LMFDB - Embedded newform 680.2.h.b.509.18

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			509.18
Character	$\chi$	$=$	680.509
Dual form			680.2.h.b.509.19

$q$-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} +(-3.33586 - 4.78247i) 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} +(-6.42896 + 5.16416i) 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} +(-9.20596 + 0.500386i) 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	$-0.816391\pi$
$7$	−4.43533			−1.67640			−0.838198	+	0.545366i	$0.816391\pi$
$8$	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	$-0.379157\pi$
$11$	2.45819			0.741173			0.370587	+	0.928798i	$0.379157\pi$
$12$	−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	$-0.739093\pi$
$19$		−	6.37197i		−	1.46183i	0.682468	−	0.730915i	$-0.260907\pi$
$20$	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	$-0.760138\pi$
$23$	−6.99487			−1.45853			−0.729266	+	0.684231i	$0.760138\pi$
$24$	−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	$-0.170700\pi$
$29$	9.25840			1.71924			0.859621	+	0.510932i	$0.170700\pi$
$30$	−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
$34$	−3.33586	−	4.78247i	−0.572095	−	0.820187i
$35$	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	$-0.962105\pi$
$47$		−	1.62850i		−	0.237540i	0.992922	−	0.118770i	$-0.0378952\pi$
$48$	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	$-0.995525\pi$
$59$		−	0.215973i		−	0.0281172i	0.999901	−	0.0140586i	$-0.00447514\pi$
$60$	−3.59423	+	9.79332i	−0.464013	+	1.26431i
$61$	4.70860			0.602874			0.301437	−	0.953486i	$-0.402534\pi$
$61$	4.70860			0.602874			0.301437	+	0.953486i	$0.402534\pi$
$62$	−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	$0.307938\pi$
$68$	−6.42896	+	5.16416i	−0.779626	+	0.626246i
$69$		−	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	$-0.281153\pi$
$73$	10.8445			1.26926			0.634629	+	0.772817i	$0.281153\pi$
$74$	−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
$85$	−9.20596	+	0.500386i	−0.998526	+	0.0542745i
$86$	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	$-0.595964\pi$
$97$	−5.84892			−0.593868			−0.296934	+	0.954898i	$0.595964\pi$
$98$	−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	$0.247201\pi$
$101$			14.0872i			1.40172i	−0.713297	+	0.700862i	$0.752799\pi$
$102$	11.1560	−	7.78148i	1.10460	−	0.770481i
$103$		−	13.4039i		−	1.32073i	−0.750945	−	0.660365i	$-0.770402\pi$
$103$		−	13.4039i		−	1.32073i	0.750945	−	0.660365i	$-0.229598\pi$
$104$	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	$-0.547009\pi$
$109$	−3.07252			−0.294294			−0.147147	+	0.989115i	$0.547009\pi$
$110$	−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	$-0.668399\pi$
$113$	−10.7302			−1.00941			−0.504707	+	0.863291i	$0.668399\pi$
$114$	−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	$0.108577\pi$
$127$			7.53988i			0.669056i	−0.942386	+	0.334528i	$0.891423\pi$
$128$	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	$-0.560219\pi$
$131$	−4.30482			−0.376114			−0.188057	+	0.982158i	$0.560219\pi$
$132$	−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
$136$	7.90129	+	8.57728i	0.677530	+	0.735495i
$137$		−	18.4366i		−	1.57514i	−0.616225	−	0.787570i	$-0.711339\pi$
$137$		−	18.4366i		−	1.57514i	0.616225	−	0.787570i	$-0.288661\pi$
$138$	−23.0226	+	1.56033i	−1.95981	+	0.132824i
$139$	14.8960			1.26346			0.631729	−	0.775189i	$-0.282345\pi$
$139$	14.8960			1.26346			0.631729	+	0.775189i	$0.282345\pi$
