LMFDB - Embedded newform 8034.2.a.y.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8034,2,Mod(1,8034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8034, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8034 = 2 \cdot 3 \cdot 13 \cdot 103 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8034.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:	$64.1518129839$
Analytic rank:	$0$
Dimension:	$13$
Coefficient field:	$\mathbb{Q}[x]/(x^{13} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{13} - 5 x^{12} - 25 x^{11} + 134 x^{10} + 196 x^{9} - 1151 x^{8} - 801 x^{7} + 4263 x^{6} + \cdots - 180 $ x^13 - 5x^12 - 25x^11 + 134x^10 + 196x^9 - 1151x^8 - 801x^7 + 4263x^6 + 2205x^5 - 6840x^4 - 3579x^3 + 3559x^2 + 1839x - 180
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Root			$-0.892751$ of defining polynomial
Character	$\chi$	$=$	8034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.04935 q^{5} -1.00000 q^{6} -0.892751 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.04935 q^{5} -1.00000 q^{6} -0.892751 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.04935 q^{10} -2.88658 q^{11} -1.00000 q^{12} +1.00000 q^{13} -0.892751 q^{14} -1.04935 q^{15} +1.00000 q^{16} +5.24247 q^{17} +1.00000 q^{18} -3.82806 q^{19} +1.04935 q^{20} +0.892751 q^{21} -2.88658 q^{22} +3.40981 q^{23} -1.00000 q^{24} -3.89887 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.892751 q^{28} +10.1001 q^{29} -1.04935 q^{30} -3.82806 q^{31} +1.00000 q^{32} +2.88658 q^{33} +5.24247 q^{34} -0.936804 q^{35} +1.00000 q^{36} -2.83071 q^{37} -3.82806 q^{38} -1.00000 q^{39} +1.04935 q^{40} +2.99710 q^{41} +0.892751 q^{42} +0.469039 q^{43} -2.88658 q^{44} +1.04935 q^{45} +3.40981 q^{46} +7.74423 q^{47} -1.00000 q^{48} -6.20299 q^{49} -3.89887 q^{50} -5.24247 q^{51} +1.00000 q^{52} +11.7592 q^{53} -1.00000 q^{54} -3.02902 q^{55} -0.892751 q^{56} +3.82806 q^{57} +10.1001 q^{58} -5.26893 q^{59} -1.04935 q^{60} -9.73575 q^{61} -3.82806 q^{62} -0.892751 q^{63} +1.00000 q^{64} +1.04935 q^{65} +2.88658 q^{66} +3.50820 q^{67} +5.24247 q^{68} -3.40981 q^{69} -0.936804 q^{70} -1.47343 q^{71} +1.00000 q^{72} -5.46808 q^{73} -2.83071 q^{74} +3.89887 q^{75} -3.82806 q^{76} +2.57700 q^{77} -1.00000 q^{78} +11.7380 q^{79} +1.04935 q^{80} +1.00000 q^{81} +2.99710 q^{82} -3.28076 q^{83} +0.892751 q^{84} +5.50116 q^{85} +0.469039 q^{86} -10.1001 q^{87} -2.88658 q^{88} +0.663018 q^{89} +1.04935 q^{90} -0.892751 q^{91} +3.40981 q^{92} +3.82806 q^{93} +7.74423 q^{94} -4.01696 q^{95} -1.00000 q^{96} +3.33231 q^{97} -6.20299 q^{98} -2.88658 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * 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
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.04935	0.469281	0.234641	−	0.972082i	$-0.424609\pi$
$5$	1.04935	0.469281	0.234641	+	0.972082i	$0.424609\pi$
$6$	−1.00000	−0.408248
$7$	−0.892751	−0.337428	−0.168714	−	0.985665i	$-0.553961\pi$
$7$	−0.892751	−0.337428	−0.168714	+	0.985665i	$0.553961\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.04935	0.331832
$11$	−2.88658	−0.870337	−0.435168	−	0.900349i	$-0.643311\pi$
$11$	−2.88658	−0.870337	−0.435168	+	0.900349i	$0.643311\pi$
$12$	−1.00000	−0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−0.892751	−0.238598
$15$	−1.04935	−0.270940
$16$	1.00000	0.250000
$17$	5.24247	1.27149	0.635743	−	0.771901i	$-0.280694\pi$
$17$	5.24247	1.27149	0.635743	+	0.771901i	$0.280694\pi$
$18$	1.00000	0.235702
$19$	−3.82806	−0.878217	−0.439109	−	0.898434i	$-0.644706\pi$
$19$	−3.82806	−0.878217	−0.439109	+	0.898434i	$0.644706\pi$
$20$	1.04935	0.234641
$21$	0.892751	0.194814
$22$	−2.88658	−0.615421
$23$	3.40981	0.710995	0.355498	−	0.934677i	$-0.384311\pi$
$23$	3.40981	0.710995	0.355498	+	0.934677i	$0.384311\pi$
$24$	−1.00000	−0.204124
$25$	−3.89887	−0.779775
$26$	1.00000	0.196116
$27$	−1.00000	−0.192450
$28$	−0.892751	−0.168714
$29$	10.1001	1.87555	0.937773	−	0.347250i	$-0.112884\pi$
$29$	10.1001	1.87555	0.937773	+	0.347250i	$0.112884\pi$
$30$	−1.04935	−0.191583
$31$	−3.82806	−0.687540	−0.343770	−	0.939054i	$-0.611704\pi$
$31$	−3.82806	−0.687540	−0.343770	+	0.939054i	$0.611704\pi$
$32$	1.00000	0.176777
$33$	2.88658	0.502489
$34$	5.24247	0.899076
$35$	−0.936804	−0.158349
$36$	1.00000	0.166667
$37$	−2.83071	−0.465365	−0.232683	−	0.972553i	$-0.574750\pi$
$37$	−2.83071	−0.465365	−0.232683	+	0.972553i	$0.574750\pi$
$38$	−3.82806	−0.620993
$39$	−1.00000	−0.160128
$40$	1.04935	0.165916
$41$	2.99710	0.468069	0.234035	−	0.972228i	$-0.424807\pi$
$41$	2.99710	0.468069	0.234035	+	0.972228i	$0.424807\pi$
$42$	0.892751	0.137755
$43$	0.469039	0.0715277	0.0357639	−	0.999360i	$-0.488614\pi$
$43$	0.469039	0.0715277	0.0357639	+	0.999360i	$0.488614\pi$
$44$	−2.88658	−0.435168
$45$	1.04935	0.156427
$46$	3.40981	0.502750
$47$	7.74423	1.12961	0.564806	−	0.825224i	$-0.308951\pi$
$47$	7.74423	1.12961	0.564806	+	0.825224i	$0.308951\pi$
$48$	−1.00000	−0.144338
$49$	−6.20299	−0.886142
$50$	−3.89887	−0.551384
$51$	−5.24247	−0.734092
$52$	1.00000	0.138675
$53$	11.7592	1.61525	0.807627	−	0.589693i	$-0.200751\pi$
$53$	11.7592	1.61525	0.807627	+	0.589693i	$0.200751\pi$
$54$	−1.00000	−0.136083
$55$	−3.02902	−0.408433
$56$	−0.892751	−0.119299
$57$	3.82806	0.507039
$58$	10.1001	1.32621
$59$	−5.26893	−0.685956	−0.342978	−	0.939344i	$-0.611436\pi$
$59$	−5.26893	−0.685956	−0.342978	+	0.939344i	$0.611436\pi$
$60$	−1.04935	−0.135470
$61$	−9.73575	−1.24654	−0.623268	−	0.782009i	$-0.714195\pi$
$61$	−9.73575	−1.24654	−0.623268	+	0.782009i	$0.714195\pi$
$62$	−3.82806	−0.486164
$63$	−0.892751	−0.112476
$64$	1.00000	0.125000
$65$	1.04935	0.130155
$66$	2.88658	0.355313
$67$	3.50820	0.428595	0.214297	−	0.976768i	$-0.431254\pi$
$67$	3.50820	0.428595	0.214297	+	0.976768i	$0.431254\pi$
$68$	5.24247	0.635743
$69$	−3.40981	−0.410493
$70$	−0.936804	−0.111970
$71$	−1.47343	−0.174864	−0.0874321	−	0.996170i	$-0.527866\pi$
