LMFDB - Embedded newform 8018.2.a.j.1.10

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			1.10
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)

$f(q)$	$=$	$q+1.00000 q^{2} -2.00763 q^{3} +1.00000 q^{4} -1.79399 q^{5} -2.00763 q^{6} -2.43862 q^{7} +1.00000 q^{8} +1.03060 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.00763 q^{3} +1.00000 q^{4} -1.79399 q^{5} -2.00763 q^{6} -2.43862 q^{7} +1.00000 q^{8} +1.03060 q^{9} -1.79399 q^{10} -1.56812 q^{11} -2.00763 q^{12} -4.34066 q^{13} -2.43862 q^{14} +3.60167 q^{15} +1.00000 q^{16} -2.98642 q^{17} +1.03060 q^{18} -1.00000 q^{19} -1.79399 q^{20} +4.89585 q^{21} -1.56812 q^{22} +1.92268 q^{23} -2.00763 q^{24} -1.78161 q^{25} -4.34066 q^{26} +3.95384 q^{27} -2.43862 q^{28} +0.562491 q^{29} +3.60167 q^{30} -4.85429 q^{31} +1.00000 q^{32} +3.14822 q^{33} -2.98642 q^{34} +4.37484 q^{35} +1.03060 q^{36} -3.93975 q^{37} -1.00000 q^{38} +8.71445 q^{39} -1.79399 q^{40} -11.0744 q^{41} +4.89585 q^{42} -8.43678 q^{43} -1.56812 q^{44} -1.84888 q^{45} +1.92268 q^{46} -6.03573 q^{47} -2.00763 q^{48} -1.05316 q^{49} -1.78161 q^{50} +5.99564 q^{51} -4.34066 q^{52} -4.46382 q^{53} +3.95384 q^{54} +2.81319 q^{55} -2.43862 q^{56} +2.00763 q^{57} +0.562491 q^{58} +14.3798 q^{59} +3.60167 q^{60} -12.9806 q^{61} -4.85429 q^{62} -2.51323 q^{63} +1.00000 q^{64} +7.78708 q^{65} +3.14822 q^{66} -15.9394 q^{67} -2.98642 q^{68} -3.86004 q^{69} +4.37484 q^{70} +8.05400 q^{71} +1.03060 q^{72} +2.43690 q^{73} -3.93975 q^{74} +3.57683 q^{75} -1.00000 q^{76} +3.82405 q^{77} +8.71445 q^{78} -2.99978 q^{79} -1.79399 q^{80} -11.0297 q^{81} -11.0744 q^{82} +9.69270 q^{83} +4.89585 q^{84} +5.35760 q^{85} -8.43678 q^{86} -1.12928 q^{87} -1.56812 q^{88} -11.2633 q^{89} -1.84888 q^{90} +10.5852 q^{91} +1.92268 q^{92} +9.74564 q^{93} -6.03573 q^{94} +1.79399 q^{95} -2.00763 q^{96} +3.44243 q^{97} -1.05316 q^{98} -1.61610 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−2.00763	−1.15911	−0.579554	−	0.814934i	$-0.696773\pi$
$3$	−2.00763	−1.15911	−0.579554	+	0.814934i	$0.696773\pi$
$4$	1.00000	0.500000
$5$	−1.79399	−0.802295	−0.401147	−	0.916013i	$-0.631389\pi$
$5$	−1.79399	−0.802295	−0.401147	+	0.916013i	$0.631389\pi$
$6$	−2.00763	−0.819614
$7$	−2.43862	−0.921710	−0.460855	−	0.887475i	$-0.652457\pi$
$7$	−2.43862	−0.921710	−0.460855	+	0.887475i	$0.652457\pi$
$8$	1.00000	0.353553
$9$	1.03060	0.343533
$10$	−1.79399	−0.567308
$11$	−1.56812	−0.472807	−0.236403	−	0.971655i	$-0.575969\pi$
$11$	−1.56812	−0.472807	−0.236403	+	0.971655i	$0.575969\pi$
$12$	−2.00763	−0.579554
$13$	−4.34066	−1.20388	−0.601941	−	0.798541i	$-0.705606\pi$
$13$	−4.34066	−1.20388	−0.601941	+	0.798541i	$0.705606\pi$
$14$	−2.43862	−0.651747
$15$	3.60167	0.929947
$16$	1.00000	0.250000
$17$	−2.98642	−0.724313	−0.362157	−	0.932117i	$-0.617959\pi$
$17$	−2.98642	−0.724313	−0.362157	+	0.932117i	$0.617959\pi$
$18$	1.03060	0.242914
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	−1.79399	−0.401147
$21$	4.89585	1.06836
$22$	−1.56812	−0.334325
$23$	1.92268	0.400906	0.200453	−	0.979703i	$-0.435759\pi$
$23$	1.92268	0.400906	0.200453	+	0.979703i	$0.435759\pi$
$24$	−2.00763	−0.409807
$25$	−1.78161	−0.356323
$26$	−4.34066	−0.851273
$27$	3.95384	0.760917
$28$	−2.43862	−0.460855
$29$	0.562491	0.104452	0.0522260	−	0.998635i	$-0.483368\pi$
$29$	0.562491	0.104452	0.0522260	+	0.998635i	$0.483368\pi$
$30$	3.60167	0.657572
$31$	−4.85429	−0.871856	−0.435928	−	0.899982i	$-0.643580\pi$
$31$	−4.85429	−0.871856	−0.435928	+	0.899982i	$0.643580\pi$
$32$	1.00000	0.176777
$33$	3.14822	0.548034
$34$	−2.98642	−0.512167
$35$	4.37484	0.739483
$36$	1.03060	0.171766
$37$	−3.93975	−0.647691	−0.323846	−	0.946110i	$-0.604976\pi$
$37$	−3.93975	−0.647691	−0.323846	+	0.946110i	$0.604976\pi$
$38$	−1.00000	−0.162221
$39$	8.71445	1.39543
$40$	−1.79399	−0.283654
$41$	−11.0744	−1.72954	−0.864768	−	0.502172i	$-0.832534\pi$
$41$	−11.0744	−1.72954	−0.864768	+	0.502172i	$0.832534\pi$
$42$	4.89585	0.755446
$43$	−8.43678	−1.28660	−0.643298	−	0.765616i	$-0.722434\pi$
$43$	−8.43678	−1.28660	−0.643298	+	0.765616i	$0.722434\pi$
$44$	−1.56812	−0.236403
$45$	−1.84888	−0.275615
$46$	1.92268	0.283484
$47$	−6.03573	−0.880401	−0.440201	−	0.897899i	$-0.645093\pi$
$47$	−6.03573	−0.880401	−0.440201	+	0.897899i	$0.645093\pi$
$48$	−2.00763	−0.289777
$49$	−1.05316	−0.150451
$50$	−1.78161	−0.251958
$51$	5.99564	0.839558
$52$	−4.34066	−0.601941
$53$	−4.46382	−0.613153	−0.306577	−	0.951846i	$-0.599184\pi$
$53$	−4.46382	−0.613153	−0.306577	+	0.951846i	$0.599184\pi$
$54$	3.95384	0.538049
$55$	2.81319	0.379331
$56$	−2.43862	−0.325874
$57$	2.00763	0.265918
$58$	0.562491	0.0738587
$59$	14.3798	1.87209	0.936043	−	0.351886i	$-0.114459\pi$
$59$	14.3798	1.87209	0.936043	+	0.351886i	$0.114459\pi$
$60$	3.60167	0.464974
$61$	−12.9806	−1.66200	−0.830998	−	0.556275i	$-0.812230\pi$
$61$	−12.9806	−1.66200	−0.830998	+	0.556275i	$0.812230\pi$
$62$	−4.85429	−0.616495
$63$	−2.51323	−0.316638
$64$	1.00000	0.125000
$65$	7.78708	0.965868
$66$	3.14822	0.387519
$67$	−15.9394	−1.94731	−0.973656	−	0.228020i	$-0.926775\pi$
$67$	−15.9394	−1.94731	−0.973656	+	0.228020i	$0.926775\pi$
$68$	−2.98642	−0.362157
$69$	−3.86004	−0.464694
$70$	4.37484	0.522894
$71$	8.05400	0.955834	0.477917	−	0.878405i	$-0.341392\pi$
$71$	8.05400	0.955834	0.477917	+	0.878405i	$0.341392\pi$
$72$	1.03060	0.121457
$73$	2.43690	0.285217	0.142609	−	0.989779i	$-0.454451\pi$
$73$	2.43690	0.285217	0.142609	+	0.989779i	$0.454451\pi$
$74$	−3.93975	−0.457987
$75$	3.57683	0.413017
