LMFDB - Embedded newform 297.2.n.b.289.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [297,2,Mod(37,297)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(297, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([10, 6]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("297.37");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.n (of order $15$, degree $8$, not minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$9$ over $\Q(\zeta_{15})$
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			289.6
Character	$\chi$	$=$	297.289
Dual form			297.2.n.b.37.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.0603978 + 0.574647i) q^{2} +(1.62972 - 0.346409i) q^{4} +(0.314048 - 2.98797i) q^{5} +(-0.779082 - 0.865259i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(0.565602 - 3.26804i) q^{11} +(-3.60501 - 1.60505i) q^{13} +(0.450163 - 0.499957i) q^{14} +(1.92600 - 0.857509i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(-0.523246 - 4.97835i) q^{20} +(1.91213 + 0.127639i) q^{22} +(-0.0427501 - 0.0740453i) q^{23} +(-3.93860 - 0.837174i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(5.15218 + 5.72208i) q^{29} +(5.96439 + 2.65552i) q^{31} +(2.72743 + 4.72404i) q^{32} +(0.0907715 - 0.157221i) q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(-3.36160 + 1.49668i) q^{38} +(6.22531 - 1.32323i) q^{40} +(-3.88703 + 4.31698i) q^{41} +(3.39229 - 5.87562i) q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(-0.320574 - 0.0681401i) q^{47} +(0.589996 - 5.61344i) q^{49} +(0.243197 - 2.31387i) q^{50} +(-6.43117 - 1.36699i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} +(1.23321 - 2.13598i) q^{56} +(-2.97699 + 3.30629i) q^{58} +(-2.24586 + 0.477372i) q^{59} +(-12.5039 + 5.56709i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +(-5.92799 + 10.2676i) q^{65} +(-5.83989 - 10.1150i) q^{67} +(-0.478226 - 0.212920i) q^{68} +(-1.35248 - 1.50208i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(-3.52850 - 0.750007i) q^{74} +(5.30529 + 9.18904i) q^{76} +(-3.26835 + 2.05668i) q^{77} +(0.928965 + 8.83851i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(-4.52916 + 2.01651i) q^{83} +(-0.631634 + 0.701501i) q^{85} +(3.58129 + 1.59449i) q^{86} +(6.95423 - 0.999772i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(-0.0953208 - 0.105864i) q^{92} +(0.0197945 - 0.188332i) q^{94} +(18.7153 - 3.97805i) q^{95} +(0.00928623 + 0.0883526i) q^{97} +3.26138 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) $ 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Character values

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

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	0.0603978	+	0.574647i	0.0427077	+	0.406337i	0.994902	+	0.100844i	$0.0321544\pi$
$2$	0.0603978	+	0.574647i	0.0427077	+	0.406337i	−0.952195	+	0.305492i	$0.901179\pi$
$3$		0			0
$3$		0			0
$4$	1.62972	−	0.346409i	0.814862	−	0.173204i
$5$	0.314048	−	2.98797i	0.140447	−	1.33626i	−0.666442	−	0.745557i	$-0.732184\pi$
$5$	0.314048	−	2.98797i	0.140447	−	1.33626i	0.806889	−	0.590704i	$-0.201150\pi$
$6$		0			0
$7$	−0.779082	−	0.865259i	−0.294465	−	0.327037i	0.577699	−	0.816250i	$-0.303951\pi$
$7$	−0.779082	−	0.865259i	−0.294465	−	0.327037i	−0.872164	+	0.489213i	$0.837284\pi$
$8$	0.654602	+	2.01466i	0.231437	+	0.712289i
$9$		0			0
$10$	1.73599			0.548970
$11$	0.565602	−	3.26804i	0.170535	−	0.985352i
$11$	0.565602	−	3.26804i	0.170535	−	0.985352i
$12$		0			0
$13$	−3.60501	−	1.60505i	−0.999849	−	0.445161i	−0.159495	−	0.987199i	$-0.550986\pi$
$13$	−3.60501	−	1.60505i	−0.999849	−	0.445161i	−0.840354	+	0.542037i	$0.817653\pi$
$14$	0.450163	−	0.499957i	0.120311	−	0.133619i
$15$		0			0
$16$	1.92600	−	0.857509i	0.481499	−	0.214377i
$17$	−0.254185	−	0.184677i	−0.0616490	−	0.0447906i	0.556534	−	0.830825i	$-0.312131\pi$
$17$	−0.254185	−	0.184677i	−0.0616490	−	0.0447906i	−0.618183	+	0.786034i	$0.712131\pi$
$18$		0			0
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	0.875222	+	0.483721i	$0.160715\pi$
$19$	1.96794	+	6.05670i	0.451477	+	1.38950i	−0.423746	+	0.905781i	$0.639285\pi$
$20$	−0.523246	−	4.97835i	−0.117001	−	1.11319i
$21$		0			0
$22$	1.91213	+	0.127639i	0.407668	+	0.0272126i
$23$	−0.0427501	−	0.0740453i	−0.00891401	−	0.0154395i	0.861534	−	0.507700i	$-0.169504\pi$
$23$	−0.0427501	−	0.0740453i	−0.00891401	−	0.0154395i	−0.870448	+	0.492260i	$0.836171\pi$
$24$		0			0
$25$	−3.93860	−	0.837174i	−0.787719	−	0.167435i
$26$	0.704604	−	2.16855i	0.138184	−	0.425287i
$27$		0			0
$28$	−1.56942	−	1.14025i	−0.296593	−	0.215487i
$29$	5.15218	+	5.72208i	0.956737	+	1.06256i	0.997987	+	0.0634149i	$0.0201991\pi$
$29$	5.15218	+	5.72208i	0.956737	+	1.06256i	−0.0412506	+	0.999149i	$0.513134\pi$
$30$		0			0
$31$	5.96439	+	2.65552i	1.07124	+	0.476945i	0.865111	−	0.501581i	$-0.167248\pi$
$31$	5.96439	+	2.65552i	1.07124	+	0.476945i	0.206125	+	0.978526i	$0.433915\pi$
$32$	2.72743	+	4.72404i	0.482146	+	0.835101i
$33$		0			0
$34$	0.0907715	−	0.157221i	0.0155672	−	0.0269632i
$35$	−2.83004	+	2.05614i	−0.478363	+	0.347551i
$36$		0			0
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	0.657694	+	0.753286i	$0.271532\pi$
$37$	−1.92922	+	5.93753i	−0.317162	+	0.976124i	−0.974855	+	0.222838i	$0.928468\pi$
$38$	−3.36160	+	1.49668i	−0.545324	+	0.242794i
$39$		0			0
$40$	6.22531	−	1.32323i	0.984308	−	0.209221i
$41$	−3.88703	+	4.31698i	−0.607052	+	0.674199i	−0.965816	−	0.259229i	$-0.916532\pi$
$41$	−3.88703	+	4.31698i	−0.607052	+	0.674199i	0.358764	+	0.933428i	$0.383198\pi$
$42$		0			0
$43$	3.39229	−	5.87562i	0.517320	−	0.896024i	−0.482478	−	0.875908i	$-0.660263\pi$
$43$	3.39229	−	5.87562i	0.517320	−	0.896024i	0.999798	−	0.0201157i	$-0.00640347\pi$
$44$	−0.210303	−	5.52194i	−0.0317043	−	0.832463i
$45$		0			0
$46$	0.0399679	−	0.0290384i	0.00589294	−	0.00428147i
$47$	−0.320574	−	0.0681401i	−0.0467605	−	0.00993925i	0.184472	−	0.982838i	$-0.440942\pi$
$47$	−0.320574	−	0.0681401i	−0.0467605	−	0.00993925i	−0.231233	+	0.972899i	$0.574276\pi$
$48$		0			0
$49$	0.589996	−	5.61344i	0.0842852	−	0.801920i
$50$	0.243197	−	2.31387i	0.0343933	−	0.327230i
$51$		0			0
$52$	−6.43117	−	1.36699i	−0.891843	−	0.189567i
$53$	−1.96000	+	1.42402i	−0.269227	+	0.195605i	−0.714205	−	0.699937i	$-0.753211\pi$
$53$	−1.96000	+	1.42402i	−0.269227	+	0.195605i	0.444978	+	0.895541i	$0.353211\pi$
$54$		0			0
$55$	−9.58718	−	2.71632i	−1.29274	−	0.366269i
$56$	1.23321	−	2.13598i	0.164795	−	0.285433i
$57$		0			0
$58$	−2.97699	+	3.30629i	−0.390899	+	0.434137i
$59$	−2.24586	+	0.477372i	−0.292386	+	0.0621485i	−0.351769	−	0.936087i	$-0.614420\pi$
$59$	−2.24586	+	0.477372i	−0.292386	+	0.0621485i	0.0593835	+	0.998235i	$0.481087\pi$
$60$		0			0
$61$	−12.5039	+	5.56709i	−1.60096	+	0.712792i	−0.996480	−	0.0838297i	$-0.973285\pi$
$61$	−12.5039	+	5.56709i	−1.60096	+	0.712792i	−0.604478	+	0.796622i	$0.706618\pi$
$62$	−1.16575	+	3.58780i	−0.148050	+	0.455652i
$63$		0			0
$64$	0.861321	−	0.625787i	0.107665	−	0.0782233i
$65$	−5.92799	+	10.2676i	−0.735277	+	1.27354i
$66$		0			0
$67$	−5.83989	−	10.1150i	−0.713456	−	1.23574i	−0.963552	−	0.267521i	$-0.913795\pi$
$67$	−5.83989	−	10.1150i	−0.713456	−	1.23574i	0.250096	−	0.968221i	$-0.419538\pi$
$68$	−0.478226	−	0.212920i	−0.0579934	−	0.0258203i
$69$		0			0
$70$	−1.35248	−	1.50208i	−0.161653	−	0.179533i
$71$	7.05272	+	5.12410i	0.837004	+	0.608119i	0.921532	−	0.388302i	$-0.126938\pi$
$71$	7.05272	+	5.12410i	0.837004	+	0.608119i	−0.0845279	+	0.996421i	$0.526938\pi$
$72$		0			0
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	−0.883525	−	0.468383i	$-0.844837\pi$
$73$	0.910538	−	2.80235i	0.106570	−	0.327990i	0.990096	+	0.140393i	$0.0448367\pi$
$74$	−3.52850	−	0.750007i	−0.410180	−	0.0871865i
$75$		0			0
$76$	5.30529	+	9.18904i	0.608559	+	1.05405i
$77$	−3.26835	+	2.05668i	−0.372463	+	0.234381i
$78$		0			0
$79$	0.928965	+	8.83851i	0.104517	+	0.994410i	0.913572	+	0.406677i	$0.133313\pi$
