LMFDB - Embedded newform 983.4.a.b.1.9

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			1.9
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)

$f(q)$	$=$	$q-5.10403 q^{2} +2.85786 q^{3} +18.0511 q^{4} +7.24893 q^{5} -14.5866 q^{6} -25.2920 q^{7} -51.3012 q^{8} -18.8326 q^{9} +O(q^{10})$	\(q-5.10403 q^{2} +2.85786 q^{3} +18.0511 q^{4} +7.24893 q^{5} -14.5866 q^{6} -25.2920 q^{7} -51.3012 q^{8} -18.8326 q^{9} -36.9987 q^{10} +68.7665 q^{11} +51.5875 q^{12} -36.1759 q^{13} +129.091 q^{14} +20.7164 q^{15} +117.434 q^{16} +120.546 q^{17} +96.1223 q^{18} -154.399 q^{19} +130.851 q^{20} -72.2810 q^{21} -350.986 q^{22} -55.8712 q^{23} -146.612 q^{24} -72.4531 q^{25} +184.643 q^{26} -130.983 q^{27} -456.549 q^{28} +44.1077 q^{29} -105.737 q^{30} +113.623 q^{31} -188.976 q^{32} +196.525 q^{33} -615.272 q^{34} -183.340 q^{35} -339.950 q^{36} -105.443 q^{37} +788.059 q^{38} -103.386 q^{39} -371.878 q^{40} +183.464 q^{41} +368.924 q^{42} +429.594 q^{43} +1241.31 q^{44} -136.516 q^{45} +285.168 q^{46} -102.529 q^{47} +335.609 q^{48} +296.686 q^{49} +369.803 q^{50} +344.505 q^{51} -653.015 q^{52} +529.102 q^{53} +668.542 q^{54} +498.483 q^{55} +1297.51 q^{56} -441.252 q^{57} -225.127 q^{58} -322.898 q^{59} +373.954 q^{60} -576.384 q^{61} -579.934 q^{62} +476.315 q^{63} +25.0680 q^{64} -262.236 q^{65} -1003.07 q^{66} +749.792 q^{67} +2176.00 q^{68} -159.672 q^{69} +935.772 q^{70} -1075.29 q^{71} +966.136 q^{72} +579.185 q^{73} +538.186 q^{74} -207.061 q^{75} -2787.08 q^{76} -1739.24 q^{77} +527.683 q^{78} -54.2223 q^{79} +851.268 q^{80} +134.150 q^{81} -936.404 q^{82} +1080.12 q^{83} -1304.75 q^{84} +873.832 q^{85} -2192.66 q^{86} +126.054 q^{87} -3527.80 q^{88} +1106.92 q^{89} +696.784 q^{90} +914.961 q^{91} -1008.54 q^{92} +324.718 q^{93} +523.309 q^{94} -1119.23 q^{95} -540.066 q^{96} +775.480 q^{97} -1514.29 q^{98} -1295.06 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.10403	−1.80455	−0.902273	−	0.431164i	$-0.858103\pi$
$2$	−5.10403	−1.80455	−0.902273	+	0.431164i	$0.858103\pi$
$3$	2.85786	0.549995	0.274998	−	0.961445i	$-0.411323\pi$
$3$	2.85786	0.549995	0.274998	+	0.961445i	$0.411323\pi$
$4$	18.0511	2.25639
$5$	7.24893	0.648364	0.324182	−	0.945995i	$-0.394911\pi$
$5$	7.24893	0.648364	0.324182	+	0.945995i	$0.394911\pi$
$6$	−14.5866	−0.992492
$7$	−25.2920	−1.36564	−0.682820	−	0.730587i	$-0.739247\pi$
$7$	−25.2920	−1.36564	−0.682820	+	0.730587i	$0.739247\pi$
$8$	−51.3012	−2.26721
$9$	−18.8326	−0.697505
$10$	−36.9987	−1.17000
$11$	68.7665	1.88490	0.942449	−	0.334349i	$-0.108516\pi$
$11$	68.7665	1.88490	0.942449	+	0.334349i	$0.108516\pi$
$12$	51.5875	1.24100
$13$	−36.1759	−0.771799	−0.385900	−	0.922541i	$-0.626109\pi$
$13$	−36.1759	−0.771799	−0.385900	+	0.922541i	$0.626109\pi$
$14$	129.091	2.46436
$15$	20.7164	0.356597
$16$	117.434	1.83490
$17$	120.546	1.71981	0.859906	−	0.510453i	$-0.170522\pi$
$17$	120.546	1.71981	0.859906	+	0.510453i	$0.170522\pi$
$18$	96.1223	1.25868
$19$	−154.399	−1.86430	−0.932149	−	0.362074i	$-0.882069\pi$
$19$	−154.399	−1.86430	−0.932149	+	0.362074i	$0.882069\pi$
$20$	130.851	1.46296
$21$	−72.2810	−0.751096
$22$	−350.986	−3.40139
$23$	−55.8712	−0.506519	−0.253260	−	0.967398i	$-0.581503\pi$
$23$	−55.8712	−0.506519	−0.253260	+	0.967398i	$0.581503\pi$
$24$	−146.612	−1.24696
$25$	−72.4531	−0.579625
$26$	184.643	1.39275
$27$	−130.983	−0.933620
$28$	−456.549	−3.08142
$29$	44.1077	0.282435	0.141217	−	0.989979i	$-0.454898\pi$
$29$	44.1077	0.282435	0.141217	+	0.989979i	$0.454898\pi$
$30$	−105.737	−0.643496
$31$	113.623	0.658299	0.329149	−	0.944278i	$-0.393238\pi$
$31$	113.623	0.658299	0.329149	+	0.944278i	$0.393238\pi$
$32$	−188.976	−1.04395
$33$	196.525	1.03669
$34$	−615.272	−3.10348
$35$	−183.340	−0.885431
$36$	−339.950	−1.57384
$37$	−105.443	−0.468508	−0.234254	−	0.972175i	$-0.575265\pi$
$37$	−105.443	−0.468508	−0.234254	+	0.972175i	$0.575265\pi$
$38$	788.059	3.36421
$39$	−103.386	−0.424486
$40$	−371.878	−1.46998
$41$	183.464	0.698835	0.349417	−	0.936967i	$-0.386380\pi$
$41$	183.464	0.698835	0.349417	+	0.936967i	$0.386380\pi$
$42$	368.924	1.35539
$43$	429.594	1.52354	0.761772	−	0.647845i	$-0.224329\pi$
$43$	429.594	1.52354	0.761772	+	0.647845i	$0.224329\pi$
$44$	1241.31	4.25306
$45$	−136.516	−0.452237
$46$	285.168	0.914038
$47$	−102.529	−0.318198	−0.159099	−	0.987263i	$-0.550859\pi$
$47$	−102.529	−0.318198	−0.159099	+	0.987263i	$0.550859\pi$
$48$	335.609	1.00919
$49$	296.686	0.864973
$50$	369.803	1.04596
$51$	344.505	0.945889
$52$	−653.015	−1.74148
$53$	529.102	1.37128	0.685639	−	0.727942i	$-0.259523\pi$
$53$	529.102	1.37128	0.685639	+	0.727942i	$0.259523\pi$
$54$	668.542	1.68476
$55$	498.483	1.22210
$56$	1297.51	3.09620
$57$	−441.252	−1.02536
$58$	−225.127	−0.509666
$59$	−322.898	−0.712505	−0.356252	−	0.934390i	$-0.615946\pi$
$59$	−322.898	−0.712505	−0.356252	+	0.934390i	$0.615946\pi$
$60$	373.954	0.804621
$61$	−576.384	−1.20981	−0.604905	−	0.796297i	$-0.706789\pi$
$61$	−576.384	−1.20981	−0.604905	+	0.796297i	$0.706789\pi$
$62$	−579.934	−1.18793
$63$	476.315	0.952541
$64$	25.0680	0.0489610
$65$	−262.236	−0.500406
$66$	−1003.07	−1.87075
$67$	749.792	1.36719	0.683595	−	0.729862i	$-0.260416\pi$
$67$	749.792	1.36719	0.683595	+	0.729862i	$0.260416\pi$
$68$	2176.00	3.88056
$69$	−159.672	−0.278583
$70$	935.772	1.59780
$71$	−1075.29	−1.79737	−0.898687	−	0.438590i	$-0.855478\pi$
$71$	−1075.29	−1.79737	−0.898687	+	0.438590i	$0.855478\pi$
$72$	966.136	1.58139
$73$	579.185	0.928610	0.464305	−	0.885675i	$-0.346304\pi$
