LMFDB - Embedded newform 983.4.a.b.1.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [983,4,Mod(1,983)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(983, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("983.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 983 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	983.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:	$57.9988775356$
Analytic rank:	$0$
Dimension:	$136$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.12
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.82266 q^{2} -8.16418 q^{3} +15.2580 q^{4} -21.8591 q^{5} +39.3730 q^{6} +14.7056 q^{7} -35.0029 q^{8} +39.6538 q^{9} +O(q^{10})$	\(q-4.82266 q^{2} -8.16418 q^{3} +15.2580 q^{4} -21.8591 q^{5} +39.3730 q^{6} +14.7056 q^{7} -35.0029 q^{8} +39.6538 q^{9} +105.419 q^{10} -31.7540 q^{11} -124.569 q^{12} -41.3143 q^{13} -70.9201 q^{14} +178.462 q^{15} +46.7428 q^{16} +21.9930 q^{17} -191.236 q^{18} +82.5207 q^{19} -333.527 q^{20} -120.059 q^{21} +153.138 q^{22} +134.395 q^{23} +285.770 q^{24} +352.822 q^{25} +199.245 q^{26} -103.307 q^{27} +224.378 q^{28} -142.993 q^{29} -860.660 q^{30} +248.657 q^{31} +54.5987 q^{32} +259.245 q^{33} -106.065 q^{34} -321.452 q^{35} +605.037 q^{36} +246.687 q^{37} -397.969 q^{38} +337.297 q^{39} +765.133 q^{40} -442.637 q^{41} +579.004 q^{42} -355.333 q^{43} -484.502 q^{44} -866.797 q^{45} -648.139 q^{46} -303.150 q^{47} -381.616 q^{48} -126.745 q^{49} -1701.54 q^{50} -179.555 q^{51} -630.374 q^{52} +45.8279 q^{53} +498.216 q^{54} +694.114 q^{55} -514.738 q^{56} -673.713 q^{57} +689.606 q^{58} +397.516 q^{59} +2722.97 q^{60} -79.0711 q^{61} -1199.19 q^{62} +583.132 q^{63} -637.253 q^{64} +903.095 q^{65} -1250.25 q^{66} -199.599 q^{67} +335.570 q^{68} -1097.22 q^{69} +1550.25 q^{70} +343.015 q^{71} -1388.00 q^{72} -817.023 q^{73} -1189.69 q^{74} -2880.50 q^{75} +1259.10 q^{76} -466.961 q^{77} -1626.67 q^{78} -260.501 q^{79} -1021.76 q^{80} -227.231 q^{81} +2134.68 q^{82} +30.0110 q^{83} -1831.86 q^{84} -480.749 q^{85} +1713.65 q^{86} +1167.42 q^{87} +1111.48 q^{88} -663.537 q^{89} +4180.26 q^{90} -607.552 q^{91} +2050.60 q^{92} -2030.08 q^{93} +1461.99 q^{94} -1803.83 q^{95} -445.753 q^{96} +1030.42 q^{97} +611.249 q^{98} -1259.16 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) $ 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * 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 $

$2$	−4.82266	−1.70507	−0.852533	−	0.522673i	$-0.824935\pi$
$2$	−4.82266	−1.70507	−0.852533	+	0.522673i	$0.824935\pi$
$3$	−8.16418	−1.57120	−0.785598	−	0.618737i	$-0.787645\pi$
$3$	−8.16418	−1.57120	−0.785598	+	0.618737i	$0.787645\pi$
$4$	15.2580	1.90725
$5$	−21.8591	−1.95514	−0.977570	−	0.210609i	$-0.932455\pi$
$5$	−21.8591	−1.95514	−0.977570	+	0.210609i	$0.932455\pi$
$6$	39.3730	2.67899
$7$	14.7056	0.794028	0.397014	−	0.917813i	$-0.370046\pi$
$7$	14.7056	0.794028	0.397014	+	0.917813i	$0.370046\pi$
$8$	−35.0029	−1.54692
$9$	39.6538	1.46866
$10$	105.419	3.33364
$11$	−31.7540	−0.870380	−0.435190	−	0.900339i	$-0.643319\pi$
$11$	−31.7540	−0.870380	−0.435190	+	0.900339i	$0.643319\pi$
$12$	−124.569	−2.99667
$13$	−41.3143	−0.881425	−0.440712	−	0.897648i	$-0.645274\pi$
$13$	−41.3143	−0.881425	−0.440712	+	0.897648i	$0.645274\pi$
$14$	−70.9201	−1.35387
$15$	178.462	3.07191
$16$	46.7428	0.730356
$17$	21.9930	0.313770	0.156885	−	0.987617i	$-0.449855\pi$
$17$	21.9930	0.313770	0.156885	+	0.987617i	$0.449855\pi$
$18$	−191.236	−2.50416
$19$	82.5207	0.996397	0.498198	−	0.867063i	$-0.333995\pi$
$19$	82.5207	0.996397	0.498198	+	0.867063i	$0.333995\pi$
$20$	−333.527	−3.72894
$21$	−120.059	−1.24757
$22$	153.138	1.48406
$23$	134.395	1.21840	0.609201	−	0.793016i	$-0.291490\pi$
$23$	134.395	1.21840	0.609201	+	0.793016i	$0.291490\pi$
$24$	285.770	2.43052
$25$	352.822	2.82258
$26$	199.245	1.50289
$27$	−103.307	−0.736353
$28$	224.378	1.51441
$29$	−142.993	−0.915625	−0.457813	−	0.889049i	$-0.651367\pi$
$29$	−142.993	−0.915625	−0.457813	+	0.889049i	$0.651367\pi$
$30$	−860.660	−5.23781
$31$	248.657	1.44065	0.720324	−	0.693637i	$-0.243993\pi$
$31$	248.657	1.44065	0.720324	+	0.693637i	$0.243993\pi$
$32$	54.5987	0.301618
$33$	259.245	1.36754
$34$	−106.065	−0.534999
$35$	−321.452	−1.55244
$36$	605.037	2.80110
$37$	246.687	1.09608	0.548042	−	0.836451i	$-0.315373\pi$
$37$	246.687	1.09608	0.548042	+	0.836451i	$0.315373\pi$
$38$	−397.969	−1.69892
$39$	337.297	1.38489
$40$	765.133	3.02445
$41$	−442.637	−1.68605	−0.843027	−	0.537871i	$-0.819229\pi$
$41$	−442.637	−1.68605	−0.843027	+	0.537871i	$0.819229\pi$
$42$	579.004	2.12720
$43$	−355.333	−1.26018	−0.630090	−	0.776522i	$-0.716982\pi$
$43$	−355.333	−1.26018	−0.630090	+	0.776522i	$0.716982\pi$
$44$	−484.502	−1.66003
$45$	−866.797	−2.87143
$46$	−648.139	−2.07746
$47$	−303.150	−0.940828	−0.470414	−	0.882446i	$-0.655895\pi$
$47$	−303.150	−0.940828	−0.470414	+	0.882446i	$0.655895\pi$
$48$	−381.616	−1.14753
$49$	−126.745	−0.369520
$50$	−1701.54	−4.81268
$51$	−179.555	−0.492994
$52$	−630.374	−1.68110
$53$	45.8279	0.118773	0.0593863	−	0.998235i	$-0.481086\pi$
$53$	45.8279	0.118773	0.0593863	+	0.998235i	$0.481086\pi$
$54$	498.216	1.25553
$55$	694.114	1.70172
$56$	−514.738	−1.22830
$57$	−673.713	−1.56554
$58$	689.606	1.56120
$59$	397.516	0.877155	0.438578	−	0.898693i	$-0.355482\pi$
$59$	397.516	0.877155	0.438578	+	0.898693i	$0.355482\pi$
$60$	2722.97	5.85890
$61$	−79.0711	−0.165967	−0.0829837	−	0.996551i	$-0.526445\pi$
$61$	−79.0711	−0.165967	−0.0829837	+	0.996551i	$0.526445\pi$
$62$	−1199.19	−2.45640
$63$	583.132	1.16616
$64$	−637.253	−1.24463
$65$	903.095	1.72331
$66$	−1250.25	−2.33174
$67$	−199.599	−0.363953	−0.181977	−	0.983303i	$-0.558250\pi$
$67$	−199.599	−0.363953	−0.181977	+	0.983303i	$0.558250\pi$
$68$	335.570	0.598438
$69$	−1097.22	−1.91435
$70$	1550.25	2.64701
$71$	343.015	0.573357	0.286678	−	0.958027i	$-0.407449\pi$
