LMFDB - Embedded newform 983.4.a.a.1.16

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:	$1$
Dimension:	$109$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	983.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-4.46204 q^{2} -5.70729 q^{3} +11.9098 q^{4} -10.3218 q^{5} +25.4662 q^{6} +32.8198 q^{7} -17.4456 q^{8} +5.57321 q^{9} +O(q^{10})$	\(q-4.46204 q^{2} -5.70729 q^{3} +11.9098 q^{4} -10.3218 q^{5} +25.4662 q^{6} +32.8198 q^{7} -17.4456 q^{8} +5.57321 q^{9} +46.0562 q^{10} +55.2787 q^{11} -67.9727 q^{12} -2.90988 q^{13} -146.443 q^{14} +58.9094 q^{15} -17.4352 q^{16} +9.44318 q^{17} -24.8679 q^{18} -110.722 q^{19} -122.930 q^{20} -187.312 q^{21} -246.656 q^{22} +51.7607 q^{23} +99.5674 q^{24} -18.4608 q^{25} +12.9840 q^{26} +122.289 q^{27} +390.877 q^{28} -161.889 q^{29} -262.856 q^{30} -54.7937 q^{31} +217.362 q^{32} -315.492 q^{33} -42.1358 q^{34} -338.759 q^{35} +66.3757 q^{36} -314.623 q^{37} +494.048 q^{38} +16.6075 q^{39} +180.070 q^{40} +379.325 q^{41} +835.795 q^{42} +104.190 q^{43} +658.358 q^{44} -57.5254 q^{45} -230.958 q^{46} -467.077 q^{47} +99.5077 q^{48} +734.140 q^{49} +82.3730 q^{50} -53.8950 q^{51} -34.6561 q^{52} +285.530 q^{53} -545.658 q^{54} -570.575 q^{55} -572.563 q^{56} +631.925 q^{57} +722.353 q^{58} +123.325 q^{59} +701.599 q^{60} -19.8015 q^{61} +244.492 q^{62} +182.912 q^{63} -830.395 q^{64} +30.0351 q^{65} +1407.74 q^{66} +875.121 q^{67} +112.466 q^{68} -295.414 q^{69} +1511.56 q^{70} -613.162 q^{71} -97.2282 q^{72} -710.907 q^{73} +1403.86 q^{74} +105.361 q^{75} -1318.68 q^{76} +1814.24 q^{77} -74.1035 q^{78} -536.451 q^{79} +179.962 q^{80} -848.416 q^{81} -1692.56 q^{82} -455.726 q^{83} -2230.85 q^{84} -97.4704 q^{85} -464.900 q^{86} +923.946 q^{87} -964.373 q^{88} -316.018 q^{89} +256.681 q^{90} -95.5017 q^{91} +616.460 q^{92} +312.724 q^{93} +2084.11 q^{94} +1142.85 q^{95} -1240.55 q^{96} -70.8410 q^{97} -3275.76 q^{98} +308.080 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) $ 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−4.46204	−1.57757	−0.788785	−	0.614670i	$-0.789289\pi$
$2$	−4.46204	−1.57757	−0.788785	+	0.614670i	$0.789289\pi$
$3$	−5.70729	−1.09837	−0.549185	−	0.835701i	$-0.685062\pi$
$3$	−5.70729	−1.09837	−0.549185	+	0.835701i	$0.685062\pi$
$4$	11.9098	1.48872
$5$	−10.3218	−0.923208	−0.461604	−	0.887086i	$-0.652726\pi$
$5$	−10.3218	−0.923208	−0.461604	+	0.887086i	$0.652726\pi$
$6$	25.4662	1.73275
$7$	32.8198	1.77210	0.886052	−	0.463586i	$-0.153438\pi$
$7$	32.8198	1.77210	0.886052	+	0.463586i	$0.153438\pi$
$8$	−17.4456	−0.770996
$9$	5.57321	0.206415
$10$	46.0562	1.45642
$11$	55.2787	1.51520	0.757599	−	0.652721i	$-0.226372\pi$
$11$	55.2787	1.51520	0.757599	+	0.652721i	$0.226372\pi$
$12$	−67.9727	−1.63517
$13$	−2.90988	−0.0620812	−0.0310406	−	0.999518i	$-0.509882\pi$
$13$	−2.90988	−0.0620812	−0.0310406	+	0.999518i	$0.509882\pi$
$14$	−146.443	−2.79562
$15$	58.9094	1.01402
$16$	−17.4352	−0.272425
$17$	9.44318	0.134724	0.0673620	−	0.997729i	$-0.478542\pi$
$17$	9.44318	0.134724	0.0673620	+	0.997729i	$0.478542\pi$
$18$	−24.8679	−0.325634
$19$	−110.722	−1.33692	−0.668459	−	0.743749i	$-0.733046\pi$
$19$	−110.722	−1.33692	−0.668459	+	0.743749i	$0.733046\pi$
$20$	−122.930	−1.37440
$21$	−187.312	−1.94642
$22$	−246.656	−2.39033
$23$	51.7607	0.469255	0.234627	−	0.972085i	$-0.424613\pi$
$23$	51.7607	0.469255	0.234627	+	0.972085i	$0.424613\pi$
$24$	99.5674	0.846838
$25$	−18.4608	−0.147687
$26$	12.9840	0.0979373
$27$	122.289	0.871649
$28$	390.877	2.63817
$29$	−161.889	−1.03662	−0.518309	−	0.855193i	$-0.673438\pi$
$29$	−161.889	−1.03662	−0.518309	+	0.855193i	$0.673438\pi$
$30$	−262.856	−1.59969
$31$	−54.7937	−0.317459	−0.158730	−	0.987322i	$-0.550740\pi$
$31$	−54.7937	−0.317459	−0.158730	+	0.987322i	$0.550740\pi$
$32$	217.362	1.20076
$33$	−315.492	−1.66425
$34$	−42.1358	−0.212536
$35$	−338.759	−1.63602
$36$	66.3757	0.307295
$37$	−314.623	−1.39794	−0.698968	−	0.715153i	$-0.746357\pi$
$37$	−314.623	−1.39794	−0.698968	+	0.715153i	$0.746357\pi$
$38$	494.048	2.10908
$39$	16.6075	0.0681881
$40$	180.070	0.711790
$41$	379.325	1.44489	0.722446	−	0.691427i	$-0.243018\pi$
$41$	379.325	1.44489	0.722446	+	0.691427i	$0.243018\pi$
$42$	835.795	3.07062
$43$	104.190	0.369508	0.184754	−	0.982785i	$-0.440851\pi$
$43$	104.190	0.369508	0.184754	+	0.982785i	$0.440851\pi$
$44$	658.358	2.25571
$45$	−57.5254	−0.190564
$46$	−230.958	−0.740282
$47$	−467.077	−1.44958	−0.724789	−	0.688971i	$-0.758063\pi$
$47$	−467.077	−1.44958	−0.724789	+	0.688971i	$0.758063\pi$
$48$	99.5077	0.299223
$49$	734.140	2.14035
$50$	82.3730	0.232986
$51$	−53.8950	−0.147977
$52$	−34.6561	−0.0924217
$53$	285.530	0.740012	0.370006	−	0.929029i	$-0.379356\pi$
$53$	285.530	0.740012	0.370006	+	0.929029i	$0.379356\pi$
$54$	−545.658	−1.37509
$55$	−570.575	−1.39884
$56$	−572.563	−1.36628
$57$	631.925	1.46843
$58$	722.353	1.63534
$59$	123.325	0.272127	0.136064	−	0.990700i	$-0.456555\pi$
$59$	123.325	0.272127	0.136064	+	0.990700i	$0.456555\pi$
$60$	701.599	1.50960
$61$	−19.8015	−0.0415628	−0.0207814	−	0.999784i	$-0.506615\pi$
$61$	−19.8015	−0.0415628	−0.0207814	+	0.999784i	$0.506615\pi$
$62$	244.492	0.500814
$63$	182.912	0.365789
$64$	−830.395	−1.62186
$65$	30.0351	0.0573138
$66$	1407.74	2.62546
$67$	875.121	1.59572	0.797859	−	0.602844i	$-0.205966\pi$
$67$	875.121	1.59572	0.797859	+	0.602844i	$0.205966\pi$
$68$	112.466	0.200567
$69$	−295.414	−0.515415
$70$	1511.56	2.58094
$71$	−613.162	−1.02491	−0.512457	−	0.858713i	$-0.671265\pi$
$71$	−613.162	−1.02491	−0.512457	+	0.858713i	$0.671265\pi$
$72$	−97.2282	−0.159145
$73$	−710.907	−1.13980	−0.569900	−	0.821714i	$-0.693018\pi$
$73$	−710.907	−1.13980	−0.569900	+	0.821714i	$0.693018\pi$
$74$	1403.86	2.20534
$75$	105.361	0.162215
$76$	−1318.68	−1.99030
$77$	1814.24	2.68509
$78$	−74.1035	−0.107571
$79$	−536.451	−0.763993	−0.381997	−	0.924164i	$-0.624763\pi$