$73$	579.185	0.928610	0.464305	+	0.885675i	$0.346304\pi$
$74$	538.186	0.845444
$75$	−207.061	−0.318791
$76$	−2787.08	−4.20658
$77$	−1739.24	−2.57409
$78$	527.683	0.766005
$79$	−54.2223	−0.0772213	−0.0386107	−	0.999254i	$-0.512293\pi$
$79$	−54.2223	−0.0772213	−0.0386107	+	0.999254i	$0.512293\pi$
$80$	851.268	1.18968
$81$	134.150	0.184019
$82$	−936.404	−1.26108
$83$	1080.12	1.42842	0.714209	−	0.699932i	$-0.246786\pi$
$83$	1080.12	1.42842	0.714209	+	0.699932i	$0.246786\pi$
$84$	−1304.75	−1.69476
$85$	873.832	1.11506
$86$	−2192.66	−2.74931
$87$	126.054	0.155338
$88$	−3527.80	−4.27347
$89$	1106.92	1.31836	0.659178	−	0.751987i	$-0.270904\pi$
$89$	1106.92	1.31836	0.659178	+	0.751987i	$0.270904\pi$
$90$	696.784	0.816083
$91$	914.961	1.05400
$92$	−1008.54	−1.14290
$93$	324.718	0.362061
$94$	523.309	0.574204
$95$	−1119.23	−1.20874
$96$	−540.066	−0.574169
$97$	775.480	0.811732	0.405866	−	0.913933i	$-0.366970\pi$
$97$	775.480	0.811732	0.405866	+	0.913933i	$0.366970\pi$
$98$	−1514.29	−1.56088
$99$	−1295.06	−1.31473
$100$	−1307.86	−1.30786
$101$	570.077	0.561632	0.280816	−	0.959762i	$-0.409395\pi$
$101$	570.077	0.561632	0.280816	+	0.959762i	$0.409395\pi$
$102$	−1758.36	−1.70690
$103$	−762.631	−0.729556	−0.364778	−	0.931095i	$-0.618855\pi$
$103$	−762.631	−0.729556	−0.364778	+	0.931095i	$0.618855\pi$
$104$	1855.87	1.74983
$105$	−523.960	−0.486983
$106$	−2700.55	−2.47453
$107$	−1802.38	−1.62844	−0.814219	−	0.580557i	$-0.802835\pi$
$107$	−1802.38	−1.62844	−0.814219	+	0.580557i	$0.802835\pi$
$108$	−2364.39	−2.10661
$109$	−1547.22	−1.35960	−0.679801	−	0.733396i	$-0.737934\pi$
$109$	−1547.22	−1.35960	−0.679801	+	0.733396i	$0.737934\pi$
$110$	−2544.27	−2.20534
$111$	−301.342	−0.257677
$112$	−2970.13	−2.50582
$113$	824.579	0.686459	0.343229	−	0.939252i	$-0.388479\pi$
$113$	824.579	0.686459	0.343229	+	0.939252i	$0.388479\pi$
$114$	2252.16	1.85030
$115$	−405.006	−0.328409
$116$	796.194	0.637282
$117$	681.288	0.538334
$118$	1648.08	1.28575
$119$	−3048.86	−2.34864
$120$	−1062.78	−0.808481
$121$	3397.84	2.55284
$122$	2941.88	2.18316
$123$	524.313	0.384356
$124$	2051.02	1.48538
$125$	−1431.32	−1.02417
$126$	−2431.13	−1.71890
$127$	2282.71	1.59494	0.797472	−	0.603355i	$-0.206170\pi$
$127$	2282.71	1.59494	0.797472	+	0.603355i	$0.206170\pi$
$128$	1383.86	0.955601
$129$	1227.72	0.837943
$130$	1338.46	0.903007
$131$	1811.91	1.20846	0.604228	−	0.796812i	$-0.293482\pi$
$131$	1811.91	1.20846	0.604228	+	0.796812i	$0.293482\pi$
$132$	3547.50	2.33917
$133$	3905.07	2.54596
$134$	−3826.96	−2.46716
$135$	−949.488	−0.605325
$136$	−6184.17	−3.89918
$137$	1321.87	0.824340	0.412170	−	0.911107i	$-0.364771\pi$
$137$	1321.87	0.824340	0.412170	+	0.911107i	$0.364771\pi$
$138$	814.970	0.502716
$139$	266.502	0.162621	0.0813107	−	0.996689i	$-0.474089\pi$
$139$	266.502	0.162621	0.0813107	+	0.996689i	$0.474089\pi$
$140$	−3309.49	−1.99788
$141$	−293.012	−0.175008
$142$	5488.32	3.24345
$143$	−2487.69	−1.45476
$144$	−2211.59	−1.27985
$145$	319.734	0.183120
$146$	−2956.18	−1.67572
$147$	847.886	0.475731
$148$	−1903.37	−1.05714
$149$	−374.275	−0.205784	−0.102892	−	0.994693i	$-0.532810\pi$
$149$	−374.275	−0.205784	−0.102892	+	0.994693i	$0.532810\pi$
$150$	1056.84	0.575273
$151$	1735.06	0.935079	0.467540	−	0.883972i	$-0.345141\pi$
$151$	1735.06	0.935079	0.467540	+	0.883972i	$0.345141\pi$
$152$	7920.87	4.22676
$153$	−2270.21	−1.19958
$154$	8877.15	4.64507
$155$	823.643	0.426817
$156$	−1866.23	−0.957805
$157$	−3359.00	−1.70750	−0.853750	−	0.520683i	$-0.825677\pi$
$157$	−3359.00	−1.70750	−0.853750	+	0.520683i	$0.825677\pi$
$158$	276.752	0.139350
$159$	1512.10	0.754196
$160$	−1369.87	−0.676861
$161$	1413.09	0.691723
$162$	−684.703	−0.332070
$163$	−2382.62	−1.14492	−0.572459	−	0.819934i	$-0.694010\pi$
$163$	−2382.62	−1.14492	−0.572459	+	0.819934i	$0.694010\pi$
$164$	3311.72	1.57684
$165$	1424.60	0.672149
$166$	−5512.97	−2.57765
$167$	3250.80	1.50632	0.753158	−	0.657840i	$-0.228530\pi$
$167$	3250.80	1.50632	0.753158	+	0.657840i	$0.228530\pi$
$168$	3708.10	1.70289
$169$	−888.304	−0.404326
$170$	−4460.06	−2.01218
$171$	2907.75	1.30036
$172$	7754.64	3.43771
$173$	15.3169	0.00673134	0.00336567	−	0.999994i	$-0.498929\pi$
$173$	15.3169	0.00673134	0.00336567	+	0.999994i	$0.498929\pi$
$174$	−643.382	−0.280314
$175$	1832.48	0.791559
$176$	8075.51	3.45860
$177$	−922.798	−0.391874
$178$	−5649.77	−2.37904
$179$	−4689.48	−1.95815	−0.979073	−	0.203508i	$-0.934766\pi$
$179$	−4689.48	−1.95815	−0.979073	+	0.203508i	$0.934766\pi$
$180$	−2464.27	−1.02042
$181$	−1469.31	−0.603388	−0.301694	−	0.953405i	$-0.597552\pi$
$181$	−1469.31	−0.603388	−0.301694	+	0.953405i	$0.597552\pi$
$182$	−4669.99	−1.90199
$183$	−1647.23	−0.665390
$184$	2866.26	1.14839
$185$	−764.351	−0.303763
$186$	−1657.37	−0.653356
$187$	8289.56	3.24167
$188$	−1850.75	−0.717979
$189$	3312.83	1.27499
$190$	5712.58	2.18123
$191$	3523.98	1.33501	0.667503	−	0.744607i	$-0.267363\pi$
$191$	3523.98	1.33501	0.667503	+	0.744607i	$0.267363\pi$
$192$	71.6409	0.0269283
$193$	4457.33	1.66241	0.831206	−	0.555965i	$-0.187651\pi$
$193$	4457.33	1.66241	0.831206	+	0.555965i	$0.187651\pi$
$194$	−3958.07	−1.46481
$195$	−749.435	−0.275221
$196$	5355.51	1.95172
$197$	−38.8404	−0.0140470	−0.00702350	−	0.999975i	$-0.502236\pi$
$197$	−38.8404	−0.0140470	−0.00702350	+	0.999975i	$0.502236\pi$
$198$	6610.00	2.37249
$199$	−640.971	−0.228328	−0.114164	−	0.993462i	$-0.536419\pi$
$199$	−640.971	−0.228328	−0.114164	+	0.993462i	$0.536419\pi$
