LMFDB - Embedded newform 4334.2.a.a.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.a (trivial)

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:	yes
Analytic conductor:	$34.6071642360$
Analytic rank:	$1$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - x^{14} - 23 x^{13} + 19 x^{12} + 194 x^{11} - 124 x^{10} - 761 x^{9} + 353 x^{8} + 1417 x^{7} - 465 x^{6} - 1128 x^{5} + 288 x^{4} + 316 x^{3} - 79 x^{2} - 20 x + 4 $ x^15 - x^14 - 23x^13 + 19x^12 + 194x^11 - 124x^10 - 761x^9 + 353x^8 + 1417x^7 - 465x^6 - 1128x^5 + 288x^4 + 316x^3 - 79x^2 - 20*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.275495$ of defining polynomial
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} +0.275495 q^{3} +1.00000 q^{4} -0.829257 q^{5} -0.275495 q^{6} +4.83738 q^{7} -1.00000 q^{8} -2.92410 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.275495 q^{3} +1.00000 q^{4} -0.829257 q^{5} -0.275495 q^{6} +4.83738 q^{7} -1.00000 q^{8} -2.92410 q^{9} +0.829257 q^{10} +1.00000 q^{11} +0.275495 q^{12} -4.69193 q^{13} -4.83738 q^{14} -0.228456 q^{15} +1.00000 q^{16} -3.61821 q^{17} +2.92410 q^{18} +3.96753 q^{19} -0.829257 q^{20} +1.33267 q^{21} -1.00000 q^{22} +3.89394 q^{23} -0.275495 q^{24} -4.31233 q^{25} +4.69193 q^{26} -1.63206 q^{27} +4.83738 q^{28} +7.12691 q^{29} +0.228456 q^{30} -5.82010 q^{31} -1.00000 q^{32} +0.275495 q^{33} +3.61821 q^{34} -4.01143 q^{35} -2.92410 q^{36} -7.26441 q^{37} -3.96753 q^{38} -1.29260 q^{39} +0.829257 q^{40} -2.08579 q^{41} -1.33267 q^{42} -10.3214 q^{43} +1.00000 q^{44} +2.42483 q^{45} -3.89394 q^{46} +5.67256 q^{47} +0.275495 q^{48} +16.4002 q^{49} +4.31233 q^{50} -0.996800 q^{51} -4.69193 q^{52} +8.95166 q^{53} +1.63206 q^{54} -0.829257 q^{55} -4.83738 q^{56} +1.09303 q^{57} -7.12691 q^{58} -9.73543 q^{59} -0.228456 q^{60} -12.1961 q^{61} +5.82010 q^{62} -14.1450 q^{63} +1.00000 q^{64} +3.89082 q^{65} -0.275495 q^{66} +12.1658 q^{67} -3.61821 q^{68} +1.07276 q^{69} +4.01143 q^{70} -7.84656 q^{71} +2.92410 q^{72} -0.146186 q^{73} +7.26441 q^{74} -1.18803 q^{75} +3.96753 q^{76} +4.83738 q^{77} +1.29260 q^{78} -6.17885 q^{79} -0.829257 q^{80} +8.32268 q^{81} +2.08579 q^{82} -13.7221 q^{83} +1.33267 q^{84} +3.00043 q^{85} +10.3214 q^{86} +1.96343 q^{87} -1.00000 q^{88} -5.85899 q^{89} -2.42483 q^{90} -22.6966 q^{91} +3.89394 q^{92} -1.60341 q^{93} -5.67256 q^{94} -3.29010 q^{95} -0.275495 q^{96} -12.1296 q^{97} -16.4002 q^{98} -2.92410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) $ 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	0.275495	0.159057	0.0795285	−	0.996833i	$-0.474659\pi$
$3$	0.275495	0.159057	0.0795285	+	0.996833i	$0.474659\pi$
$4$	1.00000	0.500000
$5$	−0.829257	−0.370855	−0.185428	−	0.982658i	$-0.559367\pi$
$5$	−0.829257	−0.370855	−0.185428	+	0.982658i	$0.559367\pi$
$6$	−0.275495	−0.112470
$7$	4.83738	1.82836	0.914178	−	0.405313i	$-0.132837\pi$
$7$	4.83738	1.82836	0.914178	+	0.405313i	$0.132837\pi$
$8$	−1.00000	−0.353553
$9$	−2.92410	−0.974701
$10$	0.829257	0.262234
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.275495	0.0795285
$13$	−4.69193	−1.30131	−0.650654	−	0.759374i	$-0.725505\pi$
$13$	−4.69193	−1.30131	−0.650654	+	0.759374i	$0.725505\pi$
$14$	−4.83738	−1.29284
$15$	−0.228456	−0.0589871
$16$	1.00000	0.250000
$17$	−3.61821	−0.877546	−0.438773	−	0.898598i	$-0.644587\pi$
$17$	−3.61821	−0.877546	−0.438773	+	0.898598i	$0.644587\pi$
$18$	2.92410	0.689218
$19$	3.96753	0.910213	0.455107	−	0.890437i	$-0.349601\pi$
$19$	3.96753	0.910213	0.455107	+	0.890437i	$0.349601\pi$
$20$	−0.829257	−0.185428
$21$	1.33267	0.290813
$22$	−1.00000	−0.213201
$23$	3.89394	0.811942	0.405971	−	0.913886i	$-0.366933\pi$
$23$	3.89394	0.811942	0.405971	+	0.913886i	$0.366933\pi$
$24$	−0.275495	−0.0562352
$25$	−4.31233	−0.862466
$26$	4.69193	0.920163
$27$	−1.63206	−0.314090
$28$	4.83738	0.914178
$29$	7.12691	1.32343	0.661717	−	0.749754i	$-0.269828\pi$
$29$	7.12691	1.32343	0.661717	+	0.749754i	$0.269828\pi$
$30$	0.228456	0.0417102
$31$	−5.82010	−1.04532	−0.522661	−	0.852541i	$-0.675060\pi$
$31$	−5.82010	−1.04532	−0.522661	+	0.852541i	$0.675060\pi$
$32$	−1.00000	−0.176777
$33$	0.275495	0.0479575
$34$	3.61821	0.620519
$35$	−4.01143	−0.678055
$36$	−2.92410	−0.487350
$37$	−7.26441	−1.19426	−0.597131	−	0.802144i	$-0.703693\pi$
$37$	−7.26441	−1.19426	−0.597131	+	0.802144i	$0.703693\pi$
$38$	−3.96753	−0.643618
$39$	−1.29260	−0.206982
$40$	0.829257	0.131117
$41$	−2.08579	−0.325746	−0.162873	−	0.986647i	$-0.552076\pi$
$41$	−2.08579	−0.325746	−0.162873	+	0.986647i	$0.552076\pi$
$42$	−1.33267	−0.205636
$43$	−10.3214	−1.57399	−0.786996	−	0.616958i	$-0.788365\pi$
$43$	−10.3214	−1.57399	−0.786996	+	0.616958i	$0.788365\pi$
$44$	1.00000	0.150756
$45$	2.42483	0.361473
$46$	−3.89394	−0.574130
$47$	5.67256	0.827428	0.413714	−	0.910407i	$-0.364231\pi$
$47$	5.67256	0.827428	0.413714	+	0.910407i	$0.364231\pi$
$48$	0.275495	0.0397643
$49$	16.4002	2.34289
$50$	4.31233	0.609856
$51$	−0.996800	−0.139580
$52$	−4.69193	−0.650654
$53$	8.95166	1.22961	0.614803	−	0.788681i	$-0.289236\pi$
$53$	8.95166	1.22961	0.614803	+	0.788681i	$0.289236\pi$
$54$	1.63206	0.222095
$55$	−0.829257	−0.111817
$56$	−4.83738	−0.646422
$57$	1.09303	0.144776
$58$	−7.12691	−0.935809
$59$	−9.73543	−1.26744	−0.633722	−	0.773560i	$-0.718474\pi$
$59$	−9.73543	−1.26744	−0.633722	+	0.773560i	$0.718474\pi$
$60$	−0.228456	−0.0294936
$61$	−12.1961	−1.56155	−0.780775	−	0.624812i	$-0.785176\pi$
$61$	−12.1961	−1.56155	−0.780775	+	0.624812i	$0.785176\pi$
$62$	5.82010	0.739154
$63$	−14.1450	−1.78210
$64$	1.00000	0.125000
$65$	3.89082	0.482597
$66$	−0.275495	−0.0339111
$67$	12.1658	1.48628	0.743142	−	0.669134i	$-0.233335\pi$
$67$	12.1658	1.48628	0.743142	+	0.669134i	$0.233335\pi$
$68$	−3.61821	−0.438773
$69$	1.07276	0.129145
$70$	4.01143	0.479458
$71$	−7.84656	−0.931216	−0.465608	−	0.884991i	$-0.654164\pi$
$71$	−7.84656	−0.931216	−0.465608	+	0.884991i	$0.654164\pi$
