LMFDB - Embedded newform 983.4.a.b.1.2

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			1.2
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)

$f(q)$	$=$	$q-5.46364 q^{2} +9.02325 q^{3} +21.8513 q^{4} +10.0186 q^{5} -49.2998 q^{6} +33.9408 q^{7} -75.6787 q^{8} +54.4191 q^{9} +O(q^{10})$	\(q-5.46364 q^{2} +9.02325 q^{3} +21.8513 q^{4} +10.0186 q^{5} -49.2998 q^{6} +33.9408 q^{7} -75.6787 q^{8} +54.4191 q^{9} -54.7380 q^{10} +44.2392 q^{11} +197.170 q^{12} -52.0613 q^{13} -185.440 q^{14} +90.4003 q^{15} +238.670 q^{16} -23.1115 q^{17} -297.326 q^{18} +62.4046 q^{19} +218.920 q^{20} +306.257 q^{21} -241.707 q^{22} -57.0386 q^{23} -682.868 q^{24} -24.6277 q^{25} +284.444 q^{26} +247.410 q^{27} +741.652 q^{28} -73.7990 q^{29} -493.915 q^{30} -272.556 q^{31} -698.577 q^{32} +399.181 q^{33} +126.273 q^{34} +340.039 q^{35} +1189.13 q^{36} -49.7278 q^{37} -340.956 q^{38} -469.762 q^{39} -758.194 q^{40} +299.261 q^{41} -1673.28 q^{42} +305.607 q^{43} +966.685 q^{44} +545.203 q^{45} +311.638 q^{46} -256.320 q^{47} +2153.58 q^{48} +808.979 q^{49} +134.557 q^{50} -208.541 q^{51} -1137.61 q^{52} +337.993 q^{53} -1351.76 q^{54} +443.214 q^{55} -2568.60 q^{56} +563.093 q^{57} +403.211 q^{58} -240.201 q^{59} +1975.37 q^{60} +560.932 q^{61} +1489.15 q^{62} +1847.03 q^{63} +1907.41 q^{64} -521.581 q^{65} -2180.98 q^{66} +920.050 q^{67} -505.016 q^{68} -514.674 q^{69} -1857.85 q^{70} -631.609 q^{71} -4118.37 q^{72} +1195.66 q^{73} +271.694 q^{74} -222.222 q^{75} +1363.62 q^{76} +1501.51 q^{77} +2566.61 q^{78} +732.714 q^{79} +2391.14 q^{80} +763.125 q^{81} -1635.05 q^{82} -497.285 q^{83} +6692.12 q^{84} -231.545 q^{85} -1669.73 q^{86} -665.907 q^{87} -3347.96 q^{88} -1316.30 q^{89} -2978.79 q^{90} -1767.00 q^{91} -1246.37 q^{92} -2459.34 q^{93} +1400.44 q^{94} +625.206 q^{95} -6303.44 q^{96} +275.311 q^{97} -4419.97 q^{98} +2407.46 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−5.46364	−1.93169	−0.965844	−	0.259125i	$-0.916566\pi$
$2$	−5.46364	−1.93169	−0.965844	+	0.259125i	$0.916566\pi$
$3$	9.02325	1.73653	0.868263	−	0.496104i	$-0.165237\pi$
$3$	9.02325	1.73653	0.868263	+	0.496104i	$0.165237\pi$
$4$	21.8513	2.73142
$5$	10.0186	0.896090	0.448045	−	0.894011i	$-0.352120\pi$
$5$	10.0186	0.896090	0.448045	+	0.894011i	$0.352120\pi$
$6$	−49.2998	−3.35443
$7$	33.9408	1.83263	0.916316	−	0.400456i	$-0.131148\pi$
$7$	33.9408	1.83263	0.916316	+	0.400456i	$0.131148\pi$
$8$	−75.6787	−3.34456
$9$	54.4191	2.01552
$10$	−54.7380	−1.73097
$11$	44.2392	1.21260	0.606300	−	0.795236i	$-0.292653\pi$
$11$	44.2392	1.21260	0.606300	+	0.795236i	$0.292653\pi$
$12$	197.170	4.74318
$13$	−52.0613	−1.11071	−0.555354	−	0.831614i	$-0.687417\pi$
$13$	−52.0613	−1.11071	−0.555354	+	0.831614i	$0.687417\pi$
$14$	−185.440	−3.54007
$15$	90.4003	1.55608
$16$	238.670	3.72922
$17$	−23.1115	−0.329727	−0.164863	−	0.986316i	$-0.552718\pi$
$17$	−23.1115	−0.329727	−0.164863	+	0.986316i	$0.552718\pi$
$18$	−297.326	−3.89336
$19$	62.4046	0.753505	0.376752	−	0.926314i	$-0.377041\pi$
$19$	62.4046	0.753505	0.376752	+	0.926314i	$0.377041\pi$
$20$	218.920	2.44760
$21$	306.257	3.18241
$22$	−241.707	−2.34237
$23$	−57.0386	−0.517103	−0.258552	−	0.965997i	$-0.583245\pi$
$23$	−57.0386	−0.517103	−0.258552	+	0.965997i	$0.583245\pi$
$24$	−682.868	−5.80791
