LMFDB - Embedded newform 8018.2.a.j.1.5

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			1.5
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.83191 q^{3} +1.00000 q^{4} +1.28371 q^{5} -2.83191 q^{6} -4.11947 q^{7} +1.00000 q^{8} +5.01973 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.83191 q^{3} +1.00000 q^{4} +1.28371 q^{5} -2.83191 q^{6} -4.11947 q^{7} +1.00000 q^{8} +5.01973 q^{9} +1.28371 q^{10} -5.23374 q^{11} -2.83191 q^{12} +5.59050 q^{13} -4.11947 q^{14} -3.63535 q^{15} +1.00000 q^{16} +0.524964 q^{17} +5.01973 q^{18} -1.00000 q^{19} +1.28371 q^{20} +11.6660 q^{21} -5.23374 q^{22} +5.73168 q^{23} -2.83191 q^{24} -3.35209 q^{25} +5.59050 q^{26} -5.71969 q^{27} -4.11947 q^{28} -6.04256 q^{29} -3.63535 q^{30} +3.63067 q^{31} +1.00000 q^{32} +14.8215 q^{33} +0.524964 q^{34} -5.28820 q^{35} +5.01973 q^{36} +0.704536 q^{37} -1.00000 q^{38} -15.8318 q^{39} +1.28371 q^{40} +8.38098 q^{41} +11.6660 q^{42} -7.73214 q^{43} -5.23374 q^{44} +6.44387 q^{45} +5.73168 q^{46} -9.79446 q^{47} -2.83191 q^{48} +9.97004 q^{49} -3.35209 q^{50} -1.48665 q^{51} +5.59050 q^{52} -14.1758 q^{53} -5.71969 q^{54} -6.71860 q^{55} -4.11947 q^{56} +2.83191 q^{57} -6.04256 q^{58} -5.63431 q^{59} -3.63535 q^{60} +6.12935 q^{61} +3.63067 q^{62} -20.6786 q^{63} +1.00000 q^{64} +7.17658 q^{65} +14.8215 q^{66} +6.03732 q^{67} +0.524964 q^{68} -16.2316 q^{69} -5.28820 q^{70} -3.00259 q^{71} +5.01973 q^{72} -0.00181745 q^{73} +0.704536 q^{74} +9.49283 q^{75} -1.00000 q^{76} +21.5602 q^{77} -15.8318 q^{78} -10.9043 q^{79} +1.28371 q^{80} +1.13848 q^{81} +8.38098 q^{82} +7.23923 q^{83} +11.6660 q^{84} +0.673900 q^{85} -7.73214 q^{86} +17.1120 q^{87} -5.23374 q^{88} -7.41940 q^{89} +6.44387 q^{90} -23.0299 q^{91} +5.73168 q^{92} -10.2817 q^{93} -9.79446 q^{94} -1.28371 q^{95} -2.83191 q^{96} +4.32411 q^{97} +9.97004 q^{98} -26.2720 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.83191	−1.63501	−0.817503	−	0.575925i	$-0.804642\pi$
$3$	−2.83191	−1.63501	−0.817503	+	0.575925i	$0.804642\pi$
$4$	1.00000	0.500000
$5$	1.28371	0.574092	0.287046	−	0.957917i	$-0.407327\pi$
$5$	1.28371	0.574092	0.287046	+	0.957917i	$0.407327\pi$
$6$	−2.83191	−1.15612
$7$	−4.11947	−1.55701	−0.778507	−	0.627636i	$-0.784023\pi$
$7$	−4.11947	−1.55701	−0.778507	+	0.627636i	$0.784023\pi$
$8$	1.00000	0.353553
$9$	5.01973	1.67324
$10$	1.28371	0.405944
$11$	−5.23374	−1.57803	−0.789016	−	0.614372i	$-0.789409\pi$
$11$	−5.23374	−1.57803	−0.789016	+	0.614372i	$0.789409\pi$
$12$	−2.83191	−0.817503
$13$	5.59050	1.55053	0.775264	−	0.631638i	$-0.217617\pi$
$13$	5.59050	1.55053	0.775264	+	0.631638i	$0.217617\pi$
$14$	−4.11947	−1.10097
$15$	−3.63535	−0.938643
$16$	1.00000	0.250000
$17$	0.524964	0.127322	0.0636612	−	0.997972i	$-0.479722\pi$
$17$	0.524964	0.127322	0.0636612	+	0.997972i	$0.479722\pi$
$18$	5.01973	1.18316
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	1.28371	0.287046
$21$	11.6660	2.54573
$22$	−5.23374	−1.11584
$23$	5.73168	1.19514	0.597569	−	0.801817i	$-0.296133\pi$
$23$	5.73168	1.19514	0.597569	+	0.801817i	$0.296133\pi$
$24$	−2.83191	−0.578062
$25$	−3.35209	−0.670418
$26$	5.59050	1.09639
$27$	−5.71969	−1.10075
$28$	−4.11947	−0.778507
$29$	−6.04256	−1.12208	−0.561038	−	0.827790i	$-0.689598\pi$
$29$	−6.04256	−1.12208	−0.561038	+	0.827790i	$0.689598\pi$
$30$	−3.63535	−0.663721
$31$	3.63067	0.652087	0.326043	−	0.945355i	$-0.394284\pi$
$31$	3.63067	0.652087	0.326043	+	0.945355i	$0.394284\pi$
$32$	1.00000	0.176777
$33$	14.8215	2.58009
$34$	0.524964	0.0900305
$35$	−5.28820	−0.893869
$36$	5.01973	0.836621
$37$	0.704536	0.115825	0.0579125	−	0.998322i	$-0.481556\pi$
$37$	0.704536	0.115825	0.0579125	+	0.998322i	$0.481556\pi$
$38$	−1.00000	−0.162221
$39$	−15.8318	−2.53512
$40$	1.28371	0.202972
$41$	8.38098	1.30889	0.654445	−	0.756110i	$-0.272902\pi$
$41$	8.38098	1.30889	0.654445	+	0.756110i	$0.272902\pi$
$42$	11.6660	1.80010
$43$	−7.73214	−1.17914	−0.589570	−	0.807717i	$-0.700703\pi$
$43$	−7.73214	−1.17914	−0.589570	+	0.807717i	$0.700703\pi$
$44$	−5.23374	−0.789016
$45$	6.44387	0.960595
$46$	5.73168	0.845091
$47$	−9.79446	−1.42867	−0.714335	−	0.699804i	$-0.753271\pi$
$47$	−9.79446	−1.42867	−0.714335	+	0.699804i	$0.753271\pi$
$48$	−2.83191	−0.408751
$49$	9.97004	1.42429
$50$	−3.35209	−0.474057
$51$	−1.48665	−0.208173
$52$	5.59050	0.775264
$53$	−14.1758	−1.94719	−0.973595	−	0.228281i	$-0.926690\pi$
$53$	−14.1758	−1.94719	−0.973595	+	0.228281i	$0.926690\pi$
$54$	−5.71969	−0.778351
$55$	−6.71860	−0.905936
$56$	−4.11947	−0.550487
$57$	2.83191	0.375096
$58$	−6.04256	−0.793427
$59$	−5.63431	−0.733524	−0.366762	−	0.930315i	$-0.619534\pi$
$59$	−5.63431	−0.733524	−0.366762	+	0.930315i	$0.619534\pi$
$60$	−3.63535	−0.469322
$61$	6.12935	0.784783	0.392391	−	0.919798i	$-0.371648\pi$
$61$	6.12935	0.784783	0.392391	+	0.919798i	$0.371648\pi$
$62$	3.63067	0.461095
$63$	−20.6786	−2.60526
$64$	1.00000	0.125000
$65$	7.17658	0.890145
$66$	14.8215	1.82440
$67$	6.03732	0.737576	0.368788	−	0.929514i	$-0.379773\pi$
$67$	6.03732	0.737576	0.368788	+	0.929514i	$0.379773\pi$
$68$	0.524964	0.0636612
$69$	−16.2316	−1.95406
$70$	−5.28820	−0.632061
$71$	−3.00259	−0.356342	−0.178171	−	0.984000i	$-0.557018\pi$
$71$	−3.00259	−0.356342	−0.178171	+	0.984000i	$0.557018\pi$
$72$	5.01973	0.591581
$73$	−0.00181745	−0.000212717 0	−0.000106358	−	1.00000i	$-0.500034\pi$
$73$	−0.00181745	−0.000212717 0	−0.000106358		1.00000i	$0.500034\pi$
$74$	0.704536	0.0819006
$75$	9.49283	1.09614
$76$	−1.00000	−0.114708
