LMFDB - Embedded newform 175.2.x.a.47.10

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [175,2,Mod(3,175)] 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("175.3"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(175, base_ring=CyclotomicField(60)) chi = DirichletCharacter(H, H._module([21, 10])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 175 = 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	175.x (of order $60$, degree $16$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			47.10
Character	$\chi$	$=$	175.47
Dual form			175.2.x.a.108.10

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0137878 - 0.263087i) q^{2} +(1.98896 - 1.61063i) q^{3} +(1.92002 + 0.201802i) q^{4} +(-2.07716 - 0.827893i) q^{5} +(-0.396312 - 0.545476i) q^{6} +(0.819241 + 2.51572i) q^{7} +(0.161989 - 1.02276i) q^{8} +(0.738101 - 3.47249i) q^{9} +(-0.246448 + 0.535059i) q^{10} +(-3.43661 + 0.730475i) q^{11} +(4.14386 - 2.69106i) q^{12} +(-1.66634 + 3.27037i) q^{13} +(0.673149 - 0.180846i) q^{14} +(-5.46481 + 1.69888i) q^{15} +(3.50997 + 0.746068i) q^{16} +(-5.50381 + 2.11271i) q^{17} +(-0.903391 - 0.242063i) q^{18} +(-0.817063 - 7.77383i) q^{19} +(-3.82112 - 2.00875i) q^{20} +(5.68132 + 3.68417i) q^{21} +(0.144795 + 0.914201i) q^{22} +(6.38626 + 0.334690i) q^{23} +(-1.32509 - 2.29513i) q^{24} +(3.62919 + 3.43933i) q^{25} +(0.837417 + 0.483483i) q^{26} +(-0.639125 - 1.25435i) q^{27} +(1.06528 + 4.99555i) q^{28} +(0.147381 - 0.202852i) q^{29} +(0.371607 + 1.46115i) q^{30} +(0.511405 - 1.14863i) q^{31} +(0.780694 - 2.91359i) q^{32} +(-5.65876 + 6.98798i) q^{33} +(0.479943 + 1.47711i) q^{34} +(0.381053 - 5.90380i) q^{35} +(2.11792 - 6.51830i) q^{36} +(-2.68029 - 4.12728i) q^{37} +(-2.05646 + 0.107775i) q^{38} +(1.95307 + 9.18847i) q^{39} +(-1.18321 + 1.99033i) q^{40} +(0.567075 - 0.184254i) q^{41} +(1.04759 - 1.44389i) q^{42} +(-5.65218 + 5.65218i) q^{43} +(-6.74578 + 0.709010i) q^{44} +(-4.40800 + 6.60185i) q^{45} +(0.176105 - 1.67553i) q^{46} +(-0.376282 + 0.980249i) q^{47} +(8.18282 - 4.16936i) q^{48} +(-5.65769 + 4.12196i) q^{49} +(0.954883 - 0.907372i) q^{50} +(-7.54405 + 13.0667i) q^{51} +(-3.85937 + 5.94290i) q^{52} +(1.86365 + 2.30142i) q^{53} +(-0.338816 + 0.150851i) q^{54} +(7.74315 + 1.32784i) q^{55} +(2.70568 - 0.430367i) q^{56} +(-14.1458 - 14.1458i) q^{57} +(-0.0513357 - 0.0415708i) q^{58} +(3.73669 - 4.15002i) q^{59} +(-10.8354 + 2.15908i) q^{60} +(2.91370 - 2.62351i) q^{61} +(-0.295140 - 0.150381i) q^{62} +(9.34049 - 0.987952i) q^{63} +(6.06975 + 1.97218i) q^{64} +(6.16876 - 5.41353i) q^{65} +(1.76043 + 1.58510i) q^{66} +(-0.424905 - 1.10691i) q^{67} +(-10.9938 + 2.94577i) q^{68} +(13.2411 - 9.62020i) q^{69} +(-1.54796 - 0.181651i) q^{70} +(7.13505 + 5.18392i) q^{71} +(-3.43196 - 1.31741i) q^{72} +(-6.72347 - 4.36627i) q^{73} +(-1.12279 + 0.648243i) q^{74} +(12.7578 + 0.995427i) q^{75} -15.0908i q^{76} +(-4.65309 - 8.04712i) q^{77} +(2.44430 - 0.387139i) q^{78} +(-4.00368 - 8.99240i) q^{79} +(-6.67311 - 4.45558i) q^{80} +(6.43796 + 2.86636i) q^{81} +(-0.0406561 - 0.151731i) q^{82} +(-6.00511 - 0.951116i) q^{83} +(10.1648 + 8.22017i) q^{84} +(13.1814 + 0.168121i) q^{85} +(1.40908 + 1.56495i) q^{86} +(-0.0335849 - 0.640839i) q^{87} +(0.190406 + 3.63316i) q^{88} +(-2.57386 - 2.85856i) q^{89} +(1.67609 + 1.25071i) q^{90} +(-9.59246 - 1.51281i) q^{91} +(12.1942 + 1.93137i) q^{92} +(-0.832857 - 3.10827i) q^{93} +(0.252703 + 0.112511i) q^{94} +(-4.73874 + 16.8239i) q^{95} +(-3.13994 - 7.05242i) q^{96} +(10.0647 - 1.59410i) q^{97} +(1.00643 + 1.54530i) q^{98} +12.4728i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) $ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{17}{20}\right)$

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 $

$2$	0.0137878	−	0.263087i	0.00974946	−	0.186031i	−0.989413	−	0.145124i	$-0.953642\pi$
$2$	0.0137878	−	0.263087i	0.00974946	−	0.186031i	0.999163	−	0.0409070i	$-0.0130247\pi$
$3$	1.98896	−	1.61063i	1.14833	−	0.929895i	0.150054	−	0.988678i	$-0.452055\pi$
$3$	1.98896	−	1.61063i	1.14833	−	0.929895i	0.998271	+	0.0587824i	$0.0187218\pi$
$4$	1.92002	+	0.201802i	0.960009	+	0.100901i
$5$	−2.07716	−	0.827893i	−0.928934	−	0.370245i
$5$	−2.07716	−	0.827893i	−0.928934	−	0.370245i
$6$	−0.396312	−	0.545476i	−0.161794	−	0.222690i
$7$	0.819241	+	2.51572i	0.309644	+	0.950853i
$7$	0.819241	+	2.51572i	0.309644	+	0.950853i
$8$	0.161989	−	1.02276i	0.0572718	−	0.361600i
$9$	0.738101	−	3.47249i	0.246034	−	1.15750i
$10$	−0.246448	+	0.535059i	−0.0779336	+	0.169201i
$11$	−3.43661	+	0.730475i	−1.03618	+	0.220246i	−0.694441	−	0.719549i	$-0.744348\pi$
$11$	−3.43661	+	0.730475i	−1.03618	+	0.220246i	−0.341737	+	0.939796i	$0.611015\pi$
$12$	4.14386	−	2.69106i	1.19623	−	0.776841i
$13$	−1.66634	+	3.27037i	−0.462159	+	0.907037i	0.535871	+	0.844300i	$0.319983\pi$
$13$	−1.66634	+	3.27037i	−0.462159	+	0.907037i	−0.998030	+	0.0627378i	$0.980017\pi$
$14$	0.673149	−	0.180846i	0.179907	−	0.0483330i
$15$	−5.46481	+	1.69888i	−1.41101	+	0.438650i
$16$	3.50997	+	0.746068i	0.877493	+	0.186517i
$17$	−5.50381	+	2.11271i	−1.33487	+	0.512408i	−0.918008	−	0.396561i	$-0.870203\pi$
$17$	−5.50381	+	2.11271i	−1.33487	+	0.512408i	−0.416862	+	0.908970i	$0.636870\pi$
$18$	−0.903391	−	0.242063i	−0.212931	−	0.0570548i
$19$	−0.817063	−	7.77383i	−0.187447	−	1.78344i	−0.534075	−	0.845437i	$-0.679340\pi$
$19$	−0.817063	−	7.77383i	−0.187447	−	1.78344i	0.346628	−	0.938003i	$-0.387327\pi$
$20$	−3.82112	−	2.00875i	−0.854427	−	0.449169i
$21$	5.68132	+	3.68417i	1.23977	+	0.803951i
$22$	0.144795	+	0.914201i	0.0308704	+	0.194908i
$23$	6.38626	+	0.334690i	1.33163	+	0.0697877i	0.704820	−	0.709386i	$-0.251028\pi$
$23$	6.38626	+	0.334690i	1.33163	+	0.0697877i	0.626808	+	0.779174i	$0.284361\pi$
$24$	−1.32509	−	2.29513i	−0.270484	−	0.468491i
$25$	3.62919	+	3.43933i	0.725837	+	0.687867i
$26$	0.837417	+	0.483483i	0.164231	+	0.0948189i
$27$	−0.639125	−	1.25435i	−0.123000	−	0.241400i
$28$	1.06528	+	4.99555i	0.201319	+	0.944071i
$29$	0.147381	−	0.202852i	0.0273679	−	0.0376687i	−0.795114	−	0.606460i	$-0.792589\pi$
$29$	0.147381	−	0.202852i	0.0273679	−	0.0376687i	0.822482	+	0.568792i	$0.192589\pi$
$30$	0.371607	+	1.46115i	0.0678458	+	0.266767i
$31$	0.511405	−	1.14863i	0.0918510	−	0.206301i	−0.861778	−	0.507286i	$-0.830649\pi$
$31$	0.511405	−	1.14863i	0.0918510	−	0.206301i	0.953629	+	0.300985i	$0.0973155\pi$
$32$	0.780694	−	2.91359i	0.138009	−	0.515055i
$33$	−5.65876	+	6.98798i	−0.985063	+	1.21645i
$34$	0.479943	+	1.47711i	0.0823095	+	0.253323i
$35$	0.381053	−	5.90380i	0.0644097	−	0.997924i
$36$	2.11792	−	6.51830i	0.352987	−	1.08638i
$37$	−2.68029	−	4.12728i	−0.440636	−	0.678520i	0.546670	−	0.837348i	$-0.315895\pi$
$37$	−2.68029	−	4.12728i	−0.440636	−	0.678520i	−0.987306	+	0.158828i	$0.949229\pi$
$38$	−2.05646	+	0.107775i	−0.333602	+	0.0174834i
$39$	1.95307	+	9.18847i	0.312741	+	1.47133i
$40$	−1.18321	+	1.99033i	−0.187082	+	0.314698i
$41$	0.567075	−	0.184254i	0.0885622	−	0.0287756i	−0.264401	−	0.964413i	$-0.585174\pi$
$41$	0.567075	−	0.184254i	0.0885622	−	0.0287756i	0.352963	+	0.935637i	$0.385174\pi$
$42$	1.04759	−	1.44389i	0.161647	−	0.222796i
$43$	−5.65218	+	5.65218i	−0.861949	+	0.861949i	−0.991564	−	0.129616i	$-0.958626\pi$
$43$	−5.65218	+	5.65218i	−0.861949	+	0.861949i	0.129616	+	0.991564i	$0.458626\pi$
$44$	−6.74578	+	0.709010i	−1.01696	+	0.106887i
$45$	−4.40800	+	6.60185i	−0.657106	+	0.984145i
$46$	0.176105	−	1.67553i	0.0259653	−	0.247043i
$47$	−0.376282	+	0.980249i	−0.0548864	+	0.142984i	−0.958282	−	0.285824i	$-0.907733\pi$
$47$	−0.376282	+	0.980249i	−0.0548864	+	0.142984i	0.903396	+	0.428808i	$0.141066\pi$
$48$	8.18282	−	4.16936i	1.18109	−	0.601795i
$49$	−5.65769	+	4.12196i	−0.808241	+	0.588852i
$50$	0.954883	−	0.907372i	0.135041	−	0.128322i
$51$	−7.54405	+	13.0667i	−1.05638	+	1.82970i
$52$	−3.85937	+	5.94290i	−0.535198	+	0.824132i
$53$	1.86365	+	2.30142i	0.255992	+	0.316124i	0.888898	−	0.458104i	$-0.151471\pi$
$53$	1.86365	+	2.30142i	0.255992	+	0.316124i	−0.632906	+	0.774229i	$0.718138\pi$
$54$	−0.338816	+	0.150851i	−0.0461071	+	0.0205282i
$55$	7.74315	+	1.32784i	1.04409	+	0.179045i
$56$	2.70568	−	0.430367i	0.361562	−	0.0575103i
$57$	−14.1458	−	14.1458i	−1.87366	−	1.87366i
$58$	−0.0513357	−	0.0415708i	−0.00674071	−	0.00545852i
$59$	3.73669	−	4.15002i	0.486476	−	0.540286i	−0.449068	−	0.893498i	$-0.648244\pi$
$59$	3.73669	−	4.15002i	0.486476	−	0.540286i	0.935543	+	0.353212i	$0.114910\pi$
$60$	−10.8354	+	2.15908i	−1.39884	+	0.278736i
$61$	2.91370	−	2.62351i	0.373062	−	0.335906i	−0.461179	−	0.887307i	$-0.652573\pi$
$61$	2.91370	−	2.62351i	0.373062	−	0.335906i	0.834240	+	0.551401i	$0.185907\pi$
$62$	−0.295140	−	0.150381i	−0.0374828	−	0.0190984i
$63$	9.34049	−	0.987952i	1.17679	−	0.124470i
$64$	6.06975	+	1.97218i	0.758719	+	0.246523i
$65$	6.16876	−	5.41353i	0.765141	−	0.671466i
$66$	1.76043	+	1.58510i	0.216694	+	0.195112i
$67$	−0.424905	−	1.10691i	−0.0519104	−	0.135231i	0.905173	−	0.425042i	$-0.139741\pi$
$67$	−0.424905	−	1.10691i	−0.0519104	−	0.135231i	−0.957084	+	0.289811i	$0.906407\pi$
$68$	−10.9938	+	2.94577i	−1.33319	+	0.357227i
$69$	13.2411	−	9.62020i	1.59404	−	1.15814i
$70$	−1.54796	−	0.181651i	−0.185017	−	0.0217114i
$71$	7.13505	+	5.18392i	0.846775	+	0.615218i	0.924255	−	0.381776i	$-0.124687\pi$
$71$	7.13505	+	5.18392i	0.846775	+	0.615218i	−0.0774798	+	0.996994i	$0.524687\pi$
$72$	−3.43196	−	1.31741i	−0.404460	−	0.155258i
$73$	−6.72347	−	4.36627i	−0.786923	−	0.511034i	0.0875197	−	0.996163i	$-0.472106\pi$
$73$	−6.72347	−	4.36627i	−0.786923	−	0.511034i	−0.874443	+	0.485129i	$0.838773\pi$
