LMFDB - Embedded newform 525.2.j.b.218.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(218,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 0]))

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

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

chi := DirichletCharacter("525.218");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.j (of order $4$, degree $2$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 105)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			218.9
Character	$\chi$	$=$	525.218
Dual form			525.2.j.b.407.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.800553 + 0.800553i) q^{2} +(1.34285 + 1.09397i) q^{3} -0.718229i q^{4} +(0.199242 + 1.95080i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.17609 - 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} +O(q^{10})$	\(q+(0.800553 + 0.800553i) q^{2} +(1.34285 + 1.09397i) q^{3} -0.718229i q^{4} +(0.199242 + 1.95080i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.17609 - 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} -5.20191i q^{11} +(0.785718 - 0.964471i) q^{12} +(3.24693 + 3.24693i) q^{13} +1.13215 q^{14} +2.04769 q^{16} +(0.844232 + 0.844232i) q^{17} +(-1.86656 + 2.83759i) q^{18} +1.32025i q^{19} +(1.72309 - 0.175985i) q^{21} +(4.16440 - 4.16440i) q^{22} +(-5.62910 + 5.62910i) q^{23} +(5.30272 - 0.541586i) q^{24} +5.19868i q^{26} +(-2.39973 + 4.60883i) q^{27} +(-0.507864 - 0.507864i) q^{28} -4.38282 q^{29} -1.70499 q^{31} +(-2.71289 - 2.71289i) q^{32} +(5.69071 - 6.98536i) q^{33} +1.35170i q^{34} +(2.11020 - 0.435588i) q^{36} +(1.71171 - 1.71171i) q^{37} +(-1.05693 + 1.05693i) q^{38} +(0.808099 + 7.91217i) q^{39} -1.82176i q^{41} +(1.52031 + 1.23854i) q^{42} +(0.281771 + 0.281771i) q^{43} -3.73616 q^{44} -9.01279 q^{46} +(-3.39588 - 3.39588i) q^{47} +(2.74973 + 2.24010i) q^{48} -1.00000i q^{49} +(0.210113 + 2.05723i) q^{51} +(2.33204 - 2.33204i) q^{52} +(3.51059 - 3.51059i) q^{53} +(-5.61073 + 1.76850i) q^{54} -3.07745i q^{56} +(-1.44431 + 1.77289i) q^{57} +(-3.50868 - 3.50868i) q^{58} -1.81772 q^{59} -2.47514 q^{61} +(-1.36494 - 1.36494i) q^{62} +(2.50636 + 1.64868i) q^{63} -8.43900i q^{64} +(10.1479 - 1.03644i) q^{66} +(-7.92132 + 7.92132i) q^{67} +(0.606352 - 0.606352i) q^{68} +(-13.7171 + 1.40098i) q^{69} +9.06358i q^{71} +(7.71322 + 5.07373i) q^{72} +(1.33856 + 1.33856i) q^{73} +2.74064 q^{74} +0.948239 q^{76} +(-3.67830 - 3.67830i) q^{77} +(-5.68718 + 6.98104i) q^{78} -11.5015i q^{79} +(-8.26437 + 3.56372i) q^{81} +(1.45841 - 1.45841i) q^{82} +(-5.46196 + 5.46196i) q^{83} +(-0.126398 - 1.23757i) q^{84} +0.451146i q^{86} +(-5.88546 - 4.79466i) q^{87} +(-11.3198 - 11.3198i) q^{88} +9.43116 q^{89} +4.59186 q^{91} +(4.04298 + 4.04298i) q^{92} +(-2.28954 - 1.86520i) q^{93} -5.43717i q^{94} +(-0.675186 - 6.61080i) q^{96} +(3.06315 - 3.06315i) q^{97} +(0.800553 - 0.800553i) q^{98} +(15.2835 - 3.15483i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{3}+O(q^{10}) $ 24 * q + 4 * q^3	$ 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) $ 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	0.800553	+	0.800553i	0.566077	+	0.566077i	0.931027	−	0.364950i	$-0.118914\pi$
$2$	0.800553	+	0.800553i	0.566077	+	0.566077i	−0.364950	+	0.931027i	$0.618914\pi$
$3$	1.34285	+	1.09397i	0.775293	+	0.631602i
$3$	1.34285	+	1.09397i	0.775293	+	0.631602i
$4$		−	0.718229i		−	0.359114i
$5$		0			0
$5$		0			0
$6$	0.199242	+	1.95080i	0.0813403	+	0.796410i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$7$	0.707107	−	0.707107i	0.267261	−	0.267261i
$8$	2.17609	−	2.17609i	0.769363	−	0.769363i
$9$	0.606476	+	2.93806i	0.202159	+	0.979353i
$10$		0			0
$11$		−	5.20191i		−	1.56843i	−0.620487	−	0.784217i	$-0.713065\pi$
$11$		−	5.20191i		−	1.56843i	0.620487	−	0.784217i	$-0.286935\pi$
$12$	0.785718	−	0.964471i	0.226817	−	0.278419i
$13$	3.24693	+	3.24693i	0.900537	+	0.900537i	0.995482	−	0.0949456i	$-0.0302677\pi$
$13$	3.24693	+	3.24693i	0.900537	+	0.900537i	−0.0949456	+	0.995482i	$0.530268\pi$
$14$	1.13215			0.302581
$15$		0			0
$16$	2.04769			0.511922
$17$	0.844232	+	0.844232i	0.204756	+	0.204756i	0.802034	−	0.597278i	$-0.203751\pi$
$17$	0.844232	+	0.844232i	0.204756	+	0.204756i	−0.597278	+	0.802034i	$0.703751\pi$
$18$	−1.86656	+	2.83759i	−0.439951	+	0.668826i
$19$			1.32025i			0.302885i	0.988466	+	0.151443i	$0.0483919\pi$
$19$			1.32025i			0.302885i	−0.988466	+	0.151443i	$0.951608\pi$
$20$		0			0
$21$	1.72309	−	0.175985i	0.376008	−	0.0384031i
$22$	4.16440	−	4.16440i	0.887854	−	0.887854i
$23$	−5.62910	+	5.62910i	−1.17375	+	1.17375i	−0.192440	+	0.981309i	$0.561640\pi$
$23$	−5.62910	+	5.62910i	−1.17375	+	1.17375i	−0.981309	+	0.192440i	$0.938360\pi$
$24$	5.30272	−	0.541586i	1.08241	−	0.110551i
$25$		0			0
$26$			5.19868i			1.01955i
$27$	−2.39973	+	4.60883i	−0.461829	+	0.886969i
$28$	−0.507864	−	0.507864i	−0.0959774	−	0.0959774i
$29$	−4.38282			−0.813870			−0.406935	−	0.913457i	$-0.633402\pi$
$29$	−4.38282			−0.813870			−0.406935	+	0.913457i	$0.633402\pi$
$30$		0			0
$31$	−1.70499			−0.306225			−0.153113	−	0.988209i	$-0.548930\pi$
$31$	−1.70499			−0.306225			−0.153113	+	0.988209i	$0.548930\pi$
$32$	−2.71289	−	2.71289i	−0.479576	−	0.479576i
$33$	5.69071	−	6.98536i	0.990625	−	1.21600i
$34$			1.35170i			0.231815i
$35$		0			0
$36$	2.11020	−	0.435588i	0.351700	−	0.0725981i
$37$	1.71171	−	1.71171i	0.281404	−	0.281404i	−0.552265	−	0.833669i	$-0.686236\pi$
$37$	1.71171	−	1.71171i	0.281404	−	0.281404i	0.833669	+	0.552265i	$0.186236\pi$
$38$	−1.05693	+	1.05693i	−0.171456	+	0.171456i
$39$	0.808099	+	7.91217i	0.129399	+	1.26696i
$40$		0			0
$41$		−	1.82176i		−	0.284511i	−0.989830	−	0.142255i	$-0.954565\pi$
$41$		−	1.82176i		−	0.284511i	0.989830	−	0.142255i	$-0.0454354\pi$
$42$	1.52031	+	1.23854i	0.234589	+	0.191110i
$43$	0.281771	+	0.281771i	0.0429697	+	0.0429697i	0.728265	−	0.685295i	$-0.240327\pi$
$43$	0.281771	+	0.281771i	0.0429697	+	0.0429697i	−0.685295	+	0.728265i	$0.740327\pi$
$44$	−3.73616			−0.563247
$45$		0			0
$46$	−9.01279			−1.32886
$47$	−3.39588	−	3.39588i	−0.495340	−	0.495340i	0.414644	−	0.909984i	$-0.363906\pi$
$47$	−3.39588	−	3.39588i	−0.495340	−	0.495340i	−0.909984	+	0.414644i	$0.863906\pi$
$48$	2.74973	+	2.24010i	0.396890	+	0.323331i
$49$		−	1.00000i		−	0.142857i
$50$		0			0
$51$	0.210113	+	2.05723i	0.0294217	+	0.288071i
$52$	2.33204	−	2.33204i	0.323396	−	0.323396i
$53$	3.51059	−	3.51059i	0.482216	−	0.482216i	−0.423623	−	0.905839i	$-0.639242\pi$
$53$	3.51059	−	3.51059i	0.482216	−	0.482216i	0.905839	+	0.423623i	$0.139242\pi$
$54$	−5.61073	+	1.76850i	−0.763523	+	0.240662i
$55$		0			0
$56$		−	3.07745i		−	0.411242i
$57$	−1.44431	+	1.77289i	−0.191303	+	0.234825i
$58$	−3.50868	−	3.50868i	−0.460713	−	0.460713i
$59$	−1.81772			−0.236647			−0.118323	−	0.992975i	$-0.537752\pi$
$59$	−1.81772			−0.236647			−0.118323	+	0.992975i	$0.537752\pi$
$60$		0			0
$61$	−2.47514			−0.316909			−0.158455	−	0.987366i	$-0.550651\pi$
$61$	−2.47514			−0.316909			−0.158455	+	0.987366i	$0.550651\pi$
$62$	−1.36494	−	1.36494i	−0.173347	−	0.173347i
$63$	2.50636	+	1.64868i	0.315772	+	0.207714i
$64$		−	8.43900i		−	1.05488i
$65$		0			0
$66$	10.1479	−	1.03644i	1.24912	−	0.127577i
$67$	−7.92132	+	7.92132i	−0.967743	+	0.967743i	−0.999496	−	0.0317530i	$-0.989891\pi$
$67$	−7.92132	+	7.92132i	−0.967743	+	0.967743i	0.0317530	+	0.999496i	$0.489891\pi$
$68$	0.606352	−	0.606352i	0.0735309	−	0.0735309i
$69$	−13.7171	+	1.40098i	−1.65134	+	0.168658i
$70$		0			0
$71$			9.06358i			1.07565i	0.843057	+	0.537825i	$0.180754\pi$
$71$			9.06358i			1.07565i	−0.843057	+	0.537825i	$0.819246\pi$
$72$	7.71322	+	5.07373i	0.909011	+	0.597944i
$73$	1.33856	+	1.33856i	0.156666	+	0.156666i	0.781088	−	0.624422i	$-0.214665\pi$
$73$	1.33856	+	1.33856i	0.156666	+	0.156666i	−0.624422	+	0.781088i	$0.714665\pi$
$74$	2.74064			0.318592
$75$		0			0
$76$	0.948239			0.108771