$77$	21.5602	2.45702
$78$	−15.8318	−1.79260
$79$	−10.9043	−1.22683	−0.613413	−	0.789762i	$-0.710204\pi$
$79$	−10.9043	−1.22683	−0.613413	+	0.789762i	$0.710204\pi$
$80$	1.28371	0.143523
$81$	1.13848	0.126498
$82$	8.38098	0.925524
$83$	7.23923	0.794609	0.397304	−	0.917687i	$-0.369946\pi$
$83$	7.23923	0.794609	0.397304	+	0.917687i	$0.369946\pi$
$84$	11.6660	1.27286
$85$	0.673900	0.0730947
$86$	−7.73214	−0.833779
$87$	17.1120	1.83460
$88$	−5.23374	−0.557919
$89$	−7.41940	−0.786455	−0.393227	−	0.919441i	$-0.628641\pi$
$89$	−7.41940	−0.786455	−0.393227	+	0.919441i	$0.628641\pi$
$90$	6.44387	0.679243
$91$	−23.0299	−2.41419
$92$	5.73168	0.597569
$93$	−10.2817	−1.06617
$94$	−9.79446	−1.01022
$95$	−1.28371	−0.131706
$96$	−2.83191	−0.289031
$97$	4.32411	0.439047	0.219523	−	0.975607i	$-0.429550\pi$
$97$	4.32411	0.439047	0.219523	+	0.975607i	$0.429550\pi$
$98$	9.97004	1.00713
$99$	−26.2720	−2.64043
$100$	−3.35209	−0.335209
$101$	12.5630	1.25006	0.625031	−	0.780600i	$-0.285086\pi$
$101$	12.5630	1.25006	0.625031	+	0.780600i	$0.285086\pi$
$102$	−1.48665	−0.147200
$103$	−2.38747	−0.235244	−0.117622	−	0.993058i	$-0.537527\pi$
$103$	−2.38747	−0.235244	−0.117622	+	0.993058i	$0.537527\pi$
$104$	5.59050	0.548194
$105$	14.9757	1.46148
$106$	−14.1758	−1.37687
$107$	12.6099	1.21905	0.609525	−	0.792767i	$-0.291360\pi$
$107$	12.6099	1.21905	0.609525	+	0.792767i	$0.291360\pi$
$108$	−5.71969	−0.550377
$109$	0.357316	0.0342247	0.0171123	−	0.999854i	$-0.494553\pi$
$109$	0.357316	0.0342247	0.0171123	+	0.999854i	$0.494553\pi$
$110$	−6.71860	−0.640593
$111$	−1.99518	−0.189374
$112$	−4.11947	−0.389253
$113$	−14.6762	−1.38062	−0.690312	−	0.723512i	$-0.742527\pi$
$113$	−14.6762	−1.38062	−0.690312	+	0.723512i	$0.742527\pi$
$114$	2.83191	0.265233
$115$	7.35781	0.686119
$116$	−6.04256	−0.561038
$117$	28.0628	2.59441
$118$	−5.63431	−0.518680
$119$	−2.16257	−0.198243
$120$	−3.63535	−0.331861
$121$	16.3921	1.49019
$122$	6.12935	0.554925
$123$	−23.7342	−2.14004
$124$	3.63067	0.326043
$125$	−10.7217	−0.958974
$126$	−20.6786	−1.84220
$127$	11.8181	1.04868	0.524342	−	0.851508i	$-0.324311\pi$
$127$	11.8181	1.04868	0.524342	+	0.851508i	$0.324311\pi$
$128$	1.00000	0.0883883
$129$	21.8968	1.92790
$130$	7.17658	0.629428
$131$	19.5959	1.71210	0.856049	−	0.516894i	$-0.172912\pi$
$131$	19.5959	1.71210	0.856049	+	0.516894i	$0.172912\pi$
$132$	14.8215	1.29005
$133$	4.11947	0.357203
$134$	6.03732	0.521545
$135$	−7.34241	−0.631934
$136$	0.524964	0.0450153
$137$	11.2612	0.962109	0.481054	−	0.876691i	$-0.340254\pi$
$137$	11.2612	0.962109	0.481054	+	0.876691i	$0.340254\pi$
$138$	−16.2316	−1.38173
$139$	22.9412	1.94585	0.972925	−	0.231121i	$-0.0742392\pi$
$139$	22.9412	1.94585	0.972925	+	0.231121i	$0.0742392\pi$
$140$	−5.28820	−0.446934
$141$	27.7371	2.33588
$142$	−3.00259	−0.251972
$143$	−29.2593	−2.44678
$144$	5.01973	0.418311
$145$	−7.75689	−0.644174
$146$	−0.00181745	−0.000150413 0
$147$	−28.2343	−2.32872
$148$	0.704536	0.0579125
$149$	5.79470	0.474720	0.237360	−	0.971422i	$-0.423718\pi$
$149$	5.79470	0.474720	0.237360	+	0.971422i	$0.423718\pi$
$150$	9.49283	0.775086
$151$	−12.6055	−1.02582	−0.512912	−	0.858441i	$-0.671433\pi$
$151$	−12.6055	−1.02582	−0.512912	+	0.858441i	$0.671433\pi$
$152$	−1.00000	−0.0811107
$153$	2.63517	0.213041
$154$	21.5602	1.73737
$155$	4.66072	0.374358
$156$	−15.8318	−1.26756
$157$	−16.4178	−1.31028	−0.655142	−	0.755506i	$-0.727391\pi$
$157$	−16.4178	−1.31028	−0.655142	+	0.755506i	$0.727391\pi$
$158$	−10.9043	−0.867497
$159$	40.1445	3.18367
$160$	1.28371	0.101486
$161$	−23.6115	−1.86085
$162$	1.13848	0.0894473
$163$	13.8959	1.08841	0.544207	−	0.838951i	$-0.316831\pi$
$163$	13.8959	1.08841	0.544207	+	0.838951i	$0.316831\pi$
$164$	8.38098	0.654445
$165$	19.0265	1.48121
$166$	7.23923	0.561873
$167$	−10.0983	−0.781426	−0.390713	−	0.920512i	$-0.627772\pi$
$167$	−10.0983	−0.781426	−0.390713	+	0.920512i	$0.627772\pi$
$168$	11.6660	0.900050
$169$	18.2537	1.40413
$170$	0.673900	0.0516858
$171$	−5.01973	−0.383868
$172$	−7.73214	−0.589570
$173$	6.86873	0.522220	0.261110	−	0.965309i	$-0.415911\pi$
$173$	6.86873	0.522220	0.261110	+	0.965309i	$0.415911\pi$
$174$	17.1120	1.29726
$175$	13.8088	1.04385
$176$	−5.23374	−0.394508
$177$	15.9559	1.19932
$178$	−7.41940	−0.556107
$179$	2.65665	0.198567	0.0992836	−	0.995059i	$-0.468345\pi$
$179$	2.65665	0.198567	0.0992836	+	0.995059i	$0.468345\pi$
$180$	6.44387	0.480297
$181$	−20.9411	−1.55654	−0.778271	−	0.627929i	$-0.783903\pi$
$181$	−20.9411	−1.55654	−0.778271	+	0.627929i	$0.783903\pi$
$182$	−23.0299	−1.70709
$183$	−17.3578	−1.28312
$184$	5.73168	0.422545
$185$	0.904419	0.0664942
$186$	−10.2817	−0.753893
$187$	−2.74752	−0.200919
$188$	−9.79446	−0.714335
$189$	23.5621	1.71389
$190$	−1.28371	−0.0931300
$191$	−8.92459	−0.645761	−0.322880	−	0.946440i	$-0.604651\pi$
$191$	−8.92459	−0.645761	−0.322880	+	0.946440i	$0.604651\pi$
$192$	−2.83191	−0.204376
$193$	21.0325	1.51395	0.756976	−	0.653442i	$-0.226676\pi$
$193$	21.0325	1.51395	0.756976	+	0.653442i	$0.226676\pi$
$194$	4.32411	0.310453
$195$	−20.3234	−1.45539
$196$	9.97004	0.712146
$197$	16.0309	1.14215	0.571077	−	0.820896i	$-0.306526\pi$
$197$	16.0309	1.14215	0.571077	+	0.820896i	$0.306526\pi$
$198$	−26.2720	−1.86707
$199$	10.3290	0.732201	0.366100	−	0.930575i	$-0.380693\pi$
$199$	10.3290	0.732201	0.366100	+	0.930575i	$0.380693\pi$
$200$	−3.35209	−0.237029
$201$	−17.0972	−1.20594
$202$	12.5630	0.883927
$203$	24.8921	1.74709
$204$	−1.48665	−0.104086
$205$	10.7587	0.751423