$76$	−1.00000	−0.114708
$77$	3.82405	0.435791
$78$	8.71445	0.986718
$79$	−2.99978	−0.337502	−0.168751	−	0.985659i	$-0.553973\pi$
$79$	−2.99978	−0.337502	−0.168751	+	0.985659i	$0.553973\pi$
$80$	−1.79399	−0.200574
$81$	−11.0297	−1.22552
$82$	−11.0744	−1.22297
$83$	9.69270	1.06391	0.531956	−	0.846772i	$-0.321457\pi$
$83$	9.69270	1.06391	0.531956	+	0.846772i	$0.321457\pi$
$84$	4.89585	0.534181
$85$	5.35760	0.581113
$86$	−8.43678	−0.909761
$87$	−1.12928	−0.121071
$88$	−1.56812	−0.167162
$89$	−11.2633	−1.19390	−0.596951	−	0.802277i	$-0.703621\pi$
$89$	−11.2633	−1.19390	−0.596951	+	0.802277i	$0.703621\pi$
$90$	−1.84888	−0.194889
$91$	10.5852	1.10963
$92$	1.92268	0.200453
$93$	9.74564	1.01058
$94$	−6.03573	−0.622538
$95$	1.79399	0.184059
$96$	−2.00763	−0.204903
$97$	3.44243	0.349526	0.174763	−	0.984611i	$-0.444084\pi$
$97$	3.44243	0.349526	0.174763	+	0.984611i	$0.444084\pi$
$98$	−1.05316	−0.106385
$99$	−1.61610	−0.162425
$100$	−1.78161	−0.178161
$101$	15.0221	1.49475	0.747376	−	0.664402i	$-0.231314\pi$
$101$	15.0221	1.49475	0.747376	+	0.664402i	$0.231314\pi$
$102$	5.99564	0.593657
$103$	1.88560	0.185793	0.0928967	−	0.995676i	$-0.470387\pi$
$103$	1.88560	0.185793	0.0928967	+	0.995676i	$0.470387\pi$
$104$	−4.34066	−0.425636
$105$	−8.78309	−0.857141
$106$	−4.46382	−0.433565
$107$	−15.1780	−1.46731	−0.733655	−	0.679522i	$-0.762187\pi$
$107$	−15.1780	−1.46731	−0.733655	+	0.679522i	$0.762187\pi$
$108$	3.95384	0.380458
$109$	−6.18520	−0.592434	−0.296217	−	0.955121i	$-0.595725\pi$
$109$	−6.18520	−0.592434	−0.296217	+	0.955121i	$0.595725\pi$
$110$	2.81319	0.268227
$111$	7.90958	0.750744
$112$	−2.43862	−0.230427
$113$	6.58029	0.619022	0.309511	−	0.950896i	$-0.399835\pi$
$113$	6.58029	0.619022	0.309511	+	0.950896i	$0.399835\pi$
$114$	2.00763	0.188032
$115$	−3.44926	−0.321645
$116$	0.562491	0.0522260
$117$	−4.47347	−0.413573
$118$	14.3798	1.32376
$119$	7.28273	0.667607
$120$	3.60167	0.328786
$121$	−8.54099	−0.776454
$122$	−12.9806	−1.17521
$123$	22.2334	2.00472
$124$	−4.85429	−0.435928
$125$	12.1661	1.08817
$126$	−2.51323	−0.223897
$127$	5.64488	0.500902	0.250451	−	0.968129i	$-0.419421\pi$
$127$	5.64488	0.500902	0.250451	+	0.968129i	$0.419421\pi$
$128$	1.00000	0.0883883
$129$	16.9380	1.49131
$130$	7.78708	0.682972
$131$	−22.2737	−1.94606	−0.973030	−	0.230679i	$-0.925905\pi$
$131$	−22.2737	−1.94606	−0.973030	+	0.230679i	$0.925905\pi$
$132$	3.14822	0.274017
$133$	2.43862	0.211455
$134$	−15.9394	−1.37696
$135$	−7.09313	−0.610480
$136$	−2.98642	−0.256083
$137$	16.4778	1.40780	0.703899	−	0.710301i	$-0.251441\pi$
$137$	16.4778	1.40780	0.703899	+	0.710301i	$0.251441\pi$
$138$	−3.86004	−0.328588
$139$	−11.6853	−0.991134	−0.495567	−	0.868570i	$-0.665040\pi$
$139$	−11.6853	−0.991134	−0.495567	+	0.868570i	$0.665040\pi$
$140$	4.37484	0.369742
$141$	12.1175	1.02048
$142$	8.05400	0.675877
$143$	6.80668	0.569203
$144$	1.03060	0.0858832
$145$	−1.00910	−0.0838013
$146$	2.43690	0.201679
$147$	2.11435	0.174389
$148$	−3.93975	−0.323846
$149$	8.74140	0.716123	0.358062	−	0.933698i	$-0.383438\pi$
$149$	8.74140	0.716123	0.358062	+	0.933698i	$0.383438\pi$
$150$	3.57683	0.292047
$151$	1.07980	0.0878725	0.0439362	−	0.999034i	$-0.486010\pi$
$151$	1.07980	0.0878725	0.0439362	+	0.999034i	$0.486010\pi$
$152$	−1.00000	−0.0811107
$153$	−3.07780	−0.248825
$154$	3.82405	0.308151
$155$	8.70853	0.699486
$156$	8.71445	0.697715
$157$	−2.01582	−0.160880	−0.0804402	−	0.996759i	$-0.525633\pi$
$157$	−2.01582	−0.160880	−0.0804402	+	0.996759i	$0.525633\pi$
$158$	−2.99978	−0.238650
$159$	8.96173	0.710711
$160$	−1.79399	−0.141827
$161$	−4.68867	−0.369519
$162$	−11.0297	−0.866572
$163$	21.8879	1.71439	0.857197	−	0.514988i	$-0.172204\pi$
$163$	21.8879	1.71439	0.857197	+	0.514988i	$0.172204\pi$
$164$	−11.0744	−0.864768
$165$	−5.64786	−0.439685
$166$	9.69270	0.752300
$167$	−4.09048	−0.316530	−0.158265	−	0.987397i	$-0.550590\pi$
$167$	−4.09048	−0.316530	−0.158265	+	0.987397i	$0.550590\pi$
$168$	4.89585	0.377723
$169$	5.84130	0.449331
$170$	5.35760	0.410909
$171$	−1.03060	−0.0788118
$172$	−8.43678	−0.643298
$173$	8.61177	0.654741	0.327370	−	0.944896i	$-0.393838\pi$
$173$	8.61177	0.654741	0.327370	+	0.944896i	$0.393838\pi$
$174$	−1.12928	−0.0856103
$175$	4.34467	0.328426
$176$	−1.56812	−0.118202
$177$	−28.8693	−2.16995
$178$	−11.2633	−0.844217
$179$	16.8064	1.25617	0.628085	−	0.778145i	$-0.283839\pi$
$179$	16.8064	1.25617	0.628085	+	0.778145i	$0.283839\pi$
$180$	−1.84888	−0.137807
$181$	6.55162	0.486978	0.243489	−	0.969904i	$-0.421708\pi$
$181$	6.55162	0.486978	0.243489	+	0.969904i	$0.421708\pi$
$182$	10.5852	0.784627
$183$	26.0603	1.92643
$184$	1.92268	0.141742
$185$	7.06786	0.519639
$186$	9.74564	0.714585
$187$	4.68307	0.342460
$188$	−6.03573	−0.440201
$189$	−9.64189	−0.701345
$190$	1.79399	0.130149
$191$	−22.4079	−1.62138	−0.810688	−	0.585478i	$-0.800907\pi$
$191$	−22.4079	−1.62138	−0.810688	+	0.585478i	$0.800907\pi$
$192$	−2.00763	−0.144889
$193$	21.0583	1.51581	0.757904	−	0.652366i	$-0.226224\pi$
$193$	21.0583	1.51581	0.757904	+	0.652366i	$0.226224\pi$
$194$	3.44243	0.247152
$195$	−15.6336	−1.11955
$196$	−1.05316	−0.0752254
$197$	17.7540	1.26492	0.632461	−	0.774592i	$-0.282045\pi$
$197$	17.7540	1.26492	0.632461	+	0.774592i	$0.282045\pi$
$198$	−1.61610	−0.114852
$199$	10.1854	0.722023	0.361012	−	0.932561i	$-0.382432\pi$
$199$	10.1854	0.722023	0.361012	+	0.932561i	$0.382432\pi$
$200$	−1.78161	−0.125979
$201$	32.0006	2.25715
$202$	15.0221	1.05695
$203$	−1.37170	−0.0962744
$204$	5.99564	0.419779
$205$	19.8674	1.38760
