LMFDB - Embedded newform 297.2.n.b.37.6

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			37.6
Character	$\chi$	$=$	297.37
Dual form			297.2.n.b.289.6

$q$-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 $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{5}\right)$

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	−0.952195	−	0.305492i	$-0.901179\pi$
$2$	0.0603978	−	0.574647i	0.0427077	−	0.406337i	0.994902	−	0.100844i	$-0.0321544\pi$
$3$		0			0
$3$		0			0
$4$	1.62972	+	0.346409i	0.814862	+	0.173204i
$5$	0.314048	+	2.98797i	0.140447	+	1.33626i	0.806889	+	0.590704i	$0.201150\pi$
$5$	0.314048	+	2.98797i	0.140447	+	1.33626i	−0.666442	+	0.745557i	$0.732184\pi$
$6$		0			0
$7$	−0.779082	+	0.865259i	−0.294465	+	0.327037i	−0.872164	−	0.489213i	$-0.837284\pi$
$7$	−0.779082	+	0.865259i	−0.294465	+	0.327037i	0.577699	+	0.816250i	$0.303951\pi$
$8$	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	−0.840354	−	0.542037i	$-0.817653\pi$
$13$	−3.60501	+	1.60505i	−0.999849	+	0.445161i	−0.159495	+	0.987199i	$0.550986\pi$
$14$	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	−0.618183	−	0.786034i	$-0.712131\pi$
$17$	−0.254185	+	0.184677i	−0.0616490	+	0.0447906i	0.556534	+	0.830825i	$0.312131\pi$
$18$		0			0
$19$	1.96794	−	6.05670i	0.451477	−	1.38950i	−0.423746	−	0.905781i	$-0.639285\pi$
$19$	1.96794	−	6.05670i	0.451477	−	1.38950i	0.875222	−	0.483721i	$-0.160715\pi$
$20$	−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	−0.870448	−	0.492260i	$-0.836171\pi$
$23$	−0.0427501	+	0.0740453i	−0.00891401	+	0.0154395i	0.861534	+	0.507700i	$0.169504\pi$
$24$		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	−0.0412506	−	0.999149i	$-0.513134\pi$
$29$	5.15218	−	5.72208i	0.956737	−	1.06256i	0.997987	−	0.0634149i	$-0.0201991\pi$
$30$		0			0
$31$	5.96439	−	2.65552i	1.07124	−	0.476945i	0.206125	−	0.978526i	$-0.433915\pi$
$31$	5.96439	−	2.65552i	1.07124	−	0.476945i	0.865111	+	0.501581i	$0.167248\pi$
$32$	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	−0.974855	−	0.222838i	$-0.928468\pi$
$37$	−1.92922	−	5.93753i	−0.317162	−	0.976124i	0.657694	−	0.753286i	$-0.271532\pi$
$38$	−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	0.358764	−	0.933428i	$-0.383198\pi$
$41$	−3.88703	−	4.31698i	−0.607052	−	0.674199i	−0.965816	+	0.259229i	$0.916532\pi$
$42$		0			0
$43$	3.39229	+	5.87562i	0.517320	+	0.896024i	0.999798	+	0.0201157i	$0.00640347\pi$
$43$	3.39229	+	5.87562i	0.517320	+	0.896024i	−0.482478	+	0.875908i	$0.660263\pi$
$44$	−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	−0.231233	−	0.972899i	$-0.574276\pi$
$47$	−0.320574	+	0.0681401i	−0.0467605	+	0.00993925i	0.184472	+	0.982838i	$0.440942\pi$
$48$		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	0.444978	−	0.895541i	$-0.353211\pi$
$53$	−1.96000	−	1.42402i	−0.269227	−	0.195605i	−0.714205	+	0.699937i	$0.753211\pi$
$54$		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	0.0593835	−	0.998235i	$-0.481087\pi$
$59$	−2.24586	−	0.477372i	−0.292386	−	0.0621485i	−0.351769	+	0.936087i	$0.614420\pi$
$60$		0			0
$61$	−12.5039	−	5.56709i	−1.60096	−	0.712792i	−0.604478	−	0.796622i	$-0.706618\pi$
$61$	−12.5039	−	5.56709i	−1.60096	−	0.712792i	−0.996480	+	0.0838297i	$0.973285\pi$
$62$	−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	0.250096	+	0.968221i	$0.419538\pi$
$67$	−5.83989	+	10.1150i	−0.713456	+	1.23574i	−0.963552	+	0.267521i	$0.913795\pi$
$68$	−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	−0.0845279	−	0.996421i	$-0.526938\pi$
$71$	7.05272	−	5.12410i	0.837004	−	0.608119i	0.921532	+	0.388302i	$0.126938\pi$
$72$		0			0
$73$	0.910538	+	2.80235i	0.106570	+	0.327990i	0.990096	−	0.140393i	$-0.0448367\pi$
$73$	0.910538	+	2.80235i	0.106570	+	0.327990i	−0.883525	+	0.468383i	$0.844837\pi$