$71$	−1.47343	−0.174864	−0.0874321	+	0.996170i	$0.527866\pi$
$72$	1.00000	0.117851
$73$	−5.46808	−0.639991	−0.319995	−	0.947419i	$-0.603681\pi$
$73$	−5.46808	−0.639991	−0.319995	+	0.947419i	$0.603681\pi$
$74$	−2.83071	−0.329063
$75$	3.89887	0.450203
$76$	−3.82806	−0.439109
$77$	2.57700	0.293676
$78$	−1.00000	−0.113228
$79$	11.7380	1.32063	0.660315	−	0.750989i	$-0.270423\pi$
$79$	11.7380	1.32063	0.660315	+	0.750989i	$0.270423\pi$
$80$	1.04935	0.117320
$81$	1.00000	0.111111
$82$	2.99710	0.330975
$83$	−3.28076	−0.360111	−0.180055	−	0.983656i	$-0.557628\pi$
$83$	−3.28076	−0.360111	−0.180055	+	0.983656i	$0.557628\pi$
$84$	0.892751	0.0974072
$85$	5.50116	0.596684
$86$	0.469039	0.0505777
$87$	−10.1001	−1.08285
$88$	−2.88658	−0.307710
$89$	0.663018	0.0702798	0.0351399	−	0.999382i	$-0.488812\pi$
$89$	0.663018	0.0702798	0.0351399	+	0.999382i	$0.488812\pi$
$90$	1.04935	0.110611
$91$	−0.892751	−0.0935858
$92$	3.40981	0.355498
$93$	3.82806	0.396951
$94$	7.74423	0.798757
$95$	−4.01696	−0.412131
$96$	−1.00000	−0.102062
$97$	3.33231	0.338345	0.169172	−	0.985586i	$-0.445891\pi$
$97$	3.33231	0.338345	0.169172	+	0.985586i	$0.445891\pi$
$98$	−6.20299	−0.626597
$99$	−2.88658	−0.290112
$100$	−3.89887	−0.389887
$101$	15.2526	1.51769	0.758846	−	0.651270i	$-0.225764\pi$
$101$	15.2526	1.51769	0.758846	+	0.651270i	$0.225764\pi$
$102$	−5.24247	−0.519082
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	1.00000	0.0980581
$105$	0.936804	0.0914227
$106$	11.7592	1.14216
$107$	10.2127	0.987299	0.493650	−	0.869661i	$-0.335663\pi$
$107$	10.2127	0.987299	0.493650	+	0.869661i	$0.335663\pi$
$108$	−1.00000	−0.0962250
$109$	−1.64471	−0.157535	−0.0787674	−	0.996893i	$-0.525098\pi$
$109$	−1.64471	−0.157535	−0.0787674	+	0.996893i	$0.525098\pi$
$110$	−3.02902	−0.288806
$111$	2.83071	0.268679
$112$	−0.892751	−0.0843571
$113$	14.7334	1.38601	0.693003	−	0.720935i	$-0.256287\pi$
$113$	14.7334	1.38601	0.693003	+	0.720935i	$0.256287\pi$
$114$	3.82806	0.358531
$115$	3.57807	0.333657
$116$	10.1001	0.937773
$117$	1.00000	0.0924500
$118$	−5.26893	−0.485044
$119$	−4.68022	−0.429035
$120$	−1.04935	−0.0957917
$121$	−2.66766	−0.242514
$122$	−9.73575	−0.881434
$123$	−2.99710	−0.270240
$124$	−3.82806	−0.343770
$125$	−9.33799	−0.835215
$126$	−0.892751	−0.0795326
$127$	11.7057	1.03871	0.519357	−	0.854557i	$-0.326172\pi$
$127$	11.7057	1.03871	0.519357	+	0.854557i	$0.326172\pi$
$128$	1.00000	0.0883883
$129$	−0.469039	−0.0412966
$130$	1.04935	0.0920336
$131$	−6.42064	−0.560974	−0.280487	−	0.959858i	$-0.590496\pi$
$131$	−6.42064	−0.560974	−0.280487	+	0.959858i	$0.590496\pi$
$132$	2.88658	0.251245
$133$	3.41751	0.296335
$134$	3.50820	0.303062
$135$	−1.04935	−0.0903132
$136$	5.24247	0.449538
$137$	11.2530	0.961407	0.480704	−	0.876883i	$-0.340381\pi$
$137$	11.2530	0.961407	0.480704	+	0.876883i	$0.340381\pi$
$138$	−3.40981	−0.290263
$139$	10.5753	0.896988	0.448494	−	0.893786i	$-0.351960\pi$
$139$	10.5753	0.896988	0.448494	+	0.893786i	$0.351960\pi$
$140$	−0.936804	−0.0791744
$141$	−7.74423	−0.652182
$142$	−1.47343	−0.123648
$143$	−2.88658	−0.241388
$144$	1.00000	0.0833333
$145$	10.5985	0.880159
$146$	−5.46808	−0.452542
$147$	6.20299	0.511614
$148$	−2.83071	−0.232683
$149$	16.4725	1.34948	0.674740	−	0.738056i	$-0.264256\pi$
$149$	16.4725	1.34948	0.674740	+	0.738056i	$0.264256\pi$
$150$	3.89887	0.318342
$151$	−4.66834	−0.379904	−0.189952	−	0.981793i	$-0.560833\pi$
$151$	−4.66834	−0.379904	−0.189952	+	0.981793i	$0.560833\pi$
$152$	−3.82806	−0.310497
$153$	5.24247	0.423828
$154$	2.57700	0.207660
$155$	−4.01696	−0.322650
$156$	−1.00000	−0.0800641
$157$	6.51808	0.520200	0.260100	−	0.965582i	$-0.416245\pi$
$157$	6.51808	0.520200	0.260100	+	0.965582i	$0.416245\pi$
$158$	11.7380	0.933827
$159$	−11.7592	−0.932568
$160$	1.04935	0.0829580
$161$	−3.04412	−0.239910
$162$	1.00000	0.0785674
$163$	11.5836	0.907297	0.453648	−	0.891181i	$-0.350122\pi$
$163$	11.5836	0.907297	0.453648	+	0.891181i	$0.350122\pi$
$164$	2.99710	0.234035
$165$	3.02902	0.235809
$166$	−3.28076	−0.254637
$167$	−21.2064	−1.64100	−0.820502	−	0.571644i	$-0.806306\pi$
$167$	−21.2064	−1.64100	−0.820502	+	0.571644i	$0.806306\pi$
$168$	0.892751	0.0688773
$169$	1.00000	0.0769231
$170$	5.50116	0.421920
$171$	−3.82806	−0.292739
$172$	0.469039	0.0357639
$173$	6.04331	0.459465	0.229732	−	0.973254i	$-0.426215\pi$
$173$	6.04331	0.459465	0.229732	+	0.973254i	$0.426215\pi$
$174$	−10.1001	−0.765688
$175$	3.48073	0.263118
$176$	−2.88658	−0.217584
$177$	5.26893	0.396037
$178$	0.663018	0.0496953
$179$	−18.5677	−1.38781	−0.693907	−	0.720065i	$-0.744112\pi$
$179$	−18.5677	−1.38781	−0.693907	+	0.720065i	$0.744112\pi$
$180$	1.04935	0.0782136
$181$	12.2559	0.910970	0.455485	−	0.890243i	$-0.349466\pi$
$181$	12.2559	0.910970	0.455485	+	0.890243i	$0.349466\pi$
$182$	−0.892751	−0.0661751
$183$	9.73575	0.719688
$184$	3.40981	0.251375
$185$	−2.97039	−0.218387
$186$	3.82806	0.280687
$187$	−15.1328	−1.10662
$188$	7.74423	0.564806
$189$	0.892751	0.0649381
$190$	−4.01696	−0.291421
$191$	−13.1689	−0.952866	−0.476433	−	0.879211i	$-0.658071\pi$
$191$	−13.1689	−0.952866	−0.476433	+	0.879211i	$0.658071\pi$
$192$	−1.00000	−0.0721688
$193$	20.4134	1.46939	0.734695	−	0.678398i	$-0.237325\pi$
$193$	20.4134	1.46939	0.734695	+	0.678398i	$0.237325\pi$
$194$	3.33231	0.239246
$195$	−1.04935	−0.0751452
$196$	−6.20299	−0.443071
$197$	6.16171	0.439004	0.219502	−	0.975612i	$-0.429557\pi$
$197$	6.16171	0.439004	0.219502	+	0.975612i	$0.429557\pi$
$198$	−2.88658	−0.205140
$199$	4.16170	0.295015	0.147508	−	0.989061i	$-0.452875\pi$
$199$	4.16170	0.295015	0.147508	+	0.989061i	$0.452875\pi$
$200$	−3.89887	−0.275692
$201$	−3.50820	−0.247449
$202$	15.2526	1.07317
$203$	−9.01690	−0.632862
$204$	−5.24247	−0.367046
$205$	3.14500	0.219656
$206$	1.00000	0.0696733
$207$	3.40981	0.236998
$208$	1.00000	0.0693375
$209$	11.0500	0.764345
$210$	0.936804	0.0646456
$211$	−15.1427	−1.04247	−0.521233	−	0.853414i	$-0.674528\pi$
