LMFDB - Embedded newform 983.4.a.b.1.5

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			1.5
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)

$f(q)$	$=$	$q-5.35973 q^{2} +4.00201 q^{3} +20.7267 q^{4} -16.3566 q^{5} -21.4497 q^{6} +27.2191 q^{7} -68.2115 q^{8} -10.9839 q^{9} +O(q^{10})$	\(q-5.35973 q^{2} +4.00201 q^{3} +20.7267 q^{4} -16.3566 q^{5} -21.4497 q^{6} +27.2191 q^{7} -68.2115 q^{8} -10.9839 q^{9} +87.6670 q^{10} -50.2187 q^{11} +82.9483 q^{12} -9.54575 q^{13} -145.887 q^{14} -65.4593 q^{15} +199.782 q^{16} -73.3080 q^{17} +58.8709 q^{18} -86.8704 q^{19} -339.018 q^{20} +108.931 q^{21} +269.159 q^{22} +18.5765 q^{23} -272.983 q^{24} +142.539 q^{25} +51.1626 q^{26} -152.012 q^{27} +564.162 q^{28} -196.813 q^{29} +350.844 q^{30} +193.511 q^{31} -525.083 q^{32} -200.976 q^{33} +392.911 q^{34} -445.213 q^{35} -227.661 q^{36} -389.748 q^{37} +465.602 q^{38} -38.2021 q^{39} +1115.71 q^{40} +283.311 q^{41} -583.841 q^{42} -120.623 q^{43} -1040.87 q^{44} +179.660 q^{45} -99.5651 q^{46} +378.974 q^{47} +799.528 q^{48} +397.881 q^{49} -763.969 q^{50} -293.379 q^{51} -197.852 q^{52} +539.365 q^{53} +814.743 q^{54} +821.408 q^{55} -1856.66 q^{56} -347.656 q^{57} +1054.86 q^{58} -64.5753 q^{59} -1356.75 q^{60} +375.356 q^{61} -1037.16 q^{62} -298.973 q^{63} +1216.05 q^{64} +156.136 q^{65} +1077.17 q^{66} -708.677 q^{67} -1519.43 q^{68} +74.3434 q^{69} +2386.22 q^{70} +283.136 q^{71} +749.231 q^{72} +1143.87 q^{73} +2088.94 q^{74} +570.441 q^{75} -1800.53 q^{76} -1366.91 q^{77} +204.753 q^{78} +329.996 q^{79} -3267.75 q^{80} -311.787 q^{81} -1518.47 q^{82} +770.739 q^{83} +2257.78 q^{84} +1199.07 q^{85} +646.509 q^{86} -787.646 q^{87} +3425.50 q^{88} -331.770 q^{89} -962.929 q^{90} -259.827 q^{91} +385.030 q^{92} +774.431 q^{93} -2031.20 q^{94} +1420.91 q^{95} -2101.39 q^{96} -1742.21 q^{97} -2132.53 q^{98} +551.599 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.35973	−1.89495	−0.947475	−	0.319830i	$-0.896374\pi$
$2$	−5.35973	−1.89495	−0.947475	+	0.319830i	$0.896374\pi$
$3$	4.00201	0.770187	0.385093	−	0.922878i	$-0.374169\pi$
$3$	4.00201	0.770187	0.385093	+	0.922878i	$0.374169\pi$
$4$	20.7267	2.59083
$5$	−16.3566	−1.46298	−0.731490	−	0.681852i	$-0.761175\pi$
$5$	−16.3566	−1.46298	−0.731490	+	0.681852i	$0.761175\pi$
$6$	−21.4497	−1.45946
$7$	27.2191	1.46969	0.734847	−	0.678233i	$-0.237254\pi$
$7$	27.2191	1.46969	0.734847	+	0.678233i	$0.237254\pi$
$8$	−68.2115	−3.01455
$9$	−10.9839	−0.406813
$10$	87.6670	2.77227
$11$	−50.2187	−1.37650	−0.688251	−	0.725473i	$-0.741621\pi$
$11$	−50.2187	−1.37650	−0.688251	+	0.725473i	$0.741621\pi$
$12$	82.9483	1.99543
$13$	−9.54575	−0.203655	−0.101827	−	0.994802i	$-0.532469\pi$
$13$	−9.54575	−0.203655	−0.101827	+	0.994802i	$0.532469\pi$
$14$	−145.887	−2.78500
$15$	−65.4593	−1.12677
$16$	199.782	3.12159
$17$	−73.3080	−1.04587	−0.522935	−	0.852372i	$-0.675163\pi$
$17$	−73.3080	−1.04587	−0.522935	+	0.852372i	$0.675163\pi$
$18$	58.8709	0.770889
$19$	−86.8704	−1.04892	−0.524459	−	0.851436i	$-0.675732\pi$
$19$	−86.8704	−1.04892	−0.524459	+	0.851436i	$0.675732\pi$
$20$	−339.018	−3.79034
$21$	108.931	1.13194
$22$	269.159	2.60840
$23$	18.5765	0.168412	0.0842060	−	0.996448i	$-0.473165\pi$
$23$	18.5765	0.168412	0.0842060	+	0.996448i	$0.473165\pi$
$24$	−272.983	−2.32177
$25$	142.539	1.14031
$26$	51.1626	0.385916
$27$	−152.012	−1.08351
$28$	564.162	3.80774
$29$	−196.813	−1.26025	−0.630124	−	0.776494i	$-0.716996\pi$
$29$	−196.813	−1.26025	−0.630124	+	0.776494i	$0.716996\pi$
$30$	350.844	2.13517
$31$	193.511	1.12115	0.560573	−	0.828105i	$-0.310581\pi$
$31$	193.511	1.12115	0.560573	+	0.828105i	$0.310581\pi$
$32$	−525.083	−2.90070
$33$	−200.976	−1.06016
$34$	392.911	1.98187
$35$	−445.213	−2.15013
$36$	−227.661	−1.05398
$37$	−389.748	−1.73173	−0.865867	−	0.500275i	$-0.833232\pi$
$37$	−389.748	−1.73173	−0.865867	+	0.500275i	$0.833232\pi$
$38$	465.602	1.98765
$39$	−38.2021	−0.156852
$40$	1115.71	4.41023
$41$	283.311	1.07916	0.539582	−	0.841933i	$-0.318582\pi$
$41$	283.311	1.07916	0.539582	+	0.841933i	$0.318582\pi$
$42$	−583.841	−2.14497
$43$	−120.623	−0.427788	−0.213894	−	0.976857i	$-0.568615\pi$
$43$	−120.623	−0.427788	−0.213894	+	0.976857i	$0.568615\pi$
$44$	−1040.87	−3.56629
$45$	179.660	0.595159
$46$	−99.5651	−0.319132
$47$	378.974	1.17615	0.588074	−	0.808807i	$-0.299886\pi$
$47$	378.974	1.17615	0.588074	+	0.808807i	$0.299886\pi$
$48$	799.528	2.40421
$49$	397.881	1.16000
$50$	−763.969	−2.16083
$51$	−293.379	−0.805516
$52$	−197.852	−0.527636
$53$	539.365	1.39788	0.698939	−	0.715181i	$-0.253656\pi$
$53$	539.365	1.39788	0.698939	+	0.715181i	$0.253656\pi$
$54$	814.743	2.05319
$55$	821.408	2.01379
$56$	−1856.66	−4.43047
$57$	−347.656	−0.807862
$58$	1054.86	2.38811
$59$	−64.5753	−0.142491	−0.0712456	−	0.997459i	$-0.522697\pi$
$59$	−64.5753	−0.142491	−0.0712456	+	0.997459i	$0.522697\pi$
$60$	−1356.75	−2.91927
$61$	375.356	0.787860	0.393930	−	0.919141i	$-0.371115\pi$
$61$	375.356	0.787860	0.393930	+	0.919141i	$0.371115\pi$
$62$	−1037.16	−2.12452
$63$	−298.973	−0.597890
$64$	1216.05	2.37510
$65$	156.136	0.297943
$66$	1077.17	2.00896
$67$	−708.677	−1.29222	−0.646109	−	0.763245i	$-0.723605\pi$
$67$	−708.677	−1.29222	−0.646109	+	0.763245i	$0.723605\pi$
$68$	−1519.43	−2.70968
$69$	74.3434	0.129709
$70$	2386.22	4.07439
$71$	283.136	0.473269	0.236634	−	0.971599i	$-0.423956\pi$
$71$	283.136	0.473269	0.236634	+	0.971599i	$0.423956\pi$
$72$	749.231	1.22636
