LMFDB - Embedded newform 1100.2.q.b.881.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1100,2,Mod(221,1100)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1100.221"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1100, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 6, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1100 = 2^{2} \cdot 5^{2} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1100.q (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [52] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$8.78354422234$
Analytic rank:	$0$
Dimension:	$52$
Relative dimension:	$13$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			881.11
Character	$\chi$	$=$	1100.881
Dual form			1100.2.q.b.221.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.36589 - 0.992379i) q^{3} +(-2.23514 + 0.0642463i) q^{5} +0.0719347 q^{7} +(-0.0462056 + 0.142206i) q^{9} +(-0.309017 - 0.951057i) q^{11} +(-0.188720 + 0.580820i) q^{13} +(-2.98921 + 2.30586i) q^{15} +(-5.73859 - 4.16933i) q^{17} +(-5.13309 - 3.72941i) q^{19} +(0.0982550 - 0.0713864i) q^{21} +(-2.28102 - 7.02024i) q^{23} +(4.99174 - 0.287200i) q^{25} +(1.64318 + 5.05720i) q^{27} +(5.84966 - 4.25003i) q^{29} +(-4.55532 - 3.30963i) q^{31} +(-1.36589 - 0.992379i) q^{33} +(-0.160784 + 0.00462154i) q^{35} +(-2.79590 + 8.60490i) q^{37} +(0.318622 + 0.980618i) q^{39} +(0.696936 - 2.14495i) q^{41} -5.82489 q^{43} +(0.0941399 - 0.320820i) q^{45} +(1.70840 - 1.24122i) q^{47} -6.99483 q^{49} -11.9758 q^{51} +(4.71286 - 3.42409i) q^{53} +(0.751800 + 2.10590i) q^{55} -10.7122 q^{57} +(-0.560805 + 1.72598i) q^{59} +(0.305261 + 0.939496i) q^{61} +(-0.00332378 + 0.0102295i) q^{63} +(0.384501 - 1.31034i) q^{65} +(-8.68855 - 6.31260i) q^{67} +(-10.0824 - 7.32526i) q^{69} +(-0.144480 + 0.104971i) q^{71} +(2.23139 + 6.86753i) q^{73} +(6.53317 - 5.34598i) q^{75} +(-0.0222290 - 0.0684139i) q^{77} +(1.69087 - 1.22849i) q^{79} +(6.90016 + 5.01326i) q^{81} +(6.37772 + 4.63369i) q^{83} +(13.0944 + 8.95037i) q^{85} +(3.77237 - 11.6102i) q^{87} +(3.10262 + 9.54889i) q^{89} +(-0.0135755 + 0.0417811i) q^{91} -9.50648 q^{93} +(11.7128 + 8.00598i) q^{95} +(-14.2422 + 10.3476i) q^{97} +0.149524 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) $ 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1100\mathbb{Z}\right)^\times$.

$n$	$101$	$177$	$551$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.36589	−	0.992379i	0.788598	−	0.572950i	−0.118949	−	0.992900i	$-0.537953\pi$
$3$	1.36589	−	0.992379i	0.788598	−	0.572950i	0.907547	+	0.419950i	$0.137953\pi$
$4$		0			0
$5$	−2.23514	+	0.0642463i	−0.999587	+	0.0287318i
$5$	−2.23514	+	0.0642463i	−0.999587	+	0.0287318i
$6$		0			0
$7$	0.0719347			0.0271888			0.0135944	−	0.999908i	$-0.495673\pi$
$7$	0.0719347			0.0271888			0.0135944	+	0.999908i	$0.495673\pi$
$8$		0			0
$9$	−0.0462056	+	0.142206i	−0.0154019	+	0.0474020i
$10$		0			0
$11$	−0.309017	−	0.951057i	−0.0931721	−	0.286754i
$11$	−0.309017	−	0.951057i	−0.0931721	−	0.286754i
$12$		0			0
$13$	−0.188720	+	0.580820i	−0.0523414	+	0.161090i	−0.973810	−	0.227362i	$-0.926990\pi$
$13$	−0.188720	+	0.580820i	−0.0523414	+	0.161090i	0.921469	+	0.388452i	$0.126990\pi$
$14$		0			0
$15$	−2.98921	+	2.30586i	−0.771811	+	0.595371i
$16$		0			0
$17$	−5.73859	−	4.16933i	−1.39181	−	1.01121i	−0.995664	−	0.0930238i	$-0.970347\pi$
$17$	−5.73859	−	4.16933i	−1.39181	−	1.01121i	−0.396148	−	0.918187i	$-0.629653\pi$
$18$		0			0
$19$	−5.13309	−	3.72941i	−1.17761	−	0.855584i	−0.185711	−	0.982604i	$-0.559459\pi$
$19$	−5.13309	−	3.72941i	−1.17761	−	0.855584i	−0.991900	+	0.127020i	$0.959459\pi$
$20$		0			0
$21$	0.0982550	−	0.0713864i	0.0214410	−	0.0155778i
$22$		0			0
$23$	−2.28102	−	7.02024i	−0.475625	−	1.46382i	−0.845114	−	0.534587i	$-0.820467\pi$
$23$	−2.28102	−	7.02024i	−0.475625	−	1.46382i	0.369489	−	0.929235i	$-0.379533\pi$
$24$		0			0
$25$	4.99174	−	0.287200i	0.998349	−	0.0574399i
$26$		0			0
$27$	1.64318	+	5.05720i	0.316231	+	0.973258i
$28$		0			0
$29$	5.84966	−	4.25003i	1.08625	−	0.789210i	0.107491	−	0.994206i	$-0.465718\pi$
$29$	5.84966	−	4.25003i	1.08625	−	0.789210i	0.978763	+	0.204996i	$0.0657182\pi$
$30$		0			0
$31$	−4.55532	−	3.30963i	−0.818160	−	0.594428i	0.0980251	−	0.995184i	$-0.468747\pi$
$31$	−4.55532	−	3.30963i	−0.818160	−	0.594428i	−0.916185	+	0.400756i	$0.868747\pi$
$32$		0			0
$33$	−1.36589	−	0.992379i	−0.237771	−	0.172751i
$34$		0			0
$35$	−0.160784	+	0.00462154i	−0.0271775	+	0.000781182i
$36$		0			0
$37$	−2.79590	+	8.60490i	−0.459644	+	1.41464i	0.405952	+	0.913894i	$0.366940\pi$
$37$	−2.79590	+	8.60490i	−0.459644	+	1.41464i	−0.865596	+	0.500743i	$0.833060\pi$
$38$		0			0
$39$	0.318622	+	0.980618i	0.0510204	+	0.157025i
$40$		0			0
$41$	0.696936	−	2.14495i	0.108843	−	0.334984i	−0.881770	−	0.471679i	$-0.843648\pi$
$41$	0.696936	−	2.14495i	0.108843	−	0.334984i	0.990613	+	0.136695i	$0.0436480\pi$
$42$		0			0
$43$	−5.82489			−0.888288			−0.444144	−	0.895955i	$-0.646492\pi$
$43$	−5.82489			−0.888288			−0.444144	+	0.895955i	$0.646492\pi$
$44$		0			0
$45$	0.0941399	−	0.320820i	0.0140335	−	0.0478250i
$46$		0			0
$47$	1.70840	−	1.24122i	0.249195	−	0.181051i	−0.456175	−	0.889890i	$-0.650781\pi$
$47$	1.70840	−	1.24122i	0.249195	−	0.181051i	0.705370	+	0.708839i	$0.250781\pi$
$48$		0			0
$49$	−6.99483			−0.999261
$50$		0			0
$51$	−11.9758			−1.67695
$52$		0			0
$53$	4.71286	−	3.42409i	0.647361	−	0.470336i	−0.215010	−	0.976612i	$-0.568978\pi$
$53$	4.71286	−	3.42409i	0.647361	−	0.470336i	0.862371	+	0.506276i	$0.168978\pi$
$54$		0			0
$55$	0.751800	+	2.10590i	0.101373	+	0.283959i
$56$		0			0
$57$	−10.7122			−1.41887
$58$		0			0
$59$	−0.560805	+	1.72598i	−0.0730107	+	0.224704i	−0.980902	−	0.194501i	$-0.937691\pi$
$59$	−0.560805	+	1.72598i	−0.0730107	+	0.224704i	0.907892	+	0.419205i	$0.137691\pi$
$60$		0			0
$61$	0.305261	+	0.939496i	0.0390846	+	0.120290i	0.968695	−	0.248253i	$-0.0798566\pi$
$61$	0.305261	+	0.939496i	0.0390846	+	0.120290i	−0.929611	+	0.368544i	$0.879857\pi$
$62$		0			0
$63$	−0.00332378	+	0.0102295i	−0.000418757	+	0.00128880i
$64$		0			0
$65$	0.384501	−	1.31034i	0.0476914	−	0.162528i
$66$		0			0
$67$	−8.68855	−	6.31260i	−1.06148	−	0.771207i	−0.0871147	−	0.996198i	$-0.527765\pi$
$67$	−8.68855	−	6.31260i	−1.06148	−	0.771207i	−0.974361	+	0.224991i	$0.927765\pi$
$68$		0			0
$69$	−10.0824	−	7.32526i	−1.21377	−	0.881858i
$70$		0			0
$71$	−0.144480	+	0.104971i	−0.0171466	+	0.0124578i	−0.596326	−	0.802743i	$-0.703373\pi$
$71$	−0.144480	+	0.104971i	−0.0171466	+	0.0124578i	0.579179	+	0.815200i	$0.303373\pi$
$72$		0			0
$73$	2.23139	+	6.86753i	0.261165	+	0.803783i	0.992552	+	0.121821i	$0.0388733\pi$
$73$	2.23139	+	6.86753i	0.261165	+	0.803783i	−0.731387	+	0.681962i	$0.761127\pi$
$74$		0			0
