LMFDB - Embedded newform 680.2.h.b.509.20

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(509,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 1, 1, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.509"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.h (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [40] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$40$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.20
Character	$\chi$	$=$	680.509
Dual form			680.2.h.b.509.17

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.0956273 + 1.41098i) q^{2} +2.33268i q^{3} +(-1.98171 - 0.269856i) q^{4} +(1.97601 - 1.04660i) q^{5} +(-3.29135 - 0.223067i) q^{6} +4.43533 q^{7} +(0.570266 - 2.77034i) q^{8} -2.44138 q^{9} +(1.28777 + 2.88819i) q^{10} -2.45819 q^{11} +(0.629486 - 4.62269i) q^{12} +3.83628 q^{13} +(-0.424138 + 6.25814i) q^{14} +(2.44138 + 4.60940i) q^{15} +(3.85436 + 1.06955i) q^{16} +(-3.53348 + 2.12474i) q^{17} +(0.233462 - 3.44473i) q^{18} +6.37197i q^{19} +(-4.19832 + 1.54082i) q^{20} +10.3462i q^{21} +(0.235070 - 3.46845i) q^{22} +6.99487 q^{23} +(6.46231 + 1.33025i) q^{24} +(2.80926 - 4.13619i) q^{25} +(-0.366853 + 5.41290i) q^{26} +1.30309i q^{27} +(-8.78954 - 1.19690i) q^{28} -9.25840 q^{29} +(-6.73722 + 3.00394i) q^{30} -7.14810i q^{31} +(-1.87770 + 5.33613i) q^{32} -5.73417i q^{33} +(-2.66007 - 5.18884i) q^{34} +(8.76427 - 4.64201i) q^{35} +(4.83810 + 0.658820i) q^{36} -1.05872i q^{37} +(-8.99070 - 0.609334i) q^{38} +8.94879i q^{39} +(-1.77259 - 6.07107i) q^{40} -5.40889i q^{41} +(-14.5982 - 0.989377i) q^{42} -1.71430 q^{43} +(4.87143 + 0.663358i) q^{44} +(-4.82419 + 2.55514i) q^{45} +(-0.668901 + 9.86960i) q^{46} +1.62850i q^{47} +(-2.49492 + 8.99096i) q^{48} +12.6721 q^{49} +(5.56742 + 4.35933i) q^{50} +(-4.95634 - 8.24246i) q^{51} +(-7.60239 - 1.03524i) q^{52} -3.10774 q^{53} +(-1.83862 - 0.124611i) q^{54} +(-4.85742 + 2.57274i) q^{55} +(2.52932 - 12.2874i) q^{56} -14.8637 q^{57} +(0.885356 - 13.0634i) q^{58} +0.215973i q^{59} +(-3.59423 - 9.79332i) q^{60} -4.70860 q^{61} +(10.0858 + 0.683553i) q^{62} -10.8283 q^{63} +(-7.34959 - 3.15966i) q^{64} +(7.58053 - 4.01504i) q^{65} +(8.09078 + 0.548343i) q^{66} +9.28922 q^{67} +(7.57571 - 3.25710i) q^{68} +16.3168i q^{69} +(5.71167 + 12.8101i) q^{70} -6.57476i q^{71} +(-1.39223 + 6.76345i) q^{72} -10.8445 q^{73} +(1.49383 + 0.101243i) q^{74} +(9.64839 + 6.55309i) q^{75} +(1.71951 - 12.6274i) q^{76} -10.9029 q^{77} +(-12.6265 - 0.855748i) q^{78} +3.29578i q^{79} +(8.73565 - 1.92052i) q^{80} -10.3638 q^{81} +(7.63182 + 0.517237i) q^{82} -2.67900 q^{83} +(2.79198 - 20.5031i) q^{84} +(-4.75845 + 7.89666i) q^{85} +(0.163933 - 2.41883i) q^{86} -21.5968i q^{87} +(-1.40182 + 6.81004i) q^{88} -4.86695 q^{89} +(-3.14392 - 7.05117i) q^{90} +17.0151 q^{91} +(-13.8618 - 1.88761i) q^{92} +16.6742 q^{93} +(-2.29777 - 0.155729i) q^{94} +(6.66890 + 12.5911i) q^{95} +(-12.4475 - 4.38005i) q^{96} +5.84892 q^{97} +(-1.21180 + 17.8801i) q^{98} +6.00138 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) $ 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$-1$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−0.0956273	+	1.41098i	−0.0676187	+	0.997711i
$2$	−0.0956273	+	1.41098i	−0.0676187	+	0.997711i
$3$			2.33268i			1.34677i	0.739291	+	0.673386i	$0.235161\pi$
$3$			2.33268i			1.34677i	−0.739291	+	0.673386i	$0.764839\pi$
$4$	−1.98171	−	0.269856i	−0.990855	−	0.134928i
$5$	1.97601	−	1.04660i	0.883700	−	0.468053i
$5$	1.97601	−	1.04660i	0.883700	−	0.468053i
$6$	−3.29135	−	0.223067i	−1.34369	−	0.0910669i
$7$	4.43533			1.67640			0.838198	−	0.545366i	$-0.183609\pi$
$7$	4.43533			1.67640			0.838198	+	0.545366i	$0.183609\pi$
$8$	0.570266	−	2.77034i	0.201619	−	0.979464i
$9$	−2.44138			−0.813792
$10$	1.28777	+	2.88819i	0.407228	+	0.913327i
$11$	−2.45819			−0.741173			−0.370587	−	0.928798i	$-0.620843\pi$
$11$	−2.45819			−0.741173			−0.370587	+	0.928798i	$0.620843\pi$
$12$	0.629486	−	4.62269i	0.181717	−	1.33446i
$13$	3.83628			1.06399			0.531996	−	0.846747i	$-0.321442\pi$
$13$	3.83628			1.06399			0.531996	+	0.846747i	$0.321442\pi$
$14$	−0.424138	+	6.25814i	−0.113356	+	1.67256i
$15$	2.44138	+	4.60940i	0.630361	+	1.19014i
$16$	3.85436	+	1.06955i	0.963589	+	0.267388i
$17$	−3.53348	+	2.12474i	−0.856994	+	0.515326i
$17$	−3.53348	+	2.12474i	−0.856994	+	0.515326i
$18$	0.233462	−	3.44473i	0.0550276	−	0.811930i
$19$			6.37197i			1.46183i	0.682468	+	0.730915i	$0.260907\pi$
$19$			6.37197i			1.46183i	−0.682468	+	0.730915i	$0.739093\pi$
$20$	−4.19832	+	1.54082i	−0.938773	+	0.344537i
$21$			10.3462i			2.25772i
$22$	0.235070	−	3.46845i	0.0501172	−	0.739477i
$23$	6.99487			1.45853			0.729266	−	0.684231i	$-0.239862\pi$
$23$	6.99487			1.45853			0.729266	+	0.684231i	$0.239862\pi$
$24$	6.46231	+	1.33025i	1.31911	+	0.271535i
$25$	2.80926	−	4.13619i	0.561852	−	0.827238i
$26$	−0.366853	+	5.41290i	−0.0719457	+	1.06156i
$27$			1.30309i			0.250779i
$28$	−8.78954	−	1.19690i	−1.66107	−	0.226193i
$29$	−9.25840			−1.71924			−0.859621	−	0.510932i	$-0.829300\pi$
$29$	−9.25840			−1.71924			−0.859621	+	0.510932i	$0.829300\pi$
$30$	−6.73722	+	3.00394i	−1.23004	+	0.548442i
$31$		−	7.14810i		−	1.28384i	−0.766773	−	0.641918i	$-0.778139\pi$
$31$		−	7.14810i		−	1.28384i	0.766773	−	0.641918i	$-0.221861\pi$
$32$	−1.87770	+	5.33613i	−0.331933	+	0.943303i
$33$		−	5.73417i		−	0.998190i
$34$	−2.66007	−	5.18884i	−0.456198	−	0.889878i
$35$	8.76427	−	4.64201i	1.48143	−	0.784643i
$36$	4.83810	+	0.658820i	0.806351	+	0.109803i
$37$		−	1.05872i		−	0.174053i	−0.996206	−	0.0870265i	$-0.972264\pi$
$37$		−	1.05872i		−	0.174053i	0.996206	−	0.0870265i	$-0.0277365\pi$
$38$	−8.99070	−	0.609334i	−1.45848	−	0.0988471i
$39$			8.94879i			1.43295i
$40$	−1.77259	−	6.07107i	−0.280270	−	0.959921i
$41$		−	5.40889i		−	0.844727i	−0.906427	−	0.422363i	$-0.861201\pi$
$41$		−	5.40889i		−	0.844727i	0.906427	−	0.422363i	$-0.138799\pi$
$42$	−14.5982	−	0.989377i	−2.25255	−	0.152664i
$43$	−1.71430			−0.261428			−0.130714	−	0.991420i	$-0.541727\pi$
$43$	−1.71430			−0.261428			−0.130714	+	0.991420i	$0.541727\pi$
$44$	4.87143	+	0.663358i	0.734395	+	0.100005i
$45$	−4.82419	+	2.55514i	−0.719148	+	0.380898i
$46$	−0.668901	+	9.86960i	−0.0986240	+	1.45519i
$47$			1.62850i			0.237540i	0.992922	+	0.118770i	$0.0378952\pi$
$47$			1.62850i			0.237540i	−0.992922	+	0.118770i	$0.962105\pi$
$48$	−2.49492	+	8.99096i	−0.360111	+	1.29773i
$49$	12.6721			1.81030
$50$	5.56742	+	4.35933i	0.787353	+	0.616503i
$51$	−4.95634	−	8.24246i	−0.694026	−	1.15418i
$52$	−7.60239	−	1.03524i	−1.05426	−	0.143562i
$53$	−3.10774			−0.426880			−0.213440	−	0.976956i	$-0.568467\pi$
$53$	−3.10774			−0.426880			−0.213440	+	0.976956i	$0.568467\pi$
$54$	−1.83862	−	0.124611i	−0.250205	−	0.0169574i
$55$	−4.85742	+	2.57274i	−0.654975	+	0.346909i
$56$	2.52932	−	12.2874i	0.337994	−	1.64197i
$57$	−14.8637			−1.96875
$58$	0.885356	−	13.0634i	0.116253	−	1.71531i
$59$			0.215973i			0.0281172i	0.999901	+	0.0140586i	$0.00447514\pi$
$59$			0.215973i			0.0281172i	−0.999901	+	0.0140586i	$0.995525\pi$
$60$	−3.59423	−	9.79332i	−0.464013	−	1.26431i
$61$	−4.70860			−0.602874			−0.301437	−	0.953486i	$-0.597466\pi$
$61$	−4.70860			−0.602874			−0.301437	+	0.953486i	$0.597466\pi$
$62$	10.0858	+	0.683553i	1.28090	+	0.0868114i
$63$	−10.8283			−1.36424
$64$	−7.34959	−	3.15966i	−0.918699	−	0.394958i
$65$	7.58053	−	4.01504i	0.940249	−	0.498005i
$66$	8.09078	+	0.548343i	0.995906	+	0.0674963i
$67$	9.28922			1.13486			0.567429	−	0.823422i	$-0.307938\pi$
$67$	9.28922			1.13486			0.567429	+	0.823422i	$0.307938\pi$
$68$	7.57571	−	3.25710i	0.918689	−	0.394981i
$69$			16.3168i			1.96431i
$70$	5.71167	+	12.8101i	0.682675	+	1.53110i
$71$		−	6.57476i		−	0.780281i	−0.920755	−	0.390140i	$-0.872426\pi$
$71$		−	6.57476i		−	0.780281i	0.920755	−	0.390140i	$-0.127574\pi$
$72$	−1.39223	+	6.76345i	−0.164076	+	0.797080i
$73$	−10.8445			−1.26926			−0.634629	−	0.772817i	$-0.718847\pi$
$73$	−10.8445			−1.26926			−0.634629	+	0.772817i	$0.718847\pi$
$74$	1.49383	+	0.101243i	0.173655	+	0.0117692i
$75$	9.64839	+	6.55309i	1.11410	+	0.756686i