$77$	−3.67830	−	3.67830i	−0.419182	−	0.419182i
$78$	−5.68718	+	6.98104i	−0.643947	+	0.790447i
$79$		−	11.5015i		−	1.29402i	−0.762481	−	0.647011i	$-0.776019\pi$
$79$		−	11.5015i		−	1.29402i	0.762481	−	0.647011i	$-0.223981\pi$
$80$		0			0
$81$	−8.26437	+	3.56372i	−0.918264	+	0.395969i
$82$	1.45841	−	1.45841i	0.161055	−	0.161055i
$83$	−5.46196	+	5.46196i	−0.599528	+	0.599528i	−0.940187	−	0.340659i	$-0.889350\pi$
$83$	−5.46196	+	5.46196i	−0.599528	+	0.599528i	0.340659	+	0.940187i	$0.389350\pi$
$84$	−0.126398	−	1.23757i	−0.0137911	−	0.135030i
$85$		0			0
$86$			0.451146i			0.0486483i
$87$	−5.88546	−	4.79466i	−0.630988	−	0.514041i
$88$	−11.3198	−	11.3198i	−1.20669	−	1.20669i
$89$	9.43116			0.999701			0.499850	−	0.866112i	$-0.333388\pi$
$89$	9.43116			0.999701			0.499850	+	0.866112i	$0.333388\pi$
$90$		0			0
$91$	4.59186			0.481357
$92$	4.04298	+	4.04298i	0.421510	+	0.421510i
$93$	−2.28954	−	1.86520i	−0.237414	−	0.193412i
$94$		−	5.43717i		−	0.560801i
$95$		0			0
$96$	−0.675186	−	6.61080i	−0.0689109	−	0.674712i
$97$	3.06315	−	3.06315i	0.311016	−	0.311016i	−0.534287	−	0.845303i	$-0.679420\pi$
$97$	3.06315	−	3.06315i	0.311016	−	0.311016i	0.845303	+	0.534287i	$0.179420\pi$
$98$	0.800553	−	0.800553i	0.0808681	−	0.0808681i
$99$	15.2835	−	3.15483i	1.53605	−	0.317072i
$100$		0			0
$101$		−	3.71640i		−	0.369796i	−0.982758	−	0.184898i	$-0.940805\pi$
$101$		−	3.71640i		−	0.369796i	0.982758	−	0.184898i	$-0.0591954\pi$
$102$	−1.47872	+	1.81513i	−0.146415	+	0.179725i
$103$	−1.18049	−	1.18049i	−0.116317	−	0.116317i	0.646553	−	0.762869i	$-0.276210\pi$
$103$	−1.18049	−	1.18049i	−0.116317	−	0.116317i	−0.762869	+	0.646553i	$0.776210\pi$
$104$	14.1312			1.38568
$105$		0			0
$106$	5.62082			0.545943
$107$	−1.38009	−	1.38009i	−0.133418	−	0.133418i	0.637244	−	0.770662i	$-0.280074\pi$
$107$	−1.38009	−	1.38009i	−0.133418	−	0.133418i	−0.770662	+	0.637244i	$0.780074\pi$
$108$	3.31019	+	1.72356i	0.318523	+	0.165849i
$109$			5.93506i			0.568475i	0.958754	+	0.284238i	$0.0917405\pi$
$109$			5.93506i			0.568475i	−0.958754	+	0.284238i	$0.908260\pi$
$110$		0			0
$111$	4.17113	−	0.426013i	0.395906	−	0.0404353i
$112$	1.44794	−	1.44794i	0.136817	−	0.136817i
$113$	0.240664	−	0.240664i	0.0226398	−	0.0226398i	−0.695696	−	0.718336i	$-0.744904\pi$
$113$	0.240664	−	0.240664i	0.0226398	−	0.0226398i	0.718336	+	0.695696i	$0.244904\pi$
$114$	−2.57554	+	0.263049i	−0.241221	+	0.0246368i
$115$		0			0
$116$			3.14787i			0.292272i
$117$	−7.57049	+	11.5089i	−0.699892	+	1.06399i
$118$	−1.45518	−	1.45518i	−0.133960	−	0.133960i
$119$	1.19392			0.109447
$120$		0			0
$121$	−16.0598			−1.45998
$122$	−1.98148	−	1.98148i	−0.179395	−	0.179395i
$123$	1.99294	−	2.44634i	0.179697	−	0.220579i
$124$			1.22457i			0.109970i
$125$		0			0
$126$	0.686624	+	3.32633i	0.0611693	+	0.296333i
$127$	4.55939	−	4.55939i	0.404581	−	0.404581i	−0.475263	−	0.879844i	$-0.657647\pi$
$127$	4.55939	−	4.55939i	0.404581	−	0.404581i	0.879844	+	0.475263i	$0.157647\pi$
$128$	1.33009	−	1.33009i	0.117565	−	0.117565i
$129$	0.0701274	+	0.686624i	0.00617437	+	0.0604538i
$130$		0			0
$131$		−	13.6784i		−	1.19509i	−0.801837	−	0.597543i	$-0.796144\pi$
$131$		−	13.6784i		−	1.19509i	0.801837	−	0.597543i	$-0.203856\pi$
$132$	−5.01709	−	4.08723i	−0.436682	−	0.355748i
$133$	0.933556	+	0.933556i	0.0809495	+	0.0809495i
$134$	−12.6829			−1.09563
$135$		0			0
$136$	3.67424			0.315064
$137$	10.0232	+	10.0232i	0.856337	+	0.856337i	0.990904	−	0.134567i	$-0.0429643\pi$
$137$	10.0232	+	10.0232i	0.856337	+	0.856337i	−0.134567	+	0.990904i	$0.542964\pi$
$138$	−12.1028	−	9.85969i	−1.03026	−	0.839313i
$139$		−	15.8262i		−	1.34236i	−0.741292	−	0.671182i	$-0.765787\pi$
$139$		−	15.8262i		−	1.34236i	0.741292	−	0.671182i	$-0.234213\pi$
$140$		0			0
$141$	−0.845170	−	8.27513i	−0.0711761	−	0.696892i
$142$	−7.25588	+	7.25588i	−0.608900	+	0.608900i
$143$	16.8902	−	16.8902i	1.41243	−	1.41243i
$144$	1.24187	+	6.01623i	0.103490	+	0.501353i
$145$		0			0
$146$			2.14317i			0.177370i
$147$	1.09397	−	1.34285i	0.0902288	−	0.110756i
$148$	−1.22940	−	1.22940i	−0.101056	−	0.101056i
$149$	−9.30594			−0.762373			−0.381186	−	0.924498i	$-0.624484\pi$
$149$	−9.30594			−0.762373			−0.381186	+	0.924498i	$0.624484\pi$
$150$		0			0
$151$	−16.8274			−1.36939			−0.684697	−	0.728827i	$-0.740066\pi$
$151$	−16.8274			−1.36939			−0.684697	+	0.728827i	$0.740066\pi$
$152$	2.87297	+	2.87297i	0.233029	+	0.233029i
$153$	−1.96840	+	2.99241i	−0.159135	+	0.241922i
$154$		−	5.88936i		−	0.474578i
$155$		0			0
$156$	5.68275	−	0.580400i	0.454984	−	0.0464692i
$157$	−6.80647	+	6.80647i	−0.543216	+	0.543216i	−0.924470	−	0.381255i	$-0.875492\pi$
$157$	−6.80647	+	6.80647i	−0.543216	+	0.543216i	0.381255	+	0.924470i	$0.375492\pi$
$158$	9.20757	−	9.20757i	0.732515	−	0.732515i
$159$	8.55464	−	0.873717i	0.678427	−	0.0692903i
$160$		0			0
$161$			7.96075i			0.627395i
$162$	−9.46902	−	3.76312i	−0.743957	−	0.295659i
$163$	−8.77966	−	8.77966i	−0.687676	−	0.687676i	0.274042	−	0.961718i	$-0.411639\pi$
$163$	−8.77966	−	8.77966i	−0.687676	−	0.687676i	−0.961718	+	0.274042i	$0.911639\pi$
$164$	−1.30844			−0.102172
$165$		0			0
$166$	−8.74519			−0.678758
$167$	12.4516	+	12.4516i	0.963532	+	0.963532i	0.999358	−	0.0358258i	$-0.0114062\pi$
$167$	12.4516	+	12.4516i	0.963532	+	0.963532i	−0.0358258	+	0.999358i	$0.511406\pi$
$168$	3.36663	−	4.13255i	0.259741	−	0.318833i
$169$			8.08513i			0.621933i
$170$		0			0
$171$	−3.87896	+	0.800698i	−0.296632	+	0.0612309i
$172$	0.202376	−	0.202376i	0.0154310	−	0.0154310i
$173$	−13.7966	+	13.7966i	−1.04894	+	1.04894i	−0.0501977	+	0.998739i	$0.515985\pi$
$173$	−13.7966	+	13.7966i	−1.04894	+	1.04894i	−0.998739	+	0.0501977i	$0.984015\pi$
$174$	−0.873244	−	8.55000i	−0.0662004	−	0.648174i
$175$		0			0
$176$		−	10.6519i		−	0.802916i
$177$	−2.44092	−	1.98852i	−0.183471	−	0.149466i
$178$	7.55015	+	7.55015i	0.565907	+	0.565907i
$179$	−7.03160			−0.525567			−0.262783	−	0.964855i	$-0.584640\pi$
$179$	−7.03160			−0.525567			−0.262783	+	0.964855i	$0.584640\pi$
$180$		0			0
$181$	14.1873			1.05454			0.527268	−	0.849699i	$-0.323216\pi$
$181$	14.1873			1.05454			0.527268	+	0.849699i	$0.323216\pi$
$182$	3.67602	+	3.67602i	0.272485	+	0.272485i
$183$	−3.32374	−	2.70772i	−0.245698	−	0.200161i
$184$			24.4988i			1.80608i
$185$		0			0
$186$	−0.339706	−	3.32609i	−0.0249085	−	0.243881i
$187$	4.39161	−	4.39161i	0.321147	−	0.321147i
$188$	−2.43902	+	2.43902i	−0.177884	+	0.177884i
$189$	1.56207	+	4.95580i	0.113624	+	0.360481i
$190$		0			0
$191$			15.6450i			1.13203i	0.824394	+	0.566017i	$0.191516\pi$
$191$			15.6450i			1.13203i	−0.824394	+	0.566017i	$0.808484\pi$
$192$	9.23199	−	11.3323i	0.666261	−	0.817838i
$193$	−9.00959	−	9.00959i	−0.648525	−	0.648525i	0.304112	−	0.952636i	$-0.401640\pi$
$193$	−9.00959	−	9.00959i	−0.648525	−	0.648525i	−0.952636	+	0.304112i	$0.901640\pi$
$194$	4.90443			0.352118
$195$		0			0
$196$	−0.718229			−0.0513021
$197$	2.78986	+	2.78986i	0.198769	+	0.198769i	0.799472	−	0.600703i	$-0.205113\pi$
$197$	2.78986	+	2.78986i	0.198769	+	0.198769i	−0.600703	+	0.799472i	$0.705113\pi$
$198$	14.7609	+	9.70965i	1.04901	+	0.690035i
$199$		−	14.4320i		−	1.02306i	−0.859266	−	0.511528i	$-0.829080\pi$
$199$		−	14.4320i		−	1.02306i	0.859266	−	0.511528i	$-0.170920\pi$
$200$		0			0
$201$	−19.3028	+	1.97146i	−1.36151	+	0.139056i
$202$	2.97518	−	2.97518i	0.209333	−	0.209333i
$203$	−3.09912	+	3.09912i	−0.217516	+	0.217516i
$204$	1.47757	−	0.150909i	0.103450	−	0.0105658i
$205$		0			0
$206$		−	1.89009i		−	0.131689i
$207$	−19.9525	−	13.1247i	−1.38680	−	0.912231i
$208$	6.64871	+	6.64871i	0.461005	+	0.461005i
$209$	6.86780			0.475056
$210$		0			0
$211$	11.9845			0.825049			0.412524	−	0.910947i	$-0.364647\pi$
$211$	11.9845			0.825049			0.412524	+	0.910947i	$0.364647\pi$
$212$	−2.52140	−	2.52140i	−0.173171	−	0.173171i
$213$	−9.91525	+	12.1710i	−0.679382	+	0.833943i
$214$		−	2.20967i		−	0.151050i