$200$	3716.93	1.31413
$201$	2142.80	0.751948
$202$	−2909.69	−1.01349
$203$	−1115.57	−0.385704
$204$	6218.69	2.13429
$205$	1329.91	0.453099
$206$	3892.49	1.31652
$207$	1052.20	0.353300
$208$	−4248.27	−1.41618
$209$	−10617.5	−3.51401
$210$	2674.31	0.878784
$211$	−1451.97	−0.473733	−0.236866	−	0.971542i	$-0.576120\pi$
$211$	−1451.97	−0.473733	−0.236866	+	0.971542i	$0.576120\pi$
$212$	9550.87	3.09414
$213$	−3073.03	−0.988548
$214$	9199.41	2.93859
$215$	3114.09	0.987811
$216$	6719.59	2.11671
$217$	−2873.75	−0.898999
$218$	7897.05	2.45347
$219$	1655.23	0.510731
$220$	8998.18	2.75753
$221$	−4360.87	−1.32735
$222$	1538.06	0.464990
$223$	2474.60	0.743101	0.371550	−	0.928413i	$-0.378826\pi$
$223$	2474.60	0.743101	0.371550	+	0.928413i	$0.378826\pi$
$224$	4779.58	1.42566
$225$	1364.48	0.404291
$226$	−4208.67	−1.23875
$227$	1514.96	0.442958	0.221479	−	0.975165i	$-0.428912\pi$
$227$	1514.96	0.442958	0.221479	+	0.975165i	$0.428912\pi$
$228$	−7965.09	−2.31360
$229$	−1169.75	−0.337551	−0.168775	−	0.985655i	$-0.553981\pi$
$229$	−1169.75	−0.337551	−0.168775	+	0.985655i	$0.553981\pi$
$230$	2067.16	0.592629
$231$	−4970.51	−1.41574
$232$	−2262.78	−0.640339
$233$	6546.28	1.84061	0.920303	−	0.391207i	$-0.127942\pi$
$233$	6546.28	1.84061	0.920303	+	0.391207i	$0.127942\pi$
$234$	−3477.31	−0.971449
$235$	−743.222	−0.206308
$236$	−5828.67	−1.60769
$237$	−154.960	−0.0424714
$238$	15561.5	4.23824
$239$	6152.67	1.66520	0.832600	−	0.553874i	$-0.186851\pi$
$239$	6152.67	1.66520	0.832600	+	0.553874i	$0.186851\pi$
$240$	2432.80	0.654320
$241$	−1569.84	−0.419593	−0.209797	−	0.977745i	$-0.567280\pi$
$241$	−1569.84	−0.419593	−0.209797	+	0.977745i	$0.567280\pi$
$242$	−17342.7	−4.60673
$243$	3919.93	1.03483
$244$	−10404.4	−2.72980
$245$	2150.65	0.560817
$246$	−2676.11	−0.693588
$247$	5585.54	1.43886
$248$	−5828.98	−1.49250
$249$	3086.84	0.785624
$250$	7305.51	1.84816
$251$	1704.82	0.428713	0.214357	−	0.976755i	$-0.431235\pi$
$251$	1704.82	0.428713	0.214357	+	0.976755i	$0.431235\pi$
$252$	8598.02	2.14930
$253$	−3842.07	−0.954738
$254$	−11651.0	−2.87815
$255$	2497.29	0.613280
$256$	−7263.80	−1.77339
$257$	4133.64	1.00331	0.501653	−	0.865069i	$-0.332726\pi$
$257$	4133.64	1.00331	0.501653	+	0.865069i	$0.332726\pi$
$258$	−6266.31	−1.51211
$259$	2666.88	0.639813
$260$	−4733.66	−1.12911
$261$	−830.665	−0.197000
$262$	−9248.06	−2.18071
$263$	−3706.08	−0.868924	−0.434462	−	0.900690i	$-0.643061\pi$
$263$	−3706.08	−0.868924	−0.434462	+	0.900690i	$0.643061\pi$
$264$	−10082.0	−2.35039
$265$	3835.42	0.889086
$266$	−19931.6	−4.59431
$267$	3163.43	0.725090
$268$	13534.6	3.08491
$269$	6204.62	1.40633	0.703164	−	0.711028i	$-0.251770\pi$
$269$	6204.62	1.40633	0.703164	+	0.711028i	$0.251770\pi$
$270$	4846.21	1.09234
$271$	5028.36	1.12713	0.563563	−	0.826073i	$-0.309430\pi$
$271$	5028.36	1.12713	0.563563	+	0.826073i	$0.309430\pi$
$272$	14156.2	3.15569
$273$	2614.83	0.579695
$274$	−6746.84	−1.48756
$275$	−4982.35	−1.09253
$276$	−2882.26	−0.628592
$277$	5494.43	1.19180	0.595900	−	0.803059i	$-0.296796\pi$
$277$	5494.43	1.19180	0.595900	+	0.803059i	$0.296796\pi$
$278$	−1360.23	−0.293458
$279$	−2139.82	−0.459167
$280$	9405.55	2.00746
$281$	1187.33	0.252065	0.126033	−	0.992026i	$-0.459776\pi$
$281$	1187.33	0.252065	0.126033	+	0.992026i	$0.459776\pi$
$282$	1495.54	0.315809
$283$	−2757.98	−0.579311	−0.289655	−	0.957131i	$-0.593541\pi$
$283$	−2757.98	−0.579311	−0.289655	+	0.957131i	$0.593541\pi$
$284$	−19410.2	−4.05558
$285$	−3198.60	−0.664803
$286$	12697.2	2.62519
$287$	−4640.17	−0.954356
$288$	3558.91	0.728163
$289$	9618.44	1.95775
$290$	−1631.93	−0.330449
$291$	2216.21	0.446449
$292$	10454.9	2.09530
$293$	3446.37	0.687164	0.343582	−	0.939123i	$-0.388360\pi$
$293$	3446.37	0.687164	0.343582	+	0.939123i	$0.388360\pi$
$294$	−4327.64	−0.858479
$295$	−2340.67	−0.461962
$296$	5409.37	1.06221
$297$	−9007.26	−1.75978
$298$	1910.31	0.371347
$299$	2021.19	0.390931
$300$	−3737.68	−0.719316
$301$	−10865.3	−2.08061
$302$	−8855.78	−1.68739
$303$	1629.20	0.308895
$304$	−18131.7	−3.42080
$305$	−4178.17	−0.784397
$306$	11587.2	2.16469
$307$	6112.06	1.13627	0.568133	−	0.822937i	$-0.307666\pi$
$307$	6112.06	1.13627	0.568133	+	0.822937i	$0.307666\pi$
$308$	−31395.3	−5.80816
$309$	−2179.49	−0.401252
$310$	−4203.90	−0.770211
$311$	4847.63	0.883871	0.441935	−	0.897047i	$-0.354292\pi$
$311$	4847.63	0.883871	0.441935	+	0.897047i	$0.354292\pi$
$312$	5303.80	0.962400
$313$	−641.591	−0.115862	−0.0579311	−	0.998321i	$-0.518450\pi$
$313$	−641.591	−0.115862	−0.0579311	+	0.998321i	$0.518450\pi$
$314$	17144.4	3.08126
$315$	3452.77	0.617593
$316$	−978.773	−0.174241
$317$	9739.95	1.72571	0.862855	−	0.505451i	$-0.168674\pi$
$317$	9739.95	1.72571	0.862855	+	0.505451i	$0.168674\pi$
$318$	−7717.79	−1.36098
$319$	3033.14	0.532361
$320$	181.716	0.0317445
$321$	−5150.96	−0.895634
$322$	−7212.47	−1.24825
$323$	−18612.3	−3.20624
$324$	2421.55	0.415217
$325$	2621.06	0.447354
$326$	12161.0	2.06606
$327$	−4421.73	−0.747775
$328$	−9411.90	−1.58441
$329$	2593.15	0.434544
$330$	−7271.18	−1.21292
$331$	−4786.76	−0.794877	−0.397438	−	0.917629i	$-0.630101\pi$
$331$	−4786.76	−0.794877	−0.397438	+	0.917629i	$0.630101\pi$
$332$	19497.4	3.22307
$333$	1985.78	0.326787
$334$	−16592.2	−2.71822
$335$	5435.19	0.886436
$336$	−8488.23	−1.37819
$337$	−6430.01	−1.03936	−0.519681	−	0.854361i	$-0.673949\pi$
$337$	−6430.01	−1.03936	−0.519681	+	0.854361i	$0.673949\pi$
$338$	4533.93	0.729625
$339$	2356.53	0.377549
$340$	15773.6	2.51602