$76$	1.71951	−	12.6274i	0.197242	−	1.44846i
$77$	−10.9029			−1.24250
$78$	−12.6265	−	0.855748i	−1.42967	−	0.0968944i
$79$			3.29578i			0.370804i	0.982663	+	0.185402i	$0.0593587\pi$
$79$			3.29578i			0.370804i	−0.982663	+	0.185402i	$0.940641\pi$
$80$	8.73565	−	1.92052i	0.976676	−	0.214720i
$81$	−10.3638			−1.15153
$82$	7.63182	+	0.517237i	0.842793	+	0.0571193i
$83$	−2.67900			−0.294059			−0.147029	−	0.989132i	$-0.546971\pi$
$83$	−2.67900			−0.294059			−0.147029	+	0.989132i	$0.546971\pi$
$84$	2.79198	−	20.5031i	0.304630	−	2.23708i
$85$	−4.75845	+	7.89666i	−0.516126	+	0.856513i
$86$	0.163933	−	2.41883i	0.0176774	−	0.260829i
$87$		−	21.5968i		−	2.31543i
$88$	−1.40182	+	6.81004i	−0.149435	+	0.725952i
$89$	−4.86695			−0.515895			−0.257948	−	0.966159i	$-0.583046\pi$
$89$	−4.86695			−0.515895			−0.257948	+	0.966159i	$0.583046\pi$
$90$	−3.14392	−	7.05117i	−0.331399	−	0.743258i
$91$	17.0151			1.78367
$92$	−13.8618	−	1.88761i	−1.44519	−	0.196797i
$93$	16.6742			1.72903
$94$	−2.29777	−	0.155729i	−0.236997	−	0.0160622i
$95$	6.66890	+	12.5911i	0.684215	+	1.29182i
$96$	−12.4475	−	4.38005i	−1.27041	−	0.447037i
$97$	5.84892			0.593868			0.296934	−	0.954898i	$-0.404036\pi$
$97$	5.84892			0.593868			0.296934	+	0.954898i	$0.404036\pi$
$98$	−1.21180	+	17.8801i	−0.122410	+	1.80616i
$99$	6.00138			0.603161
$100$	−6.68332	+	7.43864i	−0.668332	+	0.743864i
$101$		−	14.0872i		−	1.40172i	−0.713297	−	0.700862i	$-0.752799\pi$
$101$		−	14.0872i		−	1.40172i	0.713297	−	0.700862i	$-0.247201\pi$
$102$	12.1039	−	6.20507i	1.19846	−	0.614394i
$103$			13.4039i			1.32073i	0.750945	+	0.660365i	$0.229598\pi$
$103$			13.4039i			1.32073i	−0.750945	+	0.660365i	$0.770402\pi$
$104$	2.18770	−	10.6278i	0.214521	−	1.04214i
$105$	10.8283	+	20.4442i	1.05673	+	1.99515i
$106$	0.297184	−	4.38494i	0.0288651	−	0.425903i
$107$		−	10.8518i		−	1.04909i	−0.851384	−	0.524543i	$-0.824236\pi$
$107$		−	10.8518i		−	1.04909i	0.851384	−	0.524543i	$-0.175764\pi$
$108$	0.351645	−	2.58234i	0.0338371	−	0.248486i
$109$	3.07252			0.294294			0.147147	−	0.989115i	$-0.452991\pi$
$109$	3.07252			0.294294			0.147147	+	0.989115i	$0.452991\pi$
$110$	−3.16558	−	7.09973i	−0.301826	−	0.676933i
$111$	2.46966			0.234410
$112$	17.0953	+	4.74381i	1.61536	+	0.448248i
$113$	10.7302			1.00941			0.504707	−	0.863291i	$-0.331601\pi$
$113$	10.7302			1.00941			0.504707	+	0.863291i	$0.331601\pi$
$114$	1.42138	−	20.9724i	0.133124	−	1.96424i
$115$	13.8220	−	7.32083i	1.28890	−	0.682671i
$116$	18.3475	+	2.49843i	1.70352	+	0.231974i
$117$	−9.36579			−0.865868
$118$	−0.304732	−	0.0206529i	−0.0280529	−	0.00190125i
$119$	−15.6721	+	9.42393i	−1.43666	+	0.863890i
$120$	14.1618	−	4.13487i	1.29279	−	0.377460i
$121$	−4.95729			−0.450663
$122$	0.450270	−	6.64372i	0.0407656	−	0.601494i
$123$	12.6172			1.13765
$124$	−1.92896	+	14.1655i	−0.173225	+	1.27210i
$125$	1.22220	−	11.1133i	0.109317	−	0.994007i
$126$	1.03548	−	15.2785i	0.0922480	−	1.36112i
$127$		−	7.53988i		−	0.669056i	−0.942386	−	0.334528i	$-0.891423\pi$
$127$		−	7.53988i		−	0.669056i	0.942386	−	0.334528i	$-0.108577\pi$
$128$	5.16103	−	10.0680i	0.456175	−	0.889890i
$129$		−	3.99890i		−	0.352083i
$130$	4.94023	+	11.0799i	0.433287	+	0.971772i
$131$	4.30482			0.376114			0.188057	−	0.982158i	$-0.439781\pi$
$131$	4.30482			0.376114			0.188057	+	0.982158i	$0.439781\pi$
$132$	−1.54740	+	11.3635i	−0.134684	+	0.989062i
$133$			28.2618i			2.45061i
$134$	−0.888303	+	13.1069i	−0.0767377	+	1.13226i
$135$	1.36381	+	2.57492i	0.117378	+	0.221614i
$136$	3.87124	+	11.0006i	0.331956	+	0.943295i
$137$			18.4366i			1.57514i	0.616225	+	0.787570i	$0.288661\pi$
$137$			18.4366i			1.57514i	−0.616225	+	0.787570i	$0.711339\pi$
$138$	−23.0226	−	1.56033i	−1.95981	−	0.132824i
$139$	−14.8960			−1.26346			−0.631729	−	0.775189i	$-0.717655\pi$
$139$	−14.8960			−1.26346			−0.631729	+	0.775189i	$0.717655\pi$
$140$	−18.6209	+	6.83404i	−1.57375	+	0.577581i
$141$	−3.79875			−0.319913
$142$	9.27684	+	0.628727i	0.778495	+	0.0527616i
$143$	−9.43030			−0.788602
$144$	−9.40994	−	2.61118i	−0.784161	−	0.217598i
$145$	−18.2947	+	9.68984i	−1.51929	+	0.804697i
$146$	1.03703	−	15.3014i	0.0858255	−	1.26635i
$147$			29.5600i			2.43807i
$148$	−0.285703	+	2.09808i	−0.0234846	+	0.172461i
$149$			18.2481i			1.49494i	0.664296	+	0.747469i	$0.268731\pi$
$149$			18.2481i			1.49494i	−0.664296	+	0.747469i	$0.731269\pi$
$150$	−10.1689	+	12.9870i	−0.830288	+	1.06038i
$151$	6.44649			0.524608			0.262304	−	0.964985i	$-0.415518\pi$
$151$	6.44649			0.524608			0.262304	+	0.964985i	$0.415518\pi$
$152$	17.6525	+	3.63372i	1.43181	+	0.294733i
$153$	8.62655	−	5.18730i	0.697415	−	0.419368i
$154$	1.04261	−	15.3837i	0.0840162	−	1.23966i
$155$	−7.48120	−	14.1247i	−0.600904	−	1.13453i
$156$	2.41488	−	17.7339i	0.193345	−	1.41985i
$157$	15.6941			1.25253			0.626264	−	0.779611i	$-0.284583\pi$
$157$	15.6941			1.25253			0.626264	+	0.779611i	$0.284583\pi$
$158$	−4.65026	−	0.315166i	−0.369955	−	0.0250733i
$159$		−	7.24934i		−	0.574910i
$160$	1.87444	+	12.5095i	0.148187	+	0.988959i
$161$	31.0245			2.44508
$162$	0.991063	−	14.6231i	0.0778653	−	1.14890i
$163$		−	3.75801i		−	0.294350i	−0.989110	−	0.147175i	$-0.952982\pi$
$163$		−	3.75801i		−	0.294350i	0.989110	−	0.147175i	$-0.0470180\pi$
$164$	−1.45962	+	10.7189i	−0.113977	+	0.837002i
$165$	−6.00138	−	11.3308i	−0.467206	−	0.882101i
$166$	0.256186	−	3.78001i	0.0198839	−	0.293386i
$167$	−16.3629			−1.26620			−0.633099	−	0.774071i	$-0.718217\pi$
$167$	−16.3629			−1.26620			−0.633099	+	0.774071i	$0.718217\pi$
$168$	28.6625	+	5.90007i	2.21136	+	0.455201i
$169$	1.71701			0.132078
$170$	−10.6870	−	7.46919i	−0.819653	−	0.572861i
$171$		−	15.5564i		−	1.18963i
$172$	3.39724	+	0.462613i	0.259037	+	0.0352739i
$173$		−	18.2677i		−	1.38887i	−0.719557	−	0.694434i	$-0.755655\pi$
$173$		−	18.2677i		−	1.38887i	0.719557	−	0.694434i	$-0.244345\pi$
$174$	30.4727	+	2.06525i	2.31013	+	0.156566i
$175$	12.4600	−	18.3454i	0.941887	−	1.38678i
$176$	−9.47475	−	2.62917i	−0.714186	−	0.198181i
$177$	−0.503794			−0.0378675
$178$	0.465413	−	6.86715i	0.0348842	−	0.514715i
$179$		−	2.03423i		−	0.152046i	−0.997106	−	0.0760229i	$-0.975778\pi$
$179$		−	2.03423i		−	0.152046i	0.997106	−	0.0760229i	$-0.0242222\pi$
$180$	10.2497	−	3.76172i	0.763966	−	0.280382i
$181$	−1.03279			−0.0767664			−0.0383832	−	0.999263i	$-0.512221\pi$
$181$	−1.03279			−0.0767664			−0.0383832	+	0.999263i	$0.512221\pi$
$182$	−1.62711	+	24.0080i	−0.120610	+	1.77959i
$183$		−	10.9836i		−	0.811933i
$184$	3.98894	−	19.3782i	0.294068	−	1.42858i
$185$	−1.10806	−	2.09205i	−0.0814661	−	0.153811i
$186$	−1.59451	+	23.5269i	−0.116915	+	1.72508i
$187$	8.68597	−	5.22303i	0.635181	−	0.381946i
$188$	0.439459	−	3.22721i	0.0320508	−	0.235368i
$189$			5.77962i			0.420405i
$190$	−18.4035	+	8.20561i	−1.33513	+	0.595298i
$191$	9.17203			0.663665			0.331832	−	0.943338i	$-0.392333\pi$
$191$	9.17203			0.663665			0.331832	+	0.943338i	$0.392333\pi$
$192$	7.37047	−	17.1442i	0.531918	−	1.23728i
$193$	8.34085			0.600387			0.300194	−	0.953878i	$-0.402949\pi$
$193$	8.34085			0.600387			0.300194	+	0.953878i	$0.402949\pi$
$194$	−0.559316	+	8.25269i	−0.0401566	+	0.592508i
$195$	9.36579	+	17.6829i	0.670698	+	1.26630i
$196$	−25.1125	−	3.41965i	−1.79375	−	0.244261i
$197$		−	15.1384i		−	1.07857i	−0.842125	−	0.539283i	$-0.818695\pi$
$197$		−	15.1384i		−	1.07857i	0.842125	−	0.539283i	$-0.181305\pi$
$198$	−0.573895	+	8.46780i	−0.0407850	+	0.601780i
$199$		−	1.13639i		−	0.0805566i	−0.999189	−	0.0402783i	$-0.987176\pi$
$199$		−	1.13639i		−	0.0805566i	0.999189	−	0.0402783i	$-0.0128245\pi$
$200$	−9.85663	−	10.1413i	−0.696969	−	0.717101i
$201$			21.6687i			1.52839i
$202$	19.8767	+	1.34712i	1.39852	+	0.0947828i
$203$	−41.0640			−2.88213
$204$	7.59775	+	17.6717i	0.531949	+	1.23726i
$205$	−5.66094	−	10.6880i	−0.395377	−	0.746485i
$206$	−18.9127	−	1.28178i	−1.31771	−	0.0893061i
$207$	−17.0771			−1.18694
$208$	14.7864	+	4.10310i	1.02525	+	0.284499i
$209$		−	15.6635i		−	1.08347i
$210$	−29.8818	+	13.3235i	−2.06204	+	0.919407i
$211$	0.896057			0.0616871			0.0308436	−	0.999524i	$-0.490181\pi$