$140$	−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	$-0.731269\pi$
$149$		−	18.2481i		−	1.49494i	0.664296	−	0.747469i	$-0.268731\pi$
$150$	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	$-0.281783\pi$
$167$	16.3629			1.26620			0.633099	+	0.774071i	$0.281783\pi$
$168$	28.6625	−	5.90007i	2.21136	−	0.455201i
$169$	1.71701			0.132078
$170$	1.58637	+	12.9415i	0.121669	+	0.992571i
$171$			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	$0.0242222\pi$
$179$			2.03423i			0.152046i	−0.997106	+	0.0760229i	$0.975778\pi$
$180$	−10.2497	−	3.76172i	−0.763966	−	0.280382i
$181$	1.03279			0.0767664			0.0383832	−	0.999263i	$-0.487779\pi$
$181$	1.03279			0.0767664			0.0383832	+	0.999263i	$0.487779\pi$
$182$	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	$-0.597051\pi$
$193$	−8.34085			−0.600387			−0.300194	+	0.953878i	$0.597051\pi$
$194$	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
$204$	−12.0463	−	14.9967i	−0.843410	−	1.04998i
$205$	−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	$-0.509819\pi$
$211$	−0.896057			−0.0616871			−0.0308436	+	0.999524i	$0.509819\pi$
$212$	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	$0.254899\pi$
$223$			21.4412i			1.43581i	−0.696141	+	0.717905i	$0.745101\pi$
$224$	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	$0.200307\pi$
$229$			17.8132i			1.17713i	−0.808450	+	0.588565i	$0.799693\pi$
$230$	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	$-0.475062\pi$
$233$	2.38936			0.156532			0.0782661	+	0.996933i	$0.475062\pi$
$234$	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
$238$	14.7956	+	21.2118i	0.959058	+	1.37496i
$239$	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	$0.154561\pi$
$251$			14.7881i			0.933419i	−0.884411	+	0.466709i	$0.845439\pi$
$252$	−21.4586	+	2.92208i	−1.35176	+	0.184074i
$253$	−17.1947			−1.08102
$254$	10.6386	−	0.721019i	0.667525	−	0.0452407i
$255$	−1.16724	−	21.4745i	−0.0730953	−	1.34479i
$256$	13.7121	−	8.24487i	0.857007	−	0.515304i
$257$			3.16673i			0.197535i	0.995111	+	0.0987676i	$0.0314901\pi$
$257$			3.16673i			0.197535i	−0.995111	+	0.0987676i	$0.968510\pi$
$258$	−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	$-0.774742\pi$
$263$		−	21.0845i		−	1.30013i	0.759880	−	0.650063i	$-0.225258\pi$
$264$	−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	$-0.536880\pi$
$269$	−3.79202			−0.231203			−0.115602	+	0.993296i	$0.536880\pi$
$270$	−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	$0.289318\pi$
$272$	11.3468	−	11.9688i	0.687998	−	0.725712i
$273$		−	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
$306$	8.14409	+	11.6758i	0.465567	+	0.667462i
$307$	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	$-0.571569\pi$
$313$	−7.88878			−0.445900			−0.222950	+	0.974830i	$0.571569\pi$
$314$	−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	$-0.861514\pi$
$331$		−	15.3360i		−	0.842943i	0.906842	−	0.421472i	$-0.138486\pi$
$332$	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	$-0.363587\pi$
$337$	15.2572			0.831112			0.415556	+	0.909568i	$0.363587\pi$
$338$	−0.164193	−	2.42266i	−0.00893091	−	0.131775i
$339$		−	25.0301i		−	1.35945i
$340$	18.1085	−	3.47590i	0.982072	−	0.188507i
$341$		−	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	$0.223784\pi$
$349$			24.1567i			1.29308i	−0.762881	+	0.646539i	$0.776216\pi$
$350$	−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	$0.148746\pi$
$353$			16.9274i			0.900953i	−0.892788	+	0.450477i	$0.851254\pi$
$354$	−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	$-0.299731\pi$
