LMFDB - Embedded newform 8018.2.a.j.1.4

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			1.4
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.90959 q^{3} +1.00000 q^{4} -4.15278 q^{5} -2.90959 q^{6} +3.02073 q^{7} +1.00000 q^{8} +5.46571 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.90959 q^{3} +1.00000 q^{4} -4.15278 q^{5} -2.90959 q^{6} +3.02073 q^{7} +1.00000 q^{8} +5.46571 q^{9} -4.15278 q^{10} +1.94973 q^{11} -2.90959 q^{12} +7.15763 q^{13} +3.02073 q^{14} +12.0829 q^{15} +1.00000 q^{16} +1.01914 q^{17} +5.46571 q^{18} -1.00000 q^{19} -4.15278 q^{20} -8.78908 q^{21} +1.94973 q^{22} +3.81312 q^{23} -2.90959 q^{24} +12.2456 q^{25} +7.15763 q^{26} -7.17419 q^{27} +3.02073 q^{28} +10.1658 q^{29} +12.0829 q^{30} +4.20950 q^{31} +1.00000 q^{32} -5.67292 q^{33} +1.01914 q^{34} -12.5444 q^{35} +5.46571 q^{36} +9.42107 q^{37} -1.00000 q^{38} -20.8257 q^{39} -4.15278 q^{40} +0.697666 q^{41} -8.78908 q^{42} +7.53762 q^{43} +1.94973 q^{44} -22.6979 q^{45} +3.81312 q^{46} -5.51721 q^{47} -2.90959 q^{48} +2.12481 q^{49} +12.2456 q^{50} -2.96528 q^{51} +7.15763 q^{52} -3.63798 q^{53} -7.17419 q^{54} -8.09681 q^{55} +3.02073 q^{56} +2.90959 q^{57} +10.1658 q^{58} +7.99315 q^{59} +12.0829 q^{60} -1.55823 q^{61} +4.20950 q^{62} +16.5104 q^{63} +1.00000 q^{64} -29.7241 q^{65} -5.67292 q^{66} +1.68379 q^{67} +1.01914 q^{68} -11.0946 q^{69} -12.5444 q^{70} -11.8559 q^{71} +5.46571 q^{72} +3.13570 q^{73} +9.42107 q^{74} -35.6296 q^{75} -1.00000 q^{76} +5.88961 q^{77} -20.8257 q^{78} -1.68328 q^{79} -4.15278 q^{80} +4.47682 q^{81} +0.697666 q^{82} -5.75209 q^{83} -8.78908 q^{84} -4.23226 q^{85} +7.53762 q^{86} -29.5784 q^{87} +1.94973 q^{88} -8.16873 q^{89} -22.6979 q^{90} +21.6213 q^{91} +3.81312 q^{92} -12.2479 q^{93} -5.51721 q^{94} +4.15278 q^{95} -2.90959 q^{96} +11.4176 q^{97} +2.12481 q^{98} +10.6567 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.90959	−1.67985	−0.839926	−	0.542701i	$-0.817402\pi$
$3$	−2.90959	−1.67985	−0.839926	+	0.542701i	$0.817402\pi$
$4$	1.00000	0.500000
$5$	−4.15278	−1.85718	−0.928590	−	0.371107i	$-0.878978\pi$
$5$	−4.15278	−1.85718	−0.928590	+	0.371107i	$0.878978\pi$
$6$	−2.90959	−1.18783
$7$	3.02073	1.14173	0.570864	−	0.821044i	$-0.306608\pi$
$7$	3.02073	1.14173	0.570864	+	0.821044i	$0.306608\pi$
$8$	1.00000	0.353553
$9$	5.46571	1.82190
$10$	−4.15278	−1.31322
$11$	1.94973	0.587866	0.293933	−	0.955826i	$-0.405036\pi$
$11$	1.94973	0.587866	0.293933	+	0.955826i	$0.405036\pi$
$12$	−2.90959	−0.839926
$13$	7.15763	1.98517	0.992584	−	0.121560i	$-0.0387895\pi$
$13$	7.15763	1.98517	0.992584	+	0.121560i	$0.0387895\pi$
$14$	3.02073	0.807324
$15$	12.0829	3.11979
$16$	1.00000	0.250000
$17$	1.01914	0.247178	0.123589	−	0.992334i	$-0.460560\pi$
$17$	1.01914	0.247178	0.123589	+	0.992334i	$0.460560\pi$
$18$	5.46571	1.28828
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−4.15278	−0.928590
$21$	−8.78908	−1.91793
$22$	1.94973	0.415684
$23$	3.81312	0.795091	0.397545	−	0.917583i	$-0.369862\pi$
$23$	3.81312	0.795091	0.397545	+	0.917583i	$0.369862\pi$
$24$	−2.90959	−0.593917
$25$	12.2456	2.44912
$26$	7.15763	1.40373
$27$	−7.17419	−1.38067
$28$	3.02073	0.570864
$29$	10.1658	1.88775	0.943875	−	0.330302i	$-0.107151\pi$
$29$	10.1658	1.88775	0.943875	+	0.330302i	$0.107151\pi$
$30$	12.0829	2.20602
$31$	4.20950	0.756049	0.378024	−	0.925796i	$-0.376604\pi$
$31$	4.20950	0.756049	0.378024	+	0.925796i	$0.376604\pi$
$32$	1.00000	0.176777
$33$	−5.67292	−0.987528
$34$	1.01914	0.174781
$35$	−12.5444	−2.12040
$36$	5.46571	0.910951
$37$	9.42107	1.54881	0.774407	−	0.632688i	$-0.218048\pi$
$37$	9.42107	1.54881	0.774407	+	0.632688i	$0.218048\pi$
$38$	−1.00000	−0.162221
$39$	−20.8257	−3.33479
$40$	−4.15278	−0.656612
$41$	0.697666	0.108957	0.0544786	−	0.998515i	$-0.482650\pi$
$41$	0.697666	0.108957	0.0544786	+	0.998515i	$0.482650\pi$
$42$	−8.78908	−1.35618
$43$	7.53762	1.14948	0.574738	−	0.818338i	$-0.305104\pi$
$43$	7.53762	1.14948	0.574738	+	0.818338i	$0.305104\pi$
$44$	1.94973	0.293933
$45$	−22.6979	−3.38360
$46$	3.81312	0.562214
$47$	−5.51721	−0.804768	−0.402384	−	0.915471i	$-0.631818\pi$
$47$	−5.51721	−0.804768	−0.402384	+	0.915471i	$0.631818\pi$
$48$	−2.90959	−0.419963
$49$	2.12481	0.303544
$50$	12.2456	1.73179
$51$	−2.96528	−0.415222
$52$	7.15763	0.992584
$53$	−3.63798	−0.499715	−0.249857	−	0.968283i	$-0.580384\pi$
$53$	−3.63798	−0.499715	−0.249857	+	0.968283i	$0.580384\pi$
$54$	−7.17419	−0.976283
$55$	−8.09681	−1.09177
$56$	3.02073	0.403662
$57$	2.90959	0.385384
$58$	10.1658	1.33484
$59$	7.99315	1.04062	0.520309	−	0.853978i	$-0.325817\pi$
$59$	7.99315	1.04062	0.520309	+	0.853978i	$0.325817\pi$
$60$	12.0829	1.55989
$61$	−1.55823	−0.199511	−0.0997557	−	0.995012i	$-0.531806\pi$
$61$	−1.55823	−0.199511	−0.0997557	+	0.995012i	$0.531806\pi$
$62$	4.20950	0.534607
$63$	16.5104	2.08012
$64$	1.00000	0.125000
$65$	−29.7241	−3.68682
$66$	−5.67292	−0.698288
$67$	1.68379	0.205708	0.102854	−	0.994696i	$-0.467203\pi$
$67$	1.68379	0.205708	0.102854	+	0.994696i	$0.467203\pi$
$68$	1.01914	0.123589
$69$	−11.0946	−1.33563
$70$	−12.5444	−1.49935
$71$	−11.8559	−1.40704	−0.703518	−	0.710678i	$-0.748388\pi$
$71$	−11.8559	−1.40704	−0.703518	+	0.710678i	$0.748388\pi$
$72$	5.46571	0.644140
$73$	3.13570	0.367006	0.183503	−	0.983019i	$-0.441256\pi$
$73$	3.13570	0.367006	0.183503	+	0.983019i	$0.441256\pi$
$74$	9.42107	1.09518
$75$	−35.6296	−4.11415
$76$	−1.00000	−0.114708
$77$	5.88961	0.671183
$78$	−20.8257	−2.35805
