LMFDB - Embedded newform 855.2.k.j.406.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [855,2,Mod(406,855)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(855, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("855.406");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 855 = 3^{2} \cdot 5 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	855.k (of order $3$, 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:	$6.82720937282$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 3 x^{11} + 13 x^{10} - 10 x^{9} + 44 x^{8} - 20 x^{7} + 119 x^{6} + 13 x^{5} + 83 x^{4} + 14 x^{3} + 46 x^{2} + 12 x + 4 $ x^12 - 3x^11 + 13x^10 - 10x^9 + 44x^8 - 20x^7 + 119x^6 + 13x^5 + 83x^4 + 14x^3 + 46x^2 + 12*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			406.3
Root			$-0.156312 - 0.270740i$ of defining polynomial
Character	$\chi$	$=$	855.406
Dual form			855.2.k.j.676.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.656312 - 1.13677i) q^{2} +(0.138510 - 0.239907i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.11486 q^{7} -2.98887 q^{8} +O(q^{10})$	\(q+(-0.656312 - 1.13677i) q^{2} +(0.138510 - 0.239907i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.11486 q^{7} -2.98887 q^{8} +(-0.656312 + 1.13677i) q^{10} +0.692973 q^{11} +(2.07262 - 3.58988i) q^{13} +(-2.04432 - 3.54086i) q^{14} +(1.68461 + 2.91783i) q^{16} +(1.40392 + 2.43165i) q^{17} +(-1.62820 - 4.04339i) q^{19} -0.277020 q^{20} +(-0.454806 - 0.787748i) q^{22} +(1.51519 - 2.62438i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.44113 q^{26} +(0.431440 - 0.747275i) q^{28} +(1.93613 - 3.35348i) q^{29} +0.374753 q^{31} +(-0.777612 + 1.34686i) q^{32} +(1.84281 - 3.19185i) q^{34} +(-1.55743 - 2.69755i) q^{35} -1.34678 q^{37} +(-3.52778 + 4.50460i) q^{38} +(1.49443 + 2.58844i) q^{40} +(-4.77223 - 8.26575i) q^{41} +(2.32486 + 4.02677i) q^{43} +(0.0959838 - 0.166249i) q^{44} -3.97774 q^{46} +(0.0650711 - 0.112706i) q^{47} +2.70235 q^{49} +1.31262 q^{50} +(-0.574157 - 0.994469i) q^{52} +(0.442770 - 0.766900i) q^{53} +(-0.346487 - 0.600132i) q^{55} -9.30991 q^{56} -5.08282 q^{58} +(0.719490 + 1.24619i) q^{59} +(-1.63574 + 2.83319i) q^{61} +(-0.245955 - 0.426007i) q^{62} +8.77986 q^{64} -4.14523 q^{65} +(-5.44562 + 9.43209i) q^{67} +0.777826 q^{68} +(-2.04432 + 3.54086i) q^{70} +(-5.75724 - 9.97184i) q^{71} +(-2.37964 - 4.12166i) q^{73} +(0.883908 + 1.53097i) q^{74} +(-1.19556 - 0.169435i) q^{76} +2.15851 q^{77} +(-5.37760 - 9.31428i) q^{79} +(1.68461 - 2.91783i) q^{80} +(-6.26414 + 10.8498i) q^{82} +0.386145 q^{83} +(1.40392 - 2.43165i) q^{85} +(3.05166 - 5.28564i) q^{86} -2.07121 q^{88} +(-3.37096 + 5.83867i) q^{89} +(6.45591 - 11.1820i) q^{91} +(-0.419737 - 0.727006i) q^{92} -0.170828 q^{94} +(-2.68758 + 3.43175i) q^{95} +(2.16484 + 3.74962i) q^{97} +(-1.77359 - 3.07194i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) $ 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8	$ 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} - 3 q^{10} - 8 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 6 q^{19} + 10 q^{20} + 2 q^{23} - 6 q^{25} + 40 q^{26} - 26 q^{28} - 4 q^{29} + 24 q^{31} - 15 q^{32} + 7 q^{34} - 2 q^{35} + 29 q^{38} - 6 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 48 q^{46} - 6 q^{47} + 32 q^{49} + 6 q^{50} - 20 q^{52} - 26 q^{53} + 44 q^{56} - 20 q^{58} - 16 q^{59} + 20 q^{61} + 25 q^{62} + 28 q^{64} + 16 q^{65} - 12 q^{67} - 54 q^{68} - 10 q^{70} + 8 q^{71} - 4 q^{73} + 16 q^{74} - 66 q^{76} - 48 q^{77} - 12 q^{79} - 3 q^{80} + 26 q^{82} + 44 q^{83} - 4 q^{85} + 44 q^{86} - 32 q^{88} + 8 q^{89} + 2 q^{91} - 36 q^{92} - 14 q^{94} + 6 q^{95} + 30 q^{97} - 49 q^{98}+O(q^{100}) $ 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 - 3 * q^10 - 8 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 6 * q^19 + 10 * q^20 + 2 * q^23 - 6 * q^25 + 40 * q^26 - 26 * q^28 - 4 * q^29 + 24 * q^31 - 15 * q^32 + 7 * q^34 - 2 * q^35 + 29 * q^38 - 6 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 48 * q^46 - 6 * q^47 + 32 * q^49 + 6 * q^50 - 20 * q^52 - 26 * q^53 + 44 * q^56 - 20 * q^58 - 16 * q^59 + 20 * q^61 + 25 * q^62 + 28 * q^64 + 16 * q^65 - 12 * q^67 - 54 * q^68 - 10 * q^70 + 8 * q^71 - 4 * q^73 + 16 * q^74 - 66 * q^76 - 48 * q^77 - 12 * q^79 - 3 * q^80 + 26 * q^82 + 44 * q^83 - 4 * q^85 + 44 * q^86 - 32 * q^88 + 8 * q^89 + 2 * q^91 - 36 * q^92 - 14 * q^94 + 6 * q^95 + 30 * q^97 - 49 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/855\mathbb{Z}\right)^\times$.

$n$	$172$	$191$	$496$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−0.656312	−	1.13677i	−0.464082	−	0.803814i	0.535077	−	0.844803i	$-0.320283\pi$
$2$	−0.656312	−	1.13677i	−0.464082	−	0.803814i	−0.999160	+	0.0409889i	$0.986949\pi$
$3$		0			0
$3$		0			0
$4$	0.138510	−	0.239907i	0.0692550	−	0.119953i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i
$6$		0			0
$7$	3.11486			1.17731			0.588653	−	0.808386i	$-0.299658\pi$
$7$	3.11486			1.17731			0.588653	+	0.808386i	$0.299658\pi$
$8$	−2.98887			−1.05672
$9$		0			0
$10$	−0.656312	+	1.13677i	−0.207544	+	0.359477i
$11$	0.692973			0.208939			0.104470	−	0.994528i	$-0.466686\pi$
$11$	0.692973			0.208939			0.104470	+	0.994528i	$0.466686\pi$
$12$		0			0
$13$	2.07262	−	3.58988i	0.574841	−	0.995653i	−0.421218	−	0.906959i	$-0.638397\pi$
$13$	2.07262	−	3.58988i	0.574841	−	0.995653i	0.996059	−	0.0886938i	$-0.0282693\pi$
$14$	−2.04432	−	3.54086i	−0.546367	−	0.946336i
$15$		0			0
$16$	1.68461	+	2.91783i	0.421152	+	0.729457i
$17$	1.40392	+	2.43165i	0.340500	+	0.589763i	0.984526	−	0.175241i	$-0.0560704\pi$
$17$	1.40392	+	2.43165i	0.340500	+	0.589763i	−0.644026	+	0.765004i	$0.722737\pi$
$18$		0			0
$19$	−1.62820	−	4.04339i	−0.373534	−	0.927616i
$19$	−1.62820	−	4.04339i	−0.373534	−	0.927616i
$20$	−0.277020			−0.0619436
$21$		0			0
$22$	−0.454806	−	0.787748i	−0.0969650	−	0.167948i
$23$	1.51519	−	2.62438i	0.315938	−	0.547221i	−0.663698	−	0.748000i	$-0.731014\pi$
$23$	1.51519	−	2.62438i	0.315938	−	0.547221i	0.979637	+	0.200779i	$0.0643474\pi$
$24$		0			0
$25$	−0.500000	+	0.866025i	−0.100000	+	0.173205i