$206$	1.88560	0.131376
$207$	1.98151	0.137724
$208$	−4.34066	−0.300970
$209$	1.56812	0.108469
$210$	−8.78309	−0.606090
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	−4.46382	−0.306577
$213$	−16.1695	−1.10792
$214$	−15.1780	−1.03754
$215$	15.1355	1.03223
$216$	3.95384	0.269025
$217$	11.8377	0.803598
$218$	−6.18520	−0.418914
$219$	−4.89240	−0.330598
$220$	2.81319	0.189665
$221$	12.9630	0.871987
$222$	7.90958	0.530856
$223$	−18.5493	−1.24215	−0.621076	−	0.783750i	$-0.713304\pi$
$223$	−18.5493	−1.24215	−0.621076	+	0.783750i	$0.713304\pi$
$224$	−2.43862	−0.162937
$225$	−1.83613	−0.122409
$226$	6.58029	0.437715
$227$	−17.7495	−1.17807	−0.589036	−	0.808107i	$-0.700493\pi$
$227$	−17.7495	−1.17807	−0.589036	+	0.808107i	$0.700493\pi$
$228$	2.00763	0.132959
$229$	−5.45582	−0.360531	−0.180265	−	0.983618i	$-0.557696\pi$
$229$	−5.45582	−0.360531	−0.180265	+	0.983618i	$0.557696\pi$
$230$	−3.44926	−0.227437
$231$	−7.67729	−0.505129
$232$	0.562491	0.0369294
$233$	7.59030	0.497257	0.248629	−	0.968599i	$-0.420020\pi$
$233$	7.59030	0.497257	0.248629	+	0.968599i	$0.420020\pi$
$234$	−4.47347	−0.292440
$235$	10.8280	0.706341
$236$	14.3798	0.936043
$237$	6.02247	0.391201
$238$	7.28273	0.472069
$239$	−21.3228	−1.37926	−0.689630	−	0.724162i	$-0.742227\pi$
$239$	−21.3228	−1.37926	−0.689630	+	0.724162i	$0.742227\pi$
$240$	3.60167	0.232487
$241$	0.738320	0.0475594	0.0237797	−	0.999717i	$-0.492430\pi$
$241$	0.738320	0.0475594	0.0237797	+	0.999717i	$0.492430\pi$
$242$	−8.54099	−0.549036
$243$	10.2820	0.659592
$244$	−12.9806	−0.830998
$245$	1.88935	0.120706
$246$	22.2334	1.41755
$247$	4.34066	0.276189
$248$	−4.85429	−0.308248
$249$	−19.4594	−1.23319
$250$	12.1661	0.769453
$251$	−27.1705	−1.71499	−0.857494	−	0.514494i	$-0.827980\pi$
$251$	−27.1705	−1.71499	−0.857494	+	0.514494i	$0.827980\pi$
$252$	−2.51323	−0.158319
$253$	−3.01500	−0.189551
$254$	5.64488	0.354191
$255$	−10.7561	−0.673573
$256$	1.00000	0.0625000
$257$	3.47591	0.216821	0.108411	−	0.994106i	$-0.465424\pi$
$257$	3.47591	0.216821	0.108411	+	0.994106i	$0.465424\pi$
$258$	16.9380	1.05451
$259$	9.60754	0.596983
$260$	7.78708	0.482934
$261$	0.579702	0.0358827
$262$	−22.2737	−1.37607
$263$	15.5129	0.956569	0.478285	−	0.878205i	$-0.341259\pi$
$263$	15.5129	0.956569	0.478285	+	0.878205i	$0.341259\pi$
$264$	3.14822	0.193759
$265$	8.00804	0.491930
$266$	2.43862	0.149521
$267$	22.6125	1.38386
$268$	−15.9394	−0.973656
$269$	−6.93004	−0.422532	−0.211266	−	0.977429i	$-0.567759\pi$
$269$	−6.93004	−0.422532	−0.211266	+	0.977429i	$0.567759\pi$
$270$	−7.09313	−0.431674
$271$	14.8948	0.904793	0.452397	−	0.891817i	$-0.350569\pi$
$271$	14.8948	0.904793	0.452397	+	0.891817i	$0.350569\pi$
$272$	−2.98642	−0.181078
$273$	−21.2512	−1.28618
$274$	16.4778	0.995463
$275$	2.79379	0.168472
$276$	−3.86004	−0.232347
$277$	21.9705	1.32008	0.660040	−	0.751230i	$-0.270539\pi$
$277$	21.9705	1.32008	0.660040	+	0.751230i	$0.270539\pi$
$278$	−11.6853	−0.700838
$279$	−5.00282	−0.299511
$280$	4.37484	0.261447
$281$	4.45825	0.265957	0.132979	−	0.991119i	$-0.457546\pi$
$281$	4.45825	0.265957	0.132979	+	0.991119i	$0.457546\pi$
$282$	12.1175	0.721589
$283$	−5.52346	−0.328335	−0.164168	−	0.986432i	$-0.552494\pi$
$283$	−5.52346	−0.328335	−0.164168	+	0.986432i	$0.552494\pi$
$284$	8.05400	0.477917
$285$	−3.60167	−0.213344
$286$	6.80668	0.402488
$287$	27.0063	1.59413
$288$	1.03060	0.0607286
$289$	−8.08130	−0.475370
$290$	−1.00910	−0.0592565
$291$	−6.91115	−0.405139
$292$	2.43690	0.142609
$293$	−19.8393	−1.15903	−0.579513	−	0.814963i	$-0.696757\pi$
$293$	−19.8393	−1.15903	−0.579513	+	0.814963i	$0.696757\pi$
$294$	2.11435	0.123312
$295$	−25.7971	−1.50197
$296$	−3.93975	−0.228993
$297$	−6.20011	−0.359767
$298$	8.74140	0.506376
$299$	−8.34569	−0.482644
$300$	3.57683	0.206508
$301$	20.5741	1.18587
$302$	1.07980	0.0621352
$303$	−30.1588	−1.73258
$304$	−1.00000	−0.0573539
$305$	23.2870	1.33341
$306$	−3.07780	−0.175946
$307$	4.65577	0.265719	0.132859	−	0.991135i	$-0.457584\pi$
$307$	4.65577	0.265719	0.132859	+	0.991135i	$0.457584\pi$
$308$	3.82405	0.217895
$309$	−3.78559	−0.215355
$310$	8.70853	0.494611
$311$	−24.6145	−1.39576	−0.697879	−	0.716215i	$-0.745873\pi$
$311$	−24.6145	−1.39576	−0.697879	+	0.716215i	$0.745873\pi$
$312$	8.71445	0.493359
$313$	3.34650	0.189155	0.0945777	−	0.995517i	$-0.469850\pi$
$313$	3.34650	0.189155	0.0945777	+	0.995517i	$0.469850\pi$
$314$	−2.01582	−0.113760
$315$	4.50870	0.254037
$316$	−2.99978	−0.168751
$317$	5.15681	0.289636	0.144818	−	0.989458i	$-0.453740\pi$
$317$	5.15681	0.289636	0.144818	+	0.989458i	$0.453740\pi$
$318$	8.96173	0.502549
$319$	−0.882055	−0.0493856
$320$	−1.79399	−0.100287
$321$	30.4718	1.70077
$322$	−4.68867	−0.261290
$323$	2.98642	0.166169
$324$	−11.0297	−0.612759
$325$	7.73337	0.428970
$326$	21.8879	1.21226
$327$	12.4176	0.686696
$328$	−11.0744	−0.611483
$329$	14.7188	0.811474
$330$	−5.64786	−0.310904
$331$	−25.8264	−1.41955	−0.709774	−	0.704430i	$-0.751203\pi$
$331$	−25.8264	−1.41955	−0.709774	+	0.704430i	$0.751203\pi$
$332$	9.69270	0.531956
$333$	−4.06030	−0.222503
$334$	−4.09048	−0.223821
$335$	28.5951	1.56232
$336$	4.89585	0.267090
$337$	19.1488	1.04310	0.521550	−	0.853221i	$-0.325354\pi$
$337$	19.1488	1.04310	0.521550	+	0.853221i	$0.325354\pi$
$338$	5.84130	0.317725
$339$	−13.2108	−0.717514
$340$	5.35760	0.290556
$341$	7.61212	0.412219
$342$	−1.03060	−0.0557284
$343$	19.6385	1.06038
$344$	−8.43678	−0.454881
$345$	6.92485	0.372822
$346$	8.61177	0.462972
$347$	17.9943	0.965984	0.482992	−	0.875625i	$-0.339550\pi$