$75$	6.53317	−	5.34598i	0.754386	−	0.617301i
$76$		0			0
$77$	−0.0222290	−	0.0684139i	−0.00253323	−	0.00779649i
$78$		0			0
$79$	1.69087	−	1.22849i	0.190238	−	0.138216i	−0.488589	−	0.872514i	$-0.662488\pi$
$79$	1.69087	−	1.22849i	0.190238	−	0.138216i	0.678827	+	0.734298i	$0.262488\pi$
$80$		0			0
$81$	6.90016	+	5.01326i	0.766685	+	0.557029i
$82$		0			0
$83$	6.37772	+	4.63369i	0.700046	+	0.508613i	0.879947	−	0.475072i	$-0.157578\pi$
$83$	6.37772	+	4.63369i	0.700046	+	0.508613i	−0.179901	+	0.983685i	$0.557578\pi$
$84$		0			0
$85$	13.0944	+	8.95037i	1.42029	+	0.970804i
$86$		0			0
$87$	3.77237	−	11.6102i	0.404440	−	1.24474i
$88$		0			0
$89$	3.10262	+	9.54889i	0.328877	+	1.01218i	0.969660	+	0.244458i	$0.0786100\pi$
$89$	3.10262	+	9.54889i	0.328877	+	1.01218i	−0.640783	+	0.767722i	$0.721390\pi$
$90$		0			0
$91$	−0.0135755	+	0.0417811i	−0.00142310	+	0.00437985i
$92$		0			0
$93$	−9.50648			−0.985776
$94$		0			0
$95$	11.7128	+	8.00598i	1.20171	+	0.821396i
$96$		0			0
$97$	−14.2422	+	10.3476i	−1.44608	+	1.05064i	−0.459348	+	0.888257i	$0.651917\pi$
$97$	−14.2422	+	10.3476i	−1.44608	+	1.05064i	−0.986728	+	0.162379i	$0.948083\pi$
$98$		0			0
$99$	0.149524			0.0150278
$100$		0			0
$101$	4.45245			0.443035			0.221518	−	0.975156i	$-0.428899\pi$
$101$	4.45245			0.443035			0.221518	+	0.975156i	$0.428899\pi$
$102$		0			0
$103$	4.57063	−	3.32076i	0.450358	−	0.327204i	−0.339379	−	0.940650i	$-0.610217\pi$
$103$	4.57063	−	3.32076i	0.450358	−	0.327204i	0.789737	+	0.613446i	$0.210217\pi$
$104$		0			0
$105$	−0.215028	+	0.165872i	−0.0209846	+	0.0161874i
$106$		0			0
$107$	0.0211635			0.00204596			0.00102298	−	0.999999i	$-0.499674\pi$
$107$	0.0211635			0.00204596			0.00102298	+	0.999999i	$0.499674\pi$
$108$		0			0
$109$	4.93996	−	15.2036i	0.473163	−	1.45625i	−0.375257	−	0.926921i	$-0.622446\pi$
$109$	4.93996	−	15.2036i	0.473163	−	1.45625i	0.848420	−	0.529324i	$-0.177554\pi$
$110$		0			0
$111$	4.72042	+	14.5280i	0.448042	+	1.37893i
$112$		0			0
$113$	4.24204	−	13.0557i	0.399058	−	1.22817i	−0.526698	−	0.850053i	$-0.676570\pi$
$113$	4.24204	−	13.0557i	0.399058	−	1.22817i	0.925756	−	0.378122i	$-0.123430\pi$
$114$		0			0
$115$	5.54942	+	15.5447i	0.517487	+	1.44955i
$116$		0			0
$117$	−0.0738762	−	0.0536742i	−0.00682986	−	0.00496218i
$118$		0			0
$119$	−0.412803	−	0.299919i	−0.0378416	−	0.0274936i
$120$		0			0
$121$	−0.809017	+	0.587785i	−0.0735470	+	0.0534350i
$122$		0			0
$123$	−1.17666	−	3.62139i	−0.106096	−	0.326530i
$124$		0			0
$125$	−11.1388	+	0.962634i	−0.996286	+	0.0861006i
$126$		0			0
$127$	4.39054	+	13.5127i	0.389598	+	1.19906i	0.933090	+	0.359644i	$0.117102\pi$
$127$	4.39054	+	13.5127i	0.389598	+	1.19906i	−0.543492	+	0.839414i	$0.682898\pi$
$128$		0			0
$129$	−7.95618	+	5.78050i	−0.700502	+	0.508945i
$130$		0			0
$131$	−6.45666	−	4.69104i	−0.564121	−	0.409858i	0.268844	−	0.963184i	$-0.413358\pi$
$131$	−6.45666	−	4.69104i	−0.564121	−	0.409858i	−0.832965	+	0.553326i	$0.813358\pi$
$132$		0			0
$133$	−0.369247	−	0.268274i	−0.0320178	−	0.0232623i
$134$		0			0
$135$	−3.99766	−	11.1980i	−0.344064	−	0.963771i
$136$		0			0
$137$	−2.41978	+	7.44731i	−0.206736	+	0.636267i	0.792902	+	0.609349i	$0.208569\pi$
$137$	−2.41978	+	7.44731i	−0.206736	+	0.636267i	−0.999638	+	0.0269178i	$0.991431\pi$
$138$		0			0
$139$	−7.26688	−	22.3652i	−0.616369	−	1.89699i	−0.377952	−	0.925825i	$-0.623372\pi$
$139$	−7.26688	−	22.3652i	−0.616369	−	1.89699i	−0.238416	−	0.971163i	$-0.576628\pi$
$140$		0			0
$141$	1.10172	−	3.39076i	0.0927818	−	0.285553i
$142$		0			0
$143$	0.610710			0.0510701
$144$		0			0
$145$	−12.8018	+	9.87524i	−1.06313	+	0.820094i
$146$		0			0
$147$	−9.55418	+	6.94151i	−0.788015	+	0.572526i
$148$		0			0
$149$	13.9934			1.14638			0.573190	−	0.819422i	$-0.305706\pi$
$149$	13.9934			1.14638			0.573190	+	0.819422i	$0.305706\pi$
$150$		0			0
$151$	23.5831			1.91916			0.959581	−	0.281431i	$-0.0908090\pi$
$151$	23.5831			1.91916			0.959581	+	0.281431i	$0.0908090\pi$
$152$		0			0
$153$	0.858058	−	0.623416i	0.0693699	−	0.0504002i
$154$		0			0
$155$	10.3944	+	7.10485i	0.834901	+	0.570675i
$156$		0			0
$157$	0.152388			0.0121619			0.00608096	−	0.999982i	$-0.498064\pi$
$157$	0.152388			0.0121619			0.00608096	+	0.999982i	$0.498064\pi$
$158$		0			0
$159$	3.03926	−	9.35389i	0.241029	−	0.741811i
$160$		0			0
$161$	−0.164084	−	0.504999i	−0.0129316	−	0.0397995i
$162$		0			0
$163$	4.00641	−	12.3305i	0.313806	−	0.965796i	−0.662437	−	0.749118i	$-0.730478\pi$
$163$	4.00641	−	12.3305i	0.313806	−	0.965796i	0.976243	−	0.216678i	$-0.0695222\pi$
$164$		0			0
$165$	3.11672	+	2.13036i	0.242637	+	0.165848i
$166$		0			0
$167$	0.706209	+	0.513091i	0.0546481	+	0.0397042i	0.614774	−	0.788703i	$-0.289247\pi$
$167$	0.706209	+	0.513091i	0.0546481	+	0.0397042i	−0.560126	+	0.828408i	$0.689247\pi$
$168$		0			0
$169$	10.2155	+	7.42198i	0.785807	+	0.570922i
$170$		0			0
$171$	0.767521	−	0.557637i	0.0586938	−	0.0426436i
$172$		0			0
$173$	−5.06929	−	15.6017i	−0.385411	−	1.18617i	−0.936182	−	0.351516i	$-0.885666\pi$
$173$	−5.06929	−	15.6017i	−0.385411	−	1.18617i	0.550771	−	0.834656i	$-0.314334\pi$
$174$		0			0
$175$	0.359080	−	0.0206596i	0.0271439	−	0.00156172i
$176$		0			0
$177$	0.946828	+	2.91404i	0.0711679	+	0.219032i
$178$		0			0
$179$	21.4103	−	15.5555i	1.60028	−	1.16267i	0.713313	−	0.700845i	$-0.247194\pi$
$179$	21.4103	−	15.5555i	1.60028	−	1.16267i	0.886969	−	0.461828i	$-0.152806\pi$
$180$		0			0
$181$	−10.4000	−	7.55607i	−0.773029	−	0.561638i	0.129850	−	0.991534i	$-0.458550\pi$
$181$	−10.4000	−	7.55607i	−0.773029	−	0.561638i	−0.902879	+	0.429895i	$0.858550\pi$
$182$		0			0
$183$	1.34929	+	0.980316i	0.0997423	+	0.0724670i
$184$		0			0
$185$	5.69641	−	19.4128i	0.418809	−	1.42726i
$186$		0			0
$187$	−2.19195	+	6.74611i	−0.160291	+	0.493325i
$188$		0			0
$189$	0.118202	+	0.363788i	0.00859792	+	0.0264617i
$190$		0			0
$191$	−7.60028	+	23.3912i	−0.549937	+	1.69253i	0.159017	+	0.987276i	$0.449168\pi$
$191$	−7.60028	+	23.3912i	−0.549937	+	1.69253i	−0.708953	+	0.705255i	$0.750832\pi$
$192$		0			0
$193$	−15.5351			−1.11824			−0.559119	−	0.829087i	$-0.688861\pi$
$193$	−15.5351			−1.11824			−0.559119	+	0.829087i	$0.688861\pi$
$194$		0			0
$195$	−0.775168	−	2.17135i	−0.0555109	−	0.155494i
$196$		0			0
$197$	1.30233	−	0.946199i	0.0927873	−	0.0674139i	−0.540424	−	0.841393i	$-0.681736\pi$
$197$	1.30233	−	0.946199i	0.0927873	−	0.0674139i	0.633212	+	0.773979i	$0.281736\pi$
$198$		0			0
$199$	2.59050			0.183636			0.0918178	−	0.995776i	$-0.470732\pi$
$199$	2.59050			0.183636			0.0918178	+	0.995776i	$0.470732\pi$
$200$		0			0
$201$	−18.1321			−1.27894
$202$		0			0
$203$	0.420793	−	0.305724i	0.0295339	−	0.0214576i
$204$		0			0
$205$	−1.41995	+	4.83904i	−0.0991734	+	0.337973i
$206$		0			0
$207$	1.10372			0.0767136
$208$		0			0