$72$	2.92410	0.344609
$73$	−0.146186	−0.0171098	−0.00855491	−	0.999963i	$-0.502723\pi$
$73$	−0.146186	−0.0171098	−0.00855491	+	0.999963i	$0.502723\pi$
$74$	7.26441	0.844470
$75$	−1.18803	−0.137181
$76$	3.96753	0.455107
$77$	4.83738	0.551270
$78$	1.29260	0.146358
$79$	−6.17885	−0.695174	−0.347587	−	0.937648i	$-0.612999\pi$
$79$	−6.17885	−0.695174	−0.347587	+	0.937648i	$0.612999\pi$
$80$	−0.829257	−0.0927138
$81$	8.32268	0.924743
$82$	2.08579	0.230337
$83$	−13.7221	−1.50620	−0.753100	−	0.657906i	$-0.771443\pi$
$83$	−13.7221	−1.50620	−0.753100	+	0.657906i	$0.771443\pi$
$84$	1.33267	0.145406
$85$	3.00043	0.325442
$86$	10.3214	1.11298
$87$	1.96343	0.210502
$88$	−1.00000	−0.106600
$89$	−5.85899	−0.621052	−0.310526	−	0.950565i	$-0.600505\pi$
$89$	−5.85899	−0.621052	−0.310526	+	0.950565i	$0.600505\pi$
$90$	−2.42483	−0.255600
$91$	−22.6966	−2.37925
$92$	3.89394	0.405971
$93$	−1.60341	−0.166266
$94$	−5.67256	−0.585080
$95$	−3.29010	−0.337557
$96$	−0.275495	−0.0281176
$97$	−12.1296	−1.23157	−0.615786	−	0.787913i	$-0.711161\pi$
$97$	−12.1296	−1.23157	−0.615786	+	0.787913i	$0.711161\pi$
$98$	−16.4002	−1.65667
$99$	−2.92410	−0.293883
$100$	−4.31233	−0.431233
$101$	−10.1809	−1.01304	−0.506521	−	0.862228i	$-0.669069\pi$
$101$	−10.1809	−1.01304	−0.506521	+	0.862228i	$0.669069\pi$
$102$	0.996800	0.0986979
$103$	−9.12868	−0.899475	−0.449738	−	0.893161i	$-0.648483\pi$
$103$	−9.12868	−0.899475	−0.449738	+	0.893161i	$0.648483\pi$
$104$	4.69193	0.460082
$105$	−1.10513	−0.107849
$106$	−8.95166	−0.869462
$107$	3.59450	0.347494	0.173747	−	0.984790i	$-0.444413\pi$
$107$	3.59450	0.347494	0.173747	+	0.984790i	$0.444413\pi$
$108$	−1.63206	−0.157045
$109$	2.25058	0.215567	0.107783	−	0.994174i	$-0.465625\pi$
$109$	2.25058	0.215567	0.107783	+	0.994174i	$0.465625\pi$
$110$	0.829257	0.0790666
$111$	−2.00131	−0.189956
$112$	4.83738	0.457089
$113$	0.169648	0.0159591	0.00797955	−	0.999968i	$-0.497460\pi$
$113$	0.169648	0.0159591	0.00797955	+	0.999968i	$0.497460\pi$
$114$	−1.09303	−0.102372
$115$	−3.22908	−0.301113
$116$	7.12691	0.661717
$117$	13.7197	1.26839
$118$	9.73543	0.896219
$119$	−17.5027	−1.60447
$120$	0.228456	0.0208551
$121$	1.00000	0.0909091
$122$	12.1961	1.10418
$123$	−0.574625	−0.0518121
$124$	−5.82010	−0.522661
$125$	7.72232	0.690705
$126$	14.1450	1.26014
$127$	9.99362	0.886790	0.443395	−	0.896326i	$-0.353774\pi$
$127$	9.99362	0.886790	0.443395	+	0.896326i	$0.353774\pi$
$128$	−1.00000	−0.0883883
$129$	−2.84348	−0.250354
$130$	−3.89082	−0.341247
$131$	12.0832	1.05572	0.527858	−	0.849333i	$-0.322995\pi$
$131$	12.0832	1.05572	0.527858	+	0.849333i	$0.322995\pi$
$132$	0.275495	0.0239788
$133$	19.1924	1.66419
$134$	−12.1658	−1.05096
$135$	1.35340	0.116482
$136$	3.61821	0.310259
$137$	18.5604	1.58572	0.792860	−	0.609404i	$-0.208591\pi$
$137$	18.5604	1.58572	0.792860	+	0.609404i	$0.208591\pi$
$138$	−1.07276	−0.0913193
$139$	7.49907	0.636063	0.318032	−	0.948080i	$-0.396978\pi$
$139$	7.49907	0.636063	0.318032	+	0.948080i	$0.396978\pi$
$140$	−4.01143	−0.339028
$141$	1.56276	0.131608
$142$	7.84656	0.658469
$143$	−4.69193	−0.392359
$144$	−2.92410	−0.243675
$145$	−5.91004	−0.490802
$146$	0.146186	0.0120985
$147$	4.51817	0.372653
$148$	−7.26441	−0.597131
$149$	5.94309	0.486877	0.243438	−	0.969916i	$-0.421725\pi$
$149$	5.94309	0.486877	0.243438	+	0.969916i	$0.421725\pi$
$150$	1.18803	0.0970019
$151$	−23.7015	−1.92880	−0.964400	−	0.264448i	$-0.914810\pi$
$151$	−23.7015	−1.92880	−0.964400	+	0.264448i	$0.914810\pi$
$152$	−3.96753	−0.321809
$153$	10.5800	0.855345
$154$	−4.83738	−0.389807
$155$	4.82636	0.387663
$156$	−1.29260	−0.103491
$157$	−9.43485	−0.752983	−0.376491	−	0.926420i	$-0.622870\pi$
$157$	−9.43485	−0.752983	−0.376491	+	0.926420i	$0.622870\pi$
$158$	6.17885	0.491563
$159$	2.46614	0.195577
$160$	0.829257	0.0655586
$161$	18.8364	1.48452
$162$	−8.32268	−0.653892
$163$	−9.82480	−0.769537	−0.384769	−	0.923013i	$-0.625719\pi$
$163$	−9.82480	−0.769537	−0.384769	+	0.923013i	$0.625719\pi$
$164$	−2.08579	−0.162873
$165$	−0.228456	−0.0177853
$166$	13.7221	1.06504
$167$	−10.1212	−0.783206	−0.391603	−	0.920134i	$-0.628079\pi$
$167$	−10.1212	−0.783206	−0.391603	+	0.920134i	$0.628079\pi$
$168$	−1.33267	−0.102818
$169$	9.01422	0.693402
$170$	−3.00043	−0.230123
$171$	−11.6015	−0.887185
$172$	−10.3214	−0.786996
$173$	8.49931	0.646191	0.323095	−	0.946366i	$-0.395277\pi$
$173$	8.49931	0.646191	0.323095	+	0.946366i	$0.395277\pi$
$174$	−1.96343	−0.148847
$175$	−20.8604	−1.57690
$176$	1.00000	0.0753778
$177$	−2.68206	−0.201596
$178$	5.85899	0.439150
$179$	9.56658	0.715040	0.357520	−	0.933906i	$-0.383622\pi$
$179$	9.56658	0.715040	0.357520	+	0.933906i	$0.383622\pi$
$180$	2.42483	0.180736
$181$	−3.88330	−0.288644	−0.144322	−	0.989531i	$-0.546100\pi$
$181$	−3.88330	−0.288644	−0.144322	+	0.989531i	$0.546100\pi$
$182$	22.6966	1.68239
$183$	−3.35996	−0.248376
$184$	−3.89394	−0.287065
$185$	6.02406	0.442898
$186$	1.60341	0.117568
$187$	−3.61821	−0.264590
$188$	5.67256	0.413714
$189$	−7.89489	−0.574269
$190$	3.29010	0.238689
$191$	7.50821	0.543275	0.271637	−	0.962400i	$-0.412435\pi$
$191$	7.50821	0.543275	0.271637	+	0.962400i	$0.412435\pi$
$192$	0.275495	0.0198821
$193$	−3.61012	−0.259862	−0.129931	−	0.991523i	$-0.541476\pi$
$193$	−3.61012	−0.259862	−0.129931	+	0.991523i	$0.541476\pi$
$194$	12.1296	0.870853
$195$	1.07190	0.0767604
$196$	16.4002	1.17144
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	2.92410	0.207807
$199$	−3.39694	−0.240803	−0.120401	−	0.992725i	$-0.538418\pi$
$199$	−3.39694	−0.240803	−0.120401	+	0.992725i	$0.538418\pi$
$200$	4.31233	0.304928
$201$	3.35160	0.236404
$202$	10.1809	0.716329
$203$	34.4755	2.41971
$204$	−0.996800	−0.0697899
$205$	1.72966	0.120804
$206$	9.12868	0.636025
$207$	−11.3863	−0.791400
$208$	−4.69193	−0.325327
$209$	3.96753	0.274440
$210$	1.10513	0.0762611
$211$	−6.08249	−0.418736	−0.209368	−	0.977837i	$-0.567141\pi$