$206$	−2.38747	−0.166343
$207$	28.7715	1.99976
$208$	5.59050	0.387632
$209$	5.23374	0.362026
$210$	14.9757	1.03342
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−14.1758	−0.973595
$213$	8.50307	0.582621
$214$	12.6099	0.861998
$215$	−9.92582	−0.676935
$216$	−5.71969	−0.389176
$217$	−14.9564	−1.01531
$218$	0.357316	0.0242005
$219$	0.00514686	0.000347793 0
$220$	−6.71860	−0.452968
$221$	2.93481	0.197417
$222$	−1.99518	−0.133908
$223$	13.6581	0.914616	0.457308	−	0.889308i	$-0.348814\pi$
$223$	13.6581	0.914616	0.457308	+	0.889308i	$0.348814\pi$
$224$	−4.11947	−0.275244
$225$	−16.8266	−1.12177
$226$	−14.6762	−0.976248
$227$	−25.6786	−1.70435	−0.852175	−	0.523256i	$-0.824717\pi$
$227$	−25.6786	−1.70435	−0.852175	+	0.523256i	$0.824717\pi$
$228$	2.83191	0.187548
$229$	23.4863	1.55202	0.776009	−	0.630721i	$-0.217241\pi$
$229$	23.4863	1.55202	0.776009	+	0.630721i	$0.217241\pi$
$230$	7.35781	0.485160
$231$	−61.0567	−4.01724
$232$	−6.04256	−0.396713
$233$	−19.0914	−1.25072	−0.625361	−	0.780335i	$-0.715048\pi$
$233$	−19.0914	−1.25072	−0.625361	+	0.780335i	$0.715048\pi$
$234$	28.0628	1.83452
$235$	−12.5732	−0.820187
$236$	−5.63431	−0.366762
$237$	30.8799	2.00587
$238$	−2.16257	−0.140179
$239$	2.78325	0.180034	0.0900168	−	0.995940i	$-0.471308\pi$
$239$	2.78325	0.180034	0.0900168	+	0.995940i	$0.471308\pi$
$240$	−3.63535	−0.234661
$241$	27.2314	1.75413	0.877064	−	0.480374i	$-0.159499\pi$
$241$	27.2314	1.75413	0.877064	+	0.480374i	$0.159499\pi$
$242$	16.3921	1.05372
$243$	13.9350	0.893931
$244$	6.12935	0.392391
$245$	12.7986	0.817674
$246$	−23.7342	−1.51324
$247$	−5.59050	−0.355715
$248$	3.63067	0.230547
$249$	−20.5009	−1.29919
$250$	−10.7217	−0.678097
$251$	18.2310	1.15073	0.575367	−	0.817895i	$-0.304859\pi$
$251$	18.2310	1.15073	0.575367	+	0.817895i	$0.304859\pi$
$252$	−20.6786	−1.30263
$253$	−29.9982	−1.88597
$254$	11.8181	0.741531
$255$	−1.90843	−0.119510
$256$	1.00000	0.0625000
$257$	20.9695	1.30804	0.654019	−	0.756478i	$-0.273082\pi$
$257$	20.9695	1.30804	0.654019	+	0.756478i	$0.273082\pi$
$258$	21.8968	1.36323
$259$	−2.90231	−0.180341
$260$	7.17658	0.445072
$261$	−30.3320	−1.87750
$262$	19.5959	1.21064
$263$	−12.9974	−0.801452	−0.400726	−	0.916198i	$-0.631242\pi$
$263$	−12.9974	−0.801452	−0.400726	+	0.916198i	$0.631242\pi$
$264$	14.8215	0.912200
$265$	−18.1975	−1.11787
$266$	4.11947	0.252581
$267$	21.0111	1.28586
$268$	6.03732	0.368788
$269$	−12.3036	−0.750162	−0.375081	−	0.926992i	$-0.622385\pi$
$269$	−12.3036	−0.750162	−0.375081	+	0.926992i	$0.622385\pi$
$270$	−7.34241	−0.446845
$271$	20.9145	1.27046	0.635231	−	0.772322i	$-0.280905\pi$
$271$	20.9145	1.27046	0.635231	+	0.772322i	$0.280905\pi$
$272$	0.524964	0.0318306
$273$	65.2187	3.94722
$274$	11.2612	0.680314
$275$	17.5440	1.05794
$276$	−16.2316	−0.977029
$277$	−8.96764	−0.538814	−0.269407	−	0.963026i	$-0.586828\pi$
$277$	−8.96764	−0.538814	−0.269407	+	0.963026i	$0.586828\pi$
$278$	22.9412	1.37592
$279$	18.2250	1.09110
$280$	−5.28820	−0.316030
$281$	−2.55717	−0.152548	−0.0762740	−	0.997087i	$-0.524302\pi$
$281$	−2.55717	−0.152548	−0.0762740	+	0.997087i	$0.524302\pi$
$282$	27.7371	1.65172
$283$	−9.75811	−0.580060	−0.290030	−	0.957018i	$-0.593665\pi$
$283$	−9.75811	−0.580060	−0.290030	+	0.957018i	$0.593665\pi$
$284$	−3.00259	−0.178171
$285$	3.63535	0.215340
$286$	−29.2593	−1.73014
$287$	−34.5252	−2.03796
$288$	5.01973	0.295790
$289$	−16.7244	−0.983789
$290$	−7.75689	−0.455500
$291$	−12.2455	−0.717844
$292$	−0.00181745	−0.000106358 0
$293$	22.1512	1.29409	0.647044	−	0.762453i	$-0.276005\pi$
$293$	22.1512	1.29409	0.647044	+	0.762453i	$0.276005\pi$
$294$	−28.2343	−1.64666
$295$	−7.23281	−0.421110
$296$	0.704536	0.0409503
$297$	29.9354	1.73703
$298$	5.79470	0.335678
$299$	32.0430	1.85309
$300$	9.49283	0.548069
$301$	31.8523	1.83594
$302$	−12.6055	−0.725368
$303$	−35.5772	−2.04386
$304$	−1.00000	−0.0573539
$305$	7.86830	0.450537
$306$	2.63517	0.150643
$307$	18.8790	1.07748	0.538741	−	0.842471i	$-0.318900\pi$
$307$	18.8790	1.07748	0.538741	+	0.842471i	$0.318900\pi$
$308$	21.5602	1.22851
$309$	6.76109	0.384625
$310$	4.66072	0.264711
$311$	−5.03635	−0.285585	−0.142793	−	0.989753i	$-0.545608\pi$
$311$	−5.03635	−0.285585	−0.142793	+	0.989753i	$0.545608\pi$
$312$	−15.8318	−0.896300
$313$	25.5334	1.44323	0.721617	−	0.692292i	$-0.243399\pi$
$313$	25.5334	1.44323	0.721617	+	0.692292i	$0.243399\pi$
$314$	−16.4178	−0.926510
$315$	−26.5453	−1.49566
$316$	−10.9043	−0.613413
$317$	31.3517	1.76089	0.880443	−	0.474152i	$-0.157245\pi$
$317$	31.3517	1.76089	0.880443	+	0.474152i	$0.157245\pi$
$318$	40.1445	2.25119
$319$	31.6252	1.77067
$320$	1.28371	0.0717615
$321$	−35.7103	−1.99315
$322$	−23.6115	−1.31582
$323$	−0.524964	−0.0292098
$324$	1.13848	0.0632488
$325$	−18.7399	−1.03950
$326$	13.8959	0.769624
$327$	−1.01189	−0.0559575
$328$	8.38098	0.462762
$329$	40.3480	2.22446
$330$	19.0265	1.04737
$331$	16.7295	0.919538	0.459769	−	0.888039i	$-0.347932\pi$
$331$	16.7295	0.919538	0.459769	+	0.888039i	$0.347932\pi$
$332$	7.23923	0.397304
$333$	3.53658	0.193803
$334$	−10.0983	−0.552552
$335$	7.75016	0.423436
$336$	11.6660	0.636431
$337$	26.3620	1.43603	0.718014	−	0.696028i	$-0.245051\pi$
$337$	26.3620	1.43603	0.718014	+	0.696028i	$0.245051\pi$
$338$	18.2537	0.992873
$339$	41.5618	2.25733
$340$	0.673900	0.0365474
$341$	−19.0020	−1.02901
$342$	−5.01973	−0.271436
$343$	−12.2350	−0.660627
$344$	−7.73214	−0.416889
$345$	−20.8367	−1.12181
$346$	6.86873	0.369265
$347$	−15.9815	−0.857932	−0.428966	−	0.903321i	$-0.641122\pi$