$74$	−1.12279	+	0.648243i	−0.130522	+	0.0753567i
$75$	12.7578	+	0.995427i	1.47314	+	0.114942i
$76$		−	15.0908i		−	1.73103i
$77$	−4.65309	−	8.04712i	−0.530268	−	0.917055i
$78$	2.44430	−	0.387139i	0.276762	−	0.0438348i
$79$	−4.00368	−	8.99240i	−0.450449	−	1.01172i	−0.985927	−	0.167176i	$-0.946535\pi$
$79$	−4.00368	−	8.99240i	−0.450449	−	1.01172i	0.535478	−	0.844549i	$-0.320131\pi$
$80$	−6.67311	−	4.45558i	−0.746076	−	0.498149i
$81$	6.43796	+	2.86636i	0.715329	+	0.318485i
$82$	−0.0406561	−	0.151731i	−0.00448972	−	0.0167558i
$83$	−6.00511	−	0.951116i	−0.659146	−	0.104399i	−0.182105	−	0.983279i	$-0.558291\pi$
$83$	−6.00511	−	0.951116i	−0.659146	−	0.104399i	−0.477042	+	0.878881i	$0.658291\pi$
$84$	10.1648	+	8.22017i	1.10907	+	0.896895i
$85$	13.1814	+	0.168121i	1.42972	+	0.0182353i
$86$	1.40908	+	1.56495i	0.151945	+	0.168753i
$87$	−0.0335849	−	0.640839i	−0.00360068	−	0.0687051i
$88$	0.190406	+	3.63316i	0.0202973	+	0.387296i
$89$	−2.57386	−	2.85856i	−0.272829	−	0.303007i	0.591123	−	0.806581i	$-0.298685\pi$
$89$	−2.57386	−	2.85856i	−0.272829	−	0.303007i	−0.863952	+	0.503574i	$0.832018\pi$
$90$	1.67609	+	1.25071i	0.176675	+	0.131837i
$91$	−9.59246	−	1.51281i	−1.00556	−	0.158586i
$92$	12.1942	+	1.93137i	1.27133	+	0.201360i
$93$	−0.832857	−	3.10827i	−0.0863633	−	0.322312i
$94$	0.252703	+	0.112511i	0.0260643	+	0.0116046i
$95$	−4.73874	+	16.8239i	−0.486184	+	1.72610i
$96$	−3.13994	−	7.05242i	−0.320469	−	0.719784i
$97$	10.0647	−	1.59410i	1.02192	−	0.161856i	0.377085	−	0.926179i	$-0.376927\pi$
$97$	10.0647	−	1.59410i	1.02192	−	0.161856i	0.644834	+	0.764323i	$0.276927\pi$
$98$	1.00643	+	1.54530i	0.101665	+	0.156099i
$99$			12.4728i			1.25356i
$100$	6.27404	+	7.33596i	0.627404	+	0.733596i
$101$	9.38700	−	5.41959i	0.934041	−	0.539269i	0.0459539	−	0.998944i	$-0.485367\pi$
$101$	9.38700	−	5.41959i	0.934041	−	0.539269i	0.888087	+	0.459675i	$0.152034\pi$
$102$	3.33366	+	2.16490i	0.330082	+	0.214357i
$103$	4.60289	+	1.76689i	0.453537	+	0.174096i	0.574403	−	0.818572i	$-0.305234\pi$
$103$	4.60289	+	1.76689i	0.453537	+	0.174096i	−0.120867	+	0.992669i	$0.538567\pi$
$104$	3.07487	+	2.23403i	0.301516	+	0.219064i
$105$	−8.75091	−	12.3561i	−0.854001	−	1.20583i
$106$	0.631170	−	0.458572i	0.0613046	−	0.0445404i
$107$	8.33275	−	2.23275i	0.805557	−	0.215848i	0.167535	−	0.985866i	$-0.446419\pi$
$107$	8.33275	−	2.23275i	0.805557	−	0.215848i	0.638022	+	0.770018i	$0.279753\pi$
$108$	−0.974000	−	2.53736i	−0.0937232	−	0.244157i
$109$	−6.47269	−	5.82804i	−0.619972	−	0.558225i	0.298152	−	0.954518i	$-0.403630\pi$
$109$	−6.47269	−	5.82804i	−0.619972	−	0.558225i	−0.918124	+	0.396293i	$0.870296\pi$
$110$	0.456098	−	2.01882i	0.0434873	−	0.192487i
$111$	−11.9785	−	3.89204i	−1.13695	−	0.369416i
$112$	0.998616	+	9.44131i	0.0943604	+	0.892120i
$113$	−7.05314	−	3.59375i	−0.663504	−	0.338072i	0.0895963	−	0.995978i	$-0.471442\pi$
$113$	−7.05314	−	3.59375i	−0.663504	−	0.338072i	−0.753100	+	0.657906i	$0.771442\pi$
$114$	−3.91663	+	3.52655i	−0.366826	+	0.330292i
$115$	−12.9882	−	5.98235i	−1.21116	−	0.557857i
$116$	0.323909	−	0.359738i	0.0300742	−	0.0334008i
$117$	10.1264	+	8.20020i	0.936186	+	0.758109i
$118$	−1.04030	−	1.04030i	−0.0957670	−	0.0957670i
$119$	−9.82394	−	12.1152i	−0.900559	−	1.11060i
$120$	0.852309	+	5.86439i	0.0778048	+	0.535343i
$121$	1.22772	−	0.546618i	0.111611	−	0.0496925i
$122$	−0.650039	−	0.802731i	−0.0588517	−	0.0726759i
$123$	0.831124	−	1.27982i	0.0749399	−	0.115397i
$124$	1.21370	−	2.10220i	0.108994	−	0.188783i
$125$	−4.69100	−	10.1486i	−0.419576	−	0.907720i
$126$	−0.131133	−	2.47099i	−0.0116822	−	0.220133i
$127$	−8.76051	+	4.46370i	−0.777370	+	0.396090i	−0.797201	−	0.603714i	$-0.793687\pi$
$127$	−8.76051	+	4.46370i	−0.777370	+	0.396090i	0.0198315	+	0.999803i	$0.493687\pi$
$128$	2.76449	−	7.20173i	0.244348	−	0.636549i
$129$	−2.13840	+	20.3455i	−0.188275	+	1.79132i
$130$	−1.33918	−	1.69756i	−0.117454	−	0.148886i
$131$	−13.5234	+	1.42136i	−1.18154	+	0.124185i	−0.674858	−	0.737947i	$-0.735795\pi$
$131$	−13.5234	+	1.42136i	−1.18154	+	0.124185i	−0.506683	+	0.862132i	$0.669129\pi$
$132$	−12.2751	+	12.2751i	−1.06841	+	1.06841i
$133$	18.8874	−	8.42415i	1.63775	−	0.730466i
$134$	−0.297074	+	0.0965251i	−0.0256633	+	0.00833850i
$135$	0.289094	+	3.13462i	0.0248812	+	0.269785i
$136$	1.26924	+	5.97131i	0.108837	+	0.512036i
$137$	6.09072	−	0.319201i	0.520365	−	0.0272712i	0.209654	−	0.977776i	$-0.432766\pi$
$137$	6.09072	−	0.319201i	0.520365	−	0.0272712i	0.310711	+	0.950504i	$0.399433\pi$
$138$	−2.34839	−	3.61620i	−0.199908	−	0.307831i
$139$	0.132140	−	0.406687i	0.0112080	−	0.0344947i	−0.945296	−	0.326214i	$-0.894227\pi$
$139$	0.132140	−	0.406687i	0.0112080	−	0.0344947i	0.956504	+	0.291719i	$0.0942272\pi$
$140$	1.92303	−	11.2585i	0.162525	−	0.951517i
$141$	0.830405	+	2.55572i	0.0699327	+	0.215231i
$142$	1.46220	−	1.80567i	0.122705	−	0.151528i
$143$	3.33763	−	12.4562i	0.279107	−	1.04164i
$144$	5.18142	−	11.6377i	0.431785	−	0.969806i
$145$	−0.474073	+	0.299341i	−0.0393696	+	0.0248589i
$146$	−1.24141	+	1.70866i	−0.102740	+	0.141410i
$147$	−4.61396	+	17.3108i	−0.380553	+	1.42777i
$148$	−4.31331	−	8.46534i	−0.354552	−	0.695847i
$149$	−2.78363	−	1.60713i	−0.228044	−	0.131661i	0.381626	−	0.924317i	$-0.375364\pi$
$149$	−2.78363	−	1.60713i	−0.228044	−	0.131661i	−0.609669	+	0.792656i	$0.708698\pi$
$150$	0.437786	−	3.34268i	0.0357451	−	0.272929i
$151$	2.73858	+	4.74335i	0.222862	+	0.386009i	0.955676	−	0.294421i	$-0.0951267\pi$
$151$	2.73858	+	4.74335i	0.222862	+	0.386009i	−0.732814	+	0.680429i	$0.761793\pi$
$152$	−8.08312	−	0.423618i	−0.655628	−	0.0343600i
$153$	3.27401	+	20.6713i	0.264688	+	1.67118i
$154$	−2.18125	+	1.11322i	−0.175770	+	0.0897054i
$155$	−2.01322	+	1.96251i	−0.161705	+	0.157632i
$156$	1.89568	+	18.0362i	0.151776	+	1.44405i
$157$	19.5687	+	5.24342i	1.56175	+	0.418471i	0.933218	−	0.359310i	$-0.116988\pi$
$157$	19.5687	+	5.24342i	1.56175	+	0.418471i	0.628535	+	0.777781i	$0.283655\pi$
$158$	−2.42099	+	0.929331i	−0.192604	+	0.0739336i
$159$	7.41345	+	1.57578i	0.587925	+	0.124967i
$160$	−4.03377	+	5.40566i	−0.318898	+	0.427355i
$161$	4.38990	+	16.3402i	0.345973	+	1.28779i
$162$	0.842869	−	1.65422i	0.0662221	−	0.129968i
$163$	−7.30125	+	4.74149i	−0.571878	+	0.371382i	−0.797945	−	0.602730i	$-0.794080\pi$
$163$	−7.30125	+	4.74149i	−0.571878	+	0.371382i	0.226067	+	0.974112i	$0.427413\pi$
$164$	1.12598	−	0.239334i	0.0879241	−	0.0186888i
$165$	17.5394	−	9.83031i	1.36544	−	0.765289i
$166$	−0.333024	+	1.56675i	−0.0258477	+	0.121604i
$167$	−3.05970	+	19.3182i	−0.236767	+	1.49489i	0.527262	+	0.849703i	$0.323219\pi$
$167$	−3.05970	+	19.3182i	−0.236767	+	1.49489i	−0.764029	+	0.645182i	$0.776781\pi$
$168$	4.68833	−	5.21383i	0.361713	−	0.402256i
$169$	−0.277432	−	0.381852i	−0.0213409	−	0.0293732i
$170$	0.225973	−	3.46554i	0.0173314	−	0.265795i
$171$	−27.5976	−	2.90063i	−2.11044	−	0.221817i
$172$	−11.9929	+	9.71166i	−0.914451	+	0.740507i
$173$	0.439511	−	8.38638i	0.0334154	−	0.637604i	−0.929668	−	0.368400i	$-0.879906\pi$
$173$	0.439511	−	8.38638i	0.0334154	−	0.637604i	0.963083	−	0.269205i	$-0.0867609\pi$
$174$	−0.169060			−0.0128164
$175$	−5.67922	+	11.9477i	−0.429309	+	0.903158i
$176$	−12.6074			−0.950319
$177$	0.747996	−	14.2726i	0.0562229	−	1.07280i
$178$	−0.787540	+	0.637737i	−0.0590286	+	0.0478004i
$179$	−15.2840	−	1.60642i	−1.14238	−	0.120069i	−0.485623	−	0.874168i	$-0.661407\pi$
$179$	−15.2840	−	1.60642i	−1.14238	−	0.120069i	−0.656761	+	0.754099i	$0.728074\pi$
$180$	−9.79572	+	11.7861i	−0.730130	+	0.878486i
$181$	−4.54675	−	6.25807i	−0.337957	−	0.465159i	0.605886	−	0.795551i	$-0.292819\pi$
$181$	−4.54675	−	6.25807i	−0.337957	−	0.465159i	−0.943843	+	0.330393i	$0.892819\pi$
$182$	−0.530261	+	2.50280i	−0.0393056	+	0.185520i
$183$	1.56974	−	9.91094i	0.116038	−	0.732638i
$184$	1.37681	−	6.47740i	0.101500	−	0.477520i
$185$	2.15044	+	10.7920i	0.158103	+	0.793444i
$186$	−0.829229	+	0.176258i	−0.0608020	+	0.0129239i
$187$	17.3712	−	11.2810i	1.27031	−	0.824947i
$188$	−0.920285	+	1.80616i	−0.0671187	+	0.131728i
$189$	2.63200	−	2.63548i	0.191450	−	0.191703i
$190$	4.36083	+	1.47867i	0.316368	+	0.107274i
$191$	6.76057	+	1.43700i	0.489178	+	0.103978i	0.445896	−	0.895085i	$-0.352885\pi$
$191$	6.76057	+	1.43700i	0.489178	+	0.103978i	0.0432821	+	0.999063i	$0.486219\pi$
$192$	15.2489	−	5.85351i	1.10050	−	0.422441i
$193$	9.53984	+	2.55619i	0.686693	+	0.183999i	0.585262	−	0.810844i	$-0.300991\pi$
$193$	9.53984	+	2.55619i	0.686693	+	0.183999i	0.101430	+	0.994843i	$0.467658\pi$
$194$	−0.280616	−	2.66988i	−0.0201470	−	0.191686i
$195$	3.55024	−	20.7029i	0.254238	−	1.48256i
$196$	−11.6947	+	6.77251i	−0.835335	+	0.483751i
$197$	−0.927819	−	5.85802i	−0.0661044	−	0.417367i	−0.998443	−	0.0557804i	$-0.982235\pi$
$197$	−0.927819	−	5.85802i	−0.0661044	−	0.417367i	0.932339	−	0.361586i	$-0.117765\pi$
$198$	3.28143	+	0.171972i	0.233201	+	0.0122215i
$199$	0.710570	+	1.23074i	0.0503709	+	0.0872450i	0.890112	−	0.455743i	$-0.150626\pi$
$199$	0.710570	+	1.23074i	0.0503709	+	0.0872450i	−0.839741	+	0.542988i	$0.817293\pi$
$200$	4.10550	−	3.15465i	0.290303	−	0.223067i
$201$	−2.62794	−	1.51724i	−0.185361	−	0.107018i
$202$	−1.29640	−	2.54432i	−0.0912142	−	0.179018i
$203$	0.631059	+	0.204584i	0.0442916	+	0.0143589i
$204$	−17.1216	+	23.5659i	−1.19875	+	1.64994i
$205$	−1.33045	−	0.0867529i	−0.0929225	−	0.00605909i
$206$	0.528309	−	1.18660i	0.0368090	−	0.0826744i
$207$	5.87591	−	21.9292i	0.408404	−	1.52418i
$208$	−8.28871	+	10.2357i	−0.574719	+	0.709719i
$209$	8.48652	+	26.1188i	0.587025	+	1.80668i