$211$	−6.08249	−0.418736	−0.209368	+	0.977837i	$0.567141\pi$
$212$	8.95166	0.614803
$213$	−2.16169	−0.148116
$214$	−3.59450	−0.245715
$215$	8.55906	0.583723
$216$	1.63206	0.111048
$217$	−28.1540	−1.91122
$218$	−2.25058	−0.152429
$219$	−0.0402736	−0.00272144
$220$	−0.829257	−0.0559085
$221$	16.9764	1.14196
$222$	2.00131	0.134319
$223$	−6.28035	−0.420563	−0.210282	−	0.977641i	$-0.567438\pi$
$223$	−6.28035	−0.420563	−0.210282	+	0.977641i	$0.567438\pi$
$224$	−4.83738	−0.323211
$225$	12.6097	0.840647
$226$	−0.169648	−0.0112848
$227$	−20.0570	−1.33123	−0.665615	−	0.746295i	$-0.731831\pi$
$227$	−20.0570	−1.33123	−0.665615	+	0.746295i	$0.731831\pi$
$228$	1.09303	0.0723879
$229$	−5.47928	−0.362081	−0.181040	−	0.983476i	$-0.557946\pi$
$229$	−5.47928	−0.362081	−0.181040	+	0.983476i	$0.557946\pi$
$230$	3.22908	0.212919
$231$	1.33267	0.0876834
$232$	−7.12691	−0.467905
$233$	6.96448	0.456258	0.228129	−	0.973631i	$-0.426739\pi$
$233$	6.96448	0.456258	0.228129	+	0.973631i	$0.426739\pi$
$234$	−13.7197	−0.896884
$235$	−4.70401	−0.306856
$236$	−9.73543	−0.633722
$237$	−1.70224	−0.110572
$238$	17.5027	1.13453
$239$	−4.60506	−0.297876	−0.148938	−	0.988847i	$-0.547586\pi$
$239$	−4.60506	−0.297876	−0.148938	+	0.988847i	$0.547586\pi$
$240$	−0.228456	−0.0147468
$241$	7.16729	0.461686	0.230843	−	0.972991i	$-0.425852\pi$
$241$	7.16729	0.461686	0.230843	+	0.972991i	$0.425852\pi$
$242$	−1.00000	−0.0642824
$243$	7.18904	0.461177
$244$	−12.1961	−0.780775
$245$	−13.6000	−0.868872
$246$	0.574625	0.0366367
$247$	−18.6154	−1.18447
$248$	5.82010	0.369577
$249$	−3.78038	−0.239572
$250$	−7.72232	−0.488402
$251$	0.901357	0.0568931	0.0284466	−	0.999595i	$-0.490944\pi$
$251$	0.901357	0.0568931	0.0284466	+	0.999595i	$0.490944\pi$
$252$	−14.1450	−0.891050
$253$	3.89394	0.244810
$254$	−9.99362	−0.627055
$255$	0.826604	0.0517639
$256$	1.00000	0.0625000
$257$	−26.9133	−1.67881	−0.839403	−	0.543509i	$-0.817095\pi$
$257$	−26.9133	−1.67881	−0.839403	+	0.543509i	$0.817095\pi$
$258$	2.84348	0.177027
$259$	−35.1407	−2.18353
$260$	3.89082	0.241298
$261$	−20.8398	−1.28995
$262$	−12.0832	−0.746504
$263$	−7.91989	−0.488361	−0.244181	−	0.969730i	$-0.578519\pi$
$263$	−7.91989	−0.488361	−0.244181	+	0.969730i	$0.578519\pi$
$264$	−0.275495	−0.0169555
$265$	−7.42323	−0.456006
$266$	−19.1924	−1.17676
$267$	−1.61412	−0.0987826
$268$	12.1658	0.743142
$269$	−13.3200	−0.812137	−0.406069	−	0.913843i	$-0.633101\pi$
$269$	−13.3200	−0.812137	−0.406069	+	0.913843i	$0.633101\pi$
$270$	−1.35340	−0.0823652
$271$	2.17709	0.132249	0.0661243	−	0.997811i	$-0.478937\pi$
$271$	2.17709	0.132249	0.0661243	+	0.997811i	$0.478937\pi$
$272$	−3.61821	−0.219386
$273$	−6.25281	−0.378437
$274$	−18.5604	−1.12127
$275$	−4.31233	−0.260043
$276$	1.07276	0.0645725
$277$	0.716770	0.0430666	0.0215333	−	0.999768i	$-0.493145\pi$
$277$	0.716770	0.0430666	0.0215333	+	0.999768i	$0.493145\pi$
$278$	−7.49907	−0.449765
$279$	17.0186	1.01888
$280$	4.01143	0.239729
$281$	4.61908	0.275551	0.137776	−	0.990463i	$-0.456005\pi$
$281$	4.61908	0.275551	0.137776	+	0.990463i	$0.456005\pi$
$282$	−1.56276	−0.0930611
$283$	−17.5616	−1.04393	−0.521965	−	0.852967i	$-0.674801\pi$
$283$	−17.5616	−1.04393	−0.521965	+	0.852967i	$0.674801\pi$
$284$	−7.84656	−0.465608
$285$	−0.906406	−0.0536909
$286$	4.69193	0.277440
$287$	−10.0898	−0.595579
$288$	2.92410	0.172304
$289$	−3.90852	−0.229913
$290$	5.91004	0.347050
$291$	−3.34164	−0.195890
$292$	−0.146186	−0.00855491
$293$	14.6631	0.856629	0.428314	−	0.903630i	$-0.359108\pi$
$293$	14.6631	0.856629	0.428314	+	0.903630i	$0.359108\pi$
$294$	−4.51817	−0.263505
$295$	8.07318	0.470039
$296$	7.26441	0.422235
$297$	−1.63206	−0.0947017
$298$	−5.94309	−0.344274
$299$	−18.2701	−1.05659
$300$	−1.18803	−0.0685907
$301$	−49.9283	−2.87782
$302$	23.7015	1.36387
$303$	−2.80480	−0.161131
$304$	3.96753	0.227553
$305$	10.1137	0.579109
$306$	−10.5800	−0.604820
$307$	13.5913	0.775695	0.387847	−	0.921724i	$-0.373219\pi$
$307$	13.5913	0.775695	0.387847	+	0.921724i	$0.373219\pi$
$308$	4.83738	0.275635
$309$	−2.51490	−0.143068
$310$	−4.82636	−0.274119
$311$	−23.4225	−1.32817	−0.664084	−	0.747658i	$-0.731178\pi$
$311$	−23.4225	−1.32817	−0.664084	+	0.747658i	$0.731178\pi$
$312$	1.29260	0.0731792
$313$	−16.2882	−0.920664	−0.460332	−	0.887747i	$-0.652270\pi$
$313$	−16.2882	−0.920664	−0.460332	+	0.887747i	$0.652270\pi$
$314$	9.43485	0.532439
$315$	11.7298	0.660901
$316$	−6.17885	−0.347587
$317$	23.3554	1.31177	0.655884	−	0.754862i	$-0.272296\pi$
$317$	23.3554	1.31177	0.655884	+	0.754862i	$0.272296\pi$
$318$	−2.46614	−0.138294
$319$	7.12691	0.399030
$320$	−0.829257	−0.0463569
$321$	0.990267	0.0552713
$322$	−18.8364	−1.04971
$323$	−14.3554	−0.798754
$324$	8.32268	0.462371
$325$	20.2332	1.12233
$326$	9.82480	0.544145
$327$	0.620024	0.0342874
$328$	2.08579	0.115168
$329$	27.4403	1.51283
$330$	0.228456	0.0125761
$331$	34.2480	1.88244	0.941220	−	0.337793i	$-0.109680\pi$
$331$	34.2480	1.88244	0.941220	+	0.337793i	$0.109680\pi$
$332$	−13.7221	−0.753100
$333$	21.2419	1.16405
$334$	10.1212	0.553810
$335$	−10.0885	−0.551196
$336$	1.33267	0.0727032
$337$	−25.7171	−1.40090	−0.700450	−	0.713701i	$-0.747017\pi$
$337$	−25.7171	−1.40090	−0.700450	+	0.713701i	$0.747017\pi$
$338$	−9.01422	−0.490309
$339$	0.0467370	0.00253841
$340$	3.00043	0.162721
$341$	−5.82010	−0.315176
$342$	11.6015	0.627335
$343$	45.4723	2.45527
$344$	10.3214	0.556490
$345$	−0.889594	−0.0478941
$346$	−8.49931	−0.456926
$347$	26.8693	1.44242	0.721210	−	0.692717i	$-0.243586\pi$
$347$	26.8693	1.44242	0.721210	+	0.692717i	$0.243586\pi$
$348$	1.96343	0.105251
$349$	−19.8151	−1.06068	−0.530339	−	0.847786i	$-0.677935\pi$
$349$	−19.8151	−1.06068	−0.530339	+	0.847786i	$0.677935\pi$
$350$	20.8604	1.11503
$351$	7.65751	0.408728
$352$	−1.00000	−0.0533002
$353$	−23.1388	−1.23156	−0.615778	−	0.787920i	$-0.711158\pi$
$353$	−23.1388	−1.23156	−0.615778	+	0.787920i	$0.711158\pi$
