LMFDB - Embedded newform 8018.2.a.j.1.37

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			1.37
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)

$f(q)$	$=$	$q+1.00000 q^{2} +2.25942 q^{3} +1.00000 q^{4} +0.0902706 q^{5} +2.25942 q^{6} +2.22465 q^{7} +1.00000 q^{8} +2.10496 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +2.25942 q^{3} +1.00000 q^{4} +0.0902706 q^{5} +2.25942 q^{6} +2.22465 q^{7} +1.00000 q^{8} +2.10496 q^{9} +0.0902706 q^{10} +2.60751 q^{11} +2.25942 q^{12} +2.02823 q^{13} +2.22465 q^{14} +0.203959 q^{15} +1.00000 q^{16} +3.50788 q^{17} +2.10496 q^{18} -1.00000 q^{19} +0.0902706 q^{20} +5.02642 q^{21} +2.60751 q^{22} +5.88559 q^{23} +2.25942 q^{24} -4.99185 q^{25} +2.02823 q^{26} -2.02226 q^{27} +2.22465 q^{28} +7.15073 q^{29} +0.203959 q^{30} -7.83786 q^{31} +1.00000 q^{32} +5.89146 q^{33} +3.50788 q^{34} +0.200821 q^{35} +2.10496 q^{36} -1.37350 q^{37} -1.00000 q^{38} +4.58261 q^{39} +0.0902706 q^{40} +3.84368 q^{41} +5.02642 q^{42} -9.72990 q^{43} +2.60751 q^{44} +0.190016 q^{45} +5.88559 q^{46} +10.7754 q^{47} +2.25942 q^{48} -2.05091 q^{49} -4.99185 q^{50} +7.92577 q^{51} +2.02823 q^{52} -4.98609 q^{53} -2.02226 q^{54} +0.235382 q^{55} +2.22465 q^{56} -2.25942 q^{57} +7.15073 q^{58} +2.42721 q^{59} +0.203959 q^{60} -4.40040 q^{61} -7.83786 q^{62} +4.68282 q^{63} +1.00000 q^{64} +0.183089 q^{65} +5.89146 q^{66} -5.90035 q^{67} +3.50788 q^{68} +13.2980 q^{69} +0.200821 q^{70} +13.5345 q^{71} +2.10496 q^{72} +8.97044 q^{73} -1.37350 q^{74} -11.2787 q^{75} -1.00000 q^{76} +5.80082 q^{77} +4.58261 q^{78} -7.84558 q^{79} +0.0902706 q^{80} -10.8840 q^{81} +3.84368 q^{82} -17.5772 q^{83} +5.02642 q^{84} +0.316659 q^{85} -9.72990 q^{86} +16.1565 q^{87} +2.60751 q^{88} +12.1094 q^{89} +0.190016 q^{90} +4.51210 q^{91} +5.88559 q^{92} -17.7090 q^{93} +10.7754 q^{94} -0.0902706 q^{95} +2.25942 q^{96} -2.03035 q^{97} -2.05091 q^{98} +5.48872 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	2.25942	1.30447	0.652237	−	0.758015i	$-0.273831\pi$
$3$	2.25942	1.30447	0.652237	+	0.758015i	$0.273831\pi$
$4$	1.00000	0.500000
$5$	0.0902706	0.0403703	0.0201851	−	0.999796i	$-0.493574\pi$
$5$	0.0902706	0.0403703	0.0201851	+	0.999796i	$0.493574\pi$
$6$	2.25942	0.922403
$7$	2.22465	0.840840	0.420420	−	0.907330i	$-0.361883\pi$
$7$	2.22465	0.840840	0.420420	+	0.907330i	$0.361883\pi$
$8$	1.00000	0.353553
$9$	2.10496	0.701654
$10$	0.0902706	0.0285461
$11$	2.60751	0.786195	0.393098	−	0.919497i	$-0.371403\pi$
$11$	2.60751	0.786195	0.393098	+	0.919497i	$0.371403\pi$
$12$	2.25942	0.652237
$13$	2.02823	0.562529	0.281264	−	0.959630i	$-0.409246\pi$
$13$	2.02823	0.562529	0.281264	+	0.959630i	$0.409246\pi$
$14$	2.22465	0.594564
$15$	0.203959	0.0526620
$16$	1.00000	0.250000
$17$	3.50788	0.850786	0.425393	−	0.905009i	$-0.360136\pi$
$17$	3.50788	0.850786	0.425393	+	0.905009i	$0.360136\pi$
$18$	2.10496	0.496144
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	0.0902706	0.0201851
$21$	5.02642	1.09686
$22$	2.60751	0.555924
$23$	5.88559	1.22723	0.613615	−	0.789606i	$-0.289715\pi$
$23$	5.88559	1.22723	0.613615	+	0.789606i	$0.289715\pi$
$24$	2.25942	0.461201
$25$	−4.99185	−0.998370
$26$	2.02823	0.397768
$27$	−2.02226	−0.389184
$28$	2.22465	0.420420
$29$	7.15073	1.32786	0.663929	−	0.747796i	$-0.268888\pi$
$29$	7.15073	1.32786	0.663929	+	0.747796i	$0.268888\pi$
$30$	0.203959	0.0372376
$31$	−7.83786	−1.40772	−0.703861	−	0.710338i	$-0.748542\pi$
$31$	−7.83786	−1.40772	−0.703861	+	0.710338i	$0.748542\pi$
$32$	1.00000	0.176777
$33$	5.89146	1.02557
$34$	3.50788	0.601597
$35$	0.200821	0.0339449
$36$	2.10496	0.350827
$37$	−1.37350	−0.225802	−0.112901	−	0.993606i	$-0.536014\pi$
$37$	−1.37350	−0.225802	−0.112901	+	0.993606i	$0.536014\pi$
$38$	−1.00000	−0.162221
$39$	4.58261	0.733804
$40$	0.0902706	0.0142730
$41$	3.84368	0.600281	0.300141	−	0.953895i	$-0.402966\pi$
$41$	3.84368	0.600281	0.300141	+	0.953895i	$0.402966\pi$
$42$	5.02642	0.775594
$43$	−9.72990	−1.48380	−0.741898	−	0.670513i	$-0.766074\pi$
$43$	−9.72990	−1.48380	−0.741898	+	0.670513i	$0.766074\pi$
$44$	2.60751	0.393098
$45$	0.190016	0.0283260
$46$	5.88559	0.867782
$47$	10.7754	1.57175	0.785874	−	0.618387i	$-0.212214\pi$
$47$	10.7754	1.57175	0.785874	+	0.618387i	$0.212214\pi$
$48$	2.25942	0.326119
$49$	−2.05091	−0.292987
$50$	−4.99185	−0.705954
$51$	7.92577	1.10983
$52$	2.02823	0.281264
$53$	−4.98609	−0.684892	−0.342446	−	0.939537i	$-0.611255\pi$
$53$	−4.98609	−0.684892	−0.342446	+	0.939537i	$0.611255\pi$
$54$	−2.02226	−0.275195
$55$	0.235382	0.0317389
$56$	2.22465	0.297282
$57$	−2.25942	−0.299267
$58$	7.15073	0.938937
$59$	2.42721	0.315996	0.157998	−	0.987439i	$-0.449496\pi$
$59$	2.42721	0.315996	0.157998	+	0.987439i	$0.449496\pi$
$60$	0.203959	0.0263310
$61$	−4.40040	−0.563413	−0.281706	−	0.959501i	$-0.590900\pi$
$61$	−4.40040	−0.563413	−0.281706	+	0.959501i	$0.590900\pi$
$62$	−7.83786	−0.995409
$63$	4.68282	0.589979
$64$	1.00000	0.125000
$65$	0.183089	0.0227094
$66$	5.89146	0.725189
$67$	−5.90035	−0.720843	−0.360421	−	0.932790i	$-0.617367\pi$
$67$	−5.90035	−0.720843	−0.360421	+	0.932790i	$0.617367\pi$
$68$	3.50788	0.425393
$69$	13.2980	1.60089
$70$	0.200821	0.0240027
$71$	13.5345	1.60625	0.803123	−	0.595813i	$-0.203170\pi$
$71$	13.5345	1.60625	0.803123	+	0.595813i	$0.203170\pi$
$72$	2.10496	0.248072
$73$	8.97044	1.04991	0.524956	−	0.851130i	$-0.324082\pi$
$73$	8.97044	1.04991	0.524956	+	0.851130i	$0.324082\pi$
$74$	−1.37350	−0.159666
$75$	−11.2787	−1.30235
$76$	−1.00000	−0.114708
$77$	5.80082	0.661065
$78$	4.58261	0.518878