$211$	−15.1427	−1.04247	−0.521233	+	0.853414i	$0.674528\pi$
$212$	11.7592	0.807627
$213$	1.47343	0.100958
$214$	10.2127	0.698126
$215$	0.492183	0.0335666
$216$	−1.00000	−0.0680414
$217$	3.41751	0.231995
$218$	−1.64471	−0.111394
$219$	5.46808	0.369499
$220$	−3.02902	−0.204216
$221$	5.24247	0.352647
$222$	2.83071	0.189985
$223$	17.7938	1.19156	0.595781	−	0.803147i	$-0.296843\pi$
$223$	17.7938	1.19156	0.595781	+	0.803147i	$0.296843\pi$
$224$	−0.892751	−0.0596495
$225$	−3.89887	−0.259925
$226$	14.7334	0.980054
$227$	4.15039	0.275471	0.137736	−	0.990469i	$-0.456018\pi$
$227$	4.15039	0.275471	0.137736	+	0.990469i	$0.456018\pi$
$228$	3.82806	0.253520
$229$	21.1826	1.39979	0.699893	−	0.714248i	$-0.253231\pi$
$229$	21.1826	1.39979	0.699893	+	0.714248i	$0.253231\pi$
$230$	3.57807	0.235931
$231$	−2.57700	−0.169554
$232$	10.1001	0.663105
$233$	−20.0325	−1.31237	−0.656187	−	0.754598i	$-0.727832\pi$
$233$	−20.0325	−1.31237	−0.656187	+	0.754598i	$0.727832\pi$
$234$	1.00000	0.0653720
$235$	8.12637	0.530106
$236$	−5.26893	−0.342978
$237$	−11.7380	−0.762466
$238$	−4.68022	−0.303374
$239$	−11.6672	−0.754691	−0.377346	−	0.926072i	$-0.623163\pi$
$239$	−11.6672	−0.754691	−0.377346	+	0.926072i	$0.623163\pi$
$240$	−1.04935	−0.0677349
$241$	−24.2592	−1.56267	−0.781335	−	0.624111i	$-0.785461\pi$
$241$	−24.2592	−1.56267	−0.781335	+	0.624111i	$0.785461\pi$
$242$	−2.66766	−0.171484
$243$	−1.00000	−0.0641500
$244$	−9.73575	−0.623268
$245$	−6.50908	−0.415850
$246$	−2.99710	−0.191088
$247$	−3.82806	−0.243574
$248$	−3.82806	−0.243082
$249$	3.28076	0.207910
$250$	−9.33799	−0.590586
$251$	2.35132	0.148414	0.0742070	−	0.997243i	$-0.476357\pi$
$251$	2.35132	0.148414	0.0742070	+	0.997243i	$0.476357\pi$
$252$	−0.892751	−0.0562381
$253$	−9.84270	−0.618805
$254$	11.7057	0.734482
$255$	−5.50116	−0.344496
$256$	1.00000	0.0625000
$257$	4.34483	0.271023	0.135511	−	0.990776i	$-0.456732\pi$
$257$	4.34483	0.271023	0.135511	+	0.990776i	$0.456732\pi$
$258$	−0.469039	−0.0292011
$259$	2.52712	0.157027
$260$	1.04935	0.0650776
$261$	10.1001	0.625182
$262$	−6.42064	−0.396668
$263$	5.19040	0.320054	0.160027	−	0.987113i	$-0.448842\pi$
$263$	5.19040	0.320054	0.160027	+	0.987113i	$0.448842\pi$
$264$	2.88658	0.177657
$265$	12.3395	0.758009
$266$	3.41751	0.209541
$267$	−0.663018	−0.0405761
$268$	3.50820	0.214297
$269$	−1.76455	−0.107587	−0.0537933	−	0.998552i	$-0.517131\pi$
$269$	−1.76455	−0.107587	−0.0537933	+	0.998552i	$0.517131\pi$
$270$	−1.04935	−0.0638611
$271$	8.67014	0.526673	0.263337	−	0.964704i	$-0.415177\pi$
$271$	8.67014	0.526673	0.263337	+	0.964704i	$0.415177\pi$
$272$	5.24247	0.317871
$273$	0.892751	0.0540318
$274$	11.2530	0.679818
$275$	11.2544	0.678667
$276$	−3.40981	−0.205247
$277$	30.0523	1.80567	0.902833	−	0.429991i	$-0.141483\pi$
$277$	30.0523	1.80567	0.902833	+	0.429991i	$0.141483\pi$
$278$	10.5753	0.634267
$279$	−3.82806	−0.229180
$280$	−0.936804	−0.0559848
$281$	19.4106	1.15794	0.578971	−	0.815348i	$-0.303455\pi$
$281$	19.4106	1.15794	0.578971	+	0.815348i	$0.303455\pi$
$282$	−7.74423	−0.461162
$283$	−15.2057	−0.903887	−0.451943	−	0.892047i	$-0.649269\pi$
$283$	−15.2057	−0.903887	−0.451943	+	0.892047i	$0.649269\pi$
$284$	−1.47343	−0.0874321
$285$	4.01696	0.237944
$286$	−2.88658	−0.170687
$287$	−2.67567	−0.157940
$288$	1.00000	0.0589256
$289$	10.4835	0.616675
$290$	10.5985	0.622366
$291$	−3.33231	−0.195344
$292$	−5.46808	−0.319995
$293$	6.07055	0.354645	0.177323	−	0.984153i	$-0.443256\pi$
$293$	6.07055	0.354645	0.177323	+	0.984153i	$0.443256\pi$
$294$	6.20299	0.361766
$295$	−5.52892	−0.321906
$296$	−2.83071	−0.164531
$297$	2.88658	0.167496
$298$	16.4725	0.954226
$299$	3.40981	0.197195
$300$	3.89887	0.225102
$301$	−0.418735	−0.0241355
$302$	−4.66834	−0.268633
$303$	−15.2526	−0.876240
$304$	−3.82806	−0.219554
$305$	−10.2162	−0.584976
$306$	5.24247	0.299692
$307$	6.48433	0.370080	0.185040	−	0.982731i	$-0.440759\pi$
$307$	6.48433	0.370080	0.185040	+	0.982731i	$0.440759\pi$
$308$	2.57700	0.146838
$309$	−1.00000	−0.0568880
$310$	−4.01696	−0.228148
$311$	32.2896	1.83097	0.915487	−	0.402347i	$-0.131805\pi$
$311$	32.2896	1.83097	0.915487	+	0.402347i	$0.131805\pi$
$312$	−1.00000	−0.0566139
$313$	−9.14663	−0.516998	−0.258499	−	0.966011i	$-0.583228\pi$
$313$	−9.14663	−0.516998	−0.258499	+	0.966011i	$0.583228\pi$
$314$	6.51808	0.367837
$315$	−0.936804	−0.0527829
$316$	11.7380	0.660315
$317$	−23.2919	−1.30821	−0.654103	−	0.756405i	$-0.726954\pi$
$317$	−23.2919	−1.30821	−0.654103	+	0.756405i	$0.726954\pi$
$318$	−11.7592	−0.659425
$319$	−29.1548	−1.63236
$320$	1.04935	0.0586602
$321$	−10.2127	−0.570018
$322$	−3.04412	−0.169642
$323$	−20.0685	−1.11664
$324$	1.00000	0.0555556
$325$	−3.89887	−0.216271
$326$	11.5836	0.641556
$327$	1.64471	0.0909528
$328$	2.99710	0.165487
$329$	−6.91367	−0.381163
$330$	3.02902	0.166742
$331$	16.3359	0.897903	0.448951	−	0.893556i	$-0.351798\pi$
$331$	16.3359	0.897903	0.448951	+	0.893556i	$0.351798\pi$
$332$	−3.28076	−0.180055
$333$	−2.83071	−0.155122
$334$	−21.2064	−1.16036
$335$	3.68131	0.201132
$336$	0.892751	0.0487036
$337$	29.6529	1.61530	0.807648	−	0.589665i	$-0.200740\pi$
$337$	29.6529	1.61530	0.807648	+	0.589665i	$0.200740\pi$
$338$	1.00000	0.0543928
$339$	−14.7334	−0.800211
$340$	5.50116	0.298342
$341$	11.0500	0.598391
$342$	−3.82806	−0.206998
$343$	11.7870	0.636438
$344$	0.469039	0.0252889
$345$	−3.57807	−0.192637
$346$	6.04331	0.324890
$347$	−2.78071	−0.149276	−0.0746380	−	0.997211i	$-0.523780\pi$
$347$	−2.78071	−0.149276	−0.0746380	+	0.997211i	$0.523780\pi$
$348$	−10.1001	−0.541423
$349$	6.49476	0.347657	0.173828	−	0.984776i	$-0.444386\pi$
$349$	6.49476	0.347657	0.173828	+	0.984776i	$0.444386\pi$
$350$	3.48073	0.186053
$351$	−1.00000	−0.0533761
$352$	−2.88658	−0.153855
$353$	−29.1662	−1.55236	−0.776180	−	0.630512i	$-0.782845\pi$
$353$	−29.1662	−1.55236	−0.776180	+	0.630512i	$0.782845\pi$
$354$	5.26893	0.280040