$26$	−5.44113			−1.06709
$27$		0			0
$28$	0.431440	−	0.747275i	0.0815344	−	0.141222i
$29$	1.93613	−	3.35348i	0.359530	−	0.622725i	−0.628352	−	0.777929i	$-0.716270\pi$
$29$	1.93613	−	3.35348i	0.359530	−	0.622725i	0.987882	+	0.155204i	$0.0496036\pi$
$30$		0			0
$31$	0.374753			0.0673077			0.0336539	−	0.999434i	$-0.489286\pi$
$31$	0.374753			0.0673077			0.0336539	+	0.999434i	$0.489286\pi$
$32$	−0.777612	+	1.34686i	−0.137464	+	0.238094i
$33$		0			0
$34$	1.84281	−	3.19185i	0.316040	−	0.547397i
$35$	−1.55743	−	2.69755i	−0.263254	−	0.455969i
$36$		0			0
$37$	−1.34678			−0.221410			−0.110705	−	0.993853i	$-0.535311\pi$
$37$	−1.34678			−0.221410			−0.110705	+	0.993853i	$0.535311\pi$
$38$	−3.52778	+	4.50460i	−0.572281	+	0.730742i
$39$		0			0
$40$	1.49443	+	2.58844i	0.236291	+	0.409268i
$41$	−4.77223	−	8.26575i	−0.745297	−	1.29089i	−0.950056	−	0.312080i	$-0.898974\pi$
$41$	−4.77223	−	8.26575i	−0.745297	−	1.29089i	0.204759	−	0.978812i	$-0.434359\pi$
$42$		0			0
$43$	2.32486	+	4.02677i	0.354538	+	0.614077i	0.987039	−	0.160482i	$-0.0513049\pi$
$43$	2.32486	+	4.02677i	0.354538	+	0.614077i	−0.632501	+	0.774560i	$0.717972\pi$
$44$	0.0959838	−	0.166249i	0.0144701	−	0.0250629i
$45$		0			0
$46$	−3.97774			−0.586486
$47$	0.0650711	−	0.112706i	0.00949159	−	0.0164399i	−0.861241	−	0.508197i	$-0.830312\pi$
$47$	0.0650711	−	0.112706i	0.00949159	−	0.0164399i	0.870732	+	0.491758i	$0.163645\pi$
$48$		0			0
$49$	2.70235			0.386051
$50$	1.31262			0.185633
$51$		0			0
$52$	−0.574157	−	0.994469i	−0.0796212	−	0.137908i
$53$	0.442770	−	0.766900i	0.0608191	−	0.105342i	−0.834013	−	0.551745i	$-0.813962\pi$
$53$	0.442770	−	0.766900i	0.0608191	−	0.105342i	0.894832	+	0.446403i	$0.147295\pi$
$54$		0			0
$55$	−0.346487	−	0.600132i	−0.0467202	−	0.0809218i
$56$	−9.30991			−1.24409
$57$		0			0
$58$	−5.08282			−0.667407
$59$	0.719490	+	1.24619i	0.0936697	+	0.162241i	0.909053	−	0.416681i	$-0.136807\pi$
$59$	0.719490	+	1.24619i	0.0936697	+	0.162241i	−0.815383	+	0.578922i	$0.803474\pi$
$60$		0			0
$61$	−1.63574	+	2.83319i	−0.209435	+	0.362753i	−0.951537	−	0.307535i	$-0.900496\pi$
$61$	−1.63574	+	2.83319i	−0.209435	+	0.362753i	0.742101	+	0.670288i	$0.233829\pi$
$62$	−0.245955	−	0.426007i	−0.0312363	−	0.0541029i
$63$		0			0
$64$	8.77986			1.09748
$65$	−4.14523			−0.514153
$66$		0			0
$67$	−5.44562	+	9.43209i	−0.665288	+	1.15231i	0.313919	+	0.949450i	$0.398358\pi$
$67$	−5.44562	+	9.43209i	−0.665288	+	1.15231i	−0.979207	+	0.202864i	$0.934975\pi$
$68$	0.777826			0.0943253
$69$		0			0
$70$	−2.04432	+	3.54086i	−0.244343	+	0.423214i
$71$	−5.75724	−	9.97184i	−0.683259	−	1.18344i	−0.973981	−	0.226632i	$-0.927229\pi$
$71$	−5.75724	−	9.97184i	−0.683259	−	1.18344i	0.290721	−	0.956808i	$-0.406105\pi$
$72$		0			0
$73$	−2.37964	−	4.12166i	−0.278516	−	0.482404i	0.692500	−	0.721418i	$-0.256509\pi$
$73$	−2.37964	−	4.12166i	−0.278516	−	0.482404i	−0.971016	+	0.239014i	$0.923176\pi$
$74$	0.883908	+	1.53097i	0.102752	+	0.177972i
$75$		0			0
$76$	−1.19556	−	0.169435i	−0.137140	−	0.0194355i
$77$	2.15851			0.245986
$78$		0			0
$79$	−5.37760	−	9.31428i	−0.605027	−	1.04794i	−0.992047	−	0.125867i	$-0.959829\pi$
$79$	−5.37760	−	9.31428i	−0.605027	−	1.04794i	0.387020	−	0.922071i	$-0.373504\pi$
$80$	1.68461	−	2.91783i	0.188345	−	0.326223i
$81$		0			0
$82$	−6.26414	+	10.8498i	−0.691759	+	1.19816i
$83$	0.386145			0.0423850			0.0211925	−	0.999775i	$-0.493254\pi$
$83$	0.386145			0.0423850			0.0211925	+	0.999775i	$0.493254\pi$
$84$		0			0
$85$	1.40392	−	2.43165i	0.152276	−	0.263750i
$86$	3.05166	−	5.28564i	0.329069	−	0.569965i
$87$		0			0
$88$	−2.07121			−0.220791
$89$	−3.37096	+	5.83867i	−0.357321	+	0.618898i	−0.987512	−	0.157542i	$-0.949643\pi$
$89$	−3.37096	+	5.83867i	−0.357321	+	0.618898i	0.630191	+	0.776440i	$0.282976\pi$
$90$		0			0
$91$	6.45591	−	11.1820i	0.676763	−	1.17219i
$92$	−0.419737	−	0.727006i	−0.0437606	−	0.0757957i
$93$		0			0
$94$	−0.170828			−0.0176195
$95$	−2.68758	+	3.43175i	−0.275740	+	0.352090i
$96$		0			0
$97$	2.16484	+	3.74962i	0.219807	+	0.380716i	0.954749	−	0.297414i	$-0.0961240\pi$
$97$	2.16484	+	3.74962i	0.219807	+	0.380716i	−0.734942	+	0.678130i	$0.762791\pi$
$98$	−1.77359	−	3.07194i	−0.179159	−	0.310313i
$99$		0			0
$100$	0.138510	+	0.239907i	0.0138510	+	0.0239907i
$101$	0.498699	−	0.863773i	0.0496224	−	0.0859486i	−0.840147	−	0.542358i	$-0.817532\pi$
$101$	0.498699	−	0.863773i	0.0496224	−	0.0859486i	0.889770	+	0.456410i	$0.150865\pi$
$102$		0			0
$103$	−4.52737			−0.446095			−0.223047	−	0.974808i	$-0.571600\pi$
$103$	−4.52737			−0.446095			−0.223047	+	0.974808i	$0.571600\pi$
$104$	−6.19478	+	10.7297i	−0.607448	+	1.05213i
$105$		0			0
$106$	−1.16238			−0.112900
$107$	18.6472			1.80270			0.901348	−	0.433096i	$-0.142579\pi$
$107$	18.6472			1.80270			0.901348	+	0.433096i	$0.142579\pi$
$108$		0			0
$109$	−5.72633	−	9.91830i	−0.548483	−	0.950000i	−0.998379	−	0.0569194i	$-0.981872\pi$
$109$	−5.72633	−	9.91830i	−0.548483	−	0.950000i	0.449896	−	0.893081i	$-0.351461\pi$
$110$	−0.454806	+	0.787748i	−0.0433641	+	0.0751088i
$111$		0			0
$112$	5.24732	+	9.08863i	0.495825	+	0.858795i
$113$	18.2976			1.72130			0.860649	−	0.509199i	$-0.170058\pi$
$113$	18.2976			1.72130			0.860649	+	0.509199i	$0.170058\pi$
$114$		0			0
$115$	−3.03037			−0.282584
$116$	−0.536347	−	0.928980i	−0.0497986	−	0.0862537i
$117$		0			0
$118$	0.944420	−	1.63578i	0.0869409	−	0.150586i
$119$	4.37300	+	7.57427i	0.400873	+	0.694332i
$120$		0			0
$121$	−10.5198			−0.956344
$122$	4.29423			0.388781
$123$		0			0
$124$	0.0519071	−	0.0899058i	0.00466140	−	0.00807378i
$125$	1.00000			0.0894427
$126$		0			0
$127$	−5.94672	+	10.3000i	−0.527686	+	0.913979i	0.471793	+	0.881709i	$0.343607\pi$
$127$	−5.94672	+	10.3000i	−0.527686	+	0.913979i	−0.999479	+	0.0322694i	$0.989727\pi$
$128$	−4.20710	−	7.28691i	−0.371859	−	0.644078i
$129$		0			0
$130$	2.72057	+	4.71216i	0.238609	+	0.413284i
$131$	6.09045	+	10.5490i	0.532125	+	0.921668i	0.999297	+	0.0375009i	$0.0119397\pi$
$131$	6.09045	+	10.5490i	0.532125	+	0.921668i	−0.467172	+	0.884167i	$0.654727\pi$
$132$		0			0
$133$	−5.07161	−	12.5946i	−0.439764	−	1.09209i