$354$	2.68206	0.142550
$355$	6.50682	0.345346
$356$	−5.85899	−0.310526
$357$	−4.82189	−0.255202
$358$	−9.56658	−0.505609
$359$	−35.3470	−1.86554	−0.932771	−	0.360468i	$-0.882617\pi$
$359$	−35.3470	−1.86554	−0.932771	+	0.360468i	$0.882617\pi$
$360$	−2.42483	−0.127800
$361$	−3.25873	−0.171512
$362$	3.88330	0.204102
$363$	0.275495	0.0144597
$364$	−22.6966	−1.18963
$365$	0.121226	0.00634526
$366$	3.35996	0.175628
$367$	−1.43254	−0.0747779	−0.0373890	−	0.999301i	$-0.511904\pi$
$367$	−1.43254	−0.0747779	−0.0373890	+	0.999301i	$0.511904\pi$
$368$	3.89394	0.202985
$369$	6.09906	0.317505
$370$	−6.02406	−0.313176
$371$	43.3026	2.24816
$372$	−1.60341	−0.0831328
$373$	21.8486	1.13128	0.565639	−	0.824653i	$-0.308630\pi$
$373$	21.8486	1.13128	0.565639	+	0.824653i	$0.308630\pi$
$374$	3.61821	0.187093
$375$	2.12746	0.109862
$376$	−5.67256	−0.292540
$377$	−33.4390	−1.72219
$378$	7.89489	0.406069
$379$	−17.0176	−0.874135	−0.437067	−	0.899429i	$-0.643983\pi$
$379$	−17.0176	−0.874135	−0.437067	+	0.899429i	$0.643983\pi$
$380$	−3.29010	−0.168779
$381$	2.75319	0.141050
$382$	−7.50821	−0.384153
$383$	22.3816	1.14365	0.571823	−	0.820377i	$-0.306236\pi$
$383$	22.3816	1.14365	0.571823	+	0.820377i	$0.306236\pi$
$384$	−0.275495	−0.0140588
$385$	−4.01143	−0.204441
$386$	3.61012	0.183750
$387$	30.1807	1.53417
$388$	−12.1296	−0.615786
$389$	−17.5665	−0.890655	−0.445328	−	0.895368i	$-0.646913\pi$
$389$	−17.5665	−0.890655	−0.445328	+	0.895368i	$0.646913\pi$
$390$	−1.07190	−0.0542778
$391$	−14.0891	−0.712516
$392$	−16.4002	−0.828335
$393$	3.32887	0.167919
$394$	−1.00000	−0.0503793
$395$	5.12385	0.257809
$396$	−2.92410	−0.146942
$397$	−17.3428	−0.870411	−0.435205	−	0.900331i	$-0.643324\pi$
$397$	−17.3428	−0.870411	−0.435205	+	0.900331i	$0.643324\pi$
$398$	3.39694	0.170273
$399$	5.28741	0.264702
$400$	−4.31233	−0.215617
$401$	9.02318	0.450596	0.225298	−	0.974290i	$-0.427664\pi$
$401$	9.02318	0.450596	0.225298	+	0.974290i	$0.427664\pi$
$402$	−3.35160	−0.167163
$403$	27.3075	1.36028
$404$	−10.1809	−0.506521
$405$	−6.90165	−0.342946
$406$	−34.4755	−1.71099
$407$	−7.26441	−0.360083
$408$	0.996800	0.0493489
$409$	4.77298	0.236008	0.118004	−	0.993013i	$-0.462350\pi$
$409$	4.77298	0.236008	0.118004	+	0.993013i	$0.462350\pi$
$410$	−1.72966	−0.0854217
$411$	5.11329	0.252220
$412$	−9.12868	−0.449738
$413$	−47.0939	−2.31734
$414$	11.3863	0.559605
$415$	11.3792	0.558582
$416$	4.69193	0.230041
$417$	2.06596	0.101170
$418$	−3.96753	−0.194058
$419$	−25.3146	−1.23670	−0.618350	−	0.785903i	$-0.712199\pi$
$419$	−25.3146	−1.23670	−0.618350	+	0.785903i	$0.712199\pi$
$420$	−1.10513	−0.0539247
$421$	−29.7629	−1.45056	−0.725279	−	0.688455i	$-0.758289\pi$
$421$	−29.7629	−1.45056	−0.725279	+	0.688455i	$0.758289\pi$
$422$	6.08249	0.296091
$423$	−16.5871	−0.806495
$424$	−8.95166	−0.434731
$425$	15.6029	0.756854
$426$	2.16169	0.104734
$427$	−58.9971	−2.85507
$428$	3.59450	0.173747
$429$	−1.29260	−0.0624075
$430$	−8.55906	−0.412755
$431$	−6.96059	−0.335280	−0.167640	−	0.985848i	$-0.553615\pi$
$431$	−6.96059	−0.335280	−0.167640	+	0.985848i	$0.553615\pi$
$432$	−1.63206	−0.0785225
$433$	30.8500	1.48256	0.741278	−	0.671198i	$-0.234220\pi$
$433$	30.8500	1.48256	0.741278	+	0.671198i	$0.234220\pi$
$434$	28.1540	1.35144
$435$	−1.62819	−0.0780656
$436$	2.25058	0.107783
$437$	15.4493	0.739040
$438$	0.0402736	0.00192435
$439$	22.4922	1.07349	0.536747	−	0.843743i	$-0.319653\pi$
$439$	22.4922	1.07349	0.536747	+	0.843743i	$0.319653\pi$
$440$	0.829257	0.0395333
$441$	−47.9559	−2.28361
$442$	−16.9764	−0.807486
$443$	−4.94585	−0.234984	−0.117492	−	0.993074i	$-0.537486\pi$
$443$	−4.94585	−0.234984	−0.117492	+	0.993074i	$0.537486\pi$
$444$	−2.00131	−0.0949778
$445$	4.85861	0.230320
$446$	6.28035	0.297383
$447$	1.63729	0.0774412
$448$	4.83738	0.228545
$449$	29.3948	1.38723	0.693614	−	0.720347i	$-0.256017\pi$
$449$	29.3948	1.38723	0.693614	+	0.720347i	$0.256017\pi$
$450$	−12.6097	−0.594427
$451$	−2.08579	−0.0982160
$452$	0.169648	0.00797955
$453$	−6.52964	−0.306789
$454$	20.0570	0.941322
$455$	18.8214	0.882359
$456$	−1.09303	−0.0511860
$457$	−31.6624	−1.48110	−0.740552	−	0.671999i	$-0.765436\pi$
$457$	−31.6624	−1.48110	−0.740552	+	0.671999i	$0.765436\pi$
$458$	5.47928	0.256030
$459$	5.90514	0.275628
$460$	−3.22908	−0.150556
$461$	16.7107	0.778296	0.389148	−	0.921175i	$-0.372769\pi$
$461$	16.7107	0.778296	0.389148	+	0.921175i	$0.372769\pi$
$462$	−1.33267	−0.0620015
$463$	−26.5138	−1.23220	−0.616100	−	0.787668i	$-0.711288\pi$
$463$	−26.5138	−1.23220	−0.616100	+	0.787668i	$0.711288\pi$
$464$	7.12691	0.330859
$465$	1.32964	0.0616605
$466$	−6.96448	−0.322623
$467$	−15.2806	−0.707104	−0.353552	−	0.935415i	$-0.615026\pi$
$467$	−15.2806	−0.707104	−0.353552	+	0.935415i	$0.615026\pi$
$468$	13.7197	0.634193
$469$	58.8503	2.71746
$470$	4.70401	0.216980
$471$	−2.59925	−0.119767
$472$	9.73543	0.448109
$473$	−10.3214	−0.474576
$474$	1.70224	0.0781865
$475$	−17.1093	−0.785028
$476$	−17.5027	−0.802233
$477$	−26.1756	−1.19850
$478$	4.60506	0.210630
$479$	37.3582	1.70694	0.853469	−	0.521143i	$-0.174494\pi$
$479$	37.3582	1.70694	0.853469	+	0.521143i	$0.174494\pi$
$480$	0.228456	0.0104276
$481$	34.0841	1.55410
$482$	−7.16729	−0.326461
$483$	5.18934	0.236123
$484$	1.00000	0.0454545
$485$	10.0585	0.456735
$486$	−7.18904	−0.326101
$487$	−18.2127	−0.825296	−0.412648	−	0.910891i	$-0.635396\pi$
$487$	−18.2127	−0.825296	−0.412648	+	0.910891i	$0.635396\pi$
$488$	12.1961	0.552091
$489$	−2.70668	−0.122400
$490$	13.6000	0.614385
$491$	−40.6739	−1.83559	−0.917795	−	0.397055i	$-0.870032\pi$
$491$	−40.6739	−1.83559	−0.917795	+	0.397055i	$0.870032\pi$
$492$	−0.574625	−0.0259061
$493$	−25.7867	−1.16137
$494$	18.6154	0.837545
$495$	2.42483	0.108988
$496$	−5.82010	−0.261330
$497$	−37.9568	−1.70259
$498$	3.78038	0.169403
$499$	11.0473	0.494544	0.247272	−	0.968946i	$-0.420466\pi$
$499$	11.0473	0.494544	0.247272	+	0.968946i	$0.420466\pi$