$355$	−1.54614	−0.0820605
$356$	0.663018	0.0351399
$357$	4.68022	0.247704
$358$	−18.5677	−0.981333
$359$	−10.2180	−0.539283	−0.269642	−	0.962961i	$-0.586905\pi$
$359$	−10.2180	−0.539283	−0.269642	+	0.962961i	$0.586905\pi$
$360$	1.04935	0.0553053
$361$	−4.34595	−0.228734
$362$	12.2559	0.644153
$363$	2.66766	0.140016
$364$	−0.892751	−0.0467929
$365$	−5.73791	−0.300336
$366$	9.73575	0.508896
$367$	13.3939	0.699156	0.349578	−	0.936907i	$-0.386325\pi$
$367$	13.3939	0.699156	0.349578	+	0.936907i	$0.386325\pi$
$368$	3.40981	0.177749
$369$	2.99710	0.156023
$370$	−2.97039	−0.154423
$371$	−10.4981	−0.545033
$372$	3.82806	0.198476
$373$	36.1401	1.87126	0.935632	−	0.352977i	$-0.114831\pi$
$373$	36.1401	1.87126	0.935632	+	0.352977i	$0.114831\pi$
$374$	−15.1328	−0.782499
$375$	9.33799	0.482212
$376$	7.74423	0.399378
$377$	10.1001	0.520183
$378$	0.892751	0.0459182
$379$	−27.2854	−1.40156	−0.700778	−	0.713379i	$-0.747164\pi$
$379$	−27.2854	−1.40156	−0.700778	+	0.713379i	$0.747164\pi$
$380$	−4.01696	−0.206066
$381$	−11.7057	−0.599702
$382$	−13.1689	−0.673778
$383$	28.9410	1.47882	0.739409	−	0.673257i	$-0.235105\pi$
$383$	28.9410	1.47882	0.739409	+	0.673257i	$0.235105\pi$
$384$	−1.00000	−0.0510310
$385$	2.70416	0.137817
$386$	20.4134	1.03902
$387$	0.469039	0.0238426
$388$	3.33231	0.169172
$389$	38.1145	1.93248	0.966241	−	0.257639i	$-0.0829446\pi$
$389$	38.1145	1.93248	0.966241	+	0.257639i	$0.0829446\pi$
$390$	−1.04935	−0.0531357
$391$	17.8758	0.904020
$392$	−6.20299	−0.313299
$393$	6.42064	0.323878
$394$	6.16171	0.310423
$395$	12.3172	0.619747
$396$	−2.88658	−0.145056
$397$	28.3827	1.42449	0.712243	−	0.701933i	$-0.247679\pi$
$397$	28.3827	1.42449	0.712243	+	0.701933i	$0.247679\pi$
$398$	4.16170	0.208607
$399$	−3.41751	−0.171089
$400$	−3.89887	−0.194944
$401$	3.89633	0.194573	0.0972867	−	0.995256i	$-0.468984\pi$
$401$	3.89633	0.194573	0.0972867	+	0.995256i	$0.468984\pi$
$402$	−3.50820	−0.174973
$403$	−3.82806	−0.190689
$404$	15.2526	0.758846
$405$	1.04935	0.0521424
$406$	−9.01690	−0.447501
$407$	8.17106	0.405024
$408$	−5.24247	−0.259541
$409$	−32.8338	−1.62353	−0.811764	−	0.583985i	$-0.801493\pi$
$409$	−32.8338	−1.62353	−0.811764	+	0.583985i	$0.801493\pi$
$410$	3.14500	0.155320
$411$	−11.2530	−0.555069
$412$	1.00000	0.0492665
$413$	4.70384	0.231461
$414$	3.40981	0.167583
$415$	−3.44265	−0.168993
$416$	1.00000	0.0490290
$417$	−10.5753	−0.517876
$418$	11.0500	0.540473
$419$	12.6357	0.617294	0.308647	−	0.951177i	$-0.400124\pi$
$419$	12.6357	0.617294	0.308647	+	0.951177i	$0.400124\pi$
$420$	0.936804	0.0457114
$421$	−26.2171	−1.27774	−0.638870	−	0.769314i	$-0.720598\pi$
$421$	−26.2171	−1.27774	−0.638870	+	0.769314i	$0.720598\pi$
$422$	−15.1427	−0.737135
$423$	7.74423	0.376537
$424$	11.7592	0.571079
$425$	−20.4397	−0.991473
$426$	1.47343	0.0713880
$427$	8.69161	0.420616
$428$	10.2127	0.493650
$429$	2.88658	0.139365
$430$	0.492183	0.0237352
$431$	−22.0314	−1.06122	−0.530609	−	0.847617i	$-0.678037\pi$
$431$	−22.0314	−1.06122	−0.530609	+	0.847617i	$0.678037\pi$
$432$	−1.00000	−0.0481125
$433$	−14.9312	−0.717549	−0.358774	−	0.933424i	$-0.616805\pi$
$433$	−14.9312	−0.717549	−0.358774	+	0.933424i	$0.616805\pi$
$434$	3.41751	0.164046
$435$	−10.5985	−0.508160
$436$	−1.64471	−0.0787674
$437$	−13.0530	−0.624408
$438$	5.46808	0.261275
$439$	30.7140	1.46590	0.732951	−	0.680282i	$-0.238143\pi$
$439$	30.7140	1.46590	0.732951	+	0.680282i	$0.238143\pi$
$440$	−3.02902	−0.144403
$441$	−6.20299	−0.295381
$442$	5.24247	0.249359
$443$	−1.79196	−0.0851386	−0.0425693	−	0.999094i	$-0.513554\pi$
$443$	−1.79196	−0.0851386	−0.0425693	+	0.999094i	$0.513554\pi$
$444$	2.83071	0.134339
$445$	0.695735	0.0329810
$446$	17.7938	0.842561
$447$	−16.4725	−0.779123
$448$	−0.892751	−0.0421785
$449$	17.1234	0.808103	0.404051	−	0.914736i	$-0.367602\pi$
$449$	17.1234	0.808103	0.404051	+	0.914736i	$0.367602\pi$
$450$	−3.89887	−0.183795
$451$	−8.65138	−0.407378
$452$	14.7334	0.693003
$453$	4.66834	0.219338
$454$	4.15039	0.194788
$455$	−0.936804	−0.0439181
$456$	3.82806	0.179265
$457$	−22.2160	−1.03922	−0.519610	−	0.854404i	$-0.673923\pi$
$457$	−22.2160	−1.03922	−0.519610	+	0.854404i	$0.673923\pi$
$458$	21.1826	0.989798
$459$	−5.24247	−0.244697
$460$	3.57807	0.166828
$461$	−35.8738	−1.67081	−0.835404	−	0.549636i	$-0.814766\pi$
$461$	−35.8738	−1.67081	−0.835404	+	0.549636i	$0.814766\pi$
$462$	−2.57700	−0.119893
$463$	−37.5714	−1.74609	−0.873045	−	0.487640i	$-0.837858\pi$
$463$	−37.5714	−1.74609	−0.873045	+	0.487640i	$0.837858\pi$
$464$	10.1001	0.468886
$465$	4.01696	0.186282
$466$	−20.0325	−0.927989
$467$	−21.6600	−1.00231	−0.501153	−	0.865358i	$-0.667091\pi$
$467$	−21.6600	−1.00231	−0.501153	+	0.865358i	$0.667091\pi$
$468$	1.00000	0.0462250
$469$	−3.13195	−0.144620
$470$	8.12637	0.374842
$471$	−6.51808	−0.300337
$472$	−5.26893	−0.242522
$473$	−1.35392	−0.0622532
$474$	−11.7380	−0.539145
$475$	14.9251	0.684812
$476$	−4.68022	−0.214518
$477$	11.7592	0.538418
$478$	−11.6672	−0.533647
$479$	19.9197	0.910154	0.455077	−	0.890452i	$-0.349612\pi$
$479$	19.9197	0.910154	0.455077	+	0.890452i	$0.349612\pi$
$480$	−1.04935	−0.0478958
$481$	−2.83071	−0.129069
$482$	−24.2592	−1.10497
$483$	3.04412	0.138512
$484$	−2.66766	−0.121257
$485$	3.49674	0.158779
$486$	−1.00000	−0.0453609
$487$	−10.1240	−0.458761	−0.229380	−	0.973337i	$-0.573670\pi$
$487$	−10.1240	−0.458761	−0.229380	+	0.973337i	$0.573670\pi$
$488$	−9.73575	−0.440717
$489$	−11.5836	−0.523828
$490$	−6.50908	−0.294050
$491$	6.50120	0.293395	0.146697	−	0.989181i	$-0.453136\pi$
$491$	6.50120	0.293395	0.146697	+	0.989181i	$0.453136\pi$
$492$	−2.99710	−0.135120
$493$	52.9496	2.38473
$494$	−3.82806	−0.172233
$495$	−3.02902	−0.136144
$496$	−3.82806	−0.171885
$497$	1.31541	0.0590041
$498$	3.28076	0.147015
$499$	17.7920	0.796479	0.398240	−	0.917281i	$-0.369621\pi$
$499$	17.7920	0.796479	0.398240	+	0.917281i	$0.369621\pi$
$500$	−9.33799	−0.417608