$341$	7813.44	1.24083
$342$	−14841.2	−2.34656
$343$	1171.38	0.184398
$344$	−22038.7	−3.45420
$345$	−1157.45	−0.180623
$346$	−78.1779	−0.0121470
$347$	2599.16	0.402104	0.201052	−	0.979581i	$-0.435564\pi$
$347$	2599.16	0.402104	0.201052	+	0.979581i	$0.435564\pi$
$348$	2275.41	0.350502
$349$	3303.71	0.506715	0.253358	−	0.967373i	$-0.418465\pi$
$349$	3303.71	0.506715	0.253358	+	0.967373i	$0.418465\pi$
$350$	−9353.05	−1.42840
$351$	4738.44	0.720567
$352$	−12995.2	−1.96775
$353$	7859.51	1.18504	0.592521	−	0.805555i	$-0.298133\pi$
$353$	7859.51	1.18504	0.592521	+	0.805555i	$0.298133\pi$
$354$	4709.99	0.707156
$355$	−7794.71	−1.16535
$356$	19981.2	2.97472
$357$	−8713.22	−1.29174
$358$	23935.2	3.53357
$359$	4293.20	0.631161	0.315580	−	0.948899i	$-0.397801\pi$
$359$	4293.20	0.631161	0.315580	+	0.948899i	$0.397801\pi$
$360$	7003.45	1.02532
$361$	16980.2	2.47561
$362$	7499.42	1.08884
$363$	9710.54	1.40405
$364$	16516.1	2.37823
$365$	4198.47	0.602077
$366$	8407.49	1.20073
$367$	5201.25	0.739790	0.369895	−	0.929074i	$-0.379394\pi$
$367$	5201.25	0.739790	0.369895	+	0.929074i	$0.379394\pi$
$368$	−6561.16	−0.929413
$369$	−3455.11	−0.487441
$370$	3901.27	0.548155
$371$	−13382.0	−1.87267
$372$	5861.52	0.816951
$373$	−8422.54	−1.16918	−0.584588	−	0.811330i	$-0.698744\pi$
$373$	−8422.54	−1.16918	−0.584588	+	0.811330i	$0.698744\pi$
$374$	−42310.1	−5.84975
$375$	−4090.52	−0.563289
$376$	5259.83	0.721423
$377$	−1595.64	−0.217983
$378$	−16908.8	−2.30078
$379$	3247.69	0.440165	0.220083	−	0.975481i	$-0.429367\pi$
$379$	3247.69	0.440165	0.220083	+	0.975481i	$0.429367\pi$
$380$	−20203.4	−2.72739
$381$	6523.67	0.877212
$382$	−17986.5	−2.40908
$383$	−1397.63	−0.186464	−0.0932320	−	0.995644i	$-0.529720\pi$
$383$	−1397.63	−0.186464	−0.0932320	+	0.995644i	$0.529720\pi$
$384$	3954.87	0.525576
$385$	−12607.6	−1.66895
$386$	−22750.3	−2.99990
$387$	−8090.38	−1.06268
$388$	13998.3	1.83158
$389$	2535.41	0.330464	0.165232	−	0.986255i	$-0.447163\pi$
$389$	2535.41	0.330464	0.165232	+	0.986255i	$0.447163\pi$
$390$	3825.14	0.496650
$391$	−6735.07	−0.871118
$392$	−15220.3	−1.96108
$393$	5178.19	0.664645
$394$	198.242	0.0253485
$395$	−393.053	−0.0500675
$396$	−23377.2	−2.96653
$397$	−3960.52	−0.500687	−0.250343	−	0.968157i	$-0.580544\pi$
$397$	−3960.52	−0.500687	−0.250343	+	0.968157i	$0.580544\pi$
$398$	3271.53	0.412028
$399$	11160.2	1.40027
$400$	−8508.43	−1.06355
$401$	5275.40	0.656960	0.328480	−	0.944511i	$-0.393464\pi$
$401$	5275.40	0.656960	0.328480	+	0.944511i	$0.393464\pi$
$402$	−10936.9	−1.35692
$403$	−4110.41	−0.508074
$404$	10290.5	1.26726
$405$	972.440	0.119311
$406$	5693.92	0.696021
$407$	−7250.98	−0.883090
$408$	−17673.5	−2.14453
$409$	356.779	0.0431335	0.0215668	−	0.999767i	$-0.493135\pi$
$409$	356.779	0.0431335	0.0215668	+	0.999767i	$0.493135\pi$
$410$	−6787.92	−0.817638
$411$	3777.71	0.453383
$412$	−13766.3	−1.64616
$413$	8166.75	0.973025
$414$	−5370.47	−0.637546
$415$	7829.72	0.926135
$416$	6836.37	0.805722
$417$	761.625	0.0894411
$418$	54192.1	6.34120
$419$	−4263.71	−0.497126	−0.248563	−	0.968616i	$-0.579958\pi$
$419$	−4263.71	−0.497126	−0.248563	+	0.968616i	$0.579958\pi$
$420$	−9458.05	−1.09882
$421$	−13836.6	−1.60180	−0.800898	−	0.598801i	$-0.795644\pi$
$421$	−13836.6	−1.60180	−0.800898	+	0.598801i	$0.795644\pi$
$422$	7410.89	0.854873
$423$	1930.88	0.221945
$424$	−27143.5	−3.10898
$425$	−8733.96	−0.996845
$426$	15684.8	1.78388
$427$	14577.9	1.65217
$428$	−32535.0	−3.67439
$429$	−7109.47	−0.800113
$430$	−15894.4	−1.78255
$431$	9516.25	1.06353	0.531765	−	0.846892i	$-0.321529\pi$
$431$	9516.25	1.06353	0.531765	+	0.846892i	$0.321529\pi$
$432$	−15381.8	−1.71310
$433$	6109.89	0.678112	0.339056	−	0.940766i	$-0.389892\pi$
$433$	6109.89	0.678112	0.339056	+	0.940766i	$0.389892\pi$
$434$	14667.7	1.62229
$435$	913.754	0.100715
$436$	−27929.0	−3.06779
$437$	8626.48	0.944303
$438$	−8448.34	−0.921638
$439$	5737.93	0.623819	0.311909	−	0.950112i	$-0.399031\pi$
$439$	5737.93	0.623819	0.311909	+	0.950112i	$0.399031\pi$
$440$	−25572.8	−2.77076
$441$	−5587.38	−0.603323
$442$	22258.0	2.39526
$443$	4458.32	0.478151	0.239076	−	0.971001i	$-0.423156\pi$
$443$	4458.32	0.478151	0.239076	+	0.971001i	$0.423156\pi$
$444$	−5439.57	−0.581420
$445$	8024.01	0.854774
$446$	−12630.4	−1.34096
$447$	−1069.63	−0.113180
$448$	−634.020	−0.0668631
$449$	−6839.18	−0.718844	−0.359422	−	0.933175i	$-0.617026\pi$
$449$	−6839.18	−0.718844	−0.359422	+	0.933175i	$0.617026\pi$
$450$	−6964.36	−0.729562
$451$	12616.2	1.31723
$452$	14884.6	1.54892
$453$	4958.55	0.514289
$454$	−7732.40	−0.799338
$455$	6632.48	0.683375
$456$	22636.7	2.32470
$457$	3323.35	0.340175	0.170087	−	0.985429i	$-0.445595\pi$
$457$	3323.35	0.340175	0.170087	+	0.985429i	$0.445595\pi$
$458$	5970.42	0.609126
$459$	−15789.6	−1.60565
$460$	−7310.81	−0.741018
$461$	−6838.60	−0.690901	−0.345450	−	0.938437i	$-0.612274\pi$
$461$	−6838.60	−0.690901	−0.345450	+	0.938437i	$0.612274\pi$
$462$	25369.6	2.55477
$463$	−15445.1	−1.55031	−0.775157	−	0.631769i	$-0.782329\pi$
$463$	−15445.1	−1.55031	−0.775157	+	0.631769i	$0.782329\pi$
$464$	5179.74	0.518240
$465$	2353.86	0.234747
$466$	−33412.4	−3.32146
$467$	−845.134	−0.0837433	−0.0418717	−	0.999123i	$-0.513332\pi$
$467$	−845.134	−0.0837433	−0.0418717	+	0.999123i	$0.513332\pi$
$468$	12298.0	1.21469
$469$	−18963.7	−1.86709
$470$	3793.42	0.372293
$471$	−9599.56	−0.939117
$472$	16565.1	1.61540
$473$	29541.7	2.87173
$474$	790.919	0.0766416
$475$	11186.7	1.08059
$476$	−55035.3	−5.29945