$79$	−7.84558	−0.882697	−0.441348	−	0.897336i	$-0.645500\pi$
$79$	−7.84558	−0.882697	−0.441348	+	0.897336i	$0.645500\pi$
$80$	0.0902706	0.0100926
$81$	−10.8840	−1.20934
$82$	3.84368	0.424463
$83$	−17.5772	−1.92934	−0.964672	−	0.263453i	$-0.915138\pi$
$83$	−17.5772	−1.92934	−0.964672	+	0.263453i	$0.915138\pi$
$84$	5.02642	0.548428
$85$	0.316659	0.0343465
$86$	−9.72990	−1.04920
$87$	16.1565	1.73216
$88$	2.60751	0.277962
$89$	12.1094	1.28360	0.641799	−	0.766873i	$-0.278188\pi$
$89$	12.1094	1.28360	0.641799	+	0.766873i	$0.278188\pi$
$90$	0.190016	0.0200295
$91$	4.51210	0.472997
$92$	5.88559	0.613615
$93$	−17.7090	−1.83634
$94$	10.7754	1.11139
$95$	−0.0902706	−0.00926157
$96$	2.25942	0.230601
$97$	−2.03035	−0.206151	−0.103076	−	0.994674i	$-0.532868\pi$
$97$	−2.03035	−0.206151	−0.103076	+	0.994674i	$0.532868\pi$
$98$	−2.05091	−0.207173
$99$	5.48872	0.551637
$100$	−4.99185	−0.499185
$101$	6.74726	0.671377	0.335689	−	0.941973i	$-0.391031\pi$
$101$	6.74726	0.671377	0.335689	+	0.941973i	$0.391031\pi$
$102$	7.92577	0.784768
$103$	1.91556	0.188746	0.0943731	−	0.995537i	$-0.469915\pi$
$103$	1.91556	0.188746	0.0943731	+	0.995537i	$0.469915\pi$
$104$	2.02823	0.198884
$105$	0.453738	0.0442803
$106$	−4.98609	−0.484292
$107$	−9.59386	−0.927473	−0.463737	−	0.885973i	$-0.653492\pi$
$107$	−9.59386	−0.927473	−0.463737	+	0.885973i	$0.653492\pi$
$108$	−2.02226	−0.194592
$109$	13.3896	1.28249	0.641244	−	0.767337i	$-0.278419\pi$
$109$	13.3896	1.28249	0.641244	+	0.767337i	$0.278419\pi$
$110$	0.235382	0.0224428
$111$	−3.10331	−0.294553
$112$	2.22465	0.210210
$113$	−17.6784	−1.66304	−0.831521	−	0.555493i	$-0.812529\pi$
$113$	−17.6784	−1.66304	−0.831521	+	0.555493i	$0.812529\pi$
$114$	−2.25942	−0.211614
$115$	0.531296	0.0495436
$116$	7.15073	0.663929
$117$	4.26934	0.394701
$118$	2.42721	0.223443
$119$	7.80383	0.715376
$120$	0.203959	0.0186188
$121$	−4.20087	−0.381897
$122$	−4.40040	−0.398393
$123$	8.68446	0.783052
$124$	−7.83786	−0.703861
$125$	−0.901971	−0.0806747
$126$	4.68282	0.417178
$127$	−7.40036	−0.656676	−0.328338	−	0.944560i	$-0.606488\pi$
$127$	−7.40036	−0.656676	−0.328338	+	0.944560i	$0.606488\pi$
$128$	1.00000	0.0883883
$129$	−21.9839	−1.93557
$130$	0.183089	0.0160580
$131$	11.6233	1.01554	0.507768	−	0.861494i	$-0.330471\pi$
$131$	11.6233	1.01554	0.507768	+	0.861494i	$0.330471\pi$
$132$	5.89146	0.512786
$133$	−2.22465	−0.192902
$134$	−5.90035	−0.509713
$135$	−0.182551	−0.0157115
$136$	3.50788	0.300798
$137$	14.7477	1.25998	0.629989	−	0.776604i	$-0.283060\pi$
$137$	14.7477	1.25998	0.629989	+	0.776604i	$0.283060\pi$
$138$	13.2980	1.13200
$139$	−15.0659	−1.27787	−0.638937	−	0.769259i	$-0.720626\pi$
$139$	−15.0659	−1.27787	−0.638937	+	0.769259i	$0.720626\pi$
$140$	0.200821	0.0169725
$141$	24.3460	2.05030
$142$	13.5345	1.13579
$143$	5.28863	0.442257
$144$	2.10496	0.175414
$145$	0.645501	0.0536060
$146$	8.97044	0.742399
$147$	−4.63386	−0.382195
$148$	−1.37350	−0.112901
$149$	−10.7412	−0.879950	−0.439975	−	0.898010i	$-0.645013\pi$
$149$	−10.7412	−0.879950	−0.439975	+	0.898010i	$0.645013\pi$
$150$	−11.2787	−0.920900
$151$	−14.0935	−1.14691	−0.573455	−	0.819237i	$-0.694397\pi$
$151$	−14.0935	−1.14691	−0.573455	+	0.819237i	$0.694397\pi$
$152$	−1.00000	−0.0811107
$153$	7.38396	0.596958
$154$	5.80082	0.467443
$155$	−0.707529	−0.0568301
$156$	4.58261	0.366902
$157$	−15.9873	−1.27593	−0.637964	−	0.770066i	$-0.720223\pi$
$157$	−15.9873	−1.27593	−0.637964	+	0.770066i	$0.720223\pi$
$158$	−7.84558	−0.624161
$159$	−11.2657	−0.893425
$160$	0.0902706	0.00713652
$161$	13.0934	1.03190
$162$	−10.8840	−0.855129
$163$	21.7470	1.70335	0.851677	−	0.524066i	$-0.175586\pi$
$163$	21.7470	1.70335	0.851677	+	0.524066i	$0.175586\pi$
$164$	3.84368	0.300141
$165$	0.531826	0.0414026
$166$	−17.5772	−1.36425
$167$	16.8866	1.30673	0.653364	−	0.757044i	$-0.273357\pi$
$167$	16.8866	1.30673	0.653364	+	0.757044i	$0.273357\pi$
$168$	5.02642	0.387797
$169$	−8.88630	−0.683562
$170$	0.316659	0.0242866
$171$	−2.10496	−0.160971
$172$	−9.72990	−0.741898
$173$	19.6347	1.49280	0.746398	−	0.665499i	$-0.231781\pi$
$173$	19.6347	1.49280	0.746398	+	0.665499i	$0.231781\pi$
$174$	16.1565	1.22482
$175$	−11.1051	−0.839470
$176$	2.60751	0.196549
$177$	5.48409	0.412209
$178$	12.1094	0.907641
$179$	−14.2096	−1.06208	−0.531039	−	0.847347i	$-0.678198\pi$
$179$	−14.2096	−1.06208	−0.531039	+	0.847347i	$0.678198\pi$
$180$	0.190016	0.0141630
$181$	5.54986	0.412518	0.206259	−	0.978497i	$-0.433871\pi$
$181$	5.54986	0.412518	0.206259	+	0.978497i	$0.433871\pi$
$182$	4.51210	0.334459
$183$	−9.94233	−0.734958
$184$	5.88559	0.433891
$185$	−0.123987	−0.00911568
$186$	−17.7090	−1.29849
$187$	9.14685	0.668884
$188$	10.7754	0.785874
$189$	−4.49883	−0.327242
$190$	−0.0902706	−0.00654892
$191$	−18.0829	−1.30844	−0.654218	−	0.756306i	$-0.727002\pi$
$191$	−18.0829	−1.30844	−0.654218	+	0.756306i	$0.727002\pi$
$192$	2.25942	0.163059
$193$	−3.90640	−0.281189	−0.140594	−	0.990067i	$-0.544901\pi$
$193$	−3.90640	−0.281189	−0.140594	+	0.990067i	$0.544901\pi$
$194$	−2.03035	−0.145771
$195$	0.413675	0.0296239
$196$	−2.05091	−0.146494
$197$	18.1239	1.29128	0.645638	−	0.763644i	$-0.276592\pi$
$197$	18.1239	1.29128	0.645638	+	0.763644i	$0.276592\pi$
$198$	5.48872	0.390066
$199$	−6.72459	−0.476694	−0.238347	−	0.971180i	$-0.576606\pi$
$199$	−6.72459	−0.476694	−0.238347	+	0.971180i	$0.576606\pi$
$200$	−4.99185	−0.352977
$201$	−13.3314	−0.940321
$202$	6.74726	0.474736
$203$	15.9079	1.11652
$204$	7.92577	0.554915
$205$	0.346971	0.0242335
$206$	1.91556	0.133464
$207$	12.3889	0.861091
