LMFDB - Embedded newform 900.2.bj.f.523.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [900,2,Mod(127,900)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(900, base_ring=CyclotomicField(20))

chi = DirichletCharacter(H, H._module([10, 0, 1]))

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

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

chi := DirichletCharacter("900.127");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	900.bj (of order $20$, degree $8$, 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:	$7.18653618192$
Analytic rank:	$0$
Dimension:	$240$
Relative dimension:	$30$ over $\Q(\zeta_{20})$
Twist minimal:	no (minimal twist has level 300)
Sato-Tate group:	$\mathrm{SU}(2)[C_{20}]$

Embedding invariants

Embedding label			523.13
Character	$\chi$	$=$	900.523
Dual form			900.2.bj.f.487.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.210253 - 1.39850i) q^{2} +(-1.91159 + 0.588077i) q^{4} +(0.590092 - 2.15680i) q^{5} +(1.77479 + 1.77479i) q^{7} +(1.22434 + 2.54970i) q^{8} +O(q^{10})$	\(q+(-0.210253 - 1.39850i) q^{2} +(-1.91159 + 0.588077i) q^{4} +(0.590092 - 2.15680i) q^{5} +(1.77479 + 1.77479i) q^{7} +(1.22434 + 2.54970i) q^{8} +(-3.14035 - 0.371768i) q^{10} +(-0.582275 - 0.801432i) q^{11} +(-0.710606 - 4.48659i) q^{13} +(2.10889 - 2.85520i) q^{14} +(3.30833 - 2.24832i) q^{16} +(3.22163 + 1.64150i) q^{17} +(0.911162 + 2.80427i) q^{19} +(0.140352 + 4.46993i) q^{20} +(-0.998375 + 0.982813i) q^{22} +(1.25105 - 7.89882i) q^{23} +(-4.30358 - 2.54542i) q^{25} +(-6.12507 + 1.93710i) q^{26} +(-4.43639 - 2.34896i) q^{28} +(-0.616890 - 0.200440i) q^{29} +(6.41357 - 2.08390i) q^{31} +(-3.83986 - 4.15397i) q^{32} +(1.61828 - 4.85057i) q^{34} +(4.87517 - 2.78058i) q^{35} +(4.16075 - 0.658998i) q^{37} +(3.73019 - 1.86386i) q^{38} +(6.22168 - 1.13610i) q^{40} +(-9.50896 - 6.90867i) q^{41} +(1.10111 - 1.10111i) q^{43} +(1.58437 + 1.18959i) q^{44} +(-11.3095 - 0.0888373i) q^{46} +(-8.43980 + 4.30030i) q^{47} -0.700218i q^{49} +(-2.65492 + 6.55373i) q^{50} +(3.99684 + 8.15861i) q^{52} +(5.38846 - 2.74556i) q^{53} +(-2.07213 + 0.782931i) q^{55} +(-2.35224 + 6.69815i) q^{56} +(-0.150611 + 0.904861i) q^{58} +(5.91350 + 4.29641i) q^{59} +(1.00189 - 0.727914i) q^{61} +(-4.26280 - 8.53121i) q^{62} +(-5.00198 + 6.24341i) q^{64} +(-10.0960 - 1.11487i) q^{65} +(-2.66543 + 5.23120i) q^{67} +(-7.12376 - 1.24331i) q^{68} +(-4.91366 - 6.23328i) q^{70} +(-11.9160 - 3.87174i) q^{71} +(-8.37438 - 1.32637i) q^{73} +(-1.79642 - 5.68024i) q^{74} +(-3.39089 - 4.82477i) q^{76} +(0.388959 - 2.45579i) q^{77} +(2.78730 - 8.57843i) q^{79} +(-2.89696 - 8.46213i) q^{80} +(-7.66246 + 14.7508i) q^{82} +(-3.13531 - 1.59752i) q^{83} +(5.44146 - 5.97978i) q^{85} +(-1.77141 - 1.30839i) q^{86} +(1.33051 - 2.46585i) q^{88} +(-3.29356 - 4.53320i) q^{89} +(6.70159 - 9.22394i) q^{91} +(2.25362 + 15.8350i) q^{92} +(7.78845 + 10.8989i) q^{94} +(6.58592 - 0.310418i) q^{95} +(3.83895 + 7.53437i) q^{97} +(-0.979253 + 0.147223i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 240 q - 12 q^{8}+O(q^{10}) $ 240 * q - 12 * q^8	$ 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) $ 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/900\mathbb{Z}\right)^\times$.

$n$	$101$	$451$	$577$
$\chi(n)$	$1$	$-1$	$e\left(\frac{11}{20}\right)$

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 $

$2$	−0.210253	−	1.39850i	−0.148671	−	0.988887i
$2$	−0.210253	−	1.39850i	−0.148671	−	0.988887i
$3$		0			0
$3$		0			0
$4$	−1.91159	+	0.588077i	−0.955794	+	0.294039i
$5$	0.590092	−	2.15680i	0.263897	−	0.964551i
$5$	0.590092	−	2.15680i	0.263897	−	0.964551i
$6$		0			0
$7$	1.77479	+	1.77479i	0.670809	+	0.670809i	0.957903	−	0.287094i	$-0.0926891\pi$
$7$	1.77479	+	1.77479i	0.670809	+	0.670809i	−0.287094	+	0.957903i	$0.592689\pi$
$8$	1.22434	+	2.54970i	0.432870	+	0.901456i
$9$		0			0
$10$	−3.14035	−	0.371768i	−0.993065	−	0.117563i
$11$	−0.582275	−	0.801432i	−0.175562	−	0.241641i	0.712163	−	0.702014i	$-0.247716\pi$
$11$	−0.582275	−	0.801432i	−0.175562	−	0.241641i	−0.887726	+	0.460373i	$0.847716\pi$
$12$		0			0
$13$	−0.710606	−	4.48659i	−0.197087	−	1.24436i	−0.865631	−	0.500683i	$-0.833082\pi$
$13$	−0.710606	−	4.48659i	−0.197087	−	1.24436i	0.668544	−	0.743673i	$-0.266918\pi$
$14$	2.10889	−	2.85520i	0.563624	−	0.763084i
$15$		0			0
$16$	3.30833	−	2.24832i	0.827083	−	0.562080i
$17$	3.22163	+	1.64150i	0.781361	+	0.398123i	0.798702	−	0.601727i	$-0.205520\pi$
$17$	3.22163	+	1.64150i	0.781361	+	0.398123i	−0.0173417	+	0.999850i	$0.505520\pi$
$18$		0			0
$19$	0.911162	+	2.80427i	0.209035	+	0.643343i	0.999524	+	0.0308666i	$0.00982672\pi$
$19$	0.911162	+	2.80427i	0.209035	+	0.643343i	−0.790489	+	0.612477i	$0.790173\pi$
$20$	0.140352	+	4.46993i	0.0313837	+	0.999507i
$21$		0			0
$22$	−0.998375	+	0.982813i	−0.212854	+	0.209536i
$23$	1.25105	−	7.89882i	0.260862	−	1.64702i	−0.414877	−	0.909877i	$-0.636175\pi$
$23$	1.25105	−	7.89882i	0.260862	−	1.64702i	0.675739	−	0.737141i	$-0.263825\pi$
$24$		0			0
$25$	−4.30358	−	2.54542i	−0.860716	−	0.509085i
$26$	−6.12507	+	1.93710i	−1.20123	+	0.379896i
$27$		0			0
$28$	−4.43639	−	2.34896i	−0.838398	−	0.443911i
$29$	−0.616890	−	0.200440i	−0.114554	−	0.0372207i	0.251179	−	0.967941i	$-0.419182\pi$
$29$	−0.616890	−	0.200440i	−0.114554	−	0.0372207i	−0.365733	+	0.930720i	$0.619182\pi$
$30$		0			0
$31$	6.41357	−	2.08390i	1.15191	−	0.374279i	0.330048	−	0.943964i	$-0.392935\pi$
$31$	6.41357	−	2.08390i	1.15191	−	0.374279i	0.821863	+	0.569685i	$0.192935\pi$
$32$	−3.83986	−	4.15397i	−0.678797	−	0.734326i
$33$		0			0
$34$	1.61828	−	4.85057i	0.277533	−	0.831867i
$35$	4.87517	−	2.78058i	0.824054	−	0.470005i
$36$		0			0
$37$	4.16075	−	0.658998i	0.684023	−	0.108339i	0.195255	−	0.980752i	$-0.437447\pi$
$37$	4.16075	−	0.658998i	0.684023	−	0.108339i	0.488768	+	0.872414i	$0.337447\pi$
$38$	3.73019	−	1.86386i	0.605116	−	0.302359i
$39$		0			0
$40$	6.22168	−	1.13610i	0.983734	−	0.179633i
$41$	−9.50896	−	6.90867i	−1.48505	−	1.07895i	−0.975885	−	0.218283i	$-0.929954\pi$
$41$	−9.50896	−	6.90867i	−1.48505	−	1.07895i	−0.509165	−	0.860669i	$-0.670046\pi$
$42$		0			0
$43$	1.10111	−	1.10111i	0.167918	−	0.167918i	−0.618146	−	0.786063i	$-0.712116\pi$
$43$	1.10111	−	1.10111i	0.167918	−	0.167918i	0.786063	+	0.618146i	$0.212116\pi$
$44$	1.58437	+	1.18959i	0.238853	+	0.179337i
$45$		0			0
$46$	−11.3095	−	0.0888373i	−1.66750	−	0.0130983i
$47$	−8.43980	+	4.30030i	−1.23107	+	0.627262i	−0.943778	−	0.330580i	$-0.892756\pi$
$47$	−8.43980	+	4.30030i	−1.23107	+	0.627262i	−0.287294	+	0.957842i	$0.592756\pi$
$48$		0			0
$49$		−	0.700218i		−	0.100031i
$50$	−2.65492	+	6.55373i	−0.375463	+	0.926837i
$51$		0			0
$52$	3.99684	+	8.15861i	0.554263	+	1.13140i
$53$	5.38846	−	2.74556i	0.740162	−	0.377131i	−0.0428967	−	0.999080i	$-0.513659\pi$
$53$	5.38846	−	2.74556i	0.740162	−	0.377131i	0.783058	+	0.621948i	$0.213659\pi$
$54$		0			0
$55$	−2.07213	+	0.782931i	−0.279405	+	0.105570i
$56$	−2.35224	+	6.69815i	−0.314332	+	0.895078i
$57$		0			0
$58$	−0.150611	+	0.904861i	−0.0197762	+	0.118814i
$59$	5.91350	+	4.29641i	0.769872	+	0.559345i	0.901922	−	0.431898i	$-0.142156\pi$
$59$	5.91350	+	4.29641i	0.769872	+	0.559345i	−0.132051	+	0.991243i	$0.542156\pi$
$60$		0			0
$61$	1.00189	−	0.727914i	0.128279	−	0.0931999i	−0.521796	−	0.853070i	$-0.674738\pi$
$61$	1.00189	−	0.727914i	0.128279	−	0.0931999i	0.650074	+	0.759871i	$0.274738\pi$
$62$	−4.26280	−	8.53121i	−0.541376	−	1.08347i
$63$		0			0
$64$	−5.00198	+	6.24341i	−0.625247	+	0.780427i
$65$	−10.0960	−	1.11487i	−1.25225	−	0.138282i
$66$		0			0
$67$	−2.66543	+	5.23120i	−0.325634	+	0.639093i	−0.994552	−	0.104244i	$-0.966758\pi$
$67$	−2.66543	+	5.23120i	−0.325634	+	0.639093i	0.668918	+	0.743336i	$0.266758\pi$
$68$	−7.12376	−	1.24331i	−0.863883	−	0.150773i
$69$		0			0
$70$	−4.91366	−	6.23328i	−0.587295	−	0.745019i