$71$	343.015	0.573357	0.286678	+	0.958027i	$0.407449\pi$
$72$	−1388.00	−2.27190
$73$	−817.023	−1.30994	−0.654968	−	0.755656i	$-0.727318\pi$
$73$	−817.023	−1.30994	−0.654968	+	0.755656i	$0.727318\pi$
$74$	−1189.69	−1.86890
$75$	−2880.50	−4.43482
$76$	1259.10	1.90038
$77$	−466.961	−0.691106
$78$	−1626.67	−2.36133
$79$	−260.501	−0.370995	−0.185498	−	0.982645i	$-0.559390\pi$
$79$	−260.501	−0.370995	−0.185498	+	0.982645i	$0.559390\pi$
$80$	−1021.76	−1.42795
$81$	−227.231	−0.311702
$82$	2134.68	2.87483
$83$	30.0110	0.0396883	0.0198442	−	0.999803i	$-0.493683\pi$
$83$	30.0110	0.0396883	0.0198442	+	0.999803i	$0.493683\pi$
$84$	−1831.86	−2.37944
$85$	−480.749	−0.613465
$86$	1713.65	2.14869
$87$	1167.42	1.43863
$88$	1111.48	1.34641
$89$	−663.537	−0.790278	−0.395139	−	0.918621i	$-0.629304\pi$
$89$	−663.537	−0.790278	−0.395139	+	0.918621i	$0.629304\pi$
$90$	4180.26	4.89598
$91$	−607.552	−0.699876
$92$	2050.60	2.32380
$93$	−2030.08	−2.26354
$94$	1461.99	1.60417
$95$	−1803.83	−1.94810
$96$	−445.753	−0.473901
$97$	1030.42	1.07859	0.539296	−	0.842116i	$-0.318690\pi$
$97$	1030.42	1.07859	0.539296	+	0.842116i	$0.318690\pi$
$98$	611.249	0.630056
$99$	−1259.16	−1.27829
$100$	5383.36	5.38336
$101$	−606.336	−0.597353	−0.298677	−	0.954354i	$-0.596545\pi$
$101$	−606.336	−0.597353	−0.298677	+	0.954354i	$0.596545\pi$
$102$	865.931	0.840588
$103$	271.340	0.259572	0.129786	−	0.991542i	$-0.458571\pi$
$103$	271.340	0.259572	0.129786	+	0.991542i	$0.458571\pi$
$104$	1446.12	1.36350
$105$	2624.39	2.43918
$106$	−221.012	−0.202515
$107$	1180.16	1.06627	0.533134	−	0.846031i	$-0.321014\pi$
$107$	1180.16	1.06627	0.533134	+	0.846031i	$0.321014\pi$
$108$	−1576.27	−1.40441
$109$	−1768.63	−1.55417	−0.777085	−	0.629396i	$-0.783302\pi$
$109$	−1768.63	−1.55417	−0.777085	+	0.629396i	$0.783302\pi$
$110$	−3347.47	−2.90154
$111$	−2014.00	−1.72216
$112$	687.381	0.579923
$113$	518.324	0.431503	0.215751	−	0.976448i	$-0.430780\pi$
$113$	518.324	0.431503	0.215751	+	0.976448i	$0.430780\pi$
$114$	3249.09	2.66934
$115$	−2937.75	−2.38215
$116$	−2181.79	−1.74633
$117$	−1638.27	−1.29451
$118$	−1917.08	−1.49561
$119$	323.421	0.249142
$120$	−6246.68	−4.75201
$121$	−322.686	−0.242439
$122$	381.333	0.282986
$123$	3613.76	2.64912
$124$	3794.01	2.74768
$125$	−4979.99	−3.56339
$126$	−2812.25	−1.98837
$127$	2600.94	1.81730	0.908648	−	0.417564i	$-0.137116\pi$
$127$	2600.94	1.81730	0.908648	+	0.417564i	$0.137116\pi$
$128$	2636.46	1.82057
$129$	2901.00	1.97999
$130$	−4355.32	−2.93836
$131$	−447.424	−0.298409	−0.149205	−	0.988806i	$-0.547671\pi$
$131$	−447.424	−0.298409	−0.149205	+	0.988806i	$0.547671\pi$
$132$	3955.56	2.60824
$133$	1213.52	0.791167
$134$	962.596	0.620564
$135$	2258.21	1.43967
$136$	−769.819	−0.485378
$137$	−2409.04	−1.50232	−0.751160	−	0.660120i	$-0.770505\pi$
$137$	−2409.04	−1.50232	−0.751160	+	0.660120i	$0.770505\pi$
$138$	5291.52	3.26409
$139$	−2381.79	−1.45339	−0.726695	−	0.686960i	$-0.758945\pi$
$139$	−2381.79	−1.45339	−0.726695	+	0.686960i	$0.758945\pi$
$140$	−4904.71	−2.96089
$141$	2474.97	1.47823
$142$	−1654.24	−0.977612
$143$	1311.89	0.767175
$144$	1853.53	1.07264
$145$	3125.70	1.79018
$146$	3940.22	2.23353
$147$	1034.77	0.580588
$148$	3763.95	2.09051
$149$	2514.16	1.38234	0.691169	−	0.722693i	$-0.257096\pi$
$149$	2514.16	1.38234	0.691169	+	0.722693i	$0.257096\pi$
$150$	13891.7	7.56166
$151$	−1172.78	−0.632050	−0.316025	−	0.948751i	$-0.602348\pi$
$151$	−1172.78	−0.632050	−0.316025	+	0.948751i	$0.602348\pi$
$152$	−2888.46	−1.54135
$153$	872.106	0.460821
$154$	2251.99	1.17838
$155$	−5435.43	−2.81667
$156$	5146.48	2.64134
$157$	1663.60	0.845666	0.422833	−	0.906208i	$-0.361036\pi$
$157$	1663.60	0.845666	0.422833	+	0.906208i	$0.361036\pi$
$158$	1256.31	0.632571
$159$	−374.147	−0.186615
$160$	−1193.48	−0.589706
$161$	1976.35	0.967445
$162$	1095.86	0.531473
$163$	−22.6383	−0.0108783	−0.00543917	−	0.999985i	$-0.501731\pi$
$163$	−22.6383	−0.0108783	−0.00543917	+	0.999985i	$0.501731\pi$
$164$	−6753.75	−3.21573
$165$	−5666.87	−2.67373
$166$	−144.733	−0.0676713
$167$	3645.64	1.68927	0.844636	−	0.535342i	$-0.179817\pi$
$167$	3645.64	1.68927	0.844636	+	0.535342i	$0.179817\pi$
$168$	4202.42	1.92990
$169$	−490.129	−0.223090
$170$	2318.48	1.04600
$171$	3272.25	1.46337
$172$	−5421.67	−2.40348
$173$	−4388.09	−1.92844	−0.964221	−	0.265099i	$-0.914595\pi$
$173$	−4388.09	−1.92844	−0.964221	+	0.265099i	$0.914595\pi$
$174$	−5630.06	−2.45295
$175$	5188.46	2.24120
$176$	−1484.27	−0.635687
$177$	−3245.39	−1.37818
$178$	3200.01	1.34748
$179$	−1879.79	−0.784929	−0.392464	−	0.919767i	$-0.628377\pi$
$179$	−1879.79	−0.784929	−0.392464	+	0.919767i	$0.628377\pi$
$180$	−13225.6	−5.47654
$181$	858.482	0.352544	0.176272	−	0.984341i	$-0.443596\pi$
$181$	858.482	0.352544	0.176272	+	0.984341i	$0.443596\pi$
$182$	2930.01	1.19333
$183$	645.550	0.260767
$184$	−4704.20	−1.88477
$185$	−5392.36	−2.14300
$186$	9790.37	3.85949
$187$	−698.366	−0.273099
$188$	−4625.46	−1.79440
$189$	−1519.20	−0.584685
$190$	8699.26	3.32163
$191$	−657.462	−0.249069	−0.124535	−	0.992215i	$-0.539744\pi$
$191$	−657.462	−0.249069	−0.124535	+	0.992215i	$0.539744\pi$
$192$	5202.65	1.95557
$193$	−438.088	−0.163390	−0.0816949	−	0.996657i	$-0.526033\pi$
$193$	−438.088	−0.163390	−0.0816949	+	0.996657i	$0.526033\pi$
$194$	−4969.37	−1.83907
$195$	−7373.03	−2.70766
$196$	−1933.88	−0.704767
$197$	3860.02	1.39602	0.698008	−	0.716090i	$-0.254070\pi$
$197$	3860.02	1.39602	0.698008	+	0.716090i	$0.254070\pi$
$198$	6072.51	2.17957
$199$	2461.81	0.876952	0.438476	−	0.898743i	$-0.355518\pi$
$199$	2461.81	0.876952	0.438476	+	0.898743i	$0.355518\pi$
$200$	−12349.8	−4.36631
$201$	1629.56	0.571842
$202$	2924.15	1.01853
$203$	−2102.80	−0.727032
$204$	−2739.65	−0.940264
$205$	9675.65	3.29647
$206$	−1308.58	−0.442588
$207$	5329.25	1.78941
$208$	−1931.15	−0.643754
$209$	−2620.36	−0.867244
$210$	−12656.5	−4.15897
