LMFDB - Embedded newform 175.2.x.a.108.10

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			108.10
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.10

$q$-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 $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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	0.999163	+	0.0409070i	$0.0130247\pi$
$2$	0.0137878	+	0.263087i	0.00974946	+	0.186031i	−0.989413	+	0.145124i	$0.953642\pi$
$3$	1.98896	+	1.61063i	1.14833	+	0.929895i	0.998271	−	0.0587824i	$-0.0187218\pi$
$3$	1.98896	+	1.61063i	1.14833	+	0.929895i	0.150054	+	0.988678i	$0.452055\pi$
$4$	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	−0.341737	−	0.939796i	$-0.611015\pi$
$11$	−3.43661	−	0.730475i	−1.03618	−	0.220246i	−0.694441	+	0.719549i	$0.744348\pi$
$12$	4.14386	+	2.69106i	1.19623	+	0.776841i
$13$	−1.66634	−	3.27037i	−0.462159	−	0.907037i	−0.998030	−	0.0627378i	$-0.980017\pi$
$13$	−1.66634	−	3.27037i	−0.462159	−	0.907037i	0.535871	−	0.844300i	$-0.319983\pi$
$14$	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	−0.416862	−	0.908970i	$-0.636870\pi$
$17$	−5.50381	−	2.11271i	−1.33487	−	0.512408i	−0.918008	+	0.396561i	$0.870203\pi$
$18$	−0.903391	+	0.242063i	−0.212931	+	0.0570548i
$19$	−0.817063	+	7.77383i	−0.187447	+	1.78344i	0.346628	+	0.938003i	$0.387327\pi$
$19$	−0.817063	+	7.77383i	−0.187447	+	1.78344i	−0.534075	+	0.845437i	$0.679340\pi$
$20$	−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	0.626808	−	0.779174i	$-0.284361\pi$
$23$	6.38626	−	0.334690i	1.33163	−	0.0697877i	0.704820	+	0.709386i	$0.251028\pi$
$24$	−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	0.822482	−	0.568792i	$-0.192589\pi$
$29$	0.147381	+	0.202852i	0.0273679	+	0.0376687i	−0.795114	+	0.606460i	$0.792589\pi$
$30$	0.371607	−	1.46115i	0.0678458	−	0.266767i
$31$	0.511405	+	1.14863i	0.0918510	+	0.206301i	0.953629	−	0.300985i	$-0.0973155\pi$
$31$	0.511405	+	1.14863i	0.0918510	+	0.206301i	−0.861778	+	0.507286i	$0.830649\pi$
$32$	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	−0.987306	−	0.158828i	$-0.949229\pi$
$37$	−2.68029	+	4.12728i	−0.440636	+	0.678520i	0.546670	+	0.837348i	$0.315895\pi$
$38$	−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	0.352963	−	0.935637i	$-0.385174\pi$
$41$	0.567075	+	0.184254i	0.0885622	+	0.0287756i	−0.264401	+	0.964413i	$0.585174\pi$
$42$	1.04759	+	1.44389i	0.161647	+	0.222796i
$43$	−5.65218	−	5.65218i	−0.861949	−	0.861949i	0.129616	−	0.991564i	$-0.458626\pi$
$43$	−5.65218	−	5.65218i	−0.861949	−	0.861949i	−0.991564	+	0.129616i	$0.958626\pi$
$44$	−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	0.903396	−	0.428808i	$-0.141066\pi$
$47$	−0.376282	−	0.980249i	−0.0548864	−	0.142984i	−0.958282	+	0.285824i	$0.907733\pi$
$48$	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	−0.632906	−	0.774229i	$-0.718138\pi$
$53$	1.86365	−	2.30142i	0.255992	−	0.316124i	0.888898	+	0.458104i	$0.151471\pi$
$54$	−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	0.935543	−	0.353212i	$-0.114910\pi$
$59$	3.73669	+	4.15002i	0.486476	+	0.540286i	−0.449068	+	0.893498i	$0.648244\pi$
$60$	−10.8354	−	2.15908i	−1.39884	−	0.278736i
$61$	2.91370	+	2.62351i	0.373062	+	0.335906i	0.834240	−	0.551401i	$-0.185907\pi$
$61$	2.91370	+	2.62351i	0.373062	+	0.335906i	−0.461179	+	0.887307i	$0.652573\pi$
$62$	−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	−0.957084	−	0.289811i	$-0.906407\pi$
$67$	−0.424905	+	1.10691i	−0.0519104	+	0.135231i	0.905173	+	0.425042i	$0.139741\pi$
$68$	−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	−0.0774798	−	0.996994i	$-0.524687\pi$
$71$	7.13505	−	5.18392i	0.846775	−	0.615218i	0.924255	+	0.381776i	$0.124687\pi$
$72$	−3.43196	+	1.31741i	−0.404460	+	0.155258i
$73$	−6.72347	+	4.36627i	−0.786923	+	0.511034i	−0.874443	−	0.485129i	$-0.838773\pi$
$73$	−6.72347	+	4.36627i	−0.786923	+	0.511034i	0.0875197	+	0.996163i	$0.472106\pi$
$74$	−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	0.535478	+	0.844549i	$0.320131\pi$
$79$	−4.00368	+	8.99240i	−0.450449	+	1.01172i	−0.985927	+	0.167176i	$0.946535\pi$