$501$	21.2064	0.947434
$502$	2.35132	0.104945
$503$	33.1411	1.47769	0.738844	−	0.673877i	$-0.235372\pi$
$503$	33.1411	1.47769	0.738844	+	0.673877i	$0.235372\pi$
$504$	−0.892751	−0.0397663
$505$	16.0053	0.712225
$506$	−9.84270	−0.437561
$507$	−1.00000	−0.0444116
$508$	11.7057	0.519357
$509$	−9.02534	−0.400041	−0.200021	−	0.979792i	$-0.564101\pi$
$509$	−9.02534	−0.400041	−0.200021	+	0.979792i	$0.564101\pi$
$510$	−5.50116	−0.243595
$511$	4.88164	0.215951
$512$	1.00000	0.0441942
$513$	3.82806	0.169013
$514$	4.34483	0.191642
$515$	1.04935	0.0462397
$516$	−0.469039	−0.0206483
$517$	−22.3543	−0.983143
$518$	2.52712	0.111035
$519$	−6.04331	−0.265272
$520$	1.04935	0.0460168
$521$	27.9310	1.22368	0.611840	−	0.790982i	$-0.290430\pi$
$521$	27.9310	1.22368	0.611840	+	0.790982i	$0.290430\pi$
$522$	10.1001	0.442070
$523$	24.5263	1.07246	0.536230	−	0.844072i	$-0.319848\pi$
$523$	24.5263	1.07246	0.536230	+	0.844072i	$0.319848\pi$
$524$	−6.42064	−0.280487
$525$	−3.48073	−0.151911
$526$	5.19040	0.226312
$527$	−20.0685	−0.874197
$528$	2.88658	0.125622
$529$	−11.3732	−0.494486
$530$	12.3395	0.535993
$531$	−5.26893	−0.228652
$532$	3.41751	0.148168
$533$	2.99710	0.129819
$534$	−0.663018	−0.0286916
$535$	10.7167	0.463321
$536$	3.50820	0.151531
$537$	18.5677	0.801255
$538$	−1.76455	−0.0760751
$539$	17.9054	0.771242
$540$	−1.04935	−0.0451566
$541$	−13.0908	−0.562815	−0.281408	−	0.959588i	$-0.590801\pi$
$541$	−13.0908	−0.562815	−0.281408	+	0.959588i	$0.590801\pi$
$542$	8.67014	0.372414
$543$	−12.2559	−0.525949
$544$	5.24247	0.224769
$545$	−1.72587	−0.0739282
$546$	0.892751	0.0382062
$547$	−31.7085	−1.35576	−0.677879	−	0.735173i	$-0.737101\pi$
$547$	−31.7085	−1.35576	−0.677879	+	0.735173i	$0.737101\pi$
$548$	11.2530	0.480704
$549$	−9.73575	−0.415512
$550$	11.2544	0.479890
$551$	−38.6639	−1.64714
$552$	−3.40981	−0.145131
$553$	−10.4791	−0.445618
$554$	30.0523	1.27680
$555$	2.97039	0.126086
$556$	10.5753	0.448494
$557$	39.8483	1.68842	0.844212	−	0.536009i	$-0.180069\pi$
$557$	39.8483	1.68842	0.844212	+	0.536009i	$0.180069\pi$
$558$	−3.82806	−0.162055
$559$	0.469039	0.0198382
$560$	−0.936804	−0.0395872
$561$	15.1328	0.638907
$562$	19.4106	0.818788
$563$	−14.5926	−0.615005	−0.307503	−	0.951547i	$-0.599493\pi$
$563$	−14.5926	−0.615005	−0.307503	+	0.951547i	$0.599493\pi$
$564$	−7.74423	−0.326091
$565$	15.4605	0.650426
$566$	−15.2057	−0.639144
$567$	−0.892751	−0.0374920
$568$	−1.47343	−0.0618238
$569$	−16.6286	−0.697109	−0.348555	−	0.937289i	$-0.613327\pi$
$569$	−16.6286	−0.697109	−0.348555	+	0.937289i	$0.613327\pi$
$570$	4.01696	0.168252
$571$	−32.8146	−1.37325	−0.686624	−	0.727012i	$-0.740908\pi$
$571$	−32.8146	−1.37325	−0.686624	+	0.727012i	$0.740908\pi$
$572$	−2.88658	−0.120694
$573$	13.1689	0.550138
$574$	−2.67567	−0.111680
$575$	−13.2944	−0.554416
$576$	1.00000	0.0416667
$577$	−30.8376	−1.28379	−0.641894	−	0.766794i	$-0.721851\pi$
$577$	−30.8376	−1.28379	−0.641894	+	0.766794i	$0.721851\pi$
$578$	10.4835	0.436055
$579$	−20.4134	−0.848353
$580$	10.5985	0.440079
$581$	2.92891	0.121512
$582$	−3.33231	−0.138129
$583$	−33.9440	−1.40582
$584$	−5.46808	−0.226271
$585$	1.04935	0.0433851
$586$	6.07055	0.250772
$587$	21.0341	0.868170	0.434085	−	0.900872i	$-0.357072\pi$
$587$	21.0341	0.868170	0.434085	+	0.900872i	$0.357072\pi$
$588$	6.20299	0.255807
$589$	14.6540	0.603810
$590$	−5.52892	−0.227622
$591$	−6.16171	−0.253459
$592$	−2.83071	−0.116341
$593$	29.7915	1.22339	0.611696	−	0.791093i	$-0.290488\pi$
$593$	29.7915	1.22339	0.611696	+	0.791093i	$0.290488\pi$
$594$	2.88658	0.118438
$595$	−4.91117	−0.201338
$596$	16.4725	0.674740
$597$	−4.16170	−0.170327
$598$	3.40981	0.139438
$599$	0.899771	0.0367636	0.0183818	−	0.999831i	$-0.494149\pi$
$599$	0.899771	0.0367636	0.0183818	+	0.999831i	$0.494149\pi$
$600$	3.89887	0.159171
$601$	−13.2740	−0.541457	−0.270729	−	0.962656i	$-0.587265\pi$
$601$	−13.2740	−0.541457	−0.270729	+	0.962656i	$0.587265\pi$
$602$	−0.418735	−0.0170664
$603$	3.50820	0.142865
$604$	−4.66834	−0.189952
$605$	−2.79929	−0.113807
$606$	−15.2526	−0.619595
$607$	7.40817	0.300688	0.150344	−	0.988634i	$-0.451962\pi$
$607$	7.40817	0.300688	0.150344	+	0.988634i	$0.451962\pi$
$608$	−3.82806	−0.155248
$609$	9.01690	0.365383
$610$	−10.2162	−0.413640
$611$	7.74423	0.313298
$612$	5.24247	0.211914
$613$	−15.3764	−0.621045	−0.310523	−	0.950566i	$-0.600504\pi$
$613$	−15.3764	−0.621045	−0.310523	+	0.950566i	$0.600504\pi$
$614$	6.48433	0.261686
$615$	−3.14500	−0.126818
$616$	2.57700	0.103830
$617$	−2.30609	−0.0928396	−0.0464198	−	0.998922i	$-0.514781\pi$
$617$	−2.30609	−0.0928396	−0.0464198	+	0.998922i	$0.514781\pi$
$618$	−1.00000	−0.0402259
$619$	−9.14502	−0.367569	−0.183785	−	0.982967i	$-0.558835\pi$
$619$	−9.14502	−0.367569	−0.183785	+	0.982967i	$0.558835\pi$
$620$	−4.01696	−0.161325
$621$	−3.40981	−0.136831
$622$	32.2896	1.29469
$623$	−0.591911	−0.0237144
$624$	−1.00000	−0.0400320
$625$	9.69560	0.387824
$626$	−9.14663	−0.365573
$627$	−11.0500	−0.441295
$628$	6.51808	0.260100
$629$	−14.8399	−0.591705
$630$	−0.936804	−0.0373232
$631$	12.5165	0.498276	0.249138	−	0.968468i	$-0.419853\pi$
$631$	12.5165	0.498276	0.249138	+	0.968468i	$0.419853\pi$
$632$	11.7380	0.466913
$633$	15.1427	0.601868
$634$	−23.2919	−0.925041
$635$	12.2833	0.487449
$636$	−11.7592	−0.466284
$637$	−6.20299	−0.245772
$638$	−29.1548	−1.15425
$639$	−1.47343	−0.0582880
$640$	1.04935	0.0414790
$641$	−5.83269	−0.230378	−0.115189	−	0.993344i	$-0.536747\pi$
$641$	−5.83269	−0.230378	−0.115189	+	0.993344i	$0.536747\pi$
$642$	−10.2127	−0.403063
$643$	11.3158	0.446252	0.223126	−	0.974790i	$-0.428374\pi$
$643$	11.3158	0.446252	0.223126	+	0.974790i	$0.428374\pi$
$644$	−3.04412	−0.119955
$645$	−0.492183	−0.0193797
$646$	−20.0685	−0.789584
$647$	3.40230	0.133758	0.0668791	−	0.997761i	$-0.478696\pi$
$647$	3.40230	0.133758	0.0668791	+	0.997761i	$0.478696\pi$
$648$	1.00000	0.0392837
$649$	15.2092	0.597012
$650$	−3.89887	−0.152926