$71$	−11.9160	−	3.87174i	−1.41417	−	0.459491i	−0.500423	−	0.865781i	$-0.666822\pi$
$71$	−11.9160	−	3.87174i	−1.41417	−	0.459491i	−0.913744	+	0.406291i	$0.866822\pi$
$72$		0			0
$73$	−8.37438	−	1.32637i	−0.980147	−	0.155240i	−0.354254	−	0.935149i	$-0.615265\pi$
$73$	−8.37438	−	1.32637i	−0.980147	−	0.155240i	−0.625893	+	0.779909i	$0.715265\pi$
$74$	−1.79642	−	5.68024i	−0.208829	−	0.660314i
$75$		0			0
$76$	−3.39089	−	4.82477i	−0.388962	−	0.553439i
$77$	0.388959	−	2.45579i	0.0443260	−	0.279864i
$78$		0			0
$79$	2.78730	−	8.57843i	0.313596	−	0.965149i	−0.662732	−	0.748856i	$-0.730603\pi$
$79$	2.78730	−	8.57843i	0.313596	−	0.965149i	0.976328	−	0.216293i	$-0.0693967\pi$
$80$	−2.89696	−	8.46213i	−0.323890	−	0.946095i
$81$		0			0
$82$	−7.66246	+	14.7508i	−0.846177	+	1.62896i
$83$	−3.13531	−	1.59752i	−0.344145	−	0.175351i	0.273372	−	0.961908i	$-0.411861\pi$
$83$	−3.13531	−	1.59752i	−0.344145	−	0.175351i	−0.617516	+	0.786558i	$0.711861\pi$
$84$		0			0
$85$	5.44146	−	5.97978i	0.590209	−	0.648598i
$86$	−1.77141	−	1.30839i	−0.191016	−	0.141087i
$87$		0			0
$88$	1.33051	−	2.46585i	0.141833	−	0.262861i
$89$	−3.29356	−	4.53320i	−0.349117	−	0.480518i	0.597960	−	0.801526i	$-0.295978\pi$
$89$	−3.29356	−	4.53320i	−0.349117	−	0.480518i	−0.947076	+	0.321008i	$0.895978\pi$
$90$		0			0
$91$	6.70159	−	9.22394i	0.702517	−	0.966932i
$92$	2.25362	+	15.8350i	0.234956	+	1.65091i
$93$		0			0
$94$	7.78845	+	10.8989i	0.803317	+	1.12413i
$95$	6.58592	−	0.310418i	0.675701	−	0.0318482i
$96$		0			0
$97$	3.83895	+	7.53437i	0.389786	+	0.764999i	0.999621	−	0.0275298i	$-0.00876413\pi$
$97$	3.83895	+	7.53437i	0.389786	+	0.764999i	−0.609835	+	0.792529i	$0.708764\pi$
$98$	−0.979253	+	0.147223i	−0.0989194	+	0.0148718i
$99$		0			0
$100$	9.72358	+	2.33496i	0.972358	+	0.233496i
$101$	6.21954			0.618867			0.309434	−	0.950921i	$-0.399861\pi$
$101$	6.21954			0.618867			0.309434	+	0.950921i	$0.399861\pi$
$102$		0			0
$103$	6.88277	+	13.5082i	0.678180	+	1.33100i	0.931543	+	0.363632i	$0.118463\pi$
$103$	6.88277	+	13.5082i	0.678180	+	1.33100i	−0.253363	+	0.967371i	$0.581537\pi$
$104$	10.5694	−	7.30495i	1.03642	−	0.716309i
$105$		0			0
$106$	−4.97259	−	6.95848i	−0.482981	−	0.675867i
$107$	12.1376	+	12.1376i	1.17338	+	1.17338i	0.981398	+	0.191983i	$0.0614920\pi$
$107$	12.1376	+	12.1376i	1.17338	+	1.17338i	0.191983	+	0.981398i	$0.438508\pi$
$108$		0			0
$109$	9.77725	−	13.4572i	0.936490	−	1.28897i	−0.0207832	−	0.999784i	$-0.506616\pi$
$109$	9.77725	−	13.4572i	0.936490	−	1.28897i	0.957273	−	0.289184i	$-0.0933840\pi$
$110$	1.53060	+	2.73325i	0.145937	+	0.260605i
$111$		0			0
$112$	9.86191	+	1.88130i	0.931863	+	0.177766i
$113$	1.31076	+	8.27580i	0.123306	+	0.778522i	0.969400	+	0.245488i	$0.0789481\pi$
$113$	1.31076	+	8.27580i	0.123306	+	0.778522i	−0.846094	+	0.533034i	$0.821052\pi$
$114$		0			0
$115$	−16.2980	−	7.35930i	−1.51979	−	0.686258i
$116$	1.29711	+	0.0203791i	0.120434	+	0.00189215i
$117$		0			0
$118$	4.76518	−	9.17334i	0.438670	−	0.844474i
$119$	2.80440	+	8.63106i	0.257079	+	0.791208i
$120$		0			0
$121$	3.09594	−	9.52831i	0.281449	−	0.866210i
$122$	−1.22864	−	1.24809i	−0.111235	−	0.112997i
$123$		0			0
$124$	−11.0346	+	7.75522i	−0.990937	+	0.696439i
$125$	−8.02948	+	7.77994i	−0.718179	+	0.695859i
$126$		0			0
$127$	−16.4029	−	2.59797i	−1.45552	−	0.230532i	−0.622001	−	0.783017i	$-0.713680\pi$
$127$	−16.4029	−	2.59797i	−1.45552	−	0.230532i	−0.833523	+	0.552484i	$0.813680\pi$
$128$	9.78308	+	5.68255i	0.864710	+	0.502271i
$129$		0			0
$130$	0.563581	+	14.3536i	0.0494293	+	1.25890i
$131$	14.3823	−	4.67308i	1.25658	−	0.408289i	0.396308	−	0.918118i	$-0.370291\pi$
$131$	14.3823	−	4.67308i	1.25658	−	0.408289i	0.860276	+	0.509829i	$0.170291\pi$
$132$		0			0
$133$	−3.35987	+	6.59412i	−0.291338	+	0.571783i
$134$	7.87623	+	2.62772i	0.680403	+	0.227000i
$135$		0			0
$136$	−0.240970	+	10.2240i	−0.0206630	+	0.876698i
$137$	8.05142	−	1.27522i	0.687880	−	0.108949i	0.197296	−	0.980344i	$-0.436784\pi$
$137$	8.05142	−	1.27522i	0.687880	−	0.108949i	0.490583	+	0.871394i	$0.336784\pi$
$138$		0			0
$139$	−1.71761	+	1.24792i	−0.145686	+	0.105847i	−0.658241	−	0.752807i	$-0.728699\pi$
$139$	−1.71761	+	1.24792i	−0.145686	+	0.105847i	0.512555	+	0.858654i	$0.328699\pi$
$140$	−7.68411	+	8.18230i	−0.649426	+	0.691531i
$141$		0			0
$142$	−2.90924	+	17.4785i	−0.244138	+	1.46676i
$143$	−3.18193	+	3.18193i	−0.266086	+	0.266086i
$144$		0			0
$145$	−0.796330	+	1.21223i	−0.0661316	+	0.100670i
$146$	−0.0941859	+	11.9904i	−0.00779488	+	0.992334i
$147$		0			0
$148$	−7.56609	+	3.70657i	−0.621929	+	0.304678i
$149$			6.70318i			0.549146i	0.961566	+	0.274573i	$0.0885365\pi$
$149$			6.70318i			0.549146i	−0.961566	+	0.274573i	$0.911463\pi$
$150$		0			0
$151$			3.66896i			0.298576i	0.988794	+	0.149288i	$0.0476982\pi$
$151$			3.66896i			0.298576i	−0.988794	+	0.149288i	$0.952302\pi$
$152$	−6.03448	+	5.75658i	−0.489461	+	0.466920i
$153$		0			0
$154$	−3.51620	−	0.0276201i	−0.283343	−	0.00222569i
$155$	−0.709950	−	15.0625i	−0.0570245	−	1.20985i
$156$		0			0
$157$	12.4337	−	12.4337i	0.992319	−	0.992319i	−0.00765190	−	0.999971i	$-0.502436\pi$
$157$	12.4337	−	12.4337i	0.992319	−	0.992319i	0.999971	+	0.00765190i	$0.00243570\pi$
$158$	−12.5830	−	2.09439i	−1.00105	−	0.166621i
$159$		0			0
$160$	−11.2252	+	5.83058i	−0.887427	+	0.460948i
$161$	16.2391	−	11.7984i	1.27982	−	0.929846i
$162$		0			0
$163$	−9.09281	+	1.44016i	−0.712204	+	0.112802i	−0.502015	−	0.864859i	$-0.667408\pi$
$163$	−9.09281	+	1.44016i	−0.712204	+	0.112802i	−0.210189	+	0.977661i	$0.567408\pi$
$164$	22.2400	+	7.61451i	1.73666	+	0.594594i
$165$		0			0
$166$	−1.57492	+	4.72060i	−0.122237	+	0.366390i
$167$	−7.73498	+	15.1807i	−0.598550	+	1.17472i	0.370725	+	0.928743i	$0.379109\pi$
$167$	−7.73498	+	15.1807i	−0.598550	+	1.17472i	−0.969275	+	0.245979i	$0.920891\pi$
$168$		0			0
$169$	−7.26078	+	2.35917i	−0.558521	+	0.181475i
$170$	−9.50679	−	6.35259i	−0.729137	−	0.487222i
$171$		0			0
$172$	−1.45733	+	2.75240i	−0.111120	+	0.209869i
$173$	14.7932	+	2.34301i	1.12470	+	0.178136i	0.690955	−	0.722898i	$-0.257190\pi$
$173$	14.7932	+	2.34301i	1.12470	+	0.178136i	0.433749	+	0.901034i	$0.357190\pi$
$174$		0			0
$175$	−3.12037	−	12.1556i	−0.235878	−	0.918875i
$176$	−3.72823	−	1.34226i	−0.281026	−	0.101177i
$177$		0			0
$178$	−5.64718	+	5.55916i	−0.423274	+	0.416676i
$179$	0.284605	−	0.875924i	0.0212724	−	0.0654696i	−0.939857	−	0.341569i	$-0.889042\pi$
$179$	0.284605	−	0.875924i	0.0212724	−	0.0654696i	0.961129	+	0.276099i	$0.0890418\pi$
$180$		0			0
$181$	−3.55067	−	10.9278i	−0.263919	−	0.812259i	−0.991940	−	0.126705i	$-0.959560\pi$
$181$	−3.55067	−	10.9278i	−0.263919	−	0.812259i	0.728022	−	0.685554i	$-0.240440\pi$
$182$	−14.3087	−	7.43279i	−1.06063	−	0.550955i
$183$		0			0
$184$	21.6714	−	6.48105i	1.59763	−	0.477789i
$185$	1.03390	−	9.36278i	0.0760137	−	0.688365i
$186$		0			0
$187$	−0.560321	−	3.53772i	−0.0409747	−	0.258704i
$188$	13.6045	−	13.1836i	0.992211	−	0.961516i
$189$		0			0
$190$	−1.81883	−	9.14512i	−0.131952	−	0.663457i
$191$	−12.4464	+	17.1310i	−0.900587	+	1.23955i	0.0696930	+	0.997568i	$0.477798\pi$
$191$	−12.4464	+	17.1310i	−0.900587	+	1.23955i	−0.970280	+	0.241984i	$0.922202\pi$
$192$		0			0
$193$	10.4449	+	10.4449i	0.751839	+	0.751839i	0.974822	−	0.222983i	$-0.0715794\pi$
$193$	10.4449	+	10.4449i	0.751839	+	0.751839i	−0.222983	+	0.974822i	$0.571579\pi$
$194$	9.72963	−	6.95289i	0.698547	−	0.499188i
$195$		0			0
$196$	0.411782	+	1.33853i	0.0294130	+	0.0956091i
$197$	9.78412	+	19.2024i	0.697090	+	1.36812i	0.919472	+	0.393156i	$0.128617\pi$
$197$	9.78412	+	19.2024i	0.697090	+	1.36812i	−0.222382	+	0.974960i	$0.571383\pi$
$198$		0			0
$199$	10.7861			0.764606			0.382303	−	0.924037i	$-0.375131\pi$
$199$	10.7861			0.764606			0.382303	+	0.924037i	$0.375131\pi$
$200$	1.22102	−	14.0893i	0.0863393	−	0.996266i
$201$		0			0
$202$	−1.30768	−	8.69801i	−0.0920080	−	0.611990i
