LMFDB - Embedded newform 8034.2.a.x.1.13

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} - x^{12} - 40 x^{11} + 34 x^{10} + 604 x^{9} - 381 x^{8} - 4352 x^{7} + 1474 x^{6} + 15809 x^{5} + \cdots + 8832 $ x^13 - x^12 - 40x^11 + 34x^10 + 604x^9 - 381x^8 - 4352x^7 + 1474x^6 + 15809x^5 - 368x^4 - 27369x^3 - 7621x^2 + 17300*x + 8832
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Root			$3.65233$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.65233 q^{5} -1.00000 q^{6} +1.56471 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.65233 q^{5} -1.00000 q^{6} +1.56471 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.65233 q^{10} +0.593522 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.56471 q^{14} +3.65233 q^{15} +1.00000 q^{16} -3.31253 q^{17} -1.00000 q^{18} -3.02057 q^{19} +3.65233 q^{20} +1.56471 q^{21} -0.593522 q^{22} +6.72645 q^{23} -1.00000 q^{24} +8.33954 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.56471 q^{28} +7.76758 q^{29} -3.65233 q^{30} +5.43846 q^{31} -1.00000 q^{32} +0.593522 q^{33} +3.31253 q^{34} +5.71484 q^{35} +1.00000 q^{36} -2.66916 q^{37} +3.02057 q^{38} +1.00000 q^{39} -3.65233 q^{40} -1.56671 q^{41} -1.56471 q^{42} +9.36337 q^{43} +0.593522 q^{44} +3.65233 q^{45} -6.72645 q^{46} -9.06189 q^{47} +1.00000 q^{48} -4.55169 q^{49} -8.33954 q^{50} -3.31253 q^{51} +1.00000 q^{52} +0.780516 q^{53} -1.00000 q^{54} +2.16774 q^{55} -1.56471 q^{56} -3.02057 q^{57} -7.76758 q^{58} -4.34523 q^{59} +3.65233 q^{60} +12.1694 q^{61} -5.43846 q^{62} +1.56471 q^{63} +1.00000 q^{64} +3.65233 q^{65} -0.593522 q^{66} -5.60711 q^{67} -3.31253 q^{68} +6.72645 q^{69} -5.71484 q^{70} -0.247102 q^{71} -1.00000 q^{72} -13.7542 q^{73} +2.66916 q^{74} +8.33954 q^{75} -3.02057 q^{76} +0.928690 q^{77} -1.00000 q^{78} +2.31338 q^{79} +3.65233 q^{80} +1.00000 q^{81} +1.56671 q^{82} -2.60252 q^{83} +1.56471 q^{84} -12.0985 q^{85} -9.36337 q^{86} +7.76758 q^{87} -0.593522 q^{88} +9.07488 q^{89} -3.65233 q^{90} +1.56471 q^{91} +6.72645 q^{92} +5.43846 q^{93} +9.06189 q^{94} -11.0321 q^{95} -1.00000 q^{96} -5.85830 q^{97} +4.55169 q^{98} +0.593522 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) $ 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * 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
$5$	3.65233	1.63337	0.816687	−	0.577081i	$-0.195808\pi$
$5$	3.65233	1.63337	0.816687	+	0.577081i	$0.195808\pi$
$6$	−1.00000	−0.408248
$7$	1.56471	0.591404	0.295702	−	0.955280i	$-0.404446\pi$
$7$	1.56471	0.591404	0.295702	+	0.955280i	$0.404446\pi$
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	−3.65233	−1.15497
$11$	0.593522	0.178954	0.0894769	−	0.995989i	$-0.471480\pi$
$11$	0.593522	0.178954	0.0894769	+	0.995989i	$0.471480\pi$
$12$	1.00000	0.288675
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−1.56471	−0.418186
$15$	3.65233	0.943029
$16$	1.00000	0.250000
$17$	−3.31253	−0.803406	−0.401703	−	0.915770i	$-0.631582\pi$
$17$	−3.31253	−0.803406	−0.401703	+	0.915770i	$0.631582\pi$
$18$	−1.00000	−0.235702
$19$	−3.02057	−0.692967	−0.346484	−	0.938056i	$-0.612624\pi$
$19$	−3.02057	−0.692967	−0.346484	+	0.938056i	$0.612624\pi$
$20$	3.65233	0.816687
$21$	1.56471	0.341447
$22$	−0.593522	−0.126539
$23$	6.72645	1.40256	0.701281	−	0.712885i	$-0.252612\pi$
$23$	6.72645	1.40256	0.701281	+	0.712885i	$0.252612\pi$
$24$	−1.00000	−0.204124
$25$	8.33954	1.66791
$26$	−1.00000	−0.196116
$27$	1.00000	0.192450
$28$	1.56471	0.295702
$29$	7.76758	1.44240	0.721201	−	0.692725i	$-0.243590\pi$
$29$	7.76758	1.44240	0.721201	+	0.692725i	$0.243590\pi$
$30$	−3.65233	−0.666822
$31$	5.43846	0.976776	0.488388	−	0.872627i	$-0.337585\pi$
$31$	5.43846	0.976776	0.488388	+	0.872627i	$0.337585\pi$
$32$	−1.00000	−0.176777
$33$	0.593522	0.103319
$34$	3.31253	0.568094
$35$	5.71484	0.965984
$36$	1.00000	0.166667
$37$	−2.66916	−0.438808	−0.219404	−	0.975634i	$-0.570411\pi$
$37$	−2.66916	−0.438808	−0.219404	+	0.975634i	$0.570411\pi$
$38$	3.02057	0.490002
$39$	1.00000	0.160128
$40$	−3.65233	−0.577485
$41$	−1.56671	−0.244679	−0.122340	−	0.992488i	$-0.539040\pi$
$41$	−1.56671	−0.244679	−0.122340	+	0.992488i	$0.539040\pi$
$42$	−1.56471	−0.241440
$43$	9.36337	1.42790	0.713950	−	0.700196i	$-0.246904\pi$
$43$	9.36337	1.42790	0.713950	+	0.700196i	$0.246904\pi$
$44$	0.593522	0.0894769
$45$	3.65233	0.544458
$46$	−6.72645	−0.991762
$47$	−9.06189	−1.32181	−0.660906	−	0.750469i	$-0.729828\pi$
$47$	−9.06189	−1.32181	−0.660906	+	0.750469i	$0.729828\pi$
$48$	1.00000	0.144338
$49$	−4.55169	−0.650241
$50$	−8.33954	−1.17939
$51$	−3.31253	−0.463846
$52$	1.00000	0.138675
$53$	0.780516	0.107212	0.0536060	−	0.998562i	$-0.482928\pi$
$53$	0.780516	0.107212	0.0536060	+	0.998562i	$0.482928\pi$
$54$	−1.00000	−0.136083
$55$	2.16774	0.292298
$56$	−1.56471	−0.209093
$57$	−3.02057	−0.400085
$58$	−7.76758	−1.01993
$59$	−4.34523	−0.565701	−0.282850	−	0.959164i	$-0.591280\pi$
$59$	−4.34523	−0.565701	−0.282850	+	0.959164i	$0.591280\pi$
$60$	3.65233	0.471514
$61$	12.1694	1.55814	0.779069	−	0.626938i	$-0.215692\pi$
$61$	12.1694	1.55814	0.779069	+	0.626938i	$0.215692\pi$
$62$	−5.43846	−0.690685
$63$	1.56471	0.197135
$64$	1.00000	0.125000
$65$	3.65233	0.453016
$66$	−0.593522	−0.0730576
$67$	−5.60711	−0.685018	−0.342509	−	0.939515i	$-0.611277\pi$
$67$	−5.60711	−0.685018	−0.342509	+	0.939515i	$0.611277\pi$
$68$	−3.31253	−0.401703
$69$	6.72645	0.809770
$70$	−5.71484	−0.683054
$71$	−0.247102	−0.0293256	−0.0146628	−	0.999892i	$-0.504667\pi$
$71$	−0.247102	−0.0293256	−0.0146628	+	0.999892i	$0.504667\pi$
$72$	−1.00000	−0.117851
$73$	−13.7542	−1.60980	−0.804902	−	0.593408i	$-0.797782\pi$
$73$	−13.7542	−1.60980	−0.804902	+	0.593408i	$0.797782\pi$
$74$	2.66916	0.310284
$75$	8.33954	0.962968
$76$	−3.02057	−0.346484
$77$	0.928690	0.105834
$78$	−1.00000	−0.113228
$79$	2.31338	0.260276	0.130138	−	0.991496i	$-0.458458\pi$