$477$	−9964.38	−0.956473
$478$	−31403.4	−3.00493
$479$	−15162.6	−1.44634	−0.723168	−	0.690672i	$-0.757315\pi$
$479$	−15162.6	−1.44634	−0.723168	+	0.690672i	$0.757315\pi$
$480$	−3914.90	−0.372271
$481$	3814.51	0.361594
$482$	8012.48	0.757176
$483$	4038.42	0.380444
$484$	61334.7	5.76021
$485$	5621.39	0.526298
$486$	−20007.4	−1.86740
$487$	−8410.30	−0.782560	−0.391280	−	0.920272i	$-0.627968\pi$
$487$	−8410.30	−0.782560	−0.391280	+	0.920272i	$0.627968\pi$
$488$	29569.2	2.74290
$489$	−6809.20	−0.629699
$490$	−10977.0	−1.01202
$491$	−725.949	−0.0667242	−0.0333621	−	0.999443i	$-0.510621\pi$
$491$	−725.949	−0.0667242	−0.0333621	+	0.999443i	$0.510621\pi$
$492$	9464.44	0.867256
$493$	5317.03	0.485734
$494$	−28508.8	−2.59650
$495$	−9387.76	−0.852421
$496$	13343.1	1.20791
$497$	27196.3	2.45457
$498$	−15755.3	−1.41769
$499$	5829.20	0.522947	0.261474	−	0.965211i	$-0.415792\pi$
$499$	5829.20	0.522947	0.261474	+	0.965211i	$0.415792\pi$
$500$	−25837.0	−2.31093
$501$	9290.34	0.828466
$502$	−8701.43	−0.773633
$503$	3636.31	0.322336	0.161168	−	0.986927i	$-0.448474\pi$
$503$	3636.31	0.322336	0.161168	+	0.986927i	$0.448474\pi$
$504$	−24435.5	−2.15961
$505$	4132.45	0.364142
$506$	19610.0	1.72287
$507$	−2538.65	−0.222377
$508$	41205.5	3.59882
$509$	−7226.54	−0.629294	−0.314647	−	0.949209i	$-0.601886\pi$
$509$	−7226.54	−0.629294	−0.314647	+	0.949209i	$0.601886\pi$
$510$	−12746.2	−1.10669
$511$	−14648.8	−1.26815
$512$	26003.8	2.24456
$513$	20223.7	1.74055
$514$	−21098.2	−1.81051
$515$	−5528.25	−0.473017
$516$	22161.7	1.89072
$517$	−7050.53	−0.599772
$518$	−13611.8	−1.15457
$519$	43.7736	0.00370221
$520$	13453.0	1.13453
$521$	10642.0	0.894886	0.447443	−	0.894313i	$-0.352335\pi$
$521$	10642.0	0.894886	0.447443	+	0.894313i	$0.352335\pi$
$522$	4239.74	0.355495
$523$	−16673.8	−1.39406	−0.697030	−	0.717041i	$-0.745496\pi$
$523$	−16673.8	−1.39406	−0.697030	+	0.717041i	$0.745496\pi$
$524$	32707.1	2.72674
$525$	5236.98	0.435354
$526$	18916.0	1.56801
$527$	13696.8	1.13215
$528$	23078.7	1.90222
$529$	−9045.41	−0.743438
$530$	−19576.1	−1.60440
$531$	6081.03	0.496976
$532$	70490.9	5.74468
$533$	−6636.96	−0.539360
$534$	−16146.3	−1.30846
$535$	−13065.3	−1.05582
$536$	−38465.2	−3.09971
$537$	−13401.9	−1.07697
$538$	−31668.6	−2.53779
$539$	20402.1	1.63039
$540$	−17139.3	−1.36585
$541$	7961.69	0.632716	0.316358	−	0.948640i	$-0.397540\pi$
$541$	7961.69	0.632716	0.316358	+	0.948640i	$0.397540\pi$
$542$	−25664.9	−2.03395
$543$	−4199.09	−0.331860
$544$	−22780.3	−1.79540
$545$	−11215.7	−0.881517
$546$	−13346.2	−1.04609
$547$	−16565.3	−1.29485	−0.647424	−	0.762130i	$-0.724154\pi$
$547$	−16565.3	−1.29485	−0.647424	+	0.762130i	$0.724154\pi$
$548$	23861.1	1.86003
$549$	10854.8	0.843849
$550$	25430.0	1.97153
$551$	−6810.21	−0.526542
$552$	8191.36	0.631607
$553$	1371.39	0.105457
$554$	−28043.7	−2.15066
$555$	−2184.41	−0.167068
$556$	4810.65	0.366937
$557$	−21413.7	−1.62896	−0.814478	−	0.580194i	$-0.802977\pi$
$557$	−21413.7	−1.62896	−0.814478	+	0.580194i	$0.802977\pi$
$558$	10921.7	0.828588
$559$	−15540.9	−1.17587
$560$	−21530.3	−1.62468
$561$	23690.4	1.78290
$562$	−6060.18	−0.454863
$563$	10597.1	0.793278	0.396639	−	0.917975i	$-0.370176\pi$
$563$	10597.1	0.793278	0.396639	+	0.917975i	$0.370176\pi$
$564$	−5289.19	−0.394885
$565$	5977.31	0.445075
$566$	14076.8	1.04539
$567$	−3392.91	−0.251303
$568$	55163.7	4.07503
$569$	12696.3	0.935425	0.467713	−	0.883881i	$-0.345078\pi$
$569$	12696.3	0.935425	0.467713	+	0.883881i	$0.345078\pi$
$570$	16325.8	1.19967
$571$	1796.41	0.131659	0.0658296	−	0.997831i	$-0.479031\pi$
$571$	1796.41	0.131659	0.0658296	+	0.997831i	$0.479031\pi$
$572$	−44905.6	−3.28251
$573$	10071.0	0.734247
$574$	23683.5	1.72218
$575$	4048.04	0.293591
$576$	−472.097	−0.0341505
$577$	−8978.75	−0.647817	−0.323908	−	0.946088i	$-0.604997\pi$
$577$	−8978.75	−0.647817	−0.323908	+	0.946088i	$0.604997\pi$
$578$	−49092.8	−3.53286
$579$	12738.4	0.914318
$580$	5771.55	0.413191
$581$	−27318.4	−1.95071
$582$	−11311.6	−0.805638
$583$	36384.5	2.58472
$584$	−29712.9	−2.10536
$585$	4938.60	0.349036
$586$	−17590.4	−1.24002
$587$	21225.3	1.49244	0.746220	−	0.665700i	$-0.231867\pi$
$587$	21225.3	1.49244	0.746220	+	0.665700i	$0.231867\pi$
$588$	15305.3	1.07343
$589$	−17543.3	−1.22727
$590$	11946.8	0.833632
$591$	−111.000	−0.00772579
$592$	−12382.6	−0.859666
$593$	−19023.4	−1.31737	−0.658683	−	0.752421i	$-0.728886\pi$
$593$	−19023.4	−1.31737	−0.658683	+	0.752421i	$0.728886\pi$
$594$	45973.3	3.17560
$595$	−22101.0	−1.52278
$596$	−6756.08	−0.464329
$597$	−1831.80	−0.125579
$598$	−10316.2	−0.705453
$599$	−17647.8	−1.20379	−0.601894	−	0.798576i	$-0.705587\pi$
$599$	−17647.8	−1.20379	−0.601894	+	0.798576i	$0.705587\pi$
$600$	10622.5	0.722767
$601$	8132.13	0.551941	0.275970	−	0.961166i	$-0.411001\pi$
$601$	8132.13	0.551941	0.275970	+	0.961166i	$0.411001\pi$
$602$	55456.7	3.75456
$603$	−14120.6	−0.953622
$604$	31319.7	2.10990
$605$	24630.7	1.65517
$606$	−8315.49	−0.557415
$607$	15188.7	1.01563	0.507816	−	0.861466i	$-0.330453\pi$
$607$	15188.7	1.01563	0.507816	+	0.861466i	$0.330453\pi$
$608$	29177.8	1.94624
$609$	−3188.15	−0.212135
$610$	21325.5	1.41548
$611$	3709.06	0.245585
$612$	−40979.8	−2.70671
$613$	16347.2	1.07709	0.538546	−	0.842596i	$-0.318974\pi$
$613$	16347.2	1.07709	0.538546	+	0.842596i	$0.318974\pi$
$614$	−31196.1	−2.05044
$615$	3800.71	0.249202
$616$	89225.2	5.83602
$617$	11892.3	0.775956	0.387978	−	0.921669i	$-0.373174\pi$
$617$	11892.3	0.775956	0.387978	+	0.921669i	$0.373174\pi$