$134$	14.2961			1.23499
$135$		0			0
$136$	−4.19612	−	7.26790i	−0.359815	−	0.623217i
$137$	−8.40697	+	14.5613i	−0.718256	+	1.24406i	0.243435	+	0.969917i	$0.421726\pi$
$137$	−8.40697	+	14.5613i	−0.718256	+	1.24406i	−0.961690	+	0.274138i	$0.911607\pi$
$138$		0			0
$139$	−0.952762	+	1.65023i	−0.0808122	+	0.139971i	−0.903599	−	0.428379i	$-0.859085\pi$
$139$	−0.952762	+	1.65023i	−0.0808122	+	0.139971i	0.822787	+	0.568350i	$0.192418\pi$
$140$	−0.862879			−0.0729266
$141$		0			0
$142$	−7.55709	+	13.0893i	−0.634177	+	1.09843i
$143$	1.43627	−	2.48769i	0.120107	−	0.208031i
$144$		0			0
$145$	−3.87226			−0.321574
$146$	−3.12358	+	5.41019i	−0.258509	+	0.447751i
$147$		0			0
$148$	−0.186543	+	0.323102i	−0.0153337	+	0.0265588i
$149$	0.145728	+	0.252409i	0.0119385	+	0.0206782i	0.871933	−	0.489625i	$-0.162866\pi$
$149$	0.145728	+	0.252409i	0.0119385	+	0.0206782i	−0.859994	+	0.510303i	$0.829533\pi$
$150$		0			0
$151$	18.5750			1.51161			0.755807	−	0.654794i	$-0.227245\pi$
$151$	18.5750			1.51161			0.755807	+	0.654794i	$0.227245\pi$
$152$	4.86647	+	12.0852i	0.394723	+	0.980236i
$153$		0			0
$154$	−1.41666	−	2.45372i	−0.114158	−	0.197727i
$155$	−0.187377	−	0.324546i	−0.0150505	−	0.0260682i
$156$		0			0
$157$	9.88718	+	17.1251i	0.789083	+	1.36673i	0.926529	+	0.376222i	$0.122777\pi$
$157$	9.88718	+	17.1251i	0.789083	+	1.36673i	−0.137446	+	0.990509i	$0.543890\pi$
$158$	−7.05876	+	12.2261i	−0.561565	+	0.972659i
$159$		0			0
$160$	1.55522			0.122951
$161$	4.71960	−	8.17458i	0.371956	−	0.644247i
$162$		0			0
$163$	15.7513			1.23374			0.616868	−	0.787066i	$-0.288401\pi$
$163$	15.7513			1.23374			0.616868	+	0.787066i	$0.288401\pi$
$164$	−2.64401			−0.206462
$165$		0			0
$166$	−0.253432	−	0.438957i	−0.0196701	−	0.0340696i
$167$	1.83465	−	3.17771i	0.141970	−	0.245898i	−0.786269	−	0.617885i	$-0.787990\pi$
$167$	1.83465	−	3.17771i	0.141970	−	0.245898i	0.928238	+	0.371986i	$0.121323\pi$
$168$		0			0
$169$	−2.09148	−	3.62255i	−0.160883	−	0.278658i
$170$	−3.68563			−0.282675
$171$		0			0
$172$	1.28807			0.0982141
$173$	−3.50081	−	6.06357i	−0.266161	−	0.461005i	0.701706	−	0.712467i	$-0.252422\pi$
$173$	−3.50081	−	6.06357i	−0.266161	−	0.461005i	−0.967867	+	0.251462i	$0.919089\pi$
$174$		0			0
$175$	−1.55743	+	2.69755i	−0.117731	+	0.203915i
$176$	1.16739	+	2.02198i	0.0879953	+	0.152412i
$177$		0			0
$178$	8.84960			0.663305
$179$	18.4828			1.38147			0.690735	−	0.723108i	$-0.257287\pi$
$179$	18.4828			1.38147			0.690735	+	0.723108i	$0.257287\pi$
$180$		0			0
$181$	7.77997	−	13.4753i	0.578281	−	1.00161i	−0.417396	−	0.908725i	$-0.637057\pi$
$181$	7.77997	−	13.4753i	0.578281	−	1.00161i	0.995677	−	0.0928869i	$-0.0296095\pi$
$182$	−16.9484			−1.25630
$183$		0			0
$184$	−4.52870	+	7.84393i	−0.333860	+	0.578262i
$185$	0.673391	+	1.16635i	0.0495087	+	0.0857515i
$186$		0			0
$187$	0.972876	+	1.68507i	0.0711438	+	0.123225i
$188$	−0.0180260	−	0.0312220i	−0.00131468	−	0.00227710i
$189$		0			0
$190$	5.66499	+	0.802844i	0.410981	+	0.0582444i
$191$	−6.07892			−0.439855			−0.219928	−	0.975516i	$-0.570582\pi$
$191$	−6.07892			−0.439855			−0.219928	+	0.975516i	$0.570582\pi$
$192$		0			0
$193$	−6.37309	−	11.0385i	−0.458745	−	0.794570i	0.540150	−	0.841569i	$-0.318368\pi$
$193$	−6.37309	−	11.0385i	−0.458745	−	0.794570i	−0.998895	+	0.0469988i	$0.985034\pi$
$194$	2.84162	−	4.92184i	0.204017	−	0.353367i
$195$		0			0
$196$	0.374303	−	0.648312i	0.0267359	−	0.0463080i
$197$	26.8916			1.91595			0.957975	−	0.286851i	$-0.0926086\pi$
$197$	26.8916			1.91595			0.957975	+	0.286851i	$0.0926086\pi$
$198$		0			0
$199$	11.7248	−	20.3079i	0.831148	−	1.43959i	−0.0659811	−	0.997821i	$-0.521018\pi$
$199$	11.7248	−	20.3079i	0.831148	−	1.43959i	0.897129	−	0.441769i	$-0.145649\pi$
$200$	1.49443	−	2.58844i	0.105672	−	0.183030i
$201$		0			0
$202$	−1.30921			−0.0921156
$203$	6.03077	−	10.4456i	0.423277	−	0.733138i
$204$		0			0
$205$	−4.77223	+	8.26575i	−0.333307	+	0.577305i
$206$	2.97136	+	5.14655i	0.207025	+	0.358577i
$207$		0			0
$208$	13.9662			0.968382
$209$	−1.12830	−	2.80196i	−0.0780459	−	0.193815i
$210$		0			0
$211$	4.77527	+	8.27101i	0.328743	+	0.569400i	0.982263	−	0.187510i	$-0.0600416\pi$
$211$	4.77527	+	8.27101i	0.328743	+	0.569400i	−0.653520	+	0.756910i	$0.726708\pi$
$212$	−0.122656	−	0.212447i	−0.00842406	−	0.0145909i
$213$		0			0
$214$	−12.2384	−	21.1975i	−0.836599	−	1.44903i
$215$	2.32486	−	4.02677i	0.158554	−	0.274624i
$216$		0			0
$217$	1.16730			0.0792418
$218$	−7.51651	+	13.0190i	−0.509083	+	0.881757i
$219$		0			0
$220$	−0.191968			−0.0129424
$221$	11.6391			0.782932
$222$		0			0
$223$	6.59965	+	11.4309i	0.441945	+	0.765471i	0.997834	−	0.0657855i	$-0.0209553\pi$
$223$	6.59965	+	11.4309i	0.441945	+	0.765471i	−0.555889	+	0.831257i	$0.687622\pi$
$224$	−2.42215	+	4.19529i	−0.161837	+	0.280310i
$225$		0			0
$226$	−12.0090	−	20.8001i	−0.798824	−	1.38360i
$227$	8.69848			0.577339			0.288669	−	0.957429i	$-0.406787\pi$
$227$	8.69848			0.577339			0.288669	+	0.957429i	$0.406787\pi$
$228$		0			0
$229$	19.6107			1.29591			0.647955	−	0.761679i	$-0.275624\pi$
$229$	19.6107			1.29591			0.647955	+	0.761679i	$0.275624\pi$
$230$	1.98887	+	3.44482i	0.131142	+	0.227145i
$231$		0			0
$232$	−5.78684	+	10.0231i	−0.379925	+	0.658049i
$233$	13.9062	+	24.0863i	0.911027	+	1.57795i	0.812616	+	0.582799i	$0.198043\pi$
$233$	13.9062	+	24.0863i	0.911027	+	1.57795i	0.0984108	+	0.995146i	$0.468624\pi$
$234$		0			0
$235$	−0.130142			−0.00848954
$236$	0.398627			0.0259484
$237$		0			0
$238$	5.74011	−	9.94216i	0.372076	−	0.644454i
$239$	−23.5071			−1.52055			−0.760275	−	0.649601i	$-0.774936\pi$
$239$	−23.5071			−1.52055			−0.760275	+	0.649601i	$0.774936\pi$
$240$		0			0
$241$	−12.2817	+	21.2725i	−0.791132	+	1.37028i	0.134134	+	0.990963i	$0.457175\pi$
$241$	−12.2817	+	21.2725i	−0.791132	+	1.37028i	−0.925266	+	0.379318i	$0.876159\pi$
$242$	6.90426	+	11.9585i	0.443823	+	0.768723i
$243$		0			0
$244$	0.453134	+	0.784851i	0.0290089	+	0.0502449i
$245$	−1.35118	−	2.34031i	−0.0863235	−	0.149517i
$246$		0			0
$247$	−17.8899	−	2.53536i	−1.13831	−	0.161321i
$248$	−1.12009			−0.0711257
$249$		0			0
$250$	−0.656312	−	1.13677i	−0.0415088	−	0.0718953i