$79$	2.31338	0.260276	0.130138	+	0.991496i	$0.458458\pi$
$80$	3.65233	0.408343
$81$	1.00000	0.111111
$82$	1.56671	0.173014
$83$	−2.60252	−0.285663	−0.142832	−	0.989747i	$-0.545621\pi$
$83$	−2.60252	−0.285663	−0.142832	+	0.989747i	$0.545621\pi$
$84$	1.56471	0.170724
$85$	−12.0985	−1.31226
$86$	−9.36337	−1.00968
$87$	7.76758	0.832772
$88$	−0.593522	−0.0632697
$89$	9.07488	0.961935	0.480968	−	0.876738i	$-0.340285\pi$
$89$	9.07488	0.961935	0.480968	+	0.876738i	$0.340285\pi$
$90$	−3.65233	−0.384990
$91$	1.56471	0.164026
$92$	6.72645	0.701281
$93$	5.43846	0.563942
$94$	9.06189	0.934662
$95$	−11.0321	−1.13187
$96$	−1.00000	−0.102062
$97$	−5.85830	−0.594820	−0.297410	−	0.954750i	$-0.596123\pi$
$97$	−5.85830	−0.594820	−0.297410	+	0.954750i	$0.596123\pi$
$98$	4.55169	0.459790
$99$	0.593522	0.0596513
$100$	8.33954	0.833954
$101$	−2.43138	−0.241931	−0.120966	−	0.992657i	$-0.538599\pi$
$101$	−2.43138	−0.241931	−0.120966	+	0.992657i	$0.538599\pi$
$102$	3.31253	0.327989
$103$	1.00000	0.0985329
$103$	1.00000	0.0985329
$104$	−1.00000	−0.0980581
$105$	5.71484	0.557711
$106$	−0.780516	−0.0758104
$107$	11.8261	1.14327	0.571636	−	0.820507i	$-0.306309\pi$
$107$	11.8261	1.14327	0.571636	+	0.820507i	$0.306309\pi$
$108$	1.00000	0.0962250
$109$	11.5217	1.10358	0.551790	−	0.833983i	$-0.313945\pi$
$109$	11.5217	1.10358	0.551790	+	0.833983i	$0.313945\pi$
$110$	−2.16774	−0.206686
$111$	−2.66916	−0.253346
$112$	1.56471	0.147851
$113$	1.55717	0.146486	0.0732432	−	0.997314i	$-0.476665\pi$
$113$	1.55717	0.146486	0.0732432	+	0.997314i	$0.476665\pi$
$114$	3.02057	0.282903
$115$	24.5673	2.29091
$116$	7.76758	0.721201
$117$	1.00000	0.0924500
$118$	4.34523	0.400011
$119$	−5.18314	−0.475138
$120$	−3.65233	−0.333411
$121$	−10.6477	−0.967976
$122$	−12.1694	−1.10177
$123$	−1.56671	−0.141266
$124$	5.43846	0.488388
$125$	12.1971	1.09094
$126$	−1.56471	−0.139395
$127$	−7.75275	−0.687945	−0.343973	−	0.938980i	$-0.611773\pi$
$127$	−7.75275	−0.687945	−0.343973	+	0.938980i	$0.611773\pi$
$128$	−1.00000	−0.0883883
$129$	9.36337	0.824399
$130$	−3.65233	−0.320331
$131$	−5.89443	−0.514998	−0.257499	−	0.966279i	$-0.582898\pi$
$131$	−5.89443	−0.514998	−0.257499	+	0.966279i	$0.582898\pi$
$132$	0.593522	0.0516595
$133$	−4.72632	−0.409824
$134$	5.60711	0.484381
$135$	3.65233	0.314343
$136$	3.31253	0.284047
$137$	11.4227	0.975909	0.487955	−	0.872869i	$-0.337743\pi$
$137$	11.4227	0.975909	0.487955	+	0.872869i	$0.337743\pi$
$138$	−6.72645	−0.572594
$139$	18.6733	1.58384	0.791922	−	0.610622i	$-0.209080\pi$
$139$	18.6733	1.58384	0.791922	+	0.610622i	$0.209080\pi$
$140$	5.71484	0.482992
$141$	−9.06189	−0.763148
$142$	0.247102	0.0207364
$143$	0.593522	0.0496328
$144$	1.00000	0.0833333
$145$	28.3698	2.35598
$146$	13.7542	1.13830
$147$	−4.55169	−0.375417
$148$	−2.66916	−0.219404
$149$	11.3262	0.927878	0.463939	−	0.885867i	$-0.346436\pi$
$149$	11.3262	0.927878	0.463939	+	0.885867i	$0.346436\pi$
$150$	−8.33954	−0.680921
$151$	−3.57988	−0.291326	−0.145663	−	0.989334i	$-0.546532\pi$
$151$	−3.57988	−0.291326	−0.145663	+	0.989334i	$0.546532\pi$
$152$	3.02057	0.245001
$153$	−3.31253	−0.267802
$154$	−0.928690	−0.0748360
$155$	19.8631	1.59544
$156$	1.00000	0.0800641
$157$	−18.8346	−1.50316	−0.751582	−	0.659639i	$-0.770709\pi$
$157$	−18.8346	−1.50316	−0.751582	+	0.659639i	$0.770709\pi$
$158$	−2.31338	−0.184043
$159$	0.780516	0.0618989
$160$	−3.65233	−0.288742
$161$	10.5249	0.829482
$162$	−1.00000	−0.0785674
$163$	19.5242	1.52925	0.764626	−	0.644475i	$-0.222924\pi$
$163$	19.5242	1.52925	0.764626	+	0.644475i	$0.222924\pi$
$164$	−1.56671	−0.122340
$165$	2.16774	0.168759
$166$	2.60252	0.201994
$167$	−0.535319	−0.0414242	−0.0207121	−	0.999785i	$-0.506593\pi$
$167$	−0.535319	−0.0414242	−0.0207121	+	0.999785i	$0.506593\pi$
$168$	−1.56471	−0.120720
$169$	1.00000	0.0769231
$170$	12.0985	0.927909
$171$	−3.02057	−0.230989
$172$	9.36337	0.713950
$173$	5.29513	0.402582	0.201291	−	0.979532i	$-0.435486\pi$
$173$	5.29513	0.402582	0.201291	+	0.979532i	$0.435486\pi$
$174$	−7.76758	−0.588859
$175$	13.0490	0.986408
$176$	0.593522	0.0447384
$177$	−4.34523	−0.326608
$178$	−9.07488	−0.680191
$179$	−7.60749	−0.568611	−0.284305	−	0.958734i	$-0.591763\pi$
$179$	−7.60749	−0.568611	−0.284305	+	0.958734i	$0.591763\pi$
$180$	3.65233	0.272229
$181$	−5.70330	−0.423923	−0.211961	−	0.977278i	$-0.567985\pi$
$181$	−5.70330	−0.423923	−0.211961	+	0.977278i	$0.567985\pi$
$182$	−1.56471	−0.115984
$183$	12.1694	0.899591
$184$	−6.72645	−0.495881
$185$	−9.74868	−0.716737
$186$	−5.43846	−0.398767
$187$	−1.96606	−0.143772
$188$	−9.06189	−0.660906
$189$	1.56471	0.113816
$190$	11.0321	0.800356
$191$	−24.6985	−1.78712	−0.893559	−	0.448945i	$-0.851800\pi$
$191$	−24.6985	−1.78712	−0.893559	+	0.448945i	$0.851800\pi$
$192$	1.00000	0.0721688
$193$	−4.57956	−0.329644	−0.164822	−	0.986323i	$-0.552705\pi$
$193$	−4.57956	−0.329644	−0.164822	+	0.986323i	$0.552705\pi$
$194$	5.85830	0.420602
$195$	3.65233	0.261549
$196$	−4.55169	−0.325120
$197$	14.6313	1.04244	0.521220	−	0.853422i	$-0.325477\pi$
$197$	14.6313	1.04244	0.521220	+	0.853422i	$0.325477\pi$
$198$	−0.593522	−0.0421798
$199$	6.62473	0.469614	0.234807	−	0.972042i	$-0.424554\pi$
$199$	6.62473	0.469614	0.234807	+	0.972042i	$0.424554\pi$
$200$	−8.33954	−0.589695
$201$	−5.60711	−0.395495
$202$	2.43138	0.171071
$203$	12.1540	0.853043
$204$	−3.31253	−0.231923
$205$	−5.72216	−0.399653
$206$	−1.00000	−0.0696733
$207$	6.72645	0.467521
$208$	1.00000	0.0693375
$209$	−1.79278	−0.124009
$210$	−5.71484	−0.394361
$211$	−0.979136	−0.0674065	−0.0337033	−	0.999432i	$-0.510730\pi$
$211$	−0.979136	−0.0674065	−0.0337033	+	0.999432i	$0.510730\pi$
$212$	0.780516	0.0536060
$213$	−0.247102	−0.0169312
$214$	−11.8261	−0.808415
$215$	34.1982	2.33230
$216$	−1.00000	−0.0680414
$217$	8.50960	0.577669
$218$	−11.5217	−0.780349
$219$	−13.7542	−0.929420