$211$	1826.01	0.595771	0.297885	−	0.954602i	$-0.403719\pi$
$211$	1826.01	0.595771	0.297885	+	0.954602i	$0.403719\pi$
$212$	699.243	0.226529
$213$	−2800.43	−0.900856
$214$	−5691.52	−1.81806
$215$	7767.27	2.46383
$216$	3616.06	1.13908
$217$	3656.65	1.14392
$218$	8529.52	2.64996
$219$	6670.32	2.05817
$220$	10590.8	3.24560
$221$	−908.626	−0.276565
$222$	9712.81	2.93640
$223$	−2714.43	−0.815118	−0.407559	−	0.913179i	$-0.633620\pi$
$223$	−2714.43	−0.815118	−0.407559	+	0.913179i	$0.633620\pi$
$224$	802.907	0.239493
$225$	13990.7	4.14540
$226$	−2499.70	−0.735741
$227$	−3026.44	−0.884899	−0.442449	−	0.896794i	$-0.645890\pi$
$227$	−3026.44	−0.884899	−0.442449	+	0.896794i	$0.645890\pi$
$228$	−10279.5	−2.98587
$229$	−232.788	−0.0671750	−0.0335875	−	0.999436i	$-0.510693\pi$
$229$	−232.788	−0.0671750	−0.0335875	+	0.999436i	$0.510693\pi$
$230$	14167.8	4.06172
$231$	3812.35	1.08586
$232$	5005.17	1.41640
$233$	−4176.58	−1.17432	−0.587160	−	0.809471i	$-0.699754\pi$
$233$	−4176.58	−1.17432	−0.587160	+	0.809471i	$0.699754\pi$
$234$	7900.80	2.20723
$235$	6626.59	1.83945
$236$	6065.30	1.67296
$237$	2126.77	0.582906
$238$	−1559.75	−0.424804
$239$	2826.82	0.765071	0.382536	−	0.923941i	$-0.375051\pi$
$239$	2826.82	0.765071	0.382536	+	0.923941i	$0.375051\pi$
$240$	8341.80	2.24359
$241$	−1357.33	−0.362794	−0.181397	−	0.983410i	$-0.558062\pi$
$241$	−1357.33	−0.362794	−0.181397	+	0.983410i	$0.558062\pi$
$242$	1556.20	0.413374
$243$	4644.46	1.22610
$244$	−1206.47	−0.316542
$245$	2770.54	0.722463
$246$	−17427.9	−4.51693
$247$	−3409.28	−0.878249
$248$	−8703.71	−2.22857
$249$	−245.015	−0.0623582
$250$	24016.8	6.07582
$251$	5755.96	1.44746	0.723731	−	0.690082i	$-0.242426\pi$
$251$	5755.96	1.44746	0.723731	+	0.690082i	$0.242426\pi$
$252$	8897.44	2.22415
$253$	−4267.56	−1.06047
$254$	−12543.5	−3.09861
$255$	3924.92	0.963874
$256$	−7616.73	−1.85955
$257$	−512.840	−0.124475	−0.0622375	−	0.998061i	$-0.519824\pi$
$257$	−512.840	−0.124475	−0.0622375	+	0.998061i	$0.519824\pi$
$258$	−13990.5	−3.37602
$259$	3627.68	0.870321
$260$	13779.4	3.28678
$261$	−5670.21	−1.34474
$262$	2157.77	0.508808
$263$	1134.28	0.265941	0.132971	−	0.991120i	$-0.457548\pi$
$263$	1134.28	0.265941	0.132971	+	0.991120i	$0.457548\pi$
$264$	−9074.32	−2.11548
$265$	−1001.76	−0.232217
$266$	−5852.37	−1.34899
$267$	5417.23	1.24168
$268$	−3045.48	−0.694150
$269$	−7690.05	−1.74301	−0.871506	−	0.490384i	$-0.836856\pi$
$269$	−7690.05	−1.74301	−0.871506	+	0.490384i	$0.836856\pi$
$270$	−10890.6	−2.45474
$271$	4264.57	0.955919	0.477960	−	0.878382i	$-0.341376\pi$
$271$	4264.57	0.955919	0.477960	+	0.878382i	$0.341376\pi$
$272$	1028.02	0.229164
$273$	4960.16	1.09964
$274$	11618.0	2.56156
$275$	−11203.5	−2.45671
$276$	−16741.4	−3.65114
$277$	2961.80	0.642444	0.321222	−	0.947004i	$-0.395906\pi$
$277$	2961.80	0.642444	0.321222	+	0.947004i	$0.395906\pi$
$278$	11486.6	2.47813
$279$	9860.18	2.11582
$280$	11251.7	2.40150
$281$	2386.30	0.506600	0.253300	−	0.967388i	$-0.418484\pi$
$281$	2386.30	0.506600	0.253300	+	0.967388i	$0.418484\pi$
$282$	−11935.9	−2.52047
$283$	6481.48	1.36143	0.680713	−	0.732550i	$-0.261670\pi$
$283$	6481.48	1.36143	0.680713	+	0.732550i	$0.261670\pi$
$284$	5233.72	1.09354
$285$	14726.8	3.06084
$286$	−6326.81	−1.30808
$287$	−6509.24	−1.33877
$288$	2165.04	0.442974
$289$	−4429.31	−0.901548
$290$	−15074.2	−3.05237
$291$	−8412.54	−1.69468
$292$	−12466.2	−2.49838
$293$	−4101.20	−0.817729	−0.408865	−	0.912595i	$-0.634075\pi$
$293$	−4101.20	−0.817729	−0.408865	+	0.912595i	$0.634075\pi$
$294$	−4990.34	−0.989941
$295$	−8689.35	−1.71496
$296$	−8634.76	−1.69556
$297$	3280.42	0.640907
$298$	−12124.9	−2.35698
$299$	−5552.42	−1.07393
$300$	−43950.7	−8.45832
$301$	−5225.38	−1.00062
$302$	5655.92	1.07769
$303$	4950.23	0.938559
$304$	3857.25	0.727724
$305$	1728.43	0.324490
$306$	−4205.87	−0.785730
$307$	−5066.92	−0.941968	−0.470984	−	0.882142i	$-0.656101\pi$
$307$	−5066.92	−0.941968	−0.470984	+	0.882142i	$0.656101\pi$
$308$	−7124.90	−1.31811
$309$	−2215.27	−0.407839
$310$	26213.2	4.80261
$311$	−6159.67	−1.12310	−0.561548	−	0.827444i	$-0.689794\pi$
$311$	−6159.67	−1.12310	−0.561548	+	0.827444i	$0.689794\pi$
$312$	−11806.4	−2.14232
$313$	−4458.01	−0.805053	−0.402527	−	0.915408i	$-0.631868\pi$
$313$	−4458.01	−0.805053	−0.402527	+	0.915408i	$0.631868\pi$
$314$	−8022.96	−1.44192
$315$	−12746.8	−2.28000
$316$	−3974.72	−0.707581
$317$	6472.91	1.14686	0.573430	−	0.819255i	$-0.305612\pi$
$317$	6472.91	1.14686	0.573430	+	0.819255i	$0.305612\pi$
$318$	1804.38	0.318191
$319$	4540.59	0.796942
$320$	13929.8	2.43344
$321$	−9635.06	−1.67532
$322$	−9531.28	−1.64956
$323$	1814.88	0.312640
$324$	−3467.09	−0.594495
$325$	−14576.6	−2.48789
$326$	109.177	0.0185483
$327$	14439.4	2.44191
$328$	15493.6	2.60820
$329$	−4458.00	−0.747044
$330$	27329.4	4.55889
$331$	−8095.34	−1.34429	−0.672145	−	0.740420i	$-0.734627\pi$
$331$	−8095.34	−1.34429	−0.672145	+	0.740420i	$0.734627\pi$
$332$	457.908	0.0756956
$333$	9782.07	1.60977
$334$	−17581.7	−2.88032
$335$	4363.06	0.711580
$336$	−5611.90	−0.911173
$337$	8727.59	1.41075	0.705374	−	0.708835i	$-0.250779\pi$
$337$	8727.59	1.41075	0.705374	+	0.708835i	$0.250779\pi$
$338$	2363.72	0.380383
$339$	−4231.69	−0.677976
$340$	−7335.27	−1.17003
$341$	−7895.85	−1.25391
$342$	−15781.0	−2.49514
$343$	−6907.89	−1.08744
$344$	12437.7	1.94940
$345$	23984.3	3.74282
$346$	21162.3	3.28812
$347$	−239.889	−0.0371121	−0.0185561	−	0.999828i	$-0.505907\pi$
$347$	−239.889	−0.0371121	−0.0185561	+	0.999828i	$0.505907\pi$
$348$	17812.5	2.74382
$349$	8131.74	1.24723	0.623614	−	0.781733i	$-0.285664\pi$
$349$	8131.74	1.24723	0.623614	+	0.781733i	$0.285664\pi$
$350$	−25022.2	−3.82140
$351$	4268.08	0.649040
$352$	−1733.73	−0.262522
$353$	3538.61	0.533545	0.266772	−	0.963760i	$-0.414043\pi$
$353$	3538.61	0.533545	0.266772	+	0.963760i	$0.414043\pi$
$354$	15651.4	2.34989