$210$	−3.37140	+	2.13189i	−0.232648	+	0.147114i
$211$	4.15174	−	12.7778i	0.285818	−	0.879657i	−0.700335	−	0.713815i	$-0.746966\pi$
$211$	4.15174	−	12.7778i	0.285818	−	0.879657i	0.986152	−	0.165842i	$-0.0530341\pi$
$212$	3.11382	+	4.79486i	0.213858	+	0.329312i
$213$	22.5407	−	1.18131i	1.54446	−	0.0809418i
$214$	−0.472518	−	2.22302i	−0.0323007	−	0.151963i
$215$	16.4199	−	7.06107i	1.11983	−	0.481561i
$216$	−1.38643	+	0.450479i	−0.0943348	+	0.0306512i
$217$	3.30861	+	0.345543i	0.224603	+	0.0234570i
$218$	−1.62253	+	1.62253i	−0.109891	+	0.109891i
$219$	−20.4051	+	2.14467i	−1.37885	+	0.144923i
$220$	14.5990	+	4.11206i	0.984267	+	0.277235i
$221$	2.26184	−	21.5200i	0.152148	−	1.44759i
$222$	−1.18910	+	3.09772i	−0.0798074	+	0.207905i
$223$	−18.4692	+	9.41051i	−1.23679	+	0.630175i	−0.945238	−	0.326381i	$-0.894171\pi$
$223$	−18.4692	+	9.41051i	−1.23679	+	0.630175i	−0.291549	+	0.956556i	$0.594171\pi$
$224$	7.96936	−	0.422925i	0.532475	−	0.0282579i
$225$	14.6218	−	10.0637i	0.974784	−	0.670916i
$226$	−1.04272	+	1.80604i	−0.0693606	+	0.120136i
$227$	−8.00585	+	12.3279i	−0.531367	+	0.818233i	−0.997798	−	0.0663243i	$-0.978873\pi$
$227$	−8.00585	+	12.3279i	−0.531367	+	0.818233i	0.466431	+	0.884557i	$0.345539\pi$
$228$	−24.3056	−	30.0149i	−1.60968	−	1.98779i
$229$	−18.2779	+	8.13786i	−1.20784	+	0.537765i	−0.909103	−	0.416571i	$-0.863232\pi$
$229$	−18.2779	+	8.13786i	−1.20784	+	0.537765i	−0.298736	+	0.954336i	$0.596565\pi$
$230$	−1.75296	+	3.33455i	−0.115587	+	0.219874i
$231$	−22.2157	−	8.51100i	−1.46169	−	0.559983i
$232$	−0.183595	−	0.183595i	−0.0120536	−	0.0120536i
$233$	5.31044	+	4.30031i	0.347899	+	0.281723i	0.787303	−	0.616567i	$-0.211477\pi$
$233$	5.31044	+	4.30031i	0.347899	+	0.281723i	−0.439404	+	0.898290i	$0.644810\pi$
$234$	2.29699	−	2.55106i	0.150159	−	0.166768i
$235$	1.59314	−	1.72461i	0.103925	−	0.112501i
$236$	8.01200	−	7.21404i	0.521537	−	0.469594i
$237$	−22.4465	−	11.4371i	−1.45806	−	0.742918i
$238$	−3.32281	+	2.41751i	−0.215386	+	0.156704i
$239$	4.07114	+	1.32279i	0.263340	+	0.0855644i	0.437711	−	0.899116i	$-0.355789\pi$
$239$	4.07114	+	1.32279i	0.263340	+	0.0855644i	−0.174371	+	0.984680i	$0.555789\pi$
$240$	−20.4488	+	1.88591i	−1.31996	+	0.121735i
$241$	−2.71942	−	2.44858i	−0.175173	−	0.157727i	0.576880	−	0.816829i	$-0.304270\pi$
$241$	−2.71942	−	2.44858i	−0.175173	−	0.157727i	−0.752054	+	0.659102i	$0.770937\pi$
$242$	−0.126880	−	0.330535i	−0.00815619	−	0.0212476i
$243$	21.5009	−	5.76116i	1.37929	−	0.369579i
$244$	6.12380	−	4.44920i	0.392036	−	0.284831i
$245$	15.1645	−	3.87801i	0.968822	−	0.247757i
$246$	−0.325245	−	0.236304i	−0.0207368	−	0.0150662i
$247$	26.7848	+	10.2817i	1.70428	+	0.654211i
$248$	−1.09193	−	0.709111i	−0.0693379	−	0.0450286i
$249$	−13.4758	+	7.78025i	−0.853994	+	0.493054i
$250$	−2.73465	+	1.09421i	−0.172955	+	0.0692042i
$251$			23.2521i			1.46766i	0.679334	+	0.733829i	$0.262269\pi$
$251$			23.2521i			1.46766i	−0.679334	+	0.733829i	$0.737731\pi$
$252$	18.1333	−	0.0119562i	1.14229	−	0.000753172i
$253$	−22.1916	+	3.51481i	−1.39517	+	0.220974i
$254$	1.05356	+	2.36632i	0.0661059	+	0.148476i
$255$	26.4880	−	20.8959i	1.65874	−	1.30855i
$256$	9.80414	+	4.36508i	0.612759	+	0.272818i
$257$	−0.0840686	−	0.313748i	−0.00524406	−	0.0195711i	0.963254	−	0.268591i	$-0.0865581\pi$
$257$	−0.0840686	−	0.313748i	−0.00524406	−	0.0195711i	−0.968498	+	0.249020i	$0.919891\pi$
$258$	5.32315	+	0.843105i	0.331405	+	0.0524894i
$259$	8.18727	−	10.1241i	0.508732	−	0.629080i
$260$	12.9366	−	9.14921i	0.802294	−	0.567410i
$261$	−0.595620	−	0.661503i	−0.0368679	−	0.0409460i
$262$	0.187485	+	3.57742i	0.0115828	+	0.221014i
$263$	−0.353542	−	6.74598i	−0.0218003	−	0.415975i	−0.987631	−	0.156799i	$-0.949882\pi$
$263$	−0.353542	−	6.74598i	−0.0218003	−	0.415975i	0.965830	−	0.259176i	$-0.0834509\pi$
$264$	6.23037	+	6.91953i	0.383453	+	0.425867i
$265$	−1.96577	−	6.32332i	−0.120757	−	0.388439i
$266$	−1.95587	−	5.08519i	−0.119922	−	0.311793i
$267$	−9.72338	−	1.54003i	−0.595061	−	0.0942484i
$268$	−0.592447	−	2.21104i	−0.0361895	−	0.135061i
$269$	−0.532457	−	0.237065i	−0.0324645	−	0.0144541i	0.390440	−	0.920628i	$-0.372323\pi$
$269$	−0.532457	−	0.237065i	−0.0324645	−	0.0144541i	−0.422905	+	0.906174i	$0.638989\pi$
$270$	0.828664	−	0.0328373i	0.0504309	−	0.00199842i
$271$	7.55674	+	16.9727i	0.459039	+	1.03102i	0.983718	+	0.179719i	$0.0575187\pi$
$271$	7.55674	+	16.9727i	0.459039	+	1.03102i	−0.524679	+	0.851300i	$0.675815\pi$
$272$	−20.8944	+	3.30935i	−1.26691	+	0.200659i
$273$	−21.5156	+	12.4409i	−1.30218	+	0.752960i
$274$		−	1.60679i		−	0.0970698i
$275$	−14.9845	−	9.16863i	−0.903597	−	0.552889i
$276$	27.3645	−	15.7989i	1.64715	−	0.950981i
$277$	−1.25976	−	0.818099i	−0.0756917	−	0.0491548i	0.506238	−	0.862394i	$-0.331036\pi$
$277$	−1.25976	−	0.818099i	−0.0756917	−	0.0491548i	−0.581930	+	0.813239i	$0.697702\pi$
$278$	−0.105172	−	0.0403718i	−0.00630781	−	0.00242134i
$279$	−3.61115	−	2.62366i	−0.216194	−	0.157074i
$280$	−5.97644	−	1.34608i	−0.357160	−	0.0804435i
$281$	24.2076	−	17.5878i	1.44410	−	1.04920i	0.456936	−	0.889499i	$-0.348947\pi$
$281$	24.2076	−	17.5878i	1.44410	−	1.04920i	0.987165	−	0.159702i	$-0.0510533\pi$
$282$	0.683827	−	0.183231i	0.0407213	−	0.0109112i
$283$	3.21935	+	8.38668i	0.191370	+	0.498537i	0.995373	−	0.0960894i	$-0.0306335\pi$
$283$	3.21935	+	8.38668i	0.191370	+	0.498537i	−0.804002	+	0.594626i	$0.797300\pi$
$284$	12.6533	+	11.3931i	0.750836	+	0.676056i
$285$	17.6719	+	41.0944i	1.04679	+	2.43422i
$286$	−3.23105	−	1.04983i	−0.191056	−	0.0620779i
$287$	0.928102	+	1.27565i	0.0547841	+	0.0752994i
$288$	−9.54119	−	4.86148i	−0.562220	−	0.286465i
$289$	13.1949	−	11.8807i	0.776170	−	0.698867i
$290$	0.0722163	+	0.128850i	0.00424068	+	0.00756632i
$291$	17.4508	−	19.3811i	1.02299	−	1.13614i
$292$	−12.0281	−	9.74014i	−0.703889	−	0.569998i
$293$	19.5938	+	19.5938i	1.14468	+	1.14468i	0.987583	+	0.157096i	$0.0502132\pi$
$293$	19.5938	+	19.5938i	1.14468	+	1.14468i	0.157096	+	0.987583i	$0.449787\pi$
$294$	4.49064	+	1.45255i	0.261900	+	0.0847146i
$295$	−11.1975	+	5.52667i	−0.651942	+	0.321775i
$296$	−4.65539	+	2.07271i	−0.270589	+	0.120474i
$297$	3.11270	+	3.84386i	0.180617	+	0.223043i
$298$	−0.461195	+	0.710179i	−0.0267163	+	0.0411395i
$299$	−11.7362	+	20.3277i	−0.678723	+	1.17558i
$300$	24.2943	+	4.48579i	1.40263	+	0.258987i
$301$	−18.8498	−	9.58879i	−1.08648	−	0.552689i
$302$	1.28567	−	0.655084i	0.0739823	−	0.0376959i
$303$	9.94141	−	25.8983i	0.571119	−	1.48782i
$304$	2.93194	−	27.8955i	0.168158	−	1.59992i
$305$	−8.22422	+	3.03722i	−0.470917	+	0.173910i
$306$	5.48350	−	0.576339i	0.313471	−	0.0329471i
$307$	4.81162	−	4.81162i	0.274613	−	0.274613i	−0.556341	−	0.830954i	$-0.687795\pi$
$307$	4.81162	−	4.81162i	0.274613	−	0.274613i	0.830954	+	0.556341i	$0.187795\pi$
$308$	−7.31009	−	16.3896i	−0.416531	−	0.933886i
$309$	12.0008	−	3.89928i	0.682699	−	0.221822i
$310$	0.488553	+	0.556710i	0.0277479	+	0.0316190i
$311$	6.33562	+	29.8067i	0.359260	+	1.69018i	0.672166	+	0.740401i	$0.265364\pi$
$311$	6.33562	+	29.8067i	0.359260	+	1.69018i	−0.312906	+	0.949784i	$0.601303\pi$
$312$	9.71397	−	0.509088i	0.549946	−	0.0288214i
$313$	−6.76777	−	10.4215i	−0.382537	−	0.589055i	0.593984	−	0.804477i	$-0.297554\pi$
$313$	−6.76777	−	10.4215i	−0.382537	−	0.589055i	−0.976521	+	0.215421i	$0.930888\pi$
$314$	1.64929	−	5.07598i	0.0930747	−	0.286454i
$315$	−20.2196	−	5.68080i	−1.13925	−	0.320077i
$316$	−5.87245	−	18.0735i	−0.330351	−	1.01672i
$317$	1.73221	−	2.13910i	0.0972906	−	0.120144i	−0.726175	−	0.687509i	$-0.758704\pi$
$317$	1.73221	−	2.13910i	0.0972906	−	0.120144i	0.823466	+	0.567366i	$0.192037\pi$
$318$	0.516782	−	1.92866i	0.0289797	−	0.108154i
$319$	−0.358312	+	0.804782i	−0.0200616	+	0.0450591i
$320$	−10.9751	−	9.12165i	−0.613526	−	0.509915i
$321$	12.9773	−	17.8618i	0.724325	−	0.996948i
$322$	4.35944	−	0.929631i	0.242942	−	0.0518063i
$323$	20.9209	+	41.0595i	1.16407	+	2.28461i
$324$	11.7826	+	6.80267i	0.654587	+	0.377926i
$325$	−17.2953	+	6.13769i	−0.959373	+	0.340458i
$326$	1.14676	+	1.98624i	0.0635130	+	0.110008i
$327$	−22.2607	−	1.16663i	−1.23102	−	0.0645150i
$328$	−0.0965874	−	0.609829i	−0.00533315	−	0.0336722i
$329$	−2.77430	−	0.143560i	−0.152952	−	0.00791475i
$330$	−2.34440	−	4.74994i	−0.129055	−	0.261476i
$331$	−2.12996	−	20.2652i	−0.117073	−	1.11388i	−0.882486	−	0.470339i	$-0.844132\pi$
$331$	−2.12996	−	20.2652i	−0.117073	−	1.11388i	0.765413	−	0.643540i	$-0.222535\pi$
$332$	−11.3380	−	3.03800i	−0.622253	−	0.166732i
$333$	−16.3103	+	6.26092i	−0.893796	+	0.343096i
$334$	5.04018	+	1.07132i	0.275786	+	0.0586202i
$335$	−0.0338122	+	2.65101i	−0.00184736	+	0.144840i
$336$	17.1926	+	17.1700i	0.937935	+	0.936699i
$337$	6.26481	−	12.2954i	0.341266	−	0.669772i	−0.655045	−	0.755590i	$-0.727350\pi$
$337$	6.26481	−	12.2954i	0.341266	−	0.669772i	0.996311	+	0.0858177i	$0.0273503\pi$
$338$	−0.104286	+	0.0677239i	−0.00567239	+	0.00368369i
$339$	−19.8166	+	4.21215i	−1.07629	+	0.228772i
$340$	25.2746	+	2.98283i	1.37071	+	0.161767i
$341$	−0.918453	+	4.32098i	−0.0497370	+	0.233994i
$342$	−1.14363	+	7.22059i	−0.0618404	+	0.390445i
$343$	−15.0047	−	10.8563i	−0.810178	−	0.586184i
$344$	4.86523	+	6.69641i	0.262315	+	0.361046i
$345$	−35.4683	+	9.02050i	−1.90955	+	0.485647i
$346$	−2.20029	−	0.231260i	−0.118288	−	0.0124326i
$347$	−1.95331	+	1.58176i	−0.104859	+	0.0849134i	−0.680316	−	0.732919i	$-0.738158\pi$
$347$	−1.95331	+	1.58176i	−0.104859	+	0.0849134i	0.575457	+	0.817832i	$0.304824\pi$
$348$	0.0648389	−	1.23720i	0.00347573	−	0.0663209i
$349$	27.7478			1.48531			0.742654	−	0.669676i	$-0.233567\pi$