$80$	−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	−0.477042	−	0.878881i	$-0.658291\pi$
$83$	−6.00511	+	0.951116i	−0.659146	+	0.104399i	−0.182105	+	0.983279i	$0.558291\pi$
$84$	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	−0.863952	−	0.503574i	$-0.832018\pi$
$89$	−2.57386	+	2.85856i	−0.272829	+	0.303007i	0.591123	+	0.806581i	$0.298685\pi$
$90$	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	0.644834	−	0.764323i	$-0.276927\pi$
$97$	10.0647	+	1.59410i	1.02192	+	0.161856i	0.377085	+	0.926179i	$0.376927\pi$
$98$	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	0.888087	−	0.459675i	$-0.152034\pi$
$101$	9.38700	+	5.41959i	0.934041	+	0.539269i	0.0459539	+	0.998944i	$0.485367\pi$
$102$	3.33366	−	2.16490i	0.330082	−	0.214357i
$103$	4.60289	−	1.76689i	0.453537	−	0.174096i	−0.120867	−	0.992669i	$-0.538567\pi$
$103$	4.60289	−	1.76689i	0.453537	−	0.174096i	0.574403	+	0.818572i	$0.305234\pi$
$104$	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	0.638022	−	0.770018i	$-0.279753\pi$
$107$	8.33275	+	2.23275i	0.805557	+	0.215848i	0.167535	+	0.985866i	$0.446419\pi$
$108$	−0.974000	+	2.53736i	−0.0937232	+	0.244157i
$109$	−6.47269	+	5.82804i	−0.619972	+	0.558225i	−0.918124	−	0.396293i	$-0.870296\pi$
$109$	−6.47269	+	5.82804i	−0.619972	+	0.558225i	0.298152	+	0.954518i	$0.403630\pi$
$110$	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	−0.753100	−	0.657906i	$-0.771442\pi$
$113$	−7.05314	+	3.59375i	−0.663504	+	0.338072i	0.0895963	+	0.995978i	$0.471442\pi$
$114$	−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	0.0198315	−	0.999803i	$-0.493687\pi$
$127$	−8.76051	−	4.46370i	−0.777370	−	0.396090i	−0.797201	+	0.603714i	$0.793687\pi$
$128$	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	−0.506683	−	0.862132i	$-0.669129\pi$
$131$	−13.5234	−	1.42136i	−1.18154	−	0.124185i	−0.674858	+	0.737947i	$0.735795\pi$
$132$	−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	0.310711	−	0.950504i	$-0.399433\pi$
$137$	6.09072	+	0.319201i	0.520365	+	0.0272712i	0.209654	+	0.977776i	$0.432766\pi$
$138$	−2.34839	+	3.61620i	−0.199908	+	0.307831i
$139$	0.132140	+	0.406687i	0.0112080	+	0.0344947i	0.956504	−	0.291719i	$-0.0942272\pi$
$139$	0.132140	+	0.406687i	0.0112080	+	0.0344947i	−0.945296	+	0.326214i	$0.894227\pi$
$140$	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	−0.609669	−	0.792656i	$-0.708698\pi$
$149$	−2.78363	+	1.60713i	−0.228044	+	0.131661i	0.381626	+	0.924317i	$0.375364\pi$
$150$	0.437786	+	3.34268i	0.0357451	+	0.272929i
$151$	2.73858	−	4.74335i	0.222862	−	0.386009i	−0.732814	−	0.680429i	$-0.761793\pi$
$151$	2.73858	−	4.74335i	0.222862	−	0.386009i	0.955676	+	0.294421i	$0.0951267\pi$
$152$	−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	0.628535	−	0.777781i	$-0.283655\pi$
$157$	19.5687	−	5.24342i	1.56175	−	0.418471i	0.933218	+	0.359310i	$0.116988\pi$
$158$	−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	0.226067	−	0.974112i	$-0.427413\pi$
$163$	−7.30125	−	4.74149i	−0.571878	−	0.371382i	−0.797945	+	0.602730i	$0.794080\pi$
$164$	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	−0.764029	−	0.645182i	$-0.776781\pi$
$167$	−3.05970	−	19.3182i	−0.236767	−	1.49489i	0.527262	−	0.849703i	$-0.323219\pi$
$168$	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	0.963083	+	0.269205i	$0.0867609\pi$
$173$	0.439511	+	8.38638i	0.0334154	+	0.637604i	−0.929668	+	0.368400i	$0.879906\pi$
$174$	−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	−0.656761	−	0.754099i	$-0.728074\pi$
$179$	−15.2840	+	1.60642i	−1.14238	+	0.120069i	−0.485623	+	0.874168i	$0.661407\pi$
$180$	−9.79572	−	11.7861i	−0.730130	−	0.878486i
$181$	−4.54675	+	6.25807i	−0.337957	+	0.465159i	−0.943843	−	0.330393i	$-0.892819\pi$
$181$	−4.54675	+	6.25807i	−0.337957	+	0.465159i	0.605886	+	0.795551i	$0.292819\pi$
$182$	−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	0.0432821	−	0.999063i	$-0.486219\pi$
$191$	6.76057	−	1.43700i	0.489178	−	0.103978i	0.445896	+	0.895085i	$0.352885\pi$
$192$	15.2489	+	5.85351i	1.10050	+	0.422441i