$208$	2.02823	0.140632
$209$	−2.60751	−0.180366
$210$	0.453738	0.0313109
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−4.98609	−0.342446
$213$	30.5800	2.09531
$214$	−9.59386	−0.655823
$215$	−0.878325	−0.0599012
$216$	−2.02226	−0.137597
$217$	−17.4365	−1.18367
$218$	13.3896	0.906856
$219$	20.2680	1.36958
$220$	0.235382	0.0158695
$221$	7.11478	0.478592
$222$	−3.10331	−0.208280
$223$	−11.6739	−0.781743	−0.390871	−	0.920445i	$-0.627826\pi$
$223$	−11.6739	−0.781743	−0.390871	+	0.920445i	$0.627826\pi$
$224$	2.22465	0.148641
$225$	−10.5077	−0.700511
$226$	−17.6784	−1.17595
$227$	11.1124	0.737559	0.368779	−	0.929517i	$-0.379776\pi$
$227$	11.1124	0.737559	0.368779	+	0.929517i	$0.379776\pi$
$228$	−2.25942	−0.149634
$229$	8.09159	0.534708	0.267354	−	0.963598i	$-0.413851\pi$
$229$	8.09159	0.534708	0.267354	+	0.963598i	$0.413851\pi$
$230$	0.531296	0.0350326
$231$	13.1065	0.862342
$232$	7.15073	0.469469
$233$	22.0024	1.44142	0.720712	−	0.693234i	$-0.243815\pi$
$233$	22.0024	1.44142	0.720712	+	0.693234i	$0.243815\pi$
$234$	4.26934	0.279095
$235$	0.972698	0.0634518
$236$	2.42721	0.157998
$237$	−17.7264	−1.15146
$238$	7.80383	0.505847
$239$	−24.7619	−1.60171	−0.800857	−	0.598856i	$-0.795622\pi$
$239$	−24.7619	−1.60171	−0.800857	+	0.598856i	$0.795622\pi$
$240$	0.203959	0.0131655
$241$	−1.67957	−0.108191	−0.0540953	−	0.998536i	$-0.517227\pi$
$241$	−1.67957	−0.108191	−0.0540953	+	0.998536i	$0.517227\pi$
$242$	−4.20087	−0.270042
$243$	−18.5247	−1.18836
$244$	−4.40040	−0.281706
$245$	−0.185137	−0.0118280
$246$	8.68446	0.553701
$247$	−2.02823	−0.129053
$248$	−7.83786	−0.497705
$249$	−39.7141	−2.51678
$250$	−0.901971	−0.0570456
$251$	2.91526	0.184009	0.0920047	−	0.995759i	$-0.470673\pi$
$251$	2.91526	0.184009	0.0920047	+	0.995759i	$0.470673\pi$
$252$	4.68282	0.294990
$253$	15.3468	0.964842
$254$	−7.40036	−0.464340
$255$	0.715464	0.0448041
$256$	1.00000	0.0625000
$257$	−9.05942	−0.565111	−0.282556	−	0.959251i	$-0.591182\pi$
$257$	−9.05942	−0.565111	−0.282556	+	0.959251i	$0.591182\pi$
$258$	−21.9839	−1.36866
$259$	−3.05556	−0.189863
$260$	0.183089	0.0113547
$261$	15.0520	0.931697
$262$	11.6233	0.718092
$263$	13.0750	0.806242	0.403121	−	0.915147i	$-0.367925\pi$
$263$	13.0750	0.806242	0.403121	+	0.915147i	$0.367925\pi$
$264$	5.89146	0.362594
$265$	−0.450098	−0.0276493
$266$	−2.22465	−0.136402
$267$	27.3603	1.67442
$268$	−5.90035	−0.360421
$269$	2.09350	0.127643	0.0638214	−	0.997961i	$-0.479671\pi$
$269$	2.09350	0.127643	0.0638214	+	0.997961i	$0.479671\pi$
$270$	−0.182551	−0.0111097
$271$	7.83039	0.475663	0.237831	−	0.971306i	$-0.423563\pi$
$271$	7.83039	0.475663	0.237831	+	0.971306i	$0.423563\pi$
$272$	3.50788	0.212697
$273$	10.1947	0.617012
$274$	14.7477	0.890939
$275$	−13.0163	−0.784914
$276$	13.2980	0.800445
$277$	19.9567	1.19908	0.599542	−	0.800343i	$-0.295349\pi$
$277$	19.9567	1.19908	0.599542	+	0.800343i	$0.295349\pi$
$278$	−15.0659	−0.903594
$279$	−16.4984	−0.987734
$280$	0.200821	0.0120013
$281$	6.30044	0.375853	0.187926	−	0.982183i	$-0.439823\pi$
$281$	6.30044	0.375853	0.187926	+	0.982183i	$0.439823\pi$
$282$	24.3460	1.44978
$283$	2.19290	0.130354	0.0651772	−	0.997874i	$-0.479239\pi$
$283$	2.19290	0.130354	0.0651772	+	0.997874i	$0.479239\pi$
$284$	13.5345	0.803123
$285$	−0.203959	−0.0120815
$286$	5.28863	0.312723
$287$	8.55085	0.504741
$288$	2.10496	0.124036
$289$	−4.69476	−0.276163
$290$	0.645501	0.0379051
$291$	−4.58742	−0.268919
$292$	8.97044	0.524956
$293$	−0.515351	−0.0301071	−0.0150536	−	0.999887i	$-0.504792\pi$
$293$	−0.515351	−0.0301071	−0.0150536	+	0.999887i	$0.504792\pi$
$294$	−4.63386	−0.270252
$295$	0.219106	0.0127569
$296$	−1.37350	−0.0798330
$297$	−5.27308	−0.305975
$298$	−10.7412	−0.622219
$299$	11.9373	0.690352
$300$	−11.2787	−0.651174
$301$	−21.6457	−1.24764
$302$	−14.0935	−0.810988
$303$	15.2449	0.875795
$304$	−1.00000	−0.0573539
$305$	−0.397227	−0.0227451
$306$	7.38396	0.422113
$307$	25.5391	1.45760	0.728798	−	0.684729i	$-0.240079\pi$
$307$	25.5391	1.45760	0.728798	+	0.684729i	$0.240079\pi$
$308$	5.80082	0.330532
$309$	4.32806	0.246215
$310$	−0.707529	−0.0401849
$311$	−15.8495	−0.898742	−0.449371	−	0.893345i	$-0.648352\pi$
$311$	−15.8495	−0.898742	−0.449371	+	0.893345i	$0.648352\pi$
$312$	4.58261	0.259439
$313$	−8.46397	−0.478412	−0.239206	−	0.970969i	$-0.576887\pi$
$313$	−8.46397	−0.478412	−0.239206	+	0.970969i	$0.576887\pi$
$314$	−15.9873	−0.902217
$315$	0.422721	0.0238176
$316$	−7.84558	−0.441348
$317$	−14.4383	−0.810935	−0.405468	−	0.914109i	$-0.632891\pi$
$317$	−14.4383	−0.810935	−0.405468	+	0.914109i	$0.632891\pi$
$318$	−11.2657	−0.631747
$319$	18.6456	1.04396
$320$	0.0902706	0.00504628
$321$	−21.6765	−1.20987
$322$	13.0934	0.729667
$323$	−3.50788	−0.195184
$324$	−10.8840	−0.604668
$325$	−10.1246	−0.561612
$326$	21.7470	1.20445
$327$	30.2526	1.67297
$328$	3.84368	0.212232
$329$	23.9714	1.32159
$330$	0.531826	0.0292761
$331$	22.1360	1.21671	0.608354	−	0.793666i	$-0.291830\pi$
$331$	22.1360	1.21671	0.608354	+	0.793666i	$0.291830\pi$
$332$	−17.5772	−0.964672
$333$	−2.89116	−0.158435
$334$	16.8866	0.923996
$335$	−0.532628	−0.0291006
$336$	5.02642	0.274214
$337$	−24.4518	−1.33197	−0.665987	−	0.745964i	$-0.731989\pi$
$337$	−24.4518	−1.33197	−0.665987	+	0.745964i	$0.731989\pi$
$338$	−8.88630	−0.483351
$339$	−39.9428	−2.16940
$340$	0.316659	0.0171732
$341$	−20.4373	−1.10674
$342$	−2.10496	−0.113823
$343$	−20.1352	−1.08720
$344$	−9.72990	−0.524601
$345$	1.20042	0.0646283
$346$	19.6347	1.05557
$347$	−19.4337	−1.04325	−0.521627	−	0.853173i	$-0.674675\pi$