$25$	−24.6277	−0.197022
$26$	284.444	2.14554
$27$	247.410	1.76348
$28$	741.652	5.00568
$29$	−73.7990	−0.472556	−0.236278	−	0.971685i	$-0.575928\pi$
$29$	−73.7990	−0.472556	−0.236278	+	0.971685i	$0.575928\pi$
$30$	−493.915	−3.00587
$31$	−272.556	−1.57911	−0.789557	−	0.613677i	$-0.789690\pi$
$31$	−272.556	−1.57911	−0.789557	+	0.613677i	$0.789690\pi$
$32$	−698.577	−3.85913
$33$	399.181	2.10571
$34$	126.273	0.636929
$35$	340.039	1.64220
$36$	1189.13	5.50523
$37$	−49.7278	−0.220951	−0.110476	−	0.993879i	$-0.535237\pi$
$37$	−49.7278	−0.220951	−0.110476	+	0.993879i	$0.535237\pi$
$38$	−340.956	−1.45554
$39$	−469.762	−1.92877
$40$	−758.194	−2.99702
$41$	299.261	1.13992	0.569960	−	0.821673i	$-0.306959\pi$
$41$	299.261	1.13992	0.569960	+	0.821673i	$0.306959\pi$
$42$	−1673.28	−6.14743
$43$	305.607	1.08383	0.541915	−	0.840433i	$-0.317699\pi$
$43$	305.607	1.08383	0.541915	+	0.840433i	$0.317699\pi$
$44$	966.685	3.31212
$45$	545.203	1.80609
$46$	311.638	0.998882
$47$	−256.320	−0.795491	−0.397746	−	0.917496i	$-0.630207\pi$
$47$	−256.320	−0.795491	−0.397746	+	0.917496i	$0.630207\pi$
$48$	2153.58	6.47589
$49$	808.979	2.35854
$50$	134.557	0.380585
$51$	−208.541	−0.572579
$52$	−1137.61	−3.03381
$53$	337.993	0.875980	0.437990	−	0.898980i	$-0.355691\pi$
$53$	337.993	0.875980	0.437990	+	0.898980i	$0.355691\pi$
$54$	−1351.76	−3.40650
$55$	443.214	1.08660
$56$	−2568.60	−6.12934
$57$	563.093	1.30848
$58$	403.211	0.912831
$59$	−240.201	−0.530026	−0.265013	−	0.964245i	$-0.585376\pi$
$59$	−240.201	−0.530026	−0.265013	+	0.964245i	$0.585376\pi$
$60$	1975.37	4.25032
$61$	560.932	1.17738	0.588688	−	0.808360i	$-0.299644\pi$
$61$	560.932	1.17738	0.588688	+	0.808360i	$0.299644\pi$
$62$	1489.15	3.05035
$63$	1847.03	3.69371
$64$	1907.41	3.72542
$65$	−521.581	−0.995295
$66$	−2180.98	−4.06758
$67$	920.050	1.67764	0.838821	−	0.544408i	$-0.183245\pi$
$67$	920.050	1.67764	0.838821	+	0.544408i	$0.183245\pi$
$68$	−505.016	−0.900621
$69$	−514.674	−0.897963
$70$	−1857.85	−3.17222
$71$	−631.609	−1.05575	−0.527875	−	0.849322i	$-0.677011\pi$
$71$	−631.609	−1.05575	−0.527875	+	0.849322i	$0.677011\pi$
$72$	−4118.37	−6.74103
$73$	1195.66	1.91700	0.958502	−	0.285086i	$-0.0920221\pi$
$73$	1195.66	1.91700	0.958502	+	0.285086i	$0.0920221\pi$
$74$	271.694	0.426809
$75$	−222.222	−0.342134
$76$	1363.62	2.05814
$77$	1501.51	2.22225
$78$	2566.61	3.72579
$79$	732.714	1.04350	0.521752	−	0.853097i	$-0.325279\pi$
$79$	732.714	1.04350	0.521752	+	0.853097i	$0.325279\pi$
$80$	2391.14	3.34172
$81$	763.125	1.04681
$82$	−1635.05	−2.20197
$83$	−497.285	−0.657640	−0.328820	−	0.944393i	$-0.606651\pi$
$83$	−497.285	−0.657640	−0.328820	+	0.944393i	$0.606651\pi$
$84$	6692.12	8.69250
$85$	−231.545	−0.295465
$86$	−1669.73	−2.09362
$87$	−665.907	−0.820606
$88$	−3347.96	−4.05561
$89$	−1316.30	−1.56772	−0.783862	−	0.620935i	$-0.786753\pi$
$89$	−1316.30	−1.56772	−0.783862	+	0.620935i	$0.786753\pi$
$90$	−2978.79	−3.48880
$91$	−1767.00	−2.03552
$92$	−1246.37	−1.41242
$93$	−2459.34	−2.74217
$94$	1400.44	1.53664
$95$	625.206	0.675209
$96$	−6303.44	−6.70148
$97$	275.311	0.288181	0.144091	−	0.989565i	$-0.453974\pi$
$97$	275.311	0.288181	0.144091	+	0.989565i	$0.453974\pi$
$98$	−4419.97	−4.55596
$99$	2407.46	2.44402
$100$	−538.149	−0.538149
$101$	−1002.24	−0.987390	−0.493695	−	0.869635i	$-0.664354\pi$