$500$	7.72232	0.345353
$501$	−2.78835	−0.124574
$502$	−0.901357	−0.0402295
$503$	−16.2803	−0.725904	−0.362952	−	0.931808i	$-0.618231\pi$
$503$	−16.2803	−0.725904	−0.362952	+	0.931808i	$0.618231\pi$
$504$	14.1450	0.630068
$505$	8.44262	0.375692
$506$	−3.89394	−0.173107
$507$	2.48337	0.110290
$508$	9.99362	0.443395
$509$	−4.58003	−0.203006	−0.101503	−	0.994835i	$-0.532365\pi$
$509$	−4.58003	−0.203006	−0.101503	+	0.994835i	$0.532365\pi$
$510$	−0.826604	−0.0366026
$511$	−0.707158	−0.0312828
$512$	−1.00000	−0.0441942
$513$	−6.47524	−0.285889
$514$	26.9133	1.18710
$515$	7.57002	0.333575
$516$	−2.84348	−0.125177
$517$	5.67256	0.249479
$518$	35.1407	1.54399
$519$	2.34152	0.102781
$520$	−3.89082	−0.170624
$521$	21.0983	0.924334	0.462167	−	0.886793i	$-0.347072\pi$
$521$	21.0983	0.924334	0.462167	+	0.886793i	$0.347072\pi$
$522$	20.8398	0.912134
$523$	−26.1173	−1.14203	−0.571015	−	0.820939i	$-0.693450\pi$
$523$	−26.1173	−1.14203	−0.571015	+	0.820939i	$0.693450\pi$
$524$	12.0832	0.527858
$525$	−5.74693	−0.250816
$526$	7.91989	0.345324
$527$	21.0584	0.917317
$528$	0.275495	0.0119894
$529$	−7.83726	−0.340751
$530$	7.42323	0.322445
$531$	28.4674	1.23538
$532$	19.1924	0.832097
$533$	9.78638	0.423895
$534$	1.61412	0.0698499
$535$	−2.98077	−0.128870
$536$	−12.1658	−0.525481
$537$	2.63554	0.113732
$538$	13.3200	0.574268
$539$	16.4002	0.706407
$540$	1.35340	0.0582410
$541$	−46.2299	−1.98758	−0.993788	−	0.111287i	$-0.964503\pi$
$541$	−46.2299	−1.98758	−0.993788	+	0.111287i	$0.964503\pi$
$542$	−2.17709	−0.0935139
$543$	−1.06983	−0.0459108
$544$	3.61821	0.155130
$545$	−1.86631	−0.0799441
$546$	6.25281	0.267595
$547$	41.5825	1.77794	0.888969	−	0.457967i	$-0.151422\pi$
$547$	41.5825	1.77794	0.888969	+	0.457967i	$0.151422\pi$
$548$	18.5604	0.792860
$549$	35.6626	1.52204
$550$	4.31233	0.183878
$551$	28.2762	1.20461
$552$	−1.07276	−0.0456597
$553$	−29.8894	−1.27103
$554$	−0.716770	−0.0304527
$555$	1.65960	0.0704460
$556$	7.49907	0.318032
$557$	−40.7343	−1.72597	−0.862984	−	0.505232i	$-0.831407\pi$
$557$	−40.7343	−1.72597	−0.862984	+	0.505232i	$0.831407\pi$
$558$	−17.0186	−0.720454
$559$	48.4271	2.04825
$560$	−4.01143	−0.169514
$561$	−0.996800	−0.0420849
$562$	−4.61908	−0.194844
$563$	11.4817	0.483895	0.241947	−	0.970289i	$-0.422214\pi$
$563$	11.4817	0.483895	0.241947	+	0.970289i	$0.422214\pi$
$564$	1.56276	0.0658041
$565$	−0.140681	−0.00591851
$566$	17.5616	0.738169
$567$	40.2599	1.69076
$568$	7.84656	0.329235
$569$	27.8058	1.16568	0.582841	−	0.812586i	$-0.301941\pi$
$569$	27.8058	1.16568	0.582841	+	0.812586i	$0.301941\pi$
$570$	0.906406	0.0379652
$571$	−12.9931	−0.543746	−0.271873	−	0.962333i	$-0.587643\pi$
$571$	−12.9931	−0.543746	−0.271873	+	0.962333i	$0.587643\pi$
$572$	−4.69193	−0.196180
$573$	2.06847	0.0864117
$574$	10.0898	0.421138
$575$	−16.7919	−0.700272
$576$	−2.92410	−0.121838
$577$	−7.55341	−0.314453	−0.157226	−	0.987563i	$-0.550255\pi$
$577$	−7.55341	−0.314453	−0.157226	+	0.987563i	$0.550255\pi$
$578$	3.90852	0.162573
$579$	−0.994569	−0.0413329
$580$	−5.91004	−0.245401
$581$	−66.3792	−2.75387
$582$	3.34164	0.138515
$583$	8.95166	0.370740
$584$	0.146186	0.00604923
$585$	−11.3772	−0.470387
$586$	−14.6631	−0.605728
$587$	−27.0191	−1.11520	−0.557600	−	0.830110i	$-0.688278\pi$
$587$	−27.0191	−1.11520	−0.557600	+	0.830110i	$0.688278\pi$
$588$	4.51817	0.186326
$589$	−23.0914	−0.951465
$590$	−8.07318	−0.332367
$591$	0.275495	0.0113323
$592$	−7.26441	−0.298565
$593$	−38.9055	−1.59766	−0.798829	−	0.601559i	$-0.794547\pi$
$593$	−38.9055	−1.59766	−0.798829	+	0.601559i	$0.794547\pi$
$594$	1.63206	0.0669642
$595$	14.5142	0.595025
$596$	5.94309	0.243438
$597$	−0.935839	−0.0383013
$598$	18.2701	0.747119
$599$	−32.3648	−1.32239	−0.661195	−	0.750214i	$-0.729950\pi$
$599$	−32.3648	−1.32239	−0.661195	+	0.750214i	$0.729950\pi$
$600$	1.18803	0.0485009
$601$	13.9539	0.569189	0.284595	−	0.958648i	$-0.408141\pi$
$601$	13.9539	0.569189	0.284595	+	0.958648i	$0.408141\pi$
$602$	49.9283	2.03492
$603$	−35.5739	−1.44868
$604$	−23.7015	−0.964400
$605$	−0.829257	−0.0337141
$606$	2.80480	0.113937
$607$	25.2293	1.02403	0.512013	−	0.858978i	$-0.328900\pi$
$607$	25.2293	1.02403	0.512013	+	0.858978i	$0.328900\pi$
$608$	−3.96753	−0.160904
$609$	9.49784	0.384872
$610$	−10.1137	−0.409492
$611$	−26.6153	−1.07674
$612$	10.5800	0.427672
$613$	42.7405	1.72627	0.863135	−	0.504973i	$-0.168497\pi$
$613$	42.7405	1.72627	0.863135	+	0.504973i	$0.168497\pi$
$614$	−13.5913	−0.548499
$615$	0.476512	0.0192148
$616$	−4.83738	−0.194903
$617$	−16.1662	−0.650828	−0.325414	−	0.945572i	$-0.605504\pi$
$617$	−16.1662	−0.650828	−0.325414	+	0.945572i	$0.605504\pi$
$618$	2.51490	0.101164
$619$	23.6337	0.949917	0.474958	−	0.880008i	$-0.342463\pi$
$619$	23.6337	0.949917	0.474958	+	0.880008i	$0.342463\pi$
$620$	4.82636	0.193831
$621$	−6.35514	−0.255023
$622$	23.4225	0.939156
$623$	−28.3421	−1.13550
$624$	−1.29260	−0.0517455
$625$	15.1579	0.606315
$626$	16.2882	0.651008
$627$	1.09303	0.0436515
$628$	−9.43485	−0.376491
$629$	26.2842	1.04802
$630$	−11.7298	−0.467328
$631$	−15.9302	−0.634171	−0.317085	−	0.948397i	$-0.602704\pi$
$631$	−15.9302	−0.634171	−0.317085	+	0.948397i	$0.602704\pi$
$632$	6.17885	0.245781
$633$	−1.67569	−0.0666029
$634$	−23.3554	−0.927560
$635$	−8.28728	−0.328871
$636$	2.46614	0.0977887
$637$	−76.9486	−3.04882
$638$	−7.12691	−0.282157
$639$	22.9442	0.907657
$640$	0.829257	0.0327793
$641$	44.2360	1.74722	0.873608	−	0.486630i	$-0.161774\pi$
$641$	44.2360	1.74722	0.873608	+	0.486630i	$0.161774\pi$
$642$	−0.990267	−0.0390827
$643$	40.0020	1.57752	0.788762	−	0.614698i	$-0.210722\pi$
$643$	40.0020	1.57752	0.788762	+	0.614698i	$0.210722\pi$
$644$	18.8364	0.742259
$645$	2.35798	0.0928453
$646$	14.3554	0.564804
$647$	11.3381	0.445748	0.222874	−	0.974847i	$-0.428456\pi$
$647$	11.3381	0.445748	0.222874	+	0.974847i	$0.428456\pi$
$648$	−8.32268	−0.326946
$649$	−9.73543	−0.382149
$650$	−20.2332	−0.793610