$79$	−536.451	−0.763993	−0.381997	+	0.924164i	$0.624763\pi$
$80$	179.962	0.251505
$81$	−848.416	−1.16381
$82$	−1692.56	−2.27942
$83$	−455.726	−0.602680	−0.301340	−	0.953517i	$-0.597434\pi$
$83$	−455.726	−0.602680	−0.301340	+	0.953517i	$0.597434\pi$
$84$	−2230.85	−2.89769
$85$	−97.4704	−0.124378
$86$	−464.900	−0.582924
$87$	923.946	1.13859
$88$	−964.373	−1.16821
$89$	−316.018	−0.376380	−0.188190	−	0.982133i	$-0.560262\pi$
$89$	−316.018	−0.376380	−0.188190	+	0.982133i	$0.560262\pi$
$90$	256.681	0.300628
$91$	−95.5017	−0.110014
$92$	616.460	0.698591
$93$	312.724	0.348687
$94$	2084.11	2.28681
$95$	1142.85	1.23425
$96$	−1240.55	−1.31888
$97$	−70.8410	−0.0741527	−0.0370763	−	0.999312i	$-0.511804\pi$
$97$	−70.8410	−0.0741527	−0.0370763	+	0.999312i	$0.511804\pi$
$98$	−3275.76	−3.37655
$99$	308.080	0.312759
$100$	−219.865	−0.219865
$101$	1474.56	1.45271	0.726355	−	0.687319i	$-0.241213\pi$
$101$	1474.56	1.45271	0.726355	+	0.687319i	$0.241213\pi$
$102$	240.482	0.233443
$103$	169.964	0.162592	0.0812962	−	0.996690i	$-0.474094\pi$
$103$	169.964	0.162592	0.0812962	+	0.996690i	$0.474094\pi$
$104$	50.7647	0.0478643
$105$	1933.40	1.79695
$106$	−1274.05	−1.16742
$107$	546.128	0.493422	0.246711	−	0.969089i	$-0.420650\pi$
$107$	546.128	0.493422	0.246711	+	0.969089i	$0.420650\pi$
$108$	1456.44	1.29765
$109$	1144.59	1.00579	0.502897	−	0.864346i	$-0.332267\pi$
$109$	1144.59	1.00579	0.502897	+	0.864346i	$0.332267\pi$
$110$	2545.93	2.20677
$111$	1795.64	1.53545
$112$	−572.220	−0.482765
$113$	1946.72	1.62064	0.810318	−	0.585990i	$-0.199294\pi$
$113$	1946.72	1.62064	0.810318	+	0.585990i	$0.199294\pi$
$114$	−2819.67	−2.31655
$115$	−534.263	−0.433220
$116$	−1928.06	−1.54324
$117$	−16.2174	−0.0128145
$118$	−550.279	−0.429299
$119$	309.923	0.238745
$120$	−1027.71	−0.781808
$121$	1724.74	1.29582
$122$	88.3553	0.0655681
$123$	−2164.92	−1.58702
$124$	−652.581	−0.472609
$125$	1480.77	1.05955
$126$	−816.159	−0.577057
$127$	−1825.93	−1.27579	−0.637895	−	0.770124i	$-0.720194\pi$
$127$	−1825.93	−1.27579	−0.637895	+	0.770124i	$0.720194\pi$
$128$	1966.36	1.35784
$129$	−594.643	−0.405856
$130$	−134.018	−0.0904166
$131$	1231.13	0.821103	0.410552	−	0.911837i	$-0.365336\pi$
$131$	1231.13	0.821103	0.410552	+	0.911837i	$0.365336\pi$
$132$	−3757.45	−2.47760
$133$	−3633.89	−2.36916
$134$	−3904.83	−2.51736
$135$	−1262.24	−0.804714
$136$	−164.742	−0.103872
$137$	−1951.87	−1.21722	−0.608611	−	0.793469i	$-0.708273\pi$
$137$	−1951.87	−1.21722	−0.608611	+	0.793469i	$0.708273\pi$
$138$	1318.15	0.813103
$139$	−2330.95	−1.42237	−0.711183	−	0.703006i	$-0.751840\pi$
$139$	−2330.95	−1.42237	−0.711183	+	0.703006i	$0.751840\pi$
$140$	−4034.55	−2.43558
$141$	2665.74	1.59217
$142$	2735.95	1.61687
$143$	−160.854	−0.0940652
$144$	−97.1699	−0.0562326
$145$	1670.98	0.957015
$146$	3172.09	1.79811
$147$	−4189.95	−2.35090
$148$	−3747.09	−2.08114
$149$	11.3137	0.00622048	0.00311024	−	0.999995i	$-0.499010\pi$
$149$	11.3137	0.00622048	0.00311024	+	0.999995i	$0.499010\pi$
$150$	−470.127	−0.255905
$151$	−2168.65	−1.16876	−0.584379	−	0.811481i	$-0.698662\pi$
$151$	−2168.65	−1.16876	−0.584379	+	0.811481i	$0.698662\pi$
$152$	1931.62	1.03076
$153$	52.6288	0.0278090
$154$	−8095.20	−4.23591
$155$	565.568	0.293081
$156$	197.792	0.101513
$157$	1774.82	0.902203	0.451102	−	0.892473i	$-0.351031\pi$
$157$	1774.82	0.902203	0.451102	+	0.892473i	$0.351031\pi$
$158$	2393.67	1.20525
$159$	−1629.61	−0.812806
$160$	−2243.56	−1.10856
$161$	1698.78	0.831568
$162$	3785.66	1.83599
$163$	−2842.13	−1.36572	−0.682862	−	0.730547i	$-0.739265\pi$
$163$	−2842.13	−1.36572	−0.682862	+	0.730547i	$0.739265\pi$
$164$	4517.68	2.15105
$165$	3256.44	1.53645
$166$	2033.47	0.950769
$167$	−2508.14	−1.16219	−0.581095	−	0.813835i	$-0.697376\pi$
$167$	−2508.14	−1.16219	−0.581095	+	0.813835i	$0.697376\pi$
$168$	3267.78	1.50068
$169$	−2188.53	−0.996146
$170$	434.917	0.196215
$171$	−617.079	−0.275960
$172$	1240.88	0.550095
$173$	2493.75	1.09593	0.547967	−	0.836500i	$-0.315402\pi$
$173$	2493.75	1.09593	0.547967	+	0.836500i	$0.315402\pi$
$174$	−4122.68	−1.79620
$175$	−605.881	−0.261716
$176$	−963.795	−0.412777
$177$	−703.850	−0.298896
$178$	1410.08	0.593766
$179$	308.665	0.128887	0.0644433	−	0.997921i	$-0.479473\pi$
$179$	308.665	0.128887	0.0644433	+	0.997921i	$0.479473\pi$
$180$	−685.116	−0.283697
$181$	2425.01	0.995853	0.497927	−	0.867219i	$-0.334095\pi$
$181$	2425.01	0.995853	0.497927	+	0.867219i	$0.334095\pi$
$182$	426.132	0.173555
$183$	113.013	0.0456513
$184$	−903.000	−0.361794
$185$	3247.47	1.29059
$186$	−1395.39	−0.550078
$187$	522.007	0.204133
$188$	−5562.79	−2.15802
$189$	4013.50	1.54465
$190$	−5099.45	−1.94712
$191$	4540.17	1.71997	0.859987	−	0.510317i	$-0.170472\pi$
$191$	4540.17	1.71997	0.859987	+	0.510317i	$0.170472\pi$
$192$	4739.31	1.78141
$193$	−4857.77	−1.81176	−0.905880	−	0.423535i	$-0.860789\pi$
$193$	−4857.77	−1.81176	−0.905880	+	0.423535i	$0.860789\pi$
$194$	316.095	0.116981
$195$	−171.419	−0.0629518
$196$	8743.46	3.18639
$197$	−3490.97	−1.26255	−0.631273	−	0.775561i	$-0.717467\pi$
$197$	−3490.97	−1.26255	−0.631273	+	0.775561i	$0.717467\pi$
$198$	−1374.66	−0.493400
$199$	2241.97	0.798638	0.399319	−	0.916812i	$-0.369247\pi$
$199$	2241.97	0.798638	0.399319	+	0.916812i	$0.369247\pi$
$200$	322.061	0.113866
$201$	−4994.58	−1.75269
$202$	−6579.53	−2.29175
$203$	−5313.15	−1.83700
$204$	−641.878	−0.220296
$205$	−3915.31	−1.33394
$206$	−758.385	−0.256501
$207$	288.473	0.0968612
$208$	50.7343	0.0169125
$209$	−6120.59	−2.02570
$210$	−8626.89	−2.83482
$211$	−4948.13	−1.61442	−0.807211	−	0.590263i	$-0.799024\pi$
$211$	−4948.13	−1.61442	−0.807211	+	0.590263i	$0.799024\pi$
$212$	3400.61	1.10167
$213$	3499.49	1.12573
$214$	−2436.84	−0.778407
$215$	−1075.43	−0.341133
$216$	−2133.41	−0.672038
$217$	−1798.32	−0.562571
$218$	−5107.19	−1.58671
$219$	4057.36	1.25192
$220$	−6795.43	−2.08249
$221$	−27.4785	−0.00836382
$222$	−8012.24	−2.42228