$215$		0			0
$216$	4.80718	+	15.2512i	0.327087	+	1.03772i
$217$	−1.20561	+	1.20561i	−0.0818422	+	0.0818422i
$218$	−4.75133	+	4.75133i	−0.321801	+	0.321801i
$219$	0.333141	+	3.26181i	0.0225116	+	0.220413i
$220$		0			0
$221$			5.48233i			0.368781i
$222$	3.68025	+	2.99816i	0.247003	+	0.201224i
$223$	12.1834	+	12.1834i	0.815858	+	0.815858i	0.985505	−	0.169647i	$-0.0542628\pi$
$223$	12.1834	+	12.1834i	0.815858	+	0.815858i	−0.169647	+	0.985505i	$0.554263\pi$
$224$	−3.83661			−0.256344
$225$		0			0
$226$	0.385328			0.0256317
$227$	4.17335	+	4.17335i	0.276995	+	0.276995i	0.831908	−	0.554913i	$-0.187249\pi$
$227$	4.17335	+	4.17335i	0.276995	+	0.276995i	−0.554913	+	0.831908i	$0.687249\pi$
$228$	1.27334	+	1.03734i	0.0843290	+	0.0686996i
$229$			27.2705i			1.80209i	0.433730	+	0.901043i	$0.357197\pi$
$229$			27.2705i			1.80209i	−0.433730	+	0.901043i	$0.642803\pi$
$230$		0			0
$231$	−0.915459	−	8.96334i	−0.0602328	−	0.589744i
$232$	−9.53740	+	9.53740i	−0.626161	+	0.626161i
$233$	1.96791	−	1.96791i	0.128922	−	0.128922i	−0.639701	−	0.768624i	$-0.720942\pi$
$233$	1.96791	−	1.96791i	0.128922	−	0.128922i	0.768624	+	0.639701i	$0.220942\pi$
$234$	−15.2740	+	3.15288i	−0.998495	+	0.206110i
$235$		0			0
$236$			1.30554i			0.0849832i
$237$	12.5823	−	15.4448i	0.817306	−	1.00325i
$238$	0.955800	+	0.955800i	0.0619553	+	0.0619553i
$239$	1.42942			0.0924613			0.0462307	−	0.998931i	$-0.485279\pi$
$239$	1.42942			0.0924613			0.0462307	+	0.998931i	$0.485279\pi$
$240$		0			0
$241$	29.1319			1.87655			0.938274	−	0.345893i	$-0.112424\pi$
$241$	29.1319			1.87655			0.938274	+	0.345893i	$0.112424\pi$
$242$	−12.8567	−	12.8567i	−0.826463	−	0.826463i
$243$	−14.9964	−	4.25541i	−0.962018	−	0.272985i
$244$			1.77772i			0.113807i
$245$		0			0
$246$	3.55388	−	0.362971i	0.226587	−	0.0231422i
$247$	−4.28675	+	4.28675i	−0.272759	+	0.272759i
$248$	−3.71021	+	3.71021i	−0.235598	+	0.235598i
$249$	−13.3098	+	1.35938i	−0.843473	+	0.0861470i
$250$		0			0
$251$		−	12.3977i		−	0.782538i	−0.920276	−	0.391269i	$-0.872036\pi$
$251$		−	12.3977i		−	0.782538i	0.920276	−	0.391269i	$-0.127964\pi$
$252$	1.18413	−	1.80014i	0.0745931	−	0.113398i
$253$	29.2821	+	29.2821i	1.84095	+	1.84095i
$254$	7.30007			0.458047
$255$		0			0
$256$	−14.7484			−0.921774
$257$	−13.8717	−	13.8717i	−0.865290	−	0.865290i	0.126657	−	0.991947i	$-0.459575\pi$
$257$	−13.8717	−	13.8717i	−0.865290	−	0.865290i	−0.991947	+	0.126657i	$0.959575\pi$
$258$	−0.493538	+	0.605820i	−0.0307263	+	0.0377167i
$259$		−	2.42073i		−	0.150417i
$260$		0			0
$261$	−2.65808	−	12.8770i	−0.164531	−	0.797066i
$262$	10.9503	−	10.9503i	0.676511	−	0.676511i
$263$	−12.2912	+	12.2912i	−0.757909	+	0.757909i	−0.975942	−	0.218032i	$-0.930036\pi$
$263$	−12.2912	+	12.2912i	−0.757909	+	0.757909i	0.218032	+	0.975942i	$0.430036\pi$
$264$	−2.81728	−	27.5842i	−0.173392	−	1.69769i
$265$		0			0
$266$			1.49472i			0.0916473i
$267$	12.6646	+	10.3174i	0.775061	+	0.631413i
$268$	5.68932	+	5.68932i	0.347530	+	0.347530i
$269$	19.1535			1.16781			0.583906	−	0.811822i	$-0.301524\pi$
$269$	19.1535			1.16781			0.583906	+	0.811822i	$0.301524\pi$
$270$		0			0
$271$	18.4629			1.12154			0.560771	−	0.827971i	$-0.310505\pi$
$271$	18.4629			1.12154			0.560771	+	0.827971i	$0.310505\pi$
$272$	1.72872	+	1.72872i	0.104819	+	0.104819i
$273$	6.16616	+	5.02333i	0.373193	+	0.304026i
$274$			16.0482i			0.969505i
$275$		0			0
$276$	1.00622	+	9.85200i	0.0605674	+	0.593020i
$277$	7.66076	−	7.66076i	0.460290	−	0.460290i	−0.438460	−	0.898751i	$-0.644476\pi$
$277$	7.66076	−	7.66076i	0.460290	−	0.460290i	0.898751	+	0.438460i	$0.144476\pi$
$278$	12.6698	−	12.6698i	0.759881	−	0.759881i
$279$	−1.03404	−	5.00936i	−0.0619061	−	0.299903i
$280$		0			0
$281$			20.4646i			1.22082i	0.792087	+	0.610408i	$0.208995\pi$
$281$			20.4646i			1.22082i	−0.792087	+	0.610408i	$0.791005\pi$
$282$	5.94808	−	7.30129i	0.354203	−	0.434785i
$283$	−8.24528	−	8.24528i	−0.490131	−	0.490131i	0.418216	−	0.908347i	$-0.362655\pi$
$283$	−8.24528	−	8.24528i	−0.490131	−	0.490131i	−0.908347	+	0.418216i	$0.862655\pi$
$284$	6.50972			0.386281
$285$		0			0
$286$	27.0431			1.59909
$287$	−1.28818	−	1.28818i	−0.0760387	−	0.0760387i
$288$	6.32533	−	9.61593i	0.372723	−	0.566624i
$289$		−	15.5745i		−	0.916150i
$290$		0			0
$291$	7.46433	−	0.762360i	0.437567	−	0.0446903i
$292$	0.961389	−	0.961389i	0.0562610	−	0.0562610i
$293$	19.7225	−	19.7225i	1.15220	−	1.15220i	0.166088	−	0.986111i	$-0.446886\pi$
$293$	19.7225	−	19.7225i	1.15220	−	1.15220i	0.986111	−	0.166088i	$-0.0531135\pi$
$294$	1.95080	−	0.199242i	0.113773	−	0.0116200i
$295$		0			0
$296$		−	7.44968i		−	0.433004i
$297$	23.9747	+	12.4832i	1.39115	+	0.724348i
$298$	−7.44990	−	7.44990i	−0.431561	−	0.431561i
$299$	−36.5546			−2.11401
$300$		0			0
$301$	0.398485			0.0229683
$302$	−13.4712	−	13.4712i	−0.775182	−	0.775182i
$303$	4.06562	−	4.99056i	0.233564	−	0.286700i
$304$			2.70346i			0.155054i
$305$		0			0
$306$	−3.97139	+	0.819776i	−0.227029	+	0.0468635i
$307$	13.2997	−	13.2997i	0.759057	−	0.759057i	−0.217094	−	0.976151i	$-0.569658\pi$
$307$	13.2997	−	13.2997i	0.759057	−	0.759057i	0.976151	+	0.217094i	$0.0696578\pi$
$308$	−2.64186	+	2.64186i	−0.150534	+	0.150534i
$309$	−0.293801	−	2.87663i	−0.0167137	−	0.163646i
$310$		0			0
$311$			23.8049i			1.34985i	0.737885	+	0.674926i	$0.235824\pi$
$311$			23.8049i			1.34985i	−0.737885	+	0.674926i	$0.764176\pi$
$312$	18.9761	+	15.4591i	1.07431	+	0.875197i
$313$	18.9352	+	18.9352i	1.07028	+	1.07028i	0.997336	+	0.0729475i	$0.0232406\pi$
$313$	18.9352	+	18.9352i	1.07028	+	1.07028i	0.0729475	+	0.997336i	$0.476759\pi$
$314$	−10.8979			−0.615003
$315$		0			0
$316$	−8.26072			−0.464702
$317$	−11.6929	−	11.6929i	−0.656739	−	0.656739i	0.297868	−	0.954607i	$-0.403725\pi$
$317$	−11.6929	−	11.6929i	−0.656739	−	0.656739i	−0.954607	+	0.297868i	$0.903725\pi$
$318$	7.54790	+	6.14899i	0.423265	+	0.344818i
$319$			22.7990i			1.27650i
$320$		0			0
$321$	−0.343478	−	3.36302i	−0.0191711	−	0.187706i
$322$	−6.37301	+	6.37301i	−0.355154	+	0.355154i
$323$	−1.11459	+	1.11459i	−0.0620177	+	0.0620177i
$324$	2.55957	+	5.93571i	0.142198	+	0.329762i
$325$		0			0
$326$		−	14.0572i		−	0.778555i
$327$	−6.49275	+	7.96987i	−0.359050	+	0.440735i
$328$	−3.96430	−	3.96430i	−0.218892	−	0.218892i
$329$	−4.80250			−0.264771
$330$		0			0
$331$	−11.5898			−0.637031			−0.318516	−	0.947918i	$-0.603184\pi$
$331$	−11.5898			−0.637031			−0.318516	+	0.947918i	$0.603184\pi$
$332$	3.92294	+	3.92294i	0.215299	+	0.215299i
$333$	6.06723	+	3.99100i	0.332482	+	0.218706i
$334$			19.9363i			1.09087i
$335$		0			0
$336$	3.52835	−	0.360363i	0.192487	−	0.0196594i
$337$	5.46127	−	5.46127i	0.297494	−	0.297494i	−0.542537	−	0.840032i	$-0.682536\pi$
$337$	5.46127	−	5.46127i	0.297494	−	0.297494i	0.840032	+	0.542537i	$0.182536\pi$
$338$	−6.47258	+	6.47258i	−0.352062	+	0.352062i
$339$	0.586453	−	0.0598966i	0.0318517	−	0.00325314i
$340$		0			0
$341$			8.86920i			0.480294i
$342$	−3.74632	−	2.46431i	−0.202578	−	0.133255i
$343$	−0.707107	−	0.707107i	−0.0381802	−	0.0381802i
$344$	1.22632			0.0661186
$345$		0			0
$346$	−22.0898			−1.18756
$347$	20.1982	+	20.1982i	1.08430	+	1.08430i	0.996103	+	0.0881938i	$0.0281095\pi$
$347$	20.1982	+	20.1982i	1.08430	+	1.08430i	0.0881938	+	0.996103i	$0.471891\pi$
$348$	−3.44366	+	4.22711i	−0.184600	+	0.226597i
$349$			11.9748i			0.640997i	0.947249	+	0.320498i	$0.103850\pi$
$349$			11.9748i			0.640997i	−0.947249	+	0.320498i	$0.896150\pi$
$350$		0			0
$351$	−22.7563	+	7.17278i	−1.21464	+	0.382855i
$352$	−14.1122	+	14.1122i	−0.752183	+	0.752183i
$353$	−24.3423	+	24.3423i	−1.29561	+	1.29561i	−0.364345	+	0.931264i	$0.618707\pi$
$353$	−24.3423	+	24.3423i	−1.29561	+	1.29561i	−0.931264	+	0.364345i	$0.881293\pi$
$354$	−0.362166	−	3.54600i	−0.0192489	−	0.188468i
$355$		0			0
$356$		−	6.77373i		−	0.359007i
$357$	1.60326	+	1.30611i	0.0848534	+	0.0691268i
$358$	−5.62917	−	5.62917i	−0.297511	−	0.297511i