$73$	1143.87	1.83396	0.916982	−	0.398928i	$-0.130618\pi$
$73$	1143.87	1.83396	0.916982	+	0.398928i	$0.130618\pi$
$74$	2088.94	3.28155
$75$	570.441	0.878251
$76$	−1800.53	−2.71757
$77$	−1366.91	−2.02304
$78$	204.753	0.297227
$79$	329.996	0.469968	0.234984	−	0.971999i	$-0.424496\pi$
$79$	329.996	0.469968	0.234984	+	0.971999i	$0.424496\pi$
$80$	−3267.75	−4.56682
$81$	−311.787	−0.427691
$82$	−1518.47	−2.04496
$83$	770.739	1.01927	0.509636	−	0.860390i	$-0.329780\pi$
$83$	770.739	1.01927	0.509636	+	0.860390i	$0.329780\pi$
$84$	2257.78	2.93267
$85$	1199.07	1.53009
$86$	646.509	0.810637
$87$	−787.646	−0.970626
$88$	3425.50	4.14953
$89$	−331.770	−0.395141	−0.197570	−	0.980289i	$-0.563305\pi$
$89$	−331.770	−0.395141	−0.197570	+	0.980289i	$0.563305\pi$
$90$	−962.929	−1.12780
$91$	−259.827	−0.299310
$92$	385.030	0.436327
$93$	774.431	0.863492
$94$	−2031.20	−2.22874
$95$	1420.91	1.53455
$96$	−2101.39	−2.23408
$97$	−1742.21	−1.82366	−0.911830	−	0.410567i	$-0.865331\pi$
$97$	−1742.21	−1.82366	−0.911830	+	0.410567i	$0.865331\pi$
$98$	−2132.53	−2.19815
$99$	551.599	0.559978
$100$	2954.35	2.95435
$101$	1353.89	1.33383	0.666916	−	0.745133i	$-0.267614\pi$
$101$	1353.89	1.33383	0.666916	+	0.745133i	$0.267614\pi$
$102$	1572.43	1.52641
$103$	−1671.16	−1.59869	−0.799343	−	0.600875i	$-0.794819\pi$
$103$	−1671.16	−1.59869	−0.799343	+	0.600875i	$0.794819\pi$
$104$	651.130	0.613928
$105$	−1781.74	−1.65600
$106$	−2890.85	−2.64891
$107$	−1922.68	−1.73713	−0.868563	−	0.495579i	$-0.834956\pi$
$107$	−1922.68	−1.73713	−0.868563	+	0.495579i	$0.834956\pi$
$108$	−3150.70	−2.80719
$109$	−1105.37	−0.971335	−0.485667	−	0.874144i	$-0.661423\pi$
$109$	−1105.37	−0.971335	−0.485667	+	0.874144i	$0.661423\pi$
$110$	−4402.52	−3.81604
$111$	−1559.77	−1.33376
$112$	5437.88	4.58778
$113$	−484.532	−0.403372	−0.201686	−	0.979450i	$-0.564642\pi$
$113$	−484.532	−0.403372	−0.201686	+	0.979450i	$0.564642\pi$
$114$	1863.34	1.53086
$115$	−303.849	−0.246383
$116$	−4079.27	−3.26509
$117$	104.850	0.0828494
$118$	346.106	0.270014
$119$	−1995.38	−1.53711
$120$	4465.08	3.39670
$121$	1190.92	0.894756
$122$	−2011.81	−1.49295
$123$	1133.81	0.831158
$124$	4010.83	2.90470
$125$	−286.874	−0.205271
$126$	1602.41	1.13297
$127$	−24.1676	−0.0168861	−0.00844303	−	0.999964i	$-0.502688\pi$
$127$	−24.1676	−0.0168861	−0.00844303	+	0.999964i	$0.502688\pi$
$128$	−2317.03	−1.59999
$129$	−482.736	−0.329477
$130$	−836.847	−0.564587
$131$	−85.9930	−0.0573530	−0.0286765	−	0.999589i	$-0.509129\pi$
$131$	−85.9930	−0.0573530	−0.0286765	+	0.999589i	$0.509129\pi$
$132$	−4165.56	−2.74671
$133$	−2364.54	−1.54159
$134$	3798.31	2.44869
$135$	2486.40	1.58515
$136$	5000.45	3.15283
$137$	2654.52	1.65541	0.827703	−	0.561166i	$-0.189647\pi$
$137$	2654.52	1.65541	0.827703	+	0.561166i	$0.189647\pi$
$138$	−398.460	−0.245791
$139$	−1640.97	−1.00133	−0.500667	−	0.865640i	$-0.666912\pi$
$139$	−1640.97	−1.00133	−0.500667	+	0.865640i	$0.666912\pi$
$140$	−9227.78	−5.57064
$141$	1516.65	0.905854
$142$	−1517.53	−0.896820
$143$	479.375	0.280331
$144$	−2194.39	−1.26990
$145$	3219.19	1.84372
$146$	−6130.81	−3.47527
$147$	1592.32	0.893418
$148$	−8078.18	−4.48663
$149$	−1672.19	−0.919402	−0.459701	−	0.888074i	$-0.652043\pi$
$149$	−1672.19	−0.919402	−0.459701	+	0.888074i	$0.652043\pi$
$150$	−3057.41	−1.66424
$151$	3147.77	1.69644	0.848218	−	0.529647i	$-0.177676\pi$
$151$	3147.77	1.69644	0.848218	+	0.529647i	$0.177676\pi$
$152$	5925.56	3.16202
$153$	805.211	0.425473
$154$	7326.26	3.83355
$155$	−3165.18	−1.64021
$156$	−791.803	−0.406378
$157$	1244.28	0.632512	0.316256	−	0.948674i	$-0.397574\pi$
$157$	1244.28	0.632512	0.316256	+	0.948674i	$0.397574\pi$
$158$	−1768.69	−0.890566
$159$	2158.54	1.07663
$160$	8588.58	4.24367
$161$	505.637	0.247514
$162$	1671.09	0.810453
$163$	1929.79	0.927318	0.463659	−	0.886014i	$-0.346536\pi$
$163$	1929.79	0.927318	0.463659	+	0.886014i	$0.346536\pi$
$164$	5872.09	2.79594
$165$	3287.28	1.55100
$166$	−4130.95	−1.93147
$167$	2769.50	1.28330	0.641648	−	0.766999i	$-0.278251\pi$
$167$	2769.50	1.28330	0.641648	+	0.766999i	$0.278251\pi$
$168$	−7430.36	−3.41229
$169$	−2105.88	−0.958525
$170$	−6426.69	−2.89944
$171$	954.179	0.426713
$172$	−2500.12	−1.10833
$173$	746.919	0.328250	0.164125	−	0.986440i	$-0.447520\pi$
$173$	746.919	0.328250	0.164125	+	0.986440i	$0.447520\pi$
$174$	4221.57	1.83929
$175$	3879.78	1.67591
$176$	−10032.8	−4.29687
$177$	−258.431	−0.109745
$178$	1778.19	0.748771
$179$	−589.957	−0.246343	−0.123172	−	0.992385i	$-0.539307\pi$
$179$	−589.957	−0.246343	−0.123172	+	0.992385i	$0.539307\pi$
$180$	3723.76	1.54196
$181$	1852.73	0.760840	0.380420	−	0.924814i	$-0.375779\pi$
$181$	1852.73	0.760840	0.380420	+	0.924814i	$0.375779\pi$
$182$	1392.60	0.567178
$183$	1502.18	0.606799
$184$	−1267.13	−0.507686
$185$	6374.95	2.53349
$186$	−4150.74	−1.63627
$187$	3681.43	1.43964
$188$	7854.86	3.04721
$189$	−4137.63	−1.59243
$190$	−7615.66	−2.90789
$191$	3593.15	1.36121	0.680605	−	0.732651i	$-0.261717\pi$
$191$	3593.15	1.36121	0.680605	+	0.732651i	$0.261717\pi$
$192$	4866.64	1.82927
$193$	−3593.51	−1.34024	−0.670120	−	0.742253i	$-0.733757\pi$
$193$	−3593.51	−1.34024	−0.670120	+	0.742253i	$0.733757\pi$
$194$	9337.79	3.45575
$195$	624.858	0.229472
$196$	8246.74	3.00537
$197$	2085.69	0.754312	0.377156	−	0.926150i	$-0.376902\pi$
$197$	2085.69	0.754312	0.377156	+	0.926150i	$0.376902\pi$
$198$	−2956.42	−1.06113
$199$	1067.33	0.380208	0.190104	−	0.981764i	$-0.439118\pi$
$199$	1067.33	0.380208	0.190104	+	0.981764i	$0.439118\pi$