$251$	5.17195	−	8.95808i	0.326451	−	0.565429i	−0.655354	−	0.755322i	$-0.727481\pi$
$251$	5.17195	−	8.95808i	0.326451	−	0.565429i	0.981805	+	0.189893i	$0.0608140\pi$
$252$		0			0
$253$	1.04998	−	1.81863i	0.0660119	−	0.114336i
$254$	15.6116			0.979559
$255$		0			0
$256$	3.25752	−	5.64219i	0.203595	−	0.352637i
$257$	−1.34568	+	2.33079i	−0.0839413	+	0.145391i	−0.904940	−	0.425540i	$-0.860084\pi$
$257$	−1.34568	+	2.33079i	−0.0839413	+	0.145391i	0.820998	+	0.570931i	$0.193417\pi$
$258$		0			0
$259$	−4.19504			−0.260667
$260$	−0.574157	+	0.994469i	−0.0356077	+	0.0616743i
$261$		0			0
$262$	7.99447	−	13.8468i	0.493900	−	0.855459i
$263$	7.57261	+	13.1161i	0.466947	+	0.808776i	0.999287	−	0.0377547i	$-0.0120206\pi$
$263$	7.57261	+	13.1161i	0.466947	+	0.808776i	−0.532340	+	0.846531i	$0.678687\pi$
$264$		0			0
$265$	−0.885540			−0.0543983
$266$	−10.9885	+	14.0312i	−0.673750	+	0.860308i
$267$		0			0
$268$	1.50855	+	2.61288i	0.0921492	+	0.159607i
$269$	5.03811	+	8.72626i	0.307179	+	0.532050i	0.977744	−	0.209801i	$-0.0672816\pi$
$269$	5.03811	+	8.72626i	0.307179	+	0.532050i	−0.670565	+	0.741851i	$0.733948\pi$
$270$		0			0
$271$	9.60942	+	16.6440i	0.583730	+	1.01105i	0.995032	+	0.0995516i	$0.0317408\pi$
$271$	9.60942	+	16.6440i	0.583730	+	1.01105i	−0.411302	+	0.911499i	$0.634926\pi$
$272$	−4.73010	+	8.19278i	−0.286805	+	0.496760i
$273$		0			0
$274$	22.0704			1.33332
$275$	−0.346487	+	0.600132i	−0.0208939	+	0.0361893i
$276$		0			0
$277$	14.3594			0.862771			0.431386	−	0.902168i	$-0.358025\pi$
$277$	14.3594			0.862771			0.431386	+	0.902168i	$0.358025\pi$
$278$	2.50123			0.150014
$279$		0			0
$280$	4.65496	+	8.06262i	0.278187	+	0.481834i
$281$	−9.65362	+	16.7206i	−0.575887	+	0.997465i	0.420058	+	0.907497i	$0.362010\pi$
$281$	−9.65362	+	16.7206i	−0.575887	+	0.997465i	−0.995945	+	0.0899676i	$0.971324\pi$
$282$		0			0
$283$	−16.2313	−	28.1134i	−0.964850	−	1.67117i	−0.710018	−	0.704183i	$-0.751313\pi$
$283$	−16.2313	−	28.1134i	−0.964850	−	1.67117i	−0.254831	−	0.966986i	$-0.582020\pi$
$284$	−3.18975			−0.189277
$285$		0			0
$286$	−3.77056			−0.222958
$287$	−14.8648	−	25.7466i	−0.877443	−	1.51978i
$288$		0			0
$289$	4.55804	−	7.89475i	0.268120	−	0.464397i
$290$	2.54141	+	4.40185i	0.149237	+	0.258486i
$291$		0			0
$292$	−1.31842			−0.0771546
$293$	7.22833			0.422283			0.211142	−	0.977455i	$-0.432282\pi$
$293$	7.22833			0.422283			0.211142	+	0.977455i	$0.432282\pi$
$294$		0			0
$295$	0.719490	−	1.24619i	0.0418904	−	0.0725562i
$296$	4.02535			0.233969
$297$		0			0
$298$	0.191287	−	0.331318i	0.0110809	−	0.0191927i
$299$	−6.28080	−	10.8787i	−0.363228	−	0.629130i
$300$		0			0
$301$	7.24161	+	12.5428i	0.417400	+	0.722957i
$302$	−12.1910	−	21.1155i	−0.701514	−	1.21506i
$303$		0			0
$304$	9.05504	−	11.5623i	0.519342	−	0.663145i
$305$	3.27149			0.187325
$306$		0			0
$307$	6.69667	+	11.5990i	0.382199	+	0.661989i	0.991376	−	0.131046i	$-0.0418334\pi$
$307$	6.69667	+	11.5990i	0.382199	+	0.661989i	−0.609177	+	0.793034i	$0.708500\pi$
$308$	0.298976	−	0.517842i	0.0170357	−	0.0295068i
$309$		0			0
$310$	−0.245955	+	0.426007i	−0.0139693	+	0.0241956i
$311$	19.0587			1.08072			0.540361	−	0.841433i	$-0.318288\pi$
$311$	19.0587			1.08072			0.540361	+	0.841433i	$0.318288\pi$
$312$		0			0
$313$	−5.47738	+	9.48711i	−0.309600	+	0.536243i	−0.978275	−	0.207312i	$-0.933528\pi$
$313$	−5.47738	+	9.48711i	−0.309600	+	0.536243i	0.668675	+	0.743555i	$0.266862\pi$
$314$	12.9781	−	22.4788i	0.732399	−	1.26855i
$315$		0			0
$316$	−2.97941			−0.167605
$317$	−5.04659	+	8.74096i	−0.283445	+	0.490941i	−0.972231	−	0.234024i	$-0.924811\pi$
$317$	−5.04659	+	8.74096i	−0.283445	+	0.490941i	0.688786	+	0.724965i	$0.258144\pi$
$318$		0			0
$319$	1.34169	−	2.32387i	0.0751200	−	0.130112i
$320$	−4.38993	−	7.60358i	−0.245405	−	0.425053i
$321$		0			0
$322$	−12.3901			−0.690473
$323$	7.54627	−	9.63579i	0.419886	−	0.536150i
$324$		0			0
$325$	2.07262	+	3.58988i	0.114968	+	0.199131i
$326$	−10.3378	−	17.9055i	−0.572556	−	0.991695i
$327$		0			0
$328$	14.2636	+	24.7052i	0.787574	+	1.36412i
$329$	0.202687	−	0.351065i	0.0111745	−	0.0193548i
$330$		0			0
$331$	−1.50229			−0.0825736			−0.0412868	−	0.999147i	$-0.513146\pi$
$331$	−1.50229			−0.0825736			−0.0412868	+	0.999147i	$0.513146\pi$
$332$	0.0534850	−	0.0926388i	0.00293537	−	0.00508421i
$333$		0			0
$334$	−4.81641			−0.263542
$335$	10.8912			0.595052
$336$		0			0
$337$	1.46673	+	2.54045i	0.0798980	+	0.138387i	0.903206	−	0.429208i	$-0.141207\pi$
$337$	1.46673	+	2.54045i	0.0798980	+	0.138387i	−0.823308	+	0.567595i	$0.807874\pi$
$338$	−2.74533	+	4.75505i	−0.149326	+	0.258641i
$339$		0			0
$340$	−0.388913	−	0.673617i	−0.0210918	−	0.0365320i
$341$	0.259694			0.0140632
$342$		0			0
$343$	−13.3866			−0.722807
$344$	−6.94870	−	12.0355i	−0.374649	−	0.648911i
$345$		0			0
$346$	−4.59524	+	7.95919i	−0.247042	+	0.427889i
$347$	−4.86657	−	8.42915i	−0.261251	−	0.452501i	0.705323	−	0.708886i	$-0.250802\pi$
$347$	−4.86657	−	8.42915i	−0.261251	−	0.452501i	−0.966575	+	0.256385i	$0.917468\pi$
$348$		0			0
$349$	12.0493			0.644987			0.322493	−	0.946572i	$-0.395479\pi$
$349$	12.0493			0.644987			0.322493	+	0.946572i	$0.395479\pi$
$350$	4.08864			0.218547
$351$		0			0
$352$	−0.538864	+	0.933340i	−0.0287215	+	0.0497472i
$353$	−26.1484			−1.39174			−0.695870	−	0.718168i	$-0.744981\pi$
$353$	−26.1484			−1.39174			−0.695870	+	0.718168i	$0.744981\pi$
$354$		0			0
$355$	−5.75724	+	9.97184i	−0.305563	+	0.529250i
$356$	0.933824	+	1.61743i	0.0494926	+	0.0857236i
$357$		0			0
$358$	−12.1305	−	21.0106i	−0.641116	−	1.11045i
$359$	−16.6763	−	28.8843i	−0.880144	−	1.52445i	−0.851181	−	0.524873i	$-0.824113\pi$
$359$	−16.6763	−	28.8843i	−0.880144	−	1.52445i	−0.0289631	−	0.999580i	$-0.509221\pi$
$360$		0			0
$361$	−13.6979	+	13.1669i	−0.720945	+	0.692993i
$362$	−20.4243			−1.07348
$363$		0			0
$364$	−1.78842	−	3.09763i	−0.0937386	−	0.162360i
$365$	−2.37964	+	4.12166i	−0.124556	+	0.215738i
$366$		0			0
$367$	−6.49560	+	11.2507i	−0.339068	+	0.587283i	−0.984258	−	0.176740i	$-0.943445\pi$
$367$	−6.49560	+	11.2507i	−0.339068	+	0.587283i	0.645190	+	0.764022i	$0.276778\pi$