$101$	−1002.24	−0.987390	−0.493695	+	0.869635i	$0.664354\pi$
$102$	1139.39	1.10604
$103$	−818.722	−0.783214	−0.391607	−	0.920132i	$-0.628081\pi$
$103$	−818.722	−0.783214	−0.391607	+	0.920132i	$0.628081\pi$
$104$	3939.93	3.71483
$105$	3068.26	2.85173
$106$	−1846.67	−1.69212
$107$	1878.99	1.69765	0.848825	−	0.528674i	$-0.177311\pi$
$107$	1878.99	1.69765	0.848825	+	0.528674i	$0.177311\pi$
$108$	5406.23	4.81681
$109$	−1508.45	−1.32553	−0.662766	−	0.748826i	$-0.730618\pi$
$109$	−1508.45	−1.32553	−0.662766	+	0.748826i	$0.730618\pi$
$110$	−2421.56	−2.09897
$111$	−448.706	−0.383688
$112$	8100.66	6.83429
$113$	540.940	0.450331	0.225165	−	0.974321i	$-0.427708\pi$
$113$	540.940	0.450331	0.225165	+	0.974321i	$0.427708\pi$
$114$	−3076.53	−2.52758
$115$	−571.447	−0.463371
$116$	−1612.61	−1.29075
$117$	−2833.13	−2.23866
$118$	1312.37	1.02384
$119$	−784.422	−0.604268
$120$	−6841.38	−5.20441
$121$	626.103	0.470401
$122$	−3064.73	−2.27432
$123$	2700.31	1.97950
$124$	−5955.72	−4.31322
$125$	−1499.06	−1.07264
$126$	−10091.5	−7.13510
$127$	−893.216	−0.624095	−0.312048	−	0.950066i	$-0.601015\pi$
$127$	−893.216	−0.624095	−0.312048	+	0.950066i	$0.601015\pi$
$128$	−4832.79	−3.33721
$129$	2757.57	1.88210
$130$	2849.73	1.92260
$131$	−2340.95	−1.56130	−0.780648	−	0.624971i	$-0.785111\pi$
$131$	−2340.95	−1.56130	−0.780648	+	0.624971i	$0.785111\pi$
$132$	8722.64	5.75158
$133$	2118.06	1.38090
$134$	−5026.82	−3.24068
$135$	2478.70	1.58024
$136$	1749.04	1.10279
$137$	−1105.67	−0.689513	−0.344757	−	0.938692i	$-0.612039\pi$
$137$	−1105.67	−0.689513	−0.344757	+	0.938692i	$0.612039\pi$
$138$	2811.99	1.73458
$139$	603.880	0.368492	0.184246	−	0.982880i	$-0.441016\pi$
$139$	603.880	0.368492	0.184246	+	0.982880i	$0.441016\pi$
$140$	7430.31	4.48554
$141$	−2312.84	−1.38139
$142$	3450.88	2.03938
$143$	−2303.15	−1.34685
$144$	12988.2	7.51633
$145$	−739.362	−0.423453
$146$	−6532.65	−3.70305
$147$	7299.62	4.09567
$148$	−1086.62	−0.603510
$149$	710.567	0.390684	0.195342	−	0.980735i	$-0.437418\pi$
$149$	710.567	0.390684	0.195342	+	0.980735i	$0.437418\pi$
$150$	1214.14	0.660895
$151$	2150.67	1.15906	0.579532	−	0.814949i	$-0.303235\pi$
$151$	2150.67	1.15906	0.579532	+	0.814949i	$0.303235\pi$
$152$	−4722.70	−2.52014
$153$	−1257.71	−0.664572
$154$	−8203.72	−4.29269
$155$	−2730.63	−1.41503
$156$	−10264.9	−5.26829
$157$	−725.041	−0.368564	−0.184282	−	0.982873i	$-0.558996\pi$
$157$	−725.041	−0.368564	−0.184282	+	0.982873i	$0.558996\pi$
$158$	−4003.28	−2.01572
$159$	3049.80	1.52116
$160$	−6998.76	−3.45813
$161$	−1935.94	−0.947660
$162$	−4169.44	−2.02211
$163$	2226.36	1.06983	0.534914	−	0.844906i	$-0.320344\pi$
$163$	2226.36	1.06983	0.534914	+	0.844906i	$0.320344\pi$
$164$	6539.25	3.11360
$165$	3999.24	1.88691
$166$	2716.99	1.27036
$167$	−624.146	−0.289209	−0.144604	−	0.989490i	$-0.546191\pi$
$167$	−624.146	−0.289209	−0.144604	+	0.989490i	$0.546191\pi$
$168$	−23177.1	−10.6438
$169$	513.380	0.233673
$170$	1265.08	0.570746
$171$	3396.00	1.51871
$172$	6677.93	2.96039
$173$	−2504.57	−1.10069	−0.550345	−	0.834937i	$-0.685504\pi$
$173$	−2504.57	−1.10069	−0.550345	+	0.834937i	$0.685504\pi$
$174$	3638.28	1.58515
$175$	−835.885	−0.361068
$176$	10558.6	4.52205
$177$	−2167.40	−0.920404
$178$	7191.78	3.02835
$179$	3110.22	1.29871	0.649354	−	0.760486i	$-0.275039\pi$
