LMFDB - Embedded newform 8018.2.a.j.1.43

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.43
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +3.10004 q^{3} +1.00000 q^{4} +1.73533 q^{5} +3.10004 q^{6} +3.71776 q^{7} +1.00000 q^{8} +6.61026 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +3.10004 q^{3} +1.00000 q^{4} +1.73533 q^{5} +3.10004 q^{6} +3.71776 q^{7} +1.00000 q^{8} +6.61026 q^{9} +1.73533 q^{10} +0.351101 q^{11} +3.10004 q^{12} -3.27955 q^{13} +3.71776 q^{14} +5.37959 q^{15} +1.00000 q^{16} +0.752399 q^{17} +6.61026 q^{18} -1.00000 q^{19} +1.73533 q^{20} +11.5252 q^{21} +0.351101 q^{22} -6.92588 q^{23} +3.10004 q^{24} -1.98864 q^{25} -3.27955 q^{26} +11.1919 q^{27} +3.71776 q^{28} +1.99959 q^{29} +5.37959 q^{30} -1.76755 q^{31} +1.00000 q^{32} +1.08843 q^{33} +0.752399 q^{34} +6.45153 q^{35} +6.61026 q^{36} -9.46076 q^{37} -1.00000 q^{38} -10.1668 q^{39} +1.73533 q^{40} +7.34124 q^{41} +11.5252 q^{42} +4.84196 q^{43} +0.351101 q^{44} +11.4710 q^{45} -6.92588 q^{46} +9.66475 q^{47} +3.10004 q^{48} +6.82172 q^{49} -1.98864 q^{50} +2.33247 q^{51} -3.27955 q^{52} -12.6718 q^{53} +11.1919 q^{54} +0.609275 q^{55} +3.71776 q^{56} -3.10004 q^{57} +1.99959 q^{58} -2.58178 q^{59} +5.37959 q^{60} -3.16536 q^{61} -1.76755 q^{62} +24.5753 q^{63} +1.00000 q^{64} -5.69110 q^{65} +1.08843 q^{66} +14.5796 q^{67} +0.752399 q^{68} -21.4705 q^{69} +6.45153 q^{70} +2.53897 q^{71} +6.61026 q^{72} -4.14205 q^{73} -9.46076 q^{74} -6.16485 q^{75} -1.00000 q^{76} +1.30531 q^{77} -10.1668 q^{78} +2.86347 q^{79} +1.73533 q^{80} +14.8647 q^{81} +7.34124 q^{82} +13.5727 q^{83} +11.5252 q^{84} +1.30566 q^{85} +4.84196 q^{86} +6.19882 q^{87} +0.351101 q^{88} +13.1952 q^{89} +11.4710 q^{90} -12.1926 q^{91} -6.92588 q^{92} -5.47947 q^{93} +9.66475 q^{94} -1.73533 q^{95} +3.10004 q^{96} +1.69040 q^{97} +6.82172 q^{98} +2.32087 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * 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
$3$	3.10004	1.78981	0.894905	−	0.446257i	$-0.147243\pi$
$3$	3.10004	1.78981	0.894905	+	0.446257i	$0.147243\pi$
$4$	1.00000	0.500000
$5$	1.73533	0.776062	0.388031	−	0.921646i	$-0.373155\pi$
$5$	1.73533	0.776062	0.388031	+	0.921646i	$0.373155\pi$
$6$	3.10004	1.26559
$7$	3.71776	1.40518	0.702590	−	0.711595i	$-0.252027\pi$
$7$	3.71776	1.40518	0.702590	+	0.711595i	$0.252027\pi$
$8$	1.00000	0.353553
$9$	6.61026	2.20342
$10$	1.73533	0.548759
$11$	0.351101	0.105861	0.0529304	−	0.998598i	$-0.483144\pi$
$11$	0.351101	0.105861	0.0529304	+	0.998598i	$0.483144\pi$
$12$	3.10004	0.894905
$13$	−3.27955	−0.909585	−0.454792	−	0.890597i	$-0.650287\pi$
$13$	−3.27955	−0.909585	−0.454792	+	0.890597i	$0.650287\pi$
$14$	3.71776	0.993612
$15$	5.37959	1.38900
$16$	1.00000	0.250000
$17$	0.752399	0.182484	0.0912418	−	0.995829i	$-0.470916\pi$
$17$	0.752399	0.182484	0.0912418	+	0.995829i	$0.470916\pi$
$18$	6.61026	1.55805
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.73533	0.388031
$21$	11.5252	2.51500
$22$	0.351101	0.0748550
$23$	−6.92588	−1.44415	−0.722073	−	0.691817i	$-0.756810\pi$
$23$	−6.92588	−1.44415	−0.722073	+	0.691817i	$0.756810\pi$
$24$	3.10004	0.632793
$25$	−1.98864	−0.397727
$26$	−3.27955	−0.643174
$27$	11.1919	2.15389
$28$	3.71776	0.702590
$29$	1.99959	0.371315	0.185657	−	0.982615i	$-0.440559\pi$
$29$	1.99959	0.371315	0.185657	+	0.982615i	$0.440559\pi$
$30$	5.37959	0.982174
$31$	−1.76755	−0.317461	−0.158730	−	0.987322i	$-0.550740\pi$
$31$	−1.76755	−0.317461	−0.158730	+	0.987322i	$0.550740\pi$
$32$	1.00000	0.176777
$33$	1.08843	0.189471
$34$	0.752399	0.129035
$35$	6.45153	1.09051
$36$	6.61026	1.10171
$37$	−9.46076	−1.55534	−0.777669	−	0.628673i	$-0.783598\pi$
$37$	−9.46076	−1.55534	−0.777669	+	0.628673i	$0.783598\pi$
$38$	−1.00000	−0.162221
$39$	−10.1668	−1.62798
$40$	1.73533	0.274379
$41$	7.34124	1.14651	0.573255	−	0.819377i	$-0.305681\pi$
$41$	7.34124	1.14651	0.573255	+	0.819377i	$0.305681\pi$
$42$	11.5252	1.77838
$43$	4.84196	0.738392	0.369196	−	0.929352i	$-0.379633\pi$
$43$	4.84196	0.738392	0.369196	+	0.929352i	$0.379633\pi$
$44$	0.351101	0.0529304
$45$	11.4710	1.70999
$46$	−6.92588	−1.02117
$47$	9.66475	1.40975	0.704874	−	0.709332i	$-0.251003\pi$
$47$	9.66475	1.40975	0.704874	+	0.709332i	$0.251003\pi$
$48$	3.10004	0.447452
$49$	6.82172	0.974531
$50$	−1.98864	−0.281236
$51$	2.33247	0.326611
$52$	−3.27955	−0.454792
$53$	−12.6718	−1.74060	−0.870301	−	0.492521i	$-0.836076\pi$
$53$	−12.6718	−1.74060	−0.870301	+	0.492521i	$0.836076\pi$
$54$	11.1919	1.52303
$55$	0.609275	0.0821547
$56$	3.71776	0.496806
$57$	−3.10004	−0.410610
$58$	1.99959	0.262559
$59$	−2.58178	−0.336119	−0.168059	−	0.985777i	$-0.553750\pi$
$59$	−2.58178	−0.336119	−0.168059	+	0.985777i	$0.553750\pi$
$60$	5.37959	0.694502
$61$	−3.16536	−0.405283	−0.202642	−	0.979253i	$-0.564953\pi$
$61$	−3.16536	−0.405283	−0.202642	+	0.979253i	$0.564953\pi$
$62$	−1.76755	−0.224479
$63$	24.5753	3.09620
$64$	1.00000	0.125000
$65$	−5.69110	−0.705895
$66$	1.08843	0.133976
$67$	14.5796	1.78118	0.890592	−	0.454803i	$-0.150290\pi$
$67$	14.5796	1.78118	0.890592	+	0.454803i	$0.150290\pi$
$68$	0.752399	0.0912418
$69$	−21.4705	−2.58475
$70$	6.45153	0.771105
$71$	2.53897	0.301321	0.150660	−	0.988586i	$-0.451860\pi$
$71$	2.53897	0.301321	0.150660	+	0.988586i	$0.451860\pi$
$72$	6.61026	0.779026
$73$	−4.14205	−0.484791	−0.242395	−	0.970178i	$-0.577933\pi$
$73$	−4.14205	−0.484791	−0.242395	+	0.970178i	$0.577933\pi$
$74$	−9.46076	−1.09979
$75$	−6.16485	−0.711856
$76$	−1.00000	−0.114708