$651$	−3.41751	−0.133943
$652$	11.5836	0.453648
$653$	45.6839	1.78775	0.893875	−	0.448317i	$-0.147976\pi$
$653$	45.6839	1.78775	0.893875	+	0.448317i	$0.147976\pi$
$654$	1.64471	0.0643133
$655$	−6.73747	−0.263255
$656$	2.99710	0.117017
$657$	−5.46808	−0.213330
$658$	−6.91367	−0.269523
$659$	31.3686	1.22195	0.610974	−	0.791651i	$-0.290778\pi$
$659$	31.3686	1.22195	0.610974	+	0.791651i	$0.290778\pi$
$660$	3.02902	0.117904
$661$	−37.1395	−1.44456	−0.722280	−	0.691601i	$-0.756906\pi$
$661$	−37.1395	−1.44456	−0.722280	+	0.691601i	$0.756906\pi$
$662$	16.3359	0.634913
$663$	−5.24247	−0.203601
$664$	−3.28076	−0.127318
$665$	3.58614	0.139065
$666$	−2.83071	−0.109688
$667$	34.4395	1.33350
$668$	−21.2064	−0.820502
$669$	−17.7938	−0.687948
$670$	3.68131	0.142221
$671$	28.1030	1.08491
$672$	0.892751	0.0344386
$673$	−4.75206	−0.183178	−0.0915892	−	0.995797i	$-0.529195\pi$
$673$	−4.75206	−0.183178	−0.0915892	+	0.995797i	$0.529195\pi$
$674$	29.6529	1.14219
$675$	3.89887	0.150068
$676$	1.00000	0.0384615
$677$	−23.1039	−0.887954	−0.443977	−	0.896038i	$-0.646433\pi$
$677$	−23.1039	−0.887954	−0.443977	+	0.896038i	$0.646433\pi$
$678$	−14.7334	−0.565834
$679$	−2.97493	−0.114167
$680$	5.50116	0.210960
$681$	−4.15039	−0.159043
$682$	11.0500	0.423126
$683$	−21.5545	−0.824761	−0.412381	−	0.911012i	$-0.635303\pi$
$683$	−21.5545	−0.824761	−0.412381	+	0.911012i	$0.635303\pi$
$684$	−3.82806	−0.146370
$685$	11.8083	0.451171
$686$	11.7870	0.450029
$687$	−21.1826	−0.808166
$688$	0.469039	0.0178819
$689$	11.7592	0.447991
$690$	−3.57807	−0.136215
$691$	5.66392	0.215466	0.107733	−	0.994180i	$-0.465641\pi$
$691$	5.66392	0.215466	0.107733	+	0.994180i	$0.465641\pi$
$692$	6.04331	0.229732
$693$	2.57700	0.0978921
$694$	−2.78071	−0.105554
$695$	11.0972	0.420940
$696$	−10.1001	−0.382844
$697$	15.7122	0.595143
$698$	6.49476	0.245830
$699$	20.0325	0.757700
$700$	3.48073	0.131559
$701$	−39.5597	−1.49415	−0.747075	−	0.664739i	$-0.768543\pi$
$701$	−39.5597	−1.49415	−0.747075	+	0.664739i	$0.768543\pi$
$702$	−1.00000	−0.0377426
$703$	10.8361	0.408692
$704$	−2.88658	−0.108792
$705$	−8.12637	−0.306057
$706$	−29.1662	−1.09768
$707$	−13.6168	−0.512112
$708$	5.26893	0.198018
$709$	31.2324	1.17296	0.586478	−	0.809965i	$-0.300514\pi$
$709$	31.2324	1.17296	0.586478	+	0.809965i	$0.300514\pi$
$710$	−1.54614	−0.0580255
$711$	11.7380	0.440210
$712$	0.663018	0.0248477
$713$	−13.0530	−0.488838
$714$	4.68022	0.175153
$715$	−3.02902	−0.113279
$716$	−18.5677	−0.693907
$717$	11.6672	0.435721
$718$	−10.2180	−0.381331
$719$	18.4916	0.689622	0.344811	−	0.938672i	$-0.387943\pi$
$719$	18.4916	0.689622	0.344811	+	0.938672i	$0.387943\pi$
$720$	1.04935	0.0391068
$721$	−0.892751	−0.0332478
$722$	−4.34595	−0.161740
$723$	24.2592	0.902208
$724$	12.2559	0.455485
$725$	−39.3791	−1.46250
$726$	2.66766	0.0990061
$727$	−20.4004	−0.756609	−0.378304	−	0.925681i	$-0.623493\pi$
$727$	−20.4004	−0.756609	−0.378304	+	0.925681i	$0.623493\pi$
$728$	−0.892751	−0.0330876
$729$	1.00000	0.0370370
$730$	−5.73791	−0.212369
$731$	2.45892	0.0909465
$732$	9.73575	0.359844
$733$	−9.66006	−0.356803	−0.178401	−	0.983958i	$-0.557093\pi$
$733$	−9.66006	−0.356803	−0.178401	+	0.983958i	$0.557093\pi$
$734$	13.3939	0.494378
$735$	6.50908	0.240091
$736$	3.40981	0.125687
$737$	−10.1267	−0.373022
$738$	2.99710	0.110325
$739$	7.05423	0.259494	0.129747	−	0.991547i	$-0.458583\pi$
$739$	7.05423	0.259494	0.129747	+	0.991547i	$0.458583\pi$
$740$	−2.97039	−0.109194
$741$	3.82806	0.140627
$742$	−10.4981	−0.385396
$743$	−46.7259	−1.71421	−0.857104	−	0.515143i	$-0.827739\pi$
$743$	−46.7259	−1.71421	−0.857104	+	0.515143i	$0.827739\pi$
$744$	3.82806	0.140344
$745$	17.2853	0.633286
$746$	36.1401	1.32318
$747$	−3.28076	−0.120037
$748$	−15.1328	−0.553310
$749$	−9.11741	−0.333143
$750$	9.33799	0.340975
$751$	20.1656	0.735852	0.367926	−	0.929855i	$-0.380068\pi$
$751$	20.1656	0.735852	0.367926	+	0.929855i	$0.380068\pi$
$752$	7.74423	0.282403
$753$	−2.35132	−0.0856869
$754$	10.1001	0.367825
$755$	−4.89870	−0.178282
$756$	0.892751	0.0324691
$757$	1.26012	0.0457999	0.0229000	−	0.999738i	$-0.492710\pi$
$757$	1.26012	0.0457999	0.0229000	+	0.999738i	$0.492710\pi$
$758$	−27.2854	−0.991050
$759$	9.84270	0.357267
$760$	−4.01696	−0.145710
$761$	2.71141	0.0982885	0.0491443	−	0.998792i	$-0.484351\pi$
$761$	2.71141	0.0982885	0.0491443	+	0.998792i	$0.484351\pi$
$762$	−11.7057	−0.424053
$763$	1.46832	0.0531567
$764$	−13.1689	−0.476433
$765$	5.50116	0.198895
$766$	28.9410	1.04568
$767$	−5.26893	−0.190250
$768$	−1.00000	−0.0360844
$769$	−12.7129	−0.458438	−0.229219	−	0.973375i	$-0.573617\pi$
$769$	−12.7129	−0.458438	−0.229219	+	0.973375i	$0.573617\pi$
$770$	2.70416	0.0974512
$771$	−4.34483	−0.156475
$772$	20.4134	0.734695
$773$	48.6389	1.74942	0.874709	−	0.484649i	$-0.161052\pi$
$773$	48.6389	1.74942	0.874709	+	0.484649i	$0.161052\pi$
$774$	0.469039	0.0168592
$775$	14.9251	0.536126
$776$	3.33231	0.119623
$777$	−2.52712	−0.0906598
$778$	38.1145	1.36647
$779$	−11.4731	−0.411066
$780$	−1.04935	−0.0375726
$781$	4.25318	0.152191
$782$	17.8758	0.639239
$783$	−10.1001	−0.360949
$784$	−6.20299	−0.221536
$785$	6.83972	0.244120
$786$	6.42064	0.229017
$787$	−28.0907	−1.00133	−0.500663	−	0.865642i	$-0.666911\pi$
$787$	−28.0907	−1.00133	−0.500663	+	0.865642i	$0.666911\pi$
$788$	6.16171	0.219502
$789$	−5.19040	−0.184783
$790$	12.3172	0.438227
$791$	−13.1533	−0.467677
$792$	−2.88658	−0.102570
$793$	−9.73575	−0.345727
$794$	28.3827	1.00726
$795$	−12.3395	−0.437637
$796$	4.16170	0.147508
$797$	15.7990	0.559629	0.279815	−	0.960054i	$-0.409727\pi$
$797$	15.7990	0.559629	0.279815	+	0.960054i	$0.409727\pi$
$798$	−3.41751	−0.120978
$799$	40.5989	1.43629
$800$	−3.89887	−0.137846
$801$	0.663018	0.0234266
$802$	3.89633	0.137584
$803$	15.7841	0.557007
$804$	−3.50820	−0.123725
$805$	−3.19433	−0.112585
$806$	−3.82806	−0.134838
$807$	1.76455	0.0621151
$808$	15.2526	0.536585