$220$	2.16774	0.146149
$221$	−3.31253	−0.222825
$222$	2.66916	0.179143
$223$	−20.0303	−1.34133	−0.670664	−	0.741761i	$-0.733991\pi$
$223$	−20.0303	−1.34133	−0.670664	+	0.741761i	$0.733991\pi$
$224$	−1.56471	−0.104546
$225$	8.33954	0.555970
$226$	−1.55717	−0.103582
$227$	3.31462	0.219999	0.110000	−	0.993932i	$-0.464915\pi$
$227$	3.31462	0.219999	0.110000	+	0.993932i	$0.464915\pi$
$228$	−3.02057	−0.200042
$229$	5.06424	0.334654	0.167327	−	0.985901i	$-0.446486\pi$
$229$	5.06424	0.334654	0.167327	+	0.985901i	$0.446486\pi$
$230$	−24.5673	−1.61992
$231$	0.928690	0.0611033
$232$	−7.76758	−0.509966
$233$	3.20986	0.210285	0.105142	−	0.994457i	$-0.466470\pi$
$233$	3.20986	0.210285	0.105142	+	0.994457i	$0.466470\pi$
$234$	−1.00000	−0.0653720
$235$	−33.0970	−2.15901
$236$	−4.34523	−0.282850
$237$	2.31338	0.150270
$238$	5.18314	0.335973
$239$	−8.15980	−0.527814	−0.263907	−	0.964548i	$-0.585011\pi$
$239$	−8.15980	−0.527814	−0.263907	+	0.964548i	$0.585011\pi$
$240$	3.65233	0.235757
$241$	25.3901	1.63552	0.817760	−	0.575560i	$-0.195216\pi$
$241$	25.3901	1.63552	0.817760	+	0.575560i	$0.195216\pi$
$242$	10.6477	0.684462
$243$	1.00000	0.0641500
$244$	12.1694	0.779069
$245$	−16.6243	−1.06209
$246$	1.56671	0.0998899
$247$	−3.02057	−0.192194
$248$	−5.43846	−0.345342
$249$	−2.60252	−0.164928
$250$	−12.1971	−0.771414
$251$	16.9455	1.06959	0.534797	−	0.844981i	$-0.320388\pi$
$251$	16.9455	1.06959	0.534797	+	0.844981i	$0.320388\pi$
$252$	1.56471	0.0985674
$253$	3.99230	0.250994
$254$	7.75275	0.486451
$255$	−12.0985	−0.757635
$256$	1.00000	0.0625000
$257$	−2.84036	−0.177177	−0.0885883	−	0.996068i	$-0.528236\pi$
$257$	−2.84036	−0.177177	−0.0885883	+	0.996068i	$0.528236\pi$
$258$	−9.36337	−0.582938
$259$	−4.17646	−0.259513
$260$	3.65233	0.226508
$261$	7.76758	0.480801
$262$	5.89443	0.364159
$263$	11.8806	0.732591	0.366295	−	0.930499i	$-0.380626\pi$
$263$	11.8806	0.732591	0.366295	+	0.930499i	$0.380626\pi$
$264$	−0.593522	−0.0365288
$265$	2.85070	0.175117
$266$	4.72632	0.289789
$267$	9.07488	0.555373
$268$	−5.60711	−0.342509
$269$	4.82295	0.294061	0.147030	−	0.989132i	$-0.453029\pi$
$269$	4.82295	0.294061	0.147030	+	0.989132i	$0.453029\pi$
$270$	−3.65233	−0.222274
$271$	−27.8820	−1.69371	−0.846856	−	0.531822i	$-0.821508\pi$
$271$	−27.8820	−1.69371	−0.846856	+	0.531822i	$0.821508\pi$
$272$	−3.31253	−0.200851
$273$	1.56471	0.0947005
$274$	−11.4227	−0.690072
$275$	4.94971	0.298479
$276$	6.72645	0.404885
$277$	−13.5471	−0.813968	−0.406984	−	0.913435i	$-0.633419\pi$
$277$	−13.5471	−0.813968	−0.406984	+	0.913435i	$0.633419\pi$
$278$	−18.6733	−1.11995
$279$	5.43846	0.325592
$280$	−5.71484	−0.341527
$281$	−20.9745	−1.25123	−0.625616	−	0.780132i	$-0.715152\pi$
$281$	−20.9745	−1.25123	−0.625616	+	0.780132i	$0.715152\pi$
$282$	9.06189	0.539627
$283$	17.1486	1.01938	0.509688	−	0.860359i	$-0.329761\pi$
$283$	17.1486	1.01938	0.509688	+	0.860359i	$0.329761\pi$
$284$	−0.247102	−0.0146628
$285$	−11.0321	−0.653488
$286$	−0.593522	−0.0350957
$287$	−2.45145	−0.144704
$288$	−1.00000	−0.0589256
$289$	−6.02717	−0.354539
$290$	−28.3698	−1.66593
$291$	−5.85830	−0.343420
$292$	−13.7542	−0.804902
$293$	−23.5447	−1.37550	−0.687749	−	0.725948i	$-0.741401\pi$
$293$	−23.5447	−1.37550	−0.687749	+	0.725948i	$0.741401\pi$
$294$	4.55169	0.265460
$295$	−15.8702	−0.924001
$296$	2.66916	0.155142
$297$	0.593522	0.0344397
$298$	−11.3262	−0.656109
$299$	6.72645	0.389001
$300$	8.33954	0.481484
$301$	14.6509	0.844467
$302$	3.57988	0.205999
$303$	−2.43138	−0.139679
$304$	−3.02057	−0.173242
$305$	44.4469	2.54502
$306$	3.31253	0.189365
$307$	0.701523	0.0400381	0.0200190	−	0.999800i	$-0.493627\pi$
$307$	0.701523	0.0400381	0.0200190	+	0.999800i	$0.493627\pi$
$308$	0.928690	0.0529170
$309$	1.00000	0.0568880
$310$	−19.8631	−1.12815
$311$	20.5192	1.16354	0.581768	−	0.813355i	$-0.302361\pi$
$311$	20.5192	1.16354	0.581768	+	0.813355i	$0.302361\pi$
$312$	−1.00000	−0.0566139
$313$	−25.5591	−1.44469	−0.722343	−	0.691535i	$-0.756935\pi$
$313$	−25.5591	−1.44469	−0.722343	+	0.691535i	$0.756935\pi$
$314$	18.8346	1.06290
$315$	5.71484	0.321995
$316$	2.31338	0.130138
$317$	−5.60138	−0.314605	−0.157302	−	0.987550i	$-0.550280\pi$
$317$	−5.60138	−0.314605	−0.157302	+	0.987550i	$0.550280\pi$
$318$	−0.780516	−0.0437692
$319$	4.61023	0.258123
$320$	3.65233	0.204172
$321$	11.8261	0.660068
$322$	−10.5249	−0.586532
$323$	10.0057	0.556734
$324$	1.00000	0.0555556
$325$	8.33954	0.462595
$326$	−19.5242	−1.08134
$327$	11.5217	0.637152
$328$	1.56671	0.0865072
$329$	−14.1792	−0.781725
$330$	−2.16774	−0.119330
$331$	−20.5799	−1.13117	−0.565587	−	0.824689i	$-0.691350\pi$
$331$	−20.5799	−1.13117	−0.565587	+	0.824689i	$0.691350\pi$
$332$	−2.60252	−0.142832
$333$	−2.66916	−0.146269
$334$	0.535319	0.0292913
$335$	−20.4791	−1.11889
$336$	1.56471	0.0853619
$337$	−17.3293	−0.943988	−0.471994	−	0.881602i	$-0.656466\pi$
$337$	−17.3293	−0.943988	−0.471994	+	0.881602i	$0.656466\pi$
$338$	−1.00000	−0.0543928
$339$	1.55717	0.0845740
$340$	−12.0985	−0.656131
$341$	3.22785	0.174798
$342$	3.02057	0.163334
$343$	−18.0750	−0.975960
$344$	−9.36337	−0.504839
$345$	24.5673	1.32266
$346$	−5.29513	−0.284668
$347$	21.3843	1.14797	0.573984	−	0.818867i	$-0.305397\pi$
$347$	21.3843	1.14797	0.573984	+	0.818867i	$0.305397\pi$
$348$	7.76758	0.416386
$349$	28.9643	1.55042	0.775211	−	0.631702i	$-0.217643\pi$
$349$	28.9643	1.55042	0.775211	+	0.631702i	$0.217643\pi$
$350$	−13.0490	−0.697496
$351$	1.00000	0.0533761
$352$	−0.593522	−0.0316349
$353$	−0.650619	−0.0346289	−0.0173145	−	0.999850i	$-0.505512\pi$
$353$	−0.650619	−0.0346289	−0.0173145	+	0.999850i	$0.505512\pi$
$354$	4.34523	0.230946
$355$	−0.902500	−0.0478997
$356$	9.07488	0.480968
$357$	−5.18314	−0.274321
$358$	7.60749	0.402069
$359$	33.4574	1.76582	0.882908	−	0.469546i	$-0.155582\pi$
$359$	33.4574	1.76582	0.882908	+	0.469546i	$0.155582\pi$