$347$	−15.9815	−0.857932	−0.428966	+	0.903321i	$0.641122\pi$
$348$	17.1120	0.917299
$349$	−12.5484	−0.671701	−0.335851	−	0.941915i	$-0.609024\pi$
$349$	−12.5484	−0.671701	−0.335851	+	0.941915i	$0.609024\pi$
$350$	13.8088	0.738114
$351$	−31.9760	−1.70675
$352$	−5.23374	−0.278959
$353$	−22.5524	−1.20034	−0.600171	−	0.799872i	$-0.704901\pi$
$353$	−22.5524	−1.20034	−0.600171	+	0.799872i	$0.704901\pi$
$354$	15.9559	0.848044
$355$	−3.85445	−0.204573
$356$	−7.41940	−0.393227
$357$	6.12421	0.324128
$358$	2.65665	0.140408
$359$	−10.6303	−0.561046	−0.280523	−	0.959847i	$-0.590508\pi$
$359$	−10.6303	−0.561046	−0.280523	+	0.959847i	$0.590508\pi$
$360$	6.44387	0.339622
$361$	1.00000	0.0526316
$362$	−20.9411	−1.10064
$363$	−46.4209	−2.43646
$364$	−23.0299	−1.20710
$365$	−0.00233308	−0.000122119 0
$366$	−17.3578	−0.907305
$367$	−9.82680	−0.512955	−0.256477	−	0.966550i	$-0.582562\pi$
$367$	−9.82680	−0.512955	−0.256477	+	0.966550i	$0.582562\pi$
$368$	5.73168	0.298785
$369$	42.0702	2.19009
$370$	0.904419	0.0470185
$371$	58.3966	3.03180
$372$	−10.2817	−0.533083
$373$	−33.3362	−1.72608	−0.863042	−	0.505133i	$-0.831443\pi$
$373$	−33.3362	−1.72608	−0.863042	+	0.505133i	$0.831443\pi$
$374$	−2.74752	−0.142071
$375$	30.3628	1.56793
$376$	−9.79446	−0.505111
$377$	−33.7810	−1.73981
$378$	23.5621	1.21190
$379$	5.11277	0.262625	0.131313	−	0.991341i	$-0.458081\pi$
$379$	5.11277	0.262625	0.131313	+	0.991341i	$0.458081\pi$
$380$	−1.28371	−0.0658529
$381$	−33.4677	−1.71460
$382$	−8.92459	−0.456622
$383$	−21.3710	−1.09201	−0.546003	−	0.837783i	$-0.683851\pi$
$383$	−21.3710	−1.09201	−0.546003	+	0.837783i	$0.683851\pi$
$384$	−2.83191	−0.144515
$385$	27.6771	1.41055
$386$	21.0325	1.07053
$387$	−38.8133	−1.97299
$388$	4.32411	0.219523
$389$	11.0314	0.559314	0.279657	−	0.960100i	$-0.409779\pi$
$389$	11.0314	0.559314	0.279657	+	0.960100i	$0.409779\pi$
$390$	−20.3234	−1.02912
$391$	3.00892	0.152168
$392$	9.97004	0.503563
$393$	−55.4938	−2.79929
$394$	16.0309	0.807626
$395$	−13.9979	−0.704311
$396$	−26.2720	−1.32022
$397$	26.1916	1.31452	0.657259	−	0.753664i	$-0.271716\pi$
$397$	26.1916	1.31452	0.657259	+	0.753664i	$0.271716\pi$
$398$	10.3290	0.517744
$399$	−11.6660	−0.584029
$400$	−3.35209	−0.167605
$401$	34.2743	1.71157	0.855787	−	0.517328i	$-0.173073\pi$
$401$	34.2743	1.71157	0.855787	+	0.517328i	$0.173073\pi$
$402$	−17.0972	−0.852728
$403$	20.2973	1.01108
$404$	12.5630	0.625031
$405$	1.46147	0.0726212
$406$	24.8921	1.23538
$407$	−3.68736	−0.182776
$408$	−1.48665	−0.0736002
$409$	−37.4081	−1.84971	−0.924855	−	0.380319i	$-0.875814\pi$
$409$	−37.4081	−1.84971	−0.924855	+	0.380319i	$0.875814\pi$
$410$	10.7587	0.531336
$411$	−31.8907	−1.57305
$412$	−2.38747	−0.117622
$413$	23.2104	1.14211
$414$	28.7715	1.41404
$415$	9.29306	0.456179
$416$	5.59050	0.274097
$417$	−64.9676	−3.18148
$418$	5.23374	0.255991
$419$	−11.4922	−0.561429	−0.280714	−	0.959791i	$-0.590571\pi$
$419$	−11.4922	−0.561429	−0.280714	+	0.959791i	$0.590571\pi$
$420$	14.9757	0.730740
$421$	−27.6770	−1.34889	−0.674447	−	0.738323i	$-0.735618\pi$
$421$	−27.6770	−1.34889	−0.674447	+	0.738323i	$0.735618\pi$
$422$	−1.00000	−0.0486792
$423$	−49.1655	−2.39051
$424$	−14.1758	−0.688436
$425$	−1.75973	−0.0853593
$426$	8.50307	0.411975
$427$	−25.2497	−1.22192
$428$	12.6099	0.609525
$429$	82.8597	4.00050
$430$	−9.92582	−0.478666
$431$	27.9087	1.34432	0.672158	−	0.740408i	$-0.265368\pi$
$431$	27.9087	1.34432	0.672158	+	0.740408i	$0.265368\pi$
$432$	−5.71969	−0.275189
$433$	19.8795	0.955347	0.477673	−	0.878538i	$-0.341480\pi$
$433$	19.8795	0.955347	0.477673	+	0.878538i	$0.341480\pi$
$434$	−14.9564	−0.717931
$435$	21.9668	1.05323
$436$	0.357316	0.0171123
$437$	−5.73168	−0.274184
$438$	0.00514686	0.000245927 0
$439$	−18.4375	−0.879972	−0.439986	−	0.898005i	$-0.645017\pi$
$439$	−18.4375	−0.879972	−0.439986	+	0.898005i	$0.645017\pi$
$440$	−6.71860	−0.320297
$441$	50.0469	2.38318
$442$	2.93481	0.139595
$443$	33.8701	1.60922	0.804610	−	0.593804i	$-0.202375\pi$
$443$	33.8701	1.60922	0.804610	+	0.593804i	$0.202375\pi$
$444$	−1.99518	−0.0946872
$445$	−9.52435	−0.451497
$446$	13.6581	0.646731
$447$	−16.4101	−0.776170
$448$	−4.11947	−0.194627
$449$	19.6729	0.928422	0.464211	−	0.885725i	$-0.346338\pi$
$449$	19.6729	0.928422	0.464211	+	0.885725i	$0.346338\pi$
$450$	−16.8266	−0.793213
$451$	−43.8639	−2.06547
$452$	−14.6762	−0.690312
$453$	35.6978	1.67723
$454$	−25.6786	−1.20516
$455$	−29.5637	−1.38597
$456$	2.83191	0.132616
$457$	−2.54516	−0.119058	−0.0595288	−	0.998227i	$-0.518960\pi$
$457$	−2.54516	−0.119058	−0.0595288	+	0.998227i	$0.518960\pi$
$458$	23.4863	1.09744
$459$	−3.00263	−0.140151
$460$	7.35781	0.343060
$461$	−11.6962	−0.544745	−0.272373	−	0.962192i	$-0.587808\pi$
$461$	−11.6962	−0.544745	−0.272373	+	0.962192i	$0.587808\pi$
$462$	−61.0567	−2.84062
$463$	7.72399	0.358964	0.179482	−	0.983761i	$-0.442558\pi$
$463$	7.72399	0.358964	0.179482	+	0.983761i	$0.442558\pi$
$464$	−6.04256	−0.280519
$465$	−13.1987	−0.612077
$466$	−19.0914	−0.884394
$467$	10.9455	0.506498	0.253249	−	0.967401i	$-0.418501\pi$
$467$	10.9455	0.506498	0.253249	+	0.967401i	$0.418501\pi$
$468$	28.0628	1.29720
$469$	−24.8705	−1.14842
$470$	−12.5732	−0.579960
$471$	46.4938	2.14232
$472$	−5.63431	−0.259340
$473$	40.4680	1.86072
$474$	30.8799	1.41836
$475$	3.35209	0.153805
$476$	−2.16257	−0.0991213
$477$	−71.1585	−3.25812
$478$	2.78325	0.127303
$479$	22.7293	1.03853	0.519264	−	0.854614i	$-0.326206\pi$
$479$	22.7293	1.03853	0.519264	+	0.854614i	$0.326206\pi$