$651$	−7.75629	−0.303993
$652$	−9.82480	−0.384769
$653$	6.92242	0.270895	0.135448	−	0.990785i	$-0.456753\pi$
$653$	6.92242	0.270895	0.135448	+	0.990785i	$0.456753\pi$
$654$	−0.620024	−0.0242449
$655$	−10.0201	−0.391518
$656$	−2.08579	−0.0814364
$657$	0.427464	0.0166769
$658$	−27.4403	−1.06973
$659$	15.1395	0.589750	0.294875	−	0.955536i	$-0.404722\pi$
$659$	15.1395	0.589750	0.294875	+	0.955536i	$0.404722\pi$
$660$	−0.228456	−0.00889265
$661$	−34.8415	−1.35518	−0.677588	−	0.735442i	$-0.736975\pi$
$661$	−34.8415	−1.35518	−0.677588	+	0.735442i	$0.736975\pi$
$662$	−34.2480	−1.33109
$663$	4.67692	0.181636
$664$	13.7221	0.532522
$665$	−15.9155	−0.617175
$666$	−21.2419	−0.823106
$667$	27.7517	1.07455
$668$	−10.1212	−0.391603
$669$	−1.73020	−0.0668936
$670$	10.0885	0.389754
$671$	−12.1961	−0.470825
$672$	−1.33267	−0.0514090
$673$	42.6829	1.64531	0.822653	−	0.568544i	$-0.192493\pi$
$673$	42.6829	1.64531	0.822653	+	0.568544i	$0.192493\pi$
$674$	25.7171	0.990586
$675$	7.03798	0.270892
$676$	9.01422	0.346701
$677$	23.8986	0.918500	0.459250	−	0.888307i	$-0.348118\pi$
$677$	23.8986	0.918500	0.459250	+	0.888307i	$0.348118\pi$
$678$	−0.0467370	−0.00179492
$679$	−58.6753	−2.25175
$680$	−3.00043	−0.115061
$681$	−5.52560	−0.211741
$682$	5.82010	0.222863
$683$	−14.9459	−0.571887	−0.285944	−	0.958246i	$-0.592307\pi$
$683$	−14.9459	−0.571887	−0.285944	+	0.958246i	$0.592307\pi$
$684$	−11.6015	−0.443593
$685$	−15.3913	−0.588072
$686$	−45.4723	−1.73614
$687$	−1.50951	−0.0575915
$688$	−10.3214	−0.393498
$689$	−42.0006	−1.60009
$690$	0.889594	0.0338663
$691$	21.4833	0.817263	0.408632	−	0.912699i	$-0.366006\pi$
$691$	21.4833	0.817263	0.408632	+	0.912699i	$0.366006\pi$
$692$	8.49931	0.323095
$693$	−14.1450	−0.537323
$694$	−26.8693	−1.01994
$695$	−6.21866	−0.235887
$696$	−1.96343	−0.0744235
$697$	7.54684	0.285857
$698$	19.8151	0.750012
$699$	1.91868	0.0725711
$700$	−20.8604	−0.788448
$701$	35.2764	1.33237	0.666186	−	0.745785i	$-0.267926\pi$
$701$	35.2764	1.33237	0.666186	+	0.745785i	$0.267926\pi$
$702$	−7.65751	−0.289014
$703$	−28.8217	−1.08703
$704$	1.00000	0.0376889
$705$	−1.29593	−0.0488076
$706$	23.1388	0.870842
$707$	−49.2491	−1.85220
$708$	−2.68206	−0.100798
$709$	24.3875	0.915893	0.457947	−	0.888980i	$-0.348585\pi$
$709$	24.3875	0.915893	0.457947	+	0.888980i	$0.348585\pi$
$710$	−6.50682	−0.244197
$711$	18.0676	0.677587
$712$	5.85899	0.219575
$713$	−22.6631	−0.848740
$714$	4.82189	0.180455
$715$	3.89082	0.145508
$716$	9.56658	0.357520
$717$	−1.26867	−0.0473793
$718$	35.3470	1.31914
$719$	6.56128	0.244695	0.122347	−	0.992487i	$-0.460958\pi$
$719$	6.56128	0.244695	0.122347	+	0.992487i	$0.460958\pi$
$720$	2.42483	0.0903682
$721$	−44.1588	−1.64456
$722$	3.25873	0.121277
$723$	1.97455	0.0734344
$724$	−3.88330	−0.144322
$725$	−30.7336	−1.14142
$726$	−0.275495	−0.0102246
$727$	24.5434	0.910264	0.455132	−	0.890424i	$-0.349592\pi$
$727$	24.5434	0.910264	0.455132	+	0.890424i	$0.349592\pi$
$728$	22.6966	0.841193
$729$	−22.9875	−0.851389
$730$	−0.121226	−0.00448678
$731$	37.3449	1.38125
$732$	−3.35996	−0.124188
$733$	−3.91980	−0.144781	−0.0723906	−	0.997376i	$-0.523063\pi$
$733$	−3.91980	−0.144781	−0.0723906	+	0.997376i	$0.523063\pi$
$734$	1.43254	0.0528760
$735$	−3.74673	−0.138200
$736$	−3.89394	−0.143532
$737$	12.1658	0.448131
$738$	−6.09906	−0.224510
$739$	25.0985	0.923263	0.461632	−	0.887072i	$-0.347264\pi$
$739$	25.0985	0.923263	0.461632	+	0.887072i	$0.347264\pi$
$740$	6.02406	0.221449
$741$	−5.12844	−0.188398
$742$	−43.3026	−1.58969
$743$	23.4706	0.861051	0.430526	−	0.902578i	$-0.358328\pi$
$743$	23.4706	0.861051	0.430526	+	0.902578i	$0.358328\pi$
$744$	1.60341	0.0587838
$745$	−4.92835	−0.180561
$746$	−21.8486	−0.799934
$747$	40.1250	1.46810
$748$	−3.61821	−0.132295
$749$	17.3880	0.635342
$750$	−2.12746	−0.0776839
$751$	10.1705	0.371127	0.185564	−	0.982632i	$-0.440589\pi$
$751$	10.1705	0.371127	0.185564	+	0.982632i	$0.440589\pi$
$752$	5.67256	0.206857
$753$	0.248319	0.00904925
$754$	33.4390	1.21778
$755$	19.6546	0.715305
$756$	−7.89489	−0.287134
$757$	−37.6292	−1.36766	−0.683828	−	0.729643i	$-0.739686\pi$
$757$	−37.6292	−1.36766	−0.683828	+	0.729643i	$0.739686\pi$
$758$	17.0176	0.618106
$759$	1.07276	0.0389387
$760$	3.29010	0.119345
$761$	0.0484792	0.00175737	0.000878684	−	1.00000i	$-0.499720\pi$
$761$	0.0484792	0.00175737	0.000878684		1.00000i	$0.499720\pi$
$762$	−2.75319	−0.0997376
$763$	10.8869	0.394133
$764$	7.50821	0.271637
$765$	−8.77357	−0.317209
$766$	−22.3816	−0.808680
$767$	45.6780	1.64934
$768$	0.275495	0.00994107
$769$	38.9130	1.40324	0.701620	−	0.712551i	$-0.252460\pi$
$769$	38.9130	1.40324	0.701620	+	0.712551i	$0.252460\pi$
$770$	4.01143	0.144562
$771$	−7.41448	−0.267026
$772$	−3.61012	−0.129931
$773$	50.5900	1.81960	0.909798	−	0.415051i	$-0.136236\pi$
$773$	50.5900	1.81960	0.909798	+	0.415051i	$0.136236\pi$
$774$	−30.1807	−1.08482
$775$	25.0982	0.901554
$776$	12.1296	0.435426
$777$	−9.68107	−0.347307
$778$	17.5665	0.629788
$779$	−8.27543	−0.296498
$780$	1.07190	0.0383802
$781$	−7.84656	−0.280772
$782$	14.0891	0.503825
$783$	−11.6315	−0.415678
$784$	16.4002	0.585722
$785$	7.82392	0.279248
$786$	−3.32887	−0.118737
$787$	−14.1567	−0.504632	−0.252316	−	0.967645i	$-0.581192\pi$
$787$	−14.1567	−0.504632	−0.252316	+	0.967645i	$0.581192\pi$
$788$	1.00000	0.0356235
$789$	−2.18189	−0.0776773
$790$	−5.12385	−0.182299
$791$	0.820649	0.0291789
$792$	2.92410	0.103903
$793$	57.2233	2.03206
$794$	17.3428	0.615473
$795$	−2.04506	−0.0725309
$796$	−3.39694	−0.120401
$797$	14.8443	0.525811	0.262905	−	0.964822i	$-0.415319\pi$
$797$	14.8443	0.525811	0.262905	+	0.964822i	$0.415319\pi$
$798$	−5.28741	−0.187172
$799$	−20.5245	−0.726106
$800$	4.31233	0.152464
$801$	17.1323	0.605340
$802$	−9.02318	−0.318620
$803$	−0.146186	−0.00515880
$804$	3.35160	0.118202
$805$	−15.6203	−0.550542
$806$	−27.3075	−0.961866
$807$	−3.66960	−0.129176
$808$	10.1809	0.358164