$360$	−3.65233	−0.192495
$361$	−9.87614	−0.519797
$362$	5.70330	0.299759
$363$	−10.6477	−0.558861
$364$	1.56471	0.0820130
$365$	−50.2348	−2.62941
$366$	−12.1694	−0.636107
$367$	8.83655	0.461264	0.230632	−	0.973041i	$-0.425921\pi$
$367$	8.83655	0.461264	0.230632	+	0.973041i	$0.425921\pi$
$368$	6.72645	0.350641
$369$	−1.56671	−0.0815598
$370$	9.74868	0.506810
$371$	1.22128	0.0634057
$372$	5.43846	0.281971
$373$	6.53621	0.338432	0.169216	−	0.985579i	$-0.445876\pi$
$373$	6.53621	0.338432	0.169216	+	0.985579i	$0.445876\pi$
$374$	1.96606	0.101662
$375$	12.1971	0.629857
$376$	9.06189	0.467331
$377$	7.76758	0.400051
$378$	−1.56471	−0.0804799
$379$	34.1788	1.75565	0.877823	−	0.478985i	$-0.158995\pi$
$379$	34.1788	1.75565	0.877823	+	0.478985i	$0.158995\pi$
$380$	−11.0321	−0.565937
$381$	−7.75275	−0.397185
$382$	24.6985	1.26368
$383$	22.2560	1.13723	0.568614	−	0.822605i	$-0.307480\pi$
$383$	22.2560	1.13723	0.568614	+	0.822605i	$0.307480\pi$
$384$	−1.00000	−0.0510310
$385$	3.39189	0.172866
$386$	4.57956	0.233093
$387$	9.36337	0.475967
$388$	−5.85830	−0.297410
$389$	16.2990	0.826392	0.413196	−	0.910642i	$-0.364413\pi$
$389$	16.2990	0.826392	0.413196	+	0.910642i	$0.364413\pi$
$390$	−3.65233	−0.184943
$391$	−22.2816	−1.12683
$392$	4.55169	0.229895
$393$	−5.89443	−0.297334
$394$	−14.6313	−0.737116
$395$	8.44924	0.425127
$396$	0.593522	0.0298256
$397$	−8.72203	−0.437746	−0.218873	−	0.975753i	$-0.570238\pi$
$397$	−8.72203	−0.437746	−0.218873	+	0.975753i	$0.570238\pi$
$398$	−6.62473	−0.332068
$399$	−4.72632	−0.236612
$400$	8.33954	0.416977
$401$	19.4022	0.968899	0.484450	−	0.874819i	$-0.339020\pi$
$401$	19.4022	0.968899	0.484450	+	0.874819i	$0.339020\pi$
$402$	5.60711	0.279657
$403$	5.43846	0.270909
$404$	−2.43138	−0.120966
$405$	3.65233	0.181486
$406$	−12.1540	−0.603193
$407$	−1.58421	−0.0785263
$408$	3.31253	0.163994
$409$	−13.9287	−0.688731	−0.344366	−	0.938836i	$-0.611906\pi$
$409$	−13.9287	−0.688731	−0.344366	+	0.938836i	$0.611906\pi$
$410$	5.72216	0.282597
$411$	11.4227	0.563441
$412$	1.00000	0.0492665
$413$	−6.79902	−0.334558
$414$	−6.72645	−0.330587
$415$	−9.50525	−0.466595
$416$	−1.00000	−0.0490290
$417$	18.6733	0.914433
$418$	1.79278	0.0876876
$419$	−27.4558	−1.34130	−0.670651	−	0.741773i	$-0.733985\pi$
$419$	−27.4558	−1.34130	−0.670651	+	0.741773i	$0.733985\pi$
$420$	5.71484	0.278856
$421$	19.0453	0.928211	0.464106	−	0.885780i	$-0.346376\pi$
$421$	19.0453	0.928211	0.464106	+	0.885780i	$0.346376\pi$
$422$	0.979136	0.0476636
$423$	−9.06189	−0.440604
$424$	−0.780516	−0.0379052
$425$	−27.6250	−1.34001
$426$	0.247102	0.0119721
$427$	19.0416	0.921489
$428$	11.8261	0.571636
$429$	0.593522	0.0286555
$430$	−34.1982	−1.64918
$431$	−22.8753	−1.10186	−0.550932	−	0.834550i	$-0.685728\pi$
$431$	−22.8753	−1.10186	−0.550932	+	0.834550i	$0.685728\pi$
$432$	1.00000	0.0481125
$433$	−30.3703	−1.45951	−0.729753	−	0.683711i	$-0.760365\pi$
$433$	−30.3703	−1.45951	−0.729753	+	0.683711i	$0.760365\pi$
$434$	−8.50960	−0.408474
$435$	28.3698	1.36023
$436$	11.5217	0.551790
$437$	−20.3177	−0.971930
$438$	13.7542	0.657199
$439$	−21.2699	−1.01516	−0.507579	−	0.861605i	$-0.669459\pi$
$439$	−21.2699	−1.01516	−0.507579	+	0.861605i	$0.669459\pi$
$440$	−2.16774	−0.103343
$441$	−4.55169	−0.216747
$442$	3.31253	0.157561
$443$	20.0331	0.951802	0.475901	−	0.879499i	$-0.342122\pi$
$443$	20.0331	0.951802	0.475901	+	0.879499i	$0.342122\pi$
$444$	−2.66916	−0.126673
$445$	33.1445	1.57120
$446$	20.0303	0.948462
$447$	11.3262	0.535711
$448$	1.56471	0.0739255
$449$	−28.3034	−1.33572	−0.667860	−	0.744287i	$-0.732789\pi$
$449$	−28.3034	−1.33572	−0.667860	+	0.744287i	$0.732789\pi$
$450$	−8.33954	−0.393130
$451$	−0.929879	−0.0437863
$452$	1.55717	0.0732432
$453$	−3.57988	−0.168197
$454$	−3.31462	−0.155563
$455$	5.71484	0.267916
$456$	3.02057	0.141451
$457$	13.5845	0.635456	0.317728	−	0.948182i	$-0.397080\pi$
$457$	13.5845	0.635456	0.317728	+	0.948182i	$0.397080\pi$
$458$	−5.06424	−0.236636
$459$	−3.31253	−0.154615
$460$	24.5673	1.14545
$461$	−25.8954	−1.20607	−0.603035	−	0.797715i	$-0.706042\pi$
$461$	−25.8954	−1.20607	−0.603035	+	0.797715i	$0.706042\pi$
$462$	−0.928690	−0.0432066
$463$	−31.6403	−1.47045	−0.735225	−	0.677823i	$-0.762923\pi$
$463$	−31.6403	−1.47045	−0.735225	+	0.677823i	$0.762923\pi$
$464$	7.76758	0.360601
$465$	19.8631	0.921128
$466$	−3.20986	−0.148694
$467$	0.505638	0.0233981	0.0116991	−	0.999932i	$-0.496276\pi$
$467$	0.505638	0.0233981	0.0116991	+	0.999932i	$0.496276\pi$
$468$	1.00000	0.0462250
$469$	−8.77350	−0.405123
$470$	33.0970	1.52665
$471$	−18.8346	−0.867853
$472$	4.34523	0.200005
$473$	5.55737	0.255528
$474$	−2.31338	−0.106257
$475$	−25.1902	−1.15581
$476$	−5.18314	−0.237569
$477$	0.780516	0.0357374
$478$	8.15980	0.373221
$479$	−3.75281	−0.171470	−0.0857351	−	0.996318i	$-0.527324\pi$
$479$	−3.75281	−0.171470	−0.0857351	+	0.996318i	$0.527324\pi$
$480$	−3.65233	−0.166705
$481$	−2.66916	−0.121703
$482$	−25.3901	−1.15649
$483$	10.5249	0.478901
$484$	−10.6477	−0.483988
$485$	−21.3965	−0.971564
$486$	−1.00000	−0.0453609
$487$	32.4488	1.47040	0.735198	−	0.677852i	$-0.237089\pi$
$487$	32.4488	1.47040	0.735198	+	0.677852i	$0.237089\pi$
$488$	−12.1694	−0.550885
$489$	19.5242	0.882914
$490$	16.6243	0.751008
$491$	−2.82035	−0.127280	−0.0636402	−	0.997973i	$-0.520271\pi$
$491$	−2.82035	−0.127280	−0.0636402	+	0.997973i	$0.520271\pi$
$492$	−1.56671	−0.0706328
$493$	−25.7303	−1.15883
$494$	3.02057	0.135902
$495$	2.16774	0.0974328
$496$	5.43846	0.244194
$497$	−0.386643	−0.0173433
$498$	2.60252	0.116621
$499$	−20.3275	−0.909984	−0.454992	−	0.890496i	$-0.650358\pi$
$499$	−20.3275	−0.909984	−0.454992	+	0.890496i	$0.650358\pi$
$500$	12.1971	0.545472
$501$	−0.535319	−0.0239163
$502$	−16.9455	−0.756317
$503$	−32.2284	−1.43699	−0.718497	−	0.695530i	$-0.755169\pi$