$77$	1.30531	0.148754
$78$	−10.1668	−1.15116
$79$	2.86347	0.322165	0.161083	−	0.986941i	$-0.448501\pi$
$79$	2.86347	0.322165	0.161083	+	0.986941i	$0.448501\pi$
$80$	1.73533	0.194016
$81$	14.8647	1.65163
$82$	7.34124	0.810704
$83$	13.5727	1.48980	0.744899	−	0.667177i	$-0.232498\pi$
$83$	13.5727	1.48980	0.744899	+	0.667177i	$0.232498\pi$
$84$	11.5252	1.25750
$85$	1.30566	0.141619
$86$	4.84196	0.522122
$87$	6.19882	0.664583
$88$	0.351101	0.0374275
$89$	13.1952	1.39869	0.699345	−	0.714784i	$-0.253475\pi$
$89$	13.1952	1.39869	0.699345	+	0.714784i	$0.253475\pi$
$90$	11.4710	1.20915
$91$	−12.1926	−1.27813
$92$	−6.92588	−0.722073
$93$	−5.47947	−0.568194
$94$	9.66475	0.996843
$95$	−1.73533	−0.178041
$96$	3.10004	0.316397
$97$	1.69040	0.171634	0.0858172	−	0.996311i	$-0.472650\pi$
$97$	1.69040	0.171634	0.0858172	+	0.996311i	$0.472650\pi$
$98$	6.82172	0.689098
$99$	2.32087	0.233256
$100$	−1.98864	−0.198864
$101$	3.23070	0.321466	0.160733	−	0.986998i	$-0.448614\pi$
$101$	3.23070	0.321466	0.160733	+	0.986998i	$0.448614\pi$
$102$	2.33247	0.230949
$103$	−9.39478	−0.925695	−0.462848	−	0.886438i	$-0.653172\pi$
$103$	−9.39478	−0.925695	−0.462848	+	0.886438i	$0.653172\pi$
$104$	−3.27955	−0.321587
$105$	20.0000	1.95180
$106$	−12.6718	−1.23079
$107$	−11.1153	−1.07456	−0.537279	−	0.843405i	$-0.680548\pi$
$107$	−11.1153	−1.07456	−0.537279	+	0.843405i	$0.680548\pi$
$108$	11.1919	1.07694
$109$	−15.2968	−1.46516	−0.732582	−	0.680678i	$-0.761685\pi$
$109$	−15.2968	−1.46516	−0.732582	+	0.680678i	$0.761685\pi$
$110$	0.609275	0.0580921
$111$	−29.3287	−2.78376
$112$	3.71776	0.351295
$113$	4.41686	0.415503	0.207752	−	0.978182i	$-0.433385\pi$
$113$	4.41686	0.415503	0.207752	+	0.978182i	$0.433385\pi$
$114$	−3.10004	−0.290345
$115$	−12.0187	−1.12075
$116$	1.99959	0.185657
$117$	−21.6787	−2.00420
$118$	−2.58178	−0.237672
$119$	2.79724	0.256422
$120$	5.37959	0.491087
$121$	−10.8767	−0.988793
$122$	−3.16536	−0.286578
$123$	22.7581	2.05203
$124$	−1.76755	−0.158730
$125$	−12.1276	−1.08472
$126$	24.5753	2.18934
$127$	−1.09609	−0.0972621	−0.0486311	−	0.998817i	$-0.515486\pi$
$127$	−1.09609	−0.0972621	−0.0486311	+	0.998817i	$0.515486\pi$
$128$	1.00000	0.0883883
$129$	15.0103	1.32158
$130$	−5.69110	−0.499143
$131$	−3.34665	−0.292398	−0.146199	−	0.989255i	$-0.546704\pi$
$131$	−3.34665	−0.292398	−0.146199	+	0.989255i	$0.546704\pi$
$132$	1.08843	0.0947354
$133$	−3.71776	−0.322370
$134$	14.5796	1.25949
$135$	19.4217	1.67155
$136$	0.752399	0.0645177
$137$	−3.27539	−0.279835	−0.139918	−	0.990163i	$-0.544684\pi$
$137$	−3.27539	−0.279835	−0.139918	+	0.990163i	$0.544684\pi$
$138$	−21.4705	−1.82769
$139$	11.3529	0.962944	0.481472	−	0.876462i	$-0.340102\pi$
$139$	11.3529	0.962944	0.481472	+	0.876462i	$0.340102\pi$
$140$	6.45153	0.545254
$141$	29.9611	2.52318
$142$	2.53897	0.213066
$143$	−1.15145	−0.0962895
$144$	6.61026	0.550855
$145$	3.46995	0.288164
$146$	−4.14205	−0.342799
$147$	21.1476	1.74423
$148$	−9.46076	−0.777669
$149$	6.47207	0.530212	0.265106	−	0.964219i	$-0.414593\pi$
$149$	6.47207	0.530212	0.265106	+	0.964219i	$0.414593\pi$
$150$	−6.16485	−0.503358
$151$	12.6234	1.02728	0.513638	−	0.858007i	$-0.328297\pi$
$151$	12.6234	1.02728	0.513638	+	0.858007i	$0.328297\pi$
$152$	−1.00000	−0.0811107
$153$	4.97355	0.402088
$154$	1.30531	0.105185
$155$	−3.06727	−0.246369
$156$	−10.1668	−0.813992
$157$	1.06845	0.0852715	0.0426358	−	0.999091i	$-0.486425\pi$
$157$	1.06845	0.0852715	0.0426358	+	0.999091i	$0.486425\pi$
$158$	2.86347	0.227805
$159$	−39.2830	−3.11535
$160$	1.73533	0.137190
$161$	−25.7487	−2.02928
$162$	14.8647	1.16788
$163$	−11.4004	−0.892949	−0.446475	−	0.894796i	$-0.647321\pi$
$163$	−11.4004	−0.892949	−0.446475	+	0.894796i	$0.647321\pi$
$164$	7.34124	0.573255
$165$	1.88878	0.147041
$166$	13.5727	1.05345
$167$	−4.82792	−0.373596	−0.186798	−	0.982398i	$-0.559811\pi$
$167$	−4.82792	−0.373596	−0.186798	+	0.982398i	$0.559811\pi$
$168$	11.5252	0.889189
$169$	−2.24452	−0.172656
$170$	1.30566	0.100139
$171$	−6.61026	−0.505499
$172$	4.84196	0.369196
$173$	−17.2487	−1.31139	−0.655696	−	0.755025i	$-0.727625\pi$
$173$	−17.2487	−1.31139	−0.655696	+	0.755025i	$0.727625\pi$
$174$	6.19882	0.469931
$175$	−7.39327	−0.558878
$176$	0.351101	0.0264652
$177$	−8.00362	−0.601589
$178$	13.1952	0.989023
$179$	5.93539	0.443632	0.221816	−	0.975089i	$-0.428802\pi$
$179$	5.93539	0.443632	0.221816	+	0.975089i	$0.428802\pi$
$180$	11.4710	0.854995
$181$	20.9918	1.56031	0.780156	−	0.625585i	$-0.215140\pi$
$181$	20.9918	1.56031	0.780156	+	0.625585i	$0.215140\pi$
$182$	−12.1926	−0.903775
$183$	−9.81275	−0.725379
$184$	−6.92588	−0.510583
$185$	−16.4175	−1.20704
$186$	−5.47947	−0.401774
$187$	0.264168	0.0193179
$188$	9.66475	0.704874
$189$	41.6089	3.02660
$190$	−1.73533	−0.125894
$191$	−24.5408	−1.77571	−0.887855	−	0.460123i	$-0.847805\pi$
$191$	−24.5408	−1.77571	−0.887855	+	0.460123i	$0.847805\pi$
$192$	3.10004	0.223726
$193$	−11.0919	−0.798415	−0.399208	−	0.916860i	$-0.630715\pi$
$193$	−11.0919	−0.798415	−0.399208	+	0.916860i	$0.630715\pi$
$194$	1.69040	0.121364
$195$	−17.6427	−1.26342
$196$	6.82172	0.487266
$197$	8.13853	0.579846	0.289923	−	0.957050i	$-0.406370\pi$
$197$	8.13853	0.579846	0.289923	+	0.957050i	$0.406370\pi$
$198$	2.32087	0.164937
$199$	−21.6215	−1.53271	−0.766354	−	0.642418i	$-0.777931\pi$
$199$	−21.6215	−1.53271	−0.766354	+	0.642418i	$0.777931\pi$
$200$	−1.98864	−0.140618
$201$	45.1974	3.18798
$202$	3.23070	0.227311
$203$	7.43400	0.521764
$204$	2.33247	0.163305
$205$	12.7395	0.889763