$209$	−1.96066	+	6.03431i	−0.135622	+	0.417402i
$210$		0			0
$211$	4.21442	+	12.9707i	0.290133	+	0.892937i	0.984813	+	0.173618i	$0.0555458\pi$
$211$	4.21442	+	12.9707i	0.290133	+	0.892937i	−0.694680	+	0.719319i	$0.744454\pi$
$212$		0			0
$213$	−0.0931733	+	0.286758i	−0.00638413	+	0.0196483i
$214$		0			0
$215$	13.0195	−	0.374228i	0.887921	−	0.0255221i
$216$		0			0
$217$	−0.327685	−	0.238077i	−0.0222447	−	0.0161617i
$218$		0			0
$219$	9.86303	+	7.16591i	0.666482	+	0.484227i
$220$		0			0
$221$	3.50461	−	2.54625i	0.235746	−	0.171279i
$222$		0			0
$223$	−3.03071	−	9.32757i	−0.202951	−	0.624620i	−0.999791	−	0.0204296i	$-0.993497\pi$
$223$	−3.03071	−	9.32757i	−0.202951	−	0.624620i	0.796840	−	0.604190i	$-0.206503\pi$
$224$		0			0
$225$	−0.189805	+	0.723127i	−0.0126537	+	0.0482084i
$226$		0			0
$227$	−3.06424	−	9.43075i	−0.203381	−	0.625941i	−0.999776	−	0.0211648i	$-0.993263\pi$
$227$	−3.06424	−	9.43075i	−0.203381	−	0.625941i	0.796395	−	0.604776i	$-0.206737\pi$
$228$		0			0
$229$	−10.1574	+	7.37980i	−0.671222	+	0.487671i	−0.870434	−	0.492285i	$-0.836162\pi$
$229$	−10.1574	+	7.37980i	−0.671222	+	0.487671i	0.199212	+	0.979956i	$0.436162\pi$
$230$		0			0
$231$	−0.0982550	−	0.0713864i	−0.00646470	−	0.00469688i
$232$		0			0
$233$	−7.88307	−	5.72739i	−0.516437	−	0.375214i	0.298823	−	0.954309i	$-0.403406\pi$
$233$	−7.88307	−	5.72739i	−0.516437	−	0.375214i	−0.815260	+	0.579095i	$0.803406\pi$
$234$		0			0
$235$	−3.73877	+	2.88407i	−0.243891	+	0.188136i
$236$		0			0
$237$	1.09042	−	3.35597i	0.0708305	−	0.217994i
$238$		0			0
$239$	−1.11065	−	3.41823i	−0.0718420	−	0.221107i	0.908688	−	0.417476i	$-0.137085\pi$
$239$	−1.11065	−	3.41823i	−0.0718420	−	0.221107i	−0.980530	+	0.196369i	$0.937085\pi$
$240$		0			0
$241$	−6.60367	+	20.3240i	−0.425380	+	1.30918i	0.477250	+	0.878767i	$0.341633\pi$
$241$	−6.60367	+	20.3240i	−0.425380	+	1.30918i	−0.902630	+	0.430417i	$0.858367\pi$
$242$		0			0
$243$	−1.55243			−0.0995884
$244$		0			0
$245$	15.6344	−	0.449392i	0.998848	−	0.0287106i
$246$		0			0
$247$	3.13483	−	2.27759i	0.199464	−	0.144919i
$248$		0			0
$249$	13.3096			0.843465
$250$		0			0
$251$	15.3836			0.971002			0.485501	−	0.874236i	$-0.338637\pi$
$251$	15.3836			0.971002			0.485501	+	0.874236i	$0.338637\pi$
$252$		0			0
$253$	−5.97178	+	4.33875i	−0.375442	+	0.272775i
$254$		0			0
$255$	26.7677	−	0.769404i	1.67626	−	0.0481819i
$256$		0			0
$257$	−29.4530			−1.83722			−0.918612	−	0.395160i	$-0.870689\pi$
$257$	−29.4530			−1.83722			−0.918612	+	0.395160i	$0.870689\pi$
$258$		0			0
$259$	−0.201122	+	0.618991i	−0.0124971	+	0.0384622i
$260$		0			0
$261$	0.334093	+	1.02823i	0.0206798	+	0.0636459i
$262$		0			0
$263$	3.87604	−	11.9292i	0.239007	−	0.735587i	−0.757558	−	0.652768i	$-0.773608\pi$
$263$	3.87604	−	11.9292i	0.239007	−	0.735587i	0.996565	−	0.0828192i	$-0.0263924\pi$
$264$		0			0
$265$	−10.3139	+	7.95613i	−0.633581	+	0.488741i
$266$		0			0
$267$	13.7140	+	9.96377i	0.839281	+	0.609773i
$268$		0			0
$269$	5.65099	+	4.10568i	0.344547	+	0.250328i	0.746578	−	0.665298i	$-0.231696\pi$
$269$	5.65099	+	4.10568i	0.344547	+	0.250328i	−0.402031	+	0.915626i	$0.631696\pi$
$270$		0			0
$271$	16.9099	−	12.2858i	1.02720	−	0.746307i	0.0594561	−	0.998231i	$-0.481063\pi$
$271$	16.9099	−	12.2858i	1.02720	−	0.746307i	0.967747	+	0.251924i	$0.0810634\pi$
$272$		0			0
$273$	0.0229200	+	0.0705405i	0.00138718	+	0.00426930i
$274$		0			0
$275$	−1.81568	−	4.65868i	−0.109489	−	0.280929i
$276$		0			0
$277$	−10.1347	−	31.1914i	−0.608935	−	1.87411i	−0.467064	−	0.884224i	$-0.654688\pi$
$277$	−10.1347	−	31.1914i	−0.608935	−	1.87411i	−0.141871	−	0.989885i	$-0.545312\pi$
$278$		0			0
$279$	0.681131	−	0.494871i	0.0407783	−	0.0296271i
$280$		0			0
$281$	−1.94480	−	1.41298i	−0.116017	−	0.0842913i	0.528264	−	0.849080i	$-0.322843\pi$
$281$	−1.94480	−	1.41298i	−0.116017	−	0.0842913i	−0.644281	+	0.764789i	$0.722843\pi$
$282$		0			0
$283$	14.1981	+	10.3155i	0.843988	+	0.613193i	0.923482	−	0.383642i	$-0.125330\pi$
$283$	14.1981	+	10.3155i	0.843988	+	0.613193i	−0.0794938	+	0.996835i	$0.525330\pi$
$284$		0			0
$285$	23.9434	−	0.688221i	1.41828	−	0.0407667i
$286$		0			0
$287$	0.0501338	−	0.154296i	0.00295931	−	0.00910781i
$288$		0			0
$289$	10.2948	+	31.6841i	0.605577	+	1.86377i
$290$		0			0
$291$	−9.18460	+	28.2673i	−0.538411	+	1.65706i
$292$		0			0
$293$	−9.21171			−0.538154			−0.269077	−	0.963119i	$-0.586719\pi$
$293$	−9.21171			−0.538154			−0.269077	+	0.963119i	$0.586719\pi$
$294$		0			0
$295$	1.14259	−	3.89385i	0.0665244	−	0.226709i
$296$		0			0
$297$	4.30191	−	3.12552i	0.249622	−	0.181361i
$298$		0			0
$299$	4.50797			0.260703
$300$		0			0
$301$	−0.419012			−0.0241514
$302$		0			0
$303$	6.08156	−	4.41851i	0.349377	−	0.253837i
$304$		0			0
$305$	−0.742661	−	2.08030i	−0.0425246	−	0.119117i
$306$		0			0
$307$	9.70406			0.553840			0.276920	−	0.960893i	$-0.410686\pi$
$307$	9.70406			0.553840			0.276920	+	0.960893i	$0.410686\pi$
$308$		0			0
$309$	2.94754	−	9.07159i	0.167680	−	0.516065i
$310$		0			0
$311$	2.29220	+	7.05468i	0.129979	+	0.400034i	0.994775	−	0.102089i	$-0.0325526\pi$
$311$	2.29220	+	7.05468i	0.129979	+	0.400034i	−0.864796	+	0.502123i	$0.832553\pi$
$312$		0			0
$313$	−6.95507	+	21.4055i	−0.393124	+	1.20991i	0.537289	+	0.843398i	$0.319449\pi$
$313$	−6.95507	+	21.4055i	−0.393124	+	1.20991i	−0.930413	+	0.366513i	$0.880551\pi$
$314$		0			0
$315$	0.00677192	−	0.0230781i	0.000381555	−	0.00130030i
$316$		0			0
$317$	18.4100	+	13.3757i	1.03401	+	0.751253i	0.969108	−	0.246639i	$-0.0793261\pi$
$317$	18.4100	+	13.3757i	1.03401	+	0.751253i	0.0649035	+	0.997892i	$0.479326\pi$
$318$		0			0
$319$	−5.84966	−	4.25003i	−0.327518	−	0.237956i
$320$		0			0
$321$	0.0289071	−	0.0210022i	0.00161344	−	0.00117223i
$322$		0			0
$323$	13.9076	+	42.8030i	0.773837	+	2.38163i
$324$		0			0
$325$	−0.775230	+	2.95350i	−0.0430020	+	0.163831i
$326$		0			0
$327$	−8.34031	−	25.6688i	−0.461220	−	1.41949i
$328$		0			0
$329$	0.122893	−	0.0892870i	0.00677531	−	0.00492255i
$330$		0			0
$331$	−3.26772	−	2.37413i	−0.179610	−	0.130494i	0.494348	−	0.869264i	$-0.335407\pi$
$331$	−3.26772	−	2.37413i	−0.179610	−	0.130494i	−0.673958	+	0.738770i	$0.735407\pi$
$332$		0			0
$333$	−1.09448	−	0.795189i	−0.0599773	−	0.0435761i
$334$		0			0
$335$	19.8257	+	13.5514i	1.08320	+	0.740391i
$336$		0			0
$337$	−0.730540	+	2.24837i	−0.0397951	+	0.122477i	−0.968980	−	0.247137i	$-0.920510\pi$
$337$	−0.730540	+	2.24837i	−0.0397951	+	0.122477i	0.929185	+	0.369614i	$0.120510\pi$
$338$		0			0
$339$	−7.16199	−	22.0423i	−0.388986	−	1.19718i
$340$		0			0
$341$	−1.73998	+	5.35510i	−0.0942251	+	0.289995i
$342$		0			0
$343$	−1.00671			−0.0543574
$344$		0			0
$345$	23.0062	+	15.7253i	1.23861	+	0.846620i
$346$		0			0