$179$	3110.22	1.29871	0.649354	+	0.760486i	$0.275039\pi$
$180$	11913.4	4.93319
$181$	−4289.16	−1.76139	−0.880693	−	0.473688i	$-0.842922\pi$
$181$	−4289.16	−1.76139	−0.880693	+	0.473688i	$0.842922\pi$
$182$	9654.27	3.93199
$183$	5061.43	2.04455
$184$	4316.61	1.72948
$185$	−498.202	−0.197992
$186$	13437.0	5.29702
$187$	−1022.43	−0.399827
$188$	−5600.93	−2.17282
$189$	8397.29	3.23181
$190$	−3415.90	−1.30429
$191$	−2261.33	−0.856670	−0.428335	−	0.903620i	$-0.640900\pi$
$191$	−2261.33	−0.856670	−0.428335	+	0.903620i	$0.640900\pi$
$192$	17211.1	6.46928
$193$	1978.98	0.738085	0.369042	−	0.929413i	$-0.379686\pi$
$193$	1978.98	0.738085	0.369042	+	0.929413i	$0.379686\pi$
$194$	−1504.20	−0.556676
$195$	−4706.36	−1.72836
$196$	17677.3	6.44215
$197$	2170.94	0.785141	0.392571	−	0.919722i	$-0.371586\pi$
$197$	2170.94	0.785141	0.392571	+	0.919722i	$0.371586\pi$
$198$	−13153.5	−4.72109
$199$	−177.712	−0.0633048	−0.0316524	−	0.999499i	$-0.510077\pi$
$199$	−177.712	−0.0633048	−0.0316524	+	0.999499i	$0.510077\pi$
$200$	1863.79	0.658950
$201$	8301.85	2.91327
$202$	5475.87	1.90733
$203$	−2504.80	−0.866022
$204$	−4556.89	−1.56395
$205$	2998.17	1.02147
$206$	4473.20	1.51293
$207$	−3103.99	−1.04223
$208$	−12425.5	−4.14208
$209$	2760.73	0.913701
$210$	−16763.9	−5.50865
$211$	6097.13	1.98931	0.994653	−	0.103276i	$-0.0329326\pi$
$211$	6097.13	1.98931	0.994653	+	0.103276i	$0.0329326\pi$
$212$	7385.60	2.39266
$213$	−5699.17	−1.83334
$214$	−10266.1	−3.27933
$215$	3061.76	0.971210
$216$	−18723.6	−5.89807
$217$	−9250.78	−2.89393
$218$	8241.61	2.56051
$219$	10788.7	3.32893
$220$	9684.82	2.96796
$221$	1203.21	0.366230
$222$	2451.57	0.741164
$223$	−1498.34	−0.449939	−0.224970	−	0.974366i	$-0.572228\pi$
$223$	−1498.34	−0.449939	−0.224970	+	0.974366i	$0.572228\pi$
$224$	−23710.3	−7.07237
$225$	−1340.22	−0.397102
$226$	−2955.50	−0.869898
$227$	902.264	0.263812	0.131906	−	0.991262i	$-0.457890\pi$
$227$	902.264	0.263812	0.131906	+	0.991262i	$0.457890\pi$
$228$	12304.3	3.57401
$229$	−5584.47	−1.61149	−0.805747	−	0.592260i	$-0.798236\pi$
$229$	−5584.47	−1.61149	−0.805747	+	0.592260i	$0.798236\pi$
$230$	3122.18	0.895089
$231$	13548.5	3.85900
$232$	5585.01	1.58049
$233$	−1948.94	−0.547981	−0.273990	−	0.961732i	$-0.588344\pi$
$233$	−1948.94	−0.547981	−0.273990	+	0.961732i	$0.588344\pi$
$234$	15479.2	4.32439
$235$	−2567.96	−0.712832
$236$	−5248.72	−1.44772
$237$	6611.47	1.81207
$238$	4285.80	1.16726
$239$	169.458	0.0458632	0.0229316	−	0.999737i	$-0.492700\pi$
$239$	169.458	0.0458632	0.0229316	+	0.999737i	$0.492700\pi$
$240$	21575.9	5.80298
$241$	−5697.33	−1.52281	−0.761405	−	0.648276i	$-0.775490\pi$
$241$	−5697.33	−1.52281	−0.761405	+	0.648276i	$0.775490\pi$
$242$	−3420.80	−0.908667
$243$	205.806	0.0543311
$244$	12257.1	3.21591
$245$	8104.84	2.11347
$246$	−14753.5	−3.82378
$247$	−3248.86	−0.836924
$248$	20626.7	5.28143
$249$	−4487.13	−1.14201
$250$	8190.32	2.07201
$251$	5144.54	1.29371	0.646853	−	0.762614i	$-0.276085\pi$
$251$	5144.54	1.29371	0.646853	+	0.762614i	$0.276085\pi$
$252$	40360.1	10.0891
$253$	−2523.34	−0.627040
$254$	4880.21	1.20556
$255$	−2089.29	−0.513083
$256$	11145.3	2.72103
$257$	−2022.82	−0.490973	−0.245487	−	0.969400i	$-0.578948\pi$
$257$	−2022.82	−0.490973	−0.245487	+	0.969400i	$0.578948\pi$
$258$	−15066.4	−3.63563
$259$	−1687.80	−0.404922