$359$	14.2164			0.750314			0.375157	−	0.926961i	$-0.377589\pi$
$359$	14.2164			0.750314			0.375157	+	0.926961i	$0.377589\pi$
$360$		0			0
$361$	17.2569			0.908260
$362$	11.3577	+	11.3577i	0.596948	+	0.596948i
$363$	−21.5659	−	17.5689i	−1.13192	−	0.922129i
$364$		−	3.29800i		−	0.172862i
$365$		0			0
$366$	−0.493153	−	4.82850i	−0.0257775	−	0.252390i
$367$	−16.7024	+	16.7024i	−0.871859	+	0.871859i	−0.992675	−	0.120816i	$-0.961449\pi$
$367$	−16.7024	+	16.7024i	−0.871859	+	0.871859i	0.120816	+	0.992675i	$0.461449\pi$
$368$	−11.5267	+	11.5267i	−0.600868	+	0.600868i
$369$	5.35243	−	1.10485i	0.278636	−	0.0575163i
$370$		0			0
$371$		−	4.96472i		−	0.257755i
$372$	−1.33964	+	1.64441i	−0.0694572	+	0.0852589i
$373$	−4.57877	−	4.57877i	−0.237080	−	0.237080i	0.578560	−	0.815640i	$-0.303615\pi$
$373$	−4.57877	−	4.57877i	−0.237080	−	0.237080i	−0.815640	+	0.578560i	$0.803615\pi$
$374$	7.03144			0.363587
$375$		0			0
$376$	−14.7795			−0.762193
$377$	−14.2307	−	14.2307i	−0.732920	−	0.732920i
$378$	−2.71686	+	5.21790i	−0.139740	+	0.268380i
$379$		−	12.6506i		−	0.649816i	−0.945746	−	0.324908i	$-0.894667\pi$
$379$		−	12.6506i		−	0.649816i	0.945746	−	0.324908i	$-0.105333\pi$
$380$		0			0
$381$	11.1104	−	1.13474i	0.569202	−	0.0581347i
$382$	−12.5247	+	12.5247i	−0.640818	+	0.640818i
$383$	18.0165	−	18.0165i	0.920601	−	0.920601i	−0.0764705	−	0.997072i	$-0.524365\pi$
$383$	18.0165	−	18.0165i	0.920601	−	0.920601i	0.997072	+	0.0764705i	$0.0243651\pi$
$384$	3.24119	−	0.331035i	0.165401	−	0.0168930i
$385$		0			0
$386$		−	14.4253i		−	0.734229i
$387$	−0.656973	+	0.998748i	−0.0333958	+	0.0507692i
$388$	−2.20004	−	2.20004i	−0.111690	−	0.111690i
$389$	17.7215			0.898517			0.449259	−	0.893402i	$-0.351688\pi$
$389$	17.7215			0.898517			0.449259	+	0.893402i	$0.351688\pi$
$390$		0			0
$391$	−9.50453			−0.480665
$392$	−2.17609	−	2.17609i	−0.109909	−	0.109909i
$393$	14.9637	−	18.3680i	0.754819	−	0.926543i
$394$			4.46686i			0.225037i
$395$		0			0
$396$	−2.26589	−	10.9771i	−0.113865	−	0.551618i
$397$	−4.43035	+	4.43035i	−0.222353	+	0.222353i	−0.809489	−	0.587136i	$-0.800255\pi$
$397$	−4.43035	+	4.43035i	−0.222353	+	0.222353i	0.587136	+	0.809489i	$0.300255\pi$
$398$	11.5536	−	11.5536i	0.579128	−	0.579128i
$399$	0.232344	+	2.27490i	0.0116317	+	0.113887i
$400$		0			0
$401$		−	34.4780i		−	1.72175i	−0.508818	−	0.860874i	$-0.669918\pi$
$401$		−	34.4780i		−	1.72175i	0.508818	−	0.860874i	$-0.330082\pi$
$402$	−17.0312	−	13.8746i	−0.849437	−	0.692004i
$403$	−5.53599	−	5.53599i	−0.275767	−	0.275767i
$404$	−2.66923			−0.132799
$405$		0			0
$406$	−4.96203			−0.246261
$407$	−8.90417	−	8.90417i	−0.441364	−	0.441364i
$408$	4.93395	+	4.01950i	0.244267	+	0.198995i
$409$			19.5663i			0.967490i	0.875209	+	0.483745i	$0.160724\pi$
$409$			19.5663i			0.967490i	−0.875209	+	0.483745i	$0.839276\pi$
$410$		0			0
$411$	2.49457	+	24.4246i	0.123048	+	1.20478i
$412$	−0.847860	+	0.847860i	−0.0417711	+	0.0417711i
$413$	−1.28532	+	1.28532i	−0.0632465	+	0.0632465i
$414$	−5.46604	−	26.4801i	−0.268641	−	1.30143i
$415$		0			0
$416$		−	17.6171i		−	0.863751i
$417$	17.3134	−	21.2522i	0.847840	−	1.04073i
$418$	5.49804	+	5.49804i	0.268918	+	0.268918i
$419$	17.0209			0.831524			0.415762	−	0.909474i	$-0.363515\pi$
$419$	17.0209			0.831524			0.415762	+	0.909474i	$0.363515\pi$
$420$		0			0
$421$	21.7474			1.05990			0.529951	−	0.848028i	$-0.322210\pi$
$421$	21.7474			1.05990			0.529951	+	0.848028i	$0.322210\pi$
$422$	9.59425	+	9.59425i	0.467041	+	0.467041i
$423$	7.91778	−	12.0368i	0.384976	−	0.585250i
$424$		−	15.2787i		−	0.741998i
$425$		0			0
$426$	−17.6812	+	1.80585i	−0.856658	+	0.0874936i
$427$	−1.75019	+	1.75019i	−0.0846976	+	0.0846976i
$428$	−0.991221	+	0.991221i	−0.0479125	+	0.0479125i
$429$	41.1583	−	4.20365i	1.98714	−	0.202954i
$430$		0			0
$431$		−	10.7912i		−	0.519796i	−0.965636	−	0.259898i	$-0.916311\pi$
$431$		−	10.7912i		−	0.519796i	0.965636	−	0.259898i	$-0.0836889\pi$
$432$	−4.91391	+	9.43745i	−0.236420	+	0.454059i
$433$	−0.466927	−	0.466927i	−0.0224391	−	0.0224391i	0.695798	−	0.718237i	$-0.255051\pi$
$433$	−0.466927	−	0.466927i	−0.0224391	−	0.0224391i	−0.718237	+	0.695798i	$0.755051\pi$
$434$	−1.93031			−0.0926579
$435$		0			0
$436$	4.26273			0.204148
$437$	−7.43180	−	7.43180i	−0.355511	−	0.355511i
$438$	−2.34456	+	2.87795i	−0.112027	+	0.137514i
$439$		−	9.43662i		−	0.450385i	−0.974314	−	0.225193i	$-0.927699\pi$
$439$		−	9.43662i		−	0.450385i	0.974314	−	0.225193i	$-0.0723011\pi$
$440$		0			0
$441$	2.93806	−	0.606476i	0.139908	−	0.0288798i
$442$	−4.38889	+	4.38889i	−0.208758	+	0.208758i
$443$	16.8956	−	16.8956i	0.802734	−	0.802734i	−0.180788	−	0.983522i	$-0.557865\pi$
$443$	16.8956	−	16.8956i	0.802734	−	0.802734i	0.983522	+	0.180788i	$0.0578647\pi$
$444$	−0.305975	−	2.99582i	−0.0145209	−	0.142175i
$445$		0			0
$446$			19.5068i			0.923676i
$447$	−12.4965	−	10.1804i	−0.591062	−	0.481516i
$448$	−5.96728	−	5.96728i	−0.281927	−	0.281927i
$449$	11.5643			0.545753			0.272876	−	0.962049i	$-0.412025\pi$
$449$	11.5643			0.545753			0.272876	+	0.962049i	$0.412025\pi$
$450$		0			0
$451$	−9.47661			−0.446236
$452$	−0.172852	−	0.172852i	−0.00813026	−	0.00813026i
$453$	−22.5966	−	18.4086i	−1.06168	−	0.864912i
$454$			6.68197i			0.313601i
$455$		0			0
$456$	0.715027	+	7.00090i	0.0334842	+	0.327847i
$457$	17.8413	−	17.8413i	0.834580	−	0.834580i	−0.153560	−	0.988139i	$-0.549074\pi$
$457$	17.8413	−	17.8413i	0.834580	−	0.834580i	0.988139	+	0.153560i	$0.0490737\pi$
$458$	−21.8315	+	21.8315i	−1.02012	+	1.02012i
$459$	−5.91685	+	1.86499i	−0.276175	+	0.0870502i
$460$		0			0
$461$			13.0571i			0.608129i	0.952651	+	0.304064i	$0.0983438\pi$
$461$			13.0571i			0.608129i	−0.952651	+	0.304064i	$0.901656\pi$
$462$	6.44276	−	7.90850i	0.299744	−	0.367937i
$463$	−17.3925	−	17.3925i	−0.808298	−	0.808298i	0.176079	−	0.984376i	$-0.443659\pi$
$463$	−17.3925	−	17.3925i	−0.808298	−	0.808298i	−0.984376	+	0.176079i	$0.943659\pi$
$464$	−8.97466			−0.416638
$465$		0			0
$466$	3.15084			0.145960
$467$	9.40605	+	9.40605i	0.435260	+	0.435260i	0.890413	−	0.455153i	$-0.150415\pi$
$467$	9.40605	+	9.40605i	0.435260	+	0.435260i	−0.455153	+	0.890413i	$0.650415\pi$
$468$	8.26600	+	5.43734i	0.382096	+	0.251341i
$469$			11.2024i			0.517280i
$470$		0			0
$471$	−16.5861	+	1.69400i	−0.764247	+	0.0780554i
$472$	−3.95551	+	3.95551i	−0.182067	+	0.182067i
$473$	1.46575	−	1.46575i	0.0673951	−	0.0673951i
$474$	22.4371	−	2.29159i	1.03057	−	0.105256i
$475$		0			0
$476$		−	0.857511i		−	0.0393039i
$477$	12.4434	+	8.18522i	0.569744	+	0.374776i
$478$	1.14432	+	1.14432i	0.0523402	+	0.0523402i
$479$	−38.8689			−1.77596			−0.887982	−	0.459879i	$-0.847893\pi$
$479$	−38.8689			−1.77596			−0.887982	+	0.459879i	$0.847893\pi$
$480$		0			0
$481$	11.1156			0.506829
$482$	23.3216	+	23.3216i	1.06227	+	1.06227i
$483$	−8.70879	+	10.6901i	−0.396264	+	0.486415i
$484$			11.5346i			0.524301i
$485$		0			0
$486$	−8.59872	−	15.4121i	−0.390046	−	0.699106i
$487$	−23.9549	+	23.9549i	−1.08550	+	1.08550i	−0.0895148	+	0.995985i	$0.528532\pi$
$487$	−23.9549	+	23.9549i	−1.08550	+	1.08550i	−0.995985	+	0.0895148i	$0.971468\pi$
$488$	−5.38612	+	5.38612i	−0.243818	+	0.243818i
$489$	−2.18509	−	21.3944i	−0.0988131	−	0.967488i
$490$		0			0
$491$		−	25.6453i		−	1.15736i	−0.815556	−	0.578678i	$-0.803569\pi$
$491$		−	25.6453i		−	1.15736i	0.815556	−	0.578678i	$-0.196431\pi$
$492$	−1.75703	−	1.43139i	−0.0792132	−	0.0645319i
$493$	−3.70012	−	3.70012i	−0.166645	−	0.166645i
$494$	−6.86355			−0.308806
$495$		0			0
$496$	−3.49129			−0.156764
$497$	6.40892	+	6.40892i	0.287479	+	0.287479i
$498$	−11.7434	−	9.56694i	−0.526236	−	0.428705i
$499$		−	29.1057i		−	1.30295i	−0.758669	−	0.651476i	$-0.774150\pi$
$499$		−	29.1057i		−	1.30295i	0.758669	−	0.651476i	$-0.225850\pi$
$500$		0			0
$501$	3.09896	+	30.3422i	0.138451	+	1.35559i
$502$	9.92505	−	9.92505i	0.442976	−	0.442976i