$480$	−3.63535	−0.165930
$481$	3.93871	0.179590
$482$	27.2314	1.24036
$483$	66.8657	3.04249
$484$	16.3921	0.745093
$485$	5.55089	0.252053
$486$	13.9350	0.632104
$487$	30.0182	1.36026	0.680128	−	0.733094i	$-0.261924\pi$
$487$	30.0182	1.36026	0.680128	+	0.733094i	$0.261924\pi$
$488$	6.12935	0.277463
$489$	−39.3521	−1.77956
$490$	12.7986	0.578183
$491$	−13.5501	−0.611506	−0.305753	−	0.952111i	$-0.598908\pi$
$491$	−13.5501	−0.611506	−0.305753	+	0.952111i	$0.598908\pi$
$492$	−23.7342	−1.07002
$493$	−3.17212	−0.142865
$494$	−5.59050	−0.251529
$495$	−33.7255	−1.51585
$496$	3.63067	0.163022
$497$	12.3691	0.554829
$498$	−20.5009	−0.918666
$499$	8.09968	0.362592	0.181296	−	0.983429i	$-0.441971\pi$
$499$	8.09968	0.362592	0.181296	+	0.983429i	$0.441971\pi$
$500$	−10.7217	−0.479487
$501$	28.5974	1.27764
$502$	18.2310	0.813692
$503$	25.9382	1.15653	0.578263	−	0.815851i	$-0.303731\pi$
$503$	25.9382	1.15653	0.578263	+	0.815851i	$0.303731\pi$
$504$	−20.6786	−0.921099
$505$	16.1272	0.717650
$506$	−29.9982	−1.33358
$507$	−51.6930	−2.29577
$508$	11.8181	0.524342
$509$	16.6393	0.737523	0.368761	−	0.929524i	$-0.379782\pi$
$509$	16.6393	0.737523	0.368761	+	0.929524i	$0.379782\pi$
$510$	−1.90843	−0.0845065
$511$	0.00748694	0.000331203 0
$512$	1.00000	0.0441942
$513$	5.71969	0.252530
$514$	20.9695	0.924923
$515$	−3.06481	−0.135052
$516$	21.8968	0.963951
$517$	51.2617	2.25449
$518$	−2.90231	−0.127520
$519$	−19.4516	−0.853832
$520$	7.17658	0.314714
$521$	34.3543	1.50509	0.752545	−	0.658540i	$-0.228826\pi$
$521$	34.3543	1.50509	0.752545	+	0.658540i	$0.228826\pi$
$522$	−30.3320	−1.32760
$523$	20.3256	0.888778	0.444389	−	0.895834i	$-0.353421\pi$
$523$	20.3256	0.888778	0.444389	+	0.895834i	$0.353421\pi$
$524$	19.5959	0.856049
$525$	−39.1054	−1.70670
$526$	−12.9974	−0.566712
$527$	1.90597	0.0830252
$528$	14.8215	0.645023
$529$	9.85219	0.428356
$530$	−18.1975	−0.790451
$531$	−28.2827	−1.22736
$532$	4.11947	0.178602
$533$	46.8539	2.02947
$534$	21.0111	0.909239
$535$	16.1875	0.699846
$536$	6.03732	0.260772
$537$	−7.52339	−0.324658
$538$	−12.3036	−0.530444
$539$	−52.1806	−2.24758
$540$	−7.34241	−0.315967
$541$	−16.8219	−0.723230	−0.361615	−	0.932328i	$-0.617774\pi$
$541$	−16.8219	−0.723230	−0.361615	+	0.932328i	$0.617774\pi$
$542$	20.9145	0.898353
$543$	59.3034	2.54495
$544$	0.524964	0.0225076
$545$	0.458690	0.0196481
$546$	65.2187	2.79110
$547$	35.4720	1.51668	0.758338	−	0.651862i	$-0.226012\pi$
$547$	35.4720	1.51668	0.758338	+	0.651862i	$0.226012\pi$
$548$	11.2612	0.481054
$549$	30.7677	1.31313
$550$	17.5440	0.748078
$551$	6.04256	0.257422
$552$	−16.2316	−0.690864
$553$	44.9198	1.91018
$554$	−8.96764	−0.380999
$555$	−2.56123	−0.108718
$556$	22.9412	0.972925
$557$	8.67246	0.367464	0.183732	−	0.982976i	$-0.441182\pi$
$557$	8.67246	0.367464	0.183732	+	0.982976i	$0.441182\pi$
$558$	18.2250	0.771524
$559$	−43.2266	−1.82829
$560$	−5.28820	−0.223467
$561$	7.78075	0.328503
$562$	−2.55717	−0.107868
$563$	7.94154	0.334696	0.167348	−	0.985898i	$-0.446480\pi$
$563$	7.94154	0.334696	0.167348	+	0.985898i	$0.446480\pi$
$564$	27.7371	1.16794
$565$	−18.8400	−0.792605
$566$	−9.75811	−0.410164
$567$	−4.68993	−0.196958
$568$	−3.00259	−0.125986
$569$	−11.9295	−0.500109	−0.250054	−	0.968232i	$-0.580449\pi$
$569$	−11.9295	−0.500109	−0.250054	+	0.968232i	$0.580449\pi$
$570$	3.63535	0.152268
$571$	2.24578	0.0939830	0.0469915	−	0.998895i	$-0.485037\pi$
$571$	2.24578	0.0939830	0.0469915	+	0.998895i	$0.485037\pi$
$572$	−29.2593	−1.22339
$573$	25.2737	1.05582
$574$	−34.5252	−1.44105
$575$	−19.2131	−0.801243
$576$	5.01973	0.209155
$577$	17.6498	0.734771	0.367385	−	0.930069i	$-0.380253\pi$
$577$	17.6498	0.734771	0.367385	+	0.930069i	$0.380253\pi$
$578$	−16.7244	−0.695644
$579$	−59.5622	−2.47532
$580$	−7.75689	−0.322087
$581$	−29.8218	−1.23722
$582$	−12.2455	−0.507592
$583$	74.1923	3.07273
$584$	−0.00181745	−7.52067e−5 0
$585$	36.0245	1.48943
$586$	22.1512	0.915059
$587$	−24.3389	−1.00457	−0.502287	−	0.864701i	$-0.667508\pi$
$587$	−24.3389	−1.00457	−0.502287	+	0.864701i	$0.667508\pi$
$588$	−28.2343	−1.16436
$589$	−3.63067	−0.149599
$590$	−7.23281	−0.297770
$591$	−45.3981	−1.86743
$592$	0.704536	0.0289562
$593$	−1.29881	−0.0533358	−0.0266679	−	0.999644i	$-0.508490\pi$
$593$	−1.29881	−0.0533358	−0.0266679	+	0.999644i	$0.508490\pi$
$594$	29.9354	1.22826
$595$	−2.77611	−0.113809
$596$	5.79470	0.237360
$597$	−29.2507	−1.19715
$598$	32.0430	1.31034
$599$	20.2483	0.827324	0.413662	−	0.910431i	$-0.364250\pi$
$599$	20.2483	0.827324	0.413662	+	0.910431i	$0.364250\pi$
$600$	9.49283	0.387543
$601$	−33.3441	−1.36013	−0.680067	−	0.733150i	$-0.738049\pi$
$601$	−33.3441	−1.36013	−0.680067	+	0.733150i	$0.738049\pi$
$602$	31.8523	1.29820
$603$	30.3057	1.23414
$604$	−12.6055	−0.512912
$605$	21.0426	0.855504
$606$	−35.5772	−1.44523
$607$	38.9819	1.58223	0.791113	−	0.611670i	$-0.209502\pi$
$607$	38.9819	1.58223	0.791113	+	0.611670i	$0.209502\pi$
$608$	−1.00000	−0.0405554
$609$	−70.4924	−2.85650
$610$	7.86830	0.318578
$611$	−54.7560	−2.21519
$612$	2.63517	0.106521
$613$	21.3296	0.861495	0.430748	−	0.902472i	$-0.358250\pi$
$613$	21.3296	0.861495	0.430748	+	0.902472i	$0.358250\pi$
$614$	18.8790	0.761895
$615$	−30.4678	−1.22858
$616$	21.5602	0.868687
$617$	−20.2404	−0.814847	−0.407424	−	0.913239i	$-0.633573\pi$
$617$	−20.2404	−0.814847	−0.407424	+	0.913239i	$0.633573\pi$
$618$	6.76109	0.271971
$619$	43.2649	1.73896	0.869482	−	0.493965i	$-0.164453\pi$
$619$	43.2649	1.73896	0.869482	+	0.493965i	$0.164453\pi$
