−	0.156218i
$652$		0			0
$653$	−29.9343	−	8.02087i	−1.17142	−	0.313881i	−0.379902	−	0.925027i	$-0.624042\pi$
$653$	−29.9343	−	8.02087i	−1.17142	−	0.313881i	−0.791518	+	0.611146i	$0.790709\pi$
$654$		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
$659$	−28.4091	+	7.61220i	−1.10666	+	0.296529i	−0.765475	−	0.643466i	$-0.777496\pi$
$659$	−28.4091	+	7.61220i	−1.10666	+	0.296529i	−0.341188	+	0.939995i	$0.610829\pi$
$660$		0			0
$661$	22.3717	+	5.99448i	0.870159	+	0.233158i	0.666156	−	0.745812i	$-0.267938\pi$
$661$	22.3717	+	5.99448i	0.870159	+	0.233158i	0.204002	+	0.978970i	$0.434605\pi$
$662$		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
$669$	3.52411	−	12.5246i	0.136250	−	0.484230i
$670$		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
$675$	−5.74372	−	25.1709i	−0.221076	−	0.968829i
$676$		0			0
$677$	−26.8914	+	7.20552i	−1.03352	+	0.276931i	−0.735425	−	0.677606i	$-0.763017\pi$
$677$	−26.8914	+	7.20552i	−1.03352	+	0.276931i	−0.298094	+	0.954537i	$0.596351\pi$
$678$		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	0.217674	−	0.976022i	$-0.430153\pi$
$683$	31.1964	−	31.1964i	1.19370	−	1.19370i	0.976022	−	0.217674i	$-0.0698470\pi$
$684$		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
$691$	8.56164	+	31.9525i	0.325700	+	1.21553i	0.913606	+	0.406600i	$0.133286\pi$
$691$	8.56164	+	31.9525i	0.325700	+	1.21553i	−0.587906	+	0.808929i	$0.700047\pi$
$692$		0			0
$693$	2.41660	−	0.583273i	0.0917990	−	0.0221567i
$694$		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
$699$	−5.95776	−	23.3993i	−0.225343	−	0.885043i
$700$		0			0
$701$	22.9365	−	22.9365i	0.866299	−	0.866299i	−0.125761	−	0.992061i	$-0.540137\pi$
$701$	22.9365	−	22.9365i	0.866299	−	0.866299i	0.992061	+	0.125761i	$0.0401374\pi$
$702$		0			0
$703$		−	35.2257i		−	1.32856i
$704$		0			0
$705$	−1.54428	+	2.59928i	−0.0581609	+	0.0978947i
$706$		0			0
$707$	−9.73316	+	36.3246i	−0.366053	+	1.36613i
$708$		0			0
$709$	2.89716	+	10.8123i	0.108805	+	0.406066i	0.998749	−	0.0500039i	$-0.0159234\pi$
$709$	2.89716	+	10.8123i	0.108805	+	0.406066i	−0.889944	+	0.456070i	$0.849257\pi$
$710$		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
$715$	−0.0249440	+	0.0930922i	−0.000932852	+	0.00348145i
$716$		0			0
$717$	−36.7209	+	35.8153i	−1.37137	+	1.33755i
$718$		0			0
$719$	45.6552			1.70265			0.851325	−	0.524639i	$-0.175800\pi$
$719$	45.6552			1.70265			0.851325	+	0.524639i	$0.175800\pi$
$720$		0			0
$721$	−38.1488			−1.42074
$722$		0			0
$723$	−20.1144	−	5.65968i	−0.748061	−	0.210486i
$724$		0			0
$725$	12.1175	−	45.2232i	0.450033	−	1.67955i
$726$		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
$731$	3.92810	+	14.6599i	0.145286	+	0.542215i
$732$		0			0
$733$	1.38877	−	5.18294i	0.0512952	−	0.191436i	−0.935524	−	0.353263i	$-0.885072\pi$
$733$	1.38877	−	5.18294i	0.0512952	−	0.191436i	0.986819	+	0.161827i	$0.0517386\pi$
$734$		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	−0.997884	−	0.0650119i	$-0.979291\pi$
$739$	−25.3597	+	25.3597i	−0.932873	+	0.932873i	0.0650119	+	0.997884i	$0.479291\pi$
$740$		0			0
$741$	−14.5153	+	14.1573i	−0.533232	+	0.520082i
$742$		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
$747$	−27.8215	+	26.4658i	−1.01793	+	0.968332i