$203$	−0.739113	−	1.45059i	−0.0518755	−	0.101811i
$204$		0			0
$205$	−20.5118	+	16.4322i	−1.43261	+	1.14767i
$206$	17.4441	−	12.4657i	1.21539	−	0.868525i
$207$		0			0
$208$	−12.4382	−	13.2454i	−0.862435	−	0.918407i
$209$	1.71688	−	2.36309i	0.118759	−	0.163458i
$210$		0			0
$211$	13.2828	+	18.2822i	0.914424	+	1.25860i	0.965633	+	0.259909i	$0.0836925\pi$
$211$	13.2828	+	18.2822i	0.914424	+	1.25860i	−0.0512093	+	0.998688i	$0.516308\pi$
$212$	−8.68591	+	8.41720i	−0.596551	+	0.578096i
$213$		0			0
$214$	14.4224	−	19.5263i	0.985893	−	1.33479i
$215$	−1.72512	−	3.02463i	−0.117652	−	0.206278i
$216$		0			0
$217$	15.0812	+	7.68428i	1.02378	+	0.521643i
$218$	−20.8756	−	10.8440i	−1.41387	−	0.734450i
$219$		0			0
$220$	3.50062	−	2.71521i	0.236012	−	0.183059i
$221$	5.07544	−	15.6206i	0.341411	−	1.05076i
$222$		0			0
$223$	−0.0533298	+	0.336711i	−0.00357123	+	0.0225478i	−0.989410	−	0.145150i	$-0.953633\pi$
$223$	−0.0533298	+	0.336711i	−0.00357123	+	0.0225478i	0.985838	+	0.167698i	$0.0536334\pi$
$224$	0.557492	−	14.1874i	0.0372490	−	0.947935i
$225$		0			0
$226$	11.2981	−	3.57310i	0.751538	−	0.237679i
$227$	14.9903	+	2.37422i	0.994939	+	0.157583i	0.632612	−	0.774469i	$-0.281983\pi$
$227$	14.9903	+	2.37422i	0.994939	+	0.157583i	0.362326	+	0.932051i	$0.381983\pi$
$228$		0			0
$229$	17.8213	+	5.79049i	1.17766	+	0.382646i	0.831498	−	0.555527i	$-0.187484\pi$
$229$	17.8213	+	5.79049i	1.17766	+	0.382646i	0.346166	+	0.938173i	$0.387484\pi$
$230$	−6.86526	+	24.3400i	−0.452682	+	1.60493i
$231$		0			0
$232$	−0.244222	−	1.81829i	−0.0160340	−	0.119377i
$233$	−8.78825	+	17.2479i	−0.575737	+	1.12995i	0.401114	+	0.916028i	$0.368623\pi$
$233$	−8.78825	+	17.2479i	−0.575737	+	1.12995i	−0.976851	+	0.213920i	$0.931377\pi$
$234$		0			0
$235$	4.29462	+	20.7406i	0.280150	+	1.35296i
$236$	−13.8308	−	4.73536i	−0.900307	−	0.308246i
$237$		0			0
$238$	11.4809	−	5.73665i	0.744195	−	0.371852i
$239$	0.648942	−	0.471484i	0.0419765	−	0.0304977i	−0.566599	−	0.823994i	$-0.691741\pi$
$239$	0.648942	−	0.471484i	0.0419765	−	0.0304977i	0.608576	+	0.793496i	$0.291741\pi$
$240$		0			0
$241$	−10.2685	−	7.46048i	−0.661451	−	0.480572i	0.205702	−	0.978615i	$-0.434052\pi$
$241$	−10.2685	−	7.46048i	−0.661451	−	0.480572i	−0.867152	+	0.498043i	$0.834052\pi$
$242$	−13.9762	−	2.32630i	−0.898427	−	0.149540i
$243$		0			0
$244$	−1.48713	+	1.98066i	−0.0952035	+	0.126799i
$245$	−1.51023	−	0.413193i	−0.0964851	−	0.0263979i
$246$		0			0
$247$	11.9341	−	6.08074i	0.759350	−	0.386908i
$248$	13.1657	+	13.8013i	0.836024	+	0.876384i
$249$		0			0
$250$	12.5684	+	9.59345i	0.794898	+	0.606743i
$251$		−	5.05741i		−	0.319221i	−0.987180	−	0.159610i	$-0.948976\pi$
$251$		−	5.05741i		−	0.319221i	0.987180	−	0.159610i	$-0.0510238\pi$
$252$		0			0
$253$	−7.05882	+	3.59665i	−0.443784	+	0.226119i
$254$	−0.184482	+	23.4857i	−0.0115754	+	1.47362i
$255$		0			0
$256$	5.89011	−	14.8764i	0.368132	−	0.929774i
$257$	5.59294	−	5.59294i	0.348878	−	0.348878i	−0.510814	−	0.859692i	$-0.670656\pi$
$257$	5.59294	−	5.59294i	0.348878	−	0.348878i	0.859692	+	0.510814i	$0.170656\pi$
$258$		0			0
$259$	8.55406	+	6.21489i	0.531523	+	0.386174i
$260$	19.9550	−	3.80606i	1.23756	−	0.236042i
$261$		0			0
$262$	−9.55921	−	19.1310i	−0.590570	−	1.18192i
$263$	5.26506	−	0.833904i	0.324658	−	0.0514207i	0.00802154	−	0.999968i	$-0.497447\pi$
$263$	5.26506	−	0.833904i	0.324658	−	0.0514207i	0.316636	+	0.948547i	$0.397447\pi$
$264$		0			0
$265$	−2.74193	−	13.2420i	−0.168436	−	0.813447i
$266$	9.92828	+	3.31234i	0.608742	+	0.203092i
$267$		0			0
$268$	2.01885	−	11.5674i	0.123321	−	0.706590i
$269$	−14.5139	+	4.71586i	−0.884929	+	0.287531i	−0.716002	−	0.698098i	$-0.754030\pi$
$269$	−14.5139	+	4.71586i	−0.884929	+	0.287531i	−0.168926	+	0.985629i	$0.554030\pi$
$270$		0			0
$271$	15.8393	+	5.14649i	0.962167	+	0.312627i	0.747650	−	0.664093i	$-0.231182\pi$
$271$	15.8393	+	5.14649i	0.962167	+	0.312627i	0.214517	+	0.976720i	$0.431182\pi$
$272$	14.3489	−	1.81263i	0.870027	−	0.109907i
$273$		0			0
$274$	−3.47623	−	10.9918i	−0.210007	−	0.664037i
$275$	0.465882	+	4.93116i	0.0280938	+	0.297360i
$276$		0			0
$277$	−2.26929	+	14.3277i	−0.136349	+	0.860871i	0.820788	+	0.571233i	$0.193535\pi$
$277$	−2.26929	+	14.3277i	−0.136349	+	0.860871i	−0.957136	+	0.289638i	$0.906465\pi$
$278$	2.10634	+	2.13970i	0.126330	+	0.128330i
$279$		0			0
$280$	13.0585	+	9.02585i	0.780397	+	0.539398i
$281$	−0.523806	−	1.61211i	−0.0312476	−	0.0961703i	0.934216	−	0.356707i	$-0.116101\pi$
$281$	−0.523806	−	1.61211i	−0.0312476	−	0.0961703i	−0.965464	+	0.260537i	$0.916101\pi$
$282$		0			0
$283$	1.89544	+	0.965777i	0.112672	+	0.0574095i	0.509418	−	0.860519i	$-0.329861\pi$
$283$	1.89544	+	0.965777i	0.112672	+	0.0574095i	−0.396746	+	0.917928i	$0.629861\pi$
$284$	25.0553	+	0.393648i	1.48676	+	0.0233587i
$285$		0			0
$286$	5.11893	+	3.78091i	0.302689	+	0.223570i
$287$	−4.61499	−	29.1379i	−0.272414	−	1.71996i
$288$		0			0
$289$	−2.30797	−	3.17665i	−0.135763	−	0.186862i
$290$	1.86273	+	0.858790i	0.109383	+	0.0504299i
$291$		0			0
$292$	16.7884	−	2.38931i	0.982465	−	0.139824i
$293$	−12.5122	−	12.5122i	−0.730972	−	0.730972i	0.239840	−	0.970812i	$-0.422905\pi$
$293$	−12.5122	−	12.5122i	−0.730972	−	0.730972i	−0.970812	+	0.239840i	$0.922905\pi$
$294$		0			0
$295$	12.7560	−	10.2190i	0.742683	−	0.594971i
$296$	6.77443	+	9.80184i	0.393756	+	0.569720i
$297$		0			0
$298$	9.37438	−	1.40937i	0.543043	−	0.0816424i
$299$	−36.3278			−2.10089
$300$		0			0
$301$	3.90848			0.225281
$302$	5.13104	−	0.771412i	0.295258	−	0.0443898i
$303$		0			0
$304$	9.31932	+	7.22886i	0.534500	+	0.414604i
$305$	−0.978760	−	2.59041i	−0.0560436	−	0.148326i
$306$		0			0
$307$	−18.9220	−	18.9220i	−1.07994	−	1.07994i	−0.996514	−	0.0834227i	$-0.973415\pi$
$307$	−18.9220	−	18.9220i	−1.07994	−	1.07994i	−0.0834227	−	0.996514i	$-0.526585\pi$
$308$	0.700666	+	4.92320i	0.0399241	+	0.280525i
$309$		0			0
$310$	−20.9156	+	4.15980i	−1.18792	+	0.236261i
$311$	−1.35781	−	1.86887i	−0.0769945	−	0.105974i	0.768783	−	0.639510i	$-0.220863\pi$
$311$	−1.35781	−	1.86887i	−0.0769945	−	0.105974i	−0.845777	+	0.533536i	$0.820863\pi$
$312$		0			0
$313$	−1.02291	−	6.45842i	−0.0578185	−	0.365052i	−0.999586	−	0.0287858i	$-0.990836\pi$
$313$	−1.02291	−	6.45842i	−0.0578185	−	0.365052i	0.941767	−	0.336266i	$-0.109164\pi$
$314$	−20.0027	−	14.7743i	−1.12882	−	0.833761i
$315$		0			0
$316$	−0.283391	+	18.0376i	−0.0159420	+	1.01469i
$317$	17.7707	+	9.05465i	0.998105	+	0.508560i	0.875150	−	0.483853i	$-0.160763\pi$
$317$	17.7707	+	9.05465i	0.998105	+	0.508560i	0.122955	+	0.992412i	$0.460763\pi$
$318$		0			0
$319$	0.198560	+	0.611106i	0.0111172	+	0.0342154i
$320$	10.5142	+	14.4725i	0.587760	+	0.809035i
$321$		0			0
$322$	−19.9144	−	20.2297i	−1.10979	−	1.12736i
$323$	−1.66779	+	10.5300i	−0.0927982	+	0.585905i
$324$		0			0
$325$	−8.36212	+	21.1172i	−0.463847	+	1.17137i
$326$	3.92585	+	12.4135i	0.217433	+	0.687518i
$327$		0			0
$328$	5.97283	−	32.7036i	0.329795	−	1.80575i
$329$	−22.6110	−	7.34677i	−1.24659	−	0.405041i
$330$		0			0
$331$	−29.5081	+	9.58775i	−1.62191	+	0.526990i	−0.972392	−	0.233355i	$-0.925029\pi$
$331$	−29.5081	+	9.58775i	−1.62191	+	0.526990i	−0.649518	+	0.760346i	$0.725029\pi$
$332$	6.93288	+	1.20999i	0.380491	+	0.0664071i
$333$		0			0
$334$	22.8565	+	7.62554i	1.25065	+	0.417251i
$335$	9.70981	+	8.83569i	0.530503	+	0.482745i
$336$		0			0
$337$	−19.6994	+	3.12009i	−1.07310	+	0.169962i	−0.667888	−	0.744262i	$-0.732801\pi$
$337$	−19.6994	+	3.12009i	−1.07310	+	0.169962i	−0.405209	+	0.914224i	$0.632801\pi$
$338$	4.82589	+	9.65815i	0.262494	+	0.525334i
$339$		0			0
$340$	−6.88525	+	14.6309i	−0.373405	+	0.793470i
$341$	−5.40456	−	3.92664i	−0.292673	−	0.212640i
$342$		0			0
$343$	13.6663	−	13.6663i	0.737911	−	0.737911i
$344$	4.15564	+	1.45937i	0.224057	+	0.0786839i
$345$		0			0
$346$	0.166377	−	21.1808i	0.00894451	−	1.13869i
$347$	−3.24564	+	1.65374i	−0.174235	+	0.0887772i	−0.538933	−	0.842349i	$-0.681172\pi$