$79$	0.928965	+	8.83851i	0.104517	+	0.994410i	−0.809055	+	0.587733i	$0.800021\pi$
$80$	−1.95735	−	6.02412i	−0.218839	−	0.673517i
$81$		0			0
$82$	−2.71551	−	1.97293i	−0.299878	−	0.217874i
$83$	−4.52916	+	2.01651i	−0.497140	+	0.221341i	−0.639961	−	0.768408i	$-0.721049\pi$
$83$	−4.52916	+	2.01651i	−0.497140	+	0.221341i	0.142821	+	0.989749i	$0.454383\pi$
$84$		0			0
$85$	−0.631634	+	0.701501i	−0.0685104	+	0.0760885i
$86$	3.58129	+	1.59449i	0.386181	+	0.171939i
$87$		0			0
$88$	6.95423	−	0.999772i	0.741323	−	0.106576i
$89$	−2.12862			−0.225634			−0.112817	−	0.993616i	$-0.535987\pi$
$89$	−2.12862			−0.225634			−0.112817	+	0.993616i	$0.535987\pi$
$90$		0			0
$91$	1.41981	+	4.36973i	0.148837	+	0.458072i
$92$	−0.0953208	−	0.105864i	−0.00993788	−	0.0110371i
$93$		0			0
$94$	0.0197945	−	0.188332i	0.00204165	−	0.0194250i
$95$	18.7153	−	3.97805i	1.92014	−	0.408139i
$96$		0			0
$97$	0.00928623	+	0.0883526i	0.000942874	+	0.00897084i	0.994983	−	0.100042i	$-0.0318977\pi$
$97$	0.00928623	+	0.0883526i	0.000942874	+	0.00897084i	−0.994040	+	0.109013i	$0.965231\pi$
$98$	3.26138			0.329449
$99$		0			0
$100$	−6.70883			−0.670883
$101$	−0.214961	−	2.04522i	−0.0213894	−	0.203507i	0.978608	−	0.205733i	$-0.0659579\pi$
$101$	−0.214961	−	2.04522i	−0.0213894	−	0.203507i	−0.999998	+	0.00222652i	$0.999291\pi$
$102$		0			0
$103$	2.95079	−	0.627210i	0.290750	−	0.0618009i	−0.0602275	−	0.998185i	$-0.519183\pi$
$103$	2.95079	−	0.627210i	0.290750	−	0.0618009i	0.350978	+	0.936384i	$0.385849\pi$
$104$	0.873787	−	8.31352i	0.0856818	−	0.815208i
$105$		0			0
$106$	−0.936690	−	1.04030i	−0.0909794	−	0.101043i
$107$	−3.70600	−	11.4059i	−0.358272	−	1.10265i	−0.954088	−	0.299527i	$-0.903171\pi$
$107$	−3.70600	−	11.4059i	−0.358272	−	1.10265i	0.595815	−	0.803121i	$-0.296829\pi$
$108$		0			0
$109$	5.20013			0.498082			0.249041	−	0.968493i	$-0.419885\pi$
$109$	5.20013			0.498082			0.249041	+	0.968493i	$0.419885\pi$
$110$	0.981882	−	5.67330i	0.0936187	−	0.540928i
$111$		0			0
$112$	−2.24248	−	0.998415i	−0.211894	−	0.0943414i
$113$	−12.8657	+	14.2889i	−1.21031	+	1.34418i	−0.288046	+	0.957617i	$0.593005\pi$
$113$	−12.8657	+	14.2889i	−1.21031	+	1.34418i	−0.922262	+	0.386566i	$0.873661\pi$
$114$		0			0
$115$	−0.234671	+	0.104482i	−0.0218832	+	0.00974301i
$116$	10.3788	+	7.54065i	0.963649	+	0.700132i
$117$		0			0
$118$	−0.409965	−	1.26174i	−0.0377403	−	0.116153i
$119$	0.0382384	+	0.363814i	0.00350531	+	0.0333508i
$120$		0			0
$121$	−10.3602	−	3.69682i	−0.941835	−	0.336074i
$122$	−3.95432	−	6.84907i	−0.358007	−	0.620086i
$123$		0			0
$124$	10.6402	+	2.26164i	0.955518	+	0.203102i
$125$	0.903736	−	2.78141i	0.0808326	−	0.248777i
$126$		0			0
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	0.949949	−	0.312405i	$-0.101135\pi$
$127$	10.6652	+	7.74873i	0.946384	+	0.687588i	−0.00356461	+	0.999994i	$0.501135\pi$
$128$	7.71165	+	8.56465i	0.681620	+	0.757015i
$129$		0			0
$130$	−6.25827	−	2.78636i	−0.548887	−	0.244380i
$131$	−8.98588	−	15.5640i	−0.785100	−	1.35983i	−0.928939	−	0.370233i	$-0.879278\pi$
$131$	−8.98588	−	15.5640i	−0.785100	−	1.35983i	0.143839	−	0.989601i	$-0.454055\pi$
$132$		0			0
$133$	3.70742	−	6.42144i	0.321474	−	0.556810i
$134$	5.45983	−	3.96680i	0.471657	−	0.342679i
$135$		0			0
$136$	0.205670	−	0.632986i	0.0176360	−	0.0542781i
$137$	14.9837	−	6.67119i	1.28015	−	0.569958i	0.349864	−	0.936801i	$-0.386228\pi$
$137$	14.9837	−	6.67119i	1.28015	−	0.569958i	0.930283	+	0.366842i	$0.119561\pi$
$138$		0			0
$139$	11.6415	−	2.47448i	0.987421	−	0.209883i	0.314226	−	0.949348i	$-0.398255\pi$
$139$	11.6415	−	2.47448i	0.987421	−	0.209883i	0.673195	+	0.739465i	$0.264922\pi$
$140$	−3.89991	+	4.33129i	−0.329603	+	0.366061i
$141$		0			0
$142$	−2.51858	+	4.36231i	−0.211355	+	0.366077i
$143$	−7.28438	+	10.8735i	−0.609150	+	0.909287i
$144$		0			0
$145$	18.7154	−	13.5976i	1.55423	−	1.12922i
$146$	1.66535	+	0.353982i	0.137826	+	0.0292958i
$147$		0			0
$148$	−1.08729	+	10.3448i	−0.0893744	+	0.850340i
$149$	−0.473693	+	4.50689i	−0.0388065	+	0.369219i	0.957834	+	0.287321i	$0.0927647\pi$
$149$	−0.473693	+	4.50689i	−0.0388065	+	0.369219i	−0.996641	+	0.0818976i	$0.973902\pi$
$150$		0			0
$151$	2.86682	+	0.609361i	0.233298	+	0.0495891i	0.323077	−	0.946373i	$-0.395283\pi$
$151$	2.86682	+	0.609361i	0.233298	+	0.0495891i	−0.0897788	+	0.995962i	$0.528616\pi$
$152$	−10.9140	+	7.92945i	−0.885239	+	0.643164i
$153$		0			0
$154$	−1.37927	−	1.75393i	−0.111144	−	0.141336i
$155$	9.80771	−	16.9874i	0.787774	−	1.36446i
$156$		0			0
$157$	−12.0802	+	13.4165i	−0.964108	+	1.07075i	0.0333460	+	0.999444i	$0.489384\pi$
$157$	−12.0802	+	13.4165i	−0.964108	+	1.07075i	−0.997454	+	0.0713070i	$0.977283\pi$
$158$	−5.02291	+	1.06765i	−0.399602	+	0.0849379i
$159$		0			0
$160$	14.9718	−	6.66589i	1.18363	−	0.526985i
$161$	−0.0307625	+	0.0946773i	−0.00242443	+	0.00746161i
$162$		0			0
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	−0.387786	−	0.921749i	$-0.626760\pi$
$163$	4.71129	−	3.42295i	0.369017	−	0.268106i	0.756803	+	0.653643i	$0.226760\pi$
$164$	−4.83934	+	8.38199i	−0.377889	+	0.654523i
$165$		0			0
$166$	−1.43233	−	2.48087i	−0.111171	−	0.192553i
$167$	4.58758	+	2.04252i	0.354997	+	0.158055i	0.576484	−	0.817108i	$-0.304424\pi$
$167$	4.58758	+	2.04252i	0.354997	+	0.158055i	−0.221487	+	0.975163i	$0.571091\pi$
$168$		0			0
$169$	1.72118	+	1.91157i	0.132399	+	0.147044i
$170$	−0.441265	−	0.320598i	−0.0338435	−	0.0245887i
$171$		0			0
$172$	3.49313	−	10.7508i	0.266349	−	0.819738i
$173$	−15.2492	−	3.24131i	−1.15937	−	0.246433i	−0.412221	−	0.911084i	$-0.635247\pi$
$173$	−15.2492	−	3.24131i	−1.15937	−	0.246433i	−0.747153	+	0.664652i	$0.768580\pi$
$174$		0			0
$175$	2.34412	+	4.06013i	0.177199	+	0.306917i
$176$	−1.71303	−	6.77925i	−0.129124	−	0.511005i
$177$		0			0
$178$	−0.128564	−	1.22321i	−0.00963629	−	0.0916832i
$179$	−2.17822	−	6.70387i	−0.162808	−	0.501071i	0.836060	−	0.548638i	$-0.184853\pi$
$179$	−2.17822	−	6.70387i	−0.162808	−	0.501071i	−0.998868	+	0.0475668i	$0.984853\pi$
$180$		0			0
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	0.510149	−	0.860086i	$-0.329590\pi$
$181$	−2.02068	−	1.46811i	−0.150196	−	0.109124i	−0.660345	+	0.750962i	$0.729590\pi$
$182$	−2.42530	+	1.07981i	−0.179775	+	0.0800410i
$183$		0			0
$184$	0.121192	−	0.134597i	0.00893437	−	0.00992262i
$185$	17.1353	+	7.62912i	1.25981	+	0.560904i
$186$		0			0
$187$	−0.747298	+	0.726235i	−0.0546479	+	0.0531076i
$188$	−0.546051			−0.0398249
$189$		0			0
$190$	3.41633	+	10.5144i	0.247847	+	0.762795i
$191$	7.91112	+	8.78619i	0.572428	+	0.635746i	0.957944	−	0.286955i	$-0.0926431\pi$
$191$	7.91112	+	8.78619i	0.572428	+	0.635746i	−0.385516	+	0.922701i	$0.625976\pi$
$192$		0			0
$193$	−0.705218	+	6.70970i	−0.0507627	+	0.482975i	0.939376	+	0.342887i	$0.111405\pi$
$193$	−0.705218	+	6.70970i	−0.0507627	+	0.482975i	−0.990139	+	0.140087i	$0.955262\pi$
$194$	−0.0502106	+	0.0106726i	−0.00360491	+	0.000766248i
$195$		0			0
$196$	−0.983012	−	9.35274i	−0.0702152	−	0.668053i
$197$	20.6474			1.47107			0.735534	−	0.677488i	$-0.236931\pi$
$197$	20.6474			1.47107			0.735534	+	0.677488i	$0.236931\pi$
$198$		0			0
$199$	−13.2862			−0.941832			−0.470916	−	0.882178i	$-0.656077\pi$
$199$	−13.2862			−0.941832			−0.470916	+	0.882178i	$0.656077\pi$
$200$	−0.891593	−	8.48294i	−0.0630451	−	0.599834i
$201$		0			0
$202$	1.16229	−	0.247053i	0.0817788	−	0.0173826i
$203$	0.937103	−	8.91594i	0.0657718	−	0.625777i
$204$		0			0
$205$	11.6783	+	12.9701i	0.815647	+	0.905868i
$206$	0.538646	+	1.65778i	0.0375292	+	0.115503i
$207$		0			0
$208$	−8.31958			−0.576859
$209$	20.9066	−	3.00563i	1.44614	−	0.207904i
$210$		0			0
$211$	−7.62355	−	3.39422i	−0.524827	−	0.233668i	0.127182	−	0.991879i	$-0.459407\pi$
$211$	−7.62355	−	3.39422i	−0.524827	−	0.233668i	−0.652009	+	0.758211i	$0.726074\pi$
$212$	−2.70097	+	2.99973i	−0.185503	+	0.206022i
$213$		0			0
$214$	6.33052	−	2.81853i	0.432746	−	0.192671i
$215$	−16.4908	−	11.9813i	−1.12467	−	0.817117i
$216$		0			0
$217$	−2.34904	−	7.22960i	−0.159463	−	0.490778i