$347$	17.9943	0.965984	0.482992	+	0.875625i	$0.339550\pi$
$348$	−1.12928	−0.0605356
$349$	−13.2057	−0.706884	−0.353442	−	0.935456i	$-0.614989\pi$
$349$	−13.2057	−0.706884	−0.353442	+	0.935456i	$0.614989\pi$
$350$	4.34467	0.232232
$351$	−17.1623	−0.916054
$352$	−1.56812	−0.0835812
$353$	−30.3089	−1.61318	−0.806591	−	0.591110i	$-0.798690\pi$
$353$	−30.3089	−1.61318	−0.806591	+	0.591110i	$0.798690\pi$
$354$	−28.8693	−1.53439
$355$	−14.4488	−0.766861
$356$	−11.2633	−0.596951
$357$	−14.6211	−0.773829
$358$	16.8064	0.888246
$359$	21.6062	1.14033	0.570165	−	0.821530i	$-0.306879\pi$
$359$	21.6062	1.14033	0.570165	+	0.821530i	$0.306879\pi$
$360$	−1.84888	−0.0974445
$361$	1.00000	0.0526316
$362$	6.55162	0.344346
$363$	17.1472	0.899994
$364$	10.5852	0.554815
$365$	−4.37176	−0.228829
$366$	26.0603	1.36219
$367$	−9.98272	−0.521094	−0.260547	−	0.965461i	$-0.583903\pi$
$367$	−9.98272	−0.521094	−0.260547	+	0.965461i	$0.583903\pi$
$368$	1.92268	0.100227
$369$	−11.4133	−0.594152
$370$	7.06786	0.367441
$371$	10.8855	0.565149
$372$	9.74564	0.505288
$373$	−27.0164	−1.39885	−0.699427	−	0.714704i	$-0.746561\pi$
$373$	−27.0164	−1.39885	−0.699427	+	0.714704i	$0.746561\pi$
$374$	4.68307	0.242156
$375$	−24.4251	−1.26131
$376$	−6.03573	−0.311269
$377$	−2.44158	−0.125748
$378$	−9.64189	−0.495926
$379$	0.972204	0.0499388	0.0249694	−	0.999688i	$-0.492051\pi$
$379$	0.972204	0.0499388	0.0249694	+	0.999688i	$0.492051\pi$
$380$	1.79399	0.0920295
$381$	−11.3329	−0.580600
$382$	−22.4079	−1.14649
$383$	−18.3603	−0.938167	−0.469084	−	0.883154i	$-0.655416\pi$
$383$	−18.3603	−0.938167	−0.469084	+	0.883154i	$0.655416\pi$
$384$	−2.00763	−0.102452
$385$	−6.86029	−0.349633
$386$	21.0583	1.07184
$387$	−8.69493	−0.441988
$388$	3.44243	0.174763
$389$	17.7954	0.902264	0.451132	−	0.892457i	$-0.351020\pi$
$389$	17.7954	0.902264	0.451132	+	0.892457i	$0.351020\pi$
$390$	−15.6336	−0.791639
$391$	−5.74193	−0.290382
$392$	−1.05316	−0.0531924
$393$	44.7174	2.25569
$394$	17.7540	0.894435
$395$	5.38157	0.270776
$396$	−1.61610	−0.0812123
$397$	34.8852	1.75084	0.875420	−	0.483364i	$-0.160585\pi$
$397$	34.8852	1.75084	0.875420	+	0.483364i	$0.160585\pi$
$398$	10.1854	0.510547
$399$	−4.89585	−0.245099
$400$	−1.78161	−0.0890807
$401$	11.6845	0.583494	0.291747	−	0.956496i	$-0.405764\pi$
$401$	11.6845	0.583494	0.291747	+	0.956496i	$0.405764\pi$
$402$	32.0006	1.59604
$403$	21.0708	1.04961
$404$	15.0221	0.747376
$405$	19.7871	0.983227
$406$	−1.37170	−0.0680763
$407$	6.17801	0.306233
$408$	5.99564	0.296828
$409$	−16.5589	−0.818783	−0.409391	−	0.912359i	$-0.634259\pi$
$409$	−16.5589	−0.818783	−0.409391	+	0.912359i	$0.634259\pi$
$410$	19.8674	0.981180
$411$	−33.0815	−1.63179
$412$	1.88560	0.0928967
$413$	−35.0667	−1.72552
$414$	1.98151	0.0973859
$415$	−17.3886	−0.853571
$416$	−4.34066	−0.212818
$417$	23.4598	1.14883
$418$	1.56812	0.0766994
$419$	7.52769	0.367751	0.183876	−	0.982949i	$-0.441136\pi$
$419$	7.52769	0.367751	0.183876	+	0.982949i	$0.441136\pi$
$420$	−8.78309	−0.428571
$421$	−3.34379	−0.162967	−0.0814833	−	0.996675i	$-0.525966\pi$
$421$	−3.34379	−0.162967	−0.0814833	+	0.996675i	$0.525966\pi$
$422$	−1.00000	−0.0486792
$423$	−6.22041	−0.302447
$424$	−4.46382	−0.216782
$425$	5.32065	0.258089
$426$	−16.1695	−0.783414
$427$	31.6547	1.53188
$428$	−15.1780	−0.733655
$429$	−13.6653	−0.659769
$430$	15.1355	0.729897
$431$	−36.7080	−1.76816	−0.884080	−	0.467335i	$-0.845214\pi$
$431$	−36.7080	−1.76816	−0.884080	+	0.467335i	$0.845214\pi$
$432$	3.95384	0.190229
$433$	35.4441	1.70333	0.851667	−	0.524084i	$-0.175592\pi$
$433$	35.4441	1.70333	0.851667	+	0.524084i	$0.175592\pi$
$434$	11.8377	0.568230
$435$	2.02591	0.0971348
$436$	−6.18520	−0.296217
$437$	−1.92268	−0.0919742
$438$	−4.89240	−0.233768
$439$	25.0169	1.19399	0.596995	−	0.802245i	$-0.296361\pi$
$439$	25.0169	1.19399	0.596995	+	0.802245i	$0.296361\pi$
$440$	2.81319	0.134114
$441$	−1.08538	−0.0516848
$442$	12.9630	0.616588
$443$	20.7863	0.987587	0.493794	−	0.869579i	$-0.335610\pi$
$443$	20.7863	0.987587	0.493794	+	0.869579i	$0.335610\pi$
$444$	7.90958	0.375372
$445$	20.2061	0.957862
$446$	−18.5493	−0.878335
$447$	−17.5495	−0.830065
$448$	−2.43862	−0.115214
$449$	−2.12952	−0.100498	−0.0502492	−	0.998737i	$-0.516002\pi$
$449$	−2.12952	−0.100498	−0.0502492	+	0.998737i	$0.516002\pi$
$450$	−1.83613	−0.0865559
$451$	17.3661	0.817736
$452$	6.58029	0.309511
$453$	−2.16783	−0.101854
$454$	−17.7495	−0.833023
$455$	−18.9897	−0.890250
$456$	2.00763	0.0940161
$457$	8.37829	0.391920	0.195960	−	0.980612i	$-0.437218\pi$
$457$	8.37829	0.391920	0.195960	+	0.980612i	$0.437218\pi$
$458$	−5.45582	−0.254934
$459$	−11.8078	−0.551142
$460$	−3.44926	−0.160823
$461$	−26.4321	−1.23106	−0.615532	−	0.788112i	$-0.711059\pi$
$461$	−26.4321	−1.23106	−0.615532	+	0.788112i	$0.711059\pi$
$462$	−7.67729	−0.357180
$463$	7.76656	0.360943	0.180471	−	0.983580i	$-0.442238\pi$
$463$	7.76656	0.360943	0.180471	+	0.983580i	$0.442238\pi$
$464$	0.562491	0.0261130
$465$	−17.4835	−0.810780
$466$	7.59030	0.351614
$467$	8.58514	0.397273	0.198636	−	0.980073i	$-0.436349\pi$
$467$	8.58514	0.397273	0.198636	+	0.980073i	$0.436349\pi$
$468$	−4.47347	−0.206786
$469$	38.8702	1.79486
$470$	10.8280	0.499459
$471$	4.04704	0.186478
$472$	14.3798	0.661882
$473$	13.2299	0.608312
$474$	6.02247	0.276621
$475$	1.78161	0.0817460
$476$	7.28273	0.333803
$477$	−4.60041	−0.210638
$478$	−21.3228	−0.975284
$479$	−26.8403	−1.22636	−0.613182	−	0.789942i	$-0.710111\pi$
$479$	−26.8403	−1.22636	−0.613182	+	0.789942i	$0.710111\pi$
$480$	3.60167	0.164393