$347$	−19.4337	−1.04325	−0.521627	+	0.853173i	$0.674675\pi$
$348$	16.1565	0.866078
$349$	22.9166	1.22670	0.613349	−	0.789812i	$-0.289822\pi$
$349$	22.9166	1.22670	0.613349	+	0.789812i	$0.289822\pi$
$350$	−11.1051	−0.593595
$351$	−4.10160	−0.218927
$352$	2.60751	0.138981
$353$	10.9133	0.580858	0.290429	−	0.956896i	$-0.406202\pi$
$353$	10.9133	0.580858	0.290429	+	0.956896i	$0.406202\pi$
$354$	5.48409	0.291476
$355$	1.22177	0.0648446
$356$	12.1094	0.641799
$357$	17.6321	0.933189
$358$	−14.2096	−0.751002
$359$	7.93088	0.418576	0.209288	−	0.977854i	$-0.432885\pi$
$359$	7.93088	0.418576	0.209288	+	0.977854i	$0.432885\pi$
$360$	0.190016	0.0100147
$361$	1.00000	0.0526316
$362$	5.54986	0.291694
$363$	−9.49151	−0.498175
$364$	4.51210	0.236498
$365$	0.809768	0.0423852
$366$	−9.94233	−0.519694
$367$	−14.5912	−0.761655	−0.380828	−	0.924646i	$-0.624361\pi$
$367$	−14.5912	−0.761655	−0.380828	+	0.924646i	$0.624361\pi$
$368$	5.88559	0.306807
$369$	8.09079	0.421190
$370$	−0.123987	−0.00644576
$371$	−11.0923	−0.575885
$372$	−17.7090	−0.918169
$373$	−17.5135	−0.906816	−0.453408	−	0.891303i	$-0.649792\pi$
$373$	−17.5135	−0.906816	−0.453408	+	0.891303i	$0.649792\pi$
$374$	9.14685	0.472973
$375$	−2.03793	−0.105238
$376$	10.7754	0.555697
$377$	14.5033	0.746958
$378$	−4.49883	−0.231395
$379$	35.8735	1.84270	0.921348	−	0.388739i	$-0.127089\pi$
$379$	35.8735	1.84270	0.921348	+	0.388739i	$0.127089\pi$
$380$	−0.0902706	−0.00463079
$381$	−16.7205	−0.856617
$382$	−18.0829	−0.925203
$383$	−8.31301	−0.424775	−0.212388	−	0.977186i	$-0.568124\pi$
$383$	−8.31301	−0.424775	−0.212388	+	0.977186i	$0.568124\pi$
$384$	2.25942	0.115300
$385$	0.523644	0.0266874
$386$	−3.90640	−0.198831
$387$	−20.4811	−1.04111
$388$	−2.03035	−0.103076
$389$	−7.39014	−0.374695	−0.187348	−	0.982294i	$-0.559989\pi$
$389$	−7.39014	−0.374695	−0.187348	+	0.982294i	$0.559989\pi$
$390$	0.413675	0.0209472
$391$	20.6459	1.04411
$392$	−2.05091	−0.103587
$393$	26.2620	1.32474
$394$	18.1239	0.913070
$395$	−0.708226	−0.0356347
$396$	5.48872	0.275819
$397$	18.3727	0.922099	0.461050	−	0.887374i	$-0.347473\pi$
$397$	18.3727	0.922099	0.461050	+	0.887374i	$0.347473\pi$
$398$	−6.72459	−0.337073
$399$	−5.02642	−0.251636
$400$	−4.99185	−0.249593
$401$	−23.2817	−1.16263	−0.581315	−	0.813678i	$-0.697462\pi$
$401$	−23.2817	−1.16263	−0.581315	+	0.813678i	$0.697462\pi$
$402$	−13.3314	−0.664907
$403$	−15.8970	−0.791884
$404$	6.74726	0.335689
$405$	−0.982507	−0.0488212
$406$	15.9079	0.789496
$407$	−3.58142	−0.177524
$408$	7.92577	0.392384
$409$	32.3433	1.59927	0.799636	−	0.600485i	$-0.205026\pi$
$409$	32.3433	1.59927	0.799636	+	0.600485i	$0.205026\pi$
$410$	0.346971	0.0171357
$411$	33.3211	1.64361
$412$	1.91556	0.0943731
$413$	5.39971	0.265703
$414$	12.3889	0.608883
$415$	−1.58670	−0.0778881
$416$	2.02823	0.0994420
$417$	−34.0402	−1.66695
$418$	−2.60751	−0.127538
$419$	−9.36686	−0.457601	−0.228801	−	0.973473i	$-0.573480\pi$
$419$	−9.36686	−0.457601	−0.228801	+	0.973473i	$0.573480\pi$
$420$	0.453738	0.0221402
$421$	−26.6508	−1.29888	−0.649441	−	0.760412i	$-0.724997\pi$
$421$	−26.6508	−1.29888	−0.649441	+	0.760412i	$0.724997\pi$
$422$	−1.00000	−0.0486792
$423$	22.6817	1.10282
$424$	−4.98609	−0.242146
$425$	−17.5108	−0.849400
$426$	30.5800	1.48161
$427$	−9.78936	−0.473740
$428$	−9.59386	−0.463737
$429$	11.9492	0.576914
$430$	−0.878325	−0.0423566
$431$	25.1619	1.21201	0.606004	−	0.795461i	$-0.292771\pi$
$431$	25.1619	1.21201	0.606004	+	0.795461i	$0.292771\pi$
$432$	−2.02226	−0.0972961
$433$	−22.9539	−1.10310	−0.551548	−	0.834143i	$-0.685963\pi$
$433$	−22.9539	−1.10310	−0.551548	+	0.834143i	$0.685963\pi$
$434$	−17.4365	−0.836981
$435$	1.45846	0.0699276
$436$	13.3896	0.641244
$437$	−5.88559	−0.281546
$438$	20.2680	0.968441
$439$	11.8546	0.565787	0.282894	−	0.959151i	$-0.408706\pi$
$439$	11.8546	0.565787	0.282894	+	0.959151i	$0.408706\pi$
$440$	0.235382	0.0112214
$441$	−4.31709	−0.205576
$442$	7.11478	0.338415
$443$	38.4433	1.82649	0.913247	−	0.407406i	$-0.133567\pi$
$443$	38.4433	1.82649	0.913247	+	0.407406i	$0.133567\pi$
$444$	−3.10331	−0.147276
$445$	1.09313	0.0518192
$446$	−11.6739	−0.552776
$447$	−24.2687	−1.14787
$448$	2.22465	0.105105
$449$	−34.9689	−1.65029	−0.825143	−	0.564924i	$-0.808905\pi$
$449$	−34.9689	−1.65029	−0.825143	+	0.564924i	$0.808905\pi$
$450$	−10.5077	−0.495336
$451$	10.0224	0.471938
$452$	−17.6784	−0.831521
$453$	−31.8430	−1.49611
$454$	11.1124	0.521533
$455$	0.407310	0.0190950
$456$	−2.25942	−0.105807
$457$	−9.72999	−0.455150	−0.227575	−	0.973761i	$-0.573080\pi$
$457$	−9.72999	−0.455150	−0.227575	+	0.973761i	$0.573080\pi$
$458$	8.09159	0.378095
$459$	−7.09386	−0.331113
$460$	0.531296	0.0247718
$461$	−5.12953	−0.238906	−0.119453	−	0.992840i	$-0.538114\pi$
$461$	−5.12953	−0.238906	−0.119453	+	0.992840i	$0.538114\pi$
$462$	13.1065	0.609768
$463$	25.1190	1.16738	0.583690	−	0.811976i	$-0.301608\pi$
$463$	25.1190	1.16738	0.583690	+	0.811976i	$0.301608\pi$
$464$	7.15073	0.331964
$465$	−1.59860	−0.0741334
$466$	22.0024	1.01924
$467$	−32.8875	−1.52185	−0.760927	−	0.648838i	$-0.775255\pi$
$467$	−32.8875	−1.52185	−0.760927	+	0.648838i	$0.775255\pi$
$468$	4.26934	0.197350
$469$	−13.1262	−0.606114
$470$	0.972698	0.0448672
$471$	−36.1220	−1.66442
$472$	2.42721	0.111722
$473$	−25.3709	−1.16655
$474$	−17.7264	−0.814202
$475$	4.99185	0.229042
$476$	7.80383	0.357688
$477$	−10.4955	−0.480558
$478$	−24.7619	−1.13258
$479$	−36.5814	−1.67145	−0.835724	−	0.549150i	$-0.814952\pi$
$479$	−36.5814	−1.67145	−0.835724	+	0.549150i	$0.814952\pi$
$480$	0.203959	0.00930941
$481$	−2.78577	−0.127020