$193$	9.53984	−	2.55619i	0.686693	−	0.183999i	0.101430	−	0.994843i	$-0.467658\pi$
$193$	9.53984	−	2.55619i	0.686693	−	0.183999i	0.585262	+	0.810844i	$0.300991\pi$
$194$	−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	0.932339	+	0.361586i	$0.117765\pi$
$197$	−0.927819	+	5.85802i	−0.0661044	+	0.417367i	−0.998443	+	0.0557804i	$0.982235\pi$
$198$	3.28143	−	0.171972i	0.233201	−	0.0122215i
$199$	0.710570	−	1.23074i	0.0503709	−	0.0872450i	−0.839741	−	0.542988i	$-0.817293\pi$
$199$	0.710570	−	1.23074i	0.0503709	−	0.0872450i	0.890112	+	0.455743i	$0.150626\pi$
$200$	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	0.986152	+	0.165842i	$0.0530341\pi$
$211$	4.15174	+	12.7778i	0.285818	+	0.879657i	−0.700335	+	0.713815i	$0.746966\pi$
$212$	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	−0.291549	−	0.956556i	$-0.594171\pi$
$223$	−18.4692	−	9.41051i	−1.23679	−	0.630175i	−0.945238	+	0.326381i	$0.894171\pi$
$224$	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	0.466431	−	0.884557i	$-0.345539\pi$
$227$	−8.00585	−	12.3279i	−0.531367	−	0.818233i	−0.997798	+	0.0663243i	$0.978873\pi$
$228$	−24.3056	+	30.0149i	−1.60968	+	1.98779i
$229$	−18.2779	−	8.13786i	−1.20784	−	0.537765i	−0.298736	−	0.954336i	$-0.596565\pi$
$229$	−18.2779	−	8.13786i	−1.20784	−	0.537765i	−0.909103	+	0.416571i	$0.863232\pi$
$230$	−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	−0.439404	−	0.898290i	$-0.644810\pi$
$233$	5.31044	−	4.30031i	0.347899	−	0.281723i	0.787303	+	0.616567i	$0.211477\pi$
$234$	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	−0.174371	−	0.984680i	$-0.555789\pi$
$239$	4.07114	−	1.32279i	0.263340	−	0.0855644i	0.437711	+	0.899116i	$0.355789\pi$
$240$	−20.4488	−	1.88591i	−1.31996	−	0.121735i
$241$	−2.71942	+	2.44858i	−0.175173	+	0.157727i	−0.752054	−	0.659102i	$-0.770937\pi$
$241$	−2.71942	+	2.44858i	−0.175173	+	0.157727i	0.576880	+	0.816829i	$0.304270\pi$
$242$	−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	$-0.737731\pi$
$251$		−	23.2521i		−	1.46766i	0.679334	−	0.733829i	$-0.262269\pi$
$252$	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	−0.968498	−	0.249020i	$-0.919891\pi$
$257$	−0.0840686	+	0.313748i	−0.00524406	+	0.0195711i	0.963254	+	0.268591i	$0.0865581\pi$
$258$	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	0.965830	+	0.259176i	$0.0834509\pi$
$263$	−0.353542	+	6.74598i	−0.0218003	+	0.415975i	−0.987631	+	0.156799i	$0.949882\pi$
$264$	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	−0.422905	−	0.906174i	$-0.638989\pi$
$269$	−0.532457	+	0.237065i	−0.0324645	+	0.0144541i	0.390440	+	0.920628i	$0.372323\pi$
$270$	0.828664	+	0.0328373i	0.0504309	+	0.00199842i
$271$	7.55674	−	16.9727i	0.459039	−	1.03102i	−0.524679	−	0.851300i	$-0.675815\pi$
$271$	7.55674	−	16.9727i	0.459039	−	1.03102i	0.983718	−	0.179719i	$-0.0575187\pi$
$272$	−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	−0.581930	−	0.813239i	$-0.697702\pi$
$277$	−1.25976	+	0.818099i	−0.0756917	+	0.0491548i	0.506238	+	0.862394i	$0.331036\pi$
$278$	−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	0.987165	+	0.159702i	$0.0510533\pi$
$281$	24.2076	+	17.5878i	1.44410	+	1.04920i	0.456936	+	0.889499i	$0.348947\pi$
$282$	0.683827	+	0.183231i	0.0407213	+	0.0109112i
$283$	3.21935	−	8.38668i	0.191370	−	0.498537i	−0.804002	−	0.594626i	$-0.797300\pi$
$283$	3.21935	−	8.38668i	0.191370	−	0.498537i	0.995373	+	0.0960894i	$0.0306335\pi$
$284$	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	0.157096	−	0.987583i	$-0.449787\pi$
$293$	19.5938	−	19.5938i	1.14468	−	1.14468i	0.987583	−	0.157096i	$-0.0502132\pi$
$294$	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	0.830954	−	0.556341i	$-0.187795\pi$
$307$	4.81162	+	4.81162i	0.274613	+	0.274613i	−0.556341	+	0.830954i	$0.687795\pi$
$308$	−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	−0.312906	−	0.949784i	$-0.601303\pi$
$311$	6.33562	−	29.8067i	0.359260	−	1.69018i	0.672166	−	0.740401i	$-0.265364\pi$
$312$	9.71397	+	0.509088i	0.549946	+	0.0288214i
$313$	−6.76777	+	10.4215i	−0.382537	+	0.589055i	−0.976521	−	0.215421i	$-0.930888\pi$