$355$	−7498.00	−1.12099
$356$	−10124.3	−1.50726
$357$	−2640.46	−0.391451
$358$	9065.59	1.33836
$359$	−6253.75	−0.919389	−0.459694	−	0.888077i	$-0.652041\pi$
$359$	−6253.75	−0.919389	−0.459694	+	0.888077i	$0.652041\pi$
$360$	30340.4	4.44189
$361$	−49.3377	−0.00719313
$362$	−4140.17	−0.601111
$363$	2634.46	0.380919
$364$	−9270.03	−1.33484
$365$	17859.4	2.56111
$366$	−3113.27	−0.444626
$367$	9137.58	1.29967	0.649833	−	0.760077i	$-0.274839\pi$
$367$	9137.58	1.29967	0.649833	+	0.760077i	$0.274839\pi$
$368$	6281.98	0.889867
$369$	−17552.2	−2.47624
$370$	26005.5	3.65395
$371$	673.927	0.0943088
$372$	−30975.0	−4.31714
$373$	−2858.71	−0.396833	−0.198416	−	0.980118i	$-0.563580\pi$
$373$	−2858.71	−0.396833	−0.198416	+	0.980118i	$0.563580\pi$
$374$	3367.98	0.465652
$375$	40657.5	5.59879
$376$	10611.1	1.45539
$377$	5907.65	0.807055
$378$	7326.57	0.996926
$379$	−12591.7	−1.70658	−0.853290	−	0.521436i	$-0.825397\pi$
$379$	−12591.7	−1.70658	−0.853290	+	0.521436i	$0.825397\pi$
$380$	−27522.9	−3.71551
$381$	−21234.6	−2.85533
$382$	3170.71	0.424680
$383$	−2838.41	−0.378685	−0.189342	−	0.981911i	$-0.560636\pi$
$383$	−2838.41	−0.378685	−0.189342	+	0.981911i	$0.560636\pi$
$384$	−21524.5	−2.86047
$385$	10207.4	1.35121
$386$	2112.75	0.278591
$387$	−14090.3	−1.85077
$388$	15722.2	2.05715
$389$	8284.70	1.07982	0.539911	−	0.841722i	$-0.318458\pi$
$389$	8284.70	1.07982	0.539911	+	0.841722i	$0.318458\pi$
$390$	35557.6	4.61674
$391$	2955.75	0.382298
$392$	4436.45	0.571619
$393$	3652.85	0.468860
$394$	−18615.6	−2.38030
$395$	5694.32	0.725348
$396$	−19212.3	−2.43802
$397$	−12858.2	−1.62553	−0.812764	−	0.582593i	$-0.802038\pi$
$397$	−12858.2	−1.62553	−0.812764	+	0.582593i	$0.802038\pi$
$398$	−11872.5	−1.49526
$399$	−9907.36	−1.24308
$400$	16491.9	2.06149
$401$	8733.63	1.08762	0.543811	−	0.839208i	$-0.316981\pi$
$401$	8733.63	1.08762	0.543811	+	0.839208i	$0.316981\pi$
$402$	−7858.80	−0.975028
$403$	−10273.1	−1.26982
$404$	−9251.48	−1.13930
$405$	4967.08	0.609422
$406$	10141.1	1.23964
$407$	−7833.29	−0.954009
$408$	6284.94	0.762625
$409$	3289.11	0.397643	0.198822	−	0.980036i	$-0.436289\pi$
$409$	3289.11	0.397643	0.198822	+	0.980036i	$0.436289\pi$
$410$	−46662.3	−5.62071
$411$	19667.8	2.36044
$412$	4140.11	0.495069
$413$	5845.71	0.696486
$414$	−25701.2	−3.05107
$415$	−656.014	−0.0775963
$416$	−2255.71	−0.265854
$417$	19445.4	2.28356
$418$	12637.1	1.47871
$419$	−11179.6	−1.30349	−0.651744	−	0.758439i	$-0.725962\pi$
$419$	−11179.6	−1.30349	−0.651744	+	0.758439i	$0.725962\pi$
$420$	40042.9	4.65213
$421$	−7692.42	−0.890512	−0.445256	−	0.895403i	$-0.646887\pi$
$421$	−7692.42	−0.890512	−0.445256	+	0.895403i	$0.646887\pi$
$422$	−8806.21	−1.01583
$423$	−12021.0	−1.38175
$424$	−1604.11	−0.183732
$425$	7759.62	0.885640
$426$	13505.5	1.53602
$427$	−1162.79	−0.131783
$428$	18006.9	2.03364
$429$	−10710.5	−1.20538
$430$	−37458.9	−4.20099
$431$	−13939.2	−1.55784	−0.778921	−	0.627123i	$-0.784232\pi$
$431$	−13939.2	−1.55784	−0.778921	+	0.627123i	$0.784232\pi$
$432$	−4828.88	−0.537800
$433$	3552.36	0.394262	0.197131	−	0.980377i	$-0.436838\pi$
$433$	3552.36	0.394262	0.197131	+	0.980377i	$0.436838\pi$
$434$	−17634.8	−1.95045
$435$	−25518.8	−2.81272
$436$	−26985.8	−2.96419
$437$	11090.3	1.21401
$438$	−32168.7	−3.50931
$439$	−6039.99	−0.656658	−0.328329	−	0.944563i	$-0.606486\pi$
$439$	−6039.99	−0.656658	−0.328329	+	0.944563i	$0.606486\pi$
$440$	−24296.0	−2.63242
$441$	−5025.93	−0.542698
$442$	4381.99	0.471561
$443$	3710.46	0.397945	0.198972	−	0.980005i	$-0.436240\pi$
$443$	3710.46	0.397945	0.198972	+	0.980005i	$0.436240\pi$
$444$	−30729.6	−3.28460
$445$	14504.3	1.54511
$446$	13090.7	1.38983
$447$	−20526.1	−2.17192
$448$	−9371.19	−0.988275
$449$	13482.8	1.41713	0.708564	−	0.705646i	$-0.249343\pi$
$449$	13482.8	1.41713	0.708564	+	0.705646i	$0.249343\pi$
$450$	−67472.4	−7.06818
$451$	14055.5	1.46751
$452$	7908.59	0.822984
$453$	9574.79	0.993075
$454$	14595.5	1.50881
$455$	13280.6	1.36836
$456$	23581.9	2.42176
$457$	14147.5	1.44813	0.724064	−	0.689733i	$-0.242272\pi$
$457$	14147.5	1.44813	0.724064	+	0.689733i	$0.242272\pi$
$458$	1122.66	0.114538
$459$	−2272.04	−0.231046
$460$	−44824.3	−4.54335
$461$	−4501.08	−0.454742	−0.227371	−	0.973808i	$-0.573013\pi$
$461$	−4501.08	−0.454742	−0.227371	+	0.973808i	$0.573013\pi$
$462$	−18385.7	−1.85147
$463$	3791.93	0.380617	0.190309	−	0.981724i	$-0.439051\pi$
$463$	3791.93	0.380617	0.190309	+	0.981724i	$0.439051\pi$
$464$	−6683.89	−0.668732
$465$	44375.8	4.42554
$466$	20142.2	2.00229
$467$	11186.4	1.10845	0.554223	−	0.832368i	$-0.313015\pi$
$467$	11186.4	1.10845	0.554223	+	0.832368i	$0.313015\pi$
$468$	−24996.7	−2.46896
$469$	−2935.22	−0.288989
$470$	−31957.8	−3.13639
$471$	−13581.9	−1.32871
$472$	−13914.2	−1.35689
$473$	11283.2	1.09684
$474$	−10256.7	−0.993894
$475$	29115.1	2.81241
$476$	4934.76	0.475177
$477$	1817.25	0.174436
$478$	−13632.8	−1.30450
$479$	14262.7	1.36050	0.680251	−	0.732979i	$-0.261871\pi$
$479$	14262.7	1.36050	0.680251	+	0.732979i	$0.261871\pi$
$480$	9743.78	0.926544
$481$	−10191.7	−0.966115
$482$	6545.95	0.618588
$483$	−16135.3	−1.52005
$484$	−4923.54	−0.462391
$485$	−22524.1	−2.10880
$486$	−22398.6	−2.09058
$487$	6489.60	0.603844	0.301922	−	0.953333i	$-0.402372\pi$
$487$	6489.60	0.603844	0.301922	+	0.953333i	$0.402372\pi$
$488$	2767.72	0.256739
$489$	184.823	0.0170920
$490$	−13361.4	−1.23185
$491$	19027.1	1.74884	0.874419	−	0.485171i	$-0.161243\pi$
$491$	19027.1	1.74884	0.874419	+	0.485171i	$0.161243\pi$
$492$	55138.8	5.05254
$493$	−3144.85	−0.287296
$494$	16441.8	1.49747
$495$	27524.2	2.49924
$496$	11622.9	1.05219
$497$	5044.24	0.455261
$498$	1181.62	0.106325
$499$	−8686.69	−0.779298	−0.389649	−	0.920963i	$-0.627404\pi$
$499$	−8686.69	−0.779298	−0.389649	+	0.920963i	$0.627404\pi$
$500$	−75984.8	−6.79628
$501$	−29763.7	−2.65418
$502$	−27759.0	−2.46802
$503$	−15061.0	−1.33506	−0.667530	−	0.744583i	$-0.732649\pi$