$482$	−1.67957	−0.0765023
$483$	29.5834	1.34609
$484$	−4.20087	−0.190948
$485$	−0.183281	−0.00832238
$486$	−18.5247	−0.840300
$487$	12.6761	0.574409	0.287204	−	0.957869i	$-0.407274\pi$
$487$	12.6761	0.574409	0.287204	+	0.957869i	$0.407274\pi$
$488$	−4.40040	−0.199197
$489$	49.1355	2.22198
$490$	−0.185137	−0.00836364
$491$	−6.99828	−0.315828	−0.157914	−	0.987453i	$-0.550477\pi$
$491$	−6.99828	−0.315828	−0.157914	+	0.987453i	$0.550477\pi$
$492$	8.68446	0.391526
$493$	25.0839	1.12972
$494$	−2.02823	−0.0912542
$495$	0.495470	0.0222697
$496$	−7.83786	−0.351930
$497$	30.1095	1.35060
$498$	−39.7141	−1.77963
$499$	−0.547395	−0.0245048	−0.0122524	−	0.999925i	$-0.503900\pi$
$499$	−0.547395	−0.0245048	−0.0122524	+	0.999925i	$0.503900\pi$
$500$	−0.901971	−0.0403374
$501$	38.1540	1.70459
$502$	2.91526	0.130114
$503$	−20.3560	−0.907629	−0.453814	−	0.891096i	$-0.649937\pi$
$503$	−20.3560	−0.907629	−0.453814	+	0.891096i	$0.649937\pi$
$504$	4.68282	0.208589
$505$	0.609079	0.0271037
$506$	15.3468	0.682246
$507$	−20.0779	−0.891689
$508$	−7.40036	−0.328338
$509$	26.5495	1.17679	0.588394	−	0.808575i	$-0.299761\pi$
$509$	26.5495	1.17679	0.588394	+	0.808575i	$0.299761\pi$
$510$	0.715464	0.0316813
$511$	19.9561	0.882808
$512$	1.00000	0.0441942
$513$	2.02226	0.0892850
$514$	−9.05942	−0.399594
$515$	0.172919	0.00761973
$516$	−21.9839	−0.967787
$517$	28.0969	1.23570
$518$	−3.05556	−0.134254
$519$	44.3629	1.94732
$520$	0.183089	0.00802899
$521$	−13.4950	−0.591226	−0.295613	−	0.955308i	$-0.595524\pi$
$521$	−13.4950	−0.591226	−0.295613	+	0.955308i	$0.595524\pi$
$522$	15.0520	0.658809
$523$	−3.34856	−0.146422	−0.0732112	−	0.997316i	$-0.523325\pi$
$523$	−3.34856	−0.146422	−0.0732112	+	0.997316i	$0.523325\pi$
$524$	11.6233	0.507768
$525$	−25.0911	−1.09507
$526$	13.0750	0.570099
$527$	−27.4943	−1.19767
$528$	5.89146	0.256393
$529$	11.6401	0.506093
$530$	−0.450098	−0.0195510
$531$	5.10920	0.221720
$532$	−2.22465	−0.0964510
$533$	7.79584	0.337675
$534$	27.3603	1.18400
$535$	−0.866044	−0.0374423
$536$	−5.90035	−0.254856
$537$	−32.1055	−1.38545
$538$	2.09350	0.0902570
$539$	−5.34778	−0.230345
$540$	−0.182551	−0.00785574
$541$	−15.2659	−0.656332	−0.328166	−	0.944620i	$-0.606431\pi$
$541$	−15.2659	−0.656332	−0.328166	+	0.944620i	$0.606431\pi$
$542$	7.83039	0.336344
$543$	12.5394	0.538119
$544$	3.50788	0.150399
$545$	1.20869	0.0517744
$546$	10.1947	0.436294
$547$	−11.5390	−0.493371	−0.246685	−	0.969096i	$-0.579341\pi$
$547$	−11.5390	−0.493371	−0.246685	+	0.969096i	$0.579341\pi$
$548$	14.7477	0.629989
$549$	−9.26267	−0.395321
$550$	−13.0163	−0.555018
$551$	−7.15073	−0.304631
$552$	13.2980	0.566000
$553$	−17.4537	−0.742207
$554$	19.9567	0.847880
$555$	−0.280137	−0.0118912
$556$	−15.0659	−0.638937
$557$	−25.5639	−1.08318	−0.541590	−	0.840643i	$-0.682177\pi$
$557$	−25.5639	−1.08318	−0.541590	+	0.840643i	$0.682177\pi$
$558$	−16.4984	−0.698433
$559$	−19.7344	−0.834678
$560$	0.200821	0.00848624
$561$	20.6666	0.872543
$562$	6.30044	0.265768
$563$	23.2496	0.979852	0.489926	−	0.871764i	$-0.337024\pi$
$563$	23.2496	0.979852	0.489926	+	0.871764i	$0.337024\pi$
$564$	24.3460	1.02515
$565$	−1.59584	−0.0671374
$566$	2.19290	0.0921745
$567$	−24.2132	−1.01686
$568$	13.5345	0.567894
$569$	30.7441	1.28886	0.644429	−	0.764664i	$-0.277095\pi$
$569$	30.7441	1.28886	0.644429	+	0.764664i	$0.277095\pi$
$570$	−0.203959	−0.00854290
$571$	15.7927	0.660903	0.330451	−	0.943823i	$-0.392799\pi$
$571$	15.7927	0.660903	0.330451	+	0.943823i	$0.392799\pi$
$572$	5.28863	0.221129
$573$	−40.8569	−1.70682
$574$	8.55085	0.356906
$575$	−29.3800	−1.22523
$576$	2.10496	0.0877068
$577$	1.39862	0.0582252	0.0291126	−	0.999576i	$-0.490732\pi$
$577$	1.39862	0.0582252	0.0291126	+	0.999576i	$0.490732\pi$
$578$	−4.69476	−0.195276
$579$	−8.82619	−0.366804
$580$	0.645501	0.0268030
$581$	−39.1031	−1.62227
$582$	−4.58742	−0.190155
$583$	−13.0013	−0.538459
$584$	8.97044	0.371200
$585$	0.385396	0.0159342
$586$	−0.515351	−0.0212890
$587$	18.3430	0.757098	0.378549	−	0.925581i	$-0.376423\pi$
$587$	18.3430	0.757098	0.378549	+	0.925581i	$0.376423\pi$
$588$	−4.63386	−0.191097
$589$	7.83786	0.322953
$590$	0.219106	0.00902046
$591$	40.9495	1.68444
$592$	−1.37350	−0.0564505
$593$	26.0198	1.06850	0.534252	−	0.845325i	$-0.320593\pi$
$593$	26.0198	1.06850	0.534252	+	0.845325i	$0.320593\pi$
$594$	−5.27308	−0.216357
$595$	0.704456	0.0288799
$596$	−10.7412	−0.439975
$597$	−15.1937	−0.621835
$598$	11.9373	0.488152
$599$	3.65909	0.149506	0.0747531	−	0.997202i	$-0.476183\pi$
$599$	3.65909	0.149506	0.0747531	+	0.997202i	$0.476183\pi$
$600$	−11.2787	−0.460450
$601$	−37.2415	−1.51911	−0.759557	−	0.650441i	$-0.774584\pi$
$601$	−37.2415	−1.51911	−0.759557	+	0.650441i	$0.774584\pi$
$602$	−21.6457	−0.882212
$603$	−12.4200	−0.505782
$604$	−14.0935	−0.573455
$605$	−0.379215	−0.0154173
$606$	15.2449	0.619280
$607$	22.2378	0.902603	0.451301	−	0.892372i	$-0.350960\pi$
$607$	22.2378	0.902603	0.451301	+	0.892372i	$0.350960\pi$
$608$	−1.00000	−0.0405554
$609$	35.9426	1.45647
$610$	−0.397227	−0.0160832
$611$	21.8549	0.884153
$612$	7.38396	0.298479
$613$	34.4373	1.39091	0.695454	−	0.718571i	$-0.255203\pi$
$613$	34.4373	1.39091	0.695454	+	0.718571i	$0.255203\pi$
$614$	25.5391	1.03068
$615$	0.783952	0.0316120
$616$	5.80082	0.233722
$617$	−16.7676	−0.675036	−0.337518	−	0.941319i	$-0.609587\pi$
$617$	−16.7676	−0.675036	−0.337518	+	0.941319i	$0.609587\pi$
$618$	4.32806	0.174100
$619$	30.1822	1.21313	0.606563	−	0.795035i	$-0.292548\pi$
$619$	30.1822	1.21313	0.606563	+	0.795035i	$0.292548\pi$
$620$	−0.707529	−0.0284150