$313$	−6.76777	+	10.4215i	−0.382537	+	0.589055i	0.593984	+	0.804477i	$0.297554\pi$
$314$	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	0.823466	−	0.567366i	$-0.192037\pi$
$317$	1.73221	+	2.13910i	0.0972906	+	0.120144i	−0.726175	+	0.687509i	$0.758704\pi$
$318$	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	0.765413	+	0.643540i	$0.222535\pi$
$331$	−2.12996	+	20.2652i	−0.117073	+	1.11388i	−0.882486	+	0.470339i	$0.844132\pi$
$332$	−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	0.996311	−	0.0858177i	$-0.0273503\pi$
$337$	6.26481	+	12.2954i	0.341266	+	0.669772i	−0.655045	+	0.755590i	$0.727350\pi$
$338$	−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	0.575457	−	0.817832i	$-0.304824\pi$
$347$	−1.95331	−	1.58176i	−0.104859	−	0.0849134i	−0.680316	+	0.732919i	$0.738158\pi$
$348$	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	−0.0263777	−	0.999652i	$-0.508397\pi$
$353$	−18.9700	−	15.3616i	−1.00967	−	0.817614i	−0.983291	+	0.182038i	$0.941731\pi$
$354$	−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	−0.487719	−	0.873000i	$-0.662171\pi$
$359$	−7.52675	−	35.4106i	−0.397247	−	1.86890i	0.0904726	−	0.995899i	$-0.471162\pi$
$360$	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	0.628787	−	0.777577i	$-0.283552\pi$
$367$	11.0301	+	4.23406i	0.575766	+	0.221016i	−0.0530209	+	0.998593i	$0.516885\pi$
$368$	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	−0.557479	−	0.830191i	$-0.688231\pi$
$373$	−19.7985	+	1.03759i	−1.02513	+	0.0537246i	−0.467647	+	0.883916i	$0.654898\pi$
$374$	−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	0.523874	−	0.851796i	$-0.324486\pi$
$379$	−8.72393	−	12.0075i	−0.448118	−	0.616782i	−0.971992	+	0.235014i	$0.924486\pi$
$380$	−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	0.991572	+	0.129553i	$0.0413544\pi$
$383$	17.8508	+	22.0440i	0.912135	+	1.12639i	−0.0794371	+	0.996840i	$0.525312\pi$
$384$	−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	0.724622	+	0.689146i	$0.242014\pi$
$389$	−4.29281	+	20.1961i	−0.217654	+	1.02398i	−0.942276	+	0.334836i	$0.891319\pi$
$390$	−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	0.942724	−	0.333574i	$-0.108255\pi$
$397$	0.377352	+	0.983037i	0.0189388	+	0.0493372i	−0.923785	+	0.382911i	$0.874921\pi$
$398$	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	0.870604	−	0.491984i	$-0.163728\pi$
$401$	0.184864	+	0.320194i	0.00923166	+	0.0159897i	−0.861373	+	0.507974i	$0.830395\pi$
$402$	−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	0.996906	+	0.0785970i	$0.0250440\pi$
$409$	19.6346	+	21.8064i	0.970868	+	1.07826i	−0.0260387	+	0.999661i	$0.508289\pi$
$410$	−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	0.404897	−	0.914362i	$-0.367307\pi$
$419$	−6.95129	−	5.05041i	−0.339593	−	0.246729i	−0.744490	+	0.667634i	$0.767307\pi$
$420$	−14.3084	+	25.4900i	−0.698179	+	1.24378i
$421$	25.8891	−	18.8095i	1.26176	−	0.916720i	0.262914	−	0.964819i	$-0.415317\pi$
$421$	25.8891	−	18.8095i	1.26176	−	0.916720i	0.998843	+	0.0480998i	$0.0153165\pi$
$422$	−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	0.420666	−	0.907216i	$-0.361797\pi$
$431$	28.5735	−	12.7218i	1.37634	−	0.612785i	0.955673	+	0.294430i	$0.0951299\pi$
$432$	−1.30748	+	4.87957i	−0.0629060	+	0.234769i
$433$	−1.68176	+	0.266365i	−0.0808204	+	0.0128007i	−0.196714	−	0.980461i	$-0.563027\pi$
$433$	−1.68176	+	0.266365i	−0.0808204	+	0.0128007i	0.115893	+	0.993262i	$0.463027\pi$
$434$	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	−0.0488236	−	0.998807i	$-0.515547\pi$
$439$	19.8967	−	22.0975i	0.949616	−	1.05466i	0.998439	−	0.0558477i	$-0.0177861\pi$
$440$	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	0.620392	+	0.784292i	$0.286974\pi$
$443$	−6.50431	+	24.2744i	−0.309029	+	1.15331i	−0.929421	+	0.369021i	$0.879693\pi$
$444$	−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	$0.152634\pi$
$449$			19.5516i			0.922696i	−0.887219	+	0.461348i	$0.847366\pi$
$450$	−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	0.113443	−	0.993544i	$-0.463812\pi$