$218$	0.314076	+	2.98824i	0.0212719	+	0.202389i
$219$		0			0
$220$	−16.5654	−	1.10578i	−1.11684	−	0.0745514i
$221$	0.619925	+	1.07374i	0.0417007	+	0.0722277i
$222$		0			0
$223$	0.375272	+	0.0797665i	0.0251301	+	0.00534156i	0.220460	−	0.975396i	$-0.429244\pi$
$223$	0.375272	+	0.0797665i	0.0251301	+	0.00534156i	−0.195330	+	0.980738i	$0.562578\pi$
$224$	1.96263	−	6.04035i	0.131134	−	0.403588i
$225$		0			0
$226$	−8.98811	−	6.53024i	−0.597880	−	0.434385i
$227$	−12.0537	−	13.3870i	−0.800035	−	0.888529i	0.195712	−	0.980661i	$-0.437298\pi$
$227$	−12.0537	−	13.3870i	−0.800035	−	0.888529i	−0.995747	+	0.0921329i	$0.970632\pi$
$228$		0			0
$229$	12.2670	+	5.46161i	0.810624	+	0.360913i	0.769826	−	0.638254i	$-0.220343\pi$
$229$	12.2670	+	5.46161i	0.810624	+	0.360913i	0.0407985	+	0.999167i	$0.487010\pi$
$230$	−0.0742139	−	0.128542i	−0.00489352	−	0.00847583i
$231$		0			0
$232$	−8.15540	+	14.1256i	−0.535428	+	0.927389i
$233$	−2.72611	+	1.98063i	−0.178593	+	0.129756i	−0.673490	−	0.739196i	$-0.735206\pi$
$233$	−2.72611	+	1.98063i	−0.178593	+	0.129756i	0.494897	+	0.868952i	$0.335206\pi$
$234$		0			0
$235$	−0.304276	+	0.936466i	−0.0198488	+	0.0610883i
$236$	−3.49476	+	1.55597i	−0.227490	+	0.101285i
$237$		0			0
$238$	−0.206755	+	0.0439472i	−0.0134020	+	0.00284867i
$239$	15.5217	−	17.2386i	1.00401	−	1.11507i	0.0106638	−	0.999943i	$-0.496606\pi$
$239$	15.5217	−	17.2386i	1.00401	−	1.11507i	0.993351	−	0.115128i	$-0.0367278\pi$
$240$		0			0
$241$	−7.58206	+	13.1325i	−0.488404	+	0.845940i	−0.999911	−	0.0133389i	$-0.995754\pi$
$241$	−7.58206	+	13.1325i	−0.488404	+	0.845940i	0.511507	+	0.859279i	$0.329087\pi$
$242$	1.49863	−	6.17673i	0.0963358	−	0.397055i
$243$		0			0
$244$	−18.4494	+	13.4043i	−1.18110	+	0.858120i
$245$	−16.5875	−	3.52578i	−1.05974	−	0.225254i
$246$		0			0
$247$	2.62688	−	24.9931i	0.167144	−	1.59027i
$248$	−1.44566	+	13.7545i	−0.0917993	+	0.873412i
$249$		0			0
$250$	1.65291	+	0.351338i	0.104539	+	0.0222205i
$251$	−0.471095	+	0.342271i	−0.0297353	+	0.0216039i	−0.602554	−	0.798078i	$-0.705850\pi$
$251$	−0.471095	+	0.342271i	−0.0297353	+	0.0216039i	0.572818	+	0.819682i	$0.305850\pi$
$252$		0			0
$253$	−0.266163	+	0.0978289i	−0.0167335	+	0.00615045i
$254$	−3.80863	+	6.59673i	−0.238974	+	0.413916i
$255$		0			0
$256$	−3.03110	+	3.36638i	−0.189444	+	0.210399i
$257$	−10.7317	+	2.28109i	−0.669423	+	0.142290i	−0.530072	−	0.847953i	$-0.677835\pi$
$257$	−10.7317	+	2.28109i	−0.669423	+	0.142290i	−0.139351	+	0.990243i	$0.544502\pi$
$258$		0			0
$259$	6.64052	−	2.95655i	0.412622	−	0.183711i
$260$	−6.10421	+	18.7868i	−0.378567	+	1.16511i
$261$		0			0
$262$	8.40108	−	6.10374i	0.519020	−	0.377090i
$263$	−7.19768	+	12.4668i	−0.443828	+	0.768733i	−0.997970	−	0.0636896i	$-0.979713\pi$
$263$	−7.19768	+	12.4668i	−0.443828	+	0.768733i	0.554142	+	0.832422i	$0.313047\pi$
$264$		0			0
$265$	3.63940	+	6.30363i	0.223567	+	0.387229i
$266$	3.91398	+	1.74262i	0.239982	+	0.106847i
$267$		0			0
$268$	−13.0213	−	14.4617i	−0.795404	−	0.883386i
$269$	0.395590	+	0.287413i	0.0241195	+	0.0175239i	0.599780	−	0.800165i	$-0.295255\pi$
$269$	0.395590	+	0.287413i	0.0241195	+	0.0175239i	−0.575660	+	0.817689i	$0.695255\pi$
$270$		0			0
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	−0.503234	−	0.864150i	$-0.667857\pi$
$271$	6.77950	−	20.8652i	0.411825	−	1.26747i	0.915060	−	0.403318i	$-0.132143\pi$
$272$	−0.647922	−	0.137720i	−0.0392861	−	0.00835051i
$273$		0			0
$274$	4.73856	+	8.20743i	0.286267	+	0.495829i
$275$	−4.96360	+	12.3980i	−0.299316	+	0.747627i
$276$		0			0
$277$	−0.299947	−	2.85381i	−0.0180221	−	0.171469i	0.981809	−	0.189874i	$-0.0608078\pi$
$277$	−0.299947	−	2.85381i	−0.0180221	−	0.171469i	−0.999831	+	0.0184051i	$0.994141\pi$
$278$	2.12508	+	6.54031i	0.127454	+	0.392262i
$279$		0			0
$280$	−5.99497	−	4.35560i	−0.358268	−	0.260297i
$281$	−16.6065	+	7.39368i	−0.990660	+	0.441070i	−0.837089	−	0.547067i	$-0.815744\pi$
$281$	−16.6065	+	7.39368i	−0.990660	+	0.441070i	−0.153571	+	0.988138i	$0.549078\pi$
$282$		0			0
$283$	−13.7420	+	15.2620i	−0.816878	+	0.907235i	−0.997078	−	0.0763955i	$-0.975659\pi$
$283$	−13.7420	+	15.2620i	−0.816878	+	0.907235i	0.180200	+	0.983630i	$0.442326\pi$
$284$	13.2690	+	5.90775i	0.787372	+	0.350561i
$285$		0			0
$286$	−6.68838	−	3.52921i	−0.395492	−	0.208686i
$287$	6.76362			0.399244
$288$		0			0
$289$	−5.22278	−	16.0741i	−0.307223	−	0.945534i
$290$	8.94417	+	9.93350i	0.525219	+	0.583315i
$291$		0			0
$292$	0.513168	−	4.88247i	0.0300309	−	0.285725i
$293$	0.841272	−	0.178818i	0.0491476	−	0.0104467i	−0.183272	−	0.983062i	$-0.558669\pi$
$293$	0.841272	−	0.178818i	0.0491476	−	0.0104467i	0.232420	+	0.972616i	$0.425336\pi$
$294$		0			0
$295$	0.721065	+	6.86047i	0.0419820	+	0.399432i
$296$	−13.2250			−0.768685
$297$		0			0
$298$	−2.61848			−0.151684
$299$	0.0352677	+	0.335550i	0.00203959	+	0.0194054i
$300$		0			0
$301$	−7.72681	+	1.64238i	−0.445366	+	0.0946654i
$302$	−0.177018	+	1.68421i	−0.0101862	+	0.0969155i
$303$		0			0
$304$	8.98392	+	9.97766i	0.515263	+	0.572258i
$305$	12.7075	+	39.1095i	0.727627	+	2.23941i
$306$		0			0
$307$	3.48920			0.199139			0.0995696	−	0.995031i	$-0.468253\pi$
$307$	3.48920			0.199139			0.0995696	+	0.995031i	$0.468253\pi$
$308$	−4.61406	+	4.48401i	−0.262910	+	0.255500i
$309$		0			0
$310$	10.3541	+	4.60996i	0.588076	+	0.261828i
$311$	−7.25692	+	8.05963i	−0.411502	+	0.457020i	−0.912892	−	0.408202i	$-0.866156\pi$
$311$	−7.25692	+	8.05963i	−0.411502	+	0.457020i	0.501389	+	0.865222i	$0.332822\pi$
$312$		0			0
$313$	−25.8360	+	11.5029i	−1.46034	+	0.650185i	−0.974607	−	0.223923i	$-0.928114\pi$
$313$	−25.8360	+	11.5029i	−1.46034	+	0.650185i	−0.485732	+	0.874108i	$0.661447\pi$
$314$	−8.43935	−	6.13155i	−0.476260	−	0.346023i
$315$		0			0
$316$	4.57569	+	14.0825i	0.257403	+	0.792204i
$317$	−0.116291	−	1.10643i	−0.00653154	−	0.0621434i	0.990771	−	0.135549i	$-0.0432799\pi$
$317$	−0.116291	−	1.10643i	−0.00653154	−	0.0621434i	−0.997302	+	0.0734057i	$0.976613\pi$
$318$		0			0
$319$	21.6141	−	13.6011i	1.21016	−	0.761517i
$320$	−1.59933	−	2.77013i	−0.0894055	−	0.154855i
$321$		0			0
$322$	−0.0562640	−	0.0119593i	−0.00313547	−	0.000666464i
$323$	0.618308	−	1.90296i	0.0344036	−	0.105883i
$324$		0			0
$325$	12.8550	+	9.33967i	0.713065	+	0.518072i
$326$	2.25154	+	2.50059i	0.124701	+	0.138495i
$327$		0			0
$328$	−11.2417	−	5.00512i	−0.620719	−	0.276362i
$329$	0.190795	+	0.330466i	0.0105188	+	0.0182192i
$330$		0			0
$331$	6.18915	−	10.7199i	0.340187	−	0.589221i	−0.644281	−	0.764789i	$-0.722843\pi$
$331$	6.18915	−	10.7199i	0.340187	−	0.589221i	0.984467	+	0.175569i	$0.0561764\pi$
$332$	−6.68275	+	4.85530i	−0.366763	+	0.266469i
$333$		0			0
$334$	−0.896648	+	2.75960i	−0.0490624	+	0.150999i
$335$	−32.0573	+	14.2728i	−1.75148	+	0.779807i
$336$		0			0
$337$	−13.1792	+	2.80132i	−0.717916	+	0.152598i	−0.552364	−	0.833603i	$-0.686274\pi$
$337$	−13.1792	+	2.80132i	−0.717916	+	0.152598i	−0.165552	+	0.986201i	$0.552941\pi$
$338$	−0.994521	+	1.10453i	−0.0540948	+	0.0600783i
$339$		0			0
$340$	−0.786384	+	1.36206i	−0.0426477	+	0.0738679i
$341$	12.0518	−	17.9899i	0.652642	−	0.974208i
$342$		0			0
$343$	−11.9104	+	8.65342i	−0.643102	+	0.467241i
$344$	14.0580	+	2.98811i	0.757955	+	0.161108i
$345$		0			0
$346$	0.941593	−	8.95866i	0.0506204	−	0.481621i
$347$	1.01802	−	9.68582i	0.0546502	−	0.519962i	−0.932614	−	0.360875i	$-0.882478\pi$
$347$	1.01802	−	9.68582i	0.0546502	−	0.519962i	0.987265	−	0.159087i	$-0.0508551\pi$
$348$		0			0
$349$	4.34317	+	0.923168i	0.232484	+	0.0494161i	0.322680	−	0.946508i	$-0.395416\pi$
$349$	4.34317	+	0.923168i	0.232484	+	0.0494161i	−0.0901962	+	0.995924i	$0.528749\pi$
$350$	−2.19156	+	1.59226i	−0.117144	+	0.0851100i
$351$		0			0
$352$	16.9810	−	6.24142i	0.905090	−	0.332669i
$353$	16.2618	−	28.1662i	0.865527	−	1.49914i	−0.000996749	−	1.00000i	$-0.500317\pi$
$353$	16.2618	−	28.1662i	0.865527	−	1.49914i	0.866523	−	0.499137i	$-0.166349\pi$
$354$		0			0