$621$	−11.9022	−0.477619
$622$	−15.8495	−0.635507
$623$	26.9393	1.07930
$624$	4.58261	0.183451
$625$	24.8778	0.995113
$626$	−8.46397	−0.338288
$627$	−5.89146	−0.235282
$628$	−15.9873	−0.637964
$629$	−4.81807	−0.192109
$630$	0.422721	0.0168416
$631$	21.4634	0.854443	0.427221	−	0.904147i	$-0.359492\pi$
$631$	21.4634	0.854443	0.427221	+	0.904147i	$0.359492\pi$
$632$	−7.84558	−0.312080
$633$	−2.25942	−0.0898037
$634$	−14.4383	−0.573418
$635$	−0.668035	−0.0265102
$636$	−11.2657	−0.446712
$637$	−4.15971	−0.164814
$638$	18.6456	0.738188
$639$	28.4896	1.12703
$640$	0.0902706	0.00356826
$641$	29.5010	1.16522	0.582609	−	0.812753i	$-0.302032\pi$
$641$	29.5010	1.16522	0.582609	+	0.812753i	$0.302032\pi$
$642$	−21.6765	−0.855504
$643$	−45.0297	−1.77580	−0.887899	−	0.460039i	$-0.847836\pi$
$643$	−45.0297	−1.77580	−0.887899	+	0.460039i	$0.847836\pi$
$644$	13.0934	0.515952
$645$	−1.98450	−0.0781396
$646$	−3.50788	−0.138016
$647$	−12.3455	−0.485351	−0.242676	−	0.970108i	$-0.578025\pi$
$647$	−12.3455	−0.485351	−0.242676	+	0.970108i	$0.578025\pi$
$648$	−10.8840	−0.427565
$649$	6.32900	0.248435
$650$	−10.1246	−0.397120
$651$	−39.3964	−1.54407
$652$	21.7470	0.851677
$653$	−2.92487	−0.114459	−0.0572295	−	0.998361i	$-0.518227\pi$
$653$	−2.92487	−0.114459	−0.0572295	+	0.998361i	$0.518227\pi$
$654$	30.2526	1.18297
$655$	1.04925	0.0409974
$656$	3.84368	0.150070
$657$	18.8824	0.736675
$658$	23.9714	0.934504
$659$	−36.9622	−1.43984	−0.719921	−	0.694056i	$-0.755822\pi$
$659$	−36.9622	−1.43984	−0.719921	+	0.694056i	$0.755822\pi$
$660$	0.531826	0.0207013
$661$	−20.7826	−0.808350	−0.404175	−	0.914682i	$-0.632441\pi$
$661$	−20.7826	−0.808350	−0.404175	+	0.914682i	$0.632441\pi$
$662$	22.1360	0.860342
$663$	16.0752	0.624311
$664$	−17.5772	−0.682126
$665$	−0.200821	−0.00778750
$666$	−2.89116	−0.112030
$667$	42.0863	1.62959
$668$	16.8866	0.653364
$669$	−26.3762	−1.01976
$670$	−0.532628	−0.0205772
$671$	−11.4741	−0.442953
$672$	5.02642	0.193898
$673$	−30.3515	−1.16996	−0.584982	−	0.811046i	$-0.698899\pi$
$673$	−30.3515	−1.16996	−0.584982	+	0.811046i	$0.698899\pi$
$674$	−24.4518	−0.941847
$675$	10.0948	0.388550
$676$	−8.88630	−0.341781
$677$	−17.9175	−0.688626	−0.344313	−	0.938855i	$-0.611888\pi$
$677$	−17.9175	−0.688626	−0.344313	+	0.938855i	$0.611888\pi$
$678$	−39.9428	−1.53399
$679$	−4.51684	−0.173340
$680$	0.316659	0.0121433
$681$	25.1076	0.962127
$682$	−20.4373	−0.782586
$683$	−8.19568	−0.313599	−0.156800	−	0.987630i	$-0.550118\pi$
$683$	−8.19568	−0.313599	−0.156800	+	0.987630i	$0.550118\pi$
$684$	−2.10496	−0.0804853
$685$	1.33128	0.0508656
$686$	−20.1352	−0.768764
$687$	18.2823	0.697513
$688$	−9.72990	−0.370949
$689$	−10.1129	−0.385272
$690$	1.20042	0.0456991
$691$	−19.8564	−0.755375	−0.377687	−	0.925933i	$-0.623281\pi$
$691$	−19.8564	−0.755375	−0.377687	+	0.925933i	$0.623281\pi$
$692$	19.6347	0.746398
$693$	12.2105	0.463839
$694$	−19.4337	−0.737693
$695$	−1.36001	−0.0515881
$696$	16.1565	0.612410
$697$	13.4832	0.510711
$698$	22.9166	0.867407
$699$	49.7126	1.88030
$700$	−11.1051	−0.419735
$701$	−52.4909	−1.98255	−0.991277	−	0.131793i	$-0.957927\pi$
$701$	−52.4909	−1.98255	−0.991277	+	0.131793i	$0.957927\pi$
$702$	−4.10160	−0.154805
$703$	1.37350	0.0518025
$704$	2.60751	0.0982744
$705$	2.19773	0.0827713
$706$	10.9133	0.410729
$707$	15.0103	0.564521
$708$	5.48409	0.206105
$709$	−26.2064	−0.984203	−0.492102	−	0.870538i	$-0.663771\pi$
$709$	−26.2064	−0.984203	−0.492102	+	0.870538i	$0.663771\pi$
$710$	1.22177	0.0458520
$711$	−16.5147	−0.619348
$712$	12.1094	0.453821
$713$	−46.1304	−1.72760
$714$	17.6321	0.659864
$715$	0.477408	0.0178540
$716$	−14.2096	−0.531039
$717$	−55.9474	−2.08939
$718$	7.93088	0.295978
$719$	−34.0421	−1.26956	−0.634779	−	0.772694i	$-0.718909\pi$
$719$	−34.0421	−1.26956	−0.634779	+	0.772694i	$0.718909\pi$
$720$	0.190016	0.00708149
$721$	4.26147	0.158705
$722$	1.00000	0.0372161
$723$	−3.79485	−0.141132
$724$	5.54986	0.206259
$725$	−35.6954	−1.32569
$726$	−9.49151	−0.352263
$727$	−9.62996	−0.357155	−0.178578	−	0.983926i	$-0.557150\pi$
$727$	−9.62996	−0.357155	−0.178578	+	0.983926i	$0.557150\pi$
$728$	4.51210	0.167230
$729$	−9.20306	−0.340854
$730$	0.809768	0.0299708
$731$	−34.1314	−1.26239
$732$	−9.94233	−0.367479
$733$	−24.1390	−0.891593	−0.445797	−	0.895134i	$-0.647080\pi$
$733$	−24.1390	−0.891593	−0.445797	+	0.895134i	$0.647080\pi$
$734$	−14.5912	−0.538571
$735$	−0.418302	−0.0154293
$736$	5.88559	0.216946
$737$	−15.3853	−0.566723
$738$	8.09079	0.297826
$739$	13.7484	0.505744	0.252872	−	0.967500i	$-0.418625\pi$
$739$	13.7484	0.505744	0.252872	+	0.967500i	$0.418625\pi$
$740$	−0.123987	−0.00455784
$741$	−4.58261	−0.168346
$742$	−11.0923	−0.407212
$743$	14.7865	0.542463	0.271232	−	0.962514i	$-0.412569\pi$
$743$	14.7865	0.542463	0.271232	+	0.962514i	$0.412569\pi$
$744$	−17.7090	−0.649243
$745$	−0.969611	−0.0355238
$746$	−17.5135	−0.641216
$747$	−36.9993	−1.35373
$748$	9.14685	0.334442
$749$	−21.3430	−0.779857
$750$	−2.03793	−0.0744146
$751$	−8.06576	−0.294324	−0.147162	−	0.989112i	$-0.547014\pi$
$751$	−8.06576	−0.294324	−0.147162	+	0.989112i	$0.547014\pi$
$752$	10.7754	0.392937
$753$	6.58678	0.240036
$754$	14.5033	0.528179
$755$	−1.27223	−0.0463010
$756$	−4.49883	−0.163621
$757$	−23.9506	−0.870499	−0.435249	−	0.900310i	$-0.643340\pi$
$757$	−23.9506	−0.870499	−0.435249	+	0.900310i	$0.643340\pi$
$758$	35.8735	1.30298
$759$	34.6747	1.25861
$760$	−0.0902706	−0.00327446
$761$	38.8034	1.40662	0.703311	−	0.710883i	$-0.251704\pi$
$761$	38.8034	1.40662	0.703311	+	0.710883i	$0.251704\pi$
$762$	−16.7205	−0.605719
