LMFDB - Embedded newform 680.2.h.c.509.36

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 = [48] 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:	$48$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			509.36
Character	$\chi$	$=$	680.509
Dual form			680.2.h.c.509.37

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.909039 - 1.08335i) q^{2} +2.68098i q^{3} +(-0.347296 - 1.96962i) q^{4} +(-2.10758 + 0.747066i) q^{5} +(2.90444 + 2.43712i) q^{6} +0.590069 q^{7} +(-2.44949 - 1.41421i) q^{8} -4.18766 q^{9} +(-1.10654 + 2.96236i) q^{10} -5.24673 q^{11} +(5.28050 - 0.931095i) q^{12} -2.44949 q^{13} +(0.536396 - 0.639252i) q^{14} +(-2.00287 - 5.65038i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(4.03667 + 0.839805i) q^{17} +(-3.80675 + 4.53671i) q^{18} +2.57115i q^{19} +(2.20339 + 3.89167i) q^{20} +1.58196i q^{21} +(-4.76948 + 5.68404i) q^{22} -7.58646 q^{23} +(3.79148 - 6.56704i) q^{24} +(3.88378 - 3.14900i) q^{25} +(-2.22668 + 2.65366i) q^{26} -3.18410i q^{27} +(-0.204929 - 1.16221i) q^{28} -3.32207 q^{29} +(-7.94203 - 2.96661i) q^{30} -4.11271i q^{31} +(-1.93476 + 5.31570i) q^{32} -14.0664i q^{33} +(4.57930 - 3.60972i) q^{34} +(-1.24362 + 0.440821i) q^{35} +(1.45436 + 8.24809i) q^{36} -8.73391i q^{37} +(2.78546 + 2.33728i) q^{38} -6.56704i q^{39} +(6.21901 + 1.15064i) q^{40} +10.8958i q^{41} +(1.71382 + 1.43807i) q^{42} -6.08842 q^{43} +(1.82217 + 10.3340i) q^{44} +(8.82583 - 3.12846i) q^{45} +(-6.89639 + 8.21880i) q^{46} +5.98771i q^{47} +(-3.66780 - 10.0772i) q^{48} -6.65182 q^{49} +(0.119037 - 7.07007i) q^{50} +(-2.25150 + 10.8222i) q^{51} +(0.850699 + 4.82455i) q^{52} +10.8139 q^{53} +(-3.44950 - 2.89448i) q^{54} +(11.0579 - 3.91965i) q^{55} +(-1.44537 - 0.834484i) q^{56} -6.89321 q^{57} +(-3.01989 + 3.59897i) q^{58} +7.40726i q^{59} +(-10.4335 + 5.90724i) q^{60} +6.60514 q^{61} +(-4.45551 - 3.73862i) q^{62} -2.47101 q^{63} +(4.00000 + 6.92820i) q^{64} +(5.16249 - 1.82993i) q^{65} +(-15.2388 - 12.7869i) q^{66} +7.40124 q^{67} +(0.252171 - 8.24235i) q^{68} -20.3392i q^{69} +(-0.652933 + 1.74800i) q^{70} -0.239853i q^{71} +(10.2576 + 5.92225i) q^{72} -5.97435 q^{73} +(-9.46189 - 7.93947i) q^{74} +(8.44242 + 10.4124i) q^{75} +(5.06418 - 0.892951i) q^{76} -3.09593 q^{77} +(-7.11440 - 5.96969i) q^{78} +10.4890i q^{79} +(6.89986 - 5.69139i) q^{80} -4.02646 q^{81} +(11.8039 + 9.90468i) q^{82} +6.83277 q^{83} +(3.11586 - 0.549410i) q^{84} +(-9.13500 + 1.24571i) q^{85} +(-5.53461 + 6.59590i) q^{86} -8.90641i q^{87} +(12.8518 + 7.41999i) q^{88} -13.4029 q^{89} +(4.63381 - 12.4054i) q^{90} -1.44537 q^{91} +(2.63475 + 14.9424i) q^{92} +11.0261 q^{93} +(6.48679 + 5.44306i) q^{94} +(-1.92082 - 5.41890i) q^{95} +(-14.2513 - 5.18705i) q^{96} +17.0326 q^{97} +(-6.04676 + 7.20625i) q^{98} +21.9715 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) $ 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * 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 $

$2$	0.909039	−	1.08335i	0.642788	−	0.766044i
$2$	0.909039	−	1.08335i	0.642788	−	0.766044i
$3$			2.68098i			1.54787i	0.633268	+	0.773933i	$0.281713\pi$
$3$			2.68098i			1.54787i	−0.633268	+	0.773933i	$0.718287\pi$
$4$	−0.347296	−	1.96962i	−0.173648	−	0.984808i
$5$	−2.10758	+	0.747066i	−0.942538	+	0.334098i
$5$	−2.10758	+	0.747066i	−0.942538	+	0.334098i
$6$	2.90444	+	2.43712i	1.18573	+	0.994949i
$7$	0.590069			0.223025			0.111513	−	0.993763i	$-0.464430\pi$
$7$	0.590069			0.223025			0.111513	+	0.993763i	$0.464430\pi$
$8$	−2.44949	−	1.41421i	−0.866025	−	0.500000i
$9$	−4.18766			−1.39589
$10$	−1.10654	+	2.96236i	−0.349918	+	0.936780i
$11$	−5.24673			−1.58195			−0.790974	−	0.611850i	$-0.790426\pi$
$11$	−5.24673			−1.58195			−0.790974	+	0.611850i	$0.790426\pi$
$12$	5.28050	−	0.931095i	1.52435	−	0.268784i
$13$	−2.44949			−0.679366			−0.339683	−	0.940540i	$-0.610320\pi$
$13$	−2.44949			−0.679366			−0.339683	+	0.940540i	$0.610320\pi$
$14$	0.536396	−	0.639252i	0.143358	−	0.170847i
$15$	−2.00287	−	5.65038i	−0.517139	−	1.45892i
$16$	−3.75877	+	1.36808i	−0.939693	+	0.342020i
$17$	4.03667	+	0.839805i	0.979037	+	0.203683i
$17$	4.03667	+	0.839805i	0.979037	+	0.203683i
$18$	−3.80675	+	4.53671i	−0.897259	+	1.06931i
$19$			2.57115i			0.589862i	0.955518	+	0.294931i	$0.0952967\pi$
$19$			2.57115i			0.589862i	−0.955518	+	0.294931i	$0.904703\pi$
$20$	2.20339	+	3.89167i	0.492693	+	0.870203i
$21$			1.58196i			0.345213i
$22$	−4.76948	+	5.68404i	−1.01686	+	1.21184i
$23$	−7.58646			−1.58189			−0.790943	−	0.611889i	$-0.790410\pi$
$23$	−7.58646			−1.58189			−0.790943	+	0.611889i	$0.790410\pi$
$24$	3.79148	−	6.56704i	0.773933	−	1.34049i
$25$	3.88378	−	3.14900i	0.776757	−	0.629801i
$26$	−2.22668	+	2.65366i	−0.436688	+	0.520425i
$27$		−	3.18410i		−	0.612781i
$28$	−0.204929	−	1.16221i	−0.0387279	−	0.219637i
$29$	−3.32207			−0.616893			−0.308446	−	0.951242i	$-0.599809\pi$
$29$	−3.32207			−0.616893			−0.308446	+	0.951242i	$0.599809\pi$
$30$	−7.94203	−	2.96661i	−1.45001	−	0.541626i
$31$		−	4.11271i		−	0.738665i	−0.929297	−	0.369333i	$-0.879586\pi$
$31$		−	4.11271i		−	0.738665i	0.929297	−	0.369333i	$-0.120414\pi$
$32$	−1.93476	+	5.31570i	−0.342020	+	0.939693i
$33$		−	14.0664i		−	2.44864i
$34$	4.57930	−	3.60972i	0.785343	−	0.619061i
$35$	−1.24362	+	0.440821i	−0.210210	+	0.0745123i
$36$	1.45436	+	8.24809i	0.242393	+	1.37468i
$37$		−	8.73391i		−	1.43585i	−0.696122	−	0.717923i	$-0.745093\pi$
$37$		−	8.73391i		−	1.43585i	0.696122	−	0.717923i	$-0.254907\pi$
$38$	2.78546	+	2.33728i	0.451861	+	0.379156i
$39$		−	6.56704i		−	1.05157i
$40$	6.21901	+	1.15064i	0.983311	+	0.181932i
$41$			10.8958i			1.70163i	0.525463	+	0.850817i	$0.323892\pi$
$41$			10.8958i			1.70163i	−0.525463	+	0.850817i	$0.676108\pi$
$42$	1.71382	+	1.43807i	0.264448	+	0.221899i
$43$	−6.08842			−0.928476			−0.464238	−	0.885711i	$-0.653672\pi$
$43$	−6.08842			−0.928476			−0.464238	+	0.885711i	$0.653672\pi$
$44$	1.82217	+	10.3340i	0.274702	+	1.55791i
$45$	8.82583	−	3.12846i	1.31568	−	0.466364i
$46$	−6.89639	+	8.21880i	−1.01682	+	1.21180i
$47$			5.98771i			0.873397i	0.899608	+	0.436699i	$0.143852\pi$
$47$			5.98771i			0.873397i	−0.899608	+	0.436699i	$0.856148\pi$
$48$	−3.66780	−	10.0772i	−0.529401	−	1.45452i
$49$	−6.65182			−0.950260
$50$	0.119037	−	7.07007i	0.0168343	−	0.999858i
$51$	−2.25150	+	10.8222i	−0.315273	+	1.51542i
$52$	0.850699	+	4.82455i	0.117971	+	0.669045i
$53$	10.8139			1.48540			0.742699	−	0.669626i	$-0.233545\pi$
$53$	10.8139			1.48540			0.742699	+	0.669626i	$0.233545\pi$
$54$	−3.44950	−	2.89448i	−0.469418	−	0.393888i
$55$	11.0579	−	3.91965i	1.49105	−	0.528526i
$56$	−1.44537	−	0.834484i	−0.193145	−	0.111513i
$57$	−6.89321			−0.913028
$58$	−3.01989	+	3.59897i	−0.396531	+	0.472567i
$59$			7.40726i			0.964343i	0.876077	+	0.482172i	$0.160152\pi$
$59$			7.40726i			0.964343i	−0.876077	+	0.482172i	$0.839848\pi$
$60$	−10.4335	+	5.90724i	−1.34696	+	0.762622i
$61$	6.60514			0.845702			0.422851	−	0.906199i	$-0.361029\pi$
$61$	6.60514			0.845702			0.422851	+	0.906199i	$0.361029\pi$
$62$	−4.45551	−	3.73862i	−0.565850	−	0.474805i
$63$	−2.47101			−0.311318
$64$	4.00000	+	6.92820i	0.500000	+	0.866025i
$65$	5.16249	−	1.82993i	0.640329	−	0.226975i
$66$	−15.2388	−	12.7869i	−1.87577	−	1.57396i
$67$	7.40124			0.904206			0.452103	−	0.891966i	$-0.350674\pi$
$67$	7.40124			0.904206			0.452103	+	0.891966i	$0.350674\pi$
$68$	0.252171	−	8.24235i	0.0305802	−	0.999532i
$69$		−	20.3392i		−	2.44855i
$70$	−0.652933	+	1.74800i	−0.0780405	+	0.208926i
$71$		−	0.239853i		−	0.0284654i	−0.999899	−	0.0142327i	$-0.995469\pi$
$71$		−	0.239853i		−	0.0284654i	0.999899	−	0.0142327i	$-0.00453056\pi$
$72$	10.2576	+	5.92225i	1.20887	+	0.697944i
$73$	−5.97435			−0.699244			−0.349622	−	0.936891i	$-0.613690\pi$
$73$	−5.97435			−0.699244			−0.349622	+	0.936891i	$0.613690\pi$
$74$	−9.46189	−	7.93947i	−1.09992	−	0.922944i
$75$	8.44242	+	10.4124i	0.974847	+	1.20232i
$76$	5.06418	−	0.892951i	0.580901	−	0.102429i
$77$	−3.09593			−0.352814
$78$	−7.11440	−	5.96969i	−0.805548	−	0.675935i