$347$	−3.24564	+	1.65374i	−0.174235	+	0.0887772i	0.364698	+	0.931126i	$0.381172\pi$
$348$		0			0
$349$			24.4825i			1.31052i	0.755405	+	0.655258i	$0.227440\pi$
$349$			24.4825i			1.31052i	−0.755405	+	0.655258i	$0.772560\pi$
$350$	−16.3435	+	6.91957i	−0.873595	+	0.369867i
$351$		0			0
$352$	−1.09328	+	5.49614i	−0.0582719	+	0.292945i
$353$	−14.7437	+	7.51230i	−0.784729	+	0.399839i	−0.799966	−	0.600045i	$-0.795149\pi$
$353$	−14.7437	+	7.51230i	−0.784729	+	0.399839i	0.0152379	+	0.999884i	$0.495149\pi$
$354$		0			0
$355$	−15.3821	+	23.4157i	−0.816397	+	1.24278i
$356$	8.96180	+	6.72874i	0.474975	+	0.356622i
$357$		0			0
$358$	−1.28482	−	0.213853i	−0.0679046	−	0.0113025i
$359$	−6.02704	−	4.37890i	−0.318095	−	0.231109i	0.417267	−	0.908784i	$-0.362988\pi$
$359$	−6.02704	−	4.37890i	−0.318095	−	0.231109i	−0.735362	+	0.677674i	$0.762988\pi$
$360$		0			0
$361$	8.33761	−	6.05763i	0.438822	−	0.318823i
$362$	−14.5360	+	7.26321i	−0.763995	+	0.381746i
$363$		0			0
$364$	−7.38628	+	21.5734i	−0.387146	+	1.13075i
$365$	−7.80238	+	17.2792i	−0.408395	+	0.904434i
$366$		0			0
$367$	−12.3376	+	24.2139i	−0.644018	+	1.26396i	0.306080	+	0.952006i	$0.400982\pi$
$367$	−12.3376	+	24.2139i	−0.644018	+	1.26396i	−0.950098	+	0.311951i	$0.899018\pi$
$368$	−13.6202	−	28.9447i	−0.710002	−	1.50885i
$369$		0			0
$370$	−13.3112	+	0.522651i	−0.692016	+	0.0271713i
$371$	14.4362	+	4.69060i	0.749490	+	0.243524i
$372$		0			0
$373$	1.04989	+	0.166286i	0.0543613	+	0.00860998i	0.183556	−	0.983009i	$-0.441239\pi$
$373$	1.04989	+	0.166286i	0.0543613	+	0.00860998i	−0.129195	+	0.991619i	$0.541239\pi$
$374$	−4.82969	+	1.52742i	−0.249737	+	0.0789813i
$375$		0			0
$376$	−21.2977	−	16.2540i	−1.09834	−	0.838235i
$377$	−0.460925	+	2.91016i	−0.0237388	+	0.149881i
$378$		0			0
$379$	5.91385	−	18.2010i	0.303774	−	0.934921i	−0.676358	−	0.736573i	$-0.736443\pi$
$379$	5.91385	−	18.2010i	0.303774	−	0.934921i	0.980132	−	0.198347i	$-0.0635574\pi$
$380$	−12.4070	+	4.46642i	−0.636466	+	0.229123i
$381$		0			0
$382$	26.5745	+	13.8044i	1.35967	+	0.706293i
$383$	−18.3322	−	9.34072i	−0.936731	−	0.477289i	−0.0821581	−	0.996619i	$-0.526181\pi$
$383$	−18.3322	−	9.34072i	−0.936731	−	0.477289i	−0.854573	+	0.519331i	$0.826181\pi$
$384$		0			0
$385$	−5.06714	−	2.28805i	−0.258245	−	0.116610i
$386$	12.4111	−	16.8032i	0.631707	−	0.855261i
$387$		0			0
$388$	−11.7693	−	12.1450i	−0.597494	−	0.616569i
$389$	7.78730	+	10.7183i	0.394832	+	0.543439i	0.959438	−	0.281921i	$-0.0909717\pi$
$389$	7.78730	+	10.7183i	0.394832	+	0.543439i	−0.564606	+	0.825361i	$0.690972\pi$
$390$		0			0
$391$	16.9964	−	23.3935i	0.859543	−	1.18306i
$392$	1.78535	−	0.857306i	0.0901737	−	0.0433005i
$393$		0			0
$394$	24.7974	−	17.7204i	1.24927	−	0.892742i
$395$	−16.8572	−	11.0737i	−0.848178	−	0.557180i
$396$		0			0
$397$	5.75681	+	11.2984i	0.288926	+	0.567049i	0.989156	−	0.146868i	$-0.0469193\pi$
$397$	5.75681	+	11.2984i	0.288926	+	0.567049i	−0.700230	+	0.713917i	$0.746919\pi$
$398$	−2.26781	−	15.0843i	−0.113675	−	0.756109i
$399$		0			0
$400$	−19.9606	+	1.25473i	−0.998030	+	0.0627366i
$401$	−15.1445			−0.756281			−0.378141	−	0.925748i	$-0.623436\pi$
$401$	−15.1445			−0.756281			−0.378141	+	0.925748i	$0.623436\pi$
$402$		0			0
$403$	−13.9071	−	27.2942i	−0.692762	−	1.35962i
$404$	−11.8892	+	3.65757i	−0.591510	+	0.181971i
$405$		0			0
$406$	−1.87325	+	1.33864i	−0.0929676	+	0.0664355i
$407$	−2.95084	−	2.95084i	−0.146268	−	0.146268i
$408$		0			0
$409$	−15.2785	+	21.0290i	−0.755471	+	1.03982i	0.242106	+	0.970250i	$0.422162\pi$
$409$	−15.2785	+	21.0290i	−0.755471	+	1.03982i	−0.997577	+	0.0695670i	$0.977838\pi$
$410$	27.2930	+	25.2307i	1.34791	+	1.24606i
$411$		0			0
$412$	−21.1009	−	21.7745i	−1.03957	−	1.07275i
$413$	2.87000	+	18.1205i	0.141223	+	0.891650i
$414$		0			0
$415$	−5.29565	+	5.81955i	−0.259953	+	0.285671i
$416$	−15.9085	+	20.1797i	−0.779981	+	0.989391i
$417$		0			0
$418$	−3.66575	−	1.90421i	−0.179298	−	0.0931380i
$419$	−7.45434	−	22.9421i	−0.364168	−	1.12079i	−0.950500	−	0.310724i	$-0.899429\pi$
$419$	−7.45434	−	22.9421i	−0.364168	−	1.12079i	0.586332	−	0.810071i	$-0.300571\pi$
$420$		0			0
$421$	−5.40899	+	16.6472i	−0.263618	+	0.811334i	0.728390	+	0.685162i	$0.240269\pi$
$421$	−5.40899	+	16.6472i	−0.263618	+	0.811334i	−0.992009	+	0.126171i	$0.959731\pi$
$422$	22.7748	−	22.4198i	1.10866	−	1.09138i
$423$		0			0
$424$	13.5977	+	10.3775i	0.660361	+	0.503975i
$425$	−9.68624	−	15.2648i	−0.469851	−	0.740450i
$426$		0			0
$427$	3.07004	+	0.486247i	0.148570	+	0.0235311i
$428$	−30.3398	−	16.0642i	−1.46653	−	0.776491i
$429$		0			0
$430$	−3.86722	+	3.04851i	−0.186494	+	0.147012i
$431$	34.6020	−	11.2429i	1.66672	−	0.541550i	0.684455	−	0.729055i	$-0.260040\pi$
$431$	34.6020	−	11.2429i	1.66672	−	0.541550i	0.982264	+	0.187505i	$0.0600400\pi$
$432$		0			0
$433$	−16.2768	+	31.9450i	−0.782213	+	1.53518i	0.0613291	+	0.998118i	$0.480466\pi$
$433$	−16.2768	+	31.9450i	−0.782213	+	1.53518i	−0.843542	+	0.537062i	$0.819534\pi$
$434$	7.57556	−	22.7067i	0.363638	−	1.08996i
$435$		0			0
$436$	−10.7762	+	31.4744i	−0.516085	+	1.50735i
$437$	23.2903	−	3.68883i	1.11413	−	0.176460i
$438$		0			0
$439$	−13.0760	+	9.50025i	−0.624082	+	0.453422i	−0.854345	−	0.519706i	$-0.826041\pi$
$439$	−13.0760	+	9.50025i	−0.624082	+	0.453422i	0.230263	+	0.973128i	$0.426041\pi$
$440$	−4.53323	−	4.32473i	−0.216113	−	0.206173i
$441$		0			0
$442$	−22.9125	−	3.81371i	−1.08984	−	0.181399i
$443$	3.16889	−	3.16889i	0.150559	−	0.150559i	−0.627809	−	0.778367i	$-0.716048\pi$
$443$	3.16889	−	3.16889i	0.150559	−	0.150559i	0.778367	+	0.627809i	$0.216048\pi$
$444$		0			0
$445$	−11.7207	+	4.42855i	−0.555615	+	0.209934i
$446$	0.482102	+	0.00378696i	0.0228282	+	0.000179318i
$447$		0			0
$448$	−19.9582	+	2.20330i	−0.942938	+	0.104096i
$449$			32.0207i			1.51115i	0.655062	+	0.755575i	$0.272642\pi$
$449$			32.0207i			1.51115i	−0.655062	+	0.755575i	$0.727358\pi$
$450$		0			0
$451$			11.6435i			0.548272i
$452$	−7.37243	−	15.0491i	−0.346770	−	0.707849i
$453$		0			0
$454$	0.168594	−	21.4630i	0.00791251	−	1.00731i
$455$	−15.9397	−	19.8970i	−0.747263	−	0.932784i
$456$		0			0
$457$	16.1908	−	16.1908i	0.757374	−	0.757374i	−0.218469	−	0.975844i	$-0.570106\pi$
$457$	16.1908	−	16.1908i	0.757374	−	0.757374i	0.975844	+	0.218469i	$0.0701064\pi$
$458$	4.35100	−	26.1405i	0.203309	−	1.22146i
$459$		0			0
$460$	35.4828	+	4.48349i	1.65439	+	0.209044i
$461$	9.97154	−	7.24475i	0.464421	−	0.337421i	−0.330842	−	0.943686i	$-0.607333\pi$
$461$	9.97154	−	7.24475i	0.464421	−	0.337421i	0.795263	+	0.606265i	$0.207333\pi$
$462$		0			0
$463$	−32.1267	+	5.08837i	−1.49306	+	0.236477i	−0.848955	−	0.528464i	$-0.822768\pi$
$463$	−32.1267	+	5.08837i	−1.49306	+	0.236477i	−0.644100	+	0.764941i	$0.722768\pi$
$464$	−2.49153	+	0.723845i	−0.115666	+	0.0336037i
$465$		0			0
$466$	25.9689	+	8.66391i	1.20299	+	0.401348i
$467$	−0.752525	+	1.47691i	−0.0348227	+	0.0683434i	−0.907762	−	0.419485i	$-0.862211\pi$
$467$	−0.752525	+	1.47691i	−0.0348227	+	0.0683434i	0.872940	+	0.487828i	$0.162211\pi$
$468$		0			0
$469$	−14.0149	+	4.55371i	−0.647147	+	0.210271i
$470$	28.1026	−	10.3668i	1.29628	−	0.478184i
$471$		0			0
$472$	−3.71443	+	20.3379i	−0.170970	+	0.936129i
$473$	−1.52361	−	0.241317i	−0.0700558	−	0.0110957i
$474$		0			0
$475$	3.21679	−	14.3877i	0.147596	−	0.660153i
$476$	−10.4366	−	14.8498i	−0.478360	−	0.680640i
$477$		0			0
$478$	−0.795811	−	0.808412i	−0.0363995	−	0.0369759i
$479$	0.416357	−	1.28141i	0.0190238	−	0.0585493i	−0.941094	−	0.338145i	$-0.890200\pi$
$479$	0.416357	−	1.28141i	0.0190238	−	0.0585493i	0.960118	+	0.279596i	$0.0902005\pi$
$480$		0			0
$481$	−5.91331	−	18.1993i	−0.269624	−	0.829816i
$482$	−8.27448	+	15.9290i	−0.376892	+	0.725547i
$483$		0			0
$484$	−0.314771	+	20.0349i	−0.0143078	+	0.910675i
$485$	18.5155	−	3.83388i	0.840744	−	0.174088i
$486$		0			0