$367$	22.5468			1.17694			0.588468	+	0.808521i	$0.299731\pi$
$368$	−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	$0.184476\pi$
$374$	−8.20019	−	11.7562i	−0.424022	−	0.607901i
$375$	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	$-0.597651\pi$
$379$	−11.7582			−0.603979			−0.301989	+	0.953311i	$0.597651\pi$
$380$	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	$-0.790545\pi$
$383$		−	23.9366i		−	1.22311i	0.791204	−	0.611553i	$-0.209455\pi$
$384$	−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	$0.0139163\pi$
$389$			1.72401i			0.0874106i	−0.999044	+	0.0437053i	$0.986084\pi$
$390$	−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
$408$	−20.0080	+	18.4311i	−0.990544	+	0.912478i
$409$	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	$-0.702617\pi$
$419$	−24.3348			−1.18883			−0.594415	+	0.804158i	$0.702617\pi$
$420$	15.9416	−	43.4366i	0.777870	−	2.11949i
$421$			2.75894i			0.134463i	0.997737	+	0.0672313i	$0.0214165\pi$
$421$			2.75894i			0.134463i	−0.997737	+	0.0672313i	$0.978583\pi$
$422$	0.0856875	+	1.26432i	0.00417120	+	0.0615459i
$423$			3.97577i			0.193309i
$424$	−1.77224	−	8.60949i	−0.0860674	−	0.418114i
$425$	18.7148	+	8.64618i	0.907801	+	0.419401i
$426$	−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	$-0.940657\pi$
$433$		−	7.71397i		−	0.370710i	0.982672	−	0.185355i	$-0.0593434\pi$
$434$	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
$442$	−12.7973	−	18.3469i	−0.608704	−	0.872672i
$443$	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	$0.159592\pi$
$457$			20.5494i			0.961260i	−0.876924	+	0.480630i	$0.840408\pi$
$458$	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	$0.0524216\pi$
$461$			7.04005i			0.327888i	−0.986470	+	0.163944i	$0.947578\pi$
$462$	−35.8852	+	2.43208i	−1.66953	+	0.113151i
$463$		−	13.1319i		−	0.610293i	−0.952305	−	0.305147i	$-0.901295\pi$
$463$		−	13.1319i		−	0.610293i	0.952305	−	0.305147i	$-0.0987054\pi$
$464$	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
$476$	28.5145	−	22.9047i	1.30696	−	1.04984i
$477$	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	$-0.784618\pi$
$487$	−34.4121			−1.55936			−0.779680	+	0.626178i	$0.784618\pi$
$488$	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	$-0.799896\pi$
$491$		−	26.0606i		−	1.17610i	0.808825	−	0.588050i	$-0.200104\pi$
$492$	−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	$-0.453507\pi$
$499$	6.50237			0.291086			0.145543	+	0.989352i	$0.453507\pi$
$500$	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	$-0.505285\pi$
$503$	−0.744731			−0.0332059			−0.0166029	+	0.999862i	$0.505285\pi$
$504$	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	$0.133521\pi$
$509$			18.3771i			0.814550i	−0.913306	+	0.407275i	$0.866479\pi$
$510$	−30.1884	+	3.70050i	−1.33677	+	0.163861i
$511$	−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	$-0.604248\pi$
$541$	−14.9643			−0.643364			−0.321682	+	0.946848i	$0.604248\pi$
$542$	−1.93503	−	28.5514i	−0.0831168	−	1.22639i
$543$			2.40916i			0.103387i
$544$	−17.9727	−	14.8655i	−0.770573	−	0.637352i
$545$	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	$-0.630422\pi$
$571$	−19.0383			−0.796729			−0.398364	+	0.917227i	$0.630422\pi$
$572$	−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	$-0.586736\pi$
$577$		−	46.2691i		−	1.92621i	0.269128	−	0.963104i	$-0.413264\pi$
$578$	−21.9487	−	9.81091i	−0.912946	−	0.408080i
$579$		−	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	$0.148643\pi$