$457$	−6.09440	−	1.63299i	−0.285084	−	0.0763880i	−0.398527	+	0.917156i	$0.630479\pi$
$458$	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	−0.188691	−	0.982036i	$-0.560425\pi$
$461$	5.06458	−	1.64558i	0.235881	−	0.0766424i	0.424572	+	0.905394i	$0.360425\pi$
$462$	−2.54544	−	5.72732i	−0.118425	−	0.266459i
$463$	−19.8100	+	10.0937i	−0.920649	+	0.469094i	−0.849034	−	0.528338i	$-0.822815\pi$
$463$	−19.8100	+	10.0937i	−0.920649	+	0.469094i	−0.0716148	+	0.997432i	$0.522815\pi$
$464$	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	−0.753729	−	0.657185i	$-0.771747\pi$
$467$	−5.78319	+	4.68313i	−0.267614	+	0.216709i	0.486115	+	0.873895i	$0.338414\pi$
$468$	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	−0.982091	−	0.188405i	$-0.939668\pi$
$479$	−1.32701	−	12.6257i	−0.0606327	−	0.576881i	0.921459	−	0.388476i	$-0.126998\pi$
$480$	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	−0.306046	−	0.952017i	$-0.599006\pi$
$487$	−15.6668	−	0.821060i	−0.709928	−	0.0372058i	−0.403882	+	0.914811i	$0.632339\pi$
$488$	−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	−0.799705	−	0.600393i	$-0.795011\pi$
$491$	4.43552	−	13.6511i	0.200172	−	0.616067i	0.999877	−	0.0156736i	$-0.00498927\pi$
$492$	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	−0.642085	−	0.766634i	$-0.721930\pi$
$499$	−6.68368	+	3.85883i	−0.299203	+	0.172745i	0.342882	+	0.939378i	$0.388597\pi$
$500$	−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	0.929951	+	0.367684i	$0.119849\pi$
$503$	−1.52745	+	9.64392i	−0.0681055	+	0.430001i	−0.998056	+	0.0623173i	$0.980151\pi$
$504$	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	−0.327561	−	0.944830i	$-0.606227\pi$
$509$	−5.47118	+	1.16293i	−0.242506	+	0.0515462i	0.0850552	+	0.996376i	$0.472893\pi$
$510$	−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	−0.834606	−	0.550847i	$-0.814305\pi$
$521$	−35.0701	+	3.68601i	−1.53645	+	0.161487i	−0.701841	+	0.712334i	$0.747638\pi$
$522$	−0.182245	−	0.147579i	−0.00797666	−	0.00645937i
$523$	−0.924518	−	17.6409i	−0.0404264	−	0.771381i	−0.941356	−	0.337415i	$-0.890447\pi$
$523$	−0.924518	−	17.6409i	−0.0404264	−	0.771381i	0.900930	−	0.433965i	$-0.142886\pi$
$524$	−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	0.116915	−	0.993142i	$-0.462700\pi$
$541$	14.5992	−	3.10316i	0.627669	−	0.133415i	0.510754	+	0.859727i	$0.329366\pi$
$542$	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	0.190769	+	0.981635i	$0.438902\pi$
$547$	−6.87620	+	43.4146i	−0.294005	+	1.85627i	−0.484774	+	0.874639i	$0.661098\pi$
$548$	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	0.949915	−	0.312508i	$-0.101169\pi$
$557$	−0.684178	−	2.55339i	−0.0289895	−	0.108190i	−0.978905	+	0.204318i	$0.934502\pi$
$558$	−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	0.671386	−	0.741108i	$-0.265699\pi$
$563$	29.9354	+	1.56885i	1.26163	+	0.0661191i	0.590241	+	0.807227i	$0.299033\pi$
$564$	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	0.763250	−	0.646103i	$-0.223602\pi$
$569$	32.8105	+	3.44853i	1.37549	+	0.144570i	0.612239	+	0.790673i	$0.290269\pi$
$570$	11.0551	+	4.08266i	0.463046	+	0.171004i
$571$	3.39211	+	32.2738i	0.141956	+	1.35062i	0.801068	+	0.598573i	$0.204265\pi$
$571$	3.39211	+	32.2738i	0.141956	+	1.35062i	−0.659113	+	0.752044i	$0.729068\pi$
$572$	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	0.837163	−	0.546954i	$-0.184213\pi$
$577$	−0.0722936	−	0.111322i	−0.00300962	−	0.00463441i	−0.840172	+	0.542320i	$0.817546\pi$
$578$	−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	0.145762	−	0.989320i	$-0.453437\pi$
$587$	24.9989	−	12.7376i	1.03182	−	0.525736i	0.886053	+	0.463584i	$0.153437\pi$
$588$	−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	−0.790324	−	0.612689i	$-0.790088\pi$
$593$	−43.3728	−	11.6217i	−1.78111	−	0.477247i	−0.990785	+	0.135442i	$0.956754\pi$
$594$	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	0.0652335	−	0.997870i	$-0.479221\pi$
$599$	−18.7555	−	10.8285i	−0.766331	−	0.442441i	−0.831564	+	0.555429i	$0.812554\pi$
$600$	3.08471	+	12.8869i	0.125933	+	0.526105i