$260$	−11397.2	−2.71857
$261$	−4016.08	−0.952448
$262$	12790.1	3.01594
$263$	−1991.52	−0.466929	−0.233465	−	0.972365i	$-0.575006\pi$
$263$	−1991.52	−0.466929	−0.233465	+	0.972365i	$0.575006\pi$
$264$	−30209.5	−7.04267
$265$	3386.22	0.784957
$266$	−11572.3	−2.66746
$267$	−11877.3	−2.72239
$268$	20104.3	4.58234
$269$	−5419.53	−1.22838	−0.614190	−	0.789158i	$-0.710517\pi$
$269$	−5419.53	−1.22838	−0.614190	+	0.789158i	$0.710517\pi$
$270$	−13542.7	−3.05253
$271$	−647.868	−0.145222	−0.0726110	−	0.997360i	$-0.523133\pi$
$271$	−647.868	−0.145222	−0.0726110	+	0.997360i	$0.523133\pi$
$272$	−5516.02	−1.22962
$273$	−15944.1	−3.53473
$274$	6040.95	1.33192
$275$	−1089.51	−0.238909
$276$	−11246.3	−2.45271
$277$	6675.27	1.44794	0.723968	−	0.689834i	$-0.242316\pi$
$277$	6675.27	1.44794	0.723968	+	0.689834i	$0.242316\pi$
$278$	−3299.38	−0.711812
$279$	−14832.3	−3.18274
$280$	−25733.7	−5.49244
$281$	−6257.44	−1.32843	−0.664213	−	0.747543i	$-0.731233\pi$
$281$	−6257.44	−1.32843	−0.664213	+	0.747543i	$0.731233\pi$
$282$	12636.5	2.66842
$283$	−769.455	−0.161623	−0.0808116	−	0.996729i	$-0.525751\pi$
$283$	−769.455	−0.161623	−0.0808116	+	0.996729i	$0.525751\pi$
$284$	−13801.5	−2.88369
$285$	5641.40	1.17252
$286$	12583.6	2.60169
$287$	10157.2	2.08905
$288$	−38016.0	−7.77817
$289$	−4378.86	−0.891280
$290$	4039.61	0.817979
$291$	2484.20	0.500434
$292$	26126.7	5.23614
$293$	−747.473	−0.149037	−0.0745185	−	0.997220i	$-0.523742\pi$
$293$	−747.473	−0.149037	−0.0745185	+	0.997220i	$0.523742\pi$
$294$	−39882.5	−7.91155
$295$	−2406.48	−0.474951
$296$	3763.33	0.738984
$297$	10945.2	2.13840
$298$	−3882.28	−0.754679
$299$	2969.51	0.574351
$300$	−4855.85	−0.934509
$301$	10372.6	1.98626
$302$	−11750.5	−2.23895
$303$	−9043.45	−1.71463
$304$	14894.1	2.80999
$305$	5619.75	1.05504
$306$	6871.65	1.28375
$307$	−5353.73	−0.995288	−0.497644	−	0.867381i	$-0.665801\pi$
$307$	−5353.73	−0.995288	−0.497644	+	0.867381i	$0.665801\pi$
$308$	32810.1	6.06989
$309$	−7387.54	−1.36007
$310$	14919.2	2.73339
$311$	1650.58	0.300951	0.150476	−	0.988614i	$-0.451919\pi$
$311$	1650.58	0.300951	0.150476	+	0.988614i	$0.451919\pi$
$312$	35551.0	6.45089
$313$	9423.74	1.70179	0.850897	−	0.525333i	$-0.176059\pi$
$313$	9423.74	1.70179	0.850897	+	0.525333i	$0.176059\pi$
$314$	3961.36	0.711951
$315$	18504.6	3.30990
$316$	16010.8	2.85024
$317$	7121.97	1.26186	0.630930	−	0.775839i	$-0.282673\pi$
$317$	7121.97	1.26186	0.630930	+	0.775839i	$0.282673\pi$
$318$	−16663.0	−2.93841
$319$	−3264.81	−0.573022
$320$	19109.6	3.33831
$321$	16954.6	2.94801
$322$	10577.3	1.83058
$323$	−1442.26	−0.248451
$324$	16675.3	2.85928
$325$	1282.15	0.218834
$326$	−12164.0	−2.06657
$327$	−13611.1	−2.30182
$328$	−22647.7	−3.81252
$329$	−8699.70	−1.45784
$330$	−21850.4	−3.64492
$331$	−1707.63	−0.283565	−0.141782	−	0.989898i	$-0.545283\pi$
$331$	−1707.63	−0.283565	−0.141782	+	0.989898i	$0.545283\pi$
$332$	−10866.3	−1.79629
$333$	−2706.14	−0.445332
$334$	3410.11	0.558661
$335$	9217.61	1.50332
$336$	73094.3	11.8679
$337$	−10477.7	−1.69364	−0.846818	−	0.531882i	$-0.821485\pi$
$337$	−10477.7	−1.69364	−0.846818	+	0.531882i	$0.821485\pi$
$338$	−2804.92	−0.451383
$339$	4881.04	0.782011
$340$	−5059.56	−0.807038
$341$	−12057.7	−1.91483
$342$	−18554.5	−2.93367
$343$	15815.7	2.48970
$344$	−23128.0	−3.62493