$79$			10.4890i			1.18011i	0.807364	+	0.590054i	$0.200893\pi$
$79$			10.4890i			1.18011i	−0.807364	+	0.590054i	$0.799107\pi$
$80$	6.89986	−	5.69139i	0.771428	−	0.636317i
$81$	−4.02646			−0.447385
$82$	11.8039	+	9.90468i	1.30353	+	1.09379i
$83$	6.83277			0.749994			0.374997	−	0.927026i	$-0.377644\pi$
$83$	6.83277			0.749994			0.374997	+	0.927026i	$0.377644\pi$
$84$	3.11586	−	0.549410i	0.339968	−	0.0599456i
$85$	−9.13500	+	1.24571i	−0.990830	+	0.135116i
$86$	−5.53461	+	6.59590i	−0.596813	+	0.711254i
$87$		−	8.90641i		−	0.954867i
$88$	12.8518	+	7.41999i	1.37001	+	0.790974i
$89$	−13.4029			−1.42070			−0.710350	−	0.703849i	$-0.751463\pi$
$89$	−13.4029			−1.42070			−0.710350	+	0.703849i	$0.751463\pi$
$90$	4.63381	−	12.4054i	0.488446	−	1.30764i
$91$	−1.44537			−0.151516
$92$	2.63475	+	14.9424i	0.274692	+	1.55785i
$93$	11.0261			1.14335
$94$	6.48679	+	5.44306i	0.669061	+	0.561409i
$95$	−1.92082	−	5.41890i	−0.197072	−	0.555968i
$96$	−14.2513	−	5.18705i	−1.45452	−	0.529401i
$97$	17.0326			1.72940			0.864702	−	0.502286i	$-0.167507\pi$
$97$	17.0326			1.72940			0.864702	+	0.502286i	$0.167507\pi$
$98$	−6.04676	+	7.20625i	−0.610815	+	0.727941i
$99$	21.9715			2.20822
$100$	−7.55115	−	6.55592i	−0.755115	−	0.655592i
$101$		−	13.9640i		−	1.38947i	−0.719268	−	0.694733i	$-0.755523\pi$
$101$		−	13.9640i		−	1.38947i	0.719268	−	0.694733i	$-0.244477\pi$
$102$	9.67758	+	12.2770i	0.958223	+	1.21561i
$103$			7.16730i			0.706215i	0.935583	+	0.353107i	$0.114875\pi$
$103$			7.16730i			0.706215i	−0.935583	+	0.353107i	$0.885125\pi$
$104$	6.00000	+	3.46410i	0.588348	+	0.339683i
$105$	−1.18183	−	3.33412i	−0.115335	−	0.325376i
$106$	9.83022	−	11.7152i	0.954795	−	1.13788i
$107$			8.65923i			0.837120i	0.908189	+	0.418560i	$0.137465\pi$
$107$			8.65923i			0.837120i	−0.908189	+	0.418560i	$0.862535\pi$
$108$	−6.27146	+	1.10583i	−0.603472	+	0.106408i
$109$	−4.10165			−0.392867			−0.196433	−	0.980517i	$-0.562936\pi$
$109$	−4.10165			−0.392867			−0.196433	+	0.980517i	$0.562936\pi$
$110$	5.80570	−	15.5427i	0.553552	−	1.48194i
$111$	23.4155			2.22250
$112$	−2.21793	+	0.807262i	−0.209575	+	0.0762791i
$113$	1.89669			0.178426			0.0892128	−	0.996013i	$-0.471565\pi$
$113$	1.89669			0.178426			0.0892128	+	0.996013i	$0.471565\pi$
$114$	−6.26619	+	7.46776i	−0.586883	+	0.699420i
$115$	15.9891	−	5.66759i	1.49099	−	0.528506i
$116$	1.15374	+	6.54320i	0.107122	+	0.607521i
$117$	10.2576			0.948319
$118$	8.02466	+	6.73349i	0.738730	+	0.619868i
$119$	2.38192	+	0.495543i	0.218350	+	0.0454263i
$120$	−3.08484	+	16.6730i	−0.281606	+	1.52203i
$121$	16.5282			1.50256
$122$	6.00433	−	7.15568i	0.543607	−	0.647845i
$123$	−29.2114			−2.63390
$124$	−8.10047	+	1.42833i	−0.727443	+	0.128268i
$125$	−5.83287	+	9.53822i	−0.521708	+	0.853124i
$126$	−2.24624	+	2.67697i	−0.200111	+	0.238483i
$127$		−	10.0968i		−	0.895943i	−0.894048	−	0.447972i	$-0.852147\pi$
$127$		−	10.0968i		−	0.895943i	0.894048	−	0.447972i	$-0.147853\pi$
$128$	11.1418	+	1.96460i	0.984808	+	0.173648i
$129$		−	16.3230i		−	1.43716i
$130$	2.71045	−	7.25627i	0.237722	−	0.636417i
$131$	−3.48732			−0.304688			−0.152344	−	0.988327i	$-0.548682\pi$
$131$	−3.48732			−0.304688			−0.152344	+	0.988327i	$0.548682\pi$
$132$	−27.7054	+	4.88520i	−2.41144	+	0.425202i
$133$			1.51716i			0.131554i
$134$	6.72802	−	8.01814i	0.581212	−	0.692662i
$135$	2.37874	+	6.71075i	0.204729	+	0.577570i
$136$	−8.70013	−	7.76581i	−0.746030	−	0.665913i
$137$		−	6.73804i		−	0.575669i	−0.957680	−	0.287835i	$-0.907065\pi$
$137$		−	6.73804i		−	0.575669i	0.957680	−	0.287835i	$-0.0929354\pi$
$138$	−22.0344	−	18.4891i	−1.87570	−	1.57390i
$139$	−1.58506			−0.134443			−0.0672217	−	0.997738i	$-0.521413\pi$
$139$	−1.58506			−0.134443			−0.0672217	+	0.997738i	$0.521413\pi$
$140$	1.30015	+	2.29635i	0.109883	+	0.194077i
$141$	−16.0529			−1.35190
$142$	−0.259845	−	0.218036i	−0.0218057	−	0.0182972i
$143$	12.8518			1.07472
$144$	15.7405	−	5.72906i	1.31171	−	0.477422i
$145$	7.00153	−	2.48181i	0.581445	−	0.206103i
$146$	−5.43091	+	6.47231i	−0.449466	+	0.535652i
$147$		−	17.8334i		−	1.47087i
$148$	−17.2024	+	3.03326i	−1.41403	+	0.249332i
$149$			14.8180i			1.21394i	0.794726	+	0.606968i	$0.207614\pi$
$149$			14.8180i			1.21394i	−0.794726	+	0.606968i	$0.792386\pi$
$150$	18.9547	+	0.319136i	1.54765	+	0.0260573i
$151$	2.36759			0.192672			0.0963359	−	0.995349i	$-0.469288\pi$
$151$	2.36759			0.192672			0.0963359	+	0.995349i	$0.469288\pi$
$152$	3.63616	−	6.29801i	0.294931	−	0.510836i
$153$	−16.9042	−	3.51682i	−1.36663	−	0.284318i
$154$	−2.81432	+	3.35398i	−0.226785	+	0.270271i
$155$	3.07247	+	8.66787i	0.246787	+	0.696220i
$156$	−12.9345	+	2.28071i	−1.03559	+	0.182603i
$157$	−3.98012			−0.317648			−0.158824	−	0.987307i	$-0.550770\pi$
$157$	−3.98012			−0.317648			−0.158824	+	0.987307i	$0.550770\pi$
$158$	11.3633	+	9.53493i	0.904015	+	0.758559i
$159$			28.9918i			2.29920i
$160$	0.106474	−	12.6487i	0.00841747	−	0.999965i
$161$	−4.47654			−0.352801
$162$	−3.66021	+	4.36207i	−0.287573	+	0.342717i
$163$			10.1715i			0.796695i	0.917235	+	0.398348i	$0.130416\pi$
$163$			10.1715i			0.796695i	−0.917235	+	0.398348i	$0.869584\pi$
$164$	21.4605	−	3.78406i	1.67578	−	0.295486i
$165$	10.5085	+	29.6460i	0.818087	+	2.30794i
$166$	6.21126	−	7.40229i	0.482087	−	0.574529i
$167$	−13.1952			−1.02107			−0.510536	−	0.859856i	$-0.670553\pi$
$167$	−13.1952			−1.02107			−0.510536	+	0.859856i	$0.670553\pi$
$168$	2.23724	−	3.87501i	0.172606	−	0.298963i
$169$	−7.00000			−0.538462
$170$	−6.95453	+	11.0288i	−0.533388	+	0.845870i
$171$		−	10.7671i		−	0.823382i
$172$	2.11449	+	11.9919i	0.161228	+	0.914370i
$173$		−	9.02967i		−	0.686513i	−0.939242	−	0.343256i	$-0.888470\pi$
$173$		−	9.02967i		−	0.686513i	0.939242	−	0.343256i	$-0.111530\pi$
$174$	−9.64876	−	8.09627i	−0.731471	−	0.613777i
$175$	2.29170	−	1.85813i	0.173236	−	0.140461i
$176$	19.7212	−	7.17795i	1.48654	−	0.541058i
$177$	−19.8587			−1.49267
$178$	−12.1837	+	14.5200i	−0.913208	+	1.08832i
$179$		−	0.650086i		−	0.0485897i	−0.999705	−	0.0242948i	$-0.992266\pi$
$179$		−	0.650086i		−	0.0485897i	0.999705	−	0.0242948i	$-0.00773405\pi$
$180$	−9.22705	−	16.2970i	−0.687744	−	1.21471i
$181$	−13.6022			−1.01104			−0.505522	−	0.862814i	$-0.668700\pi$
$181$	−13.6022			−1.01104			−0.505522	+	0.862814i	$0.668700\pi$
$182$	−1.31390	+	1.56584i	−0.0973924	+	0.116068i
$183$			17.7083i			1.30903i
$184$	18.5830	+	10.7289i	1.36995	+	0.790943i
$185$	6.52481	+	18.4074i	0.479714	+	1.35334i
$186$	10.0232	−	11.9451i	0.734934	−	0.875860i
$187$	−21.1793	−	4.40623i	−1.54879	−	0.322215i
$188$	11.7935	−	2.07951i	0.860129	−	0.151664i
$189$		−	1.87884i		−	0.136666i
$190$	−7.61667	−	2.84507i	−0.552571	−	0.206403i
$191$	−2.68686			−0.194414			−0.0972070	−	0.995264i	$-0.530991\pi$
$191$	−2.68686			−0.194414			−0.0972070	+	0.995264i	$0.530991\pi$
$192$	−18.5744	+	10.7239i	−1.34049	+	0.773933i
$193$	1.50477			0.108316			0.0541578	−	0.998532i	$-0.482753\pi$
$193$	1.50477			0.108316			0.0541578	+	0.998532i	$0.482753\pi$
$194$	15.4833	−	18.4523i	1.11164	−	1.32480i
$195$	4.90601	+	13.8406i	0.351327	+	0.991143i
$196$	2.31015	+	13.1015i	0.165011	+	0.935823i
$197$		−	10.7106i		−	0.763098i	−0.924349	−	0.381549i	$-0.875391\pi$
$197$		−	10.7106i		−	0.763098i	0.924349	−	0.381549i	$-0.124609\pi$
$198$	19.9730	−	23.8029i	1.41942	−	1.69160i
$199$		−	19.4313i		−	1.37744i	−0.725025	−	0.688722i	$-0.758172\pi$
$199$		−	19.4313i		−	1.37744i	0.725025	−	0.688722i	$-0.241828\pi$
$200$	−13.9667	+	2.22095i	−0.987591	+	0.157045i
$201$			19.8426i			1.39959i
$202$	−15.1279	−	12.6938i	−1.06439	−	0.893131i
$203$	−1.96025			−0.137583
$204$	22.0976	+	0.676066i	1.54714	+	0.0473341i
$205$	−8.13986	−	22.9637i	−0.568513	−	1.60385i
$206$	7.76470	+	6.51535i	0.540992	+	0.453946i
$207$	31.7696			2.20814
$208$	9.20707	−	3.35110i	0.638395	−	0.232357i
$209$		−	13.4901i		−	0.933132i
$210$	−4.68635	−	1.75050i	−0.323389	−	0.120796i
$211$	−12.9096			−0.888732			−0.444366	−	0.895845i	$-0.646571\pi$
$211$	−12.9096			−0.888732			−0.444366	+	0.895845i	$0.646571\pi$