$200$	−9722.78	−3.43752
$201$	−2836.13	−0.995249
$202$	−7256.47	−2.52754
$203$	−5357.07	−1.85218
$204$	−6080.77	−2.08696
$205$	−4634.01	−1.57880
$206$	8956.98	3.02943
$207$	−204.044	−0.0685121
$208$	−1907.07	−0.635727
$209$	4362.52	1.44384
$210$	9549.66	3.13804
$211$	−2129.96	−0.694942	−0.347471	−	0.937691i	$-0.612960\pi$
$211$	−2129.96	−0.694942	−0.347471	+	0.937691i	$0.612960\pi$
$212$	11179.2	3.62167
$213$	1133.11	0.364505
$214$	10305.0	3.29177
$215$	1972.99	0.625846
$216$	10369.0	3.26629
$217$	5267.19	1.64774
$218$	5924.50	1.84063
$219$	4577.76	1.41249
$220$	17025.1	5.21741
$221$	699.780	0.212997
$222$	8359.96	2.52740
$223$	630.427	0.189312	0.0946559	−	0.995510i	$-0.469825\pi$
$223$	630.427	0.189312	0.0946559	+	0.995510i	$0.469825\pi$
$224$	−14292.3	−4.26315
$225$	−1565.64	−0.463892
$226$	2596.96	0.764369
$227$	−1466.92	−0.428913	−0.214456	−	0.976734i	$-0.568798\pi$
$227$	−1466.92	−0.428913	−0.214456	+	0.976734i	$0.568798\pi$
$228$	−7205.75	−2.09304
$229$	6228.65	1.79738	0.898691	−	0.438582i	$-0.144519\pi$
$229$	6228.65	1.79738	0.898691	+	0.438582i	$0.144519\pi$
$230$	1628.55	0.466884
$231$	−5470.38	−1.55812
$232$	13424.9	3.79908
$233$	−5969.13	−1.67833	−0.839165	−	0.543877i	$-0.816956\pi$
$233$	−5969.13	−1.67833	−0.839165	+	0.543877i	$0.816956\pi$
$234$	−561.967	−0.156995
$235$	−6198.72	−1.72068
$236$	−1338.43	−0.369171
$237$	1320.65	0.361963
$238$	10694.7	2.91275
$239$	6683.88	1.80897	0.904485	−	0.426504i	$-0.140255\pi$
$239$	6683.88	1.80897	0.904485	+	0.426504i	$0.140255\pi$
$240$	−13077.6	−3.51730
$241$	−497.806	−0.133056	−0.0665280	−	0.997785i	$-0.521192\pi$
$241$	−497.806	−0.133056	−0.0665280	+	0.997785i	$0.521192\pi$
$242$	−6383.01	−1.69552
$243$	2856.55	0.754106
$244$	7779.89	2.04121
$245$	−6507.98	−1.69706
$246$	−6076.93	−1.57500
$247$	829.243	0.213617
$248$	−13199.7	−3.37975
$249$	3084.50	0.785029
$250$	1537.57	0.388977
$251$	937.235	0.235688	0.117844	−	0.993032i	$-0.462402\pi$
$251$	937.235	0.235688	0.117844	+	0.993032i	$0.462402\pi$
$252$	−6196.72	−1.54903
$253$	−932.890	−0.231819
$254$	129.532	0.0319982
$255$	4798.69	1.17845
$256$	2690.24	0.656797
$257$	2754.40	0.668540	0.334270	−	0.942477i	$-0.391510\pi$
$257$	2754.40	0.668540	0.334270	+	0.942477i	$0.391510\pi$
$258$	2587.33	0.624342
$259$	−10608.6	−2.54512
$260$	3236.18	0.771921
$261$	2161.78	0.512685
$262$	460.899	0.108681
$263$	4198.19	0.984301	0.492151	−	0.870510i	$-0.336211\pi$
$263$	4198.19	0.984301	0.492151	+	0.870510i	$0.336211\pi$
$264$	13708.9	3.19592
$265$	−8822.19	−2.04507
$266$	12673.3	2.92123
$267$	−1327.74	−0.304332
$268$	−14688.5	−3.34792
$269$	−980.083	−0.222144	−0.111072	−	0.993812i	$-0.535428\pi$
$269$	−980.083	−0.222144	−0.111072	+	0.993812i	$0.535428\pi$
$270$	−13326.4	−3.00378
$271$	2091.50	0.468817	0.234409	−	0.972138i	$-0.424685\pi$
$271$	2091.50	0.468817	0.234409	+	0.972138i	$0.424685\pi$
$272$	−14645.6	−3.26478
$273$	−1039.83	−0.230525
$274$	−14227.5	−3.13691
$275$	−7158.11	−1.56964
$276$	1540.89	0.336054
$277$	1487.45	0.322643	0.161322	−	0.986902i	$-0.448424\pi$
$277$	1487.45	0.322643	0.161322	+	0.986902i	$0.448424\pi$
$278$	8795.16	1.89748
$279$	−2125.51	−0.456096
$280$	30368.6	6.48169
$281$	−1688.47	−0.358454	−0.179227	−	0.983808i	$-0.557360\pi$
$281$	−1688.47	−0.358454	−0.179227	+	0.983808i	$0.557360\pi$
$282$	−8128.86	−1.71655
$283$	3161.74	0.664120	0.332060	−	0.943258i	$-0.392256\pi$
$283$	3161.74	0.664120	0.332060	+	0.943258i	$0.392256\pi$
$284$	5868.47	1.22616
$285$	5686.47	1.18189
$286$	−2569.32	−0.531214
$287$	7711.48	1.58604
$288$	5767.48	1.18004
$289$	461.064	0.0938456
$290$	−17254.0	−3.49375
$291$	−6972.35	−1.40456
$292$	23708.5	4.75150
$293$	−3349.69	−0.667888	−0.333944	−	0.942593i	$-0.608380\pi$
$293$	−3349.69	−0.667888	−0.333944	+	0.942593i	$0.608380\pi$
$294$	−8534.41	−1.69298
$295$	1056.23	0.208462
$296$	26585.3	5.22040
$297$	7633.85	1.49145
$298$	8962.46	1.74222
$299$	−177.327	−0.0342979
$300$	11823.3	2.27540
$301$	−3283.26	−0.628718
$302$	−16871.2	−3.21466
$303$	5418.27	1.02730
$304$	−17355.1	−3.27429
$305$	−6139.55	−1.15262
$306$	−4315.71	−0.806251
$307$	−1441.84	−0.268047	−0.134023	−	0.990978i	$-0.542790\pi$
$307$	−1441.84	−0.268047	−0.134023	+	0.990978i	$0.542790\pi$
$308$	−28331.5	−5.24135
$309$	−6688.01	−1.23129
$310$	16964.5	3.10812
$311$	138.431	0.0252403	0.0126201	−	0.999920i	$-0.495983\pi$
$311$	138.431	0.0252403	0.0126201	+	0.999920i	$0.495983\pi$
$312$	2605.83	0.472839
$313$	4357.26	0.786859	0.393429	−	0.919355i	$-0.371289\pi$
$313$	4357.26	0.786859	0.393429	+	0.919355i	$0.371289\pi$
$314$	−6669.00	−1.19858
$315$	4890.19	0.874701
$316$	6839.73	1.21761
$317$	3086.60	0.546879	0.273439	−	0.961889i	$-0.411839\pi$
$317$	3086.60	0.546879	0.273439	+	0.961889i	$0.411839\pi$
$318$	−11569.2	−2.04015
$319$	9883.68	1.73473
$320$	−19890.5	−3.47472
$321$	−7694.58	−1.33791
$322$	−2710.08	−0.469027
$323$	6368.30	1.09703
$324$	−6462.30	−1.10808
$325$	−1360.64	−0.232230
$326$	−10343.1	−1.75722
$327$	−4423.71	−0.748109
$328$	−19325.1	−3.25320
$329$	10315.3	1.72858
$330$	−17618.9	−2.93906
$331$	11133.2	1.84876	0.924378	−	0.381477i	$-0.124584\pi$
$331$	11133.2	1.84876	0.924378	+	0.381477i	$0.124584\pi$
$332$	15974.9	2.64076
$333$	4280.97	0.704491
$334$	−14843.8	−2.43178
$335$	11591.6	1.89049
$336$	21762.4	3.53345
$337$	4249.42	0.686886	0.343443	−	0.939173i	$-0.388407\pi$
$337$	4249.42	0.686886	0.343443	+	0.939173i	$0.388407\pi$
$338$	11286.9	1.81636
$339$	−1939.10	−0.310671
$340$	24852.7	3.96420