$345$	−5156.31	−0.804656
$346$	13684.1	2.12619
$347$	−3024.63	−0.467927	−0.233963	−	0.972245i	$-0.575170\pi$
$347$	−3024.63	−0.467927	−0.233963	+	0.972245i	$0.575170\pi$
$348$	−14551.0	−2.24142
$349$	1790.41	0.274608	0.137304	−	0.990529i	$-0.456156\pi$
$349$	1790.41	0.274608	0.137304	+	0.990529i	$0.456156\pi$
$350$	4566.97	0.697471
$351$	−12880.5	−1.95871
$352$	−30904.5	−4.67958
$353$	4857.62	0.732422	0.366211	−	0.930532i	$-0.380655\pi$
$353$	4857.62	0.732422	0.366211	+	0.930532i	$0.380655\pi$
$354$	11841.9	1.77793
$355$	−6327.84	−0.946047
$356$	−28762.9	−4.28211
$357$	−7078.04	−1.04933
$358$	−16993.1	−2.50870
$359$	−7713.51	−1.13399	−0.566996	−	0.823720i	$-0.691895\pi$
$359$	−7713.51	−1.13399	−0.566996	+	0.823720i	$0.691895\pi$
$360$	−41260.2	−6.04057
$361$	−2964.67	−0.432230
$362$	23434.4	3.40245
$363$	5649.49	0.816863
$364$	−38611.4	−5.55985
$365$	11978.8	1.71781
$366$	−27653.8	−3.94942
$367$	−12360.3	−1.75804	−0.879022	−	0.476781i	$-0.841803\pi$
$367$	−12360.3	−1.75804	−0.879022	+	0.476781i	$0.841803\pi$
$368$	−13613.4	−1.92839
$369$	16285.5	2.29753
$370$	2722.00	0.382459
$371$	11471.8	1.60535
$372$	−53739.9	−7.49002
$373$	1342.37	0.186341	0.0931705	−	0.995650i	$-0.470300\pi$
$373$	1342.37	0.186341	0.0931705	+	0.995650i	$0.470300\pi$
$374$	5586.20	0.772341
$375$	−13526.4	−1.86267
$376$	19397.9	2.66056
$377$	3842.07	0.524872
$378$	−45879.7	−6.24286
$379$	11823.8	1.60249	0.801247	−	0.598333i	$-0.204170\pi$
$379$	11823.8	1.60249	0.801247	+	0.598333i	$0.204170\pi$
$380$	13661.6	1.84428
$381$	−8059.71	−1.08376
$382$	12355.1	1.65482
$383$	891.097	0.118885	0.0594424	−	0.998232i	$-0.481068\pi$
$383$	891.097	0.118885	0.0594424	+	0.998232i	$0.481068\pi$
$384$	−43607.5	−5.79515
$385$	15043.1	1.99134
$386$	−10812.4	−1.42575
$387$	16630.9	2.18448
$388$	6015.91	0.787143
$389$	9001.92	1.17330	0.586652	−	0.809839i	$-0.300446\pi$
$389$	9001.92	1.17330	0.586652	+	0.809839i	$0.300446\pi$
$390$	25713.8	3.33864
$391$	1318.25	0.170503
$392$	−61222.4	−7.88827
$393$	−21123.0	−2.71123
$394$	−11861.2	−1.51665
$395$	7340.77	0.935074
$396$	52606.1	6.67565
$397$	−8180.23	−1.03414	−0.517071	−	0.855943i	$-0.672978\pi$
$397$	−8180.23	−1.03414	−0.517071	+	0.855943i	$0.672978\pi$
$398$	970.954	0.122285
$399$	19111.8	2.39796
$400$	−5877.90	−0.734738
$401$	−5777.12	−0.719441	−0.359720	−	0.933060i	$-0.617128\pi$
$401$	−5777.12	−0.719441	−0.359720	+	0.933060i	$0.617128\pi$
$402$	−45358.3	−5.62752
$403$	14189.6	1.75394
$404$	−21900.2	−2.69697
$405$	7645.44	0.938037
$406$	13685.3	1.67288
$407$	−2199.91	−0.267926
$408$	15782.1	1.91502
$409$	8481.14	1.02534	0.512672	−	0.858585i	$-0.328656\pi$
$409$	8481.14	1.02534	0.512672	+	0.858585i	$0.328656\pi$
$410$	−16380.9	−1.97316
$411$	−9976.70	−1.19736
$412$	−17890.2	−2.13928
$413$	−8152.62	−0.971342
$414$	16959.1	2.01327
$415$	−4982.10	−0.589305
$416$	36368.8	4.28637
$417$	5448.96	0.639896
$418$	−15083.6	−1.76498
$419$	10804.5	1.25974	0.629872	−	0.776699i	$-0.283107\pi$
$419$	10804.5	1.25974	0.629872	+	0.776699i	$0.283107\pi$
$420$	67045.6	7.78926
$421$	3603.22	0.417127	0.208563	−	0.978009i	$-0.433121\pi$
$421$	3603.22	0.417127	0.208563	+	0.978009i	$0.433121\pi$
$422$	−33312.5	−3.84272
$423$	−13948.7	−1.60333
$424$	−25578.9	−2.92976
$425$	569.183	0.0649634
$426$	31138.2	3.54143
$427$	19038.5	2.15770