$79$	−1.68328	−0.189384	−0.0946918	−	0.995507i	$-0.530187\pi$
$79$	−1.68328	−0.189384	−0.0946918	+	0.995507i	$0.530187\pi$
$80$	−4.15278	−0.464295
$81$	4.47682	0.497424
$82$	0.697666	0.0770443
$83$	−5.75209	−0.631374	−0.315687	−	0.948863i	$-0.602235\pi$
$83$	−5.75209	−0.631374	−0.315687	+	0.948863i	$0.602235\pi$
$84$	−8.78908	−0.958967
$85$	−4.23226	−0.459053
$86$	7.53762	0.812802
$87$	−29.5784	−3.17114
$88$	1.94973	0.207842
$89$	−8.16873	−0.865884	−0.432942	−	0.901422i	$-0.642524\pi$
$89$	−8.16873	−0.865884	−0.432942	+	0.901422i	$0.642524\pi$
$90$	−22.6979	−2.39257
$91$	21.6213	2.26652
$92$	3.81312	0.397545
$93$	−12.2479	−1.27005
$94$	−5.51721	−0.569057
$95$	4.15278	0.426066
$96$	−2.90959	−0.296959
$97$	11.4176	1.15928	0.579642	−	0.814871i	$-0.303193\pi$
$97$	11.4176	1.15928	0.579642	+	0.814871i	$0.303193\pi$
$98$	2.12481	0.214638
$99$	10.6567	1.07103
$100$	12.2456	1.22456
$101$	17.1859	1.71006	0.855031	−	0.518577i	$-0.173538\pi$
$101$	17.1859	1.71006	0.855031	+	0.518577i	$0.173538\pi$
$102$	−2.96528	−0.293606
$103$	−0.905175	−0.0891896	−0.0445948	−	0.999005i	$-0.514200\pi$
$103$	−0.905175	−0.0891896	−0.0445948	+	0.999005i	$0.514200\pi$
$104$	7.15763	0.701863
$105$	36.4991	3.56195
$106$	−3.63798	−0.353352
$107$	−6.25612	−0.604802	−0.302401	−	0.953181i	$-0.597788\pi$
$107$	−6.25612	−0.604802	−0.302401	+	0.953181i	$0.597788\pi$
$108$	−7.17419	−0.690337
$109$	6.87919	0.658907	0.329453	−	0.944172i	$-0.393136\pi$
$109$	6.87919	0.658907	0.329453	+	0.944172i	$0.393136\pi$
$110$	−8.09681	−0.772000
$111$	−27.4114	−2.60178
$112$	3.02073	0.285432
$113$	−15.0441	−1.41523	−0.707616	−	0.706598i	$-0.750229\pi$
$113$	−15.0441	−1.41523	−0.707616	+	0.706598i	$0.750229\pi$
$114$	2.90959	0.272508
$115$	−15.8351	−1.47663
$116$	10.1658	0.943875
$117$	39.1215	3.61678
$118$	7.99315	0.735829
$119$	3.07854	0.282210
$120$	12.0829	1.10301
$121$	−7.19855	−0.654413
$122$	−1.55823	−0.141076
$123$	−2.02992	−0.183032
$124$	4.20950	0.378024
$125$	−30.0893	−2.69127
$126$	16.5104	1.47086
$127$	−15.5694	−1.38156	−0.690779	−	0.723066i	$-0.742732\pi$
$127$	−15.5694	−1.38156	−0.690779	+	0.723066i	$0.742732\pi$
$128$	1.00000	0.0883883
$129$	−21.9314	−1.93095
$130$	−29.7241	−2.60697
$131$	−15.0676	−1.31646	−0.658229	−	0.752818i	$-0.728694\pi$
$131$	−15.0676	−1.31646	−0.658229	+	0.752818i	$0.728694\pi$
$132$	−5.67292	−0.493764
$133$	−3.02073	−0.261930
$134$	1.68379	0.145457
$135$	29.7928	2.56416
$136$	1.01914	0.0873905
$137$	3.33949	0.285312	0.142656	−	0.989772i	$-0.454436\pi$
$137$	3.33949	0.285312	0.142656	+	0.989772i	$0.454436\pi$
$138$	−11.0946	−0.944436
$139$	19.3076	1.63765	0.818826	−	0.574042i	$-0.194625\pi$
$139$	19.3076	1.63765	0.818826	+	0.574042i	$0.194625\pi$
$140$	−12.5444	−1.06020
$141$	16.0528	1.35189
$142$	−11.8559	−0.994924
$143$	13.9554	1.16701
$144$	5.46571	0.455475
$145$	−42.2165	−3.50589
$146$	3.13570	0.259513
$147$	−6.18231	−0.509909
$148$	9.42107	0.774407
$149$	5.10176	0.417953	0.208976	−	0.977921i	$-0.432987\pi$
$149$	5.10176	0.417953	0.208976	+	0.977921i	$0.432987\pi$
$150$	−35.6296	−2.90915
$151$	12.0241	0.978505	0.489252	−	0.872142i	$-0.337270\pi$
$151$	12.0241	0.978505	0.489252	+	0.872142i	$0.337270\pi$
$152$	−1.00000	−0.0811107
$153$	5.57031	0.450333
$154$	5.88961	0.474598
$155$	−17.4811	−1.40412
$156$	−20.8257	−1.66739
$157$	−2.70273	−0.215701	−0.107851	−	0.994167i	$-0.534397\pi$
$157$	−2.70273	−0.215701	−0.107851	+	0.994167i	$0.534397\pi$
$158$	−1.68328	−0.133914
$159$	10.5850	0.839447
$160$	−4.15278	−0.328306
$161$	11.5184	0.907778
$162$	4.47682	0.351732
$163$	13.4310	1.05200	0.525999	−	0.850485i	$-0.323692\pi$
$163$	13.4310	1.05200	0.525999	+	0.850485i	$0.323692\pi$
$164$	0.697666	0.0544786
$165$	23.5584	1.83402
$166$	−5.75209	−0.446449
$167$	−9.30505	−0.720046	−0.360023	−	0.932943i	$-0.617231\pi$
$167$	−9.30505	−0.720046	−0.360023	+	0.932943i	$0.617231\pi$
$168$	−8.78908	−0.678092
$169$	38.2316	2.94089
$170$	−4.23226	−0.324600
$171$	−5.46571	−0.417973
$172$	7.53762	0.574738
$173$	−5.62614	−0.427747	−0.213874	−	0.976861i	$-0.568608\pi$
$173$	−5.62614	−0.427747	−0.213874	+	0.976861i	$0.568608\pi$
$174$	−29.5784	−2.24234
$175$	36.9906	2.79623
$176$	1.94973	0.146967
$177$	−23.2568	−1.74809
$178$	−8.16873	−0.612272
$179$	6.67942	0.499243	0.249622	−	0.968343i	$-0.419694\pi$
$179$	6.67942	0.499243	0.249622	+	0.968343i	$0.419694\pi$
$180$	−22.6979	−1.69180
$181$	−16.2828	−1.21029	−0.605145	−	0.796116i	$-0.706885\pi$
$181$	−16.2828	−1.21029	−0.605145	+	0.796116i	$0.706885\pi$
$182$	21.6213	1.60267
$183$	4.53382	0.335149
$184$	3.81312	0.281107
$185$	−39.1236	−2.87643
$186$	−12.2479	−0.898061
$187$	1.98705	0.145307
$188$	−5.51721	−0.402384
$189$	−21.6713	−1.57635
$190$	4.15278	0.301274
$191$	16.0005	1.15775	0.578877	−	0.815415i	$-0.303491\pi$
$191$	16.0005	1.15775	0.578877	+	0.815415i	$0.303491\pi$
$192$	−2.90959	−0.209981
$193$	−12.4466	−0.895926	−0.447963	−	0.894052i	$-0.647850\pi$
$193$	−12.4466	−0.895926	−0.447963	+	0.894052i	$0.647850\pi$
$194$	11.4176	0.819737
$195$	86.4848	6.19330
$196$	2.12481	0.151772
$197$	14.3766	1.02429	0.512144	−	0.858899i	$-0.328851\pi$
$197$	14.3766	1.02429	0.512144	+	0.858899i	$0.328851\pi$
$198$	10.6567	0.757336
$199$	19.1040	1.35425	0.677125	−	0.735868i	$-0.263226\pi$
$199$	19.1040	1.35425	0.677125	+	0.735868i	$0.263226\pi$
$200$	12.2456	0.865894
$201$	−4.89914	−0.345558
$202$	17.1859	1.20920
$203$	30.7083	2.15530
$204$	−2.96528	−0.207611
$205$	−2.89725	−0.202353
$206$	−0.905175	−0.0630665