$503$	−15061.0	−1.33506	−0.667530	+	0.744583i	$0.732649\pi$
$504$	−20411.3	−1.80395
$505$	13254.0	1.16791
$506$	20581.0	1.80818
$507$	4001.50	0.350518
$508$	39685.2	3.46604
$509$	−15360.9	−1.33764	−0.668822	−	0.743423i	$-0.733201\pi$
$509$	−15360.9	−1.33764	−0.668822	+	0.743423i	$0.733201\pi$
$510$	−18928.5	−1.64347
$511$	−12014.8	−1.04013
$512$	15641.2	1.35009
$513$	−8525.00	−0.733700
$514$	2473.25	0.212238
$515$	−5931.26	−0.507500
$516$	44263.5	3.77634
$517$	9626.20	0.818878
$518$	−17495.1	−1.48395
$519$	35825.2	3.02996
$520$	−31610.9	−2.66583
$521$	−7790.70	−0.655119	−0.327559	−	0.944831i	$-0.606226\pi$
$521$	−7790.70	−0.655119	−0.327559	+	0.944831i	$0.606226\pi$
$522$	27345.5	2.29287
$523$	−20365.8	−1.70274	−0.851370	−	0.524566i	$-0.824228\pi$
$523$	−20365.8	−1.70274	−0.851370	+	0.524566i	$0.824228\pi$
$524$	−6826.80	−0.569141
$525$	−42359.5	−3.52137
$526$	−5470.23	−0.453447
$527$	5468.72	0.452033
$528$	12117.8	0.998789
$529$	5894.93	0.484502
$530$	4831.14	0.395946
$531$	15763.0	1.28824
$532$	18515.8	1.50895
$533$	18287.2	1.48613
$534$	−26125.4	−2.11715
$535$	−25797.3	−2.08470
$536$	6986.53	0.563008
$537$	15346.9	1.23328
$538$	37086.5	2.97195
$539$	4024.66	0.321623
$540$	34455.8	2.74582
$541$	3629.89	0.288468	0.144234	−	0.989544i	$-0.453928\pi$
$541$	3629.89	0.288468	0.144234	+	0.989544i	$0.453928\pi$
$542$	−20566.6	−1.62991
$543$	−7008.80	−0.553916
$544$	1200.79	0.0946387
$545$	38660.8	3.03862
$546$	−23921.1	−1.87496
$547$	−5086.27	−0.397575	−0.198787	−	0.980043i	$-0.563700\pi$
$547$	−5086.27	−0.397575	−0.198787	+	0.980043i	$0.563700\pi$
$548$	−36757.1	−2.86530
$549$	−3135.47	−0.243749
$550$	54030.6	4.18886
$551$	−11799.9	−0.912326
$552$	38405.9	2.96135
$553$	−3830.82	−0.294581
$554$	−14283.7	−1.09541
$555$	44024.2	3.36707
$556$	−36341.4	−2.77198
$557$	25513.8	1.94085	0.970427	−	0.241395i	$-0.0776051\pi$
$557$	25513.8	1.94085	0.970427	+	0.241395i	$0.0776051\pi$
$558$	−47552.3	−3.60761
$559$	14680.3	1.11075
$560$	−15025.6	−1.13383
$561$	5701.58	0.429092
$562$	−11508.3	−0.863787
$563$	3334.17	0.249589	0.124794	−	0.992183i	$-0.460173\pi$
$563$	3334.17	0.249589	0.124794	+	0.992183i	$0.460173\pi$
$564$	37763.1	2.81935
$565$	−11330.1	−0.843649
$566$	−31257.9	−2.32132
$567$	−3341.57	−0.247500
$568$	−12006.5	−0.886939
$569$	−3158.07	−0.232677	−0.116338	−	0.993210i	$-0.537116\pi$
$569$	−3158.07	−0.232677	−0.116338	+	0.993210i	$0.537116\pi$
$570$	−71022.2	−5.21894
$571$	15491.1	1.13535	0.567674	−	0.823253i	$-0.307843\pi$
$571$	15491.1	1.13535	0.567674	+	0.823253i	$0.307843\pi$
$572$	20016.9	1.46319
$573$	5367.63	0.391337
$574$	31391.8	2.28270
$575$	47417.4	3.43903
$576$	−25269.5	−1.82794
$577$	−16343.7	−1.17920	−0.589599	−	0.807696i	$-0.700714\pi$
$577$	−16343.7	−1.17920	−0.589599	+	0.807696i	$0.700714\pi$
$578$	21361.0	1.53720
$579$	3576.62	0.256718
$580$	47692.0	3.41432
$581$	441.329	0.0315136
$582$	40570.8	2.88954
$583$	−1455.22	−0.103377
$584$	28598.2	2.02637
$585$	35811.1	2.53095
$586$	19778.7	1.39428
$587$	4773.93	0.335675	0.167837	−	0.985815i	$-0.446322\pi$
$587$	4773.93	0.335675	0.167837	+	0.985815i	$0.446322\pi$
$588$	15788.5	1.10733
$589$	20519.3	1.43546
$590$	41905.8	2.92412
$591$	−31513.9	−2.19341
$592$	11530.8	0.800531
$593$	−10722.1	−0.742501	−0.371250	−	0.928533i	$-0.621071\pi$
$593$	−10722.1	−0.742501	−0.371250	+	0.928533i	$0.621071\pi$
$594$	−15820.3	−1.09279
$595$	−7069.70	−0.487108
$596$	38361.1	2.63647
$597$	−20098.7	−1.37786
$598$	26777.4	1.83112
$599$	20664.3	1.40955	0.704775	−	0.709431i	$-0.251048\pi$
$599$	20664.3	1.40955	0.704775	+	0.709431i	$0.251048\pi$
$600$	100826.	6.86033
$601$	−19870.1	−1.34862	−0.674308	−	0.738451i	$-0.735558\pi$
$601$	−19870.1	−1.34862	−0.674308	+	0.738451i	$0.735558\pi$
$602$	25200.2	1.70612
$603$	−7914.84	−0.534523
$604$	−17894.3	−1.20548
$605$	7053.64	0.474002
$606$	−23873.3	−1.60031
$607$	26043.4	1.74146	0.870732	−	0.491758i	$-0.163645\pi$
$607$	26043.4	1.74146	0.870732	+	0.491758i	$0.163645\pi$
$608$	4505.52	0.300531
$609$	17167.6	1.14231
$610$	−8335.60	−0.553277
$611$	12524.4	0.829269
$612$	13306.6	0.878901
$613$	−21439.6	−1.41262	−0.706311	−	0.707902i	$-0.749642\pi$
$613$	−21439.6	−1.41262	−0.706311	+	0.707902i	$0.749642\pi$
$614$	24436.0	1.60612
$615$	−78993.7	−5.17941
$616$	16345.0	1.06909
$617$	22269.5	1.45306	0.726529	−	0.687136i	$-0.241132\pi$
$617$	22269.5	1.45306	0.726529	+	0.687136i	$0.241132\pi$
$618$	10683.5	0.695392
$619$	−18603.9	−1.20801	−0.604003	−	0.796982i	$-0.706429\pi$
$619$	−18603.9	−1.20801	−0.604003	+	0.796982i	$0.706429\pi$
$620$	−82933.8	−5.37210
$621$	−13884.0	−0.897174
$622$	29706.0	1.91495
$623$	−9757.71	−0.627503
$624$	15766.2	1.01146
$625$	64755.6	4.14436
$626$	21499.4	1.37267
$627$	21393.1	1.36261
$628$	25383.2	1.61290
$629$	5425.39	0.343918
$630$	61473.3	3.88755
$631$	9010.22	0.568449	0.284224	−	0.958758i	$-0.408264\pi$
$631$	9010.22	0.568449	0.284224	+	0.958758i	$0.408264\pi$
$632$	9118.28	0.573901
$633$	−14907.9	−0.936073
$634$	−31216.6	−1.95547
$635$	−56854.4	−3.55307
$636$	−5708.74	−0.355922
$637$	5236.39	0.325704
$638$	−21897.7	−1.35884
$639$	13601.8	0.842065
$640$	−57630.8	−3.55946
$641$	3173.49	0.195547	0.0977734	−	0.995209i	$-0.468828\pi$
$641$	3173.49	0.195547	0.0977734	+	0.995209i	$0.468828\pi$
$642$	46466.6	2.85653
$643$	−1731.26	−0.106181	−0.0530905	−	0.998590i	$-0.516907\pi$
$643$	−1731.26	−0.106181	−0.0530905	+	0.998590i	$0.516907\pi$
$644$	30155.2	1.84516
$645$	−63413.4	−3.87116
$646$	−8752.54	−0.533071
$647$	16399.6	0.996500	0.498250	−	0.867033i	$-0.333976\pi$
$647$	16399.6	0.996500	0.498250	+	0.867033i	$0.333976\pi$
$648$	7953.74	0.482180
$649$	−12622.7	−0.763458
$650$	70297.9	4.24202
$651$	−29853.5	−1.79732
$652$	−345.415	−0.0207477
$653$	−19707.9	−1.18106	−0.590528	−	0.807017i	$-0.701080\pi$
$653$	−19707.9	−1.18106	−0.590528	+	0.807017i	$0.701080\pi$