$503$	−32.2284	−1.43699	−0.718497	+	0.695530i	$0.755169\pi$
$504$	−1.56471	−0.0696977
$505$	−8.88021	−0.395164
$506$	−3.99230	−0.177479
$507$	1.00000	0.0444116
$508$	−7.75275	−0.343973
$509$	−17.2405	−0.764170	−0.382085	−	0.924127i	$-0.624794\pi$
$509$	−17.2405	−0.764170	−0.382085	+	0.924127i	$0.624794\pi$
$510$	12.0985	0.535728
$511$	−21.5213	−0.952045
$512$	−1.00000	−0.0441942
$513$	−3.02057	−0.133362
$514$	2.84036	0.125283
$515$	3.65233	0.160941
$516$	9.36337	0.412199
$517$	−5.37843	−0.236543
$518$	4.17646	0.183503
$519$	5.29513	0.232431
$520$	−3.65233	−0.160165
$521$	35.5137	1.55588	0.777941	−	0.628337i	$-0.216264\pi$
$521$	35.5137	1.55588	0.777941	+	0.628337i	$0.216264\pi$
$522$	−7.76758	−0.339978
$523$	−1.78895	−0.0782252	−0.0391126	−	0.999235i	$-0.512453\pi$
$523$	−1.78895	−0.0782252	−0.0391126	+	0.999235i	$0.512453\pi$
$524$	−5.89443	−0.257499
$525$	13.0490	0.569503
$526$	−11.8806	−0.518020
$527$	−18.0150	−0.784747
$528$	0.593522	0.0258298
$529$	22.2452	0.967182
$530$	−2.85070	−0.123827
$531$	−4.34523	−0.188567
$532$	−4.72632	−0.204912
$533$	−1.56671	−0.0678618
$534$	−9.07488	−0.392708
$535$	43.1929	1.86739
$536$	5.60711	0.242190
$537$	−7.60749	−0.328288
$538$	−4.82295	−0.207932
$539$	−2.70153	−0.116363
$540$	3.65233	0.157171
$541$	−38.3448	−1.64857	−0.824285	−	0.566174i	$-0.808423\pi$
$541$	−38.3448	−1.64857	−0.824285	+	0.566174i	$0.808423\pi$
$542$	27.8820	1.19764
$543$	−5.70330	−0.244752
$544$	3.31253	0.142023
$545$	42.0811	1.80256
$546$	−1.56471	−0.0669633
$547$	22.4260	0.958867	0.479433	−	0.877578i	$-0.340842\pi$
$547$	22.4260	0.958867	0.479433	+	0.877578i	$0.340842\pi$
$548$	11.4227	0.487955
$549$	12.1694	0.519379
$550$	−4.94971	−0.211056
$551$	−23.4625	−0.999538
$552$	−6.72645	−0.286297
$553$	3.61977	0.153928
$554$	13.5471	0.575562
$555$	−9.74868	−0.413808
$556$	18.6733	0.791922
$557$	−38.1214	−1.61525	−0.807627	−	0.589693i	$-0.799249\pi$
$557$	−38.1214	−1.61525	−0.807627	+	0.589693i	$0.799249\pi$
$558$	−5.43846	−0.230228
$559$	9.36337	0.396028
$560$	5.71484	0.241496
$561$	−1.96606	−0.0830071
$562$	20.9745	0.884754
$563$	44.4666	1.87404	0.937022	−	0.349271i	$-0.113571\pi$
$563$	44.4666	1.87404	0.937022	+	0.349271i	$0.113571\pi$
$564$	−9.06189	−0.381574
$565$	5.68731	0.239267
$566$	−17.1486	−0.720808
$567$	1.56471	0.0657116
$568$	0.247102	0.0103682
$569$	−10.2749	−0.430748	−0.215374	−	0.976532i	$-0.569097\pi$
$569$	−10.2749	−0.430748	−0.215374	+	0.976532i	$0.569097\pi$
$570$	11.0321	0.462086
$571$	−10.3078	−0.431368	−0.215684	−	0.976463i	$-0.569198\pi$
$571$	−10.3078	−0.431368	−0.215684	+	0.976463i	$0.569198\pi$
$572$	0.593522	0.0248164
$573$	−24.6985	−1.03179
$574$	2.45145	0.102321
$575$	56.0956	2.33935
$576$	1.00000	0.0416667
$577$	5.29394	0.220390	0.110195	−	0.993910i	$-0.464853\pi$
$577$	5.29394	0.220390	0.110195	+	0.993910i	$0.464853\pi$
$578$	6.02717	0.250697
$579$	−4.57956	−0.190320
$580$	28.3698	1.17799
$581$	−4.07218	−0.168942
$582$	5.85830	0.242834
$583$	0.463254	0.0191860
$584$	13.7542	0.569151
$585$	3.65233	0.151005
$586$	23.5447	0.972625
$587$	−19.1000	−0.788342	−0.394171	−	0.919037i	$-0.628968\pi$
$587$	−19.1000	−0.788342	−0.394171	+	0.919037i	$0.628968\pi$
$588$	−4.55169	−0.187708
$589$	−16.4273	−0.676873
$590$	15.8702	0.653367
$591$	14.6313	0.601853
$592$	−2.66916	−0.109702
$593$	45.9837	1.88833	0.944163	−	0.329478i	$-0.106873\pi$
$593$	45.9837	1.88833	0.944163	+	0.329478i	$0.106873\pi$
$594$	−0.593522	−0.0243525
$595$	−18.9306	−0.776077
$596$	11.3262	0.463939
$597$	6.62473	0.271132
$598$	−6.72645	−0.275065
$599$	10.8849	0.444743	0.222372	−	0.974962i	$-0.428620\pi$
$599$	10.8849	0.444743	0.222372	+	0.974962i	$0.428620\pi$
$600$	−8.33954	−0.340460
$601$	−5.30294	−0.216312	−0.108156	−	0.994134i	$-0.534495\pi$
$601$	−5.30294	−0.216312	−0.108156	+	0.994134i	$0.534495\pi$
$602$	−14.6509	−0.597128
$603$	−5.60711	−0.228339
$604$	−3.57988	−0.145663
$605$	−38.8891	−1.58107
$606$	2.43138	0.0987680
$607$	27.3754	1.11113	0.555566	−	0.831473i	$-0.312502\pi$
$607$	27.3754	1.11113	0.555566	+	0.831473i	$0.312502\pi$
$608$	3.02057	0.122500
$609$	12.1540	0.492505
$610$	−44.4469	−1.79960
$611$	−9.06189	−0.366605
$612$	−3.31253	−0.133901
$613$	−21.8218	−0.881374	−0.440687	−	0.897661i	$-0.645265\pi$
$613$	−21.8218	−0.881374	−0.440687	+	0.897661i	$0.645265\pi$
$614$	−0.701523	−0.0283112
$615$	−5.72216	−0.230740
$616$	−0.928690	−0.0374180
$617$	31.7586	1.27855	0.639277	−	0.768977i	$-0.279234\pi$
$617$	31.7586	1.27855	0.639277	+	0.768977i	$0.279234\pi$
$618$	−1.00000	−0.0402259
$619$	−43.5286	−1.74956	−0.874780	−	0.484519i	$-0.838994\pi$
$619$	−43.5286	−1.74956	−0.874780	+	0.484519i	$0.838994\pi$
$620$	19.8631	0.797720
$621$	6.72645	0.269923
$622$	−20.5192	−0.822745
$623$	14.1995	0.568892
$624$	1.00000	0.0400320
$625$	2.85028	0.114011
$626$	25.5591	1.02155
$627$	−1.79278	−0.0715967
$628$	−18.8346	−0.751582
$629$	8.84167	0.352541
$630$	−5.71484	−0.227685
$631$	−9.18788	−0.365764	−0.182882	−	0.983135i	$-0.558543\pi$
$631$	−9.18788	−0.365764	−0.182882	+	0.983135i	$0.558543\pi$
$632$	−2.31338	−0.0920213
$633$	−0.979136	−0.0389172
$634$	5.60138	0.222459
$635$	−28.3156	−1.12367
$636$	0.780516	0.0309495
$637$	−4.55169	−0.180344
$638$	−4.61023	−0.182521
$639$	−0.247102	−0.00977522
$640$	−3.65233	−0.144371
$641$	−10.4847	−0.414121	−0.207061	−	0.978328i	$-0.566390\pi$
$641$	−10.4847	−0.414121	−0.207061	+	0.978328i	$0.566390\pi$
$642$	−11.8261	−0.466739
$643$	1.12629	0.0444166	0.0222083	−	0.999753i	$-0.492930\pi$
$643$	1.12629	0.0444166	0.0222083	+	0.999753i	$0.492930\pi$
$644$	10.5249	0.414741
$645$	34.1982	1.34655
$646$	−10.0057	−0.393670
$647$	−18.6789	−0.734342	−0.367171	−	0.930154i	$-0.619674\pi$
$647$	−18.6789	−0.734342	−0.367171	+	0.930154i	$0.619674\pi$
$648$	−1.00000	−0.0392837
$649$	−2.57899	−0.101234
$650$	−8.33954	−0.327104
$651$	8.50960	0.333518