$809$	−2.79386	−0.0982271	−0.0491135	−	0.998793i	$-0.515640\pi$
$809$	−2.79386	−0.0982271	−0.0491135	+	0.998793i	$0.515640\pi$
$810$	6.90165	0.242499
$811$	−8.96871	−0.314934	−0.157467	−	0.987524i	$-0.550333\pi$
$811$	−8.96871	−0.314934	−0.157467	+	0.987524i	$0.550333\pi$
$812$	34.4755	1.20985
$813$	0.599777	0.0210351
$814$	7.26441	0.254617
$815$	8.14729	0.285387
$816$	−0.996800	−0.0348950
$817$	−40.9503	−1.43267
$818$	−4.77298	−0.166883
$819$	66.3673	2.31906
$820$	1.72966	0.0604022
$821$	28.1486	0.982392	0.491196	−	0.871049i	$-0.336560\pi$
$821$	28.1486	0.982392	0.491196	+	0.871049i	$0.336560\pi$
$822$	−5.11329	−0.178346
$823$	−24.6879	−0.860566	−0.430283	−	0.902694i	$-0.641586\pi$
$823$	−24.6879	−0.860566	−0.430283	+	0.902694i	$0.641586\pi$
$824$	9.12868	0.318013
$825$	−1.18803	−0.0413617
$826$	47.0939	1.63861
$827$	44.8396	1.55923	0.779613	−	0.626261i	$-0.215416\pi$
$827$	44.8396	1.55923	0.779613	+	0.626261i	$0.215416\pi$
$828$	−11.3863	−0.395700
$829$	−12.0773	−0.419463	−0.209732	−	0.977759i	$-0.567259\pi$
$829$	−12.0773	−0.419463	−0.209732	+	0.977759i	$0.567259\pi$
$830$	−11.3792	−0.394977
$831$	0.197467	0.00685004
$832$	−4.69193	−0.162663
$833$	−59.3395	−2.05599
$834$	−2.06596	−0.0715382
$835$	8.39312	0.290456
$836$	3.96753	0.137220
$837$	9.49875	0.328325
$838$	25.3146	0.874479
$839$	−53.8304	−1.85843	−0.929216	−	0.369537i	$-0.879516\pi$
$839$	−53.8304	−1.85843	−0.929216	+	0.369537i	$0.879516\pi$
$840$	1.10513	0.0381306
$841$	21.7929	0.751478
$842$	29.7629	1.02570
$843$	1.27253	0.0438283
$844$	−6.08249	−0.209368
$845$	−7.47511	−0.257152
$846$	16.5871	0.570278
$847$	4.83738	0.166214
$848$	8.95166	0.307401
$849$	−4.83813	−0.166044
$850$	−15.6029	−0.535177
$851$	−28.2871	−0.969670
$852$	−2.16169	−0.0740582
$853$	23.6977	0.811393	0.405697	−	0.914008i	$-0.367029\pi$
$853$	23.6977	0.811393	0.405697	+	0.914008i	$0.367029\pi$
$854$	58.9971	2.01884
$855$	9.62059	0.329017
$856$	−3.59450	−0.122858
$857$	−34.2047	−1.16841	−0.584204	−	0.811607i	$-0.698593\pi$
$857$	−34.2047	−1.16841	−0.584204	+	0.811607i	$0.698593\pi$
$858$	1.29260	0.0441287
$859$	−10.7322	−0.366180	−0.183090	−	0.983096i	$-0.558610\pi$
$859$	−10.7322	−0.366180	−0.183090	+	0.983096i	$0.558610\pi$
$860$	8.55906	0.291862
$861$	−2.77967	−0.0947311
$862$	6.96059	0.237079
$863$	12.8060	0.435922	0.217961	−	0.975957i	$-0.430059\pi$
$863$	12.8060	0.435922	0.217961	+	0.975957i	$0.430059\pi$
$864$	1.63206	0.0555238
$865$	−7.04812	−0.239643
$866$	−30.8500	−1.04833
$867$	−1.07678	−0.0365693
$868$	−28.1540	−0.955610
$869$	−6.17885	−0.209603
$870$	1.62819	0.0552007
$871$	−57.0809	−1.93411
$872$	−2.25058	−0.0762144
$873$	35.4681	1.20041
$874$	−15.4493	−0.522580
$875$	37.3558	1.26286
$876$	−0.0402736	−0.00136072
$877$	−40.5951	−1.37080	−0.685399	−	0.728168i	$-0.740372\pi$
$877$	−40.5951	−1.37080	−0.685399	+	0.728168i	$0.740372\pi$
$878$	−22.4922	−0.759075
$879$	4.03962	0.136253
$880$	−0.829257	−0.0279543
$881$	−26.1642	−0.881496	−0.440748	−	0.897631i	$-0.645287\pi$
$881$	−26.1642	−0.881496	−0.440748	+	0.897631i	$0.645287\pi$
$882$	47.9559	1.61476
$883$	2.99051	0.100639	0.0503194	−	0.998733i	$-0.483976\pi$
$883$	2.99051	0.100639	0.0503194	+	0.998733i	$0.483976\pi$
$884$	16.9764	0.570979
$885$	2.22412	0.0747629
$886$	4.94585	0.166159
$887$	−24.8922	−0.835797	−0.417899	−	0.908494i	$-0.637233\pi$
$887$	−24.8922	−0.835797	−0.417899	+	0.908494i	$0.637233\pi$
$888$	2.00131	0.0671595
$889$	48.3429	1.62137
$890$	−4.85861	−0.162861
$891$	8.32268	0.278820
$892$	−6.28035	−0.210282
$893$	22.5060	0.753136
$894$	−1.63729	−0.0547592
$895$	−7.93316	−0.265176
$896$	−4.83738	−0.161605
$897$	−5.03331	−0.168057
$898$	−29.3948	−0.980918
$899$	−41.4793	−1.38341
$900$	12.6097	0.420323
$901$	−32.3890	−1.07904
$902$	2.08579	0.0694492
$903$	−13.7550	−0.457737
$904$	−0.169648	−0.00564239
$905$	3.22026	0.107045
$906$	6.52964	0.216933
$907$	−1.84829	−0.0613714	−0.0306857	−	0.999529i	$-0.509769\pi$
$907$	−1.84829	−0.0613714	−0.0306857	+	0.999529i	$0.509769\pi$
$908$	−20.0570	−0.665615
$909$	29.7701	0.987413
$910$	−18.8214	−0.623922
$911$	−2.63136	−0.0871808	−0.0435904	−	0.999049i	$-0.513880\pi$
$911$	−2.63136	−0.0871808	−0.0435904	+	0.999049i	$0.513880\pi$
$912$	1.09303	0.0361940
$913$	−13.7221	−0.454137
$914$	31.6624	1.04730
$915$	2.78627	0.0921114
$916$	−5.47928	−0.181040
$917$	58.4511	1.93023
$918$	−5.90514	−0.194899
$919$	−42.5543	−1.40374	−0.701868	−	0.712307i	$-0.747650\pi$
$919$	−42.5543	−1.40374	−0.701868	+	0.712307i	$0.747650\pi$
$920$	3.22908	0.106459
$921$	3.74432	0.123380
$922$	−16.7107	−0.550339
$923$	36.8155	1.21180
$924$	1.33267	0.0438417
$925$	31.3265	1.03001
$926$	26.5138	0.871298
$927$	26.6932	0.876719
$928$	−7.12691	−0.233952
$929$	−19.6061	−0.643255	−0.321628	−	0.946866i	$-0.604230\pi$
$929$	−19.6061	−0.643255	−0.321628	+	0.946866i	$0.604230\pi$
$930$	−1.32964	−0.0436006
$931$	65.0682	2.13253
$932$	6.96448	0.228129
$933$	−6.45277	−0.211254
$934$	15.2806	0.499998
$935$	3.00043	0.0981246
$936$	−13.7197	−0.448442
$937$	27.8111	0.908550	0.454275	−	0.890861i	$-0.349898\pi$
$937$	27.8111	0.908550	0.454275	+	0.890861i	$0.349898\pi$
$938$	−58.8503	−1.92153
$939$	−4.48732	−0.146438
$940$	−4.70401	−0.153428
$941$	−22.8584	−0.745161	−0.372581	−	0.928000i	$-0.621527\pi$
$941$	−22.8584	−0.745161	−0.372581	+	0.928000i	$0.621527\pi$
$942$	2.59925	0.0846882
$943$	−8.12193	−0.264487
$944$	−9.73543	−0.316861
$945$	6.54689	0.212970
$946$	10.3214	0.335576
$947$	−5.64337	−0.183385	−0.0916925	−	0.995787i	$-0.529228\pi$
$947$	−5.64337	−0.183385	−0.0916925	+	0.995787i	$0.529228\pi$
$948$	−1.70224	−0.0552862
$949$	0.685896	0.0222651
$950$	17.1093	0.555099
$951$	6.43428	0.208646
$952$	17.5027	0.567265
$953$	−3.87642	−0.125570	−0.0627848	−	0.998027i	$-0.519998\pi$
$953$	−3.87642	−0.125570	−0.0627848	+	0.998027i	$0.519998\pi$
$954$	26.1756	0.847466
$955$	−6.22624	−0.201476
$956$	−4.60506	−0.148938