$341$	−9717.86	−1.54326
$342$	−5114.14	−0.808599
$343$	1493.80	0.235154
$344$	8227.90	1.28959
$345$	−1216.01	−0.189761
$346$	−4003.28	−0.622017
$347$	−5849.94	−0.905017	−0.452509	−	0.891760i	$-0.649471\pi$
$347$	−5849.94	−0.905017	−0.452509	+	0.891760i	$0.649471\pi$
$348$	−16325.3	−2.51473
$349$	−3991.18	−0.612158	−0.306079	−	0.952006i	$-0.599017\pi$
$349$	−3991.18	−0.612158	−0.306079	+	0.952006i	$0.599017\pi$
$350$	−20794.6	−3.17576
$351$	1451.07	0.220662
$352$	26369.0	3.99282
$353$	4562.12	0.687868	0.343934	−	0.938994i	$-0.388240\pi$
$353$	4562.12	0.687868	0.343934	+	0.938994i	$0.388240\pi$
$354$	1385.12	0.207961
$355$	−4631.15	−0.692382
$356$	−6876.48	−1.02374
$357$	−7985.52	−1.18386
$358$	3162.01	0.466808
$359$	−1945.47	−0.286011	−0.143005	−	0.989722i	$-0.545677\pi$
$359$	−1945.47	−0.286011	−0.143005	+	0.989722i	$0.545677\pi$
$360$	−12254.9	−1.79414
$361$	687.465	0.100228
$362$	−9930.10	−1.44175
$363$	4766.07	0.689129
$364$	−5385.35	−0.775464
$365$	−18709.8	−2.68305
$366$	−8051.26	−1.14985
$367$	11593.4	1.64896	0.824480	−	0.565891i	$-0.191468\pi$
$367$	11593.4	1.64896	0.824480	+	0.565891i	$0.191468\pi$
$368$	3711.25	0.525713
$369$	−3111.87	−0.439018
$370$	−34168.0	−4.80084
$371$	14681.0	2.05445
$372$	16051.4	2.23716
$373$	−7213.83	−1.00139	−0.500694	−	0.865624i	$-0.666922\pi$
$373$	−7213.83	−1.00139	−0.500694	+	0.865624i	$0.666922\pi$
$374$	−19731.5	−2.72805
$375$	−1148.07	−0.158097
$376$	−25850.4	−3.54556
$377$	1878.72	0.256656
$378$	22176.6	3.01757
$379$	−6497.06	−0.880558	−0.440279	−	0.897861i	$-0.645120\pi$
$379$	−6497.06	−0.880558	−0.440279	+	0.897861i	$0.645120\pi$
$380$	29450.6	3.97575
$381$	−96.7190	−0.0130054
$382$	−19258.3	−2.57942
$383$	14203.2	1.89490	0.947451	−	0.319900i	$-0.103649\pi$
$383$	14203.2	1.89490	0.947451	+	0.319900i	$0.103649\pi$
$384$	−9272.76	−1.23229
$385$	22358.0	2.95966
$386$	19260.2	2.53969
$387$	1324.92	0.174030
$388$	−36110.3	−4.72480
$389$	−12232.7	−1.59440	−0.797200	−	0.603715i	$-0.793687\pi$
$389$	−12232.7	−1.59440	−0.797200	+	0.603715i	$0.793687\pi$
$390$	−3349.07	−0.434837
$391$	−1361.81	−0.176137
$392$	−27140.0	−3.49689
$393$	−344.145	−0.0441725
$394$	−11178.7	−1.42938
$395$	−5397.62	−0.687554
$396$	11432.8	1.45081
$397$	11769.0	1.48784	0.743919	−	0.668270i	$-0.232965\pi$
$397$	11769.0	1.48784	0.743919	+	0.668270i	$0.232965\pi$
$398$	−5720.62	−0.720475
$399$	−9462.89	−1.18731
$400$	28476.6	3.55958
$401$	−8356.67	−1.04068	−0.520340	−	0.853959i	$-0.674195\pi$
$401$	−8356.67	−1.04068	−0.520340	+	0.853959i	$0.674195\pi$
$402$	15200.9	1.88595
$403$	−1847.20	−0.228327
$404$	28061.6	3.45574
$405$	5099.77	0.625703
$406$	28712.4	3.50979
$407$	19572.6	2.38373
$408$	20011.8	2.42827
$409$	1908.84	0.230773	0.115386	−	0.993321i	$-0.463189\pi$
$409$	1908.84	0.230773	0.115386	+	0.993321i	$0.463189\pi$
$410$	24837.0	2.99174
$411$	10623.4	1.27497
$412$	−34637.7	−4.14193
$413$	−1757.68	−0.209419
$414$	1093.62	0.129827
$415$	−12606.7	−1.49117
$416$	5012.31	0.590742
$417$	−6567.18	−0.771214
$418$	−23381.9	−2.73600
$419$	1420.00	0.165564	0.0827822	−	0.996568i	$-0.473619\pi$
$419$	1420.00	0.165564	0.0827822	+	0.996568i	$0.473619\pi$
$420$	−36929.6	−4.29043
$421$	−11592.9	−1.34205	−0.671025	−	0.741434i	$-0.734146\pi$
$421$	−11592.9	−1.34205	−0.671025	+	0.741434i	$0.734146\pi$
$422$	11416.0	1.31688
$423$	−4162.62	−0.478472
$424$	−36790.9	−4.21397
$425$	−10449.2	−1.19262
$426$	−6073.17	−0.690719
$427$	10216.9	1.15791
$428$	−39850.7	−4.50060
$429$	1918.46	0.215907
$430$	−10574.7	−1.18595
$431$	6847.35	0.765255	0.382628	−	0.923903i	$-0.375019\pi$
$431$	6847.35	0.765255	0.382628	+	0.923903i	$0.375019\pi$
$432$	−30369.2	−3.38227
$433$	−7802.88	−0.866010	−0.433005	−	0.901392i	$-0.642547\pi$
$433$	−7802.88	−0.866010	−0.433005	+	0.901392i	$0.642547\pi$
$434$	−28230.7	−3.12239
$435$	12883.2	1.42001
$436$	−22910.7	−2.51657
$437$	−1613.75	−0.176650
$438$	−24535.5	−2.67661
$439$	9937.65	1.08041	0.540203	−	0.841535i	$-0.318347\pi$
$439$	9937.65	1.08041	0.540203	+	0.841535i	$0.318347\pi$
$440$	−56029.5	−6.07068
$441$	−4370.30	−0.471903
$442$	−3750.63	−0.403618
$443$	−9441.65	−1.01261	−0.506305	−	0.862354i	$-0.668989\pi$
$443$	−9441.65	−1.01261	−0.506305	+	0.862354i	$0.668989\pi$
$444$	−32328.9	−3.45555
$445$	5426.63	0.578083
$446$	−3378.92	−0.358736
$447$	−6692.10	−0.708111
$448$	33099.8	3.49067
$449$	−11765.7	−1.23666	−0.618328	−	0.785920i	$-0.712190\pi$
$449$	−11765.7	−1.23666	−0.618328	+	0.785920i	$0.712190\pi$
$450$	8391.39	0.879053
$451$	−14227.5	−1.48547
$452$	−10042.7	−1.04507
$453$	12597.4	1.30657
$454$	7862.31	0.812768
$455$	4249.89	0.437885
$456$	23714.1	2.43534
$457$	−5460.87	−0.558968	−0.279484	−	0.960150i	$-0.590163\pi$
$457$	−5460.87	−0.558968	−0.279484	+	0.960150i	$0.590163\pi$
$458$	−33383.8	−3.40595
$459$	11143.7	1.13321
$460$	−6297.78	−0.638338
$461$	−6801.76	−0.687179	−0.343589	−	0.939120i	$-0.611643\pi$
$461$	−6801.76	−0.687179	−0.343589	+	0.939120i	$0.611643\pi$
$462$	29319.8	2.95255
$463$	−2639.03	−0.264894	−0.132447	−	0.991190i	$-0.542283\pi$
$463$	−2639.03	−0.264894	−0.132447	+	0.991190i	$0.542283\pi$
$464$	−39319.6	−3.93398
$465$	−12667.1	−1.26327
$466$	31992.9	3.18035
$467$	−5008.86	−0.496322	−0.248161	−	0.968719i	$-0.579826\pi$
$467$	−5008.86	−0.496322	−0.248161	+	0.968719i	$0.579826\pi$
$468$	2173.19	0.214649
$469$	−19289.6	−1.89917
$470$	33223.5	3.26060
$471$	4979.62	0.487152
$472$	4404.78	0.429547
$473$	6057.55	0.588851
$474$	−7078.31	−0.685902
$475$	−12382.4	−1.19609