$347$	−6.61053	+	4.80283i	−0.354872	+	0.257830i	−0.750910	−	0.660404i	$-0.770385\pi$
$347$	−6.61053	+	4.80283i	−0.354872	+	0.257830i	0.396038	+	0.918234i	$0.370385\pi$
$348$		0			0
$349$	30.9193			1.65507			0.827537	−	0.561411i	$-0.189741\pi$
$349$	30.9193			1.65507			0.827537	+	0.561411i	$0.189741\pi$
$350$		0			0
$351$	−3.24742			−0.173335
$352$		0			0
$353$	−0.431015	+	0.313151i	−0.0229406	+	0.0166673i	−0.599196	−	0.800602i	$-0.704513\pi$
$353$	−0.431015	+	0.313151i	−0.0229406	+	0.0166673i	0.576256	+	0.817269i	$0.304513\pi$
$354$		0			0
$355$	0.316190	−	0.243908i	0.0167816	−	0.0129453i
$356$		0			0
$357$	−0.861478			−0.0455943
$358$		0			0
$359$	9.46465	−	29.1292i	0.499525	−	1.53738i	−0.310259	−	0.950652i	$-0.600416\pi$
$359$	9.46465	−	29.1292i	0.499525	−	1.53738i	0.809784	−	0.586728i	$-0.199584\pi$
$360$		0			0
$361$	6.56879	+	20.2167i	0.345726	+	1.06403i
$362$		0			0
$363$	−0.521724	+	1.60570i	−0.0273834	+	0.0842775i
$364$		0			0
$365$	−5.42870	−	15.2066i	−0.284151	−	0.795948i
$366$		0			0
$367$	17.4028	+	12.6439i	0.908420	+	0.660006i	0.940615	−	0.339476i	$-0.110250\pi$
$367$	17.4028	+	12.6439i	0.908420	+	0.660006i	−0.0321945	+	0.999482i	$0.510250\pi$
$368$		0			0
$369$	0.272822	+	0.198217i	0.0142026	+	0.0103188i
$370$		0			0
$371$	0.339018	−	0.246311i	0.0176009	−	0.0127878i
$372$		0			0
$373$	−11.6438	−	35.8359i	−0.602893	−	1.85551i	−0.510671	−	0.859776i	$-0.670603\pi$
$373$	−11.6438	−	35.8359i	−0.602893	−	1.85551i	−0.0922218	−	0.995738i	$-0.529397\pi$
$374$		0			0
$375$	−14.2591	+	12.3688i	−0.736338	+	0.638721i
$376$		0			0
$377$	1.36455	+	4.19966i	0.0702780	+	0.216294i
$378$		0			0
$379$	−8.98082	+	6.52495i	−0.461314	+	0.335164i	−0.794046	−	0.607857i	$-0.792029\pi$
$379$	−8.98082	+	6.52495i	−0.461314	+	0.335164i	0.332733	+	0.943021i	$0.392029\pi$
$380$		0			0
$381$	19.4067	+	14.0998i	0.994237	+	0.722355i
$382$		0			0
$383$	−8.28533	−	6.01965i	−0.423361	−	0.307590i	0.355628	−	0.934628i	$-0.384267\pi$
$383$	−8.28533	−	6.01965i	−0.423361	−	0.307590i	−0.778989	+	0.627038i	$0.784267\pi$
$384$		0			0
$385$	0.0540805	+	0.151487i	0.00275620	+	0.00772049i
$386$		0			0
$387$	0.269143	−	0.828335i	0.0136813	−	0.0421067i
$388$		0			0
$389$	−2.02448	−	6.23070i	−0.102645	−	0.315909i	0.886525	−	0.462680i	$-0.153112\pi$
$389$	−2.02448	−	6.23070i	−0.102645	−	0.315909i	−0.989171	+	0.146771i	$0.953112\pi$
$390$		0			0
$391$	−16.1799	+	49.7966i	−0.818252	+	2.51832i
$392$		0			0
$393$	−13.4744			−0.679693
$394$		0			0
$395$	−3.70042	+	2.85449i	−0.186188	+	0.143625i
$396$		0			0
$397$	−14.4034	+	10.4647i	−0.722886	+	0.525208i	−0.887305	−	0.461183i	$-0.847425\pi$
$397$	−14.4034	+	10.4647i	−0.722886	+	0.525208i	0.164419	+	0.986391i	$0.447425\pi$
$398$		0			0
$399$	−0.770580			−0.0385773
$400$		0			0
$401$	5.98243			0.298748			0.149374	−	0.988781i	$-0.452274\pi$
$401$	5.98243			0.298748			0.149374	+	0.988781i	$0.452274\pi$
$402$		0			0
$403$	2.78198	−	2.02123i	0.138580	−	0.100684i
$404$		0			0
$405$	−15.7449	−	10.7621i	−0.782373	−	0.534771i
$406$		0			0
$407$	9.04773			0.448479
$408$		0			0
$409$	4.41043	−	13.5739i	0.218082	−	0.671187i	−0.780839	−	0.624733i	$-0.785208\pi$
$409$	4.41043	−	13.5739i	0.218082	−	0.671187i	0.998920	−	0.0464539i	$-0.0147921\pi$
$410$		0			0
$411$	4.08540	+	12.5736i	0.201518	+	0.620208i
$412$		0			0
$413$	−0.0403414	+	0.124158i	−0.00198507	+	0.00610941i
$414$		0			0
$415$	−14.5528	−	9.94721i	−0.714370	−	0.488289i
$416$		0			0
$417$	−32.1205	−	23.3369i	−1.57295	−	1.14281i
$418$		0			0
$419$	12.5221	+	9.09785i	0.611745	+	0.444459i	0.850028	−	0.526737i	$-0.176585\pi$
$419$	12.5221	+	9.09785i	0.611745	+	0.444459i	−0.238283	+	0.971196i	$0.576585\pi$
$420$		0			0
$421$	−1.58053	+	1.14832i	−0.0770305	+	0.0559659i	−0.625634	−	0.780117i	$-0.715160\pi$
$421$	−1.58053	+	1.14832i	−0.0770305	+	0.0559659i	0.548604	+	0.836083i	$0.315160\pi$
$422$		0			0
$423$	0.0975721	+	0.300296i	0.00474412	+	0.0146009i
$424$		0			0
$425$	−29.8430	−	19.1641i	−1.44760	−	0.929595i
$426$		0			0
$427$	0.0219588	+	0.0675823i	0.00106266	+	0.00327054i
$428$		0			0
$429$	0.834164	−	0.606056i	0.0402738	−	0.0292606i
$430$		0			0
$431$	−14.4968	−	10.5326i	−0.698287	−	0.507335i	0.181087	−	0.983467i	$-0.442038\pi$
$431$	−14.4968	−	10.5326i	−0.698287	−	0.507335i	−0.879374	+	0.476132i	$0.842038\pi$
$432$		0			0
$433$	−5.23692	−	3.80485i	−0.251670	−	0.182849i	0.454796	−	0.890595i	$-0.349712\pi$
$433$	−5.23692	−	3.80485i	−0.251670	−	0.182849i	−0.706467	+	0.707746i	$0.749712\pi$
$434$		0			0
$435$	−7.68588	+	26.1927i	−0.368510	+	1.25585i
$436$		0			0
$437$	−14.4727	+	44.5424i	−0.692323	+	2.13075i
$438$		0			0
$439$	10.2428	+	31.5240i	0.488861	+	1.50456i	0.826310	+	0.563216i	$0.190436\pi$
$439$	10.2428	+	31.5240i	0.488861	+	1.50456i	−0.337449	+	0.941344i	$0.609564\pi$
$440$		0			0
$441$	0.323200	−	0.994707i	0.0153905	−	0.0473670i
$442$		0			0
$443$	−41.0466			−1.95018			−0.975092	−	0.221800i	$-0.928807\pi$
$443$	−41.0466			−1.95018			−0.975092	+	0.221800i	$0.928807\pi$
$444$		0			0
$445$	−7.54829	−	21.1438i	−0.357823	−	1.00231i
$446$		0			0
$447$	19.1134	−	13.8867i	0.904034	−	0.656819i
$448$		0			0
$449$	16.0959			0.759611			0.379805	−	0.925066i	$-0.375991\pi$
$449$	16.0959			0.759611			0.379805	+	0.925066i	$0.375991\pi$
$450$		0			0
$451$	−2.25533			−0.106199
$452$		0			0
$453$	32.2119	−	23.4033i	1.51345	−	1.09958i
$454$		0			0
$455$	0.0276589	−	0.0942589i	0.00129667	−	0.00441893i
$456$		0			0
$457$	−1.05732			−0.0494593			−0.0247297	−	0.999694i	$-0.507872\pi$
$457$	−1.05732			−0.0494593			−0.0247297	+	0.999694i	$0.507872\pi$
$458$		0			0
$459$	11.6556	−	35.8721i	0.544035	−	1.67437i
$460$		0			0
$461$	−9.67386	−	29.7731i	−0.450557	−	1.38667i	−0.876273	−	0.481815i	$-0.839978\pi$
$461$	−9.67386	−	29.7731i	−0.450557	−	1.38667i	0.425716	−	0.904857i	$-0.360022\pi$
$462$		0			0
$463$	7.31024	−	22.4986i	0.339736	−	1.04560i	−0.624607	−	0.780940i	$-0.714741\pi$
$463$	7.31024	−	22.4986i	0.339736	−	1.04560i	0.964342	−	0.264659i	$-0.0852593\pi$
$464$		0			0
$465$	21.2484	−	0.610757i	0.985369	−	0.0283232i
$466$		0			0
$467$	−20.2065	−	14.6809i	−0.935044	−	0.679349i	0.0121787	−	0.999926i	$-0.496123\pi$
$467$	−20.2065	−	14.6809i	−0.935044	−	0.679349i	−0.947223	+	0.320577i	$0.896123\pi$
$468$		0			0
$469$	−0.625008	−	0.454095i	−0.0288602	−	0.0209682i
$470$		0			0
$471$	0.208146	−	0.151227i	0.00959086	−	0.00696817i
$472$		0			0
$473$	1.79999	+	5.53980i	0.0827637	+	0.254720i
$474$		0			0
$475$	−26.6941	−	17.1420i	−1.22481	−	0.786530i
$476$		0			0
$477$	0.269167	+	0.828410i	0.0123243	+	0.0379303i
$478$		0			0
$479$	−6.76191	+	4.91282i	−0.308960	+	0.224472i	−0.731450	−	0.681895i	$-0.761156\pi$
$479$	−6.76191	+	4.91282i	−0.308960	+	0.224472i	0.422490	+	0.906367i	$0.361156\pi$
$480$		0			0
$481$	−4.47026	−	3.24783i	−0.203826	−	0.148088i