$74$	−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	−0.809055	−	0.587733i	$-0.800021\pi$
$79$	0.928965	−	8.83851i	0.104517	−	0.994410i	0.913572	−	0.406677i	$-0.133313\pi$
$80$	−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	0.142821	−	0.989749i	$-0.454383\pi$
$83$	−4.52916	−	2.01651i	−0.497140	−	0.221341i	−0.639961	+	0.768408i	$0.721049\pi$
$84$		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	−0.994040	−	0.109013i	$-0.965231\pi$
$97$	0.00928623	−	0.0883526i	0.000942874	−	0.00897084i	0.994983	+	0.100042i	$0.0318977\pi$
$98$	3.26138			0.329449
$99$		0			0
$100$	−6.70883			−0.670883
$101$	−0.214961	+	2.04522i	−0.0213894	+	0.203507i	−0.999998	−	0.00222652i	$-0.999291\pi$
$101$	−0.214961	+	2.04522i	−0.0213894	+	0.203507i	0.978608	+	0.205733i	$0.0659579\pi$
$102$		0			0
$103$	2.95079	+	0.627210i	0.290750	+	0.0618009i	0.350978	−	0.936384i	$-0.385849\pi$
$103$	2.95079	+	0.627210i	0.290750	+	0.0618009i	−0.0602275	+	0.998185i	$0.519183\pi$
$104$	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	0.595815	+	0.803121i	$0.296829\pi$
$107$	−3.70600	+	11.4059i	−0.358272	+	1.10265i	−0.954088	+	0.299527i	$0.903171\pi$
$108$		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	−0.922262	−	0.386566i	$-0.873661\pi$
$113$	−12.8657	−	14.2889i	−1.21031	−	1.34418i	−0.288046	−	0.957617i	$-0.593005\pi$
$114$		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	−0.00356461	−	0.999994i	$-0.501135\pi$
$127$	10.6652	−	7.74873i	0.946384	−	0.687588i	0.949949	+	0.312405i	$0.101135\pi$
$128$	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	0.143839	+	0.989601i	$0.454055\pi$
$131$	−8.98588	+	15.5640i	−0.785100	+	1.35983i	−0.928939	+	0.370233i	$0.879278\pi$
$132$		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	0.930283	−	0.366842i	$-0.119561\pi$
$137$	14.9837	+	6.67119i	1.28015	+	0.569958i	0.349864	+	0.936801i	$0.386228\pi$
$138$		0			0
$139$	11.6415	+	2.47448i	0.987421	+	0.209883i	0.673195	−	0.739465i	$-0.264922\pi$
$139$	11.6415	+	2.47448i	0.987421	+	0.209883i	0.314226	+	0.949348i	$0.398255\pi$
$140$	−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	−0.996641	−	0.0818976i	$-0.973902\pi$
$149$	−0.473693	−	4.50689i	−0.0388065	−	0.369219i	0.957834	−	0.287321i	$-0.0927647\pi$
$150$		0			0
$151$	2.86682	−	0.609361i	0.233298	−	0.0495891i	−0.0897788	−	0.995962i	$-0.528616\pi$
$151$	2.86682	−	0.609361i	0.233298	−	0.0495891i	0.323077	+	0.946373i	$0.395283\pi$
$152$	−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	−0.997454	−	0.0713070i	$-0.977283\pi$
$157$	−12.0802	−	13.4165i	−0.964108	−	1.07075i	0.0333460	−	0.999444i	$-0.489384\pi$
$158$	−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	0.756803	−	0.653643i	$-0.226760\pi$
$163$	4.71129	+	3.42295i	0.369017	+	0.268106i	−0.387786	+	0.921749i	$0.626760\pi$
$164$	−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	−0.221487	−	0.975163i	$-0.571091\pi$
$167$	4.58758	−	2.04252i	0.354997	−	0.158055i	0.576484	+	0.817108i	$0.304424\pi$
$168$		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	−0.747153	−	0.664652i	$-0.768580\pi$
$173$	−15.2492	+	3.24131i	−1.15937	+	0.246433i	−0.412221	+	0.911084i	$0.635247\pi$
$174$		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	−0.998868	−	0.0475668i	$-0.984853\pi$
$179$	−2.17822	+	6.70387i	−0.162808	+	0.501071i	0.836060	+	0.548638i	$0.184853\pi$
$180$		0			0
$181$	−2.02068	+	1.46811i	−0.150196	+	0.109124i	−0.660345	−	0.750962i	$-0.729590\pi$
$181$	−2.02068	+	1.46811i	−0.150196	+	0.109124i	0.510149	+	0.860086i	$0.329590\pi$
$182$	−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	−0.385516	−	0.922701i	$-0.625976\pi$
$191$	7.91112	−	8.78619i	0.572428	−	0.635746i	0.957944	+	0.286955i	$0.0926431\pi$
$192$		0			0
$193$	−0.705218	−	6.70970i	−0.0507627	−	0.482975i	−0.990139	−	0.140087i	$-0.955262\pi$