$481$	17.1011	0.779743
$482$	0.738320	0.0336296
$483$	9.41315	0.428313
$484$	−8.54099	−0.388227
$485$	−6.17567	−0.280423
$486$	10.2820	0.466402
$487$	−2.04309	−0.0925810	−0.0462905	−	0.998928i	$-0.514740\pi$
$487$	−2.04309	−0.0925810	−0.0462905	+	0.998928i	$0.514740\pi$
$488$	−12.9806	−0.587605
$489$	−43.9430	−1.98717
$490$	1.88935	0.0853520
$491$	27.0638	1.22137	0.610685	−	0.791873i	$-0.290894\pi$
$491$	27.0638	1.22137	0.610685	+	0.791873i	$0.290894\pi$
$492$	22.2334	1.00236
$493$	−1.67983	−0.0756560
$494$	4.34066	0.195295
$495$	2.89927	0.130312
$496$	−4.85429	−0.217964
$497$	−19.6406	−0.881001
$498$	−19.4594	−0.871997
$499$	−15.2351	−0.682015	−0.341008	−	0.940061i	$-0.610768\pi$
$499$	−15.2351	−0.682015	−0.341008	+	0.940061i	$0.610768\pi$
$500$	12.1661	0.544085
$501$	8.21218	0.366893
$502$	−27.1705	−1.21268
$503$	−39.1190	−1.74423	−0.872115	−	0.489302i	$-0.837252\pi$
$503$	−39.1190	−1.74423	−0.872115	+	0.489302i	$0.837252\pi$
$504$	−2.51323	−0.111948
$505$	−26.9494	−1.19923
$506$	−3.01500	−0.134033
$507$	−11.7272	−0.520823
$508$	5.64488	0.250451
$509$	19.3701	0.858564	0.429282	−	0.903171i	$-0.358767\pi$
$509$	19.3701	0.858564	0.429282	+	0.903171i	$0.358767\pi$
$510$	−10.7561	−0.476288
$511$	−5.94266	−0.262888
$512$	1.00000	0.0441942
$513$	−3.95384	−0.174566
$514$	3.47591	0.153316
$515$	−3.38274	−0.149061
$516$	16.9380	0.745653
$517$	9.46476	0.416260
$518$	9.60754	0.422131
$519$	−17.2893	−0.758916
$520$	7.78708	0.341486
$521$	11.8930	0.521042	0.260521	−	0.965468i	$-0.416106\pi$
$521$	11.8930	0.521042	0.260521	+	0.965468i	$0.416106\pi$
$522$	0.579702	0.0253729
$523$	14.1575	0.619066	0.309533	−	0.950889i	$-0.399827\pi$
$523$	14.1575	0.619066	0.309533	+	0.950889i	$0.399827\pi$
$524$	−22.2737	−0.973030
$525$	−8.72251	−0.380682
$526$	15.5129	0.676397
$527$	14.4969	0.631497
$528$	3.14822	0.137009
$529$	−19.3033	−0.839274
$530$	8.00804	0.347847
$531$	14.8198	0.643123
$532$	2.43862	0.105727
$533$	48.0703	2.08216
$534$	22.6125	0.978539
$535$	27.2291	1.17721
$536$	−15.9394	−0.688479
$537$	−33.7411	−1.45604
$538$	−6.93004	−0.298775
$539$	1.65148	0.0711342
$540$	−7.09313	−0.305240
$541$	−0.952493	−0.0409509	−0.0204754	−	0.999790i	$-0.506518\pi$
$541$	−0.952493	−0.0409509	−0.0204754	+	0.999790i	$0.506518\pi$
$542$	14.8948	0.639786
$543$	−13.1533	−0.564461
$544$	−2.98642	−0.128042
$545$	11.0962	0.475307
$546$	−21.2512	−0.909467
$547$	4.26440	0.182333	0.0911664	−	0.995836i	$-0.470941\pi$
$547$	4.26440	0.182333	0.0911664	+	0.995836i	$0.470941\pi$
$548$	16.4778	0.703899
$549$	−13.3778	−0.570950
$550$	2.79379	0.119128
$551$	−0.562491	−0.0239629
$552$	−3.86004	−0.164294
$553$	7.31531	0.311079
$554$	21.9705	0.933438
$555$	−14.1897	−0.602318
$556$	−11.6853	−0.495567
$557$	43.2644	1.83317	0.916586	−	0.399837i	$-0.130933\pi$
$557$	43.2644	1.83317	0.916586	+	0.399837i	$0.130933\pi$
$558$	−5.00282	−0.211786
$559$	36.6212	1.54891
$560$	4.37484	0.184871
$561$	−9.40190	−0.396949
$562$	4.45825	0.188060
$563$	−5.26828	−0.222032	−0.111016	−	0.993819i	$-0.535410\pi$
$563$	−5.26828	−0.222032	−0.111016	+	0.993819i	$0.535410\pi$
$564$	12.1175	0.510240
$565$	−11.8050	−0.496638
$566$	−5.52346	−0.232168
$567$	26.8971	1.12957
$568$	8.05400	0.337938
$569$	−25.8701	−1.08453	−0.542265	−	0.840207i	$-0.682433\pi$
$569$	−25.8701	−1.08453	−0.542265	+	0.840207i	$0.682433\pi$
$570$	−3.60167	−0.150857
$571$	22.2409	0.930753	0.465377	−	0.885113i	$-0.345919\pi$
$571$	22.2409	0.930753	0.465377	+	0.885113i	$0.345919\pi$
$572$	6.80668	0.284602
$573$	44.9868	1.87935
$574$	27.0063	1.12722
$575$	−3.42547	−0.142852
$576$	1.03060	0.0429416
$577$	−13.5623	−0.564606	−0.282303	−	0.959325i	$-0.591098\pi$
$577$	−13.5623	−0.564606	−0.282303	+	0.959325i	$0.591098\pi$
$578$	−8.08130	−0.336138
$579$	−42.2773	−1.75699
$580$	−1.00910	−0.0419007
$581$	−23.6368	−0.980618
$582$	−6.91115	−0.286476
$583$	6.99982	0.289903
$584$	2.43690	0.100840
$585$	8.02535	0.331807
$586$	−19.8393	−0.819555
$587$	−23.9666	−0.989208	−0.494604	−	0.869118i	$-0.664687\pi$
$587$	−23.9666	−0.989208	−0.494604	+	0.869118i	$0.664687\pi$
$588$	2.11435	0.0871945
$589$	4.85429	0.200017
$590$	−25.7971	−1.06205
$591$	−35.6436	−1.46618
$592$	−3.93975	−0.161923
$593$	45.1261	1.85311	0.926553	−	0.376164i	$-0.122757\pi$
$593$	45.1261	1.85311	0.926553	+	0.376164i	$0.122757\pi$
$594$	−6.20011	−0.254393
$595$	−13.0651	−0.535617
$596$	8.74140	0.358062
$597$	−20.4485	−0.836903
$598$	−8.34569	−0.341281
$599$	42.9732	1.75584	0.877918	−	0.478810i	$-0.158932\pi$
$599$	42.9732	1.75584	0.877918	+	0.478810i	$0.158932\pi$
$600$	3.57683	0.146023
$601$	−17.6388	−0.719501	−0.359751	−	0.933049i	$-0.617138\pi$
$601$	−17.6388	−0.719501	−0.359751	+	0.933049i	$0.617138\pi$
$602$	20.5741	0.838536
$603$	−16.4272	−0.668966
$604$	1.07980	0.0439362
$605$	15.3224	0.622945
$606$	−30.1588	−1.22512
$607$	−24.9758	−1.01374	−0.506868	−	0.862024i	$-0.669197\pi$
$607$	−24.9758	−1.01374	−0.506868	+	0.862024i	$0.669197\pi$
$608$	−1.00000	−0.0405554
$609$	2.75387	0.111593
$610$	23.2870	0.942864
$611$	26.1990	1.05990
$612$	−3.07780	−0.124413
$613$	−41.6642	−1.68280	−0.841401	−	0.540411i	$-0.818269\pi$
$613$	−41.6642	−1.68280	−0.841401	+	0.540411i	$0.818269\pi$
$614$	4.65577	0.187891
$615$	−39.8864	−1.60838
$616$	3.82405	0.154075
$617$	−24.4712	−0.985173	−0.492587	−	0.870263i	$-0.663949\pi$
$617$	−24.4712	−0.985173	−0.492587	+	0.870263i	$0.663949\pi$
$618$	−3.78559	−0.152279
$619$	−2.64664	−0.106377	−0.0531887	−	0.998584i	$-0.516938\pi$
$619$	−2.64664	−0.106377	−0.0531887	+	0.998584i	$0.516938\pi$