$652$	19.5242	0.764626
$653$	−15.9150	−0.622803	−0.311402	−	0.950278i	$-0.600798\pi$
$653$	−15.9150	−0.622803	−0.311402	+	0.950278i	$0.600798\pi$
$654$	−11.5217	−0.450534
$655$	−21.5284	−0.841185
$656$	−1.56671	−0.0611698
$657$	−13.7542	−0.536601
$658$	14.1792	0.552763
$659$	31.3756	1.22222	0.611109	−	0.791546i	$-0.290724\pi$
$659$	31.3756	1.22222	0.611109	+	0.791546i	$0.290724\pi$
$660$	2.16774	0.0843793
$661$	−45.9559	−1.78748	−0.893739	−	0.448588i	$-0.851927\pi$
$661$	−45.9559	−1.78748	−0.893739	+	0.448588i	$0.851927\pi$
$662$	20.5799	0.799861
$663$	−3.31253	−0.128648
$664$	2.60252	0.100997
$665$	−17.2621	−0.669395
$666$	2.66916	0.103428
$667$	52.2483	2.02306
$668$	−0.535319	−0.0207121
$669$	−20.0303	−0.774416
$670$	20.4791	0.791175
$671$	7.22284	0.278835
$672$	−1.56471	−0.0603599
$673$	−23.6387	−0.911204	−0.455602	−	0.890183i	$-0.650576\pi$
$673$	−23.6387	−0.911204	−0.455602	+	0.890183i	$0.650576\pi$
$674$	17.3293	0.667500
$675$	8.33954	0.320989
$676$	1.00000	0.0384615
$677$	41.8223	1.60736	0.803681	−	0.595060i	$-0.202872\pi$
$677$	41.8223	1.60736	0.803681	+	0.595060i	$0.202872\pi$
$678$	−1.55717	−0.0598028
$679$	−9.16653	−0.351779
$680$	12.0985	0.463954
$681$	3.31462	0.127016
$682$	−3.22785	−0.123601
$683$	28.1779	1.07820	0.539098	−	0.842243i	$-0.318765\pi$
$683$	28.1779	1.07820	0.539098	+	0.842243i	$0.318765\pi$
$684$	−3.02057	−0.115495
$685$	41.7196	1.59402
$686$	18.0750	0.690108
$687$	5.06424	0.193213
$688$	9.36337	0.356975
$689$	0.780516	0.0297353
$690$	−24.5673	−0.935260
$691$	−34.9961	−1.33132	−0.665658	−	0.746257i	$-0.731849\pi$
$691$	−34.9961	−1.33132	−0.665658	+	0.746257i	$0.731849\pi$
$692$	5.29513	0.201291
$693$	0.928690	0.0352780
$694$	−21.3843	−0.811736
$695$	68.2010	2.58701
$696$	−7.76758	−0.294429
$697$	5.18978	0.196577
$698$	−28.9643	−1.09631
$699$	3.20986	0.121408
$700$	13.0490	0.493204
$701$	10.5866	0.399850	0.199925	−	0.979811i	$-0.435930\pi$
$701$	10.5866	0.399850	0.199925	+	0.979811i	$0.435930\pi$
$702$	−1.00000	−0.0377426
$703$	8.06240	0.304079
$704$	0.593522	0.0223692
$705$	−33.0970	−1.24651
$706$	0.650619	0.0244864
$707$	−3.80440	−0.143079
$708$	−4.34523	−0.163304
$709$	−13.7738	−0.517286	−0.258643	−	0.965973i	$-0.583275\pi$
$709$	−13.7738	−0.517286	−0.258643	+	0.965973i	$0.583275\pi$
$710$	0.902500	0.0338702
$711$	2.31338	0.0867585
$712$	−9.07488	−0.340095
$713$	36.5815	1.36999
$714$	5.18314	0.193974
$715$	2.16774	0.0810690
$716$	−7.60749	−0.284305
$717$	−8.15980	−0.304733
$718$	−33.4574	−1.24862
$719$	36.5615	1.36351	0.681757	−	0.731579i	$-0.261216\pi$
$719$	36.5615	1.36351	0.681757	+	0.731579i	$0.261216\pi$
$720$	3.65233	0.136114
$721$	1.56471	0.0582728
$722$	9.87614	0.367552
$723$	25.3901	0.944268
$724$	−5.70330	−0.211961
$725$	64.7781	2.40580
$726$	10.6477	0.395174
$727$	−19.8221	−0.735161	−0.367580	−	0.929992i	$-0.619814\pi$
$727$	−19.8221	−0.735161	−0.367580	+	0.929992i	$0.619814\pi$
$728$	−1.56471	−0.0579920
$729$	1.00000	0.0370370
$730$	50.2348	1.85927
$731$	−31.0164	−1.14718
$732$	12.1694	0.449796
$733$	−32.9623	−1.21749	−0.608745	−	0.793366i	$-0.708327\pi$
$733$	−32.9623	−1.21749	−0.608745	+	0.793366i	$0.708327\pi$
$734$	−8.83655	−0.326163
$735$	−16.6243	−0.613196
$736$	−6.72645	−0.247940
$737$	−3.32795	−0.122587
$738$	1.56671	0.0576715
$739$	14.8921	0.547813	0.273907	−	0.961756i	$-0.411684\pi$
$739$	14.8921	0.547813	0.273907	+	0.961756i	$0.411684\pi$
$740$	−9.74868	−0.358369
$741$	−3.02057	−0.110964
$742$	−1.22128	−0.0448346
$743$	16.3961	0.601515	0.300758	−	0.953701i	$-0.402760\pi$
$743$	16.3961	0.601515	0.300758	+	0.953701i	$0.402760\pi$
$744$	−5.43846	−0.199384
$745$	41.3670	1.51557
$746$	−6.53621	−0.239308
$747$	−2.60252	−0.0952210
$748$	−1.96606	−0.0718862
$749$	18.5044	0.676136
$750$	−12.1971	−0.445376
$751$	21.0966	0.769825	0.384912	−	0.922953i	$-0.374232\pi$
$751$	21.0966	0.769825	0.384912	+	0.922953i	$0.374232\pi$
$752$	−9.06189	−0.330453
$753$	16.9455	0.617530
$754$	−7.76758	−0.282878
$755$	−13.0749	−0.475845
$756$	1.56471	0.0569079
$757$	−34.1425	−1.24093	−0.620465	−	0.784234i	$-0.713056\pi$
$757$	−34.1425	−1.24093	−0.620465	+	0.784234i	$0.713056\pi$
$758$	−34.1788	−1.24143
$759$	3.99230	0.144911
$760$	11.0321	0.400178
$761$	−23.9219	−0.867167	−0.433583	−	0.901113i	$-0.642751\pi$
$761$	−23.9219	−0.867167	−0.433583	+	0.901113i	$0.642751\pi$
$762$	7.75275	0.280852
$763$	18.0281	0.652662
$764$	−24.6985	−0.893559
$765$	−12.0985	−0.437420
$766$	−22.2560	−0.804141
$767$	−4.34523	−0.156897
$768$	1.00000	0.0360844
$769$	−46.0192	−1.65949	−0.829747	−	0.558139i	$-0.811515\pi$
$769$	−46.0192	−1.65949	−0.829747	+	0.558139i	$0.811515\pi$
$770$	−3.39189	−0.122235
$771$	−2.84036	−0.102293
$772$	−4.57956	−0.164822
$773$	27.6422	0.994221	0.497110	−	0.867687i	$-0.334394\pi$
$773$	27.6422	0.994221	0.497110	+	0.867687i	$0.334394\pi$
$774$	−9.36337	−0.336559
$775$	45.3543	1.62917
$776$	5.85830	0.210301
$777$	−4.17646	−0.149830
$778$	−16.2990	−0.584347
$779$	4.73237	0.169555
$780$	3.65233	0.130775
$781$	−0.146661	−0.00524793
$782$	22.2816	0.796787
$783$	7.76758	0.277591
$784$	−4.55169	−0.162560
$785$	−68.7903	−2.45523
$786$	5.89443	0.210247
$787$	8.23300	0.293475	0.146737	−	0.989175i	$-0.453123\pi$
$787$	8.23300	0.293475	0.146737	+	0.989175i	$0.453123\pi$
$788$	14.6313	0.521220
$789$	11.8806	0.422962
$790$	−8.44924	−0.300610
$791$	2.43652	0.0866327
$792$	−0.593522	−0.0210899
$793$	12.1694	0.432150
$794$	8.72203	0.309533
$795$	2.85070	0.101104
$796$	6.62473	0.234807
$797$	−20.0785	−0.711218	−0.355609	−	0.934635i	$-0.615727\pi$
$797$	−20.0785	−0.711218	−0.355609	+	0.934635i	$0.615727\pi$
$798$	4.72632	0.167310
$799$	30.0177	1.06195
$800$	−8.33954	−0.294847
$801$	9.07488	0.320645
$802$	−19.4022	−0.685115
$803$	−8.16341	−0.288080
$804$	−5.60711	−0.197748
$805$	38.4406	1.35485
$806$	−5.43846	−0.191562
$807$	4.82295	0.169776