$193$	−0.705218	−	6.70970i	−0.0507627	−	0.482975i	0.939376	−	0.342887i	$-0.111405\pi$
$194$	−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	−0.652009	−	0.758211i	$-0.726074\pi$
$211$	−7.62355	+	3.39422i	−0.524827	+	0.233668i	0.127182	+	0.991879i	$0.459407\pi$
$212$	−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	−0.195330	−	0.980738i	$-0.562578\pi$
$223$	0.375272	−	0.0797665i	0.0251301	−	0.00534156i	0.220460	+	0.975396i	$0.429244\pi$
$224$	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	−0.995747	−	0.0921329i	$-0.970632\pi$
$227$	−12.0537	+	13.3870i	−0.800035	+	0.888529i	0.195712	+	0.980661i	$0.437298\pi$
$228$		0			0
$229$	12.2670	−	5.46161i	0.810624	−	0.360913i	0.0407985	−	0.999167i	$-0.487010\pi$
$229$	12.2670	−	5.46161i	0.810624	−	0.360913i	0.769826	+	0.638254i	$0.220343\pi$
$230$	−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	0.494897	−	0.868952i	$-0.335206\pi$
$233$	−2.72611	−	1.98063i	−0.178593	−	0.129756i	−0.673490	+	0.739196i	$0.735206\pi$
$234$		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	0.993351	+	0.115128i	$0.0367278\pi$
$239$	15.5217	+	17.2386i	1.00401	+	1.11507i	0.0106638	+	0.999943i	$0.496606\pi$
$240$		0			0
$241$	−7.58206	−	13.1325i	−0.488404	−	0.845940i	0.511507	−	0.859279i	$-0.329087\pi$
$241$	−7.58206	−	13.1325i	−0.488404	−	0.845940i	−0.999911	+	0.0133389i	$0.995754\pi$
$242$	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	0.572818	−	0.819682i	$-0.305850\pi$
$251$	−0.471095	−	0.342271i	−0.0297353	−	0.0216039i	−0.602554	+	0.798078i	$0.705850\pi$
$252$		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	−0.139351	−	0.990243i	$-0.544502\pi$
$257$	−10.7317	−	2.28109i	−0.669423	−	0.142290i	−0.530072	+	0.847953i	$0.677835\pi$
$258$		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	0.554142	−	0.832422i	$-0.313047\pi$
$263$	−7.19768	−	12.4668i	−0.443828	−	0.768733i	−0.997970	+	0.0636896i	$0.979713\pi$
$264$		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	−0.575660	−	0.817689i	$-0.695255\pi$
$269$	0.395590	−	0.287413i	0.0241195	−	0.0175239i	0.599780	+	0.800165i	$0.295255\pi$
$270$		0			0
$271$	6.77950	+	20.8652i	0.411825	+	1.26747i	0.915060	+	0.403318i	$0.132143\pi$
$271$	6.77950	+	20.8652i	0.411825	+	1.26747i	−0.503234	+	0.864150i	$0.667857\pi$
$272$	−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	−0.999831	−	0.0184051i	$-0.994141\pi$
$277$	−0.299947	+	2.85381i	−0.0180221	+	0.171469i	0.981809	+	0.189874i	$0.0608078\pi$
$278$	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	−0.153571	−	0.988138i	$-0.549078\pi$
$281$	−16.6065	−	7.39368i	−0.990660	−	0.441070i	−0.837089	+	0.547067i	$0.815744\pi$
$282$		0			0
$283$	−13.7420	−	15.2620i	−0.816878	−	0.907235i	0.180200	−	0.983630i	$-0.442326\pi$
$283$	−13.7420	−	15.2620i	−0.816878	−	0.907235i	−0.997078	+	0.0763955i	$0.975659\pi$
$284$	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	0.232420	−	0.972616i	$-0.425336\pi$
$293$	0.841272	+	0.178818i	0.0491476	+	0.0104467i	−0.183272	+	0.983062i	$0.558669\pi$
$294$		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	0.501389	−	0.865222i	$-0.332822\pi$
$311$	−7.25692	−	8.05963i	−0.411502	−	0.457020i	−0.912892	+	0.408202i	$0.866156\pi$
$312$		0			0
$313$	−25.8360	−	11.5029i	−1.46034	−	0.650185i	−0.485732	−	0.874108i	$-0.661447\pi$
$313$	−25.8360	−	11.5029i	−1.46034	−	0.650185i	−0.974607	+	0.223923i	$0.928114\pi$
$314$	−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	−0.997302	−	0.0734057i	$-0.976613\pi$
$317$	−0.116291	+	1.10643i	−0.00653154	+	0.0621434i	0.990771	+	0.135549i	$0.0432799\pi$
$318$		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	0.984467	−	0.175569i	$-0.0561764\pi$
$331$	6.18915	+	10.7199i	0.340187	+	0.589221i	−0.644281	+	0.764789i	$0.722843\pi$
$332$	−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	−0.165552	−	0.986201i	$-0.552941\pi$