$355$	17.5256	−	19.4641i	0.930160	−	1.03305i
$356$	−3.46907	+	0.737373i	−0.183860	+	0.0390807i
$357$		0			0
$358$	3.72080	−	1.65661i	0.196650	−	0.0875543i
$359$	8.58143	−	26.4109i	0.452911	−	1.39392i	−0.420660	−	0.907218i	$-0.638201\pi$
$359$	8.58143	−	26.4109i	0.452911	−	1.39392i	0.873571	−	0.486697i	$-0.161799\pi$
$360$		0			0
$361$	−17.4395	+	12.6705i	−0.917868	+	0.666870i
$362$	0.721600	−	1.24985i	0.0379264	−	0.0656905i
$363$		0			0
$364$	3.82761	+	6.62962i	0.200621	+	0.347487i
$365$	−8.08737	−	3.60073i	−0.423312	−	0.188471i
$366$		0			0
$367$	0.784353	+	0.871112i	0.0409429	+	0.0454717i	0.763268	−	0.646082i	$-0.223593\pi$
$367$	0.784353	+	0.871112i	0.0409429	+	0.0454717i	−0.722326	+	0.691553i	$0.756927\pi$
$368$	−0.145831	−	0.105952i	−0.00760197	−	0.00552315i
$369$		0			0
$370$	−3.34912	+	10.3075i	−0.174112	+	0.535862i
$371$	2.75915	+	0.586475i	0.143248	+	0.0304483i
$372$		0			0
$373$	−10.8834	−	18.8506i	−0.563520	−	0.976046i	−0.997186	−	0.0749719i	$-0.976113\pi$
$373$	−10.8834	−	18.8506i	−0.563520	−	0.976046i	0.433665	−	0.901074i	$-0.357220\pi$
$374$	−0.462464	−	0.385570i	−0.0239134	−	0.0199373i
$375$		0			0
$376$	−0.0725693	−	0.690451i	−0.00374248	−	0.0356073i
$377$	−9.38942	−	28.8977i	−0.483580	−	1.48831i
$378$		0			0
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	0.871749	−	0.489953i	$-0.162986\pi$
$379$	13.1440	+	9.54967i	0.675161	+	0.490533i	−0.196588	+	0.980486i	$0.562986\pi$
$380$	29.1227	−	12.9663i	1.49396	−	0.665155i
$381$		0			0
$382$	−4.57114	+	5.07676i	−0.233880	+	0.259750i
$383$	−5.65791	−	2.51906i	−0.289105	−	0.128718i	0.257060	−	0.966396i	$-0.417246\pi$
$383$	−5.65791	−	2.51906i	−0.289105	−	0.128718i	−0.546165	+	0.837677i	$0.683913\pi$
$384$		0			0
$385$	5.11888	+	10.4116i	0.260882	+	0.530626i
$386$	−3.89830			−0.198418
$387$		0			0
$388$	0.0457401	+	0.140773i	0.00232210	+	0.00714669i
$389$	0.483924	+	0.537452i	0.0245359	+	0.0272499i	0.755288	−	0.655393i	$-0.227497\pi$
$389$	0.483924	+	0.537452i	0.0245359	+	0.0272499i	−0.730752	+	0.682643i	$0.760830\pi$
$390$		0			0
$391$	−0.00280798	+	0.0267162i	−0.000142006	+	0.00135110i
$392$	11.6954	−	2.48593i	0.590705	−	0.125558i
$393$		0			0
$394$	1.24706	+	11.8650i	0.0628259	+	0.597749i
$395$	26.7009			1.34347
$396$		0			0
$397$	4.08994			0.205268			0.102634	−	0.994719i	$-0.467273\pi$
$397$	4.08994			0.205268			0.102634	+	0.994719i	$0.467273\pi$
$398$	−0.802456	−	7.63486i	−0.0402235	−	0.382701i
$399$		0			0
$400$	−8.30361	+	1.76499i	−0.415180	+	0.0882493i
$401$	−0.590196	+	5.61534i	−0.0294730	+	0.280417i	0.969852	+	0.243693i	$0.0783588\pi$
$401$	−0.590196	+	5.61534i	−0.0294730	+	0.280417i	−0.999325	+	0.0367238i	$0.988308\pi$
$402$		0			0
$403$	−17.2394	−	19.1463i	−0.858757	−	0.953746i
$404$	−1.05881	−	3.25868i	−0.0526777	−	0.162125i
$405$		0			0
$406$	5.18012			0.257085
$407$	18.3129	+	9.66305i	0.907738	+	0.478980i
$408$		0			0
$409$	8.63188	+	3.84316i	0.426819	+	0.190032i	0.608892	−	0.793253i	$-0.291614\pi$
$409$	8.63188	+	3.84316i	0.426819	+	0.190032i	−0.182073	+	0.983285i	$0.558281\pi$
$410$	−6.74786	+	7.49426i	−0.333253	+	0.370115i
$411$		0			0
$412$	4.59171	−	2.04436i	0.226217	−	0.100718i
$413$	2.16276	+	1.57134i	0.106422	+	0.0773204i
$414$		0			0
$415$	4.60290	+	14.1663i	0.225948	+	0.695395i
$416$	−2.25006	−	21.4079i	−0.110318	−	1.04961i
$417$		0			0
$418$	2.98989	+	11.8324i	0.146240	+	0.578741i
$419$	0.0757820	+	0.131258i	0.00370219	+	0.00641238i	0.867871	−	0.496790i	$-0.165488\pi$
$419$	0.0757820	+	0.131258i	0.00370219	+	0.00641238i	−0.864168	+	0.503203i	$0.832155\pi$
$420$		0			0
$421$	−16.6056	−	3.52962i	−0.809306	−	0.172023i	−0.215367	−	0.976533i	$-0.569095\pi$
$421$	−16.6056	−	3.52962i	−0.809306	−	0.172023i	−0.593939	+	0.804510i	$0.702428\pi$
$422$	1.49003	−	4.58585i	0.0725337	−	0.223236i
$423$		0			0
$424$	−4.15194	−	3.01656i	−0.201636	−	0.146497i
$425$	0.846527	+	0.940164i	0.0410626	+	0.0456047i
$426$		0			0
$427$	14.5585	+	6.48187i	0.704536	+	0.313680i
$428$	−9.99085	−	17.3047i	−0.482926	−	0.836453i
$429$		0			0
$430$	5.88900	−	10.2000i	0.283993	−	0.491890i
$431$	−20.5242	+	14.9117i	−0.988618	+	0.718273i	−0.959618	−	0.281307i	$-0.909232\pi$
$431$	−20.5242	+	14.9117i	−0.988618	+	0.718273i	−0.0289998	+	0.999579i	$0.509232\pi$
$432$		0			0
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	−0.749999	−	0.661439i	$-0.769946\pi$
$433$	5.10950	−	15.7254i	0.245547	−	0.755716i	0.995546	−	0.0942769i	$-0.0300539\pi$
$434$	4.01259	−	1.78652i	0.192611	−	0.0857558i
$435$		0			0
$436$	8.47477	−	1.80137i	0.405868	−	0.0862699i
$437$	0.364341	−	0.404641i	0.0174288	−	0.0193566i
$438$		0			0
$439$	19.6207	−	33.9840i	0.936443	−	1.62197i	0.164403	−	0.986393i	$-0.447430\pi$
$439$	19.6207	−	33.9840i	0.936443	−	1.62197i	0.772040	−	0.635574i	$-0.219237\pi$
$440$	−0.803326	−	21.0930i	−0.0382971	−	1.00557i
$441$		0			0
$442$	−0.579580	+	0.421089i	−0.0275678	+	0.0200292i
$443$	31.4859	+	6.69254i	1.49594	+	0.317972i	0.881951	−	0.471341i	$-0.156230\pi$
$443$	31.4859	+	6.69254i	1.49594	+	0.317972i	0.613991	+	0.789313i	$0.289563\pi$
$444$		0			0
$445$	−0.668490	+	6.36026i	−0.0316895	+	0.301505i
$446$	−0.0231720	+	0.220466i	−0.00109722	+	0.0104394i
$447$		0			0
$448$	−1.21251	−	0.257726i	−0.0572856	−	0.0121764i
$449$	−20.9085	+	15.1909i	−0.986731	+	0.716902i	−0.959203	−	0.282719i	$-0.908764\pi$
$449$	−20.9085	+	15.1909i	−0.986731	+	0.716902i	−0.0275281	+	0.999621i	$0.508764\pi$
$450$		0			0
$451$	11.9096	+	15.1447i	0.560799	+	0.713134i
$452$	−16.0178	+	27.7437i	−0.753415	+	1.30495i
$453$		0			0
$454$	6.96480	−	7.73519i	0.326874	−	0.363030i
$455$	13.5025	−	2.87005i	0.633007	−	0.134550i
$456$		0			0
$457$	−11.6169	+	5.17218i	−0.543416	+	0.241944i	−0.660038	−	0.751232i	$-0.729460\pi$
$457$	−11.6169	+	5.17218i	−0.543416	+	0.241944i	0.116623	+	0.993176i	$0.462793\pi$
$458$	−2.39760	+	7.37904i	−0.112032	+	0.344800i
$459$		0			0
$460$	−0.346255	+	0.251569i	−0.0161442	+	0.0117295i
$461$	−9.51087	+	16.4733i	−0.442965	+	0.767238i	−0.997908	−	0.0646502i	$-0.979407\pi$
$461$	−9.51087	+	16.4733i	−0.442965	+	0.767238i	0.554943	+	0.831889i	$0.312740\pi$
$462$		0			0
$463$	11.4334	+	19.8032i	0.531353	+	0.920331i	0.999330	+	0.0365903i	$0.0116497\pi$
$463$	11.4334	+	19.8032i	0.531353	+	0.920331i	−0.467977	+	0.883741i	$0.655017\pi$
$464$	14.8298	+	6.60266i	0.688457	+	0.306521i
$465$		0			0
$466$	−1.30281	−	1.44692i	−0.0603517	−	0.0670274i
$467$	12.8819	+	9.35921i	0.596101	+	0.433093i	0.844493	−	0.535567i	$-0.179902\pi$
$467$	12.8819	+	9.35921i	0.596101	+	0.433093i	−0.248392	+	0.968660i	$0.579902\pi$
$468$		0			0
$469$	−4.20232	+	12.9334i	−0.194045	+	0.597210i
$470$	−0.556515	−	0.118291i	−0.0256701	−	0.00545635i
$471$		0			0
$472$	−2.43188	−	4.21215i	−0.111936	−	0.193880i
$473$	−17.2831	−	14.4094i	−0.794677	−	0.662545i
$474$		0			0
$475$	−2.68041	−	25.5024i	−0.122986	−	1.17013i
$476$	0.188347	+	0.579671i	0.00863285	+	0.0265692i
$477$		0			0
$478$	10.8436	+	7.87832i	0.495973	+	0.360346i
$479$	14.9730	−	6.66640i	0.684133	−	0.304596i	−0.0350809	−	0.999384i	$-0.511169\pi$
$479$	14.9730	−	6.66640i	0.684133	−	0.304596i	0.719214	+	0.694789i	$0.244502\pi$
$480$		0			0
$481$	16.4849	−	18.3083i	0.751647	−	0.834788i
$482$	−8.00450	−	3.56383i	−0.364595	−	0.162328i
$483$		0			0
$484$	−18.1649	−	2.43594i	−0.825676	−	0.110724i
$485$	0.266911			0.0121198
$486$		0			0
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	0.974044	+	0.226361i	$0.0726828\pi$
$487$	7.04142	+	21.6713i	0.319077	+	0.982019i	−0.654966	+	0.755658i	$0.727317\pi$
$488$	−19.4008	−	21.5468i	−0.878234	−	0.975378i
$489$		0			0
$490$	1.02423	−	9.74490i	0.0462700	−	0.440230i
$491$	−42.6893	+	9.07389i	−1.92654	+	0.409499i	−0.927147	+	0.374698i	$0.877747\pi$
$491$	−42.6893	+	9.07389i	−1.92654	+	0.409499i	−0.999394	+	0.0348013i	$0.988920\pi$
$492$		0			0
$493$	−0.252876	−	2.40596i	−0.0113890	−	0.108359i
$494$	14.5209			0.653324
$495$		0			0
$496$	13.7645			0.618045