$223$	4344.05	1.30448	0.652241	−	0.758012i	$-0.273829\pi$
$223$	4344.05	1.30448	0.652241	+	0.758012i	$0.273829\pi$
$224$	7133.77	2.12788
$225$	−102.886	−0.0304848
$226$	−8686.33	−2.55667
$227$	362.635	0.106030	0.0530152	−	0.998594i	$-0.483117\pi$
$227$	362.635	0.106030	0.0530152	+	0.998594i	$0.483117\pi$
$228$	7526.10	2.18609
$229$	−2714.36	−0.783274	−0.391637	−	0.920120i	$-0.628091\pi$
$229$	−2714.36	−0.783274	−0.391637	+	0.920120i	$0.628091\pi$
$230$	2383.90	0.683434
$231$	−10354.4	−2.94922
$232$	2824.25	0.799229
$233$	−5462.36	−1.53584	−0.767921	−	0.640545i	$-0.778709\pi$
$233$	−5462.36	−1.53584	−0.767921	+	0.640545i	$0.778709\pi$
$234$	72.3625	0.0202157
$235$	4821.06	1.33826
$236$	1468.77	0.405122
$237$	3061.68	0.839147
$238$	−1382.89	−0.376636
$239$	3940.13	1.06638	0.533192	−	0.845994i	$-0.320992\pi$
$239$	3940.13	1.06638	0.533192	+	0.845994i	$0.320992\pi$
$240$	−1027.10	−0.276245
$241$	6500.63	1.73752	0.868761	−	0.495232i	$-0.164917\pi$
$241$	6500.63	1.73752	0.868761	+	0.495232i	$0.164917\pi$
$242$	−7695.86	−2.04425
$243$	1540.36	0.406641
$244$	−235.832	−0.0618755
$245$	−7577.64	−1.97599
$246$	9659.95	2.50364
$247$	322.189	0.0829975
$248$	955.911	0.244760
$249$	2600.96	0.661965
$250$	−6607.26	−1.67152
$251$	4533.97	1.14017	0.570083	−	0.821587i	$-0.306911\pi$
$251$	4533.97	1.14017	0.570083	+	0.821587i	$0.306911\pi$
$252$	2178.44	0.544559
$253$	2861.27	0.711014
$254$	8147.38	2.01265
$255$	556.292	0.136613
$256$	−2130.82	−0.520219
$257$	−3205.52	−0.778034	−0.389017	−	0.921231i	$-0.627185\pi$
$257$	−3205.52	−0.778034	−0.389017	+	0.921231i	$0.627185\pi$
$258$	2653.32	0.640266
$259$	−10325.9	−2.47729
$260$	357.712	0.0853245
$261$	−902.238	−0.213974
$262$	−5493.36	−1.29535
$263$	−4733.83	−1.10989	−0.554944	−	0.831888i	$-0.687260\pi$
$263$	−4733.83	−1.10989	−0.554944	+	0.831888i	$0.687260\pi$
$264$	5503.96	1.28313
$265$	−2947.18	−0.683185
$266$	16214.6	3.73751
$267$	1803.61	0.413404
$268$	10422.5	2.37558
$269$	−3865.37	−0.876119	−0.438059	−	0.898946i	$-0.644334\pi$
$269$	−3865.37	−0.876119	−0.438059	+	0.898946i	$0.644334\pi$
$270$	5632.17	1.26949
$271$	−5315.53	−1.19150	−0.595748	−	0.803172i	$-0.703144\pi$
$271$	−5315.53	−1.19150	−0.595748	+	0.803172i	$0.703144\pi$
$272$	−164.644	−0.0367021
$273$	545.056	0.120836
$274$	8709.31	1.92025
$275$	−1020.49	−0.223775
$276$	−3518.32	−0.767311
$277$	3472.55	0.753232	0.376616	−	0.926369i	$-0.377088\pi$
$277$	3472.55	0.753232	0.376616	+	0.926369i	$0.377088\pi$
$278$	10400.8	2.24388
$279$	−305.376	−0.0655283
$280$	5909.87	1.26136
$281$	−2590.79	−0.550012	−0.275006	−	0.961443i	$-0.588680\pi$
$281$	−2590.79	−0.550012	−0.275006	+	0.961443i	$0.588680\pi$
$282$	−11894.7	−2.51176
$283$	−1478.51	−0.310558	−0.155279	−	0.987871i	$-0.549628\pi$
$283$	−1478.51	−0.310558	−0.155279	+	0.987871i	$0.549628\pi$
$284$	−7302.63	−1.52581
$285$	−6522.59	−1.35567
$286$	717.739	0.148394
$287$	12449.4	2.56050
$288$	1211.40	0.247856
$289$	−4823.83	−0.981849
$290$	−7455.97	−1.50976
$291$	404.310	0.0814470
$292$	−8466.75	−1.69685
$293$	7475.57	1.49054	0.745269	−	0.666764i	$-0.232321\pi$
$293$	7475.57	1.49054	0.745269	+	0.666764i	$0.232321\pi$
$294$	18695.7	3.70870
$295$	−1272.93	−0.251230
$296$	5488.80	1.07780
$297$	6759.98	1.32072
$298$	−50.4820	−0.00981324
$299$	−150.618	−0.0291319
$300$	1254.83	0.241493
$301$	3419.50	0.654806
$302$	9676.62	1.84380
$303$	−8415.72	−1.59561
$304$	1930.47	0.364210
$305$	204.387	0.0383711
$306$	−234.832	−0.0438707
$307$	−1414.23	−0.262913	−0.131457	−	0.991322i	$-0.541965\pi$
$307$	−1414.23	−0.262913	−0.131457	+	0.991322i	$0.541965\pi$
$308$	21607.2	3.99735
$309$	−970.033	−0.178587
$310$	−2523.59	−0.462355
$311$	4721.68	0.860906	0.430453	−	0.902613i	$-0.358354\pi$
$311$	4721.68	0.860906	0.430453	+	0.902613i	$0.358354\pi$
$312$	−289.729	−0.0525727
$313$	−8664.43	−1.56467	−0.782336	−	0.622857i	$-0.785972\pi$
$313$	−8664.43	−1.56467	−0.782336	+	0.622857i	$0.785972\pi$
$314$	−7919.31	−1.42329
$315$	−1887.97	−0.337699
$316$	−6389.02	−1.13738
$317$	−5273.97	−0.934434	−0.467217	−	0.884143i	$-0.654743\pi$
$317$	−5273.97	−0.934434	−0.467217	+	0.884143i	$0.654743\pi$
$318$	7271.37	1.28226
$319$	−8949.00	−1.57068
$320$	8571.15	1.49732
$321$	−3116.91	−0.541960
$322$	−7580.01	−1.31186
$323$	−1045.57	−0.180115
$324$	−10104.5	−1.73259
$325$	53.7188	0.00916857
$326$	12681.7	2.15452
$327$	−6532.50	−1.10473
$328$	−6617.56	−1.11401
$329$	−15329.4	−2.56880
$330$	−14530.4	−2.42385
$331$	7529.36	1.25030	0.625152	−	0.780503i	$-0.285037\pi$
$331$	7529.36	1.25030	0.625152	+	0.780503i	$0.285037\pi$
$332$	−5427.60	−0.897224
$333$	−1753.46	−0.288555
$334$	11191.4	1.83344
$335$	−9032.81	−1.47318
$336$	3265.83	0.530254
$337$	1521.00	0.245858	0.122929	−	0.992415i	$-0.460771\pi$
$337$	1521.00	0.245858	0.122929	+	0.992415i	$0.460771\pi$
$338$	9765.32	1.57149
$339$	−11110.5	−1.78006
$340$	−1160.85	−0.185165
$341$	−3028.93	−0.481013
$342$	2753.43	0.435346
$343$	12837.2	2.02082
$344$	−1817.66	−0.284889
$345$	3049.20	0.475835
$346$	−11127.2	−1.72891
$347$	8682.94	1.34330	0.671649	−	0.740870i	$-0.265586\pi$
$347$	8682.94	1.34330	0.671649	+	0.740870i	$0.265586\pi$
$348$	11004.0	1.69505
$349$	8438.80	1.29432	0.647161	−	0.762353i	$-0.275956\pi$
$349$	8438.80	1.29432	0.647161	+	0.762353i	$0.275956\pi$
$350$	2703.47	0.412875
$351$	−355.846	−0.0541130
$352$	12015.5	1.81940
$353$	−171.504	−0.0258591	−0.0129295	−	0.999916i	$-0.504116\pi$
$353$	−171.504	−0.0258591	−0.0129295	+	0.999916i	$0.504116\pi$
$354$	3140.61	0.471529
$355$	6328.92	0.946209
$356$	−3763.71	−0.560326
$357$	−1768.82	−0.262230
$358$	−1377.27	−0.203327
$359$	2031.61	0.298674	0.149337	−	0.988786i	$-0.452286\pi$
$359$	2031.61	0.298674	0.149337	+	0.988786i	$0.452286\pi$
$360$	1003.57	0.146924
$361$	5400.45	0.787352
$362$	−10820.5	−1.57103
$363$	−9843.60	−1.42329
$364$	−1137.41	−0.163781
$365$	7337.83	1.05227
$366$	−504.270	−0.0720180
