LMFDB - Embedded newform 297.2.t.a.260.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(8,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.8"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([5, 9])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.t (of order $30$, degree $8$, not minimal)

Newform invariants

comment:select newform

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

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$80$
Relative dimension:	$10$ over $\Q(\zeta_{30})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			260.1
Character	$\chi$	$=$	297.260
Dual form			297.2.t.a.8.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.245046 + 2.33146i) q^{2} +(-3.41935 - 0.726805i) q^{4} +(2.90568 - 0.305399i) q^{5} +(0.977562 + 0.880201i) q^{7} +(1.08356 - 3.33484i) q^{8} +6.84930i q^{10} +(-2.72590 + 1.88930i) q^{11} +(2.40347 + 5.39828i) q^{13} +(-2.29170 + 2.06345i) q^{14} +(1.12249 + 0.499763i) q^{16} +(3.07734 - 2.23582i) q^{17} +(-2.83716 - 0.921851i) q^{19} +(-10.1575 - 1.06759i) q^{20} +(-3.73685 - 6.81829i) q^{22} +(-0.0733618 - 0.0423554i) q^{23} +(3.45895 - 0.735222i) q^{25} +(-13.1748 + 4.28075i) q^{26} +(-2.70289 - 3.72021i) q^{28} +(2.94645 - 3.27237i) q^{29} +(-2.35549 + 1.04873i) q^{31} +(2.06622 - 3.57881i) q^{32} +(4.45863 + 7.72257i) q^{34} +(3.10929 + 2.25903i) q^{35} +(-2.11787 - 6.51815i) q^{37} +(2.84449 - 6.38883i) q^{38} +(2.13000 - 10.0209i) q^{40} +(3.02460 + 3.35916i) q^{41} +(2.93163 - 1.69258i) q^{43} +(10.6940 - 4.47897i) q^{44} +(0.116727 - 0.160661i) q^{46} +(0.987907 + 4.64774i) q^{47} +(-0.550825 - 5.24075i) q^{49} +(0.866537 + 8.24455i) q^{50} +(-4.29480 - 20.2054i) q^{52} +(-2.46224 + 3.38898i) q^{53} +(-7.34360 + 6.32218i) q^{55} +(3.99457 - 2.30627i) q^{56} +(6.90737 + 7.67141i) q^{58} +(2.91842 - 13.7301i) q^{59} +(-3.99395 + 8.97056i) q^{61} +(-1.86787 - 5.74871i) q^{62} +(9.82561 + 7.13872i) q^{64} +(8.63232 + 14.9516i) q^{65} +(1.89207 - 3.27716i) q^{67} +(-12.1475 + 5.40842i) q^{68} +(-6.02876 + 6.69561i) q^{70} +(-2.61027 - 3.59273i) q^{71} +(8.30569 - 2.69868i) q^{73} +(15.7158 - 3.34049i) q^{74} +(9.03125 + 5.21419i) q^{76} +(-4.32770 - 0.552436i) q^{77} +(5.53218 + 0.581456i) q^{79} +(3.41421 + 1.10934i) q^{80} +(-8.57291 + 6.22858i) q^{82} +(-1.15281 - 0.513262i) q^{83} +(8.25894 - 7.43639i) q^{85} +(3.22779 + 7.24973i) q^{86} +(3.34684 + 11.1376i) q^{88} +13.6071i q^{89} +(-2.40203 + 7.39268i) q^{91} +(0.220065 + 0.198148i) q^{92} +(-11.0781 + 1.16435i) q^{94} +(-8.52541 - 1.81213i) q^{95} +(1.43965 - 13.6973i) q^{97} +12.3536 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) $ 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{7}{10}\right)$

Coefficient data

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

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

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

$2$	−0.245046	+	2.33146i	−0.173274	+	1.64859i	0.469791	+	0.882777i	$0.344329\pi$
$2$	−0.245046	+	2.33146i	−0.173274	+	1.64859i	−0.643065	+	0.765812i	$0.722338\pi$
$3$		0			0
$3$		0			0
$4$	−3.41935	−	0.726805i	−1.70967	−	0.363402i
$5$	2.90568	−	0.305399i	1.29946	−	0.136579i	0.570591	−	0.821234i	$-0.306714\pi$
$5$	2.90568	−	0.305399i	1.29946	−	0.136579i	0.728867	+	0.684656i	$0.240047\pi$
$6$		0			0
$7$	0.977562	+	0.880201i	0.369484	+	0.332685i	0.832867	−	0.553473i	$-0.186698\pi$
$7$	0.977562	+	0.880201i	0.369484	+	0.332685i	−0.463383	+	0.886158i	$0.653365\pi$
$8$	1.08356	−	3.33484i	0.383095	−	1.17904i
$9$		0			0
$10$			6.84930i			2.16594i
$11$	−2.72590	+	1.88930i	−0.821891	+	0.569645i
$11$	−2.72590	+	1.88930i	−0.821891	+	0.569645i
$12$		0			0
$13$	2.40347	+	5.39828i	0.666602	+	1.49721i	0.856898	+	0.515485i	$0.172388\pi$
$13$	2.40347	+	5.39828i	0.666602	+	1.49721i	−0.190297	+	0.981727i	$0.560945\pi$
$14$	−2.29170	+	2.06345i	−0.612482	+	0.551481i
$15$		0			0
$16$	1.12249	+	0.499763i	0.280621	+	0.124941i
$17$	3.07734	−	2.23582i	0.746365	−	0.542266i	−0.148333	−	0.988938i	$-0.547391\pi$
$17$	3.07734	−	2.23582i	0.746365	−	0.542266i	0.894698	+	0.446671i	$0.147391\pi$
$18$		0			0
$19$	−2.83716	−	0.921851i	−0.650890	−	0.211487i	−0.0350836	−	0.999384i	$-0.511170\pi$
$19$	−2.83716	−	0.921851i	−0.650890	−	0.211487i	−0.615807	+	0.787897i	$0.711170\pi$
$20$	−10.1575	−	1.06759i	−2.27128	−	0.238721i
$21$		0			0
$22$	−3.73685	−	6.81829i	−0.796698	−	1.45366i
$23$	−0.0733618	−	0.0423554i	−0.0152970	−	0.00883172i	0.492332	−	0.870407i	$-0.336145\pi$
$23$	−0.0733618	−	0.0423554i	−0.0152970	−	0.00883172i	−0.507629	+	0.861576i	$0.669478\pi$
$24$		0			0
$25$	3.45895	−	0.735222i	0.691789	−	0.147044i
$26$	−13.1748	+	4.28075i	−2.58379	+	0.839525i
$27$		0			0
$28$	−2.70289	−	3.72021i	−0.510799	−	0.703054i
$29$	2.94645	−	3.27237i	0.547143	−	0.607664i	−0.404625	−	0.914483i	$-0.632598\pi$
$29$	2.94645	−	3.27237i	0.547143	−	0.607664i	0.951768	+	0.306819i	$0.0992646\pi$
$30$		0			0
$31$	−2.35549	+	1.04873i	−0.423058	+	0.188358i	−0.607212	−	0.794540i	$-0.707712\pi$
$31$	−2.35549	+	1.04873i	−0.423058	+	0.188358i	0.184154	+	0.982897i	$0.441045\pi$
$32$	2.06622	−	3.57881i	0.365260	−	0.632649i
$33$		0			0
$34$	4.45863	+	7.72257i	0.764649	+	1.32441i
$35$	3.10929	+	2.25903i	0.525566	+	0.381846i
$36$		0			0
$37$	−2.11787	−	6.51815i	−0.348176	−	1.07158i	−0.959861	−	0.280475i	$-0.909508\pi$
$37$	−2.11787	−	6.51815i	−0.348176	−	1.07158i	0.611685	−	0.791102i	$-0.290492\pi$
$38$	2.84449	−	6.38883i	0.461437	−	1.03641i
$39$		0			0
$40$	2.13000	−	10.0209i	0.336783	−	1.58444i
$41$	3.02460	+	3.35916i	0.472364	+	0.524613i	0.931494	−	0.363756i	$-0.118506\pi$
$41$	3.02460	+	3.35916i	0.472364	+	0.524613i	−0.459131	+	0.888369i	$0.651839\pi$
$42$		0			0
$43$	2.93163	−	1.69258i	0.447069	−	0.258116i	−0.259522	−	0.965737i	$-0.583565\pi$
$43$	2.93163	−	1.69258i	0.447069	−	0.258116i	0.706592	+	0.707621i	$0.250232\pi$
$44$	10.6940	−	4.47897i	1.61218	−	0.675230i
$45$		0			0
$46$	0.116727	−	0.160661i	0.0172104	−	0.0236881i
$47$	0.987907	+	4.64774i	0.144101	+	0.677942i	0.989586	+	0.143943i	$0.0459782\pi$
$47$	0.987907	+	4.64774i	0.144101	+	0.677942i	−0.845485	+	0.533999i	$0.820688\pi$
$48$		0			0
$49$	−0.550825	−	5.24075i	−0.0786893	−	0.748679i
$50$	0.866537	+	8.24455i	0.122547	+	1.16596i
$51$		0			0
$52$	−4.29480	−	20.2054i	−0.595581	−	2.80199i
$53$	−2.46224	+	3.38898i	−0.338215	+	0.465512i	−0.943919	−	0.330177i	$-0.892891\pi$
$53$	−2.46224	+	3.38898i	−0.338215	+	0.465512i	0.605704	+	0.795690i	$0.292891\pi$
$54$		0			0
$55$	−7.34360	+	6.32218i	−0.990211	+	0.852482i
$56$	3.99457	−	2.30627i	0.533797	−	0.308188i
$57$		0			0
$58$	6.90737	+	7.67141i	0.906982	+	1.00731i
$59$	2.91842	−	13.7301i	0.379947	−	1.78751i	−0.207489	−	0.978237i	$-0.566529\pi$
$59$	2.91842	−	13.7301i	0.379947	−	1.78751i	0.587436	−	0.809271i	$-0.300137\pi$
$60$		0			0
$61$	−3.99395	+	8.97056i	−0.511373	+	1.14856i	0.454783	+	0.890602i	$0.349717\pi$
$61$	−3.99395	+	8.97056i	−0.511373	+	1.14856i	−0.966156	+	0.257960i	$0.916950\pi$
$62$	−1.86787	−	5.74871i	−0.237219	−	0.730086i
$63$		0			0
$64$	9.82561	+	7.13872i	1.22820	+	0.892340i
$65$	8.63232	+	14.9516i	1.07071	+	1.85452i
$66$		0			0
$67$	1.89207	−	3.27716i	0.231153	−	0.400369i	−0.726995	−	0.686643i	$-0.759083\pi$
$67$	1.89207	−	3.27716i	0.231153	−	0.400369i	0.958148	+	0.286274i	$0.0924168\pi$
$68$	−12.1475	+	5.40842i	−1.47310	+	0.655868i
$69$		0			0
$70$	−6.02876	+	6.69561i	−0.720574	+	0.800279i
$71$	−2.61027	−	3.59273i	−0.309782	−	0.426379i	0.625531	−	0.780199i	$-0.284882\pi$
$71$	−2.61027	−	3.59273i	−0.309782	−	0.426379i	−0.935313	+	0.353821i	$0.884882\pi$
$72$		0			0
$73$	8.30569	−	2.69868i	0.972108	−	0.315857i	0.220441	−	0.975400i	$-0.429250\pi$
$73$	8.30569	−	2.69868i	0.972108	−	0.315857i	0.751667	+	0.659543i	$0.229250\pi$