$957$	1.96343	0.0634686
$958$	−37.3582	−1.20699
$959$	89.7835	2.89926
$960$	−0.228456	−0.00737339
$961$	2.87358	0.0926961
$962$	−34.0841	−1.09892
$963$	−10.5107	−0.338702
$964$	7.16729	0.230843
$965$	2.99372	0.0963711
$966$	−5.18934	−0.166964
$967$	42.7324	1.37418	0.687091	−	0.726572i	$-0.258888\pi$
$967$	42.7324	1.37418	0.687091	+	0.726572i	$0.258888\pi$
$968$	−1.00000	−0.0321412
$969$	−3.95483	−0.127047
$970$	−10.0585	−0.322960
$971$	−23.2887	−0.747371	−0.373685	−	0.927556i	$-0.621906\pi$
$971$	−23.2887	−0.747371	−0.373685	+	0.927556i	$0.621906\pi$
$972$	7.18904	0.230588
$973$	36.2758	1.16295
$974$	18.2127	0.583572
$975$	5.57413	0.178515
$976$	−12.1961	−0.390388
$977$	−22.7720	−0.728541	−0.364270	−	0.931293i	$-0.618682\pi$
$977$	−22.7720	−0.728541	−0.364270	+	0.931293i	$0.618682\pi$
$978$	2.70668	0.0865501
$979$	−5.85899	−0.187254
$980$	−13.6000	−0.434436
$981$	−6.58094	−0.210113
$982$	40.6739	1.29796
$983$	51.6985	1.64892	0.824462	−	0.565917i	$-0.191478\pi$
$983$	51.6985	1.64892	0.824462	+	0.565917i	$0.191478\pi$
$984$	0.574625	0.0183184
$985$	−0.829257	−0.0264223
$986$	25.7867	0.821216
$987$	7.55966	0.240627
$988$	−18.6154	−0.592234
$989$	−40.1907	−1.27799
$990$	−2.42483	−0.0770663
$991$	−28.4828	−0.904787	−0.452393	−	0.891819i	$-0.649430\pi$
$991$	−28.4828	−0.904787	−0.452393	+	0.891819i	$0.649430\pi$
$992$	5.82010	0.184788
$993$	9.43515	0.299415
$994$	37.9568	1.20392
$995$	2.81694	0.0893029
$996$	−3.78038	−0.119786
$997$	48.3041	1.52980	0.764902	−	0.644146i	$-0.222787\pi$
$997$	48.3041	1.52980	0.764902	+	0.644146i	$0.222787\pi$
$998$	−11.0473	−0.349696
$999$	11.8559	0.375106

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.a.1.9	✓	15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.a.1.9	✓	15	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.275495 q^{3} +1.00000 q^{4} -0.829257 q^{5} -0.275495 q^{6} +4.83738 q^{7} -1.00000 q^{8} -2.92410 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.275495 q^{3} +1.00000 q^{4} -0.829257 q^{5} -0.275495 q^{6} +4.83738 q^{7} -1.00000 q^{8} -2.92410 q^{9} +0.829257 q^{10} +1.00000 q^{11} +0.275495 q^{12} -4.69193 q^{13} -4.83738 q^{14} -0.228456 q^{15} +1.00000 q^{16} -3.61821 q^{17} +2.92410 q^{18} +3.96753 q^{19} -0.829257 q^{20} +1.33267 q^{21} -1.00000 q^{22} +3.89394 q^{23} -0.275495 q^{24} -4.31233 q^{25} +4.69193 q^{26} -1.63206 q^{27} +4.83738 q^{28} +7.12691 q^{29} +0.228456 q^{30} -5.82010 q^{31} -1.00000 q^{32} +0.275495 q^{33} +3.61821 q^{34} -4.01143 q^{35} -2.92410 q^{36} -7.26441 q^{37} -3.96753 q^{38} -1.29260 q^{39} +0.829257 q^{40} -2.08579 q^{41} -1.33267 q^{42} -10.3214 q^{43} +1.00000 q^{44} +2.42483 q^{45} -3.89394 q^{46} +5.67256 q^{47} +0.275495 q^{48} +16.4002 q^{49} +4.31233 q^{50} -0.996800 q^{51} -4.69193 q^{52} +8.95166 q^{53} +1.63206 q^{54} -0.829257 q^{55} -4.83738 q^{56} +1.09303 q^{57} -7.12691 q^{58} -9.73543 q^{59} -0.228456 q^{60} -12.1961 q^{61} +5.82010 q^{62} -14.1450 q^{63} +1.00000 q^{64} +3.89082 q^{65} -0.275495 q^{66} +12.1658 q^{67} -3.61821 q^{68} +1.07276 q^{69} +4.01143 q^{70} -7.84656 q^{71} +2.92410 q^{72} -0.146186 q^{73} +7.26441 q^{74} -1.18803 q^{75} +3.96753 q^{76} +4.83738 q^{77} +1.29260 q^{78} -6.17885 q^{79} -0.829257 q^{80} +8.32268 q^{81} +2.08579 q^{82} -13.7221 q^{83} +1.33267 q^{84} +3.00043 q^{85} +10.3214 q^{86} +1.96343 q^{87} -1.00000 q^{88} -5.85899 q^{89} -2.42483 q^{90} -22.6966 q^{91} +3.89394 q^{92} -1.60341 q^{93} -5.67256 q^{94} -3.29010 q^{95} -0.275495 q^{96} -12.1296 q^{97} -16.4002 q^{98} -2.92410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9}+O(q^{10}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9	\( 15 q - 15 q^{2} - q^{3} + 15 q^{4} - 7 q^{5} + q^{6} + q^{7} - 15 q^{8} + 2 q^{9} + 7 q^{10} + 15 q^{11} - q^{12} - q^{13} - q^{14} - 6 q^{15} + 15 q^{16} - 6 q^{17} - 2 q^{18} - 14 q^{19} - 7 q^{20} - 3 q^{21} - 15 q^{22} + 2 q^{23} + q^{24} - 10 q^{25} + q^{26} - 7 q^{27} + q^{28} + 8 q^{29} + 6 q^{30} - 33 q^{31} - 15 q^{32} - q^{33} + 6 q^{34} - 8 q^{35} + 2 q^{36} - 9 q^{37} + 14 q^{38} - 9 q^{39} + 7 q^{40} - 10 q^{41} + 3 q^{42} - 6 q^{43} + 15 q^{44} - 20 q^{45} - 2 q^{46} - q^{47} - q^{48} - 30 q^{49} + 10 q^{50} + 12 q^{51} - q^{52} + 6 q^{53} + 7 q^{54} - 7 q^{55} - q^{56} - 24 q^{57} - 8 q^{58} - 15 q^{59} - 6 q^{60} - 25 q^{61} + 33 q^{62} + 12 q^{63} + 15 q^{64} + 31 q^{65} + q^{66} - 13 q^{67} - 6 q^{68} - 43 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} - 4 q^{73} + 9 q^{74} - 5 q^{75} - 14 q^{76} + q^{77} + 9 q^{78} - 20 q^{79} - 7 q^{80} + 11 q^{81} + 10 q^{82} + q^{83} - 3 q^{84} - q^{85} + 6 q^{86} + 22 q^{87} - 15 q^{88} - 41 q^{89} + 20 q^{90} - 31 q^{91} + 2 q^{92} + 14 q^{93} + q^{94} + 41 q^{95} + q^{96} - 57 q^{97} + 30 q^{98} + 2 q^{99}+O(q^{100}) \) 15 * q - 15 * q^2 - q^3 + 15 * q^4 - 7 * q^5 + q^6 + q^7 - 15 * q^8 + 2 * q^9 + 7 * q^10 + 15 * q^11 - q^12 - q^13 - q^14 - 6 * q^15 + 15 * q^16 - 6 * q^17 - 2 * q^18 - 14 * q^19 - 7 * q^20 - 3 * q^21 - 15 * q^22 + 2 * q^23 + q^24 - 10 * q^25 + q^26 - 7 * q^27 + q^28 + 8 * q^29 + 6 * q^30 - 33 * q^31 - 15 * q^32 - q^33 + 6 * q^34 - 8 * q^35 + 2 * q^36 - 9 * q^37 + 14 * q^38 - 9 * q^39 + 7 * q^40 - 10 * q^41 + 3 * q^42 - 6 * q^43 + 15 * q^44 - 20 * q^45 - 2 * q^46 - q^47 - q^48 - 30 * q^49 + 10 * q^50 + 12 * q^51 - q^52 + 6 * q^53 + 7 * q^54 - 7 * q^55 - q^56 - 24 * q^57 - 8 * q^58 - 15 * q^59 - 6 * q^60 - 25 * q^61 + 33 * q^62 + 12 * q^63 + 15 * q^64 + 31 * q^65 + q^66 - 13 * q^67 - 6 * q^68 - 43 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 - 4 * q^73 + 9 * q^74 - 5 * q^75 - 14 * q^76 + q^77 + 9 * q^78 - 20 * q^79 - 7 * q^80 + 11 * q^81 + 10 * q^82 + q^83 - 3 * q^84 - q^85 + 6 * q^86 + 22 * q^87 - 15 * q^88 - 41 * q^89 + 20 * q^90 - 31 * q^91 + 2 * q^92 + 14 * q^93 + q^94 + 41 * q^95 + q^96 - 57 * q^97 + 30 * q^98 + 2 * q^99

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