$206$	−9.39478	−0.654565
$207$	−45.7818	−3.18206
$208$	−3.27955	−0.227396
$209$	−0.351101	−0.0242862
$210$	20.0000	1.38013
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−12.6718	−0.870301
$213$	7.87092	0.539307
$214$	−11.1153	−0.759827
$215$	8.40239	0.573038
$216$	11.1919	0.761515
$217$	−6.57131	−0.446090
$218$	−15.2968	−1.03603
$219$	−12.8405	−0.867683
$220$	0.609275	0.0410773
$221$	−2.46753	−0.165984
$222$	−29.3287	−1.96842
$223$	−9.23464	−0.618397	−0.309199	−	0.950997i	$-0.600061\pi$
$223$	−9.23464	−0.618397	−0.309199	+	0.950997i	$0.600061\pi$
$224$	3.71776	0.248403
$225$	−13.1454	−0.876359
$226$	4.41686	0.293805
$227$	4.48137	0.297439	0.148719	−	0.988879i	$-0.452485\pi$
$227$	4.48137	0.297439	0.148719	+	0.988879i	$0.452485\pi$
$228$	−3.10004	−0.205305
$229$	0.681758	0.0450518	0.0225259	−	0.999746i	$-0.492829\pi$
$229$	0.681758	0.0450518	0.0225259	+	0.999746i	$0.492829\pi$
$230$	−12.0187	−0.792488
$231$	4.04651	0.266241
$232$	1.99959	0.131280
$233$	−29.9511	−1.96216	−0.981080	−	0.193603i	$-0.937983\pi$
$233$	−29.9511	−1.96216	−0.981080	+	0.193603i	$0.937983\pi$
$234$	−21.6787	−1.41718
$235$	16.7715	1.09405
$236$	−2.58178	−0.168059
$237$	8.87686	0.576614
$238$	2.79724	0.181318
$239$	13.9618	0.903112	0.451556	−	0.892243i	$-0.350869\pi$
$239$	13.9618	0.903112	0.451556	+	0.892243i	$0.350869\pi$
$240$	5.37959	0.347251
$241$	12.9567	0.834614	0.417307	−	0.908766i	$-0.362974\pi$
$241$	12.9567	0.834614	0.417307	+	0.908766i	$0.362974\pi$
$242$	−10.8767	−0.699183
$243$	12.5054	0.802221
$244$	−3.16536	−0.202642
$245$	11.8379	0.756297
$246$	22.7581	1.45101
$247$	3.27955	0.208673
$248$	−1.76755	−0.112239
$249$	42.0759	2.66645
$250$	−12.1276	−0.767015
$251$	−7.56776	−0.477673	−0.238836	−	0.971060i	$-0.576766\pi$
$251$	−7.56776	−0.477673	−0.238836	+	0.971060i	$0.576766\pi$
$252$	24.5753	1.54810
$253$	−2.43168	−0.152879
$254$	−1.09609	−0.0687747
$255$	4.04760	0.253470
$256$	1.00000	0.0625000
$257$	18.6452	1.16305	0.581527	−	0.813527i	$-0.302455\pi$
$257$	18.6452	1.16305	0.581527	+	0.813527i	$0.302455\pi$
$258$	15.0103	0.934498
$259$	−35.1728	−2.18553
$260$	−5.69110	−0.352947
$261$	13.2178	0.818162
$262$	−3.34665	−0.206757
$263$	−19.1324	−1.17975	−0.589876	−	0.807494i	$-0.700823\pi$
$263$	−19.1324	−1.17975	−0.589876	+	0.807494i	$0.700823\pi$
$264$	1.08843	0.0669881
$265$	−21.9897	−1.35082
$266$	−3.71776	−0.227950
$267$	40.9057	2.50339
$268$	14.5796	0.890592
$269$	−12.4630	−0.759884	−0.379942	−	0.925010i	$-0.624056\pi$
$269$	−12.4630	−0.759884	−0.379942	+	0.925010i	$0.624056\pi$
$270$	19.4217	1.18197
$271$	4.83946	0.293976	0.146988	−	0.989138i	$-0.453042\pi$
$271$	4.83946	0.293976	0.146988	+	0.989138i	$0.453042\pi$
$272$	0.752399	0.0456209
$273$	−37.7975	−2.28761
$274$	−3.27539	−0.197873
$275$	−0.698212	−0.0421037
$276$	−21.4705	−1.29237
$277$	−10.5967	−0.636692	−0.318346	−	0.947975i	$-0.603127\pi$
$277$	−10.5967	−0.636692	−0.318346	+	0.947975i	$0.603127\pi$
$278$	11.3529	0.680904
$279$	−11.6839	−0.699499
$280$	6.45153	0.385553
$281$	−1.82039	−0.108595	−0.0542976	−	0.998525i	$-0.517292\pi$
$281$	−1.82039	−0.108595	−0.0542976	+	0.998525i	$0.517292\pi$
$282$	29.9611	1.78416
$283$	−8.61545	−0.512135	−0.256068	−	0.966659i	$-0.582427\pi$
$283$	−8.61545	−0.512135	−0.256068	+	0.966659i	$0.582427\pi$
$284$	2.53897	0.150660
$285$	−5.37959	−0.318659
$286$	−1.15145	−0.0680869
$287$	27.2929	1.61105
$288$	6.61026	0.389513
$289$	−16.4339	−0.966700
$290$	3.46995	0.203762
$291$	5.24032	0.307193
$292$	−4.14205	−0.242395
$293$	21.4225	1.25152	0.625759	−	0.780016i	$-0.284789\pi$
$293$	21.4225	1.25152	0.625759	+	0.780016i	$0.284789\pi$
$294$	21.1476	1.23335
$295$	−4.48023	−0.260849
$296$	−9.46076	−0.549895
$297$	3.92950	0.228013
$298$	6.47207	0.374917
$299$	22.7138	1.31357
$300$	−6.16485	−0.355928
$301$	18.0012	1.03757
$302$	12.6234	0.726394
$303$	10.0153	0.575364
$304$	−1.00000	−0.0573539
$305$	−5.49294	−0.314525
$306$	4.97355	0.284319
$307$	31.8435	1.81741	0.908704	−	0.417442i	$-0.137073\pi$
$307$	31.8435	1.81741	0.908704	+	0.417442i	$0.137073\pi$
$308$	1.30531	0.0743768
$309$	−29.1242	−1.65682
$310$	−3.06727	−0.174209
$311$	4.38707	0.248768	0.124384	−	0.992234i	$-0.460305\pi$
$311$	4.38707	0.248768	0.124384	+	0.992234i	$0.460305\pi$
$312$	−10.1668	−0.575579
$313$	−27.9212	−1.57820	−0.789099	−	0.614266i	$-0.789452\pi$
$313$	−27.9212	−1.57820	−0.789099	+	0.614266i	$0.789452\pi$
$314$	1.06845	0.0602961
$315$	42.6463	2.40284
$316$	2.86347	0.161083
$317$	−8.74704	−0.491283	−0.245641	−	0.969361i	$-0.578999\pi$
$317$	−8.74704	−0.491283	−0.245641	+	0.969361i	$0.578999\pi$
$318$	−39.2830	−2.20288
$319$	0.702059	0.0393077
$320$	1.73533	0.0970078
$321$	−34.4579	−1.92325
$322$	−25.7487	−1.43492
$323$	−0.752399	−0.0418646
$324$	14.8647	0.825817
$325$	6.52184	0.361767
$326$	−11.4004	−0.631411
$327$	−47.4206	−2.62237
$328$	7.34124	0.405352
$329$	35.9312	1.98095
$330$	1.88878	0.103974
$331$	−3.27865	−0.180211	−0.0901055	−	0.995932i	$-0.528720\pi$
$331$	−3.27865	−0.180211	−0.0901055	+	0.995932i	$0.528720\pi$
$332$	13.5727	0.744899
$333$	−62.5380	−3.42706
$334$	−4.82792	−0.264172
$335$	25.3004	1.38231
$336$	11.5252	0.628751
$337$	20.0280	1.09099	0.545497	−	0.838113i	$-0.316341\pi$
$337$	20.0280	1.09099	0.545497	+	0.838113i	$0.316341\pi$
$338$	−2.24452	−0.122086
$339$	13.6924	0.743671
$340$	1.30566	0.0708093
$341$	−0.620587	−0.0336067
$342$	−6.61026	−0.357442
$343$	−0.662803	−0.0357880
$344$	4.84196	0.261061
$345$	−37.2584	−2.00592
$346$	−17.2487	−0.927294