$207$	20.8414	1.44858
$208$	7.15763	0.496292
$209$	−1.94973	−0.134866
$210$	36.4991	2.51868
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−3.63798	−0.249857
$213$	34.4958	2.36361
$214$	−6.25612	−0.427660
$215$	−31.3021	−2.13478
$216$	−7.17419	−0.488142
$217$	12.7158	0.863203
$218$	6.87919	0.465917
$219$	−9.12361	−0.616516
$220$	−8.09681	−0.545887
$221$	7.29462	0.490689
$222$	−27.4114	−1.83974
$223$	−17.1649	−1.14945	−0.574724	−	0.818347i	$-0.694891\pi$
$223$	−17.1649	−1.14945	−0.574724	+	0.818347i	$0.694891\pi$
$224$	3.02073	0.201831
$225$	66.9308	4.46205
$226$	−15.0441	−1.00072
$227$	−14.3527	−0.952622	−0.476311	−	0.879277i	$-0.658026\pi$
$227$	−14.3527	−0.952622	−0.476311	+	0.879277i	$0.658026\pi$
$228$	2.90959	0.192692
$229$	6.65984	0.440095	0.220047	−	0.975489i	$-0.429379\pi$
$229$	6.65984	0.440095	0.220047	+	0.975489i	$0.429379\pi$
$230$	−15.8351	−1.04413
$231$	−17.1363	−1.12749
$232$	10.1658	0.667421
$233$	9.07581	0.594576	0.297288	−	0.954788i	$-0.403918\pi$
$233$	9.07581	0.594576	0.297288	+	0.954788i	$0.403918\pi$
$234$	39.1215	2.55745
$235$	22.9118	1.49460
$236$	7.99315	0.520309
$237$	4.89764	0.318136
$238$	3.07854	0.199552
$239$	−14.6906	−0.950257	−0.475128	−	0.879916i	$-0.657598\pi$
$239$	−14.6906	−0.950257	−0.475128	+	0.879916i	$0.657598\pi$
$240$	12.0829	0.779947
$241$	−23.1588	−1.49179	−0.745894	−	0.666065i	$-0.767977\pi$
$241$	−23.1588	−1.49179	−0.745894	+	0.666065i	$0.767977\pi$
$242$	−7.19855	−0.462740
$243$	8.49686	0.545074
$244$	−1.55823	−0.0997557
$245$	−8.82386	−0.563736
$246$	−2.02992	−0.129423
$247$	−7.15763	−0.455429
$248$	4.20950	0.267304
$249$	16.7362	1.06061
$250$	−30.0893	−1.90302
$251$	−12.5886	−0.794588	−0.397294	−	0.917691i	$-0.630051\pi$
$251$	−12.5886	−0.794588	−0.397294	+	0.917691i	$0.630051\pi$
$252$	16.5104	1.04006
$253$	7.43456	0.467407
$254$	−15.5694	−0.976909
$255$	12.3141	0.771141
$256$	1.00000	0.0625000
$257$	−23.4693	−1.46397	−0.731986	−	0.681319i	$-0.761406\pi$
$257$	−23.4693	−1.46397	−0.731986	+	0.681319i	$0.761406\pi$
$258$	−21.9314	−1.36539
$259$	28.4585	1.76833
$260$	−29.7241	−1.84341
$261$	55.5635	3.43930
$262$	−15.0676	−0.930877
$263$	6.34196	0.391062	0.195531	−	0.980698i	$-0.437357\pi$
$263$	6.34196	0.391062	0.195531	+	0.980698i	$0.437357\pi$
$264$	−5.67292	−0.349144
$265$	15.1077	0.928060
$266$	−3.02073	−0.185213
$267$	23.7676	1.45456
$268$	1.68379	0.102854
$269$	19.2182	1.17176	0.585878	−	0.810400i	$-0.300750\pi$
$269$	19.2182	1.17176	0.585878	+	0.810400i	$0.300750\pi$
$270$	29.7928	1.81313
$271$	−27.7948	−1.68842	−0.844208	−	0.536015i	$-0.819929\pi$
$271$	−27.7948	−1.68842	−0.844208	+	0.536015i	$0.819929\pi$
$272$	1.01914	0.0617944
$273$	−62.9089	−3.80742
$274$	3.33949	0.201746
$275$	23.8756	1.43975
$276$	−11.0946	−0.667817
$277$	−8.51136	−0.511398	−0.255699	−	0.966756i	$-0.582306\pi$
$277$	−8.51136	−0.511398	−0.255699	+	0.966756i	$0.582306\pi$
$278$	19.3076	1.15799
$279$	23.0079	1.37745
$280$	−12.5444	−0.749673
$281$	29.3230	1.74926	0.874632	−	0.484787i	$-0.161103\pi$
$281$	29.3230	1.74926	0.874632	+	0.484787i	$0.161103\pi$
$282$	16.0528	0.955931
$283$	1.05656	0.0628062	0.0314031	−	0.999507i	$-0.490002\pi$
$283$	1.05656	0.0628062	0.0314031	+	0.999507i	$0.490002\pi$
$284$	−11.8559	−0.703518
$285$	−12.0829	−0.715728
$286$	13.9554	0.825203
$287$	2.10746	0.124399
$288$	5.46571	0.322070
$289$	−15.9614	−0.938903
$290$	−42.2165	−2.47904
$291$	−33.2206	−1.94742
$292$	3.13570	0.183503
$293$	−12.4399	−0.726745	−0.363373	−	0.931644i	$-0.618375\pi$
$293$	−12.4399	−0.726745	−0.363373	+	0.931644i	$0.618375\pi$
$294$	−6.18231	−0.360560
$295$	−33.1938	−1.93262
$296$	9.42107	0.547589
$297$	−13.9877	−0.811651
$298$	5.10176	0.295537
$299$	27.2929	1.57839
$300$	−35.6296	−2.05708
$301$	22.7691	1.31239
$302$	12.0241	0.691907
$303$	−50.0039	−2.87265
$304$	−1.00000	−0.0573539
$305$	6.47100	0.370528
$306$	5.57031	0.318434
$307$	−17.3312	−0.989141	−0.494571	−	0.869137i	$-0.664675\pi$
$307$	−17.3312	−0.989141	−0.494571	+	0.869137i	$0.664675\pi$
$308$	5.88961	0.335592
$309$	2.63369	0.149825
$310$	−17.4811	−0.992862
$311$	−2.20615	−0.125099	−0.0625496	−	0.998042i	$-0.519923\pi$
$311$	−2.20615	−0.125099	−0.0625496	+	0.998042i	$0.519923\pi$
$312$	−20.8257	−1.17903
$313$	18.6570	1.05456	0.527278	−	0.849693i	$-0.323213\pi$
$313$	18.6570	1.05456	0.527278	+	0.849693i	$0.323213\pi$
$314$	−2.70273	−0.152524
$315$	−68.5641	−3.86315
$316$	−1.68328	−0.0946918
$317$	4.76007	0.267352	0.133676	−	0.991025i	$-0.457322\pi$
$317$	4.76007	0.267352	0.133676	+	0.991025i	$0.457322\pi$
$318$	10.5850	0.593578
$319$	19.8207	1.10974
$320$	−4.15278	−0.232148
$321$	18.2027	1.01598
$322$	11.5184	0.641896
$323$	−1.01914	−0.0567064
$324$	4.47682	0.248712
$325$	87.6494	4.86191
$326$	13.4310	0.743875
$327$	−20.0156	−1.10687
$328$	0.697666	0.0385222
$329$	−16.6660	−0.918826
$330$	23.5584	1.29685
$331$	11.8428	0.650938	0.325469	−	0.945553i	$-0.394478\pi$
$331$	11.8428	0.650938	0.325469	+	0.945553i	$0.394478\pi$
$332$	−5.75209	−0.315687
$333$	51.4928	2.82179
$334$	−9.30505	−0.509150
$335$	−6.99241	−0.382036
$336$	−8.78908	−0.479484
$337$	−23.8124	−1.29714	−0.648572	−	0.761153i	$-0.724634\pi$
$337$	−23.8124	−1.29714	−0.648572	+	0.761153i	$0.724634\pi$
$338$	38.2316	2.07953
$339$	43.7722	2.37738
$340$	−4.23226	−0.229527
$341$	8.20740	0.444455
$342$	−5.46571	−0.295551
$343$	−14.7266	−0.795164
$344$	7.53762	0.406401
$345$	46.0735	2.48051
$346$	−5.62614	−0.302463
$347$	34.6997	1.86278	0.931388	−	0.364027i	$-0.118599\pi$