$74$	15.7158	−	3.34049i	1.82692	−	0.388324i
$75$		0			0
$76$	9.03125	+	5.21419i	1.03596	+	0.598109i
$77$	−4.32770	−	0.552436i	−0.493188	−	0.0629559i
$78$		0			0
$79$	5.53218	+	0.581456i	0.622419	+	0.0654189i	0.410488	−	0.911866i	$-0.365358\pi$
$79$	5.53218	+	0.581456i	0.622419	+	0.0654189i	0.211931	+	0.977285i	$0.432025\pi$
$80$	3.41421	+	1.10934i	0.381720	+	0.124028i
$81$		0			0
$82$	−8.57291	+	6.22858i	−0.946719	+	0.687832i
$83$	−1.15281	−	0.513262i	−0.126537	−	0.0563378i	0.342492	−	0.939521i	$-0.388729\pi$
$83$	−1.15281	−	0.513262i	−0.126537	−	0.0563378i	−0.469028	+	0.883183i	$0.655396\pi$
$84$		0			0
$85$	8.25894	−	7.43639i	0.895808	−	0.806589i
$86$	3.22779	+	7.24973i	0.348061	+	0.781758i
$87$		0			0
$88$	3.34684	+	11.1376i	0.356775	+	1.18727i
$89$			13.6071i			1.44234i	0.692756	+	0.721172i	$0.256396\pi$
$89$			13.6071i			1.44234i	−0.692756	+	0.721172i	$0.743604\pi$
$90$		0			0
$91$	−2.40203	+	7.39268i	−0.251801	+	0.774964i
$92$	0.220065	+	0.198148i	0.0229434	+	0.0206583i
$93$		0			0
$94$	−11.0781	+	1.16435i	−1.14262	+	0.120094i
$95$	−8.52541	−	1.81213i	−0.874689	−	0.185921i
$96$		0			0
$97$	1.43965	−	13.6973i	0.146174	−	1.39075i	−0.637916	−	0.770106i	$-0.720203\pi$
$97$	1.43965	−	13.6973i	0.146174	−	1.39075i	0.784090	−	0.620647i	$-0.213130\pi$
$98$	12.3536			1.24790
$99$		0			0
$100$	−12.3617			−1.23617
$101$	1.30686	−	12.4339i	0.130037	−	1.23722i	−0.713696	−	0.700456i	$-0.752980\pi$
$101$	1.30686	−	12.4339i	0.130037	−	1.23722i	0.843733	−	0.536763i	$-0.180353\pi$
$102$		0			0
$103$	−5.85523	−	1.24457i	−0.576933	−	0.122631i	−0.0898018	−	0.995960i	$-0.528623\pi$
$103$	−5.85523	−	1.24457i	−0.576933	−	0.122631i	−0.487131	+	0.873329i	$0.661957\pi$
$104$	20.6067	−	2.16585i	2.02065	−	0.212379i
$105$		0			0
$106$	−7.29790	−	6.57106i	−0.708835	−	0.638238i
$107$	0.951472	−	2.92833i	0.0919823	−	0.283092i	−0.894473	−	0.447122i	$-0.852449\pi$
$107$	0.951472	−	2.92833i	0.0919823	−	0.283092i	0.986455	+	0.164029i	$0.0524491\pi$
$108$		0			0
$109$		−	9.98777i		−	0.956655i	−0.878181	−	0.478328i	$-0.841243\pi$
$109$		−	9.98777i		−	0.956655i	0.878181	−	0.478328i	$-0.158757\pi$
$110$	−12.9404	−	18.6705i	−1.23382	−	1.78016i
$111$		0			0
$112$	0.657408	+	1.47656i	0.0621192	+	0.139522i
$113$	3.50337	−	3.15445i	0.329569	−	0.296745i	−0.487689	−	0.873018i	$-0.662160\pi$
$113$	3.50337	−	3.15445i	0.329569	−	0.296745i	0.817258	+	0.576272i	$0.195493\pi$
$114$		0			0
$115$	−0.226101	−	0.100667i	−0.0210840	−	0.00938721i
$116$	−12.4533	+	9.04787i	−1.15626	+	0.840074i
$117$		0			0
$118$	31.2960	+	10.1687i	2.88103	+	0.936104i
$119$	4.97627	+	0.523027i	0.456174	+	0.0479458i
$120$		0			0
$121$	3.86110	−	10.3001i	0.351009	−	0.936372i
$122$	−19.9358	−	11.5099i	−1.80490	−	1.04206i
$123$		0			0
$124$	8.81646	−	1.87400i	0.791741	−	0.168290i
$125$	−4.06738	+	1.32157i	−0.363797	+	0.118205i
$126$		0			0
$127$	−1.75209	−	2.41154i	−0.155473	−	0.213990i	0.724174	−	0.689617i	$-0.242221\pi$
$127$	−1.75209	−	2.41154i	−0.155473	−	0.213990i	−0.879647	+	0.475627i	$0.842221\pi$
$128$	−13.5211	+	15.0167i	−1.19510	+	1.32730i
$129$		0			0
$130$	−36.9744	+	16.4621i	−3.24287	+	1.44382i
$131$	3.89251	−	6.74202i	0.340090	−	0.589053i	−0.644359	−	0.764723i	$-0.722876\pi$
$131$	3.89251	−	6.74202i	0.340090	−	0.589053i	0.984449	+	0.175670i	$0.0562092\pi$
$132$		0			0
$133$	−1.96209	−	3.39844i	−0.170135	−	0.294682i
$134$	7.17692	+	5.21434i	0.619991	+	0.450450i
$135$		0			0
$136$	−4.12163	−	12.6851i	−0.353427	−	1.08774i
$137$	2.55508	−	5.73881i	0.218295	−	0.490299i	−0.770890	−	0.636968i	$-0.780188\pi$
$137$	2.55508	−	5.73881i	0.218295	−	0.490299i	0.989186	+	0.146669i	$0.0468551\pi$
$138$		0			0
$139$	−0.109057	+	0.513071i	−0.00925006	+	0.0435181i	−0.982531	−	0.186101i	$-0.940415\pi$
$139$	−0.109057	+	0.513071i	−0.00925006	+	0.0435181i	0.973281	+	0.229619i	$0.0737481\pi$
$140$	−8.98988	−	9.98427i	−0.759783	−	0.843825i
$141$		0			0
$142$	9.01593	−	5.20535i	0.756600	−	0.436823i
$143$	−16.7506	−	10.1743i	−1.40075	−	0.850819i
$144$		0			0
$145$	7.56206	−	10.4083i	0.627995	−	0.864361i
$146$	4.25659	+	20.0257i	0.352278	+	1.65734i
$147$		0			0
$148$	2.50433	+	23.8271i	0.205855	+	1.95858i
$149$	1.00519	+	9.56377i	0.0823486	+	0.783494i	0.955290	+	0.295670i	$0.0955428\pi$
$149$	1.00519	+	9.56377i	0.0823486	+	0.783494i	−0.872942	+	0.487825i	$0.837791\pi$
$150$		0			0
$151$	2.08034	+	9.78722i	0.169295	+	0.796472i	0.978057	+	0.208336i	$0.0668048\pi$
$151$	2.08034	+	9.78722i	0.169295	+	0.796472i	−0.808762	+	0.588136i	$0.799862\pi$
$152$	−6.14845	+	8.46262i	−0.498705	+	0.686409i
$153$		0			0
$154$	2.34847	−	9.95448i	0.189245	−	0.802155i
$155$	−6.52400	+	3.76663i	−0.524021	+	0.302543i
$156$		0			0
$157$	2.19583	+	2.43872i	0.175246	+	0.194631i	0.824369	−	0.566053i	$-0.191530\pi$
$157$	2.19583	+	2.43872i	0.175246	+	0.194631i	−0.649122	+	0.760684i	$0.724864\pi$
$158$	−2.71128	+	12.7556i	−0.215698	+	1.01478i
$159$		0			0
$160$	4.91082	−	11.0299i	0.388234	−	0.871988i
$161$	−0.0344344	−	0.105978i	−0.00271381	−	0.00835225i
$162$		0			0
$163$	−7.00394	−	5.08866i	−0.548591	−	0.398575i	0.278675	−	0.960386i	$-0.410105\pi$
$163$	−7.00394	−	5.08866i	−0.548591	−	0.398575i	−0.827266	+	0.561811i	$0.810105\pi$
$164$	−7.90072	−	13.6844i	−0.616942	−	1.06858i
$165$		0			0
$166$	1.47914	−	2.56194i	0.114803	−	0.198845i
$167$	−18.1258	+	8.07010i	−1.40261	+	0.624483i	−0.961959	−	0.273194i	$-0.911920\pi$
$167$	−18.1258	+	8.07010i	−1.40261	+	0.624483i	−0.440654	+	0.897677i	$0.645253\pi$
$168$		0			0
$169$	−14.6660	+	16.2883i	−1.12816	+	1.25294i
$170$	15.3138	+	21.0776i	1.17451	+	1.61658i
$171$		0			0
$172$	−11.2544	+	3.65679i	−0.858143	+	0.278828i
$173$	−6.83074	+	1.45192i	−0.519331	+	0.110387i	−0.460118	−	0.887858i	$-0.652193\pi$
$173$	−6.83074	+	1.45192i	−0.519331	+	0.110387i	−0.0592139	+	0.998245i	$0.518859\pi$
$174$		0			0
$175$	4.02848	+	2.32584i	0.304524	+	0.175817i
$176$	−4.00399	+	0.758405i	−0.301812	+	0.0571669i
$177$		0			0
$178$	−31.7243	−	3.33435i	−2.37783	−	0.249920i
$179$	−14.8154	−	4.81380i	−1.10735	−	0.359800i	−0.302424	−	0.953173i	$-0.597796\pi$
$179$	−14.8154	−	4.81380i	−1.10735	−	0.359800i	−0.804928	+	0.593373i	$0.797796\pi$
$180$		0			0
$181$	−13.0927	+	9.51241i	−0.973173	+	0.707052i	−0.956173	−	0.292804i	$-0.905412\pi$
$181$	−13.0927	+	9.51241i	−0.973173	+	0.707052i	−0.0170005	+	0.999855i	$0.505412\pi$
$182$	−16.6471	−	7.41177i	−1.23397	−	0.549397i
$183$		0			0
$184$	−0.220740	+	0.198755i	−0.0162732	+	0.0146524i
$185$	−8.14449	−	18.2928i	−0.598795	−	1.34492i
$186$		0			0
$187$	−4.16441	+	11.9087i	−0.304532	+	0.870847i
$188$		−	16.6103i		−	1.21143i
$189$		0			0
$190$	6.31403	−	19.4326i	0.458068	−	1.40979i
$191$	10.9393	+	9.84977i	0.791538	+	0.712704i	0.962116	−	0.272640i	$-0.0878968\pi$
$191$	10.9393	+	9.84977i	0.791538	+	0.712704i	−0.170578	+	0.985344i	$0.554564\pi$
$192$		0			0
$193$	−6.81432	+	0.716214i	−0.490506	+	0.0515542i	−0.346553	−	0.938030i	$-0.612648\pi$
$193$	−6.81432	+	0.716214i	−0.490506	+	0.0515542i	−0.143953	+	0.989585i	$0.545981\pi$
$194$	31.5820	+	6.71295i	2.26745	+	0.481962i
$195$		0			0
$196$	−1.92554	+	18.3203i	−0.137539	+	1.30859i
$197$	8.81639			0.628141			0.314071	−	0.949400i	$-0.398307\pi$
$197$	8.81639			0.628141			0.314071	+	0.949400i	$0.398307\pi$
$198$		0			0
$199$	8.40540			0.595843			0.297921	−	0.954590i	$-0.403707\pi$
$199$	8.40540			0.595843			0.297921	+	0.954590i	$0.403707\pi$
$200$	1.29611	−	12.3317i	0.0916490	−	0.871982i
$201$		0			0
$202$	28.6689	+	6.09375i	2.01713	+	0.428755i
$203$	5.76068	−	0.605472i	0.404321	−	0.0424958i
$204$		0			0
$205$	9.81440	+	8.83693i	0.685468	+	0.617198i
$206$	4.33646	−	13.3462i	0.302135	−	0.929877i
$207$		0			0
$208$			7.26065i			0.503435i
$209$	9.47549	−	2.84738i	0.655433	−	0.196957i
$210$		0			0