$347$	−5.20405	−0.279368	−0.139684	−	0.990196i	$-0.544609\pi$
$347$	−5.20405	−0.279368	−0.139684	+	0.990196i	$0.544609\pi$
$348$	6.19882	0.332292
$349$	−13.4254	−0.718643	−0.359321	−	0.933214i	$-0.616992\pi$
$349$	−13.4254	−0.718643	−0.359321	+	0.933214i	$0.616992\pi$
$350$	−7.39327	−0.395187
$351$	−36.7046	−1.95915
$352$	0.351101	0.0187137
$353$	9.77014	0.520012	0.260006	−	0.965607i	$-0.416275\pi$
$353$	9.77014	0.520012	0.260006	+	0.965607i	$0.416275\pi$
$354$	−8.00362	−0.425387
$355$	4.40595	0.233844
$356$	13.1952	0.699345
$357$	8.67155	0.458947
$358$	5.93539	0.313695
$359$	−27.7370	−1.46390	−0.731951	−	0.681357i	$-0.761390\pi$
$359$	−27.7370	−1.46390	−0.731951	+	0.681357i	$0.761390\pi$
$360$	11.4710	0.604573
$361$	1.00000	0.0526316
$362$	20.9918	1.10331
$363$	−33.7183	−1.76975
$364$	−12.1926	−0.639065
$365$	−7.18782	−0.376228
$366$	−9.81275	−0.512921
$367$	17.4207	0.909355	0.454677	−	0.890656i	$-0.349755\pi$
$367$	17.4207	0.909355	0.454677	+	0.890656i	$0.349755\pi$
$368$	−6.92588	−0.361036
$369$	48.5275	2.52624
$370$	−16.4175	−0.853506
$371$	−47.1106	−2.44586
$372$	−5.47947	−0.284097
$373$	−14.8013	−0.766384	−0.383192	−	0.923669i	$-0.625175\pi$
$373$	−14.8013	−0.766384	−0.383192	+	0.923669i	$0.625175\pi$
$374$	0.264168	0.0136598
$375$	−37.5960	−1.94145
$376$	9.66475	0.498422
$377$	−6.55777	−0.337742
$378$	41.6089	2.14013
$379$	−21.6776	−1.11350	−0.556752	−	0.830679i	$-0.687953\pi$
$379$	−21.6776	−1.11350	−0.556752	+	0.830679i	$0.687953\pi$
$380$	−1.73533	−0.0890205
$381$	−3.39792	−0.174081
$382$	−24.5408	−1.25562
$383$	−6.00591	−0.306888	−0.153444	−	0.988157i	$-0.549036\pi$
$383$	−6.00591	−0.306888	−0.153444	+	0.988157i	$0.549036\pi$
$384$	3.10004	0.158198
$385$	2.26514	0.115442
$386$	−11.0919	−0.564565
$387$	32.0066	1.62699
$388$	1.69040	0.0858172
$389$	−23.2504	−1.17884	−0.589422	−	0.807825i	$-0.700645\pi$
$389$	−23.2504	−1.17884	−0.589422	+	0.807825i	$0.700645\pi$
$390$	−17.6427	−0.893371
$391$	−5.21102	−0.263533
$392$	6.82172	0.344549
$393$	−10.3748	−0.523337
$394$	8.13853	0.410013
$395$	4.96905	0.250020
$396$	2.32087	0.116628
$397$	−39.1450	−1.96463	−0.982316	−	0.187229i	$-0.940049\pi$
$397$	−39.1450	−1.96463	−0.982316	+	0.187229i	$0.940049\pi$
$398$	−21.6215	−1.08379
$399$	−11.5252	−0.576982
$400$	−1.98864	−0.0994318
$401$	19.2227	0.959936	0.479968	−	0.877286i	$-0.340648\pi$
$401$	19.2227	0.959936	0.479968	+	0.877286i	$0.340648\pi$
$402$	45.1974	2.25424
$403$	5.79677	0.288758
$404$	3.23070	0.160733
$405$	25.7951	1.28177
$406$	7.43400	0.368943
$407$	−3.32168	−0.164650
$408$	2.33247	0.115474
$409$	−0.152173	−0.00752447	−0.00376224	−	0.999993i	$-0.501198\pi$
$409$	−0.152173	−0.00752447	−0.00376224	+	0.999993i	$0.501198\pi$
$410$	12.7395	0.629157
$411$	−10.1538	−0.500852
$412$	−9.39478	−0.462848
$413$	−9.59842	−0.472308
$414$	−45.7818	−2.25005
$415$	23.5531	1.15618
$416$	−3.27955	−0.160793
$417$	35.1946	1.72349
$418$	−0.351101	−0.0171729
$419$	27.1022	1.32403	0.662015	−	0.749490i	$-0.269701\pi$
$419$	27.1022	1.32403	0.662015	+	0.749490i	$0.269701\pi$
$420$	20.0000	0.975900
$421$	9.67776	0.471665	0.235833	−	0.971794i	$-0.424218\pi$
$421$	9.67776	0.471665	0.235833	+	0.971794i	$0.424218\pi$
$422$	−1.00000	−0.0486792
$423$	63.8865	3.10627
$424$	−12.6718	−0.615396
$425$	−1.49625	−0.0725787
$426$	7.87092	0.381348
$427$	−11.7680	−0.569496
$428$	−11.1153	−0.537279
$429$	−3.56956	−0.172340
$430$	8.40239	0.405199
$431$	28.4143	1.36867	0.684335	−	0.729168i	$-0.260093\pi$
$431$	28.4143	1.36867	0.684335	+	0.729168i	$0.260093\pi$
$432$	11.1919	0.538472
$433$	6.23986	0.299868	0.149934	−	0.988696i	$-0.452094\pi$
$433$	6.23986	0.299868	0.149934	+	0.988696i	$0.452094\pi$
$434$	−6.57131	−0.315433
$435$	10.7570	0.515758
$436$	−15.2968	−0.732582
$437$	6.92588	0.331310
$438$	−12.8405	−0.613544
$439$	32.5502	1.55353	0.776767	−	0.629788i	$-0.216858\pi$
$439$	32.5502	1.55353	0.776767	+	0.629788i	$0.216858\pi$
$440$	0.609275	0.0290461
$441$	45.0933	2.14730
$442$	−2.46753	−0.117369
$443$	20.3511	0.966912	0.483456	−	0.875369i	$-0.339381\pi$
$443$	20.3511	0.966912	0.483456	+	0.875369i	$0.339381\pi$
$444$	−29.3287	−1.39188
$445$	22.8980	1.08547
$446$	−9.23464	−0.437273
$447$	20.0637	0.948979
$448$	3.71776	0.175648
$449$	−16.6193	−0.784314	−0.392157	−	0.919898i	$-0.628271\pi$
$449$	−16.6193	−0.784314	−0.392157	+	0.919898i	$0.628271\pi$
$450$	−13.1454	−0.619680
$451$	2.57752	0.121370
$452$	4.41686	0.207752
$453$	39.1330	1.83863
$454$	4.48137	0.210321
$455$	−21.1581	−0.991909
$456$	−3.10004	−0.145173
$457$	−2.63080	−0.123064	−0.0615319	−	0.998105i	$-0.519599\pi$
$457$	−2.63080	−0.123064	−0.0615319	+	0.998105i	$0.519599\pi$
$458$	0.681758	0.0318564
$459$	8.42080	0.393049
$460$	−12.0187	−0.560374
$461$	21.7075	1.01102	0.505510	−	0.862821i	$-0.331305\pi$
$461$	21.7075	1.01102	0.505510	+	0.862821i	$0.331305\pi$
$462$	4.04651	0.188261
$463$	37.3602	1.73628	0.868138	−	0.496322i	$-0.165317\pi$
$463$	37.3602	1.73628	0.868138	+	0.496322i	$0.165317\pi$
$464$	1.99959	0.0928287
$465$	−9.50868	−0.440954
$466$	−29.9511	−1.38746
$467$	10.1334	0.468919	0.234460	−	0.972126i	$-0.424668\pi$
$467$	10.1334	0.468919	0.234460	+	0.972126i	$0.424668\pi$
$468$	−21.6787	−1.00210
$469$	54.2035	2.50288
$470$	16.7715	0.773612
$471$	3.31224	0.152620
$472$	−2.58178	−0.118836
$473$	1.70002	0.0781668
$474$	8.87686	0.407728
$475$	1.98864	0.0912449
$476$	2.79724	0.128211
$477$	−83.7636	−3.83527
$478$	13.9618	0.638597
$479$	−42.3174	−1.93353	−0.966765	−	0.255666i	$-0.917705\pi$
$479$	−42.3174	−1.93353	−0.966765	+	0.255666i	$0.917705\pi$