$763$	29.7872	1.07837
$764$	−18.0829	−0.654218
$765$	0.666555	0.0240993
$766$	−8.31301	−0.300361
$767$	4.92294	0.177757
$768$	2.25942	0.0815297
$769$	−10.0388	−0.362010	−0.181005	−	0.983482i	$-0.557935\pi$
$769$	−10.0388	−0.362010	−0.181005	+	0.983482i	$0.557935\pi$
$770$	0.523644	0.0188708
$771$	−20.4690	−0.737173
$772$	−3.90640	−0.140594
$773$	−1.32912	−0.0478052	−0.0239026	−	0.999714i	$-0.507609\pi$
$773$	−1.32912	−0.0478052	−0.0239026	+	0.999714i	$0.507609\pi$
$774$	−20.4811	−0.736177
$775$	39.1254	1.40543
$776$	−2.03035	−0.0728855
$777$	−6.90378	−0.247672
$778$	−7.39014	−0.264949
$779$	−3.84368	−0.137714
$780$	0.413675	0.0148119
$781$	35.2913	1.26282
$782$	20.6459	0.738297
$783$	−14.4607	−0.516782
$784$	−2.05091	−0.0732468
$785$	−1.44319	−0.0515095
$786$	26.2620	0.936733
$787$	−27.2763	−0.972296	−0.486148	−	0.873876i	$-0.661598\pi$
$787$	−27.2763	−0.972296	−0.486148	+	0.873876i	$0.661598\pi$
$788$	18.1239	0.645638
$789$	29.5420	1.05172
$790$	−0.708226	−0.0251975
$791$	−39.3283	−1.39835
$792$	5.48872	0.195033
$793$	−8.92500	−0.316936
$794$	18.3727	0.652023
$795$	−1.01696	−0.0360678
$796$	−6.72459	−0.238347
$797$	−24.5622	−0.870037	−0.435018	−	0.900422i	$-0.643258\pi$
$797$	−24.5622	−0.870037	−0.435018	+	0.900422i	$0.643258\pi$
$798$	−5.02642	−0.177933
$799$	37.7987	1.33722
$800$	−4.99185	−0.176489
$801$	25.4899	0.900643
$802$	−23.2817	−0.822104
$803$	23.3906	0.825435
$804$	−13.3314	−0.470160
$805$	1.18195	0.0416582
$806$	−15.8970	−0.559946
$807$	4.73008	0.166507
$808$	6.74726	0.237368
$809$	41.6308	1.46366	0.731830	−	0.681488i	$-0.238667\pi$
$809$	41.6308	1.46366	0.731830	+	0.681488i	$0.238667\pi$
$810$	−0.982507	−0.0345218
$811$	−11.0581	−0.388303	−0.194152	−	0.980972i	$-0.562195\pi$
$811$	−11.0581	−0.388303	−0.194152	+	0.980972i	$0.562195\pi$
$812$	15.9079	0.558258
$813$	17.6921	0.620490
$814$	−3.58142	−0.125529
$815$	1.96311	0.0687649
$816$	7.92577	0.277457
$817$	9.72990	0.340406
$818$	32.3433	1.13086
$819$	9.49781	0.331880
$820$	0.346971	0.0121168
$821$	−37.4344	−1.30647	−0.653234	−	0.757156i	$-0.726588\pi$
$821$	−37.4344	−1.30647	−0.653234	+	0.757156i	$0.726588\pi$
$822$	33.3211	1.16221
$823$	−10.9793	−0.382715	−0.191357	−	0.981520i	$-0.561289\pi$
$823$	−10.9793	−0.382715	−0.191357	+	0.981520i	$0.561289\pi$
$824$	1.91556	0.0667318
$825$	−29.4093	−1.02390
$826$	5.39971	0.187880
$827$	6.01005	0.208990	0.104495	−	0.994525i	$-0.466677\pi$
$827$	6.01005	0.208990	0.104495	+	0.994525i	$0.466677\pi$
$828$	12.3889	0.430545
$829$	16.5815	0.575898	0.287949	−	0.957646i	$-0.407027\pi$
$829$	16.5815	0.575898	0.287949	+	0.957646i	$0.407027\pi$
$830$	−1.58670	−0.0550752
$831$	45.0906	1.56417
$832$	2.02823	0.0703161
$833$	−7.19436	−0.249270
$834$	−34.0402	−1.17871
$835$	1.52437	0.0527529
$836$	−2.60751	−0.0901828
$837$	15.8502	0.547863
$838$	−9.36686	−0.323573
$839$	2.47599	0.0854807	0.0427403	−	0.999086i	$-0.486391\pi$
$839$	2.47599	0.0854807	0.0427403	+	0.999086i	$0.486391\pi$
$840$	0.453738	0.0156555
$841$	22.1330	0.763206
$842$	−26.6508	−0.918448
$843$	14.2353	0.490291
$844$	−1.00000	−0.0344214
$845$	−0.802172	−0.0275956
$846$	22.6817	0.779814
$847$	−9.34548	−0.321114
$848$	−4.98609	−0.171223
$849$	4.95468	0.170044
$850$	−17.5108	−0.600616
$851$	−8.08385	−0.277111
$852$	30.5800	1.04765
$853$	−51.2929	−1.75624	−0.878118	−	0.478445i	$-0.841201\pi$
$853$	−51.2929	−1.75624	−0.878118	+	0.478445i	$0.841201\pi$
$854$	−9.78936	−0.334985
$855$	−0.190016	−0.00649842
$856$	−9.59386	−0.327911
$857$	1.63880	0.0559805	0.0279902	−	0.999608i	$-0.491089\pi$
$857$	1.63880	0.0559805	0.0279902	+	0.999608i	$0.491089\pi$
$858$	11.9492	0.407939
$859$	24.4951	0.835761	0.417881	−	0.908502i	$-0.362773\pi$
$859$	24.4951	0.835761	0.417881	+	0.908502i	$0.362773\pi$
$860$	−0.878325	−0.0299506
$861$	19.3199	0.658422
$862$	25.1619	0.857019
$863$	13.3226	0.453507	0.226754	−	0.973952i	$-0.427189\pi$
$863$	13.3226	0.453507	0.226754	+	0.973952i	$0.427189\pi$
$864$	−2.02226	−0.0687987
$865$	1.77243	0.0602646
$866$	−22.9539	−0.780006
$867$	−10.6074	−0.360247
$868$	−17.4365	−0.591835
$869$	−20.4575	−0.693972
$870$	1.45846	0.0494463
$871$	−11.9672	−0.405495
$872$	13.3896	0.453428
$873$	−4.27382	−0.144647
$874$	−5.88559	−0.199083
$875$	−2.00657	−0.0678346
$876$	20.2680	0.684791
$877$	47.2831	1.59664	0.798318	−	0.602236i	$-0.205723\pi$
$877$	47.2831	1.59664	0.798318	+	0.602236i	$0.205723\pi$
$878$	11.8546	0.400072
$879$	−1.16439	−0.0392740
$880$	0.235382	0.00793473
$881$	−11.5007	−0.387467	−0.193733	−	0.981054i	$-0.562060\pi$
$881$	−11.5007	−0.387467	−0.193733	+	0.981054i	$0.562060\pi$
$882$	−4.31709	−0.145364
$883$	0.00605963	0.000203923 0	0.000101961	−	1.00000i	$-0.499968\pi$
$883$	0.00605963	0.000203923 0	0.000101961		1.00000i	$0.499968\pi$
$884$	7.11478	0.239296
$885$	0.495052	0.0166410
$886$	38.4433	1.29153
$887$	−33.0152	−1.10854	−0.554271	−	0.832337i	$-0.687003\pi$
$887$	−33.0152	−1.10854	−0.554271	+	0.832337i	$0.687003\pi$
$888$	−3.10331	−0.104140
$889$	−16.4632	−0.552159
$890$	1.09313	0.0366417
$891$	−28.3802	−0.950774
$892$	−11.6739	−0.390871
$893$	−10.7754	−0.360584
$894$	−24.2687	−0.811668
$895$	−1.28271	−0.0428764
$896$	2.22465	0.0743205
$897$	26.9713	0.900546
$898$	−34.9689	−1.16693
$899$	−56.0465	−1.86925
$900$	−10.5077	−0.350255
$901$	−17.4906	−0.582697
$902$	10.0224	0.333711
$903$	−48.9066	−1.62751
$904$	−17.6784	−0.587974
$905$	0.500989	0.0166534
$906$	−31.8430	−1.05791
$907$	48.5868	1.61330	0.806648	−	0.591032i	$-0.201279\pi$
$907$	48.5868	1.61330	0.806648	+	0.591032i	$0.201279\pi$
$908$	11.1124	0.368779