$211$	7.08524	+	15.9137i	0.487768	+	1.09555i	0.974986	+	0.222265i	$0.0713450\pi$
$211$	7.08524	+	15.9137i	0.487768	+	1.09555i	−0.487218	+	0.873280i	$0.661988\pi$
$212$	10.8824	−	9.79854i	0.747405	−	0.672967i
$213$		0			0
$214$	6.59412	+	2.93589i	0.450765	+	0.200693i
$215$	8.00146	−	5.81340i	0.545695	−	0.396471i
$216$		0			0
$217$	−3.22573	−	1.04810i	−0.218977	−	0.0711499i
$218$	23.2861	+	2.44746i	1.57713	+	0.165763i
$219$		0			0
$220$	29.7053	−	16.2804i	2.00273	−	1.09762i
$221$	19.4659	+	11.2386i	1.30942	+	0.755992i
$222$		0			0
$223$	−16.7641	+	3.56332i	−1.12261	+	0.238618i	−0.731577	−	0.681759i	$-0.761215\pi$
$223$	−16.7641	+	3.56332i	−1.12261	+	0.238618i	−0.391032	+	0.920377i	$0.627882\pi$
$224$	5.16993	−	1.67981i	0.345431	−	0.112237i
$225$		0			0
$226$	6.49597	+	8.94094i	0.432106	+	0.594742i
$227$	−11.5707	+	12.8506i	−0.767976	+	0.852924i	−0.992588	−	0.121524i	$-0.961222\pi$
$227$	−11.5707	+	12.8506i	−0.767976	+	0.852924i	0.224612	+	0.974448i	$0.427888\pi$
$228$		0			0
$229$	14.4376	−	6.42803i	0.954063	−	0.424776i	0.130151	−	0.991494i	$-0.458454\pi$
$229$	14.4376	−	6.42803i	0.954063	−	0.424776i	0.823912	+	0.566718i	$0.191787\pi$
$230$	0.290105	−	0.502476i	0.0191290	−	0.0331323i
$231$		0			0
$232$	−7.72018	−	13.3718i	−0.506855	−	0.877898i
$233$	−2.75423	−	2.00107i	−0.180436	−	0.131094i	0.493901	−	0.869518i	$-0.335570\pi$
$233$	−2.75423	−	2.00107i	−0.180436	−	0.131094i	−0.674337	+	0.738424i	$0.735570\pi$
$234$		0			0
$235$	4.28995	+	13.2031i	0.279846	+	0.861276i
$236$	−19.9582	+	44.8269i	−1.29917	+	2.91798i
$237$		0			0
$238$	−2.43883	+	11.4738i	−0.158086	+	0.743735i
$239$	3.88504	+	4.31478i	0.251302	+	0.279100i	0.855576	−	0.517677i	$-0.173203\pi$
$239$	3.88504	+	4.31478i	0.251302	+	0.279100i	−0.604273	+	0.796777i	$0.706537\pi$
$240$		0			0
$241$	2.60691	−	1.50510i	0.167926	−	0.0969521i	−0.413681	−	0.910422i	$-0.635757\pi$
$241$	2.60691	−	1.50510i	0.167926	−	0.0969521i	0.581608	+	0.813470i	$0.302424\pi$
$242$	23.0681	+	11.5260i	1.48287	+	0.740918i
$243$		0			0
$244$	20.1765	−	27.7706i	1.29167	−	1.77783i
$245$	−3.20104	−	15.0597i	−0.204507	−	0.962129i
$246$		0			0
$247$	−1.84263	−	17.5314i	−0.117244	−	1.11550i
$248$	0.945049	+	8.99154i	0.0600106	+	0.570963i
$249$		0			0
$250$	−2.08449	−	9.80676i	−0.131835	−	0.620234i
$251$	9.41803	−	12.9628i	0.594461	−	0.818205i	−0.400726	−	0.916198i	$-0.631242\pi$
$251$	9.41803	−	12.9628i	0.594461	−	0.818205i	0.995187	+	0.0979925i	$0.0312421\pi$
$252$		0			0
$253$	0.279999	−	0.0231455i	0.0176034	−	0.00145514i
$254$	6.05175	−	3.49398i	0.379721	−	0.219232i
$255$		0			0
$256$	−15.4441	−	17.1524i	−0.965254	−	1.07202i
$257$	−2.58695	+	12.1706i	−0.161369	+	0.759183i	0.820805	+	0.571209i	$0.193525\pi$
$257$	−2.58695	+	12.1706i	−0.161369	+	0.759183i	−0.982174	+	0.187974i	$0.939808\pi$
$258$		0			0
$259$	3.66693	−	8.23605i	0.227852	−	0.511763i
$260$	−18.6500	−	57.3988i	−1.15662	−	3.55972i
$261$		0			0
$262$	14.7649	+	10.7273i	0.912178	+	0.662736i
$263$	−7.64365	−	13.2392i	−0.471328	−	0.816363i	0.528134	−	0.849161i	$-0.322892\pi$
$263$	−7.64365	−	13.2392i	−0.471328	−	0.816363i	−0.999462	+	0.0327974i	$0.989558\pi$
$264$		0			0
$265$	−6.11948	+	10.5992i	−0.375917	+	0.651107i
$266$	8.40412	−	3.74176i	0.515290	−	0.229422i
$267$		0			0
$268$	−8.85150	+	9.83059i	−0.540692	+	0.600499i
$269$	1.18129	+	1.62591i	0.0720247	+	0.0991335i	0.843509	−	0.537114i	$-0.180486\pi$
$269$	1.18129	+	1.62591i	0.0720247	+	0.0991335i	−0.771485	+	0.636248i	$0.780486\pi$
$270$		0			0
$271$	−20.2438	+	6.57759i	−1.22972	+	0.399560i	−0.850613	−	0.525792i	$-0.823769\pi$
$271$	−20.2438	+	6.57759i	−1.22972	+	0.399560i	−0.379107	+	0.925353i	$0.623769\pi$
$272$	4.57165	−	0.971735i	0.277197	−	0.0589201i
$273$		0			0
$274$	12.7537	+	7.36333i	0.770477	+	0.444835i
$275$	−8.03970	+	8.53913i	−0.484812	+	0.514929i
$276$		0			0
$277$	−24.5518	−	2.58049i	−1.47517	−	0.155047i	−0.667469	−	0.744637i	$-0.732623\pi$
$277$	−24.5518	−	2.58049i	−1.47517	−	0.155047i	−0.807702	+	0.589590i	$0.799289\pi$
$278$	−1.16948	−	0.379987i	−0.0701407	−	0.0227901i
$279$		0			0
$280$	10.9026	−	7.92121i	0.651555	−	0.473383i
$281$	−11.8982	−	5.29740i	−0.709785	−	0.316017i	0.0198983	−	0.999802i	$-0.493666\pi$
$281$	−11.8982	−	5.29740i	−0.709785	−	0.316017i	−0.729683	+	0.683785i	$0.760332\pi$
$282$		0			0
$283$	−14.6910	+	13.2278i	−0.873287	+	0.786311i	−0.978090	−	0.208182i	$-0.933245\pi$
$283$	−14.6910	+	13.2278i	−0.873287	+	0.786311i	0.104803	+	0.994493i	$0.466579\pi$
$284$	6.31421	+	14.1820i	0.374680	+	0.841544i
$285$		0			0
$286$	27.8256	−	36.5601i	1.64536	−	2.16184i
$287$			5.94605i			0.350984i
$288$		0			0
$289$	−0.782142	+	2.40719i	−0.0460084	+	0.141599i
$290$	22.4134	+	20.1811i	1.31616	+	1.18508i
$291$		0			0
$292$	−30.3615	+	3.19112i	−1.77677	+	0.186746i
$293$	4.33566	+	0.921573i	0.253292	+	0.0538389i	0.332808	−	0.942995i	$-0.392004\pi$
$293$	4.33566	+	0.921573i	0.253292	+	0.0538389i	−0.0795156	+	0.996834i	$0.525337\pi$
$294$		0			0
$295$	4.28684	−	40.7865i	0.249589	−	2.37468i
$296$	−24.0318			−1.39682
$297$		0			0
$298$	−22.5438			−1.30593
$299$	0.0523237	−	0.497827i	0.00302596	−	0.0287901i
$300$		0			0
$301$	4.35566	+	0.925824i	0.251056	+	0.0533636i
$302$	−23.3283	+	2.45190i	−1.34239	+	0.141091i
$303$		0			0
$304$	−2.72397	−	2.45267i	−0.156230	−	0.140670i
$305$	−8.86552	+	27.2853i	−0.507638	+	1.56235i
$306$		0			0
$307$			11.0942i			0.633182i	0.948562	+	0.316591i	$0.102538\pi$
$307$			11.0942i			0.633182i	−0.948562	+	0.316591i	$0.897462\pi$
$308$	14.3964	+	5.03437i	0.820312	+	0.286860i
$309$		0			0
$310$	−7.18307	−	16.1334i	−0.407971	−	0.916317i
$311$	5.83088	−	5.25015i	0.330639	−	0.297709i	−0.487044	−	0.873377i	$-0.661925\pi$
$311$	5.83088	−	5.25015i	0.330639	−	0.297709i	0.817683	+	0.575669i	$0.195258\pi$
$312$		0			0
$313$	29.5491	+	13.1561i	1.67021	+	0.743627i	0.999999	+	0.00146091i	$0.000465022\pi$
$313$	29.5491	+	13.1561i	1.67021	+	0.743627i	0.670216	+	0.742166i	$0.266202\pi$
$314$	−6.22384	+	4.52188i	−0.351232	+	0.255185i
$315$		0			0
$316$	−18.4939	−	6.00902i	−1.04036	−	0.338034i
$317$	−11.9644	−	1.25751i	−0.671988	−	0.0706288i	−0.237612	−	0.971360i	$-0.576365\pi$
$317$	−11.9644	−	1.25751i	−0.671988	−	0.0706288i	−0.434377	+	0.900731i	$0.643031\pi$
$318$		0			0
$319$	−1.84927	+	14.4869i	−0.103539	+	0.811110i
$320$	30.7302	+	17.7421i	1.71787	+	0.991813i
$321$		0			0
$322$	0.255522	−	0.0543128i	0.0142397	−	0.00302673i
$323$	−10.7920	+	3.50654i	−0.600484	+	0.195109i
$324$		0			0
$325$	12.2824	+	16.9053i	0.681305	+	0.937735i
$326$	13.5803	−	15.0824i	0.752143	−	0.835339i
$327$		0			0
$328$	14.4796	−	6.44673i	0.799502	−	0.355961i
$329$	−3.12520	+	5.41301i	−0.172298	+	0.298429i
$330$		0			0
$331$	15.0373	+	26.0453i	0.826524	+	1.43158i	0.900749	+	0.434340i	$0.143018\pi$
$331$	15.0373	+	26.0453i	0.826524	+	1.43158i	−0.0742249	+	0.997242i	$0.523648\pi$
$332$	3.56880	+	2.59289i	0.195863	+	0.142303i
$333$		0			0
$334$	−14.3735	−	44.2370i	−0.786481	−	2.42054i
$335$	4.49690	−	10.1002i	0.245692	−	0.551833i
$336$		0			0
$337$	4.57335	−	21.5159i	0.249126	−	1.17205i	−0.658603	−	0.752490i	$-0.728853\pi$
$337$	4.57335	−	21.5159i	0.249126	−	1.17205i	0.907730	−	0.419556i	$-0.137814\pi$
$338$	−34.3815	−	38.1846i	−1.87011	−	2.07697i
$339$		0			0
$340$	−33.6450	+	19.4250i	−1.82466	+	1.05347i
$341$	4.43947	−	7.30896i	0.240411	−	0.395802i
$342$		0			0
$343$	9.48682	−	13.0575i	0.512240	−	0.705038i
$344$	−2.46789	−	11.6105i	−0.133060	−	0.625998i
$345$		0			0
$346$	−1.71124	−	16.2814i	−0.0919968	−	0.875291i
$347$	1.58495	+	15.0798i	0.0850847	+	0.809527i	0.950970	+	0.309284i	$0.100089\pi$
$347$	1.58495	+	15.0798i	0.0850847	+	0.809527i	−0.865885	+	0.500243i	$0.833244\pi$
$348$		0			0
$349$	3.90788	+	18.3851i	0.209184	+	0.984133i	0.949958	+	0.312379i	$0.101126\pi$