$808$	2.43138	0.0855356
$809$	−7.80171	−0.274293	−0.137147	−	0.990551i	$-0.543793\pi$
$809$	−7.80171	−0.274293	−0.137147	+	0.990551i	$0.543793\pi$
$810$	−3.65233	−0.128330
$811$	30.8227	1.08233	0.541166	−	0.840916i	$-0.317983\pi$
$811$	30.8227	1.08233	0.541166	+	0.840916i	$0.317983\pi$
$812$	12.1540	0.426522
$813$	−27.8820	−0.977865
$814$	1.58421	0.0555265
$815$	71.3088	2.49784
$816$	−3.31253	−0.115962
$817$	−28.2828	−0.989488
$818$	13.9287	0.487006
$819$	1.56471	0.0546753
$820$	−5.72216	−0.199826
$821$	49.7601	1.73664	0.868320	−	0.496005i	$-0.165200\pi$
$821$	49.7601	1.73664	0.868320	+	0.496005i	$0.165200\pi$
$822$	−11.4227	−0.398413
$823$	−12.7952	−0.446013	−0.223007	−	0.974817i	$-0.571587\pi$
$823$	−12.7952	−0.446013	−0.223007	+	0.974817i	$0.571587\pi$
$824$	−1.00000	−0.0348367
$825$	4.94971	0.172327
$826$	6.79902	0.236568
$827$	−35.6163	−1.23850	−0.619249	−	0.785195i	$-0.712563\pi$
$827$	−35.6163	−1.23850	−0.619249	+	0.785195i	$0.712563\pi$
$828$	6.72645	0.233760
$829$	2.17950	0.0756972	0.0378486	−	0.999283i	$-0.487950\pi$
$829$	2.17950	0.0756972	0.0378486	+	0.999283i	$0.487950\pi$
$830$	9.50525	0.329932
$831$	−13.5471	−0.469945
$832$	1.00000	0.0346688
$833$	15.0776	0.522407
$834$	−18.6733	−0.646602
$835$	−1.95516	−0.0676612
$836$	−1.79278	−0.0620045
$837$	5.43846	0.187981
$838$	27.4558	0.948443
$839$	31.0033	1.07035	0.535176	−	0.844741i	$-0.320245\pi$
$839$	31.0033	1.07035	0.535176	+	0.844741i	$0.320245\pi$
$840$	−5.71484	−0.197181
$841$	31.3353	1.08053
$842$	−19.0453	−0.656344
$843$	−20.9745	−0.722399
$844$	−0.979136	−0.0337033
$845$	3.65233	0.125644
$846$	9.06189	0.311554
$847$	−16.6606	−0.572465
$848$	0.780516	0.0268030
$849$	17.1486	0.588537
$850$	27.6250	0.947528
$851$	−17.9540	−0.615455
$852$	−0.247102	−0.00846558
$853$	2.34066	0.0801427	0.0400713	−	0.999197i	$-0.487241\pi$
$853$	2.34066	0.0801427	0.0400713	+	0.999197i	$0.487241\pi$
$854$	−19.0416	−0.651591
$855$	−11.0321	−0.377291
$856$	−11.8261	−0.404208
$857$	43.4059	1.48272	0.741358	−	0.671109i	$-0.234182\pi$
$857$	43.4059	1.48272	0.741358	+	0.671109i	$0.234182\pi$
$858$	−0.593522	−0.0202625
$859$	32.2410	1.10005	0.550024	−	0.835149i	$-0.314618\pi$
$859$	32.2410	1.10005	0.550024	+	0.835149i	$0.314618\pi$
$860$	34.1982	1.16615
$861$	−2.45145	−0.0835451
$862$	22.8753	0.779136
$863$	−7.49830	−0.255245	−0.127622	−	0.991823i	$-0.540735\pi$
$863$	−7.49830	−0.255245	−0.127622	+	0.991823i	$0.540735\pi$
$864$	−1.00000	−0.0340207
$865$	19.3396	0.657566
$866$	30.3703	1.03203
$867$	−6.02717	−0.204693
$868$	8.50960	0.288835
$869$	1.37304	0.0465773
$870$	−28.3698	−0.961826
$871$	−5.60711	−0.189990
$872$	−11.5217	−0.390174
$873$	−5.85830	−0.198273
$874$	20.3177	0.687258
$875$	19.0850	0.645189
$876$	−13.7542	−0.464710
$877$	16.3580	0.552372	0.276186	−	0.961104i	$-0.410929\pi$
$877$	16.3580	0.552372	0.276186	+	0.961104i	$0.410929\pi$
$878$	21.2699	0.717825
$879$	−23.5447	−0.794145
$880$	2.16774	0.0730746
$881$	−11.1363	−0.375190	−0.187595	−	0.982246i	$-0.560069\pi$
$881$	−11.1363	−0.375190	−0.187595	+	0.982246i	$0.560069\pi$
$882$	4.55169	0.153263
$883$	13.8356	0.465606	0.232803	−	0.972524i	$-0.425210\pi$
$883$	13.8356	0.465606	0.232803	+	0.972524i	$0.425210\pi$
$884$	−3.31253	−0.111412
$885$	−15.8702	−0.533472
$886$	−20.0331	−0.673025
$887$	−40.5596	−1.36186	−0.680929	−	0.732349i	$-0.738424\pi$
$887$	−40.5596	−1.36186	−0.680929	+	0.732349i	$0.738424\pi$
$888$	2.66916	0.0895713
$889$	−12.1308	−0.406854
$890$	−33.1445	−1.11101
$891$	0.593522	0.0198838
$892$	−20.0303	−0.670664
$893$	27.3721	0.915972
$894$	−11.3262	−0.378805
$895$	−27.7851	−0.928754
$896$	−1.56471	−0.0522732
$897$	6.72645	0.224590
$898$	28.3034	0.944496
$899$	42.2436	1.40890
$900$	8.33954	0.277985
$901$	−2.58548	−0.0861348
$902$	0.929879	0.0309616
$903$	14.6509	0.487553
$904$	−1.55717	−0.0517908
$905$	−20.8303	−0.692424
$906$	3.57988	0.118933
$907$	−2.46745	−0.0819305	−0.0409652	−	0.999161i	$-0.513043\pi$
$907$	−2.46745	−0.0819305	−0.0409652	+	0.999161i	$0.513043\pi$
$908$	3.31462	0.110000
$909$	−2.43138	−0.0806437
$910$	−5.71484	−0.189445
$911$	35.6779	1.18206	0.591030	−	0.806649i	$-0.298721\pi$
$911$	35.6779	1.18206	0.591030	+	0.806649i	$0.298721\pi$
$912$	−3.02057	−0.100021
$913$	−1.54465	−0.0511205
$914$	−13.5845	−0.449335
$915$	44.4469	1.46937
$916$	5.06424	0.167327
$917$	−9.22306	−0.304572
$918$	3.31253	0.109330
$919$	37.5006	1.23703	0.618515	−	0.785773i	$-0.287735\pi$
$919$	37.5006	1.23703	0.618515	+	0.785773i	$0.287735\pi$
$920$	−24.5673	−0.809959
$921$	0.701523	0.0231160
$922$	25.8954	0.852820
$923$	−0.247102	−0.00813347
$924$	0.928690	0.0305516
$925$	−22.2596	−0.731891
$926$	31.6403	1.03976
$927$	1.00000	0.0328443
$928$	−7.76758	−0.254983
$929$	11.1479	0.365752	0.182876	−	0.983136i	$-0.441459\pi$
$929$	11.1479	0.365752	0.182876	+	0.983136i	$0.441459\pi$
$930$	−19.8631	−0.651336
$931$	13.7487	0.450596
$932$	3.20986	0.105142
$933$	20.5192	0.671768
$934$	−0.505638	−0.0165450
$935$	−7.18070	−0.234834
$936$	−1.00000	−0.0326860
$937$	−20.6791	−0.675557	−0.337779	−	0.941226i	$-0.609676\pi$
$937$	−20.6791	−0.675557	−0.337779	+	0.941226i	$0.609676\pi$
$938$	8.77350	0.286465
$939$	−25.5591	−0.834089
$940$	−33.0970	−1.07951
$941$	13.2189	0.430923	0.215462	−	0.976512i	$-0.430874\pi$
$941$	13.2189	0.430923	0.215462	+	0.976512i	$0.430874\pi$
$942$	18.8346	0.613664
$943$	−10.5384	−0.343178
$944$	−4.34523	−0.141425
$945$	5.71484	0.185904
$946$	−5.55737	−0.180686
$947$	−28.0664	−0.912036	−0.456018	−	0.889970i	$-0.650725\pi$
$947$	−28.0664	−0.912036	−0.456018	+	0.889970i	$0.650725\pi$
$948$	2.31338	0.0751351
$949$	−13.7542	−0.446479
$950$	25.1902	0.817278
$951$	−5.60138	−0.181637
$952$	5.18314	0.167986
$953$	23.8537	0.772697	0.386349	−	0.922353i	$-0.373736\pi$
$953$	23.8537	0.772697	0.386349	+	0.922353i	$0.373736\pi$
$954$	−0.780516	−0.0252701