$601$		−	27.1300i		−	1.10666i	−0.832963	−	0.553328i	$-0.813357\pi$
$601$		−	27.1300i		−	1.10666i	0.832963	−	0.553328i	$-0.186643\pi$
$602$	−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	−0.981807	−	0.189882i	$-0.939189\pi$
$607$	−0.901633	+	3.36494i	−0.0365961	+	0.136579i	0.945211	+	0.326461i	$0.105856\pi$
$608$	−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	−0.710555	−	0.703642i	$-0.751556\pi$
$613$	1.72465	−	32.9083i	0.0696581	−	1.32916i	0.780213	−	0.625514i	$-0.215111\pi$
$614$	−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	−0.892856	−	0.450342i	$-0.851302\pi$
$617$	−39.8140	+	6.30591i	−1.60285	+	0.253866i	−0.709994	+	0.704208i	$0.751302\pi$
$618$	−0.860387	+	3.21101i	−0.0346098	+	0.129166i
$619$	26.1694	−	11.6513i	1.05184	−	0.468307i	0.193342	−	0.981131i	$-0.438067\pi$
$619$	26.1694	−	11.6513i	1.05184	−	0.468307i	0.858494	+	0.512824i	$0.171401\pi$
$620$	−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	−0.996595	−	0.0824526i	$-0.973725\pi$
$631$	−34.7400	−	25.2401i	−1.38298	−	1.00479i	−0.386382	−	0.922339i	$-0.626275\pi$
$632$	−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	0.997186	−	0.0749634i	$-0.0238840\pi$
$641$	20.7202	+	23.0121i	0.818399	+	0.908924i	−0.178787	+	0.983888i	$0.557217\pi$
$642$	−4.52028	+	3.66045i	−0.178401	+	0.144466i
$643$	−10.0822	+	10.0822i	−0.397604	+	0.397604i	−0.877387	−	0.479783i	$-0.840715\pi$
$643$	−10.0822	+	10.0822i	−0.397604	+	0.397604i	0.479783	+	0.877387i	$0.340715\pi$
$644$	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	−0.996105	−	0.0881806i	$-0.971895\pi$
$647$	−17.8753	+	22.0741i	−0.702749	+	0.867823i	0.293355	+	0.956003i	$0.405228\pi$
$648$	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	0.937672	+	0.347521i	$0.112977\pi$
$653$	12.0968	+	31.5132i	0.473383	+	1.23321i	−0.464289	+	0.885684i	$0.653690\pi$
$654$	−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	0.273476	−	0.961879i	$-0.411827\pi$
$659$	−1.81381	−	0.589344i	−0.0706562	−	0.0229576i	−0.344132	+	0.938921i	$0.611827\pi$
$660$	35.6598	+	15.3349i	1.38806	+	0.596910i
$661$	2.24221	−	10.5488i	0.0872120	−	0.410300i	−0.912786	−	0.408437i	$-0.866074\pi$
$661$	2.24221	−	10.5488i	0.0872120	−	0.410300i	0.999998	−	0.00186255i	$-0.000592870\pi$
$662$	−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	0.0870048	+	0.996208i	$0.472270\pi$
$673$	−19.9777	+	39.2085i	−0.770084	+	1.51138i	−0.857089	+	0.515168i	$0.827730\pi$
$674$	−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	−0.226364	−	0.974043i	$-0.572684\pi$
$677$	−9.09823	+	0.476818i	−0.349674	+	0.0183256i	−0.123309	+	0.992368i	$0.539351\pi$
$678$	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	−0.199212	−	0.979956i	$-0.563838\pi$
$683$	−26.2120	−	10.0618i	−1.00297	−	0.385006i	−0.803762	+	0.594951i	$0.797172\pi$
$684$	−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	0.477257	+	0.878764i	$0.341631\pi$
$691$	10.4802	+	49.3056i	0.398686	+	1.87567i	−0.0785710	+	0.996909i	$0.525036\pi$
$692$	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	−0.999984	−	0.00565112i	$-0.998201\pi$
$709$	−2.36320	−	11.1180i	−0.0887517	−	0.417544i	0.911232	−	0.411893i	$-0.135132\pi$
$710$	−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	0.485650	+	0.874153i	$0.338583\pi$
$719$	−4.58882	+	43.6597i	−0.171134	+	1.62823i	−0.656784	+	0.754078i	$0.728084\pi$
$720$	−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	0.418058	+	0.908420i	$0.362711\pi$
$727$	−15.1693	+	29.7714i	−0.562598	+	1.10416i	−0.980656	+	0.195740i	$0.937289\pi$
$728$	−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	−0.995212	−	0.0977448i	$-0.968837\pi$
$733$	−23.9308	−	29.5521i	−0.883904	−	1.09153i	0.111307	−	0.993786i	$-0.464496\pi$
$734$	−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	−0.694720	−	0.719281i	$-0.744472\pi$
$739$	6.32030	−	29.7347i	0.232496	−	1.09381i	0.927216	−	0.374528i	$-0.122195\pi$
$740$	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	0.840008	−	0.542573i	$-0.182550\pi$
$743$	8.10749	+	8.10749i	0.297435	+	0.297435i	−0.542573	+	0.840008i	$0.682550\pi$