$497$	−1.06098	−	10.0945i	−0.0475914	−	0.452801i
$498$		0			0
$499$	19.6642	−	4.17976i	0.880291	−	0.187112i	0.254472	−	0.967080i	$-0.418098\pi$
$499$	19.6642	−	4.17976i	0.880291	−	0.187112i	0.625819	+	0.779969i	$0.284765\pi$
$500$	0.509335	−	4.84600i	0.0227781	−	0.216720i
$501$		0			0
$502$	−0.225138	−	0.250041i	−0.0100484	−	0.0111599i
$503$	3.27815	+	10.0891i	0.146165	+	0.449850i	0.997159	−	0.0753254i	$-0.0239995\pi$
$503$	3.27815	+	10.0891i	0.146165	+	0.449850i	−0.850994	+	0.525176i	$0.824000\pi$
$504$		0			0
$505$	−6.17856			−0.274942
$506$	−0.0722927	−	0.147041i	−0.00321380	−	0.00653676i
$507$		0			0
$508$	20.0656	+	8.93377i	0.890266	+	0.396372i
$509$	29.7551	−	33.0464i	1.31887	−	1.46476i	0.533399	−	0.845864i	$-0.320914\pi$
$509$	29.7551	−	33.0464i	1.31887	−	1.46476i	0.785475	−	0.618894i	$-0.212419\pi$
$510$		0			0
$511$	−3.13414	+	1.39541i	−0.138646	+	0.0617292i
$512$	16.5301	+	12.0098i	0.730534	+	0.530764i
$513$		0			0
$514$	−1.95899	−	6.02915i	−0.0864073	−	0.265934i
$515$	−0.947394	−	9.01385i	−0.0417472	−	0.397198i
$516$		0			0
$517$	−0.404002	+	1.00911i	−0.0177680	+	0.0443805i
$518$	2.10004	+	3.63738i	0.0922707	+	0.159817i
$519$		0			0
$520$	−24.5661	−	5.22169i	−1.07730	−	0.228986i
$521$	−5.23819	+	16.1215i	−0.229489	+	0.706296i	0.768315	+	0.640071i	$0.221095\pi$
$521$	−5.23819	+	16.1215i	−0.229489	+	0.706296i	−0.997805	+	0.0662243i	$0.978905\pi$
$522$		0			0
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.0931472	−	0.995652i	$-0.529693\pi$
$523$	−24.4438	−	17.7595i	−1.06885	−	0.776567i	−0.975706	+	0.219085i	$0.929693\pi$
$524$	−20.0360	−	22.2523i	−0.875277	−	0.972094i
$525$		0			0
$526$	−7.59870	−	3.38316i	−0.331319	−	0.147513i
$527$	−1.02565	−	1.77648i	−0.0446780	−	0.0773845i
$528$		0			0
$529$	11.4963	−	19.9123i	0.499841	−	0.865750i
$530$	−3.40255	+	2.47210i	−0.147797	+	0.107381i
$531$		0			0
$532$	3.81763	−	11.7495i	0.165515	−	0.509404i
$533$	20.9417	−	9.32386i	0.907087	−	0.403861i
$534$		0			0
$535$	−35.2443	+	7.49141i	−1.52374	+	0.323882i
$536$	16.5554	−	18.3867i	0.715086	−	0.794183i
$537$		0			0
$538$	−0.141268	+	0.244683i	−0.00609050	+	0.0105491i
$539$	−18.0112	−	5.10310i	−0.775799	−	0.219806i
$540$		0			0
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	−0.774216	−	0.632922i	$-0.781855\pi$
$541$	−9.57164	+	6.95421i	−0.411517	+	0.298985i	0.362699	+	0.931906i	$0.381855\pi$
$542$	12.3996	+	2.63561i	0.532607	+	0.113209i
$543$		0			0
$544$	0.179148	−	1.70447i	0.00768089	−	0.0730788i
$545$	1.63309	−	15.5378i	0.0699539	−	0.665567i
$546$		0			0
$547$	−2.49018	−	0.529304i	−0.106472	−	0.0226314i	0.154367	−	0.988014i	$-0.450666\pi$
$547$	−2.49018	−	0.529304i	−0.106472	−	0.0226314i	−0.260840	+	0.965382i	$0.583999\pi$
$548$	22.1084	−	16.0627i	0.944424	−	0.686164i
$549$		0			0
$550$	−7.42425	−	2.10350i	−0.316571	−	0.0896937i
$551$	−24.5177	+	42.4659i	−1.04449	+	1.80911i
$552$		0			0
$553$	6.92386	−	7.68972i	0.294432	−	0.327000i
$554$	1.62181	−	0.344727i	0.0689043	−	0.0146461i
$555$		0			0
$556$	18.1153	−	8.06545i	0.768260	−	0.342051i
$557$	−2.98987	+	9.20189i	−0.126685	+	0.389896i	−0.994204	−	0.107507i	$-0.965713\pi$
$557$	−2.98987	+	9.20189i	−0.126685	+	0.389896i	0.867519	+	0.497404i	$0.165713\pi$
$558$		0			0
$559$	−21.6599	+	15.7368i	−0.916117	+	0.665598i
$560$	−3.68748	+	6.38690i	−0.155824	+	0.269896i
$561$		0			0
$562$	−5.25175	−	9.09630i	−0.221532	−	0.383704i
$563$	21.9134	+	9.75648i	0.923540	+	0.411187i	0.812720	−	0.582654i	$-0.197986\pi$
$563$	21.9134	+	9.75648i	0.923540	+	0.411187i	0.110820	+	0.993840i	$0.464652\pi$
$564$		0			0
$565$	38.6542	+	42.9298i	1.62619	+	1.80607i
$566$	−9.60027	−	6.97501i	−0.403530	−	0.293181i
$567$		0			0
$568$	−5.70659	+	17.5631i	−0.239443	+	0.736930i
$569$	−36.7971	−	7.82146i	−1.54261	−	0.327893i	−0.643444	−	0.765493i	$-0.722495\pi$
$569$	−36.7971	−	7.82146i	−1.54261	−	0.327893i	−0.899169	+	0.437601i	$0.855828\pi$
$570$		0			0
$571$	7.37740	+	12.7780i	0.308735	+	0.534744i	0.978086	−	0.208202i	$-0.0667612\pi$
$571$	7.37740	+	12.7780i	0.308735	+	0.534744i	−0.669351	+	0.742946i	$0.733428\pi$
$572$	−8.10485	+	20.2442i	−0.338881	+	0.846451i
$573$		0			0
$574$	0.408508	+	3.88669i	0.0170508	+	0.162227i
$575$	0.106386	+	0.327424i	0.00443662	+	0.0136545i
$576$		0			0
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	0.896226	−	0.443598i	$-0.146298\pi$
$577$	18.0466	+	13.1116i	0.751289	+	0.545843i	−0.144937	+	0.989441i	$0.546298\pi$
$578$	8.92147	−	3.97210i	0.371084	−	0.165217i
$579$		0			0
$580$	25.7907	−	28.6435i	1.07090	−	1.18935i
$581$	5.27339	+	2.34787i	0.218777	+	0.0974059i
$582$		0			0
$583$	3.54519	+	7.21079i	0.146827	+	0.298640i
$584$	6.24181			0.258288
$585$		0			0
$586$	0.153568	+	0.472634i	0.00634384	+	0.0195243i
$587$	1.67294	+	1.85799i	0.0690496	+	0.0766873i	0.776680	−	0.629896i	$-0.216902\pi$
$587$	1.67294	+	1.85799i	0.0690496	+	0.0766873i	−0.707630	+	0.706583i	$0.750236\pi$
$588$		0			0
$589$	−4.34610	+	41.3504i	−0.179078	+	1.70381i
$590$	−3.89880	+	0.828715i	−0.160511	+	0.0341177i
$591$		0			0
$592$	1.37581	+	13.0900i	0.0565456	+	0.537995i
$593$	10.8953			0.447417			0.223708	−	0.974656i	$-0.428184\pi$
$593$	10.8953			0.447417			0.223708	+	0.974656i	$0.428184\pi$
$594$		0			0
$595$	1.09907			0.0450577
$596$	0.789236	+	7.50908i	0.0323284	+	0.307584i
$597$		0			0
$598$	−0.190693	+	0.0405330i	−0.00779800	+	0.00165752i
$599$	−3.85063	+	36.6363i	−0.157332	+	1.49692i	0.576225	+	0.817291i	$0.304525\pi$
$599$	−3.85063	+	36.6363i	−0.157332	+	1.49692i	−0.733558	+	0.679627i	$0.762142\pi$
$600$		0			0
$601$	−10.3409	−	11.4848i	−0.421815	−	0.468474i	0.494356	−	0.869259i	$-0.335404\pi$
$601$	−10.3409	−	11.4848i	−0.421815	−	0.468474i	−0.916172	+	0.400786i	$0.868737\pi$
$602$	−1.41047	−	4.34099i	−0.0574866	−	0.176925i
$603$		0			0
$604$	4.88321			0.198695
$605$	−14.2996	+	29.7949i	−0.581361	+	1.21134i
$606$		0			0
$607$	−23.2743	−	10.3624i	−0.944675	−	0.420596i	−0.124186	−	0.992259i	$-0.539632\pi$
$607$	−23.2743	−	10.3624i	−0.944675	−	0.420596i	−0.820489	+	0.571663i	$0.806299\pi$
$608$	−23.2447	+	25.8158i	−0.942696	+	1.04697i
$609$		0			0
$610$	−21.7067	+	9.66443i	−0.878877	+	0.391301i
$611$	1.04630	+	0.760183i	0.0423289	+	0.0307537i
$612$		0			0
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	−0.850672	−	0.525697i	$-0.823805\pi$
$613$	−11.6728	−	35.9252i	−0.471461	−	1.45101i	0.379211	−	0.925310i	$-0.376195\pi$
$614$	0.210740	+	2.00506i	0.00850478	+	0.0809175i
$615$		0			0
$616$	−6.28298	−	5.23830i	−0.253148	−	0.211057i
$617$	20.9464	+	36.2802i	0.843271	+	1.46059i	0.887115	+	0.461549i	$0.152706\pi$
$617$	20.9464	+	36.2802i	0.843271	+	1.46059i	−0.0438437	+	0.999038i	$0.513960\pi$
$618$		0			0
$619$	5.85872	+	1.24531i	0.235482	+	0.0500532i	0.324141	−	0.946009i	$-0.394925\pi$
$619$	5.85872	+	1.24531i	0.235482	+	0.0500532i	−0.0886590	+	0.996062i	$0.528258\pi$
$620$	10.0993	−	31.0823i	0.405596	−	1.24830i
$621$		0			0
$622$	−5.06974	−	3.68338i	−0.203278	−	0.147690i
$623$	1.65837	+	1.84181i	0.0664413	+	0.0737905i
$624$		0			0
$625$	−26.4193	−	11.7626i	−1.05677	−	0.470505i
$626$	−8.17057	−	14.1518i	−0.326562	−	0.565621i
$627$		0			0
$628$	−15.0399	+	26.0498i	−0.600157	+	1.03950i
$629$	1.58690	−	1.15295i	0.0632739	−	0.0459712i
$630$		0			0
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	0.727332	+	0.686286i	$0.240760\pi$
$631$	−6.64368	+	20.4471i	−0.264481	+	0.813988i	−0.991813	+	0.127702i	$0.959240\pi$
$632$	−17.1985	+	7.65725i	−0.684118	+	0.304589i
$633$		0			0
$634$	0.628784	−	0.133652i	0.0249722	−	0.00530801i
$635$	26.5024	−	29.4338i	1.05171	−	1.16805i
$636$		0			0
$637$	−11.1368	+	19.2895i	−0.441256	+	0.764278i
$638$	9.12129	+	11.5990i	0.361115	+	0.459208i
$639$		0			0
$640$	28.0127	−	20.3525i	1.10730	−	0.804501i
$641$	12.5565	+	2.66896i	0.495951	+	0.105418i	0.449095	−	0.893484i	$-0.351746\pi$
$641$	12.5565	+	2.66896i	0.495951	+	0.105418i	0.0468561	+	0.998902i	$0.485080\pi$
$642$		0			0
$643$	−2.96396	+	28.2002i	−0.116887	+	1.11211i	0.766103	+	0.642718i	$0.222193\pi$