$212$	−3.75561	−	21.2991i	−0.257937	−	1.46283i
$213$	0.643043			0.0440606
$214$	9.38098	+	7.87158i	0.641271	+	0.538090i
$215$	12.8318	−	4.54846i	0.875124	−	0.310202i
$216$	−4.50300	+	7.79943i	−0.306391	+	0.530684i
$217$		−	2.42679i		−	0.164741i
$218$	−3.72856	+	4.44352i	−0.252530	+	0.300953i
$219$		−	16.0171i		−	1.08234i
$220$	−11.5606	−	20.4185i	−0.779414	−	1.37662i
$221$	−9.88779	−	2.05709i	−0.665125	−	0.138375i
$222$	21.2856	−	25.3671i	1.42859	−	1.70253i
$223$			9.88986i			0.662274i	0.943583	+	0.331137i	$0.107432\pi$
$223$			9.88986i			0.662274i	−0.943583	+	0.331137i	$0.892568\pi$
$224$	−1.14164	+	3.13663i	−0.0762791	+	0.209575i
$225$	−16.2640	+	13.1870i	−1.08427	+	0.879131i
$226$	1.72417	−	2.05478i	0.114690	−	0.136682i
$227$		−	15.1612i		−	1.00629i	−0.864203	−	0.503143i	$-0.832177\pi$
$227$		−	15.1612i		−	1.00629i	0.864203	−	0.503143i	$-0.167823\pi$
$228$	2.39399	+	13.5770i	0.158546	+	0.899157i
$229$		−	5.19117i		−	0.343042i	−0.985180	−	0.171521i	$-0.945132\pi$
$229$		−	5.19117i		−	0.343042i	0.985180	−	0.171521i	$-0.0548682\pi$
$230$	8.39471	−	22.4738i	0.553531	−	1.48188i
$231$		−	8.30014i		−	0.546109i
$232$	8.13738	+	4.69812i	0.534245	+	0.308446i
$233$	6.57405			0.430680			0.215340	−	0.976539i	$-0.430914\pi$
$233$	6.57405			0.430680			0.215340	+	0.976539i	$0.430914\pi$
$234$	9.32459	−	11.1126i	0.609568	−	0.726455i
$235$	−4.47322	−	12.6196i	−0.291801	−	0.823211i
$236$	14.5895	−	2.57251i	0.949693	−	0.167456i
$237$	−28.1209			−1.82665
$238$	2.70210	−	2.12998i	0.175151	−	0.138066i
$239$	−8.86248			−0.573266			−0.286633	−	0.958040i	$-0.592536\pi$
$239$	−8.86248			−0.573266			−0.286633	+	0.958040i	$0.592536\pi$
$240$	15.2585	+	18.4984i	0.984933	+	1.19407i
$241$		−	19.3789i		−	1.24830i	−0.781303	−	0.624152i	$-0.785445\pi$
$241$		−	19.3789i		−	1.24830i	0.781303	−	0.624152i	$-0.214555\pi$
$242$	15.0247	−	17.9058i	0.965827	−	1.15103i
$243$		−	20.3472i		−	1.30527i
$244$	−2.29394	−	13.0096i	−0.146855	−	0.832853i
$245$	14.0192	−	4.96935i	0.895656	−	0.317480i
$246$	−26.5543	+	31.6461i	−1.69304	+	2.01768i
$247$		−	6.29801i		−	0.400733i
$248$	−5.81626	+	10.0741i	−0.369333	+	0.639703i
$249$			18.3185i			1.16089i
$250$	5.03093	+	14.9897i	0.318184	+	0.948029i
$251$			16.7259i			1.05573i	0.849329	+	0.527864i	$0.177007\pi$
$251$			16.7259i			1.05573i	−0.849329	+	0.527864i	$0.822993\pi$
$252$	0.858173	+	4.86694i	0.0540598	+	0.306588i
$253$	39.8041			2.50246
$254$	−10.9383	−	9.17836i	−0.686332	−	0.575901i
$255$	−3.33972	−	24.4908i	−0.209141	−	1.53367i
$256$	12.2567	−	10.2846i	0.766044	−	0.642788i
$257$			17.7274i			1.10580i	0.833247	+	0.552901i	$0.186479\pi$
$257$			17.7274i			1.10580i	−0.833247	+	0.552901i	$0.813521\pi$
$258$	−17.6835	−	14.8382i	−1.10093	−	0.923786i
$259$		−	5.15361i		−	0.320230i
$260$	−5.39718	−	9.53260i	−0.334719	−	0.591187i
$261$	13.9117			0.861113
$262$	−3.17011	+	3.77799i	−0.195850	+	0.233405i
$263$			12.7203i			0.784367i	0.919887	+	0.392183i	$0.128280\pi$
$263$			12.7203i			0.784367i	−0.919887	+	0.392183i	$0.871720\pi$
$264$	−19.8929	+	34.4555i	−1.22432	+	2.12059i
$265$	−22.7911	+	8.07867i	−1.40004	+	0.496269i
$266$	1.64361	+	1.37915i	0.100776	+	0.0845614i
$267$		−	35.9328i		−	2.19905i
$268$	−2.57043	−	14.5776i	−0.157014	−	0.890469i
$269$	−3.92774			−0.239478			−0.119739	−	0.992805i	$-0.538206\pi$
$269$	−3.92774			−0.239478			−0.119739	+	0.992805i	$0.538206\pi$
$270$	9.43246	+	3.52333i	0.574041	+	0.214423i
$271$	−13.0760			−0.794312			−0.397156	−	0.917751i	$-0.630003\pi$
$271$	−13.0760			−0.794312			−0.397156	+	0.917751i	$0.630003\pi$
$272$	−16.3218	+	2.36586i	−0.989657	+	0.143451i
$273$		−	3.87501i		−	0.234526i
$274$	−7.29966	−	6.12514i	−0.440988	−	0.370033i
$275$	−20.3772	+	16.5220i	−1.22879	+	0.996312i
$276$	−40.0603	+	7.06372i	−2.41135	+	0.425186i
$277$			8.80827i			0.529238i	0.964353	+	0.264619i	$0.0852461\pi$
$277$			8.80827i			0.529238i	−0.964353	+	0.264619i	$0.914754\pi$
$278$	−1.44088	+	1.71718i	−0.0864185	+	0.102990i
$279$			17.2227i			1.03109i
$280$	3.66964	+	0.678955i	0.219303	+	0.0405753i
$281$	−27.7050			−1.65274			−0.826371	−	0.563126i	$-0.809599\pi$
$281$	−27.7050			−1.65274			−0.826371	+	0.563126i	$0.809599\pi$
$282$	−14.5928	+	17.3910i	−0.868986	+	1.03562i
$283$			4.87332i			0.289689i	0.989454	+	0.144844i	$0.0462682\pi$
$283$			4.87332i			0.289689i	−0.989454	+	0.144844i	$0.953732\pi$
$284$	−0.472419	+	0.0833002i	−0.0280329	+	0.00494296i
$285$	14.5280	−	5.14968i	0.860564	−	0.305041i
$286$	11.6828	−	13.9230i	0.690818	−	0.823285i
$287$			6.42926i			0.379507i
$288$	8.10212	−	22.2604i	0.477422	−	1.31171i
$289$	15.5895	+	6.78004i	0.917027	+	0.398826i
$290$	3.67600	−	9.84117i	0.215862	−	0.577893i
$291$			45.6642i			2.67688i
$292$	2.07487	+	11.7672i	0.121423	+	0.688621i
$293$	−16.8991			−0.987254			−0.493627	−	0.869674i	$-0.664329\pi$
$293$	−16.8991			−0.987254			−0.493627	+	0.869674i	$0.664329\pi$
$294$	−19.3198	−	16.2113i	−1.12676	−	0.945460i
$295$	−5.53371	−	15.6114i	−0.322185	−	0.908930i
$296$	−12.3516	+	21.3936i	−0.717923	+	1.24348i
$297$			16.7061i			0.969388i
$298$	16.0531	+	13.4701i	0.929929	+	0.780303i
$299$	18.5830			1.07468
$300$	17.5763	−	20.2445i	1.01477	−	1.16882i
$301$	−3.59259			−0.207073
$302$	2.15223	−	2.56493i	0.123847	−	0.147595i
$303$	37.4371			2.15071
$304$	−3.51754	−	9.66436i	−0.201745	−	0.554289i
$305$	−13.9209	+	4.93448i	−0.797106	+	0.282547i
$306$	−19.1766	+	15.1163i	−1.09625	+	0.864140i
$307$	−1.27785			−0.0729310			−0.0364655	−	0.999335i	$-0.511610\pi$
$307$	−1.27785			−0.0729310			−0.0364655	+	0.999335i	$0.511610\pi$
$308$	1.07521	+	6.09779i	0.0612655	+	0.347454i
$309$	−19.2154			−1.09313
$310$	12.1833	+	4.55087i	0.691967	+	0.258472i
$311$			28.2277i			1.60064i	0.599571	+	0.800322i	$0.295338\pi$
$311$			28.2277i			1.60064i	−0.599571	+	0.800322i	$0.704662\pi$
$312$	−9.28719	+	16.0859i	−0.525784	+	0.910684i
$313$	2.22638			0.125843			0.0629213	−	0.998018i	$-0.479958\pi$
$313$	2.22638			0.125843			0.0629213	+	0.998018i	$0.479958\pi$
$314$	−3.61808	+	4.31187i	−0.204180	+	0.243333i
$315$	5.20785	−	1.84601i	0.293429	−	0.104011i
$316$	20.6593	−	3.64280i	1.16218	−	0.204924i
$317$		−	27.5279i		−	1.54612i	−0.634333	−	0.773060i	$-0.718725\pi$
$317$		−	27.5279i		−	1.54612i	0.634333	−	0.773060i	$-0.281275\pi$
$318$	31.4082	+	26.3546i	1.76129	+	1.47789i
$319$	17.4300			0.975893
$320$	−13.6061	−	11.6135i	−0.760607	−	0.649213i
$321$	−23.2152			−1.29575
$322$	−4.06935	+	4.84966i	−0.226776	+	0.270261i
$323$	−2.15926	+	10.3789i	−0.120145	+	0.577497i
$324$	1.39838	+	7.93059i	0.0776876	+	0.440588i
$325$	−9.51329	+	7.71345i	−0.527702	+	0.427865i
$326$	11.0193	+	9.24631i	0.610304	+	0.512106i
$327$		−	10.9964i		−	0.608105i
$328$	15.4089	−	26.6891i	0.850817	−	1.47366i
$329$			3.53316i			0.194790i
$330$	41.6697	+	15.5650i	2.29384	+	0.856824i
$331$		−	25.4287i		−	1.39769i	−0.715275	−	0.698843i	$-0.753699\pi$
$331$		−	25.4287i		−	1.39769i	0.715275	−	0.698843i	$-0.246301\pi$
$332$	−2.37300	−	13.4579i	−0.130235	−	0.738600i
$333$			36.5747i			2.00428i
$334$	−11.9949	+	14.2950i	−0.656333	+	0.782187i
$335$	−15.5987	+	5.52922i	−0.852249	+	0.302094i
$336$	−2.16425	−	5.94624i	−0.118070	−	0.324394i
$337$	13.0469			0.710708			0.355354	−	0.934732i	$-0.384360\pi$
$337$	13.0469			0.710708			0.355354	+	0.934732i	$0.384360\pi$
$338$	−6.36327	+	7.58345i	−0.346116	+	0.412485i
$339$			5.08499i			0.276179i
$340$	5.62611	+	17.5598i	0.305119	+	0.952314i
$341$			21.5783i			1.16853i
$342$	−11.6646	−	9.78773i	−0.630747	−	0.529260i
$343$	−8.05552			−0.434957
$344$	14.9135	+	8.61033i	0.804084	+	0.464238i
$345$	15.1947	+	42.8664i	0.818056	+	2.30785i
$346$	−9.78229	−	8.20832i	−0.525899	−	0.441282i
$347$			26.0425i			1.39804i	0.715104	+	0.699018i	$0.246379\pi$
$347$			26.0425i			1.39804i	−0.715104	+	0.699018i	$0.753621\pi$
$348$	−17.5422	+	3.09316i	−0.940361	+	0.165811i
$349$			18.6985i			1.00091i	0.865763	+	0.500455i	$0.166834\pi$
$349$			18.6985i			1.00091i	−0.865763	+	0.500455i	$0.833166\pi$
$350$	0.0702399	−	4.17183i	0.00375448	−	0.222994i