$480$	5.37959	0.245544
$481$	31.0271	1.41471
$482$	12.9567	0.590161
$483$	−79.8221	−3.63203
$484$	−10.8767	−0.494397
$485$	2.93340	0.133199
$486$	12.5054	0.567256
$487$	14.7169	0.666888	0.333444	−	0.942770i	$-0.391789\pi$
$487$	14.7169	0.666888	0.333444	+	0.942770i	$0.391789\pi$
$488$	−3.16536	−0.143289
$489$	−35.3418	−1.59821
$490$	11.8379	0.534783
$491$	−26.8044	−1.20966	−0.604832	−	0.796353i	$-0.706760\pi$
$491$	−26.8044	−1.20966	−0.604832	+	0.796353i	$0.706760\pi$
$492$	22.7581	1.02602
$493$	1.50449	0.0677589
$494$	3.27955	0.147554
$495$	4.02746	0.181021
$496$	−1.76755	−0.0793652
$497$	9.43929	0.423410
$498$	42.0759	1.88547
$499$	−16.4246	−0.735264	−0.367632	−	0.929971i	$-0.619831\pi$
$499$	−16.4246	−0.735264	−0.367632	+	0.929971i	$0.619831\pi$
$500$	−12.1276	−0.542362
$501$	−14.9668	−0.668665
$502$	−7.56776	−0.337766
$503$	27.5604	1.22886	0.614430	−	0.788971i	$-0.289386\pi$
$503$	27.5604	1.22886	0.614430	+	0.788971i	$0.289386\pi$
$504$	24.5753	1.09467
$505$	5.60632	0.249478
$506$	−2.43168	−0.108101
$507$	−6.95811	−0.309021
$508$	−1.09609	−0.0486311
$509$	3.15059	0.139647	0.0698237	−	0.997559i	$-0.477756\pi$
$509$	3.15059	0.139647	0.0698237	+	0.997559i	$0.477756\pi$
$510$	4.04760	0.179231
$511$	−15.3991	−0.681218
$512$	1.00000	0.0441942
$513$	−11.1919	−0.494136
$514$	18.6452	0.822403
$515$	−16.3030	−0.718397
$516$	15.0103	0.660790
$517$	3.39330	0.149237
$518$	−35.1728	−1.54540
$519$	−53.4716	−2.34714
$520$	−5.69110	−0.249571
$521$	−40.1741	−1.76006	−0.880029	−	0.474919i	$-0.842477\pi$
$521$	−40.1741	−1.76006	−0.880029	+	0.474919i	$0.842477\pi$
$522$	13.2178	0.578528
$523$	16.2791	0.711835	0.355917	−	0.934517i	$-0.384168\pi$
$523$	16.2791	0.711835	0.355917	+	0.934517i	$0.384168\pi$
$524$	−3.34665	−0.146199
$525$	−22.9194	−1.00029
$526$	−19.1324	−0.834210
$527$	−1.32990	−0.0579314
$528$	1.08843	0.0473677
$529$	24.9678	1.08556
$530$	−21.9897	−0.955171
$531$	−17.0662	−0.740610
$532$	−3.71776	−0.161185
$533$	−24.0760	−1.04285
$534$	40.9057	1.77016
$535$	−19.2887	−0.833924
$536$	14.5796	0.629744
$537$	18.4000	0.794017
$538$	−12.4630	−0.537319
$539$	2.39511	0.103165
$540$	19.4217	0.835776
$541$	−9.18498	−0.394893	−0.197447	−	0.980314i	$-0.563265\pi$
$541$	−9.18498	−0.394893	−0.197447	+	0.980314i	$0.563265\pi$
$542$	4.83946	0.207873
$543$	65.0756	2.79266
$544$	0.752399	0.0322588
$545$	−26.5449	−1.13706
$546$	−37.7975	−1.61758
$547$	2.87883	0.123090	0.0615450	−	0.998104i	$-0.480397\pi$
$547$	2.87883	0.123090	0.0615450	+	0.998104i	$0.480397\pi$
$548$	−3.27539	−0.139918
$549$	−20.9238	−0.893008
$550$	−0.698212	−0.0297718
$551$	−1.99959	−0.0851855
$552$	−21.4705	−0.913846
$553$	10.6457	0.452700
$554$	−10.5967	−0.450209
$555$	−50.8950	−2.16037
$556$	11.3529	0.481472
$557$	18.1580	0.769380	0.384690	−	0.923046i	$-0.374308\pi$
$557$	18.1580	0.769380	0.384690	+	0.923046i	$0.374308\pi$
$558$	−11.6839	−0.494621
$559$	−15.8795	−0.671630
$560$	6.45153	0.272627
$561$	0.818931	0.0345753
$562$	−1.82039	−0.0767884
$563$	−14.4464	−0.608843	−0.304421	−	0.952537i	$-0.598463\pi$
$563$	−14.4464	−0.608843	−0.304421	+	0.952537i	$0.598463\pi$
$564$	29.9611	1.26159
$565$	7.66470	0.322456
$566$	−8.61545	−0.362134
$567$	55.2634	2.32084
$568$	2.53897	0.106533
$569$	−43.3171	−1.81595	−0.907974	−	0.419026i	$-0.862372\pi$
$569$	−43.3171	−1.81595	−0.907974	+	0.419026i	$0.862372\pi$
$570$	−5.37959	−0.225326
$571$	25.9611	1.08644	0.543219	−	0.839591i	$-0.317205\pi$
$571$	25.9611	1.08644	0.543219	+	0.839591i	$0.317205\pi$
$572$	−1.15145	−0.0481447
$573$	−76.0775	−3.17818
$574$	27.2929	1.13919
$575$	13.7730	0.574376
$576$	6.61026	0.275427
$577$	21.4138	0.891469	0.445734	−	0.895165i	$-0.352943\pi$
$577$	21.4138	0.891469	0.445734	+	0.895165i	$0.352943\pi$
$578$	−16.4339	−0.683560
$579$	−34.3855	−1.42901
$580$	3.46995	0.144082
$581$	50.4600	2.09343
$582$	5.24032	0.217218
$583$	−4.44907	−0.184262
$584$	−4.14205	−0.171399
$585$	−37.6196	−1.55538
$586$	21.4225	0.884957
$587$	46.6066	1.92366	0.961831	−	0.273644i	$-0.0882290\pi$
$587$	46.6066	1.92366	0.961831	+	0.273644i	$0.0882290\pi$
$588$	21.1476	0.872113
$589$	1.76755	0.0728305
$590$	−4.48023	−0.184448
$591$	25.2298	1.03781
$592$	−9.46076	−0.388835
$593$	−8.47897	−0.348190	−0.174095	−	0.984729i	$-0.555700\pi$
$593$	−8.47897	−0.348190	−0.174095	+	0.984729i	$0.555700\pi$
$594$	3.92950	0.161229
$595$	4.85412	0.199000
$596$	6.47207	0.265106
$597$	−67.0276	−2.74326
$598$	22.7138	0.928836
$599$	44.8446	1.83230	0.916151	−	0.400833i	$-0.131279\pi$
$599$	44.8446	1.83230	0.916151	+	0.400833i	$0.131279\pi$
$600$	−6.16485	−0.251679
$601$	42.3239	1.72643	0.863213	−	0.504839i	$-0.168448\pi$
$601$	42.3239	1.72643	0.863213	+	0.504839i	$0.168448\pi$
$602$	18.0012	0.733675
$603$	96.3750	3.92469
$604$	12.6234	0.513638
$605$	−18.8747	−0.767365
$606$	10.0153	0.406844
$607$	17.0076	0.690317	0.345158	−	0.938544i	$-0.387825\pi$
$607$	17.0076	0.690317	0.345158	+	0.938544i	$0.387825\pi$
$608$	−1.00000	−0.0405554
$609$	23.0457	0.933859
$610$	−5.49294	−0.222403
$611$	−31.6961	−1.28229
$612$	4.97355	0.201044
$613$	0.729020	0.0294448	0.0147224	−	0.999892i	$-0.495314\pi$
$613$	0.729020	0.0294448	0.0147224	+	0.999892i	$0.495314\pi$
$614$	31.8435	1.28510
$615$	39.4929	1.59251
$616$	1.30531	0.0525923
$617$	17.8269	0.717683	0.358841	−	0.933399i	$-0.383172\pi$
$617$	17.8269	0.717683	0.358841	+	0.933399i	$0.383172\pi$
$618$	−29.1242	−1.17155
$619$	30.8609	1.24041	0.620203	−	0.784442i	$-0.287050\pi$
$619$	30.8609	1.24041	0.620203	+	0.784442i	$0.287050\pi$