$349$	3.90788	+	18.3851i	0.209184	+	0.984133i	−0.740774	+	0.671755i	$0.765541\pi$
$350$	−6.40977	+	8.82229i	−0.342616	+	0.471571i
$351$		0			0
$352$	1.12910	+	13.6592i	0.0601815	+	0.728037i
$353$	−7.65781	+	4.42124i	−0.407584	+	0.235319i	−0.689751	−	0.724046i	$-0.742280\pi$
$353$	−7.65781	+	4.42124i	−0.407584	+	0.235319i	0.282167	+	0.959365i	$0.408947\pi$
$354$		0			0
$355$	−8.68182	−	9.64213i	−0.460783	−	0.511751i
$356$	9.88967	−	46.5273i	0.524152	−	2.46594i
$357$		0			0
$358$	14.8536	−	33.3618i	0.785038	−	1.76322i
$359$	5.57195	+	17.1487i	0.294076	+	0.905074i	0.983530	+	0.180744i	$0.0578507\pi$
$359$	5.57195	+	17.1487i	0.294076	+	0.905074i	−0.689454	+	0.724330i	$0.742149\pi$
$360$		0			0
$361$	−8.17163	−	5.93703i	−0.430086	−	0.312476i
$362$	−18.9695	−	32.8561i	−0.997012	−	1.72688i
$363$		0			0
$364$	13.5864	−	23.5324i	0.712122	−	1.23343i
$365$	23.3095	−	10.3780i	1.22007	−	0.543212i
$366$		0			0
$367$	20.9560	−	23.2740i	1.09390	−	1.21489i	0.118845	−	0.992913i	$-0.462081\pi$
$367$	20.9560	−	23.2740i	1.09390	−	1.21489i	0.975051	−	0.221982i	$-0.0712525\pi$
$368$	−0.0611798	−	0.0842068i	−0.00318922	−	0.00438958i
$369$		0			0
$370$	44.6447	−	14.5059i	2.32097	−	0.754128i
$371$	−5.38998	+	1.14567i	−0.279834	+	0.0594805i
$372$		0			0
$373$	2.91679	+	1.68401i	0.151026	+	0.0871948i	0.573609	−	0.819130i	$-0.305543\pi$
$373$	2.91679	+	1.68401i	0.151026	+	0.0871948i	−0.422583	+	0.906324i	$0.638876\pi$
$374$	−26.7440	−	12.6273i	−1.38290	−	0.652942i
$375$		0			0
$376$	16.5699	+	1.74157i	0.854529	+	0.0898146i
$377$	24.7469	+	8.04074i	1.27453	+	0.414119i
$378$		0			0
$379$	−19.5313	+	14.1903i	−1.00326	+	0.728908i	−0.962784	−	0.270273i	$-0.912886\pi$
$379$	−19.5313	+	14.1903i	−1.00326	+	0.728908i	−0.0404716	+	0.999181i	$0.512886\pi$
$380$	27.8343	+	12.3926i	1.42787	+	0.635728i
$381$		0			0
$382$	−25.6449	+	23.0908i	−1.31211	+	1.18143i
$383$	3.68064	+	8.26684i	0.188072	+	0.422416i	0.982831	−	0.184509i	$-0.0590695\pi$
$383$	3.68064	+	8.26684i	0.188072	+	0.422416i	−0.794759	+	0.606925i	$0.792403\pi$
$384$		0			0
$385$	−12.7436	−	0.283524i	−0.649475	−	0.0144497i
$386$		−	16.0628i		−	0.817575i
$387$		0			0
$388$	−14.8779	+	45.7896i	−0.755313	+	2.32461i
$389$	−19.3868	−	17.4559i	−0.982948	−	0.885050i	0.0104299	−	0.999946i	$-0.496680\pi$
$389$	−19.3868	−	17.4559i	−0.982948	−	0.885050i	−0.993378	+	0.114896i	$0.963347\pi$
$390$		0			0
$391$	−0.320459	+	0.0336815i	−0.0162063	+	0.00170335i
$392$	−18.0739	−	3.84173i	−0.912871	−	0.194037i
$393$		0			0
$394$	−2.16042	+	20.5550i	−0.108840	+	1.03555i
$395$	16.2523			0.817742
$396$		0			0
$397$	19.8829			0.997896			0.498948	−	0.866632i	$-0.333720\pi$
$397$	19.8829			0.997896			0.498948	+	0.866632i	$0.333720\pi$
$398$	−2.05971	+	19.5968i	−0.103244	+	0.982300i
$399$		0			0
$400$	4.25005	+	0.903376i	0.212503	+	0.0451688i
$401$	−9.88172	+	1.03861i	−0.493470	+	0.0518658i	−0.347995	−	0.937496i	$-0.613137\pi$
$401$	−9.88172	+	1.03861i	−0.493470	+	0.0518658i	−0.145474	+	0.989362i	$0.546471\pi$
$402$		0			0
$403$	−11.3227	−	10.1950i	−0.564023	−	0.507848i
$404$	−13.5056	+	41.5660i	−0.671929	+	2.06799i
$405$		0			0
$406$			13.5792i			0.673922i
$407$	18.0879	+	13.7665i	0.896582	+	0.682382i
$408$		0			0
$409$	0.000627409		0.00140918i	3.10234e−5		6.96796e-5i	0.913561	−	0.406702i	$-0.133321\pi$
$409$	0.000627409		0.00140918i	3.10234e−5		6.96796e-5i	−0.913530	+	0.406771i	$0.866655\pi$
$410$	−23.0079	+	20.7164i	−1.13628	+	1.02311i
$411$		0			0
$412$	19.1165	+	8.51122i	0.941803	+	0.419318i
$413$	14.9382	−	10.8532i	0.735061	−	0.534053i
$414$		0			0
$415$	−3.50643	−	1.13931i	−0.172124	−	0.0559264i
$416$	24.2855	+	2.55251i	1.19069	+	0.125147i
$417$		0			0
$418$	4.31660	+	22.7894i	0.211132	+	1.11467i
$419$	−13.3723	−	7.72050i	−0.653279	−	0.377171i	0.136432	−	0.990649i	$-0.456436\pi$
$419$	−13.3723	−	7.72050i	−0.653279	−	0.377171i	−0.789711	+	0.613478i	$0.789770\pi$
$420$		0			0
$421$	−23.9785	+	5.09679i	−1.16864	+	0.248403i	−0.751058	−	0.660236i	$-0.770456\pi$
$421$	−23.9785	+	5.09679i	−1.16864	+	0.248403i	−0.417584	+	0.908638i	$0.637123\pi$
$422$	−38.8383	+	12.6193i	−1.89062	+	0.614300i
$423$		0			0
$424$	8.63374	+	11.8833i	0.419292	+	0.577105i
$425$	9.00054	−	9.99611i	0.436590	−	0.484883i
$426$		0			0
$427$	−11.8002	+	5.25380i	−0.571053	+	0.254249i
$428$	−5.38174	+	9.32145i	−0.260136	+	0.450569i
$429$		0			0
$430$	11.5930	+	20.0796i	0.559062	+	0.968324i
$431$	9.71012	+	7.05482i	0.467720	+	0.339818i	0.796552	−	0.604570i	$-0.206655\pi$
$431$	9.71012	+	7.05482i	0.467720	+	0.339818i	−0.328832	+	0.944388i	$0.606655\pi$
$432$		0			0
$433$	0.277208	+	0.853159i	0.0133218	+	0.0410002i	0.957496	−	0.288445i	$-0.0931383\pi$
$433$	0.277208	+	0.853159i	0.0133218	+	0.0410002i	−0.944175	+	0.329445i	$0.893138\pi$
$434$	3.23406	−	7.26382i	0.155240	−	0.348674i
$435$		0			0
$436$	−7.25916	+	34.1517i	−0.347651	+	1.63557i
$437$	0.169094	+	0.187798i	0.00808887	+	0.00898360i
$438$		0			0
$439$	3.76825	−	2.17560i	0.179849	−	0.103836i	−0.407373	−	0.913262i	$-0.633555\pi$
$439$	3.76825	−	2.17560i	0.179849	−	0.103836i	0.587222	+	0.809426i	$0.300222\pi$
$440$	13.1263	+	31.3402i	0.625770	+	1.49408i
$441$		0			0
$442$	−30.9724	+	42.6299i	−1.47321	+	2.02770i
$443$	−7.99334	−	37.6057i	−0.379775	−	1.78670i	−0.588256	−	0.808675i	$-0.700185\pi$
$443$	−7.99334	−	37.6057i	−0.379775	−	1.78670i	0.208480	−	0.978027i	$-0.433148\pi$
$444$		0			0
$445$	4.15558	+	39.5377i	0.196993	+	1.87427i
$446$	−4.19976	−	39.9580i	−0.198864	−	1.89207i
$447$		0			0
$448$	3.32163	+	15.6271i	0.156932	+	0.738309i
$449$	10.6492	−	14.6573i	0.502566	−	0.691723i	−0.480078	−	0.877226i	$-0.659392\pi$
$449$	10.6492	−	14.6573i	0.502566	−	0.691723i	0.982644	+	0.185503i	$0.0593916\pi$
$450$		0			0
$451$	−14.5912	−	3.44237i	−0.687075	−	0.162095i
$452$	−14.2719	+	8.23989i	−0.671294	+	0.387572i
$453$		0			0
$454$	−27.1253	−	30.1256i	−1.27305	−	1.41387i
$455$	−4.72180	+	22.2143i	−0.221361	+	1.04142i
$456$		0			0
$457$	−13.0983	+	29.4192i	−0.612711	+	1.37617i	0.294563	+	0.955632i	$0.404826\pi$
$457$	−13.0983	+	29.4192i	−0.612711	+	1.37617i	−0.907274	+	0.420540i	$0.861841\pi$
$458$	11.4488	+	35.2358i	0.534967	+	1.64646i
$459$		0			0
$460$	0.699953	+	0.508545i	0.0326355	+	0.0237111i
$461$	19.5476	+	33.8574i	0.910420	+	1.57689i	0.813471	+	0.581605i	$0.197575\pi$
$461$	19.5476	+	33.8574i	0.910420	+	1.57689i	0.0969489	+	0.995289i	$0.469092\pi$
$462$		0			0
$463$	8.51825	−	14.7540i	0.395877	−	0.685679i	−0.597336	−	0.801991i	$-0.703774\pi$
$463$	8.51825	−	14.7540i	0.395877	−	0.685679i	0.993213	+	0.116313i	$0.0371074\pi$
$464$	4.94276	−	2.20066i	0.229462	−	0.102163i
$465$		0			0
$466$	5.34032	−	5.93102i	0.247385	−	0.274749i
$467$	−13.3070	−	18.3156i	−0.615776	−	0.847543i	0.381261	−	0.924468i	$-0.375490\pi$
$467$	−13.3070	−	18.3156i	−0.615776	−	0.847543i	−0.997037	+	0.0769242i	$0.975490\pi$
$468$		0			0
$469$	4.73418	−	1.53823i	0.218604	−	0.0710287i
$470$	−31.8337	+	6.76647i	−1.46838	+	0.312114i
$471$		0			0
$472$	−42.6255	−	24.6098i	−1.96200	−	1.13276i
$473$	−4.79356	+	10.1525i	−0.220408	+	0.466814i
$474$		0			0
$475$	−10.4914	−	1.10269i	−0.481377	−	0.0505947i
$476$	−16.6355	−	5.40519i	−0.762485	−	0.247746i
$477$		0			0
$478$	−11.0117	+	8.00049i	−0.503665	+	0.365934i
$479$	12.4237	+	5.53139i	0.567654	+	0.252736i	0.670435	−	0.741968i	$-0.266107\pi$
$479$	12.4237	+	5.53139i	0.567654	+	0.252736i	−0.102781	+	0.994704i	$0.532774\pi$
$480$		0			0
$481$	30.0965	−	27.0990i	1.37228	−	1.23561i
$482$	2.87027	+	6.44673i	0.130737	+	0.293640i
$483$		0			0
$484$	−20.6886	+	32.4133i	−0.940391	+	1.47333i
$485$		−	40.2397i		−	1.82719i
$486$		0			0
$487$	2.70549	−	8.32664i	0.122597	−	0.377316i	−0.870858	−	0.491534i	$-0.836436\pi$
$487$	2.70549	−	8.32664i	0.122597	−	0.377316i	0.993456	+	0.114218i	$0.0364362\pi$
$488$	25.5877	+	23.0393i	1.15830	+	1.04294i