$367$	−10114.4	−1.43860	−0.719301	−	0.694698i	$-0.755538\pi$
$367$	−10114.4	−1.43860	−0.719301	+	0.694698i	$0.755538\pi$
$368$	−902.458	−0.127837
$369$	2114.05	0.298247
$370$	−14490.3	−2.03599
$371$	9371.06	1.31138
$372$	3724.47	0.519099
$373$	1596.82	0.221663	0.110832	−	0.993839i	$-0.464649\pi$
$373$	1596.82	0.221663	0.110832	+	0.993839i	$0.464649\pi$
$374$	−2329.22	−0.322034
$375$	−8451.20	−1.16378
$376$	8148.46	1.11762
$377$	471.076	0.0643545
$378$	−17908.4	−2.43680
$379$	−206.933	−0.0280460	−0.0140230	−	0.999902i	$-0.504464\pi$
$379$	−206.933	−0.0280460	−0.0140230	+	0.999902i	$0.504464\pi$
$380$	13611.1	1.83746
$381$	10421.1	1.40129
$382$	−20258.4	−2.71338
$383$	−2868.55	−0.382705	−0.191353	−	0.981521i	$-0.561287\pi$
$383$	−2868.55	−0.382705	−0.191353	+	0.981521i	$0.561287\pi$
$384$	−11222.6	−1.49141
$385$	−18726.2	−2.47889
$386$	21675.5	2.85818
$387$	580.673	0.0762720
$388$	−843.701	−0.110393
$389$	−2260.86	−0.294680	−0.147340	−	0.989086i	$-0.547071\pi$
$389$	−2260.86	−0.294680	−0.147340	+	0.989086i	$0.547071\pi$
$390$	764.880	0.0993108
$391$	488.786	0.0632199
$392$	−12807.6	−1.65020
$393$	−7026.43	−0.901874
$394$	15576.9	1.99175
$395$	5537.13	0.705325
$396$	3669.17	0.465613
$397$	−7366.58	−0.931280	−0.465640	−	0.884974i	$-0.654176\pi$
$397$	−7366.58	−0.931280	−0.465640	+	0.884974i	$0.654176\pi$
$398$	−10003.8	−1.25991
$399$	20739.7	2.60221
$400$	321.868	0.0402335
$401$	650.496	0.0810080	0.0405040	−	0.999179i	$-0.487104\pi$
$401$	650.496	0.0810080	0.0405040	+	0.999179i	$0.487104\pi$
$402$	22286.0	2.76499
$403$	159.443	0.0197082
$404$	17561.7	2.16269
$405$	8757.16	1.07444
$406$	23707.5	2.89799
$407$	−17392.0	−2.11815
$408$	940.233	0.114089
$409$	1953.99	0.236232	0.118116	−	0.993000i	$-0.462315\pi$
$409$	1953.99	0.236232	0.118116	+	0.993000i	$0.462315\pi$
$410$	17470.3	2.10438
$411$	11139.9	1.33696
$412$	2024.23	0.242055
$413$	4047.49	0.482237
$414$	−1287.18	−0.152805
$415$	4703.90	0.556399
$416$	−632.496	−0.0745449
$417$	13303.4	1.56228
$418$	27310.3	3.19567
$419$	−3118.76	−0.363632	−0.181816	−	0.983333i	$-0.558197\pi$
$419$	−3118.76	−0.363632	−0.181816	+	0.983333i	$0.558197\pi$
$420$	23026.4	2.67517
$421$	9337.44	1.08095	0.540474	−	0.841361i	$-0.318245\pi$
$421$	9337.44	1.08095	0.540474	+	0.841361i	$0.318245\pi$
$422$	22078.7	2.54686
$423$	−2603.11	−0.299215
$424$	−4981.26	−0.570546
$425$	−174.329	−0.0198969
$426$	−15614.9	−1.77592
$427$	−649.883	−0.0736535
$428$	6504.27	0.734569
$429$	918.044	0.103318
$430$	4798.60	0.538160
$431$	−15124.7	−1.69033	−0.845166	−	0.534504i	$-0.820498\pi$
$431$	−15124.7	−1.69033	−0.845166	+	0.534504i	$0.820498\pi$
$432$	−2132.13	−0.237459
$433$	16011.8	1.77709	0.888544	−	0.458792i	$-0.151718\pi$
$433$	16011.8	1.77709	0.888544	+	0.458792i	$0.151718\pi$
$434$	8024.17	0.887494
$435$	−9536.76	−1.05116
$436$	13631.8	1.49735
$437$	−5731.07	−0.627356
$438$	−18104.1	−1.97499
$439$	−10062.7	−1.09400	−0.547001	−	0.837132i	$-0.684231\pi$
$439$	−10062.7	−1.09400	−0.547001	+	0.837132i	$0.684231\pi$
$440$	9954.05	1.07850
$441$	4091.52	0.441801
$442$	122.610	0.0131945
$443$	−3931.79	−0.421682	−0.210841	−	0.977520i	$-0.567620\pi$
$443$	−3931.79	−0.421682	−0.210841	+	0.977520i	$0.567620\pi$
$444$	21385.8	2.28586
$445$	3261.87	0.347477
$446$	−19383.3	−2.05791
$447$	−64.5704	−0.00683239
$448$	−27253.4	−2.87411
$449$	1101.21	0.115745	0.0578724	−	0.998324i	$-0.481568\pi$
$449$	1101.21	0.115745	0.0578724	+	0.998324i	$0.481568\pi$
$450$	459.082	0.0480918
$451$	20968.6	2.18930
$452$	23185.0	2.41268
$453$	12377.1	1.28373
$454$	−1618.09	−0.167270
$455$	985.748	0.101566
$456$	−11024.3	−1.13215
$457$	−9927.88	−1.01621	−0.508104	−	0.861296i	$-0.669653\pi$
$457$	−9927.88	−1.01621	−0.508104	+	0.861296i	$0.669653\pi$
$458$	12111.6	1.23567
$459$	1154.80	0.117432
$460$	−6362.96	−0.644945
$461$	−1512.55	−0.152812	−0.0764061	−	0.997077i	$-0.524345\pi$
$461$	−1512.55	−0.152812	−0.0764061	+	0.997077i	$0.524345\pi$
$462$	46201.7	4.65259
$463$	8571.68	0.860389	0.430194	−	0.902736i	$-0.358445\pi$
$463$	8571.68	0.860389	0.430194	+	0.902736i	$0.358445\pi$
$464$	2822.56	0.282401
$465$	−3227.86	−0.321911
$466$	24373.3	2.42290
$467$	−14778.5	−1.46439	−0.732194	−	0.681096i	$-0.761503\pi$
$467$	−14778.5	−1.46439	−0.732194	+	0.681096i	$0.761503\pi$
$468$	−193.145	−0.0190772
$469$	28721.3	2.82778
$470$	−21511.8	−2.11120
$471$	−10129.4	−0.990952
$472$	−2151.48	−0.209809
$473$	5759.50	0.559877
$474$	−13661.4	−1.32381
$475$	2044.03	0.197445
$476$	3691.12	0.355425
$477$	1591.32	0.152750
$478$	−17581.0	−1.68230
$479$	−8114.31	−0.774013	−0.387006	−	0.922077i	$-0.626491\pi$
$479$	−8114.31	−0.774013	−0.387006	+	0.922077i	$0.626491\pi$
$480$	12804.7	1.21760
$481$	915.514	0.0867856
$482$	−29006.1	−2.74106
$483$	−9695.43	−0.913369
$484$	20541.3	1.92912
$485$	731.205	0.0684583
$486$	−6873.13	−0.641505
$487$	−8615.16	−0.801623	−0.400811	−	0.916161i	$-0.631272\pi$
$487$	−8615.16	−0.801623	−0.400811	+	0.916161i	$0.631272\pi$
$488$	345.451	0.0320447
$489$	16220.9	1.50007
$490$	33811.7	3.11726
$491$	−5196.70	−0.477646	−0.238823	−	0.971063i	$-0.576762\pi$
$491$	−5196.70	−0.477646	−0.238823	+	0.971063i	$0.576762\pi$
$492$	−25783.7	−2.36264
$493$	−1528.74	−0.139657
$494$	−1437.62	−0.130934
$495$	−3179.93	−0.288742
$496$	955.338	0.0864838
$497$	−20123.8	−1.81625
$498$	−11605.6	−1.04430
$499$	8312.20	0.745702	0.372851	−	0.927891i	$-0.378380\pi$
$499$	8312.20	0.745702	0.372851	+	0.927891i	$0.378380\pi$
$500$	17635.7	1.57738
$501$	14314.7	1.27651
$502$	−20230.8	−1.79869
$503$	10199.2	0.904092	0.452046	−	0.891995i	$-0.350694\pi$
$503$	10199.2	0.904092	0.452046	+	0.891995i	$0.350694\pi$
$504$	−3191.01	−0.282022
$505$	−15220.0	−1.34115
$506$	−12767.1	−1.12167
$507$	12490.6	1.09414
$508$	−21746.5	−1.89930
$509$	−9301.01	−0.809941	−0.404970	−	0.914330i	$-0.632718\pi$
$509$	−9301.01	−0.809941	−0.404970	+	0.914330i	$0.632718\pi$