$487$	5.18153	+	32.7149i	0.234798	+	1.48245i	0.770171	+	0.637838i	$0.220171\pi$
$487$	5.18153	+	32.7149i	0.234798	+	1.48245i	−0.535373	+	0.844616i	$0.679829\pi$
$488$	3.08262	+	1.66330i	0.139544	+	0.0752941i
$489$		0			0
$490$	−0.260318	+	2.19893i	−0.0117600	+	0.0993374i
$491$	1.80230	−	2.48065i	0.0813366	−	0.111950i	−0.766410	−	0.642352i	$-0.777959\pi$
$491$	1.80230	−	2.48065i	0.0813366	−	0.111950i	0.847747	+	0.530402i	$0.177959\pi$
$492$		0			0
$493$	−1.65837	−	1.65837i	−0.0746892	−	0.0746892i
$494$	−11.0131	−	15.4113i	−0.495502	−	0.693389i
$495$		0			0
$496$	16.5329	−	21.3140i	0.742351	−	0.957026i
$497$	−14.2769	−	28.0199i	−0.640405	−	1.25687i
$498$		0			0
$499$	−38.2306			−1.71144			−0.855718	−	0.517443i	$-0.826884\pi$
$499$	−38.2306			−1.71144			−0.855718	+	0.517443i	$0.826884\pi$
$500$	10.7739	−	19.5940i	0.481821	−	0.876269i
$501$		0			0
$502$	−7.07277	+	1.06334i	−0.315673	+	0.0474590i
$503$	14.4347	+	28.3298i	0.643613	+	1.26316i	0.950295	+	0.311350i	$0.100781\pi$
$503$	14.4347	+	28.3298i	0.643613	+	1.26316i	−0.306682	+	0.951812i	$0.599219\pi$
$504$		0			0
$505$	3.67010	−	13.4143i	0.163317	−	0.596929i
$506$	6.51404	+	9.11554i	0.289585	+	0.405235i
$507$		0			0
$508$	32.8834	−	4.67994i	1.45897	−	0.207639i
$509$	−0.131687	+	0.181251i	−0.00583691	+	0.00803381i	−0.811925	−	0.583761i	$-0.801580\pi$
$509$	−0.131687	+	0.181251i	−0.00583691	+	0.00803381i	0.806089	+	0.591795i	$0.201580\pi$
$510$		0			0
$511$	−12.5088	−	17.2168i	−0.553355	−	0.761628i
$512$	−22.0430	−	5.10949i	−0.974171	−	0.225810i
$513$		0			0
$514$	−8.99764	−	6.64577i	−0.396869	−	0.293133i
$515$	33.1960	−	6.87369i	1.46279	−	0.302891i
$516$		0			0
$517$	8.36068	+	4.25998i	0.367702	+	0.187354i
$518$	6.89298	−	13.2695i	0.302860	−	0.583029i
$519$		0			0
$520$	−9.51837	−	27.1068i	−0.417408	−	1.18871i
$521$	2.36876	−	7.29029i	0.103777	−	0.319393i	−0.885664	−	0.464326i	$-0.846297\pi$
$521$	2.36876	−	7.29029i	0.103777	−	0.319393i	0.989441	+	0.144933i	$0.0462966\pi$
$522$		0			0
$523$	2.40963	−	15.2138i	0.105366	−	0.665253i	−0.877311	−	0.479923i	$-0.840665\pi$
$523$	2.40963	−	15.2138i	0.105366	−	0.665253i	0.982676	−	0.185330i	$-0.0593353\pi$
$524$	−24.7448	+	17.3909i	−1.08098	+	0.759724i
$525$		0			0
$526$	−2.27321	−	7.18784i	−0.0991166	−	0.313405i
$527$	24.0829	+	3.81435i	1.04907	+	0.166156i
$528$		0			0
$529$	−38.9519	−	12.6563i	−1.69356	−	0.550272i
$530$	−17.9423	+	6.61875i	−0.779366	+	0.287500i
$531$		0			0
$532$	2.54484	−	14.5811i	0.110333	−	0.632171i
$533$	−24.2392	+	47.5721i	−1.04992	+	2.06058i
$534$		0			0
$535$	33.3406	−	19.0160i	1.44144	−	0.822134i
$536$	−16.6014	−	0.391281i	−0.717071	−	0.0169008i
$537$		0			0
$538$	9.64671	+	19.3061i	0.415899	+	0.832347i
$539$	−0.561177	+	0.407719i	−0.0241716	+	0.0175617i
$540$		0			0
$541$	−0.252310	−	0.183314i	−0.0108476	−	0.00788127i	0.582348	−	0.812939i	$-0.302134\pi$
$541$	−0.252310	−	0.183314i	−0.0108476	−	0.00788127i	−0.593196	+	0.805058i	$0.702134\pi$
$542$	3.86709	−	23.2332i	0.166106	−	0.997953i
$543$		0			0
$544$	−5.55184	−	19.6857i	−0.238033	−	0.844018i
$545$	−23.2551	−	29.0286i	−0.996138	−	1.24345i
$546$		0			0
$547$	34.1386	−	17.3945i	1.45966	−	0.743735i	0.469405	−	0.882983i	$-0.344468\pi$
$547$	34.1386	−	17.3945i	1.45966	−	0.743735i	0.990258	+	0.139248i	$0.0444684\pi$
$548$	−14.6411	+	7.17255i	−0.625436	+	0.306396i
$549$		0			0
$550$	6.79826	−	1.68833i	0.289879	−	0.0719905i
$551$		−	1.91256i		−	0.0814777i
$552$		0			0
$553$	20.1718	−	10.2781i	0.857794	−	0.437068i
$554$	20.5144	+	0.161143i	0.871575	+	0.00684630i
$555$		0			0
$556$	2.54949	−	3.39559i	0.108123	−	0.144005i
$557$	−10.7978	+	10.7978i	−0.457518	+	0.457518i	−0.897840	−	0.440322i	$-0.854864\pi$
$557$	−10.7978	+	10.7978i	−0.457518	+	0.457518i	0.440322	+	0.897840i	$0.354864\pi$
$558$		0			0
$559$	−5.72268	−	4.15777i	−0.242044	−	0.175855i
$560$	9.87702	−	20.1600i	0.417380	−	0.851917i
$561$		0			0
$562$	−2.14440	+	1.07149i	−0.0904559	+	0.0451982i
$563$	−19.0254	+	3.01333i	−0.801826	+	0.126997i	−0.543881	−	0.839163i	$-0.683046\pi$
$563$	−19.0254	+	3.01333i	−0.801826	+	0.126997i	−0.257946	+	0.966159i	$0.583046\pi$
$564$		0			0
$565$	18.6227	+	2.05644i	0.783464	+	0.0865151i
$566$	0.952112	−	2.85383i	0.0400203	−	0.119955i
$567$		0			0
$568$	−4.71745	−	35.1225i	−0.197940	−	1.47371i
$569$	−15.7909	+	5.13076i	−0.661987	+	0.215093i	−0.620692	−	0.784054i	$-0.713148\pi$
$569$	−15.7909	+	5.13076i	−0.661987	+	0.215093i	−0.0412948	+	0.999147i	$0.513148\pi$
$570$		0			0
$571$	−18.7027	−	6.07687i	−0.782683	−	0.254309i	−0.109698	−	0.993965i	$-0.534988\pi$
$571$	−18.7027	−	6.07687i	−0.782683	−	0.254309i	−0.672985	+	0.739656i	$0.734988\pi$
$572$	4.21131	−	7.95375i	0.176084	−	0.332563i
$573$		0			0
$574$	−39.7789	+	12.5804i	−1.66034	+	0.525095i
$575$	−25.4898	+	30.8088i	−1.06300	+	1.28481i
$576$		0			0
$577$	1.60647	−	10.1429i	0.0668783	−	0.422253i	−0.931420	−	0.363945i	$-0.881430\pi$
$577$	1.60647	−	10.1429i	0.0668783	−	0.422253i	0.998299	−	0.0583078i	$-0.0185705\pi$
$578$	−3.95728	+	3.89559i	−0.164601	+	0.162035i
$579$		0			0
$580$	0.809370	−	2.78559i	0.0336072	−	0.115665i
$581$	−2.72926	−	8.39979i	−0.113229	−	0.348482i
$582$		0			0
$583$	−5.33794	−	2.71982i	−0.221075	−	0.112643i
$584$	−6.87125	−	22.9761i	−0.284334	−	0.950759i
$585$		0			0
$586$	−14.8676	+	20.1290i	−0.614174	+	0.831523i
$587$	−0.441412	−	2.78696i	−0.0182190	−	0.115030i	0.976903	−	0.213684i	$-0.0685463\pi$
$587$	−0.441412	−	2.78696i	−0.0182190	−	0.115030i	−0.995122	+	0.0986539i	$0.968546\pi$
$588$		0			0
$589$	11.6876	+	16.0866i	0.481579	+	0.662837i
$590$	−16.9732	−	15.6907i	−0.698775	−	0.645974i
$591$		0			0
$592$	12.2835	−	11.5349i	0.504849	−	0.474081i
$593$	25.1359	+	25.1359i	1.03221	+	1.03221i	0.999464	+	0.0327451i	$0.0104249\pi$
$593$	25.1359	+	25.1359i	1.03221	+	1.03221i	0.0327451	+	0.999464i	$0.489575\pi$
$594$		0			0
$595$	20.2703	−	0.955414i	0.831003	−	0.0391682i
$596$	−3.94199	−	12.8137i	−0.161470	−	0.524870i
$597$		0			0
$598$	7.63803	+	50.8043i	0.312342	+	2.07754i
$599$	37.4833			1.53153			0.765763	−	0.643123i	$-0.222362\pi$
$599$	37.4833			1.53153			0.765763	+	0.643123i	$0.222362\pi$
$600$		0			0
$601$	6.04452			0.246561			0.123280	−	0.992372i	$-0.460659\pi$
$601$	6.04452			0.246561			0.123280	+	0.992372i	$0.460659\pi$
$602$	−0.821771	−	5.46600i	−0.0334929	−	0.222778i
$603$		0			0
$604$	−2.15763	−	7.01355i	−0.0877929	−	0.285377i
$605$	−18.7238	−	12.2999i	−0.761230	−	0.500062i
$606$		0			0
$607$	15.4953	+	15.4953i	0.628933	+	0.628933i	0.947800	−	0.318866i	$-0.103302\pi$
$607$	15.4953	+	15.4953i	0.628933	+	0.628933i	−0.318866	+	0.947800i	$0.603302\pi$
$608$	8.15013	−	14.5529i	0.330531	−	0.590200i
$609$		0			0
$610$	−3.41689	+	1.91343i	−0.138346	+	0.0774727i
$611$	25.2910	+	34.8101i	1.02317	+	1.40827i
$612$		0			0
$613$	−1.58245	−	9.99119i	−0.0639145	−	0.403540i	−0.998817	−	0.0486348i	$-0.984513\pi$
$613$	−1.58245	−	9.99119i	−0.0639145	−	0.403540i	0.934902	−	0.354906i	$-0.115487\pi$
$614$	−22.4840	+	30.4408i	−0.907379	+	1.22849i
$615$		0			0
$616$	6.73776	−	2.01500i	0.271472	−	0.0811866i
$617$	−4.47285	−	2.27903i	−0.180070	−	0.0917504i	0.361632	−	0.932321i	$-0.382220\pi$
$617$	−4.47285	−	2.27903i	−0.180070	−	0.0917504i	−0.541702	+	0.840571i	$0.682220\pi$
$618$		0			0
$619$	6.25004	+	19.2356i	0.251210	+	0.773146i	0.994553	+	0.104235i	$0.0332393\pi$
$619$	6.25004	+	19.2356i	0.251210	+	0.773146i	−0.743342	+	0.668911i	$0.766761\pi$
$620$	10.2150	+	28.3758i	0.410246	+	1.13960i
$621$		0			0
$622$	−2.32812	+	2.29183i	−0.0933492	+	0.0918941i
$623$	2.20010	−	13.8909i	0.0881452	−	0.556527i
$624$		0			0
$625$	12.0416	+	21.9089i	0.481666	+	0.876355i
$626$	−8.81702	+	2.78845i	−0.352399	+	0.111449i
$627$		0			0
$628$	−16.4562	+	31.0801i	−0.656672	+	1.24023i
$629$	14.4862	+	4.70684i	0.577601	+	0.187674i
$630$		0			0
$631$	−29.5030	+	9.58611i	−1.17450	+	0.381617i	−0.830319	−	0.557288i	$-0.811842\pi$