$620$	4.66072	0.187179
$621$	−32.7835	−1.31555
$622$	−5.03635	−0.201939
$623$	30.5640	1.22452
$624$	−15.8318	−0.633780
$625$	2.99699	0.119879
$626$	25.5334	1.02052
$627$	−14.8215	−0.591914
$628$	−16.4178	−0.655142
$629$	0.369856	0.0147471
$630$	−26.5453	−1.05759
$631$	−39.4632	−1.57101	−0.785503	−	0.618858i	$-0.787596\pi$
$631$	−39.4632	−1.57101	−0.785503	+	0.618858i	$0.787596\pi$
$632$	−10.9043	−0.433748
$633$	2.83191	0.112558
$634$	31.3517	1.24513
$635$	15.1710	0.602041
$636$	40.1445	1.59183
$637$	55.7375	2.20840
$638$	31.6252	1.25205
$639$	−15.0722	−0.596246
$640$	1.28371	0.0507430
$641$	−26.9674	−1.06515	−0.532574	−	0.846383i	$-0.678775\pi$
$641$	−26.9674	−1.06515	−0.532574	+	0.846383i	$0.678775\pi$
$642$	−35.7103	−1.40937
$643$	−1.14849	−0.0452922	−0.0226461	−	0.999744i	$-0.507209\pi$
$643$	−1.14849	−0.0452922	−0.0226461	+	0.999744i	$0.507209\pi$
$644$	−23.6115	−0.930423
$645$	28.1090	1.10679
$646$	−0.524964	−0.0206544
$647$	−23.6049	−0.928003	−0.464002	−	0.885834i	$-0.653587\pi$
$647$	−23.6049	−0.928003	−0.464002	+	0.885834i	$0.653587\pi$
$648$	1.13848	0.0447237
$649$	29.4885	1.15752
$650$	−18.7399	−0.735039
$651$	42.3553	1.66003
$652$	13.8959	0.544207
$653$	−5.96224	−0.233320	−0.116660	−	0.993172i	$-0.537219\pi$
$653$	−5.96224	−0.233320	−0.116660	+	0.993172i	$0.537219\pi$
$654$	−1.01189	−0.0395679
$655$	25.1554	0.982902
$656$	8.38098	0.327222
$657$	−0.00912311	−0.000355926 0
$658$	40.3480	1.57293
$659$	−5.28961	−0.206054	−0.103027	−	0.994679i	$-0.532853\pi$
$659$	−5.28961	−0.206054	−0.103027	+	0.994679i	$0.532853\pi$
$660$	19.0265	0.740605
$661$	−35.1871	−1.36862	−0.684310	−	0.729191i	$-0.739897\pi$
$661$	−35.1871	−1.36862	−0.684310	+	0.729191i	$0.739897\pi$
$662$	16.7295	0.650211
$663$	−8.31113	−0.322777
$664$	7.23923	0.280937
$665$	5.28820	0.205068
$666$	3.53658	0.137040
$667$	−34.6340	−1.34104
$668$	−10.0983	−0.390713
$669$	−38.6786	−1.49540
$670$	7.75016	0.299415
$671$	−32.0794	−1.23841
$672$	11.6660	0.450025
$673$	23.4092	0.902357	0.451178	−	0.892434i	$-0.351004\pi$
$673$	23.4092	0.902357	0.451178	+	0.892434i	$0.351004\pi$
$674$	26.3620	1.01543
$675$	19.1729	0.737966
$676$	18.2537	0.702067
$677$	37.0478	1.42386	0.711931	−	0.702249i	$-0.247821\pi$
$677$	37.0478	1.42386	0.711931	+	0.702249i	$0.247821\pi$
$678$	41.5618	1.59617
$679$	−17.8130	−0.683602
$680$	0.673900	0.0258429
$681$	72.7196	2.78662
$682$	−19.0020	−0.727623
$683$	−19.2393	−0.736171	−0.368086	−	0.929792i	$-0.619987\pi$
$683$	−19.2393	−0.736171	−0.368086	+	0.929792i	$0.619987\pi$
$684$	−5.01973	−0.191934
$685$	14.4561	0.552339
$686$	−12.2350	−0.467134
$687$	−66.5112	−2.53756
$688$	−7.73214	−0.294785
$689$	−79.2497	−3.01917
$690$	−20.8367	−0.793239
$691$	−2.61908	−0.0996344	−0.0498172	−	0.998758i	$-0.515864\pi$
$691$	−2.61908	−0.0996344	−0.0498172	+	0.998758i	$0.515864\pi$
$692$	6.86873	0.261110
$693$	108.227	4.11119
$694$	−15.9815	−0.606650
$695$	29.4499	1.11710
$696$	17.1120	0.648629
$697$	4.39971	0.166651
$698$	−12.5484	−0.474964
$699$	54.0653	2.04494
$700$	13.8088	0.521925
$701$	40.8641	1.54342	0.771709	−	0.635976i	$-0.219402\pi$
$701$	40.8641	1.54342	0.771709	+	0.635976i	$0.219402\pi$
$702$	−31.9760	−1.20685
$703$	−0.704536	−0.0265721
$704$	−5.23374	−0.197254
$705$	35.6063	1.34101
$706$	−22.5524	−0.848770
$707$	−51.7528	−1.94636
$708$	15.9559	0.599658
$709$	50.5698	1.89919	0.949593	−	0.313484i	$-0.101496\pi$
$709$	50.5698	1.89919	0.949593	+	0.313484i	$0.101496\pi$
$710$	−3.85445	−0.144655
$711$	−54.7364	−2.05278
$712$	−7.41940	−0.278054
$713$	20.8098	0.779334
$714$	6.12421	0.229193
$715$	−37.5604	−1.40468
$716$	2.65665	0.0992836
$717$	−7.88192	−0.294356
$718$	−10.6303	−0.396719
$719$	−11.9160	−0.444393	−0.222197	−	0.975002i	$-0.571323\pi$
$719$	−11.9160	−0.444393	−0.222197	+	0.975002i	$0.571323\pi$
$720$	6.44387	0.240149
$721$	9.83510	0.366278
$722$	1.00000	0.0372161
$723$	−77.1169	−2.86801
$724$	−20.9411	−0.778271
$725$	20.2552	0.752260
$726$	−46.4209	−1.72284
$727$	51.0029	1.89159	0.945797	−	0.324758i	$-0.105283\pi$
$727$	51.0029	1.89159	0.945797	+	0.324758i	$0.105283\pi$
$728$	−23.0299	−0.853546
$729$	−42.8781	−1.58808
$730$	−0.00233308	−8.63511e−5 0
$731$	−4.05909	−0.150131
$732$	−17.3578	−0.641562
$733$	−12.2799	−0.453568	−0.226784	−	0.973945i	$-0.572821\pi$
$733$	−12.2799	−0.453568	−0.226784	+	0.973945i	$0.572821\pi$
$734$	−9.82680	−0.362714
$735$	−36.2446	−1.33690
$736$	5.73168	0.211273
$737$	−31.5978	−1.16392
$738$	42.0702	1.54863
$739$	−20.6690	−0.760322	−0.380161	−	0.924920i	$-0.624131\pi$
$739$	−20.6690	−0.760322	−0.380161	+	0.924920i	$0.624131\pi$
$740$	0.904419	0.0332471
$741$	15.8318	0.581596
$742$	58.3966	2.14381
$743$	2.61303	0.0958629	0.0479315	−	0.998851i	$-0.484737\pi$
$743$	2.61303	0.0958629	0.0479315	+	0.998851i	$0.484737\pi$
$744$	−10.2817	−0.376946
$745$	7.43871	0.272533
$746$	−33.3362	−1.22053
$747$	36.3390	1.32957
$748$	−2.74752	−0.100459
$749$	−51.9463	−1.89808
$750$	30.3628	1.10869
$751$	−39.7386	−1.45008	−0.725041	−	0.688705i	$-0.758179\pi$
$751$	−39.7386	−1.45008	−0.725041	+	0.688705i	$0.758179\pi$
$752$	−9.79446	−0.357167
$753$	−51.6287	−1.88146
$754$	−33.7810	−1.23023
$755$	−16.1818	−0.588918
$756$	23.5621	0.856945
$757$	−1.80296	−0.0655298	−0.0327649	−	0.999463i	$-0.510431\pi$
$757$	−1.80296	−0.0655298	−0.0327649	+	0.999463i	$0.510431\pi$
$758$	5.11277	0.185704
$759$	84.9521	3.08357
$760$	−1.28371	−0.0465650
$761$	−7.51392	−0.272380	−0.136190	−	0.990683i	$-0.543486\pi$
$761$	−7.51392	−0.272380	−0.136190	+	0.990683i	$0.543486\pi$