$368$	10.2100			0.532233
$369$		0			0
$370$	0.883908	−	1.53097i	0.0459522	−	0.0795916i
$371$	1.37917	−	2.38879i	0.0716028	−	0.124020i
$372$		0			0
$373$	−36.5438			−1.89216			−0.946082	−	0.323926i	$-0.894997\pi$
$373$	−36.5438			−1.89216			−0.946082	+	0.323926i	$0.894997\pi$
$374$	1.27702	−	2.21186i	0.0660331	−	0.114373i
$375$		0			0
$376$	−0.194489	+	0.336865i	−0.0100300	+	0.0173725i
$377$	−8.02571	−	13.9009i	−0.413345	−	0.715935i
$378$		0			0
$379$	−32.7622			−1.68288			−0.841441	−	0.540350i	$-0.818292\pi$
$379$	−32.7622			−1.68288			−0.841441	+	0.540350i	$0.818292\pi$
$380$	0.451043	+	1.12010i	0.0231380	+	0.0574599i
$381$		0			0
$382$	3.98967	+	6.91030i	0.204129	+	0.353562i
$383$	−19.3221	−	33.4669i	−0.987315	−	1.71008i	−0.631162	−	0.775651i	$-0.717422\pi$
$383$	−19.3221	−	33.4669i	−0.987315	−	1.71008i	−0.356153	−	0.934428i	$-0.615912\pi$
$384$		0			0
$385$	−1.07926	−	1.86933i	−0.0550040	−	0.0952698i
$386$	−8.36547	+	14.4894i	−0.425791	+	0.737492i
$387$		0			0
$388$	1.19941			0.0608909
$389$	−17.7295	+	30.7085i	−0.898923	+	1.55698i	−0.0700500	+	0.997543i	$0.522316\pi$
$389$	−17.7295	+	30.7085i	−0.898923	+	1.55698i	−0.828873	+	0.559437i	$0.811017\pi$
$390$		0			0
$391$	8.50878			0.430308
$392$	−8.07698			−0.407949
$393$		0			0
$394$	−17.6493	−	30.5695i	−0.889159	−	1.54007i
$395$	−5.37760	+	9.31428i	−0.270576	+	0.468652i
$396$		0			0
$397$	−6.08814	−	10.5450i	−0.305555	−	0.529237i	0.671830	−	0.740706i	$-0.265509\pi$
$397$	−6.08814	−	10.5450i	−0.305555	−	0.529237i	−0.977385	+	0.211469i	$0.932175\pi$
$398$	−30.7804			−1.54288
$399$		0			0
$400$	−3.36922			−0.168461
$401$	15.4557	+	26.7701i	0.771822	+	1.33684i	0.936563	+	0.350498i	$0.113988\pi$
$401$	15.4557	+	26.7701i	0.771822	+	1.33684i	−0.164741	+	0.986337i	$0.552679\pi$
$402$		0			0
$403$	0.776720	−	1.34532i	0.0386912	−	0.0670151i
$404$	−0.138150	−	0.239282i	−0.00687321	−	0.0119047i
$405$		0			0
$406$	−15.8323			−0.785742
$407$	−0.933283			−0.0462611
$408$		0			0
$409$	−6.96184	+	12.0583i	−0.344241	+	0.596243i	−0.985216	−	0.171319i	$-0.945197\pi$
$409$	−6.96184	+	12.0583i	−0.344241	+	0.596243i	0.640975	+	0.767562i	$0.278530\pi$
$410$	12.5283			0.618728
$411$		0			0
$412$	−0.627086	+	1.08614i	−0.0308943	+	0.0535105i
$413$	2.24111	+	3.88172i	0.110278	+	0.191007i
$414$		0			0
$415$	−0.193073	−	0.334412i	−0.00947757	−	0.0164156i
$416$	3.22338	+	5.58306i	0.158039	+	0.273732i
$417$		0			0
$418$	−2.44465	+	3.12157i	−0.119572	+	0.152681i
$419$	−19.7638			−0.965525			−0.482763	−	0.875751i	$-0.660367\pi$
$419$	−19.7638			−0.965525			−0.482763	+	0.875751i	$0.660367\pi$
$420$		0			0
$421$	1.07302	+	1.85853i	0.0522959	+	0.0905791i	0.890988	−	0.454026i	$-0.150013\pi$
$421$	1.07302	+	1.85853i	0.0522959	+	0.0905791i	−0.838692	+	0.544605i	$0.816679\pi$
$422$	6.26813	−	10.8567i	0.305128	−	0.528497i
$423$		0			0
$424$	−1.32338	+	2.29216i	−0.0642691	+	0.111317i
$425$	−2.80783			−0.136200
$426$		0			0
$427$	−5.09511	+	8.82499i	−0.246570	+	0.427071i
$428$	2.58283	−	4.47359i	0.124846	−	0.216239i
$429$		0			0
$430$	−6.10333			−0.294329
$431$	14.0250	−	24.2920i	0.675559	−	1.17010i	−0.300746	−	0.953704i	$-0.597236\pi$
$431$	14.0250	−	24.2920i	0.675559	−	1.17010i	0.976305	−	0.216398i	$-0.0694310\pi$
$432$		0			0
$433$	5.38799	−	9.33227i	0.258930	−	0.448480i	−0.707025	−	0.707188i	$-0.749963\pi$
$433$	5.38799	−	9.33227i	0.258930	−	0.448480i	0.965956	+	0.258708i	$0.0832967\pi$
$434$	−0.766116	−	1.32695i	−0.0367747	−	0.0636957i
$435$		0			0
$436$	−3.17262			−0.151941
$437$	−13.0784	−	1.85348i	−0.625625	−	0.0886638i
$438$		0			0
$439$	9.03536	+	15.6497i	0.431234	+	0.746920i	0.996980	−	0.0776600i	$-0.0247449\pi$
$439$	9.03536	+	15.6497i	0.431234	+	0.746920i	−0.565745	+	0.824580i	$0.691412\pi$
$440$	1.03560	+	1.79372i	0.0493704	+	0.0855121i
$441$		0			0
$442$	−7.63889	−	13.2310i	−0.363345	−	0.629332i
$443$	−1.78684	+	3.09491i	−0.0848956	+	0.147043i	−0.905347	−	0.424673i	$-0.860389\pi$
$443$	−1.78684	+	3.09491i	−0.0848956	+	0.147043i	0.820451	+	0.571717i	$0.193722\pi$
$444$		0			0
$445$	6.74192			0.319598
$446$	8.66285	−	15.0045i	0.410198	−	0.710483i
$447$		0			0
$448$	27.3480			1.29207
$449$	−12.7199			−0.600291			−0.300145	−	0.953893i	$-0.597035\pi$
$449$	−12.7199			−0.600291			−0.300145	+	0.953893i	$0.597035\pi$
$450$		0			0
$451$	−3.30703	−	5.72794i	−0.155722	−	0.269718i
$452$	2.53441	−	4.38972i	0.119209	−	0.206475i
$453$		0			0
$454$	−5.70892	−	9.88813i	−0.267933	−	0.464073i
$455$	−12.9118			−0.605316
$456$		0			0
$457$	29.7579			1.39202			0.696008	−	0.718034i	$-0.254958\pi$
$457$	29.7579			1.39202			0.696008	+	0.718034i	$0.254958\pi$
$458$	−12.8707	−	22.2927i	−0.601409	−	1.04167i
$459$		0			0
$460$	−0.419737	+	0.727006i	−0.0195704	+	0.0338969i
$461$	17.2888	+	29.9450i	0.805218	+	1.39468i	0.916144	+	0.400850i	$0.131285\pi$
$461$	17.2888	+	29.9450i	0.805218	+	1.39468i	−0.110926	+	0.993829i	$0.535382\pi$
$462$		0			0
$463$	0.783874			0.0364297			0.0182149	−	0.999834i	$-0.494202\pi$
$463$	0.783874			0.0364297			0.0182149	+	0.999834i	$0.494202\pi$
$464$	13.0465			0.605668
$465$		0			0
$466$	18.2536	−	31.6162i	0.845583	−	1.46459i
$467$	−14.2134			−0.657720			−0.328860	−	0.944379i	$-0.606664\pi$
$467$	−14.2134			−0.657720			−0.328860	+	0.944379i	$0.606664\pi$
$468$		0			0
$469$	−16.9623	+	29.3796i	−0.783248	+	1.35663i
$470$	0.0854138	+	0.147941i	0.00393985	+	0.00682401i
$471$		0			0
$472$	−2.15046	−	3.72471i	−0.0989831	−	0.171444i
$473$	1.61107	+	2.79045i	0.0740769	+	0.128305i
$474$		0			0
$475$	4.31577	+	0.611633i	0.198021	+	0.0280637i
$476$	2.42282			0.111050
$477$		0			0
$478$	15.4280	+	26.7221i	0.705660	+	1.22224i
$479$	9.33951	−	16.1765i	0.426733	−	0.739123i	−0.569848	−	0.821750i	$-0.692998\pi$
$479$	9.33951	−	16.1765i	0.426733	−	0.739123i	0.996581	+	0.0826272i	$0.0263311\pi$
$480$		0			0
$481$	−2.79136	+	4.83478i	−0.127275	+	0.220447i
$482$	32.2424			1.46860
$483$		0			0
$484$	−1.45710	+	2.52377i	−0.0662317	+	0.114717i
$485$	2.16484	−	3.74962i	0.0983005	−	0.170261i
$486$		0			0
$487$	−14.6054			−0.661833			−0.330916	−	0.943660i	$-0.607358\pi$