$347$	34.6997	1.86278	0.931388	+	0.364027i	$0.118599\pi$
$348$	−29.5784	−1.58557
$349$	−29.2926	−1.56800	−0.784000	−	0.620761i	$-0.786824\pi$
$349$	−29.2926	−1.56800	−0.784000	+	0.620761i	$0.786824\pi$
$350$	36.9906	1.97723
$351$	−51.3502	−2.74087
$352$	1.94973	0.103921
$353$	−5.86582	−0.312206	−0.156103	−	0.987741i	$-0.549893\pi$
$353$	−5.86582	−0.312206	−0.156103	+	0.987741i	$0.549893\pi$
$354$	−23.2568	−1.23608
$355$	49.2349	2.61312
$356$	−8.16873	−0.432942
$357$	−8.95730	−0.474070
$358$	6.67942	0.353018
$359$	−0.441918	−0.0233235	−0.0116618	−	0.999932i	$-0.503712\pi$
$359$	−0.441918	−0.0233235	−0.0116618	+	0.999932i	$0.503712\pi$
$360$	−22.6979	−1.19628
$361$	1.00000	0.0526316
$362$	−16.2828	−0.855804
$363$	20.9448	1.09932
$364$	21.6213	1.13326
$365$	−13.0219	−0.681597
$366$	4.53382	0.236986
$367$	17.2015	0.897911	0.448955	−	0.893554i	$-0.351796\pi$
$367$	17.2015	0.897911	0.448955	+	0.893554i	$0.351796\pi$
$368$	3.81312	0.198773
$369$	3.81324	0.198509
$370$	−39.1236	−2.03394
$371$	−10.9893	−0.570539
$372$	−12.2479	−0.635025
$373$	10.6175	0.549755	0.274877	−	0.961479i	$-0.411363\pi$
$373$	10.6175	0.549755	0.274877	+	0.961479i	$0.411363\pi$
$374$	1.98705	0.102748
$375$	87.5476	4.52094
$376$	−5.51721	−0.284528
$377$	72.7633	3.74750
$378$	−21.6713	−1.11465
$379$	−17.9307	−0.921037	−0.460519	−	0.887650i	$-0.652337\pi$
$379$	−17.9307	−0.921037	−0.460519	+	0.887650i	$0.652337\pi$
$380$	4.15278	0.213033
$381$	45.3004	2.32081
$382$	16.0005	0.818655
$383$	17.9992	0.919716	0.459858	−	0.887992i	$-0.347900\pi$
$383$	17.9992	0.919716	0.459858	+	0.887992i	$0.347900\pi$
$384$	−2.90959	−0.148479
$385$	−24.4583	−1.24651
$386$	−12.4466	−0.633515
$387$	41.1984	2.09423
$388$	11.4176	0.579642
$389$	−31.9610	−1.62049	−0.810243	−	0.586094i	$-0.800665\pi$
$389$	−31.9610	−1.62049	−0.810243	+	0.586094i	$0.800665\pi$
$390$	86.4848	4.37933
$391$	3.88610	0.196529
$392$	2.12481	0.107319
$393$	43.8404	2.21145
$394$	14.3766	0.724281
$395$	6.99028	0.351719
$396$	10.6567	0.535517
$397$	7.68750	0.385825	0.192912	−	0.981216i	$-0.438207\pi$
$397$	7.68750	0.385825	0.192912	+	0.981216i	$0.438207\pi$
$398$	19.1040	0.957599
$399$	8.78908	0.440004
$400$	12.2456	0.612279
$401$	31.2202	1.55906	0.779532	−	0.626362i	$-0.215457\pi$
$401$	31.2202	1.55906	0.779532	+	0.626362i	$0.215457\pi$
$402$	−4.89914	−0.244347
$403$	30.1300	1.50088
$404$	17.1859	0.855031
$405$	−18.5912	−0.923807
$406$	30.7083	1.52403
$407$	18.3686	0.910495
$408$	−2.96528	−0.146803
$409$	33.3660	1.64984	0.824921	−	0.565249i	$-0.191220\pi$
$409$	33.3660	1.64984	0.824921	+	0.565249i	$0.191220\pi$
$410$	−2.89725	−0.143085
$411$	−9.71653	−0.479281
$412$	−0.905175	−0.0445948
$413$	24.1451	1.18810
$414$	20.8414	1.02430
$415$	23.8872	1.17258
$416$	7.15763	0.350931
$417$	−56.1773	−2.75101
$418$	−1.94973	−0.0953645
$419$	−13.8340	−0.675837	−0.337919	−	0.941175i	$-0.609723\pi$
$419$	−13.8340	−0.675837	−0.337919	+	0.941175i	$0.609723\pi$
$420$	36.4991	1.78097
$421$	17.9771	0.876152	0.438076	−	0.898938i	$-0.355660\pi$
$421$	17.9771	0.876152	0.438076	+	0.898938i	$0.355660\pi$
$422$	−1.00000	−0.0486792
$423$	−30.1554	−1.46621
$424$	−3.63798	−0.176676
$425$	12.4800	0.605367
$426$	34.4958	1.67132
$427$	−4.70700	−0.227788
$428$	−6.25612	−0.302401
$429$	−40.6046	−1.96041
$430$	−31.3021	−1.50952
$431$	34.4107	1.65750	0.828752	−	0.559616i	$-0.189052\pi$
$431$	34.4107	1.65750	0.828752	+	0.559616i	$0.189052\pi$
$432$	−7.17419	−0.345168
$433$	−32.8764	−1.57994	−0.789969	−	0.613147i	$-0.789903\pi$
$433$	−32.8764	−1.57994	−0.789969	+	0.613147i	$0.789903\pi$
$434$	12.7158	0.610376
$435$	122.833	5.88938
$436$	6.87919	0.329453
$437$	−3.81312	−0.182406
$438$	−9.12361	−0.435943
$439$	12.5408	0.598539	0.299270	−	0.954169i	$-0.403257\pi$
$439$	12.5408	0.598539	0.299270	+	0.954169i	$0.403257\pi$
$440$	−8.09681	−0.386000
$441$	11.6136	0.553027
$442$	7.29462	0.346970
$443$	−7.63728	−0.362858	−0.181429	−	0.983404i	$-0.558072\pi$
$443$	−7.63728	−0.362858	−0.181429	+	0.983404i	$0.558072\pi$
$444$	−27.4114	−1.30089
$445$	33.9229	1.60810
$446$	−17.1649	−0.812783
$447$	−14.8440	−0.702098
$448$	3.02073	0.142716
$449$	−16.9124	−0.798148	−0.399074	−	0.916919i	$-0.630668\pi$
$449$	−16.9124	−0.798148	−0.399074	+	0.916919i	$0.630668\pi$
$450$	66.9308	3.15515
$451$	1.36026	0.0640522
$452$	−15.0441	−0.707616
$453$	−34.9851	−1.64374
$454$	−14.3527	−0.673606
$455$	−89.7883	−4.20934
$456$	2.90959	0.136254
$457$	−17.7455	−0.830102	−0.415051	−	0.909798i	$-0.636236\pi$
$457$	−17.7455	−0.830102	−0.415051	+	0.909798i	$0.636236\pi$
$458$	6.65984	0.311194
$459$	−7.31150	−0.341271
$460$	−15.8351	−0.738313
$461$	−28.6682	−1.33521	−0.667606	−	0.744515i	$-0.732681\pi$
$461$	−28.6682	−1.33521	−0.667606	+	0.744515i	$0.732681\pi$
$462$	−17.1363	−0.797255
$463$	2.56062	0.119002	0.0595011	−	0.998228i	$-0.481049\pi$
$463$	2.56062	0.119002	0.0595011	+	0.998228i	$0.481049\pi$
$464$	10.1658	0.471938
$465$	50.8629	2.35871
$466$	9.07581	0.420429
$467$	−20.0042	−0.925682	−0.462841	−	0.886441i	$-0.653170\pi$
$467$	−20.0042	−0.925682	−0.462841	+	0.886441i	$0.653170\pi$
$468$	39.1215	1.80839
$469$	5.08627	0.234862
$470$	22.9118	1.05684
$471$	7.86384	0.362346
$472$	7.99315	0.367914
$473$	14.6963	0.675738
$474$	4.89764	0.224956
$475$	−12.2456	−0.561866
$476$	3.07854	0.141105
$477$	−19.8841	−0.910431
$478$	−14.6906	−0.671933
$479$	5.04331	0.230435	0.115217	−	0.993340i	$-0.463244\pi$
$479$	5.04331	0.230435	0.115217	+	0.993340i	$0.463244\pi$