$211$	0.896057			0.0616871			0.0308436	+	0.999524i	$0.490181\pi$
$212$	6.15864	+	0.838641i	0.422977	+	0.0575981i
$213$	15.3368			1.05086
$214$	15.3117	+	1.03773i	1.04669	+	0.0709379i
$215$	−3.38747	+	1.79418i	−0.231024	+	0.122362i
$216$	3.61000	+	0.743106i	0.245629	+	0.0505619i
$217$		−	31.7042i		−	2.15222i
$218$	−0.293816	+	4.33525i	−0.0198998	+	0.293620i
$219$		−	25.2968i		−	1.70940i
$220$	10.3203	−	3.78763i	0.695793	−	0.255362i
$221$	−13.5554	+	8.15110i	−0.911834	+	0.548302i
$222$	−0.236167	+	3.48463i	−0.0158505	+	0.233873i
$223$		−	21.4412i		−	1.43581i	−0.696141	−	0.717905i	$-0.745101\pi$
$223$		−	21.4412i		−	1.43581i	0.696141	−	0.717905i	$-0.254899\pi$
$224$	−8.32819	+	23.6675i	−0.556451	+	1.58135i
$225$	−6.85846	+	10.0980i	−0.457231	+	0.673200i
$226$	−1.02610	+	15.1401i	−0.0682552	+	1.00710i
$227$			20.2679i			1.34523i	0.739993	+	0.672614i	$0.234829\pi$
$227$			20.2679i			1.34523i	−0.739993	+	0.672614i	$0.765171\pi$
$228$	29.4556	+	4.01107i	1.95075	+	0.265639i
$229$		−	17.8132i		−	1.17713i	−0.808450	−	0.588565i	$-0.799693\pi$
$229$		−	17.8132i		−	1.17713i	0.808450	−	0.588565i	$-0.200307\pi$
$230$	9.00776	+	20.2025i	0.593954	+	1.33212i
$231$		−	25.4329i		−	1.67336i
$232$	−5.27975	+	25.6489i	−0.346633	+	1.68394i
$233$	−2.38936			−0.156532			−0.0782661	−	0.996933i	$-0.524938\pi$
$233$	−2.38936			−0.156532			−0.0782661	+	0.996933i	$0.524938\pi$
$234$	0.895626	−	13.2149i	0.0585489	−	0.863886i
$235$	1.70438	+	3.21793i	0.111182	+	0.209915i
$236$	0.0582815	−	0.427995i	0.00379380	−	0.0278601i
$237$	−7.68798			−0.499388
$238$	−11.7983	−	23.0142i	−0.764768	−	1.49179i
$239$	3.32924			0.215351			0.107675	−	0.994186i	$-0.465659\pi$
$239$	3.32924			0.215351			0.107675	+	0.994186i	$0.465659\pi$
$240$	4.47994	+	20.3774i	0.289179	+	1.31536i
$241$		−	18.0407i		−	1.16210i	−0.813867	−	0.581052i	$-0.802641\pi$
$241$		−	18.0407i		−	1.16210i	0.813867	−	0.581052i	$-0.197359\pi$
$242$	0.474052	−	6.99462i	0.0304732	−	0.449631i
$243$		−	20.2661i		−	1.30007i
$244$	9.33108	+	1.27064i	0.597361	+	0.0813445i
$245$	25.0403	−	13.2626i	1.59977	−	0.847319i
$246$	−1.20655	+	17.8026i	−0.0769267	+	1.13505i
$247$			24.4446i			1.55537i
$248$	−19.8027	−	4.07632i	−1.25747	−	0.258846i
$249$		−	6.24924i		−	0.396030i
$250$	15.5638	+	2.78724i	0.984340	+	0.176280i
$251$		−	14.7881i		−	0.933419i	−0.884411	−	0.466709i	$-0.845439\pi$
$251$		−	14.7881i		−	0.933419i	0.884411	−	0.466709i	$-0.154561\pi$
$252$	21.4586	+	2.92208i	1.35176	+	0.184074i
$253$	−17.1947			−1.08102
$254$	10.6386	+	0.721019i	0.667525	+	0.0452407i
$255$	−18.4203	−	11.0999i	−1.15353	−	0.695103i
$256$	13.7121	+	8.24487i	0.857007	+	0.515304i
$257$		−	3.16673i		−	0.197535i	−0.995111	−	0.0987676i	$-0.968510\pi$
$257$		−	3.16673i		−	0.197535i	0.995111	−	0.0987676i	$-0.0314901\pi$
$258$	5.64235	+	0.382404i	0.351277	+	0.0238074i
$259$		−	4.69579i		−	0.291782i
$260$	−16.1059	+	5.91100i	−0.998846	+	0.366585i
$261$	22.6032			1.39911
$262$	−0.411658	+	6.07400i	−0.0254323	+	0.375253i
$263$			21.0845i			1.30013i	0.759880	+	0.650063i	$0.225258\pi$
$263$			21.0845i			1.30013i	−0.759880	+	0.650063i	$0.774742\pi$
$264$	−15.8856	−	3.27000i	−0.977692	−	0.201255i
$265$	−6.14093	+	3.25256i	−0.377234	+	0.199803i
$266$	−39.8767	−	2.70260i	−2.44500	−	0.165707i
$267$		−	11.3530i		−	0.694793i
$268$	−18.4085	−	2.50675i	−1.12448	−	0.153124i
$269$	3.79202			0.231203			0.115602	−	0.993296i	$-0.463120\pi$
$269$	3.79202			0.231203			0.115602	+	0.993296i	$0.463120\pi$
$270$	−3.76356	+	1.67807i	−0.229043	+	0.102124i
$271$	20.2352			1.22920			0.614599	−	0.788839i	$-0.289318\pi$
$271$	20.2352			1.22920			0.614599	+	0.788839i	$0.289318\pi$
$272$	−15.8918	+	4.41028i	−0.963582	+	0.267412i
$273$			39.6908i			2.40220i
$274$	−26.0135	−	1.76304i	−1.57154	−	0.106509i
$275$	−6.90570	+	10.1676i	−0.416430	+	0.613126i
$276$	4.40317	−	32.3351i	0.265040	−	1.94635i
$277$			11.7708i			0.707241i	0.935389	+	0.353621i	$0.115050\pi$
$277$			11.7708i			0.707241i	−0.935389	+	0.353621i	$0.884950\pi$
$278$	1.42446	−	21.0178i	0.0854334	−	1.26057i
$279$			17.4512i			1.04478i
$280$	−7.86200	−	26.9272i	−0.469844	−	1.60921i
$281$	−12.1576			−0.725262			−0.362631	−	0.931933i	$-0.618121\pi$
$281$	−12.1576			−0.725262			−0.362631	+	0.931933i	$0.618121\pi$
$282$	0.363264	−	5.35995i	0.0216321	−	0.319180i
$283$			0.633186i			0.0376390i	0.999823	+	0.0188195i	$0.00599079\pi$
$283$			0.633186i			0.0376390i	−0.999823	+	0.0188195i	$0.994009\pi$
$284$	−1.77424	+	13.0293i	−0.105282	+	0.773145i
$285$	−29.3710	+	15.5564i	−1.73979	+	0.921481i
$286$	0.901795	−	13.3059i	0.0533242	−	0.786797i
$287$		−	23.9902i		−	1.41610i
$288$	4.58416	−	13.0275i	0.270124	−	0.767653i
$289$	7.97093	−	15.0155i	0.468878	−	0.883263i
$290$	−11.9227	−	26.7400i	−0.700123	−	1.57023i
$291$			13.6436i			0.799804i
$292$	21.4907	+	2.92646i	1.25765	+	0.171258i
$293$	−24.3103			−1.42022			−0.710111	−	0.704090i	$-0.751355\pi$
$293$	−24.3103			−1.42022			−0.710111	+	0.704090i	$0.751355\pi$
$294$	−41.7084	−	2.82674i	−2.43249	−	0.164859i
$295$	0.226037	+	0.426765i	0.0131604	+	0.0248472i
$296$	−2.93303	−	0.603754i	−0.170479	−	0.0350925i
$297$		−	3.20324i		−	0.185871i
$298$	−25.7476	−	1.74501i	−1.49152	−	0.101086i
$299$	26.8343			1.55186
$300$	−17.3519	−	15.5900i	−1.00181	−	0.900090i
$301$	−7.60346			−0.438256
$302$	−0.616460	+	9.09585i	−0.0354733	+	0.523407i
$303$	32.8608			1.88780
$304$	−6.81516	+	24.5598i	−0.390876	+	1.40860i
$305$	−9.30425	+	4.92801i	−0.532760	+	0.282177i
$306$	6.49422	+	12.6679i	0.371250	+	0.724176i
$307$	5.01197			0.286048			0.143024	−	0.989719i	$-0.454317\pi$
$307$	5.01197			0.286048			0.143024	+	0.989719i	$0.454317\pi$
$308$	21.6064	+	2.94221i	1.23114	+	0.167648i
$309$	−31.2671			−1.77872
$310$	20.6451	−	9.20508i	1.17256	−	0.522814i
$311$			3.69611i			0.209587i	0.994494	+	0.104794i	$0.0334182\pi$
$311$			3.69611i			0.209587i	−0.994494	+	0.104794i	$0.966582\pi$
$312$	24.7912	+	5.10319i	1.40353	+	0.288911i
$313$	7.88878			0.445900			0.222950	−	0.974830i	$-0.428431\pi$
$313$	7.88878			0.445900			0.222950	+	0.974830i	$0.428431\pi$
$314$	−1.50079	+	22.1440i	−0.0846943	+	1.24966i
$315$	−21.3969	+	11.3329i	−1.20558	+	0.638537i
$316$	0.889384	−	6.53128i	0.0500318	−	0.367413i
$317$			11.9767i			0.672678i	0.941741	+	0.336339i	$0.109189\pi$
$317$			11.9767i			0.672678i	−0.941741	+	0.336339i	$0.890811\pi$
$318$	10.2287	+	0.693235i	0.573594	+	0.0388747i
$319$	22.7589			1.27426
$320$	−17.8298	+	1.44854i	−0.996716	+	0.0809759i
$321$	25.3138			1.41288
$322$	−2.96679	+	43.7749i	−0.165333	+	2.43948i
$323$	−13.5388	−	22.5152i	−0.753319	−	1.25278i
$324$	20.5381	+	2.79673i	1.14100	+	0.155374i
$325$	10.7771	−	15.8676i	0.597806	−	0.880174i
$326$	5.30246	+	0.359368i	0.293676	+	0.0199035i
$327$			7.16718i			0.396346i
$328$	−14.9845	−	3.08451i	−0.827379	−	0.170313i
$329$			7.22291i			0.398212i
$330$	16.5614	−	7.38427i	0.911674	−	0.406491i
$331$			15.3360i			0.842943i	0.906842	+	0.421472i	$0.138486\pi$
$331$			15.3360i			0.842943i	−0.906842	+	0.421472i	$0.861514\pi$
$332$	5.30900	+	0.722944i	0.291369	+	0.0396767i
$333$			2.58474i			0.141643i
$334$	1.56474	−	23.0876i	0.0856186	−	1.26330i
$335$	18.3556	−	9.72209i	1.00287	−	0.531174i
$336$	−11.0658	+	39.8779i	−0.603688	+	2.17552i
$337$	−15.2572			−0.831112			−0.415556	−	0.909568i	$-0.636413\pi$
$337$	−15.2572			−0.831112			−0.415556	+	0.909568i	$0.636413\pi$
$338$	−0.164193	+	2.42266i	−0.00893091	+	0.131775i
$339$			25.0301i			1.35945i
$340$	11.5608	−	14.3648i	0.626974	−	0.779040i
$341$			17.5714i			0.951545i
$342$	21.9497	+	1.48761i	1.18690	+	0.0804410i
$343$	25.1578			1.35839
$344$	−0.977604	+	4.74919i	−0.0527089	+	0.256059i
$345$	17.0771	+	32.2422i	0.919401	+	1.73586i
$346$	25.7753	+	1.74689i	1.38569	+	0.0939134i
$347$		−	17.9160i		−	0.961781i	−0.876781	−	0.480891i	$-0.840313\pi$
$347$		−	17.9160i		−	0.961781i	0.876781	−	0.480891i	$-0.159687\pi$
$348$	−5.82803	+	42.7987i	−0.312415	+	2.29425i
$349$		−	24.1567i		−	1.29308i	−0.762881	−	0.646539i	$-0.776216\pi$
$349$		−	24.1567i		−	1.29308i	0.762881	−	0.646539i	$-0.223784\pi$
$350$	24.6934	+	19.3351i	1.31992	+	1.03350i
$351$			4.99900i			0.266827i