$762$	−33.4677	−1.21241
$763$	−1.47195	−0.0532883
$764$	−8.92459	−0.322880
$765$	3.38279	0.122305
$766$	−21.3710	−0.772165
$767$	−31.4986	−1.13735
$768$	−2.83191	−0.102188
$769$	−15.6871	−0.565691	−0.282845	−	0.959165i	$-0.591278\pi$
$769$	−15.6871	−0.565691	−0.282845	+	0.959165i	$0.591278\pi$
$770$	27.6771	0.997412
$771$	−59.3836	−2.13865
$772$	21.0325	0.756976
$773$	−16.5299	−0.594540	−0.297270	−	0.954793i	$-0.596076\pi$
$773$	−16.5299	−0.594540	−0.297270	+	0.954793i	$0.596076\pi$
$774$	−38.8133	−1.39511
$775$	−12.1703	−0.437171
$776$	4.32411	0.155226
$777$	8.21910	0.294859
$778$	11.0314	0.395495
$779$	−8.38098	−0.300280
$780$	−20.3234	−0.727696
$781$	15.7148	0.562319
$782$	3.00892	0.107599
$783$	34.5616	1.23513
$784$	9.97004	0.356073
$785$	−21.0757	−0.752223
$786$	−55.4938	−1.97940
$787$	−14.3823	−0.512675	−0.256338	−	0.966587i	$-0.582516\pi$
$787$	−14.3823	−0.512675	−0.256338	+	0.966587i	$0.582516\pi$
$788$	16.0309	0.571077
$789$	36.8074	1.31038
$790$	−13.9979	−0.498023
$791$	60.4583	2.14965
$792$	−26.2720	−0.933533
$793$	34.2661	1.21683
$794$	26.1916	0.929505
$795$	51.5339	1.82772
$796$	10.3290	0.366100
$797$	29.9228	1.05992	0.529959	−	0.848023i	$-0.322207\pi$
$797$	29.9228	1.05992	0.529959	+	0.848023i	$0.322207\pi$
$798$	−11.6660	−0.412971
$799$	−5.14174	−0.181902
$800$	−3.35209	−0.118514
$801$	−37.2434	−1.31593
$802$	34.2743	1.21027
$803$	0.00951207	0.000335674 0
$804$	−17.0972	−0.602970
$805$	−30.3103	−1.06830
$806$	20.2973	0.714940
$807$	34.8426	1.22652
$808$	12.5630	0.441964
$809$	8.99588	0.316278	0.158139	−	0.987417i	$-0.449451\pi$
$809$	8.99588	0.316278	0.158139	+	0.987417i	$0.449451\pi$
$810$	1.46147	0.0513510
$811$	8.61968	0.302678	0.151339	−	0.988482i	$-0.451641\pi$
$811$	8.61968	0.302678	0.151339	+	0.988482i	$0.451641\pi$
$812$	24.8921	0.873543
$813$	−59.2279	−2.07721
$814$	−3.68736	−0.129242
$815$	17.8383	0.624849
$816$	−1.48665	−0.0520432
$817$	7.73214	0.270513
$818$	−37.4081	−1.30794
$819$	−115.604	−4.03953
$820$	10.7587	0.375711
$821$	−13.2047	−0.460847	−0.230423	−	0.973090i	$-0.574011\pi$
$821$	−13.2047	−0.460847	−0.230423	+	0.973090i	$0.574011\pi$
$822$	−31.8907	−1.11232
$823$	0.0138661	0.000483342 0	0.000241671	−	1.00000i	$-0.499923\pi$
$823$	0.0138661	0.000483342 0	0.000241671		1.00000i	$0.499923\pi$
$824$	−2.38747	−0.0831713
$825$	−49.6830	−1.72974
$826$	23.2104	0.807592
$827$	38.0651	1.32365	0.661827	−	0.749656i	$-0.269781\pi$
$827$	38.0651	1.32365	0.661827	+	0.749656i	$0.269781\pi$
$828$	28.7715	0.999878
$829$	8.32910	0.289282	0.144641	−	0.989484i	$-0.453797\pi$
$829$	8.32910	0.289282	0.144641	+	0.989484i	$0.453797\pi$
$830$	9.29306	0.322567
$831$	25.3956	0.880963
$832$	5.59050	0.193816
$833$	5.23391	0.181344
$834$	−64.9676	−2.24964
$835$	−12.9632	−0.448611
$836$	5.23374	0.181013
$837$	−20.7663	−0.717788
$838$	−11.4922	−0.396990
$839$	−26.5057	−0.915078	−0.457539	−	0.889189i	$-0.651269\pi$
$839$	−26.5057	−0.915078	−0.457539	+	0.889189i	$0.651269\pi$
$840$	14.9757	0.516711
$841$	7.51252	0.259053
$842$	−27.6770	−0.953812
$843$	7.24169	0.249417
$844$	−1.00000	−0.0344214
$845$	23.4325	0.806102
$846$	−49.1655	−1.69035
$847$	−67.5266	−2.32024
$848$	−14.1758	−0.486798
$849$	27.6341	0.948401
$850$	−1.75973	−0.0603581
$851$	4.03818	0.138427
$852$	8.50307	0.291310
$853$	−33.2364	−1.13799	−0.568996	−	0.822340i	$-0.692668\pi$
$853$	−33.2364	−1.13799	−0.568996	+	0.822340i	$0.692668\pi$
$854$	−25.2497	−0.864026
$855$	−6.44387	−0.220376
$856$	12.6099	0.430999
$857$	22.0699	0.753895	0.376948	−	0.926235i	$-0.376974\pi$
$857$	22.0699	0.753895	0.376948	+	0.926235i	$0.376974\pi$
$858$	82.8597	2.82878
$859$	−52.1401	−1.77900	−0.889498	−	0.456939i	$-0.848946\pi$
$859$	−52.1401	−1.77900	−0.889498	+	0.456939i	$0.848946\pi$
$860$	−9.92582	−0.338468
$861$	97.7723	3.33207
$862$	27.9087	0.950575
$863$	−18.5005	−0.629764	−0.314882	−	0.949131i	$-0.601965\pi$
$863$	−18.5005	−0.629764	−0.314882	+	0.949131i	$0.601965\pi$
$864$	−5.71969	−0.194588
$865$	8.81745	0.299802
$866$	19.8795	0.675532
$867$	47.3621	1.60850
$868$	−14.9564	−0.507654
$869$	57.0701	1.93597
$870$	21.9668	0.744745
$871$	33.7516	1.14363
$872$	0.357316	0.0121002
$873$	21.7058	0.734631
$874$	−5.73168	−0.193877
$875$	44.1675	1.49314
$876$	0.00514686	0.000173896 0
$877$	44.6124	1.50645	0.753227	−	0.657761i	$-0.228496\pi$
$877$	44.6124	1.50645	0.753227	+	0.657761i	$0.228496\pi$
$878$	−18.4375	−0.622234
$879$	−62.7303	−2.11584
$880$	−6.71860	−0.226484
$881$	−51.9611	−1.75061	−0.875307	−	0.483567i	$-0.839341\pi$
$881$	−51.9611	−1.75061	−0.875307	+	0.483567i	$0.839341\pi$
$882$	50.0469	1.68517
$883$	2.67045	0.0898677	0.0449339	−	0.998990i	$-0.485692\pi$
$883$	2.67045	0.0898677	0.0449339	+	0.998990i	$0.485692\pi$
$884$	2.93481	0.0987084
$885$	20.4827	0.688517
$886$	33.8701	1.13789
$887$	41.5772	1.39603	0.698014	−	0.716084i	$-0.254067\pi$
$887$	41.5772	1.39603	0.698014	+	0.716084i	$0.254067\pi$
$888$	−1.99518	−0.0669540
$889$	−48.6842	−1.63281
$890$	−9.52435	−0.319257
$891$	−5.95850	−0.199617
$892$	13.6581	0.457308
$893$	9.79446	0.327759
$894$	−16.4101	−0.548835
$895$	3.41036	0.113996
$896$	−4.11947	−0.137622
$897$	−90.7430	−3.02982
$898$	19.6729	0.656494
$899$	−21.9385	−0.731690
$900$	−16.8266	−0.560886
$901$	−7.44176	−0.247921
$902$	−43.8639	−1.46051
$903$	−90.2030	−3.00177
$904$	−14.6762	−0.488124
$905$	−26.8823	−0.893598
$906$	35.6978	1.18598
$907$	−38.7421	−1.28641	−0.643205	−	0.765694i	$-0.722396\pi$
$907$	−38.7421	−1.28641	−0.643205	+	0.765694i	$0.722396\pi$