$349$	27.7478			1.48531			0.742654	+	0.669676i	$0.233567\pi$
$350$	3.06497	+	1.65886i	0.163830	+	0.0886699i
$351$	5.16719			0.275804
$352$	−0.554640	+	10.5832i	−0.0295624	+	0.564085i
$353$	−18.9700	+	15.3616i	−1.00967	+	0.817614i	−0.983291	−	0.182038i	$-0.941731\pi$
$353$	−18.9700	+	15.3616i	−1.00967	+	0.817614i	−0.0263777	+	0.999652i	$0.508397\pi$
$354$	−3.74463	−	0.393577i	−0.199025	−	0.0209184i
$355$	−10.5289	−	16.6749i	−0.558817	−	0.885012i
$356$	−4.36500	−	6.00791i	−0.231345	−	0.318418i
$357$	−39.0525	−	8.27395i	−2.06688	−	0.437904i
$358$	−0.633362	+	3.99889i	−0.0334742	+	0.211348i
$359$	−7.52675	+	35.4106i	−0.397247	+	1.86890i	0.0904726	+	0.995899i	$0.471162\pi$
$359$	−7.52675	+	35.4106i	−0.397247	+	1.86890i	−0.487719	+	0.873000i	$0.662171\pi$
$360$	6.03806	+	5.57776i	0.318233	+	0.293974i
$361$	−41.1801	+	8.75310i	−2.16737	+	0.460690i
$362$	−1.70911	+	1.10991i	−0.0898287	+	0.0583355i
$363$	1.56149	−	3.06460i	0.0819571	−	0.160850i
$364$	−18.1124	−	4.84041i	−0.949349	−	0.253707i
$365$	10.3509	+	14.6358i	0.541792	+	0.766071i
$366$	−2.58580	−	0.549628i	−0.135162	−	0.0287295i
$367$	11.0301	−	4.23406i	0.575766	−	0.221016i	−0.0530209	−	0.998593i	$-0.516885\pi$
$367$	11.0301	−	4.23406i	0.575766	−	0.221016i	0.628787	+	0.777577i	$0.283552\pi$
$368$	22.1659	+	5.93934i	1.15548	+	0.309609i
$369$	−0.221261	−	2.10516i	−0.0115184	−	0.109590i
$370$	2.86889	−	0.416954i	0.149146	−	0.0216764i
$371$	−4.26294	+	6.57384i	−0.221321	+	0.341297i
$372$	−0.971847	−	6.13600i	−0.0503879	−	0.318137i
$373$	−19.7985	−	1.03759i	−1.02513	−	0.0537246i	−0.467647	−	0.883916i	$-0.654898\pi$
$373$	−19.7985	−	1.03759i	−1.02513	−	0.0537246i	−0.557479	+	0.830191i	$0.688231\pi$
$374$	−2.72837	−	4.72568i	−0.141081	−	0.244359i
$375$	−25.6758	−	12.6297i	−1.32589	−	0.652197i
$376$	0.941605	+	0.543636i	0.0485596	+	0.0280359i
$377$	0.417815	+	0.820009i	0.0215186	+	0.0422326i
$378$	−0.657070	−	0.728784i	−0.0337961	−	0.0374846i
$379$	−8.72393	+	12.0075i	−0.448118	+	0.616782i	−0.971992	−	0.235014i	$-0.924486\pi$
$379$	−8.72393	+	12.0075i	−0.448118	+	0.616782i	0.523874	+	0.851796i	$0.324486\pi$
$380$	−12.4936	+	31.3460i	−0.640907	+	1.60802i
$381$	−10.2349	+	22.9880i	−0.524351	+	1.17771i
$382$	0.471271	−	1.75881i	0.0241123	−	0.0899884i
$383$	17.8508	−	22.0440i	0.912135	−	1.12639i	−0.0794371	−	0.996840i	$-0.525312\pi$
$383$	17.8508	−	22.0440i	0.912135	−	1.12639i	0.991572	−	0.129553i	$-0.0413544\pi$
$384$	−6.10085	−	18.7765i	−0.311333	−	0.958184i
$385$	3.00304	+	20.5674i	0.153049	+	1.04821i
$386$	0.804035	−	2.47457i	0.0409243	−	0.125952i
$387$	15.4553	+	23.7990i	0.785635	+	1.20977i
$388$	19.6462	−	1.02961i	0.997383	−	0.0522706i
$389$	−4.29281	−	20.1961i	−0.217654	−	1.02398i	−0.942276	−	0.334836i	$-0.891319\pi$
$389$	−4.29281	−	20.1961i	−0.217654	−	1.02398i	0.724622	−	0.689146i	$-0.242014\pi$
$390$	−5.39771	−	1.21947i	−0.273324	−	0.0617502i
$391$	−35.8559	+	11.6503i	−1.81331	+	0.589180i
$392$	3.29929	+	6.45417i	0.166639	+	0.325985i
$393$	−24.6081	+	24.6081i	−1.24131	+	1.24131i
$394$	−1.55396	+	0.163328i	−0.0782875	+	0.00822835i
$395$	0.871524	+	21.9933i	0.0438511	+	1.10660i
$396$	−2.51703	+	23.9480i	−0.126486	+	1.20343i
$397$	0.377352	−	0.983037i	0.0189388	−	0.0493372i	−0.923785	−	0.382911i	$-0.874921\pi$
$397$	0.377352	−	0.983037i	0.0189388	−	0.0493372i	0.942724	+	0.333574i	$0.108255\pi$
$398$	0.333590	−	0.169973i	0.0167214	−	0.00851996i
$399$	23.9981	−	47.1758i	1.20141	−	2.36175i
$400$	10.1724	+	14.7796i	0.508618	+	0.738979i
$401$	0.184864	−	0.320194i	0.00923166	−	0.0159897i	−0.861373	−	0.507974i	$-0.830395\pi$
$401$	0.184864	−	0.320194i	0.00923166	−	0.0159897i	0.870604	+	0.491984i	$0.163728\pi$
$402$	−0.435401	+	0.670459i	−0.0217158	+	0.0334395i
$403$	2.90429	+	3.58649i	0.144673	+	0.178656i
$404$	19.1169	−	8.51139i	0.951101	−	0.423458i
$405$	−10.9996	−	11.2838i	−0.546576	−	0.560699i
$406$	0.0625242	−	0.163203i	0.00310303	−	0.00809962i
$407$	12.2260	+	12.2260i	0.606019	+	0.606019i
$408$	12.1420	+	9.83241i	0.601119	+	0.486777i
$409$	19.6346	−	21.8064i	0.970868	−	1.07826i	−0.0260387	−	0.999661i	$-0.508289\pi$
$409$	19.6346	−	21.8064i	0.970868	−	1.07826i	0.996906	−	0.0785970i	$-0.0250440\pi$
$410$	−0.0411676	+	0.348828i	−0.00203312	+	0.0172274i
$411$	11.6001	−	10.4447i	0.572189	−	0.515201i
$412$	8.48108	+	4.32133i	0.417833	+	0.212897i
$413$	13.5015	+	6.00060i	0.664367	+	0.295270i
$414$	−5.68828	−	1.84823i	−0.279564	−	0.0908357i
$415$	11.6861	+	6.94721i	0.573650	+	0.341025i
$416$	8.22762	+	7.40818i	0.403392	+	0.363216i
$417$	−0.392198	−	1.02171i	−0.0192060	−	0.0500334i
$418$	6.98854	−	1.87257i	0.341821	−	0.0915906i
$419$	−6.95129	+	5.05041i	−0.339593	+	0.246729i	−0.744490	−	0.667634i	$-0.767307\pi$
$419$	−6.95129	+	5.05041i	−0.339593	+	0.246729i	0.404897	+	0.914362i	$0.367307\pi$
$420$	−14.3084	−	25.4900i	−0.698179	−	1.24378i
$421$	25.8891	+	18.8095i	1.26176	+	0.916720i	0.998843	−	0.0480998i	$-0.0153165\pi$
$421$	25.8891	+	18.8095i	1.26176	+	0.916720i	0.262914	+	0.964819i	$0.415317\pi$
$422$	−3.30442	−	1.26845i	−0.160857	−	0.0617471i
$423$	3.12617	+	2.03016i	0.152000	+	0.0987097i
$424$	2.65569	−	1.53326i	0.128972	−	0.0744619i
$425$	−27.2407	−	11.2620i	−1.32137	−	0.546287i
$426$		−	5.94645i		−	0.288107i
$427$	8.98704	+	5.18077i	0.434914	+	0.250715i
$428$	16.4496	−	2.60536i	0.795122	−	0.125935i
$429$	−13.4239	−	30.1506i	−0.648112	−	1.45568i
$430$	−1.63128	−	4.41722i	−0.0786675	−	0.213017i
$431$	28.5735	+	12.7218i	1.37634	+	0.612785i	0.955673	−	0.294430i	$-0.0951299\pi$
$431$	28.5735	+	12.7218i	1.37634	+	0.612785i	0.420666	+	0.907216i	$0.361797\pi$
$432$	−1.30748	−	4.87957i	−0.0629060	−	0.234769i
$433$	−1.68176	−	0.266365i	−0.0808204	−	0.0128007i	0.115893	−	0.993262i	$-0.463027\pi$
$433$	−1.68176	−	0.266365i	−0.0808204	−	0.0128007i	−0.196714	+	0.980461i	$0.563027\pi$
$434$	0.136526	−	0.865688i	0.00655348	−	0.0415543i
$435$	−0.460785	+	1.35893i	−0.0220929	+	0.0651557i
$436$	−11.2516	−	12.4962i	−0.538853	−	0.598457i
$437$	−2.61616	−	49.9192i	−0.125148	−	2.38796i
$438$	0.282892	+	5.39790i	0.0135171	+	0.257922i
$439$	19.8967	+	22.0975i	0.949616	+	1.05466i	0.998439	+	0.0558477i	$0.0177861\pi$
$439$	19.8967	+	22.0975i	0.949616	+	1.05466i	−0.0488236	+	0.998807i	$0.515547\pi$
$440$	2.61237	−	7.70429i	0.124540	−	0.367288i
$441$	10.1375	+	22.6887i	0.482739	+	1.08041i
$442$	−5.63045	−	0.891775i	−0.267813	−	0.0424174i
$443$	−6.50431	−	24.2744i	−0.309029	−	1.15331i	−0.929421	−	0.369021i	$-0.879693\pi$
$443$	−6.50431	−	24.2744i	−0.309029	−	1.15331i	0.620392	−	0.784292i	$-0.286974\pi$
$444$	−22.2135	−	9.89008i	−1.05421	−	0.469362i
$445$	2.97974	+	8.06858i	0.141253	+	0.382487i
$446$	2.22114	+	4.98876i	0.105174	+	0.236224i
$447$	−8.12500	+	1.28687i	−0.384299	+	0.0608671i
$448$	0.0111335	+	16.8855i	0.000526008	+	0.797764i
$449$		−	19.5516i		−	0.922696i	−0.887219	−	0.461348i	$-0.847366\pi$
$449$		−	19.5516i		−	0.922696i	0.887219	−	0.461348i	$-0.152634\pi$
$450$	−2.44604	−	3.98555i	−0.115307	−	0.187881i
$451$	−1.81423	+	1.04744i	−0.0854285	+	0.0493222i
$452$	−12.8169	−	8.32341i	−0.602858	−	0.391500i
$453$	13.0867	+	5.02351i	0.614866	+	0.236025i
$454$	3.13294	+	2.27621i	0.147036	+	0.106828i
$455$	18.6726	+	11.0839i	0.875386	+	0.519621i
$456$	−16.7593	+	12.1763i	−0.784825	+	0.570209i
$457$	−6.09440	+	1.63299i	−0.285084	+	0.0763880i	−0.398527	−	0.917156i	$-0.630479\pi$
$457$	−6.09440	+	1.63299i	−0.285084	+	0.0763880i	0.113443	+	0.993544i	$0.463812\pi$
$458$	1.88895	+	4.92089i	0.0882650	+	0.229938i
$459$	6.16771	+	5.55343i	0.287884	+	0.259212i
$460$	−23.7303	−	14.1073i	−1.10643	−	0.657755i
$461$	5.06458	+	1.64558i	0.235881	+	0.0766424i	0.424572	−	0.905394i	$-0.360425\pi$
$461$	5.06458	+	1.64558i	0.235881	+	0.0766424i	−0.188691	+	0.982036i	$0.560425\pi$
$462$	−2.54544	+	5.72732i	−0.118425	+	0.266459i
$463$	−19.8100	−	10.0937i	−0.920649	−	0.469094i	−0.0716148	−	0.997432i	$-0.522815\pi$
$463$	−19.8100	−	10.0937i	−0.920649	−	0.469094i	−0.849034	+	0.528338i	$0.822815\pi$
$464$	0.668643	−	0.602049i	0.0310410	−	0.0279494i
$465$	−0.843335	+	7.14588i	−0.0391087	+	0.331382i
$466$	1.20458	−	1.33782i	0.0558009	−	0.0619732i
$467$	−5.78319	−	4.68313i	−0.267614	−	0.216709i	0.486115	−	0.873895i	$-0.338414\pi$
$467$	−5.78319	−	4.68313i	−0.267614	−	0.216709i	−0.753729	+	0.657185i	$0.771747\pi$
$468$	17.7881	+	17.7881i	0.822254	+	0.822254i
$469$	2.43659	−	1.97577i	0.112511	−	0.0912326i
$470$	−0.431757	−	0.442913i	−0.0199155	−	0.0204301i
$471$	47.3665	−	21.0889i	2.18253	−	0.971727i
$472$	−3.63917	−	4.49400i	−0.167506	−	0.206853i
$473$	15.2956	−	23.5531i	0.703291	−	1.08297i
$474$	−3.31844	+	5.74771i	−0.152421	+	0.264001i
$475$	23.7715	−	31.0228i	1.09071	−	1.42343i
$476$	−16.4173	−	25.2439i	−0.752485	−	1.15705i
$477$	9.36722	−	4.77284i	0.428895	−	0.218533i
$478$	0.404142	−	1.05283i	0.0184850	−	0.0481552i
$479$	−1.32701	+	12.6257i	−0.0606327	+	0.576881i	0.921459	+	0.388476i	$0.126998\pi$
$479$	−1.32701	+	12.6257i	−0.0606327	+	0.576881i	−0.982091	+	0.188405i	$0.939668\pi$
$480$	0.683505	+	17.2485i	0.0311976	+	0.787284i
$481$	17.9640	−	1.88809i	0.819087	−	0.0860895i
$482$	−0.681684	+	0.681684i	−0.0310498	+	0.0310498i
$483$	35.0493	+	25.4295i	1.59480	+	1.15708i
$484$	2.46756	−	0.801759i	0.112162	−	0.0364436i
$485$	−22.2258	−	5.02133i	−1.00922	−	0.228007i
$486$	−1.21924	−	5.73606i	−0.0553057	−	0.260193i
$487$	−15.6668	+	0.821060i	−0.709928	+	0.0372058i	−0.403882	−	0.914811i	$-0.632339\pi$
$487$	−15.6668	+	0.821060i	−0.709928	+	0.0372058i	−0.306046	+	0.952017i	$0.599006\pi$
$488$	−2.21123	−	3.40500i	−0.100098	−	0.154137i