$337$	−13.1792	−	2.80132i	−0.717916	−	0.152598i	−0.552364	+	0.833603i	$0.686274\pi$
$338$	−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	0.987265	+	0.159087i	$0.0508551\pi$
$347$	1.01802	+	9.68582i	0.0546502	+	0.519962i	−0.932614	+	0.360875i	$0.882478\pi$
$348$		0			0
$349$	4.34317	−	0.923168i	0.232484	−	0.0494161i	−0.0901962	−	0.995924i	$-0.528749\pi$
$349$	4.34317	−	0.923168i	0.232484	−	0.0494161i	0.322680	+	0.946508i	$0.395416\pi$
$350$	−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	0.866523	+	0.499137i	$0.166349\pi$
$353$	16.2618	+	28.1662i	0.865527	+	1.49914i	−0.000996749		1.00000i	$0.500317\pi$
$354$		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	0.873571	+	0.486697i	$0.161799\pi$
$359$	8.58143	+	26.4109i	0.452911	+	1.39392i	−0.420660	+	0.907218i	$0.638201\pi$
$360$		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	−0.722326	−	0.691553i	$-0.756927\pi$
$367$	0.784353	−	0.871112i	0.0409429	−	0.0454717i	0.763268	+	0.646082i	$0.223593\pi$
$368$	−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	0.433665	+	0.901074i	$0.357220\pi$
$373$	−10.8834	+	18.8506i	−0.563520	+	0.976046i	−0.997186	+	0.0749719i	$0.976113\pi$
$374$	−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	−0.196588	−	0.980486i	$-0.562986\pi$
$379$	13.1440	−	9.54967i	0.675161	−	0.490533i	0.871749	+	0.489953i	$0.162986\pi$
$380$	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	−0.546165	−	0.837677i	$-0.683913\pi$
$383$	−5.65791	+	2.51906i	−0.289105	+	0.128718i	0.257060	+	0.966396i	$0.417246\pi$
$384$		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	−0.730752	−	0.682643i	$-0.760830\pi$
$389$	0.483924	−	0.537452i	0.0245359	−	0.0272499i	0.755288	+	0.655393i	$0.227497\pi$
$390$		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	−0.999325	−	0.0367238i	$-0.988308\pi$
$401$	−0.590196	−	5.61534i	−0.0294730	−	0.280417i	0.969852	−	0.243693i	$-0.0783588\pi$
$402$		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	−0.182073	−	0.983285i	$-0.558281\pi$
$409$	8.63188	−	3.84316i	0.426819	−	0.190032i	0.608892	+	0.793253i	$0.291614\pi$
$410$	−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	−0.864168	−	0.503203i	$-0.832155\pi$
$419$	0.0757820	−	0.131258i	0.00370219	−	0.00641238i	0.867871	+	0.496790i	$0.165488\pi$
$420$		0			0
$421$	−16.6056	+	3.52962i	−0.809306	+	0.172023i	−0.593939	−	0.804510i	$-0.702428\pi$
$421$	−16.6056	+	3.52962i	−0.809306	+	0.172023i	−0.215367	+	0.976533i	$0.569095\pi$
$422$	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	−0.0289998	−	0.999579i	$-0.509232\pi$
$431$	−20.5242	−	14.9117i	−0.988618	−	0.718273i	−0.959618	+	0.281307i	$0.909232\pi$
$432$		0			0
$433$	5.10950	+	15.7254i	0.245547	+	0.755716i	0.995546	+	0.0942769i	$0.0300539\pi$
$433$	5.10950	+	15.7254i	0.245547	+	0.755716i	−0.749999	+	0.661439i	$0.769946\pi$
$434$	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	0.772040	+	0.635574i	$0.219237\pi$
$439$	19.6207	+	33.9840i	0.936443	+	1.62197i	0.164403	+	0.986393i	$0.447430\pi$
$440$	−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	0.613991	−	0.789313i	$-0.289563\pi$
$443$	31.4859	−	6.69254i	1.49594	−	0.317972i	0.881951	+	0.471341i	$0.156230\pi$
$444$		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	−0.0275281	−	0.999621i	$-0.508764\pi$
$449$	−20.9085	−	15.1909i	−0.986731	−	0.716902i	−0.959203	+	0.282719i	$0.908764\pi$
$450$		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	0.116623	−	0.993176i	$-0.462793\pi$
$457$	−11.6169	−	5.17218i	−0.543416	−	0.241944i	−0.660038	+	0.751232i	$0.729460\pi$
$458$	−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	0.554943	−	0.831889i	$-0.312740\pi$
$461$	−9.51087	−	16.4733i	−0.442965	−	0.767238i	−0.997908	+	0.0646502i	$0.979407\pi$
$462$		0			0