$476$	−41357.6	−3.98240
$477$	−5924.36	−0.568674
$478$	−35823.8	−3.42791
$479$	−4014.18	−0.382908	−0.191454	−	0.981502i	$-0.561320\pi$
$479$	−4014.18	−0.382908	−0.191454	+	0.981502i	$0.561320\pi$
$480$	34371.6	3.26842
$481$	3720.43	0.352676
$482$	2668.10	0.252135
$483$	2023.56	0.190632
$484$	24683.8	2.31817
$485$	28496.7	2.66798
$486$	−15310.3	−1.42899
$487$	−90.0330	−0.00837739	−0.00418869	−	0.999991i	$-0.501333\pi$
$487$	−90.0330	−0.00837739	−0.00418869	+	0.999991i	$0.501333\pi$
$488$	−25603.6	−2.37504
$489$	7723.03	0.714208
$490$	34881.0	3.21584
$491$	8775.58	0.806591	0.403296	−	0.915070i	$-0.367865\pi$
$491$	8775.58	0.806591	0.403296	+	0.915070i	$0.367865\pi$
$492$	23500.2	2.15339
$493$	14427.9	1.31806
$494$	−4444.51	−0.404794
$495$	−9022.30	−0.819237
$496$	38659.9	3.49976
$497$	7706.72	0.695560
$498$	−16532.1	−1.48759
$499$	20774.8	1.86375	0.931874	−	0.362783i	$-0.118173\pi$
$499$	20774.8	1.86375	0.931874	+	0.362783i	$0.118173\pi$
$500$	−5945.95	−0.531822
$501$	11083.6	0.988378
$502$	−5023.33	−0.446618
$503$	9605.57	0.851474	0.425737	−	0.904847i	$-0.360015\pi$
$503$	9605.57	0.851474	0.425737	+	0.904847i	$0.360015\pi$
$504$	20393.4	1.80237
$505$	−22145.0	−1.95137
$506$	5000.03	0.439286
$507$	−8427.74	−0.738243
$508$	−500.915	−0.0437490
$509$	16477.6	1.43489	0.717444	−	0.696616i	$-0.245312\pi$
$509$	16477.6	1.43489	0.717444	+	0.696616i	$0.245312\pi$
$510$	−25719.7	−2.23311
$511$	31135.0	2.69537
$512$	4117.27	0.355389
$513$	13205.3	1.13651
$514$	−14762.8	−1.26685
$515$	27334.6	2.33884
$516$	−10005.5	−0.853620
$517$	−19031.6	−1.61897
$518$	56859.2	4.82287
$519$	2989.18	0.252814
$520$	−10650.3	−0.898165
$521$	−13164.6	−1.10701	−0.553504	−	0.832847i	$-0.686709\pi$
$521$	−13164.6	−1.10701	−0.553504	+	0.832847i	$0.686709\pi$
$522$	−11586.5	−0.971512
$523$	5999.37	0.501595	0.250797	−	0.968040i	$-0.419307\pi$
$523$	5999.37	0.501595	0.250797	+	0.968040i	$0.419307\pi$
$524$	−1782.35	−0.148592
$525$	15526.9	1.29076
$526$	−22501.1	−1.86520
$527$	−14185.9	−1.17257
$528$	−40151.3	−3.30939
$529$	−11821.9	−0.971637
$530$	47284.5	3.87530
$531$	709.291	0.0579672
$532$	−49009.0	−3.99400
$533$	−2704.41	−0.219777
$534$	7116.35	0.576694
$535$	31448.5	2.54138
$536$	48339.9	3.89546
$537$	−2361.01	−0.189730
$538$	5252.98	0.420951
$539$	−19981.1	−1.59674
$540$	51534.8	4.10686
$541$	19097.8	1.51770	0.758852	−	0.651264i	$-0.225761\pi$
$541$	19097.8	1.51770	0.758852	+	0.651264i	$0.225761\pi$
$542$	−11209.9	−0.888385
$543$	7414.62	0.585989
$544$	38492.8	3.03376
$545$	18080.2	1.42104
$546$	5573.20	0.436833
$547$	5573.42	0.435653	0.217827	−	0.975987i	$-0.430103\pi$
$547$	5573.42	0.435653	0.217827	+	0.975987i	$0.430103\pi$
$548$	55019.3	4.28888
$549$	−4122.89	−0.320511
$550$	38365.5	2.97439
$551$	17097.2	1.32190
$552$	−5071.08	−0.391013
$553$	8982.21	0.690710
$554$	−7972.33	−0.611393
$555$	25512.6	1.95126
$556$	−34011.9	−2.59429
$557$	−3368.91	−0.256275	−0.128138	−	0.991756i	$-0.540900\pi$
$557$	−3368.91	−0.256275	−0.128138	+	0.991756i	$0.540900\pi$
$558$	11392.2	0.864280
$559$	1151.44	0.0871212
$560$	−88945.3	−6.71183
$561$	14733.1	1.10879
$562$	9049.72	0.679251
$563$	12958.2	0.970020	0.485010	−	0.874509i	$-0.338816\pi$
$563$	12958.2	0.970020	0.485010	+	0.874509i	$0.338816\pi$
$564$	31435.2	2.34692
$565$	7925.31	0.590124
$566$	−16946.1	−1.25847
$567$	−8486.56	−0.628575
$568$	−19313.1	−1.42669
$569$	−1678.65	−0.123678	−0.0618390	−	0.998086i	$-0.519697\pi$
$569$	−1678.65	−0.123678	−0.0618390	+	0.998086i	$0.519697\pi$
$570$	−30477.9	−2.23961
$571$	7896.03	0.578702	0.289351	−	0.957223i	$-0.406561\pi$
$571$	7896.03	0.578702	0.289351	+	0.957223i	$0.406561\pi$
$572$	9935.86	0.726292
$573$	14379.8	1.04839
$574$	−41331.4	−3.00547
$575$	2647.88	0.192042
$576$	−13357.0	−0.966219
$577$	6659.83	0.480507	0.240253	−	0.970710i	$-0.422769\pi$
$577$	6659.83	0.480507	0.240253	+	0.970710i	$0.422769\pi$
$578$	−2471.18	−0.177833
$579$	−14381.2	−1.03223
$580$	66723.1	4.77677
$581$	20978.8	1.49802
$582$	37369.9	2.66157
$583$	−27086.2	−1.92418
$584$	−78024.8	−5.52858
$585$	−1714.99	−0.121207
$586$	17953.4	1.26561
$587$	5032.81	0.353878	0.176939	−	0.984222i	$-0.443380\pi$
$587$	5032.81	0.353878	0.176939	+	0.984222i	$0.443380\pi$
$588$	33003.5	2.31470
$589$	−16810.3	−1.17599
$590$	−5661.12	−0.395025
$591$	8346.96	0.580961
$592$	−77864.5	−5.40576
$593$	9661.53	0.669058	0.334529	−	0.942385i	$-0.391423\pi$
$593$	9661.53	0.669058	0.334529	+	0.942385i	$0.391423\pi$
$594$	−40915.3	−2.82622
$595$	32637.6	2.24876
$596$	−34658.9	−2.38202
$597$	4271.48	0.292831
$598$	950.424	0.0649928
$599$	−22492.9	−1.53428	−0.767140	−	0.641479i	$-0.778321\pi$
$599$	−22492.9	−1.53428	−0.767140	+	0.641479i	$0.778321\pi$
$600$	−38910.6	−2.64753
$601$	−23419.0	−1.58948	−0.794742	−	0.606947i	$-0.792394\pi$
$601$	−23419.0	−1.58948	−0.794742	+	0.606947i	$0.792394\pi$
$602$	17597.4	1.19139
$603$	7784.06	0.525691
$604$	65242.8	4.39519
$605$	−19479.4	−1.30901
$606$	−29040.5	−1.94668
$607$	4997.53	0.334174	0.167087	−	0.985942i	$-0.446564\pi$
$607$	4997.53	0.334174	0.167087	+	0.985942i	$0.446564\pi$
$608$	45614.2	3.04260
$609$	−21439.0	−1.42652
$610$	32906.3	2.18416
$611$	−3617.59	−0.239528
$612$	16689.3	1.10233
$613$	12058.0	0.794480	0.397240	−	0.917715i	$-0.369968\pi$
$613$	12058.0	0.794480	0.397240	+	0.917715i	$0.369968\pi$
$614$	7727.89	0.507935
$615$	−18545.3	−1.21597
$616$	93239.0	6.09855
$617$	−14057.3	−0.917221	−0.458610	−	0.888637i	$-0.651653\pi$