$489$	−6.88511	+	21.1902i	−0.311355	+	0.958254i
$490$	−0.811170	−	4.04305i	−0.0366449	−	0.182646i
$491$	4.43552	+	13.6511i	0.200172	+	0.616067i	0.999877	+	0.0156736i	$0.00498927\pi$
$491$	4.43552	+	13.6511i	0.200172	+	0.616067i	−0.799705	+	0.600393i	$0.795011\pi$
$492$	1.85404	−	2.28955i	0.0835868	−	0.103221i
$493$	−0.382586	+	1.42783i	−0.0172308	+	0.0643063i
$494$	3.07430	−	6.90498i	0.138319	−	0.310670i
$495$	10.3261	−	25.9079i	0.464125	−	1.16448i
$496$	2.65198	−	3.65013i	0.119077	−	0.163896i
$497$	−7.19596	+	22.1967i	−0.322783	+	0.995657i
$498$	1.86108	+	3.65258i	0.0833972	+	0.163676i
$499$	−6.68368	−	3.85883i	−0.299203	−	0.172745i	0.342882	−	0.939378i	$-0.388597\pi$
$499$	−6.68368	−	3.85883i	−0.299203	−	0.172745i	−0.642085	+	0.766634i	$0.721930\pi$
$500$	−6.95879	−	20.4322i	−0.311207	−	0.913756i
$501$	25.0287	+	43.3511i	1.11820	+	1.93678i
$502$	6.11732	+	0.320595i	0.273030	+	0.0143089i
$503$	−1.52745	−	9.64392i	−0.0681055	−	0.430001i	−0.998056	−	0.0623173i	$-0.980151\pi$
$503$	−1.52745	−	9.64392i	−0.0681055	−	0.430001i	0.929951	−	0.367684i	$-0.119849\pi$
$504$	0.502621	−	9.71312i	0.0223885	−	0.432657i
$505$	−23.9851	+	3.48591i	−1.06732	+	0.155121i
$506$	0.618727	+	5.88679i	0.0275058	+	0.261700i
$507$	−1.16682	−	0.312649i	−0.0518203	−	0.0138852i
$508$	−17.7211	+	6.80251i	−0.786248	+	0.301812i
$509$	−5.47118	−	1.16293i	−0.242506	−	0.0515462i	0.0850552	−	0.996376i	$-0.472893\pi$
$509$	−5.47118	−	1.16293i	−0.242506	−	0.0515462i	−0.327561	+	0.944830i	$0.606227\pi$
$510$	−5.13224	−	7.25677i	−0.227259	−	0.321335i
$511$	5.47617	−	20.4914i	0.242252	−	0.906486i
$512$	8.28783	−	16.2658i	0.366274	−	0.718853i
$513$	−9.22892	+	5.99333i	−0.407467	+	0.264612i
$514$	−0.0837023	+	0.0177915i	−0.00369195	+	0.000784748i
$515$	−8.09815	−	7.48081i	−0.356847	−	0.329644i
$516$	−8.21152	+	38.6322i	−0.361492	+	1.70069i
$517$	0.577090	−	3.64360i	0.0253804	−	0.160245i
$518$	−2.55063	−	2.29356i	−0.112068	−	0.100773i
$519$	−12.6331	−	17.3880i	−0.554534	−	0.763250i
$520$	−4.53747	−	7.18610i	−0.198981	−	0.315131i
$521$	−35.0701	−	3.68601i	−1.53645	−	0.161487i	−0.701841	−	0.712334i	$-0.747638\pi$
$521$	−35.0701	−	3.68601i	−1.53645	−	0.161487i	−0.834606	+	0.550847i	$0.814305\pi$
$522$	−0.182245	+	0.147579i	−0.00797666	+	0.00645937i
$523$	−0.924518	+	17.6409i	−0.0404264	+	0.771381i	0.900930	+	0.433965i	$0.142886\pi$
$523$	−0.924518	+	17.6409i	−0.0404264	+	0.771381i	−0.941356	+	0.337415i	$0.890447\pi$
$524$	−26.2519			−1.14682
$525$	7.94748	+	32.9105i	0.346856	+	1.43633i
$526$	−1.77966			−0.0775967
$527$	−0.387939	+	7.40232i	−0.0168989	+	0.322450i
$528$	−25.0756	+	20.3058i	−1.09127	+	0.883697i
$529$	17.7983	+	1.87068i	0.773841	+	0.0813340i
$530$	−1.69069	+	0.429985i	−0.0734388	+	0.0186774i
$531$	−11.6528	−	16.0388i	−0.505690	−	0.696023i
$532$	37.9642	−	12.3630i	1.64596	−	0.536004i
$533$	−0.342360	+	2.16157i	−0.0148292	+	0.0936282i
$534$	−0.539227	+	2.53686i	−0.0233346	+	0.109781i
$535$	−19.1569	−	2.26084i	−0.828226	−	0.0977447i
$536$	−1.20094	+	0.255267i	−0.0518726	+	0.0110259i
$537$	−32.9867	+	21.4218i	−1.42348	+	0.924418i
$538$	−0.0697102	+	0.136814i	−0.00300542	+	0.00589847i
$539$	16.4323	−	18.2984i	0.707789	−	0.788167i
$540$	−0.0775070	+	6.07687i	−0.00333537	+	0.261507i
$541$	14.5992	+	3.10316i	0.627669	+	0.133415i	0.510754	−	0.859727i	$-0.329366\pi$
$541$	14.5992	+	3.10316i	0.627669	+	0.133415i	0.116915	+	0.993142i	$0.462700\pi$
$542$	4.56950	−	1.75406i	0.196277	−	0.0753435i
$543$	−19.1227	−	5.12391i	−0.820634	−	0.219888i
$544$	1.85879	+	17.6852i	0.0796951	+	0.758248i
$545$	8.61983	+	17.4645i	0.369233	+	0.748096i
$546$	2.97640	+	5.83201i	0.127378	+	0.249587i
$547$	−6.87620	−	43.4146i	−0.294005	−	1.85627i	−0.484774	−	0.874639i	$-0.661098\pi$
$547$	−6.87620	−	43.4146i	−0.294005	−	1.85627i	0.190769	−	0.981635i	$-0.438902\pi$
$548$	11.7587	+	0.616248i	0.502307	+	0.0263248i
$549$	−6.95951	−	12.0542i	−0.297025	−	0.514462i
$550$	−2.61875	+	3.81580i	−0.111664	+	0.162706i
$551$	−1.69736	−	0.979969i	−0.0723098	−	0.0417481i
$552$	−7.69424	−	15.1008i	−0.327489	−	0.642733i
$553$	19.3424	−	17.4391i	0.822522	−	0.741585i
$554$	−0.232601	+	0.320147i	−0.00988226	+	0.0136018i
$555$	21.6590	+	18.0013i	0.919374	+	0.764112i
$556$	0.335782	−	0.754180i	0.0142403	−	0.0319843i
$557$	−0.684178	+	2.55339i	−0.0289895	+	0.108190i	−0.978905	−	0.204318i	$-0.934502\pi$
$557$	−0.684178	+	2.55339i	−0.0289895	+	0.108190i	0.949915	+	0.312508i	$0.101169\pi$
$558$	−0.740040	+	0.913874i	−0.0313284	+	0.0386874i
$559$	−9.06628	−	27.9031i	−0.383463	−	1.18018i
$560$	5.74211	−	20.4379i	0.242649	−	0.863657i
$561$	16.3811	−	50.4159i	0.691611	−	2.12856i
$562$	−4.29336	−	6.61120i	−0.181105	−	0.278877i
$563$	29.9354	−	1.56885i	1.26163	−	0.0661191i	0.590241	−	0.807227i	$-0.299033\pi$
$563$	29.9354	−	1.56885i	1.26163	−	0.0661191i	0.671386	+	0.741108i	$0.265699\pi$
$564$	1.07864	+	5.07461i	0.0454190	+	0.213680i
$565$	11.6753	+	13.3040i	0.491182	+	0.559705i
$566$	2.25082	−	0.731335i	0.0946089	−	0.0307403i
$567$	−1.93673	+	18.5443i	−0.0813349	+	0.778789i
$568$	6.45771	−	6.45771i	0.270959	−	0.270959i
$569$	32.8105	−	3.44853i	1.37549	−	0.144570i	0.612239	−	0.790673i	$-0.290269\pi$
$569$	32.8105	−	3.44853i	1.37549	−	0.144570i	0.763250	+	0.646103i	$0.223602\pi$
$570$	11.0551	−	4.08266i	0.463046	−	0.171004i
$571$	3.39211	−	32.2738i	0.141956	−	1.35062i	−0.659113	−	0.752044i	$-0.729068\pi$
$571$	3.39211	−	32.2738i	0.141956	−	1.35062i	0.801068	−	0.598573i	$-0.204265\pi$
$572$	8.92201	−	23.2426i	0.373048	−	0.971823i
$573$	15.7610	−	8.03061i	0.658424	−	0.335484i
$574$	0.348405	−	0.226583i	0.0145421	−	0.00945741i
$575$	22.0258	+	23.1791i	0.918540	+	0.966637i
$576$	11.3285	−	19.6215i	0.472020	−	0.817562i
$577$	−0.0722936	+	0.111322i	−0.00300962	+	0.00463441i	−0.840172	−	0.542320i	$-0.817546\pi$
$577$	−0.0722936	+	0.111322i	−0.00300962	+	0.00463441i	0.837163	+	0.546954i	$0.184213\pi$
$578$	−2.94374	−	3.63522i	−0.122443	−	0.151205i
$579$	23.0914	−	10.2810i	0.959646	−	0.427262i
$580$	−0.970636	+	0.479071i	−0.0403035	+	0.0198923i
$581$	−2.52689	−	15.8864i	−0.104833	−	0.659077i
$582$	−4.85831	−	4.85831i	−0.201384	−	0.201384i
$583$	−8.08578	−	6.54774i	−0.334879	−	0.271180i
$584$	−5.55478	+	6.16921i	−0.229858	+	0.255284i
$585$	−14.2453	−	25.4167i	−0.588969	−	1.05085i
$586$	5.42502	−	4.88471i	0.224106	−	0.201786i
$587$	24.9989	+	12.7376i	1.03182	+	0.525736i	0.886053	−	0.463584i	$-0.153437\pi$
$587$	24.9989	+	12.7376i	1.03182	+	0.525736i	0.145762	+	0.989320i	$0.453437\pi$
$588$	−12.3523	+	32.3060i	−0.509399	+	1.33228i
$589$	−9.34714	−	3.03707i	−0.385142	−	0.125140i
$590$	1.29961	+	3.02211i	0.0535040	+	0.124418i
$591$	−11.2805	−	10.1570i	−0.464017	−	0.417802i
$592$	−6.32850	−	16.4863i	−0.260100	−	0.677583i
$593$	−43.3728	+	11.6217i	−1.78111	+	0.477247i	−0.990785	−	0.135442i	$-0.956754\pi$
$593$	−43.3728	+	11.6217i	−1.78111	+	0.477247i	−0.790324	+	0.612689i	$0.790088\pi$
$594$	1.05419	−	0.765913i	0.0432539	−	0.0314258i
$595$	10.3758	+	33.2984i	0.425366	+	1.36510i
$596$	−5.02030	−	3.64746i	−0.205639	−	0.149406i
$597$	3.39556	+	1.30343i	0.138971	+	0.0533460i
$598$	5.18615	+	3.36793i	0.212078	+	0.137725i
$599$	−18.7555	+	10.8285i	−0.766331	+	0.442441i	−0.831564	−	0.555429i	$-0.812554\pi$
$599$	−18.7555	+	10.8285i	−0.766331	+	0.442441i	0.0652335	+	0.997870i	$0.479221\pi$
$600$	3.08471	−	12.8869i	0.125933	−	0.526105i
$601$			27.1300i			1.10666i	0.832963	+	0.553328i	$0.186643\pi$
$601$			27.1300i			1.10666i	−0.832963	+	0.553328i	$0.813357\pi$
$602$	−2.78259	+	4.82693i	−0.113410	+	0.196731i
$603$	−4.15737	+	0.658463i	−0.169301	+	0.0268147i
$604$	4.30090	+	9.65998i	0.175001	+	0.393059i
$605$	−3.00272	+	0.118988i	−0.122078	+	0.00483756i
$606$	−6.67644	−	2.97254i	−0.271212	−	0.120751i
$607$	−0.901633	−	3.36494i	−0.0365961	−	0.136579i	0.945211	−	0.326461i	$-0.105856\pi$
$607$	−0.901633	−	3.36494i	−0.0365961	−	0.136579i	−0.981807	+	0.189882i	$0.939189\pi$
$608$	−23.2877	−	3.68840i	−0.944439	−	0.149584i
$609$	1.58466	−	0.609492i	0.0642135	−	0.0246979i
$610$	0.685659	+	2.20556i	0.0277615	+	0.0893006i
$611$	−2.57876	−	2.86401i	−0.104326	−	0.115865i
$612$	2.11466	+	40.3500i	0.0854799	+	1.63105i
$613$	1.72465	+	32.9083i	0.0696581	+	1.32916i	0.780213	+	0.625514i	$0.215111\pi$
$613$	1.72465	+	32.9083i	0.0696581	+	1.32916i	−0.710555	+	0.703642i	$0.751556\pi$
$614$	−1.19953	−	1.33222i	−0.0484092	−	0.0537639i
$615$	−2.78593	+	1.97031i	−0.112340	+	0.0794504i
$616$	−8.98402	+	3.45544i	−0.361977	+	0.139224i
$617$	−39.8140	−	6.30591i	−1.60285	−	0.253866i	−0.709994	−	0.704208i	$-0.751302\pi$
$617$	−39.8140	−	6.30591i	−1.60285	−	0.253866i	−0.892856	+	0.450342i	$0.851302\pi$
$618$	−0.860387	−	3.21101i	−0.0346098	−	0.129166i
$619$	26.1694	+	11.6513i	1.05184	+	0.468307i	0.858494	−	0.512824i	$-0.171401\pi$
$619$	26.1694	+	11.6513i	1.05184	+	0.468307i	0.193342	+	0.981131i	$0.438067\pi$
$620$	−4.26145	+	3.36178i	−0.171144	+	0.135012i
$621$	−3.66180	−	8.22453i	−0.146943	−	0.330039i
$622$	7.92913	−	1.25585i	0.317929	−	0.0503550i
$623$	5.08273	−	8.81697i	0.203635	−	0.353244i
$624$			33.7084i			1.34942i
$625$	1.34197	+	24.9640i	0.0536789	+	0.998558i
$626$	−2.83506	+	1.63683i	−0.113312	+	0.0654207i
$627$	58.9470	+	38.2806i	2.35412	+	1.52878i
$628$	36.5142	+	14.0165i	1.45707	+	0.559318i
$629$	23.4715	+	17.0531i	0.935872	+	0.679951i
$630$	−1.77333	+	5.24120i	−0.0706511	+	0.208814i
$631$	−34.7400	+	25.2401i	−1.38298	+	1.00479i	−0.386382	+	0.922339i	$0.626275\pi$
$631$	−34.7400	+	25.2401i	−1.38298	+	1.00479i	−0.996595	+	0.0824526i	$0.973725\pi$
$632$	−9.84562	+	2.63813i	−0.391638	+	0.104939i