$487$	−14.6054			−0.661833			−0.330916	+	0.943660i	$0.607358\pi$
$488$	4.88902	−	8.46804i	0.221316	−	0.383330i
$489$		0			0
$490$	−1.77359	+	3.07194i	−0.0801225	+	0.138776i
$491$	−1.65767	−	2.87116i	−0.0748094	−	0.129574i	0.826194	−	0.563386i	$-0.190501\pi$
$491$	−1.65767	−	2.87116i	−0.0748094	−	0.129574i	−0.901003	+	0.433812i	$0.857168\pi$
$492$		0			0
$493$	10.8727			0.489680
$494$	8.85923	+	22.0006i	0.398596	+	0.989854i
$495$		0			0
$496$	0.631313	+	1.09347i	0.0283468	+	0.0490981i
$497$	−17.9330	−	31.0609i	−0.804405	−	1.39327i
$498$		0			0
$499$	4.63324	+	8.02501i	0.207412	+	0.359249i	0.950899	−	0.309502i	$-0.100162\pi$
$499$	4.63324	+	8.02501i	0.207412	+	0.359249i	−0.743486	+	0.668751i	$0.766829\pi$
$500$	0.138510	−	0.239907i	0.00619436	−	0.0107289i
$501$		0			0
$502$	−13.5776			−0.606000
$503$	16.6005	−	28.7530i	0.740181	−	1.28203i	−0.212231	−	0.977219i	$-0.568073\pi$
$503$	16.6005	−	28.7530i	0.740181	−	1.28203i	0.952413	−	0.304812i	$-0.0985936\pi$
$504$		0			0
$505$	−0.997399			−0.0443837
$506$	−2.75647			−0.122540
$507$		0			0
$508$	1.64736	+	2.85331i	0.0730898	+	0.126595i
$509$	−18.3832	+	31.8406i	−0.814820	+	1.41131i	0.0946365	+	0.995512i	$0.469831\pi$
$509$	−18.3832	+	31.8406i	−0.814820	+	1.41131i	−0.909457	+	0.415798i	$0.863502\pi$
$510$		0			0
$511$	−7.41226	−	12.8384i	−0.327899	−	0.567938i
$512$	−25.3802			−1.12166
$513$		0			0
$514$	3.53274			0.155823
$515$	2.26368	+	3.92081i	0.0997498	+	0.172772i
$516$		0			0
$517$	0.0450925	−	0.0781025i	0.00198317	−	0.00343495i
$518$	2.75325	+	4.76877i	0.120971	+	0.209528i
$519$		0			0
$520$	12.3896			0.543318
$521$	−5.40142			−0.236640			−0.118320	−	0.992975i	$-0.537751\pi$
$521$	−5.40142			−0.236640			−0.118320	+	0.992975i	$0.537751\pi$
$522$		0			0
$523$	−5.04334	+	8.73533i	−0.220530	+	0.381969i	−0.954969	−	0.296705i	$-0.904112\pi$
$523$	−5.04334	+	8.73533i	−0.220530	+	0.381969i	0.734439	+	0.678675i	$0.237445\pi$
$524$	3.37435			0.147409
$525$		0			0
$526$	9.93998	−	17.2166i	0.433404	−	0.750677i
$527$	0.526123	+	0.911271i	0.0229183	+	0.0396956i
$528$		0			0
$529$	6.90842	+	11.9657i	0.300366	+	0.520249i
$530$	0.581190	+	1.00665i	0.0252453	+	0.0437261i
$531$		0			0
$532$	−3.72399	−	0.527765i	−0.161455	−	0.0228815i
$533$	−39.5640			−1.71371
$534$		0			0
$535$	−9.32362	−	16.1490i	−0.403095	−	0.698181i
$536$	16.2763	−	28.1913i	0.703027	−	1.21768i
$537$		0			0
$538$	6.61314	−	11.4543i	0.285113	−	0.493830i
$539$	1.87266			0.0806611
$540$		0			0
$541$	−4.85048	+	8.40128i	−0.208538	+	0.361199i	−0.951254	−	0.308407i	$-0.900204\pi$
$541$	−4.85048	+	8.40128i	−0.208538	+	0.361199i	0.742716	+	0.669607i	$0.233537\pi$
$542$	12.6135	−	21.8473i	0.541798	−	0.938422i
$543$		0			0
$544$	−4.36681			−0.187225
$545$	−5.72633	+	9.91830i	−0.245289	+	0.424853i
$546$		0			0
$547$	−2.05849	+	3.56540i	−0.0880145	+	0.152446i	−0.906672	−	0.421837i	$-0.861386\pi$
$547$	−2.05849	+	3.56540i	−0.0880145	+	0.152446i	0.818657	+	0.574282i	$0.194719\pi$
$548$	2.32890	+	4.03377i	0.0994857	+	0.172314i
$549$		0			0
$550$	0.909613			0.0387860
$551$	−16.7118	−	2.36840i	−0.711947	−	0.100897i
$552$		0			0
$553$	−16.7505	−	29.0127i	−0.712302	−	1.23374i
$554$	−9.42422	−	16.3232i	−0.400397	−	0.693508i
$555$		0			0
$556$	0.263934	+	0.457147i	0.0111933	+	0.0193874i
$557$	−16.8094	+	29.1147i	−0.712237	+	1.23363i	0.251779	+	0.967785i	$0.418985\pi$
$557$	−16.8094	+	29.1147i	−0.712237	+	1.23363i	−0.964016	+	0.265846i	$0.914349\pi$
$558$		0			0
$559$	19.2742			0.815211
$560$	5.24732	−	9.08863i	0.221740	−	0.384065i
$561$		0			0
$562$	25.3431			1.06904
$563$	34.8168			1.46735			0.733677	−	0.679498i	$-0.237802\pi$
$563$	34.8168			1.46735			0.733677	+	0.679498i	$0.237802\pi$
$564$		0			0
$565$	−9.14882	−	15.8462i	−0.384894	−	0.666656i
$566$	−21.3056	+	36.9023i	−0.895539	+	1.55112i
$567$		0			0
$568$	17.2076	+	29.8045i	0.722017	+	1.25057i
$569$	−35.0377			−1.46886			−0.734429	−	0.678686i	$-0.762550\pi$
$569$	−35.0377			−1.46886			−0.734429	+	0.678686i	$0.762550\pi$
$570$		0			0
$571$	35.7203			1.49485			0.747424	−	0.664347i	$-0.231290\pi$
$571$	35.7203			1.49485			0.747424	+	0.664347i	$0.231290\pi$
$572$	−0.397875	−	0.689140i	−0.0166360	−	0.0288144i
$573$		0			0
$574$	−19.5119	+	33.7956i	−0.814412	+	1.41060i
$575$	1.51519	+	2.62438i	0.0631877	+	0.109444i
$576$		0			0
$577$	28.5678			1.18929			0.594647	−	0.803987i	$-0.297292\pi$
$577$	28.5678			1.18929			0.594647	+	0.803987i	$0.297292\pi$
$578$	−11.9660			−0.497719
$579$		0			0
$580$	−0.536347	+	0.928980i	−0.0222706	+	0.0385738i
$581$	1.20279			0.0499001
$582$		0			0
$583$	0.306828	−	0.531441i	0.0127075	−	0.0220100i
$584$	7.11245	+	12.3191i	0.294315	+	0.509769i
$585$		0			0
$586$	−4.74404	−	8.21691i	−0.195974	−	0.339437i
$587$	−10.8661	−	18.8206i	−0.448492	−	0.776811i	0.549796	−	0.835299i	$-0.314705\pi$
$587$	−10.8661	−	18.8206i	−0.448492	−	0.776811i	−0.998288	+	0.0584879i	$0.981372\pi$
$588$		0			0
$589$	−0.610173	−	1.51527i	−0.0251417	−	0.0624357i
$590$	−1.88884			−0.0777623
$591$		0			0
$592$	−2.26880	−	3.92968i	−0.0932472	−	0.161509i
$593$	4.15459	−	7.19595i	0.170608	−	0.295502i	−0.768024	−	0.640421i	$-0.778760\pi$
$593$	4.15459	−	7.19595i	0.170608	−	0.295502i	0.938633	+	0.344918i	$0.112093\pi$
$594$		0			0
$595$	4.37300	−	7.57427i	0.179276	−	0.310515i
$596$	0.0807395			0.00330722
$597$		0			0
$598$	−8.24433	+	14.2796i	−0.337136	+	0.583936i
$599$	7.98082	−	13.8232i	0.326087	−	0.564800i	−0.655644	−	0.755070i	$-0.727603\pi$
$599$	7.98082	−	13.8232i	0.326087	−	0.564800i	0.981732	+	0.190270i	$0.0609363\pi$
$600$		0			0
$601$	10.2096			0.416457			0.208228	−	0.978080i	$-0.433230\pi$
$601$	10.2096			0.416457			0.208228	+	0.978080i	$0.433230\pi$
$602$	9.50551	−	16.4640i	0.387416	−	0.671024i
$603$		0			0
$604$	2.57283	−	4.45627i	0.104687	−	0.181323i
$605$	5.25989	+	9.11040i	0.213845	+	0.370391i
$606$		0			0
$607$	−11.4506			−0.464764			−0.232382	−	0.972625i	$-0.574652\pi$
$607$	−11.4506			−0.464764			−0.232382	+	0.972625i	$0.574652\pi$
$608$	6.71199	+	0.951226i	0.272207	+	0.0385773i
$609$		0			0
$610$	−2.14711	−	3.71891i	−0.0869341	−	0.150574i
$611$	−0.269735	−	0.467195i	−0.0109123	−	0.0189007i