$482$		0			0
$483$	−0.725271	−	0.526940i	−0.0330010	−	0.0239766i
$484$		0			0
$485$	31.1686	−	24.0433i	1.41529	−	1.09175i
$486$		0			0
$487$	−1.16406	+	3.58261i	−0.0527486	+	0.162343i	−0.973961	−	0.226718i	$-0.927201\pi$
$487$	−1.16406	+	3.58261i	−0.0527486	+	0.162343i	0.921212	+	0.389061i	$0.127201\pi$
$488$		0			0
$489$	−6.76416	−	20.8179i	−0.305886	−	0.941420i
$490$		0			0
$491$	7.61112	−	23.4246i	0.343485	−	1.05714i	−0.618905	−	0.785466i	$-0.712423\pi$
$491$	7.61112	−	23.4246i	0.343485	−	1.05714i	0.962390	−	0.271672i	$-0.0875765\pi$
$492$		0			0
$493$	−51.2885			−2.30992
$494$		0			0
$495$	−0.334209	+	0.00960639i	−0.0150216	+	0.000431775i
$496$		0			0
$497$	−0.0103931	+	0.00755105i	−0.000466195	+	0.000338711i
$498$		0			0
$499$	0.0632242			0.00283030			0.00141515	−	0.999999i	$-0.499550\pi$
$499$	0.0632242			0.00283030			0.00141515	+	0.999999i	$0.499550\pi$
$500$		0			0
$501$	1.47379			0.0658439
$502$		0			0
$503$	−19.8116	+	14.3940i	−0.883357	+	0.641796i	−0.934137	−	0.356913i	$-0.883829\pi$
$503$	−19.8116	+	14.3940i	−0.883357	+	0.641796i	0.0507804	+	0.998710i	$0.483829\pi$
$504$		0			0
$505$	−9.95187	+	0.286053i	−0.442852	+	0.0127292i
$506$		0			0
$507$	21.3187			0.946795
$508$		0			0
$509$	−11.5610	+	35.5811i	−0.512432	+	1.57710i	0.275474	+	0.961309i	$0.411165\pi$
$509$	−11.5610	+	35.5811i	−0.512432	+	1.57710i	−0.787906	+	0.615796i	$0.788835\pi$
$510$		0			0
$511$	0.160515	+	0.494013i	0.00710075	+	0.0218539i
$512$		0			0
$513$	10.4257	−	32.0871i	0.460308	−	1.41668i
$514$		0			0
$515$	−10.0027	+	7.71602i	−0.440771	+	0.340008i
$516$		0			0
$517$	−1.70840	−	1.24122i	−0.0751353	−	0.0545890i
$518$		0			0
$519$	−22.4068	−	16.2795i	−0.983551	−	0.714592i
$520$		0			0
$521$	6.39913	−	4.64924i	0.280351	−	0.203687i	−0.438719	−	0.898624i	$-0.644568\pi$
$521$	6.39913	−	4.64924i	0.280351	−	0.203687i	0.719071	+	0.694937i	$0.244568\pi$
$522$		0			0
$523$	−7.42314	−	22.8461i	−0.324591	−	0.998990i	−0.971625	−	0.236528i	$-0.923991\pi$
$523$	−7.42314	−	22.8461i	−0.324591	−	0.998990i	0.647033	−	0.762462i	$-0.276009\pi$
$524$		0			0
$525$	0.469962	−	0.384562i	0.0205108	−	0.0167836i
$526$		0			0
$527$	12.3422	+	37.9852i	0.537633	+	1.65466i
$528$		0			0
$529$	−25.4734	+	18.5075i	−1.10754	+	0.804674i
$530$		0			0
$531$	−0.219533	−	0.159500i	−0.00952691	−	0.00692171i
$532$		0			0
$533$	1.11430	+	0.809588i	0.0482658	+	0.0350671i
$534$		0			0
$535$	−0.0473036	+	0.00135968i	−0.00204511	+	5.87840e-5i
$536$		0			0
$537$	13.8072	−	42.4943i	0.595826	−	1.83376i
$538$		0			0
$539$	2.16152	+	6.65247i	0.0931033	+	0.286542i
$540$		0			0
$541$	7.85253	−	24.1676i	0.337607	−	1.03905i	−0.627817	−	0.778361i	$-0.716052\pi$
$541$	7.85253	−	24.1676i	0.337607	−	1.03905i	0.965424	−	0.260685i	$-0.0839485\pi$
$542$		0			0
$543$	−21.7038			−0.931400
$544$		0			0
$545$	−10.0648	+	34.2997i	−0.431127	+	1.46924i
$546$		0			0
$547$	10.2376	−	7.43807i	0.437729	−	0.318029i	−0.347003	−	0.937864i	$-0.612801\pi$
$547$	10.2376	−	7.43807i	0.437729	−	0.318029i	0.784732	+	0.619835i	$0.212801\pi$
$548$		0			0
$549$	−0.147707			−0.00630397
$550$		0			0
$551$	−45.8769			−1.95442
$552$		0			0
$553$	0.121632	−	0.0883711i	0.00517233	−	0.00375792i
$554$		0			0
$555$	−11.4842	−	32.1688i	−0.487477	−	1.36549i
$556$		0			0
$557$	−37.4281			−1.58588			−0.792940	−	0.609300i	$-0.791450\pi$
$557$	−37.4281			−1.58588			−0.792940	+	0.609300i	$0.791450\pi$
$558$		0			0
$559$	1.09927	−	3.38321i	0.0464943	−	0.143095i
$560$		0			0
$561$	3.70074	+	11.3897i	0.156245	+	0.480874i
$562$		0			0
$563$	5.51971	−	16.9879i	0.232628	−	0.715956i	−0.764799	−	0.644269i	$-0.777162\pi$
$563$	5.51971	−	16.9879i	0.232628	−	0.715956i	0.997427	−	0.0716868i	$-0.0228382\pi$
$564$		0			0
$565$	−8.64281	+	29.4539i	−0.363606	+	1.23913i
$566$		0			0
$567$	0.496361	+	0.360627i	0.0208452	+	0.0151449i
$568$		0			0
$569$	−20.2206	−	14.6911i	−0.847690	−	0.615883i	0.0768179	−	0.997045i	$-0.475524\pi$
$569$	−20.2206	−	14.6911i	−0.847690	−	0.615883i	−0.924508	+	0.381162i	$0.875524\pi$
$570$		0			0
$571$	−30.4372	+	22.1139i	−1.27376	+	0.925439i	−0.999346	−	0.0361733i	$-0.988483\pi$
$571$	−30.4372	+	22.1139i	−1.27376	+	0.925439i	−0.274412	+	0.961612i	$0.588483\pi$
$572$		0			0
$573$	12.8318	+	39.4923i	0.536057	+	1.64981i
$574$		0			0
$575$	−13.4025	−	34.3882i	−0.558921	−	1.43409i
$576$		0			0
$577$	0.284159	+	0.874553i	0.0118297	+	0.0364081i	0.956797	−	0.290756i	$-0.0939069\pi$
$577$	0.284159	+	0.874553i	0.0118297	+	0.0364081i	−0.944967	+	0.327164i	$0.893907\pi$
$578$		0			0
$579$	−21.2192	+	15.4167i	−0.881841	+	0.640695i
$580$		0			0
$581$	0.458779	+	0.333323i	0.0190334	+	0.0138286i
$582$		0			0
$583$	−4.71286	−	3.42409i	−0.195187	−	0.141812i
$584$		0			0
$585$	0.168572	+	0.115223i	0.00696961	+	0.00476390i
$586$		0			0
$587$	13.6565	−	42.0304i	0.563664	−	1.73478i	−0.108223	−	0.994127i	$-0.534516\pi$
$587$	13.6565	−	42.0304i	0.563664	−	1.73478i	0.671888	−	0.740653i	$-0.265484\pi$
$588$		0			0
$589$	11.0399	+	33.9773i	0.454891	+	1.40001i
$590$		0			0
$591$	0.839856	−	2.58481i	0.0345471	−	0.106325i
$592$		0			0
$593$	−4.85529			−0.199383			−0.0996914	−	0.995018i	$-0.531786\pi$
$593$	−4.85529			−0.199383			−0.0996914	+	0.995018i	$0.531786\pi$
$594$		0			0
$595$	0.941944	+	0.643842i	0.0386159	+	0.0263949i
$596$		0			0
$597$	3.53834	−	2.57076i	0.144815	−	0.105214i
$598$		0			0
$599$	22.9942			0.939516			0.469758	−	0.882795i	$-0.344341\pi$
$599$	22.9942			0.939516			0.469758	+	0.882795i	$0.344341\pi$
$600$		0			0
$601$	4.36380			0.178003			0.0890016	−	0.996031i	$-0.471632\pi$
$601$	4.36380			0.178003			0.0890016	+	0.996031i	$0.471632\pi$
$602$		0			0
$603$	1.29915	−	0.943888i	0.0529055	−	0.0384381i
$604$		0			0
$605$	1.77051	−	1.36576i	0.0719814	−	0.0555261i
$606$		0			0
$607$	−13.1083			−0.532050			−0.266025	−	0.963966i	$-0.585710\pi$
$607$	−13.1083			−0.532050			−0.266025	+	0.963966i	$0.585710\pi$
$608$		0			0
$609$	0.271364	−	0.835172i	0.0109962	−	0.0338429i
$610$		0			0
$611$	0.398519	+	1.22651i	0.0161223	+	0.0496195i
$612$		0			0
$613$	−10.2030	+	31.4016i	−0.412095	+	1.26830i	0.502729	+	0.864444i	$0.332329\pi$
$613$	−10.2030	+	31.4016i	−0.412095	+	1.26830i	−0.914824	+	0.403853i	$0.867671\pi$
$614$		0			0
$615$	2.86267	+	8.01873i	0.115434	+	0.323347i
$616$		0			0
$617$	−0.722310	−	0.524789i	−0.0290791	−	0.0211272i	0.573151	−	0.819450i	$-0.305721\pi$
$617$	−0.722310	−	0.524789i	−0.0290791	−	0.0211272i	−0.602230	+	0.798323i	$0.705721\pi$
$618$		0			0
$619$	−18.5063	−	13.4456i	−0.743832	−	0.540425i	0.150077	−	0.988674i	$-0.452048\pi$
$619$	−18.5063	−	13.4456i	−0.743832	−	0.540425i	−0.893909	+	0.448249i	$0.852048\pi$
$620$		0			0
$621$	31.7546	−	23.0711i	1.27427	−	0.925811i
$622$		0			0
$623$	0.223186	+	0.686896i	0.00894176	+	0.0275199i