$351$			7.79943i			0.416303i
$352$	10.1511	−	27.8901i	0.541058	−	1.48654i
$353$		−	15.1999i		−	0.809010i	−0.914536	−	0.404505i	$-0.867444\pi$
$353$		−	15.1999i		−	0.809010i	0.914536	−	0.404505i	$-0.132556\pi$
$354$	−18.0524	+	21.5140i	−0.959472	+	1.14345i
$355$	0.179186	+	0.505510i	0.00951023	+	0.0268297i
$356$	4.65476	+	26.3985i	0.246702	+	1.39912i
$357$	−1.32854	+	6.38587i	−0.0703139	+	0.337976i
$358$	−0.704271	−	0.590953i	−0.0372219	−	0.0312329i
$359$	−18.9154			−0.998317			−0.499158	−	0.866511i	$-0.666357\pi$
$359$	−18.9154			−0.998317			−0.499158	+	0.866511i	$0.666357\pi$
$360$	−26.0431	−	4.81848i	−1.37259	−	0.253956i
$361$	12.3892			0.652062
$362$	−12.3649	+	14.7359i	−0.649886	+	0.774504i
$363$			44.3117i			2.32576i
$364$	0.501971	+	2.84682i	0.0263104	+	0.149214i
$365$	12.5914	−	4.46323i	0.659065	−	0.233616i
$366$	19.1843	+	16.0975i	1.00278	+	0.841430i
$367$	−12.9709			−0.677073			−0.338537	−	0.940953i	$-0.609932\pi$
$367$	−12.9709			−0.677073			−0.338537	+	0.940953i	$0.609932\pi$
$368$	28.5158	−	10.3789i	1.48649	−	0.541037i
$369$		−	45.6278i		−	2.37529i
$370$	25.8730	+	9.66440i	1.34507	+	0.502428i
$371$	6.38092			0.331281
$372$	−3.82933	−	21.7172i	−0.198541	−	1.12598i
$373$	3.90153			0.202014			0.101007	−	0.994886i	$-0.467794\pi$
$373$	3.90153			0.202014			0.101007	+	0.994886i	$0.467794\pi$
$374$	−24.0263	+	18.9392i	−1.24237	+	0.979323i
$375$	−25.5718	−	15.6378i	−1.32052	−	0.807533i
$376$	8.46790	−	14.6668i	0.436699	−	0.756384i
$377$	8.13738			0.419096
$378$	−2.03544	−	1.70794i	−0.104692	−	0.0878470i
$379$	−19.9672			−1.02565			−0.512824	−	0.858494i	$-0.671401\pi$
$379$	−19.9672			−1.02565			−0.512824	+	0.858494i	$0.671401\pi$
$380$	−10.0061	+	5.66524i	−0.513300	+	0.290621i
$381$	27.0693			1.38680
$382$	−2.44246	+	2.91081i	−0.124967	+	0.148930i
$383$			28.0933i			1.43550i	0.696301	+	0.717750i	$0.254828\pi$
$383$			28.0933i			1.43550i	−0.696301	+	0.717750i	$0.745172\pi$
$384$	−5.26707	+	29.8710i	−0.268784	+	1.52435i
$385$	6.52492	−	2.31287i	0.332541	−	0.117875i
$386$	1.36789	−	1.63019i	0.0696240	−	0.0829746i
$387$	25.4963			1.29605
$388$	−5.91538	−	33.5478i	−0.300308	−	1.70313i
$389$		−	6.13012i		−	0.310810i	−0.987851	−	0.155405i	$-0.950332\pi$
$389$		−	6.13012i		−	0.310810i	0.987851	−	0.155405i	$-0.0496682\pi$
$390$	19.4539	+	7.26667i	0.985088	+	0.367962i
$391$	−30.6241	−	6.37115i	−1.54873	−	0.322203i
$392$	16.2936	+	9.40709i	0.822949	+	0.475130i
$393$		−	9.34944i		−	0.471617i
$394$	−11.6033	−	9.73634i	−0.584567	−	0.490510i
$395$	−7.83600	−	22.1065i	−0.394272	−	1.11230i
$396$	−7.63063	−	43.2755i	−0.383454	−	2.17467i
$397$		−	5.63325i		−	0.282725i	−0.989958	−	0.141362i	$-0.954852\pi$
$397$		−	5.63325i		−	0.282725i	0.989958	−	0.141362i	$-0.0451483\pi$
$398$	−21.0509	−	17.6638i	−1.05518	−	0.885405i
$399$	−4.06747			−0.203628
$400$	−10.2902	+	17.1497i	−0.514508	+	0.857486i
$401$		−	1.02106i		−	0.0509893i	−0.999675	−	0.0254946i	$-0.991884\pi$
$401$		−	1.02106i		−	0.0509893i	0.999675	−	0.0254946i	$-0.00811608\pi$
$402$	21.4965	+	18.0377i	1.07215	+	0.899639i
$403$			10.0741i			0.501824i
$404$	−27.5036	+	4.84963i	−1.36836	+	0.241278i
$405$	8.48609	−	3.00804i	0.421677	−	0.149470i
$406$	−1.78194	+	2.12364i	−0.0884364	+	0.105394i
$407$			45.8245i			2.27143i
$408$	20.8200	−	23.3249i	1.03074	−	1.15475i
$409$	30.6157			1.51385			0.756925	−	0.653502i	$-0.226701\pi$
$409$	30.6157			1.51385			0.756925	+	0.653502i	$0.226701\pi$
$410$	−32.2772	−	12.0566i	−1.59406	−	0.595432i
$411$	18.0646			0.891059
$412$	14.1168	−	2.48918i	0.695486	−	0.122633i
$413$			4.37079i			0.215073i
$414$	28.8798	−	34.4176i	1.41936	−	1.69153i
$415$	−14.4006	+	5.10453i	−0.706898	+	0.250572i
$416$	4.73917	−	13.0208i	0.232357	−	0.638395i
$417$		−	4.24953i		−	0.208100i
$418$	−14.6145	−	12.2631i	−0.714820	−	0.599805i
$419$	16.4593			0.804088			0.402044	−	0.915620i	$-0.368300\pi$
$419$	16.4593			0.804088			0.402044	+	0.915620i	$0.368300\pi$
$420$	−6.15648	+	3.48568i	−0.300405	+	0.170084i
$421$			35.3101i			1.72091i	0.509527	+	0.860455i	$0.329820\pi$
$421$			35.3101i			1.72091i	−0.509527	+	0.860455i	$0.670180\pi$
$422$	−11.7353	+	13.9856i	−0.571266	+	0.680808i
$423$		−	25.0745i		−	1.21916i
$424$	−26.4884	−	15.2931i	−1.28639	−	0.742699i
$425$	18.3221	−	9.44987i	0.888753	−	0.458386i
$426$	0.584551	−	0.696641i	0.0283216	−	0.0337524i
$427$	3.89749			0.188613
$428$	17.0554	−	3.00732i	0.824402	−	0.145364i
$429$			34.4555i			1.66353i
$430$	6.73707	−	18.0361i	0.324890	−	0.869778i
$431$		−	8.63834i		−	0.416094i	−0.978119	−	0.208047i	$-0.933289\pi$
$431$		−	8.63834i		−	0.416094i	0.978119	−	0.208047i	$-0.0667108\pi$
$432$	4.35611	+	11.9683i	0.209584	+	0.575826i
$433$			31.8980i			1.53292i	0.642292	+	0.766460i	$0.277984\pi$
$433$			31.8980i			1.53292i	−0.642292	+	0.766460i	$0.722016\pi$
$434$	−2.62906	−	2.20604i	−0.126199	−	0.105893i
$435$	6.65368	+	18.7710i	0.319019	+	0.899999i
$436$	1.42449	+	8.07867i	0.0682206	+	0.386898i
$437$		−	19.5059i		−	0.933096i
$438$	−17.3522	−	14.5602i	−0.829118	−	0.695712i
$439$			24.7914i			1.18323i	0.806222	+	0.591614i	$0.201509\pi$
$439$			24.7914i			1.18323i	−0.806222	+	0.591614i	$0.798491\pi$
$440$	−32.6294	−	6.03708i	−1.55555	−	0.287806i
$441$	27.8556			1.32646
$442$	−11.2169	+	8.84196i	−0.533535	+	0.420569i
$443$	−13.4991			−0.641364			−0.320682	−	0.947187i	$-0.603912\pi$
$443$	−13.4991			−0.641364			−0.320682	+	0.947187i	$0.603912\pi$
$444$	−8.13210	−	46.1195i	−0.385933	−	2.18873i
$445$	28.2476	−	10.0128i	1.33906	−	0.474653i
$446$	10.7142	+	8.99027i	0.507331	+	0.425702i
$447$	−39.7267			−1.87901
$448$	2.36028	+	4.08812i	0.111513	+	0.193145i
$449$		−	28.4034i		−	1.34044i	−0.742163	−	0.670220i	$-0.766200\pi$
$449$		−	28.4034i		−	1.34044i	0.742163	−	0.670220i	$-0.233800\pi$
$450$	−0.498486	+	29.6071i	−0.0234989	+	1.39569i
$451$		−	57.1671i		−	2.69190i
$452$	−0.658714	−	3.73575i	−0.0309833	−	0.175715i
$453$			6.34747i			0.298230i
$454$	−16.4249	−	13.7822i	−0.770861	−	0.646829i
$455$	3.04623	−	1.07979i	0.142809	−	0.0506211i
$456$	16.8848	+	9.74847i	0.790705	+	0.456514i
$457$		−	8.91339i		−	0.416951i	−0.978028	−	0.208475i	$-0.933150\pi$
$457$		−	8.91339i		−	0.416951i	0.978028	−	0.208475i	$-0.0668501\pi$
$458$	−5.62386	−	4.71898i	−0.262786	−	0.220503i
$459$	2.67403	−	12.8532i	0.124813	−	0.599935i
$460$	−16.7159	−	29.5240i	−0.779384	−	1.37656i
$461$		−	36.8616i		−	1.71682i	−0.512968	−	0.858408i	$-0.671454\pi$
$461$		−	36.8616i		−	1.71682i	0.512968	−	0.858408i	$-0.328546\pi$
$462$	−8.99196	−	7.54515i	−0.418344	−	0.351032i
$463$		−	15.6345i		−	0.726597i	−0.931673	−	0.363298i	$-0.881651\pi$
$463$		−	15.6345i		−	0.726597i	0.931673	−	0.363298i	$-0.118349\pi$
$464$	12.4869	−	4.54486i	0.579690	−	0.210990i
$465$	−23.2384	+	8.23724i	−1.07766	+	0.381993i
$466$	5.97606	−	7.12200i	0.276836	−	0.329920i
$467$	−2.86172			−0.132425			−0.0662124	−	0.997806i	$-0.521091\pi$
$467$	−2.86172			−0.132425			−0.0662124	+	0.997806i	$0.521091\pi$
$468$	−3.56244	−	20.2036i	−0.164674	−	0.933912i
$469$	4.36725			0.201661
$470$	−17.7378	−	6.62563i	−0.818182	−	0.305617i
$471$		−	10.6706i		−	0.491677i
$472$	10.4754	−	18.1440i	0.482172	−	0.835146i
$473$	31.9443			1.46880
$474$	−25.5630	+	30.4648i	−1.17415	+	1.39929i
$475$	8.09656	+	9.98579i	0.371496	+	0.458180i
$476$	0.148798	−	4.86356i	0.00682016	−	0.222921i
$477$	−45.2848			−2.07345
$478$	−8.05634	+	9.60117i	−0.368488	+	0.439147i
$479$		−	13.1532i		−	0.600985i	−0.953784	−	0.300492i	$-0.902849\pi$
$479$		−	13.1532i		−	0.600985i	0.953784	−	0.300492i	$-0.0971510\pi$
$480$	33.9108	+	0.285454i	1.54781	+	0.0130291i
$481$			21.3936i			0.975465i
$482$	−20.9941	−	17.6162i	−0.956257	−	0.802395i
$483$		−	12.0015i		−	0.546088i
$484$	−5.74017	−	32.5541i	−0.260917	−	1.47973i
$485$	−35.8977	+	12.7245i	−1.63003	+	0.577791i
$486$	−22.0431	−	18.4964i	−0.999897	−	0.839013i
$487$	17.0600			0.773062			0.386531	−	0.922276i	$-0.373673\pi$
$487$	17.0600			0.773062			0.386531	+	0.922276i	$0.373673\pi$
$488$	−16.1792	−	9.34108i	−0.732399	−	0.422851i
$489$	−27.2697			−1.23318