$489$		0			0
$490$	35.8954	−	3.77276i	1.62159	−	0.170436i
$491$	−32.8423	−	6.98084i	−1.48215	−	0.315041i	−0.605376	−	0.795940i	$-0.706977\pi$
$491$	−32.8423	−	6.98084i	−1.48215	−	0.315041i	−0.876776	+	0.480899i	$0.840310\pi$
$492$		0			0
$493$	1.75082	−	16.6579i	0.0788530	−	0.750236i
$494$	41.3253			1.85931
$495$		0			0
$496$	−3.16812			−0.142253
$497$	0.610622	−	5.80968i	0.0273901	−	0.260600i
$498$		0			0
$499$	−2.19779	−	0.467155i	−0.0983866	−	0.0209127i	0.158455	−	0.987366i	$-0.449349\pi$
$499$	−2.19779	−	0.467155i	−0.0983866	−	0.0209127i	−0.256842	+	0.966453i	$0.582682\pi$
$500$	14.8683	−	1.56272i	0.664931	−	0.0698871i
$501$		0			0
$502$	27.9144	+	25.1342i	1.24588	+	1.12180i
$503$	−5.15181	+	15.8556i	−0.229708	+	0.706968i	0.768072	+	0.640364i	$0.221216\pi$
$503$	−5.15181	+	15.8556i	−0.229708	+	0.706968i	−0.997779	+	0.0666040i	$0.978784\pi$
$504$		0			0
$505$		−	36.5280i		−	1.62547i
$506$	−0.0146500	+	0.658478i	−0.000651274	+	0.0292729i
$507$		0			0
$508$	4.23828	+	9.51933i	0.188043	+	0.422352i
$509$	−7.78076	+	7.00582i	−0.344876	+	0.310528i	−0.823306	−	0.567598i	$-0.807873\pi$
$509$	−7.78076	+	7.00582i	−0.344876	+	0.310528i	0.478430	+	0.878126i	$0.341206\pi$
$510$		0			0
$511$	10.4947	+	4.67255i	0.464259	+	0.206701i
$512$	11.0790	−	8.04940i	0.489629	−	0.355737i
$513$		0			0
$514$	−27.7414	−	9.01372i	−1.22362	−	0.397578i
$515$	−17.3935	−	1.82813i	−0.766449	−	0.0805570i
$516$		0			0
$517$	−11.4739	−	10.8028i	−0.504622	−	0.475108i
$518$	18.3034	+	10.5675i	0.804207	+	0.464309i
$519$		0			0
$520$	59.2149	−	12.5865i	2.59674	−	0.551955i
$521$	−5.99155	+	1.94677i	−0.262494	+	0.0852896i	−0.437308	−	0.899312i	$-0.644068\pi$
$521$	−5.99155	+	1.94677i	−0.262494	+	0.0852896i	0.174813	+	0.984602i	$0.444068\pi$
$522$		0			0
$523$	−12.7364	−	17.5301i	−0.556923	−	0.766538i	0.434008	−	0.900909i	$-0.357099\pi$
$523$	−12.7364	−	17.5301i	−0.556923	−	0.766538i	−0.990931	+	0.134370i	$0.957099\pi$
$524$	−18.2100	+	20.2242i	−0.795506	+	0.883499i
$525$		0			0
$526$	32.7396	−	14.5766i	1.42752	−	0.635571i
$527$	−4.90387	+	8.49375i	−0.213616	+	0.369994i
$528$		0			0
$529$	−11.4964	−	19.9124i	−0.499844	−	0.865755i
$530$	−23.2121	−	16.8646i	−1.00827	−	0.732551i
$531$		0			0
$532$	4.23907	+	13.0465i	0.183787	+	0.565638i
$533$	−10.8641	+	24.4013i	−0.470579	+	1.05694i
$534$		0			0
$535$	1.87036	−	8.79936i	0.0808628	−	0.380429i
$536$	−8.87865	−	9.86074i	−0.383499	−	0.425919i
$537$		0			0
$538$	−4.08021	+	2.35571i	−0.175910	+	0.101562i
$539$	11.4028	+	13.2451i	0.491155	+	0.570507i
$540$		0			0
$541$	13.1964	−	18.1633i	0.567357	−	0.780899i	−0.424882	−	0.905249i	$-0.639684\pi$
$541$	13.1964	−	18.1633i	0.567357	−	0.780899i	0.992238	+	0.124349i	$0.0396844\pi$
$542$	−10.3747	−	48.8093i	−0.445633	−	2.09654i
$543$		0			0
$544$	−1.64309	−	15.6329i	−0.0704467	−	0.670256i
$545$	−3.05025	−	29.0212i	−0.130659	−	1.24313i
$546$		0			0
$547$	4.87105	+	22.9165i	0.208271	+	0.979839i	0.950748	+	0.309966i	$0.100318\pi$
$547$	4.87105	+	22.9165i	0.208271	+	0.979839i	−0.742476	+	0.669872i	$0.766349\pi$
$548$	−12.9077	+	17.7659i	−0.551390	+	0.758923i
$549$		0			0
$550$	−17.9385	−	20.8367i	−0.764901	−	0.888480i
$551$	−11.3762	+	6.56806i	−0.484643	+	0.279809i
$552$		0			0
$553$	4.89626	+	5.43784i	0.208210	+	0.231241i
$554$	12.0326	−	56.6090i	0.511217	−	2.40509i
$555$		0			0
$556$	0.745805	−	1.67511i	0.0316292	−	0.0710403i
$557$	1.09525	+	3.37084i	0.0464074	+	0.142827i	0.971575	−	0.236731i	$-0.0760760\pi$
$557$	1.09525	+	3.37084i	0.0464074	+	0.142827i	−0.925168	+	0.379558i	$0.876076\pi$
$558$		0			0
$559$	16.1831	+	11.7577i	0.684471	+	0.497297i
$560$	2.36115	+	4.08964i	0.0997770	+	0.172819i
$561$		0			0
$562$	15.2663	−	26.4419i	0.643968	−	1.11539i
$563$	16.8560	−	7.50476i	0.710394	−	0.316288i	−0.0195365	−	0.999809i	$-0.506219\pi$
$563$	16.8560	−	7.50476i	0.710394	−	0.316288i	0.729931	+	0.683521i	$0.239552\pi$
$564$		0			0
$565$	9.21629	−	10.2357i	0.387732	−	0.430620i
$566$	−27.2401	−	37.4927i	−1.14499	−	1.57594i
$567$		0			0
$568$	−14.8096	+	4.81192i	−0.621395	+	0.201904i
$569$	14.0177	−	2.97956i	0.587654	−	0.124910i	0.0955176	−	0.995428i	$-0.469549\pi$
$569$	14.0177	−	2.97956i	0.587654	−	0.124910i	0.492137	+	0.870518i	$0.336216\pi$
$570$		0			0
$571$	−34.7935	−	20.0880i	−1.45606	−	0.840658i	−0.457247	−	0.889340i	$-0.651165\pi$
$571$	−34.7935	−	20.0880i	−1.45606	−	0.840658i	−0.998814	+	0.0486820i	$0.984498\pi$
$572$	49.8813	+	46.9639i	2.08564	+	1.96366i
$573$		0			0
$574$	−13.8630	−	1.45706i	−0.578629	−	0.0608163i
$575$	−0.284895	−	0.0925680i	−0.0118809	−	0.00386035i
$576$		0			0
$577$	24.3026	−	17.6568i	1.01173	−	0.735064i	0.0471580	−	0.998887i	$-0.484984\pi$
$577$	24.3026	−	17.6568i	1.01173	−	0.735064i	0.964571	+	0.263823i	$0.0849836\pi$
$578$	−5.42059	−	2.41340i	−0.225467	−	0.100384i
$579$		0			0
$580$	−33.4221	+	30.0934i	−1.38778	+	1.24956i
$581$	−0.675165	−	1.51645i	−0.0280106	−	0.0629128i
$582$		0			0
$583$	0.309028	−	13.8899i	0.0127986	−	0.575263i
$584$		−	30.6223i		−	1.26716i
$585$		0			0
$586$	−3.21104	+	9.88258i	−0.132647	+	0.408246i
$587$	−9.08473	−	8.17993i	−0.374967	−	0.337622i	0.460003	−	0.887917i	$-0.347848\pi$
$587$	−9.08473	−	8.17993i	−0.374967	−	0.337622i	−0.834970	+	0.550296i	$0.814515\pi$
$588$		0			0
$589$	7.64968	−	0.804014i	0.315200	−	0.0331288i
$590$	94.0416	+	19.9892i	3.87163	+	0.822940i
$591$		0			0
$592$	0.880244	−	8.37496i	0.0361778	−	0.344209i
$593$	−26.0062			−1.06795			−0.533973	−	0.845502i	$-0.679301\pi$
$593$	−26.0062			−1.06795			−0.533973	+	0.845502i	$0.679301\pi$
$594$		0			0
$595$	14.6191			0.599327
$596$	3.51389	−	33.4324i	0.143935	−	1.36945i
$597$		0			0
$598$	1.14784	+	0.243981i	0.0469387	+	0.00997713i
$599$	16.4733	−	1.73141i	0.673081	−	0.0707437i	0.238179	−	0.971221i	$-0.423450\pi$
$599$	16.4733	−	1.73141i	0.673081	−	0.0707437i	0.434902	+	0.900478i	$0.356783\pi$
$600$		0			0
$601$	−24.7472	−	22.2825i	−1.00946	−	0.908920i	−0.0136061	−	0.999907i	$-0.504331\pi$
$601$	−24.7472	−	22.2825i	−1.00946	−	0.908920i	−0.995852	+	0.0909872i	$0.970998\pi$
$602$	−3.22586	+	9.92816i	−0.131476	+	0.404642i
$603$		0			0
$604$		−	34.9779i		−	1.42323i
$605$	8.07347	−	31.1079i	0.328233	−	1.26472i
$606$		0			0
$607$	18.1403	+	40.7438i	0.736293	+	1.65374i	0.756541	+	0.653946i	$0.226888\pi$
$607$	18.1403	+	40.7438i	0.736293	+	1.65374i	−0.0202479	+	0.999795i	$0.506446\pi$
$608$	−9.16134	+	8.24891i	−0.371542	+	0.334537i
$609$		0			0
$610$	−61.4420	−	27.3557i	−2.48771	−	1.10760i
$611$	−22.7154	+	16.5037i	−0.918966	+	0.667668i
$612$		0			0
$613$	−11.7116	−	3.80532i	−0.473026	−	0.153695i	0.0627963	−	0.998026i	$-0.479998\pi$
$613$	−11.7116	−	3.80532i	−0.473026	−	0.153695i	−0.535822	+	0.844331i	$0.679998\pi$
$614$	−25.8657	−	2.71860i	−1.04386	−	0.109714i
$615$		0			0
$616$	−6.53159	+	13.8336i	−0.263165	+	0.557372i
$617$	13.5088	+	7.79934i	0.543846	+	0.313989i	0.746636	−	0.665233i	$-0.231668\pi$
$617$	13.5088	+	7.79934i	0.543846	+	0.313989i	−0.202790	+	0.979222i	$0.565001\pi$
$618$		0			0
$619$	36.1986	−	7.69425i	1.45494	−	0.309258i	0.588486	−	0.808507i	$-0.299724\pi$
$619$	36.1986	−	7.69425i	1.45494	−	0.309258i	0.866458	+	0.499250i	$0.166391\pi$
$620$	25.0455	−	8.13776i	1.00585	−	0.326820i
$621$		0			0
$622$	10.8117	+	14.8810i	0.433508	+	0.596673i
$623$	−11.9769	+	13.3017i	−0.479846	+	0.532923i
$624$		0			0
$625$	−27.5674	+	12.2738i	−1.10269	+	0.490951i
$626$	−37.9138	+	65.6686i	−1.51534	+	2.62465i
$627$		0			0
$628$	−5.73584	−	9.93476i	−0.228885	−	0.396440i
$629$	−21.0908	−	15.3234i	−0.840947	−	0.610984i
$630$		0			0
$631$	13.3328	+	41.0343i	0.530772	+	1.63355i	0.752611	+	0.658465i	$0.228794\pi$
$631$	13.3328	+	41.0343i	0.530772	+	1.63355i	−0.221840	+	0.975083i	$0.571206\pi$
$632$	7.93349	−	17.8189i	0.315577	−	0.708798i
$633$		0			0