$631$	−29.5030	+	9.58611i	−1.17450	+	0.381617i	−0.344177	+	0.938905i	$0.611842\pi$
$632$	25.2851	−	3.39614i	1.00579	−	0.135091i
$633$		0			0
$634$	8.92654	−	26.7561i	0.354518	−	1.06262i
$635$	−15.2825	+	33.8448i	−0.606469	+	1.34309i
$636$		0			0
$637$	−3.14159	+	0.497579i	−0.124474	+	0.0197148i
$638$	0.812882	−	0.406173i	0.0321823	−	0.0160805i
$639$		0			0
$640$	18.0291	−	17.7469i	0.712661	−	0.701509i
$641$	−7.01361	−	5.09569i	−0.277021	−	0.201267i	0.440596	−	0.897705i	$-0.354767\pi$
$641$	−7.01361	−	5.09569i	−0.277021	−	0.201267i	−0.717617	+	0.696438i	$0.754767\pi$
$642$		0			0
$643$	19.1482	−	19.1482i	0.755130	−	0.755130i	−0.220302	−	0.975432i	$-0.570704\pi$
$643$	19.1482	−	19.1482i	0.755130	−	0.755130i	0.975432	+	0.220302i	$0.0707043\pi$
$644$	−24.1041	+	32.1036i	−0.949836	+	1.26506i
$645$		0			0
$646$	15.0768	+	0.118430i	0.593190	+	0.00465956i
$647$	−40.2378	+	20.5022i	−1.58191	+	0.806023i	−0.999974	−	0.00721134i	$-0.997705\pi$
$647$	−40.2378	+	20.5022i	−1.58191	+	0.806023i	−0.581936	+	0.813235i	$0.697705\pi$
$648$		0			0
$649$		−	7.24095i		−	0.284232i
$650$	31.2905	+	7.25443i	1.22731	+	0.284542i
$651$		0			0
$652$	16.5348	−	8.10026i	0.647552	−	0.317231i
$653$	15.4764	−	7.88563i	0.605639	−	0.308588i	−0.124147	−	0.992264i	$-0.539620\pi$
$653$	15.4764	−	7.88563i	0.605639	−	0.308588i	0.729786	+	0.683675i	$0.239620\pi$
$654$		0			0
$655$	−1.59204	−	33.7772i	−0.0622063	−	1.31979i
$656$	−46.9917	−	1.47695i	−1.83472	−	0.0576653i
$657$		0			0
$658$	−5.52039	+	33.1662i	−0.215207	+	1.29295i
$659$	6.41486	+	4.66067i	0.249888	+	0.181554i	0.705677	−	0.708534i	$-0.250643\pi$
$659$	6.41486	+	4.66067i	0.249888	+	0.181554i	−0.455789	+	0.890088i	$0.650643\pi$
$660$		0			0
$661$	37.5286	−	27.2661i	1.45969	−	1.06053i	0.476248	−	0.879311i	$-0.341996\pi$
$661$	37.5286	−	27.2661i	1.45969	−	1.06053i	0.983443	−	0.181217i	$-0.0580037\pi$
$662$	19.6126	+	39.2511i	0.762266	+	1.52554i
$663$		0			0
$664$	0.234513	−	9.95002i	0.00910089	−	0.386136i
$665$	12.2396	+	11.1377i	0.474630	+	0.431902i
$666$		0			0
$667$	−2.35500	+	4.62194i	−0.0911858	+	0.178962i
$668$	5.85863	−	33.5681i	0.226677	−	1.29879i
$669$		0			0
$670$	10.3152	−	15.4369i	0.398510	−	0.596378i
$671$	−1.16675	−	0.379099i	−0.0450418	−	0.0146350i
$672$		0			0
$673$	21.4521	+	3.39769i	0.826919	+	0.130971i	0.555528	−	0.831498i	$-0.312516\pi$
$673$	21.4521	+	3.39769i	0.826919	+	0.130971i	0.271391	+	0.962469i	$0.412516\pi$
$674$	8.50530	+	26.8936i	0.327612	+	1.03590i
$675$		0			0
$676$	12.4922	−	8.77965i	0.480471	−	0.337679i
$677$	−0.733481	+	4.63102i	−0.0281900	+	0.177984i	−0.997766	−	0.0668060i	$-0.978719\pi$
$677$	−0.733481	+	4.63102i	−0.0281900	+	0.177984i	0.969576	+	0.244790i	$0.0787192\pi$
$678$		0			0
$679$	−6.55860	+	20.1853i	−0.251696	+	0.774640i
$680$	21.9089	+	6.55281i	0.840167	+	0.251289i
$681$		0			0
$682$	−4.35507	+	8.38385i	−0.166764	+	0.321034i
$683$	−26.7626	−	13.6362i	−1.02404	−	0.521775i	−0.140476	−	0.990084i	$-0.544863\pi$
$683$	−26.7626	−	13.6362i	−1.02404	−	0.521775i	−0.883565	+	0.468309i	$0.844863\pi$
$684$		0			0
$685$	2.00069	−	18.1178i	0.0764423	−	0.692246i
$686$	−21.9857	−	16.2389i	−0.839416	−	0.620004i
$687$		0			0
$688$	1.16719	−	6.11848i	0.0444986	−	0.233265i
$689$	−16.1472	−	22.2248i	−0.615161	−	0.846697i
$690$		0			0
$691$	3.45831	−	4.75996i	0.131560	−	0.181077i	−0.738155	−	0.674632i	$-0.764303\pi$
$691$	3.45831	−	4.75996i	0.131560	−	0.181077i	0.869715	+	0.493554i	$0.164303\pi$
$692$	−29.6563	+	4.22066i	−1.12736	+	0.160445i
$693$		0			0
$694$	2.99515	+	4.19131i	0.113694	+	0.159100i
$695$	1.67796	+	4.44093i	0.0636487	+	0.168454i
$696$		0			0
$697$	−19.2938	−	37.8662i	−0.730804	−	1.43428i
$698$	34.2386	−	5.14752i	1.29595	−	0.194836i
$699$		0			0
$700$	13.1133	+	21.4014i	0.495635	+	0.808897i
$701$	32.3819			1.22305			0.611524	−	0.791226i	$-0.290557\pi$
$701$	32.3819			1.22305			0.611524	+	0.791226i	$0.290557\pi$
$702$		0			0
$703$	5.63913	+	11.0674i	0.212684	+	0.417415i
$704$	7.91620	+	0.373364i	0.298353	+	0.0140717i
$705$		0			0
$706$	13.6058	+	19.0395i	0.512062	+	0.716563i
$707$	11.0384	+	11.0384i	0.415142	+	0.415142i
$708$		0			0
$709$	16.8589	−	23.2043i	0.633149	−	0.871454i	−0.365078	−	0.930977i	$-0.618958\pi$
$709$	16.8589	−	23.2043i	0.633149	−	0.871454i	0.998227	+	0.0595224i	$0.0189578\pi$
$710$	35.9809	+	16.5886i	1.35034	+	0.622558i
$711$		0			0
$712$	7.52587	−	13.9478i	0.282044	−	0.522716i
$713$	−8.43662	−	53.2667i	−0.315954	−	1.99485i
$714$		0			0
$715$	4.98515	+	8.74042i	0.186434	+	0.326873i
$716$	−0.0289364	+	1.84177i	−0.00108140	+	0.0688303i
$717$		0			0
$718$	−4.85667	+	9.34947i	−0.181249	+	0.348919i
$719$	−3.24857	−	9.99806i	−0.121151	−	0.372865i	0.872029	−	0.489454i	$-0.162804\pi$
$719$	−3.24857	−	9.99806i	−0.121151	−	0.372865i	−0.993180	+	0.116589i	$0.962804\pi$
$720$		0			0
$721$	−11.7588	+	36.1898i	−0.437920	+	1.34778i
$722$	−10.2246	−	10.3865i	−0.380520	−	0.386545i
$723$		0			0
$724$	13.2138	+	18.8014i	0.491087	+	0.698749i
$725$	2.14463	+	2.43285i	0.0796496	+	0.0903539i
$726$		0			0
$727$	19.0292	+	3.01393i	0.705755	+	0.111781i	0.498987	−	0.866609i	$-0.333706\pi$
$727$	19.0292	+	3.01393i	0.705755	+	0.111781i	0.206768	+	0.978390i	$0.433706\pi$
$728$	31.7234	+	5.79381i	1.17575	+	0.214733i
$729$		0			0
$730$	25.8054	+	7.27860i	0.955100	+	0.269393i
$731$	5.35484	−	1.73989i	0.198056	−	0.0643523i
$732$		0			0
$733$	−16.7661	+	32.9054i	−0.619271	+	1.21539i	0.341979	+	0.939708i	$0.388903\pi$
$733$	−16.7661	+	32.9054i	−0.619271	+	1.21539i	−0.961250	+	0.275680i	$0.911097\pi$
$734$	36.4571	+	12.1631i	1.34566	+	0.448946i
$735$		0			0
$736$	−37.6153	+	25.1335i	−1.38652	+	0.926434i
$737$	5.74446	−	0.909833i	0.211600	−	0.0335141i
$738$		0			0
$739$	−0.146989	+	0.106794i	−0.00540707	+	0.00392846i	−0.590486	−	0.807048i	$-0.701064\pi$
$739$	−0.146989	+	0.106794i	−0.00540707	+	0.00392846i	0.585078	+	0.810977i	$0.301064\pi$
$740$	3.52965	+	18.5058i	0.129752	+	0.680286i
$741$		0			0
$742$	3.52454	−	21.1752i	0.129390	−	0.777366i
$743$	14.3370	−	14.3370i	0.525973	−	0.525973i	−0.393396	−	0.919369i	$-0.628700\pi$
$743$	14.3370	−	14.3370i	0.525973	−	0.525973i	0.919369	+	0.393396i	$0.128700\pi$
$744$		0			0
$745$	14.4574	+	3.95550i	0.529679	+	0.144918i
$746$	0.0118080	−	1.50323i	0.000432322	−	0.0550372i
$747$		0			0
$748$	3.15156	+	6.43316i	0.115232	+	0.235220i
$749$			43.0833i			1.57423i
$750$		0			0
$751$		−	12.5620i		−	0.458394i	−0.973380	−	0.229197i	$-0.926390\pi$
$751$		−	12.5620i		−	0.458394i	0.973380	−	0.229197i	$-0.0736101\pi$
$752$	−18.2532	+	33.2022i	−0.665626	+	1.21076i
$753$		0			0
$754$	4.16677	+	0.0327303i	0.151745	+	0.00119197i
$755$	7.91323	+	2.16503i	0.287992	+	0.0787934i
$756$		0			0
$757$	−30.6304	+	30.6304i	−1.11328	+	1.11328i	−0.120579	+	0.992704i	$0.538475\pi$
$757$	−30.6304	+	30.6304i	−1.11328	+	1.11328i	−0.992704	+	0.120579i	$0.961525\pi$
$758$	−26.6974	−	4.44369i	−0.969693	−	0.161402i
$759$		0			0
$760$	8.85489	+	16.4121i	0.321201	+	0.595329i
$761$	26.3840	−	19.1691i	0.956420	−	0.694880i	0.00410353	−	0.999992i	$-0.498694\pi$
$761$	26.3840	−	19.1691i	0.956420	−	0.694880i	0.952317	+	0.305112i	$0.0986938\pi$
$762$		0			0
$763$	41.2364	−	6.53120i	1.49286	−	0.236445i
$764$	13.7180	−	40.0667i	0.496300	−	1.44956i
$765$		0			0
$766$	−9.20856	+	27.6014i	−0.332719	+	0.997280i
$767$	15.0740	−	29.5845i	0.544292	−	1.06823i
$768$		0			0
$769$	12.4755	−	4.05354i	0.449879	−	0.146175i	−0.0753100	−	0.997160i	$-0.523995\pi$
$769$	12.4755	−	4.05354i	0.449879	−	0.146175i	0.525189	+	0.850986i	$0.323995\pi$
$770$	−2.13445	+	7.56744i	−0.0769203	+	0.272712i
$771$		0			0
$772$	−26.1087	−	13.8239i	−0.939673	−	0.497533i
$773$	45.2454	+	7.16616i	1.62736	+	0.257749i	0.902355	−	0.430993i	$-0.141837\pi$
$773$	45.2454	+	7.16616i	1.62736	+	0.257749i	0.725007	+	0.688742i	$0.241837\pi$
$774$		0			0
$775$	−32.9057	−	7.35704i	−1.18201	−	0.264273i
$776$	−14.5102	+	19.0128i	−0.520886	+	0.682521i