$620$	−3.06727	−0.123185
$621$	−77.5140	−3.11053
$622$	4.38707	0.175905
$623$	49.0566	1.96541
$624$	−10.1668	−0.406996
$625$	−11.1021	−0.444086
$626$	−27.9212	−1.11595
$627$	−1.08843	−0.0434676
$628$	1.06845	0.0426358
$629$	−7.11826	−0.283824
$630$	42.6463	1.69907
$631$	−4.70983	−0.187495	−0.0937477	−	0.995596i	$-0.529885\pi$
$631$	−4.70983	−0.187495	−0.0937477	+	0.995596i	$0.529885\pi$
$632$	2.86347	0.113903
$633$	−3.10004	−0.123216
$634$	−8.74704	−0.347390
$635$	−1.90207	−0.0754815
$636$	−39.2830	−1.55767
$637$	−22.3722	−0.886419
$638$	0.702059	0.0277948
$639$	16.7833	0.663936
$640$	1.73533	0.0685949
$641$	−22.3062	−0.881042	−0.440521	−	0.897742i	$-0.645206\pi$
$641$	−22.3062	−0.881042	−0.440521	+	0.897742i	$0.645206\pi$
$642$	−34.4579	−1.35995
$643$	−6.80290	−0.268280	−0.134140	−	0.990962i	$-0.542827\pi$
$643$	−6.80290	−0.268280	−0.134140	+	0.990962i	$0.542827\pi$
$644$	−25.7487	−1.01464
$645$	26.0477	1.02563
$646$	−0.752399	−0.0296027
$647$	38.5285	1.51471	0.757355	−	0.653003i	$-0.226491\pi$
$647$	38.5285	1.51471	0.757355	+	0.653003i	$0.226491\pi$
$648$	14.8647	0.583941
$649$	−0.906464	−0.0355818
$650$	6.52184	0.255808
$651$	−20.3713	−0.798416
$652$	−11.4004	−0.446475
$653$	12.1794	0.476615	0.238308	−	0.971190i	$-0.423407\pi$
$653$	12.1794	0.476615	0.238308	+	0.971190i	$0.423407\pi$
$654$	−47.4206	−1.85429
$655$	−5.80754	−0.226919
$656$	7.34124	0.286627
$657$	−27.3800	−1.06820
$658$	35.9312	1.40074
$659$	−29.1482	−1.13545	−0.567727	−	0.823217i	$-0.692177\pi$
$659$	−29.1482	−1.13545	−0.567727	+	0.823217i	$0.692177\pi$
$660$	1.88878	0.0735206
$661$	45.7410	1.77912	0.889560	−	0.456818i	$-0.151011\pi$
$661$	45.7410	1.77912	0.889560	+	0.456818i	$0.151011\pi$
$662$	−3.27865	−0.127428
$663$	−7.64945	−0.297080
$664$	13.5727	0.526723
$665$	−6.45153	−0.250180
$666$	−62.5380	−2.42330
$667$	−13.8489	−0.536233
$668$	−4.82792	−0.186798
$669$	−28.6278	−1.10681
$670$	25.3004	0.977441
$671$	−1.11136	−0.0429036
$672$	11.5252	0.444594
$673$	12.8728	0.496211	0.248105	−	0.968733i	$-0.420192\pi$
$673$	12.8728	0.496211	0.248105	+	0.968733i	$0.420192\pi$
$674$	20.0280	0.771449
$675$	−22.2567	−0.856660
$676$	−2.24452	−0.0863278
$677$	1.00243	0.0385264	0.0192632	−	0.999814i	$-0.493868\pi$
$677$	1.00243	0.0385264	0.0192632	+	0.999814i	$0.493868\pi$
$678$	13.6924	0.525855
$679$	6.28451	0.241177
$680$	1.30566	0.0500697
$681$	13.8924	0.532359
$682$	−0.620587	−0.0237635
$683$	−7.55624	−0.289132	−0.144566	−	0.989495i	$-0.546179\pi$
$683$	−7.55624	−0.289132	−0.144566	+	0.989495i	$0.546179\pi$
$684$	−6.61026	−0.252749
$685$	−5.68388	−0.217170
$686$	−0.662803	−0.0253060
$687$	2.11348	0.0806342
$688$	4.84196	0.184598
$689$	41.5578	1.58322
$690$	−37.2584	−1.41840
$691$	41.3882	1.57448	0.787240	−	0.616646i	$-0.211509\pi$
$691$	41.3882	1.57448	0.787240	+	0.616646i	$0.211509\pi$
$692$	−17.2487	−0.655696
$693$	8.62842	0.327766
$694$	−5.20405	−0.197543
$695$	19.7011	0.747304
$696$	6.19882	0.234966
$697$	5.52354	0.209219
$698$	−13.4254	−0.508157
$699$	−92.8495	−3.51189
$700$	−7.39327	−0.279439
$701$	−18.1830	−0.686764	−0.343382	−	0.939196i	$-0.611573\pi$
$701$	−18.1830	−0.686764	−0.343382	+	0.939196i	$0.611573\pi$
$702$	−36.7046	−1.38532
$703$	9.46076	0.356819
$704$	0.351101	0.0132326
$705$	51.9924	1.95815
$706$	9.77014	0.367704
$707$	12.0109	0.451718
$708$	−8.00362	−0.300794
$709$	−15.6607	−0.588149	−0.294074	−	0.955783i	$-0.595011\pi$
$709$	−15.6607	−0.588149	−0.294074	+	0.955783i	$0.595011\pi$
$710$	4.40595	0.165352
$711$	18.9282	0.709865
$712$	13.1952	0.494512
$713$	12.2418	0.458460
$714$	8.67155	0.324525
$715$	−1.99815	−0.0747266
$716$	5.93539	0.221816
$717$	43.2821	1.61640
$718$	−27.7370	−1.03514
$719$	−8.86763	−0.330707	−0.165353	−	0.986234i	$-0.552876\pi$
$719$	−8.86763	−0.330707	−0.165353	+	0.986234i	$0.552876\pi$
$720$	11.4710	0.427498
$721$	−34.9275	−1.30077
$722$	1.00000	0.0372161
$723$	40.1663	1.49380
$724$	20.9918	0.780156
$725$	−3.97646	−0.147682
$726$	−33.7183	−1.25140
$727$	−41.6682	−1.54539	−0.772694	−	0.634779i	$-0.781091\pi$
$727$	−41.6682	−1.54539	−0.772694	+	0.634779i	$0.781091\pi$
$728$	−12.1926	−0.451887
$729$	−5.82691	−0.215811
$730$	−7.18782	−0.266033
$731$	3.64308	0.134744
$732$	−9.81275	−0.362690
$733$	24.8732	0.918714	0.459357	−	0.888252i	$-0.348080\pi$
$733$	24.8732	0.918714	0.459357	+	0.888252i	$0.348080\pi$
$734$	17.4207	0.643011
$735$	36.6980	1.35363
$736$	−6.92588	−0.255291
$737$	5.11892	0.188558
$738$	48.5275	1.78632
$739$	42.8333	1.57565	0.787824	−	0.615900i	$-0.211208\pi$
$739$	42.8333	1.57565	0.787824	+	0.615900i	$0.211208\pi$
$740$	−16.4175	−0.603520
$741$	10.1668	0.373485
$742$	−47.1106	−1.72948
$743$	−20.6014	−0.755791	−0.377896	−	0.925848i	$-0.623352\pi$
$743$	−20.6014	−0.755791	−0.377896	+	0.925848i	$0.623352\pi$
$744$	−5.47947	−0.200887
$745$	11.2312	0.411478
$746$	−14.8013	−0.541915
$747$	89.7190	3.28265
$748$	0.264168	0.00965893
$749$	−41.3240	−1.50995
$750$	−37.5960	−1.37281
$751$	−17.6587	−0.644374	−0.322187	−	0.946676i	$-0.604418\pi$
$751$	−17.6587	−0.644374	−0.322187	+	0.946676i	$0.604418\pi$
$752$	9.66475	0.352437
$753$	−23.4604	−0.854943
$754$	−6.55777	−0.238820
$755$	21.9057	0.797231
$756$	41.6089	1.51330
$757$	32.3760	1.17672	0.588362	−	0.808597i	$-0.299773\pi$
$757$	32.3760	1.17672	0.588362	+	0.808597i	$0.299773\pi$
$758$	−21.6776	−0.787366
$759$	−7.53831	−0.273623
$760$	−1.73533	−0.0629470
$761$	−45.1688	−1.63737	−0.818684	−	0.574245i	$-0.805296\pi$
$761$	−45.1688	−1.63737	−0.818684	+	0.574245i	$0.805296\pi$