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	−0.467977	−	0.883741i	$-0.655017\pi$
$463$	11.4334	−	19.8032i	0.531353	−	0.920331i	0.999330	−	0.0365903i	$-0.0116497\pi$
$464$	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	−0.248392	−	0.968660i	$-0.579902\pi$
$467$	12.8819	−	9.35921i	0.596101	−	0.433093i	0.844493	+	0.535567i	$0.179902\pi$
$468$		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	0.719214	−	0.694789i	$-0.244502\pi$
$479$	14.9730	+	6.66640i	0.684133	+	0.304596i	−0.0350809	+	0.999384i	$0.511169\pi$
$480$		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	−0.654966	−	0.755658i	$-0.727317\pi$
$487$	7.04142	−	21.6713i	0.319077	−	0.982019i	0.974044	−	0.226361i	$-0.0726828\pi$
$488$	−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	−0.999394	−	0.0348013i	$-0.988920\pi$
$491$	−42.6893	−	9.07389i	−1.92654	−	0.409499i	−0.927147	−	0.374698i	$-0.877747\pi$
$492$		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	0.625819	−	0.779969i	$-0.284765\pi$
$499$	19.6642	+	4.17976i	0.880291	+	0.187112i	0.254472	+	0.967080i	$0.418098\pi$
$500$	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	−0.850994	−	0.525176i	$-0.824000\pi$
$503$	3.27815	−	10.0891i	0.146165	−	0.449850i	0.997159	+	0.0753254i	$0.0239995\pi$
$504$		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	0.785475	+	0.618894i	$0.212419\pi$
$509$	29.7551	+	33.0464i	1.31887	+	1.46476i	0.533399	+	0.845864i	$0.320914\pi$
$510$		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	−0.997805	−	0.0662243i	$-0.978905\pi$
$521$	−5.23819	−	16.1215i	−0.229489	−	0.706296i	0.768315	−	0.640071i	$-0.221095\pi$
$522$		0			0
$523$	−24.4438	+	17.7595i	−1.06885	+	0.776567i	−0.975706	−	0.219085i	$-0.929693\pi$
$523$	−24.4438	+	17.7595i	−1.06885	+	0.776567i	−0.0931472	+	0.995652i	$0.529693\pi$
$524$	−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	0.362699	−	0.931906i	$-0.381855\pi$
$541$	−9.57164	−	6.95421i	−0.411517	−	0.298985i	−0.774216	+	0.632922i	$0.781855\pi$
$542$	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	−0.260840	−	0.965382i	$-0.583999\pi$
$547$	−2.49018	+	0.529304i	−0.106472	+	0.0226314i	0.154367	+	0.988014i	$0.450666\pi$
$548$	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	0.867519	−	0.497404i	$-0.165713\pi$
$557$	−2.98987	−	9.20189i	−0.126685	−	0.389896i	−0.994204	+	0.107507i	$0.965713\pi$
$558$		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	0.110820	−	0.993840i	$-0.464652\pi$
$563$	21.9134	−	9.75648i	0.923540	−	0.411187i	0.812720	+	0.582654i	$0.197986\pi$
$564$		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	−0.899169	−	0.437601i	$-0.855828\pi$
$569$	−36.7971	+	7.82146i	−1.54261	+	0.327893i	−0.643444	+	0.765493i	$0.722495\pi$
$570$		0			0
$571$	7.37740	−	12.7780i	0.308735	−	0.534744i	−0.669351	−	0.742946i	$-0.733428\pi$
$571$	7.37740	−	12.7780i	0.308735	−	0.534744i	0.978086	+	0.208202i	$0.0667612\pi$
$572$	−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	−0.144937	−	0.989441i	$-0.546298\pi$
$577$	18.0466	−	13.1116i	0.751289	−	0.545843i	0.896226	+	0.443598i	$0.146298\pi$
$578$	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	−0.707630	−	0.706583i	$-0.750236\pi$
$587$	1.67294	−	1.85799i	0.0690496	−	0.0766873i	0.776680	+	0.629896i	$0.216902\pi$
$588$		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	−0.733558	−	0.679627i	$-0.762142\pi$
$599$	−3.85063	−	36.6363i	−0.157332	−	1.49692i	0.576225	−	0.817291i	$-0.304525\pi$
$600$		0			0
$601$	−10.3409	+	11.4848i	−0.421815	+	0.468474i	−0.916172	−	0.400786i	$-0.868737\pi$
$601$	−10.3409	+	11.4848i	−0.421815	+	0.468474i	0.494356	+	0.869259i	$0.335404\pi$
$602$	−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	−0.820489	−	0.571663i	$-0.806299\pi$
$607$	−23.2743	+	10.3624i	−0.944675	+	0.420596i	−0.124186	+	0.992259i	$0.539632\pi$