$777$		0			0
$778$	13.3522	−	13.1441i	0.478700	−	0.471238i
$779$	10.7095	−	32.9606i	0.383709	−	1.18094i
$780$		0			0
$781$	3.83544	+	11.8043i	0.137243	+	0.422390i
$782$	−36.2893	−	18.8508i	−1.29770	−	0.674104i
$783$		0			0
$784$	−1.57431	−	2.31655i	−0.0562255	−	0.0827340i
$785$	−19.4800	−	34.1541i	−0.695272	−	1.21901i
$786$		0			0
$787$	1.69779	+	10.7194i	0.0605197	+	0.382107i	0.999294	+	0.0375734i	$0.0119628\pi$
$787$	1.69779	+	10.7194i	0.0605197	+	0.382107i	−0.938774	+	0.344533i	$0.888037\pi$
$788$	−29.9957	−	30.9533i	−1.06855	−	1.10266i
$789$		0			0
$790$	−11.9423	+	25.9030i	−0.424887	+	0.921589i
$791$	−12.3615	+	17.0142i	−0.439525	+	0.604954i
$792$		0			0
$793$	−3.97780	−	3.97780i	−0.141256	−	0.141256i
$794$	14.5904	−	10.4264i	0.517792	−	0.370019i
$795$		0			0
$796$	−20.6186	+	6.34306i	−0.730806	+	0.224824i
$797$	−13.5415	−	26.5768i	−0.479666	−	0.941397i	−0.996361	−	0.0852282i	$-0.972838\pi$
$797$	−13.5415	−	26.5768i	−0.479666	−	0.941397i	0.516696	−	0.856169i	$-0.327162\pi$
$798$		0			0
$799$	−34.2489			−1.21164
$800$	5.95152	+	27.6510i	0.210418	+	0.977612i
$801$		0			0
$802$	3.18418	+	21.1796i	0.112437	+	0.747876i
$803$	3.81319	+	7.48381i	0.134565	+	0.264098i
$804$		0			0
$805$	−15.8643	−	41.9867i	−0.559142	−	1.47984i
$806$	−35.2469	+	25.1877i	−1.24152	+	0.887200i
$807$		0			0
$808$	7.61484	+	15.8580i	0.267889	+	0.557882i
$809$	−4.38125	+	6.03028i	−0.154037	+	0.212013i	−0.879060	−	0.476711i	$-0.841829\pi$
$809$	−4.38125	+	6.03028i	−0.154037	+	0.212013i	0.725023	+	0.688724i	$0.241829\pi$
$810$		0			0
$811$	−0.930193	−	1.28030i	−0.0326635	−	0.0449575i	0.792373	−	0.610037i	$-0.208845\pi$
$811$	−0.930193	−	1.28030i	−0.0326635	−	0.0449575i	−0.825036	+	0.565080i	$0.808845\pi$
$812$	2.26594	+	2.33828i	0.0795188	+	0.0820574i
$813$		0			0
$814$	−3.50632	+	4.74717i	−0.122896	+	0.166388i
$815$	−2.25946	+	20.4612i	−0.0791454	+	0.716725i
$816$		0			0
$817$	4.09110	+	2.08452i	0.143129	+	0.0729281i
$818$	32.6213	+	16.9455i	1.14058	+	0.592484i
$819$		0			0
$820$	29.5467	−	43.4741i	1.03181	−	1.51818i
$821$	−9.93549	+	30.5783i	−0.346751	+	1.06719i	0.613888	+	0.789393i	$0.289604\pi$
$821$	−9.93549	+	30.5783i	−0.346751	+	1.06719i	−0.960640	+	0.277798i	$0.910396\pi$
$822$		0			0
$823$	−4.78704	+	30.2242i	−0.166866	+	1.05355i	0.752053	+	0.659103i	$0.229064\pi$
$823$	−4.78704	+	30.2242i	−0.166866	+	1.05355i	−0.918919	+	0.394447i	$0.870936\pi$
$824$	−26.0151	+	34.0877i	−0.906277	+	1.18750i
$825$		0			0
$826$	24.7380	−	7.82357i	0.860745	−	0.272217i
$827$	−50.7210	−	8.03342i	−1.76374	−	0.279349i	−0.811425	−	0.584457i	$-0.801308\pi$
$827$	−50.7210	−	8.03342i	−1.76374	−	0.279349i	−0.952318	+	0.305107i	$0.901308\pi$
$828$		0			0
$829$	−25.8242	−	8.39079i	−0.896912	−	0.291424i	−0.175950	−	0.984399i	$-0.556300\pi$
$829$	−25.8242	−	8.39079i	−0.896912	−	0.291424i	−0.720962	+	0.692975i	$0.756300\pi$
$830$	9.25205	+	6.18237i	0.321144	+	0.214593i
$831$		0			0
$832$	31.5661	+	18.0052i	1.09436	+	0.624218i
$833$	1.14941	−	2.25584i	0.0398247	−	0.0781604i
$834$		0			0
$835$	28.1775	+	25.6408i	0.975123	+	0.887338i
$836$	−1.89230	+	5.52691i	−0.0654464	+	0.191152i
$837$		0			0
$838$	−30.5171	+	15.2485i	−1.05420	+	0.526751i
$839$	12.9256	−	9.39100i	0.446241	−	0.324213i	−0.341869	−	0.939748i	$-0.611060\pi$
$839$	12.9256	−	9.39100i	0.446241	−	0.324213i	0.788110	+	0.615535i	$0.211060\pi$
$840$		0			0
$841$	−23.1211	−	16.7985i	−0.797280	−	0.579258i
$842$	24.4183	+	4.06434i	0.841509	+	0.140066i
$843$		0			0
$844$	−36.1425	−	27.1367i	−1.24408	−	0.934083i
$845$	0.803731	+	17.0522i	0.0276492	+	0.586613i
$846$		0			0
$847$	22.4054	−	11.4161i	0.769860	−	0.392263i
$848$	11.6539	−	21.1982i	0.400197	−	0.727949i
$849$		0			0
$850$	−19.3112	+	16.7556i	−0.662367	+	0.574714i
$851$		−	33.6895i		−	1.15486i
$852$		0			0
$853$	45.1378	−	22.9989i	1.54549	−	0.787466i	0.546732	−	0.837308i	$-0.315872\pi$
$853$	45.1378	−	22.9989i	1.54549	−	0.787466i	0.998757	+	0.0498414i	$0.0158716\pi$
$854$	0.0345285	−	4.39568i	0.00118154	−	0.150417i
$855$		0			0
$856$	−16.0867	+	45.8077i	−0.549831	+	1.56567i
$857$	33.6931	−	33.6931i	1.15093	−	1.15093i	0.164569	−	0.986366i	$-0.447377\pi$
$857$	33.6931	−	33.6931i	1.15093	−	1.15093i	0.986366	−	0.164569i	$-0.0526232\pi$
$858$		0			0
$859$	28.7062	+	20.8562i	0.979441	+	0.711606i	0.957584	−	0.288155i	$-0.0930420\pi$
$859$	28.7062	+	20.8562i	0.979441	+	0.711606i	0.0218576	+	0.999761i	$0.493042\pi$
$860$	5.07643	+	4.76734i	0.173105	+	0.162565i
$861$		0			0
$862$	−22.9983	−	46.0269i	−0.783325	−	1.56768i
$863$	31.6541	−	5.01352i	1.07752	−	0.170662i	0.407647	−	0.913140i	$-0.366349\pi$
$863$	31.6541	−	5.01352i	1.07752	−	0.170662i	0.669871	+	0.742477i	$0.266349\pi$
$864$		0			0
$865$	13.7827	−	30.5233i	0.468627	−	1.03782i
$866$	48.0973	+	16.0465i	1.63441	+	0.545283i
$867$		0			0
$868$	−33.3481	−	5.82023i	−1.13191	−	0.197552i
$869$	−8.49801	+	2.76117i	−0.288275	+	0.0936663i
$870$		0			0
$871$	25.3643	+	8.24136i	0.859437	+	0.279248i
$872$	46.2826	+	8.45284i	1.56733	+	0.286249i
$873$		0			0
$874$	−10.0557	−	31.7959i	−0.340138	−	1.07551i
$875$	−28.0584	−	0.442893i	−0.948549	−	0.0149725i
$876$		0			0
$877$	3.21039	−	20.2696i	0.108407	−	0.684457i	−0.872299	−	0.488972i	$-0.837372\pi$
$877$	3.21039	−	20.2696i	0.108407	−	0.684457i	0.980707	−	0.195485i	$-0.0626280\pi$
$878$	16.0353	+	16.2892i	0.541166	+	0.549735i
$879$		0			0
$880$	−5.09500	+	7.24900i	−0.171752	+	0.244364i
$881$	10.4735	+	32.2341i	0.352861	+	1.08599i	0.957239	+	0.289297i	$0.0934214\pi$
$881$	10.4735	+	32.2341i	0.352861	+	1.08599i	−0.604379	+	0.796697i	$0.706579\pi$
$882$		0			0
$883$	−18.4629	−	9.40734i	−0.621327	−	0.316582i	0.114838	−	0.993384i	$-0.463365\pi$
$883$	−18.4629	−	9.40734i	−0.621327	−	0.316582i	−0.736165	+	0.676802i	$0.763365\pi$
$884$	−0.516031	+	32.8449i	−0.0173560	+	1.10469i
$885$		0			0
$886$	−5.09795	−	3.76541i	−0.171269	−	0.126502i
$887$	−4.49497	−	28.3801i	−0.150926	−	0.952911i	−0.940633	−	0.339426i	$-0.889767\pi$
$887$	−4.49497	−	28.3801i	−0.150926	−	0.952911i	0.789706	−	0.613485i	$-0.210233\pi$
$888$		0			0
$889$	−24.5009	−	33.7227i	−0.821735	−	1.13102i
$890$	8.65764	+	15.4603i	0.290205	+	0.518229i
$891$		0			0
$892$	−0.0960675	−	0.675014i	−0.00321658	−	0.0226012i
$893$	−19.7492	−	19.7492i	−0.660882	−	0.660882i
$894$		0			0
$895$	−1.72125	−	1.13071i	−0.0575351	−	0.0377955i
$896$	7.27759	+	27.4483i	0.243127	+	0.916983i
$897$		0			0
$898$	44.7808	−	6.73245i	1.49436	−	0.224665i
$899$	−4.37416			−0.145886
$900$		0			0
$901$	21.8665			0.728478
$902$	16.2834	−	2.44809i	0.542179	−	0.0815125i
$903$		0			0
$904$	−19.4960	+	13.4744i	−0.648428	+	0.448153i
$905$	−25.6644	+	1.20965i	−0.853112	+	0.0402103i
$906$		0			0
$907$	−1.04173	−	1.04173i	−0.0345900	−	0.0345900i	0.689600	−	0.724190i	$-0.257786\pi$
$907$	−1.04173	−	1.04173i	−0.0345900	−	0.0345900i	−0.724190	+	0.689600i	$0.757786\pi$
$908$	−30.0514	+	4.27689i	−0.997291	+	0.141934i
$909$		0			0
$910$	−24.4745	+	26.4750i	−0.811321	+	0.877637i
$911$	−1.07000	−	1.47273i	−0.0354508	−	0.0487938i	0.790924	−	0.611915i	$-0.209600\pi$
$911$	−1.07000	−	1.47273i	−0.0354508	−	0.0487938i	−0.826374	+	0.563121i	$0.809600\pi$
$912$		0			0
$913$	0.545307	+	3.44293i	0.0180470	+	0.113944i
$914$	−26.0470	−	19.2386i	−0.861557	−	0.636357i
$915$		0			0
$916$	−37.4722	−	0.588731i	−1.23812	−	0.0194522i
$917$	33.8193	+	17.2318i	1.11681	+	0.569044i
$918$		0			0
$919$	−11.4266	−	35.1676i	−0.376930	−	1.16007i	−0.942167	−	0.335144i	$-0.891215\pi$
$919$	−11.4266	−	35.1676i	−0.376930	−	1.16007i	0.565237	−	0.824929i	$-0.308785\pi$
$920$	−1.19022	−	50.5652i	−0.0392404	−	1.66709i
$921$		0			0
$922$	−12.2283	−	12.4219i	−0.402718	−	0.409095i
$923$	−8.90332	+	56.2134i	−0.293056	+	1.85029i
$924$		0			0
$925$	−19.5836	−	7.75482i	−0.643903	−	0.254977i
$926$	13.8708	+	43.8593i	0.455824	+	1.44131i
$927$		0			0
$928$	1.53615	+	3.33220i	0.0504265	+	0.109385i