$352$	4.61574	−	13.1172i	0.246020	−	0.699151i
$353$		−	16.9274i		−	0.900953i	−0.892788	−	0.450477i	$-0.851254\pi$
$353$		−	16.9274i		−	0.900953i	0.892788	−	0.450477i	$-0.148746\pi$
$354$	0.0481765	−	0.710842i	0.00256055	−	0.0377808i
$355$	−6.88114	−	12.9918i	−0.365213	−	0.689534i
$356$	9.64488	+	1.31337i	0.511178	+	0.0696087i
$357$	−21.9830	−	36.5580i	−1.16346	−	1.93485i
$358$	2.87026	+	0.194528i	0.151698	+	0.0102811i
$359$	−19.3984			−1.02381			−0.511904	−	0.859043i	$-0.671059\pi$
$359$	−19.3984			−1.02381			−0.511904	+	0.859043i	$0.671059\pi$
$360$	4.32755	+	14.8218i	0.228082	+	0.781176i
$361$	−21.6020			−1.13695
$362$	0.0987626	−	1.45724i	0.00519085	−	0.0765907i
$363$		−	11.5637i		−	0.606939i
$364$	−33.7191	−	4.59163i	−1.76736	−	0.240667i
$365$	−21.4290	+	11.3499i	−1.12164	+	0.594080i
$366$	15.4976	+	1.05033i	0.810075	+	0.0549019i
$367$	−22.5468			−1.17694			−0.588468	−	0.808521i	$-0.700269\pi$
$367$	−22.5468			−1.17694			−0.588468	+	0.808521i	$0.700269\pi$
$368$	26.9607	+	7.48138i	1.40542	+	0.389994i
$369$			13.2051i			0.687432i
$370$	3.05780	−	1.36339i	0.158967	−	0.0708792i
$371$	−13.7838			−0.715621
$372$	−33.0434	−	4.49963i	−1.71322	−	0.233295i
$373$	32.3191			1.67342			0.836710	−	0.547646i	$-0.184476\pi$
$373$	32.3191			1.67342			0.836710	+	0.547646i	$0.184476\pi$
$374$	6.53896	+	12.7552i	0.338121	+	0.659554i
$375$	25.9238	+	2.85100i	1.33870	+	0.147225i
$376$	4.51149	+	0.928675i	0.232662	+	0.0478928i
$377$	−35.5178			−1.82926
$378$	−8.15490	−	0.552689i	−0.419443	−	0.0284273i
$379$	11.7582			0.603979			0.301989	−	0.953311i	$-0.402349\pi$
$379$	11.7582			0.603979			0.301989	+	0.953311i	$0.402349\pi$
$380$	−9.81805	−	26.7516i	−0.503655	−	1.37233i
$381$	17.5881			0.901066
$382$	−0.877096	+	12.9415i	−0.0448762	+	0.662146i
$383$			23.9366i			1.22311i	0.791204	+	0.611553i	$0.209455\pi$
$383$			23.9366i			1.22311i	−0.791204	+	0.611553i	$0.790545\pi$
$384$	23.4853	+	12.0390i	1.19848	+	0.614364i
$385$	−21.5443	+	11.4110i	−1.09800	+	0.581556i
$386$	−0.797613	+	11.7687i	−0.0405974	+	0.599013i
$387$	4.18524			0.212748
$388$	−11.5909	−	1.57836i	−0.588437	−	0.0801293i
$389$		−	1.72401i		−	0.0874106i	−0.999044	−	0.0437053i	$-0.986084\pi$
$389$		−	1.72401i		−	0.0874106i	0.999044	−	0.0437053i	$-0.0139163\pi$
$390$	−25.8458	+	11.5239i	−1.30875	+	0.583538i
$391$	−24.7162	+	14.8623i	−1.24995	+	0.751619i
$392$	7.22649	−	35.1061i	0.364993	−	1.77313i
$393$			10.0418i			0.506540i
$394$	21.3599	+	1.44764i	1.07610	+	0.0729312i
$395$	3.44936	+	6.51250i	0.173556	+	0.327679i
$396$	−11.8930	−	1.61951i	−0.597645	−	0.0813832i
$397$		−	0.572727i		−	0.0287444i	−0.999897	−	0.0143722i	$-0.995425\pi$
$397$		−	0.572727i		−	0.0287444i	0.999897	−	0.0143722i	$-0.00457496\pi$
$398$	1.60342	+	0.108670i	0.0803722	+	0.00544713i
$399$	−65.9256			−3.30041
$400$	15.2518	−	12.9377i	0.762588	−	0.646885i
$401$			0.0285393i			0.00142518i	1.00000		0.000712592i	$0.000226825\pi$
$401$			0.0285393i			0.00142518i	−1.00000		0.000712592i	$0.999773\pi$
$402$	−30.5741	−	2.07212i	−1.52490	−	0.103348i
$403$		−	27.4221i		−	1.36599i
$404$	−3.80150	+	27.9167i	−0.189132	+	1.38891i
$405$	−20.4790	+	10.8468i	−1.01761	+	0.538980i
$406$	3.92684	−	57.9404i	0.194886	−	2.87553i
$407$			2.60255i			0.129003i
$408$	−25.6609	+	9.03036i	−1.27040	+	0.447069i
$409$	4.23076			0.209197			0.104599	−	0.994515i	$-0.466644\pi$
$409$	4.23076			0.209197			0.104599	+	0.994515i	$0.466644\pi$
$410$	15.6219	−	6.96539i	0.771511	−	0.343996i
$411$	−43.0065			−2.12135
$412$	3.61713	−	26.5628i	0.178203	−	1.30865i
$413$			0.957909i			0.0471356i
$414$	1.63304	−	24.0954i	0.0802595	−	1.18423i
$415$	−5.29374	+	2.80384i	−0.259860	+	0.137635i
$416$	−7.20335	+	20.4709i	−0.353174	+	1.00367i
$417$		−	34.7474i		−	1.70159i
$418$	22.1009	+	1.49786i	1.08099	+	0.0732628i
$419$	24.3348			1.18883			0.594415	−	0.804158i	$-0.297383\pi$
$419$	24.3348			1.18883			0.594415	+	0.804158i	$0.297383\pi$
$420$	−15.9416	−	43.4366i	−0.777870	−	2.11949i
$421$		−	2.75894i		−	0.134463i	−0.997737	−	0.0672313i	$-0.978583\pi$
$421$		−	2.75894i		−	0.134463i	0.997737	−	0.0672313i	$-0.0214165\pi$
$422$	−0.0856875	+	1.26432i	−0.00417120	+	0.0615459i
$423$		−	3.97577i		−	0.193309i
$424$	−1.77224	+	8.60949i	−0.0860674	+	0.418114i
$425$	−1.13812	+	20.5841i	−0.0552068	+	0.998475i
$426$	−1.46662	+	21.6399i	−0.0710578	+	1.04845i
$427$	−20.8842			−1.01066
$428$	−2.92843	+	21.5052i	−0.141551	+	1.03949i
$429$		−	21.9978i		−	1.06207i
$430$	−2.20761	−	4.95122i	−0.106461	−	0.238769i
$431$		−	4.51067i		−	0.217272i	−0.994082	−	0.108636i	$-0.965352\pi$
$431$		−	4.51067i		−	0.217272i	0.994082	−	0.108636i	$-0.0346482\pi$
$432$	−1.39372	+	5.02256i	−0.0670553	+	0.241648i
$433$			7.71397i			0.370710i	0.982672	+	0.185355i	$0.0593434\pi$
$433$			7.71397i			0.370710i	−0.982672	+	0.185355i	$0.940657\pi$
$434$	44.7338	+	3.03178i	2.14729	+	0.145530i
$435$	−22.6032	−	42.6757i	−1.08374	−	2.04614i
$436$	−6.08884	−	0.829136i	−0.291602	−	0.0397084i
$437$			44.5711i			2.13213i
$438$	35.6932	+	2.41906i	1.70549	+	0.115587i
$439$			35.7538i			1.70643i	0.521557	+	0.853217i	$0.325352\pi$
$439$			35.7538i			1.70643i	−0.521557	+	0.853217i	$0.674648\pi$
$440$	4.35736	+	14.9239i	0.207729	+	0.711468i
$441$	−30.9375			−1.47321
$442$	−10.2047	−	19.9058i	−0.485390	−	0.946823i
$443$	0.775272			0.0368343			0.0184171	−	0.999830i	$-0.494137\pi$
$443$	0.775272			0.0368343			0.0184171	+	0.999830i	$0.494137\pi$
$444$	−4.89415	−	0.666452i	−0.232266	−	0.0316284i
$445$	−9.61715	+	5.09374i	−0.455897	+	0.241467i
$446$	30.2530	+	2.05036i	1.43252	+	0.0970876i
$447$	−42.5668			−2.01334
$448$	−32.5979	−	14.0141i	−1.54010	−	0.662106i
$449$		−	26.7849i		−	1.26406i	−0.774945	−	0.632028i	$-0.782223\pi$
$449$		−	26.7849i		−	1.26406i	0.774945	−	0.632028i	$-0.217777\pi$
$450$	−13.5922	−	10.6428i	−0.640742	−	0.501705i
$451$			13.2961i			0.626089i
$452$	−21.2642	−	2.89561i	−1.00018	−	0.136198i
$453$			15.0376i			0.706527i
$454$	−28.5976	−	1.93817i	−1.34215	−	0.0909626i
$455$	33.6221	−	17.8080i	1.57623	−	0.834853i
$456$	−8.47629	+	41.1777i	−0.396938	+	1.92832i
$457$		−	20.5494i		−	0.961260i	−0.876924	−	0.480630i	$-0.840408\pi$
$457$		−	20.5494i		−	0.961260i	0.876924	−	0.480630i	$-0.159592\pi$
$458$	25.1340	+	1.70343i	1.17444	+	0.0795960i
$459$	−2.76872	−	4.60443i	−0.129233	−	0.214916i
$460$	−29.3667	+	10.7778i	−1.36923	+	0.502519i
$461$		−	7.04005i		−	0.327888i	−0.986470	−	0.163944i	$-0.947578\pi$
$461$		−	7.04005i		−	0.327888i	0.986470	−	0.163944i	$-0.0524216\pi$
$462$	35.8852	+	2.43208i	1.66953	+	0.113151i
$463$			13.1319i			0.610293i	0.952305	+	0.305147i	$0.0987054\pi$
$463$			13.1319i			0.610293i	−0.952305	+	0.305147i	$0.901295\pi$
$464$	−35.6852	−	9.90234i	−1.65664	−	0.459705i
$465$	32.9484	−	17.4512i	1.52795	−	0.809280i
$466$	0.228488	−	3.37133i	0.0105845	−	0.156174i
$467$	−26.5329			−1.22779			−0.613897	−	0.789386i	$-0.710399\pi$
$467$	−26.5329			−1.22779			−0.613897	+	0.789386i	$0.710399\pi$
$468$	18.5603	+	2.52741i	0.857950	+	0.116830i
$469$	41.2007			1.90247
$470$	−4.70341	+	2.09712i	−0.216952	+	0.0967330i
$471$			36.6093i			1.68687i
$472$	0.598318	+	0.123162i	0.0275398	+	0.00566898i
$473$	4.21407			0.193763
$474$	0.735181	−	10.8476i	0.0337680	−	0.498245i
$475$	26.3557	+	17.9005i	1.20928	+	0.821332i
$476$	33.6007	−	14.4463i	1.54009	−	0.662145i
$477$	7.58716			0.347392
$478$	−0.318367	+	4.69749i	−0.0145618	+	0.214858i
$479$			36.7590i			1.67956i	0.542925	+	0.839781i	$0.317317\pi$
$479$			36.7590i			1.67956i	−0.542925	+	0.839781i	$0.682683\pi$
$480$	−29.1805	+	4.37245i	−1.33190	+	0.199574i
$481$		−	4.06156i		−	0.185191i
$482$	25.4550	+	1.72518i	1.15944	+	0.0785799i
$483$			72.3702i			3.29296i
$484$	9.82391	+	1.33775i	0.446541	+	0.0608069i
$485$	11.5575	−	6.12147i	0.524801	−	0.277962i
$486$	28.5951	+	1.93800i	1.29710	+	0.0879093i
$487$	34.4121			1.55936			0.779680	−	0.626178i	$-0.215382\pi$
$487$	34.4121			1.55936			0.779680	+	0.626178i	$0.215382\pi$
$488$	−2.68515	+	13.0444i	−0.121551	+	0.590493i
$489$	8.76621			0.396422
$490$	16.3187	+	36.5996i	0.737206	+	1.65340i