$608$	−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	0.379211	+	0.925310i	$0.376195\pi$
$613$	−11.6728	+	35.9252i	−0.471461	+	1.45101i	−0.850672	+	0.525697i	$0.823805\pi$
$614$	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	−0.0438437	−	0.999038i	$-0.513960\pi$
$617$	20.9464	−	36.2802i	0.843271	−	1.46059i	0.887115	−	0.461549i	$-0.152706\pi$
$618$		0			0
$619$	5.85872	−	1.24531i	0.235482	−	0.0500532i	−0.0886590	−	0.996062i	$-0.528258\pi$
$619$	5.85872	−	1.24531i	0.235482	−	0.0500532i	0.324141	+	0.946009i	$0.394925\pi$
$620$	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	−0.991813	−	0.127702i	$-0.959240\pi$
$631$	−6.64368	−	20.4471i	−0.264481	−	0.813988i	0.727332	−	0.686286i	$-0.240760\pi$
$632$	−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	0.0468561	−	0.998902i	$-0.485080\pi$
$641$	12.5565	−	2.66896i	0.495951	−	0.105418i	0.449095	+	0.893484i	$0.351746\pi$
$642$		0			0
$643$	−2.96396	−	28.2002i	−0.116887	−	1.11211i	−0.882990	−	0.469391i	$-0.844473\pi$
$643$	−2.96396	−	28.2002i	−0.116887	−	1.11211i	0.766103	−	0.642718i	$-0.222193\pi$
$644$	−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	0.273717	−	0.961810i	$-0.411747\pi$
$647$	−14.1536	−	10.2832i	−0.556436	−	0.404274i	−0.830153	+	0.557536i	$0.811747\pi$
$648$		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	−0.390468	−	0.920617i	$-0.627687\pi$
$653$	−28.6619	−	6.09227i	−1.12163	−	0.238409i	−0.731159	+	0.682207i	$0.761020\pi$
$654$		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	0.999047	+	0.0436422i	$0.0138961\pi$
$659$	13.7935	+	23.8911i	0.537319	+	0.930664i	−0.461728	+	0.887021i	$0.652771\pi$
$660$		0			0
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	0.416960	+	0.908925i	$0.363096\pi$
$661$	−14.8776	+	25.7688i	−0.578672	+	1.00229i	−0.995632	+	0.0933649i	$0.970238\pi$
$662$	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	0.957707	+	0.287745i	$0.0929055\pi$
$673$	−1.00908	+	9.60079i	−0.0388973	+	0.370083i	−0.996604	+	0.0823384i	$0.973761\pi$
$674$	−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	0.408458	−	0.912777i	$-0.366067\pi$
$677$	0.0896326	+	0.0399070i	0.00344486	+	0.00153375i	−0.405013	+	0.914311i	$0.632733\pi$
$678$		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	0.711992	+	0.702188i	$0.247793\pi$
$691$	−3.42871	+	32.6220i	−0.130434	+	1.24100i	−0.842426	+	0.538812i	$0.818873\pi$
$692$	−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	−0.886927	−	0.461909i	$-0.847165\pi$
$701$	2.70365	−	8.32098i	0.102115	−	0.314279i	0.989043	+	0.147630i	$0.0471646\pi$
$702$		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	0.810911	−	0.585169i	$-0.198972\pi$
$709$	24.4610	+	10.8907i	0.918651	+	0.409010i	0.107740	+	0.994179i	$0.465639\pi$
$710$	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	0.999532	−	0.0305782i	$-0.00973486\pi$
$719$	4.63672	+	14.2703i	0.172920	+	0.532194i	−0.826612	+	0.562772i	$0.809735\pi$
$720$		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	−0.999925	−	0.0122391i	$-0.996104\pi$
$727$	−13.7663	−	23.8438i	−0.510562	−	0.884319i	0.489363	−	0.872080i	$-0.337229\pi$
$728$	−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	−0.764273	−	0.644893i	$-0.776902\pi$
$733$	−46.6964	−	9.92564i	−1.72477	−	0.366612i	−0.960500	+	0.278281i	$0.910235\pi$
$734$	−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	0.565416	−	0.824806i	$-0.308716\pi$
$739$	−1.20421	−	0.874910i	−0.0442976	−	0.0321841i	−0.609714	+	0.792622i	$0.708716\pi$
$740$	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	−0.972541	−	0.232733i	$-0.925233\pi$
$743$	−1.89825	−	18.0607i	−0.0696402	−	0.662582i	0.902901	−	0.429850i	$-0.141433\pi$
$744$		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	0.687100	−	0.726563i	$-0.258883\pi$
$751$	−2.94060	−	3.26586i	−0.107304	−	0.119173i	−0.794404	+	0.607390i	$0.792217\pi$