$929$	36.8445	+	11.9715i	1.20883	+	0.392772i	0.843002	−	0.537911i	$-0.180786\pi$
$929$	36.8445	+	11.9715i	1.20883	+	0.392772i	0.365827	+	0.930683i	$0.380786\pi$
$930$		0			0
$931$	1.96360	−	0.638012i	0.0643544	−	0.0209100i
$932$	6.65641	−	38.1391i	0.218038	−	1.24929i
$933$		0			0
$934$	2.22368	+	0.741878i	0.0727610	+	0.0242750i
$935$	−7.96081	−	0.879084i	−0.260346	−	0.0287491i
$936$		0			0
$937$	14.1890	−	2.24732i	0.463536	−	0.0734168i	0.0797013	−	0.996819i	$-0.474603\pi$
$937$	14.1890	−	2.24732i	0.463536	−	0.0734168i	0.383834	+	0.923402i	$0.374603\pi$
$938$	9.31503	+	18.6423i	0.304146	+	0.608694i
$939$		0			0
$940$	−20.4066	−	37.1218i	−0.665589	−	1.21078i
$941$	−28.0766	−	20.3988i	−0.915270	−	0.664982i	0.0270725	−	0.999633i	$-0.491382\pi$
$941$	−28.0766	−	20.3988i	−0.915270	−	0.664982i	−0.942342	+	0.334651i	$0.891382\pi$
$942$		0			0
$943$	−66.4665	+	66.4665i	−2.16445	+	2.16445i
$944$	29.2235	+	0.918497i	0.951144	+	0.0298945i
$945$		0			0
$946$	−0.0171359	+	2.18150i	−0.000557137	+	0.0709268i
$947$	−2.50903	+	1.27841i	−0.0815325	+	0.0415429i	−0.494281	−	0.869302i	$-0.664569\pi$
$947$	−2.50903	+	1.27841i	−0.0815325	+	0.0415429i	0.412749	+	0.910845i	$0.364569\pi$
$948$		0			0
$949$			38.5149i			1.25025i
$950$	−20.7975	−	1.47361i	−0.674760	−	0.0478103i
$951$		0			0
$952$	−18.5731	+	17.7178i	−0.601958	+	0.574236i
$953$	25.2286	−	12.8546i	0.817234	−	0.416401i	0.00518178	−	0.999987i	$-0.498351\pi$
$953$	25.2286	−	12.8546i	0.817234	−	0.416401i	0.812052	+	0.583585i	$0.198351\pi$
$954$		0			0
$955$	29.6036	+	36.9532i	0.957948	+	1.19578i
$956$	−0.963240	+	1.28291i	−0.0311534	+	0.0414923i
$957$		0			0
$958$	−1.87960	−	0.312852i	−0.0607270	−	0.0101078i
$959$	16.5529	+	12.0264i	0.534520	+	0.388351i
$960$		0			0
$961$	11.7117	−	8.50908i	0.377798	−	0.274486i
$962$	−24.2083	+	12.0962i	−0.780508	+	0.389997i
$963$		0			0
$964$	24.0164	+	8.22271i	0.773517	+	0.264836i
$965$	28.6910	−	16.3641i	0.923596	−	0.526779i
$966$		0			0
$967$	11.2935	−	22.1648i	0.363175	−	0.712771i	−0.635041	−	0.772479i	$-0.719017\pi$
$967$	11.2935	−	22.1648i	0.363175	−	0.712771i	0.998216	+	0.0597073i	$0.0190167\pi$
$968$	28.0849	−	3.77219i	0.902682	−	0.121243i
$969$		0			0
$970$	−9.25461	−	25.0877i	−0.297148	−	0.805519i
$971$	−13.7509	−	4.46795i	−0.441289	−	0.143383i	0.0799415	−	0.996800i	$-0.474527\pi$
$971$	−13.7509	−	4.46795i	−0.441289	−	0.143383i	−0.521230	+	0.853416i	$0.674527\pi$
$972$		0			0
$973$	−5.26320	−	0.833609i	−0.168730	−	0.0267243i
$974$	44.6622	−	14.1248i	1.43107	−	0.452587i
$975$		0			0
$976$	1.67799	−	4.66075i	0.0537112	−	0.149187i
$977$	−0.0404109	+	0.255144i	−0.00129286	+	0.00816278i	−0.988326	−	0.152352i	$-0.951315\pi$
$977$	−0.0404109	+	0.255144i	−0.00129286	+	0.00816278i	0.987033	+	0.160515i	$0.0513153\pi$
$978$		0			0
$979$	−1.71529	+	5.27913i	−0.0548211	+	0.168722i
$980$	3.12993	−	0.0982772i	0.0999819	−	0.00313935i
$981$		0			0
$982$	−3.84812	−	1.99894i	−0.122799	−	0.0637889i
$983$	−10.9161	−	5.56205i	−0.348171	−	0.177402i	0.271156	−	0.962536i	$-0.412594\pi$
$983$	−10.9161	−	5.56205i	−0.348171	−	0.177402i	−0.619326	+	0.785134i	$0.712594\pi$
$984$		0			0
$985$	47.1893	−	9.77120i	1.50358	−	0.311336i
$986$	−1.97055	+	2.66790i	−0.0627550	+	0.0849633i
$987$		0			0
$988$	−19.2372	+	18.6420i	−0.612016	+	0.593083i
$989$	−7.31992	−	10.0750i	−0.232760	−	0.320367i
$990$		0			0
$991$	−9.47852	+	13.0461i	−0.301095	+	0.414422i	−0.932578	−	0.360968i	$-0.882447\pi$
$991$	−9.47852	+	13.0461i	−0.301095	+	0.414422i	0.631483	+	0.775390i	$0.282447\pi$
$992$	−33.2836	−	18.6399i	−1.05676	−	0.591819i
$993$		0			0
$994$	−36.1840	+	25.8574i	−1.14769	+	0.820148i
$995$	6.36479	−	23.2635i	0.201778	−	0.737502i
$996$		0			0
$997$	15.2660	+	29.9612i	0.483479	+	0.948881i	0.995927	+	0.0901629i	$0.0287388\pi$
$997$	15.2660	+	29.9612i	0.483479	+	0.948881i	−0.512448	+	0.858718i	$0.671261\pi$
$998$	8.03810	+	53.4653i	0.254442	+	1.69242i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	900.2.bj.f.523.13		240
3.2	odd	2		300.2.w.a.223.18	yes	240
4.3	odd	2	inner	900.2.bj.f.523.20		240
12.11	even	2		300.2.w.a.223.11	yes	240
25.12	odd	20	inner	900.2.bj.f.487.20		240
75.62	even	20		300.2.w.a.187.11	✓	240
100.87	even	20	inner	900.2.bj.f.487.13		240
300.287	odd	20		300.2.w.a.187.18	yes	240

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
300.2.w.a.187.11	✓	240	75.62	even	20
300.2.w.a.187.18	yes	240	300.287	odd	20
300.2.w.a.223.11	yes	240	12.11	even	2
300.2.w.a.223.18	yes	240	3.2	odd	2
900.2.bj.f.487.13		240	100.87	even	20	inner
900.2.bj.f.487.20		240	25.12	odd	20	inner
900.2.bj.f.523.13		240	1.1	even	1	trivial
900.2.bj.f.523.20		240	4.3	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	900.bj (of order \(20\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.210253 - 1.39850i) q^{2} +(-1.91159 + 0.588077i) q^{4} +(0.590092 - 2.15680i) q^{5} +(1.77479 + 1.77479i) q^{7} +(1.22434 + 2.54970i) q^{8} +O(q^{10})\)	\(q+(-0.210253 - 1.39850i) q^{2} +(-1.91159 + 0.588077i) q^{4} +(0.590092 - 2.15680i) q^{5} +(1.77479 + 1.77479i) q^{7} +(1.22434 + 2.54970i) q^{8} +(-3.14035 - 0.371768i) q^{10} +(-0.582275 - 0.801432i) q^{11} +(-0.710606 - 4.48659i) q^{13} +(2.10889 - 2.85520i) q^{14} +(3.30833 - 2.24832i) q^{16} +(3.22163 + 1.64150i) q^{17} +(0.911162 + 2.80427i) q^{19} +(0.140352 + 4.46993i) q^{20} +(-0.998375 + 0.982813i) q^{22} +(1.25105 - 7.89882i) q^{23} +(-4.30358 - 2.54542i) q^{25} +(-6.12507 + 1.93710i) q^{26} +(-4.43639 - 2.34896i) q^{28} +(-0.616890 - 0.200440i) q^{29} +(6.41357 - 2.08390i) q^{31} +(-3.83986 - 4.15397i) q^{32} +(1.61828 - 4.85057i) q^{34} +(4.87517 - 2.78058i) q^{35} +(4.16075 - 0.658998i) q^{37} +(3.73019 - 1.86386i) q^{38} +(6.22168 - 1.13610i) q^{40} +(-9.50896 - 6.90867i) q^{41} +(1.10111 - 1.10111i) q^{43} +(1.58437 + 1.18959i) q^{44} +(-11.3095 - 0.0888373i) q^{46} +(-8.43980 + 4.30030i) q^{47} -0.700218i q^{49} +(-2.65492 + 6.55373i) q^{50} +(3.99684 + 8.15861i) q^{52} +(5.38846 - 2.74556i) q^{53} +(-2.07213 + 0.782931i) q^{55} +(-2.35224 + 6.69815i) q^{56} +(-0.150611 + 0.904861i) q^{58} +(5.91350 + 4.29641i) q^{59} +(1.00189 - 0.727914i) q^{61} +(-4.26280 - 8.53121i) q^{62} +(-5.00198 + 6.24341i) q^{64} +(-10.0960 - 1.11487i) q^{65} +(-2.66543 + 5.23120i) q^{67} +(-7.12376 - 1.24331i) q^{68} +(-4.91366 - 6.23328i) q^{70} +(-11.9160 - 3.87174i) q^{71} +(-8.37438 - 1.32637i) q^{73} +(-1.79642 - 5.68024i) q^{74} +(-3.39089 - 4.82477i) q^{76} +(0.388959 - 2.45579i) q^{77} +(2.78730 - 8.57843i) q^{79} +(-2.89696 - 8.46213i) q^{80} +(-7.66246 + 14.7508i) q^{82} +(-3.13531 - 1.59752i) q^{83} +(5.44146 - 5.97978i) q^{85} +(-1.77141 - 1.30839i) q^{86} +(1.33051 - 2.46585i) q^{88} +(-3.29356 - 4.53320i) q^{89} +(6.70159 - 9.22394i) q^{91} +(2.25362 + 15.8350i) q^{92} +(7.78845 + 10.8989i) q^{94} +(6.58592 - 0.310418i) q^{95} +(3.83895 + 7.53437i) q^{97} +(-0.979253 + 0.147223i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 240 q - 12 q^{8}+O(q^{10}) \) 240 * q - 12 * q^8	\( 240 q - 12 q^{8} + 8 q^{10} + 4 q^{13} - 20 q^{17} + 20 q^{20} - 12 q^{22} + 20 q^{25} + 4 q^{28} + 20 q^{32} - 4 q^{37} + 76 q^{38} - 92 q^{40} + 140 q^{44} + 164 q^{50} - 172 q^{52} + 4 q^{53} - 120 q^{58} + 44 q^{62} - 60 q^{64} + 20 q^{65} - 16 q^{68} - 44 q^{70} - 44 q^{73} + 48 q^{77} + 4 q^{80} + 24 q^{82} - 64 q^{85} + 60 q^{88} + 260 q^{89} - 144 q^{92} + 40 q^{94} - 180 q^{97} - 256 q^{98}+O(q^{100}) \) 240 * q - 12 * q^8 + 8 * q^10 + 4 * q^13 - 20 * q^17 + 20 * q^20 - 12 * q^22 + 20 * q^25 + 4 * q^28 + 20 * q^32 - 4 * q^37 + 76 * q^38 - 92 * q^40 + 140 * q^44 + 164 * q^50 - 172 * q^52 + 4 * q^53 - 120 * q^58 + 44 * q^62 - 60 * q^64 + 20 * q^65 - 16 * q^68 - 44 * q^70 - 44 * q^73 + 48 * q^77 + 4 * q^80 + 24 * q^82 - 64 * q^85 + 60 * q^88 + 260 * q^89 - 144 * q^92 + 40 * q^94 - 180 * q^97 - 256 * q^98

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