$909$	14.2027	0.471075
$910$	0.407310	0.0135022
$911$	30.3216	1.00460	0.502301	−	0.864693i	$-0.332487\pi$
$911$	30.3216	1.00460	0.502301	+	0.864693i	$0.332487\pi$
$912$	−2.25942	−0.0748168
$913$	−45.8327	−1.51684
$914$	−9.72999	−0.321839
$915$	−0.897500	−0.0296704
$916$	8.09159	0.267354
$917$	25.8579	0.853904
$918$	−7.09386	−0.234132
$919$	−3.25304	−0.107308	−0.0536539	−	0.998560i	$-0.517087\pi$
$919$	−3.25304	−0.107308	−0.0536539	+	0.998560i	$0.517087\pi$
$920$	0.531296	0.0175163
$921$	57.7036	1.90140
$922$	−5.12953	−0.168932
$923$	27.4510	0.903559
$924$	13.1065	0.431171
$925$	6.85630	0.225434
$926$	25.1190	0.825463
$927$	4.03219	0.132435
$928$	7.15073	0.234734
$929$	−22.3640	−0.733738	−0.366869	−	0.930273i	$-0.619570\pi$
$929$	−22.3640	−0.733738	−0.366869	+	0.930273i	$0.619570\pi$
$930$	−1.59860	−0.0524202
$931$	2.05091	0.0672159
$932$	22.0024	0.720712
$933$	−35.8106	−1.17239
$934$	−32.8875	−1.07611
$935$	0.825692	0.0270030
$936$	4.26934	0.139548
$937$	13.7606	0.449541	0.224770	−	0.974412i	$-0.427837\pi$
$937$	13.7606	0.449541	0.224770	+	0.974412i	$0.427837\pi$
$938$	−13.1262	−0.428587
$939$	−19.1236	−0.624076
$940$	0.972698	0.0317259
$941$	−0.969236	−0.0315962	−0.0157981	−	0.999875i	$-0.505029\pi$
$941$	−0.969236	−0.0315962	−0.0157981	+	0.999875i	$0.505029\pi$
$942$	−36.1220	−1.17692
$943$	22.6223	0.736683
$944$	2.42721	0.0789991
$945$	−0.406113	−0.0132108
$946$	−25.3709	−0.824878
$947$	−17.8326	−0.579483	−0.289741	−	0.957105i	$-0.593569\pi$
$947$	−17.8326	−0.579483	−0.289741	+	0.957105i	$0.593569\pi$
$948$	−17.7264	−0.575728
$949$	18.1941	0.590605
$950$	4.99185	0.161957
$951$	−32.6221	−1.05784
$952$	7.80383	0.252923
$953$	−13.1540	−0.426099	−0.213050	−	0.977041i	$-0.568340\pi$
$953$	−13.1540	−0.426099	−0.213050	+	0.977041i	$0.568340\pi$
$954$	−10.4955	−0.339806
$955$	−1.63236	−0.0528219
$956$	−24.7619	−0.800857
$957$	42.1283	1.36181
$958$	−36.5814	−1.18189
$959$	32.8084	1.05944
$960$	0.203959	0.00658275
$961$	30.4321	0.981680
$962$	−2.78577	−0.0898167
$963$	−20.1947	−0.650765
$964$	−1.67957	−0.0540953
$965$	−0.352633	−0.0113517
$966$	29.5834	0.951831
$967$	13.4444	0.432343	0.216172	−	0.976355i	$-0.430643\pi$
$967$	13.4444	0.432343	0.216172	+	0.976355i	$0.430643\pi$
$968$	−4.20087	−0.135021
$969$	−7.92577	−0.254612
$970$	−0.183281	−0.00588481
$971$	−26.9282	−0.864168	−0.432084	−	0.901833i	$-0.642222\pi$
$971$	−26.9282	−0.864168	−0.432084	+	0.901833i	$0.642222\pi$
$972$	−18.5247	−0.594182
$973$	−33.5165	−1.07449
$974$	12.6761	0.406168
$975$	−22.8757	−0.732608
$976$	−4.40040	−0.140853
$977$	25.2331	0.807280	0.403640	−	0.914918i	$-0.367745\pi$
$977$	25.2331	0.807280	0.403640	+	0.914918i	$0.367745\pi$
$978$	49.1355	1.57118
$979$	31.5756	1.00916
$980$	−0.185137	−0.00591399
$981$	28.1845	0.899863
$982$	−6.99828	−0.223324
$983$	−23.5385	−0.750760	−0.375380	−	0.926871i	$-0.622488\pi$
$983$	−23.5385	−0.750760	−0.375380	+	0.926871i	$0.622488\pi$
$984$	8.68446	0.276851
$985$	1.63606	0.0521291
$986$	25.0839	0.798835
$987$	54.1615	1.72398
$988$	−2.02823	−0.0645265
$989$	−57.2662	−1.82096
$990$	0.495470	0.0157471
$991$	−41.4691	−1.31731	−0.658654	−	0.752446i	$-0.728874\pi$
$991$	−41.4691	−1.31731	−0.658654	+	0.752446i	$0.728874\pi$
$992$	−7.83786	−0.248852
$993$	50.0145	1.58716
$994$	30.1095	0.955016
$995$	−0.607033	−0.0192443
$996$	−39.7141	−1.25839
$997$	−2.29979	−0.0728352	−0.0364176	−	0.999337i	$-0.511595\pi$
$997$	−2.29979	−0.0728352	−0.0364176	+	0.999337i	$0.511595\pi$
$998$	−0.547395	−0.0173275
$999$	2.77757	0.0878786

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.37	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.37	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +2.25942 q^{3} +1.00000 q^{4} +0.0902706 q^{5} +2.25942 q^{6} +2.22465 q^{7} +1.00000 q^{8} +2.10496 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +2.25942 q^{3} +1.00000 q^{4} +0.0902706 q^{5} +2.25942 q^{6} +2.22465 q^{7} +1.00000 q^{8} +2.10496 q^{9} +0.0902706 q^{10} +2.60751 q^{11} +2.25942 q^{12} +2.02823 q^{13} +2.22465 q^{14} +0.203959 q^{15} +1.00000 q^{16} +3.50788 q^{17} +2.10496 q^{18} -1.00000 q^{19} +0.0902706 q^{20} +5.02642 q^{21} +2.60751 q^{22} +5.88559 q^{23} +2.25942 q^{24} -4.99185 q^{25} +2.02823 q^{26} -2.02226 q^{27} +2.22465 q^{28} +7.15073 q^{29} +0.203959 q^{30} -7.83786 q^{31} +1.00000 q^{32} +5.89146 q^{33} +3.50788 q^{34} +0.200821 q^{35} +2.10496 q^{36} -1.37350 q^{37} -1.00000 q^{38} +4.58261 q^{39} +0.0902706 q^{40} +3.84368 q^{41} +5.02642 q^{42} -9.72990 q^{43} +2.60751 q^{44} +0.190016 q^{45} +5.88559 q^{46} +10.7754 q^{47} +2.25942 q^{48} -2.05091 q^{49} -4.99185 q^{50} +7.92577 q^{51} +2.02823 q^{52} -4.98609 q^{53} -2.02226 q^{54} +0.235382 q^{55} +2.22465 q^{56} -2.25942 q^{57} +7.15073 q^{58} +2.42721 q^{59} +0.203959 q^{60} -4.40040 q^{61} -7.83786 q^{62} +4.68282 q^{63} +1.00000 q^{64} +0.183089 q^{65} +5.89146 q^{66} -5.90035 q^{67} +3.50788 q^{68} +13.2980 q^{69} +0.200821 q^{70} +13.5345 q^{71} +2.10496 q^{72} +8.97044 q^{73} -1.37350 q^{74} -11.2787 q^{75} -1.00000 q^{76} +5.80082 q^{77} +4.58261 q^{78} -7.84558 q^{79} +0.0902706 q^{80} -10.8840 q^{81} +3.84368 q^{82} -17.5772 q^{83} +5.02642 q^{84} +0.316659 q^{85} -9.72990 q^{86} +16.1565 q^{87} +2.60751 q^{88} +12.1094 q^{89} +0.190016 q^{90} +4.51210 q^{91} +5.88559 q^{92} -17.7090 q^{93} +10.7754 q^{94} -0.0902706 q^{95} +2.25942 q^{96} -2.03035 q^{97} -2.05091 q^{98} +5.48872 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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