$633$	−12.3225	−	32.1013i	−0.489777	−	1.27591i
$634$	−0.538887	−	0.485216i	−0.0214019	−	0.0192704i
$635$	21.8925	−	2.01906i	0.868776	−	0.0801238i
$636$	13.9160	+	4.52157i	0.551804	+	0.179292i
$637$	−4.05272	−	25.3713i	−0.160575	−	1.00525i
$638$	0.206787	+	0.105363i	0.00818680	+	0.00417138i
$639$	23.2675	−	20.9502i	0.920448	−	0.828775i
$640$	−11.7045	+	12.6705i	−0.462663	+	0.500844i
$641$	20.7202	−	23.0121i	0.818399	−	0.908924i	−0.178787	−	0.983888i	$-0.557217\pi$
$641$	20.7202	−	23.0121i	0.818399	−	0.908924i	0.997186	+	0.0749634i	$0.0238840\pi$
$642$	−4.52028	−	3.66045i	−0.178401	−	0.144466i
$643$	−10.0822	−	10.0822i	−0.397604	−	0.397604i	0.479783	−	0.877387i	$-0.340715\pi$
$643$	−10.0822	−	10.0822i	−0.397604	−	0.397604i	−0.877387	+	0.479783i	$0.840715\pi$
$644$	5.13120	+	32.2595i	0.202198	+	1.27120i
$645$	21.2857	−	40.4904i	0.838123	−	1.59431i
$646$	11.0907	−	4.93789i	0.436357	−	0.194279i
$647$	−17.8753	−	22.0741i	−0.702749	−	0.867823i	0.293355	−	0.956003i	$-0.405228\pi$
$647$	−17.8753	−	22.0741i	−0.702749	−	0.867823i	−0.996105	+	0.0881806i	$0.971895\pi$
$648$	3.97448	−	6.12017i	0.156132	−	0.240423i
$649$	−9.81009	+	16.9916i	−0.385080	+	0.666977i
$650$	1.37628	+	4.63481i	0.0539823	+	0.181792i
$651$	7.13722	−	4.64166i	0.279730	−	0.181921i
$652$	−14.9754	+	7.63034i	−0.586481	+	0.298827i
$653$	12.0968	−	31.5132i	0.473383	−	1.23321i	−0.464289	−	0.885684i	$-0.653690\pi$
$653$	12.0968	−	31.5132i	0.473383	−	1.23321i	0.937672	−	0.347521i	$-0.112977\pi$
$654$	−0.613853	+	5.84042i	−0.0240036	+	0.228379i
$655$	29.2669	+	8.24350i	1.14355	+	0.322100i
$656$	2.12788	−	0.223650i	0.0830799	−	0.00873205i
$657$	−20.1244	+	20.1244i	−0.785129	+	0.785129i
$658$	−0.0760204	+	0.727903i	−0.00296359	+	0.0283766i
$659$	−1.81381	+	0.589344i	−0.0706562	+	0.0229576i	−0.344132	−	0.938921i	$-0.611827\pi$
$659$	−1.81381	+	0.589344i	−0.0706562	+	0.0229576i	0.273476	+	0.961879i	$0.411827\pi$
$660$	35.6598	−	15.3349i	1.38806	−	0.596910i
$661$	2.24221	+	10.5488i	0.0872120	+	0.410300i	0.999998	+	0.00186255i	$0.000592870\pi$
$661$	2.24221	+	10.5488i	0.0872120	+	0.410300i	−0.912786	+	0.408437i	$0.866074\pi$
$662$	−5.36090	+	0.280953i	−0.208357	+	0.0109195i
$663$	−30.1619	−	46.4453i	−1.17139	−	1.80379i
$664$	−1.94553	+	5.98771i	−0.0755010	+	0.232368i
$665$	−46.2065	+	1.86153i	−1.79181	+	0.0721871i
$666$	1.42229	+	4.37734i	0.0551124	+	0.169619i
$667$	1.00910	−	1.24614i	0.0390727	−	0.0482507i
$668$	−9.77313	+	36.4738i	−0.378134	+	1.41121i
$669$	−21.5776	+	48.4640i	−0.834238	+	1.87373i
$670$	0.696982	+	0.0454473i	0.0269268	+	0.00175578i
$671$	−8.09687	+	11.1444i	−0.312576	+	0.430224i
$672$	15.1695	−	13.6768i	0.585177	−	0.527595i
$673$	−19.9777	−	39.2085i	−0.770084	−	1.51138i	−0.857089	−	0.515168i	$-0.827730\pi$
$673$	−19.9777	−	39.2085i	−0.770084	−	1.51138i	0.0870048	−	0.996208i	$-0.472270\pi$
$674$	−3.14838	−	1.81772i	−0.121271	−	0.0700159i
$675$	1.99464	−	6.75044i	0.0767735	−	0.259825i
$676$	−0.455616	−	0.789150i	−0.0175237	−	0.0303519i
$677$	−9.09823	−	0.476818i	−0.349674	−	0.0183256i	−0.123309	−	0.992368i	$-0.539351\pi$
$677$	−9.09823	−	0.476818i	−0.349674	−	0.0183256i	−0.226364	+	0.974043i	$0.572684\pi$
$678$	0.834934	+	5.27157i	0.0320655	+	0.202453i
$679$	12.2557	+	24.0141i	0.470332	+	0.921576i
$680$	2.30719	−	13.4542i	0.0884768	−	0.515944i
$681$	3.93239	+	37.4141i	0.150689	+	1.43371i
$682$	1.12413	+	0.301210i	0.0430452	+	0.0115339i
$683$	−26.2120	+	10.0618i	−1.00297	+	0.385006i	−0.803762	−	0.594951i	$-0.797172\pi$
$683$	−26.2120	+	10.0618i	−1.00297	+	0.385006i	−0.199212	+	0.979956i	$0.563838\pi$
$684$	−52.4026	−	11.1385i	−2.00366	−	0.425892i
$685$	−12.9157	−	4.37943i	−0.493482	−	0.167330i
$686$	−3.06303	+	3.79786i	−0.116947	+	0.145003i
$687$	−23.2470	+	45.6248i	−0.886927	+	1.74069i
$688$	−24.0559	+	15.6221i	−0.917122	+	0.595586i
$689$	−10.6320	+	2.25989i	−0.405046	+	0.0860951i
$690$	1.88415	+	9.45563i	0.0717283	+	0.359970i
$691$	10.4802	−	49.3056i	0.398686	−	1.87567i	−0.0785710	−	0.996909i	$-0.525036\pi$
$691$	10.4802	−	49.3056i	0.398686	−	1.87567i	0.477257	−	0.878764i	$-0.341631\pi$
$692$	2.53626	−	16.0133i	0.0964141	−	0.608735i
$693$	−31.3780	+	10.2182i	−1.19195	+	0.388158i
$694$	0.389209	+	0.535701i	0.0147742	+	0.0203349i
$695$	−0.611170	+	0.735355i	−0.0231830	+	0.0278936i
$696$	−0.660865	−	0.0694597i	−0.0250500	−	0.00263286i
$697$	−2.73180	+	2.21217i	−0.103474	+	0.0837917i
$698$	0.382582	−	7.30010i	0.0144809	−	0.276313i
$699$	17.4884			0.661473
$700$	−13.3153	+	21.7936i	−0.503270	+	0.823722i
$701$	−10.4471			−0.394583			−0.197292	−	0.980345i	$-0.563215\pi$
$701$	−10.4471			−0.394583			−0.197292	+	0.980345i	$0.563215\pi$
$702$	0.0712443	−	1.35942i	0.00268894	−	0.0513081i
$703$	−29.8948	+	24.2083i	−1.12750	+	0.913035i
$704$	−22.3000	−	2.34383i	−0.840464	−	0.0883363i
$705$	0.390983	−	5.99613i	0.0147253	−	0.225827i
$706$	3.77988	+	5.20256i	0.142258	+	0.195801i
$707$	21.3244	+	19.1751i	0.801986	+	0.721154i
$708$	4.31641	−	27.2528i	0.162221	−	1.02422i
$709$	−2.36320	+	11.1180i	−0.0887517	+	0.417544i	0.911232	+	0.411893i	$0.135132\pi$
$709$	−2.36320	+	11.1180i	−0.0887517	+	0.417544i	−0.999984	+	0.00565112i	$0.998201\pi$
$710$	−4.53212	+	2.54011i	−0.170088	+	0.0953287i
$711$	−34.1811	+	7.26543i	−1.28189	+	0.272475i
$712$	−3.34056	+	2.16939i	−0.125193	+	0.0813012i
$713$	3.65040	−	7.16432i	0.136709	−	0.268306i
$714$	−2.71522	+	10.1601i	−0.101615	+	0.380233i
$715$	−17.2452	+	23.1103i	−0.644934	+	0.864278i
$716$	−29.0215	−	6.16871i	−1.08458	−	0.230535i
$717$	10.2279	−	3.92610i	0.381966	−	0.146623i
$718$	9.21230	+	2.46843i	0.343800	+	0.0921209i
$719$	−4.58882	−	43.6597i	−0.171134	−	1.62823i	−0.656784	−	0.754078i	$-0.728084\pi$
$719$	−4.58882	−	43.6597i	−0.171134	−	1.62823i	0.485650	−	0.874153i	$-0.338583\pi$
$720$	−20.3974	+	19.8836i	−0.760166	+	0.741019i
$721$	−0.674108	+	13.0271i	−0.0251051	+	0.485154i
$722$	1.73505	+	10.9546i	0.0645717	+	0.407690i
$723$	−9.35255	−	0.490146i	−0.347825	−	0.0182287i
$724$	−7.46696	−	12.9332i	−0.277507	−	0.480657i
$725$	1.23255	−	0.229296i	0.0457756	−	0.00851586i
$726$	−0.784728	−	0.453063i	−0.0291240	−	0.0168147i
$727$	−15.1693	−	29.7714i	−0.562598	−	1.10416i	−0.980656	−	0.195740i	$-0.937289\pi$
$727$	−15.1693	−	29.7714i	−0.562598	−	1.10416i	0.418058	−	0.908420i	$-0.362711\pi$
$728$	−3.10112	+	9.56573i	−0.114935	+	0.354529i
$729$	21.0586	−	28.9847i	0.779949	−	1.07351i
$730$	3.99320	−	2.52140i	0.147795	−	0.0933212i
$731$	19.1671	−	43.0499i	0.708919	−	1.59226i
$732$	5.01398	−	18.7124i	0.185322	−	0.691631i
$733$	−23.9308	+	29.5521i	−0.883904	+	1.09153i	0.111307	+	0.993786i	$0.464496\pi$
$733$	−23.9308	+	29.5521i	−0.883904	+	1.09153i	−0.995212	+	0.0977448i	$0.968837\pi$
$734$	−0.961845	−	2.96026i	−0.0355024	−	0.109265i
$735$	23.9155	−	32.1375i	0.882135	−	1.18541i
$736$	5.96087	−	18.3457i	0.219721	−	0.676230i
$737$	2.26881	+	3.49366i	0.0835726	+	0.128691i
$738$	−0.556892	+	0.0291854i	−0.0204995	+	0.00107433i
$739$	6.32030	+	29.7347i	0.232496	+	1.09381i	0.927216	+	0.374528i	$0.122195\pi$
$739$	6.32030	+	29.7347i	0.232496	+	1.09381i	−0.694720	+	0.719281i	$0.744472\pi$
$740$	1.95103	+	21.1548i	0.0717212	+	0.777667i
$741$	69.8339	−	22.6904i	2.56541	−	0.833553i
$742$	1.67072	+	1.21217i	0.0613340	+	0.0445000i
$743$	8.10749	−	8.10749i	0.297435	−	0.297435i	−0.542573	−	0.840008i	$-0.682550\pi$
$743$	8.10749	−	8.10749i	0.297435	−	0.297435i	0.840008	+	0.542573i	$0.182550\pi$
$744$	−3.31392	+	0.348307i	−0.121494	+	0.0127696i
$745$	4.45151	+	5.64281i	0.163091	+	0.206737i
$746$	−0.545955	+	5.19442i	−0.0199888	+	0.190181i
$747$	−7.73511	+	20.1507i	−0.283013	+	0.737274i
$748$	35.6295	−	18.1542i	1.30274	−	0.663781i
$749$	12.4435	+	19.1337i	0.454676	+	0.699130i
$750$	−3.67674	+	6.58085i	−0.134255	+	0.240299i
$751$	−22.9279	+	39.7123i	−0.836652	+	1.44912i	0.0560263	+	0.998429i	$0.482157\pi$
$751$	−22.9279	+	39.7123i	−0.836652	+	1.44912i	−0.892678	+	0.450694i	$0.851176\pi$
$752$	−2.05207	+	3.15991i	−0.0748313	+	0.115230i
$753$	37.4504	+	46.2474i	1.36477	+	1.68535i
$754$	0.221495	−	0.0986157i	0.00806636	−	0.00359137i
$755$	−1.76147	−	12.1200i	−0.0641065	−	0.441090i
$756$	5.58534	−	4.52902i	0.203137	−	0.164719i
$757$	24.8825	+	24.8825i	0.904371	+	0.904371i	0.995811	−	0.0914400i	$-0.0291470\pi$
$757$	24.8825	+	24.8825i	0.904371	+	0.904371i	−0.0914400	+	0.995811i	$0.529147\pi$
$758$	3.03873	+	2.46071i	0.110372	+	0.0893771i
$759$	−38.4771	+	42.7332i	−1.39663	+	1.55112i
$760$	16.4392	+	7.57189i	0.596313	+	0.274661i
$761$	−18.8581	+	16.9799i	−0.683606	+	0.615522i	−0.935957	−	0.352114i	$-0.885463\pi$
$761$	−18.8581	+	16.9799i	−0.683606	+	0.615522i	0.252351	+	0.967636i	$0.418796\pi$
$762$	5.90674	+	3.00963i	0.213979	+	0.109028i
$763$	9.35902	−	21.0581i	0.338819	−	0.762353i
$764$	12.6904	+	4.12337i	0.459124	+	0.149178i
$765$	10.3130	−	45.6482i	0.372867	−	1.65041i
$766$	−5.55336	−	5.00027i	−0.200651	−	0.180667i
$767$	7.34550	+	19.1357i	0.265231	+	0.690950i
$768$	26.5305	−	7.10883i	0.957338	−	0.256518i
$769$	8.55473	−	6.21537i	0.308491	−	0.224132i	−0.422757	−	0.906243i	$-0.638938\pi$
$769$	8.55473	−	6.21537i	0.308491	−	0.224132i	0.731249	+	0.682111i	$0.238938\pi$
$770$	5.45243	−	0.506483i	0.196492	−	0.0182524i
$771$	−0.672540	−	0.488629i	−0.0242209	−	0.0175975i
$772$	17.8008	+	6.83310i	0.640666	+	0.245929i
$773$	5.99102	+	3.89062i	0.215482	+	0.139936i	0.647867	−	0.761753i	$-0.275661\pi$
$773$	5.99102	+	3.89062i	0.215482	+	0.139936i	−0.432385	+	0.901689i	$0.642328\pi$
$774$	6.47431	−	3.73794i	0.232714	−	0.134358i
$775$	5.80652	−	2.40971i	0.208576	−	0.0865595i
$776$		−	10.5520i		−	0.378796i