$510$	−2482.20	−0.215517
$511$	−23331.8	−2.01984
$512$	−6223.09	−0.537157
$513$	−13540.1	−1.16532
$514$	14303.1	1.22740
$515$	−1754.33	−0.150107
$516$	−7082.08	−0.604208
$517$	−25819.4	−2.19640
$518$	46074.4	3.90809
$519$	−14232.6	−1.20374
$520$	−523.982	−0.0441887
$521$	14584.6	1.22641	0.613207	−	0.789922i	$-0.289879\pi$
$521$	14584.6	1.22641	0.613207	+	0.789922i	$0.289879\pi$
$522$	4025.82	0.337558
$523$	7276.77	0.608395	0.304198	−	0.952609i	$-0.401612\pi$
$523$	7276.77	0.608395	0.304198	+	0.952609i	$0.401612\pi$
$524$	14662.5	1.22240
$525$	3457.94	0.287461
$526$	21122.5	1.75092
$527$	−517.426	−0.0427694
$528$	5500.66	0.453382
$529$	−9487.83	−0.779800
$530$	13150.4	1.07777
$531$	687.314	0.0561711
$532$	−43278.9	−3.52702
$533$	−1103.79	−0.0897006
$534$	−8047.77	−0.652174
$535$	−5637.01	−0.455531
$536$	−15267.1	−1.23029
$537$	−1761.64	−0.141565
$538$	17247.4	1.38214
$539$	40582.4	3.24305
$540$	−15033.0	−1.19800
$541$	7177.23	0.570375	0.285188	−	0.958472i	$-0.407944\pi$
$541$	7177.23	0.570375	0.285188	+	0.958472i	$0.407944\pi$
$542$	23718.1	1.87967
$543$	−13840.2	−1.09381
$544$	2052.58	0.161772
$545$	−11814.2	−0.928558
$546$	−2432.06	−0.190628
$547$	−20588.7	−1.60934	−0.804669	−	0.593723i	$-0.797657\pi$
$547$	−20588.7	−1.60934	−0.804669	+	0.593723i	$0.797657\pi$
$548$	−23246.3	−1.81211
$549$	−110.358	−0.00857918
$550$	4553.48	0.353020
$551$	17924.7	1.38588
$552$	5153.68	0.397383
$553$	−17606.2	−1.35388
$554$	−15494.6	−1.18828
$555$	−18534.2	−1.41754
$556$	−27761.2	−2.11751
$557$	5138.84	0.390915	0.195457	−	0.980712i	$-0.437381\pi$
$557$	5138.84	0.390915	0.195457	+	0.980712i	$0.437381\pi$
$558$	1362.60	0.103375
$559$	−303.181	−0.0229395
$560$	5906.33	0.445693
$561$	−2979.25	−0.224214
$562$	11560.2	0.867681
$563$	−17090.4	−1.27935	−0.639677	−	0.768644i	$-0.720932\pi$
$563$	−17090.4	−1.27935	−0.639677	+	0.768644i	$0.720932\pi$
$564$	31748.5	2.37030
$565$	−20093.6	−1.49618
$566$	6597.15	0.489927
$567$	−27844.9	−2.06239
$568$	10697.0	0.790204
$569$	4519.31	0.332969	0.166484	−	0.986044i	$-0.446758\pi$
$569$	4519.31	0.332969	0.166484	+	0.986044i	$0.446758\pi$
$570$	29104.1	2.13866
$571$	−4982.15	−0.365142	−0.182571	−	0.983193i	$-0.558442\pi$
$571$	−4982.15	−0.365142	−0.182571	+	0.983193i	$0.558442\pi$
$572$	−1915.74	−0.140037
$573$	−25912.1	−1.88917
$574$	−55549.6	−4.03936
$575$	−955.547	−0.0693027
$576$	−4627.96	−0.334777
$577$	−14799.9	−1.06781	−0.533907	−	0.845543i	$-0.679277\pi$
$577$	−14799.9	−1.06781	−0.533907	+	0.845543i	$0.679277\pi$
$578$	21524.1	1.54894
$579$	27724.7	1.98998
$580$	19901.0	1.42473
$581$	−14956.8	−1.06801
$582$	−1804.05	−0.128488
$583$	15783.8	1.12126
$584$	12402.2	0.878781
$585$	167.392	0.0118304
$586$	−33356.3	−2.35143
$587$	−8229.83	−0.578673	−0.289337	−	0.957227i	$-0.593435\pi$
$587$	−8229.83	−0.578673	−0.289337	+	0.957227i	$0.593435\pi$
$588$	−49901.5	−3.49983
$589$	6066.89	0.424417
$590$	5679.86	0.396333
$591$	19924.0	1.38674
$592$	5485.51	0.380833
$593$	−8334.86	−0.577186	−0.288593	−	0.957452i	$-0.593188\pi$
$593$	−8334.86	−0.577186	−0.288593	+	0.957452i	$0.593188\pi$
$594$	−30163.3	−2.08353
$595$	−3198.96	−0.220411
$596$	134.743	0.00926058
$597$	−12795.6	−0.877200
$598$	672.061	0.0459576
$599$	−21695.8	−1.47991	−0.739954	−	0.672658i	$-0.765153\pi$
$599$	−21695.8	−1.47991	−0.739954	+	0.672658i	$0.765153\pi$
$600$	−1838.10	−0.125067
$601$	−15732.6	−1.06780	−0.533899	−	0.845548i	$-0.679274\pi$
$601$	−15732.6	−1.06780	−0.533899	+	0.845548i	$0.679274\pi$
$602$	−15257.9	−1.03300
$603$	4877.23	0.329380
$604$	−25828.2	−1.73996
$605$	−17802.4	−1.19631
$606$	37551.3	2.51719
$607$	−17808.5	−1.19082	−0.595409	−	0.803423i	$-0.703010\pi$
$607$	−17808.5	−1.19082	−0.595409	+	0.803423i	$0.703010\pi$
$608$	−24066.8	−1.60533
$609$	30323.7	2.01770
$610$	−911.984	−0.0605330
$611$	1359.14	0.0899915
$612$	626.798	0.0414000
$613$	−19461.6	−1.28229	−0.641146	−	0.767419i	$-0.721541\pi$
$613$	−19461.6	−1.28229	−0.641146	+	0.767419i	$0.721541\pi$
$614$	6310.35	0.414764
$615$	22345.8	1.46515
$616$	−31650.6	−2.07019
$617$	−25712.2	−1.67769	−0.838843	−	0.544373i	$-0.816768\pi$
$617$	−25712.2	−1.67769	−0.838843	+	0.544373i	$0.816768\pi$
$618$	4328.33	0.281733
$619$	−3376.81	−0.219266	−0.109633	−	0.993972i	$-0.534968\pi$
$619$	−3376.81	−0.219266	−0.109633	+	0.993972i	$0.534968\pi$
$620$	6735.80	0.436317
$621$	6329.77	0.409026
$622$	−21068.3	−1.35814
$623$	−10371.7	−0.666985
$624$	−289.556	−0.0185761
$625$	−12976.6	−0.830502
$626$	38661.0	2.46838
$627$	34932.0	2.22496
$628$	21137.7	1.34313
$629$	−2971.04	−0.188336
$630$	8424.21	0.532744
$631$	−8779.27	−0.553878	−0.276939	−	0.960887i	$-0.589320\pi$
$631$	−8779.27	−0.553878	−0.276939	+	0.960887i	$0.589320\pi$
$632$	9358.74	0.589036
$633$	28240.4	1.77323
$634$	23532.6	1.47413
$635$	18846.9	1.17782
$636$	−19408.3	−1.21004
$637$	−2136.26	−0.132876
$638$	39930.8	2.47786
$639$	−3417.28	−0.211558
$640$	−20296.3	−1.25357
$641$	4999.03	0.308034	0.154017	−	0.988068i	$-0.450779\pi$
$641$	4999.03	0.308034	0.154017	+	0.988068i	$0.450779\pi$
$642$	13907.8	0.854979
$643$	−19683.6	−1.20722	−0.603611	−	0.797279i	$-0.706272\pi$
$643$	−19683.6	−1.20722	−0.603611	+	0.797279i	$0.706272\pi$
$644$	20232.1	1.23798
$645$	6137.78	0.374690
$646$	4665.38	0.284144
$647$	8213.13	0.499059	0.249530	−	0.968367i	$-0.419724\pi$
$647$	8213.13	0.499059	0.249530	+	0.968367i	$0.419724\pi$
$648$	14801.2	0.897291
$649$	6817.23	0.412326
$650$	−239.696	−0.0144640
$651$	10263.5	0.617910
$652$	−33849.2	−2.03319
$653$	−30188.1	−1.80911	−0.904556	−	0.426355i	$-0.859797\pi$
$653$	−30188.1	−1.80911	−0.904556	+	0.426355i	$0.859797\pi$
$654$	29148.3	1.74279
$655$	−12707.5	−0.758049
$656$	−6613.60	−0.393624
$657$	−3962.03	−0.235272
$658$	68400.3	4.05246
$659$	4719.39	0.278970	0.139485	−	0.990224i	$-0.455455\pi$
$659$	4719.39	0.278970	0.139485	+	0.990224i	$0.455455\pi$
$660$	38783.5	2.28734
$661$	6750.25	0.397208	0.198604	−	0.980080i	$-0.436359\pi$