$480$	12.0829	0.551506
$481$	67.4325	3.07466
$482$	−23.1588	−1.05485
$483$	−33.5138	−1.52493
$484$	−7.19855	−0.327207
$485$	−47.4149	−2.15300
$486$	8.49686	0.385426
$487$	11.0808	0.502118	0.251059	−	0.967972i	$-0.419221\pi$
$487$	11.0808	0.502118	0.251059	+	0.967972i	$0.419221\pi$
$488$	−1.55823	−0.0705379
$489$	−39.0787	−1.76720
$490$	−8.82386	−0.398621
$491$	9.19476	0.414954	0.207477	−	0.978240i	$-0.433475\pi$
$491$	9.19476	0.414954	0.207477	+	0.978240i	$0.433475\pi$
$492$	−2.02992	−0.0915159
$493$	10.3604	0.466610
$494$	−7.15763	−0.322037
$495$	−44.2548	−1.98910
$496$	4.20950	0.189012
$497$	−35.8134	−1.60645
$498$	16.7362	0.749968
$499$	−29.6428	−1.32699	−0.663496	−	0.748180i	$-0.730928\pi$
$499$	−29.6428	−1.32699	−0.663496	+	0.748180i	$0.730928\pi$
$500$	−30.0893	−1.34564
$501$	27.0739	1.20957
$502$	−12.5886	−0.561859
$503$	3.40931	0.152013	0.0760067	−	0.997107i	$-0.475783\pi$
$503$	3.40931	0.152013	0.0760067	+	0.997107i	$0.475783\pi$
$504$	16.5104	0.735432
$505$	−71.3693	−3.17589
$506$	7.43456	0.330507
$507$	−111.238	−4.94026
$508$	−15.5694	−0.690779
$509$	32.1399	1.42458	0.712289	−	0.701886i	$-0.247659\pi$
$509$	32.1399	1.42458	0.712289	+	0.701886i	$0.247659\pi$
$510$	12.3141	0.545279
$511$	9.47211	0.419022
$512$	1.00000	0.0441942
$513$	7.17419	0.316748
$514$	−23.4693	−1.03518
$515$	3.75899	0.165641
$516$	−21.9314	−0.965474
$517$	−10.7571	−0.473096
$518$	28.4585	1.25039
$519$	16.3697	0.718552
$520$	−29.7241	−1.30349
$521$	−3.70118	−0.162152	−0.0810759	−	0.996708i	$-0.525836\pi$
$521$	−3.70118	−0.162152	−0.0810759	+	0.996708i	$0.525836\pi$
$522$	55.5635	2.43195
$523$	−16.1140	−0.704614	−0.352307	−	0.935884i	$-0.614603\pi$
$523$	−16.1140	−0.704614	−0.352307	+	0.935884i	$0.614603\pi$
$524$	−15.0676	−0.658229
$525$	−107.627	−4.69725
$526$	6.34196	0.276522
$527$	4.29007	0.186878
$528$	−5.67292	−0.246882
$529$	−8.46011	−0.367831
$530$	15.1077	0.656238
$531$	43.6882	1.89591
$532$	−3.02073	−0.130965
$533$	4.99363	0.216298
$534$	23.7676	1.02853
$535$	25.9803	1.12323
$536$	1.68379	0.0727287
$537$	−19.4344	−0.838655
$538$	19.2182	0.828556
$539$	4.14280	0.178443
$540$	29.7928	1.28208
$541$	−26.9278	−1.15772	−0.578859	−	0.815428i	$-0.696502\pi$
$541$	−26.9278	−1.15772	−0.578859	+	0.815428i	$0.696502\pi$
$542$	−27.7948	−1.19389
$543$	47.3762	2.03311
$544$	1.01914	0.0436952
$545$	−28.5678	−1.22371
$546$	−62.9089	−2.69225
$547$	−3.90587	−0.167003	−0.0835016	−	0.996508i	$-0.526610\pi$
$547$	−3.90587	−0.167003	−0.0835016	+	0.996508i	$0.526610\pi$
$548$	3.33949	0.142656
$549$	−8.51684	−0.363490
$550$	23.8756	1.01806
$551$	−10.1658	−0.433080
$552$	−11.0946	−0.472218
$553$	−5.08473	−0.216225
$554$	−8.51136	−0.361613
$555$	113.834	4.83197
$556$	19.3076	0.818826
$557$	38.7742	1.64292	0.821458	−	0.570269i	$-0.193161\pi$
$557$	38.7742	1.64292	0.821458	+	0.570269i	$0.193161\pi$
$558$	23.0079	0.974002
$559$	53.9514	2.28190
$560$	−12.5444	−0.530099
$561$	−5.78149	−0.244095
$562$	29.3230	1.23692
$563$	34.8720	1.46968	0.734840	−	0.678240i	$-0.237257\pi$
$563$	34.8720	1.46968	0.734840	+	0.678240i	$0.237257\pi$
$564$	16.0528	0.675945
$565$	62.4749	2.62834
$566$	1.05656	0.0444107
$567$	13.5233	0.567924
$568$	−11.8559	−0.497462
$569$	−14.2554	−0.597616	−0.298808	−	0.954313i	$-0.596589\pi$
$569$	−14.2554	−0.597616	−0.298808	+	0.954313i	$0.596589\pi$
$570$	−12.0829	−0.506096
$571$	5.78533	0.242109	0.121054	−	0.992646i	$-0.461372\pi$
$571$	5.78533	0.242109	0.121054	+	0.992646i	$0.461372\pi$
$572$	13.9554	0.583507
$573$	−46.5548	−1.94485
$574$	2.10746	0.0879637
$575$	46.6939	1.94727
$576$	5.46571	0.227738
$577$	−28.9710	−1.20608	−0.603038	−	0.797712i	$-0.706043\pi$
$577$	−28.9710	−1.20608	−0.603038	+	0.797712i	$0.706043\pi$
$578$	−15.9614	−0.663905
$579$	36.2145	1.50502
$580$	−42.2165	−1.75295
$581$	−17.3755	−0.720858
$582$	−33.2206	−1.37704
$583$	−7.09308	−0.293765
$584$	3.13570	0.129756
$585$	−162.463	−6.71701
$586$	−12.4399	−0.513886
$587$	−45.7854	−1.88976	−0.944882	−	0.327410i	$-0.893824\pi$
$587$	−45.7854	−1.88976	−0.944882	+	0.327410i	$0.893824\pi$
$588$	−6.18231	−0.254954
$589$	−4.20950	−0.173450
$590$	−33.1938	−1.36657
$591$	−41.8299	−1.72065
$592$	9.42107	0.387204
$593$	10.5318	0.432489	0.216244	−	0.976339i	$-0.430619\pi$
$593$	10.5318	0.432489	0.216244	+	0.976339i	$0.430619\pi$
$594$	−13.9877	−0.573924
$595$	−12.7845	−0.524114
$596$	5.10176	0.208976
$597$	−55.5849	−2.27494
$598$	27.2929	1.11609
$599$	−35.3648	−1.44497	−0.722483	−	0.691389i	$-0.756999\pi$
$599$	−35.3648	−1.44497	−0.722483	+	0.691389i	$0.756999\pi$
$600$	−35.6296	−1.45457
$601$	−21.9281	−0.894464	−0.447232	−	0.894418i	$-0.647590\pi$
$601$	−21.9281	−0.894464	−0.447232	+	0.894418i	$0.647590\pi$
$602$	22.7691	0.927999
$603$	9.20310	0.374779
$604$	12.0241	0.489252
$605$	29.8940	1.21536
$606$	−50.0039	−2.03127
$607$	19.6293	0.796728	0.398364	−	0.917228i	$-0.369578\pi$
$607$	19.6293	0.796728	0.398364	+	0.917228i	$0.369578\pi$
$608$	−1.00000	−0.0405554
$609$	−89.3485	−3.62058
$610$	6.47100	0.262003
$611$	−39.4901	−1.59760
$612$	5.57031	0.225167
$613$	−33.3190	−1.34574	−0.672870	−	0.739760i	$-0.734939\pi$
$613$	−33.3190	−1.34574	−0.672870	+	0.739760i	$0.734939\pi$
$614$	−17.3312	−0.699429
$615$	8.42982	0.339923
$616$	5.88961	0.237299
$617$	−2.01887	−0.0812767	−0.0406384	−	0.999174i	$-0.512939\pi$
$617$	−2.01887	−0.0812767	−0.0406384	+	0.999174i	$0.512939\pi$
$618$	2.63369	0.105942
$619$	15.6910	0.630676	0.315338	−	0.948979i	$-0.397882\pi$
$619$	15.6910	0.630676	0.315338	+	0.948979i	$0.397882\pi$