$620$	8.70853	0.349743
$621$	7.60197	0.305056
$622$	−24.6145	−0.986950
$623$	27.4667	1.10043
$624$	8.71445	0.348857
$625$	−12.9178	−0.516711
$626$	3.34650	0.133753
$627$	−3.14822	−0.125728
$628$	−2.01582	−0.0804402
$629$	11.7658	0.469131
$630$	4.50870	0.179631
$631$	7.39706	0.294472	0.147236	−	0.989101i	$-0.452962\pi$
$631$	7.39706	0.294472	0.147236	+	0.989101i	$0.452962\pi$
$632$	−2.99978	−0.119325
$633$	2.00763	0.0797963
$634$	5.15681	0.204803
$635$	−10.1268	−0.401871
$636$	8.96173	0.355356
$637$	4.57139	0.181125
$638$	−0.882055	−0.0349209
$639$	8.30044	0.328360
$640$	−1.79399	−0.0709135
$641$	40.8577	1.61378	0.806892	−	0.590700i	$-0.201148\pi$
$641$	40.8577	1.61378	0.806892	+	0.590700i	$0.201148\pi$
$642$	30.4718	1.20263
$643$	21.0525	0.830230	0.415115	−	0.909769i	$-0.363741\pi$
$643$	21.0525	0.830230	0.415115	+	0.909769i	$0.363741\pi$
$644$	−4.68867	−0.184760
$645$	−30.3865	−1.19647
$646$	2.98642	0.117499
$647$	−11.4788	−0.451277	−0.225638	−	0.974211i	$-0.572447\pi$
$647$	−11.4788	−0.451277	−0.225638	+	0.974211i	$0.572447\pi$
$648$	−11.0297	−0.433286
$649$	−22.5492	−0.885135
$650$	7.73337	0.303328
$651$	−23.7659	−0.931458
$652$	21.8879	0.857197
$653$	31.3640	1.22737	0.613685	−	0.789551i	$-0.289687\pi$
$653$	31.3640	1.22737	0.613685	+	0.789551i	$0.289687\pi$
$654$	12.4176	0.485567
$655$	39.9587	1.56131
$656$	−11.0744	−0.432384
$657$	2.51146	0.0979815
$658$	14.7188	0.573799
$659$	2.78257	0.108393	0.0541967	−	0.998530i	$-0.482740\pi$
$659$	2.78257	0.108393	0.0541967	+	0.998530i	$0.482740\pi$
$660$	−5.64786	−0.219843
$661$	39.1029	1.52093	0.760464	−	0.649380i	$-0.224972\pi$
$661$	39.1029	1.52093	0.760464	+	0.649380i	$0.224972\pi$
$662$	−25.8264	−1.00377
$663$	−26.0250	−1.01073
$664$	9.69270	0.376150
$665$	−4.37484	−0.169649
$666$	−4.06030	−0.157333
$667$	1.08149	0.0418755
$668$	−4.09048	−0.158265
$669$	37.2402	1.43979
$670$	28.5951	1.10473
$671$	20.3552	0.785803
$672$	4.89585	0.188861
$673$	−47.2618	−1.82181	−0.910905	−	0.412616i	$-0.864615\pi$
$673$	−47.2618	−1.82181	−0.910905	+	0.412616i	$0.864615\pi$
$674$	19.1488	0.737583
$675$	−7.04422	−0.271132
$676$	5.84130	0.224665
$677$	−37.7782	−1.45194	−0.725968	−	0.687729i	$-0.758608\pi$
$677$	−37.7782	−1.45194	−0.725968	+	0.687729i	$0.758608\pi$
$678$	−13.2108	−0.507359
$679$	−8.39477	−0.322162
$680$	5.35760	0.205454
$681$	35.6344	1.36551
$682$	7.61212	0.291483
$683$	14.2962	0.547029	0.273515	−	0.961868i	$-0.411814\pi$
$683$	14.2962	0.547029	0.273515	+	0.961868i	$0.411814\pi$
$684$	−1.03060	−0.0394059
$685$	−29.5610	−1.12947
$686$	19.6385	0.749803
$687$	10.9533	0.417894
$688$	−8.43678	−0.321649
$689$	19.3759	0.738164
$690$	6.92485	0.263625
$691$	38.5441	1.46629	0.733144	−	0.680073i	$-0.238052\pi$
$691$	38.5441	1.46629	0.733144	+	0.680073i	$0.238052\pi$
$692$	8.61177	0.327370
$693$	3.94106	0.149708
$694$	17.9943	0.683054
$695$	20.9633	0.795182
$696$	−1.12928	−0.0428051
$697$	33.0729	1.25273
$698$	−13.2057	−0.499842
$699$	−15.2386	−0.576375
$700$	4.34467	0.164213
$701$	−24.8451	−0.938387	−0.469194	−	0.883095i	$-0.655455\pi$
$701$	−24.8451	−0.938387	−0.469194	+	0.883095i	$0.655455\pi$
$702$	−17.1623	−0.647748
$703$	3.93975	0.148591
$704$	−1.56812	−0.0591009
$705$	−21.7387	−0.818726
$706$	−30.3089	−1.14069
$707$	−36.6330	−1.37773
$708$	−28.8693	−1.08498
$709$	−12.8176	−0.481376	−0.240688	−	0.970603i	$-0.577373\pi$
$709$	−12.8176	−0.481376	−0.240688	+	0.970603i	$0.577373\pi$
$710$	−14.4488	−0.542252
$711$	−3.09157	−0.115943
$712$	−11.2633	−0.422108
$713$	−9.33324	−0.349533
$714$	−14.6211	−0.547179
$715$	−12.2111	−0.456669
$716$	16.8064	0.628085
$717$	42.8085	1.59871
$718$	21.6062	0.806336
$719$	−20.0904	−0.749245	−0.374623	−	0.927177i	$-0.622228\pi$
$719$	−20.0904	−0.749245	−0.374623	+	0.927177i	$0.622228\pi$
$720$	−1.84888	−0.0689036
$721$	−4.59825	−0.171248
$722$	1.00000	0.0372161
$723$	−1.48228	−0.0551265
$724$	6.55162	0.243489
$725$	−1.00214	−0.0372186
$726$	17.1472	0.636392
$727$	−7.51975	−0.278892	−0.139446	−	0.990230i	$-0.544532\pi$
$727$	−7.51975	−0.278892	−0.139446	+	0.990230i	$0.544532\pi$
$728$	10.5852	0.392313
$729$	12.4465	0.460980
$730$	−4.37176	−0.161806
$731$	25.1958	0.931899
$732$	26.0603	0.963217
$733$	17.4972	0.646274	0.323137	−	0.946352i	$-0.395263\pi$
$733$	17.4972	0.646274	0.323137	+	0.946352i	$0.395263\pi$
$734$	−9.98272	−0.368469
$735$	−3.79312	−0.139911
$736$	1.92268	0.0708709
$737$	24.9950	0.920703
$738$	−11.4133	−0.420129
$739$	−27.4871	−1.01113	−0.505565	−	0.862789i	$-0.668716\pi$
$739$	−27.4871	−1.01113	−0.505565	+	0.862789i	$0.668716\pi$
$740$	7.06786	0.259820
$741$	−8.71445	−0.320133
$742$	10.8855	0.399621
$743$	−44.5321	−1.63373	−0.816863	−	0.576832i	$-0.804289\pi$
$743$	−44.5321	−1.63373	−0.816863	+	0.576832i	$0.804289\pi$
$744$	9.74564	0.357292
$745$	−15.6820	−0.574542
$746$	−27.0164	−0.989139
$747$	9.98928	0.365489
$748$	4.68307	0.171230
$749$	37.0132	1.35243
$750$	−24.4251	−0.891880
$751$	25.6955	0.937644	0.468822	−	0.883293i	$-0.344679\pi$
$751$	25.6955	0.937644	0.468822	+	0.883293i	$0.344679\pi$
$752$	−6.03573	−0.220100
$753$	54.5485	1.98786
$754$	−2.44158	−0.0889171
$755$	−1.93714	−0.0704996
$756$	−9.64189	−0.350672
$757$	18.4588	0.670895	0.335447	−	0.942059i	$-0.391113\pi$
$757$	18.4588	0.670895	0.335447	+	0.942059i	$0.391113\pi$
$758$	0.972204	0.0353120
$759$	6.05301	0.219710
$760$	1.79399	0.0650747
$761$	18.1033	0.656243	0.328121	−	0.944636i	$-0.393584\pi$
$761$	18.1033	0.656243	0.328121	+	0.944636i	$0.393584\pi$
$762$	−11.3329	−0.410546
$763$	15.0833	0.546053