$491$			26.0606i			1.17610i	0.808825	+	0.588050i	$0.200104\pi$
$491$			26.0606i			1.17610i	−0.808825	+	0.588050i	$0.799896\pi$
$492$	−25.0036	−	3.40482i	−1.12725	−	0.153501i
$493$	32.7144	−	19.6717i	1.47338	−	0.885970i
$494$	−34.4908	−	2.33757i	−1.55181	−	0.105172i
$495$	11.8588	−	6.28104i	0.533013	−	0.282312i
$496$	7.64527	−	27.5513i	0.343283	−	1.23709i
$497$		−	29.1612i		−	1.30806i
$498$	8.81753	+	0.597598i	0.395123	+	0.0267790i
$499$	−6.50237			−0.291086			−0.145543	−	0.989352i	$-0.546493\pi$
$499$	−6.50237			−0.291086			−0.145543	+	0.989352i	$0.546493\pi$
$500$	−5.42105	+	21.6936i	−0.242437	+	0.970167i
$501$		−	38.1693i		−	1.70528i
$502$	20.8657	+	1.41415i	0.931283	+	0.0631166i
$503$	0.744731			0.0332059			0.0166029	−	0.999862i	$-0.494715\pi$
$503$	0.744731			0.0332059			0.0166029	+	0.999862i	$0.494715\pi$
$504$	−6.17501	+	29.9981i	−0.275057	+	1.33622i
$505$	−14.7436	−	27.8364i	−0.656082	−	1.23870i
$506$	1.64429	−	24.2614i	0.0730975	−	1.07855i
$507$			4.00522i			0.177878i
$508$	−2.03468	+	14.9419i	−0.0902744	+	0.662938i
$509$		−	18.3771i		−	0.814550i	−0.913306	−	0.407275i	$-0.866479\pi$
$509$		−	18.3771i		−	0.814550i	0.913306	−	0.407275i	$-0.133521\pi$
$510$	17.4232	−	24.9292i	0.771513	−	1.10388i
$511$	−48.0991			−2.12778
$512$	−12.9446	+	18.5590i	−0.572075	+	0.820202i
$513$	−8.30323			−0.366596
$514$	4.46818	+	0.302826i	0.197083	+	0.0133571i
$515$	14.0286	+	26.4864i	0.618172	+	1.16713i
$516$	−1.07913	+	7.92466i	−0.0475058	+	0.348864i
$517$		−	4.00316i		−	0.176059i
$518$	6.62565	+	0.449045i	0.291114	+	0.0197299i
$519$	42.6126			1.87049
$520$	−6.80012	−	23.2903i	−0.298205	−	1.02135i
$521$		−	16.6952i		−	0.731431i	−0.930727	−	0.365716i	$-0.880824\pi$
$521$		−	16.6952i		−	0.731431i	0.930727	−	0.365716i	$-0.119176\pi$
$522$	−2.16149	+	31.8927i	−0.0946057	+	1.39590i
$523$	−16.4104			−0.717578			−0.358789	−	0.933419i	$-0.616810\pi$
$523$	−16.4104			−0.717578			−0.358789	+	0.933419i	$0.616810\pi$
$524$	−8.53091	−	1.16168i	−0.372675	−	0.0507483i
$525$	42.7938	+	29.0651i	1.86767	+	1.26851i
$526$	−29.7498	−	2.01625i	−1.29715	−	0.0879129i
$527$	15.1879	+	25.2577i	0.661594	+	1.10024i
$528$	6.13299	−	22.1015i	0.266904	−	0.961845i
$529$	25.9282			1.12731
$530$	−4.00204	−	8.97574i	−0.173837	−	0.389881i
$531$		−	0.527271i		−	0.0228816i
$532$	7.62660	−	56.0067i	0.330655	−	2.42820i
$533$		−	20.7500i		−	0.898782i
$534$	16.0188	+	1.08566i	0.693203	+	0.0469810i
$535$	−11.3575	−	21.4434i	−0.491029	−	0.927078i
$536$	5.29732	−	25.7343i	0.228810	−	1.11155i
$537$	4.74521			0.204771
$538$	−0.362620	+	5.35045i	−0.0156337	+	0.230674i
$539$	−31.1505			−1.34175
$540$	−2.00782	−	5.47077i	−0.0864028	−	0.235425i
$541$	14.9643			0.643364			0.321682	−	0.946848i	$-0.395752\pi$
$541$	14.9643			0.643364			0.321682	+	0.946848i	$0.395752\pi$
$542$	−1.93503	+	28.5514i	−0.0831168	+	1.22639i
$543$		−	2.40916i		−	0.103387i
$544$	−4.70311	−	22.8447i	−0.201644	−	0.979459i
$545$	6.07133	−	3.21569i	0.260067	−	0.137745i
$546$	−56.0028	−	3.79552i	−2.39670	−	0.162433i
$547$			9.14081i			0.390833i	0.980720	+	0.195416i	$0.0626059\pi$
$547$			9.14081i			0.390833i	−0.980720	+	0.195416i	$0.937394\pi$
$548$	4.97521	−	36.5359i	0.212530	−	1.56074i
$549$	11.4955			0.490614
$550$	−13.6858	−	10.7161i	−0.583565	−	0.456935i
$551$		−	58.9943i		−	2.51324i
$552$	45.2030	+	9.30490i	1.92397	+	0.396043i
$553$			14.6178i			0.621614i
$554$	−16.6084	−	1.12561i	−0.705623	−	0.0478227i
$555$	4.88008	−	2.58474i	0.207148	−	0.109716i
$556$	29.5195	+	4.01976i	1.25190	+	0.170476i
$557$	−17.6080			−0.746077			−0.373039	−	0.927816i	$-0.621684\pi$
$557$	−17.6080			−0.746077			−0.373039	+	0.927816i	$0.621684\pi$
$558$	−24.6232	−	1.66881i	−1.04239	−	0.0706464i
$559$	−6.57651			−0.278157
$560$	38.7455	−	8.51812i	1.63730	−	0.359956i
$561$	12.1836	+	20.2616i	0.514393	+	0.855443i
$562$	1.16260	−	17.1541i	0.0490413	−	0.723602i
$563$	44.4958			1.87528			0.937638	−	0.347614i	$-0.113008\pi$
$563$	44.4958			1.87528			0.937638	+	0.347614i	$0.113008\pi$
$564$	7.52803	+	1.02512i	0.316987	+	0.0431651i
$565$	21.2030	−	11.2302i	0.892019	−	0.472459i
$566$	−0.893411	−	0.0605499i	−0.0375529	−	0.00254510i
$567$	−45.9669			−1.93043
$568$	−18.2143	−	3.74936i	−0.764257	−	0.157320i
$569$	19.3399			0.810769			0.405384	−	0.914146i	$-0.367138\pi$
$569$	19.3399			0.810769			0.405384	+	0.914146i	$0.367138\pi$
$570$	−19.1410	−	42.9294i	−0.801729	−	1.79811i
$571$	19.0383			0.796729			0.398364	−	0.917227i	$-0.369578\pi$
$571$	19.0383			0.796729			0.398364	+	0.917227i	$0.369578\pi$
$572$	18.6881	+	2.54482i	0.781390	+	0.106404i
$573$			21.3954i			0.893805i
$574$	33.8496	+	2.29412i	1.41286	+	0.0957546i
$575$	19.6504	−	28.9321i	0.819479	−	1.20655i
$576$	17.9431	+	7.71393i	0.747630	+	0.321414i
$577$			46.2691i			1.92621i	0.269128	+	0.963104i	$0.413264\pi$
$577$			46.2691i			1.92621i	−0.269128	+	0.963104i	$0.586736\pi$
$578$	20.4242	+	12.6827i	0.849536	+	0.527530i
$579$			19.4565i			0.808584i
$580$	38.8697	−	14.2655i	1.61398	−	0.592343i
$581$	−11.8822			−0.492959
$582$	−19.2508	−	1.30470i	−0.797973	−	0.0540817i
$583$	7.63942			0.316392
$584$	−6.18427	+	30.0431i	−0.255907	+	1.24319i
$585$	−18.5069	+	9.80223i	−0.765168	+	0.405272i
$586$	2.32473	−	34.3012i	0.0960335	−	1.41697i
$587$	10.5537			0.435597			0.217798	−	0.975994i	$-0.430113\pi$
$587$	10.5537			0.435597			0.217798	+	0.975994i	$0.430113\pi$
$588$	7.97693	−	58.5793i	0.328963	−	2.41577i
$589$	45.5475			1.87675
$590$	−0.623771	+	0.278122i	−0.0256802	+	0.0114501i
$591$	35.3130			1.45258
$592$	1.13236	−	4.08070i	0.0465397	−	0.167716i
$593$		−	21.9255i		−	0.900374i	−0.892934	−	0.450187i	$-0.851357\pi$
$593$		−	21.9255i		−	0.900374i	0.892934	−	0.450187i	$-0.148643\pi$
$594$	4.51969	+	0.306317i	0.185445	+	0.0125683i
$595$	−21.1053	+	35.0243i	−0.865232	+	1.43585i
$596$	4.92434	−	36.1624i	0.201709	−	1.48127i
$597$	2.65083			0.108491
$598$	−2.56609	+	37.8625i	−0.104935	+	1.54831i
$599$	−30.1539			−1.23205			−0.616027	−	0.787725i	$-0.711259\pi$
$599$	−30.1539			−1.23205			−0.616027	+	0.787725i	$0.711259\pi$
$600$	23.6565	−	22.9923i	0.965771	−	0.938658i
$601$			10.9973i			0.448589i	0.974521	+	0.224294i	$0.0720077\pi$
$601$			10.9973i			0.448589i	−0.974521	+	0.224294i	$0.927992\pi$
$602$	0.727099	−	10.7283i	0.0296343	−	0.437253i
$603$	−22.6785			−0.923539
$604$	−12.7751	−	1.73962i	−0.519811	−	0.0707842i
$605$	−9.79567	+	5.18829i	−0.398251	+	0.210934i
$606$	−3.14239	+	46.3658i	−0.127651	+	1.88348i
$607$	14.5176			0.589250			0.294625	−	0.955613i	$-0.404805\pi$
$607$	14.5176			0.589250			0.294625	+	0.955613i	$0.404805\pi$
$608$	−34.0017	−	11.9646i	−1.37895	−	0.485229i
$609$		−	95.7891i		−	3.88157i
$610$	−6.06357	−	13.5993i	−0.245507	−	0.550621i
$611$			6.24736i			0.252741i
$612$	−18.4952	+	7.95180i	−0.747622	+	0.321433i
$613$	−1.50630			−0.0608388			−0.0304194	−	0.999537i	$-0.509684\pi$
$613$	−1.50630			−0.0608388			−0.0304194	+	0.999537i	$0.509684\pi$
$614$	−0.479281	+	7.07178i	−0.0193422	+	0.285394i
$615$	24.9317	−	13.2051i	1.00534	−	0.532483i
$616$	−6.21755	+	30.2047i	−0.250512	+	1.21698i
$617$	−0.545393			−0.0219567			−0.0109783	−	0.999940i	$-0.503495\pi$
$617$	−0.545393			−0.0219567			−0.0109783	+	0.999940i	$0.503495\pi$
$618$	2.98999	−	44.1171i	0.120275	−	1.77465i
$619$	−44.4056			−1.78481			−0.892405	−	0.451235i	$-0.850984\pi$
$619$	−44.4056			−1.78481			−0.892405	+	0.451235i	$0.850984\pi$
$620$	11.0139	+	30.0100i	0.442330	+	1.20523i
$621$			9.11492i			0.365769i
$622$	−5.21513	−	0.353449i	−0.209107	−	0.0141720i
$623$	−21.5865			−0.864845
$624$	−9.57120	+	34.4918i	−0.383154	+	1.38078i
$625$	−9.21612	−	23.2393i	−0.368645	−	0.929570i
$626$	−0.754382	+	11.1309i	−0.0301512	+	0.444879i
$627$	36.5379			1.45919
$628$	−31.1012	−	4.23515i	−1.24107	−	0.169001i
$629$	2.24952	+	3.74098i	0.0896941	+	0.149163i
$630$	−13.9443	−	31.2742i	−0.555555	−	1.24600i
$631$	−10.3315			−0.411290			−0.205645	−	0.978627i	$-0.565929\pi$
$631$	−10.3315			−0.411290			−0.205645	+	0.978627i	$0.565929\pi$
$632$	9.13043	+	1.87947i	0.363189	+	0.0747613i
$633$			2.09021i			0.0830784i
$634$	−16.8988	−	1.14530i	−0.671139	−	0.0454856i