$620$	−17.4811	−0.702059
$621$	−27.3560	−1.09776
$622$	−2.20615	−0.0884584
$623$	−24.6755	−0.988604
$624$	−20.8257	−0.833697
$625$	63.7265	2.54906
$626$	18.6570	0.745683
$627$	5.67292	0.226554
$628$	−2.70273	−0.107851
$629$	9.60138	0.382832
$630$	−68.5641	−2.73166
$631$	−20.2060	−0.804390	−0.402195	−	0.915554i	$-0.631753\pi$
$631$	−20.2060	−0.804390	−0.402195	+	0.915554i	$0.631753\pi$
$632$	−1.68328	−0.0669572
$633$	2.90959	0.115646
$634$	4.76007	0.189047
$635$	64.6561	2.56580
$636$	10.5850	0.419723
$637$	15.2086	0.602586
$638$	19.8207	0.784708
$639$	−64.8008	−2.56348
$640$	−4.15278	−0.164153
$641$	7.16583	0.283033	0.141517	−	0.989936i	$-0.454802\pi$
$641$	7.16583	0.283033	0.141517	+	0.989936i	$0.454802\pi$
$642$	18.2027	0.718405
$643$	−28.5747	−1.12687	−0.563437	−	0.826159i	$-0.690521\pi$
$643$	−28.5747	−1.12687	−0.563437	+	0.826159i	$0.690521\pi$
$644$	11.5184	0.453889
$645$	91.0761	3.58612
$646$	−1.01914	−0.0400975
$647$	−19.5375	−0.768099	−0.384049	−	0.923313i	$-0.625471\pi$
$647$	−19.5375	−0.768099	−0.384049	+	0.923313i	$0.625471\pi$
$648$	4.47682	0.175866
$649$	15.5845	0.611745
$650$	87.6494	3.43789
$651$	−36.9976	−1.45005
$652$	13.4310	0.525999
$653$	31.5416	1.23432	0.617160	−	0.786838i	$-0.288283\pi$
$653$	31.5416	1.23432	0.617160	+	0.786838i	$0.288283\pi$
$654$	−20.0156	−0.782672
$655$	62.5723	2.44490
$656$	0.697666	0.0272393
$657$	17.1388	0.668650
$658$	−16.6660	−0.649708
$659$	−21.0459	−0.819831	−0.409916	−	0.912123i	$-0.634442\pi$
$659$	−21.0459	−0.819831	−0.409916	+	0.912123i	$0.634442\pi$
$660$	23.5584	0.917009
$661$	1.86235	0.0724369	0.0362184	−	0.999344i	$-0.488469\pi$
$661$	1.86235	0.0724369	0.0362184	+	0.999344i	$0.488469\pi$
$662$	11.8428	0.460283
$663$	−21.2243	−0.824285
$664$	−5.75209	−0.223224
$665$	12.5444	0.486452
$666$	51.4928	1.99531
$667$	38.7636	1.50093
$668$	−9.30505	−0.360023
$669$	49.9429	1.93090
$670$	−6.99241	−0.270140
$671$	−3.03814	−0.117286
$672$	−8.78908	−0.339046
$673$	20.7209	0.798734	0.399367	−	0.916791i	$-0.369230\pi$
$673$	20.7209	0.798734	0.399367	+	0.916791i	$0.369230\pi$
$674$	−23.8124	−0.917220
$675$	−87.8522	−3.38143
$676$	38.2316	1.47045
$677$	38.2054	1.46835	0.734177	−	0.678958i	$-0.237568\pi$
$677$	38.2054	1.46835	0.734177	+	0.678958i	$0.237568\pi$
$678$	43.7722	1.68106
$679$	34.4895	1.32359
$680$	−4.23226	−0.162300
$681$	41.7605	1.60026
$682$	8.20740	0.314277
$683$	−24.4622	−0.936022	−0.468011	−	0.883723i	$-0.655029\pi$
$683$	−24.4622	−0.936022	−0.468011	+	0.883723i	$0.655029\pi$
$684$	−5.46571	−0.208986
$685$	−13.8682	−0.529875
$686$	−14.7266	−0.562266
$687$	−19.3774	−0.739294
$688$	7.53762	0.287369
$689$	−26.0393	−0.992018
$690$	46.0735	1.75399
$691$	−36.0523	−1.37149	−0.685746	−	0.727841i	$-0.740524\pi$
$691$	−36.0523	−1.37149	−0.685746	+	0.727841i	$0.740524\pi$
$692$	−5.62614	−0.213874
$693$	32.1909	1.22283
$694$	34.6997	1.31718
$695$	−80.1804	−3.04141
$696$	−29.5784	−1.12117
$697$	0.711019	0.0269318
$698$	−29.2926	−1.10874
$699$	−26.4069	−0.998800
$700$	36.9906	1.39811
$701$	−28.0614	−1.05986	−0.529932	−	0.848040i	$-0.677782\pi$
$701$	−28.0614	−1.05986	−0.529932	+	0.848040i	$0.677782\pi$
$702$	−51.3502	−1.93809
$703$	−9.42107	−0.355322
$704$	1.94973	0.0734833
$705$	−66.6638	−2.51070
$706$	−5.86582	−0.220763
$707$	51.9140	1.95243
$708$	−23.2568	−0.874043
$709$	−13.5688	−0.509586	−0.254793	−	0.966996i	$-0.582007\pi$
$709$	−13.5688	−0.509586	−0.254793	+	0.966996i	$0.582007\pi$
$710$	49.2349	1.84775
$711$	−9.20030	−0.345038
$712$	−8.16873	−0.306136
$713$	16.0513	0.601127
$714$	−8.95730	−0.335218
$715$	−57.9539	−2.16735
$716$	6.67942	0.249622
$717$	42.7436	1.59629
$718$	−0.441918	−0.0164922
$719$	−45.3428	−1.69100	−0.845500	−	0.533975i	$-0.820698\pi$
$719$	−45.3428	−1.69100	−0.845500	+	0.533975i	$0.820698\pi$
$720$	−22.6979	−0.845900
$721$	−2.73429	−0.101830
$722$	1.00000	0.0372161
$723$	67.3825	2.50598
$724$	−16.2828	−0.605145
$725$	124.487	4.62332
$726$	20.9448	0.777335
$727$	2.59966	0.0964162	0.0482081	−	0.998837i	$-0.484649\pi$
$727$	2.59966	0.0964162	0.0482081	+	0.998837i	$0.484649\pi$
$728$	21.6213	0.801337
$729$	−38.1528	−1.41307
$730$	−13.0219	−0.481962
$731$	7.68188	0.284125
$732$	4.53382	0.167575
$733$	50.3954	1.86140	0.930698	−	0.365788i	$-0.119201\pi$
$733$	50.3954	1.86140	0.930698	+	0.365788i	$0.119201\pi$
$734$	17.2015	0.634919
$735$	25.6738	0.946992
$736$	3.81312	0.140553
$737$	3.28294	0.120929
$738$	3.81324	0.140367
$739$	−51.5853	−1.89759	−0.948797	−	0.315885i	$-0.897699\pi$
$739$	−51.5853	−1.89759	−0.948797	+	0.315885i	$0.897699\pi$
$740$	−39.1236	−1.43821
$741$	20.8257	0.765053
$742$	−10.9893	−0.403432
$743$	12.8723	0.472240	0.236120	−	0.971724i	$-0.424124\pi$
$743$	12.8723	0.472240	0.236120	+	0.971724i	$0.424124\pi$
$744$	−12.2479	−0.449030
$745$	−21.1865	−0.776213
$746$	10.6175	0.388735
$747$	−31.4392	−1.15030
$748$	1.98705	0.0726536
$749$	−18.8981	−0.690520
$750$	87.5476	3.19679
$751$	−40.4289	−1.47527	−0.737635	−	0.675199i	$-0.764058\pi$
$751$	−40.4289	−1.47527	−0.737635	+	0.675199i	$0.764058\pi$
$752$	−5.51721	−0.201192
$753$	36.6278	1.33479
$754$	72.7633	2.64988
$755$	−49.9333	−1.81726
$756$	−21.6713	−0.788177
$757$	24.2399	0.881014	0.440507	−	0.897749i	$-0.354799\pi$
$757$	24.2399	0.881014	0.440507	+	0.897749i	$0.354799\pi$
$758$	−17.9307	−0.651272
$759$	−21.6315	−0.785174
$760$	4.15278	0.150637
$761$	−9.40814	−0.341045	−0.170522	−	0.985354i	$-0.554546\pi$
$761$	−9.40814	−0.341045	−0.170522	+	0.985354i	$0.554546\pi$