$748$		0			0
$749$	−1.79034	−	6.68164i	−0.0654176	−	0.244142i
$750$		0			0
$751$	15.0045	−	8.66287i	0.547523	−	0.316112i	−0.200599	−	0.979673i	$-0.564289\pi$
$751$	15.0045	−	8.66287i	0.547523	−	0.316112i	0.748122	+	0.663561i	$0.230956\pi$
$752$		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	−0.0563619	+	0.998410i	$0.517950\pi$
$757$	−29.0206	+	29.0206i	−1.05477	+	1.05477i	−0.998410	+	0.0563619i	$0.982050\pi$
$758$		0			0
$759$	0.0595015	−	0.100151i	0.00215977	−	0.00363526i
$760$		0			0
$761$	−9.85285	−	17.0656i	−0.357166	−	0.618629i	0.630320	−	0.776335i	$-0.282924\pi$
$761$	−9.85285	−	17.0656i	−0.357166	−	0.618629i	−0.987486	+	0.157706i	$0.949590\pi$
$762$		0			0
$763$	−24.7100	+	6.62101i	−0.894560	+	0.239697i
$764$		0			0
$765$	1.84859	−	0.446178i	0.0668360	−	0.0161316i
$766$		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
$771$	−29.3289	−	30.0705i	−1.05626	−	1.08296i
$772$		0			0
$773$	18.7350	+	18.7350i	0.673853	+	0.673853i	0.958602	−	0.284749i	$-0.0919104\pi$
$773$	18.7350	+	18.7350i	0.673853	+	0.673853i	−0.284749	+	0.958602i	$0.591910\pi$
$774$		0			0
$775$	−19.7308			−0.708751
$776$		0			0
$777$	16.4739	−	9.23894i	0.590998	−	0.331445i
$778$		0			0
$779$	−62.3687	−	16.7116i	−2.23459	−	0.598757i
$780$		0			0
$781$	0.387276	−	0.103770i	0.0138578	−	0.00371319i
$782$		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
$787$	34.0663	+	9.12803i	1.21433	+	0.325379i	0.808460	−	0.588551i	$-0.200301\pi$
$787$	34.0663	+	9.12803i	1.21433	+	0.325379i	0.405872	+	0.913930i	$0.366968\pi$
$788$		0			0
$789$	14.4677	−	51.4177i	0.515062	−	1.83052i
$790$		0			0
$791$			27.9703i			0.994511i
$792$		0			0
$793$			12.7380i			0.452338i
$794$		0			0
$795$	−1.46458	−	1.50161i	−0.0519433	−	0.0532566i
$796$		0			0
$797$	−11.1029	−	2.97502i	−0.393286	−	0.105381i	0.0567557	−	0.998388i	$-0.481924\pi$
$797$	−11.1029	−	2.97502i	−0.393286	−	0.105381i	−0.450042	+	0.893007i	$0.648591\pi$
$798$		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
$803$	−1.93565	+	0.518655i	−0.0683076	+	0.0183030i
$804$		0			0
$805$	0.0765542	+	0.0205126i	0.00269818	+	0.000722976i
$806$		0			0
$807$	−11.0423	−	6.56042i	−0.388707	−	0.230938i
$808$		0			0
$809$	25.8320			0.908205			0.454102	−	0.890950i	$-0.349960\pi$
$809$	25.8320			0.908205			0.454102	+	0.890950i	$0.349960\pi$
$810$		0			0
$811$	16.1463	+	16.1463i	0.566973	+	0.566973i	0.931279	−	0.364306i	$-0.118694\pi$
$811$	16.1463	+	16.1463i	0.566973	+	0.566973i	−0.364306	+	0.931279i	$0.618694\pi$
$812$		0			0
$813$	11.4607	−	2.91804i	0.401944	−	0.102340i
$814$		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
$819$	−10.4280	−	3.07516i	−0.364382	−	0.107455i
$820$		0			0
$821$	−7.01329	+	1.87921i	−0.244766	+	0.0655848i	−0.379116	−	0.925349i	$-0.623772\pi$
$821$	−7.01329	+	1.87921i	−0.244766	+	0.0655848i	0.134350	+	0.990934i	$0.457105\pi$
$822$		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	$-0.845716\pi$
$827$	−12.0458	+	12.0458i	−0.418875	+	0.418875i	0.465941	+	0.884816i	$0.345716\pi$
$828$		0			0
$829$	22.8912	+	22.8912i	0.795046	+	0.795046i	0.982310	−	0.187264i	$-0.0599619\pi$
$829$	22.8912	+	22.8912i	0.795046	+	0.795046i	−0.187264	+	0.982310i	$0.559962\pi$
$830$		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