$635$	−7.89124	−	14.8989i	−0.313154	−	0.591245i
$636$	−1.95628	+	14.3661i	−0.0775714	+	0.569653i
$637$	48.6138			1.92615
$638$	−2.17638	+	32.1123i	−0.0861635	+	1.27134i
$639$			16.0515i			0.634987i
$640$	−0.338843	−	25.2960i	−0.0133939	−	0.999910i
$641$			18.9391i			0.748048i	0.927419	+	0.374024i	$0.122022\pi$
$641$			18.9391i			0.748048i	−0.927419	+	0.374024i	$0.877978\pi$
$642$	−2.42069	+	35.7172i	−0.0955371	+	1.40965i
$643$			37.5006i			1.47888i	0.673224	+	0.739439i	$0.264909\pi$
$643$			37.5006i			1.47888i	−0.673224	+	0.739439i	$0.735091\pi$
$644$	−61.4817	−	8.37215i	−2.42272	−	0.329909i
$645$	−4.18524	−	7.90187i	−0.164794	−	0.311136i
$646$	33.0631	−	16.9499i	1.30085	−	0.666884i
$647$		−	27.4611i		−	1.07961i	−0.841791	−	0.539804i	$-0.818498\pi$
$647$		−	27.4611i		−	1.07961i	0.841791	−	0.539804i	$-0.181502\pi$
$648$	−5.91013	+	28.7113i	−0.232172	+	1.12789i
$649$		−	0.530902i		−	0.0208397i
$650$	21.3582	+	16.7236i	0.837736	+	0.655954i
$651$	73.9555			2.89855
$652$	−1.01412	+	7.44728i	−0.0397160	+	0.291658i
$653$		−	4.08558i		−	0.159881i	−0.996800	−	0.0799406i	$-0.974527\pi$
$653$		−	4.08558i		−	0.159881i	0.996800	−	0.0799406i	$-0.0254731\pi$
$654$	−10.1127	−	0.685378i	−0.395439	−	0.0268004i
$655$	8.50639	−	4.50542i	0.332372	−	0.176041i
$656$	5.78509	−	20.8478i	0.225870	−	0.813969i
$657$	26.4756			1.03291
$658$	−10.1914	−	0.690708i	−0.397301	−	0.0269266i
$659$		−	38.3536i		−	1.49404i	−0.664799	−	0.747022i	$-0.731483\pi$
$659$		−	38.3536i		−	1.49404i	0.664799	−	0.747022i	$-0.268517\pi$
$660$	8.83531	+	24.0739i	0.343914	+	0.937074i
$661$		−	14.3360i		−	0.557607i	−0.960348	−	0.278804i	$-0.910062\pi$
$661$		−	14.3360i		−	0.557607i	0.960348	−	0.278804i	$-0.0899378\pi$
$662$	−21.6387	−	1.46654i	−0.841014	−	0.0569987i
$663$	−19.0139	−	31.6203i	−0.738438	−	1.22803i
$664$	−1.52774	+	7.42175i	−0.0592879	+	0.288020i
$665$	29.5788	+	55.8457i	1.14702	+	2.16560i
$666$	−3.64701	−	0.247172i	−0.141319	−	0.00957772i
$667$	−64.7613			−2.50757
$668$	32.4265	+	4.41562i	1.25462	+	0.170845i
$669$	50.0154			1.93371
$670$	11.9623	+	26.8291i	0.462146	+	1.03650i
$671$	11.5746			0.446834
$672$	−55.2086	−	19.4270i	−2.12972	−	0.749412i
$673$	6.34888			0.244731			0.122366	−	0.992485i	$-0.460952\pi$
$673$	6.34888			0.244731			0.122366	+	0.992485i	$0.460952\pi$
$674$	1.45900	−	21.5275i	0.0561987	−	0.829210i
$675$	5.38981	+	3.66071i	0.207454	+	0.140901i
$676$	−3.40261	−	0.463344i	−0.130870	−	0.0178209i
$677$		−	21.7279i		−	0.835072i	−0.908660	−	0.417536i	$-0.862894\pi$
$677$		−	21.7279i		−	0.835072i	0.908660	−	0.417536i	$-0.137106\pi$
$678$	−35.3169	−	2.39356i	−1.35634	−	0.0919242i
$679$	25.9419			0.995557
$680$	19.1629	+	17.6857i	0.734862	+	0.678216i
$681$	−47.2785			−1.81171
$682$	−24.7928	−	1.68031i	−0.949367	−	0.0643423i
$683$		−	1.22743i		−	0.0469664i	−0.999724	−	0.0234832i	$-0.992524\pi$
$683$		−	1.22743i		−	0.0469664i	0.999724	−	0.0234832i	$-0.00747562\pi$
$684$	−4.19798	+	30.8283i	−0.160514	+	1.17875i
$685$	19.2957	+	36.4309i	0.737250	+	1.39195i
$686$	−2.40577	+	35.4970i	−0.0918527	+	1.35528i
$687$	41.5525			1.58533
$688$	−6.60750	−	1.83353i	−0.251909	−	0.0699026i
$689$	−11.9221			−0.454197
$690$	−47.1260	+	21.0122i	−1.79405	+	0.799920i
$691$	−45.6561			−1.73684			−0.868419	−	0.495831i	$-0.834864\pi$
$691$	−45.6561			−1.73684			−0.868419	+	0.495831i	$0.834864\pi$
$692$	−4.92964	+	36.2013i	−0.187397	+	1.37617i
$693$	26.6181			1.01114
$694$	25.2791	+	1.71326i	0.959580	+	0.0650344i
$695$	−29.4346	+	15.5901i	−1.11652	+	0.591366i
$696$	−59.8307	−	12.3159i	−2.26788	−	0.466835i
$697$	11.4925	+	19.1122i	0.435310	+	0.723926i
$698$	34.0845	+	2.31004i	1.29012	+	0.0874363i
$699$		−	5.57360i		−	0.210813i
$700$	−29.6427	+	32.9928i	−1.12039	+	1.24701i
$701$			12.9121i			0.487683i	0.969815	+	0.243841i	$0.0784077\pi$
$701$			12.9121i			0.487683i	−0.969815	+	0.243841i	$0.921592\pi$
$702$	−7.05347	−	0.478041i	−0.266216	−	0.0180425i
$703$	6.74616			0.254436
$704$	18.0667	+	7.76706i	0.680915	+	0.292732i
$705$	−7.50639	+	3.97577i	−0.282707	+	0.149736i
$706$	23.8841	+	1.61872i	0.898891	+	0.0609213i
$707$		−	62.4812i		−	2.34985i
$708$	0.998374	+	0.135952i	0.0375212	+	0.00510938i
$709$	−50.9488			−1.91342			−0.956712	−	0.291036i	$-0.906000\pi$
$709$	−50.9488			−1.91342			−0.956712	+	0.291036i	$0.906000\pi$
$710$	18.9892	−	8.46676i	0.712651	−	0.317752i
$711$		−	8.04623i		−	0.301757i
$712$	−2.77545	+	13.4831i	−0.104015	+	0.505301i
$713$		−	50.0000i		−	1.87252i
$714$	53.6847	−	27.5215i	2.00910	−	1.02997i
$715$	−18.6344	+	9.86975i	−0.696887	+	0.369108i
$716$	−0.548950	+	4.03126i	−0.0205152	+	0.150655i
$717$			7.76605i			0.290028i
$718$	1.85501	−	27.3707i	0.0692285	−	1.02146i
$719$			21.2170i			0.791259i	0.918410	+	0.395630i	$0.129474\pi$
$719$			21.2170i			0.791259i	−0.918410	+	0.395630i	$0.870526\pi$
$720$	−21.3270	+	4.68870i	−0.794811	+	0.174738i
$721$			59.4509i			2.21407i
$722$	2.06574	−	30.4799i	0.0768790	−	1.13435i
$723$	42.0831			1.56509
$724$	2.04669	+	0.278704i	0.0760645	+	0.0103579i
$725$	−26.0093	+	38.2945i	−0.965959	+	1.42222i
$726$	16.3162	+	1.10581i	0.605550	+	0.0410405i
$727$			25.0074i			0.927473i	0.885973	+	0.463736i	$0.153492\pi$
$727$			25.0074i			0.927473i	−0.885973	+	0.463736i	$0.846508\pi$
$728$	9.70315	−	47.1378i	0.359623	−	1.74704i
$729$	16.1829			0.599368
$730$	−13.9652	−	31.3211i	−0.516876	−	1.15925i
$731$	6.05743	−	3.64244i	0.224042	−	0.134720i
$732$	−2.96400	+	21.7664i	−0.109552	+	0.804508i
$733$	−13.6267			−0.503315			−0.251658	−	0.967816i	$-0.580976\pi$
$733$	−13.6267			−0.503315			−0.251658	+	0.967816i	$0.580976\pi$
$734$	2.15609	−	31.8131i	0.0795829	−	1.17424i
$735$	30.9375	+	58.4109i	1.14115	+	2.15452i
$736$	−13.1342	+	37.3255i	−0.484134	+	1.37584i
$737$	−22.8347			−0.841127
$738$	−18.6321	−	1.26277i	−0.685859	−	0.0464833i
$739$			17.6145i			0.647960i	0.946064	+	0.323980i	$0.105021\pi$
$739$			17.6145i			0.647960i	−0.946064	+	0.323980i	$0.894979\pi$
$740$	1.63130	+	4.44486i	0.0599678	+	0.163396i
$741$	−57.0214			−2.09473
$742$	1.31811	−	19.4487i	0.0483894	−	0.713983i
$743$	6.03503			0.221404			0.110702	−	0.993854i	$-0.464690\pi$
$743$	6.03503			0.221404			0.110702	+	0.993854i	$0.464690\pi$
$744$	9.50873	−	46.1932i	0.348607	−	1.69353i
$745$	19.0984	+	36.0584i	0.699711	+	1.32108i
$746$	−3.09059	+	45.6015i	−0.113154	+	1.66959i
$747$	6.54045			0.239303
$748$	−18.6225	+	8.00657i	−0.680908	+	0.292749i
$749$		−	48.1315i		−	1.75869i
$750$	−6.50172	+	36.3053i	−0.237409	+	1.32568i
$751$			20.3013i			0.740806i	0.928871	+	0.370403i	$0.120780\pi$
$751$			20.3013i			0.740806i	−0.928871	+	0.370403i	$0.879220\pi$
$752$	−1.74176	+	6.27680i	−0.0635155	+	0.228891i
$753$	34.4959			1.25710
$754$	3.39647	−	50.1148i	0.123692	−	1.82507i
$755$	12.7384	−	6.74689i	0.463596	−	0.245545i
$756$	1.55966	−	11.4535i	0.0567244	−	0.416561i
$757$	17.5220			0.636847			0.318424	−	0.947949i	$-0.396847\pi$
$757$	17.5220			0.636847			0.318424	+	0.947949i	$0.396847\pi$
$758$	−1.12441	+	16.5906i	−0.0408403	+	0.602596i
$759$		−	40.1098i		−	1.45589i
$760$	38.6847	−	11.2949i	1.40324	−	0.409708i
$761$	−49.0266			−1.77721			−0.888607	−	0.458670i	$-0.848326\pi$
$761$	−49.0266			−1.77721			−0.888607	+	0.458670i	$0.848326\pi$
$762$	−1.68190	+	24.8164i	−0.0609289	+	0.899003i
$763$	13.6276			0.493353
$764$	−18.1763	−	2.47513i	−0.657596	−	0.0895469i
$765$	11.6172	−	19.2787i	0.420019	−	0.697023i
$766$	−33.7740	−	2.28900i	−1.22031	−	0.0827048i
$767$			0.828530i			0.0299165i
$768$	−19.2326	+	31.9859i	−0.693997	+	1.15419i
$769$	−11.7225			−0.422724			−0.211362	−	0.977408i	$-0.567790\pi$
$769$	−11.7225			−0.422724			−0.211362	+	0.977408i	$0.567790\pi$
$770$	−14.0404	−	31.4897i	−0.505980	−	1.13481i
$771$	7.38696			0.266035
$772$	−16.5292	−	2.25083i	−0.594897	−	0.0810090i
$773$	−38.4421			−1.38267			−0.691334	−	0.722536i	$-0.742976\pi$
$773$	−38.4421			−1.38267			−0.691334	+	0.722536i	$0.742976\pi$
$774$	−0.400223	+	5.90528i	−0.0143857	+	0.212261i
$775$	−29.5659	−	20.0809i	−1.06204	−	0.721326i
$776$	3.33544	−	16.2035i	0.119735	−	0.581672i
$777$	10.9537			0.392964
$778$	2.43253	+	0.164862i	0.0872105	+	0.00591059i