$617$	−14057.3	−0.917221	−0.458610	+	0.888637i	$0.651653\pi$
$618$	35845.9	2.33323
$619$	−17070.1	−1.10841	−0.554203	−	0.832381i	$-0.686977\pi$
$619$	−17070.1	−1.10841	−0.554203	+	0.832381i	$0.686977\pi$
$620$	−65603.6	−4.24952
$621$	−2823.86	−0.182476
$622$	−741.955	−0.0478290
$623$	−9030.48	−0.580736
$624$	−7632.09	−0.489628
$625$	−13125.1	−0.840003
$626$	−23353.7	−1.49106
$627$	17458.8	1.11202
$628$	25789.8	1.63873
$629$	28571.6	1.81117
$630$	−26210.1	−1.65752
$631$	−24426.6	−1.54106	−0.770528	−	0.637406i	$-0.780007\pi$
$631$	−24426.6	−1.54106	−0.770528	+	0.637406i	$0.780007\pi$
$632$	−22509.5	−1.41674
$633$	−8524.13	−0.535235
$634$	−16543.3	−1.03631
$635$	395.300	0.0247040
$636$	44739.4	2.78936
$637$	−3798.07	−0.236240
$638$	−52973.8	−3.28723
$639$	−3109.95	−0.192532
$640$	37898.7	2.34075
$641$	16090.2	0.991456	0.495728	−	0.868478i	$-0.334901\pi$
$641$	16090.2	0.991456	0.495728	+	0.868478i	$0.334901\pi$
$642$	41240.8	2.53527
$643$	5142.75	0.315413	0.157706	−	0.987486i	$-0.449590\pi$
$643$	5142.75	0.315413	0.157706	+	0.987486i	$0.449590\pi$
$644$	10480.2	0.641268
$645$	7895.92	0.482018
$646$	−34132.3	−2.07882
$647$	−8650.56	−0.525639	−0.262820	−	0.964845i	$-0.584652\pi$
$647$	−8650.56	−0.525639	−0.262820	+	0.964845i	$0.584652\pi$
$648$	21267.4	1.28930
$649$	3242.89	0.196139
$650$	7292.65	0.440064
$651$	21079.3	1.26907
$652$	39998.1	2.40253
$653$	−2738.58	−0.164118	−0.0820590	−	0.996627i	$-0.526150\pi$
$653$	−2738.58	−0.164118	−0.0820590	+	0.996627i	$0.526150\pi$
$654$	23709.9	1.41763
$655$	1406.55	0.0839063
$656$	56600.3	3.36871
$657$	−12564.2	−0.746080
$658$	−55287.3	−3.27557
$659$	−17222.8	−1.01807	−0.509034	−	0.860747i	$-0.669997\pi$
$659$	−17222.8	−1.01807	−0.509034	+	0.860747i	$0.669997\pi$
$660$	68134.4	4.01838
$661$	−6555.61	−0.385754	−0.192877	−	0.981223i	$-0.561782\pi$
$661$	−6555.61	−0.385754	−0.192877	+	0.981223i	$0.561782\pi$
$662$	−59671.2	−3.50330
$663$	2800.52	0.164047
$664$	−52573.2	−3.07265
$665$	38675.8	2.25531
$666$	−22944.8	−1.33497
$667$	−3656.10	−0.212241
$668$	57402.6	3.32481
$669$	2522.97	0.145805
$670$	−62127.5	−3.58238
$671$	−18849.9	−1.08449
$672$	−57197.9	−3.28342
$673$	24595.3	1.40873	0.704367	−	0.709836i	$-0.251231\pi$
$673$	24595.3	1.40873	0.704367	+	0.709836i	$0.251231\pi$
$674$	−22775.7	−1.30162
$675$	−21667.6	−1.23554
$676$	−43647.9	−2.48338
$677$	5942.73	0.337367	0.168684	−	0.985670i	$-0.446048\pi$
$677$	5942.73	0.337367	0.168684	+	0.985670i	$0.446048\pi$
$678$	10393.1	0.588707
$679$	−47421.6	−2.68022
$680$	−81790.4	−4.61253
$681$	−5870.64	−0.330343
$682$	52085.1	2.92440
$683$	−1664.96	−0.0932766	−0.0466383	−	0.998912i	$-0.514851\pi$
$683$	−1664.96	−0.0932766	−0.0466383	+	0.998912i	$0.514851\pi$
$684$	19777.0	1.10554
$685$	−43418.9	−2.42183
$686$	−8006.38	−0.445605
$687$	24927.1	1.38432
$688$	−24098.3	−1.33538
$689$	−5148.64	−0.284685
$690$	6517.46	0.359588
$691$	1130.28	0.0622253	0.0311127	−	0.999516i	$-0.490095\pi$
$691$	1130.28	0.0622253	0.0311127	+	0.999516i	$0.490095\pi$
$692$	15481.2	0.850441
$693$	15014.1	0.822997
$694$	31354.1	1.71496
$695$	26840.7	1.46493
$696$	53726.5	2.92600
$697$	−20769.0	−1.12867
$698$	21391.6	1.16001
$699$	−23888.5	−1.29263
$700$	80414.9	4.34200
$701$	−33742.4	−1.81802	−0.909011	−	0.416772i	$-0.863161\pi$
$701$	−33742.4	−1.81802	−0.909011	+	0.416772i	$0.863161\pi$
$702$	−7777.33	−0.418143
$703$	33857.5	1.81645
$704$	−61068.5	−3.26932
$705$	−24807.3	−1.32525
$706$	−24451.7	−1.30347
$707$	36851.7	1.96032
$708$	−5356.41	−0.284331
$709$	20288.4	1.07468	0.537340	−	0.843366i	$-0.319429\pi$
$709$	20288.4	1.07468	0.537340	+	0.843366i	$0.319429\pi$
$710$	24821.7	1.31203
$711$	−3624.66	−0.191189
$712$	22630.5	1.19117
$713$	3594.76	0.188814
$714$	42800.2	2.24336
$715$	−7840.95	−0.410119
$716$	−12227.8	−0.638235
$717$	26748.9	1.39325
$718$	10427.2	0.541976
$719$	−11587.3	−0.601021	−0.300510	−	0.953779i	$-0.597157\pi$
$719$	−11587.3	−0.601021	−0.300510	+	0.953779i	$0.597157\pi$
$720$	35892.8	1.85784
$721$	−45487.6	−2.34958
$722$	−3684.62	−0.189927
$723$	−1992.22	−0.102478
$724$	38400.8	1.97121
$725$	−28053.4	−1.43707
$726$	−25544.8	−1.30587
$727$	−2331.37	−0.118935	−0.0594676	−	0.998230i	$-0.518940\pi$
$727$	−2331.37	−0.118935	−0.0594676	+	0.998230i	$0.518940\pi$
$728$	17723.2	0.902287
$729$	19850.2	1.00849
$730$	100279.	5.08425
$731$	8842.66	0.447411
$732$	31135.2	1.57212
$733$	−17629.9	−0.888369	−0.444184	−	0.895935i	$-0.646506\pi$
$733$	−17629.9	−0.888369	−0.444184	+	0.895935i	$0.646506\pi$
$734$	−62137.2	−3.12470
$735$	−26045.0	−1.30705
$736$	−9754.23	−0.488513
$737$	35588.8	1.77874
$738$	16678.8	0.831916
$739$	1255.82	0.0625117	0.0312558	−	0.999511i	$-0.490049\pi$
$739$	1255.82	0.0625117	0.0312558	+	0.999511i	$0.490049\pi$
$740$	132132.	6.56386
$741$	3318.64	0.164525
$742$	−78686.4	−3.89309
$743$	21569.4	1.06501	0.532507	−	0.846426i	$-0.321250\pi$
$743$	21569.4	1.06501	0.532507	+	0.846426i	$0.321250\pi$
$744$	−52825.1	−2.60304
$745$	27351.3	1.34507
$746$	38664.2	1.89758
$747$	−8465.75	−0.414653
$748$	76303.9	3.72988
$749$	−52333.6	−2.55304
$750$	6153.36	0.299585
$751$	2125.00	0.103252	0.0516260	−	0.998666i	$-0.483560\pi$
$751$	2125.00	0.103252	0.0516260	+	0.998666i	$0.483560\pi$
$752$	75712.0	3.67145
$753$	3750.82	0.181524
$754$	−10069.4	−0.486350
$755$	−51486.8	−2.48185
$756$	−85759.4	−4.12571
$757$	11161.2	0.535881	0.267941	−	0.963435i	$-0.413657\pi$
$757$	11161.2	0.535881	0.267941	+	0.963435i	$0.413657\pi$
$758$	34822.5	1.66861
$759$	−3733.43	−0.178544