$762$	−3.39792	−0.123094
$763$	−56.8697	−2.05882
$764$	−24.5408	−0.887855
$765$	8.63074	0.312045
$766$	−6.00591	−0.217002
$767$	8.46708	0.305729
$768$	3.10004	0.111863
$769$	12.7741	0.460647	0.230323	−	0.973114i	$-0.426022\pi$
$769$	12.7741	0.460647	0.230323	+	0.973114i	$0.426022\pi$
$770$	2.26514	0.0816299
$771$	57.8008	2.08165
$772$	−11.0919	−0.399208
$773$	21.9571	0.789742	0.394871	−	0.918737i	$-0.370789\pi$
$773$	21.9571	0.789742	0.394871	+	0.918737i	$0.370789\pi$
$774$	32.0066	1.15045
$775$	3.51501	0.126263
$776$	1.69040	0.0606819
$777$	−109.037	−3.91168
$778$	−23.2504	−0.833569
$779$	−7.34124	−0.263027
$780$	−17.6427	−0.631708
$781$	0.891436	0.0318981
$782$	−5.21102	−0.186346
$783$	22.3793	0.799772
$784$	6.82172	0.243633
$785$	1.85411	0.0661760
$786$	−10.3748	−0.370055
$787$	−3.37254	−0.120218	−0.0601090	−	0.998192i	$-0.519145\pi$
$787$	−3.37254	−0.120218	−0.0601090	+	0.998192i	$0.519145\pi$
$788$	8.13853	0.289923
$789$	−59.3111	−2.11153
$790$	4.96905	0.176791
$791$	16.4208	0.583857
$792$	2.32087	0.0824684
$793$	10.3810	0.368639
$794$	−39.1450	−1.38920
$795$	−68.1689	−2.41770
$796$	−21.6215	−0.766354
$797$	30.8540	1.09291	0.546453	−	0.837490i	$-0.315978\pi$
$797$	30.8540	1.09291	0.546453	+	0.837490i	$0.315978\pi$
$798$	−11.5252	−0.407988
$799$	7.27175	0.257256
$800$	−1.98864	−0.0703089
$801$	87.2238	3.08190
$802$	19.2227	0.678777
$803$	−1.45428	−0.0513204
$804$	45.1974	1.59399
$805$	−44.6825	−1.57485
$806$	5.79677	0.204182
$807$	−38.6359	−1.36005
$808$	3.23070	0.113656
$809$	−38.9691	−1.37008	−0.685040	−	0.728506i	$-0.740215\pi$
$809$	−38.9691	−1.37008	−0.685040	+	0.728506i	$0.740215\pi$
$810$	25.7951	0.906349
$811$	−16.6761	−0.585577	−0.292789	−	0.956177i	$-0.594583\pi$
$811$	−16.6761	−0.585577	−0.292789	+	0.956177i	$0.594583\pi$
$812$	7.43400	0.260882
$813$	15.0025	0.526162
$814$	−3.32168	−0.116425
$815$	−19.7835	−0.692985
$816$	2.33247	0.0816527
$817$	−4.84196	−0.169399
$818$	−0.152173	−0.00532061
$819$	−80.5961	−2.81626
$820$	12.7395	0.444881
$821$	−7.26920	−0.253697	−0.126848	−	0.991922i	$-0.540486\pi$
$821$	−7.26920	−0.253697	−0.126848	+	0.991922i	$0.540486\pi$
$822$	−10.1538	−0.354156
$823$	10.8910	0.379636	0.189818	−	0.981819i	$-0.439210\pi$
$823$	10.8910	0.379636	0.189818	+	0.981819i	$0.439210\pi$
$824$	−9.39478	−0.327283
$825$	−2.16449	−0.0753577
$826$	−9.59842	−0.333972
$827$	49.5583	1.72331	0.861655	−	0.507495i	$-0.169428\pi$
$827$	49.5583	1.72331	0.861655	+	0.507495i	$0.169428\pi$
$828$	−45.7818	−1.59103
$829$	15.5170	0.538928	0.269464	−	0.963010i	$-0.413153\pi$
$829$	15.5170	0.538928	0.269464	+	0.963010i	$0.413153\pi$
$830$	23.5531	0.817540
$831$	−32.8501	−1.13956
$832$	−3.27955	−0.113698
$833$	5.13265	0.177836
$834$	35.1946	1.21869
$835$	−8.37803	−0.289934
$836$	−0.351101	−0.0121431
$837$	−19.7823	−0.683776
$838$	27.1022	0.936231
$839$	33.5435	1.15805	0.579024	−	0.815310i	$-0.303434\pi$
$839$	33.5435	1.15805	0.579024	+	0.815310i	$0.303434\pi$
$840$	20.0000	0.690066
$841$	−25.0016	−0.862125
$842$	9.67776	0.333518
$843$	−5.64328	−0.194365
$844$	−1.00000	−0.0344214
$845$	−3.89498	−0.133991
$846$	63.8865	2.19646
$847$	−40.4370	−1.38943
$848$	−12.6718	−0.435150
$849$	−26.7083	−0.916625
$850$	−1.49625	−0.0513209
$851$	65.5240	2.24614
$852$	7.87092	0.269653
$853$	−20.3615	−0.697164	−0.348582	−	0.937278i	$-0.613337\pi$
$853$	−20.3615	−0.697164	−0.348582	+	0.937278i	$0.613337\pi$
$854$	−11.7680	−0.402694
$855$	−11.4710	−0.392299
$856$	−11.1153	−0.379913
$857$	−12.7900	−0.436898	−0.218449	−	0.975848i	$-0.570100\pi$
$857$	−12.7900	−0.436898	−0.218449	+	0.975848i	$0.570100\pi$
$858$	−3.56956	−0.121863
$859$	−20.7426	−0.707729	−0.353865	−	0.935297i	$-0.615133\pi$
$859$	−20.7426	−0.707729	−0.353865	+	0.935297i	$0.615133\pi$
$860$	8.40239	0.286519
$861$	84.6093	2.88348
$862$	28.4143	0.967796
$863$	17.8871	0.608882	0.304441	−	0.952531i	$-0.401530\pi$
$863$	17.8871	0.608882	0.304441	+	0.952531i	$0.401530\pi$
$864$	11.1919	0.380758
$865$	−29.9321	−1.01772
$866$	6.23986	0.212039
$867$	−50.9458	−1.73021
$868$	−6.57131	−0.223045
$869$	1.00537	0.0341047
$870$	10.7570	0.364696
$871$	−47.8147	−1.62014
$872$	−15.2968	−0.518014
$873$	11.1740	0.378182
$874$	6.92588	0.234271
$875$	−45.0874	−1.52423
$876$	−12.8405	−0.433841
$877$	46.9121	1.58411	0.792054	−	0.610451i	$-0.209012\pi$
$877$	46.9121	1.58411	0.792054	+	0.610451i	$0.209012\pi$
$878$	32.5502	1.09851
$879$	66.4108	2.23998
$880$	0.609275	0.0205387
$881$	−22.2504	−0.749636	−0.374818	−	0.927098i	$-0.622295\pi$
$881$	−22.2504	−0.749636	−0.374818	+	0.927098i	$0.622295\pi$
$882$	45.0933	1.51837
$883$	−3.22230	−0.108439	−0.0542196	−	0.998529i	$-0.517267\pi$
$883$	−3.22230	−0.108439	−0.0542196	+	0.998529i	$0.517267\pi$
$884$	−2.46753	−0.0829921
$885$	−13.8889	−0.466870
$886$	20.3511	0.683710
$887$	−57.0542	−1.91569	−0.957846	−	0.287281i	$-0.907249\pi$
$887$	−57.0542	−1.91569	−0.957846	+	0.287281i	$0.907249\pi$
$888$	−29.3287	−0.984208
$889$	−4.07499	−0.136671
$890$	22.8980	0.767544
$891$	5.21901	0.174843
$892$	−9.23464	−0.309199
$893$	−9.66475	−0.323419
$894$	20.0637	0.671030
$895$	10.2999	0.344286
$896$	3.71776	0.124202
$897$	70.4137	2.35105
$898$	−16.6193	−0.554594
$899$	−3.53437	−0.117878
$900$	−13.1454	−0.438180
$901$	−9.53423	−0.317631
$902$	2.57752	0.0858219
$903$	55.8045	1.85706
$904$	4.41686	0.146903
$905$	36.4277	1.21090
$906$	39.1330	1.30011
$907$	−30.3769	−1.00865	−0.504324	−	0.863515i	$-0.668258\pi$
$907$	−30.3769	−1.00865	−0.504324	+	0.863515i	$0.668258\pi$