$762$	45.3004	1.64106
$763$	20.7802	0.752293
$764$	16.0005	0.578877
$765$	−23.1323	−0.836350
$766$	17.9992	0.650338
$767$	57.2119	2.06580
$768$	−2.90959	−0.104991
$769$	−46.7257	−1.68497	−0.842485	−	0.538720i	$-0.818908\pi$
$769$	−46.7257	−1.68497	−0.842485	+	0.538720i	$0.818908\pi$
$770$	−24.4583	−0.881415
$771$	68.2859	2.45926
$772$	−12.4466	−0.447963
$773$	−23.5066	−0.845473	−0.422736	−	0.906253i	$-0.638930\pi$
$773$	−23.5066	−0.845473	−0.422736	+	0.906253i	$0.638930\pi$
$774$	41.1984	1.48085
$775$	51.5478	1.85165
$776$	11.4176	0.409869
$777$	−82.8025	−2.97052
$778$	−31.9610	−1.14586
$779$	−0.697666	−0.0249965
$780$	86.4848	3.09665
$781$	−23.1158	−0.827148
$782$	3.88610	0.138967
$783$	−72.9317	−2.60637
$784$	2.12481	0.0758860
$785$	11.2239	0.400596
$786$	43.8404	1.56373
$787$	−6.72057	−0.239563	−0.119781	−	0.992800i	$-0.538219\pi$
$787$	−6.72057	−0.239563	−0.119781	+	0.992800i	$0.538219\pi$
$788$	14.3766	0.512144
$789$	−18.4525	−0.656926
$790$	6.99028	0.248703
$791$	−45.4442	−1.61581
$792$	10.6567	0.378668
$793$	−11.1533	−0.396064
$794$	7.68750	0.272819
$795$	−43.9573	−1.55900
$796$	19.1040	0.677125
$797$	28.2983	1.00238	0.501189	−	0.865338i	$-0.332896\pi$
$797$	28.2983	1.00238	0.501189	+	0.865338i	$0.332896\pi$
$798$	8.78908	0.311130
$799$	−5.62280	−0.198920
$800$	12.2456	0.432947
$801$	−44.6479	−1.57756
$802$	31.2202	1.10243
$803$	6.11378	0.215751
$804$	−4.89914	−0.172779
$805$	−47.8334	−1.68591
$806$	30.1300	1.06129
$807$	−55.9171	−1.96837
$808$	17.1859	0.604598
$809$	1.85205	0.0651146	0.0325573	−	0.999470i	$-0.489635\pi$
$809$	1.85205	0.0651146	0.0325573	+	0.999470i	$0.489635\pi$
$810$	−18.5912	−0.653230
$811$	45.4507	1.59599	0.797995	−	0.602664i	$-0.205894\pi$
$811$	45.4507	1.59599	0.797995	+	0.602664i	$0.205894\pi$
$812$	30.7083	1.07765
$813$	80.8716	2.83629
$814$	18.3686	0.643817
$815$	−55.7760	−1.95375
$816$	−2.96528	−0.103805
$817$	−7.53762	−0.263708
$818$	33.3660	1.16661
$819$	118.175	4.12938
$820$	−2.89725	−0.101177
$821$	−5.32174	−0.185730	−0.0928651	−	0.995679i	$-0.529603\pi$
$821$	−5.32174	−0.185730	−0.0928651	+	0.995679i	$0.529603\pi$
$822$	−9.71653	−0.338903
$823$	−13.8074	−0.481294	−0.240647	−	0.970613i	$-0.577360\pi$
$823$	−13.8074	−0.481294	−0.240647	+	0.970613i	$0.577360\pi$
$824$	−0.905175	−0.0315333
$825$	−69.4682	−2.41857
$826$	24.1451	0.840117
$827$	−35.4391	−1.23234	−0.616170	−	0.787614i	$-0.711316\pi$
$827$	−35.4391	−1.23234	−0.616170	+	0.787614i	$0.711316\pi$
$828$	20.8414	0.724289
$829$	26.9862	0.937271	0.468636	−	0.883392i	$-0.344746\pi$
$829$	26.9862	0.937271	0.468636	+	0.883392i	$0.344746\pi$
$830$	23.8872	0.829136
$831$	24.7646	0.859073
$832$	7.15763	0.248146
$833$	2.16547	0.0750292
$834$	−56.1773	−1.94526
$835$	38.6418	1.33726
$836$	−1.94973	−0.0674329
$837$	−30.1998	−1.04386
$838$	−13.8340	−0.477889
$839$	5.72977	0.197814	0.0989068	−	0.995097i	$-0.468465\pi$
$839$	5.72977	0.197814	0.0989068	+	0.995097i	$0.468465\pi$
$840$	36.4991	1.25934
$841$	74.3445	2.56360
$842$	17.9771	0.619533
$843$	−85.3179	−2.93851
$844$	−1.00000	−0.0344214
$845$	−158.768	−5.46177
$846$	−30.1554	−1.03677
$847$	−21.7449	−0.747162
$848$	−3.63798	−0.124929
$849$	−3.07417	−0.105505
$850$	12.4800	0.428059
$851$	35.9237	1.23145
$852$	34.4958	1.18181
$853$	9.82818	0.336510	0.168255	−	0.985743i	$-0.446187\pi$
$853$	9.82818	0.336510	0.168255	+	0.985743i	$0.446187\pi$
$854$	−4.70700	−0.161070
$855$	22.6979	0.776251
$856$	−6.25612	−0.213830
$857$	25.3796	0.866950	0.433475	−	0.901166i	$-0.357287\pi$
$857$	25.3796	0.866950	0.433475	+	0.901166i	$0.357287\pi$
$858$	−40.6046	−1.38622
$859$	−9.13659	−0.311736	−0.155868	−	0.987778i	$-0.549817\pi$
$859$	−9.13659	−0.311736	−0.155868	+	0.987778i	$0.549817\pi$
$860$	−31.3021	−1.06739
$861$	−6.13184	−0.208973
$862$	34.4107	1.17203
$863$	−22.9804	−0.782263	−0.391131	−	0.920335i	$-0.627916\pi$
$863$	−22.9804	−0.782263	−0.391131	+	0.920335i	$0.627916\pi$
$864$	−7.17419	−0.244071
$865$	23.3641	0.794404
$866$	−32.8764	−1.11719
$867$	46.4410	1.57722
$868$	12.7158	0.431601
$869$	−3.28194	−0.111332
$870$	122.833	4.16442
$871$	12.0519	0.408364
$872$	6.87919	0.232959
$873$	62.4053	2.11210
$874$	−3.81312	−0.128981
$875$	−90.8918	−3.07270
$876$	−9.12361	−0.308258
$877$	−38.9306	−1.31459	−0.657296	−	0.753632i	$-0.728300\pi$
$877$	−38.9306	−1.31459	−0.657296	+	0.753632i	$0.728300\pi$
$878$	12.5408	0.423231
$879$	36.1949	1.22082
$880$	−8.09681	−0.272943
$881$	−23.5053	−0.791912	−0.395956	−	0.918269i	$-0.629587\pi$
$881$	−23.5053	−0.791912	−0.395956	+	0.918269i	$0.629587\pi$
$882$	11.6136	0.391049
$883$	−13.9825	−0.470548	−0.235274	−	0.971929i	$-0.575599\pi$
$883$	−13.9825	−0.470548	−0.235274	+	0.971929i	$0.575599\pi$
$884$	7.29462	0.245345
$885$	96.5803	3.24651
$886$	−7.63728	−0.256580
$887$	−19.4188	−0.652021	−0.326010	−	0.945366i	$-0.605704\pi$
$887$	−19.4188	−0.652021	−0.326010	+	0.945366i	$0.605704\pi$
$888$	−27.4114	−0.919868
$889$	−47.0308	−1.57736
$890$	33.9229	1.13710
$891$	8.72859	0.292419
$892$	−17.1649	−0.574724
$893$	5.51721	0.184626
$894$	−14.8440	−0.496459
$895$	−27.7382	−0.927185
$896$	3.02073	0.100915
$897$	−79.4111	−2.65146
$898$	−16.9124	−0.564376
$899$	42.7932	1.42723
$900$	66.9308	2.23103
$901$	−3.70761	−0.123518
$902$	1.36026	0.0452917
$903$	−66.2487	−2.20462
$904$	−15.0441	−0.500360
$905$	67.6188	2.24772
$906$	−34.9851	−1.16230
$907$	28.6747	0.952126	0.476063	−	0.879411i	$-0.342063\pi$
$907$	28.6747	0.952126	0.476063	+	0.879411i	$0.342063\pi$