$760$	−96922.1	−4.62597
$761$	−41049.6	−1.95539	−0.977693	−	0.210041i	$-0.932640\pi$
$761$	−41049.6	−1.95539	−0.977693	+	0.210041i	$0.932640\pi$
$762$	518.388	0.0246446
$763$	−30087.3	−1.42757
$764$	74474.0	3.52667
$765$	−13170.5	−0.622459
$766$	−76125.1	−3.59075
$767$	616.419	0.0290190
$768$	10766.4	0.505856
$769$	10874.8	0.509954	0.254977	−	0.966947i	$-0.417932\pi$
$769$	10874.8	0.509954	0.254977	+	0.966947i	$0.417932\pi$
$770$	−119833.	−5.60841
$771$	11023.1	0.514900
$772$	−74481.4	−3.47234
$773$	16592.3	0.772034	0.386017	−	0.922492i	$-0.373851\pi$
$773$	16592.3	0.772034	0.386017	+	0.922492i	$0.373851\pi$
$774$	−7101.21	−0.329777
$775$	27582.8	1.27845
$776$	118839.	5.49752
$777$	−42455.7	−1.96022
$778$	65563.9	3.02131
$779$	−24611.3	−1.13195
$780$	12951.2	0.594523
$781$	−14218.7	−0.651455
$782$	7298.92	0.333771
$783$	29917.9	1.36549
$784$	79489.3	3.62105
$785$	−20352.2	−0.925352
$786$	1844.52	0.0837047
$787$	34594.9	1.56693	0.783465	−	0.621436i	$-0.213450\pi$
$787$	34594.9	1.56693	0.783465	+	0.621436i	$0.213450\pi$
$788$	43229.5	1.95430
$789$	16801.2	0.758096
$790$	28929.8	1.30288
$791$	−13188.5	−0.592833
$792$	−37625.4	−1.68808
$793$	−3583.05	−0.160451
$794$	−63078.9	−2.81938
$795$	−35306.5	−1.57508
$796$	22122.3	0.985055
$797$	−18341.1	−0.815152	−0.407576	−	0.913171i	$-0.633626\pi$
$797$	−18341.1	−0.815152	−0.407576	+	0.913171i	$0.633626\pi$
$798$	50718.5	2.24989
$799$	−27781.8	−1.23010
$800$	−74844.7	−3.30770
$801$	3644.14	0.160748
$802$	44789.5	1.97203
$803$	−57443.5	−2.52445
$804$	−58783.5	−2.57853
$805$	−8270.51	−0.362108
$806$	9900.51	0.432668
$807$	−3922.30	−0.171092
$808$	−92350.8	−4.02090
$809$	10091.6	0.438569	0.219285	−	0.975661i	$-0.429628\pi$
$809$	10091.6	0.438569	0.219285	+	0.975661i	$0.429628\pi$
$810$	−27333.4	−1.18568
$811$	24208.7	1.04819	0.524096	−	0.851659i	$-0.324403\pi$
$811$	24208.7	1.04819	0.524096	+	0.851659i	$0.324403\pi$
$812$	−111034.	−4.79869
$813$	8370.19	0.361077
$814$	−104904.	−4.51706
$815$	−31564.8	−1.35665
$816$	−58611.8	−2.51449
$817$	10478.6	0.448715
$818$	−10230.9	−0.437303
$819$	2853.92	0.121763
$820$	−96047.6	−4.09040
$821$	35113.8	1.49267	0.746334	−	0.665572i	$-0.231812\pi$
$821$	35113.8	1.49267	0.746334	+	0.665572i	$0.231812\pi$
$822$	−56938.5	−2.41601
$823$	−40044.3	−1.69606	−0.848029	−	0.529951i	$-0.822210\pi$
$823$	−40044.3	−1.69606	−0.848029	+	0.529951i	$0.822210\pi$
$824$	113993.	4.81932
$825$	−28646.8	−1.20891
$826$	9420.70	0.396838
$827$	−6351.64	−0.267071	−0.133536	−	0.991044i	$-0.542633\pi$
$827$	−6351.64	−0.267071	−0.133536	+	0.991044i	$0.542633\pi$
$828$	−4229.14	−0.177504
$829$	−14751.7	−0.618032	−0.309016	−	0.951057i	$-0.600000\pi$
$829$	−14751.7	−0.618032	−0.309016	+	0.951057i	$0.600000\pi$
$830$	67568.3	2.82570
$831$	5952.79	0.248496
$832$	−11608.1	−0.483700
$833$	−29167.8	−1.21321
$834$	35198.3	1.46141
$835$	−45299.7	−1.87744
$836$	90420.5	3.74074
$837$	−29415.9	−1.21477
$838$	−7610.81	−0.313736
$839$	12439.3	0.511861	0.255931	−	0.966695i	$-0.417618\pi$
$839$	12439.3	0.511861	0.255931	+	0.966695i	$0.417618\pi$
$840$	121535.	4.99211
$841$	14346.2	0.588226
$842$	62134.8	2.54312
$843$	−6757.25	−0.276076
$844$	−44147.1	−1.80048
$845$	34445.0	1.40230
$846$	22310.5	0.906680
$847$	32415.8	1.31502
$848$	107755.	4.36360
$849$	12653.3	0.511496
$850$	56005.0	2.25995
$851$	−7240.16	−0.291645
$852$	23485.7	0.944373
$853$	22824.3	0.916166	0.458083	−	0.888909i	$-0.348536\pi$
$853$	22824.3	0.916166	0.458083	+	0.888909i	$0.348536\pi$
$854$	−54759.6	−2.19419
$855$	−15607.1	−0.624272
$856$	131149.	5.23665
$857$	1511.19	0.0602350	0.0301175	−	0.999546i	$-0.490412\pi$
$857$	1511.19	0.0602350	0.0301175	+	0.999546i	$0.490412\pi$
$858$	−10282.4	−0.409134
$859$	−1058.50	−0.0420438	−0.0210219	−	0.999779i	$-0.506692\pi$
$859$	−1058.50	−0.0420438	−0.0210219	+	0.999779i	$0.506692\pi$
$860$	40893.5	1.62146
$861$	30861.4	1.22155
$862$	−36699.9	−1.45012
$863$	−19450.4	−0.767208	−0.383604	−	0.923498i	$-0.625317\pi$
$863$	−19450.4	−0.767208	−0.383604	+	0.923498i	$0.625317\pi$
$864$	79819.0	3.14294
$865$	−12217.1	−0.480223
$866$	41821.3	1.64105
$867$	1845.18	0.0722787
$868$	109171.	4.26903
$869$	−16572.0	−0.646912
$870$	−69050.5	−2.69084
$871$	6764.85	0.263167
$872$	75399.1	2.92814
$873$	19136.4	0.741888
$874$	8649.26	0.334743
$875$	−7808.47	−0.301685
$876$	94881.7	3.65954
$877$	47013.6	1.81019	0.905095	−	0.425208i	$-0.139799\pi$
$877$	47013.6	1.81019	0.905095	+	0.425208i	$0.139799\pi$
$878$	−53263.1	−2.04732
$879$	−13405.5	−0.514398
$880$	164102.	6.28624
$881$	−5138.49	−0.196504	−0.0982521	−	0.995162i	$-0.531325\pi$
$881$	−5138.49	−0.196504	−0.0982521	+	0.995162i	$0.531325\pi$
$882$	23423.6	0.894233
$883$	13668.3	0.520922	0.260461	−	0.965484i	$-0.416125\pi$
$883$	13668.3	0.520922	0.260461	+	0.965484i	$0.416125\pi$
$884$	14504.1	0.551839
$885$	4227.05	0.160555
$886$	50604.7	1.91885
$887$	−37986.7	−1.43796	−0.718979	−	0.695031i	$-0.755390\pi$
$887$	−37986.7	−1.43796	−0.718979	+	0.695031i	$0.755390\pi$
$888$	106394.	4.02068
$889$	−657.822	−0.0248174
$890$	−29085.2	−1.09544
$891$	15657.5	0.588717
$892$	13066.7	0.490476
$893$	−32921.6	−1.23368
$894$	35867.8	1.34183
$895$	9649.70	0.360395
$896$	−63067.5	−2.35149
$897$	−709.663	−0.0264158
$898$	63061.1	2.34340
$899$	−38085.4	−1.41292
$900$	−32450.4	−1.20187
$901$	−39539.8	−1.46200
$902$	76255.6	2.81489
$903$	−13139.6	−0.484230
$904$	33050.7	1.21598
$905$	−30304.3	−1.11309
$906$	−67518.6	−2.47589
$907$	31783.5	1.16356	0.581782	−	0.813345i	$-0.302356\pi$