$779$	34.4653			1.23485
$780$	−13.7885	−	37.5699i	−0.493706	−	1.34522i
$781$			16.1620i			0.578323i
$782$	−18.6068	−	36.2953i	−0.665379	−	1.29792i
$783$		−	12.0645i		−	0.431150i
$784$	48.8429	+	13.5535i	1.74439	+	0.484054i
$785$	31.0118	−	16.4255i	1.10686	−	0.586250i
$786$	−14.1687	−	0.960266i	−0.505380	−	0.0342515i
$787$		−	7.70519i		−	0.274661i	−0.990525	−	0.137330i	$-0.956148\pi$
$787$		−	7.70519i		−	0.274661i	0.990525	−	0.137330i	$-0.0438522\pi$
$788$	−4.08518	+	29.9999i	−0.145529	+	1.06870i
$789$	−49.1833			−1.75097
$790$	−9.51884	+	4.24419i	−0.338665	+	0.151002i
$791$	47.5920			1.69218
$792$	3.42238	−	16.6259i	0.121609	−	0.590774i
$793$	−18.0635			−0.641453
$794$	0.808105	+	0.0547684i	0.0286786	+	0.00194366i
$795$	−7.58716	−	14.3248i	−0.269089	−	0.508048i
$796$	−0.306662	+	2.25200i	−0.0108693	+	0.0798199i
$797$	0.584825			0.0207156			0.0103578	−	0.999946i	$-0.496703\pi$
$797$	0.584825			0.0207156			0.0103578	+	0.999946i	$0.496703\pi$
$798$	6.30428	−	93.0194i	0.223169	−	3.29285i
$799$	−3.46013	−	5.75425i	−0.122411	−	0.203571i
$800$	16.7963	+	22.7571i	0.593839	+	0.804584i
$801$	11.8821			0.419832
$802$	−0.0402683	−	0.00272913i	−0.00142192	−	9.63691e-5i
$803$	26.6580			0.940739
$804$	5.84743	−	42.9412i	0.206223	−	1.51442i
$805$	61.3049	−	32.4703i	2.16071	−	1.14443i
$806$	38.6919	+	2.62230i	1.36286	+	0.0923666i
$807$			8.84555i			0.311378i
$808$	−39.0263	−	8.03343i	−1.37294	−	0.282615i
$809$		−	9.44747i		−	0.332155i	−0.986113	−	0.166078i	$-0.946890\pi$
$809$		−	9.44747i		−	0.332155i	0.986113	−	0.166078i	$-0.0531102\pi$
$810$	−13.3462	−	29.9327i	−0.468936	−	1.05173i
$811$	−50.4495			−1.77152			−0.885761	−	0.464142i	$-0.846363\pi$
$811$	−50.4495			−1.77152			−0.885761	+	0.464142i	$0.846363\pi$
$812$	81.3771	+	11.0814i	2.85577	+	0.388880i
$813$			47.2021i			1.65545i
$814$	−3.67213	−	0.248875i	−0.128708	−	0.00872305i
$815$	−3.93313	−	7.42587i	−0.137771	−	0.260117i
$816$	−10.2877	−	37.0704i	−0.360143	−	1.29772i
$817$		−	10.9234i		−	0.382163i
$818$	−0.404576	+	5.96950i	−0.0141457	+	0.208719i
$819$	−41.5404			−1.45154
$820$	8.33412	+	22.7082i	0.291040	+	0.793006i
$821$	28.4106			0.991537			0.495769	−	0.868455i	$-0.334886\pi$
$821$	28.4106			0.991537			0.495769	+	0.868455i	$0.334886\pi$
$822$	4.11260	−	60.6812i	0.143443	−	2.11650i
$823$	−2.79256			−0.0973425			−0.0486712	−	0.998815i	$-0.515499\pi$
$823$	−2.79256			−0.0973425			−0.0486712	+	0.998815i	$0.515499\pi$
$824$	37.1335	+	7.64381i	1.29361	+	0.266285i
$825$	−23.7176	−	16.1088i	−0.825741	−	0.560835i
$826$	−1.35159	−	0.0916023i	−0.0470278	−	0.00318725i
$827$			19.6144i			0.682061i	0.940052	+	0.341030i	$0.110776\pi$
$827$			19.6144i			0.682061i	−0.940052	+	0.341030i	$0.889224\pi$
$828$	33.8419	+	4.60836i	1.17609	+	0.160152i
$829$		−	25.3514i		−	0.880489i	−0.897878	−	0.440245i	$-0.854892\pi$
$829$		−	25.3514i		−	0.880489i	0.897878	−	0.440245i	$-0.145108\pi$
$830$	−3.44993	−	7.73747i	−0.119749	−	0.268572i
$831$	−27.4576			−0.952492
$832$	−28.1951	−	12.1213i	−0.977488	−	0.420232i
$833$	−44.7767	+	26.9250i	−1.55142	+	0.932897i
$834$	49.0278	+	3.32280i	1.69769	+	0.115059i
$835$	−32.3333	+	17.1254i	−1.11894	+	0.592648i
$836$	−4.22689	+	31.0406i	−0.146190	+	1.07356i
$837$	9.31459			0.321959
$838$	−2.32707	+	34.3358i	−0.0803872	+	1.18611i
$839$		−	2.75256i		−	0.0950291i	−0.998871	−	0.0475145i	$-0.984870\pi$
$839$		−	2.75256i		−	0.0950291i	0.998871	−	0.0475145i	$-0.0151300\pi$
$840$	62.8124	−	18.3395i	2.16724	−	0.632773i
$841$	56.7180			1.95579
$842$	3.89280	+	0.263830i	0.134155	+	0.00909219i
$843$		−	28.3597i		−	0.976761i
$844$	−1.77573	−	0.241806i	−0.0611230	−	0.00832331i
$845$	3.39283	−	1.79702i	0.116717	−	0.0618193i
$846$	5.60972	+	0.380192i	0.192866	+	0.0130713i
$847$	−21.9872			−0.755489
$848$	−11.9783	−	3.32389i	−0.411337	−	0.114143i
$849$	−1.47702			−0.0506911
$850$	−28.9348	−	3.57426i	−0.992457	−	0.122596i
$851$		−	7.40564i		−	0.253862i
$852$	−30.3931	−	4.13872i	−1.04125	−	0.141790i
$853$		−	47.7663i		−	1.63549i	−0.575583	−	0.817743i	$-0.695225\pi$
$853$		−	47.7663i		−	1.63549i	0.575583	−	0.817743i	$-0.304775\pi$
$854$	1.99710	−	29.4671i	0.0683392	−	1.00834i
$855$	−16.2813	−	30.7396i	−0.556809	−	1.05127i
$856$	−30.0633	−	6.18843i	−1.02754	−	0.211516i
$857$	39.9732			1.36546			0.682729	−	0.730672i	$-0.260793\pi$
$857$	39.9732			1.36546			0.682729	+	0.730672i	$0.260793\pi$
$858$	31.0384	+	2.10359i	1.05964	+	0.0718155i
$859$			27.0787i			0.923913i	0.886902	+	0.461957i	$0.152852\pi$
$859$			27.0787i			0.923913i	−0.886902	+	0.461957i	$0.847148\pi$
$860$	7.19716	−	2.64142i	0.245421	−	0.0900716i
$861$	55.9614			1.90716
$862$	6.36446	+	0.431344i	0.216774	+	0.0146916i
$863$		−	1.87893i		−	0.0639594i	−0.999489	−	0.0319797i	$-0.989819\pi$
$863$		−	1.87893i		−	0.0639594i	0.999489	−	0.0319797i	$-0.0101812\pi$
$864$	−6.95344	−	2.44680i	−0.236561	−	0.0832418i
$865$	−19.1190	−	36.0972i	−0.650064	−	1.22734i
$866$	−10.8842	−	0.737666i	−0.369861	−	0.0250669i
$867$	35.0262	+	18.5936i	1.18955	+	0.631472i
$868$	−8.55555	+	62.8285i	−0.290394	+	2.13254i
$869$		−	8.10165i		−	0.274830i
$870$	62.3759	−	27.8117i	2.11474	−	0.942905i
$871$	35.6360			1.20748
$872$	1.75215	−	8.51192i	0.0593353	−	0.288250i
$873$	−14.2794			−0.483285
$874$	−62.8888	−	4.26222i	−2.12725	−	0.144172i
$875$	5.42087	−	49.2913i	0.183259	−	1.66635i
$876$	−6.82649	+	50.1309i	−0.230646	+	1.69377i
$877$			34.9661i			1.18072i	0.807139	+	0.590361i	$0.201015\pi$
$877$			34.9661i			1.18072i	−0.807139	+	0.590361i	$0.798985\pi$
$878$	−50.4477	−	3.41903i	−1.70253	−	0.115387i
$879$		−	56.7080i		−	1.91271i
$880$	−21.4739	+	4.72100i	−0.723886	+	0.159145i
$881$			58.8637i			1.98317i	0.129466	+	0.991584i	$0.458674\pi$
$881$			58.8637i			1.98317i	−0.129466	+	0.991584i	$0.541326\pi$
$882$	2.95847	−	43.6520i	0.0996167	−	1.46984i
$883$	12.7513			0.429115			0.214558	−	0.976711i	$-0.431169\pi$
$883$	12.7513			0.429115			0.214558	+	0.976711i	$0.431169\pi$
$884$	29.0625	−	12.4951i	0.977477	−	0.420256i
$885$	−0.995504	+	0.527271i	−0.0334635	+	0.0177240i
$886$	−0.0741372	+	1.09389i	−0.00249069	+	0.0367500i
$887$	−17.4369			−0.585474			−0.292737	−	0.956193i	$-0.594566\pi$
$887$	−17.4369			−0.585474			−0.292737	+	0.956193i	$0.594566\pi$
$888$	1.40836	−	6.84180i	0.0472615	−	0.229596i
$889$		−	33.4418i		−	1.12160i
$890$	−6.26749	−	14.0567i	−0.210087	−	0.471181i
$891$	25.4762			0.853486
$892$	−5.78603	+	42.4903i	−0.193731	+	1.42268i
$893$	−10.3767			−0.347244
$894$	4.07055	−	60.0608i	0.136139	−	2.00873i
$895$	−2.12903	−	4.01967i	−0.0711655	−	0.134363i
$896$	22.8909	−	44.6547i	0.764730	−	1.49181i
$897$			62.5956i			2.09001i
$898$	37.7928	+	2.56137i	1.26116	+	0.0854739i
$899$			66.1800i			2.20723i
$900$	16.3165	−	18.1605i	0.543883	−	0.605350i
$901$	10.9811	−	6.60314i	0.365834	−	0.219983i
$902$	−18.7605	−	1.27147i	−0.624656	−	0.0423353i
$903$		−	17.7364i		−	0.590231i
$904$	6.11907	−	29.7264i	0.203517	−	0.988684i
$905$	−2.04080	+	1.08091i	−0.0678385	+	0.0359308i
$906$	−21.2177	−	1.43800i	−0.704910	−	0.0477744i
$907$			16.1397i			0.535910i	0.963431	+	0.267955i	$0.0863478\pi$
$907$			16.1397i			0.535910i	−0.963431	+	0.267955i	$0.913652\pi$
$908$	5.46941	−	40.1651i	0.181509	−	1.33293i
$909$			34.3921i			1.14071i
$910$	21.9115	+	49.1430i	0.726360	+	1.62907i
$911$			28.4224i			0.941675i	0.882220	+	0.470837i	$0.156048\pi$
$911$			28.4224i			0.941675i	−0.882220	+	0.470837i	$0.843952\pi$
$912$	−57.2902	−	15.8975i	−1.89707	−	0.526420i
$913$	6.58550			0.217948
$914$	28.9947	+	1.96508i	0.959060	+	0.0649991i
$915$	−11.4955	−	21.7038i	−0.380028	−	0.717506i
$916$	−4.80700	+	35.3006i	−0.158828	+	1.16637i
$917$	19.0933			0.630516
$918$	6.76151	−	3.46630i	0.223163	−	0.114405i
$919$	−48.7201			−1.60713			−0.803565	−	0.595217i	$-0.797066\pi$
$919$	−48.7201			−1.60713			−0.803565	+	0.595217i	$0.797066\pi$
$920$	−12.3990	−	42.4664i	−0.408783	−	1.40008i
$921$			11.6913i			0.385242i
$922$	9.93334	+	0.673221i	0.327137	+	0.0221713i
$923$		−	25.2226i		−	0.830212i
$924$	−6.86322	+	50.4007i	−0.225783	+	1.65806i
$925$	−4.37908	−	2.97423i	−0.143983	−	0.0977921i
$926$	−18.5289	−	1.25577i	−0.608896	−	0.0412672i