$490$	7.36049	−	19.7051i	0.332513	−	0.890185i
$491$			14.7216i			0.664376i	0.943213	+	0.332188i	$0.107787\pi$
$491$			14.7216i			0.664376i	−0.943213	+	0.332188i	$0.892213\pi$
$492$	10.1450	+	57.5351i	0.457372	+	2.59388i
$493$	−13.4101	−	2.78989i	−0.603961	−	0.125650i
$494$	−6.82295	−	5.72513i	−0.306979	−	0.257586i
$495$	−46.3068	+	16.4142i	−2.08133	+	0.737763i
$496$	5.62652	+	15.4587i	0.252638	+	0.694118i
$497$		−	0.141530i		−	0.00634849i
$498$	19.8454	+	16.6523i	0.889294	+	0.746206i
$499$	−1.06323			−0.0475968			−0.0237984	−	0.999717i	$-0.507576\pi$
$499$	−1.06323			−0.0475968			−0.0237984	+	0.999717i	$0.507576\pi$
$500$	20.8124	+	8.17592i	0.930757	+	0.365638i
$501$		−	35.3760i		−	1.58048i
$502$	18.1200	+	15.2045i	0.808734	+	0.678609i
$503$	−27.4571			−1.22425			−0.612125	−	0.790761i	$-0.709685\pi$
$503$	−27.4571			−1.22425			−0.612125	+	0.790761i	$0.709685\pi$
$504$	6.05272	+	3.49454i	0.269609	+	0.155659i
$505$	10.4320	+	29.4301i	0.464218	+	1.30962i
$506$	36.1835	−	43.1218i	1.60855	−	1.91700i
$507$		−	18.7669i		−	0.833466i
$508$	−19.8868	+	3.50657i	−0.882332	+	0.155579i
$509$			16.8197i			0.745520i	0.927928	+	0.372760i	$0.121588\pi$
$509$			16.8197i			0.745520i	−0.927928	+	0.372760i	$0.878412\pi$
$510$	−29.5680	−	18.6450i	−1.30929	−	0.825614i
$511$	−3.52528			−0.155949
$512$		−	22.6274i		−	1.00000i
$513$	8.18681			0.361457
$514$	19.2049	+	16.1149i	0.847094	+	0.710796i
$515$	−5.35445	−	15.1057i	−0.235945	−	0.665635i
$516$	−32.1499	+	5.66890i	−1.41532	+	0.249559i
$517$		−	31.4159i		−	1.38167i
$518$	−5.58317	−	4.68483i	−0.245310	−	0.205840i
$519$	24.2084			1.06263
$520$	−15.2334	−	2.81847i	−0.668028	−	0.123598i
$521$			29.1842i			1.27858i	0.768964	+	0.639292i	$0.220772\pi$
$521$			29.1842i			1.27858i	−0.768964	+	0.639292i	$0.779228\pi$
$522$	12.6463	−	15.0713i	0.553513	−	0.659651i
$523$	42.9036			1.87604			0.938021	−	0.346578i	$-0.112656\pi$
$523$	42.9036			1.87604			0.938021	+	0.346578i	$0.112656\pi$
$524$	1.21113	+	6.86868i	0.0529086	+	0.300059i
$525$	4.98161	+	6.14401i	0.217415	+	0.268146i
$526$	13.7805	+	11.5632i	0.600860	+	0.504181i
$527$	3.45388	−	16.6017i	0.150453	−	0.723181i
$528$	19.2439	+	52.8723i	0.837485	+	2.30097i
$529$	34.5544			1.50237
$530$	−11.9659	+	32.0345i	−0.519767	+	1.39149i
$531$		−	31.0191i		−	1.34611i
$532$	2.98821	−	0.526903i	0.129556	−	0.0228441i
$533$		−	26.6891i		−	1.15603i
$534$	−38.9278	−	32.6643i	−1.68457	−	1.41352i
$535$	−6.46902	−	18.2500i	−0.279680	−	0.789017i
$536$	−18.1293	−	10.4669i	−0.783065	−	0.452103i
$537$	1.74287			0.0752103
$538$	−3.57047	+	4.25512i	−0.153934	+	0.183451i
$539$	34.9003			1.50326
$540$	12.3915	−	7.01582i	0.533244	−	0.301913i
$541$	26.2365			1.12799			0.563997	−	0.825777i	$-0.309263\pi$
$541$	26.2365			1.12799			0.563997	+	0.825777i	$0.309263\pi$
$542$	−11.8866	+	14.1659i	−0.510574	+	0.608479i
$543$		−	36.4672i		−	1.56496i
$544$	−12.2741	+	19.8329i	−0.526249	+	0.850330i
$545$	8.64455	−	3.06420i	0.370292	−	0.131256i
$546$	−4.19799	−	3.52253i	−0.179657	−	0.150750i
$547$			3.46142i			0.148000i	0.997258	+	0.0739999i	$0.0235765\pi$
$547$			3.46142i			0.148000i	−0.997258	+	0.0739999i	$0.976424\pi$
$548$	−13.2713	+	2.34010i	−0.566924	+	0.0999640i
$549$	−27.6601			−1.18050
$550$	−0.624554	+	37.0947i	−0.0266311	+	1.58172i
$551$		−	8.54154i		−	0.363882i
$552$	−28.7639	+	49.8206i	−1.22427	+	2.12051i
$553$			6.18925i			0.263194i
$554$	9.54244	+	8.00706i	0.405419	+	0.340187i
$555$	−49.3499	+	17.4929i	−2.09479	+	0.742532i
$556$	0.550487	+	3.12197i	0.0233458	+	0.132401i
$557$	4.47936			0.189797			0.0948983	−	0.995487i	$-0.469747\pi$
$557$	4.47936			0.189797			0.0948983	+	0.995487i	$0.469747\pi$
$558$	18.6582	+	15.6561i	0.789864	+	0.662774i
$559$	14.9135			0.630775
$560$	4.07139	−	3.35831i	0.172048	−	0.141915i
$561$	11.8130	−	56.7814i	0.498746	−	2.39731i
$562$	−25.1849	+	30.0142i	−1.06236	+	1.26607i
$563$	0.670970			0.0282780			0.0141390	−	0.999900i	$-0.495499\pi$
$563$	0.670970			0.0282780			0.0141390	+	0.999900i	$0.495499\pi$
$564$	5.57513	+	31.6181i	0.234755	+	1.33136i
$565$	−3.99743	+	1.41695i	−0.168173	+	0.0596117i
$566$	5.27951	+	4.43004i	0.221915	+	0.186208i
$567$	−2.37589			−0.0997781
$568$	−0.339204	+	0.587519i	−0.0142327	+	0.0246517i
$569$	22.3013			0.934919			0.467459	−	0.884015i	$-0.345169\pi$
$569$	22.3013			0.934919			0.467459	+	0.884015i	$0.345169\pi$
$570$	7.62759	−	20.4202i	0.319485	−	0.855306i
$571$	−41.6316			−1.74223			−0.871114	−	0.491081i	$-0.836602\pi$
$571$	−41.6316			−1.74223			−0.871114	+	0.491081i	$0.836602\pi$
$572$	−4.46339	−	25.3131i	−0.186624	−	1.05839i
$573$		−	7.20341i		−	0.300927i
$574$	6.96514	+	5.84444i	0.290719	+	0.243942i
$575$	−29.4642	+	23.8898i	−1.22874	+	0.996273i
$576$	−16.7507	−	29.0130i	−0.697944	−	1.20887i
$577$		−	35.7159i		−	1.48687i	−0.668807	−	0.743436i	$-0.733195\pi$
$577$		−	35.7159i		−	1.48687i	0.668807	−	0.743436i	$-0.266805\pi$
$578$	21.5166	−	10.7255i	0.894972	−	0.446123i
$579$			4.03426i			0.167658i
$580$	−7.31981	−	12.9284i	−0.303939	−	0.536822i
$581$	4.03181			0.167268
$582$	49.4704	+	41.5106i	2.05061	+	1.72067i
$583$	−56.7374			−2.34982
$584$	14.6341	+	8.44900i	0.605563	+	0.349622i
$585$	−21.6188	+	7.66314i	−0.893827	+	0.316832i
$586$	−15.3619	+	18.3076i	−0.634594	+	0.756280i
$587$	−27.8951			−1.15135			−0.575677	−	0.817677i	$-0.695261\pi$
$587$	−27.8951			−1.15135			−0.575677	+	0.817677i	$0.695261\pi$
$588$	−35.1250	+	6.19348i	−1.44853	+	0.255415i
$589$	10.5744			0.435711
$590$	−21.9430	−	8.19641i	−0.903378	−	0.337441i
$591$	28.7149			1.18117
$592$	11.9487	+	32.8288i	0.491088	+	1.34925i
$593$			10.8444i			0.445325i	0.974896	+	0.222662i	$0.0714748\pi$
$593$			10.8444i			0.445325i	−0.974896	+	0.222662i	$0.928525\pi$
$594$	18.0986	+	15.1865i	0.742594	+	0.623111i
$595$	−5.39028	+	0.735053i	−0.220980	+	0.0301342i
$596$	29.1857	−	5.14623i	1.19549	−	0.210798i
$597$	52.0948			2.13210
$598$	16.8926	−	20.1319i	0.690791	−	0.823253i
$599$	45.5313			1.86036			0.930178	−	0.367108i	$-0.119652\pi$
$599$	45.5313			1.86036			0.930178	+	0.367108i	$0.119652\pi$
$600$	−5.95433	−	37.4443i	−0.243085	−	1.52866i
$601$		−	6.37954i		−	0.260227i	−0.991499	−	0.130113i	$-0.958466\pi$
$601$		−	6.37954i		−	0.260227i	0.991499	−	0.130113i	$-0.0415341\pi$
$602$	−3.26580	+	3.89203i	−0.133104	+	0.158627i
$603$	−30.9939			−1.26217
$604$	−0.822256	−	4.66324i	−0.0334571	−	0.189745i
$605$	−34.8344	+	12.3476i	−1.41622	+	0.502002i
$606$	34.0318	−	40.5575i	1.38245	−	1.64754i
$607$	16.5424			0.671434			0.335717	−	0.941963i	$-0.391021\pi$
$607$	16.5424			0.671434			0.335717	+	0.941963i	$0.391021\pi$
$608$	−13.6675	−	4.97455i	−0.554289	−	0.201745i
$609$		−	5.25540i		−	0.212959i
$610$	−7.30884	+	19.5668i	−0.295926	+	0.792237i
$611$		−	14.6668i		−	0.593357i
$612$	−1.05601	+	34.5162i	−0.0426866	+	1.39524i
$613$	−18.9747			−0.766379			−0.383189	−	0.923670i	$-0.625174\pi$
$613$	−18.9747			−0.766379			−0.383189	+	0.923670i	$0.625174\pi$
$614$	−1.16162	+	1.38436i	−0.0468791	+	0.0558684i
$615$	61.5653	−	21.8228i	2.48255	−	0.879981i
$616$	7.58345	+	4.37831i	0.305546	+	0.176407i
$617$	−0.795132			−0.0320108			−0.0160054	−	0.999872i	$-0.505095\pi$
$617$	−0.795132			−0.0320108			−0.0160054	+	0.999872i	$0.505095\pi$
$618$	−17.4675	+	20.8170i	−0.702648	+	0.837383i
$619$	1.58506			0.0637091			0.0318545	−	0.999493i	$-0.489859\pi$
$619$	1.58506			0.0637091			0.0318545	+	0.999493i	$0.489859\pi$
$620$	16.0053	−	9.06191i	0.642789	−	0.363935i
$621$			24.1561i			0.969351i
$622$	30.5804	+	25.6600i	1.22616	+	1.02887i
$623$	−7.90861			−0.316852
$624$	8.98424	+	24.6840i	0.359657	+	0.988150i
$625$	5.16756	−	24.4601i	0.206702	−	0.978404i
$626$	2.02387	−	2.41195i	0.0808901	−	0.0964010i
$627$	36.1668			1.44436
$628$	1.38228	+	7.83931i	0.0551590	+	0.312822i
$629$	7.33478	−	35.2559i	0.292457	−	1.40575i
$630$	2.73427	−	7.32002i	0.108936	−	0.291637i
$631$	−24.9094			−0.991627			−0.495814	−	0.868429i	$-0.665130\pi$
$631$	−24.9094			−0.991627			−0.495814	+	0.868429i	$0.665130\pi$
$632$	14.8337	−	25.6928i	0.590054	−	1.02200i