$643$	−2.96396	+	28.2002i	−0.116887	+	1.11211i	−0.882990	+	0.469391i	$0.844473\pi$
$644$	−0.0173374	+	0.164954i	−0.000683189	+	0.00650011i
$645$		0			0
$646$	1.13087	+	0.240374i	0.0444936	+	0.00945741i
$647$	−14.1536	+	10.2832i	−0.556436	+	0.404274i	−0.830153	−	0.557536i	$-0.811747\pi$
$647$	−14.1536	+	10.2832i	−0.556436	+	0.404274i	0.273717	+	0.961810i	$0.411747\pi$
$648$		0			0
$649$	0.289810	+	7.60956i	0.0113760	+	0.298701i
$650$	−4.59060	+	7.95116i	−0.180058	+	0.311870i
$651$		0			0
$652$	6.49236	−	7.21050i	0.254261	−	0.282385i
$653$	−28.6619	+	6.09227i	−1.12163	+	0.238409i	−0.731159	−	0.682207i	$-0.761020\pi$
$653$	−28.6619	+	6.09227i	−1.12163	+	0.238409i	−0.390468	+	0.920617i	$0.627687\pi$
$654$		0			0
$655$	−49.3268	+	21.9617i	−1.92736	+	0.858114i
$656$	−3.78455	+	11.6477i	−0.147762	+	0.454764i
$657$		0			0
$658$	−0.178378	+	0.129599i	−0.00695388	+	0.00505229i
$659$	13.7935	−	23.8911i	0.537319	−	0.930664i	−0.461728	−	0.887021i	$-0.652771\pi$
$659$	13.7935	−	23.8911i	0.537319	−	0.930664i	0.999047	−	0.0436422i	$-0.0138961\pi$
$660$		0			0
$661$	−14.8776	−	25.7688i	−0.578672	−	1.00229i	−0.995632	−	0.0933649i	$-0.970238\pi$
$661$	−14.8776	−	25.7688i	−0.578672	−	1.00229i	0.416960	−	0.908925i	$-0.363096\pi$
$662$	6.53398	+	2.90912i	0.253950	+	0.113066i
$663$		0			0
$664$	−7.02738	−	7.80469i	−0.272715	−	0.302881i
$665$	−18.0228	−	13.0943i	−0.698893	−	0.507775i
$666$		0			0
$667$	0.203437	−	0.626115i	0.00787711	−	0.0242433i
$668$	8.18403	+	1.73957i	0.316650	+	0.0673060i
$669$		0			0
$670$	−10.1380	−	17.5596i	−0.391666	−	0.678385i
$671$	11.1213	+	44.0120i	0.429331	+	1.69906i
$672$		0			0
$673$	−1.00908	−	9.60079i	−0.0388973	−	0.370083i	−0.996604	−	0.0823384i	$-0.973761\pi$
$673$	−1.00908	−	9.60079i	−0.0388973	−	0.370083i	0.957707	−	0.287745i	$-0.0929055\pi$
$674$	−2.40577	−	7.40418i	−0.0926666	−	0.285198i
$675$		0			0
$676$	3.46724	+	2.51910i	0.133355	+	0.0968883i
$677$	0.0896326	−	0.0399070i	0.00344486	−	0.00153375i	−0.405013	−	0.914311i	$-0.632733\pi$
$677$	0.0896326	−	0.0399070i	0.00344486	−	0.00153375i	0.408458	+	0.912777i	$0.366067\pi$
$678$		0			0
$679$	0.0692131	−	0.0768689i	0.00265615	−	0.00294996i
$680$	−1.82675	−	0.813323i	−0.0700528	−	0.0311895i
$681$		0			0
$682$	11.0657	+	5.83898i	0.423729	+	0.223586i
$683$	−30.5246			−1.16799			−0.583996	−	0.811756i	$-0.698512\pi$
$683$	−30.5246			−1.16799			−0.583996	+	0.811756i	$0.698512\pi$
$684$		0			0
$685$	−15.2277	−	46.8660i	−0.581820	−	1.79066i
$686$	−5.69202	−	6.32163i	−0.217323	−	0.241361i
$687$		0			0
$688$	1.49514	−	14.2253i	0.0570018	−	0.542336i
$689$	9.35145	−	1.98771i	0.356262	−	0.0757258i
$690$		0			0
$691$	−3.42871	−	32.6220i	−0.130434	−	1.24100i	−0.842426	−	0.538812i	$-0.818873\pi$
$691$	−3.42871	−	32.6220i	−0.130434	−	1.24100i	0.711992	−	0.702188i	$-0.247793\pi$
$692$	−25.9748			−0.987413
$693$		0			0
$694$	5.62741			0.213614
$695$	−3.73768	−	35.5616i	−0.141778	−	1.34893i
$696$		0			0
$697$	1.78527	−	0.379471i	0.0676220	−	0.0143735i
$698$	−0.268178	+	2.55154i	−0.0101507	+	0.0965773i
$699$		0			0
$700$	5.22673	+	5.80487i	0.197552	+	0.219404i
$701$	2.70365	+	8.32098i	0.102115	+	0.314279i	0.989043	−	0.147630i	$-0.0471646\pi$
$701$	2.70365	+	8.32098i	0.102115	+	0.314279i	−0.886927	+	0.461909i	$0.847165\pi$
$702$		0			0
$703$	−39.7584			−1.49952
$704$	−1.55793	−	3.16878i	−0.0587168	−	0.119428i
$705$		0			0
$706$	17.1678	+	7.64360i	0.646119	+	0.287671i
$707$	−1.60217	+	1.77939i	−0.0602558	+	0.0669208i
$708$		0			0
$709$	24.4610	−	10.8907i	0.918651	−	0.409010i	0.107740	−	0.994179i	$-0.465639\pi$
$709$	24.4610	−	10.8907i	0.918651	−	0.409010i	0.810911	+	0.585169i	$0.198972\pi$
$710$	12.2435	+	8.89542i	0.459490	+	0.333839i
$711$		0			0
$712$	−1.39340	−	4.28845i	−0.0522199	−	0.160716i
$713$	−0.0583495	−	0.555159i	−0.00218521	−	0.0207909i
$714$		0			0
$715$	30.2020	+	25.1803i	1.12949	+	0.941690i
$716$	−5.87217	−	10.1709i	−0.219453	−	0.380105i
$717$		0			0
$718$	15.6953	+	3.33613i	0.585742	+	0.124503i
$719$	4.63672	−	14.2703i	0.172920	−	0.532194i	−0.826612	−	0.562772i	$-0.809735\pi$
$719$	4.63672	−	14.2703i	0.172920	−	0.532194i	0.999532	+	0.0305782i	$0.00973486\pi$
$720$		0			0
$721$	−2.84161	−	2.06455i	−0.105827	−	0.0768879i
$722$	−8.33438	−	9.25627i	−0.310174	−	0.344483i
$723$		0			0
$724$	−3.80172	−	1.69263i	−0.141290	−	0.0629062i
$725$	−15.5020	−	26.8502i	−0.575730	−	0.997193i
$726$		0			0
$727$	−13.7663	+	23.8438i	−0.510562	+	0.884319i	0.489363	+	0.872080i	$0.337229\pi$
$727$	−13.7663	+	23.8438i	−0.510562	+	0.884319i	−0.999925	+	0.0122391i	$0.996104\pi$
$728$	−7.87410	+	5.72087i	−0.291834	+	0.212029i
$729$		0			0
$730$	1.58069	−	4.86486i	0.0585039	−	0.180057i
$731$	−1.94736	+	0.867021i	−0.0720257	+	0.0320679i
$732$		0			0
$733$	−46.6964	+	9.92564i	−1.72477	+	0.366612i	−0.960500	−	0.278281i	$-0.910235\pi$
$733$	−46.6964	+	9.92564i	−1.72477	+	0.366612i	−0.764273	+	0.644893i	$0.776902\pi$
$734$	−0.453208	+	0.503339i	−0.0167282	+	0.0185786i
$735$		0			0
$736$	0.233195	−	0.403906i	0.00859570	−	0.0148882i
$737$	−36.3593	+	13.3640i	−1.33931	+	0.492267i
$738$		0			0
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	−0.609714	−	0.792622i	$-0.708716\pi$
$739$	−1.20421	+	0.874910i	−0.0442976	+	0.0321841i	0.565416	+	0.824806i	$0.308716\pi$
$740$	30.5686	+	6.49755i	1.12372	+	0.238855i
$741$		0			0
$742$	−0.170370	+	1.62096i	−0.00625446	+	0.0595072i
$743$	−1.89825	+	18.0607i	−0.0696402	+	0.662582i	0.902901	+	0.429850i	$0.141433\pi$
$743$	−1.89825	+	18.0607i	−0.0696402	+	0.662582i	−0.972541	+	0.232733i	$0.925233\pi$
$744$		0			0
$745$	13.3177	+	2.83076i	0.487922	+	0.103711i
$746$	10.1751	−	7.39264i	0.372537	−	0.270664i
$747$		0			0
$748$	−0.966316	+	1.44243i	−0.0353320	+	0.0527406i
$749$	−6.98177	+	12.0928i	−0.255108	+	0.441860i
$750$		0			0
$751$	−2.94060	+	3.26586i	−0.107304	+	0.119173i	−0.794404	−	0.607390i	$-0.792217\pi$
$751$	−2.94060	+	3.26586i	−0.107304	+	0.119173i	0.687100	+	0.726563i	$0.258883\pi$
$752$	−0.675855	+	0.143657i	−0.0246459	+	0.00523865i
$753$		0			0
$754$	16.0389	−	7.14096i	0.584101	−	0.260058i
$755$	2.72107	−	8.37459i	0.0990299	−	0.304783i
$756$		0			0
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	−0.366708	−	0.930336i	$-0.619515\pi$
$757$	11.1369	−	8.09140i	0.404776	−	0.294087i	0.771483	+	0.636249i	$0.219515\pi$
$758$	−4.69382	+	8.12993i	−0.170487	+	0.295292i
$759$		0			0
$760$	20.2655	+	35.1008i	0.735105	+	1.27324i
$761$	28.4168	+	12.6520i	1.03011	+	0.458634i	0.850984	−	0.525192i	$-0.176006\pi$
$761$	28.4168	+	12.6520i	1.03011	+	0.458634i	0.179126	+	0.983826i	$0.442673\pi$
$762$		0			0
$763$	−4.05133	−	4.49945i	−0.146668	−	0.162891i
$764$	15.9365	+	11.5786i	0.576564	+	0.418898i
$765$		0			0
$766$	1.10585	−	3.40344i	0.0399558	−	0.122971i
$767$	8.86254	+	1.88379i	0.320008	+	0.0680197i
$768$		0			0
$769$	−10.9677	−	18.9966i	−0.395504	−	0.685034i	0.597661	−	0.801749i	$-0.296097\pi$
$769$	−10.9677	−	18.9966i	−0.395504	−	0.685034i	−0.993165	+	0.116715i	$0.962764\pi$
$770$	−5.67384	+	3.57039i	−0.204471	+	0.128668i
$771$		0			0
$772$	1.17499	+	11.1793i	0.0422887	+	0.402350i
$773$	3.92965	+	12.0942i	0.141340	+	0.434999i	0.996522	−	0.0833281i	$-0.0265549\pi$
$773$	3.92965	+	12.0942i	0.141340	+	0.434999i	−0.855182	+	0.518327i	$0.826555\pi$
$774$		0			0
$775$	−21.2682	−	15.4522i	−0.763976	−	0.555061i
$776$	−0.171921	+	0.0765443i	−0.00617162	+	0.00274778i
$777$		0			0
$778$	−0.279617	+	0.310546i	−0.0100248	+	0.0111336i
$779$	−33.7961	−	15.0470i	−1.21087	−	0.539114i
$780$		0			0
$781$	20.7348	−	20.1504i	0.741950	−	0.721038i
$782$	−0.0155220			−0.000555064
$783$		0			0
$784$	−3.67724	−	11.3174i	−0.131330	−	0.404193i
$785$	36.2942	+	40.3088i	1.29540	+	1.43868i
$786$		0			0
$787$	1.80433	−	17.1671i	0.0643176	−	0.611941i	−0.914127	−	0.405429i	$-0.867122\pi$
$787$	1.80433	−	17.1671i	0.0643176	−	0.611941i	0.978444	−	0.206512i	$-0.0662112\pi$
$788$	33.6496	−	7.15244i	1.19872	−	0.254795i