$612$		0			0
$613$	13.0849	+	22.6637i	0.528494	+	0.915378i	0.999448	+	0.0332202i	$0.0105763\pi$
$613$	13.0849	+	22.6637i	0.528494	+	0.915378i	−0.470954	+	0.882158i	$0.656090\pi$
$614$	8.79021	−	15.2251i	0.354744	−	0.614435i
$615$		0			0
$616$	−6.45152			−0.259939
$617$	−15.2975	+	26.4961i	−0.615854	+	1.06669i	0.374379	+	0.927276i	$0.377856\pi$
$617$	−15.2975	+	26.4961i	−0.615854	+	1.06669i	−0.990234	+	0.139416i	$0.955478\pi$
$618$		0			0
$619$	28.4931			1.14523			0.572616	−	0.819823i	$-0.305928\pi$
$619$	28.4931			1.14523			0.572616	+	0.819823i	$0.305928\pi$
$620$	−0.103814			−0.00416928
$621$		0			0
$622$	−12.5085	−	21.6653i	−0.501544	−	0.868700i
$623$	−10.5001	+	18.1866i	−0.420676	+	0.728633i
$624$		0			0
$625$	−0.500000	−	0.866025i	−0.0200000	−	0.0346410i
$626$	14.3795			0.574720
$627$		0			0
$628$	5.47790			0.218592
$629$	−1.89077	−	3.27491i	−0.0753899	−	0.130579i
$630$		0			0
$631$	5.50411	−	9.53340i	0.219115	−	0.379518i	−0.735423	−	0.677609i	$-0.763016\pi$
$631$	5.50411	−	9.53340i	0.219115	−	0.379518i	0.954538	+	0.298090i	$0.0963496\pi$
$632$	16.0729	+	27.8392i	0.639347	+	1.10738i
$633$		0			0
$634$	13.2486			0.526167
$635$	11.8934			0.471976
$636$		0			0
$637$	5.60094	−	9.70112i	0.221918	−	0.384372i
$638$	−3.52226			−0.139447
$639$		0			0
$640$	−4.20710	+	7.28691i	−0.166300	+	0.288041i
$641$	−11.0021	−	19.0562i	−0.434557	−	0.752675i	0.562702	−	0.826660i	$-0.309762\pi$
$641$	−11.0021	−	19.0562i	−0.434557	−	0.752675i	−0.997259	+	0.0739847i	$0.976428\pi$
$642$		0			0
$643$	−23.4637	−	40.6403i	−0.925319	−	1.60270i	−0.791048	−	0.611754i	$-0.790464\pi$
$643$	−23.4637	−	40.6403i	−0.925319	−	1.60270i	−0.134271	−	0.990945i	$-0.542869\pi$
$644$	−1.30742	−	2.26452i	−0.0515197	−	0.0892347i
$645$		0			0
$646$	−15.9063	−	2.25425i	−0.625826	−	0.0886924i
$647$	−0.973639			−0.0382777			−0.0191389	−	0.999817i	$-0.506092\pi$
$647$	−0.973639			−0.0382777			−0.0191389	+	0.999817i	$0.506092\pi$
$648$		0			0
$649$	0.498588	+	0.863579i	0.0195713	+	0.0338984i
$650$	2.72057	−	4.71216i	0.106709	−	0.184826i
$651$		0			0
$652$	2.18171	−	3.77884i	0.0854425	−	0.147991i
$653$	43.3819			1.69766			0.848832	−	0.528662i	$-0.177306\pi$
$653$	43.3819			1.69766			0.848832	+	0.528662i	$0.177306\pi$
$654$		0			0
$655$	6.09045	−	10.5490i	0.237974	−	0.412182i
$656$	16.0787	−	27.8491i	0.627767	−	1.08733i
$657$		0			0
$658$	−0.532104			−0.0207436
$659$	1.95482	−	3.38584i	0.0761489	−	0.131894i	−0.825436	−	0.564495i	$-0.809071\pi$
$659$	1.95482	−	3.38584i	0.0761489	−	0.131894i	0.901585	+	0.432601i	$0.142404\pi$
$660$		0			0
$661$	19.3249	−	33.4717i	0.751652	−	1.30190i	−0.195370	−	0.980730i	$-0.562591\pi$
$661$	19.3249	−	33.4717i	0.751652	−	1.30190i	0.947022	−	0.321169i	$-0.104076\pi$
$662$	0.985973	+	1.70776i	0.0383209	+	0.0663738i
$663$		0			0
$664$	−1.15414			−0.0447892
$665$	−8.37143	+	10.6894i	−0.324630	+	0.414518i
$666$		0			0
$667$	−5.86720	−	10.1623i	−0.227179	−	0.393485i
$668$	−0.508235	−	0.880289i	−0.0196642	−	0.0340594i
$669$		0			0
$670$	−7.14805	−	12.3808i	−0.276153	−	0.478311i
$671$	−1.13353	+	1.96332i	−0.0437593	+	0.0757933i
$672$		0			0
$673$	−19.0257			−0.733387			−0.366693	−	0.930342i	$-0.619510\pi$
$673$	−19.0257			−0.733387			−0.366693	+	0.930342i	$0.619510\pi$
$674$	1.92527	−	3.33466i	0.0741585	−	0.128446i
$675$		0			0
$676$	−1.15877			−0.0445679
$677$	−3.39483			−0.130474			−0.0652369	−	0.997870i	$-0.520780\pi$
$677$	−3.39483			−0.130474			−0.0652369	+	0.997870i	$0.520780\pi$
$678$		0			0
$679$	6.74319	+	11.6795i	0.258780	+	0.448220i
$680$	−4.19612	+	7.26790i	−0.160914	+	0.278711i
$681$		0			0
$682$	−0.170440	−	0.295211i	−0.00652649	−	0.0113042i
$683$	6.42057			0.245676			0.122838	−	0.992427i	$-0.460800\pi$
$683$	6.42057			0.245676			0.122838	+	0.992427i	$0.460800\pi$
$684$		0			0
$685$	16.8139			0.642427
$686$	8.78576	+	15.2174i	0.335442	+	0.581002i
$687$		0			0
$688$	−7.83296	+	13.5671i	−0.298629	+	0.517240i
$689$	−1.83539	−	3.17898i	−0.0699226	−	0.121110i
$690$		0			0
$691$	9.32092			0.354584			0.177292	−	0.984158i	$-0.443266\pi$
$691$	9.32092			0.354584			0.177292	+	0.984158i	$0.443266\pi$
$692$	−1.93959			−0.0737321
$693$		0			0
$694$	−6.38798	+	11.0643i	−0.242484	+	0.419995i
$695$	1.90552			0.0722806
$696$		0			0
$697$	13.3996	−	23.2088i	0.507547	−	0.879097i
$698$	−7.90813	−	13.6973i	−0.299327	−	0.518450i
$699$		0			0
$700$	0.431440	+	0.747275i	0.0163069	+	0.0282443i
$701$	12.1943	+	21.1211i	0.460572	+	0.797735i	0.998990	−	0.0449438i	$-0.0143109\pi$
$701$	12.1943	+	21.1211i	0.460572	+	0.797735i	−0.538417	+	0.842678i	$0.680978\pi$
$702$		0			0
$703$	2.19283	+	5.44556i	0.0827040	+	0.205383i
$704$	6.08421			0.229307
$705$		0			0
$706$	17.1615	+	29.7246i	0.645882	+	1.11870i
$707$	1.55338	−	2.69053i	0.0584208	−	0.101188i
$708$		0			0
$709$	−8.78866	+	15.2224i	−0.330065	+	0.571689i	−0.982524	−	0.186135i	$-0.940404\pi$
$709$	−8.78866	+	15.2224i	−0.330065	+	0.571689i	0.652459	+	0.757824i	$0.273737\pi$
$710$	15.1142			0.567225
$711$		0			0
$712$	10.0754	−	17.4510i	0.377590	−	0.654005i
$713$	0.567822	−	0.983496i	0.0212651	−	0.0368322i
$714$		0			0
$715$	−2.87254			−0.107427
$716$	2.56006	−	4.43415i	0.0956738	−	0.165712i
$717$		0			0
$718$	−21.8898	+	37.9142i	−0.816918	+	1.41494i
$719$	−9.54695	−	16.5358i	−0.356041	−	0.616681i	0.631255	−	0.775576i	$-0.282540\pi$
$719$	−9.54695	−	16.5358i	−0.356041	−	0.616681i	−0.987296	+	0.158895i	$0.949207\pi$
$720$		0			0
$721$	−14.1021			−0.525190
$722$	23.9577	+	6.92979i	0.891615	+	0.257900i
$723$		0			0
$724$	−2.15521	−	3.73293i	−0.0800977	−	0.138733i
$725$	1.93613	+	3.35348i	0.0719061	+	0.124545i
$726$		0			0
$727$	−0.846286	−	1.46581i	−0.0313870	−	0.0543639i	0.849905	−	0.526936i	$-0.176659\pi$
$727$	−0.846286	−	1.46581i	−0.0313870	−	0.0543639i	−0.881292	+	0.472572i	$0.843326\pi$
$728$	−19.2959	+	33.4214i	−0.715153	+	1.23868i
$729$		0			0
$730$	6.24715			0.231217
$731$	−6.52782	+	11.3065i	−0.241440	+	0.418186i
$732$		0			0
$733$	−18.4707			−0.682233			−0.341116	−	0.940021i	$-0.610805\pi$
$733$	−18.4707			−0.682233			−0.341116	+	0.940021i	$0.610805\pi$
$734$	17.0526			0.629422