$428$	41058.4	4.63699
$429$	−20781.9	−2.33883
$430$	−16728.3	−1.87607
$431$	3675.25	0.410743	0.205372	−	0.978684i	$-0.434160\pi$
$431$	3675.25	0.410743	0.205372	+	0.978684i	$0.434160\pi$
$432$	59049.3	6.57641
$433$	−11458.8	−1.27176	−0.635881	−	0.771787i	$-0.719363\pi$
$433$	−11458.8	−1.27176	−0.635881	+	0.771787i	$0.719363\pi$
$434$	50542.9	5.59018
$435$	−6671.45	−0.735337
$436$	−32961.6	−3.62058
$437$	−3559.47	−0.389640
$438$	−58945.7	−6.43045
$439$	−10139.5	−1.10235	−0.551177	−	0.834388i	$-0.685821\pi$
$439$	−10139.5	−1.10235	−0.551177	+	0.834388i	$0.685821\pi$
$440$	−33541.9	−3.63419
$441$	44023.9	4.75369
$442$	−6573.92	−0.707442
$443$	−2459.93	−0.263826	−0.131913	−	0.991261i	$-0.542112\pi$
$443$	−2459.93	−0.263826	−0.131913	+	0.991261i	$0.542112\pi$
$444$	−9804.83	−1.04801
$445$	−13187.5	−1.40482
$446$	8186.40	0.869142
$447$	6411.62	0.678433
$448$	64739.1	6.82731
$449$	−12015.8	−1.26294	−0.631469	−	0.775401i	$-0.717548\pi$
$449$	−12015.8	−1.26294	−0.631469	+	0.775401i	$0.717548\pi$
$450$	7322.47	0.767077
$451$	13239.1	1.38227
$452$	11820.3	1.23004
$453$	19406.0	2.01275
$454$	−4929.64	−0.509603
$455$	−17702.9	−1.82401
$456$	−42614.1	−4.37629
$457$	14058.8	1.43905	0.719523	−	0.694469i	$-0.244361\pi$
$457$	14058.8	1.43905	0.719523	+	0.694469i	$0.244361\pi$
$458$	30511.5	3.11290
$459$	−5718.00	−0.581467
$460$	−12486.9	−1.26566
$461$	−6306.07	−0.637099	−0.318550	−	0.947906i	$-0.603196\pi$
$461$	−6306.07	−0.637099	−0.318550	+	0.947906i	$0.603196\pi$
$462$	−74024.3	−7.45438
$463$	8407.25	0.843883	0.421942	−	0.906623i	$-0.361349\pi$
$463$	8407.25	0.843883	0.421942	+	0.906623i	$0.361349\pi$
$464$	−17613.6	−1.76227
$465$	−24639.2	−2.45724
$466$	10648.3	1.05853
$467$	−6970.57	−0.690706	−0.345353	−	0.938473i	$-0.612241\pi$
$467$	−6970.57	−0.690706	−0.345353	+	0.938473i	$0.612241\pi$
$468$	−61907.7	−6.11471
$469$	31227.2	3.07450
$470$	14030.4	1.37697
$471$	−6542.23	−0.640021
$472$	18178.1	1.77270
$473$	13519.8	1.31425
$474$	−36122.7	−3.50036
$475$	−1536.88	−0.148457
$476$	−17140.7	−1.65051
$477$	18393.3	1.76556
$478$	−925.855	−0.0885934
$479$	5608.45	0.534982	0.267491	−	0.963560i	$-0.413805\pi$
$479$	5608.45	0.534982	0.267491	+	0.963560i	$0.413805\pi$
$480$	−63151.6	−6.00513
$481$	2588.89	0.245412
$482$	31128.1	2.94159
$483$	−17468.5	−1.64564
$484$	13681.2	1.28486
$485$	2758.23	0.258236
$486$	−1124.45	−0.104951
$487$	12457.1	1.15910	0.579552	−	0.814935i	$-0.303227\pi$
$487$	12457.1	1.15910	0.579552	+	0.814935i	$0.303227\pi$
$488$	−42450.6	−3.93780
$489$	20089.0	1.85779
$490$	−44281.9	−4.08255
$491$	9901.71	0.910097	0.455049	−	0.890467i	$-0.349622\pi$
$491$	9901.71	0.910097	0.455049	+	0.890467i	$0.349622\pi$
$492$	59005.3	5.40684
$493$	1705.60	0.155814
$494$	17750.6	1.61668
$495$	24119.3	2.19007
$496$	−65051.0	−5.88886
$497$	−21437.3	−1.93480
$498$	24516.1	2.20601
$499$	−9126.53	−0.818757	−0.409378	−	0.912365i	$-0.634254\pi$
$499$	−9126.53	−0.818757	−0.409378	+	0.912365i	$0.634254\pi$
$500$	−32756.5	−2.92983
$501$	−5631.83	−0.502219
$502$	−28107.9	−2.49904
$503$	2585.98	0.229231	0.114616	−	0.993410i	$-0.463436\pi$
$503$	2585.98	0.229231	0.114616	+	0.993410i	$0.463436\pi$
$504$	−139781.	−12.3538
$505$	−10041.0	−0.884791
$506$	13786.6	1.21124
$507$	4632.36	0.405779
$508$	−19518.0	−1.70466