$835$	−0.538048	−	2.00802i	−0.0186199	−	0.0694905i
$836$		0			0
$837$	19.7171	+	6.08305i	0.681524	+	0.210261i
$838$		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
$843$	7.66597	+	2.15701i	0.264030	+	0.0742914i
$844$		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
$851$	0.229075	−	0.854919i	0.00785258	−	0.0293062i
$852$		0			0
$853$	12.2179	+	45.5977i	0.418331	+	1.56123i	0.778068	+	0.628180i	$0.216200\pi$
$853$	12.2179	+	45.5977i	0.418331	+	1.56123i	−0.359737	+	0.933054i	$0.617133\pi$
$854$		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	$-0.537090\pi$
$857$	23.4789	−	40.6666i	0.802023	−	1.38914i	0.918283	−	0.395926i	$-0.129576\pi$
$858$		0			0
$859$	−4.21294	+	15.7229i	−0.143744	+	0.536459i	0.856064	+	0.516869i	$0.172903\pi$
$859$	−4.21294	+	15.7229i	−0.143744	+	0.536459i	−0.999808	+	0.0195896i	$0.993764\pi$
$860$		0			0
$861$	−8.54249	−	33.5509i	−0.291127	−	1.14341i
$862$		0			0
$863$	51.2010			1.74290			0.871451	−	0.490482i	$-0.163179\pi$
$863$	51.2010			1.74290			0.871451	+	0.490482i	$0.163179\pi$
$864$		0			0
$865$	2.63008			0.0894253
$866$		0			0
$867$	1.78547	+	7.01249i	0.0606377	+	0.238157i
$868$		0			0
$869$	−1.35625	+	5.06161i	−0.0460078	+	0.171703i
$870$		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
$875$	−1.07271	−	4.00341i	−0.0362642	−	0.135340i
$876$		0			0
$877$	8.77699	−	32.7562i	0.296378	−	1.10610i	−0.643739	−	0.765245i	$-0.722618\pi$
$877$	8.77699	−	32.7562i	0.296378	−	1.10610i	0.940117	−	0.340852i	$-0.110716\pi$
$878$		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	−0.805301	−	0.592866i	$-0.797996\pi$
$883$	−6.31259	+	6.31259i	−0.212436	+	0.212436i	0.592866	+	0.805301i	$0.297996\pi$
$884$		0			0
$885$	−0.821929	−	0.231270i	−0.0276289	−	0.00777407i
$886$		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
$891$	3.02241	+	0.973947i	0.101255	+	0.0326284i
$892$		0			0
$893$	19.3622	+	72.2606i	0.647930	+	2.41811i
$894$		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
$907$	10.5600	−	2.82954i	0.350639	−	0.0939534i	−0.0792006	−	0.996859i	$-0.525237\pi$
$907$	10.5600	−	2.82954i	0.350639	−	0.0939534i	0.429840	+	0.902905i	$0.358570\pi$
$908$		0			0
$909$	−34.8038	+	33.1078i	−1.15437	+	1.09812i
$910$		0			0
$911$	−4.41606	+	7.64884i	−0.146311	+	0.253417i	−0.929861	−	0.367911i	$-0.880073\pi$
$911$	−4.41606	+	7.64884i	−0.146311	+	0.253417i	0.783551	+	0.621328i	$0.213407\pi$
$912$		0			0
$913$	2.25804	+	3.91103i	0.0747301	+	0.129436i
$914$		0			0
$915$	2.45293	−	0.624547i	0.0810913	−	0.0206469i
$916$		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
$923$	−1.69366	−	0.453816i	−0.0557476	−	0.0149375i
$924$		0			0
$925$	−22.2838	+	5.97091i	−0.732685	+	0.196322i
$926$		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
$931$	−10.8746	−	2.91384i	−0.356401	−	0.0954973i
$932$		0			0
$933$	16.4613	+	16.8775i	0.538918	+	0.552544i
$934$		0			0
$935$		−	0.223655i		−	0.00731431i
$936$		0			0
$937$			8.98159i			0.293416i	0.989180	+	0.146708i	$0.0468677\pi$
$937$			8.98159i			0.293416i	−0.989180	+	0.146708i	$0.953132\pi$
$938$		0			0
$939$	−4.93565	+	17.5412i	−0.161069	+	0.572435i
$940$		0			0
$941$	38.5789	+	10.3372i	1.25764	+	0.336982i	0.825282	−	0.564721i	$-0.191016\pi$