$503$	−10.1763	+	10.1763i	−0.453738	+	0.453738i	−0.896593	−	0.442855i	$-0.853965\pi$
$503$	−10.1763	+	10.1763i	−0.453738	+	0.453738i	0.442855	+	0.896593i	$0.353965\pi$
$504$	9.04173	−	1.86640i	0.402751	−	0.0831361i
$505$		0			0
$506$			46.8837i			2.08423i
$507$	−8.84486	+	10.8571i	−0.392814	+	0.482181i
$508$	−3.27469	−	3.27469i	−0.145291	−	0.145291i
$509$	−31.2970			−1.38721			−0.693607	−	0.720354i	$-0.743979\pi$
$509$	−31.2970			−1.38721			−0.693607	+	0.720354i	$0.743979\pi$
$510$		0			0
$511$	1.89300			0.0837415
$512$	−14.4671	−	14.4671i	−0.639360	−	0.639360i
$513$	−6.08479	−	3.16824i	−0.268650	−	0.139881i
$514$		−	22.2100i		−	0.979641i
$515$		0			0
$516$	0.493153	−	0.0503675i	0.0217098	−	0.00221731i
$517$	−17.6651	+	17.6651i	−0.776908	+	0.776908i
$518$	1.93792	−	1.93792i	0.0851474	−	0.0851474i
$519$	−33.6198	+	3.43371i	−1.47574	+	0.150723i
$520$		0			0
$521$		−	24.4644i		−	1.07180i	−0.844280	−	0.535902i	$-0.819972\pi$
$521$		−	24.4644i		−	1.07180i	0.844280	−	0.535902i	$-0.180028\pi$
$522$	8.18078	−	12.4366i	0.358063	−	0.544337i
$523$	−1.82790	−	1.82790i	−0.0799284	−	0.0799284i	0.666012	−	0.745941i	$-0.268000\pi$
$523$	−1.82790	−	1.82790i	−0.0799284	−	0.0799284i	−0.745941	+	0.666012i	$0.768000\pi$
$524$	−9.82422			−0.429173
$525$		0			0
$526$	−19.6796			−0.858069
$527$	−1.43941	−	1.43941i	−0.0627015	−	0.0627015i
$528$	11.6528	−	14.3039i	0.507123	−	0.622495i
$529$		−	40.3736i		−	1.75537i
$530$		0			0
$531$	−1.10240	−	5.34056i	−0.0478402	−	0.231761i
$532$	0.670507	−	0.670507i	0.0290701	−	0.0290701i
$533$	5.91512	−	5.91512i	0.256212	−	0.256212i
$534$	1.87909	+	18.3983i	0.0813160	+	0.796172i
$535$		0			0
$536$			34.4749i			1.48909i
$537$	−9.44237	−	7.69234i	−0.407468	−	0.331949i
$538$	15.3334	+	15.3334i	0.661071	+	0.661071i
$539$	−5.20191			−0.224062
$540$		0			0
$541$	41.8839			1.80073			0.900364	−	0.435137i	$-0.143300\pi$
$541$	41.8839			1.80073			0.900364	+	0.435137i	$0.143300\pi$
$542$	14.7805	+	14.7805i	0.634879	+	0.634879i
$543$	19.0514	+	15.5205i	0.817575	+	0.666047i
$544$		−	4.58061i		−	0.196392i
$545$		0			0
$546$	0.914892	+	8.95779i	0.0391538	+	0.383358i
$547$	21.6813	−	21.6813i	0.927024	−	0.927024i	−0.0704885	−	0.997513i	$-0.522456\pi$
$547$	21.6813	−	21.6813i	0.927024	−	0.927024i	0.997513	+	0.0704885i	$0.0224558\pi$
$548$	7.19893	−	7.19893i	0.307523	−	0.307523i
$549$	−1.50111	−	7.27211i	−0.0640660	−	0.310366i
$550$		0			0
$551$		−	5.78641i		−	0.246509i
$552$	−26.8009	+	32.8982i	−1.14072	+	1.40024i
$553$	−8.13280	−	8.13280i	−0.345842	−	0.345842i
$554$	12.2657			0.521119
$555$		0			0
$556$	−11.3669			−0.482063
$557$	−13.1204	−	13.1204i	−0.555929	−	0.555929i	0.372217	−	0.928146i	$-0.378598\pi$
$557$	−13.1204	−	13.1204i	−0.555929	−	0.555929i	−0.928146	+	0.372217i	$0.878598\pi$
$558$	3.18246	−	4.83806i	0.134724	−	0.204811i
$559$			1.82978i			0.0773916i
$560$		0			0
$561$	10.7015	−	1.09299i	0.451819	−	0.0461460i
$562$	−16.3830	+	16.3830i	−0.691076	+	0.691076i
$563$	15.9166	−	15.9166i	0.670804	−	0.670804i	−0.287097	−	0.957901i	$-0.592690\pi$
$563$	15.9166	−	15.9166i	0.670804	−	0.670804i	0.957901	+	0.287097i	$0.0926903\pi$
$564$	−5.94344	+	0.607025i	−0.250264	+	0.0255604i
$565$		0			0
$566$		−	13.2016i		−	0.554903i
$567$	−3.32386	+	8.36373i	−0.139589	+	0.351244i
$568$	19.7231	+	19.7231i	0.827565	+	0.827565i
$569$	−27.8303			−1.16671			−0.583354	−	0.812218i	$-0.698260\pi$
$569$	−27.8303			−1.16671			−0.583354	+	0.812218i	$0.698260\pi$
$570$		0			0
$571$	−4.11555			−0.172230			−0.0861151	−	0.996285i	$-0.527445\pi$
$571$	−4.11555			−0.172230			−0.0861151	+	0.996285i	$0.527445\pi$
$572$	−12.1311	−	12.1311i	−0.507225	−	0.507225i
$573$	−17.1151	+	21.0089i	−0.714994	+	0.877658i
$574$		−	2.06251i		−	0.0860874i
$575$		0			0
$576$	24.7943	−	5.11805i	1.03310	−	0.213252i
$577$	15.3143	−	15.3143i	0.637542	−	0.637542i	−0.312406	−	0.949949i	$-0.601135\pi$
$577$	15.3143	−	15.3143i	0.637542	−	0.637542i	0.949949	+	0.312406i	$0.101135\pi$
$578$	12.4683	−	12.4683i	0.518611	−	0.518611i
$579$	−2.24231	−	21.9547i	−0.0931874	−	0.912406i
$580$		0			0
$581$			7.72438i			0.320461i
$582$	6.58590	+	5.36528i	0.272994	+	0.222398i
$583$	−18.2617	−	18.2617i	−0.756324	−	0.756324i
$584$	5.82563			0.241066
$585$		0			0
$586$	31.5778			1.30447
$587$	−23.2211	−	23.2211i	−0.958439	−	0.958439i	0.0407314	−	0.999170i	$-0.487031\pi$
$587$	−23.2211	−	23.2211i	−0.958439	−	0.958439i	−0.999170	+	0.0407314i	$0.987031\pi$
$588$	−0.964471	−	0.785718i	−0.0397741	−	0.0324025i
$589$		−	2.25101i		−	0.0927512i
$590$		0			0
$591$	0.694342	+	6.79837i	0.0285614	+	0.279647i
$592$	3.50506	−	3.50506i	0.144057	−	0.144057i
$593$	−24.2941	+	24.2941i	−0.997641	+	0.997641i	−0.999997	−	0.00235668i	$-0.999250\pi$
$593$	−24.2941	+	24.2941i	−0.997641	+	0.997641i	0.00235668	+	0.999997i	$0.499250\pi$
$594$	9.19956	+	29.1865i	0.377463	+	1.19754i
$595$		0			0
$596$			6.68380i			0.273779i
$597$	15.7881	−	19.3799i	0.646164	−	0.793169i
$598$	−29.2639	−	29.2639i	−1.19669	−	1.19669i
$599$	22.7865			0.931029			0.465515	−	0.885040i	$-0.345869\pi$
$599$	22.7865			0.931029			0.465515	+	0.885040i	$0.345869\pi$
$600$		0			0
$601$	−41.7276			−1.70210			−0.851052	−	0.525082i	$-0.824035\pi$
$601$	−41.7276			−1.70210			−0.851052	+	0.525082i	$0.824035\pi$
$602$	0.319008	+	0.319008i	0.0130018	+	0.0130018i
$603$	−28.0774	−	18.4692i	−1.14340	−	0.752124i
$604$			12.0859i			0.491769i
$605$		0			0
$606$	7.24995	−	0.740464i	0.294509	−	0.0300793i
$607$	17.5164	−	17.5164i	0.710968	−	0.710968i	−0.255770	−	0.966738i	$-0.582329\pi$
$607$	17.5164	−	17.5164i	0.710968	−	0.710968i	0.966738	+	0.255770i	$0.0823289\pi$
$608$	3.58168	−	3.58168i	0.145256	−	0.145256i
$609$	−7.55198	+	0.771312i	−0.306022	+	0.0312551i
$610$		0			0
$611$		−	22.0524i		−	0.892144i
$612$	2.14923	+	1.41376i	0.0868776	+	0.0571478i
$613$	25.9860	+	25.9860i	1.04956	+	1.04956i	0.998706	+	0.0508591i	$0.0161959\pi$
$613$	25.9860	+	25.9860i	1.04956	+	1.04956i	0.0508591	+	0.998706i	$0.483804\pi$
$614$	21.2943			0.859369
$615$		0			0
$616$	−16.0086			−0.645005
$617$	8.12737	+	8.12737i	0.327196	+	0.327196i	0.851519	−	0.524323i	$-0.175682\pi$
$617$	8.12737	+	8.12737i	0.327196	+	0.327196i	−0.524323	+	0.851519i	$0.675682\pi$
$618$	2.06769	−	2.53810i	0.0831747	−	0.102097i
$619$			7.20599i			0.289633i	0.989459	+	0.144817i	$0.0462592\pi$
$619$			7.20599i			0.289633i	−0.989459	+	0.144817i	$0.953741\pi$
$620$		0			0
$621$	−12.4352	−	39.4519i	−0.499008	−	1.58315i
$622$	−19.0571	+	19.0571i	−0.764120	+	0.764120i
$623$	6.66884	−	6.66884i	0.267181	−	0.267181i
$624$	1.65474	+	16.2017i	0.0662424	+	0.648586i
$625$		0			0
$626$			30.3173i			1.21172i
$627$	9.22241	+	7.51314i	0.368307	+	0.300046i
$628$	4.88860	+	4.88860i	0.195077	+	0.195077i
$629$	2.89017			0.115238
$630$		0			0
$631$	−29.8770			−1.18938			−0.594692	−	0.803954i	$-0.702726\pi$
$631$	−29.8770			−1.18938			−0.594692	+	0.803954i	$0.702726\pi$
$632$	−25.0283	−	25.0283i	−0.995572	−	0.995572i
$633$	16.0934	+	13.1107i	0.639655	+	0.521102i
$634$		−	18.7216i		−	0.743530i
$635$		0			0
$636$	−0.627529	−	6.14419i	−0.0248831	−	0.243633i
$637$	3.24693	−	3.24693i	0.128648	−	0.128648i
$638$	−18.2518	+	18.2518i	−0.722597	+	0.722597i
$639$	−26.6293	+	5.49684i	−1.05344	+	0.217452i
$640$		0			0
$641$		−	19.3661i		−	0.764917i	−0.923973	−	0.382458i	$-0.875078\pi$
$641$		−	19.3661i		−	0.764917i	0.923973	−	0.382458i	$-0.124922\pi$
$642$	2.41731	−	2.96725i	0.0954035	−	0.117108i
$643$	−11.6091	−	11.6091i	−0.457819	−	0.457819i	0.440120	−	0.897939i	$-0.354936\pi$
$643$	−11.6091	−	11.6091i	−0.457819	−	0.457819i	−0.897939	+	0.440120i	$0.854936\pi$
$644$	5.71764			0.225307
$645$		0			0
$646$	−1.78458			−0.0702135
$647$	−10.6517	−	10.6517i	−0.418760	−	0.418760i	0.466016	−	0.884776i	$-0.345689\pi$
$647$	−10.6517	−	10.6517i	−0.418760	−	0.418760i	−0.884776	+	0.466016i	$0.845689\pi$
$648$	−10.2290	+	25.7390i	−0.401834	+	1.01112i