$654$	−69636.5	−4.16361
$655$	9780.30	0.583432
$656$	−20690.1	−1.23142
$657$	−32398.0	−1.92385
$658$	21499.4	1.27376
$659$	−19555.3	−1.15594	−0.577972	−	0.816057i	$-0.696156\pi$
$659$	−19555.3	−1.15594	−0.577972	+	0.816057i	$0.696156\pi$
$660$	−86465.2	−5.09947
$661$	7230.65	0.425476	0.212738	−	0.977109i	$-0.431762\pi$
$661$	7230.65	0.425476	0.212738	+	0.977109i	$0.431762\pi$
$662$	39041.0	2.29210
$663$	7418.18	0.434538
$664$	−1050.47	−0.0613948
$665$	−26526.4	−1.54684
$666$	−47175.5	−2.74477
$667$	−19217.5	−1.11560
$668$	55625.3	3.22186
$669$	22161.0	1.28071
$670$	−21041.5	−1.21329
$671$	2510.82	0.144455
$672$	−6555.07	−0.376291
$673$	10310.0	0.590523	0.295262	−	0.955416i	$-0.404593\pi$
$673$	10310.0	0.590523	0.295262	+	0.955416i	$0.404593\pi$
$674$	−42090.2	−2.40542
$675$	−36449.1	−2.07841
$676$	−7478.39	−0.425489
$677$	−5303.47	−0.301076	−0.150538	−	0.988604i	$-0.548101\pi$
$677$	−5303.47	−0.301076	−0.150538	+	0.988604i	$0.548101\pi$
$678$	20408.0	1.15599
$679$	15153.0	0.856432
$680$	16827.6	0.948983
$681$	24708.4	1.39035
$682$	38078.9	2.13800
$683$	−1518.20	−0.0850549	−0.0425274	−	0.999095i	$-0.513541\pi$
$683$	−1518.20	−0.0850549	−0.0425274	+	0.999095i	$0.513541\pi$
$684$	49928.1	2.79101
$685$	52659.5	2.93725
$686$	33314.4	1.85415
$687$	1900.52	0.105545
$688$	−16609.3	−0.920380
$689$	−1893.35	−0.104689
$690$	−115668.	−6.38175
$691$	−1408.76	−0.0775569	−0.0387784	−	0.999248i	$-0.512347\pi$
$691$	−1408.76	−0.0775569	−0.0387784	+	0.999248i	$0.512347\pi$
$692$	−66953.6	−3.67802
$693$	−18516.8	−1.01500
$694$	1156.90	0.0632787
$695$	52064.0	2.84158
$696$	−40863.1	−2.22545
$697$	−9734.92	−0.529033
$698$	−39216.6	−2.12661
$699$	34098.3	1.84509
$700$	79165.6	4.27454
$701$	−8987.48	−0.484240	−0.242120	−	0.970246i	$-0.577843\pi$
$701$	−8987.48	−0.484240	−0.242120	+	0.970246i	$0.577843\pi$
$702$	−20583.5	−1.10666
$703$	20356.8	1.09213
$704$	20235.3	1.08331
$705$	−54100.6	−2.89014
$706$	−17065.5	−0.909729
$707$	−8916.54	−0.474315
$708$	−49518.2	−2.62854
$709$	9650.09	0.511166	0.255583	−	0.966787i	$-0.417733\pi$
$709$	9650.09	0.511166	0.255583	+	0.966787i	$0.417733\pi$
$710$	36160.3	1.91137
$711$	−10329.8	−0.544865
$712$	23225.7	1.22250
$713$	33418.2	1.75529
$714$	12734.0	0.667450
$715$	−28676.8	−1.49993
$716$	−28681.9	−1.49706
$717$	−23078.7	−1.20208
$718$	30159.7	1.56762
$719$	−19227.8	−0.997322	−0.498661	−	0.866797i	$-0.666175\pi$
$719$	−19227.8	−0.997322	−0.498661	+	0.866797i	$0.666175\pi$
$720$	−40516.5	−2.09717
$721$	3990.22	0.206108
$722$	237.939	0.0122648
$723$	11081.5	0.570021
$724$	13098.7	0.672390
$725$	−50451.1	−2.58442
$726$	−12705.1	−0.649492
$727$	−33858.6	−1.72730	−0.863648	−	0.504095i	$-0.831826\pi$
$727$	−33858.6	−1.72730	−0.863648	+	0.504095i	$0.831826\pi$
$728$	21266.1	1.08265
$729$	−31782.9	−1.61474
$730$	−86129.9	−4.36686
$731$	−7814.85	−0.395407
$732$	9849.81	0.497349
$733$	−491.138	−0.0247484	−0.0123742	−	0.999923i	$-0.503939\pi$
$733$	−491.138	−0.0247484	−0.0123742	+	0.999923i	$0.503939\pi$
$734$	−44067.4	−2.21602
$735$	−22619.2	−1.13513
$736$	7337.78	0.367492
$737$	6338.05	0.316778
$738$	84648.2	4.22215
$739$	−14804.6	−0.736935	−0.368468	−	0.929641i	$-0.620117\pi$
$739$	−14804.6	−0.736935	−0.368468	+	0.929641i	$0.620117\pi$
$740$	−82276.8	−4.08723
$741$	27834.0	1.37990
$742$	−3250.12	−0.160803
$743$	11207.2	0.553368	0.276684	−	0.960961i	$-0.410764\pi$
$743$	11207.2	0.553368	0.276684	+	0.960961i	$0.410764\pi$
$744$	71058.6	3.50153
$745$	−54957.5	−2.70267
$746$	13786.6	0.676626
$747$	1190.05	0.0582886
$748$	−10655.7	−0.520869
$749$	17355.0	0.846646
$750$	−196077.	−9.54631
$751$	28158.6	1.36820	0.684102	−	0.729386i	$-0.260194\pi$
$751$	28158.6	1.36820	0.684102	+	0.729386i	$0.260194\pi$
$752$	−14170.1	−0.687139
$753$	−46992.7	−2.27425
$754$	−28490.6	−1.37608
$755$	25636.0	1.23575
$756$	−23179.9	−1.11514
$757$	18752.5	0.900357	0.450179	−	0.892939i	$-0.351360\pi$
$757$	18752.5	0.900357	0.450179	+	0.892939i	$0.351360\pi$
$758$	60725.6	2.90983
$759$	34841.1	1.66621
$760$	63139.3	3.01356
$761$	28823.7	1.37300	0.686502	−	0.727128i	$-0.259145\pi$
$761$	28823.7	1.37300	0.686502	+	0.727128i	$0.259145\pi$
$762$	102407.	4.86852
$763$	−26008.8	−1.23405
$764$	−10031.6	−0.475038
$765$	−19063.5	−0.900970
$766$	13688.7	0.645682
$767$	−16423.1	−0.773147
$768$	62184.3	2.92172
$769$	5814.04	0.272639	0.136320	−	0.990665i	$-0.456473\pi$
$769$	5814.04	0.272639	0.136320	+	0.990665i	$0.456473\pi$
$770$	−49226.6	−2.30390
$771$	4186.91	0.195575
$772$	−6684.35	−0.311625
$773$	−25519.6	−1.18742	−0.593711	−	0.804679i	$-0.702338\pi$
$773$	−25519.6	−1.18742	−0.593711	+	0.804679i	$0.702338\pi$
$774$	67952.6	3.15569
$775$	87731.7	4.06634
$776$	−36067.7	−1.66850
$777$	−29617.0	−1.36744
$778$	−39954.3	−1.84117
$779$	−36526.7	−1.67998
$780$	−112498.	−5.16418
$781$	−10892.1	−0.499038
$782$	−14254.5	−0.651843
$783$	14772.2	0.674223
$784$	−5924.43	−0.269881
$785$	−36364.8	−1.65340
$786$	−17616.4	−0.799437
$787$	2736.26	0.123935	0.0619677	−	0.998078i	$-0.480262\pi$
$787$	2736.26	0.123935	0.0619677	+	0.998078i	$0.480262\pi$
$788$	58896.2	2.66255
$789$	−9260.44	−0.417846
$790$	−27461.8	−1.23677
$791$	7622.27	0.342625
$792$	44074.4	1.97742
$793$	3266.77	0.146288
$794$	62010.7	2.77163
$795$	8178.54	0.364859
$796$	37562.4	1.67257
$797$	−27587.0	−1.22608	−0.613038	−	0.790054i	$-0.710053\pi$
$797$	−27587.0	−1.22608	−0.613038	+	0.790054i	$0.710053\pi$
$798$	47779.8	2.11953
$799$	−6667.18	−0.295204
$800$	19263.6	0.851340
$801$	−26311.7	−1.16065
$802$	−42119.3	−1.85447
$803$	25943.7	1.14014
$804$	24863.8	1.09065
$805$	−43201.4	−1.89149
$806$	49543.6	2.16513
$807$	62782.9	2.73862
$808$	21223.5	0.924060
$809$	−18023.4	−0.783274	−0.391637	−	0.920120i	$-0.628091\pi$
$809$	−18023.4	−0.783274	−0.391637	+	0.920120i	$0.628091\pi$
$810$	−23954.5	−1.03911
$811$	−10624.4	−0.460015	−0.230008	−	0.973189i	$-0.573875\pi$