$764$	−22.4079	−0.810688
$765$	5.52153	0.199631
$766$	−18.3603	−0.663385
$767$	−62.4176	−2.25377
$768$	−2.00763	−0.0724443
$769$	−45.5260	−1.64171	−0.820855	−	0.571137i	$-0.806503\pi$
$769$	−45.5260	−1.64171	−0.820855	+	0.571137i	$0.806503\pi$
$770$	−6.86029	−0.247228
$771$	−6.97836	−0.251320
$772$	21.0583	0.757904
$773$	−22.0175	−0.791913	−0.395956	−	0.918269i	$-0.629587\pi$
$773$	−22.0175	−0.791913	−0.395956	+	0.918269i	$0.629587\pi$
$774$	−8.69493	−0.312533
$775$	8.64847	0.310662
$776$	3.44243	0.123576
$777$	−19.2884	−0.691969
$778$	17.7954	0.637997
$779$	11.0744	0.396783
$780$	−15.6336	−0.559773
$781$	−12.6297	−0.451925
$782$	−5.74193	−0.205331
$783$	2.22400	0.0794793
$784$	−1.05316	−0.0376127
$785$	3.61636	0.129073
$786$	44.7174	1.59502
$787$	−28.0918	−1.00137	−0.500683	−	0.865631i	$-0.666918\pi$
$787$	−28.0918	−1.00137	−0.500683	+	0.865631i	$0.666918\pi$
$788$	17.7540	0.632461
$789$	−31.1443	−1.10877
$790$	5.38157	0.191468
$791$	−16.0468	−0.570559
$792$	−1.61610	−0.0574258
$793$	56.3444	2.00085
$794$	34.8852	1.23803
$795$	−16.0772	−0.570200
$796$	10.1854	0.361012
$797$	−9.55800	−0.338562	−0.169281	−	0.985568i	$-0.554144\pi$
$797$	−9.55800	−0.338562	−0.169281	+	0.985568i	$0.554144\pi$
$798$	−4.89585	−0.173311
$799$	18.0252	0.637686
$800$	−1.78161	−0.0629896
$801$	−11.6079	−0.410145
$802$	11.6845	0.412592
$803$	−3.82136	−0.134853
$804$	32.0006	1.12857
$805$	8.41142	0.296463
$806$	21.0708	0.742187
$807$	13.9130	0.489760
$808$	15.0221	0.528474
$809$	3.15214	0.110823	0.0554116	−	0.998464i	$-0.482353\pi$
$809$	3.15214	0.110823	0.0554116	+	0.998464i	$0.482353\pi$
$810$	19.7871	0.695246
$811$	−42.8175	−1.50353	−0.751763	−	0.659433i	$-0.770796\pi$
$811$	−42.8175	−1.50353	−0.751763	+	0.659433i	$0.770796\pi$
$812$	−1.37170	−0.0481372
$813$	−29.9033	−1.04875
$814$	6.17801	0.216539
$815$	−39.2666	−1.37545
$816$	5.99564	0.209889
$817$	8.43678	0.295165
$818$	−16.5589	−0.578967
$819$	10.9091	0.381194
$820$	19.8674	0.693799
$821$	−5.54040	−0.193361	−0.0966807	−	0.995315i	$-0.530823\pi$
$821$	−5.54040	−0.193361	−0.0966807	+	0.995315i	$0.530823\pi$
$822$	−33.0815	−1.15385
$823$	−10.4057	−0.362718	−0.181359	−	0.983417i	$-0.558050\pi$
$823$	−10.4057	−0.362718	−0.181359	+	0.983417i	$0.558050\pi$
$824$	1.88560	0.0656879
$825$	−5.60891	−0.195277
$826$	−35.0667	−1.22013
$827$	−55.2056	−1.91969	−0.959843	−	0.280538i	$-0.909487\pi$
$827$	−55.2056	−1.91969	−0.959843	+	0.280538i	$0.909487\pi$
$828$	1.98151	0.0688622
$829$	−43.3892	−1.50697	−0.753484	−	0.657466i	$-0.771628\pi$
$829$	−43.3892	−1.50697	−0.753484	+	0.657466i	$0.771628\pi$
$830$	−17.3886	−0.603566
$831$	−44.1088	−1.53012
$832$	−4.34066	−0.150485
$833$	3.14517	0.108974
$834$	23.4598	0.812347
$835$	7.33826	0.253951
$836$	1.56812	0.0542347
$837$	−19.1931	−0.663410
$838$	7.52769	0.260040
$839$	−43.8812	−1.51495	−0.757474	−	0.652865i	$-0.773567\pi$
$839$	−43.8812	−1.51495	−0.757474	+	0.652865i	$0.773567\pi$
$840$	−8.78309	−0.303045
$841$	−28.6836	−0.989090
$842$	−3.34379	−0.115235
$843$	−8.95055	−0.308273
$844$	−1.00000	−0.0344214
$845$	−10.4792	−0.360496
$846$	−6.22041	−0.213862
$847$	20.8282	0.715665
$848$	−4.46382	−0.153288
$849$	11.0891	0.380576
$850$	5.32065	0.182497
$851$	−7.57488	−0.259663
$852$	−16.1695	−0.553958
$853$	−6.94606	−0.237829	−0.118914	−	0.992905i	$-0.537941\pi$
$853$	−6.94606	−0.237829	−0.118914	+	0.992905i	$0.537941\pi$
$854$	31.6547	1.08320
$855$	1.84888	0.0632303
$856$	−15.1780	−0.518772
$857$	−3.03688	−0.103738	−0.0518690	−	0.998654i	$-0.516518\pi$
$857$	−3.03688	−0.103738	−0.0518690	+	0.998654i	$0.516518\pi$
$858$	−13.6653	−0.466527
$859$	−12.6581	−0.431889	−0.215945	−	0.976406i	$-0.569283\pi$
$859$	−12.6581	−0.431889	−0.215945	+	0.976406i	$0.569283\pi$
$860$	15.1355	0.516115
$861$	−54.2187	−1.84777
$862$	−36.7080	−1.25028
$863$	−14.4476	−0.491803	−0.245902	−	0.969295i	$-0.579084\pi$
$863$	−14.4476	−0.491803	−0.245902	+	0.969295i	$0.579084\pi$
$864$	3.95384	0.134512
$865$	−15.4494	−0.525295
$866$	35.4441	1.20444
$867$	16.2243	0.551006
$868$	11.8377	0.401799
$869$	4.70403	0.159573
$870$	2.02591	0.0686847
$871$	69.1877	2.34433
$872$	−6.18520	−0.209457
$873$	3.54776	0.120074
$874$	−1.92268	−0.0650356
$875$	−29.6685	−1.00298
$876$	−4.89240	−0.165299
$877$	21.0284	0.710080	0.355040	−	0.934851i	$-0.384467\pi$
$877$	21.0284	0.710080	0.355040	+	0.934851i	$0.384467\pi$
$878$	25.0169	0.844278
$879$	39.8301	1.34344
$880$	2.81319	0.0948326
$881$	−43.6644	−1.47109	−0.735546	−	0.677474i	$-0.763074\pi$
$881$	−43.6644	−1.47109	−0.735546	+	0.677474i	$0.763074\pi$
$882$	−1.08538	−0.0365467
$883$	−17.7562	−0.597543	−0.298771	−	0.954325i	$-0.596577\pi$
$883$	−17.7562	−0.597543	−0.298771	+	0.954325i	$0.596577\pi$
$884$	12.9630	0.435994
$885$	51.7912	1.74094
$886$	20.7863	0.698330
$887$	−37.3649	−1.25459	−0.627295	−	0.778782i	$-0.715838\pi$
$887$	−37.3649	−1.25459	−0.627295	+	0.778782i	$0.715838\pi$
$888$	7.90958	0.265428
$889$	−13.7657	−0.461687
$890$	20.2061	0.677311
$891$	17.2959	0.579433
$892$	−18.5493	−0.621076
$893$	6.03573	0.201978
$894$	−17.5495	−0.586944
$895$	−30.1505	−1.00782
$896$	−2.43862	−0.0814684
$897$	16.7551	0.559437
$898$	−2.12952	−0.0710631
$899$	−2.73049	−0.0910671
$900$	−1.83613	−0.0612043
$901$	13.3309	0.444115
$902$	17.3661	0.578227
$903$	−41.3052	−1.37455
$904$	6.58029	0.218857
$905$	−11.7535	−0.390700
$906$	−2.16783	−0.0720215
$907$	−35.1732	−1.16791	−0.583953	−	0.811787i	$-0.698495\pi$
$907$	−35.1732	−1.16791	−0.583953	+	0.811787i	$0.698495\pi$
$908$	−17.7495	−0.589036