$752$	−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	0.771483	−	0.636249i	$-0.219515\pi$
$757$	11.1369	+	8.09140i	0.404776	+	0.294087i	−0.366708	+	0.930336i	$0.619515\pi$
$758$	−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	0.179126	−	0.983826i	$-0.442673\pi$
$761$	28.4168	−	12.6520i	1.03011	−	0.458634i	0.850984	+	0.525192i	$0.176006\pi$
$762$		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	−0.993165	−	0.116715i	$-0.962764\pi$
$769$	−10.9677	+	18.9966i	−0.395504	+	0.685034i	0.597661	+	0.801749i	$0.296097\pi$
$770$	−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	−0.855182	−	0.518327i	$-0.826555\pi$
$773$	3.92965	−	12.0942i	0.141340	−	0.434999i	0.996522	+	0.0833281i	$0.0265549\pi$
$774$		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	0.978444	+	0.206512i	$0.0662112\pi$
$787$	1.80433	+	17.1671i	0.0643176	+	0.611941i	−0.914127	+	0.405429i	$0.867122\pi$
$788$	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	0.842748	+	0.538309i	$0.180936\pi$
$797$	3.67956	+	35.0087i	0.130337	+	1.24007i	−0.712411	+	0.701762i	$0.752397\pi$
$798$		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	−0.825096	−	0.564992i	$-0.808879\pi$
$809$	−15.4367	+	11.2154i	−0.542725	+	0.394313i	0.282371	+	0.959305i	$0.408879\pi$
$810$		0			0
$811$	−9.59769	+	29.5387i	−0.337020	+	1.03724i	0.628698	+	0.777650i	$0.283588\pi$
$811$	−9.59769	+	29.5387i	−0.337020	+	1.03724i	−0.965718	+	0.259593i	$0.916412\pi$
$812$	−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	−0.995231	−	0.0975412i	$-0.968902\pi$
$821$	−22.7561	+	25.2732i	−0.794195	+	0.882042i	0.201037	+	0.979584i	$0.435569\pi$
$822$		0			0
$823$	14.2111	−	6.32720i	0.495368	−	0.220552i	−0.143818	−	0.989604i	$-0.545938\pi$
$823$	14.2111	−	6.32720i	0.495368	−	0.220552i	0.639186	+	0.769052i	$0.279271\pi$
$824$	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	0.789949	−	0.613172i	$-0.210107\pi$
$827$	12.9667	+	9.42084i	0.450895	+	0.327595i	−0.339054	+	0.940767i	$0.610107\pi$
$828$		0			0
$829$	5.90205	+	18.1646i	0.204987	+	0.630884i	0.999714	+	0.0239173i	$0.00761382\pi$
$829$	5.90205	+	18.1646i	0.204987	+	0.630884i	−0.794727	+	0.606967i	$0.792386\pi$
$830$	−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	−0.182720	−	0.983165i	$-0.558490\pi$
$839$	1.45541	−	0.309356i	0.0502462	−	0.0106802i	0.232966	+	0.972485i	$0.425157\pi$
$840$		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	0.901287	−	0.433222i	$-0.142624\pi$
$853$	34.5339	+	15.3755i	1.18242	+	0.526447i	0.281132	+	0.959669i	$0.409290\pi$
$854$	−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	0.984177	−	0.177189i	$-0.0567005\pi$
$857$	9.91348	+	17.1706i	0.338638	+	0.586538i	−0.645539	+	0.763727i	$0.723367\pi$
$858$		0			0
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	−0.700272	−	0.713876i	$-0.746938\pi$
$859$	7.85764	−	13.6098i	0.268099	−	0.464362i	0.968371	+	0.249515i	$0.0802711\pi$
$860$	−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	−0.470218	−	0.882550i	$-0.655825\pi$
$863$	6.57548	−	4.77736i	0.223832	−	0.162623i	0.694050	+	0.719927i	$0.255825\pi$
$864$		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	0.713842	−	0.700307i	$-0.246953\pi$
$877$	−1.69526	−	1.88278i	−0.0572449	−	0.0635769i	−0.771087	+	0.636730i	$0.780287\pi$
$878$	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	−0.713315	−	0.700844i	$-0.752807\pi$
$883$	8.19295	−	25.2153i	0.275715	−	0.848563i	0.989029	−	0.147719i	$-0.0471930\pi$
$884$	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	−0.661511	−	0.749935i	$-0.730085\pi$
$887$	−46.7841	−	9.94428i	−1.57086	−	0.333896i	−0.909347	+	0.416039i	$0.863418\pi$
$888$		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	0.970258	−	0.242074i	$-0.0778277\pi$