$811$	−10624.4	−0.460015	−0.230008	+	0.973189i	$0.573875\pi$
$812$	−32084.5	−1.38663
$813$	−34816.7	−1.50194
$814$	37777.3	1.62665
$815$	494.854	0.0212687
$816$	−8392.90	−0.360061
$817$	−29322.3	−1.25564
$818$	−15862.3	−0.678008
$819$	−24091.7	−1.02788
$820$	147631.	6.28720
$821$	16052.5	0.682381	0.341190	−	0.939994i	$-0.389170\pi$
$821$	16052.5	0.682381	0.341190	+	0.939994i	$0.389170\pi$
$822$	−94851.0	−4.02471
$823$	−6721.26	−0.284676	−0.142338	−	0.989818i	$-0.545462\pi$
$823$	−6721.26	−0.284676	−0.142338	+	0.989818i	$0.545462\pi$
$824$	−9497.69	−0.401538
$825$	91467.3	3.85998
$826$	−28191.8	−1.18755
$827$	27009.0	1.13566	0.567832	−	0.823145i	$-0.307782\pi$
$827$	27009.0	1.13566	0.567832	+	0.823145i	$0.307782\pi$
$828$	81313.8	3.41286
$829$	−24852.7	−1.04122	−0.520609	−	0.853795i	$-0.674295\pi$
$829$	−24852.7	−1.04122	−0.520609	+	0.853795i	$0.674295\pi$
$830$	3163.73	0.132307
$831$	−24180.6	−1.00941
$832$	26327.7	1.09705
$833$	−2787.51	−0.115944
$834$	−93778.4	−3.89362
$835$	−79690.6	−3.30276
$836$	−39981.5	−1.65405
$837$	−25688.1	−1.06083
$838$	53915.6	2.22253
$839$	−35728.5	−1.47018	−0.735092	−	0.677967i	$-0.762861\pi$
$839$	−35728.5	−1.47018	−0.735092	+	0.677967i	$0.762861\pi$
$840$	−91861.2	−3.77323
$841$	−3942.01	−0.161631
$842$	37097.9	1.51838
$843$	−19482.2	−0.795968
$844$	27861.3	1.13628
$845$	10713.8	0.436172
$846$	57973.3	2.35598
$847$	−4745.29	−0.192503
$848$	2142.13	0.0867463
$849$	−52915.9	−2.13907
$850$	−37422.0	−1.51007
$851$	33153.4	1.33547
$852$	−42729.0	−1.71816
$853$	20468.7	0.821613	0.410806	−	0.911723i	$-0.365247\pi$
$853$	20468.7	0.821613	0.410806	+	0.911723i	$0.365247\pi$
$854$	5607.73	0.224698
$855$	−71528.7	−2.86109
$856$	−41309.1	−1.64943
$857$	−15116.7	−0.602538	−0.301269	−	0.953539i	$-0.597410\pi$
$857$	−15116.7	−0.602538	−0.301269	+	0.953539i	$0.597410\pi$
$858$	51653.2	2.05526
$859$	32519.0	1.29166	0.645829	−	0.763482i	$-0.276512\pi$
$859$	32519.0	1.29166	0.645829	+	0.763482i	$0.276512\pi$
$860$	118513.	4.69914
$861$	53142.5	2.10348
$862$	67224.2	2.65622
$863$	−27484.6	−1.08411	−0.542055	−	0.840343i	$-0.682354\pi$
$863$	−27484.6	−1.08411	−0.542055	+	0.840343i	$0.682354\pi$
$864$	−5640.45	−0.222097
$865$	95919.9	3.77038
$866$	−17131.8	−0.672243
$867$	36161.6	1.41651
$868$	55793.2	2.18173
$869$	8271.93	0.322907
$870$	123068.	4.79587
$871$	8246.28	0.320797
$872$	61907.3	2.40418
$873$	40860.1	1.58408
$874$	−53484.9	−2.06997
$875$	−73233.8	−2.82943
$876$	101776.	3.92544
$877$	41148.9	1.58438	0.792189	−	0.610276i	$-0.208942\pi$
$877$	41148.9	1.58438	0.792189	+	0.610276i	$0.208942\pi$
$878$	29128.8	1.11965
$879$	33482.9	1.28481
$880$	32444.8	1.24286
$881$	−42748.8	−1.63478	−0.817391	−	0.576083i	$-0.804580\pi$
$881$	−42748.8	−1.63478	−0.817391	+	0.576083i	$0.804580\pi$
$882$	24238.3	0.925336
$883$	−5837.29	−0.222469	−0.111235	−	0.993794i	$-0.535481\pi$
$883$	−5837.29	−0.222469	−0.111235	+	0.993794i	$0.535481\pi$
$884$	−13863.8	−0.527479
$885$	70941.4	2.69454
$886$	−17894.3	−0.678522
$887$	−42974.1	−1.62675	−0.813376	−	0.581738i	$-0.802373\pi$
$887$	−42974.1	−1.62675	−0.813376	+	0.581738i	$0.802373\pi$
$888$	70495.7	2.66405
$889$	38248.5	1.44298
$890$	−69949.5	−2.63451
$891$	7215.49	0.271300
$892$	−41416.7	−1.55464
$893$	−25016.1	−0.937438
$894$	98990.2	3.70328
$895$	41090.6	1.53465
$896$	38770.8	1.44558
$897$	45330.9	1.68735
$898$	−65022.7	−2.41630
$899$	−35556.2	−1.31909
$900$	213470.	7.90631
$901$	1007.89	0.0372673
$902$	−67784.7	−2.50220
$903$	42661.0	1.57217
$904$	−18142.8	−0.667502
$905$	−18765.7	−0.689273
$906$	−46175.9	−1.69326
$907$	23540.7	0.861803	0.430901	−	0.902399i	$-0.358196\pi$
$907$	23540.7	0.861803	0.430901	+	0.902399i	$0.358196\pi$
$908$	−46177.5	−1.68772
$909$	−24043.5	−0.877308
$910$	−64047.5	−2.33314
$911$	−30755.9	−1.11854	−0.559269	−	0.828986i	$-0.688918\pi$
$911$	−30755.9	−1.11854	−0.559269	+	0.828986i	$0.688918\pi$
$912$	−31491.2	−1.14340
$913$	−952.967	−0.0345439
$914$	−68228.8	−2.46915
$915$	−14111.2	−0.509837
$916$	−3551.88	−0.128120
$917$	−6579.64	−0.236945
$918$	10957.3	0.393948
$919$	−7411.94	−0.266047	−0.133024	−	0.991113i	$-0.542469\pi$
$919$	−7411.94	−0.266047	−0.133024	+	0.991113i	$0.542469\pi$
$920$	102830.	3.68500
$921$	41367.2	1.48002
$922$	21707.2	0.775366
$923$	−14171.4	−0.505371
$924$	58168.9	2.07101
$925$	87036.6	3.09378
$926$	−18287.2	−0.648978
$927$	10759.7	0.381223
$928$	−7807.23	−0.276169
$929$	50327.3	1.77738	0.888689	−	0.458511i	$-0.151617\pi$
$929$	50327.3	1.77738	0.888689	+	0.458511i	$0.151617\pi$
$930$	−214009.	−7.54585
$931$	−10459.1	−0.368188
$932$	−63726.2	−2.23972
$933$	50288.6	1.76460
$934$	−53948.1	−1.88997
$935$	15265.7	0.533947
$936$	57344.1	2.00251
$937$	37658.3	1.31296	0.656480	−	0.754343i	$-0.272045\pi$
$937$	37658.3	1.31296	0.656480	+	0.754343i	$0.272045\pi$
$938$	14155.6	0.492745
$939$	36396.0	1.26490
$940$	101109.	3.50830
$941$	39852.9	1.38062	0.690312	−	0.723512i	$-0.257473\pi$
$941$	39852.9	1.38062	0.690312	+	0.723512i	$0.257473\pi$
$942$	65500.9	2.26553
$943$	−59488.0	−2.05429
$944$	18581.0	0.640636
$945$	33208.4	1.14314
$946$	−54415.1	−1.87018
$947$	39985.9	1.37209	0.686044	−	0.727560i	$-0.259346\pi$
$947$	39985.9	1.37209	0.686044	+	0.727560i	$0.259346\pi$
$948$	32450.3	1.11175
$949$	33754.7	1.15461
$950$	−140412.	−4.79534
$951$	−52845.9	−1.80194
$952$	−11320.7	−0.385404
$953$	40712.7	1.38386	0.691928	−	0.721967i	$-0.256762\pi$
$953$	40712.7	1.38386	0.691928	+	0.721967i	$0.256762\pi$
$954$	−8763.97	−0.297426
$955$	14371.5	0.486966
$956$	43131.7	1.45918
$957$	−37070.2	−1.25215
$958$	−68784.2	−2.31975
$959$	−35426.3	−1.19288
$960$	−113725.	−3.82341
$961$	32039.3	1.07547
$962$	49151.1	1.64729
$963$	46797.9	1.56598
$964$	−20710.2	−0.691940
$965$	9576.22	0.319450
$966$	77815.0	2.59178
$967$	16687.6	0.554951	0.277475	−	0.960733i	$-0.410502\pi$
$967$	16687.6	0.554951	0.277475	+	0.960733i	$0.410502\pi$
$968$	11294.9	0.375034