$593$			21.9255i			0.900374i	−0.892934	+	0.450187i	$0.851357\pi$
$594$	4.51969	−	0.306317i	0.185445	−	0.0125683i
$595$	40.8314	−	2.21938i	1.67393	−	0.0909855i
$596$	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	$-0.595195\pi$
$607$	−14.5176			−0.589250			−0.294625	+	0.955613i	$0.595195\pi$
$608$	−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
$612$	15.6955	−	12.6077i	0.634453	−	0.509634i
$613$	−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	$-0.496505\pi$
$617$	0.545393			0.0219567			0.0109783	+	0.999940i	$0.496505\pi$
$618$	−2.98999	−	44.1171i	−0.120275	−	1.77465i
$619$	44.4056			1.78481			0.892405	−	0.451235i	$-0.149016\pi$
$619$	44.4056			1.78481			0.892405	+	0.451235i	$0.149016\pi$
$620$	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
$646$	−30.4738	+	21.2560i	−1.19897	+	0.836306i
$647$			27.4611i			1.07961i	0.841791	+	0.539804i	$0.181502\pi$
$647$			27.4611i			1.07961i	−0.841791	+	0.539804i	$0.818498\pi$
$648$	−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	$0.268517\pi$
$659$			38.3536i			1.49404i	−0.664799	+	0.747022i	$0.731483\pi$
$660$	−8.83531	+	24.0739i	−0.343914	+	0.937074i
$661$			14.3360i			0.557607i	0.960348	+	0.278804i	$0.0899378\pi$
$661$			14.3360i			0.557607i	−0.960348	+	0.278804i	$0.910062\pi$
$662$	−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	$-0.539048\pi$
$673$	−6.34888			−0.244731			−0.122366	+	0.992485i	$0.539048\pi$
$674$	−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
$680$	−6.63608	−	25.2183i	−0.254482	−	0.967077i
$681$	−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	$-0.165136\pi$
$691$	45.6561			1.73684			0.868419	+	0.495831i	$0.165136\pi$
$692$	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	$-0.921592\pi$
$701$		−	12.9121i		−	0.487683i	0.969815	−	0.243841i	$-0.0784077\pi$
$702$	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	$-0.0940001\pi$
$709$	50.9488			1.91342			0.956712	+	0.291036i	$0.0940001\pi$
$710$	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
$714$	−49.4803	+	34.5134i	−1.85175	+	1.29163i
$715$	−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	$-0.846508\pi$
$727$		−	25.0074i		−	0.927473i	0.885973	−	0.463736i	$-0.153492\pi$
$728$	−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	$-0.894979\pi$
$739$		−	17.6145i		−	0.647960i	0.946064	−	0.323980i	$-0.105021\pi$
$740$	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	$-0.535310\pi$
$743$	−6.03503			−0.221404			−0.110702	+	0.993854i	$0.535310\pi$
$744$	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
$748$	−15.8036	+	12.6945i	−0.577837	+	0.464157i
$749$			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
$765$	22.4752	−	1.22163i	0.812593	−	0.0441682i
$766$	−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
$782$	23.3339	+	33.4528i	0.834419	+	1.19627i
$783$			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	$-0.153637\pi$
$811$	50.4495			1.77152			0.885761	+	0.464142i	$0.153637\pi$
$812$	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
$816$	27.9192	+	26.4683i	0.977368	+	0.926576i
$817$			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	$-0.665114\pi$
$821$	−28.4106			−0.991537			−0.495769	+	0.868455i	$0.665114\pi$
$822$	−4.11260	−	60.6812i	−0.143443	−	2.11650i
$823$	2.79256			0.0973425			0.0486712	−	0.998815i	$-0.484501\pi$
$823$	2.79256			0.0973425			0.0486712	+	0.998815i	$0.484501\pi$
$824$	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	$0.145108\pi$
$829$			25.3514i			0.880489i	−0.897878	+	0.440245i	$0.854892\pi$