$634$	5.86366	−	27.5864i	0.232876	−	1.09559i
$635$	−5.82748	−	6.47208i	−0.231257	−	0.256836i
$636$		0			0
$637$	26.9671	−	15.5695i	1.06848	−	0.616885i
$638$	−33.3224	−	7.86144i	−1.31925	−	0.311238i
$639$		0			0
$640$	−34.7017	+	47.7629i	−1.37171	+	1.88799i
$641$	10.3254	+	48.5772i	0.407829	+	1.91868i	0.394796	+	0.918769i	$0.370815\pi$
$641$	10.3254	+	48.5772i	0.407829	+	1.91868i	0.0130324	+	0.999915i	$0.495852\pi$
$642$		0			0
$643$	−3.46705	−	32.9868i	−0.136727	−	1.30087i	−0.820698	−	0.571363i	$-0.806415\pi$
$643$	−3.46705	−	32.9868i	−0.136727	−	1.30087i	0.683970	−	0.729510i	$-0.260252\pi$
$644$	0.0407177	+	0.387404i	0.00160450	+	0.0152658i
$645$		0			0
$646$	−5.53081	−	26.0204i	−0.217607	−	1.02376i
$647$	25.8770	−	35.6166i	1.01733	−	1.40023i	0.103268	−	0.994654i	$-0.467070\pi$
$647$	25.8770	−	35.6166i	1.01733	−	1.40023i	0.914060	−	0.405578i	$-0.132930\pi$
$648$		0			0
$649$	17.9849	+	42.9407i	0.705970	+	1.68557i
$650$	−42.4236	+	24.4933i	−1.66399	+	0.960706i
$651$		0			0
$652$	20.2505	+	22.4904i	0.793069	+	0.880793i
$653$	−1.42386	+	6.69872i	−0.0557198	+	0.262141i	−0.997186	−	0.0749660i	$-0.976115\pi$
$653$	−1.42386	+	6.69872i	−0.0557198	+	0.262141i	0.941466	+	0.337107i	$0.109448\pi$
$654$		0			0
$655$	9.25136	−	20.7789i	0.361481	−	0.811899i
$656$	1.71629	+	5.28219i	0.0670098	+	0.206235i
$657$		0			0
$658$	−11.8544	−	8.61271i	−0.462132	−	0.335759i
$659$	−5.89894	−	10.2173i	−0.229790	−	0.398008i	0.727956	−	0.685624i	$-0.240471\pi$
$659$	−5.89894	−	10.2173i	−0.229790	−	0.398008i	−0.957746	+	0.287616i	$0.907137\pi$
$660$		0			0
$661$	−22.4153	+	38.8245i	−0.871855	+	1.51010i	−0.0117796	+	0.999931i	$0.503750\pi$
$661$	−22.4153	+	38.8245i	−0.871855	+	1.51010i	−0.860076	+	0.510167i	$0.829584\pi$
$662$	−64.4084	+	28.6765i	−2.50330	+	1.11454i
$663$		0			0
$664$	−2.96078	+	3.28827i	−0.114900	+	0.127610i
$665$	−6.73908	−	9.27555i	−0.261330	−	0.359690i
$666$		0			0
$667$	−0.354760	+	0.115268i	−0.0137364	+	0.00446321i
$668$	67.8437	−	14.4206i	2.62495	−	0.557950i
$669$		0			0
$670$	22.4462	+	12.9593i	0.867174	+	0.500663i
$671$	−6.06094	−	31.9986i	−0.233980	−	1.23529i
$672$		0			0
$673$	37.7995	+	3.97289i	1.45706	+	0.153144i	0.799687	−	0.600418i	$-0.204999\pi$
$673$	37.7995	+	3.97289i	1.45706	+	0.153144i	0.657378	+	0.753561i	$0.271666\pi$
$674$	49.0427	+	15.9349i	1.88906	+	0.613791i
$675$		0			0
$676$	61.9866	−	45.0359i	2.38410	−	1.73215i
$677$	24.5059	+	10.9107i	0.941837	+	0.419333i	0.819451	−	0.573150i	$-0.194279\pi$
$677$	24.5059	+	10.9107i	0.941837	+	0.419333i	0.122386	+	0.992483i	$0.460945\pi$
$678$		0			0
$679$	13.4637	−	12.1228i	0.516691	−	0.465231i
$680$	−15.8501	−	35.6000i	−0.607825	−	1.36520i
$681$		0			0
$682$	15.9526	+	12.1415i	0.610859	+	0.464920i
$683$			4.41371i			0.168886i	0.996428	+	0.0844429i	$0.0269111\pi$
$683$			4.41371i			0.168886i	−0.996428	+	0.0844429i	$0.973089\pi$
$684$		0			0
$685$	5.67161	−	17.4554i	0.216701	−	0.666938i
$686$	28.1183	+	25.3178i	1.07356	+	0.966638i
$687$		0			0
$688$	4.13660	−	0.434774i	0.157706	−	0.0165756i
$689$	−24.2126	−	5.14654i	−0.922425	−	0.196068i
$690$		0			0
$691$	−1.73073	+	16.4668i	−0.0658399	+	0.626425i	0.910993	+	0.412422i	$0.135317\pi$
$691$	−1.73073	+	16.4668i	−0.0658399	+	0.626425i	−0.976833	+	0.214003i	$0.931350\pi$
$692$	24.4119			0.928003
$693$		0			0
$694$	−35.5463			−1.34932
$695$	−0.160192	+	1.52412i	−0.00607643	+	0.0578133i
$696$		0			0
$697$	16.8182	+	3.57482i	0.637036	+	0.135406i
$698$	−43.8217	+	4.60585i	−1.65868	+	0.174334i
$699$		0			0
$700$	−12.0843	−	10.8808i	−0.456745	−	0.411255i
$701$	3.17601	−	9.77475i	0.119956	−	0.369187i	−0.872992	−	0.487734i	$-0.837824\pi$
$701$	3.17601	−	9.77475i	0.119956	−	0.369187i	0.992948	+	0.118547i	$0.0378236\pi$
$702$		0			0
$703$			20.4454i			0.771114i
$704$	−40.2708	−	0.895960i	−1.51776	−	0.0337677i
$705$		0			0
$706$	−8.43141	−	18.9373i	−0.317320	−	0.712713i
$707$	12.2219	−	11.0046i	0.459650	−	0.413871i
$708$		0			0
$709$	−43.9649	−	19.5745i	−1.65114	−	0.735134i	−0.651416	−	0.758721i	$-0.725825\pi$
$709$	−43.9649	−	19.5745i	−1.65114	−	0.735134i	−0.999722	+	0.0235867i	$0.992491\pi$
$710$	24.6077	−	17.8785i	0.923509	−	0.670969i
$711$		0			0
$712$	45.3774	+	14.7440i	1.70059	+	0.552555i
$713$	0.217222	+	0.0228310i	0.00813504	+	0.000855027i
$714$		0			0
$715$	−51.7790	−	24.4476i	−1.93642	−	0.914290i
$716$	47.1602	+	27.2279i	1.76246	+	1.01756i
$717$		0			0
$718$	−41.3469	+	8.78854i	−1.54305	+	0.327986i
$719$	46.0534	−	14.9636i	1.71750	−	0.558050i	0.725947	−	0.687750i	$-0.241402\pi$
$719$	46.0534	−	14.9636i	1.71750	−	0.558050i	0.991553	+	0.129700i	$0.0414016\pi$
$720$		0			0
$721$	−4.62838	−	6.37042i	−0.172370	−	0.237247i
$722$	15.8444	−	17.5970i	0.589666	−	0.654891i
$723$		0			0
$724$	51.6822	−	23.0104i	1.92075	−	0.855174i
$725$	7.78571	−	13.4852i	0.289154	−	0.500829i
$726$		0			0
$727$	−14.4674	−	25.0583i	−0.536568	−	0.929363i	−0.999086	−	0.0427527i	$-0.986387\pi$
$727$	−14.4674	−	25.0583i	−0.536568	−	0.929363i	0.462518	−	0.886610i	$-0.346946\pi$
$728$	22.0507	+	16.0208i	0.817253	+	0.593769i
$729$		0			0
$730$	18.4841	+	56.8881i	0.684126	+	2.10552i
$731$	5.23733	−	11.7632i	0.193710	−	0.435079i
$732$		0			0
$733$	−3.48446	+	16.3931i	−0.128701	+	0.605492i	0.865766	+	0.500448i	$0.166832\pi$
$733$	−3.48446	+	16.3931i	−0.128701	+	0.605492i	−0.994468	+	0.105044i	$0.966502\pi$
$734$	49.1272	+	54.5613i	1.81332	+	2.01389i
$735$		0			0
$736$	−0.303164	+	0.175032i	−0.0111748	+	0.00645175i
$737$	1.03394	+	12.5079i	0.0380855	+	0.460735i
$738$		0			0
$739$	16.0114	−	22.0378i	0.588990	−	0.810675i	−0.405655	−	0.914026i	$-0.632957\pi$
$739$	16.0114	−	22.0378i	0.588990	−	0.810675i	0.994645	+	0.103351i	$0.0329566\pi$
$740$	14.5535	+	68.4690i	0.534999	+	2.51697i
$741$		0			0
$742$	−1.35030	−	12.8472i	−0.0495711	−	0.471637i
$743$	4.63093	+	44.0604i	0.169892	+	1.61642i	0.664491	+	0.747296i	$0.268649\pi$
$743$	4.63093	+	44.0604i	0.169892	+	1.61642i	−0.494598	+	0.869122i	$0.664685\pi$
$744$		0			0
$745$	5.84153	+	27.4822i	0.214017	+	1.00687i
$746$	−4.64095	+	6.38772i	−0.169917	+	0.233871i
$747$		0			0
$748$	22.8948	−	37.6931i	0.837118	−	1.37820i
$749$	3.50764	−	2.02514i	0.128166	−	0.0739970i
$750$		0			0
$751$	18.9151	+	21.0073i	0.690221	+	0.766568i	0.981787	−	0.189982i	$-0.0608431\pi$
$751$	18.9151	+	21.0073i	0.690221	+	0.766568i	−0.291566	+	0.956551i	$0.594176\pi$
$752$	−1.21385	+	5.71074i	−0.0442647	+	0.208249i
$753$		0			0
$754$	−24.8108	+	55.7259i	−0.903554	+	2.02942i
$755$	9.03379	+	27.8031i	0.328773	+	1.01186i
$756$		0			0
$757$	−13.9254	−	10.1174i	−0.506129	−	0.367724i	0.305224	−	0.952280i	$-0.401269\pi$
$757$	−13.9254	−	10.1174i	−0.506129	−	0.367724i	−0.811353	+	0.584556i	$0.801269\pi$
$758$	−28.2980	−	49.0137i	−1.02783	−	1.78026i
$759$		0			0
$760$	−15.2809	+	26.4674i	−0.554298	+	0.960072i
$761$	44.2426	−	19.6981i	1.60379	−	0.714054i	0.607046	−	0.794666i	$-0.292354\pi$
$761$	44.2426	−	19.6981i	1.60379	−	0.714054i	0.996746	+	0.0806124i	$0.0256876\pi$
$762$		0			0
$763$	8.79125	−	9.76367i	0.318265	−	0.353469i
$764$	−30.2463	−	41.6305i	−1.09427	−	1.50614i
$765$		0			0
$766$	−20.1757	+	6.55549i	−0.728978	+	0.236859i
$767$	81.1332	−	17.2454i	2.92955	−	0.622695i
$768$		0			0
$769$	8.98495	+	5.18746i	0.324006	+	0.187065i	0.653177	−	0.757206i	$-0.273436\pi$
$769$	8.98495	+	5.18746i	0.324006	+	0.187065i	−0.329171	+	0.944270i	$0.606769\pi$
$770$	3.78380	−	29.6417i	0.136359	−	1.06821i
$771$		0			0
$772$	23.8211	+	2.50370i	0.857340	+	0.0901100i
$773$	−7.58873	−	2.46573i	−0.272947	−	0.0886860i	0.169345	−	0.985557i	$-0.445835\pi$
$773$	−7.58873	−	2.46573i	−0.272947	−	0.0886860i	−0.442293	+	0.896871i	$0.645835\pi$
$774$		0			0
$775$	−7.37646	+	5.35931i	−0.264970	+	0.192512i
$776$	−44.1185	−	19.6428i	−1.58376	−	0.705136i
$777$		0			0