$744$	−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	−0.892678	−	0.450694i	$-0.851176\pi$
$751$	−22.9279	−	39.7123i	−0.836652	−	1.44912i	0.0560263	−	0.998429i	$-0.482157\pi$
$752$	−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	−0.0914400	−	0.995811i	$-0.529147\pi$
$757$	24.8825	−	24.8825i	0.904371	−	0.904371i	0.995811	+	0.0914400i	$0.0291470\pi$
$758$	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	0.252351	−	0.967636i	$-0.418796\pi$
$761$	−18.8581	−	16.9799i	−0.683606	−	0.615522i	−0.935957	+	0.352114i	$0.885463\pi$
$762$	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	0.731249	−	0.682111i	$-0.238938\pi$
$769$	8.55473	+	6.21537i	0.308491	+	0.224132i	−0.422757	+	0.906243i	$0.638938\pi$
$770$	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	−0.432385	−	0.901689i	$-0.642328\pi$
$773$	5.99102	−	3.89062i	0.215482	−	0.139936i	0.647867	+	0.761753i	$0.275661\pi$
$774$	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	−0.960046	−	0.279842i	$-0.909718\pi$
$787$	0.673066	−	12.8429i	0.0239922	−	0.457799i	0.984038	−	0.177957i	$-0.0569487\pi$
$788$	−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	0.438594	−	0.898685i	$-0.355477\pi$
$797$	16.3180	+	2.58451i	0.578012	+	0.0915481i	0.139418	+	0.990234i	$0.455477\pi$
$798$	−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	−0.993218	−	0.116267i	$-0.962907\pi$
$809$	−27.9141	+	25.1340i	−0.981407	+	0.883663i	0.0118109	+	0.999930i	$0.496240\pi$
$810$	−3.12030	−	2.73828i	−0.109636	−	0.0962134i
$811$	−19.9913	+	6.49556i	−0.701989	+	0.228090i	−0.638197	−	0.769873i	$-0.720319\pi$
$811$	−19.9913	+	6.49556i	−0.701989	+	0.228090i	−0.0637922	+	0.997963i	$0.520319\pi$
$812$	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	−0.580320	−	0.814389i	$-0.697072\pi$
$821$	−45.0953	−	20.0777i	−1.57384	−	0.700718i	−0.993518	+	0.113671i	$0.963739\pi$
$822$	−2.58794	+	3.19584i	−0.0902648	+	0.111468i
$823$	28.3335	+	43.6298i	0.987645	+	1.52084i	0.847559	+	0.530701i	$0.178071\pi$
$823$	28.3335	+	43.6298i	0.987645	+	1.52084i	0.140086	+	0.990139i	$0.455262\pi$
$824$	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	0.928196	−	0.372093i	$-0.121360\pi$
$827$	33.7254	+	17.1839i	1.17275	+	0.597544i	0.244550	+	0.969637i	$0.421360\pi$
$828$	15.7072	+	40.9187i	0.545864	+	1.42202i
$829$	3.99905	+	38.0484i	0.138893	+	1.32147i	0.812750	+	0.582613i	$0.197970\pi$
$829$	3.99905	+	38.0484i	0.138893	+	1.32147i	−0.673857	+	0.738862i	$0.735364\pi$
$830$	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	−0.999631	−	0.0271505i	$-0.991357\pi$
$839$	−5.99213	−	18.4419i	−0.206871	−	0.636684i	0.792760	−	0.609534i	$-0.208643\pi$
$840$	−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	−0.949886	−	0.312595i	$-0.898802\pi$
$853$	1.46342	−	9.23966i	0.0501065	−	0.316360i	0.999993	−	0.00376463i	$-0.00119832\pi$
$854$	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	0.0213003	−	0.999773i	$-0.493219\pi$
$857$	15.7975	−	4.23294i	0.539633	−	0.144594i	0.518333	+	0.855179i	$0.326553\pi$
$858$	−8.11731	−	3.11595i	−0.277121	−	0.106377i
$859$	−47.3304	+	10.0604i	−1.61489	+	0.343256i	−0.924797	−	0.380461i	$-0.875765\pi$
$859$	−47.3304	+	10.0604i	−1.61489	+	0.343256i	−0.690096	+	0.723717i	$0.742432\pi$
$860$	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	−0.993653	−	0.112485i	$-0.964119\pi$
$863$	−44.0820	−	28.6272i	−1.50057	−	0.974481i	−0.506916	−	0.861996i	$-0.669214\pi$
$864$	−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	−0.910607	−	0.413274i	$-0.864385\pi$
$877$	−1.42703	−	27.2293i	−0.0481873	−	0.919469i	0.862419	−	0.506195i	$-0.168948\pi$
$878$	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	−0.815669	−	0.578519i	$-0.803631\pi$
$881$	−0.398014	+	0.547820i	−0.0134094	+	0.0184565i	0.802260	+	0.596975i	$0.203631\pi$
$882$	6.10888	+	2.35423i	0.205697	+	0.0792709i
$883$	4.97481	+	31.4097i	0.167416	+	1.05702i	0.918097	+	0.396356i	$0.129726\pi$
$883$	4.97481	+	31.4097i	0.167416	+	1.05702i	−0.750681	+	0.660665i	$0.770274\pi$
$884$	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	0.535015	−	0.844843i	$-0.320306\pi$