$649$			9.45560i			0.371165i
$650$		0			0
$651$	−2.93785	+	0.300053i	−0.115143	+	0.0117600i
$652$	−6.30580	+	6.30580i	−0.246954	+	0.246954i
$653$	−3.67307	+	3.67307i	−0.143738	+	0.143738i	−0.775314	−	0.631576i	$-0.782408\pi$
$653$	−3.67307	+	3.67307i	−0.143738	+	0.143738i	0.631576	+	0.775314i	$0.282408\pi$
$654$	−11.5781	+	1.18251i	−0.452740	+	0.0462400i
$655$		0			0
$656$		−	3.73039i		−	0.145647i
$657$	−3.12095	+	4.74456i	−0.121760	+	0.185103i
$658$	−3.84466	−	3.84466i	−0.149880	−	0.149880i
$659$	45.6844			1.77961			0.889807	−	0.456338i	$-0.150839\pi$
$659$	45.6844			1.77961			0.889807	+	0.456338i	$0.150839\pi$
$660$		0			0
$661$	−21.8518			−0.849935			−0.424968	−	0.905209i	$-0.639715\pi$
$661$	−21.8518			−0.849935			−0.424968	+	0.905209i	$0.639715\pi$
$662$	−9.27823	−	9.27823i	−0.360609	−	0.360609i
$663$	−5.99748	+	7.36192i	−0.232923	+	0.285913i
$664$			23.7714i			0.922510i
$665$		0			0
$666$	1.66213	+	8.05215i	0.0644062	+	0.312014i
$667$	24.6714	−	24.6714i	0.955279	−	0.955279i
$668$	8.94308	−	8.94308i	0.346018	−	0.346018i
$669$	3.03220	+	29.6886i	0.117232	+	1.14783i
$670$		0			0
$671$			12.8755i			0.497051i
$672$	−5.15197	−	4.19712i	−0.198742	−	0.161907i
$673$	−12.1963	−	12.1963i	−0.470132	−	0.470132i	0.431825	−	0.901957i	$-0.357870\pi$
$673$	−12.1963	−	12.1963i	−0.470132	−	0.470132i	−0.901957	+	0.431825i	$0.857870\pi$
$674$	8.74408			0.336809
$675$		0			0
$676$	5.80698			0.223345
$677$	30.0858	+	30.0858i	1.15629	+	1.15629i	0.985267	+	0.171025i	$0.0547080\pi$
$677$	30.0858	+	30.0858i	1.15629	+	1.15629i	0.171025	+	0.985267i	$0.445292\pi$
$678$	0.517437	+	0.421536i	0.0198721	+	0.0161890i
$679$		−	4.33195i		−	0.166245i
$680$		0			0
$681$	1.03867	+	10.1697i	0.0398018	+	0.389703i
$682$	−7.10027	+	7.10027i	−0.271883	+	0.271883i
$683$	−1.48486	+	1.48486i	−0.0568166	+	0.0568166i	−0.734944	−	0.678128i	$-0.762792\pi$
$683$	−1.48486	+	1.48486i	−0.0568166	+	0.0568166i	0.678128	+	0.734944i	$0.262792\pi$
$684$	0.575084	+	2.78598i	0.0219889	+	0.106525i
$685$		0			0
$686$		−	1.13215i		−	0.0432258i
$687$	−29.8330	+	36.6201i	−1.13820	+	1.39714i
$688$	0.576980	+	0.576980i	0.0219972	+	0.0219972i
$689$	22.7973			0.868507
$690$		0			0
$691$	42.2833			1.60853			0.804267	−	0.594269i	$-0.202558\pi$
$691$	42.2833			1.60853			0.804267	+	0.594269i	$0.202558\pi$
$692$	9.90912	+	9.90912i	0.376688	+	0.376688i
$693$	8.57627	−	13.0379i	0.325785	−	0.495268i
$694$			32.3395i			1.22759i
$695$		0			0
$696$	−23.2409	+	2.37368i	−0.880943	+	0.0899740i
$697$	1.53799	−	1.53799i	0.0582553	−	0.0582553i
$698$	−9.58647	+	9.58647i	−0.362853	+	0.362853i
$699$	4.79544	−	0.489776i	0.181380	−	0.0185250i
$700$		0			0
$701$			42.8399i			1.61804i	0.587781	+	0.809020i	$0.300002\pi$
$701$			42.8399i			1.61804i	−0.587781	+	0.809020i	$0.699998\pi$
$702$	−23.9598	−	12.4755i	−0.904306	−	0.470856i
$703$	2.25988	+	2.25988i	0.0852332	+	0.0852332i
$704$	−43.8989			−1.65450
$705$		0			0
$706$	−38.9746			−1.46683
$707$	−2.62789	−	2.62789i	−0.0988320	−	0.0988320i
$708$	−1.42821	+	1.75314i	−0.0536756	+	0.0658869i
$709$		−	21.7856i		−	0.818175i	−0.912495	−	0.409087i	$-0.865847\pi$
$709$		−	21.7856i		−	0.818175i	0.912495	−	0.409087i	$-0.134153\pi$
$710$		0			0
$711$	33.7921	−	6.97539i	1.26730	−	0.261598i
$712$	20.5230	−	20.5230i	0.769133	−	0.769133i
$713$	9.59756	−	9.59756i	0.359432	−	0.359432i
$714$	0.237880	+	2.32911i	0.00890244	+	0.0871646i
$715$		0			0
$716$			5.05030i			0.188739i
$717$	1.91949	+	1.56373i	0.0716846	+	0.0583987i
$718$	11.3810	+	11.3810i	0.424735	+	0.424735i
$719$	45.9617			1.71408			0.857041	−	0.515249i	$-0.172301\pi$
$719$	45.9617			1.71408			0.857041	+	0.515249i	$0.172301\pi$
$720$		0			0
$721$	−1.66946			−0.0621740
$722$	13.8151	+	13.8151i	0.514145	+	0.514145i
$723$	39.1196	+	31.8693i	1.45487	+	1.18523i
$724$		−	10.1898i		−	0.378699i
$725$		0			0
$726$	−3.19980	−	31.3295i	−0.118756	−	1.16275i
$727$	4.37251	−	4.37251i	0.162168	−	0.162168i	−0.621359	−	0.783526i	$-0.713419\pi$
$727$	4.37251	−	4.37251i	0.162168	−	0.162168i	0.783526	+	0.621359i	$0.213419\pi$
$728$	9.99228	−	9.99228i	0.370338	−	0.370338i
$729$	−15.4826	−	22.1199i	−0.573428	−	0.819256i
$730$		0			0
$731$			0.475760i			0.0175966i
$732$	−1.94476	+	2.38720i	−0.0718805	+	0.0882336i
$733$	32.0267	+	32.0267i	1.18293	+	1.18293i	0.978981	+	0.203952i	$0.0653787\pi$
$733$	32.0267	+	32.0267i	1.18293	+	1.18293i	0.203952	+	0.978981i	$0.434621\pi$
$734$	−26.7423			−0.987078
$735$		0			0
$736$	30.5423			1.12580
$737$	41.2059	+	41.2059i	1.51784	+	1.51784i
$738$	5.16940	+	3.40041i	0.190288	+	0.125171i
$739$		−	19.8100i		−	0.728722i	−0.931258	−	0.364361i	$-0.881287\pi$
$739$		−	19.8100i		−	0.728722i	0.931258	−	0.364361i	$-0.118713\pi$
$740$		0			0
$741$	−10.4460	+	1.06689i	−0.383744	+	0.0391932i
$742$	3.97452	−	3.97452i	0.145909	−	0.145909i
$743$	−14.6828	+	14.6828i	−0.538660	+	0.538660i	−0.923135	−	0.384475i	$-0.874382\pi$
$743$	−14.6828	+	14.6828i	−0.538660	+	0.538660i	0.384475	+	0.923135i	$0.374382\pi$
$744$	−9.04108	+	0.923399i	−0.331462	+	0.0338535i
$745$		0			0
$746$		−	7.33110i		−	0.268411i
$747$	−19.3601	−	12.7350i	−0.708350	−	0.465950i
$748$	−3.15418	−	3.15418i	−0.115328	−	0.115328i
$749$	−1.95174			−0.0713151
$750$		0			0
$751$	−26.6832			−0.973682			−0.486841	−	0.873491i	$-0.661851\pi$
$751$	−26.6832			−0.973682			−0.486841	+	0.873491i	$0.661851\pi$
$752$	−6.95371	−	6.95371i	−0.253576	−	0.253576i
$753$	13.5627	−	16.6483i	0.494252	−	0.606696i
$754$		−	22.7849i		−	0.829777i
$755$		0			0
$756$	3.55940	−	1.12192i	0.129454	−	0.0408039i
$757$	4.11078	−	4.11078i	0.149409	−	0.149409i	−0.628445	−	0.777854i	$-0.716308\pi$
$757$	4.11078	−	4.11078i	0.149409	−	0.149409i	0.777854	+	0.628445i	$0.216308\pi$
$758$	10.1275	−	10.1275i	0.367846	−	0.367846i
$759$	7.28774	+	71.3549i	0.264528	+	2.59002i
$760$		0			0
$761$		−	22.2859i		−	0.807862i	−0.914789	−	0.403931i	$-0.867644\pi$
$761$		−	22.2859i		−	0.807862i	0.914789	−	0.403931i	$-0.132356\pi$
$762$	9.80288	+	7.98603i	0.355121	+	0.289303i
$763$	4.19672	+	4.19672i	0.151931	+	0.151931i
$764$	11.2367			0.406530
$765$		0			0
$766$	28.8464			1.04226
$767$	−5.90201	−	5.90201i	−0.213109	−	0.213109i
$768$	−19.8048	−	16.1342i	−0.714645	−	0.582194i
$769$			37.7021i			1.35957i	0.733410	+	0.679786i	$0.237927\pi$
$769$			37.7021i			1.35957i	−0.733410	+	0.679786i	$0.762073\pi$
$770$		0			0
$771$	−3.45239	−	33.8026i	−0.124335	−	1.21737i
$772$	−6.47095	+	6.47095i	−0.232895	+	0.232895i
$773$	20.5564	−	20.5564i	0.739362	−	0.739362i	−0.233093	−	0.972455i	$-0.574884\pi$
$773$	20.5564	−	20.5564i	0.739362	−	0.739362i	0.972455	+	0.233093i	$0.0748845\pi$
$774$	−1.32549	+	0.273609i	−0.0476438	+	0.00983467i
$775$		0			0
$776$		−	13.3314i		−	0.478568i
$777$	2.64820	−	3.25067i	0.0950035	−	0.116617i
$778$	14.1870	+	14.1870i	0.508630	+	0.508630i
$779$	2.40517			0.0861741
$780$		0			0
$781$	47.1479			1.68708
$782$	−7.60888	−	7.60888i	−0.272093	−	0.272093i
$783$	10.5176	−	20.1997i	0.375868	−	0.721877i
$784$		−	2.04769i		−	0.0731318i
$785$		0			0
$786$	26.6838	−	2.72531i	0.951779	−	0.0972088i
$787$	−9.45113	+	9.45113i	−0.336896	+	0.336896i	−0.855198	−	0.518302i	$-0.826564\pi$
$787$	−9.45113	+	9.45113i	−0.336896	+	0.336896i	0.518302	+	0.855198i	$0.326564\pi$
$788$	2.00376	−	2.00376i	0.0713809	−	0.0713809i
$789$	−29.9514	+	3.05905i	−1.06630	+	0.108905i
$790$		0			0
$791$		−	0.340350i		−	0.0121015i
$792$	26.3930	−	40.1234i	0.937836	−	1.42572i
$793$	−8.03662	−	8.03662i	−0.285389	−	0.285389i
$794$	−7.09346			−0.251737
$795$		0			0
$796$	−10.3655			−0.367394
$797$	5.16008	+	5.16008i	0.182779	+	0.182779i	0.792566	−	0.609786i	$-0.208745\pi$
$797$	5.16008	+	5.16008i	0.182779	+	0.182779i	−0.609786	+	0.792566i	$0.708745\pi$
$798$	−1.63518	+	2.00718i	−0.0578846	+	0.0710535i
$799$		−	5.73382i		−	0.202848i
$800$		0			0
$801$	5.71977	+	27.7093i	0.202098	+	0.979060i
$802$	27.6015	−	27.6015i	0.974641	−	0.974641i