$778$	45.4484	−	40.9219i	1.62940	−	1.46712i
$779$	−5.48465	−	12.3187i	−0.196508	−	0.441364i
$780$		0			0
$781$	13.9031	+	4.86185i	0.497491	+	0.173971i
$782$		−	0.755389i		−	0.0270126i
$783$		0			0
$784$	2.00084	−	6.15795i	0.0714585	−	0.219927i
$785$	7.12515	+	6.41551i	0.254308	+	0.228980i
$786$		0			0
$787$	−17.6056	+	1.85042i	−0.627572	+	0.0659604i	−0.412975	−	0.910742i	$-0.635510\pi$
$787$	−17.6056	+	1.85042i	−0.627572	+	0.0659604i	−0.214597	+	0.976703i	$0.568844\pi$
$788$	−30.1463	−	6.40779i	−1.07392	−	0.228268i
$789$		0			0
$790$	−3.98256	+	37.8916i	−0.141693	+	1.34812i
$791$	6.20131			0.220493
$792$		0			0
$793$	−58.0249			−2.06052
$794$	−4.87223	+	46.3562i	−0.172909	+	1.64512i
$795$		0			0
$796$	−28.7410	−	6.10908i	−1.01870	−	0.216531i
$797$	31.2927	−	3.28900i	1.10845	−	0.116502i	0.467430	−	0.884030i	$-0.345180\pi$
$797$	31.2927	−	3.28900i	1.10845	−	0.116502i	0.641015	+	0.767528i	$0.278513\pi$
$798$		0			0
$799$	13.4316	+	12.0939i	0.475177	+	0.427852i
$800$	4.51574	−	13.8980i	0.159656	−	0.491370i
$801$		0			0
$802$		−	23.2933i		−	0.822516i
$803$	−17.5419	+	23.0483i	−0.619040	+	0.813356i
$804$		0			0
$805$	−0.132421	−	0.297422i	−0.00466722	−	0.0104828i
$806$	26.5437	−	23.9001i	0.934963	−	0.841845i
$807$		0			0
$808$	−40.0490	−	17.8310i	−1.40892	−	0.627292i
$809$	−17.3896	+	12.6343i	−0.611384	+	0.444197i	−0.849902	−	0.526942i	$-0.823339\pi$
$809$	−17.3896	+	12.6343i	−0.611384	+	0.444197i	0.238517	+	0.971138i	$0.423339\pi$
$810$		0			0
$811$	31.2311	+	10.1476i	1.09667	+	0.356331i	0.800822	−	0.598903i	$-0.204396\pi$
$811$	31.2311	+	10.1476i	1.09667	+	0.356331i	0.295852	+	0.955234i	$0.404396\pi$
$812$	−20.1379	−	2.11657i	−0.706700	−	0.0742772i
$813$		0			0
$814$	−36.5285	+	38.7976i	−1.28032	+	1.35986i
$815$	−21.9053	−	12.6470i	−0.767308	−	0.443005i
$816$		0			0
$817$	−9.87782	+	2.09960i	−0.345581	+	0.0734556i
$818$	−0.00343919	+	0.00111746i	−0.000120249	+	3.90711e-5i
$819$		0			0
$820$	−27.1361	−	37.3497i	−0.947635	−	1.30431i
$821$	−37.5063	+	41.6550i	−1.30898	+	1.45377i	−0.499884	+	0.866092i	$0.666624\pi$
$821$	−37.5063	+	41.6550i	−1.30898	+	1.45377i	−0.809095	+	0.587677i	$0.800042\pi$
$822$		0			0
$823$	48.7936	−	21.7243i	1.70084	−	0.757261i	0.701847	−	0.712328i	$-0.252359\pi$
$823$	48.7936	−	21.7243i	1.70084	−	0.757261i	0.998990	−	0.0449335i	$-0.0143076\pi$
$824$	−10.4949	+	18.1777i	−0.365607	+	0.633250i
$825$		0			0
$826$	21.6433	+	37.4873i	0.753067	+	1.30435i
$827$	15.2821	+	11.1031i	0.531410	+	0.386092i	0.820885	−	0.571094i	$-0.193481\pi$
$827$	15.2821	+	11.1031i	0.531410	+	0.386092i	−0.289475	+	0.957186i	$0.593481\pi$
$828$		0			0
$829$	−8.51237	−	26.1984i	−0.295647	−	0.909907i	−0.983003	−	0.183587i	$-0.941229\pi$
$829$	−8.51237	−	26.1984i	−0.295647	−	0.909907i	0.687357	−	0.726320i	$-0.258771\pi$
$830$	3.51548	−	7.89590i	0.122024	−	0.274071i
$831$		0			0
$832$	−14.9213	+	70.1990i	−0.517302	+	2.43371i
$833$	−13.4125	−	14.8960i	−0.464714	−	0.516117i
$834$		0			0
$835$	−50.2030	+	28.9847i	−1.73735	+	1.00306i
$836$	−34.4695	+	2.84934i	−1.19215	+	0.0985464i
$837$		0			0
$838$	21.2768	−	29.2850i	0.734996	−	1.01164i
$839$	−0.747267	−	3.51562i	−0.0257985	−	0.121373i	0.963364	−	0.268197i	$-0.0864279\pi$
$839$	−0.747267	−	3.51562i	−0.0257985	−	0.121373i	−0.989162	+	0.146825i	$0.953095\pi$
$840$		0			0
$841$	1.00452	+	9.55736i	0.0346386	+	0.329564i
$842$	−6.00711	−	57.1539i	−0.207019	−	1.96965i
$843$		0			0
$844$	−12.6607	−	59.5641i	−0.435801	−	2.05028i
$845$	−37.6403	+	51.8074i	−1.29487	+	1.78223i
$846$		0			0
$847$	12.8406	−	6.67044i	0.441209	−	0.229199i
$848$	−4.45751	+	2.57355i	−0.153072	+	0.0883759i
$849$		0			0
$850$	21.1000	+	23.4339i	0.723723	+	0.803775i
$851$	−0.120708	+	0.567886i	−0.00413782	+	0.0194669i
$852$		0			0
$853$	5.57862	−	12.5298i	0.191008	−	0.429012i	−0.792501	−	0.609871i	$-0.791221\pi$
$853$	5.57862	−	12.5298i	0.191008	−	0.429012i	0.983509	+	0.180859i	$0.0578879\pi$
$854$	−9.35741	−	28.7991i	−0.320204	−	0.985486i
$855$		0			0
$856$	−8.73455	−	6.34602i	−0.298541	−	0.216902i
$857$	−1.82655	−	3.16368i	−0.0623939	−	0.108069i	0.833141	−	0.553060i	$-0.186540\pi$
$857$	−1.82655	−	3.16368i	−0.0623939	−	0.108069i	−0.895535	+	0.444991i	$0.853207\pi$
$858$		0			0
$859$	−12.4493	+	21.5628i	−0.424764	+	0.735713i	−0.996398	−	0.0847953i	$-0.972976\pi$
$859$	−12.4493	+	21.5628i	−0.424764	+	0.735713i	0.571634	+	0.820509i	$0.306310\pi$
$860$	−31.5850	+	14.0625i	−1.07704	+	0.479529i
$861$		0			0
$862$	−18.8274	+	20.9100i	−0.641265	+	0.712196i
$863$	−4.84824	−	6.67303i	−0.165036	−	0.227152i	0.718487	−	0.695540i	$-0.244835\pi$
$863$	−4.84824	−	6.67303i	−0.165036	−	0.227152i	−0.883523	+	0.468388i	$0.844835\pi$
$864$		0			0
$865$	−19.4045	+	6.30490i	−0.659773	+	0.214373i
$866$	−2.05703	+	0.437235i	−0.0699008	+	0.0148579i
$867$		0			0
$868$	10.2681	+	5.92831i	0.348523	+	0.201220i
$869$	−16.1787	+	8.86695i	−0.548826	+	0.300791i
$870$		0			0
$871$	22.2385	+	2.33737i	0.753524	+	0.0791986i
$872$	−33.3076	−	10.8223i	−1.12794	−	0.366490i
$873$		0			0
$874$	−0.479279	+	0.348216i	−0.0162118	+	0.0117786i
$875$	−5.13936	−	2.28819i	−0.173742	−	0.0773550i
$876$		0			0
$877$	−7.38760	+	6.65182i	−0.249462	+	0.224616i	−0.784369	−	0.620294i	$-0.787013\pi$
$877$	−7.38760	+	6.65182i	−0.249462	+	0.224616i	0.534908	+	0.844911i	$0.320346\pi$
$878$	4.14893	+	9.31864i	0.140019	+	0.314489i
$879$		0			0
$880$	−11.4027	+	3.42649i	−0.384384	+	0.115507i
$881$			46.2212i			1.55723i	0.627501	+	0.778616i	$0.284078\pi$
$881$			46.2212i			1.55723i	−0.627501	+	0.778616i	$0.715922\pi$
$882$		0			0
$883$	9.04674	−	27.8430i	0.304447	−	0.936991i	−0.675436	−	0.737419i	$-0.736045\pi$
$883$	9.04674	−	27.8430i	0.304447	−	0.936991i	0.979883	−	0.199573i	$-0.0639554\pi$
$884$	−58.3923	−	52.5767i	−1.96395	−	1.76834i
$885$		0			0
$886$	89.6349	−	9.42100i	3.01134	−	0.316505i
$887$	49.0001	+	10.4153i	1.64526	+	0.349711i	0.935115	−	0.354343i	$-0.115296\pi$
$887$	49.0001	+	10.4153i	1.64526	+	0.349711i	0.710146	+	0.704054i	$0.248629\pi$
$888$		0			0
$889$	0.409867	−	3.89962i	0.0137465	−	0.130789i
$890$	−93.1987			−3.12403
$891$		0			0
$892$	59.9122			2.00601
$893$	1.48167	−	14.0971i	0.0495820	−	0.471742i
$894$		0			0
$895$	−44.5188	−	9.46275i	−1.48810	−	0.316305i
$896$	−26.4354	+	2.77847i	−0.883143	+	0.0928221i
$897$		0			0
$898$	31.5634	+	28.4198i	1.05328	+	0.948382i
$899$	−3.50850	+	10.7981i	−0.117015	+	0.360136i
$900$		0			0
$901$			15.9342i			0.530845i
$902$	11.6013	−	33.1753i	0.386280	−	1.10462i
$903$		0			0
$904$	−6.72349	−	15.1012i	−0.223620	−	0.502258i
$905$	−35.1381	+	31.6385i	−1.16803	+	1.05170i
$906$		0			0
$907$	12.7171	+	5.66202i	0.422264	+	0.188004i	0.606857	−	0.794811i	$-0.292430\pi$
$907$	12.7171	+	5.66202i	0.422264	+	0.188004i	−0.184593	+	0.982815i	$0.559097\pi$
$908$	48.9042	−	35.5310i	1.62294	−	1.17914i
$909$		0			0
$910$	−50.6347	−	16.4522i	−1.67852	−	0.545385i
$911$	−13.8046	−	1.45092i	−0.457367	−	0.0480712i	−0.126956	−	0.991908i	$-0.540521\pi$
$911$	−13.8046	−	1.45092i	−0.457367	−	0.0480712i	−0.330411	+	0.943837i	$0.607187\pi$
$912$		0			0
$913$	4.11214	−	0.778891i	0.136092	−	0.0257775i
$914$	−65.3799	−	37.7471i	−2.16257	−	1.24856i
$915$		0			0
$916$	−54.0391	+	11.4864i	−1.78550	+	0.379520i
$917$	9.73950	−	3.16456i	0.321627	−	0.104503i
$918$		0			0
$919$	11.1835	+	15.3927i	0.368908	+	0.507759i	0.952604	−	0.304214i	$-0.0983938\pi$
$919$	11.1835	+	15.3927i	0.368908	+	0.507759i	−0.583695	+	0.811973i	$0.698394\pi$
$920$	−0.580700	+	0.644933i	−0.0191451	+	0.0212628i
$921$		0			0
$922$	−83.7270	+	37.2777i	−2.75740	+	1.22767i
$923$	13.1208	−	22.7260i	0.431878	−	0.748034i
$924$		0			0
$925$	−12.1179	−	20.9888i	−0.398434	−	0.690108i
$926$	32.3111	+	23.4754i	1.06181	+	0.771448i
$927$		0			0
$928$	−5.62314	−	17.3062i	−0.184588	−	0.568105i