$908$	−25.6786	−0.852175
$909$	63.0627	2.09166
$910$	−29.5637	−0.980027
$911$	−11.9422	−0.395663	−0.197832	−	0.980236i	$-0.563390\pi$
$911$	−11.9422	−0.395663	−0.197832	+	0.980236i	$0.563390\pi$
$912$	2.83191	0.0937740
$913$	−37.8883	−1.25392
$914$	−2.54516	−0.0841864
$915$	−22.2823	−0.736631
$916$	23.4863	0.776009
$917$	−80.7246	−2.66576
$918$	−3.00263	−0.0991015
$919$	6.08053	0.200578	0.100289	−	0.994958i	$-0.468023\pi$
$919$	6.08053	0.200578	0.100289	+	0.994958i	$0.468023\pi$
$920$	7.35781	0.242580
$921$	−53.4637	−1.76169
$922$	−11.6962	−0.385193
$923$	−16.7860	−0.552517
$924$	−61.0567	−2.00862
$925$	−2.36167	−0.0776512
$926$	7.72399	0.253826
$927$	−11.9844	−0.393620
$928$	−6.04256	−0.198357
$929$	31.7492	1.04166	0.520828	−	0.853661i	$-0.325623\pi$
$929$	31.7492	1.04166	0.520828	+	0.853661i	$0.325623\pi$
$930$	−13.1987	−0.432804
$931$	−9.97004	−0.326755
$932$	−19.0914	−0.625361
$933$	14.2625	0.466933
$934$	10.9455	0.358148
$935$	−3.52702	−0.115346
$936$	28.0628	0.917262
$937$	7.04364	0.230106	0.115053	−	0.993359i	$-0.463296\pi$
$937$	7.04364	0.230106	0.115053	+	0.993359i	$0.463296\pi$
$938$	−24.8705	−0.812052
$939$	−72.3084	−2.35970
$940$	−12.5732	−0.410094
$941$	55.6064	1.81272	0.906359	−	0.422509i	$-0.138851\pi$
$941$	55.6064	1.81272	0.906359	+	0.422509i	$0.138851\pi$
$942$	46.4938	1.51485
$943$	48.0371	1.56430
$944$	−5.63431	−0.183381
$945$	30.2469	0.983930
$946$	40.4680	1.31573
$947$	3.42796	0.111394	0.0556969	−	0.998448i	$-0.482262\pi$
$947$	3.42796	0.111394	0.0556969	+	0.998448i	$0.482262\pi$
$948$	30.8799	1.00293
$949$	−0.0101605	−0.000329823 0
$950$	3.35209	0.108756
$951$	−88.7852	−2.87906
$952$	−2.16257	−0.0700894
$953$	29.8183	0.965910	0.482955	−	0.875645i	$-0.339563\pi$
$953$	29.8183	0.965910	0.482955	+	0.875645i	$0.339563\pi$
$954$	−71.1585	−2.30384
$955$	−11.4566	−0.370726
$956$	2.78325	0.0900168
$957$	−89.5598	−2.89506
$958$	22.7293	0.734350
$959$	−46.3902	−1.49802
$960$	−3.63535	−0.117330
$961$	−17.8183	−0.574783
$962$	3.93871	0.126989
$963$	63.2985	2.03977
$964$	27.2314	0.877064
$965$	26.9996	0.869148
$966$	66.8657	2.15137
$967$	30.8109	0.990811	0.495405	−	0.868662i	$-0.335020\pi$
$967$	30.8109	0.990811	0.495405	+	0.868662i	$0.335020\pi$
$968$	16.3921	0.526861
$969$	1.48665	0.0477581
$970$	5.55089	0.178228
$971$	−46.9490	−1.50667	−0.753333	−	0.657640i	$-0.771555\pi$
$971$	−46.9490	−1.50667	−0.753333	+	0.657640i	$0.771555\pi$
$972$	13.9350	0.446965
$973$	−94.5057	−3.02972
$974$	30.0182	0.961846
$975$	53.0697	1.69959
$976$	6.12935	0.196196
$977$	18.1762	0.581509	0.290754	−	0.956798i	$-0.406094\pi$
$977$	18.1762	0.581509	0.290754	+	0.956798i	$0.406094\pi$
$978$	−39.3521	−1.25834
$979$	38.8312	1.24105
$980$	12.7986	0.408837
$981$	1.79363	0.0572662
$982$	−13.5501	−0.432400
$983$	−1.29361	−0.0412597	−0.0206298	−	0.999787i	$-0.506567\pi$
$983$	−1.29361	−0.0412597	−0.0206298	+	0.999787i	$0.506567\pi$
$984$	−23.7342	−0.756619
$985$	20.5790	0.655702
$986$	−3.17212	−0.101021
$987$	−114.262	−3.63700
$988$	−5.59050	−0.177858
$989$	−44.3182	−1.40924
$990$	−33.7255	−1.07187
$991$	36.4309	1.15727	0.578633	−	0.815588i	$-0.303586\pi$
$991$	36.4309	1.15727	0.578633	+	0.815588i	$0.303586\pi$
$992$	3.63067	0.115274
$993$	−47.3765	−1.50345
$994$	12.3691	0.392323
$995$	13.2594	0.420351
$996$	−20.5009	−0.649595
$997$	−32.6614	−1.03440	−0.517198	−	0.855866i	$-0.673025\pi$
$997$	−32.6614	−1.03440	−0.517198	+	0.855866i	$0.673025\pi$
$998$	8.09968	0.256391
$999$	−4.02973	−0.127495

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.5	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.5	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.83191 q^{3} +1.00000 q^{4} +1.28371 q^{5} -2.83191 q^{6} -4.11947 q^{7} +1.00000 q^{8} +5.01973 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.83191 q^{3} +1.00000 q^{4} +1.28371 q^{5} -2.83191 q^{6} -4.11947 q^{7} +1.00000 q^{8} +5.01973 q^{9} +1.28371 q^{10} -5.23374 q^{11} -2.83191 q^{12} +5.59050 q^{13} -4.11947 q^{14} -3.63535 q^{15} +1.00000 q^{16} +0.524964 q^{17} +5.01973 q^{18} -1.00000 q^{19} +1.28371 q^{20} +11.6660 q^{21} -5.23374 q^{22} +5.73168 q^{23} -2.83191 q^{24} -3.35209 q^{25} +5.59050 q^{26} -5.71969 q^{27} -4.11947 q^{28} -6.04256 q^{29} -3.63535 q^{30} +3.63067 q^{31} +1.00000 q^{32} +14.8215 q^{33} +0.524964 q^{34} -5.28820 q^{35} +5.01973 q^{36} +0.704536 q^{37} -1.00000 q^{38} -15.8318 q^{39} +1.28371 q^{40} +8.38098 q^{41} +11.6660 q^{42} -7.73214 q^{43} -5.23374 q^{44} +6.44387 q^{45} +5.73168 q^{46} -9.79446 q^{47} -2.83191 q^{48} +9.97004 q^{49} -3.35209 q^{50} -1.48665 q^{51} +5.59050 q^{52} -14.1758 q^{53} -5.71969 q^{54} -6.71860 q^{55} -4.11947 q^{56} +2.83191 q^{57} -6.04256 q^{58} -5.63431 q^{59} -3.63535 q^{60} +6.12935 q^{61} +3.63067 q^{62} -20.6786 q^{63} +1.00000 q^{64} +7.17658 q^{65} +14.8215 q^{66} +6.03732 q^{67} +0.524964 q^{68} -16.2316 q^{69} -5.28820 q^{70} -3.00259 q^{71} +5.01973 q^{72} -0.00181745 q^{73} +0.704536 q^{74} +9.49283 q^{75} -1.00000 q^{76} +21.5602 q^{77} -15.8318 q^{78} -10.9043 q^{79} +1.28371 q^{80} +1.13848 q^{81} +8.38098 q^{82} +7.23923 q^{83} +11.6660 q^{84} +0.673900 q^{85} -7.73214 q^{86} +17.1120 q^{87} -5.23374 q^{88} -7.41940 q^{89} +6.44387 q^{90} -23.0299 q^{91} +5.73168 q^{92} -10.2817 q^{93} -9.79446 q^{94} -1.28371 q^{95} -2.83191 q^{96} +4.32411 q^{97} +9.97004 q^{98} -26.2720 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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