$908$	4.48137	0.148719
$909$	21.3557	0.708325
$910$	−21.1581	−0.701386
$911$	−21.2285	−0.703331	−0.351665	−	0.936126i	$-0.614385\pi$
$911$	−21.2285	−0.703331	−0.351665	+	0.936126i	$0.614385\pi$
$912$	−3.10004	−0.102653
$913$	4.76539	0.157711
$914$	−2.63080	−0.0870192
$915$	−17.0283	−0.562940
$916$	0.681758	0.0225259
$917$	−12.4420	−0.410872
$918$	8.42080	0.277928
$919$	−48.6280	−1.60409	−0.802044	−	0.597265i	$-0.796254\pi$
$919$	−48.6280	−1.60409	−0.802044	+	0.597265i	$0.796254\pi$
$920$	−12.0187	−0.396244
$921$	98.7163	3.25281
$922$	21.7075	0.714899
$923$	−8.32670	−0.274077
$924$	4.04651	0.133120
$925$	18.8140	0.618600
$926$	37.3602	1.22773
$927$	−62.1019	−2.03969
$928$	1.99959	0.0656398
$929$	−8.09057	−0.265443	−0.132721	−	0.991153i	$-0.542372\pi$
$929$	−8.09057	−0.265443	−0.132721	+	0.991153i	$0.542372\pi$
$930$	−9.50868	−0.311802
$931$	−6.82172	−0.223573
$932$	−29.9511	−0.981080
$933$	13.6001	0.445247
$934$	10.1334	0.331576
$935$	0.458418	0.0149919
$936$	−21.6787	−0.708590
$937$	−9.57968	−0.312955	−0.156477	−	0.987682i	$-0.550014\pi$
$937$	−9.57968	−0.312955	−0.156477	+	0.987682i	$0.550014\pi$
$938$	54.2035	1.76981
$939$	−86.5567	−2.82467
$940$	16.7715	0.547027
$941$	46.1734	1.50521	0.752604	−	0.658473i	$-0.228797\pi$
$941$	46.1734	1.50521	0.752604	+	0.658473i	$0.228797\pi$
$942$	3.31224	0.107918
$943$	−50.8445	−1.65573
$944$	−2.58178	−0.0840297
$945$	72.2051	2.34883
$946$	1.70002	0.0552723
$947$	−47.1625	−1.53258	−0.766288	−	0.642498i	$-0.777898\pi$
$947$	−47.1625	−1.53258	−0.766288	+	0.642498i	$0.777898\pi$
$948$	8.87686	0.288307
$949$	13.5841	0.440958
$950$	1.98864	0.0645199
$951$	−27.1162	−0.879303
$952$	2.79724	0.0906590
$953$	12.9228	0.418610	0.209305	−	0.977850i	$-0.432880\pi$
$953$	12.9228	0.418610	0.209305	+	0.977850i	$0.432880\pi$
$954$	−83.7636	−2.71195
$955$	−42.5864	−1.37806
$956$	13.9618	0.451556
$957$	2.17641	0.0703534
$958$	−42.3174	−1.36721
$959$	−12.1771	−0.393219
$960$	5.37959	0.173625
$961$	−27.8758	−0.899219
$962$	31.0271	1.00035
$963$	−73.4750	−2.36770
$964$	12.9567	0.417307
$965$	−19.2482	−0.619620
$966$	−79.8221	−2.56824
$967$	−32.3219	−1.03940	−0.519701	−	0.854348i	$-0.673957\pi$
$967$	−32.3219	−1.03940	−0.519701	+	0.854348i	$0.673957\pi$
$968$	−10.8767	−0.349591
$969$	−2.33247	−0.0749297
$970$	2.93340	0.0941859
$971$	−25.3033	−0.812021	−0.406011	−	0.913868i	$-0.633080\pi$
$971$	−25.3033	−0.812021	−0.406011	+	0.913868i	$0.633080\pi$
$972$	12.5054	0.401111
$973$	42.2075	1.35311
$974$	14.7169	0.471561
$975$	20.2180	0.647493
$976$	−3.16536	−0.101321
$977$	−25.6983	−0.822162	−0.411081	−	0.911599i	$-0.634849\pi$
$977$	−25.6983	−0.822162	−0.411081	+	0.911599i	$0.634849\pi$
$978$	−35.3418	−1.13010
$979$	4.63285	0.148067
$980$	11.8379	0.378149
$981$	−101.116	−3.22837
$982$	−26.8044	−0.855362
$983$	17.5857	0.560898	0.280449	−	0.959869i	$-0.409517\pi$
$983$	17.5857	0.560898	0.280449	+	0.959869i	$0.409517\pi$
$984$	22.7581	0.725503
$985$	14.1230	0.449997
$986$	1.50449	0.0479128
$987$	111.388	3.54553
$988$	3.27955	0.104337
$989$	−33.5348	−1.06634
$990$	4.02746	0.128001
$991$	30.2210	0.960001	0.480001	−	0.877268i	$-0.340636\pi$
$991$	30.2210	0.960001	0.480001	+	0.877268i	$0.340636\pi$
$992$	−1.76755	−0.0561197
$993$	−10.1640	−0.322543
$994$	9.43929	0.299396
$995$	−37.5204	−1.18948
$996$	42.0759	1.33323
$997$	−11.0113	−0.348732	−0.174366	−	0.984681i	$-0.555788\pi$
$997$	−11.0113	−0.348732	−0.174366	+	0.984681i	$0.555788\pi$
$998$	−16.4246	−0.519910
$999$	−105.884	−3.35003

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.43	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.43	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +3.10004 q^{3} +1.00000 q^{4} +1.73533 q^{5} +3.10004 q^{6} +3.71776 q^{7} +1.00000 q^{8} +6.61026 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +3.10004 q^{3} +1.00000 q^{4} +1.73533 q^{5} +3.10004 q^{6} +3.71776 q^{7} +1.00000 q^{8} +6.61026 q^{9} +1.73533 q^{10} +0.351101 q^{11} +3.10004 q^{12} -3.27955 q^{13} +3.71776 q^{14} +5.37959 q^{15} +1.00000 q^{16} +0.752399 q^{17} +6.61026 q^{18} -1.00000 q^{19} +1.73533 q^{20} +11.5252 q^{21} +0.351101 q^{22} -6.92588 q^{23} +3.10004 q^{24} -1.98864 q^{25} -3.27955 q^{26} +11.1919 q^{27} +3.71776 q^{28} +1.99959 q^{29} +5.37959 q^{30} -1.76755 q^{31} +1.00000 q^{32} +1.08843 q^{33} +0.752399 q^{34} +6.45153 q^{35} +6.61026 q^{36} -9.46076 q^{37} -1.00000 q^{38} -10.1668 q^{39} +1.73533 q^{40} +7.34124 q^{41} +11.5252 q^{42} +4.84196 q^{43} +0.351101 q^{44} +11.4710 q^{45} -6.92588 q^{46} +9.66475 q^{47} +3.10004 q^{48} +6.82172 q^{49} -1.98864 q^{50} +2.33247 q^{51} -3.27955 q^{52} -12.6718 q^{53} +11.1919 q^{54} +0.609275 q^{55} +3.71776 q^{56} -3.10004 q^{57} +1.99959 q^{58} -2.58178 q^{59} +5.37959 q^{60} -3.16536 q^{61} -1.76755 q^{62} +24.5753 q^{63} +1.00000 q^{64} -5.69110 q^{65} +1.08843 q^{66} +14.5796 q^{67} +0.752399 q^{68} -21.4705 q^{69} +6.45153 q^{70} +2.53897 q^{71} +6.61026 q^{72} -4.14205 q^{73} -9.46076 q^{74} -6.16485 q^{75} -1.00000 q^{76} +1.30531 q^{77} -10.1668 q^{78} +2.86347 q^{79} +1.73533 q^{80} +14.8647 q^{81} +7.34124 q^{82} +13.5727 q^{83} +11.5252 q^{84} +1.30566 q^{85} +4.84196 q^{86} +6.19882 q^{87} +0.351101 q^{88} +13.1952 q^{89} +11.4710 q^{90} -12.1926 q^{91} -6.92588 q^{92} -5.47947 q^{93} +9.66475 q^{94} -1.73533 q^{95} +3.10004 q^{96} +1.69040 q^{97} +6.82172 q^{98} +2.32087 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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