$633$		−	34.6103i		−	1.37564i
$634$	−29.8223	−	25.0239i	−1.18440	−	0.993826i
$635$	7.54296	+	21.2797i	0.299333	+	0.844461i
$636$	57.1026	−	10.0687i	2.26427	−	0.399251i
$637$	16.2936			0.645574
$638$	15.8445	−	18.8828i	0.627292	−	0.747577i
$639$			1.00443i			0.0397345i
$640$	−24.9500	+	4.18312i	−0.986235	+	0.165352i
$641$			26.7986i			1.05848i	0.848472	+	0.529240i	$0.177523\pi$
$641$			26.7986i			1.05848i	−0.848472	+	0.529240i	$0.822477\pi$
$642$	−21.1036	+	25.1502i	−0.832891	+	0.992601i
$643$			8.22151i			0.324225i	0.986772	+	0.162112i	$0.0518307\pi$
$643$			8.22151i			0.324225i	−0.986772	+	0.162112i	$0.948169\pi$
$644$	1.55468	+	8.81706i	0.0612632	+	0.347441i
$645$	12.1943	+	34.4019i	0.480151	+	1.35457i
$646$	9.28112	+	11.7741i	0.365161	+	0.463244i
$647$			2.52907i			0.0994281i	0.998763	+	0.0497141i	$0.0158310\pi$
$647$			2.52907i			0.0994281i	−0.998763	+	0.0497141i	$0.984169\pi$
$648$	9.86278	+	5.69428i	0.387447	+	0.223692i
$649$		−	38.8639i		−	1.52554i
$650$	−0.291579	+	17.3181i	−0.0114367	+	0.679270i
$651$	6.50617			0.254997
$652$	20.0340	−	3.53253i	0.784592	−	0.138345i
$653$			11.8623i			0.464207i	0.972691	+	0.232104i	$0.0745608\pi$
$653$			11.8623i			0.464207i	−0.972691	+	0.232104i	$0.925439\pi$
$654$	−11.9130	−	9.99619i	−0.465835	−	0.390882i
$655$	7.34980	−	2.60526i	0.287180	−	0.101796i
$656$	−14.9063	−	40.9547i	−0.581993	−	1.59901i
$657$	25.0186			0.976067
$658$	3.82765	+	3.21178i	0.149217	+	0.125208i
$659$		−	22.2352i		−	0.866160i	−0.901356	−	0.433080i	$-0.857427\pi$
$659$		−	22.2352i		−	0.866160i	0.901356	−	0.433080i	$-0.142573\pi$
$660$	54.7417	−	30.9937i	2.13082	−	1.20643i
$661$			31.2369i			1.21498i	0.794329	+	0.607488i	$0.207823\pi$
$661$			31.2369i			1.21498i	−0.794329	+	0.607488i	$0.792177\pi$
$662$	−27.5482	−	23.1157i	−1.07069	−	0.898415i
$663$	5.51503	−	26.5090i	0.214186	−	1.02952i
$664$	−16.7368	−	9.66300i	−0.649514	−	0.374997i
$665$	−1.13342	−	3.19753i	−0.0439520	−	0.123995i
$666$	39.6232	+	33.2478i	1.53537	+	1.28833i
$667$	25.2028			0.975855
$668$	4.58263	+	25.9894i	0.177307	+	1.00556i
$669$	−26.5145			−1.02511
$670$	−8.18975	+	21.9251i	−0.316398	+	0.847042i
$671$	−34.6554			−1.33786
$672$	−8.40925	−	3.06072i	−0.324394	−	0.118070i
$673$	38.4573			1.48242			0.741210	−	0.671273i	$-0.234252\pi$
$673$	38.4573			1.48242			0.741210	+	0.671273i	$0.234252\pi$
$674$	11.8601	−	14.1343i	0.456834	−	0.544434i
$675$	−10.0268	−	12.3664i	−0.385930	−	0.475982i
$676$	2.43107	+	13.7873i	0.0935029	+	0.530281i
$677$			44.7009i			1.71799i	0.511980	+	0.858997i	$0.328912\pi$
$677$			44.7009i			1.71799i	−0.511980	+	0.858997i	$0.671088\pi$
$678$	5.50883	+	4.62246i	0.211565	+	0.177524i
$679$	10.0504			0.385700
$680$	24.1378	+	9.86750i	0.925642	+	0.378401i
$681$	40.6470			1.55760
$682$	23.3769	+	19.6155i	0.895146	+	0.751117i
$683$		−	43.2946i		−	1.65662i	−0.560268	−	0.828311i	$-0.689302\pi$
$683$		−	43.2946i		−	1.65662i	0.560268	−	0.828311i	$-0.310698\pi$
$684$	−21.2071	+	3.73938i	−0.810873	+	0.142979i
$685$	5.03376	+	14.2010i	0.192330	+	0.542591i
$686$	−7.32278	+	8.72695i	−0.279585	+	0.333196i
$687$	13.9174			0.530984
$688$	22.8850	−	8.32945i	0.872482	−	0.317557i
$689$	−26.4884			−1.00913
$690$	60.2519	+	22.5061i	2.29375	+	0.856791i
$691$	39.0764			1.48653			0.743267	−	0.668994i	$-0.233275\pi$
$691$	39.0764			1.48653			0.743267	+	0.668994i	$0.233275\pi$
$692$	−17.7850	+	3.13597i	−0.676083	+	0.119212i
$693$	12.9647			0.492489
$694$	28.2132	+	23.6737i	1.07096	+	0.898641i
$695$	3.34065	−	1.18415i	0.126718	−	0.0449173i
$696$	−12.5956	+	21.8162i	−0.477434	+	0.826939i
$697$	−9.15032	+	43.9827i	−0.346593	+	1.66596i
$698$	20.2571	+	16.9977i	0.766741	+	0.643372i
$699$			17.6249i			0.666635i
$700$	−4.45570	−	3.86845i	−0.168410	−	0.146214i
$701$			2.70302i			0.102092i	0.998696	+	0.0510458i	$0.0162554\pi$
$701$			2.70302i			0.102092i	−0.998696	+	0.0510458i	$0.983745\pi$
$702$	8.44952	+	7.08999i	0.318906	+	0.267594i
$703$	22.4562			0.846952
$704$	−20.9869	−	36.3504i	−0.790974	−	1.37001i
$705$	33.8329	−	11.9926i	1.27422	−	0.451668i
$706$	−16.4668	−	13.8173i	−0.619738	−	0.520022i
$707$		−	8.23970i		−	0.309886i
$708$	6.89686	+	39.1141i	0.259200	+	1.47000i
$709$	−46.1190			−1.73203			−0.866017	−	0.500014i	$-0.833328\pi$
$709$	−46.1190			−1.73203			−0.866017	+	0.500014i	$0.833328\pi$
$710$	0.710532	+	0.265407i	0.0266658	+	0.00996054i
$711$		−	43.9245i		−	1.64730i
$712$	32.8302	+	18.9545i	1.23036	+	0.710350i
$713$			31.2010i			1.16848i
$714$	5.71044	+	7.24428i	0.213708	+	0.271110i
$715$	−27.0862	+	9.60115i	−1.01297	+	0.359063i
$716$	−1.28042	+	0.225772i	−0.0478515	+	0.00843751i
$717$		−	23.7601i		−	0.887339i
$718$	−17.1948	+	20.4920i	−0.641706	+	0.764755i
$719$			7.11654i			0.265402i	0.991156	+	0.132701i	$0.0423651\pi$
$719$			7.11654i			0.265402i	−0.991156	+	0.132701i	$0.957635\pi$
$720$	−28.8943	+	23.8336i	−1.07683	+	0.888227i
$721$			4.22920i			0.157504i
$722$	11.2623	−	13.4218i	0.419138	−	0.499509i
$723$	51.9545			1.93221
$724$	4.72399	+	26.7911i	0.175566	+	0.995683i
$725$	−12.9022	+	10.4612i	−0.479176	+	0.388520i
$726$	48.0051	+	40.2810i	1.78164	+	1.49497i
$727$		−	19.9877i		−	0.741301i	−0.928772	−	0.370651i	$-0.879135\pi$
$727$		−	19.9877i		−	0.741301i	0.928772	−	0.370651i	$-0.120865\pi$
$728$	3.54041	+	2.04406i	0.131216	+	0.0757579i
$729$	42.4711			1.57300
$730$	6.61084	−	17.6982i	0.244678	−	0.655039i
$731$	−24.5770	−	5.11309i	−0.909012	−	0.189114i
$732$	34.8785	−	6.15001i	1.28915	−	0.227311i
$733$	−42.5930			−1.57321			−0.786604	−	0.617458i	$-0.788163\pi$
$733$	−42.5930			−1.57321			−0.786604	+	0.617458i	$0.788163\pi$
$734$	−11.7910	+	14.0520i	−0.435214	+	0.518668i
$735$	13.3227	+	37.5853i	0.491416	+	1.38636i
$736$	14.6780	−	40.3274i	0.541037	−	1.48649i
$737$	−38.8323			−1.43041
$738$	−49.4309	−	41.4775i	−1.81958	−	1.52681i
$739$			22.9061i			0.842614i	0.906918	+	0.421307i	$0.138428\pi$
$739$			22.9061i			0.842614i	−0.906918	+	0.421307i	$0.861572\pi$
$740$	33.9895	−	19.2442i	1.24948	−	0.707431i
$741$	16.8848			0.620280
$742$	5.80051	−	6.91278i	0.212943	−	0.253776i
$743$	28.2281			1.03559			0.517795	−	0.855505i	$-0.326753\pi$
$743$	28.2281			1.03559			0.517795	+	0.855505i	$0.326753\pi$
$744$	−27.0083	−	15.5933i	−0.990174	−	0.571677i
$745$	−11.0700	−	31.2301i	−0.405574	−	1.14418i
$746$	3.54665	−	4.22673i	0.129852	−	0.154751i
$747$	−28.6134			−1.04691
$748$	−1.32307	+	43.2454i	−0.0483764	+	1.58121i
$749$			5.10954i			0.186699i
$750$	−40.1870	+	13.4878i	−1.46742	+	0.492506i
$751$		−	39.6316i		−	1.44618i	−0.690754	−	0.723089i	$-0.742721\pi$
$751$		−	39.6316i		−	1.44618i	0.690754	−	0.723089i	$-0.257279\pi$
$752$	−8.19167	−	22.5064i	−0.298720	−	0.820725i
$753$	−44.8418			−1.63412
$754$	7.39719	−	8.81563i	0.269390	−	0.321046i
$755$	−4.98989	+	1.76875i	−0.181601	+	0.0643713i
$756$	−3.70060	+	0.652515i	−0.134589	+	0.0237317i
$757$	23.6246			0.858649			0.429324	−	0.903150i	$-0.358752\pi$
$757$	23.6246			0.858649			0.429324	+	0.903150i	$0.358752\pi$
$758$	−18.1510	+	21.6315i	−0.659274	+	0.785692i
$759$			106.714i			3.87348i
$760$	−2.95846	+	15.9900i	−0.107315	+	0.580018i
$761$	−38.5749			−1.39834			−0.699170	−	0.714955i	$-0.746447\pi$
$761$	−38.5749			−1.39834			−0.699170	+	0.714955i	$0.746447\pi$
$762$	24.6070	−	29.3255i	0.891418	−	1.06235i
$763$	−2.42026			−0.0876191
$764$	0.933135	+	5.29207i	0.0337597	+	0.191461i
$765$	38.2543	−	5.21660i	1.38309	−	0.188607i
$766$	30.4349	+	25.5379i	1.09966	+	0.922722i
$767$		−	18.1440i		−	0.655142i
$768$	27.5728	+	32.8600i	0.994949	+	1.18573i
$769$	−13.5299			−0.487901			−0.243950	−	0.969788i	$-0.578443\pi$
$769$	−13.5299			−0.487901			−0.243950	+	0.969788i	$0.578443\pi$
$770$	3.42576	−	9.17126i	0.123456	−	0.330509i
$771$	−47.5267			−1.71163
$772$	−0.522601	−	2.96382i	−0.0188088	−	0.106670i
$773$	5.05914			0.181965			0.0909823	−	0.995853i	$-0.470999\pi$
$773$	5.05914			0.181965			0.0909823	+	0.995853i	$0.470999\pi$
$774$	23.1771	−	27.6214i	0.833084	−	0.992830i
$775$	−12.9510	−	15.9729i	−0.465212	−	0.573763i