$777$	−0.0219716	−	33.3230i	−0.000788227	−	1.19546i
$778$	−5.37252	+	0.850924i	−0.192614	+	0.0305071i
$779$	−1.89569	−	4.25780i	−0.0679203	−	0.152552i
$780$	10.9944	−	39.0334i	0.393663	−	1.39762i
$781$	−28.3072	−	12.6032i	−1.01291	−	0.450976i
$782$	2.57067	+	9.59386i	0.0919268	+	0.343076i
$783$	−0.348642	−	0.0552195i	−0.0124595	−	0.00197339i
$784$	−22.9336	+	10.2470i	−0.819057	+	0.365963i
$785$	−36.3064	−	27.0922i	−1.29583	−	0.966963i
$786$	6.13479	+	6.81337i	0.218821	+	0.243025i
$787$	0.673066	+	12.8429i	0.0239922	+	0.457799i	0.984038	+	0.177957i	$0.0569487\pi$
$787$	0.673066	+	12.8429i	0.0239922	+	0.457799i	−0.960046	+	0.279842i	$0.909718\pi$
$788$	−0.599270	−	11.4347i	−0.0213481	−	0.407346i
$789$	−11.5684	−	12.8480i	−0.411847	−	0.457402i
$790$	5.79817	+	0.0739524i	0.206290	+	0.00263111i
$791$	3.26266	−	20.6879i	0.116007	−	0.735576i
$792$	12.7566	+	2.02045i	0.453288	+	0.0717937i
$793$	3.72464	+	13.9005i	0.132266	+	0.493623i
$794$	−0.253422	−	0.112831i	−0.00899359	−	0.00400421i
$795$	−14.0943	−	9.41069i	−0.499875	−	0.333763i
$796$	1.11594	+	2.50644i	0.0395535	+	0.0888386i
$797$	16.3180	−	2.58451i	0.578012	−	0.0915481i	0.139418	−	0.990234i	$-0.455477\pi$
$797$	16.3180	−	2.58451i	0.578012	−	0.0915481i	0.438594	+	0.898685i	$0.355477\pi$
$798$	−12.0805	−	6.96405i	−0.427644	−	0.246525i
$799$		−	6.19008i		−	0.218989i
$800$	12.8541	−	7.88889i	0.454461	−	0.278915i
$801$	−11.8261	+	6.82780i	−0.417855	+	0.241249i
$802$	−0.0816900	−	0.0530501i	−0.00288457	−	0.00187326i
$803$	26.2954	+	10.0939i	0.927946	+	0.356205i
$804$	−4.73952	−	3.44346i	−0.167150	−	0.121442i
$805$	4.40944	−	37.5757i	0.155412	−	1.32437i
$806$	0.983605	−	0.714631i	0.0346460	−	0.0251718i
$807$	−1.44086	+	0.386077i	−0.0507206	+	0.0135905i
$808$	−4.02234	−	10.4786i	−0.141506	−	0.368634i
$809$	−27.9141	−	25.1340i	−0.981407	−	0.883663i	0.0118109	−	0.999930i	$-0.496240\pi$
$809$	−27.9141	−	25.1340i	−0.981407	−	0.883663i	−0.993218	+	0.116267i	$0.962907\pi$
$810$	−3.12030	+	2.73828i	−0.109636	+	0.0962134i
$811$	−19.9913	−	6.49556i	−0.701989	−	0.228090i	−0.0637922	−	0.997963i	$-0.520319\pi$
$811$	−19.9913	−	6.49556i	−0.701989	−	0.228090i	−0.638197	+	0.769873i	$0.720319\pi$
$812$	1.17036	+	0.520153i	0.0410716	+	0.0182538i
$813$	42.3667	+	21.5869i	1.48587	+	0.757086i
$814$	3.38507	−	3.04793i	0.118647	−	0.106830i
$815$	19.0913	−	3.80417i	0.668739	−	0.133254i
$816$	−36.2280	+	40.2353i	−1.26823	+	1.40852i
$817$	48.5573	+	39.3209i	1.69880	+	1.37566i
$818$	−5.46627	−	5.46627i	−0.191124	−	0.191124i
$819$	−12.3334	+	32.1931i	−0.430965	+	1.12492i
$820$	−2.53698	−	0.435054i	−0.0885951	−	0.0151928i
$821$	−45.0953	+	20.0777i	−1.57384	+	0.700718i	−0.993518	−	0.113671i	$-0.963739\pi$
$821$	−45.0953	+	20.0777i	−1.57384	+	0.700718i	−0.580320	+	0.814389i	$0.697072\pi$
$822$	−2.58794	−	3.19584i	−0.0902648	−	0.111468i
$823$	28.3335	−	43.6298i	0.987645	−	1.52084i	0.140086	−	0.990139i	$-0.455262\pi$
$823$	28.3335	−	43.6298i	0.987645	−	1.52084i	0.847559	−	0.530701i	$-0.178071\pi$
$824$	2.55272	−	4.42144i	0.0889282	−	0.154028i
$825$	−44.5707	+	5.89833i	−1.55175	+	0.205354i
$826$	1.76484	−	3.46935i	0.0614066	−	0.120714i
$827$	33.7254	−	17.1839i	1.17275	−	0.597544i	0.244550	−	0.969637i	$-0.421360\pi$
$827$	33.7254	−	17.1839i	1.17275	−	0.597544i	0.928196	+	0.372093i	$0.121360\pi$
$828$	15.7072	−	40.9187i	0.545864	−	1.42202i
$829$	3.99905	−	38.0484i	0.138893	−	1.32147i	−0.673857	−	0.738862i	$-0.735364\pi$
$829$	3.99905	−	38.0484i	0.138893	−	1.32147i	0.812750	−	0.582613i	$-0.197970\pi$
$830$	1.98885	−	2.97869i	0.0690339	−	0.103392i
$831$	−3.82326	+	0.401841i	−0.132628	+	0.0139397i
$832$	−16.5640	+	16.5640i	−0.574254	+	0.574254i
$833$	22.4303	−	34.6396i	0.777164	−	1.20019i
$834$	−0.274207	+	0.0890952i	−0.00949500	+	0.00308511i
$835$	22.3489	−	37.5938i	0.773414	−	1.30099i
$836$	11.0234	+	51.8612i	0.381254	+	1.79366i
$837$	−1.76764	+	0.0926383i	−0.0610987	+	0.00320205i
$838$	1.23286	+	1.89843i	0.0425883	+	0.0655802i
$839$	−5.99213	+	18.4419i	−0.206871	+	0.636684i	0.792760	+	0.609534i	$0.208643\pi$
$839$	−5.99213	+	18.4419i	−0.206871	+	0.636684i	−0.999631	+	0.0271505i	$0.991357\pi$
$840$	−14.0549	+	6.94852i	−0.484940	+	0.239747i
$841$	8.94206	+	27.5208i	0.308347	+	0.948995i
$842$	5.30550	−	6.55174i	0.182840	−	0.225788i
$843$	19.8204	−	73.9707i	0.682651	−	2.54769i
$844$	10.5500	−	23.6957i	0.363146	−	0.815639i
$845$	0.260137	+	1.02285i	0.00894900	+	0.0351872i
$846$	0.577212	−	0.794464i	0.0198449	−	0.0273142i
$847$	2.38094	+	2.64080i	0.0818100	+	0.0907388i
$848$	4.82435	+	9.46833i	0.165669	+	0.325144i
$849$	19.9110	+	11.4956i	0.683342	+	0.394528i
$850$	−3.33848	+	7.01140i	−0.114509	+	0.240489i
$851$	−15.7357	−	27.2550i	−0.539411	−	0.934288i
$852$	43.5169	+	2.28062i	1.49086	+	0.0781329i
$853$	1.46342	+	9.23966i	0.0501065	+	0.316360i	0.999993	+	0.00376463i	$0.00119832\pi$
$853$	1.46342	+	9.23966i	0.0501065	+	0.316360i	−0.949886	+	0.312595i	$0.898802\pi$
$854$	1.48691	−	2.29295i	0.0508809	−	0.0784630i
$855$	54.9233	+	28.8730i	1.87834	+	0.987435i
$856$	−0.933754	−	8.88408i	−0.0319151	−	0.303652i
$857$	15.7975	+	4.23294i	0.539633	+	0.144594i	0.518333	−	0.855179i	$-0.326553\pi$
$857$	15.7975	+	4.23294i	0.539633	+	0.144594i	0.0213003	+	0.999773i	$0.493219\pi$
$858$	−8.11731	+	3.11595i	−0.277121	+	0.106377i
$859$	−47.3304	−	10.0604i	−1.61489	−	0.343256i	−0.690096	−	0.723717i	$-0.742432\pi$
$859$	−47.3304	−	10.0604i	−1.61489	−	0.343256i	−0.924797	+	0.380461i	$0.875765\pi$
$860$	32.9514	−	10.2438i	1.12363	−	0.349312i
$861$	3.90056	+	1.04239i	0.132931	+	0.0355247i
$862$	3.74090	−	7.34193i	0.127416	−	0.250067i
$863$	−44.0820	+	28.6272i	−1.50057	+	0.974481i	−0.506916	+	0.861996i	$0.669214\pi$
$863$	−44.0820	+	28.6272i	−1.50057	+	0.974481i	−0.993653	+	0.112485i	$0.964119\pi$
$864$	−4.15363	+	0.882882i	−0.141309	+	0.0300362i
$865$	−7.85596	+	17.0560i	−0.267111	+	0.579921i
$866$	−0.0932651	+	0.438778i	−0.00316928	+	0.0149103i
$867$	7.10866	−	44.8823i	0.241423	−	1.52428i
$868$	6.28285	+	1.33113i	0.213254	+	0.0451816i
$869$	20.3278	+	27.9788i	0.689574	+	0.949117i
$870$	0.351164	+	0.139963i	0.0119056	+	0.00474520i
$871$	4.32806	+	0.454897i	0.146651	+	0.0154136i
$872$	−7.00919	+	5.67593i	−0.237361	+	0.192211i
$873$	1.89330	−	36.1263i	0.0640784	−	1.22269i
$874$	−13.1692			−0.445454
$875$	21.6880	−	20.1154i	0.733189	−	0.680025i
$876$	−39.6110			−1.33833
$877$	−1.42703	+	27.2293i	−0.0481873	+	0.919469i	0.862419	+	0.506195i	$0.168948\pi$
$877$	−1.42703	+	27.2293i	−0.0481873	+	0.919469i	−0.910607	+	0.413274i	$0.864385\pi$
$878$	6.08790	−	4.92988i	0.205457	−	0.166375i
$879$	70.5293	+	7.41293i	2.37890	+	0.250032i
$880$	26.1876	+	10.4376i	0.882784	+	0.351851i
$881$	−0.398014	−	0.547820i	−0.0134094	−	0.0184565i	0.802260	−	0.596975i	$-0.203631\pi$
$881$	−0.398014	−	0.547820i	−0.0134094	−	0.0184565i	−0.815669	+	0.578519i	$0.803631\pi$
$882$	6.10888	−	2.35423i	0.205697	−	0.0792709i
$883$	4.97481	−	31.4097i	0.167416	−	1.05702i	−0.750681	−	0.660665i	$-0.770274\pi$
$883$	4.97481	−	31.4097i	0.167416	−	1.05702i	0.918097	−	0.396356i	$-0.129726\pi$
$884$	8.68556	−	40.8623i	0.292127	−	1.37435i
$885$	−13.3699	+	29.0273i	−0.449425	+	0.975740i
$886$	−6.47597	+	1.37651i	−0.217565	+	0.0462448i
$887$	−0.571156	+	0.370913i	−0.0191775	+	0.0124540i	−0.554192	−	0.832389i	$-0.686973\pi$
$887$	−0.571156	+	0.370913i	−0.0191775	+	0.0124540i	0.535015	+	0.844843i	$0.320306\pi$
$888$	−5.92101	+	11.6206i	−0.198696	+	0.389963i
$889$	−18.4064	−	18.3821i	−0.617331	−	0.616517i
$890$	2.16382	−	0.672683i	0.0725315	−	0.0225484i
$891$	−24.2186	−	5.14782i	−0.811353	−	0.172458i
$892$	−37.3602	+	14.3412i	−1.25091	+	0.480180i
$893$	7.92774	+	2.12423i	0.265292	+	0.0710847i
$894$	0.226534	+	2.15533i	0.00757643	+	0.0720849i
$895$	30.4175	+	15.9903i	1.01674	+	0.534498i
$896$	20.3823	+	1.05472i	0.680926	+	0.0352356i
$897$	9.39753	+	59.3337i	0.313774	+	1.98109i
$898$	−5.14377	−	0.269574i	−0.171650	−	0.00899579i
$899$	−0.157632	−	0.273026i	−0.00525731	−	0.00910592i
$900$	30.1049	−	16.3719i	1.00350	−	0.545729i
$901$	−15.1194	−	8.72921i	−0.503701	−	0.290812i
$902$	0.250555	+	0.491742i	0.00834256	+	0.0163732i
$903$	−52.9354	+	11.2882i	−1.76158	+	0.375649i
$904$	−4.81808	+	6.63152i	−0.160247	+	0.220561i
$905$	4.26332	+	16.7632i	0.141718	+	0.557229i
$906$	1.50206	−	3.37368i	0.0499025	−	0.112083i
$907$	−11.3108	+	42.2126i	−0.375570	+	1.40165i	0.476941	+	0.878936i	$0.341746\pi$
$907$	−11.3108	+	42.2126i	−0.375570	+	1.40165i	−0.852510	+	0.522710i	$0.824921\pi$
$908$	−17.8592	+	22.0543i	−0.592678	+	0.731896i
$909$	−11.8909	−	36.5965i	−0.394397	−	1.21383i
$910$	3.17349	−	4.75971i	0.105200	−	0.157783i
$911$	−8.28755	+	25.5065i	−0.274579	+	0.845067i	0.714752	+	0.699378i	$0.246540\pi$
$911$	−8.28755	+	25.5065i	−0.274579	+	0.845067i	−0.989331	+	0.145689i	$0.953460\pi$
$912$	−39.0978	−	60.2053i	−1.29466	−	1.99360i
$913$	21.3320	−	1.11796i	0.705986	−	0.0369992i
$914$	0.345590	+	1.62587i	0.0114311	+	0.0537791i
$915$	−11.4658	+	19.2870i	−0.379048	+	0.637610i
$916$	−36.7362	+	11.9363i	−1.21380	+	0.394387i
$917$	−14.6546	−	32.8565i	−0.483939	−	1.08502i
$918$	1.54608	−	1.54608i	0.0510281	−	0.0510281i
$919$	−43.3179	+	4.55289i	−1.42892	+	0.150186i	−0.787176	−	0.616729i	$-0.788458\pi$
$919$	−43.3179	+	4.55289i	−1.42892	+	0.150186i	−0.641749	+	0.766915i	$0.721791\pi$
$920$	−8.22246	+	12.3147i	−0.271086	+	0.406005i
$921$	1.82039	−	17.3198i	0.0599838	−	0.570707i
$922$	0.502761	−	1.30974i	0.0165575	−	0.0431339i
$923$	−28.8427	+	14.6961i	−0.949370	+	0.483728i
$924$	−40.9370	−	20.8245i	−1.34673	−	0.685074i