$624$		0			0
$625$	24.8350	−	2.86725i	0.993401	−	0.114690i
$626$		0			0
$627$	3.31026	+	10.1879i	0.132199	+	0.406867i
$628$		0			0
$629$	51.9212	−	37.7230i	2.07023	−	1.50411i
$630$		0			0
$631$	−24.4855	−	17.7897i	−0.974751	−	0.708198i	−0.0182216	−	0.999834i	$-0.505800\pi$
$631$	−24.4855	−	17.7897i	−0.974751	−	0.708198i	−0.956529	+	0.291636i	$0.905800\pi$
$632$		0			0
$633$	18.6282	+	13.5342i	0.740406	+	0.537937i
$634$		0			0
$635$	−10.6816	−	29.9208i	−0.423888	−	1.18737i
$636$		0			0
$637$	1.32006	−	4.06273i	0.0523028	−	0.160971i
$638$		0			0
$639$	−0.00825172	−	0.0253962i	−0.000326433	−	0.00100466i
$640$		0			0
$641$	−0.559205	+	1.72106i	−0.0220873	+	0.0679777i	−0.961493	−	0.274831i	$-0.911378\pi$
$641$	−0.559205	+	1.72106i	−0.0220873	+	0.0679777i	0.939405	+	0.342808i	$0.111378\pi$
$642$		0			0
$643$	−7.07286			−0.278926			−0.139463	−	0.990227i	$-0.544538\pi$
$643$	−7.07286			−0.278926			−0.139463	+	0.990227i	$0.544538\pi$
$644$		0			0
$645$	17.4118	−	13.4314i	0.685590	−	0.528861i
$646$		0			0
$647$	5.12654	−	3.72465i	0.201545	−	0.146431i	−0.482435	−	0.875932i	$-0.660248\pi$
$647$	5.12654	−	3.72465i	0.201545	−	0.146431i	0.683980	+	0.729501i	$0.260248\pi$
$648$		0			0
$649$	1.81480			0.0712373
$650$		0			0
$651$	−0.683846			−0.0268020
$652$		0			0
$653$	−21.6978	+	15.7644i	−0.849099	+	0.616907i	−0.924898	−	0.380216i	$-0.875850\pi$
$653$	−21.6978	+	15.7644i	−0.849099	+	0.616907i	0.0757983	+	0.997123i	$0.475850\pi$
$654$		0			0
$655$	14.7329	+	10.0703i	0.575664	+	0.393480i
$656$		0			0
$657$	−1.07971			−0.0421234
$658$		0			0
$659$	−1.36469	+	4.20009i	−0.0531608	+	0.163612i	−0.974112	−	0.226066i	$-0.927414\pi$
$659$	−1.36469	+	4.20009i	−0.0531608	+	0.163612i	0.920951	+	0.389678i	$0.127414\pi$
$660$		0			0
$661$	10.0351	+	30.8848i	0.390319	+	1.20128i	0.932548	+	0.361047i	$0.117581\pi$
$661$	10.0351	+	30.8848i	0.390319	+	1.20128i	−0.542229	+	0.840231i	$0.682419\pi$
$662$		0			0
$663$	2.26008	−	6.95580i	0.0877742	−	0.270141i
$664$		0			0
$665$	0.842556	+	0.575908i	0.0326729	+	0.0223327i
$666$		0			0
$667$	−43.1794	−	31.3717i	−1.67191	−	1.21472i
$668$		0			0
$669$	−13.3961	−	9.73284i	−0.517923	−	0.376293i
$670$		0			0
$671$	0.799183	−	0.580640i	0.0308521	−	0.0224154i
$672$		0			0
$673$	−2.17495	−	6.69381i	−0.0838381	−	0.258027i	0.900346	−	0.435174i	$-0.143313\pi$
$673$	−2.17495	−	6.69381i	−0.0838381	−	0.258027i	−0.984184	+	0.177147i	$0.943313\pi$
$674$		0			0
$675$	9.65478	+	24.7723i	0.371613	+	0.953487i
$676$		0			0
$677$	−8.22777	−	25.3225i	−0.316219	−	0.973222i	−0.975250	−	0.221106i	$-0.929033\pi$
$677$	−8.22777	−	25.3225i	−0.316219	−	0.973222i	0.659031	−	0.752116i	$-0.270967\pi$
$678$		0			0
$679$	−1.02451	+	0.744348i	−0.0393170	+	0.0285655i
$680$		0			0
$681$	−13.5443	−	9.84051i	−0.519018	−	0.377089i
$682$		0			0
$683$	−4.72642	−	3.43395i	−0.180852	−	0.131396i	0.493676	−	0.869646i	$-0.335653\pi$
$683$	−4.72642	−	3.43395i	−0.180852	−	0.131396i	−0.674528	+	0.738249i	$0.735653\pi$
$684$		0			0
$685$	4.93009	−	16.8013i	0.188369	−	0.641944i
$686$		0			0
$687$	−6.55039	+	20.1600i	−0.249913	+	0.769153i
$688$		0			0
$689$	1.09937	+	3.38352i	0.0418827	+	0.128902i
$690$		0			0
$691$	6.09934	−	18.7719i	0.232030	−	0.714115i	−0.765472	−	0.643470i	$-0.777494\pi$
$691$	6.09934	−	18.7719i	0.232030	−	0.714115i	0.997502	−	0.0706451i	$-0.0225058\pi$
$692$		0			0
$693$	0.0107560			0.000408586
$694$		0			0
$695$	17.6794	+	49.5225i	0.670618	+	1.87850i
$696$		0			0
$697$	−12.9424	+	9.40321i	−0.490229	+	0.356172i
$698$		0			0
$699$	−16.4512			−0.622240
$700$		0			0
$701$	26.3612			0.995648			0.497824	−	0.867278i	$-0.334133\pi$
$701$	26.3612			0.995648			0.497824	+	0.867278i	$0.334133\pi$
$702$		0			0
$703$	46.4428	−	33.7427i	1.75162	−	1.27263i
$704$		0			0
$705$	−2.24467	+	7.64961i	−0.0845391	+	0.288101i
$706$		0			0
$707$	0.320285			0.0120456
$708$		0			0
$709$	−5.81767	+	17.9049i	−0.218487	+	0.672434i	0.780400	+	0.625280i	$0.215015\pi$
$709$	−5.81767	+	17.9049i	−0.218487	+	0.672434i	−0.998888	+	0.0471544i	$0.984985\pi$
$710$		0			0
$711$	0.0965711	+	0.297215i	0.00362170	+	0.0111464i
$712$		0			0
$713$	−12.8437	+	39.5288i	−0.481000	+	1.48036i
$714$		0			0
$715$	−1.36503	+	0.0392359i	−0.0510491	+	0.00146734i
$716$		0			0
$717$	−4.90921	−	3.56675i	−0.183338	−	0.133203i
$718$		0			0
$719$	−24.1452	−	17.5425i	−0.900465	−	0.654226i	0.0381206	−	0.999273i	$-0.487863\pi$
$719$	−24.1452	−	17.5425i	−0.900465	−	0.654226i	−0.938585	+	0.345047i	$0.887863\pi$
$720$		0			0
$721$	0.328787	−	0.238878i	0.0122447	−	0.00889627i
$722$		0			0
$723$	11.1492	+	34.3137i	0.414644	+	1.27614i
$724$		0			0
$725$	27.9794	−	22.8951i	1.03913	−	0.850301i
$726$		0			0
$727$	8.89220	+	27.3674i	0.329793	+	1.01500i	0.969230	+	0.246156i	$0.0791676\pi$
$727$	8.89220	+	27.3674i	0.329793	+	1.01500i	−0.639437	+	0.768844i	$0.720832\pi$
$728$		0			0
$729$	−22.8209	+	16.5804i	−0.845220	+	0.614088i
$730$		0			0
$731$	33.4267	+	24.2859i	1.23633	+	0.898246i
$732$		0			0
$733$	25.6566	+	18.6406i	0.947646	+	0.688505i	0.950249	−	0.311491i	$-0.100828\pi$
$733$	25.6566	+	18.6406i	0.947646	+	0.688505i	−0.00260260	+	0.999997i	$0.500828\pi$
$734$		0			0
$735$	20.9090	−	16.1291i	0.771240	−	0.594931i
$736$		0			0
$737$	−3.31873	+	10.2140i	−0.122247	+	0.376238i
$738$		0			0
$739$	−0.712986	−	2.19434i	−0.0262276	−	0.0807202i	0.937086	−	0.349099i	$-0.113512\pi$
$739$	−0.712986	−	2.19434i	−0.0262276	−	0.0807202i	−0.963314	+	0.268378i	$0.913512\pi$
$740$		0			0
$741$	2.02161	−	6.22187i	0.0742657	−	0.228566i
$742$		0			0
$743$	26.9274			0.987871			0.493935	−	0.869499i	$-0.335558\pi$
$743$	26.9274			0.987871			0.493935	+	0.869499i	$0.335558\pi$
$744$		0			0
$745$	−31.2772	+	0.899022i	−1.14591	+	0.0329376i
$746$		0			0
$747$	−0.953624	+	0.692849i	−0.0348913	+	0.0253500i
$748$		0			0
$749$	0.00152239			5.56270e−5
$750$		0			0
$751$	−23.7671			−0.867272			−0.433636	−	0.901088i	$-0.642770\pi$
$751$	−23.7671			−0.867272			−0.433636	+	0.901088i	$0.642770\pi$
$752$		0			0
$753$	21.0123	−	15.2663i	0.765730	−	0.556336i
$754$		0			0
$755$	−52.7116	+	1.51513i	−1.91837	+	0.0551411i
$756$		0			0
$757$	23.7228			0.862219			0.431109	−	0.902300i	$-0.358122\pi$
$757$	23.7228			0.862219			0.431109	+	0.902300i	$0.358122\pi$
$758$		0			0
$759$	−3.85112	+	11.8525i	−0.139787	+	0.430219i
$760$		0			0
$761$	−14.8034	−	45.5602i	−0.536623	−	1.65155i	−0.740117	−	0.672479i	$-0.765230\pi$
$761$	−14.8034	−	45.5602i	−0.536623	−	1.65155i	0.203494	−	0.979076i	$-0.434770\pi$
$762$		0			0
$763$	0.355355	−	1.09367i	0.0128647	−	0.0395935i
$764$		0			0
$765$	−1.87783	+	1.44855i	−0.0678932	+	0.0523725i
$766$		0			0
$767$	−0.896649	−	0.651454i	−0.0323761	−	0.0235226i
$768$		0			0