$735$		0			0
$736$	2.35645	+	4.08150i	0.0868601	+	0.150446i
$737$	−3.77367	+	6.53619i	−0.139005	+	0.240763i
$738$		0			0
$739$	8.97295	+	15.5416i	0.330075	+	0.571707i	0.982526	−	0.186124i	$-0.0595925\pi$
$739$	8.97295	+	15.5416i	0.330075	+	0.571707i	−0.652451	+	0.757831i	$0.726259\pi$
$740$	0.373086			0.0137149
$741$		0			0
$742$	−3.62065			−0.132918
$743$	15.3279	+	26.5486i	0.562324	+	0.973975i	0.997293	+	0.0735289i	$0.0234261\pi$
$743$	15.3279	+	26.5486i	0.562324	+	0.973975i	−0.434969	+	0.900446i	$0.643241\pi$
$744$		0			0
$745$	0.145728	−	0.252409i	0.00533908	−	0.00924756i
$746$	23.9841	+	41.5417i	0.878120	+	1.52095i
$747$		0			0
$748$	0.539013			0.0197083
$749$	58.0835			2.12233
$750$		0			0
$751$	−13.8978	+	24.0717i	−0.507139	+	0.878390i	0.492827	+	0.870127i	$0.335964\pi$
$751$	−13.8978	+	24.0717i	−0.507139	+	0.878390i	−0.999966	+	0.00826290i	$0.997370\pi$
$752$	0.438478			0.0159896
$753$		0			0
$754$	−10.5347	+	18.2467i	−0.383652	+	0.664506i
$755$	−9.28752	−	16.0865i	−0.338007	−	0.585446i
$756$		0			0
$757$	3.66800	+	6.35317i	0.133316	+	0.230910i	0.924953	−	0.380082i	$-0.124104\pi$
$757$	3.66800	+	6.35317i	0.133316	+	0.230910i	−0.791637	+	0.610992i	$0.790771\pi$
$758$	21.5022	+	37.2429i	0.780996	+	1.35272i
$759$		0			0
$760$	8.03282	−	10.2571i	0.291381	−	0.372063i
$761$	−32.6306			−1.18286			−0.591430	−	0.806356i	$-0.701436\pi$
$761$	−32.6306			−1.18286			−0.591430	+	0.806356i	$0.701436\pi$
$762$		0			0
$763$	−17.8367	−	30.8941i	−0.645733	−	1.11844i
$764$	−0.841992	+	1.45837i	−0.0304622	+	0.0527621i
$765$		0			0
$766$	−25.3627	+	43.9294i	−0.916391	+	1.58724i
$767$	5.96491			0.215381
$768$		0			0
$769$	15.2386	−	26.3941i	0.549519	−	0.951796i	−0.448788	−	0.893638i	$-0.648144\pi$
$769$	15.2386	−	26.3941i	0.549519	−	0.951796i	0.998307	−	0.0581573i	$-0.0185225\pi$
$770$	−1.41666	+	2.45372i	−0.0510528	+	0.0884261i
$771$		0			0
$772$	−3.53095			−0.127082
$773$	−19.9777	+	34.6024i	−0.718548	+	1.24456i	0.243027	+	0.970020i	$0.421860\pi$
$773$	−19.9777	+	34.6024i	−0.718548	+	1.24456i	−0.961575	+	0.274542i	$0.911474\pi$
$774$		0			0
$775$	−0.187377	+	0.324546i	−0.00673077	+	0.0116580i
$776$	−6.47044	−	11.2071i	−0.232275	−	0.402312i
$777$		0			0
$778$	46.5444			1.66870
$779$	−25.6515	+	32.7542i	−0.919059	+	1.17354i
$780$		0			0
$781$	−3.98961	−	6.91022i	−0.142760	−	0.247267i
$782$	−5.58441	−	9.67249i	−0.199698	−	0.345888i
$783$		0

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:	\( N \)	\(=\)	\( 855 = 3^{2} \cdot 5 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	855.k (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.656312 - 1.13677i) q^{2} +(0.138510 - 0.239907i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.11486 q^{7} -2.98887 q^{8} +O(q^{10})\)	\(q+(-0.656312 - 1.13677i) q^{2} +(0.138510 - 0.239907i) q^{4} +(-0.500000 - 0.866025i) q^{5} +3.11486 q^{7} -2.98887 q^{8} +(-0.656312 + 1.13677i) q^{10} +0.692973 q^{11} +(2.07262 - 3.58988i) q^{13} +(-2.04432 - 3.54086i) q^{14} +(1.68461 + 2.91783i) q^{16} +(1.40392 + 2.43165i) q^{17} +(-1.62820 - 4.04339i) q^{19} -0.277020 q^{20} +(-0.454806 - 0.787748i) q^{22} +(1.51519 - 2.62438i) q^{23} +(-0.500000 + 0.866025i) q^{25} -5.44113 q^{26} +(0.431440 - 0.747275i) q^{28} +(1.93613 - 3.35348i) q^{29} +0.374753 q^{31} +(-0.777612 + 1.34686i) q^{32} +(1.84281 - 3.19185i) q^{34} +(-1.55743 - 2.69755i) q^{35} -1.34678 q^{37} +(-3.52778 + 4.50460i) q^{38} +(1.49443 + 2.58844i) q^{40} +(-4.77223 - 8.26575i) q^{41} +(2.32486 + 4.02677i) q^{43} +(0.0959838 - 0.166249i) q^{44} -3.97774 q^{46} +(0.0650711 - 0.112706i) q^{47} +2.70235 q^{49} +1.31262 q^{50} +(-0.574157 - 0.994469i) q^{52} +(0.442770 - 0.766900i) q^{53} +(-0.346487 - 0.600132i) q^{55} -9.30991 q^{56} -5.08282 q^{58} +(0.719490 + 1.24619i) q^{59} +(-1.63574 + 2.83319i) q^{61} +(-0.245955 - 0.426007i) q^{62} +8.77986 q^{64} -4.14523 q^{65} +(-5.44562 + 9.43209i) q^{67} +0.777826 q^{68} +(-2.04432 + 3.54086i) q^{70} +(-5.75724 - 9.97184i) q^{71} +(-2.37964 - 4.12166i) q^{73} +(0.883908 + 1.53097i) q^{74} +(-1.19556 - 0.169435i) q^{76} +2.15851 q^{77} +(-5.37760 - 9.31428i) q^{79} +(1.68461 - 2.91783i) q^{80} +(-6.26414 + 10.8498i) q^{82} +0.386145 q^{83} +(1.40392 - 2.43165i) q^{85} +(3.05166 - 5.28564i) q^{86} -2.07121 q^{88} +(-3.37096 + 5.83867i) q^{89} +(6.45591 - 11.1820i) q^{91} +(-0.419737 - 0.727006i) q^{92} -0.170828 q^{94} +(-2.68758 + 3.43175i) q^{95} +(2.16484 + 3.74962i) q^{97} +(-1.77359 - 3.07194i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8}+O(q^{10}) \) 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8	\( 12 q - 3 q^{2} - 5 q^{4} - 6 q^{5} + 4 q^{7} + 12 q^{8} - 3 q^{10} - 8 q^{13} - 10 q^{14} - 3 q^{16} - 4 q^{17} - 6 q^{19} + 10 q^{20} + 2 q^{23} - 6 q^{25} + 40 q^{26} - 26 q^{28} - 4 q^{29} + 24 q^{31} - 15 q^{32} + 7 q^{34} - 2 q^{35} + 29 q^{38} - 6 q^{40} - 12 q^{41} - 4 q^{43} - 6 q^{44} + 48 q^{46} - 6 q^{47} + 32 q^{49} + 6 q^{50} - 20 q^{52} - 26 q^{53} + 44 q^{56} - 20 q^{58} - 16 q^{59} + 20 q^{61} + 25 q^{62} + 28 q^{64} + 16 q^{65} - 12 q^{67} - 54 q^{68} - 10 q^{70} + 8 q^{71} - 4 q^{73} + 16 q^{74} - 66 q^{76} - 48 q^{77} - 12 q^{79} - 3 q^{80} + 26 q^{82} + 44 q^{83} - 4 q^{85} + 44 q^{86} - 32 q^{88} + 8 q^{89} + 2 q^{91} - 36 q^{92} - 14 q^{94} + 6 q^{95} + 30 q^{97} - 49 q^{98}+O(q^{100}) \) 12 * q - 3 * q^2 - 5 * q^4 - 6 * q^5 + 4 * q^7 + 12 * q^8 - 3 * q^10 - 8 * q^13 - 10 * q^14 - 3 * q^16 - 4 * q^17 - 6 * q^19 + 10 * q^20 + 2 * q^23 - 6 * q^25 + 40 * q^26 - 26 * q^28 - 4 * q^29 + 24 * q^31 - 15 * q^32 + 7 * q^34 - 2 * q^35 + 29 * q^38 - 6 * q^40 - 12 * q^41 - 4 * q^43 - 6 * q^44 + 48 * q^46 - 6 * q^47 + 32 * q^49 + 6 * q^50 - 20 * q^52 - 26 * q^53 + 44 * q^56 - 20 * q^58 - 16 * q^59 + 20 * q^61 + 25 * q^62 + 28 * q^64 + 16 * q^65 - 12 * q^67 - 54 * q^68 - 10 * q^70 + 8 * q^71 - 4 * q^73 + 16 * q^74 - 66 * q^76 - 48 * q^77 - 12 * q^79 - 3 * q^80 + 26 * q^82 + 44 * q^83 - 4 * q^85 + 44 * q^86 - 32 * q^88 + 8 * q^89 + 2 * q^91 - 36 * q^92 - 14 * q^94 + 6 * q^95 + 30 * q^97 - 49 * q^98

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