$925$	4.46783	−	24.1971i	0.146901	−	0.795594i
$926$	−2.92866	+	5.07259i	−0.0962417	+	0.166696i
$927$	9.53289	−	14.6794i	0.313101	−	0.482134i
$928$	−0.475969	−	0.587772i	−0.0156244	−	0.0192946i
$929$	38.1215	−	16.9728i	1.25073	−	0.556859i	0.328863	−	0.944378i	$-0.393334\pi$
$929$	38.1215	−	16.9728i	1.25073	−	0.556859i	0.921862	+	0.387519i	$0.126668\pi$
$930$	1.86836	+	0.320397i	0.0612660	+	0.0105062i
$931$	36.6661	+	40.6140i	1.20168	+	1.33107i
$932$	9.32834	+	9.32834i	0.305560	+	0.305560i
$933$	60.6088	+	49.0800i	1.98424	+	1.60681i
$934$	−1.31181	+	1.45691i	−0.0429237	+	0.0476716i
$935$	−45.4222	+	9.05091i	−1.48546	+	0.295996i
$936$	10.0272	−	9.02853i	0.327749	−	0.295107i
$937$	18.2151	+	9.28106i	0.595062	+	0.303199i	0.725462	−	0.688262i	$-0.241626\pi$
$937$	18.2151	+	9.28106i	0.595062	+	0.303199i	−0.130400	+	0.991461i	$0.541626\pi$
$938$	−0.486205	−	0.668277i	−0.0158752	−	0.0218200i
$939$	−30.2459	−	9.82748i	−0.987037	−	0.320708i
$940$	3.40689	−	2.98979i	0.111120	−	0.0975161i
$941$	−2.78647	−	2.50895i	−0.0908362	−	0.0817893i	0.622462	−	0.782650i	$-0.286133\pi$
$941$	−2.78647	−	2.50895i	−0.0908362	−	0.0817893i	−0.713298	+	0.700861i	$0.752799\pi$
$942$	−4.89515	−	12.7523i	−0.159493	−	0.415492i
$943$	3.68316	−	0.986899i	0.119940	−	0.0321379i
$944$	16.2119	−	11.7786i	0.527652	−	0.383361i
$945$	−7.64898	+	3.29529i	−0.248821	+	0.107196i
$946$	−5.98563	−	4.34882i	−0.194610	−	0.141392i
$947$	−51.1715	−	19.6429i	−1.66285	−	0.638308i	−0.668427	−	0.743778i	$-0.733032\pi$
$947$	−51.1715	−	19.6429i	−1.66285	−	0.638308i	−0.994423	+	0.105470i	$0.966365\pi$
$948$	−40.7898	−	26.4892i	−1.32479	−	0.860328i
$949$	25.4829	−	14.7126i	0.827210	−	0.477590i
$950$	−7.83396	−	6.68173i	−0.254167	−	0.216784i
$951$		−	7.04452i		−	0.228434i
$952$	−13.9823	+	8.08500i	−0.453170	+	0.262036i
$953$	23.8338	−	3.77491i	0.772054	−	0.122281i	0.242036	−	0.970267i	$-0.422185\pi$
$953$	23.8338	−	3.77491i	0.772054	−	0.122281i	0.530019	+	0.847986i	$0.322185\pi$
$954$	−1.12652	−	2.53020i	−0.0364724	−	0.0819183i
$955$	−12.8531	−	8.58192i	−0.415917	−	0.277704i
$956$	7.54972	+	3.36135i	0.244176	+	0.108714i
$957$	0.583535	+	2.17778i	0.0188630	+	0.0703977i
$958$	3.30335	+	0.523200i	0.106727	+	0.0169038i
$959$	5.79279	+	15.0610i	0.187059	+	0.486346i
$960$	−36.5205	−	0.465799i	−1.17870	−	0.0150336i
$961$	19.6852	+	21.8627i	0.635007	+	0.705247i
$962$	−0.249048	−	4.75213i	−0.00802965	−	0.153215i
$963$	−1.60281	−	30.5834i	−0.0516497	−	0.985535i
$964$	−4.72721	−	5.25010i	−0.152253	−	0.169094i
$965$	−17.6995	−	13.2076i	−0.569768	−	0.425167i
$966$	7.17344	−	8.87042i	0.230802	−	0.285401i
$967$	−4.38267	−	0.694147i	−0.140937	−	0.0223222i	0.0855672	−	0.996332i	$-0.472730\pi$
$967$	−4.38267	−	0.694147i	−0.140937	−	0.0223222i	−0.226504	+	0.974010i	$0.572730\pi$
$968$	−0.360181	−	1.34421i	−0.0115766	−	0.0432046i
$969$	107.742	+	47.9699i	3.46118	+	1.54102i
$970$	−1.62749	+	5.77809i	−0.0522557	+	0.185523i
$971$	−1.14821	−	2.57893i	−0.0368479	−	0.0827617i	0.894184	−	0.447700i	$-0.147757\pi$
$971$	−1.14821	−	2.57893i	−0.0368479	−	0.0827617i	−0.931032	+	0.364938i	$0.881090\pi$
$972$	42.4448	−	6.72260i	1.36142	−	0.215627i
$973$	1.13136		0.000745968i	0.0362699		2.39146e-5i
$974$			4.13304i			0.132431i
$975$	−24.5142	+	40.0639i	−0.785081	+	1.28307i
$976$	12.1843	−	7.03463i	0.390011	−	0.225173i
$977$	−19.1854	−	12.4592i	−0.613797	−	0.398604i	0.199965	−	0.979803i	$-0.435917\pi$
$977$	−19.1854	−	12.4592i	−0.613797	−	0.398604i	−0.813762	+	0.581199i	$0.802584\pi$
$978$	5.47994	+	2.10355i	0.175229	+	0.0672642i
$979$	10.9335	+	7.94364i	0.349436	+	0.253880i
$980$	29.8987	−	4.38563i	0.955077	−	0.140094i
$981$	−25.0153	+	18.1747i	−0.798677	+	0.580273i
$982$	3.65259	−	0.978710i	0.116559	−	0.0312319i
$983$	−9.71403	−	25.3059i	−0.309829	−	0.807133i	−0.996762	−	0.0804117i	$-0.974377\pi$
$983$	−9.71403	−	25.3059i	−0.309829	−	0.807133i	0.686932	−	0.726721i	$-0.258957\pi$
$984$	−1.17431	−	1.05736i	−0.0374358	−	0.0337073i
$985$	−2.92259	+	12.9362i	−0.0931214	+	0.412181i
$986$	0.370369	+	0.120340i	0.0117950	+	0.00383241i
$987$	−5.74918	+	4.18282i	−0.182998	+	0.133141i
$988$	49.3525	+	25.1463i	1.57011	+	0.800012i
$989$	−37.9880	+	34.2046i	−1.20795	+	1.08764i
$990$	−6.67367	−	3.07389i	−0.212103	−	0.0976945i
$991$	11.0607	−	12.2841i	0.351354	−	0.390219i	−0.541398	−	0.840767i	$-0.682105\pi$
$991$	11.0607	−	12.2841i	0.351354	−	0.390219i	0.892752	+	0.450548i	$0.148771\pi$
$992$	−2.94740	−	2.38676i	−0.0935800	−	0.0757796i
$993$	−36.8761	−	36.8761i	−1.17023	−	1.17023i
$994$	5.74045	+	2.19921i	0.182076	+	0.0697547i
$995$	−0.457043	−	3.14473i	−0.0144892	−	0.0996945i
$996$	−27.4439	+	12.2188i	−0.869592	+	0.387167i
$997$	1.92253	+	2.37413i	0.0608872	+	0.0751895i	0.806680	−	0.590989i	$-0.201262\pi$
$997$	1.92253	+	2.37413i	0.0608872	+	0.0751895i	−0.745792	+	0.666178i	$0.767929\pi$
$998$	−1.10736	+	1.70519i	−0.0350529	+	0.0539767i
$999$	−3.46403	+	5.99987i	−0.109597	+	0.189827i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.47.10	yes	288
5.2	odd	4		875.2.bb.a.243.10		288
5.3	odd	4		875.2.bb.b.243.9		288
5.4	even	2		875.2.bb.c.257.9		288
7.3	odd	6	inner	175.2.x.a.122.10	yes	288
25.6	even	5		875.2.bb.b.607.10		288
25.8	odd	20	inner	175.2.x.a.33.10	✓	288
25.17	odd	20		875.2.bb.c.768.9		288
25.19	even	10		875.2.bb.a.607.9		288
35.3	even	12		875.2.bb.b.493.10		288
35.17	even	12		875.2.bb.a.493.9		288
35.24	odd	6		875.2.bb.c.507.9		288
175.17	even	60		875.2.bb.c.143.9		288
175.31	odd	30		875.2.bb.b.857.9		288
175.94	odd	30		875.2.bb.a.857.10		288
175.108	even	60	inner	175.2.x.a.108.10	yes	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.10	✓	288	25.8	odd	20	inner
175.2.x.a.47.10	yes	288	1.1	even	1	trivial
175.2.x.a.108.10	yes	288	175.108	even	60	inner
175.2.x.a.122.10	yes	288	7.3	odd	6	inner
875.2.bb.a.243.10		288	5.2	odd	4
875.2.bb.a.493.9		288	35.17	even	12
875.2.bb.a.607.9		288	25.19	even	10
875.2.bb.a.857.10		288	175.94	odd	30
875.2.bb.b.243.9		288	5.3	odd	4
875.2.bb.b.493.10		288	35.3	even	12
875.2.bb.b.607.10		288	25.6	even	5
875.2.bb.b.857.9		288	175.31	odd	30
875.2.bb.c.143.9		288	175.17	even	60
875.2.bb.c.257.9		288	5.4	even	2
875.2.bb.c.507.9		288	35.24	odd	6
875.2.bb.c.768.9		288	25.17	odd	20

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:	\( N \)	\(=\)	\( 175 = 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	175.x (of order \(60\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.0137878 - 0.263087i) q^{2} +(1.98896 - 1.61063i) q^{3} +(1.92002 + 0.201802i) q^{4} +(-2.07716 - 0.827893i) q^{5} +(-0.396312 - 0.545476i) q^{6} +(0.819241 + 2.51572i) q^{7} +(0.161989 - 1.02276i) q^{8} +(0.738101 - 3.47249i) q^{9} +(-0.246448 + 0.535059i) q^{10} +(-3.43661 + 0.730475i) q^{11} +(4.14386 - 2.69106i) q^{12} +(-1.66634 + 3.27037i) q^{13} +(0.673149 - 0.180846i) q^{14} +(-5.46481 + 1.69888i) q^{15} +(3.50997 + 0.746068i) q^{16} +(-5.50381 + 2.11271i) q^{17} +(-0.903391 - 0.242063i) q^{18} +(-0.817063 - 7.77383i) q^{19} +(-3.82112 - 2.00875i) q^{20} +(5.68132 + 3.68417i) q^{21} +(0.144795 + 0.914201i) q^{22} +(6.38626 + 0.334690i) q^{23} +(-1.32509 - 2.29513i) q^{24} +(3.62919 + 3.43933i) q^{25} +(0.837417 + 0.483483i) q^{26} +(-0.639125 - 1.25435i) q^{27} +(1.06528 + 4.99555i) q^{28} +(0.147381 - 0.202852i) q^{29} +(0.371607 + 1.46115i) q^{30} +(0.511405 - 1.14863i) q^{31} +(0.780694 - 2.91359i) q^{32} +(-5.65876 + 6.98798i) q^{33} +(0.479943 + 1.47711i) q^{34} +(0.381053 - 5.90380i) q^{35} +(2.11792 - 6.51830i) q^{36} +(-2.68029 - 4.12728i) q^{37} +(-2.05646 + 0.107775i) q^{38} +(1.95307 + 9.18847i) q^{39} +(-1.18321 + 1.99033i) q^{40} +(0.567075 - 0.184254i) q^{41} +(1.04759 - 1.44389i) q^{42} +(-5.65218 + 5.65218i) q^{43} +(-6.74578 + 0.709010i) q^{44} +(-4.40800 + 6.60185i) q^{45} +(0.176105 - 1.67553i) q^{46} +(-0.376282 + 0.980249i) q^{47} +(8.18282 - 4.16936i) q^{48} +(-5.65769 + 4.12196i) q^{49} +(0.954883 - 0.907372i) q^{50} +(-7.54405 + 13.0667i) q^{51} +(-3.85937 + 5.94290i) q^{52} +(1.86365 + 2.30142i) q^{53} +(-0.338816 + 0.150851i) q^{54} +(7.74315 + 1.32784i) q^{55} +(2.70568 - 0.430367i) q^{56} +(-14.1458 - 14.1458i) q^{57} +(-0.0513357 - 0.0415708i) q^{58} +(3.73669 - 4.15002i) q^{59} +(-10.8354 + 2.15908i) q^{60} +(2.91370 - 2.62351i) q^{61} +(-0.295140 - 0.150381i) q^{62} +(9.34049 - 0.987952i) q^{63} +(6.06975 + 1.97218i) q^{64} +(6.16876 - 5.41353i) q^{65} +(1.76043 + 1.58510i) q^{66} +(-0.424905 - 1.10691i) q^{67} +(-10.9938 + 2.94577i) q^{68} +(13.2411 - 9.62020i) q^{69} +(-1.54796 - 0.181651i) q^{70} +(7.13505 + 5.18392i) q^{71} +(-3.43196 - 1.31741i) q^{72} +(-6.72347 - 4.36627i) q^{73} +(-1.12279 + 0.648243i) q^{74} +(12.7578 + 0.995427i) q^{75} -15.0908i q^{76} +(-4.65309 - 8.04712i) q^{77} +(2.44430 - 0.387139i) q^{78} +(-4.00368 - 8.99240i) q^{79} +(-6.67311 - 4.45558i) q^{80} +(6.43796 + 2.86636i) q^{81} +(-0.0406561 - 0.151731i) q^{82} +(-6.00511 - 0.951116i) q^{83} +(10.1648 + 8.22017i) q^{84} +(13.1814 + 0.168121i) q^{85} +(1.40908 + 1.56495i) q^{86} +(-0.0335849 - 0.640839i) q^{87} +(0.190406 + 3.63316i) q^{88} +(-2.57386 - 2.85856i) q^{89} +(1.67609 + 1.25071i) q^{90} +(-9.59246 - 1.51281i) q^{91} +(12.1942 + 1.93137i) q^{92} +(-0.832857 - 3.10827i) q^{93} +(0.252703 + 0.112511i) q^{94} +(-4.73874 + 16.8239i) q^{95} +(-3.13994 - 7.05242i) q^{96} +(10.0647 - 1.59410i) q^{97} +(1.00643 + 1.54530i) q^{98} +12.4728i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100}) \) 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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