$618$	11124.2	0.724078
$619$	−19702.0	−1.27930	−0.639652	−	0.768664i	$-0.720922\pi$
$619$	−19702.0	−1.27930	−0.639652	+	0.768664i	$0.720922\pi$
$620$	14867.7	0.963065
$621$	7318.19	0.472896
$622$	−24742.4	−1.59499
$623$	−27996.3	−1.80040
$624$	−12141.0	−0.778890
$625$	−1318.91	−0.0844106
$626$	3274.70	0.209079
$627$	−30343.4	−1.93269
$628$	−60633.7	−3.85278
$629$	−12710.8	−0.805745
$630$	−17623.1	−1.11448
$631$	14406.6	0.908900	0.454450	−	0.890772i	$-0.349836\pi$
$631$	14406.6	0.908900	0.454450	+	0.890772i	$0.349836\pi$
$632$	2781.67	0.175077
$633$	−4149.52	−0.260551
$634$	−49713.0	−3.11413
$635$	16547.2	1.03410
$636$	27295.1	1.70176
$637$	−10732.9	−0.667585
$638$	−15481.2	−0.960670
$639$	20250.6	1.25368
$640$	10031.5	0.619577
$641$	−4010.11	−0.247098	−0.123549	−	0.992338i	$-0.539428\pi$
$641$	−4010.11	−0.247098	−0.123549	+	0.992338i	$0.539428\pi$
$642$	26290.6	1.61621
$643$	−15735.0	−0.965049	−0.482525	−	0.875882i	$-0.660280\pi$
$643$	−15735.0	−0.965049	−0.482525	+	0.875882i	$0.660280\pi$
$644$	25507.9	1.56080
$645$	8899.64	0.543291
$646$	94997.8	5.78581
$647$	−13305.0	−0.808460	−0.404230	−	0.914657i	$-0.632461\pi$
$647$	−13305.0	−0.808460	−0.404230	+	0.914657i	$0.632461\pi$
$648$	−6882.02	−0.417209
$649$	−22204.6	−1.34300
$650$	−13377.9	−0.807271
$651$	−8212.77	−0.494445
$652$	−43009.0	−2.58338
$653$	4294.46	0.257359	0.128679	−	0.991686i	$-0.458926\pi$
$653$	4294.46	0.257359	0.128679	+	0.991686i	$0.458926\pi$
$654$	22568.7	1.34939
$655$	13134.4	0.783518
$656$	21544.8	1.28229
$657$	−10907.6	−0.647710
$658$	−13235.5	−0.784156
$659$	−16194.7	−0.957292	−0.478646	−	0.878008i	$-0.658872\pi$
$659$	−16194.7	−0.957292	−0.478646	+	0.878008i	$0.658872\pi$
$660$	25715.5	1.51663
$661$	5617.55	0.330556	0.165278	−	0.986247i	$-0.447148\pi$
$661$	5617.55	0.330556	0.165278	+	0.986247i	$0.447148\pi$
$662$	24431.8	1.43439
$663$	−12462.8	−0.730036
$664$	−55411.5	−3.23853
$665$	28307.6	1.65071
$666$	−10135.5	−0.589702
$667$	−2464.35	−0.143059
$668$	58680.6	3.39883
$669$	7072.06	0.408702
$670$	−27741.3	−1.59961
$671$	−39635.9	−2.28037
$672$	13659.4	0.784109
$673$	−6233.41	−0.357029	−0.178514	−	0.983937i	$-0.557129\pi$
$673$	−6233.41	−0.357029	−0.178514	+	0.983937i	$0.557129\pi$
$674$	32818.9	1.87558
$675$	9490.14	0.541149
$676$	−16034.9	−0.912317
$677$	−11362.9	−0.645066	−0.322533	−	0.946558i	$-0.604534\pi$
$677$	−11362.9	−0.645066	−0.322533	+	0.946558i	$0.604534\pi$
$678$	−12027.8	−0.681305
$679$	−19613.4	−1.10853
$680$	−44828.6	−2.52809
$681$	4329.54	0.243625
$682$	−39880.0	−2.23913
$683$	10467.8	0.586439	0.293220	−	0.956045i	$-0.405273\pi$
$683$	10467.8	0.586439	0.293220	+	0.956045i	$0.405273\pi$
$684$	52488.1	2.93411
$685$	9582.11	0.534472
$686$	−5978.76	−0.332755
$687$	−3342.97	−0.185651
$688$	50448.8	2.79555
$689$	−19140.7	−1.05835
$690$	5907.66	0.325943
$691$	27083.7	1.49105	0.745524	−	0.666479i	$-0.232199\pi$
$691$	27083.7	1.49105	0.745524	+	0.666479i	$0.232199\pi$
$692$	276.487	0.0151885
$693$	32754.5	1.79544
$694$	−13266.2	−0.725616
$695$	1931.85	0.105438
$696$	−6466.70	−0.352183
$697$	22115.9	1.20186
$698$	−16862.2	−0.914392
$699$	18708.3	1.01232
$700$	33078.4	1.78606
$701$	9454.90	0.509425	0.254712	−	0.967017i	$-0.418019\pi$
$701$	9454.90	0.509425	0.254712	+	0.967017i	$0.418019\pi$
$702$	−24185.1	−1.30030
$703$	16280.4	0.873438
$704$	1723.84	0.0922865
$705$	−2124.02	−0.113469
$706$	−40115.2	−2.13846
$707$	−14418.4	−0.766987
$708$	−16657.5	−0.884221
$709$	25511.1	1.35133	0.675663	−	0.737210i	$-0.263857\pi$
$709$	25511.1	1.35133	0.675663	+	0.737210i	$0.263857\pi$
$710$	39784.4	2.10293
$711$	1021.15	0.0538623
$712$	−56786.5	−2.98899
$713$	−6348.24	−0.333441
$714$	44472.5	2.33101
$715$	−18033.1	−0.943216
$716$	−84650.3	−4.41834
$717$	17583.5	0.915852
$718$	−21912.6	−1.13896
$719$	6843.48	0.354963	0.177482	−	0.984124i	$-0.443205\pi$
$719$	6843.48	0.354963	0.177482	+	0.984124i	$0.443205\pi$
$720$	−16031.6	−0.829810
$721$	19288.5	0.996311
$722$	−86667.5	−4.46735
$723$	−4486.37	−0.230774
$724$	−26522.7	−1.36148
$725$	−3195.74	−0.163706
$726$	−49562.9	−2.53368
$727$	9038.62	0.461106	0.230553	−	0.973060i	$-0.425947\pi$
$727$	9038.62	0.461106	0.230553	+	0.973060i	$0.425947\pi$
$728$	−46938.6	−2.38964
$729$	7580.57	0.385133
$730$	−21429.1	−1.08648
$731$	51786.0	2.62021
$732$	−29734.2	−1.50138
$733$	−25203.8	−1.27002	−0.635009	−	0.772504i	$-0.719004\pi$
$733$	−25203.8	−1.27002	−0.635009	+	0.772504i	$0.719004\pi$
$734$	−26547.3	−1.33499
$735$	6146.26	0.308447
$736$	10558.3	0.528782
$737$	51560.6	2.57701
$738$	17635.0	0.879609
$739$	−2539.12	−0.126391	−0.0631956	−	0.998001i	$-0.520129\pi$
$739$	−2539.12	−0.126391	−0.0631956	+	0.998001i	$0.520129\pi$
$740$	−13797.4	−0.685408
$741$	15962.7	0.791369
$742$	68302.3	3.37932
$743$	−39774.7	−1.96392	−0.981960	−	0.189089i	$-0.939447\pi$
$743$	−39774.7	−1.96392	−0.981960	+	0.189089i	$0.939447\pi$
$744$	−16658.4	−0.820869
$745$	−2713.09	−0.133423
$746$	42988.9	2.10983
$747$	−20341.5	−0.996329
$748$	149636.	7.31447
$749$	45585.9	2.22386
$750$	20878.1	1.01648
$751$	15269.6	0.741941	0.370970	−	0.928645i	$-0.379025\pi$
$751$	15269.6	0.741941	0.370970	+	0.928645i	$0.379025\pi$
$752$	−12040.3	−0.583863
$753$	4872.12	0.235790
$754$	8144.18	0.393360
$755$	12577.3	0.606271
$756$	59800.3	2.87687
$757$	−1575.57	−0.0756475	−0.0378238	−	0.999284i	$-0.512043\pi$
$757$	−1575.57	−0.0756475	−0.0378238	+	0.999284i	$0.512043\pi$
$758$	−16576.3	−0.794299
$759$	−10980.1	−0.525101
$760$	57417.8	2.74048