$887$	−0.571156	−	0.370913i	−0.0191775	−	0.0124540i	−0.554192	+	0.832389i	$0.686973\pi$
$888$	−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	−0.852510	−	0.522710i	$-0.824921\pi$
$907$	−11.3108	−	42.2126i	−0.375570	−	1.40165i	0.476941	−	0.878936i	$-0.341746\pi$
$908$	−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	−0.989331	−	0.145689i	$-0.953460\pi$
$911$	−8.28755	−	25.5065i	−0.274579	−	0.845067i	0.714752	−	0.699378i	$-0.246540\pi$
$912$	−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	−0.641749	−	0.766915i	$-0.721791\pi$
$919$	−43.3179	−	4.55289i	−1.42892	−	0.150186i	−0.787176	+	0.616729i	$0.788458\pi$
$920$	−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	0.921862	−	0.387519i	$-0.126668\pi$
$929$	38.1215	+	16.9728i	1.25073	+	0.556859i	0.328863	+	0.944378i	$0.393334\pi$
$930$	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	−0.130400	−	0.991461i	$-0.541626\pi$
$937$	18.2151	−	9.28106i	0.595062	−	0.303199i	0.725462	+	0.688262i	$0.241626\pi$
$938$	−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	−0.713298	−	0.700861i	$-0.752799\pi$
$941$	−2.78647	+	2.50895i	−0.0908362	+	0.0817893i	0.622462	+	0.782650i	$0.286133\pi$
$942$	−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	−0.994423	−	0.105470i	$-0.966365\pi$
$947$	−51.1715	+	19.6429i	−1.66285	+	0.638308i	−0.668427	+	0.743778i	$0.733032\pi$
$948$	−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	0.530019	−	0.847986i	$-0.322185\pi$
$953$	23.8338	+	3.77491i	0.772054	+	0.122281i	0.242036	+	0.970267i	$0.422185\pi$
$954$	−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	−0.226504	−	0.974010i	$-0.572730\pi$
$967$	−4.38267	+	0.694147i	−0.140937	+	0.0223222i	0.0855672	+	0.996332i	$0.472730\pi$
$968$	−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	−0.931032	−	0.364938i	$-0.881090\pi$
$971$	−1.14821	+	2.57893i	−0.0368479	+	0.0827617i	0.894184	+	0.447700i	$0.147757\pi$
$972$	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	−0.813762	−	0.581199i	$-0.802584\pi$
$977$	−19.1854	+	12.4592i	−0.613797	+	0.398604i	0.199965	+	0.979803i	$0.435917\pi$
$978$	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	0.686932	+	0.726721i	$0.258957\pi$
$983$	−9.71403	+	25.3059i	−0.309829	+	0.807133i	−0.996762	+	0.0804117i	$0.974377\pi$
$984$	−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	0.892752	−	0.450548i	$-0.148771\pi$
$991$	11.0607	+	12.2841i	0.351354	+	0.390219i	−0.541398	+	0.840767i	$0.682105\pi$
$992$	−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	−0.745792	−	0.666178i	$-0.767929\pi$
$997$	1.92253	−	2.37413i	0.0608872	−	0.0751895i	0.806680	+	0.590989i	$0.201262\pi$
$998$	−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.108.10	yes	288
5.2	odd	4		875.2.bb.b.857.9		288
5.3	odd	4		875.2.bb.a.857.10		288
5.4	even	2		875.2.bb.c.143.9		288
7.5	odd	6	inner	175.2.x.a.33.10	✓	288
25.3	odd	20		875.2.bb.c.507.9		288
25.4	even	10		875.2.bb.a.493.9		288
25.21	even	5		875.2.bb.b.493.10		288
25.22	odd	20	inner	175.2.x.a.122.10	yes	288
35.12	even	12		875.2.bb.b.607.10		288
35.19	odd	6		875.2.bb.c.768.9		288
35.33	even	12		875.2.bb.a.607.9		288
175.47	even	60	inner	175.2.x.a.47.10	yes	288
175.54	odd	30		875.2.bb.a.243.10		288
175.96	odd	30		875.2.bb.b.243.9		288
175.103	even	60		875.2.bb.c.257.9		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.10	✓	288	7.5	odd	6	inner
175.2.x.a.47.10	yes	288	175.47	even	60	inner
175.2.x.a.108.10	yes	288	1.1	even	1	trivial
175.2.x.a.122.10	yes	288	25.22	odd	20	inner
875.2.bb.a.243.10		288	175.54	odd	30
875.2.bb.a.493.9		288	25.4	even	10
875.2.bb.a.607.9		288	35.33	even	12
875.2.bb.a.857.10		288	5.3	odd	4
875.2.bb.b.243.9		288	175.96	odd	30
875.2.bb.b.493.10		288	25.21	even	5
875.2.bb.b.607.10		288	35.12	even	12
875.2.bb.b.857.9		288	5.2	odd	4
875.2.bb.c.143.9		288	5.4	even	2
875.2.bb.c.257.9		288	175.103	even	60
875.2.bb.c.507.9		288	25.3	odd	20
875.2.bb.c.768.9		288	35.19	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Fields

Representations

Groups

Database

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