$909$	15.4817	0.513496
$910$	−18.9897	−0.629502
$911$	−38.8799	−1.28815	−0.644075	−	0.764962i	$-0.722758\pi$
$911$	−38.8799	−1.28815	−0.644075	+	0.764962i	$0.722758\pi$
$912$	2.00763	0.0664794
$913$	−15.1993	−0.503025
$914$	8.37829	0.277129
$915$	−46.7519	−1.54557
$916$	−5.45582	−0.180265
$917$	54.3169	1.79370
$918$	−11.8078	−0.389716
$919$	10.4829	0.345798	0.172899	−	0.984940i	$-0.444687\pi$
$919$	10.4829	0.345798	0.172899	+	0.984940i	$0.444687\pi$
$920$	−3.44926	−0.113719
$921$	−9.34708	−0.307997
$922$	−26.4321	−0.870493
$923$	−34.9596	−1.15071
$924$	−7.67729	−0.252564
$925$	7.01912	0.230787
$926$	7.76656	0.255225
$927$	1.94329	0.0638261
$928$	0.562491	0.0184647
$929$	−21.2402	−0.696869	−0.348434	−	0.937333i	$-0.613287\pi$
$929$	−21.2402	−0.696869	−0.348434	+	0.937333i	$0.613287\pi$
$930$	−17.4835	−0.573308
$931$	1.05316	0.0345158
$932$	7.59030	0.248629
$933$	49.4169	1.61784
$934$	8.58514	0.280914
$935$	−8.40137	−0.274754
$936$	−4.47347	−0.146220
$937$	−24.8936	−0.813239	−0.406620	−	0.913598i	$-0.633293\pi$
$937$	−24.8936	−0.813239	−0.406620	+	0.913598i	$0.633293\pi$
$938$	38.8702	1.26916
$939$	−6.71855	−0.219252
$940$	10.8280	0.353171
$941$	8.16223	0.266081	0.133041	−	0.991111i	$-0.457526\pi$
$941$	8.16223	0.266081	0.133041	+	0.991111i	$0.457526\pi$
$942$	4.04704	0.131860
$943$	−21.2926	−0.693382
$944$	14.3798	0.468021
$945$	17.2974	0.562685
$946$	13.2299	0.430141
$947$	44.4251	1.44362	0.721811	−	0.692090i	$-0.243310\pi$
$947$	44.4251	1.44362	0.721811	+	0.692090i	$0.243310\pi$
$948$	6.02247	0.195601
$949$	−10.5777	−0.343368
$950$	1.78161	0.0578032
$951$	−10.3530	−0.335719
$952$	7.28273	0.236035
$953$	8.42769	0.273000	0.136500	−	0.990640i	$-0.456415\pi$
$953$	8.42769	0.273000	0.136500	+	0.990640i	$0.456415\pi$
$954$	−4.60041	−0.148944
$955$	40.1994	1.30082
$956$	−21.3228	−0.689630
$957$	1.77084	0.0572433
$958$	−26.8403	−0.867170
$959$	−40.1831	−1.29758
$960$	3.60167	0.116243
$961$	−7.43588	−0.239867
$962$	17.1011	0.551362
$963$	−15.6424	−0.504069
$964$	0.738320	0.0237797
$965$	−37.7783	−1.21613
$966$	9.41315	0.302863
$967$	17.6656	0.568086	0.284043	−	0.958812i	$-0.408324\pi$
$967$	17.6656	0.568086	0.284043	+	0.958812i	$0.408324\pi$
$968$	−8.54099	−0.274518
$969$	−5.99564	−0.192608
$970$	−6.17567	−0.198289
$971$	52.1695	1.67420	0.837099	−	0.547051i	$-0.184250\pi$
$971$	52.1695	1.67420	0.837099	+	0.547051i	$0.184250\pi$
$972$	10.2820	0.329796
$973$	28.4960	0.913538
$974$	−2.04309	−0.0654647
$975$	−15.5258	−0.497223
$976$	−12.9806	−0.415499
$977$	−22.8120	−0.729819	−0.364909	−	0.931043i	$-0.618900\pi$
$977$	−22.8120	−0.729819	−0.364909	+	0.931043i	$0.618900\pi$
$978$	−43.9430	−1.40514
$979$	17.6622	0.564485
$980$	1.88935	0.0603530
$981$	−6.37445	−0.203521
$982$	27.0638	0.863640
$983$	−14.4751	−0.461682	−0.230841	−	0.972991i	$-0.574148\pi$
$983$	−14.4751	−0.461682	−0.230841	+	0.972991i	$0.574148\pi$
$984$	22.2334	0.708775
$985$	−31.8505	−1.01484
$986$	−1.67983	−0.0534968
$987$	−29.5500	−0.940587
$988$	4.34066	0.138095
$989$	−16.2212	−0.515805
$990$	2.89927	0.0921448
$991$	−29.6521	−0.941929	−0.470964	−	0.882152i	$-0.656094\pi$
$991$	−29.6521	−0.941929	−0.470964	+	0.882152i	$0.656094\pi$
$992$	−4.85429	−0.154124
$993$	51.8500	1.64541
$994$	−19.6406	−0.622962
$995$	−18.2724	−0.579275
$996$	−19.4594	−0.616595
$997$	−21.5565	−0.682700	−0.341350	−	0.939936i	$-0.610884\pi$
$997$	−21.5565	−0.682700	−0.341350	+	0.939936i	$0.610884\pi$
$998$	−15.2351	−0.482257
$999$	−15.5771	−0.492839

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.10	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.10	✓	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.00763 q^{3} +1.00000 q^{4} -1.79399 q^{5} -2.00763 q^{6} -2.43862 q^{7} +1.00000 q^{8} +1.03060 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.00763 q^{3} +1.00000 q^{4} -1.79399 q^{5} -2.00763 q^{6} -2.43862 q^{7} +1.00000 q^{8} +1.03060 q^{9} -1.79399 q^{10} -1.56812 q^{11} -2.00763 q^{12} -4.34066 q^{13} -2.43862 q^{14} +3.60167 q^{15} +1.00000 q^{16} -2.98642 q^{17} +1.03060 q^{18} -1.00000 q^{19} -1.79399 q^{20} +4.89585 q^{21} -1.56812 q^{22} +1.92268 q^{23} -2.00763 q^{24} -1.78161 q^{25} -4.34066 q^{26} +3.95384 q^{27} -2.43862 q^{28} +0.562491 q^{29} +3.60167 q^{30} -4.85429 q^{31} +1.00000 q^{32} +3.14822 q^{33} -2.98642 q^{34} +4.37484 q^{35} +1.03060 q^{36} -3.93975 q^{37} -1.00000 q^{38} +8.71445 q^{39} -1.79399 q^{40} -11.0744 q^{41} +4.89585 q^{42} -8.43678 q^{43} -1.56812 q^{44} -1.84888 q^{45} +1.92268 q^{46} -6.03573 q^{47} -2.00763 q^{48} -1.05316 q^{49} -1.78161 q^{50} +5.99564 q^{51} -4.34066 q^{52} -4.46382 q^{53} +3.95384 q^{54} +2.81319 q^{55} -2.43862 q^{56} +2.00763 q^{57} +0.562491 q^{58} +14.3798 q^{59} +3.60167 q^{60} -12.9806 q^{61} -4.85429 q^{62} -2.51323 q^{63} +1.00000 q^{64} +7.78708 q^{65} +3.14822 q^{66} -15.9394 q^{67} -2.98642 q^{68} -3.86004 q^{69} +4.37484 q^{70} +8.05400 q^{71} +1.03060 q^{72} +2.43690 q^{73} -3.93975 q^{74} +3.57683 q^{75} -1.00000 q^{76} +3.82405 q^{77} +8.71445 q^{78} -2.99978 q^{79} -1.79399 q^{80} -11.0297 q^{81} -11.0744 q^{82} +9.69270 q^{83} +4.89585 q^{84} +5.35760 q^{85} -8.43678 q^{86} -1.12928 q^{87} -1.56812 q^{88} -11.2633 q^{89} -1.84888 q^{90} +10.5852 q^{91} +1.92268 q^{92} +9.74564 q^{93} -6.03573 q^{94} +1.79399 q^{95} -2.00763 q^{96} +3.44243 q^{97} -1.05316 q^{98} -1.61610 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 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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