$761$	26372.4	1.25624	0.628120	−	0.778117i	$-0.283825\pi$
$761$	26372.4	1.25624	0.628120	+	0.778117i	$0.283825\pi$
$762$	−33297.0	−1.58297
$763$	39132.3	1.85673
$764$	63611.7	3.01229
$765$	−16456.6	−0.777762
$766$	7133.56	0.336483
$767$	11681.1	0.549911
$768$	−20758.9	−0.975355
$769$	14862.1	0.696934	0.348467	−	0.937321i	$-0.386702\pi$
$769$	14862.1	0.696934	0.348467	+	0.937321i	$0.386702\pi$
$770$	64349.8	3.01170
$771$	11813.4	0.551813
$772$	80459.7	3.75105
$773$	21150.6	0.984133	0.492066	−	0.870558i	$-0.336242\pi$
$773$	21150.6	0.984133	0.492066	+	0.870558i	$0.336242\pi$
$774$	41293.5	1.91766
$775$	−8232.32	−0.381566
$776$	−39783.0	−1.84037
$777$	7621.56	0.351894
$778$	−12940.8	−0.596338
$779$	−28326.7	−1.30284
$780$	−13528.1	−0.621006
$781$	−73944.1	−3.38787
$782$	34376.0	1.57197
$783$	−5777.37	−0.263687
$784$	34840.9	1.58714
$785$	−24349.2	−1.10708
$786$	−26429.7	−1.19938
$787$	−37720.0	−1.70848	−0.854239	−	0.519880i	$-0.825976\pi$
$787$	−37720.0	−1.70848	−0.854239	+	0.519880i	$0.825976\pi$
$788$	−701.112	−0.0316955
$789$	−10591.5	−0.477904
$790$	2006.16	0.0903491
$791$	−20855.3	−0.937456
$792$	66437.8	2.98076
$793$	20851.2	0.933731
$794$	20214.6	0.903513
$795$	10961.1	0.488993
$796$	−11570.2	−0.515196
$797$	3293.04	0.146356	0.0731779	−	0.997319i	$-0.476686\pi$
$797$	3293.04	0.146356	0.0731779	+	0.997319i	$0.476686\pi$
$798$	−56961.7	−2.52685
$799$	−12359.4	−0.547241
$800$	13691.9	0.605101
$801$	−20846.3	−0.919560
$802$	−26925.8	−1.18552
$803$	39828.6	1.75034
$804$	38679.9	1.69669
$805$	10243.4	0.448488
$806$	20979.6	0.916844
$807$	17731.9	0.773474
$808$	−29245.6	−1.27334
$809$	11983.9	0.520803	0.260402	−	0.965500i	$-0.416145\pi$
$809$	11983.9	0.520803	0.260402	+	0.965500i	$0.416145\pi$
$810$	−4963.36	−0.215302
$811$	−340.473	−0.0147418	−0.00737090	−	0.999973i	$-0.502346\pi$
$811$	−340.473	−0.0147418	−0.00737090	+	0.999973i	$0.502346\pi$
$812$	−20137.3	−0.870298
$813$	14370.4	0.619914
$814$	37009.2	1.59358
$815$	−17271.5	−0.742323
$816$	40456.5	1.73561
$817$	−66329.1	−2.84034
$818$	−1821.01	−0.0778365
$819$	−17231.1	−0.735170
$820$	24006.4	1.02237
$821$	19202.9	0.816305	0.408153	−	0.912914i	$-0.366173\pi$
$821$	19202.9	0.816305	0.408153	+	0.912914i	$0.366173\pi$
$822$	−19281.5	−0.818151
$823$	12483.5	0.528732	0.264366	−	0.964422i	$-0.414837\pi$
$823$	12483.5	0.528732	0.264366	+	0.964422i	$0.414837\pi$
$824$	39123.8	1.65406
$825$	−14238.8	−0.600889
$826$	−41683.3	−1.75587
$827$	−24111.2	−1.01382	−0.506910	−	0.861999i	$-0.669212\pi$
$827$	−24111.2	−1.01382	−0.506910	+	0.861999i	$0.669212\pi$
$828$	18993.4	0.797182
$829$	7288.85	0.305371	0.152685	−	0.988275i	$-0.451208\pi$
$829$	7288.85	0.305371	0.152685	+	0.988275i	$0.451208\pi$
$830$	−39963.1	−1.67125
$831$	15702.3	0.655484
$832$	−906.858	−0.0377880
$833$	35764.4	1.48759
$834$	−3887.35	−0.161401
$835$	23564.8	0.976640
$836$	−191658.	−7.92898
$837$	−14882.7	−0.614601
$838$	21762.1	0.897087
$839$	−1882.49	−0.0774622	−0.0387311	−	0.999250i	$-0.512332\pi$
$839$	−1882.49	−0.0774622	−0.0387311	+	0.999250i	$0.512332\pi$
$840$	26879.7	1.10409
$841$	−22443.5	−0.920231
$842$	70622.6	2.89052
$843$	3393.23	0.138635
$844$	−26209.6	−1.06893
$845$	−6439.25	−0.262150
$846$	−9855.28	−0.400510
$847$	−85938.1	−3.48627
$848$	62134.4	2.51616
$849$	−7881.93	−0.318618
$850$	44578.4	1.79885
$851$	5891.25	0.237308
$852$	−55471.6	−2.23055
$853$	2074.96	0.0832886	0.0416443	−	0.999132i	$-0.486740\pi$
$853$	2074.96	0.0832886	0.0416443	+	0.999132i	$0.486740\pi$
$854$	−74406.1	−2.98141
$855$	21078.1	0.843105
$856$	92464.3	3.69202
$857$	−27146.8	−1.08205	−0.541025	−	0.841006i	$-0.681964\pi$
$857$	−27146.8	−1.08205	−0.541025	+	0.841006i	$0.681964\pi$
$858$	36286.9	1.44384
$859$	−5686.93	−0.225885	−0.112943	−	0.993602i	$-0.536028\pi$
$859$	−5686.93	−0.225885	−0.112943	+	0.993602i	$0.536028\pi$
$860$	56212.8	2.22889
$861$	−13260.9	−0.524892
$862$	−48571.2	−1.91919
$863$	−11137.8	−0.439321	−0.219660	−	0.975576i	$-0.570495\pi$
$863$	−11137.8	−0.439321	−0.219660	+	0.975576i	$0.570495\pi$
$864$	24752.7	0.974656
$865$	111.031	0.00436436
$866$	−31185.0	−1.22368
$867$	27488.1	1.07675
$868$	−51874.4	−2.02849
$869$	−3728.68	−0.145554
$870$	−4663.83	−0.181745
$871$	−27124.4	−1.05520
$872$	79374.1	3.08251
$873$	−14604.3	−0.566187
$874$	−44029.8	−1.70404
$875$	36201.0	1.39865
$876$	29878.7	1.15241
$877$	19540.2	0.752366	0.376183	−	0.926545i	$-0.377236\pi$
$877$	19540.2	0.752366	0.376183	+	0.926545i	$0.377236\pi$
$878$	−29286.5	−1.12571
$879$	9849.24	0.377937
$880$	58538.8	2.24243
$881$	−36647.5	−1.40146	−0.700729	−	0.713428i	$-0.747142\pi$
$881$	−36647.5	−1.40146	−0.700729	+	0.713428i	$0.747142\pi$
$882$	28518.1	1.08872
$883$	30708.5	1.17035	0.585177	−	0.810906i	$-0.301025\pi$
$883$	30708.5	1.17035	0.585177	+	0.810906i	$0.301025\pi$
$884$	−78718.6	−2.99502
$885$	−6689.30	−0.254077
$886$	−22755.4	−0.862847
$887$	−387.870	−0.0146825	−0.00734126	−	0.999973i	$-0.502337\pi$
$887$	−387.870	−0.0146825	−0.00734126	+	0.999973i	$0.502337\pi$
$888$	15459.2	0.584209
$889$	−57734.4	−2.17812
$890$	−40954.8	−1.54248
$891$	9225.00	0.346856
$892$	44669.3	1.67672
$893$	15830.4	0.593217
$894$	5459.40	0.204239
$895$	−33993.7	−1.26959
$896$	−35000.6	−1.30501
$897$	5776.28	0.215010
$898$	34907.4	1.29719
$899$	5011.64	0.185926
$900$	24630.4	0.912238
$901$	63781.3	2.35834
$902$	−64393.3	−2.37701
$903$	−31051.5	−1.14433
$904$	−42301.9	−1.55635
$905$	−10650.9	−0.391215
$906$	−25308.6	−0.928059
$907$	−39242.6	−1.43664	−0.718318	−	0.695715i	$-0.755088\pi$