$941$	38.5789	+	10.3372i	1.25764	+	0.336982i	0.432354	+	0.901704i	$0.357683\pi$
$942$		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
$947$	7.36412	−	1.97321i	0.239302	−	0.0641207i	−0.137175	−	0.990547i	$-0.543802\pi$
$947$	7.36412	−	1.97321i	0.239302	−	0.0641207i	0.376476	+	0.926426i	$0.377136\pi$
$948$		0			0
$949$	8.46512	+	2.26822i	0.274789	+	0.0736296i
$950$		0			0
$951$	−29.3515	+	16.4610i	−0.951786	+	0.533784i
$952$		0			0
$953$	9.35277			0.302966			0.151483	−	0.988460i	$-0.451595\pi$
$953$	9.35277			0.302966			0.151483	+	0.988460i	$0.451595\pi$
$954$		0			0
$955$	−0.865105	−	0.865105i	−0.0279941	−	0.0279941i
$956$		0			0
$957$	4.02066	+	4.12233i	0.129970	+	0.133256i
$958$		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
$963$	2.49923	−	8.47497i	0.0805366	−	0.273102i
$964$		0			0
$965$	2.67747	−	0.717426i	0.0861908	−	0.0230948i
$966$		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	0.161822	−	0.986820i	$-0.448263\pi$
$971$	35.7927	−	35.7927i	1.14864	−	1.14864i	0.986820	−	0.161822i	$-0.0517370\pi$
$972$		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
$979$	−0.279179	−	1.04191i	−0.00892259	−	0.0332996i
$980$		0			0
$981$	−31.3420	−	9.24263i	−1.00067	−	0.295094i
$982$		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
$987$	−28.7156	+	28.0075i	−0.914028	+	0.891487i
$988$		0			0
$989$	−0.571303	+	0.571303i	−0.0181664	+	0.0181664i
$990$		0			0
$991$			51.8246i			1.64626i	0.567852	+	0.823131i	$0.307775\pi$
$991$			51.8246i			1.64626i	−0.567852	+	0.823131i	$0.692225\pi$
$992$		0			0
$993$	−10.8065	−	19.2690i	−0.342934	−	0.611483i
$994$		0			0
$995$	0.253236	−	0.945091i	0.00802813	−	0.0299614i
$996$		0			0
$997$	−12.2448	−	45.6984i	−0.387798	−	1.44728i	−0.833709	−	0.552204i	$-0.813787\pi$
$997$	−12.2448	−	45.6984i	−0.387798	−	1.44728i	0.445911	−	0.895077i	$-0.352880\pi$
$998$		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.47.14		88
3.2	odd	2		1728.2.z.a.1007.12		88
4.3	odd	2		144.2.u.a.83.13	yes	88
9.4	even	3		1728.2.z.a.1583.12		88
9.5	odd	6	inner	576.2.y.a.239.2		88
12.11	even	2		432.2.v.a.35.10		88
16.5	even	4		144.2.u.a.11.6	✓	88
16.11	odd	4	inner	576.2.y.a.335.2		88
36.23	even	6		144.2.u.a.131.6	yes	88
36.31	odd	6		432.2.v.a.179.17		88
48.5	odd	4		432.2.v.a.251.17		88
48.11	even	4		1728.2.z.a.143.12		88
144.5	odd	12		144.2.u.a.59.13	yes	88
144.59	even	12	inner	576.2.y.a.527.14		88
144.85	even	12		432.2.v.a.395.10		88
144.139	odd	12		1728.2.z.a.719.12		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.6	✓	88	16.5	even	4
144.2.u.a.59.13	yes	88	144.5	odd	12
144.2.u.a.83.13	yes	88	4.3	odd	2
144.2.u.a.131.6	yes	88	36.23	even	6
432.2.v.a.35.10		88	12.11	even	2
432.2.v.a.179.17		88	36.31	odd	6
432.2.v.a.251.17		88	48.5	odd	4
432.2.v.a.395.10		88	144.85	even	12
576.2.y.a.47.14		88	1.1	even	1	trivial
576.2.y.a.239.2		88	9.5	odd	6	inner
576.2.y.a.335.2		88	16.11	odd	4	inner
576.2.y.a.527.14		88	144.59	even	12	inner
1728.2.z.a.143.12		88	48.11	even	4
1728.2.z.a.719.12		88	144.139	odd	12
1728.2.z.a.1007.12		88	3.2	odd	2
1728.2.z.a.1583.12		88	9.4	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

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

Properties

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