$908$	−14.3527	−0.476311
$909$	93.9331	3.11556
$910$	−89.7883	−2.97645
$911$	−30.8665	−1.02265	−0.511327	−	0.859386i	$-0.670846\pi$
$911$	−30.8665	−1.02265	−0.511327	+	0.859386i	$0.670846\pi$
$912$	2.90959	0.0963461
$913$	−11.2150	−0.371163
$914$	−17.7455	−0.586970
$915$	−18.8280	−0.622433
$916$	6.65984	0.220047
$917$	−45.5150	−1.50304
$918$	−7.31150	−0.241315
$919$	−25.9388	−0.855643	−0.427821	−	0.903863i	$-0.640719\pi$
$919$	−25.9388	−0.855643	−0.427821	+	0.903863i	$0.640719\pi$
$920$	−15.8351	−0.522066
$921$	50.4265	1.66161
$922$	−28.6682	−0.944137
$923$	−84.8600	−2.79320
$924$	−17.1363	−0.563744
$925$	115.367	3.79323
$926$	2.56062	0.0841473
$927$	−4.94742	−0.162495
$928$	10.1658	0.333710
$929$	−32.5571	−1.06816	−0.534082	−	0.845433i	$-0.679343\pi$
$929$	−32.5571	−1.06816	−0.534082	+	0.845433i	$0.679343\pi$
$930$	50.8629	1.66786
$931$	−2.12481	−0.0696377
$932$	9.07581	0.297288
$933$	6.41898	0.210148
$934$	−20.0042	−0.654556
$935$	−8.25177	−0.269862
$936$	39.1215	1.27873
$937$	20.4620	0.668464	0.334232	−	0.942491i	$-0.391523\pi$
$937$	20.4620	0.668464	0.334232	+	0.942491i	$0.391523\pi$
$938$	5.08627	0.166073
$939$	−54.2842	−1.77150
$940$	22.9118	0.747299
$941$	33.0659	1.07792	0.538958	−	0.842333i	$-0.318818\pi$
$941$	33.0659	1.07792	0.538958	+	0.842333i	$0.318818\pi$
$942$	7.86384	0.256218
$943$	2.66029	0.0866308
$944$	7.99315	0.260155
$945$	89.9961	2.92757
$946$	14.6963	0.477819
$947$	−7.41391	−0.240920	−0.120460	−	0.992718i	$-0.538437\pi$
$947$	−7.41391	−0.240920	−0.120460	+	0.992718i	$0.538437\pi$
$948$	4.89764	0.159068
$949$	22.4442	0.728569
$950$	−12.2456	−0.397299
$951$	−13.8499	−0.449112
$952$	3.07854	0.0997762
$953$	−15.8671	−0.513987	−0.256994	−	0.966413i	$-0.582732\pi$
$953$	−15.8671	−0.513987	−0.256994	+	0.966413i	$0.582732\pi$
$954$	−19.8841	−0.643772
$955$	−66.4465	−2.15016
$956$	−14.6906	−0.475128
$957$	−57.6700	−1.86421
$958$	5.04331	0.162942
$959$	10.0877	0.325748
$960$	12.0829	0.389973
$961$	−13.2801	−0.428390
$962$	67.4325	2.17411
$963$	−34.1941	−1.10189
$964$	−23.1588	−0.745894
$965$	51.6880	1.66390
$966$	−33.5138	−1.07829
$967$	9.86280	0.317166	0.158583	−	0.987346i	$-0.449307\pi$
$967$	9.86280	0.317166	0.158583	+	0.987346i	$0.449307\pi$
$968$	−7.19855	−0.231370
$969$	2.96528	0.0952584
$970$	−47.4149	−1.52240
$971$	0.323688	0.0103876	0.00519382	−	0.999987i	$-0.498347\pi$
$971$	0.323688	0.0103876	0.00519382	+	0.999987i	$0.498347\pi$
$972$	8.49686	0.272537
$973$	58.3231	1.86975
$974$	11.0808	0.355051
$975$	−255.024	−8.16729
$976$	−1.55823	−0.0498778
$977$	22.5466	0.721331	0.360665	−	0.932695i	$-0.382550\pi$
$977$	22.5466	0.721331	0.360665	+	0.932695i	$0.382550\pi$
$978$	−39.0787	−1.24960
$979$	−15.9268	−0.509024
$980$	−8.82386	−0.281868
$981$	37.5996	1.20046
$982$	9.19476	0.293417
$983$	15.5583	0.496233	0.248116	−	0.968730i	$-0.420188\pi$
$983$	15.5583	0.496233	0.248116	+	0.968730i	$0.420188\pi$
$984$	−2.02992	−0.0647115
$985$	−59.7028	−1.90229
$986$	10.3604	0.329943
$987$	48.4912	1.54349
$988$	−7.15763	−0.227714
$989$	28.7418	0.913937
$990$	−44.2548	−1.40651
$991$	−5.67356	−0.180227	−0.0901133	−	0.995932i	$-0.528723\pi$
$991$	−5.67356	−0.180227	−0.0901133	+	0.995932i	$0.528723\pi$
$992$	4.20950	0.133652
$993$	−34.4576	−1.09348
$994$	−35.8134	−1.13593
$995$	−79.3349	−2.51509
$996$	16.7362	0.530307
$997$	24.7691	0.784445	0.392223	−	0.919870i	$-0.371706\pi$
$997$	24.7691	0.784445	0.392223	+	0.919870i	$0.371706\pi$
$998$	−29.6428	−0.938325
$999$	−67.5885	−2.13841

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.4	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.4	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.90959 q^{3} +1.00000 q^{4} -4.15278 q^{5} -2.90959 q^{6} +3.02073 q^{7} +1.00000 q^{8} +5.46571 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.90959 q^{3} +1.00000 q^{4} -4.15278 q^{5} -2.90959 q^{6} +3.02073 q^{7} +1.00000 q^{8} +5.46571 q^{9} -4.15278 q^{10} +1.94973 q^{11} -2.90959 q^{12} +7.15763 q^{13} +3.02073 q^{14} +12.0829 q^{15} +1.00000 q^{16} +1.01914 q^{17} +5.46571 q^{18} -1.00000 q^{19} -4.15278 q^{20} -8.78908 q^{21} +1.94973 q^{22} +3.81312 q^{23} -2.90959 q^{24} +12.2456 q^{25} +7.15763 q^{26} -7.17419 q^{27} +3.02073 q^{28} +10.1658 q^{29} +12.0829 q^{30} +4.20950 q^{31} +1.00000 q^{32} -5.67292 q^{33} +1.01914 q^{34} -12.5444 q^{35} +5.46571 q^{36} +9.42107 q^{37} -1.00000 q^{38} -20.8257 q^{39} -4.15278 q^{40} +0.697666 q^{41} -8.78908 q^{42} +7.53762 q^{43} +1.94973 q^{44} -22.6979 q^{45} +3.81312 q^{46} -5.51721 q^{47} -2.90959 q^{48} +2.12481 q^{49} +12.2456 q^{50} -2.96528 q^{51} +7.15763 q^{52} -3.63798 q^{53} -7.17419 q^{54} -8.09681 q^{55} +3.02073 q^{56} +2.90959 q^{57} +10.1658 q^{58} +7.99315 q^{59} +12.0829 q^{60} -1.55823 q^{61} +4.20950 q^{62} +16.5104 q^{63} +1.00000 q^{64} -29.7241 q^{65} -5.67292 q^{66} +1.68379 q^{67} +1.01914 q^{68} -11.0946 q^{69} -12.5444 q^{70} -11.8559 q^{71} +5.46571 q^{72} +3.13570 q^{73} +9.42107 q^{74} -35.6296 q^{75} -1.00000 q^{76} +5.88961 q^{77} -20.8257 q^{78} -1.68328 q^{79} -4.15278 q^{80} +4.47682 q^{81} +0.697666 q^{82} -5.75209 q^{83} -8.78908 q^{84} -4.23226 q^{85} +7.53762 q^{86} -29.5784 q^{87} +1.94973 q^{88} -8.16873 q^{89} -22.6979 q^{90} +21.6213 q^{91} +3.81312 q^{92} -12.2479 q^{93} -5.51721 q^{94} +4.15278 q^{95} -2.90959 q^{96} +11.4176 q^{97} +2.12481 q^{98} +10.6567 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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