$661$	6750.25	0.397208	0.198604	+	0.980080i	$0.436359\pi$
$662$	−33596.3	−1.97244
$663$	156.828	0.00918656
$664$	7950.43	0.464663
$665$	37508.2	2.18723
$666$	7823.99	0.455216
$667$	−8379.47	−0.486438
$668$	−29871.4	−1.73018
$669$	−24792.8	−1.43280
$670$	40304.8	2.32404
$671$	−1094.60	−0.0629758
$672$	−40714.5	−2.33720
$673$	8623.30	0.493913	0.246957	−	0.969027i	$-0.420569\pi$
$673$	8623.30	0.493913	0.246957	+	0.969027i	$0.420569\pi$
$674$	−6786.75	−0.387857
$675$	−2257.56	−0.128731
$676$	−26065.0	−1.48299
$677$	922.397	0.0523643	0.0261821	−	0.999657i	$-0.491665\pi$
$677$	922.397	0.0523643	0.0261821	+	0.999657i	$0.491665\pi$
$678$	49575.5	2.80816
$679$	−2324.99	−0.131406
$680$	1700.43	0.0958951
$681$	−2069.66	−0.116461
$682$	13515.2	0.758832
$683$	−15531.3	−0.870116	−0.435058	−	0.900402i	$-0.643272\pi$
$683$	−15531.3	−0.870116	−0.435058	+	0.900402i	$0.643272\pi$
$684$	−7349.28	−0.410828
$685$	20146.7	1.12375
$686$	−57279.9	−3.18798
$687$	15491.6	0.860324
$688$	−1816.57	−0.100663
$689$	−830.859	−0.0459408
$690$	−13605.6	−0.750663
$691$	25847.6	1.42299	0.711496	−	0.702690i	$-0.248018\pi$
$691$	25847.6	1.42299	0.711496	+	0.702690i	$0.248018\pi$
$692$	29700.1	1.63154
$693$	10111.1	0.554242
$694$	−38743.6	−2.11915
$695$	24059.6	1.31314
$696$	−16118.8	−0.877848
$697$	3582.03	0.194662
$698$	−37654.2	−2.04188
$699$	31175.3	1.68692
$700$	−7215.92	−0.389623
$701$	−22664.4	−1.22115	−0.610573	−	0.791960i	$-0.709061\pi$
$701$	−22664.4	−1.22115	−0.610573	+	0.791960i	$0.709061\pi$
$702$	1587.80	0.0853670
$703$	34835.8	1.86893
$704$	−45903.2	−2.45744
$705$	−27515.2	−1.46991
$706$	765.259	0.0407945
$707$	48394.7	2.57435
$708$	−8382.71	−0.444974
$709$	−19054.9	−1.00934	−0.504669	−	0.863313i	$-0.668386\pi$
$709$	−19054.9	−1.00934	−0.504669	+	0.863313i	$0.668386\pi$
$710$	−28239.9	−1.49271
$711$	−2989.75	−0.157700
$712$	5513.14	0.290188
$713$	−2836.16	−0.148969
$714$	7892.56	0.413686
$715$	1660.30	0.0868418
$716$	3676.13	0.191876
$717$	−22487.5	−1.17128
$718$	−9065.11	−0.471179
$719$	−14553.9	−0.754892	−0.377446	−	0.926032i	$-0.623198\pi$
$719$	−14553.9	−0.754892	−0.377446	+	0.926032i	$0.623198\pi$
$720$	1002.97	0.0519144
$721$	5578.18	0.288131
$722$	−24097.0	−1.24210
$723$	−37101.0	−1.90844
$724$	28881.3	1.48255
$725$	2988.60	0.153095
$726$	43922.5	2.24534
$727$	2583.82	0.131814	0.0659068	−	0.997826i	$-0.479006\pi$
$727$	2583.82	0.131814	0.0659068	+	0.997826i	$0.479006\pi$
$728$	1666.09	0.0848206
$729$	14116.0	0.717165
$730$	−32741.7	−1.66003
$731$	983.885	0.0497816
$732$	1345.96	0.0679621
$733$	26552.5	1.33798	0.668990	−	0.743272i	$-0.266727\pi$
$733$	26552.5	1.33798	0.668990	+	0.743272i	$0.266727\pi$
$734$	45130.8	2.26949
$735$	43247.8	2.17037
$736$	11250.8	0.563465
$737$	48375.6	2.41783
$738$	−9432.99	−0.470506
$739$	13965.3	0.695156	0.347578	−	0.937651i	$-0.387004\pi$
$739$	13965.3	0.695156	0.347578	+	0.937651i	$0.387004\pi$
$740$	38676.7	1.92133
$741$	−1838.83	−0.0911619
$742$	−41814.0	−2.06879
$743$	−7580.87	−0.374314	−0.187157	−	0.982330i	$-0.559927\pi$
$743$	−7580.87	−0.374314	−0.187157	+	0.982330i	$0.559927\pi$
$744$	−5455.67	−0.268837
$745$	−116.777	−0.00574280
$746$	−7125.09	−0.349689
$747$	−2539.85	−0.124402
$748$	6217.00	0.303898
$749$	17923.8	0.874395
$750$	37709.6	1.83595
$751$	−18089.5	−0.878954	−0.439477	−	0.898254i	$-0.644836\pi$
$751$	−18089.5	−0.878954	−0.439477	+	0.898254i	$0.644836\pi$
$752$	8143.57	0.394901
$753$	−25876.7	−1.25232
$754$	−2101.96	−0.101524
$755$	22384.4	1.07901
$756$	47800.0	2.29956
$757$	−24935.6	−1.19722	−0.598612	−	0.801039i	$-0.704281\pi$
$757$	−24935.6	−1.19722	−0.598612	+	0.801039i	$0.704281\pi$
$758$	923.342	0.0442444
$759$	−16330.1	−0.780955
$760$	−19937.8	−0.951605
$761$	1982.92	0.0944556	0.0472278	−	0.998884i	$-0.484961\pi$
$761$	1982.92	0.0944556	0.0472278	+	0.998884i	$0.484961\pi$
$762$	−46499.5	−2.21063
$763$	37565.2	1.78237
$764$	54072.4	2.56057
$765$	−543.223	−0.0256735
$766$	12799.6	0.603744
$767$	−358.860	−0.0168940
$768$	12161.2	0.571393
$769$	−8136.59	−0.381551	−0.190776	−	0.981634i	$-0.561100\pi$
$769$	−8136.59	−0.381551	−0.190776	+	0.981634i	$0.561100\pi$
$770$	83556.9	3.91063
$771$	18294.8	0.854568
$772$	−57855.0	−2.69721
$773$	−36988.0	−1.72104	−0.860522	−	0.509414i	$-0.829862\pi$
$773$	−36988.0	−1.72104	−0.860522	+	0.509414i	$0.829862\pi$
$774$	−2590.98	−0.120324
$775$	1011.54	0.0468845
$776$	1235.87	0.0571714
$777$	58932.7	2.72098
$778$	10088.1	0.464878
$779$	−41999.7	−1.93170
$780$	−2041.57	−0.0937178
$781$	−33894.8	−1.55295
$782$	−2180.98	−0.0997337
$783$	−19797.2	−0.903568
$784$	−12799.9	−0.583085
$785$	−18319.3	−0.832921
$786$	31352.2	1.42277
$787$	−2077.02	−0.0940759	−0.0470380	−	0.998893i	$-0.514978\pi$
$787$	−2077.02	−0.0940759	−0.0470380	+	0.998893i	$0.514978\pi$
$788$	−41576.8	−1.87958
$789$	27017.3	1.21907
$790$	−24706.9	−1.11270
$791$	63890.9	2.87193
$792$	−5374.65	−0.241136
$793$	57.6201	0.00258026
$794$	32870.0	1.46916
$795$	16820.4	0.750389
$796$	26701.4	1.18895
$797$	−17824.8	−0.792204	−0.396102	−	0.918206i	$-0.629637\pi$
$797$	−17824.8	−0.792204	−0.396102	+	0.918206i	$0.629637\pi$
$798$	−92541.2	−4.10517
$799$	−4410.69	−0.195293
$800$	−4012.68	−0.177337
$801$	−1761.23	−0.0776905
$802$	−2902.54	−0.127796
$803$	−39298.1	−1.72702
$804$	−59484.4	−2.60927
$805$	−17534.4	−0.767710
$806$	−711.441	−0.0310911
$807$	22060.8	0.962302
$808$	−25724.6	−1.12003
$809$	785.015	0.0341158	0.0170579	−	0.999855i	$-0.494570\pi$
$809$	785.015	0.0341158	0.0170579	+	0.999855i	$0.494570\pi$
$810$	−39074.8	−1.69500
$811$	−14206.0	−0.615092	−0.307546	−	0.951533i	$-0.599508\pi$
$811$	−14206.0	−0.615092	−0.307546	+	0.951533i	$0.599508\pi$
$812$	−63278.5	−2.73478
$813$	30337.3	1.30870
$814$	77603.6	3.34153
$815$	29335.9	1.26085
$816$	939.669	0.0403125
$817$	−11536.2	−0.494002
$818$	−8718.80	−0.372672
$819$	−532.251	−0.0227086
$820$	−46630.5	−1.98586