$776$	−41.7213	−	24.0878i	−1.49771	−	0.864702i
$777$	13.8167			0.495673
$778$	−6.64107	−	5.57252i	−0.238094	−	0.199785i
$779$	−28.0147			−1.00373
$780$	25.5567	−	14.4697i	0.915078	−	0.518100i
$781$			1.25845i			0.0450307i
$782$	−34.7407	+	27.3850i	−1.24232	+	0.979285i
$783$			10.5778i			0.378020i
$784$	25.0027	−	9.10022i	0.892952	−	0.325008i
$785$	8.38842	−	2.97341i	0.299396	−	0.106126i
$786$	−10.1287	−	8.49900i	−0.361279	−	0.303149i
$787$		−	24.0659i		−	0.857855i	−0.903339	−	0.428928i	$-0.858892\pi$
$787$		−	24.0659i		−	0.857855i	0.903339	−	0.428928i	$-0.141108\pi$
$788$	−21.0957	+	3.71975i	−0.751504	+	0.132511i
$789$	−34.1029			−1.21409
$790$	−31.0723	−	11.6065i	−1.10550	−	0.412941i
$791$	1.11918			0.0397934
$792$	−53.8190	−	31.0724i	−1.91238	−	1.10411i
$793$	−16.1792			−0.574541
$794$	−6.10279	−	5.12084i	−0.216580	−	0.181732i
$795$	−21.6588	−	61.1024i	−0.768157	−	2.16708i
$796$	−38.2721	+	6.74840i	−1.35652	+	0.239191i
$797$	−11.6549			−0.412838			−0.206419	−	0.978464i	$-0.566181\pi$
$797$	−11.6549			−0.412838			−0.206419	+	0.978464i	$0.566181\pi$
$798$	−3.69749	+	4.40649i	−0.130890	+	0.155988i
$799$	−5.02851	+	24.1704i	−0.177896	+	0.855088i
$800$	9.22499	+	26.7376i	0.326153	+	0.945317i
$801$	56.1266			1.98314
$802$	−1.10617	−	0.928183i	−0.0390601	−	0.0327753i
$803$	31.3458			1.10617
$804$	39.0823	−	6.89126i	1.37833	−	0.243036i
$805$	9.43466	−	3.34427i	0.332528	−	0.117870i
$806$	10.9137	+	9.15771i	0.384420	+	0.322566i
$807$		−	10.5302i		−	0.370680i
$808$	−19.7480	+	34.2046i	−0.694733	+	1.20331i
$809$			0.998466i			0.0351042i	0.999846	+	0.0175521i	$0.00558729\pi$
$809$			0.998466i			0.0351042i	−0.999846	+	0.0175521i	$0.994413\pi$
$810$	4.45543	−	11.9278i	0.156548	−	0.419101i
$811$	38.7092			1.35926			0.679632	−	0.733553i	$-0.262139\pi$
$811$	38.7092			1.35926			0.679632	+	0.733553i	$0.262139\pi$
$812$	0.680788	+	3.86094i	0.0238910	+	0.135492i
$813$		−	35.0566i		−	1.22949i
$814$	49.6439	+	41.6562i	1.74002	+	1.46005i
$815$	−7.59880	−	21.4373i	−0.266174	−	0.750916i
$816$	−6.34283	−	43.7586i	−0.222043	−	1.53186i
$817$		−	15.6543i		−	0.547673i
$818$	27.8309	−	33.1676i	0.973084	−	1.15968i
$819$	6.05272			0.211499
$820$	−42.4027	+	24.0076i	−1.48077	+	0.838382i
$821$	36.8698			1.28676			0.643382	−	0.765545i	$-0.277531\pi$
$821$	36.8698			1.28676			0.643382	+	0.765545i	$0.277531\pi$
$822$	16.4214	−	19.5702i	0.572762	−	0.682591i
$823$	10.6486			0.371186			0.185593	−	0.982627i	$-0.440579\pi$
$823$	10.6486			0.371186			0.185593	+	0.982627i	$0.440579\pi$
$824$	10.1361	−	17.5562i	0.353107	−	0.611600i
$825$	−44.2951	−	54.6308i	−1.54216	−	1.90200i
$826$	4.73510	+	3.97322i	0.164755	+	0.138246i
$827$			0.372763i			0.0129622i	0.999979	+	0.00648112i	$0.00206302\pi$
$827$			0.372763i			0.0129622i	−0.999979	+	0.00648112i	$0.997937\pi$
$828$	−11.0335	−	62.5738i	−0.383439	−	2.17459i
$829$			41.9147i			1.45576i	0.685705	+	0.727879i	$0.259494\pi$
$829$			41.9147i			1.45576i	−0.685705	+	0.727879i	$0.740506\pi$
$830$	−7.56072	+	20.2411i	−0.262436	+	0.702580i
$831$	−23.6148			−0.819189
$832$	−9.79796	−	16.9706i	−0.339683	−	0.588348i
$833$	−26.8512	−	5.58623i	−0.930339	−	0.193551i
$834$	−4.60373	−	3.86299i	−0.159414	−	0.133764i
$835$	27.8099	−	9.85767i	0.962400	−	0.341139i
$836$	−26.5704	+	4.68507i	−0.918955	+	0.162037i
$837$	−13.0953			−0.452640
$838$	14.9621	−	17.8312i	0.516858	−	0.615967i
$839$			20.2832i			0.700256i	0.936702	+	0.350128i	$0.113862\pi$
$839$			20.2832i			0.700256i	−0.936702	+	0.350128i	$0.886138\pi$
$840$	−1.82027	+	9.83825i	−0.0628051	+	0.339452i
$841$	−17.9638			−0.619443
$842$	38.2532	+	32.0983i	1.31829	+	1.10618i
$843$		−	74.2766i		−	2.55822i
$844$	4.48345	+	25.4269i	0.154327	+	0.875230i
$845$	14.7531	−	5.22946i	0.507521	−	0.179899i
$846$	−27.1645	−	22.7937i	−0.933935	−	0.783664i
$847$	9.75275			0.335108
$848$	−40.6468	+	14.7942i	−1.39582	+	0.508036i
$849$	−13.0653			−0.448399
$850$	6.41799	−	28.4396i	0.220135	−	0.975469i
$851$			66.2595i			2.27135i
$852$	−0.223326	−	1.26655i	−0.00765104	−	0.0433912i
$853$			43.1040i			1.47585i	0.674881	+	0.737926i	$0.264195\pi$
$853$			43.1040i			1.47585i	−0.674881	+	0.737926i	$0.735805\pi$
$854$	3.54297	−	4.22235i	0.121238	−	0.144486i
$855$	8.04375	+	22.6925i	0.275090	+	0.776069i
$856$	12.2460	−	21.2107i	0.418560	−	0.724967i
$857$	−14.2658			−0.487310			−0.243655	−	0.969862i	$-0.578346\pi$
$857$	−14.2658			−0.487310			−0.243655	+	0.969862i	$0.578346\pi$
$858$	37.3273	+	31.3214i	1.27433	+	1.06929i
$859$		−	54.5523i		−	1.86130i	−0.365912	−	0.930650i	$-0.619243\pi$
$859$		−	54.5523i		−	1.86130i	0.365912	−	0.930650i	$-0.380757\pi$
$860$	−13.4152	−	23.6941i	−0.457453	−	0.807963i
$861$	−17.2367			−0.587426
$862$	−9.35835	−	7.85259i	−0.318747	−	0.267460i
$863$		−	4.40558i		−	0.149968i	−0.997185	−	0.0749838i	$-0.976109\pi$
$863$		−	4.40558i		−	0.149968i	0.997185	−	0.0749838i	$-0.0238905\pi$
$864$	16.9258	+	6.16047i	0.575826	+	0.209584i
$865$	6.74576	+	19.0307i	0.229363	+	0.647065i
$866$	34.5567	+	28.9965i	1.17429	+	0.985342i
$867$	−18.1772	+	41.7950i	−0.617328	+	1.41943i
$868$	−4.77983	+	0.842814i	−0.162238	+	0.0286070i
$869$		−	55.0331i		−	1.86687i
$870$	26.3840	+	9.85528i	0.894501	+	0.334125i
$871$	−18.1293			−0.614287
$872$	10.0469	+	5.80061i	0.340232	+	0.196433i
$873$	−71.3270			−2.41405
$874$	−21.1318	−	17.7317i	−0.714793	−	0.599782i
$875$	−3.44180	+	5.62821i	−0.116354	+	0.190268i
$876$	−31.5476	+	5.56269i	−1.06589	+	0.187946i
$877$			50.7096i			1.71234i	0.516694	+	0.856170i	$0.327163\pi$
$877$			50.7096i			1.71234i	−0.516694	+	0.856170i	$0.672837\pi$
$878$	26.8577	+	22.5363i	0.906405	+	0.760564i
$879$		−	45.3061i		−	1.52814i
$880$	−36.2017	+	29.8612i	−1.22036	+	1.00662i
$881$			19.6951i			0.663545i	0.943359	+	0.331773i	$0.107647\pi$
$881$			19.6951i			0.663545i	−0.943359	+	0.331773i	$0.892353\pi$
$882$	25.3218	−	30.1774i	0.852630	−	1.01612i
$883$	20.3159			0.683683			0.341842	−	0.939758i	$-0.388949\pi$
$883$	20.3159			0.683683			0.341842	+	0.939758i	$0.388949\pi$
$884$	−0.617691	+	20.1896i	−0.0207752	+	0.679048i
$885$	41.8539	−	14.8358i	1.40690	−	0.498700i
$886$	−12.2712	+	14.6243i	−0.412261	+	0.491313i
$887$	5.06252			0.169983			0.0849914	−	0.996382i	$-0.472914\pi$
$887$	5.06252			0.169983			0.0849914	+	0.996382i	$0.472914\pi$
$888$	−57.3559	−	33.1145i	−1.92474	−	1.11125i
$889$		−	5.95779i		−	0.199818i
$890$	14.8308	−	39.7041i	0.497128	−	1.33088i
$891$	21.1258			0.707740
$892$	19.4792	−	3.43471i	0.652213	−	0.115003i
$893$	−15.3953			−0.515184
$894$	−36.1131	+	43.0380i	−1.20780	+	1.43940i
$895$	0.485657	+	1.37011i	0.0162337	+	0.0457976i
$896$	6.57445	+	1.15925i	0.219637	+	0.0387279i
$897$			49.8206i			1.66346i
$898$	−30.7708	−	25.8198i	−1.02684	−	0.861618i
$899$			13.6627i			0.455677i
$900$	31.6217	+	27.4540i	1.05406	+	0.915133i
$901$	43.6520	+	9.08153i	1.45426	+	0.302550i
$902$	−61.9320	−	51.9672i	−2.06211	−	1.73032i
$903$		−	9.63167i		−	0.320522i
$904$	−4.64592	−	2.68233i	−0.154521	−	0.0892128i
$905$	28.6677	−	10.1617i	0.952947	−	0.337788i
$906$	6.87653	+	5.77010i	0.228457	+	0.191699i
$907$			40.3689i			1.34043i	0.742168	+	0.670214i	$0.233798\pi$
$907$			40.3689i			1.34043i	−0.742168	+	0.670214i	$0.766202\pi$
$908$	−29.8618	+	5.26544i	−0.990999	+	0.174740i
$909$			58.4763i			1.93954i
$910$	1.59935	−	4.28170i	0.0530181	−	0.141937i
$911$		−	29.5250i		−	0.978208i	−0.872225	−	0.489104i	$-0.837324\pi$
$911$		−	29.5250i		−	0.978208i	0.872225	−	0.489104i	$-0.162676\pi$
$912$	25.9100	−	9.43046i	0.857965	−	0.312274i
$913$	−35.8497			−1.18645
$914$	−9.65633	−	8.10262i	−0.319403	−	0.268011i
$915$	−13.2292	−	37.3216i	−0.437345	−	1.23381i
$916$	−10.2246	+	1.80288i	−0.337831	+	0.0595687i
$917$	−2.05776			−0.0679532
$918$	−11.4937	−	14.5810i	−0.379349	−	0.481243i
$919$	−34.2077			−1.12841			−0.564204	−	0.825636i	$-0.690817\pi$
$919$	−34.2077			−1.12841			−0.564204	+	0.825636i	$0.690817\pi$
$920$	−47.1803	−	8.72926i	−1.55549	−	0.287795i
$921$		−	3.42590i		−	0.112887i
$922$	−39.9340	−	33.5086i	−1.31516	−	1.10355i