$927$		−	32.7241i		−	1.07480i
$928$	17.3845	−	49.4040i	0.570673	−	1.62177i
$929$			53.8045i			1.76527i	0.470061	+	0.882634i	$0.344232\pi$
$929$			53.8045i			1.76527i	−0.470061	+	0.882634i	$0.655768\pi$
$930$	21.4725	+	48.1583i	0.704110	+	1.57917i
$931$			80.7465i			2.64636i
$932$	4.73502	+	0.644783i	0.155101	+	0.0211206i
$933$	−8.62183			−0.282266
$934$	2.53727	−	37.4373i	0.0830219	−	1.22498i
$935$	11.6972	−	19.4115i	0.382539	−	0.634824i
$936$	−5.34099	+	25.9465i	−0.174576	+	0.848086i
$937$		−	17.3019i		−	0.565230i	−0.959233	−	0.282615i	$-0.908798\pi$
$937$		−	17.3019i		−	0.565230i	0.959233	−	0.282615i	$-0.0912019\pi$
$938$	−3.93991	+	58.1333i	−0.128643	+	1.89812i
$939$			18.4020i			0.600525i
$940$	−2.50922	−	6.83694i	−0.0818416	−	0.222997i
$941$	−31.7594			−1.03533			−0.517663	−	0.855585i	$-0.673198\pi$
$941$	−31.7594			−1.03533			−0.517663	+	0.855585i	$0.673198\pi$
$942$	−51.6549	−	3.50085i	−1.68301	−	0.114064i
$943$		−	37.8345i		−	1.23206i
$944$	−0.230994	+	0.832435i	−0.00751821	+	0.0270935i
$945$	6.04894	+	11.4206i	0.196772	+	0.371512i
$946$	−0.402980	+	5.94595i	−0.0131020	+	0.193320i
$947$			6.57610i			0.213694i	0.994275	+	0.106847i	$0.0340756\pi$
$947$			6.57610i			0.213694i	−0.994275	+	0.106847i	$0.965924\pi$
$948$	15.2354	+	2.07465i	0.494821	+	0.0673814i
$949$	−41.6026			−1.35048
$950$	−27.7775	+	35.4755i	−0.901222	+	1.15098i
$951$	−27.9377			−0.905943
$952$	17.1702	+	48.7913i	0.556491	+	1.58134i
$953$		−	0.331815i		−	0.0107486i	−0.999986	−	0.00537428i	$-0.998289\pi$
$953$		−	0.331815i		−	0.0107486i	0.999986	−	0.00537428i	$-0.00171069\pi$
$954$	−0.725539	+	10.7053i	−0.0234902	+	0.346597i
$955$	18.1241	−	9.59944i	0.586481	−	0.310631i
$956$	−6.59760	−	0.898416i	−0.213382	−	0.0290568i
$957$			53.0892i			1.71613i
$958$	−51.8661	−	3.51517i	−1.67572	−	0.113570i
$959$			81.7722i			2.64056i
$960$	−3.37898	−	41.5911i	−0.109056	−	1.34235i
$961$	−20.0953			−0.648237
$962$	5.73076	+	0.388396i	0.184767	+	0.0125224i
$963$			26.4934i			0.853739i
$964$	−4.86838	+	35.7514i	−0.156800	+	1.15148i
$965$	16.4816	−	8.72953i	0.530562	−	0.281013i
$966$	−102.113	−	6.92057i	−3.28542	−	0.222666i
$967$		−	26.9044i		−	0.865188i	−0.901589	−	0.432594i	$-0.857598\pi$
$967$		−	26.9044i		−	0.865188i	0.901589	−	0.432594i	$-0.142402\pi$
$968$	−2.82697	+	13.7334i	−0.0908623	+	0.441408i
$969$	52.5207	−	31.5816i	1.68721	−	1.01455i
$970$	7.53204	+	16.8928i	0.241839	+	0.542395i
$971$			23.4854i			0.753681i	0.926278	+	0.376841i	$0.122990\pi$
$971$			23.4854i			0.753681i	−0.926278	+	0.376841i	$0.877010\pi$
$972$	−5.46894	+	40.1616i	−0.175416	+	1.28819i
$973$	−66.0684			−2.11806
$974$	−3.29073	+	48.5547i	−0.105442	+	1.55579i
$975$	37.0139	+	25.1395i	1.18539	+	0.805107i
$976$	−18.1486	−	5.03609i	−0.580923	−	0.161201i
$977$			22.0297i			0.704793i	0.935851	+	0.352396i	$0.114633\pi$
$977$			22.0297i			0.704793i	−0.935851	+	0.352396i	$0.885367\pi$
$978$	−0.838289	+	12.3689i	−0.0268055	+	0.395514i
$979$	11.9639			0.382368
$980$	−53.2017	+	19.5255i	−1.69946	+	0.623718i
$981$	−7.50117			−0.239494
$982$	−36.7709	−	2.49211i	−1.17341	−	0.0795264i
$983$	−55.0949			−1.75725			−0.878627	−	0.477508i	$-0.841540\pi$
$983$	−55.0949			−1.75725			−0.878627	+	0.477508i	$0.841540\pi$
$984$	7.19515	−	34.9539i	0.229373	−	1.11429i
$985$	−15.8438	−	29.9137i	−0.504826	−	0.953128i
$986$	24.6280	+	48.0403i	0.784314	+	1.52992i
$987$	−16.8487			−0.536300
$988$	6.59653	−	48.4422i	0.209863	−	1.54115i
$989$	−11.9913			−0.381300
$990$	7.72837	+	17.3331i	0.245624	+	0.550883i
$991$		−	22.4296i		−	0.712501i	−0.934391	−	0.356250i	$-0.884055\pi$
$991$		−	22.4296i		−	0.712501i	0.934391	−	0.356250i	$-0.115945\pi$
$992$	38.1432	+	13.4220i	1.21105	+	0.426147i
$993$	−35.7739			−1.13525
$994$	41.1458	+	2.78861i	1.30507	+	0.0884493i
$995$	−1.18935	−	2.24552i	−0.0377048	−	0.0711879i
$996$	−1.68639	+	12.3842i	−0.0534354	+	0.392408i
$997$			37.3152i			1.18178i	0.806750	+	0.590892i	$0.201224\pi$
$997$			37.3152i			1.18178i	−0.806750	+	0.590892i	$0.798776\pi$
$998$	0.621805	−	9.17470i	0.0196829	−	0.290420i
$999$	1.37961			0.0436489

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.b.509.20	yes	40
5.4	even	2	inner	680.2.h.b.509.21	yes	40
8.5	even	2	inner	680.2.h.b.509.23	yes	40
17.16	even	2	inner	680.2.h.b.509.19	yes	40
40.29	even	2	inner	680.2.h.b.509.18	yes	40
85.84	even	2	inner	680.2.h.b.509.22	yes	40
136.101	even	2	inner	680.2.h.b.509.24	yes	40
680.509	even	2	inner	680.2.h.b.509.17	✓	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.b.509.17	✓	40	680.509	even	2	inner
680.2.h.b.509.18	yes	40	40.29	even	2	inner
680.2.h.b.509.19	yes	40	17.16	even	2	inner
680.2.h.b.509.20	yes	40	1.1	even	1	trivial
680.2.h.b.509.21	yes	40	5.4	even	2	inner
680.2.h.b.509.22	yes	40	85.84	even	2	inner
680.2.h.b.509.23	yes	40	8.5	even	2	inner
680.2.h.b.509.24	yes	40	136.101	even	2	inner

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:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0956273 + 1.41098i) q^{2} +2.33268i q^{3} +(-1.98171 - 0.269856i) q^{4} +(1.97601 - 1.04660i) q^{5} +(-3.29135 - 0.223067i) q^{6} +4.43533 q^{7} +(0.570266 - 2.77034i) q^{8} -2.44138 q^{9} +(1.28777 + 2.88819i) q^{10} -2.45819 q^{11} +(0.629486 - 4.62269i) q^{12} +3.83628 q^{13} +(-0.424138 + 6.25814i) q^{14} +(2.44138 + 4.60940i) q^{15} +(3.85436 + 1.06955i) q^{16} +(-3.53348 + 2.12474i) q^{17} +(0.233462 - 3.44473i) q^{18} +6.37197i q^{19} +(-4.19832 + 1.54082i) q^{20} +10.3462i q^{21} +(0.235070 - 3.46845i) q^{22} +6.99487 q^{23} +(6.46231 + 1.33025i) q^{24} +(2.80926 - 4.13619i) q^{25} +(-0.366853 + 5.41290i) q^{26} +1.30309i q^{27} +(-8.78954 - 1.19690i) q^{28} -9.25840 q^{29} +(-6.73722 + 3.00394i) q^{30} -7.14810i q^{31} +(-1.87770 + 5.33613i) q^{32} -5.73417i q^{33} +(-2.66007 - 5.18884i) q^{34} +(8.76427 - 4.64201i) q^{35} +(4.83810 + 0.658820i) q^{36} -1.05872i q^{37} +(-8.99070 - 0.609334i) q^{38} +8.94879i q^{39} +(-1.77259 - 6.07107i) q^{40} -5.40889i q^{41} +(-14.5982 - 0.989377i) q^{42} -1.71430 q^{43} +(4.87143 + 0.663358i) q^{44} +(-4.82419 + 2.55514i) q^{45} +(-0.668901 + 9.86960i) q^{46} +1.62850i q^{47} +(-2.49492 + 8.99096i) q^{48} +12.6721 q^{49} +(5.56742 + 4.35933i) q^{50} +(-4.95634 - 8.24246i) q^{51} +(-7.60239 - 1.03524i) q^{52} -3.10774 q^{53} +(-1.83862 - 0.124611i) q^{54} +(-4.85742 + 2.57274i) q^{55} +(2.52932 - 12.2874i) q^{56} -14.8637 q^{57} +(0.885356 - 13.0634i) q^{58} +0.215973i q^{59} +(-3.59423 - 9.79332i) q^{60} -4.70860 q^{61} +(10.0858 + 0.683553i) q^{62} -10.8283 q^{63} +(-7.34959 - 3.15966i) q^{64} +(7.58053 - 4.01504i) q^{65} +(8.09078 + 0.548343i) q^{66} +9.28922 q^{67} +(7.57571 - 3.25710i) q^{68} +16.3168i q^{69} +(5.71167 + 12.8101i) q^{70} -6.57476i q^{71} +(-1.39223 + 6.76345i) q^{72} -10.8445 q^{73} +(1.49383 + 0.101243i) q^{74} +(9.64839 + 6.55309i) q^{75} +(1.71951 - 12.6274i) q^{76} -10.9029 q^{77} +(-12.6265 - 0.855748i) q^{78} +3.29578i q^{79} +(8.73565 - 1.92052i) q^{80} -10.3638 q^{81} +(7.63182 + 0.517237i) q^{82} -2.67900 q^{83} +(2.79198 - 20.5031i) q^{84} +(-4.75845 + 7.89666i) q^{85} +(0.163933 - 2.41883i) q^{86} -21.5968i q^{87} +(-1.40182 + 6.81004i) q^{88} -4.86695 q^{89} +(-3.14392 - 7.05117i) q^{90} +17.0151 q^{91} +(-13.8618 - 1.88761i) q^{92} +16.6742 q^{93} +(-2.29777 - 0.155729i) q^{94} +(6.66890 + 12.5911i) q^{95} +(-12.4475 - 4.38005i) q^{96} +5.84892 q^{97} +(-1.21180 + 17.8801i) q^{98} +6.00138 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 12 q^{4} - 56 q^{9} + 56 q^{15} - 4 q^{16} - 36 q^{26} - 28 q^{30} + 24 q^{34} + 88 q^{36} + 8 q^{49} - 16 q^{50} - 88 q^{55} - 88 q^{60} - 132 q^{64} + 208 q^{66} + 72 q^{70} - 20 q^{76} - 56 q^{81}+ \cdots - 36 q^{94}+O(q^{100}) \) 40 * q + 12 * q^4 - 56 * q^9 + 56 * q^15 - 4 * q^16 - 36 * q^26 - 28 * q^30 + 24 * q^34 + 88 * q^36 + 8 * q^49 - 16 * q^50 - 88 * q^55 - 88 * q^60 - 132 * q^64 + 208 * q^66 + 72 * q^70 - 20 * q^76 - 56 * q^81 + 144 * q^84 + 256 * q^86 - 96 * q^89 - 36 * q^94

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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