$821$	−17779.1	−0.755780	−0.377890	−	0.925851i	$-0.623350\pi$
$821$	−17779.1	−0.755780	−0.377890	+	0.925851i	$0.623350\pi$
$822$	−49706.6	−2.10914
$823$	38036.5	1.61102	0.805510	−	0.592583i	$-0.201892\pi$
$823$	38036.5	1.61102	0.805510	+	0.592583i	$0.201892\pi$
$824$	−2965.13	−0.125358
$825$	5824.25	0.245787
$826$	−18060.1	−0.760763
$827$	27945.2	1.17503	0.587515	−	0.809213i	$-0.300106\pi$
$827$	27945.2	1.17503	0.587515	+	0.809213i	$0.300106\pi$
$828$	3435.66	0.144200
$829$	8714.87	0.365115	0.182557	−	0.983195i	$-0.441562\pi$
$829$	8714.87	0.365115	0.182557	+	0.983195i	$0.441562\pi$
$830$	−20989.0	−0.877757
$831$	−19818.9	−0.827327
$832$	2416.35	0.100687
$833$	6932.62	0.288357
$834$	−59360.5	−2.46461
$835$	25888.5	1.07294
$836$	−72895.0	−3.01570
$837$	−6700.67	−0.276713
$838$	13916.0	0.573654
$839$	−17155.4	−0.705924	−0.352962	−	0.935638i	$-0.614826\pi$
$839$	−17155.4	−0.705924	−0.352962	+	0.935638i	$0.614826\pi$
$840$	−33729.4	−1.38544
$841$	1818.90	0.0745787
$842$	−41664.0	−1.70527
$843$	14786.4	0.604116
$844$	−58931.2	−2.40343
$845$	22589.6	0.919650
$846$	11615.2	0.472032
$847$	56605.7	2.29633
$848$	−4978.28	−0.201598
$849$	8438.26	0.341108
$850$	777.863	0.0313888
$851$	−16285.1	−0.655989
$852$	41678.2	1.67591
$853$	−12274.2	−0.492685	−0.246342	−	0.969183i	$-0.579229\pi$
$853$	−12274.2	−0.492685	−0.246342	+	0.969183i	$0.579229\pi$
$854$	2899.80	0.116193
$855$	6369.35	0.254769
$856$	−9527.55	−0.380426
$857$	−7027.38	−0.280106	−0.140053	−	0.990144i	$-0.544727\pi$
$857$	−7027.38	−0.280106	−0.140053	+	0.990144i	$0.544727\pi$
$858$	−4096.35	−0.162992
$859$	23043.6	0.915292	0.457646	−	0.889134i	$-0.348693\pi$
$859$	23043.6	0.915292	0.457646	+	0.889134i	$0.348693\pi$
$860$	−12808.1	−0.507852
$861$	−71052.2	−2.81237
$862$	67487.2	2.66662
$863$	15303.3	0.603628	0.301814	−	0.953367i	$-0.402408\pi$
$863$	15303.3	0.603628	0.301814	+	0.953367i	$0.402408\pi$
$864$	26580.9	1.04665
$865$	−25740.0	−1.01177
$866$	−71445.4	−2.80348
$867$	27531.0	1.07843
$868$	−21417.6	−0.837512
$869$	−29654.3	−1.15760
$870$	42553.4	1.65827
$871$	−2546.50	−0.0990641
$872$	−19968.1	−0.775463
$873$	−394.811	−0.0153062
$874$	25572.3	0.989697
$875$	48598.6	1.87764
$876$	48322.3	1.86376
$877$	35190.6	1.35496	0.677480	−	0.735541i	$-0.263072\pi$
$877$	35190.6	1.35496	0.677480	+	0.735541i	$0.263072\pi$
$878$	44900.2	1.72586
$879$	−42665.3	−1.63716
$880$	9948.08	0.381079
$881$	−24727.9	−0.945635	−0.472818	−	0.881160i	$-0.656763\pi$
$881$	−24727.9	−0.945635	−0.472818	+	0.881160i	$0.656763\pi$
$882$	−18256.5	−0.696971
$883$	−20288.2	−0.773219	−0.386609	−	0.922244i	$-0.626354\pi$
$883$	−20288.2	−0.773219	−0.386609	+	0.922244i	$0.626354\pi$
$884$	−327.263	−0.0124514
$885$	7264.99	0.275943
$886$	17543.8	0.665232
$887$	−7075.42	−0.267835	−0.133917	−	0.990993i	$-0.542756\pi$
$887$	−7075.42	−0.267835	−0.133917	+	0.990993i	$0.542756\pi$
$888$	−31326.2	−1.18383
$889$	−59926.7	−2.26083
$890$	−14554.6	−0.548169
$891$	−46899.4	−1.76340
$892$	51736.8	1.94201
$893$	51715.9	1.93797
$894$	288.116	0.0107786
$895$	−3185.97	−0.118989
$896$	64535.6	2.40623
$897$	859.618	0.0319976
$898$	−4913.65	−0.182596
$899$	8870.47	0.329084
$900$	−1225.35	−0.0453834
$901$	2696.31	0.0996973
$902$	−93562.7	−3.45377
$903$	−19516.1	−0.719219
$904$	−33961.8	−1.24950
$905$	−25030.4	−0.919380
$906$	−55227.3	−2.02517
$907$	−33322.0	−1.21989	−0.609943	−	0.792445i	$-0.708808\pi$
$907$	−33322.0	−1.21989	−0.609943	+	0.792445i	$0.708808\pi$
$908$	4318.90	0.157850
$909$	8218.00	0.299861
$910$	−4398.44	−0.160227
$911$	12674.4	0.460945	0.230472	−	0.973079i	$-0.425973\pi$
$911$	12674.4	0.460945	0.230472	+	0.973079i	$0.425973\pi$
$912$	−11017.7	−0.400037
$913$	−25192.0	−0.913178
$914$	44298.6	1.60314
$915$	−1166.50	−0.0421456
$916$	−32327.4	−1.16608
$917$	40405.5	1.45508
$918$	−5152.75	−0.185257
$919$	38442.0	1.37985	0.689926	−	0.723880i	$-0.257643\pi$
$919$	38442.0	1.37985	0.689926	+	0.723880i	$0.257643\pi$
$920$	9320.56	0.334011
$921$	8071.42	0.288776
$922$	6749.06	0.241072
$923$	1784.23	0.0636279
$924$	−123319.	−4.39057
$925$	5808.20	0.206457
$926$	−38247.2	−1.35732
$927$	947.243	0.0335615
$928$	−35188.4	−1.24474
$929$	−3869.62	−0.136661	−0.0683305	−	0.997663i	$-0.521767\pi$
$929$	−3869.62	−0.136661	−0.0683305	+	0.997663i	$0.521767\pi$
$930$	14402.9	0.507837
$931$	−81285.8	−2.86148
$932$	−65055.6	−2.28644
$933$	−26948.0	−0.945593
$934$	65942.4	2.31017
$935$	−5388.04	−0.188458
$936$	282.922	0.00987992
$937$	−1018.02	−0.0354933	−0.0177467	−	0.999843i	$-0.505649\pi$
$937$	−1018.02	−0.0354933	−0.0177467	+	0.999843i	$0.505649\pi$
$938$	−128156.	−4.46101
$939$	49450.4	1.71859
$940$	57417.9	1.99230
$941$	52160.0	1.80698	0.903489	−	0.428610i	$-0.140997\pi$
$941$	52160.0	1.80698	0.903489	+	0.428610i	$0.140997\pi$
$942$	45197.8	1.56330
$943$	19634.1	0.678022
$944$	−2150.19	−0.0741342
$945$	−41426.5	−1.42604
$946$	−25699.1	−0.883245
$947$	1706.03	0.0585411	0.0292705	−	0.999572i	$-0.490682\pi$
$947$	1706.03	0.0585411	0.0292705	+	0.999572i	$0.490682\pi$
$948$	36464.0	1.24926
$949$	2068.65	0.0707601
$950$	−9120.54	−0.311483
$951$	30100.1	1.02635
$952$	−5406.81	−0.184071
$953$	−12115.9	−0.411829	−0.205915	−	0.978570i	$-0.566017\pi$
$953$	−12115.9	−0.411829	−0.205915	+	0.978570i	$0.566017\pi$
$954$	−7100.53	−0.240973
$955$	−46862.6	−1.58789
$956$	46926.1	1.58755
$957$	51074.6	1.72519
$958$	36206.4	1.22106
$959$	−64059.9	−2.15704
$960$	−48918.1	−1.64461
$961$	−26788.7	−0.899220
$962$	−4085.06	−0.136910
$963$	3043.68	0.101850
$964$	77421.2	2.58669
$965$	50140.8	1.67263
$966$	43261.4	1.44090
$967$	−24059.0	−0.800088	−0.400044	−	0.916496i	$-0.631005\pi$
$967$	−24059.0	−0.800088	−0.400044	+	0.916496i	$0.631005\pi$
$968$	−30089.2	−0.999074
$969$	5967.38	0.197833
$970$	−3262.66	−0.107998
$971$	−34143.9	−1.12846	−0.564228	−	0.825619i	$-0.690826\pi$
$971$	−34143.9	−1.12846	−0.564228	+	0.825619i	$0.690826\pi$