$907$	31783.5	1.16356	0.581782	+	0.813345i	$0.302356\pi$
$908$	−30404.5	−1.11124
$909$	−14871.0	−0.542619
$910$	−22778.2	−0.829770
$911$	−9407.69	−0.342141	−0.171071	−	0.985259i	$-0.554723\pi$
$911$	−9407.69	−0.342141	−0.171071	+	0.985259i	$0.554723\pi$
$912$	−69455.3	−2.52181
$913$	−38705.5	−1.40303
$914$	29268.8	1.05922
$915$	−24570.5	−0.887734
$916$	129099.	4.65672
$917$	−2340.65	−0.0842914
$918$	−59727.2	−2.14738
$919$	−4214.84	−0.151289	−0.0756445	−	0.997135i	$-0.524101\pi$
$919$	−4214.84	−0.151289	−0.0756445	+	0.997135i	$0.524101\pi$
$920$	20726.0	0.742735
$921$	−5770.27	−0.206446
$922$	36455.6	1.30217
$923$	−2702.75	−0.0963835
$924$	−113383.	−4.03682
$925$	−55554.2	−1.97471
$926$	14144.5	0.501961
$927$	18356.0	0.650365
$928$	103343.	3.65561
$929$	26217.8	0.925919	0.462960	−	0.886379i	$-0.346787\pi$
$929$	26217.8	0.925919	0.462960	+	0.886379i	$0.346787\pi$
$930$	67892.0	2.39384
$931$	−34564.0	−1.21675
$932$	−123720.	−4.34827
$933$	554.003	0.0194397
$934$	26846.1	0.940505
$935$	−60215.8	−2.10617
$936$	−7151.97	−0.249754
$937$	20072.0	0.699810	0.349905	−	0.936785i	$-0.386214\pi$
$937$	20072.0	0.699810	0.349905	+	0.936785i	$0.386214\pi$
$938$	103387.	3.59883
$939$	17437.8	0.606028
$940$	−128479.	−4.45800
$941$	−12095.1	−0.419011	−0.209506	−	0.977807i	$-0.567185\pi$
$941$	−12095.1	−0.419011	−0.209506	+	0.977807i	$0.567185\pi$
$942$	−26689.4	−0.923129
$943$	5262.93	0.181744
$944$	−12901.0	−0.444799
$945$	67677.7	2.32969
$946$	−32466.8	−1.11584
$947$	−27766.2	−0.952778	−0.476389	−	0.879234i	$-0.658055\pi$
$947$	−27766.2	−0.952778	−0.476389	+	0.879234i	$0.658055\pi$
$948$	27372.6	0.937787
$949$	−10919.1	−0.373496
$950$	66366.3	2.26653
$951$	12352.6	0.421199
$952$	136108.	4.63370
$953$	−1806.67	−0.0614099	−0.0307050	−	0.999528i	$-0.509775\pi$
$953$	−1806.67	−0.0614099	−0.0307050	+	0.999528i	$0.509775\pi$
$954$	31752.9	1.07761
$955$	−58771.7	−1.99142
$956$	138535.	4.68674
$957$	39554.6	1.33607
$958$	21514.9	0.725591
$959$	72253.6	2.43294
$960$	−79601.7	−2.67618
$961$	7655.37	0.256969
$962$	−19940.5	−0.668303
$963$	21118.6	0.706684
$964$	−10317.9	−0.344726
$965$	58777.6	1.96074
$966$	−10845.7	−0.361238
$967$	48736.6	1.62075	0.810374	−	0.585913i	$-0.199264\pi$
$967$	48736.6	1.62075	0.810374	+	0.585913i	$0.199264\pi$
$968$	−81234.5	−2.69729
$969$	25486.0	0.844920
$970$	−152735.	−5.05569
$971$	12292.6	0.406269	0.203135	−	0.979151i	$-0.434887\pi$
$971$	12292.6	0.406269	0.203135	+	0.979151i	$0.434887\pi$
$972$	59206.8	1.95376
$973$	−44665.8	−1.47166
$974$	482.553	0.0158747
$975$	−5445.29	−0.178860
$976$	74989.3	2.45937
$977$	−56000.6	−1.83379	−0.916897	−	0.399123i	$-0.869315\pi$
$977$	−56000.6	−1.83379	−0.916897	+	0.399123i	$0.869315\pi$
$978$	−41393.3	−1.35339
$979$	16661.0	0.543911
$980$	−134889.	−4.39680
$981$	12141.3	0.395151
$982$	−47034.7	−1.52845
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	−77339.1	−2.50557
$985$	−34114.9	−1.10354
$986$	−77329.9	−2.49765
$987$	41282.0	1.33133
$988$	17187.4	0.553447
$989$	−2240.76	−0.0720447
$990$	48357.1	1.55241
$991$	−14128.2	−0.452873	−0.226436	−	0.974026i	$-0.572708\pi$
$991$	−14128.2	−0.452873	−0.226436	+	0.974026i	$0.572708\pi$
$992$	−101609.	−3.25211
$993$	44555.3	1.42389
$994$	−41305.9	−1.31805
$995$	−17458.0	−0.556236
$996$	63931.5	2.03388
$997$	34603.1	1.09919	0.549595	−	0.835432i	$-0.314782\pi$
$997$	34603.1	1.09919	0.549595	+	0.835432i	$0.314782\pi$
$998$	−111348.	−3.53171
$999$	59246.3	1.87635

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.5	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-5.35973 q^{2} +4.00201 q^{3} +20.7267 q^{4} -16.3566 q^{5} -21.4497 q^{6} +27.2191 q^{7} -68.2115 q^{8} -10.9839 q^{9} +O(q^{10})\)	\(q-5.35973 q^{2} +4.00201 q^{3} +20.7267 q^{4} -16.3566 q^{5} -21.4497 q^{6} +27.2191 q^{7} -68.2115 q^{8} -10.9839 q^{9} +87.6670 q^{10} -50.2187 q^{11} +82.9483 q^{12} -9.54575 q^{13} -145.887 q^{14} -65.4593 q^{15} +199.782 q^{16} -73.3080 q^{17} +58.8709 q^{18} -86.8704 q^{19} -339.018 q^{20} +108.931 q^{21} +269.159 q^{22} +18.5765 q^{23} -272.983 q^{24} +142.539 q^{25} +51.1626 q^{26} -152.012 q^{27} +564.162 q^{28} -196.813 q^{29} +350.844 q^{30} +193.511 q^{31} -525.083 q^{32} -200.976 q^{33} +392.911 q^{34} -445.213 q^{35} -227.661 q^{36} -389.748 q^{37} +465.602 q^{38} -38.2021 q^{39} +1115.71 q^{40} +283.311 q^{41} -583.841 q^{42} -120.623 q^{43} -1040.87 q^{44} +179.660 q^{45} -99.5651 q^{46} +378.974 q^{47} +799.528 q^{48} +397.881 q^{49} -763.969 q^{50} -293.379 q^{51} -197.852 q^{52} +539.365 q^{53} +814.743 q^{54} +821.408 q^{55} -1856.66 q^{56} -347.656 q^{57} +1054.86 q^{58} -64.5753 q^{59} -1356.75 q^{60} +375.356 q^{61} -1037.16 q^{62} -298.973 q^{63} +1216.05 q^{64} +156.136 q^{65} +1077.17 q^{66} -708.677 q^{67} -1519.43 q^{68} +74.3434 q^{69} +2386.22 q^{70} +283.136 q^{71} +749.231 q^{72} +1143.87 q^{73} +2088.94 q^{74} +570.441 q^{75} -1800.53 q^{76} -1366.91 q^{77} +204.753 q^{78} +329.996 q^{79} -3267.75 q^{80} -311.787 q^{81} -1518.47 q^{82} +770.739 q^{83} +2257.78 q^{84} +1199.07 q^{85} +646.509 q^{86} -787.646 q^{87} +3425.50 q^{88} -331.770 q^{89} -962.929 q^{90} -259.827 q^{91} +385.030 q^{92} +774.431 q^{93} -2031.20 q^{94} +1420.91 q^{95} -2101.39 q^{96} -1742.21 q^{97} -2132.53 q^{98} +551.599 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 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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