$803$	6.96304	−	6.96304i	0.245720	−	0.245720i
$804$	1.41596	+	13.8638i	0.0499371	+	0.488939i
$805$		0			0
$806$		−	8.86371i		−	0.312211i
$807$	25.7203	+	20.9533i	0.905396	+	0.737592i
$808$	−8.08721	−	8.08721i	−0.284507	−	0.284507i
$809$	−12.8615			−0.452187			−0.226093	−	0.974106i	$-0.572595\pi$
$809$	−12.8615			−0.452187			−0.226093	+	0.974106i	$0.572595\pi$
$810$		0			0
$811$	0.485057			0.0170327			0.00851633	−	0.999964i	$-0.497289\pi$
$811$	0.485057			0.0170327			0.00851633	+	0.999964i	$0.497289\pi$
$812$	2.22588	+	2.22588i	0.0781131	+	0.0781131i
$813$	24.7929	+	20.1978i	0.869524	+	0.708368i
$814$		−	14.2565i		−	0.499691i
$815$		0			0
$816$	0.430246	+	4.21258i	0.0150616	+	0.147470i
$817$	−0.372008	+	0.372008i	−0.0130149	+	0.0130149i
$818$	−15.6638	+	15.6638i	−0.547673	+	0.547673i
$819$	2.78485	+	13.4911i	0.0973105	+	0.471419i
$820$		0			0
$821$			28.1679i			0.983066i	0.870859	+	0.491533i	$0.163563\pi$
$821$			28.1679i			0.983066i	−0.870859	+	0.491533i	$0.836437\pi$
$822$	−17.5562	+	21.5502i	−0.612341	+	0.751651i
$823$	−7.62024	−	7.62024i	−0.265625	−	0.265625i	0.561710	−	0.827334i	$-0.310144\pi$
$823$	−7.62024	−	7.62024i	−0.265625	−	0.265625i	−0.827334	+	0.561710i	$0.810144\pi$
$824$	−5.13769			−0.178980
$825$		0			0
$826$	−2.05794			−0.0716047
$827$	24.0314	+	24.0314i	0.835652	+	0.835652i	0.988283	−	0.152631i	$-0.0487746\pi$
$827$	24.0314	+	24.0314i	0.835652	+	0.835652i	−0.152631	+	0.988283i	$0.548775\pi$
$828$	−9.42655	+	14.3305i	−0.327595	+	0.498019i
$829$			18.7082i			0.649763i	0.945755	+	0.324881i	$0.105324\pi$
$829$			18.7082i			0.649763i	−0.945755	+	0.324881i	$0.894676\pi$
$830$		0			0
$831$	18.6678	−	1.90661i	0.647580	−	0.0661397i
$832$	27.4009	−	27.4009i	0.949954	−	0.949954i
$833$	0.844232	−	0.844232i	0.0292509	−	0.0292509i
$834$	30.8738	−	3.15326i	1.06907	−	0.109188i
$835$		0			0
$836$		−	4.93265i		−	0.170599i
$837$	4.09152	−	7.85801i	0.141424	−	0.271612i
$838$	13.6261	+	13.6261i	0.470706	+	0.470706i
$839$	1.64172			0.0566785			0.0283392	−	0.999598i	$-0.490978\pi$
$839$	1.64172			0.0566785			0.0283392	+	0.999598i	$0.490978\pi$
$840$		0			0
$841$	−9.79087			−0.337616
$842$	17.4099	+	17.4099i	0.599986	+	0.599986i
$843$	−22.3876	+	27.4809i	−0.771070	+	0.946491i
$844$		−	8.60763i		−	0.296287i
$845$		0			0
$846$	15.9747	−	3.29751i	0.549222	−	0.113371i
$847$	−11.3560	+	11.3560i	−0.390197	+	0.390197i
$848$	7.18859	−	7.18859i	0.246857	−	0.246857i
$849$	−2.05209	−	20.0922i	−0.0704276	−	0.689563i
$850$		0			0
$851$			19.2708i			0.660595i
$852$	8.74156	+	7.12142i	0.299481	+	0.243976i
$853$	−3.77850	−	3.77850i	−0.129373	−	0.129373i	0.639455	−	0.768828i	$-0.279160\pi$
$853$	−3.77850	−	3.77850i	−0.129373	−	0.129373i	−0.768828	+	0.639455i	$0.779160\pi$
$854$	−2.80224			−0.0958907
$855$		0			0
$856$	−6.00639			−0.205294
$857$	−8.38908	−	8.38908i	−0.286566	−	0.286566i	0.549155	−	0.835721i	$-0.314950\pi$
$857$	−8.38908	−	8.38908i	−0.286566	−	0.286566i	−0.835721	+	0.549155i	$0.814950\pi$
$858$	36.3147	+	29.5842i	1.23976	+	1.00999i
$859$			12.4393i			0.424424i	0.977224	+	0.212212i	$0.0680668\pi$
$859$			12.4393i			0.424424i	−0.977224	+	0.212212i	$0.931933\pi$
$860$		0			0
$861$	−0.320602	−	3.13905i	−0.0109261	−	0.106978i
$862$	8.63896	−	8.63896i	0.294244	−	0.294244i
$863$	−8.43057	+	8.43057i	−0.286980	+	0.286980i	−0.835885	−	0.548905i	$-0.815045\pi$
$863$	−8.43057	+	8.43057i	−0.286980	+	0.286980i	0.548905	+	0.835885i	$0.315045\pi$
$864$	19.0134	−	5.99303i	0.646851	−	0.203887i
$865$		0			0
$866$		−	0.747600i		−	0.0254045i
$867$	17.0380	−	20.9142i	0.578642	−	0.710285i
$868$	0.865904	+	0.865904i	0.0293907	+	0.0293907i
$869$	−59.8298			−2.02959
$870$		0			0
$871$	−51.4399			−1.74298
$872$	12.9152	+	12.9152i	0.437364	+	0.437364i
$873$	10.8574	+	7.14199i	0.367469	+	0.241720i
$874$		−	11.8991i		−	0.402493i
$875$		0			0
$876$	2.34273	−	0.239271i	0.0791534	−	0.00808423i
$877$	2.56130	−	2.56130i	0.0864889	−	0.0864889i	−0.662539	−	0.749028i	$-0.730521\pi$
$877$	2.56130	−	2.56130i	0.0864889	−	0.0864889i	0.749028	+	0.662539i	$0.230521\pi$
$878$	7.55451	−	7.55451i	0.254953	−	0.254953i
$879$	48.0600	−	4.90854i	1.62102	−	0.165561i
$880$		0			0
$881$			16.9744i			0.571882i	0.958247	+	0.285941i	$0.0923061\pi$
$881$			16.9744i			0.571882i	−0.958247	+	0.285941i	$0.907694\pi$
$882$	2.83759	+	1.86656i	0.0955466	+	0.0628502i
$883$	−21.2023	−	21.2023i	−0.713513	−	0.713513i	0.253756	−	0.967268i	$-0.418334\pi$
$883$	−21.2023	−	21.2023i	−0.713513	−	0.713513i	−0.967268	+	0.253756i	$0.918334\pi$
$884$	3.93756			0.132435
$885$		0			0
$886$	27.0517			0.908818
$887$	−12.5527	−	12.5527i	−0.421480	−	0.421480i	0.464233	−	0.885713i	$-0.346330\pi$
$887$	−12.5527	−	12.5527i	−0.421480	−	0.421480i	−0.885713	+	0.464233i	$0.846330\pi$
$888$	8.14969	−	10.0038i	0.273486	−	0.335705i
$889$		−	6.44795i		−	0.216257i
$890$		0			0
$891$	18.5382	+	42.9905i	0.621051	+	1.44024i
$892$	8.75044	−	8.75044i	0.292986	−	0.292986i
$893$	4.48340	−	4.48340i	0.150031	−	0.150031i
$894$	−1.85414	−	18.1540i	−0.0620116	−	0.607161i
$895$		0			0
$896$		−	1.88104i		−	0.0628410i
$897$	−49.0873	−	39.9895i	−1.63898	−	1.33521i
$898$	9.25783	+	9.25783i	0.308938	+	0.308938i
$899$	7.47267			0.249227
$900$		0			0
$901$	5.92750			0.197474
$902$	−7.58653	−	7.58653i	−0.252604	−	0.252604i
$903$	0.535104	+	0.435929i	0.0178071	+	0.0145068i
$904$		−	1.04741i		−	0.0348364i
$905$		0			0
$906$	−3.35273	−	32.8269i	−0.111387	−	1.09060i
$907$	8.60959	−	8.60959i	0.285877	−	0.285877i	−0.549571	−	0.835447i	$-0.685209\pi$
$907$	8.60959	−	8.60959i	0.285877	−	0.285877i	0.835447	+	0.549571i	$0.185209\pi$
$908$	2.99742	−	2.99742i	0.0994728	−	0.0994728i
$909$	10.9190	−	2.25391i	0.362160	−	0.0747574i
$910$		0			0
$911$		−	23.0151i		−	0.762525i	−0.924467	−	0.381263i	$-0.875489\pi$
$911$		−	23.0151i		−	0.762525i	0.924467	−	0.381263i	$-0.124511\pi$
$912$	−2.95749	+	3.63033i	−0.0979323	+	0.120212i
$913$	28.4126	+	28.4126i	0.940320	+	0.940320i
$914$	28.5658			0.944872
$915$		0			0
$916$	19.5865			0.647155
$917$	−9.67209	−	9.67209i	−0.319400	−	0.319400i
$918$	−6.22977	−	3.24373i	−0.205613	−	0.107059i
$919$		−	22.0977i		−	0.728935i	−0.931216	−	0.364468i	$-0.881251\pi$
$919$		−	22.0977i		−	0.728935i	0.931216	−	0.364468i	$-0.118749\pi$
$920$		0			0
$921$	32.4090	−	3.31005i	1.06791	−	0.109070i
$922$	−10.4529	+	10.4529i	−0.344248	+	0.344248i
$923$	−29.4288	+	29.4288i	−0.968662	+	0.968662i
$924$	−6.43773	+	0.657509i	−0.211786	+	0.0216305i
$925$		0			0
$926$		−	27.8472i		−	0.915117i
$927$	2.75240	−	4.18428i	0.0904008	−	0.137430i
$928$	11.8901	+	11.8901i	0.390312	+	0.390312i
$929$	51.7684			1.69846			0.849232	−	0.528019i	$-0.177065\pi$
$929$	51.7684			1.69846			0.849232	+	0.528019i	$0.177065\pi$
$930$		0			0
$931$	1.32025			0.0432693
$932$	−1.41341	−	1.41341i	−0.0462979	−	0.0462979i
$933$	−26.0418	+	31.9663i	−0.852569	+	1.04653i
$934$			15.0601i			0.492781i
$935$		0			0
$936$	8.57024	+	41.5183i	0.280127	+	1.35707i
$937$	−32.8470	+	32.8470i	−1.07307	+	1.07307i	−0.0759541	+	0.997111i	$0.524200\pi$
$937$	−32.8470	+	32.8470i	−1.07307	+	1.07307i	−0.997111	+	0.0759541i	$0.975800\pi$
$938$	−8.96814	+	8.96814i	−0.292820	+	0.292820i
$939$	4.71262	+	46.1417i	0.153790	+	1.50578i
$940$		0			0
$941$		−	15.0930i		−	0.492018i	−0.969268	−	0.246009i	$-0.920881\pi$
$941$		−	15.0930i		−	0.492018i	0.969268	−	0.246009i	$-0.0791193\pi$
$942$	−14.6342	−	11.9219i	−0.476808	−	0.388437i
$943$	10.2549	+	10.2549i	0.333944	+	0.333944i
$944$	−3.72212			−0.121145
$945$		0			0
$946$	2.34682			0.0763016
$947$	−27.9272	−	27.9272i	−0.907512	−	0.907512i	0.0885587	−	0.996071i	$-0.471774\pi$
$947$	−27.9272	−	27.9272i	−0.907512	−	0.907512i	−0.996071	+	0.0885587i	$0.971774\pi$
$948$	−11.0929	−	9.03695i	−0.360280	−	0.293506i
$949$			8.69240i			0.282167i
$950$		0			0
$951$	−2.91014	−	28.4934i	−0.0943678	−	0.923963i
$952$	2.59808	−	2.59808i	0.0842043	−	0.0842043i