$929$	−6.58671	+	14.7940i	−0.216103	+	0.485375i	−0.988772	−	0.149434i	$-0.952255\pi$
$929$	−6.58671	+	14.7940i	−0.216103	+	0.485375i	0.772669	+	0.634809i	$0.218921\pi$
$930$		0			0
$931$	−3.26841	+	15.3767i	−0.107118	+	0.503949i
$932$	7.96330	+	8.84414i	0.260847	+	0.289699i
$933$		0			0
$934$	45.9628	−	26.5366i	1.50395	−	0.868305i
$935$	−8.46353	+	35.8745i	−0.276787	+	1.17322i
$936$		0			0
$937$	−24.7387	+	34.0498i	−0.808177	+	1.11236i	0.183425	+	0.983034i	$0.441281\pi$
$937$	−24.7387	+	34.0498i	−0.808177	+	1.11236i	−0.991602	+	0.129326i	$0.958719\pi$
$938$	2.42622	+	11.4145i	0.0792189	+	0.372696i
$939$		0			0
$940$	−5.07275	−	48.2640i	−0.165455	−	1.57420i
$941$	−0.0442293	−	0.420814i	−0.00144183	−	0.0137181i	0.993777	−	0.111385i	$-0.0355287\pi$
$941$	−0.0442293	−	0.420814i	−0.00144183	−	0.0137181i	−0.995219	+	0.0976669i	$0.968862\pi$
$942$		0			0
$943$	−0.0796115	−	0.374543i	−0.00259251	−	0.0121968i
$944$	10.1377	−	13.9533i	0.329954	−	0.454142i
$945$		0			0
$946$	−22.4955	−	13.6638i	−0.731393	−	0.444249i
$947$	10.8999	−	6.29305i	0.354199	−	0.204497i	−0.312334	−	0.949972i	$-0.601111\pi$
$947$	10.8999	−	6.29305i	0.354199	−	0.204497i	0.666533	+	0.745475i	$0.267778\pi$
$948$		0			0
$949$	34.5307	+	38.3502i	1.12091	+	1.24490i
$950$	5.14173	−	24.1900i	0.166820	−	0.784826i
$951$		0			0
$952$	7.13627	−	16.0283i	0.231288	−	0.519481i
$953$	−16.7845	−	51.6574i	−0.543703	−	1.67335i	−0.724053	−	0.689745i	$-0.757723\pi$
$953$	−16.7845	−	51.6574i	−0.543703	−	1.67335i	0.180349	−	0.983603i	$-0.442277\pi$
$954$		0			0
$955$	34.7941	+	25.2794i	1.12591	+	0.818022i
$956$	−10.1483	−	17.5774i	−0.328220	−	0.568494i
$957$		0			0
$958$	−15.9406	+	27.6099i	−0.515017	+	0.892036i
$959$	7.54905	−	3.36105i	0.243772	−	0.108534i
$960$		0			0
$961$	−16.2946	+	18.0969i	−0.525631	+	0.583772i
$962$	55.8052	+	76.8092i	1.79923	+	2.47643i
$963$		0			0
$964$	−10.0079	+	3.25175i	−0.322332	+	0.104732i
$965$	−19.5815	+	4.16217i	−0.630350	+	0.133985i
$966$		0			0
$967$	23.2525	+	13.4249i	0.747751	+	0.431714i	0.824881	−	0.565307i	$-0.191242\pi$
$967$	23.2525	+	13.4249i	0.747751	+	0.431714i	−0.0771296	+	0.997021i	$0.524576\pi$
$968$	−30.1655	−	24.0369i	−0.969554	−	0.772575i
$969$		0			0
$970$	93.8170	+	9.86057i	3.01228	+	0.316604i
$971$	−25.9476	−	8.43088i	−0.832697	−	0.270560i	−0.138516	−	0.990360i	$-0.544233\pi$
$971$	−25.9476	−	8.43088i	−0.832697	−	0.270560i	−0.694181	+	0.719801i	$0.744233\pi$
$972$		0			0
$973$	−0.558215	+	0.405567i	−0.0178956	+	0.0130019i
$974$	18.7502	+	8.34815i	0.600797	+	0.267492i
$975$		0			0
$976$	−8.96630	+	8.07329i	−0.287004	+	0.258420i
$977$	−14.0102	−	31.4674i	−0.448226	−	1.00673i	−0.986470	−	0.163942i	$-0.947579\pi$
$977$	−14.0102	−	31.4674i	−0.448226	−	1.00673i	0.538244	−	0.842789i	$-0.319088\pi$
$978$		0			0
$979$	−25.7078	−	37.0915i	−0.821624	−	1.18545i
$980$			53.8209i			1.71925i
$981$		0			0
$982$	24.3234	−	74.8598i	0.776191	−	2.38887i
$983$	−12.1930	−	10.9786i	−0.388896	−	0.350163i	0.451371	−	0.892336i	$-0.350935\pi$
$983$	−12.1930	−	10.9786i	−0.388896	−	0.350163i	−0.840267	+	0.542173i	$0.817602\pi$
$984$		0			0
$985$	25.6176	−	2.69251i	0.816243	−	0.0857906i
$986$	38.4082	+	8.16393i	1.22317	+	0.259992i
$987$		0			0
$988$	−6.44135	+	61.2853i	−0.204927	+	1.94975i
$989$	−0.286760			−0.00911842
$990$		0			0
$991$	59.6539			1.89497			0.947484	−	0.319804i	$-0.103617\pi$
$991$	59.6539			1.89497			0.947484	+	0.319804i	$0.103617\pi$
$992$	−1.11376	+	10.5967i	−0.0353620	+	0.336447i
$993$		0			0
$994$	13.3954	+	2.84728i	0.424876	+	0.0903102i
$995$	24.4234	−	2.56700i	0.774273	−	0.0813793i
$996$		0			0
$997$	−30.2638	−	27.2496i	−0.958463	−	0.863004i	0.0321797	−	0.999482i	$-0.489755\pi$
$997$	−30.2638	−	27.2496i	−0.958463	−	0.863004i	−0.990643	+	0.136478i	$0.956422\pi$
$998$	1.62771	−	5.00958i	0.0515243	−	0.158575i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.t.a.260.1		80
3.2	odd	2		99.2.p.a.95.10	yes	80
9.2	odd	6	inner	297.2.t.a.62.1		80
9.4	even	3		891.2.k.a.161.2		80
9.5	odd	6		891.2.k.a.161.19		80
9.7	even	3		99.2.p.a.29.10	✓	80
11.8	odd	10	inner	297.2.t.a.206.1		80
33.8	even	10		99.2.p.a.41.10	yes	80
99.41	even	30		891.2.k.a.404.2		80
99.52	odd	30		99.2.p.a.74.10	yes	80
99.74	even	30	inner	297.2.t.a.8.1		80
99.85	odd	30		891.2.k.a.404.19		80

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.p.a.29.10	✓	80	9.7	even	3
99.2.p.a.41.10	yes	80	33.8	even	10
99.2.p.a.74.10	yes	80	99.52	odd	30
99.2.p.a.95.10	yes	80	3.2	odd	2
297.2.t.a.8.1		80	99.74	even	30	inner
297.2.t.a.62.1		80	9.2	odd	6	inner
297.2.t.a.206.1		80	11.8	odd	10	inner
297.2.t.a.260.1		80	1.1	even	1	trivial
891.2.k.a.161.2		80	9.4	even	3
891.2.k.a.161.19		80	9.5	odd	6
891.2.k.a.404.2		80	99.41	even	30
891.2.k.a.404.19		80	99.85	odd	30

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:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.t (of order \(30\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.245046 + 2.33146i) q^{2} +(-3.41935 - 0.726805i) q^{4} +(2.90568 - 0.305399i) q^{5} +(0.977562 + 0.880201i) q^{7} +(1.08356 - 3.33484i) q^{8} +6.84930i q^{10} +(-2.72590 + 1.88930i) q^{11} +(2.40347 + 5.39828i) q^{13} +(-2.29170 + 2.06345i) q^{14} +(1.12249 + 0.499763i) q^{16} +(3.07734 - 2.23582i) q^{17} +(-2.83716 - 0.921851i) q^{19} +(-10.1575 - 1.06759i) q^{20} +(-3.73685 - 6.81829i) q^{22} +(-0.0733618 - 0.0423554i) q^{23} +(3.45895 - 0.735222i) q^{25} +(-13.1748 + 4.28075i) q^{26} +(-2.70289 - 3.72021i) q^{28} +(2.94645 - 3.27237i) q^{29} +(-2.35549 + 1.04873i) q^{31} +(2.06622 - 3.57881i) q^{32} +(4.45863 + 7.72257i) q^{34} +(3.10929 + 2.25903i) q^{35} +(-2.11787 - 6.51815i) q^{37} +(2.84449 - 6.38883i) q^{38} +(2.13000 - 10.0209i) q^{40} +(3.02460 + 3.35916i) q^{41} +(2.93163 - 1.69258i) q^{43} +(10.6940 - 4.47897i) q^{44} +(0.116727 - 0.160661i) q^{46} +(0.987907 + 4.64774i) q^{47} +(-0.550825 - 5.24075i) q^{49} +(0.866537 + 8.24455i) q^{50} +(-4.29480 - 20.2054i) q^{52} +(-2.46224 + 3.38898i) q^{53} +(-7.34360 + 6.32218i) q^{55} +(3.99457 - 2.30627i) q^{56} +(6.90737 + 7.67141i) q^{58} +(2.91842 - 13.7301i) q^{59} +(-3.99395 + 8.97056i) q^{61} +(-1.86787 - 5.74871i) q^{62} +(9.82561 + 7.13872i) q^{64} +(8.63232 + 14.9516i) q^{65} +(1.89207 - 3.27716i) q^{67} +(-12.1475 + 5.40842i) q^{68} +(-6.02876 + 6.69561i) q^{70} +(-2.61027 - 3.59273i) q^{71} +(8.30569 - 2.69868i) q^{73} +(15.7158 - 3.34049i) q^{74} +(9.03125 + 5.21419i) q^{76} +(-4.32770 - 0.552436i) q^{77} +(5.53218 + 0.581456i) q^{79} +(3.41421 + 1.10934i) q^{80} +(-8.57291 + 6.22858i) q^{82} +(-1.15281 - 0.513262i) q^{83} +(8.25894 - 7.43639i) q^{85} +(3.22779 + 7.24973i) q^{86} +(3.34684 + 11.1376i) q^{88} +13.6071i q^{89} +(-2.40203 + 7.39268i) q^{91} +(0.220065 + 0.198148i) q^{92} +(-11.0781 + 1.16435i) q^{94} +(-8.52541 - 1.81213i) q^{95} +(1.43965 - 13.6973i) q^{97} +12.3536 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 80 q + 15 q^{2} + 5 q^{4} + 6 q^{5} - 5 q^{7} + 3 q^{11} - 5 q^{13} + 9 q^{14} + 5 q^{16} - 50 q^{19} + 3 q^{20} - 11 q^{22} + 42 q^{23} - 2 q^{25} - 20 q^{28} - 30 q^{29} - 6 q^{31} - 10 q^{34} - 6 q^{37}+ \cdots + 27 q^{97}+O(q^{100}) \) 80 * q + 15 * q^2 + 5 * q^4 + 6 * q^5 - 5 * q^7 + 3 * q^11 - 5 * q^13 + 9 * q^14 + 5 * q^16 - 50 * q^19 + 3 * q^20 - 11 * q^22 + 42 * q^23 - 2 * q^25 - 20 * q^28 - 30 * q^29 - 6 * q^31 - 10 * q^34 - 6 * q^37 - 9 * q^38 + 15 * q^40 + 15 * q^41 - 40 * q^46 + 21 * q^47 - q^49 - 60 * q^50 - 5 * q^52 - 18 * q^55 - 90 * q^56 - 29 * q^58 - 81 * q^59 - 5 * q^61 - 8 * q^64 + 10 * q^67 - 180 * q^68 + 30 * q^70 - 20 * q^73 + 15 * q^74 - 33 * q^77 - 5 * q^79 - 2 * q^82 + 60 * q^83 - 5 * q^85 + 48 * q^86 - 59 * q^88 + 52 * q^91 + 213 * q^92 - 5 * q^94 + 135 * q^95 + 27 * q^97

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