$972$	18345.3	0.605377
$973$	−76501.5	−2.52058
$974$	38441.2	1.26462
$975$	−306.589	−0.0100705
$976$	345.244	0.0113227
$977$	10022.0	0.328181	0.164091	−	0.986445i	$-0.447531\pi$
$977$	10022.0	0.328181	0.164091	+	0.986445i	$0.447531\pi$
$978$	−72378.2	−2.36646
$979$	−17469.1	−0.570290
$980$	−90248.1	−2.94170
$981$	6379.02	0.207611
$982$	23187.9	0.753519
$983$	983.000	0.0318950
$983$	983.000	0.0318950
$984$	37768.4	1.22359
$985$	36033.1	1.16559
$986$	6821.31	0.220319
$987$	87489.2	2.82149
$988$	3837.20	0.123560
$989$	5392.96	0.173393
$990$	14189.0	0.455511
$991$	49079.5	1.57322	0.786610	−	0.617450i	$-0.211834\pi$
$991$	49079.5	1.57322	0.786610	+	0.617450i	$0.211834\pi$
$992$	−11910.0	−0.381194
$993$	−42972.2	−1.37330
$994$	89793.4	2.86527
$995$	−23141.1	−0.737309
$996$	30976.9	0.985483
$997$	−52518.0	−1.66827	−0.834134	−	0.551563i	$-0.814032\pi$
$997$	−52518.0	−1.66827	−0.834134	+	0.551563i	$0.814032\pi$
$998$	−37089.4	−1.17640
$999$	−38474.9	−1.21851

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.a.1.16	✓	109

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.a.1.16	✓	109	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 983 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	983.a (trivial)

\(f(q)\)	\(=\)	\(q-4.46204 q^{2} -5.70729 q^{3} +11.9098 q^{4} -10.3218 q^{5} +25.4662 q^{6} +32.8198 q^{7} -17.4456 q^{8} +5.57321 q^{9} +O(q^{10})\)	\(q-4.46204 q^{2} -5.70729 q^{3} +11.9098 q^{4} -10.3218 q^{5} +25.4662 q^{6} +32.8198 q^{7} -17.4456 q^{8} +5.57321 q^{9} +46.0562 q^{10} +55.2787 q^{11} -67.9727 q^{12} -2.90988 q^{13} -146.443 q^{14} +58.9094 q^{15} -17.4352 q^{16} +9.44318 q^{17} -24.8679 q^{18} -110.722 q^{19} -122.930 q^{20} -187.312 q^{21} -246.656 q^{22} +51.7607 q^{23} +99.5674 q^{24} -18.4608 q^{25} +12.9840 q^{26} +122.289 q^{27} +390.877 q^{28} -161.889 q^{29} -262.856 q^{30} -54.7937 q^{31} +217.362 q^{32} -315.492 q^{33} -42.1358 q^{34} -338.759 q^{35} +66.3757 q^{36} -314.623 q^{37} +494.048 q^{38} +16.6075 q^{39} +180.070 q^{40} +379.325 q^{41} +835.795 q^{42} +104.190 q^{43} +658.358 q^{44} -57.5254 q^{45} -230.958 q^{46} -467.077 q^{47} +99.5077 q^{48} +734.140 q^{49} +82.3730 q^{50} -53.8950 q^{51} -34.6561 q^{52} +285.530 q^{53} -545.658 q^{54} -570.575 q^{55} -572.563 q^{56} +631.925 q^{57} +722.353 q^{58} +123.325 q^{59} +701.599 q^{60} -19.8015 q^{61} +244.492 q^{62} +182.912 q^{63} -830.395 q^{64} +30.0351 q^{65} +1407.74 q^{66} +875.121 q^{67} +112.466 q^{68} -295.414 q^{69} +1511.56 q^{70} -613.162 q^{71} -97.2282 q^{72} -710.907 q^{73} +1403.86 q^{74} +105.361 q^{75} -1318.68 q^{76} +1814.24 q^{77} -74.1035 q^{78} -536.451 q^{79} +179.962 q^{80} -848.416 q^{81} -1692.56 q^{82} -455.726 q^{83} -2230.85 q^{84} -97.4704 q^{85} -464.900 q^{86} +923.946 q^{87} -964.373 q^{88} -316.018 q^{89} +256.681 q^{90} -95.5017 q^{91} +616.460 q^{92} +312.724 q^{93} +2084.11 q^{94} +1142.85 q^{95} -1240.55 q^{96} -70.8410 q^{97} -3275.76 q^{98} +308.080 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9}+O(q^{10}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9	\( 109 q - 19 q^{2} - 23 q^{3} + 385 q^{4} - 50 q^{5} - 83 q^{6} - 225 q^{7} - 225 q^{8} + 714 q^{9} - 243 q^{10} - 126 q^{11} - 280 q^{12} - 458 q^{13} - 177 q^{14} - 314 q^{15} + 1009 q^{16} - 594 q^{17} - 671 q^{18} - 491 q^{19} - 500 q^{20} - 660 q^{21} - 899 q^{22} - 487 q^{23} - 811 q^{24} + 705 q^{25} - 104 q^{26} - 842 q^{27} - 2648 q^{28} - 820 q^{29} - 728 q^{30} - 965 q^{31} - 1669 q^{32} - 2196 q^{33} - 508 q^{34} - 846 q^{35} + 1358 q^{36} - 3209 q^{37} - 1136 q^{38} - 1326 q^{39} - 3234 q^{40} - 1961 q^{41} - 2240 q^{42} - 2999 q^{43} - 1922 q^{44} - 2234 q^{45} - 2962 q^{46} - 1903 q^{47} - 2787 q^{48} + 1186 q^{49} - 2309 q^{50} - 2436 q^{51} - 4897 q^{52} - 1825 q^{53} - 3306 q^{54} - 2888 q^{55} - 1820 q^{56} - 6684 q^{57} - 4813 q^{58} - 1537 q^{59} - 3869 q^{60} - 2276 q^{61} - 1950 q^{62} - 6491 q^{63} - 89 q^{64} - 5546 q^{65} - 3527 q^{66} - 5005 q^{67} - 4183 q^{68} - 3018 q^{69} - 2993 q^{70} - 2014 q^{71} - 9549 q^{72} - 12904 q^{73} - 2714 q^{74} - 3379 q^{75} - 6293 q^{76} - 3258 q^{77} - 4593 q^{78} - 5005 q^{79} - 3988 q^{80} + 249 q^{81} - 5116 q^{82} - 2854 q^{83} - 4158 q^{84} - 11742 q^{85} - 2709 q^{86} - 2412 q^{87} - 10451 q^{88} - 2519 q^{89} - 8095 q^{90} - 2438 q^{91} - 6660 q^{92} - 10668 q^{93} - 4281 q^{94} - 4482 q^{95} - 6515 q^{96} - 16628 q^{97} - 5708 q^{98} - 6308 q^{99}+O(q^{100}) \) 109 * q - 19 * q^2 - 23 * q^3 + 385 * q^4 - 50 * q^5 - 83 * q^6 - 225 * q^7 - 225 * q^8 + 714 * q^9 - 243 * q^10 - 126 * q^11 - 280 * q^12 - 458 * q^13 - 177 * q^14 - 314 * q^15 + 1009 * q^16 - 594 * q^17 - 671 * q^18 - 491 * q^19 - 500 * q^20 - 660 * q^21 - 899 * q^22 - 487 * q^23 - 811 * q^24 + 705 * q^25 - 104 * q^26 - 842 * q^27 - 2648 * q^28 - 820 * q^29 - 728 * q^30 - 965 * q^31 - 1669 * q^32 - 2196 * q^33 - 508 * q^34 - 846 * q^35 + 1358 * q^36 - 3209 * q^37 - 1136 * q^38 - 1326 * q^39 - 3234 * q^40 - 1961 * q^41 - 2240 * q^42 - 2999 * q^43 - 1922 * q^44 - 2234 * q^45 - 2962 * q^46 - 1903 * q^47 - 2787 * q^48 + 1186 * q^49 - 2309 * q^50 - 2436 * q^51 - 4897 * q^52 - 1825 * q^53 - 3306 * q^54 - 2888 * q^55 - 1820 * q^56 - 6684 * q^57 - 4813 * q^58 - 1537 * q^59 - 3869 * q^60 - 2276 * q^61 - 1950 * q^62 - 6491 * q^63 - 89 * q^64 - 5546 * q^65 - 3527 * q^66 - 5005 * q^67 - 4183 * q^68 - 3018 * q^69 - 2993 * q^70 - 2014 * q^71 - 9549 * q^72 - 12904 * q^73 - 2714 * q^74 - 3379 * q^75 - 6293 * q^76 - 3258 * q^77 - 4593 * q^78 - 5005 * q^79 - 3988 * q^80 + 249 * q^81 - 5116 * q^82 - 2854 * q^83 - 4158 * q^84 - 11742 * q^85 - 2709 * q^86 - 2412 * q^87 - 10451 * q^88 - 2519 * q^89 - 8095 * q^90 - 2438 * q^91 - 6660 * q^92 - 10668 * q^93 - 4281 * q^94 - 4482 * q^95 - 6515 * q^96 - 16628 * q^97 - 5708 * q^98 - 6308 * q^99

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