$809$	−0.849569	−0.0298693	−0.0149346	−	0.999888i	$-0.504754\pi$
$809$	−0.849569	−0.0298693	−0.0149346	+	0.999888i	$0.504754\pi$
$810$	1.04935	0.0368702
$811$	37.4304	1.31436	0.657180	−	0.753734i	$-0.271749\pi$
$811$	37.4304	1.31436	0.657180	+	0.753734i	$0.271749\pi$
$812$	−9.01690	−0.316431
$813$	−8.67014	−0.304075
$814$	8.17106	0.286395
$815$	12.1552	0.425778
$816$	−5.24247	−0.183523
$817$	−1.79551	−0.0628169
$818$	−32.8338	−1.14801
$819$	−0.892751	−0.0311953
$820$	3.14500	0.109828
$821$	29.5102	1.02991	0.514957	−	0.857216i	$-0.327808\pi$
$821$	29.5102	1.02991	0.514957	+	0.857216i	$0.327808\pi$
$822$	−11.2530	−0.392493
$823$	57.0294	1.98792	0.993960	−	0.109741i	$-0.0350021\pi$
$823$	57.0294	1.98792	0.993960	+	0.109741i	$0.0350021\pi$
$824$	1.00000	0.0348367
$825$	−11.2544	−0.391828
$826$	4.70384	0.163668
$827$	44.0496	1.53175	0.765877	−	0.642987i	$-0.222305\pi$
$827$	44.0496	1.53175	0.765877	+	0.642987i	$0.222305\pi$
$828$	3.40981	0.118499
$829$	−6.09056	−0.211534	−0.105767	−	0.994391i	$-0.533730\pi$
$829$	−6.09056	−0.211534	−0.105767	+	0.994391i	$0.533730\pi$
$830$	−3.44265	−0.119496
$831$	−30.0523	−1.04250
$832$	1.00000	0.0346688
$833$	−32.5190	−1.12672
$834$	−10.5753	−0.366194
$835$	−22.2529	−0.770093
$836$	11.0500	0.382172
$837$	3.82806	0.132317
$838$	12.6357	0.436493
$839$	−11.7654	−0.406187	−0.203094	−	0.979159i	$-0.565100\pi$
$839$	−11.7654	−0.406187	−0.203094	+	0.979159i	$0.565100\pi$
$840$	0.936804	0.0323228
$841$	73.0124	2.51767
$842$	−26.2171	−0.903499
$843$	−19.4106	−0.668538
$844$	−15.1427	−0.521233
$845$	1.04935	0.0360986
$846$	7.74423	0.266252
$847$	2.38156	0.0818312
$848$	11.7592	0.403814
$849$	15.2057	0.521859
$850$	−20.4397	−0.701077
$851$	−9.65218	−0.330872
$852$	1.47343	0.0504789
$853$	−23.7063	−0.811687	−0.405843	−	0.913943i	$-0.633022\pi$
$853$	−23.7063	−0.811687	−0.405843	+	0.913943i	$0.633022\pi$
$854$	8.69161	0.297421
$855$	−4.01696	−0.137377
$856$	10.2127	0.349063
$857$	−55.7724	−1.90515	−0.952574	−	0.304308i	$-0.901575\pi$
$857$	−55.7724	−1.90515	−0.952574	+	0.304308i	$0.901575\pi$
$858$	2.88658	0.0985462
$859$	−32.2117	−1.09905	−0.549525	−	0.835477i	$-0.685191\pi$
$859$	−32.2117	−1.09905	−0.549525	+	0.835477i	$0.685191\pi$
$860$	0.492183	0.0167833
$861$	2.67567	0.0911866
$862$	−22.0314	−0.750394
$863$	−33.4454	−1.13849	−0.569247	−	0.822167i	$-0.692765\pi$
$863$	−33.4454	−1.13849	−0.569247	+	0.822167i	$0.692765\pi$
$864$	−1.00000	−0.0340207
$865$	6.34152	0.215618
$866$	−14.9312	−0.507383
$867$	−10.4835	−0.356038
$868$	3.41751	0.115998
$869$	−33.8827	−1.14939
$870$	−10.5985	−0.359323
$871$	3.50820	0.118871
$872$	−1.64471	−0.0556970
$873$	3.33231	0.112782
$874$	−13.0530	−0.441523
$875$	8.33650	0.281825
$876$	5.46808	0.184749
$877$	−21.8407	−0.737507	−0.368753	−	0.929527i	$-0.620215\pi$
$877$	−21.8407	−0.737507	−0.368753	+	0.929527i	$0.620215\pi$
$878$	30.7140	1.03655
$879$	−6.07055	−0.204754
$880$	−3.02902	−0.102108
$881$	−28.3700	−0.955811	−0.477906	−	0.878411i	$-0.658604\pi$
$881$	−28.3700	−0.955811	−0.477906	+	0.878411i	$0.658604\pi$
$882$	−6.20299	−0.208866
$883$	−54.4627	−1.83282	−0.916408	−	0.400245i	$-0.868925\pi$
$883$	−54.4627	−1.83282	−0.916408	+	0.400245i	$0.868925\pi$
$884$	5.24247	0.176323
$885$	5.52892	0.185853
$886$	−1.79196	−0.0602021
$887$	−28.9181	−0.970975	−0.485487	−	0.874244i	$-0.661358\pi$
$887$	−28.9181	−0.970975	−0.485487	+	0.874244i	$0.661358\pi$
$888$	2.83071	0.0949923
$889$	−10.4503	−0.350491
$890$	0.695735	0.0233211
$891$	−2.88658	−0.0967041
$892$	17.7938	0.595781
$893$	−29.6454	−0.992045
$894$	−16.4725	−0.550923
$895$	−19.4839	−0.651275
$896$	−0.892751	−0.0298247
$897$	−3.40981	−0.113850
$898$	17.1234	0.571415
$899$	−38.6639	−1.28951
$900$	−3.89887	−0.129962
$901$	61.6474	2.05377
$902$	−8.65138	−0.288059
$903$	0.418735	0.0139346
$904$	14.7334	0.490027
$905$	12.8606	0.427501
$906$	4.66834	0.155095
$907$	−5.45993	−0.181294	−0.0906470	−	0.995883i	$-0.528893\pi$
$907$	−5.45993	−0.181294	−0.0906470	+	0.995883i	$0.528893\pi$
$908$	4.15039	0.137736
$909$	15.2526	0.505897
$910$	−0.936804	−0.0310548
$911$	−19.0428	−0.630917	−0.315458	−	0.948939i	$-0.602158\pi$
$911$	−19.0428	−0.630917	−0.315458	+	0.948939i	$0.602158\pi$
$912$	3.82806	0.126760
$913$	9.47019	0.313418
$914$	−22.2160	−0.734840
$915$	10.2162	0.337736
$916$	21.1826	0.699893
$917$	5.73204	0.189288
$918$	−5.24247	−0.173027
$919$	4.20450	0.138694	0.0693469	−	0.997593i	$-0.477908\pi$
$919$	4.20450	0.138694	0.0693469	+	0.997593i	$0.477908\pi$
$920$	3.57807	0.117965
$921$	−6.48433	−0.213666
$922$	−35.8738	−1.18144
$923$	−1.47343	−0.0484986
$924$	−2.57700	−0.0847770
$925$	11.0366	0.362880
$926$	−37.5714	−1.23467
$927$	1.00000	0.0328443
$928$	10.1001	0.331553
$929$	−50.1718	−1.64608	−0.823042	−	0.567981i	$-0.807725\pi$
$929$	−50.1718	−1.64608	−0.823042	+	0.567981i	$0.807725\pi$
$930$	4.01696	0.131721
$931$	23.7454	0.778225
$932$	−20.0325	−0.656187
$933$	−32.2896	−1.05711
$934$	−21.6600	−0.708738
$935$	−15.8795	−0.519316
$936$	1.00000	0.0326860
$937$	32.2206	1.05260	0.526301	−	0.850299i	$-0.323579\pi$
$937$	32.2206	1.05260	0.526301	+	0.850299i	$0.323579\pi$
$938$	−3.13195	−0.102262
$939$	9.14663	0.298489
$940$	8.12637	0.265053
$941$	24.3448	0.793616	0.396808	−	0.917902i	$-0.370118\pi$
$941$	24.3448	0.793616	0.396808	+	0.917902i	$0.370118\pi$
$942$	−6.51808	−0.212371
$943$	10.2196	0.332795
$944$	−5.26893	−0.171489
$945$	0.936804	0.0304742
$946$	−1.35392	−0.0440197
$947$	37.4640	1.21742	0.608708	−	0.793394i	$-0.291688\pi$
$947$	37.4640	1.21742	0.608708	+	0.793394i	$0.291688\pi$
$948$	−11.7380	−0.381233
$949$	−5.46808	−0.177501
$950$	14.9251	0.484235
$951$	23.2919	0.755293
$952$	−4.68022	−0.151687
$953$	−1.78454	−0.0578069	−0.0289034	−	0.999582i	$-0.509202\pi$
$953$	−1.78454	−0.0578069	−0.0289034	+	0.999582i	$0.509202\pi$
$954$	11.7592	0.380719
$955$	−13.8187	−0.447162
$956$	−11.6672	−0.377346
$957$	29.1548	0.942441
$958$	19.9197	0.643576