$907$	43.3554	+	19.3030i	1.43959	+	0.640947i	0.469333	+	0.883021i	$0.344494\pi$
$908$	−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	0.828067	+	0.560629i	$0.189440\pi$
$911$	−2.97198	+	28.2765i	−0.0984660	+	0.936841i	−0.926533	+	0.376213i	$0.877226\pi$
$912$		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	−0.967110	−	0.254358i	$-0.918136\pi$
$919$	−31.0442	+	22.5550i	−1.02406	+	0.744020i	−0.0569449	+	0.998377i	$0.518136\pi$
$920$	−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	0.196176	−	0.980569i	$-0.437148\pi$
$929$	−12.2302	−	5.44526i	−0.401261	−	0.178653i	−0.597437	+	0.801916i	$0.703814\pi$
$930$		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	0.863961	−	0.503559i	$-0.167976\pi$
$937$	19.9588	+	14.5010i	0.652027	+	0.473725i	−0.211934	+	0.977284i	$0.567976\pi$
$938$	−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	0.999519	+	0.0310154i	$0.00987409\pi$
$941$	0.867827	+	8.25682i	0.0282903	+	0.269165i	−0.971229	+	0.238149i	$0.923459\pi$
$942$		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	0.990102	+	0.140351i	$0.0448231\pi$
$947$	18.9748	+	32.8653i	0.616598	+	1.06798i	−0.373503	+	0.927629i	$0.621844\pi$
$948$		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	0.828778	+	0.559578i	$0.189037\pi$
$953$	15.0400	+	46.2884i	0.487194	+	1.49943i	−0.341583	+	0.939852i	$0.610963\pi$
$954$		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	−0.940684	−	0.339283i	$-0.889816\pi$
$967$	−5.48901	+	9.50724i	−0.176515	+	0.305732i	0.764170	+	0.645015i	$0.223149\pi$
$968$	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	−0.994702	−	0.102796i	$-0.967221\pi$
$971$	−4.03687	+	12.4242i	−0.129549	+	0.398712i	0.865153	+	0.501508i	$0.167221\pi$
$972$		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	−0.238438	−	0.971158i	$-0.576635\pi$
$977$	10.1187	−	4.50514i	0.323726	−	0.144132i	0.562164	+	0.827025i	$0.309969\pi$
$978$		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	−0.391849	−	0.920029i	$-0.628165\pi$
$983$	17.6861	−	19.6424i	0.564100	−	0.626496i	0.955949	+	0.293533i	$0.0948312\pi$
$984$		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	−0.461788	−	0.886990i	$-0.652792\pi$
$997$	14.7966	−	16.4333i	0.468613	−	0.520447i	0.930401	+	0.366543i	$0.119459\pi$
$998$	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.37.6		72
3.2	odd	2		99.2.m.b.4.4	✓	72
9.2	odd	6		99.2.m.b.70.6	yes	72
9.4	even	3		891.2.f.e.730.6		36
9.5	odd	6		891.2.f.f.730.4		36
9.7	even	3	inner	297.2.n.b.235.4		72
11.3	even	5	inner	297.2.n.b.91.4		72
33.5	odd	10		1089.2.e.p.364.8		36
33.14	odd	10		99.2.m.b.58.6	yes	72
33.17	even	10		1089.2.e.o.364.11		36
99.5	odd	30		9801.2.a.cm.1.11		18
99.14	odd	30		891.2.f.f.487.4		36
99.25	even	15	inner	297.2.n.b.289.6		72
99.38	odd	30		1089.2.e.p.727.8		36
99.47	odd	30		99.2.m.b.25.4	yes	72
99.49	even	15		9801.2.a.cp.1.8		18
99.50	even	30		9801.2.a.co.1.8		18
99.58	even	15		891.2.f.e.487.6		36
99.83	even	30		1089.2.e.o.727.11		36
99.94	odd	30		9801.2.a.cn.1.11		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.m.b.4.4	✓	72	3.2	odd	2
99.2.m.b.25.4	yes	72	99.47	odd	30
99.2.m.b.58.6	yes	72	33.14	odd	10
99.2.m.b.70.6	yes	72	9.2	odd	6
297.2.n.b.37.6		72	1.1	even	1	trivial
297.2.n.b.91.4		72	11.3	even	5	inner
297.2.n.b.235.4		72	9.7	even	3	inner
297.2.n.b.289.6		72	99.25	even	15	inner
891.2.f.e.487.6		36	99.58	even	15
891.2.f.e.730.6		36	9.4	even	3
891.2.f.f.487.4		36	99.14	odd	30
891.2.f.f.730.4		36	9.5	odd	6
1089.2.e.o.364.11		36	33.17	even	10
1089.2.e.o.727.11		36	99.83	even	30
1089.2.e.p.364.8		36	33.5	odd	10
1089.2.e.p.727.8		36	99.38	odd	30
9801.2.a.cm.1.11		18	99.5	odd	30
9801.2.a.cn.1.11		18	99.94	odd	30
9801.2.a.co.1.8		18	99.50	even	30
9801.2.a.cp.1.8		18	99.49	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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