$955$	−90.2071	−2.91903
$956$	−8.15980	−0.263907
$957$	4.61023	0.149028
$958$	3.75281	0.121248
$959$	17.8732	0.577157
$960$	3.65233	0.117879
$961$	−1.42318	−0.0459090
$962$	2.66916	0.0860573
$963$	11.8261	0.381091
$964$	25.3901	0.817760
$965$	−16.7261	−0.538431
$966$	−10.5249	−0.338634
$967$	−15.2202	−0.489447	−0.244724	−	0.969593i	$-0.578697\pi$
$967$	−15.2202	−0.489447	−0.244724	+	0.969593i	$0.578697\pi$
$968$	10.6477	0.342231
$969$	10.0057	0.321430
$970$	21.3965	0.686999
$971$	50.8080	1.63050	0.815252	−	0.579106i	$-0.196598\pi$
$971$	50.8080	1.63050	0.815252	+	0.579106i	$0.196598\pi$
$972$	1.00000	0.0320750
$973$	29.2182	0.936693
$974$	−32.4488	−1.03973
$975$	8.33954	0.267079
$976$	12.1694	0.389534
$977$	17.6462	0.564552	0.282276	−	0.959333i	$-0.408911\pi$
$977$	17.6462	0.564552	0.282276	+	0.959333i	$0.408911\pi$
$978$	−19.5242	−0.624314
$979$	5.38614	0.172142
$980$	−16.6243	−0.531043
$981$	11.5217	0.367860
$982$	2.82035	0.0900009
$983$	−1.70092	−0.0542511	−0.0271255	−	0.999632i	$-0.508635\pi$
$983$	−1.70092	−0.0542511	−0.0271255	+	0.999632i	$0.508635\pi$
$984$	1.56671	0.0499450
$985$	53.4386	1.70269
$986$	25.7303	0.819420
$987$	−14.1792	−0.451329
$988$	−3.02057	−0.0960972
$989$	62.9823	2.00272
$990$	−2.16774	−0.0688954
$991$	3.75492	0.119279	0.0596396	−	0.998220i	$-0.481005\pi$
$991$	3.75492	0.119279	0.0596396	+	0.998220i	$0.481005\pi$
$992$	−5.43846	−0.172671
$993$	−20.5799	−0.653084
$994$	0.386643	0.0122636
$995$	24.1957	0.767056
$996$	−2.60252	−0.0824638
$997$	−41.6370	−1.31866	−0.659329	−	0.751854i	$-0.729160\pi$
$997$	−41.6370	−1.31866	−0.659329	+	0.751854i	$0.729160\pi$
$998$	20.3275	0.643456
$999$	−2.66916	−0.0844486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8034.2.a.x.1.13	✓	13

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8034.2.a.x.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.65233 q^{5} -1.00000 q^{6} +1.56471 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +1.00000 q^{3} +1.00000 q^{4} +3.65233 q^{5} -1.00000 q^{6} +1.56471 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.65233 q^{10} +0.593522 q^{11} +1.00000 q^{12} +1.00000 q^{13} -1.56471 q^{14} +3.65233 q^{15} +1.00000 q^{16} -3.31253 q^{17} -1.00000 q^{18} -3.02057 q^{19} +3.65233 q^{20} +1.56471 q^{21} -0.593522 q^{22} +6.72645 q^{23} -1.00000 q^{24} +8.33954 q^{25} -1.00000 q^{26} +1.00000 q^{27} +1.56471 q^{28} +7.76758 q^{29} -3.65233 q^{30} +5.43846 q^{31} -1.00000 q^{32} +0.593522 q^{33} +3.31253 q^{34} +5.71484 q^{35} +1.00000 q^{36} -2.66916 q^{37} +3.02057 q^{38} +1.00000 q^{39} -3.65233 q^{40} -1.56671 q^{41} -1.56471 q^{42} +9.36337 q^{43} +0.593522 q^{44} +3.65233 q^{45} -6.72645 q^{46} -9.06189 q^{47} +1.00000 q^{48} -4.55169 q^{49} -8.33954 q^{50} -3.31253 q^{51} +1.00000 q^{52} +0.780516 q^{53} -1.00000 q^{54} +2.16774 q^{55} -1.56471 q^{56} -3.02057 q^{57} -7.76758 q^{58} -4.34523 q^{59} +3.65233 q^{60} +12.1694 q^{61} -5.43846 q^{62} +1.56471 q^{63} +1.00000 q^{64} +3.65233 q^{65} -0.593522 q^{66} -5.60711 q^{67} -3.31253 q^{68} +6.72645 q^{69} -5.71484 q^{70} -0.247102 q^{71} -1.00000 q^{72} -13.7542 q^{73} +2.66916 q^{74} +8.33954 q^{75} -3.02057 q^{76} +0.928690 q^{77} -1.00000 q^{78} +2.31338 q^{79} +3.65233 q^{80} +1.00000 q^{81} +1.56671 q^{82} -2.60252 q^{83} +1.56471 q^{84} -12.0985 q^{85} -9.36337 q^{86} +7.76758 q^{87} -0.593522 q^{88} +9.07488 q^{89} -3.65233 q^{90} +1.56471 q^{91} +6.72645 q^{92} +5.43846 q^{93} +9.06189 q^{94} -11.0321 q^{95} -1.00000 q^{96} -5.85830 q^{97} +4.55169 q^{98} +0.593522 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9}+O(q^{10}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9	\( 13 q - 13 q^{2} + 13 q^{3} + 13 q^{4} + q^{5} - 13 q^{6} - q^{7} - 13 q^{8} + 13 q^{9} - q^{10} + 6 q^{11} + 13 q^{12} + 13 q^{13} + q^{14} + q^{15} + 13 q^{16} + 18 q^{17} - 13 q^{18} - q^{19} + q^{20} - q^{21} - 6 q^{22} + 20 q^{23} - 13 q^{24} + 16 q^{25} - 13 q^{26} + 13 q^{27} - q^{28} + 25 q^{29} - q^{30} - 5 q^{31} - 13 q^{32} + 6 q^{33} - 18 q^{34} + 26 q^{35} + 13 q^{36} - 6 q^{37} + q^{38} + 13 q^{39} - q^{40} + 13 q^{41} + q^{42} - 2 q^{43} + 6 q^{44} + q^{45} - 20 q^{46} + 5 q^{47} + 13 q^{48} - 16 q^{50} + 18 q^{51} + 13 q^{52} + 21 q^{53} - 13 q^{54} + 2 q^{55} + q^{56} - q^{57} - 25 q^{58} + 22 q^{59} + q^{60} + 2 q^{61} + 5 q^{62} - q^{63} + 13 q^{64} + q^{65} - 6 q^{66} - q^{67} + 18 q^{68} + 20 q^{69} - 26 q^{70} + 32 q^{71} - 13 q^{72} - 13 q^{73} + 6 q^{74} + 16 q^{75} - q^{76} + 33 q^{77} - 13 q^{78} - 7 q^{79} + q^{80} + 13 q^{81} - 13 q^{82} + 17 q^{83} - q^{84} - 25 q^{85} + 2 q^{86} + 25 q^{87} - 6 q^{88} - 12 q^{89} - q^{90} - q^{91} + 20 q^{92} - 5 q^{93} - 5 q^{94} + 36 q^{95} - 13 q^{96} - 42 q^{97} + 6 q^{99}+O(q^{100}) \) 13 * q - 13 * q^2 + 13 * q^3 + 13 * q^4 + q^5 - 13 * q^6 - q^7 - 13 * q^8 + 13 * q^9 - q^10 + 6 * q^11 + 13 * q^12 + 13 * q^13 + q^14 + q^15 + 13 * q^16 + 18 * q^17 - 13 * q^18 - q^19 + q^20 - q^21 - 6 * q^22 + 20 * q^23 - 13 * q^24 + 16 * q^25 - 13 * q^26 + 13 * q^27 - q^28 + 25 * q^29 - q^30 - 5 * q^31 - 13 * q^32 + 6 * q^33 - 18 * q^34 + 26 * q^35 + 13 * q^36 - 6 * q^37 + q^38 + 13 * q^39 - q^40 + 13 * q^41 + q^42 - 2 * q^43 + 6 * q^44 + q^45 - 20 * q^46 + 5 * q^47 + 13 * q^48 - 16 * q^50 + 18 * q^51 + 13 * q^52 + 21 * q^53 - 13 * q^54 + 2 * q^55 + q^56 - q^57 - 25 * q^58 + 22 * q^59 + q^60 + 2 * q^61 + 5 * q^62 - q^63 + 13 * q^64 + q^65 - 6 * q^66 - q^67 + 18 * q^68 + 20 * q^69 - 26 * q^70 + 32 * q^71 - 13 * q^72 - 13 * q^73 + 6 * q^74 + 16 * q^75 - q^76 + 33 * q^77 - 13 * q^78 - 7 * q^79 + q^80 + 13 * q^81 - 13 * q^82 + 17 * q^83 - q^84 - 25 * q^85 + 2 * q^86 + 25 * q^87 - 6 * q^88 - 12 * q^89 - q^90 - q^91 + 20 * q^92 - 5 * q^93 - 5 * q^94 + 36 * q^95 - 13 * q^96 - 42 * q^97 + 6 * q^99

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