$789$		0			0
$790$	1.61268	+	15.3436i	0.0573765	+	0.545901i
$791$	22.3870			0.795991
$792$		0			0
$793$	54.0120			1.91802
$794$	0.247023	+	2.35027i	0.00876652	+	0.0834079i
$795$		0			0
$796$	−21.6528	+	4.60245i	−0.767463	+	0.163129i
$797$	3.67956	−	35.0087i	0.130337	−	1.24007i	−0.712411	−	0.701762i	$-0.752397\pi$
$797$	3.67956	−	35.0087i	0.130337	−	1.24007i	0.842748	−	0.538309i	$-0.180936\pi$
$798$		0			0
$799$	0.0689013	+	0.0765227i	0.00243755	+	0.00270718i
$800$	−6.78739	−	20.8894i	−0.239970	−	0.738553i
$801$		0			0
$802$	−3.26248			−0.115202
$803$	−8.64318	−	4.56069i	−0.305011	−	0.160943i
$804$		0			0
$805$	0.273232	+	0.121651i	0.00963016	+	0.00428762i
$806$	9.96114	−	11.0630i	0.350866	−	0.389677i
$807$		0			0
$808$	3.97970	−	1.77188i	0.140005	−	0.0623344i
$809$	−15.4367	−	11.2154i	−0.542725	−	0.394313i	0.282371	−	0.959305i	$-0.408879\pi$
$809$	−15.4367	−	11.2154i	−0.542725	−	0.394313i	−0.825096	+	0.564992i	$0.808879\pi$
$810$		0			0
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	−0.965718	−	0.259593i	$-0.916412\pi$
$811$	−9.59769	−	29.5387i	−0.337020	−	1.03724i	0.628698	−	0.777650i	$-0.283588\pi$
$812$	−1.56134	−	14.8551i	−0.0547923	−	0.521314i
$813$		0			0
$814$	−4.44678	+	11.1071i	−0.155860	+	0.389303i
$815$	−8.74810	−	15.1522i	−0.306433	−	0.530757i
$816$		0			0
$817$	42.2627	+	8.98321i	1.47858	+	0.314283i
$818$	−1.68711	+	5.19240i	−0.0589885	+	0.181548i
$819$		0			0
$820$	23.5253	+	17.0922i	0.821540	+	0.596884i
$821$	−22.7561	−	25.2732i	−0.794195	−	0.882042i	0.201037	−	0.979584i	$-0.435569\pi$
$821$	−22.7561	−	25.2732i	−0.794195	−	0.882042i	−0.995231	+	0.0975412i	$0.968902\pi$
$822$		0			0
$823$	14.2111	+	6.32720i	0.495368	+	0.220552i	0.639186	−	0.769052i	$-0.279271\pi$
$823$	14.2111	+	6.32720i	0.495368	+	0.220552i	−0.143818	+	0.989604i	$0.545938\pi$
$824$	3.19521	+	5.53426i	0.111310	+	0.192795i
$825$		0			0
$826$	−0.772337	+	1.33773i	−0.0268730	+	0.0465455i
$827$	12.9667	−	9.42084i	0.450895	−	0.327595i	−0.339054	−	0.940767i	$-0.610107\pi$
$827$	12.9667	−	9.42084i	0.450895	−	0.327595i	0.789949	+	0.613172i	$0.210107\pi$
$828$		0			0
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	−0.794727	−	0.606967i	$-0.792386\pi$
$829$	5.90205	−	18.1646i	0.204987	−	0.630884i	0.999714	−	0.0239173i	$-0.00761382\pi$
$830$	−7.86260	+	3.50065i	−0.272915	+	0.121509i
$831$		0			0
$832$	−4.10949	+	0.873499i	−0.142471	+	0.0302831i
$833$	−1.18664	+	1.31790i	−0.0411146	+	0.0456624i
$834$		0			0
$835$	7.54371	−	13.0661i	0.261061	−	0.452171i
$836$	33.0308	−	12.1406i	1.14240	−	0.419891i
$837$		0			0
$838$	−0.0708501	+	0.0514756i	−0.00244747	+	0.00177819i
$839$	1.45541	+	0.309356i	0.0502462	+	0.0106802i	0.232966	−	0.972485i	$-0.425157\pi$
$839$	1.45541	+	0.309356i	0.0502462	+	0.0106802i	−0.182720	+	0.983165i	$0.558490\pi$
$840$		0			0
$841$	−3.16588	+	30.1213i	−0.109168	+	1.03867i
$842$	1.02535	−	9.75552i	0.0353358	−	0.336198i
$843$		0			0
$844$	−13.6001	−	2.89079i	−0.468134	−	0.0995049i
$845$	6.25224	−	4.54252i	0.215084	−	0.156267i
$846$		0			0
$847$	4.87274	+	11.8444i	0.167429	+	0.406977i
$848$	−2.55384	+	4.42338i	−0.0876993	+	0.151900i
$849$		0			0
$850$	−0.489134	+	0.543238i	−0.0167772	+	0.0186329i
$851$	0.522121	−	0.110980i	0.0178981	−	0.00380435i
$852$		0			0
$853$	34.5339	−	15.3755i	1.18242	−	0.526447i	0.281132	−	0.959669i	$-0.409290\pi$
$853$	34.5339	−	15.3755i	1.18242	−	0.526447i	0.901287	+	0.433222i	$0.142624\pi$
$854$	−2.84548	+	8.75750i	−0.0973704	+	0.299675i
$855$		0			0
$856$	20.5530	−	14.9326i	0.702487	−	0.510387i
$857$	9.91348	−	17.1706i	0.338638	−	0.586538i	−0.645539	−	0.763727i	$-0.723367\pi$
$857$	9.91348	−	17.1706i	0.338638	−	0.586538i	0.984177	+	0.177189i	$0.0567005\pi$
$858$		0			0
$859$	7.85764	+	13.6098i	0.268099	+	0.464362i	0.968371	−	0.249515i	$-0.0802711\pi$
$859$	7.85764	+	13.6098i	0.268099	+	0.464362i	−0.700272	+	0.713876i	$0.746938\pi$
$860$	−31.0259	−	13.8136i	−1.05798	−	0.471041i
$861$		0			0
$862$	−9.80860	−	10.8936i	−0.334082	−	0.371036i
$863$	6.57548	+	4.77736i	0.223832	+	0.162623i	0.694050	−	0.719927i	$-0.255825\pi$
$863$	6.57548	+	4.77736i	0.223832	+	0.162623i	−0.470218	+	0.882550i	$0.655825\pi$
$864$		0			0
$865$	−14.4739	+	44.5462i	−0.492128	+	1.51462i
$866$	9.34517	+	1.98638i	0.317562	+	0.0674998i
$867$		0			0
$868$	−6.33269	−	10.9685i	−0.214945	−	0.372296i
$869$	29.4100	+	1.96318i	0.997667	+	0.0665963i
$870$		0			0
$871$	4.81776	+	45.8379i	0.163244	+	1.55316i
$872$	3.40401	+	10.4765i	0.115274	+	0.354778i
$873$		0			0
$874$	0.254531	+	0.184928i	0.00860964	+	0.00625527i
$875$	−3.11073	+	1.38498i	−0.105162	+	0.0468210i
$876$		0			0
$877$	−1.69526	+	1.88278i	−0.0572449	+	0.0635769i	−0.771087	−	0.636730i	$-0.780287\pi$
$877$	−1.69526	+	1.88278i	−0.0572449	+	0.0635769i	0.713842	+	0.700307i	$0.246953\pi$
$878$	20.7138	+	9.22239i	0.699058	+	0.311241i
$879$		0			0
$880$	−20.7942	+	2.98947i	−0.700971	+	0.100775i
$881$	47.4109			1.59731			0.798657	−	0.601786i	$-0.205544\pi$
$881$	47.4109			1.59731			0.798657	+	0.601786i	$0.205544\pi$
$882$		0			0
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	0.989029	+	0.147719i	$0.0471930\pi$
$883$	8.19295	+	25.2153i	0.275715	+	0.848563i	−0.713315	+	0.700844i	$0.752807\pi$
$884$	1.38226	+	1.53515i	0.0464904	+	0.0516328i
$885$		0			0
$886$	−1.94417	+	18.4975i	−0.0653156	+	0.621436i
$887$	−46.7841	+	9.94428i	−1.57086	+	0.333896i	−0.909347	−	0.416039i	$-0.863418\pi$
$887$	−46.7841	+	9.94428i	−1.57086	+	0.333896i	−0.661511	+	0.749935i	$0.730085\pi$
$888$		0			0
$889$	−1.60442	−	15.2651i	−0.0538106	−	0.511974i
$890$	−3.69528			−0.123866
$891$		0			0
$892$	0.639221			0.0214027
$893$	−0.218166	−	2.07571i	−0.00730066	−	0.0694612i
$894$		0			0
$895$	−20.7150	+	4.40311i	−0.692427	+	0.147180i
$896$	1.40263	−	13.3451i	0.0468586	−	0.445830i
$897$		0			0
$898$	−9.99221	−	11.0975i	−0.333445	−	0.370328i
$899$	15.5345	+	47.8104i	0.518106	+	1.59457i
$900$		0			0
$901$	0.761187			0.0253588
$902$	−7.98352	+	7.75850i	−0.265822	+	0.258330i
$903$		0			0
$904$	−37.2091	−	16.5666i	−1.23756	−	0.550995i
$905$	−5.02126	+	5.57667i	−0.166912	+	0.185375i
$906$		0			0
$907$	43.3554	−	19.3030i	1.43959	−	0.640947i	0.469333	−	0.883021i	$-0.344494\pi$
$907$	43.3554	−	19.3030i	1.43959	−	0.640947i	0.970258	+	0.242074i	$0.0778277\pi$
$908$	−24.2817	−	17.6417i	−0.805815	−	0.585459i
$909$		0			0
$910$	2.46479	+	7.58583i	0.0817068	+	0.251468i
$911$	−2.97198	−	28.2765i	−0.0984660	−	0.936841i	−0.926533	−	0.376213i	$-0.877226\pi$
$911$	−2.97198	−	28.2765i	−0.0984660	−	0.936841i	0.828067	−	0.560629i	$-0.189440\pi$
$912$		0			0
$913$	4.02834	+	15.9420i	0.133319	+	0.527604i
$914$	−3.67381	−	6.36322i	−0.121519	−	0.210477i
$915$		0			0
$916$	21.8837	+	4.65153i	0.723059	+	0.153691i
$917$	−6.46615	+	19.9008i	−0.213531	+	0.657181i
$918$		0			0
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.0569449	−	0.998377i	$-0.518136\pi$
$919$	−31.0442	−	22.5550i	−1.02406	−	0.744020i	−0.967110	+	0.254358i	$0.918136\pi$
$920$	−0.364112	−	0.404387i	−0.0120044	−	0.0133322i
$921$		0			0
$922$	−10.0408	−	4.47044i	−0.330675	−	0.147226i
$923$	−17.2007	−	29.7924i	−0.566167	−	0.980629i
$924$		0			0
$925$	12.5692	−	21.7704i	0.413272	−	0.715808i
$926$	−10.6893	+	7.76621i	−0.351271	+	0.255214i
$927$		0			0
$928$	−12.9791	+	39.9457i	−0.426061	+	1.31128i
$929$	−12.2302	+	5.44526i	−0.401261	+	0.178653i	−0.597437	−	0.801916i	$-0.703814\pi$
$929$	−12.2302	+	5.44526i	−0.401261	+	0.178653i	0.196176	+	0.980569i	$0.437148\pi$
$930$		0			0
$931$	35.1600	−	7.47348i	1.15232	−	0.244934i
$932$	−3.75669	+	4.17223i	−0.123055	+	0.136666i
$933$		0			0
$934$	−4.60021	+	7.96779i	−0.150523	+	0.260714i
$935$	1.93528	+	2.46098i	0.0632905	+	0.0804826i
$936$		0			0
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	−0.211934	−	0.977284i	$-0.567976\pi$
$937$	19.9588	−	14.5010i	0.652027	−	0.473725i	0.863961	+	0.503559i	$0.167976\pi$
$938$	−7.68596	−	1.63370i	−0.250956	−	0.0533422i