$769$	8.60094	+	6.24895i	0.310158	+	0.225343i	0.731964	−	0.681343i	$-0.238604\pi$
$769$	8.60094	+	6.24895i	0.310158	+	0.225343i	−0.421806	+	0.906686i	$0.638604\pi$
$770$		0			0
$771$	−40.2295	+	29.2285i	−1.44883	+	1.05264i
$772$		0			0
$773$	4.63963	+	14.2793i	0.166876	+	0.513591i	0.999170	−	0.0407439i	$-0.0129728\pi$
$773$	4.63963	+	14.2793i	0.166876	+	0.513591i	−0.832294	+	0.554335i	$0.812973\pi$
$774$		0			0
$775$	−23.6895	−	15.2126i	−0.850953	−	0.546451i
$776$		0			0
$777$	0.339562	+	1.04506i	0.0121817	+	0.0374915i
$778$		0			0
$779$	−11.5768	+	8.41105i	−0.414782	+	0.301357i
$780$		0			0
$781$	0.144480	+	0.104971i	0.00516990	+	0.00375615i
$782$		0			0
$783$	31.1053	+	22.5993i	1.11161	+	0.807633i
$784$		0			0
$785$	−0.340610	+	0.00979039i	−0.0121569	+	0.000349434i
$786$		0			0
$787$	−9.87155	+	30.3815i	−0.351883	+	1.08298i	0.605912	+	0.795532i	$0.292808\pi$
$787$	−9.87155	+	30.3815i	−0.351883	+	1.08298i	−0.957795	+	0.287453i	$0.907192\pi$
$788$		0			0
$789$	−6.54405	−	20.1405i	−0.232974	−	0.717022i
$790$		0			0
$791$	0.305150	−	0.939155i	0.0108499	−	0.0333925i
$792$		0			0
$793$	−0.603286			−0.0214233
$794$		0			0
$795$	−6.19224	+	21.1026i	−0.219616	+	0.748430i
$796$		0			0
$797$	2.21625	−	1.61020i	0.0785037	−	0.0570363i	−0.547841	−	0.836582i	$-0.684550\pi$
$797$	2.21625	−	1.61020i	0.0785037	−	0.0570363i	0.626345	+	0.779546i	$0.284550\pi$
$798$		0			0
$799$	−14.9789			−0.529914
$800$		0			0
$801$	−1.50127			−0.0530447
$802$		0			0
$803$	5.84187	−	4.24436i	0.206155	−	0.149780i
$804$		0			0
$805$	0.399196	+	1.11820i	0.0140698	+	0.0394115i
$806$		0			0
$807$	11.7930			0.415134
$808$		0			0
$809$	−2.65341	+	8.16637i	−0.0932891	+	0.287114i	−0.986804	−	0.161919i	$-0.948232\pi$
$809$	−2.65341	+	8.16637i	−0.0932891	+	0.287114i	0.893515	+	0.449033i	$0.148232\pi$
$810$		0			0
$811$	7.33135	+	22.5636i	0.257439	+	0.792315i	0.993339	+	0.115225i	$0.0367590\pi$
$811$	7.33135	+	22.5636i	0.257439	+	0.792315i	−0.735901	+	0.677089i	$0.763241\pi$
$812$		0			0
$813$	10.9050	−	33.5620i	0.382454	−	1.17707i
$814$		0			0
$815$	−8.16272	+	27.8178i	−0.285927	+	0.974413i
$816$		0			0
$817$	29.8997	+	21.7234i	1.04606	+	0.760006i
$818$		0			0
$819$	−0.00531426	−	0.00386104i	−0.000185695	−	0.000134916i
$820$		0			0
$821$	42.3966	−	30.8030i	1.47965	−	1.07503i	0.501985	−	0.864876i	$-0.332603\pi$
$821$	42.3966	−	30.8030i	1.47965	−	1.07503i	0.977668	−	0.210154i	$-0.0673967\pi$
$822$		0			0
$823$	−2.62226	−	8.07048i	−0.0914061	−	0.281319i	0.894894	−	0.446278i	$-0.147251\pi$
$823$	−2.62226	−	8.07048i	−0.0914061	−	0.281319i	−0.986300	+	0.164959i	$0.947251\pi$
$824$		0			0
$825$	−7.10319	−	4.56142i	−0.247301	−	0.158808i
$826$		0			0
$827$	−4.13882	−	12.7380i	−0.143921	−	0.442943i	0.852950	−	0.521993i	$-0.174811\pi$
$827$	−4.13882	−	12.7380i	−0.143921	−	0.442943i	−0.996871	+	0.0790500i	$0.974811\pi$
$828$		0			0
$829$	−14.0994	+	10.2438i	−0.489694	+	0.355783i	−0.805066	−	0.593185i	$-0.797870\pi$
$829$	−14.0994	+	10.2438i	−0.489694	+	0.355783i	0.315373	+	0.948968i	$0.397870\pi$
$830$		0			0
$831$	−44.7966	−	32.5466i	−1.55398	−	1.12903i
$832$		0			0
$833$	40.1404	+	29.1637i	1.39078	+	1.01046i
$834$		0			0
$835$	−1.61144	−	1.10146i	−0.0557663	−	0.0381176i
$836$		0			0
$837$	9.25225	−	28.4755i	0.319804	−	0.984257i
$838$		0			0
$839$	6.66570	+	20.5149i	0.230125	+	0.708253i	0.997731	+	0.0673305i	$0.0214482\pi$
$839$	6.66570	+	20.5149i	0.230125	+	0.708253i	−0.767605	+	0.640923i	$0.778552\pi$
$840$		0			0
$841$	7.19429	−	22.1418i	0.248079	−	0.763509i
$842$		0			0
$843$	−4.05860			−0.139785
$844$		0			0
$845$	−23.3099	−	15.9329i	−0.801886	−	0.548108i
$846$		0			0
$847$	−0.0581964	+	0.0422821i	−0.00199965	+	0.00145283i
$848$		0			0
$849$	29.6299			1.01690
$850$		0			0
$851$	66.7860			2.28939
$852$		0			0
$853$	−20.9925	+	15.2520i	−0.718770	+	0.522217i	−0.885991	−	0.463703i	$-0.846521\pi$
$853$	−20.9925	+	15.2520i	−0.718770	+	0.522217i	0.167221	+	0.985919i	$0.446521\pi$
$854$		0			0
$855$	−1.67970	+	1.29571i	−0.0574444	+	0.0443123i
$856$		0			0
$857$	37.3189			1.27479			0.637394	−	0.770538i	$-0.280012\pi$
$857$	37.3189			1.27479			0.637394	+	0.770538i	$0.280012\pi$
$858$		0			0
$859$	15.8461	−	48.7694i	0.540663	−	1.66399i	−0.190422	−	0.981702i	$-0.560986\pi$
$859$	15.8461	−	48.7694i	0.540663	−	1.66399i	0.731085	−	0.682287i	$-0.239014\pi$
$860$		0			0
$861$	−0.0846427	−	0.260503i	−0.00288462	−	0.00887794i
$862$		0			0
$863$	5.04401	−	15.5239i	0.171700	−	0.528438i	−0.827767	−	0.561072i	$-0.810389\pi$
$863$	5.04401	−	15.5239i	0.171700	−	0.528438i	0.999467	+	0.0326330i	$0.0103893\pi$
$864$		0			0
$865$	12.3329	+	34.5463i	0.419332	+	1.17461i
$866$		0			0
$867$	45.5042	+	33.0608i	1.54541	+	1.12280i
$868$		0			0
$869$	−1.69087	−	1.22849i	−0.0573589	−	0.0416737i
$870$		0			0
$871$	5.30619	−	3.85517i	0.179793	−	0.130627i
$872$		0			0
$873$	−0.813418	−	2.50344i	−0.0275300	−	0.0847287i
$874$		0			0
$875$	−0.801267	+	0.0692468i	−0.0270878	+	0.00234097i
$876$		0			0
$877$	11.3077	+	34.8014i	0.381832	+	1.17516i	0.938752	+	0.344593i	$0.111983\pi$
$877$	11.3077	+	34.8014i	0.381832	+	1.17516i	−0.556920	+	0.830566i	$0.688017\pi$
$878$		0			0
$879$	−12.5822	+	9.14150i	−0.424387	+	0.308335i
$880$		0			0
$881$	−42.7038	−	31.0261i	−1.43873	−	1.04530i	−0.988306	−	0.152482i	$-0.951274\pi$
$881$	−42.7038	−	31.0261i	−1.43873	−	1.04530i	−0.450422	−	0.892816i	$-0.648726\pi$
$882$		0			0
$883$	−13.5075	−	9.81377i	−0.454563	−	0.330260i	0.336831	−	0.941565i	$-0.390645\pi$
$883$	−13.5075	−	9.81377i	−0.454563	−	0.330260i	−0.791395	+	0.611305i	$0.790645\pi$
$884$		0			0
$885$	−2.30351	−	6.45246i	−0.0774317	−	0.216897i
$886$		0			0
$887$	−1.11209	+	3.42267i	−0.0373404	+	0.114922i	−0.967989	−	0.250991i	$-0.919243\pi$
$887$	−1.11209	+	3.42267i	−0.0373404	+	0.114922i	0.930649	+	0.365913i	$0.119243\pi$
$888$		0			0
$889$	0.315832	+	0.972032i	0.0105927	+	0.0326009i
$890$		0			0
$891$	2.63563	−	8.11163i	0.0882968	−	0.271750i
$892$		0			0
$893$	−13.3984			−0.448360
$894$		0			0
$895$	−46.8558	+	36.1444i	−1.56622	+	1.20817i
$896$		0			0
$897$	6.15740	−	4.47361i	0.205590	−	0.149370i
$898$		0			0
$899$	−40.7131			−1.35786
$900$		0			0
$901$	−41.3213			−1.37661
$902$		0			0
$903$	−0.572325	+	0.415818i	−0.0190458	+	0.0138376i
$904$		0			0
$905$	23.7310	+	16.2207i	0.788847	+	0.539196i
$906$		0			0
$907$	32.4598			1.07781			0.538904	−	0.842367i	$-0.318838\pi$
$907$	32.4598			1.07781			0.538904	+	0.842367i	$0.318838\pi$
$908$		0			0
$909$	−0.205728	+	0.633165i	−0.00682356	+	0.0210008i
$910$		0			0
$911$	−12.3091	−	37.8834i	−0.407817	−	1.25513i	−0.918520	−	0.395375i	$-0.870615\pi$
$911$	−12.3091	−	37.8834i	−0.407817	−	1.25513i	0.510702	−	0.859758i	$-0.329385\pi$
$912$		0			0
$913$	2.43607	−	7.49746i	0.0806222	−	0.248130i
$914$		0			0