$953$	11.2553	−	11.2553i	0.364595	−	0.364595i	−0.500906	−	0.865501i	$-0.667000\pi$
$953$	11.2553	−	11.2553i	0.364595	−	0.364595i	0.865501	+	0.500906i	$0.167000\pi$
$954$	3.40889	+	16.5143i	0.110367	+	0.534670i
$955$		0			0
$956$		−	1.02665i		−	0.0332042i
$957$	−24.9414	+	30.6156i	−0.806240	+	0.989662i
$958$	−31.1166	−	31.1166i	−1.00533	−	1.00533i
$959$	14.1749			0.457732
$960$		0			0
$961$	−28.0930			−0.906226
$962$	8.89866	+	8.89866i	0.286904	+	0.286904i
$963$	3.21779	−	4.89178i	0.103692	−	0.157635i
$964$		−	20.9233i		−	0.673896i
$965$		0			0
$966$	−15.5298	+	1.58612i	−0.499664	+	0.0510325i
$967$	−21.6914	+	21.6914i	−0.697548	+	0.697548i	−0.963881	−	0.266333i	$-0.914188\pi$
$967$	−21.6914	+	21.6914i	−0.697548	+	0.697548i	0.266333	+	0.963881i	$0.414188\pi$
$968$	−34.9476	+	34.9476i	−1.12326	+	1.12326i
$969$	−2.71606	+	0.277401i	−0.0872524	+	0.00891141i
$970$		0			0
$971$			57.5902i			1.84816i	0.382201	+	0.924079i	$0.375166\pi$
$971$			57.5902i			1.84816i	−0.382201	+	0.924079i	$0.624834\pi$
$972$	−3.05636	+	10.7708i	−0.0980328	+	0.345475i
$973$	−11.1908	−	11.1908i	−0.358762	−	0.358762i
$974$	−38.3544			−1.22895
$975$		0			0
$976$	−5.06832			−0.162233
$977$	−7.49722	−	7.49722i	−0.239857	−	0.239857i	0.576934	−	0.816791i	$-0.304249\pi$
$977$	−7.49722	−	7.49722i	−0.239857	−	0.239857i	−0.816791	+	0.576934i	$0.804249\pi$
$978$	15.3781	−	18.8766i	0.491736	−	0.603608i
$979$		−	49.0600i		−	1.56796i
$980$		0			0
$981$	−17.4375	+	3.59947i	−0.556738	+	0.114922i
$982$	20.5304	−	20.5304i	0.655152	−	0.655152i
$983$	−1.92238	+	1.92238i	−0.0613143	+	0.0613143i	−0.737099	−	0.675785i	$-0.763805\pi$
$983$	−1.92238	+	1.92238i	−0.0613143	+	0.0613143i	0.675785	+	0.737099i	$0.263805\pi$
$984$	−0.986639	−	9.66026i	−0.0314529	−	0.307958i
$985$		0			0
$986$		−	5.92428i		−	0.188668i
$987$	−6.44903	−	5.25377i	−0.205275	−	0.167229i
$988$	3.07887	+	3.07887i	0.0979519	+	0.0979519i
$989$	−3.17224			−0.100871
$990$		0			0
$991$	−31.7442			−1.00839			−0.504194	−	0.863591i	$-0.668210\pi$
$991$	−31.7442			−1.00839			−0.504194	+	0.863591i	$0.668210\pi$
$992$	4.62545	+	4.62545i	0.146858	+	0.146858i
$993$	−15.5633	−	12.6788i	−0.493886	−	0.402350i
$994$			10.2614i			0.325471i
$995$		0			0
$996$	0.976344	+	9.55947i	0.0309366	+	0.302903i
$997$	−12.7289	+	12.7289i	−0.403128	+	0.403128i	−0.879334	−	0.476206i	$-0.842012\pi$
$997$	−12.7289	+	12.7289i	−0.403128	+	0.403128i	0.476206	+	0.879334i	$0.342012\pi$
$998$	23.3007	−	23.3007i	0.737571	−	0.737571i
$999$	3.78134	+	11.9966i	0.119636	+	0.379557i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.j.b.218.9		24
3.2	odd	2	inner	525.2.j.b.218.4		24
5.2	odd	4	inner	525.2.j.b.407.4		24
5.3	odd	4		105.2.j.a.92.9	yes	24
5.4	even	2		105.2.j.a.8.4	✓	24
15.2	even	4	inner	525.2.j.b.407.9		24
15.8	even	4		105.2.j.a.92.4	yes	24
15.14	odd	2		105.2.j.a.8.9	yes	24
35.3	even	12		735.2.y.g.422.9		48
35.4	even	6		735.2.y.j.128.9		48
35.9	even	6		735.2.y.j.263.4		48
35.13	even	4		735.2.j.h.197.9		24
35.18	odd	12		735.2.y.j.422.9		48
35.19	odd	6		735.2.y.g.263.4		48
35.23	odd	12		735.2.y.j.557.4		48
35.24	odd	6		735.2.y.g.128.9		48
35.33	even	12		735.2.y.g.557.4		48
35.34	odd	2		735.2.j.h.638.4		24
105.23	even	12		735.2.y.j.557.9		48
105.38	odd	12		735.2.y.g.422.4		48
105.44	odd	6		735.2.y.j.263.9		48
105.53	even	12		735.2.y.j.422.4		48
105.59	even	6		735.2.y.g.128.4		48
105.68	odd	12		735.2.y.g.557.9		48
105.74	odd	6		735.2.y.j.128.4		48
105.83	odd	4		735.2.j.h.197.4		24
105.89	even	6		735.2.y.g.263.9		48
105.104	even	2		735.2.j.h.638.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.2.j.a.8.4	✓	24	5.4	even	2
105.2.j.a.8.9	yes	24	15.14	odd	2
105.2.j.a.92.4	yes	24	15.8	even	4
105.2.j.a.92.9	yes	24	5.3	odd	4
525.2.j.b.218.4		24	3.2	odd	2	inner
525.2.j.b.218.9		24	1.1	even	1	trivial
525.2.j.b.407.4		24	5.2	odd	4	inner
525.2.j.b.407.9		24	15.2	even	4	inner
735.2.j.h.197.4		24	105.83	odd	4
735.2.j.h.197.9		24	35.13	even	4
735.2.j.h.638.4		24	35.34	odd	2
735.2.j.h.638.9		24	105.104	even	2
735.2.y.g.128.4		48	105.59	even	6
735.2.y.g.128.9		48	35.24	odd	6
735.2.y.g.263.4		48	35.19	odd	6
735.2.y.g.263.9		48	105.89	even	6
735.2.y.g.422.4		48	105.38	odd	12
735.2.y.g.422.9		48	35.3	even	12
735.2.y.g.557.4		48	35.33	even	12
735.2.y.g.557.9		48	105.68	odd	12
735.2.y.j.128.4		48	105.74	odd	6
735.2.y.j.128.9		48	35.4	even	6
735.2.y.j.263.4		48	35.9	even	6
735.2.y.j.263.9		48	105.44	odd	6
735.2.y.j.422.4		48	105.53	even	12
735.2.y.j.422.9		48	35.18	odd	12
735.2.y.j.557.4		48	35.23	odd	12
735.2.y.j.557.9		48	105.23	even	12

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.800553 + 0.800553i) q^{2} +(1.34285 + 1.09397i) q^{3} -0.718229i q^{4} +(0.199242 + 1.95080i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.17609 - 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} +O(q^{10})\)	\(q+(0.800553 + 0.800553i) q^{2} +(1.34285 + 1.09397i) q^{3} -0.718229i q^{4} +(0.199242 + 1.95080i) q^{6} +(0.707107 - 0.707107i) q^{7} +(2.17609 - 2.17609i) q^{8} +(0.606476 + 2.93806i) q^{9} -5.20191i q^{11} +(0.785718 - 0.964471i) q^{12} +(3.24693 + 3.24693i) q^{13} +1.13215 q^{14} +2.04769 q^{16} +(0.844232 + 0.844232i) q^{17} +(-1.86656 + 2.83759i) q^{18} +1.32025i q^{19} +(1.72309 - 0.175985i) q^{21} +(4.16440 - 4.16440i) q^{22} +(-5.62910 + 5.62910i) q^{23} +(5.30272 - 0.541586i) q^{24} +5.19868i q^{26} +(-2.39973 + 4.60883i) q^{27} +(-0.507864 - 0.507864i) q^{28} -4.38282 q^{29} -1.70499 q^{31} +(-2.71289 - 2.71289i) q^{32} +(5.69071 - 6.98536i) q^{33} +1.35170i q^{34} +(2.11020 - 0.435588i) q^{36} +(1.71171 - 1.71171i) q^{37} +(-1.05693 + 1.05693i) q^{38} +(0.808099 + 7.91217i) q^{39} -1.82176i q^{41} +(1.52031 + 1.23854i) q^{42} +(0.281771 + 0.281771i) q^{43} -3.73616 q^{44} -9.01279 q^{46} +(-3.39588 - 3.39588i) q^{47} +(2.74973 + 2.24010i) q^{48} -1.00000i q^{49} +(0.210113 + 2.05723i) q^{51} +(2.33204 - 2.33204i) q^{52} +(3.51059 - 3.51059i) q^{53} +(-5.61073 + 1.76850i) q^{54} -3.07745i q^{56} +(-1.44431 + 1.77289i) q^{57} +(-3.50868 - 3.50868i) q^{58} -1.81772 q^{59} -2.47514 q^{61} +(-1.36494 - 1.36494i) q^{62} +(2.50636 + 1.64868i) q^{63} -8.43900i q^{64} +(10.1479 - 1.03644i) q^{66} +(-7.92132 + 7.92132i) q^{67} +(0.606352 - 0.606352i) q^{68} +(-13.7171 + 1.40098i) q^{69} +9.06358i q^{71} +(7.71322 + 5.07373i) q^{72} +(1.33856 + 1.33856i) q^{73} +2.74064 q^{74} +0.948239 q^{76} +(-3.67830 - 3.67830i) q^{77} +(-5.68718 + 6.98104i) q^{78} -11.5015i q^{79} +(-8.26437 + 3.56372i) q^{81} +(1.45841 - 1.45841i) q^{82} +(-5.46196 + 5.46196i) q^{83} +(-0.126398 - 1.23757i) q^{84} +0.451146i q^{86} +(-5.88546 - 4.79466i) q^{87} +(-11.3198 - 11.3198i) q^{88} +9.43116 q^{89} +4.59186 q^{91} +(4.04298 + 4.04298i) q^{92} +(-2.28954 - 1.86520i) q^{93} -5.43717i q^{94} +(-0.675186 - 6.61080i) q^{96} +(3.06315 - 3.06315i) q^{97} +(0.800553 - 0.800553i) q^{98} +(15.2835 - 3.15483i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{3}+O(q^{10}) \) 24 * q + 4 * q^3	\( 24 q + 4 q^{3} - 16 q^{12} + 8 q^{13} - 16 q^{16} + 20 q^{18} + 4 q^{21} - 8 q^{22} + 16 q^{27} - 28 q^{33} + 16 q^{36} + 16 q^{37} + 20 q^{42} + 40 q^{43} - 64 q^{46} - 16 q^{48} - 20 q^{51} - 4 q^{57} - 40 q^{58} + 32 q^{61} + 8 q^{63} - 16 q^{66} - 24 q^{67} + 8 q^{72} - 32 q^{73} + 32 q^{76} - 60 q^{78} + 52 q^{81} + 80 q^{82} - 4 q^{87} - 96 q^{88} - 24 q^{91} + 76 q^{93} - 96 q^{96} - 24 q^{97}+O(q^{100}) \) 24 * q + 4 * q^3 - 16 * q^12 + 8 * q^13 - 16 * q^16 + 20 * q^18 + 4 * q^21 - 8 * q^22 + 16 * q^27 - 28 * q^33 + 16 * q^36 + 16 * q^37 + 20 * q^42 + 40 * q^43 - 64 * q^46 - 16 * q^48 - 20 * q^51 - 4 * q^57 - 40 * q^58 + 32 * q^61 + 8 * q^63 - 16 * q^66 - 24 * q^67 + 8 * q^72 - 32 * q^73 + 32 * q^76 - 60 * q^78 + 52 * q^81 + 80 * q^82 - 4 * q^87 - 96 * q^88 - 24 * q^91 + 76 * q^93 - 96 * q^96 - 24 * q^97

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