$939$		0			0
$940$	−0.171486	+	1.63158i	−0.00559327	+	0.0532164i
$941$	0.867827	−	8.25682i	0.0282903	−	0.269165i	−0.971229	−	0.238149i	$-0.923459\pi$
$941$	0.867827	−	8.25682i	0.0282903	−	0.269165i	0.999519	−	0.0310154i	$-0.00987409\pi$
$942$		0			0
$943$	0.485823	+	0.103265i	0.0158206	+	0.00336277i
$944$	−3.91616	+	2.84526i	−0.127460	+	0.0926053i
$945$		0			0
$946$	7.23646	−	10.8020i	0.235278	−	0.351202i
$947$	18.9748	−	32.8653i	0.616598	−	1.06798i	−0.373503	−	0.927629i	$-0.621844\pi$
$947$	18.9748	−	32.8653i	0.616598	−	1.06798i	0.990102	−	0.140351i	$-0.0448231\pi$
$948$		0			0
$949$	−7.78041	+	8.64102i	−0.252563	+	0.280499i
$950$	14.4930	−	3.08058i	0.470214	−	0.0999472i
$951$		0			0
$952$	−0.707930	+	0.315191i	−0.0229442	+	0.0102154i
$953$	15.0400	−	46.2884i	0.487194	−	1.49943i	−0.341583	−	0.939852i	$-0.610963\pi$
$953$	15.0400	−	46.2884i	0.487194	−	1.49943i	0.828778	−	0.559578i	$-0.189037\pi$
$954$		0			0
$955$	28.7373	−	20.8789i	0.929918	−	0.675625i
$956$	19.3245	−	33.4710i	0.624998	−	1.08253i
$957$		0			0
$958$	4.73516	+	8.20154i	0.152986	+	0.264980i
$959$	−17.4459	−	7.76740i	−0.563356	−	0.250822i
$960$		0			0
$961$	7.77911	+	8.63958i	0.250939	+	0.278696i
$962$	11.5165	+	8.36721i	0.371306	+	0.269770i
$963$		0			0
$964$	−7.80746	+	24.0289i	−0.251461	+	0.773918i
$965$	19.8269	+	4.21434i	0.638250	+	0.135664i
$966$		0			0
$967$	−5.48901	−	9.50724i	−0.176515	−	0.305732i	0.764170	−	0.645015i	$-0.223149\pi$
$967$	−5.48901	−	9.50724i	−0.176515	−	0.305732i	−0.940684	+	0.339283i	$0.889816\pi$
$968$	0.666025	−	23.2922i	0.0214069	−	0.748639i
$969$		0			0
$970$	0.0161208	+	0.153380i	0.000517609	+	0.00492472i
$971$	−4.03687	−	12.4242i	−0.129549	−	0.398712i	0.865153	−	0.501508i	$-0.167221\pi$
$971$	−4.03687	−	12.4242i	−0.129549	−	0.398712i	−0.994702	+	0.102796i	$0.967221\pi$
$972$		0			0
$973$	−11.2108	−	8.14510i	−0.359401	−	0.261120i
$974$	−12.0280	+	5.35523i	−0.385403	+	0.171592i
$975$		0			0
$976$	−19.3086	+	21.4444i	−0.618053	+	0.686418i
$977$	10.1187	+	4.50514i	0.323726	+	0.144132i	0.562164	−	0.827025i	$-0.309969\pi$
$977$	10.1187	+	4.50514i	0.323726	+	0.144132i	−0.238438	+	0.971158i	$0.576635\pi$
$978$		0			0
$979$	−1.20395	+	6.95643i	−0.0384785	+	0.222328i
$980$	−28.2544			−0.902554
$981$		0			0
$982$	−7.79262	−	23.9832i	−0.248673	−	0.765336i
$983$	17.6861	+	19.6424i	0.564100	+	0.626496i	0.955949	−	0.293533i	$-0.0948312\pi$
$983$	17.6861	+	19.6424i	0.564100	+	0.626496i	−0.391849	+	0.920029i	$0.628165\pi$
$984$		0			0
$985$	6.48429	−	61.6939i	0.206607	−	1.96573i
$986$	1.36730	−	0.290629i	0.0435438	−	0.00925552i
$987$		0			0
$988$	−4.37673	−	41.6418i	−0.139242	−	1.32480i
$989$	−0.580083			−0.0184456
$990$		0			0
$991$	−18.9911			−0.603272			−0.301636	−	0.953423i	$-0.597533\pi$
$991$	−18.9911			−0.603272			−0.301636	+	0.953423i	$0.597533\pi$
$992$	3.72266	+	35.4188i	0.118195	+	1.12455i
$993$		0			0
$994$	5.73671	−	1.21937i	0.181957	−	0.0386762i
$995$	−4.17250	+	39.6987i	−0.132277	+	1.25853i
$996$		0			0
$997$	14.7966	+	16.4333i	0.468613	+	0.520447i	0.930401	−	0.366543i	$-0.119459\pi$
$997$	14.7966	+	16.4333i	0.468613	+	0.520447i	−0.461788	+	0.886990i	$0.652792\pi$
$998$	3.58956	+	11.0475i	0.113625	+	0.349703i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.n.b.289.6		72
3.2	odd	2		99.2.m.b.25.4	yes	72
9.2	odd	6		891.2.f.f.487.4		36
9.4	even	3	inner	297.2.n.b.91.4		72
9.5	odd	6		99.2.m.b.58.6	yes	72
9.7	even	3		891.2.f.e.487.6		36
11.4	even	5	inner	297.2.n.b.235.4		72
33.2	even	10		1089.2.e.o.727.11		36
33.20	odd	10		1089.2.e.p.727.8		36
33.26	odd	10		99.2.m.b.70.6	yes	72
99.2	even	30		9801.2.a.co.1.8		18
99.4	even	15	inner	297.2.n.b.37.6		72
99.20	odd	30		9801.2.a.cm.1.11		18
99.59	odd	30		99.2.m.b.4.4	✓	72
99.68	even	30		1089.2.e.o.364.11		36
99.70	even	15		891.2.f.e.730.6		36
99.79	odd	30		9801.2.a.cn.1.11		18
99.86	odd	30		1089.2.e.p.364.8		36
99.92	odd	30		891.2.f.f.730.4		36
99.97	even	15		9801.2.a.cp.1.8		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	99.59	odd	30
99.2.m.b.25.4	yes	72	3.2	odd	2
99.2.m.b.58.6	yes	72	9.5	odd	6
99.2.m.b.70.6	yes	72	33.26	odd	10
297.2.n.b.37.6		72	99.4	even	15	inner
297.2.n.b.91.4		72	9.4	even	3	inner
297.2.n.b.235.4		72	11.4	even	5	inner
297.2.n.b.289.6		72	1.1	even	1	trivial
891.2.f.e.487.6		36	9.7	even	3
891.2.f.e.730.6		36	99.70	even	15
891.2.f.f.487.4		36	9.2	odd	6
891.2.f.f.730.4		36	99.92	odd	30
1089.2.e.o.364.11		36	99.68	even	30
1089.2.e.o.727.11		36	33.2	even	10
1089.2.e.p.364.8		36	99.86	odd	30
1089.2.e.p.727.8		36	33.20	odd	10
9801.2.a.cm.1.11		18	99.20	odd	30
9801.2.a.cn.1.11		18	99.79	odd	30
9801.2.a.co.1.8		18	99.2	even	30
9801.2.a.cp.1.8		18	99.97	even	15

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 $\F_{q}$

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.n (of order \(15\), degree \(8\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.0603978 + 0.574647i) q^{2} +(1.62972 - 0.346409i) q^{4} +(0.314048 - 2.98797i) q^{5} +(-0.779082 - 0.865259i) q^{7} +(0.654602 + 2.01466i) q^{8} +1.73599 q^{10} +(0.565602 - 3.26804i) q^{11} +(-3.60501 - 1.60505i) q^{13} +(0.450163 - 0.499957i) q^{14} +(1.92600 - 0.857509i) q^{16} +(-0.254185 - 0.184677i) q^{17} +(1.96794 + 6.05670i) q^{19} +(-0.523246 - 4.97835i) q^{20} +(1.91213 + 0.127639i) q^{22} +(-0.0427501 - 0.0740453i) q^{23} +(-3.93860 - 0.837174i) q^{25} +(0.704604 - 2.16855i) q^{26} +(-1.56942 - 1.14025i) q^{28} +(5.15218 + 5.72208i) q^{29} +(5.96439 + 2.65552i) q^{31} +(2.72743 + 4.72404i) q^{32} +(0.0907715 - 0.157221i) q^{34} +(-2.83004 + 2.05614i) q^{35} +(-1.92922 + 5.93753i) q^{37} +(-3.36160 + 1.49668i) q^{38} +(6.22531 - 1.32323i) q^{40} +(-3.88703 + 4.31698i) q^{41} +(3.39229 - 5.87562i) q^{43} +(-0.210303 - 5.52194i) q^{44} +(0.0399679 - 0.0290384i) q^{46} +(-0.320574 - 0.0681401i) q^{47} +(0.589996 - 5.61344i) q^{49} +(0.243197 - 2.31387i) q^{50} +(-6.43117 - 1.36699i) q^{52} +(-1.96000 + 1.42402i) q^{53} +(-9.58718 - 2.71632i) q^{55} +(1.23321 - 2.13598i) q^{56} +(-2.97699 + 3.30629i) q^{58} +(-2.24586 + 0.477372i) q^{59} +(-12.5039 + 5.56709i) q^{61} +(-1.16575 + 3.58780i) q^{62} +(0.861321 - 0.625787i) q^{64} +(-5.92799 + 10.2676i) q^{65} +(-5.83989 - 10.1150i) q^{67} +(-0.478226 - 0.212920i) q^{68} +(-1.35248 - 1.50208i) q^{70} +(7.05272 + 5.12410i) q^{71} +(0.910538 - 2.80235i) q^{73} +(-3.52850 - 0.750007i) q^{74} +(5.30529 + 9.18904i) q^{76} +(-3.26835 + 2.05668i) q^{77} +(0.928965 + 8.83851i) q^{79} +(-1.95735 - 6.02412i) q^{80} +(-2.71551 - 1.97293i) q^{82} +(-4.52916 + 2.01651i) q^{83} +(-0.631634 + 0.701501i) q^{85} +(3.58129 + 1.59449i) q^{86} +(6.95423 - 0.999772i) q^{88} -2.12862 q^{89} +(1.41981 + 4.36973i) q^{91} +(-0.0953208 - 0.105864i) q^{92} +(0.0197945 - 0.188332i) q^{94} +(18.7153 - 3.97805i) q^{95} +(0.00928623 + 0.0883526i) q^{97} +3.26138 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + q^{2} + 11 q^{4} + 8 q^{5} - 2 q^{7} - 6 q^{8} - 8 q^{10} + 2 q^{11} - 11 q^{13} + 10 q^{14} - 9 q^{16} + 20 q^{17} + 8 q^{19} + 45 q^{20} - 16 q^{22} - 20 q^{23} + 11 q^{25} + 12 q^{26} - 54 q^{28}+ \cdots + 328 q^{98}+O(q^{100}) \) 72 * q + q^2 + 11 * q^4 + 8 * q^5 - 2 * q^7 - 6 * q^8 - 8 * q^10 + 2 * q^11 - 11 * q^13 + 10 * q^14 - 9 * q^16 + 20 * q^17 + 8 * q^19 + 45 * q^20 - 16 * q^22 - 20 * q^23 + 11 * q^25 + 12 * q^26 - 54 * q^28 + 23 * q^29 + 3 * q^31 - 18 * q^32 + 8 * q^34 - 18 * q^35 - 42 * q^37 + q^38 - 25 * q^40 - 10 * q^41 - 8 * q^43 - 38 * q^44 - 18 * q^46 + 34 * q^47 + q^49 - 27 * q^52 - 4 * q^53 + 18 * q^55 - 114 * q^56 + q^58 + 16 * q^59 - 3 * q^61 - 184 * q^62 + 26 * q^64 - 84 * q^65 + 10 * q^67 + 23 * q^68 - 46 * q^70 + 48 * q^71 - 40 * q^73 - 68 * q^74 + 16 * q^76 + 26 * q^77 + 19 * q^79 + 56 * q^80 + 94 * q^82 - 7 * q^83 + 25 * q^85 + 77 * q^86 + 18 * q^88 + 56 * q^89 + 20 * q^91 - 50 * q^92 - 63 * q^94 + 77 * q^95 - 33 * q^97 + 328 * q^98

Introduction

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