$915$	−3.07884	−	2.10446i	−0.101783	−	0.0695713i
$916$		0			0
$917$	−0.464458	−	0.337448i	−0.0153377	−	0.0111435i
$918$		0			0
$919$	−23.8408	−	17.3214i	−0.786435	−	0.571379i	0.120468	−	0.992717i	$-0.461560\pi$
$919$	−23.8408	−	17.3214i	−0.786435	−	0.571379i	−0.906903	+	0.421339i	$0.861560\pi$
$920$		0			0
$921$	13.2547	−	9.63010i	0.436757	−	0.317323i
$922$		0			0
$923$	−0.0337029	−	0.103727i	−0.00110935	−	0.00341421i
$924$		0			0
$925$	−11.4851	+	43.7565i	−0.377628	+	1.43870i
$926$		0			0
$927$	0.261043	+	0.803409i	0.00857379	+	0.0263874i
$928$		0			0
$929$	−12.4595	+	9.05232i	−0.408781	+	0.296997i	−0.773108	−	0.634274i	$-0.781299\pi$
$929$	−12.4595	+	9.05232i	−0.408781	+	0.296997i	0.364327	+	0.931271i	$0.381299\pi$
$930$		0			0
$931$	35.9051	+	26.0865i	1.17674	+	0.854952i
$932$		0			0
$933$	10.1318	+	7.36119i	0.331701	+	0.240995i
$934$		0			0
$935$	4.46590	−	15.2194i	0.146051	−	0.497726i
$936$		0			0
$937$	6.03486	−	18.5734i	0.197150	−	0.606766i	−0.802794	−	0.596256i	$-0.796654\pi$
$937$	6.03486	−	18.5734i	0.197150	−	0.606766i	0.999945	−	0.0105104i	$-0.00334563\pi$
$938$		0			0
$939$	11.7425	+	36.1397i	0.383202	+	1.17937i
$940$		0			0
$941$	−6.71302	+	20.6606i	−0.218838	+	0.673515i	0.780021	+	0.625754i	$0.215209\pi$
$941$	−6.71302	+	20.6606i	−0.218838	+	0.673515i	−0.998859	+	0.0477609i	$0.984791\pi$
$942$		0			0
$943$	−16.6478			−0.542126
$944$		0			0
$945$	−0.287570	−	0.805525i	−0.00935466	−	0.0262037i
$946$		0			0
$947$	−24.4051	+	17.7313i	−0.793059	+	0.576191i	−0.908870	−	0.417080i	$-0.863053\pi$
$947$	−24.4051	+	17.7313i	−0.793059	+	0.576191i	0.115811	+	0.993271i	$0.463053\pi$
$948$		0			0
$949$	−4.40990			−0.143152
$950$		0			0
$951$	38.4199			1.24585
$952$		0			0
$953$	5.43279	−	3.94715i	0.175985	−	0.127861i	−0.496306	−	0.868148i	$-0.665310\pi$
$953$	5.43279	−	3.94715i	0.175985	−	0.127861i	0.672291	+	0.740287i	$0.265310\pi$
$954$		0			0
$955$	15.4849	−	52.7711i	0.501080	−	1.70763i
$956$		0			0
$957$	−12.2076			−0.394617
$958$		0			0
$959$	−0.174066	+	0.535720i	−0.00562088	+	0.0172993i
$960$		0			0
$961$	0.217738	+	0.670129i	0.00702381	+	0.0216171i
$962$		0			0
$963$	−0.000977873		0.00300958i	−3.15115e−5		9.69825e-5i
$964$		0			0
$965$	34.7231	−	0.998071i	1.11778	−	0.0321290i
$966$		0			0
$967$	−9.15005	−	6.64790i	−0.294246	−	0.213782i	0.430861	−	0.902418i	$-0.358210\pi$
$967$	−9.15005	−	6.64790i	−0.294246	−	0.213782i	−0.725107	+	0.688636i	$0.758210\pi$
$968$		0			0
$969$	61.4730	+	44.6628i	1.97480	+	1.43478i
$970$		0			0
$971$	−7.35518	+	5.34385i	−0.236039	+	0.171492i	−0.699517	−	0.714616i	$-0.746601\pi$
$971$	−7.35518	+	5.34385i	−0.236039	+	0.171492i	0.463478	+	0.886109i	$0.346601\pi$
$972$		0			0
$973$	−0.522741	−	1.60883i	−0.0167583	−	0.0515767i
$974$		0			0
$975$	1.87211	+	4.80349i	0.0599556	+	0.153835i
$976$		0			0
$977$	7.45171	+	22.9340i	0.238401	+	0.733723i	0.996652	+	0.0817604i	$0.0260542\pi$
$977$	7.45171	+	22.9340i	0.238401	+	0.733723i	−0.758251	+	0.651963i	$0.773946\pi$
$978$		0			0
$979$	8.12277	−	5.90154i	0.259605	−	0.188614i
$980$		0			0
$981$	1.93380	+	1.40499i	0.0617414	+	0.0448577i
$982$		0			0
$983$	33.0752	+	24.0306i	1.05494	+	0.766456i	0.973145	−	0.230194i	$-0.0739360\pi$
$983$	33.0752	+	24.0306i	1.05494	+	0.766456i	0.0817911	+	0.996649i	$0.473936\pi$
$984$		0			0
$985$	−2.85011	+	2.19856i	−0.0908121	+	0.0700520i
$986$		0			0
$987$	0.0792521	−	0.243913i	0.00252262	−	0.00776383i
$988$		0			0
$989$	13.2867	+	40.8922i	0.422492	+	1.30030i
$990$		0			0
$991$	14.6701	−	45.1500i	0.466012	−	1.43424i	−0.391693	−	0.920096i	$-0.628111\pi$
$991$	14.6701	−	45.1500i	0.466012	−	1.43424i	0.857705	−	0.514142i	$-0.171889\pi$
$992$		0			0
$993$	−6.81939			−0.216407
$994$		0			0
$995$	−5.79014	+	0.166430i	−0.183560	+	0.00527619i
$996$		0			0
$997$	−10.3842	+	7.54455i	−0.328870	+	0.238938i	−0.739951	−	0.672661i	$-0.765151\pi$
$997$	−10.3842	+	7.54455i	−0.328870	+	0.238938i	0.411081	+	0.911599i	$0.365151\pi$
$998$		0			0
$999$	−48.1109			−1.52216

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1100.2.q.b.881.11	yes	52
25.21	even	5	inner	1100.2.q.b.221.11	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1100.2.q.b.221.11	✓	52	25.21	even	5	inner
1100.2.q.b.881.11	yes	52	1.1	even	1	trivial

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 1100 = 2^{2} \cdot 5^{2} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1100.q (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.36589 - 0.992379i) q^{3} +(-2.23514 + 0.0642463i) q^{5} +0.0719347 q^{7} +(-0.0462056 + 0.142206i) q^{9} +(-0.309017 - 0.951057i) q^{11} +(-0.188720 + 0.580820i) q^{13} +(-2.98921 + 2.30586i) q^{15} +(-5.73859 - 4.16933i) q^{17} +(-5.13309 - 3.72941i) q^{19} +(0.0982550 - 0.0713864i) q^{21} +(-2.28102 - 7.02024i) q^{23} +(4.99174 - 0.287200i) q^{25} +(1.64318 + 5.05720i) q^{27} +(5.84966 - 4.25003i) q^{29} +(-4.55532 - 3.30963i) q^{31} +(-1.36589 - 0.992379i) q^{33} +(-0.160784 + 0.00462154i) q^{35} +(-2.79590 + 8.60490i) q^{37} +(0.318622 + 0.980618i) q^{39} +(0.696936 - 2.14495i) q^{41} -5.82489 q^{43} +(0.0941399 - 0.320820i) q^{45} +(1.70840 - 1.24122i) q^{47} -6.99483 q^{49} -11.9758 q^{51} +(4.71286 - 3.42409i) q^{53} +(0.751800 + 2.10590i) q^{55} -10.7122 q^{57} +(-0.560805 + 1.72598i) q^{59} +(0.305261 + 0.939496i) q^{61} +(-0.00332378 + 0.0102295i) q^{63} +(0.384501 - 1.31034i) q^{65} +(-8.68855 - 6.31260i) q^{67} +(-10.0824 - 7.32526i) q^{69} +(-0.144480 + 0.104971i) q^{71} +(2.23139 + 6.86753i) q^{73} +(6.53317 - 5.34598i) q^{75} +(-0.0222290 - 0.0684139i) q^{77} +(1.69087 - 1.22849i) q^{79} +(6.90016 + 5.01326i) q^{81} +(6.37772 + 4.63369i) q^{83} +(13.0944 + 8.95037i) q^{85} +(3.77237 - 11.6102i) q^{87} +(3.10262 + 9.54889i) q^{89} +(-0.0135755 + 0.0417811i) q^{91} -9.50648 q^{93} +(11.7128 + 8.00598i) q^{95} +(-14.2422 + 10.3476i) q^{97} +0.149524 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q - 3 q^{5} - 9 q^{9} + 13 q^{11} + 12 q^{13} - 15 q^{15} + 8 q^{17} - 10 q^{19} - 6 q^{21} + 22 q^{23} + 5 q^{25} + 21 q^{27} + 12 q^{29} - 12 q^{31} + 30 q^{35} + 15 q^{37} - 20 q^{39} - 68 q^{43}+ \cdots - 56 q^{99}+O(q^{100}) \) 52 * q - 3 * q^5 - 9 * q^9 + 13 * q^11 + 12 * q^13 - 15 * q^15 + 8 * q^17 - 10 * q^19 - 6 * q^21 + 22 * q^23 + 5 * q^25 + 21 * q^27 + 12 * q^29 - 12 * q^31 + 30 * q^35 + 15 * q^37 - 20 * q^39 - 68 * q^43 - 7 * q^45 + 19 * q^47 + 68 * q^49 + 34 * q^51 + 3 * q^53 - 2 * q^55 - 24 * q^57 - 37 * q^59 + 10 * q^61 - 8 * q^63 + 12 * q^65 + 2 * q^67 + 27 * q^69 - 3 * q^71 + 4 * q^73 + 68 * q^75 - 17 * q^79 - 39 * q^81 + 78 * q^83 + 13 * q^85 + 13 * q^87 - 7 * q^89 - 2 * q^91 - 94 * q^93 + 18 * q^95 + 15 * q^97 - 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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