$969$	−14817.0	−0.491218
$970$	108626.	3.59564
$971$	32499.8	1.07412	0.537058	−	0.843545i	$-0.319535\pi$
$971$	32499.8	1.07412	0.537058	+	0.843545i	$0.319535\pi$
$972$	70865.2	2.33848
$973$	−35025.7	−1.15403
$974$	−31297.1	−1.02959
$975$	119006.	3.90896
$976$	−3696.00	−0.121215
$977$	−39682.4	−1.29944	−0.649720	−	0.760173i	$-0.725114\pi$
$977$	−39682.4	−1.29944	−0.649720	+	0.760173i	$0.725114\pi$
$978$	−891.338	−0.0291430
$979$	21069.9	0.687842
$980$	42273.0	1.37792
$981$	−70133.0	−2.28254
$982$	−91761.0	−2.98189
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	−126492.	−4.09799
$985$	−84376.7	−2.72941
$986$	15166.5	0.489858
$987$	36395.9	1.17375
$988$	−52018.9	−1.67504
$989$	−47754.9	−1.53541
$990$	−132740.	−4.26137
$991$	−36490.6	−1.16969	−0.584845	−	0.811145i	$-0.698845\pi$
$991$	−36490.6	−1.16969	−0.584845	+	0.811145i	$0.698845\pi$
$992$	13576.4	0.434526
$993$	66091.8	2.11214
$994$	−24326.6	−0.776251
$995$	−53813.1	−1.71456
$996$	−3738.44	−0.118933
$997$	−2853.32	−0.0906373	−0.0453187	−	0.998973i	$-0.514430\pi$
$997$	−2853.32	−0.0906373	−0.0453187	+	0.998973i	$0.514430\pi$
$998$	41892.9	1.32875
$999$	−25484.6	−0.807104

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.12	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.12	✓	136	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:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-4.82266 q^{2} -8.16418 q^{3} +15.2580 q^{4} -21.8591 q^{5} +39.3730 q^{6} +14.7056 q^{7} -35.0029 q^{8} +39.6538 q^{9} +O(q^{10})\)	\(q-4.82266 q^{2} -8.16418 q^{3} +15.2580 q^{4} -21.8591 q^{5} +39.3730 q^{6} +14.7056 q^{7} -35.0029 q^{8} +39.6538 q^{9} +105.419 q^{10} -31.7540 q^{11} -124.569 q^{12} -41.3143 q^{13} -70.9201 q^{14} +178.462 q^{15} +46.7428 q^{16} +21.9930 q^{17} -191.236 q^{18} +82.5207 q^{19} -333.527 q^{20} -120.059 q^{21} +153.138 q^{22} +134.395 q^{23} +285.770 q^{24} +352.822 q^{25} +199.245 q^{26} -103.307 q^{27} +224.378 q^{28} -142.993 q^{29} -860.660 q^{30} +248.657 q^{31} +54.5987 q^{32} +259.245 q^{33} -106.065 q^{34} -321.452 q^{35} +605.037 q^{36} +246.687 q^{37} -397.969 q^{38} +337.297 q^{39} +765.133 q^{40} -442.637 q^{41} +579.004 q^{42} -355.333 q^{43} -484.502 q^{44} -866.797 q^{45} -648.139 q^{46} -303.150 q^{47} -381.616 q^{48} -126.745 q^{49} -1701.54 q^{50} -179.555 q^{51} -630.374 q^{52} +45.8279 q^{53} +498.216 q^{54} +694.114 q^{55} -514.738 q^{56} -673.713 q^{57} +689.606 q^{58} +397.516 q^{59} +2722.97 q^{60} -79.0711 q^{61} -1199.19 q^{62} +583.132 q^{63} -637.253 q^{64} +903.095 q^{65} -1250.25 q^{66} -199.599 q^{67} +335.570 q^{68} -1097.22 q^{69} +1550.25 q^{70} +343.015 q^{71} -1388.00 q^{72} -817.023 q^{73} -1189.69 q^{74} -2880.50 q^{75} +1259.10 q^{76} -466.961 q^{77} -1626.67 q^{78} -260.501 q^{79} -1021.76 q^{80} -227.231 q^{81} +2134.68 q^{82} +30.0110 q^{83} -1831.86 q^{84} -480.749 q^{85} +1713.65 q^{86} +1167.42 q^{87} +1111.48 q^{88} -663.537 q^{89} +4180.26 q^{90} -607.552 q^{91} +2050.60 q^{92} -2030.08 q^{93} +1461.99 q^{94} -1803.83 q^{95} -445.753 q^{96} +1030.42 q^{97} +611.249 q^{98} -1259.16 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9} + 257 q^{10} + 204 q^{11} + 296 q^{12} + 530 q^{13} + 103 q^{14} + 226 q^{15} + 2737 q^{16} + 664 q^{17} + 949 q^{18} + 421 q^{19} + 500 q^{20} + 684 q^{21} + 905 q^{22} + 617 q^{23} + 917 q^{24} + 5430 q^{25} + 572 q^{26} + 886 q^{27} + 2728 q^{28} + 688 q^{29} + 712 q^{30} + 1019 q^{31} + 2363 q^{32} + 1764 q^{33} + 1260 q^{34} + 834 q^{35} + 7190 q^{36} + 3303 q^{37} + 384 q^{38} + 1950 q^{39} + 2766 q^{40} + 1975 q^{41} + 448 q^{42} + 3021 q^{43} + 2038 q^{44} + 2266 q^{45} + 2742 q^{46} + 1293 q^{47} + 2589 q^{48} + 10447 q^{49} + 2191 q^{50} + 1032 q^{51} + 4983 q^{52} + 2415 q^{53} + 1878 q^{54} + 2612 q^{55} + 1540 q^{56} + 7908 q^{57} + 5743 q^{58} + 1059 q^{59} + 2611 q^{60} + 4312 q^{61} + 3258 q^{62} + 5605 q^{63} + 13735 q^{64} + 3554 q^{65} + 433 q^{66} + 5715 q^{67} + 5881 q^{68} + 1398 q^{69} + 4287 q^{70} + 2530 q^{71} + 9891 q^{72} + 14106 q^{73} + 2318 q^{74} + 2621 q^{75} + 4651 q^{76} + 4750 q^{77} + 6639 q^{78} + 4791 q^{79} + 4812 q^{80} + 19932 q^{81} + 5380 q^{82} + 4284 q^{83} + 9282 q^{84} + 12058 q^{85} + 2451 q^{86} + 6984 q^{87} + 11197 q^{88} + 5313 q^{89} + 5405 q^{90} + 6298 q^{91} + 6588 q^{92} + 5700 q^{93} + 4743 q^{94} + 5778 q^{95} + 9613 q^{96} + 15382 q^{97} + 6640 q^{98} + 8542 q^{99}+O(q^{100}) \) 136 * q + 17 * q^2 + 25 * q^3 + 601 * q^4 + 50 * q^5 + 61 * q^6 + 223 * q^7 + 207 * q^8 + 1443 * q^9 + 257 * q^10 + 204 * q^11 + 296 * q^12 + 530 * q^13 + 103 * q^14 + 226 * q^15 + 2737 * q^16 + 664 * q^17 + 949 * q^18 + 421 * q^19 + 500 * q^20 + 684 * q^21 + 905 * q^22 + 617 * q^23 + 917 * q^24 + 5430 * q^25 + 572 * q^26 + 886 * q^27 + 2728 * q^28 + 688 * q^29 + 712 * q^30 + 1019 * q^31 + 2363 * q^32 + 1764 * q^33 + 1260 * q^34 + 834 * q^35 + 7190 * q^36 + 3303 * q^37 + 384 * q^38 + 1950 * q^39 + 2766 * q^40 + 1975 * q^41 + 448 * q^42 + 3021 * q^43 + 2038 * q^44 + 2266 * q^45 + 2742 * q^46 + 1293 * q^47 + 2589 * q^48 + 10447 * q^49 + 2191 * q^50 + 1032 * q^51 + 4983 * q^52 + 2415 * q^53 + 1878 * q^54 + 2612 * q^55 + 1540 * q^56 + 7908 * q^57 + 5743 * q^58 + 1059 * q^59 + 2611 * q^60 + 4312 * q^61 + 3258 * q^62 + 5605 * q^63 + 13735 * q^64 + 3554 * q^65 + 433 * q^66 + 5715 * q^67 + 5881 * q^68 + 1398 * q^69 + 4287 * q^70 + 2530 * q^71 + 9891 * q^72 + 14106 * q^73 + 2318 * q^74 + 2621 * q^75 + 4651 * q^76 + 4750 * q^77 + 6639 * q^78 + 4791 * q^79 + 4812 * q^80 + 19932 * q^81 + 5380 * q^82 + 4284 * q^83 + 9282 * q^84 + 12058 * q^85 + 2451 * q^86 + 6984 * q^87 + 11197 * q^88 + 5313 * q^89 + 5405 * q^90 + 6298 * q^91 + 6588 * q^92 + 5700 * q^93 + 4743 * q^94 + 5778 * q^95 + 9613 * q^96 + 15382 * q^97 + 6640 * q^98 + 8542 * q^99

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