$959$	−10.0461	−0.324406
$960$	−1.04935	−0.0338675
$961$	−16.3460	−0.527289
$962$	−2.83071	−0.0912656
$963$	10.2127	0.329100
$964$	−24.2592	−0.781335
$965$	21.4207	0.689557
$966$	3.04412	0.0979428
$967$	0.813078	0.0261468	0.0130734	−	0.999915i	$-0.495838\pi$
$967$	0.813078	0.0261468	0.0130734	+	0.999915i	$0.495838\pi$
$968$	−2.66766	−0.0857418
$969$	20.0685	0.644693
$970$	3.49674	0.112274
$971$	0.869530	0.0279045	0.0139523	−	0.999903i	$-0.495559\pi$
$971$	0.869530	0.0279045	0.0139523	+	0.999903i	$0.495559\pi$
$972$	−1.00000	−0.0320750
$973$	−9.44115	−0.302669
$974$	−10.1240	−0.324393
$975$	3.89887	0.124864
$976$	−9.73575	−0.311634
$977$	−47.3297	−1.51421	−0.757106	−	0.653292i	$-0.773387\pi$
$977$	−47.3297	−1.51421	−0.757106	+	0.653292i	$0.773387\pi$
$978$	−11.5836	−0.370402
$979$	−1.91386	−0.0611671
$980$	−6.50908	−0.207925
$981$	−1.64471	−0.0525116
$982$	6.50120	0.207461
$983$	−20.4703	−0.652902	−0.326451	−	0.945214i	$-0.605853\pi$
$983$	−20.4703	−0.652902	−0.326451	+	0.945214i	$0.605853\pi$
$984$	−2.99710	−0.0955442
$985$	6.46576	0.206016
$986$	52.9496	1.68626
$987$	6.91367	0.220065
$988$	−3.82806	−0.121787
$989$	1.59933	0.0508559
$990$	−3.02902	−0.0962685
$991$	5.56427	0.176755	0.0883775	−	0.996087i	$-0.471832\pi$
$991$	5.56427	0.176755	0.0883775	+	0.996087i	$0.471832\pi$
$992$	−3.82806	−0.121541
$993$	−16.3359	−0.518404
$994$	1.31541	0.0417222
$995$	4.36706	0.138445
$996$	3.28076	0.103955
$997$	30.3814	0.962189	0.481094	−	0.876669i	$-0.340239\pi$
$997$	30.3814	0.962189	0.481094	+	0.876669i	$0.340239\pi$
$998$	17.7920	0.563196
$999$	2.83071	0.0895596

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.y.1.9	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.y.1.9	✓	13	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:	\( N \)	\(=\)	\( 8034 = 2 \cdot 3 \cdot 13 \cdot 103 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.04935 q^{5} -1.00000 q^{6} -0.892751 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.04935 q^{5} -1.00000 q^{6} -0.892751 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.04935 q^{10} -2.88658 q^{11} -1.00000 q^{12} +1.00000 q^{13} -0.892751 q^{14} -1.04935 q^{15} +1.00000 q^{16} +5.24247 q^{17} +1.00000 q^{18} -3.82806 q^{19} +1.04935 q^{20} +0.892751 q^{21} -2.88658 q^{22} +3.40981 q^{23} -1.00000 q^{24} -3.89887 q^{25} +1.00000 q^{26} -1.00000 q^{27} -0.892751 q^{28} +10.1001 q^{29} -1.04935 q^{30} -3.82806 q^{31} +1.00000 q^{32} +2.88658 q^{33} +5.24247 q^{34} -0.936804 q^{35} +1.00000 q^{36} -2.83071 q^{37} -3.82806 q^{38} -1.00000 q^{39} +1.04935 q^{40} +2.99710 q^{41} +0.892751 q^{42} +0.469039 q^{43} -2.88658 q^{44} +1.04935 q^{45} +3.40981 q^{46} +7.74423 q^{47} -1.00000 q^{48} -6.20299 q^{49} -3.89887 q^{50} -5.24247 q^{51} +1.00000 q^{52} +11.7592 q^{53} -1.00000 q^{54} -3.02902 q^{55} -0.892751 q^{56} +3.82806 q^{57} +10.1001 q^{58} -5.26893 q^{59} -1.04935 q^{60} -9.73575 q^{61} -3.82806 q^{62} -0.892751 q^{63} +1.00000 q^{64} +1.04935 q^{65} +2.88658 q^{66} +3.50820 q^{67} +5.24247 q^{68} -3.40981 q^{69} -0.936804 q^{70} -1.47343 q^{71} +1.00000 q^{72} -5.46808 q^{73} -2.83071 q^{74} +3.89887 q^{75} -3.82806 q^{76} +2.57700 q^{77} -1.00000 q^{78} +11.7380 q^{79} +1.04935 q^{80} +1.00000 q^{81} +2.99710 q^{82} -3.28076 q^{83} +0.892751 q^{84} +5.50116 q^{85} +0.469039 q^{86} -10.1001 q^{87} -2.88658 q^{88} +0.663018 q^{89} +1.04935 q^{90} -0.892751 q^{91} +3.40981 q^{92} +3.82806 q^{93} +7.74423 q^{94} -4.01696 q^{95} -1.00000 q^{96} +3.33231 q^{97} -6.20299 q^{98} -2.88658 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9	\( 13 q + 13 q^{2} - 13 q^{3} + 13 q^{4} + 3 q^{5} - 13 q^{6} + 5 q^{7} + 13 q^{8} + 13 q^{9} + 3 q^{10} + 8 q^{11} - 13 q^{12} + 13 q^{13} + 5 q^{14} - 3 q^{15} + 13 q^{16} - q^{17} + 13 q^{18} + 5 q^{19} + 3 q^{20} - 5 q^{21} + 8 q^{22} - 9 q^{23} - 13 q^{24} + 24 q^{25} + 13 q^{26} - 13 q^{27} + 5 q^{28} - q^{29} - 3 q^{30} + 5 q^{31} + 13 q^{32} - 8 q^{33} - q^{34} + 28 q^{35} + 13 q^{36} + 35 q^{37} + 5 q^{38} - 13 q^{39} + 3 q^{40} + 24 q^{41} - 5 q^{42} + 9 q^{43} + 8 q^{44} + 3 q^{45} - 9 q^{46} - 8 q^{47} - 13 q^{48} - 16 q^{49} + 24 q^{50} + q^{51} + 13 q^{52} + 32 q^{53} - 13 q^{54} - 4 q^{55} + 5 q^{56} - 5 q^{57} - q^{58} + 12 q^{59} - 3 q^{60} + 17 q^{61} + 5 q^{62} + 5 q^{63} + 13 q^{64} + 3 q^{65} - 8 q^{66} + 20 q^{67} - q^{68} + 9 q^{69} + 28 q^{70} + 16 q^{71} + 13 q^{72} + 46 q^{73} + 35 q^{74} - 24 q^{75} + 5 q^{76} - 7 q^{77} - 13 q^{78} + 17 q^{79} + 3 q^{80} + 13 q^{81} + 24 q^{82} + 13 q^{83} - 5 q^{84} + 11 q^{85} + 9 q^{86} + q^{87} + 8 q^{88} + 14 q^{89} + 3 q^{90} + 5 q^{91} - 9 q^{92} - 5 q^{93} - 8 q^{94} + 2 q^{95} - 13 q^{96} + 46 q^{97} - 16 q^{98} + 8 q^{99}+O(q^{100}) \) 13 * q + 13 * q^2 - 13 * q^3 + 13 * q^4 + 3 * q^5 - 13 * q^6 + 5 * q^7 + 13 * q^8 + 13 * q^9 + 3 * q^10 + 8 * q^11 - 13 * q^12 + 13 * q^13 + 5 * q^14 - 3 * q^15 + 13 * q^16 - q^17 + 13 * q^18 + 5 * q^19 + 3 * q^20 - 5 * q^21 + 8 * q^22 - 9 * q^23 - 13 * q^24 + 24 * q^25 + 13 * q^26 - 13 * q^27 + 5 * q^28 - q^29 - 3 * q^30 + 5 * q^31 + 13 * q^32 - 8 * q^33 - q^34 + 28 * q^35 + 13 * q^36 + 35 * q^37 + 5 * q^38 - 13 * q^39 + 3 * q^40 + 24 * q^41 - 5 * q^42 + 9 * q^43 + 8 * q^44 + 3 * q^45 - 9 * q^46 - 8 * q^47 - 13 * q^48 - 16 * q^49 + 24 * q^50 + q^51 + 13 * q^52 + 32 * q^53 - 13 * q^54 - 4 * q^55 + 5 * q^56 - 5 * q^57 - q^58 + 12 * q^59 - 3 * q^60 + 17 * q^61 + 5 * q^62 + 5 * q^63 + 13 * q^64 + 3 * q^65 - 8 * q^66 + 20 * q^67 - q^68 + 9 * q^69 + 28 * q^70 + 16 * q^71 + 13 * q^72 + 46 * q^73 + 35 * q^74 - 24 * q^75 + 5 * q^76 - 7 * q^77 - 13 * q^78 + 17 * q^79 + 3 * q^80 + 13 * q^81 + 24 * q^82 + 13 * q^83 - 5 * q^84 + 11 * q^85 + 9 * q^86 + q^87 + 8 * q^88 + 14 * q^89 + 3 * q^90 + 5 * q^91 - 9 * q^92 - 5 * q^93 - 8 * q^94 + 2 * q^95 - 13 * q^96 + 46 * q^97 - 16 * q^98 + 8 * q^99

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