$923$			0.587519i			0.0193384i
$924$	−16.3481	+	2.88261i	−0.537812	+	0.0948308i
$925$	−27.5031	−	33.9206i	−0.904297	−	1.11530i
$926$	−16.9376	−	14.2124i	−0.556605	−	0.467047i
$927$		−	30.0142i		−	0.985797i
$928$	6.42740	−	17.6591i	0.210990	−	0.579690i
$929$			32.8396i			1.07743i	0.842487	+	0.538716i	$0.181090\pi$
$929$			32.8396i			1.07743i	−0.842487	+	0.538716i	$0.818910\pi$
$930$	−12.2008	+	32.6633i	−0.400080	+	1.07107i
$931$		−	17.1028i		−	0.560522i
$932$	−2.28314	−	12.9483i	−0.0747868	−	0.424137i
$933$	−75.6778			−2.47758
$934$	−2.60142	+	3.10025i	−0.0851210	+	0.101443i
$935$	47.9289	−	6.53588i	1.56744	−	0.213746i
$936$	−25.1260	−	14.5065i	−0.821268	−	0.474160i
$937$		−	47.3997i		−	1.54848i	−0.632892	−	0.774240i	$-0.718132\pi$
$937$		−	47.3997i		−	1.54848i	0.632892	−	0.774240i	$-0.281868\pi$
$938$	3.97000	−	4.73126i	0.129625	−	0.154481i
$939$			5.96889i			0.194787i
$940$	−23.3022	+	13.1933i	−0.760034	+	0.430316i
$941$	22.1334			0.721527			0.360764	−	0.932657i	$-0.382516\pi$
$941$	22.1334			0.721527			0.360764	+	0.932657i	$0.382516\pi$
$942$	−11.5600	−	9.70002i	−0.376646	−	0.316044i
$943$		−	82.6604i		−	2.69179i
$944$	−10.1337	−	27.8422i	−0.329825	−	0.906186i
$945$	1.40362	+	3.95981i	0.0456597	+	0.128813i
$946$	29.0386	−	34.6069i	0.944127	−	1.12517i
$947$			1.44639i			0.0470013i	0.999724	+	0.0235006i	$0.00748117\pi$
$947$			1.44639i			0.0470013i	−0.999724	+	0.0235006i	$0.992519\pi$
$948$	9.76628	+	55.3873i	0.317194	+	1.79890i
$949$	14.6341			0.475043
$950$	18.1782	+	0.306062i	0.589779	+	0.00992995i
$951$	73.8017			2.39318
$952$	−5.13367	−	4.58236i	−0.166383	−	0.148515i
$953$			31.5446i			1.02183i	0.859631	+	0.510915i	$0.170693\pi$
$953$			31.5446i			1.02183i	−0.859631	+	0.510915i	$0.829307\pi$
$954$	−41.1656	+	49.0593i	−1.33279	+	1.58835i
$955$	5.66276	−	2.00726i	0.183243	−	0.0649534i
$956$	3.07791	+	17.4557i	0.0995466	+	0.564557i
$957$			46.7295i			1.51055i
$958$	−14.2495	−	11.9568i	−0.460381	−	0.386306i
$959$		−	3.97591i		−	0.128389i
$960$	31.1355	−	36.4778i	1.00489	−	1.17732i
$961$	14.0856			0.454374
$962$	23.1768	+	19.4476i	0.747250	+	0.627017i
$963$		−	36.2620i		−	1.16853i
$964$	−38.1690	+	6.73022i	−1.22934	+	0.216766i
$965$	−3.17142	+	1.12416i	−0.102092	+	0.0361881i
$966$	−13.0018	−	10.9098i	−0.418328	−	0.351018i
$967$			30.2037i			0.971286i	0.874157	+	0.485643i	$0.161414\pi$
$967$			30.2037i			0.971286i	−0.874157	+	0.485643i	$0.838586\pi$
$968$	−40.4855	−	23.3743i	−1.30125	−	0.751280i
$969$	−27.8256	−	5.78895i	−0.893888	−	0.185968i
$970$	−18.8473	+	50.4568i	−0.605149	+	1.62007i
$971$		−	38.3436i		−	1.23050i	−0.788331	−	0.615252i	$-0.789054\pi$
$971$		−	38.3436i		−	1.23050i	0.788331	−	0.615252i	$-0.210946\pi$
$972$	−40.0761	+	7.06651i	−1.28544	+	0.226658i
$973$	−0.935297			−0.0299842
$974$	15.5082	−	18.4819i	0.496915	−	0.592200i
$975$	−20.6796	−	25.5050i	−0.662278	−	0.816812i
$976$	−24.8272	+	9.03636i	−0.794700	+	0.289247i
$977$		−	12.1582i		−	0.388975i	−0.980905	−	0.194487i	$-0.937696\pi$
$977$		−	12.1582i		−	0.388975i	0.980905	−	0.194487i	$-0.0623043\pi$
$978$	−24.7892	+	29.5426i	−0.792671	+	0.944669i
$979$	70.3211			2.24747
$980$	−14.6565	−	25.8867i	−0.468186	−	0.826919i
$981$	17.1763			0.548398
$982$	15.9486	+	13.3825i	0.508941	+	0.427052i
$983$	42.5044			1.35568			0.677839	−	0.735210i	$-0.262917\pi$
$983$	42.5044			1.35568			0.677839	+	0.735210i	$0.262917\pi$
$984$	71.5529	+	41.3111i	2.28102	+	1.31695i
$985$	8.00152	+	22.5734i	0.254950	+	0.719249i
$986$	−15.2127	+	11.9917i	−0.484472	+	0.381894i
$987$	−9.47235			−0.301508
$988$	−12.4047	+	2.18727i	−0.394645	+	0.0695865i
$989$	46.1896			1.46874
$990$	−24.3123	+	65.0876i	−0.772696	+	2.06862i
$991$			40.8846i			1.29874i	0.760472	+	0.649371i	$0.224968\pi$
$991$			40.8846i			1.29874i	−0.760472	+	0.649371i	$0.775032\pi$
$992$	21.8620	+	7.95711i	0.694118	+	0.252638i
$993$	68.1738			2.16343
$994$	−0.153327	−	0.128656i	−0.00486323	−	0.00408073i
$995$	14.5164	+	40.9529i	0.460202	+	1.29829i
$996$	36.0805	−	6.36196i	1.14325	−	0.201586i
$997$			6.50535i			0.206026i	0.994680	+	0.103013i	$0.0328484\pi$
$997$			6.50535i			0.206026i	−0.994680	+	0.103013i	$0.967152\pi$
$998$	−0.966519	+	1.15185i	−0.0305946	+	0.0364613i
$999$	−27.8097			−0.879860

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.h.c.509.36	yes	48
5.4	even	2	inner	680.2.h.c.509.13	yes	48
8.5	even	2	inner	680.2.h.c.509.9	✓	48
17.16	even	2	inner	680.2.h.c.509.33	yes	48
40.29	even	2	inner	680.2.h.c.509.40	yes	48
85.84	even	2	inner	680.2.h.c.509.16	yes	48
136.101	even	2	inner	680.2.h.c.509.12	yes	48
680.509	even	2	inner	680.2.h.c.509.37	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.h.c.509.9	✓	48	8.5	even	2	inner
680.2.h.c.509.12	yes	48	136.101	even	2	inner
680.2.h.c.509.13	yes	48	5.4	even	2	inner
680.2.h.c.509.16	yes	48	85.84	even	2	inner
680.2.h.c.509.33	yes	48	17.16	even	2	inner
680.2.h.c.509.36	yes	48	1.1	even	1	trivial
680.2.h.c.509.37	yes	48	680.509	even	2	inner
680.2.h.c.509.40	yes	48	40.29	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+(0.909039 - 1.08335i) q^{2} +2.68098i q^{3} +(-0.347296 - 1.96962i) q^{4} +(-2.10758 + 0.747066i) q^{5} +(2.90444 + 2.43712i) q^{6} +0.590069 q^{7} +(-2.44949 - 1.41421i) q^{8} -4.18766 q^{9} +(-1.10654 + 2.96236i) q^{10} -5.24673 q^{11} +(5.28050 - 0.931095i) q^{12} -2.44949 q^{13} +(0.536396 - 0.639252i) q^{14} +(-2.00287 - 5.65038i) q^{15} +(-3.75877 + 1.36808i) q^{16} +(4.03667 + 0.839805i) q^{17} +(-3.80675 + 4.53671i) q^{18} +2.57115i q^{19} +(2.20339 + 3.89167i) q^{20} +1.58196i q^{21} +(-4.76948 + 5.68404i) q^{22} -7.58646 q^{23} +(3.79148 - 6.56704i) q^{24} +(3.88378 - 3.14900i) q^{25} +(-2.22668 + 2.65366i) q^{26} -3.18410i q^{27} +(-0.204929 - 1.16221i) q^{28} -3.32207 q^{29} +(-7.94203 - 2.96661i) q^{30} -4.11271i q^{31} +(-1.93476 + 5.31570i) q^{32} -14.0664i q^{33} +(4.57930 - 3.60972i) q^{34} +(-1.24362 + 0.440821i) q^{35} +(1.45436 + 8.24809i) q^{36} -8.73391i q^{37} +(2.78546 + 2.33728i) q^{38} -6.56704i q^{39} +(6.21901 + 1.15064i) q^{40} +10.8958i q^{41} +(1.71382 + 1.43807i) q^{42} -6.08842 q^{43} +(1.82217 + 10.3340i) q^{44} +(8.82583 - 3.12846i) q^{45} +(-6.89639 + 8.21880i) q^{46} +5.98771i q^{47} +(-3.66780 - 10.0772i) q^{48} -6.65182 q^{49} +(0.119037 - 7.07007i) q^{50} +(-2.25150 + 10.8222i) q^{51} +(0.850699 + 4.82455i) q^{52} +10.8139 q^{53} +(-3.44950 - 2.89448i) q^{54} +(11.0579 - 3.91965i) q^{55} +(-1.44537 - 0.834484i) q^{56} -6.89321 q^{57} +(-3.01989 + 3.59897i) q^{58} +7.40726i q^{59} +(-10.4335 + 5.90724i) q^{60} +6.60514 q^{61} +(-4.45551 - 3.73862i) q^{62} -2.47101 q^{63} +(4.00000 + 6.92820i) q^{64} +(5.16249 - 1.82993i) q^{65} +(-15.2388 - 12.7869i) q^{66} +7.40124 q^{67} +(0.252171 - 8.24235i) q^{68} -20.3392i q^{69} +(-0.652933 + 1.74800i) q^{70} -0.239853i q^{71} +(10.2576 + 5.92225i) q^{72} -5.97435 q^{73} +(-9.46189 - 7.93947i) q^{74} +(8.44242 + 10.4124i) q^{75} +(5.06418 - 0.892951i) q^{76} -3.09593 q^{77} +(-7.11440 - 5.96969i) q^{78} +10.4890i q^{79} +(6.89986 - 5.69139i) q^{80} -4.02646 q^{81} +(11.8039 + 9.90468i) q^{82} +6.83277 q^{83} +(3.11586 - 0.549410i) q^{84} +(-9.13500 + 1.24571i) q^{85} +(-5.53461 + 6.59590i) q^{86} -8.90641i q^{87} +(12.8518 + 7.41999i) q^{88} -13.4029 q^{89} +(4.63381 - 12.4054i) q^{90} -1.44537 q^{91} +(2.63475 + 14.9424i) q^{92} +11.0261 q^{93} +(6.48679 + 5.44306i) q^{94} +(-1.92082 - 5.41890i) q^{95} +(-14.2513 - 5.18705i) q^{96} +17.0326 q^{97} +(-6.04676 + 7.20625i) q^{98} +21.9715 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 96 q^{9} - 48 q^{15} + 24 q^{34} - 96 q^{36} + 96 q^{49} + 48 q^{60} + 192 q^{64} - 144 q^{66} - 96 q^{70} + 96 q^{76} - 192 q^{84} - 192 q^{86} - 48 q^{89} - 144 q^{94}+O(q^{100}) \) 48 * q - 96 * q^9 - 48 * q^15 + 24 * q^34 - 96 * q^36 + 96 * q^49 + 48 * q^60 + 192 * q^64 - 144 * q^66 - 96 * q^70 + 96 * q^76 - 192 * q^84 - 192 * q^86 - 48 * q^89 - 144 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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