$907$	−39242.6	−1.43664	−0.718318	+	0.695715i	$0.755088\pi$
$908$	27346.7	0.999485
$909$	−10736.1	−0.391741
$910$	−33852.4	−1.23318
$911$	−23531.5	−0.855799	−0.427899	−	0.903826i	$-0.640746\pi$
$911$	−23531.5	−0.855799	−0.427899	+	0.903826i	$0.640746\pi$
$912$	−51817.9	−1.88143
$913$	74276.2	2.69243
$914$	−16962.5	−0.613861
$915$	−11940.6	−0.431415
$916$	−21115.2	−0.761645
$917$	−45826.9	−1.65031
$918$	80590.4	2.89747
$919$	17460.0	0.626715	0.313358	−	0.949635i	$-0.398546\pi$
$919$	17460.0	0.626715	0.313358	+	0.949635i	$0.398546\pi$
$920$	20777.3	0.744572
$921$	17467.4	0.624941
$922$	34904.4	1.24676
$923$	38899.6	1.38721
$924$	−89723.3	−3.19446
$925$	7639.70	0.271559
$926$	78832.3	2.79761
$927$	14362.3	0.508869
$928$	−8335.29	−0.294848
$929$	3333.60	0.117731	0.0588654	−	0.998266i	$-0.481252\pi$
$929$	3333.60	0.117731	0.0588654	+	0.998266i	$0.481252\pi$
$930$	−12014.2	−0.423612
$931$	−45808.1	−1.61257
$932$	118168.	4.15312
$933$	13853.8	0.486125
$934$	4313.59	0.151119
$935$	60090.4	2.10178
$936$	−34950.8	−1.22052
$937$	41220.2	1.43714	0.718572	−	0.695453i	$-0.244796\pi$
$937$	41220.2	1.43714	0.718572	+	0.695453i	$0.244796\pi$
$938$	96791.5	3.36925
$939$	−1833.58	−0.0637237
$940$	−13416.0	−0.465512
$941$	−30726.3	−1.06445	−0.532225	−	0.846603i	$-0.678644\pi$
$941$	−30726.3	−1.06445	−0.532225	+	0.846603i	$0.678644\pi$
$942$	48996.4	1.69468
$943$	−10250.3	−0.353973
$944$	−37919.2	−1.30738
$945$	24014.5	0.826656
$946$	−150782.	−5.18217
$947$	−934.028	−0.0320505	−0.0160252	−	0.999872i	$-0.505101\pi$
$947$	−934.028	−0.0320505	−0.0160252	+	0.999872i	$0.505101\pi$
$948$	−2797.19	−0.0958319
$949$	−20952.5	−0.716700
$950$	−57097.3	−1.94998
$951$	27835.4	0.949133
$952$	156410.	5.32487
$953$	−3002.13	−0.102045	−0.0510223	−	0.998698i	$-0.516248\pi$
$953$	−3002.13	−0.102045	−0.0510223	+	0.998698i	$0.516248\pi$
$954$	50858.5	1.72600
$955$	25545.1	0.865570
$956$	111062.	3.75734
$957$	8668.28	0.292796
$958$	77390.2	2.60998
$959$	−33432.6	−1.12575
$960$	519.319	0.0174593
$961$	−16880.9	−0.566643
$962$	−19469.4	−0.652513
$963$	33943.6	1.13584
$964$	−28337.3	−0.946765
$965$	32310.8	1.07785
$966$	−20612.2	−0.686530
$967$	18031.4	0.599639	0.299820	−	0.953996i	$-0.403073\pi$
$967$	18031.4	0.599639	0.299820	+	0.953996i	$0.403073\pi$
$968$	−174313.	−5.78784
$969$	−53191.4	−1.76342
$970$	−28691.8	−0.949729
$971$	−47274.0	−1.56240	−0.781202	−	0.624279i	$-0.785393\pi$
$971$	−47274.0	−1.56240	−0.781202	+	0.624279i	$0.785393\pi$
$972$	70759.1	2.33498
$973$	−6740.37	−0.222082
$974$	42926.4	1.41217
$975$	7490.61	0.246043
$976$	−67686.9	−2.21988
$977$	21815.3	0.714363	0.357182	−	0.934035i	$-0.383738\pi$
$977$	21815.3	0.714363	0.357182	+	0.934035i	$0.383738\pi$
$978$	34754.4	1.13632
$979$	76119.3	2.48497
$980$	38821.7	1.26542
$981$	29138.2	0.948330
$982$	3705.26	0.120407
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	−26897.9	−0.871416
$985$	−281.551	−0.00910757
$986$	−27138.3	−0.876530
$987$	7410.87	0.238997
$988$	100825.	3.24664
$989$	−24001.9	−0.771705
$990$	47915.4	1.53823
$991$	−26200.1	−0.839833	−0.419916	−	0.907563i	$-0.637941\pi$
$991$	−26200.1	−0.839833	−0.419916	+	0.907563i	$0.637941\pi$
$992$	−21472.0	−0.687233
$993$	−13679.9	−0.437179
$994$	−138811.	−4.42938
$995$	−4646.35	−0.148039
$996$	55720.8	1.77267
$997$	−34080.7	−1.08260	−0.541298	−	0.840831i	$-0.682067\pi$
$997$	−34080.7	−1.08260	−0.541298	+	0.840831i	$0.682067\pi$
$998$	−29752.4	−0.943683
$999$	13811.3	0.437408

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.9	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-5.10403 q^{2} +2.85786 q^{3} +18.0511 q^{4} +7.24893 q^{5} -14.5866 q^{6} -25.2920 q^{7} -51.3012 q^{8} -18.8326 q^{9} +O(q^{10})\)	\(q-5.10403 q^{2} +2.85786 q^{3} +18.0511 q^{4} +7.24893 q^{5} -14.5866 q^{6} -25.2920 q^{7} -51.3012 q^{8} -18.8326 q^{9} -36.9987 q^{10} +68.7665 q^{11} +51.5875 q^{12} -36.1759 q^{13} +129.091 q^{14} +20.7164 q^{15} +117.434 q^{16} +120.546 q^{17} +96.1223 q^{18} -154.399 q^{19} +130.851 q^{20} -72.2810 q^{21} -350.986 q^{22} -55.8712 q^{23} -146.612 q^{24} -72.4531 q^{25} +184.643 q^{26} -130.983 q^{27} -456.549 q^{28} +44.1077 q^{29} -105.737 q^{30} +113.623 q^{31} -188.976 q^{32} +196.525 q^{33} -615.272 q^{34} -183.340 q^{35} -339.950 q^{36} -105.443 q^{37} +788.059 q^{38} -103.386 q^{39} -371.878 q^{40} +183.464 q^{41} +368.924 q^{42} +429.594 q^{43} +1241.31 q^{44} -136.516 q^{45} +285.168 q^{46} -102.529 q^{47} +335.609 q^{48} +296.686 q^{49} +369.803 q^{50} +344.505 q^{51} -653.015 q^{52} +529.102 q^{53} +668.542 q^{54} +498.483 q^{55} +1297.51 q^{56} -441.252 q^{57} -225.127 q^{58} -322.898 q^{59} +373.954 q^{60} -576.384 q^{61} -579.934 q^{62} +476.315 q^{63} +25.0680 q^{64} -262.236 q^{65} -1003.07 q^{66} +749.792 q^{67} +2176.00 q^{68} -159.672 q^{69} +935.772 q^{70} -1075.29 q^{71} +966.136 q^{72} +579.185 q^{73} +538.186 q^{74} -207.061 q^{75} -2787.08 q^{76} -1739.24 q^{77} +527.683 q^{78} -54.2223 q^{79} +851.268 q^{80} +134.150 q^{81} -936.404 q^{82} +1080.12 q^{83} -1304.75 q^{84} +873.832 q^{85} -2192.66 q^{86} +126.054 q^{87} -3527.80 q^{88} +1106.92 q^{89} +696.784 q^{90} +914.961 q^{91} -1008.54 q^{92} +324.718 q^{93} +523.309 q^{94} -1119.23 q^{95} -540.066 q^{96} +775.480 q^{97} -1514.29 q^{98} -1295.06 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 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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