$830$	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
$850$	10.4099	−	27.2330i	0.357057	−	0.934083i
$851$			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	$-0.739207\pi$
$857$	−39.9732			−1.36546			−0.682729	+	0.730672i	$0.739207\pi$
$858$	31.0384	−	2.10359i	1.05964	−	0.0718155i
$859$		−	27.0787i		−	0.923913i	−0.886902	−	0.461957i	$-0.847148\pi$
$859$		−	27.0787i		−	0.923913i	0.886902	−	0.461957i	$-0.152852\pi$
$860$	−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	$0.0101812\pi$
$863$			1.87893i			0.0639594i	−0.999489	+	0.0319797i	$0.989819\pi$
$864$	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	$0.431169\pi$
$884$	−24.6632	+	19.8111i	−0.829515	+	0.666320i
$885$	−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	$-0.405434\pi$
$887$	17.4369			0.585474			0.292737	+	0.956193i	$0.405434\pi$
$888$	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
$918$	6.23197	−	4.34691i	0.205686	−	0.143470i
$919$	−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
$935$	−22.6300	+	1.23005i	−0.740081	+	0.0402268i
$936$	−5.34099	−	25.9465i	−0.174576	−	0.848086i
$937$			17.3019i			0.565230i	0.959233	+	0.282615i	$0.0912019\pi$
$937$			17.3019i			0.565230i	−0.959233	+	0.282615i	$0.908798\pi$
$938$	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	$-0.326802\pi$
$941$	31.7594			1.03533			0.517663	+	0.855585i	$0.326802\pi$
$942$	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
$952$	−35.0448	−	38.0430i	−1.13581	−	1.23298i
$953$			0.331815i			0.0107486i	0.999986	+	0.00537428i	$0.00171069\pi$
$953$			0.331815i			0.0107486i	−0.999986	+	0.00537428i	$0.998289\pi$
$954$	−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	$0.142402\pi$
$967$			26.9044i			0.865188i	−0.901589	+	0.432594i	$0.857598\pi$
$968$	−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	$-0.877010\pi$
$971$		−	23.4854i		−	0.753681i	0.926278	−	0.376841i	$-0.122990\pi$
$972$	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	$-0.885367\pi$
$977$		−	22.0297i		−	0.704793i	0.935851	−	0.352396i	$-0.114633\pi$
$978$	−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	$-0.158460\pi$
$983$	55.0949			1.75725			0.878627	+	0.477508i	$0.158460\pi$
$984$	7.19515	+	34.9539i	0.229373	+	1.11429i
$985$	−15.8438	+	29.9137i	−0.504826	+	0.953128i
$986$	−30.8847	−	44.2780i	−0.983570	−	1.41010i
$987$	−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.509.18	yes	40
5.4	even	2	inner	680.2.h.b.509.23	yes	40
8.5	even	2	inner	680.2.h.b.509.21	yes	40
17.16	even	2	inner	680.2.h.b.509.17	✓	40
40.29	even	2	inner	680.2.h.b.509.20	yes	40
85.84	even	2	inner	680.2.h.b.509.24	yes	40
136.101	even	2	inner	680.2.h.b.509.22	yes	40
680.509	even	2	inner	680.2.h.b.509.19	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.b.509.17	✓	40	17.16	even	2	inner
680.2.h.b.509.18	yes	40	1.1	even	1	trivial
680.2.h.b.509.19	yes	40	680.509	even	2	inner
680.2.h.b.509.20	yes	40	40.29	even	2	inner
680.2.h.b.509.21	yes	40	8.5	even	2	inner
680.2.h.b.509.22	yes	40	136.101	even	2	inner
680.2.h.b.509.23	yes	40	5.4	even	2	inner
680.2.h.b.509.24	yes	40	85.84	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} +(-3.33586 - 4.78247i) 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} +(-6.42896 + 5.16416i) 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} +(-9.20596 + 0.500386i) 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

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Database

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