$509$	18790.8	1.63632	0.818160	−	0.574990i	$-0.194994\pi$
$509$	18790.8	1.63632	0.818160	+	0.574990i	$0.194994\pi$
$510$	11415.1	0.991116
$511$	40581.6	3.51316
$512$	−22231.7	−1.91896
$513$	15439.5	1.32879
$514$	11052.0	0.948407
$515$	−8202.45	−0.701831
$516$	60256.7	5.14080
$517$	−11339.4	−0.964613
$518$	9221.53	0.782183
$519$	−22599.4	−1.91138
$520$	39472.6	3.32882
$521$	1503.35	0.126417	0.0632083	−	0.998000i	$-0.479867\pi$
$521$	1503.35	0.126417	0.0632083	+	0.998000i	$0.479867\pi$
$522$	21942.4	1.83983
$523$	−15101.8	−1.26263	−0.631315	−	0.775526i	$-0.717485\pi$
$523$	−15101.8	−1.26263	−0.631315	+	0.775526i	$0.717485\pi$
$524$	−51152.9	−4.26455
$525$	−7542.41	−0.627005
$526$	10880.9	0.901961
$527$	6299.17	0.520676
$528$	95272.6	7.85267
$529$	−8913.60	−0.732604
$530$	−18501.1	−1.51629
$531$	−13071.5	−1.06828
$532$	46282.5	3.77181
$533$	−15579.9	−1.26612
$534$	64893.3	5.25882
$535$	18824.8	1.52125
$536$	−69628.1	−5.61097
$537$	28064.3	2.25524
$538$	29610.3	2.37285
$539$	35788.6	2.85997
$540$	54162.9	4.31629
$541$	−21969.4	−1.74591	−0.872954	−	0.487802i	$-0.837799\pi$
$541$	−21969.4	−1.74591	−0.872954	+	0.487802i	$0.837799\pi$
$542$	3539.71	0.280523
$543$	−38702.2	−3.05869
$544$	16145.1	1.27246
$545$	−15112.5	−1.18780
$546$	87112.9	6.82800
$547$	16600.5	1.29760	0.648801	−	0.760958i	$-0.275271\pi$
$547$	16600.5	1.29760	0.648801	+	0.760958i	$0.275271\pi$
$548$	−24160.3	−1.88335
$549$	30525.4	2.37303
$550$	5952.69	0.461497
$551$	−4605.40	−0.356073
$552$	38949.8	3.00329
$553$	24868.9	1.91236
$554$	−36471.3	−2.79696
$555$	−4495.41	−0.343819
$556$	13195.6	1.00651
$557$	4799.21	0.365079	0.182540	−	0.983199i	$-0.441568\pi$
$557$	4799.21	0.365079	0.182540	+	0.983199i	$0.441568\pi$
$558$	81038.1	6.14806
$559$	−15910.3	−1.20382
$560$	81157.2	6.12414
$561$	−9225.66	−0.694310
$562$	34188.4	2.56610
$563$	−14604.8	−1.09329	−0.546643	−	0.837366i	$-0.684094\pi$
$563$	−14604.8	−1.09329	−0.546643	+	0.837366i	$0.684094\pi$
$564$	−50538.6	−3.77315
$565$	5419.46	0.403537
$566$	4204.02	0.312206
$567$	25901.1	1.91842
$568$	47799.3	3.53101
$569$	−2279.13	−0.167919	−0.0839596	−	0.996469i	$-0.526757\pi$
$569$	−2279.13	−0.167919	−0.0839596	+	0.996469i	$0.526757\pi$
$570$	−30822.5	−2.26494
$571$	10705.6	0.784618	0.392309	−	0.919834i	$-0.371676\pi$
$571$	10705.6	0.784618	0.392309	+	0.919834i	$0.371676\pi$
$572$	−50326.9	−3.67880
$573$	−20404.5	−1.48763
$574$	−55495.0	−4.03540
$575$	1404.73	0.101881
$576$	103800.	7.50866
$577$	951.196	0.0686288	0.0343144	−	0.999411i	$-0.489075\pi$
$577$	951.196	0.0686288	0.0343144	+	0.999411i	$0.489075\pi$
$578$	23924.5	1.72167
$579$	17856.9	1.28170
$580$	−16156.1	−1.15663
$581$	−16878.3	−1.20521
$582$	−13572.8	−0.966682
$583$	14952.5	1.06221
$584$	−90485.9	−6.41153
$585$	−28384.0	−2.00604
$586$	4083.92	0.287893
$587$	−18603.5	−1.30809	−0.654046	−	0.756455i	$-0.726930\pi$
$587$	−18603.5	−1.30809	−0.654046	+	0.756455i	$0.726930\pi$
$588$	159507.	11.1870
$589$	−17008.8	−1.18987
$590$	13148.1	0.917457
$591$	19588.9	1.36342
$592$	−11868.5	−0.823975
$593$	5714.87	0.395753	0.197877	−	0.980227i	$-0.436595\pi$
$593$	5714.87	0.395753	0.197877	+	0.980227i	$0.436595\pi$
$594$	−59800.6	−4.13072
$595$	−7858.81	−0.541479
$596$	15526.8	1.06712
$597$	−1603.54	−0.109931
$598$	−16224.3	−1.10947
$599$	2841.85	0.193848	0.0969240	−	0.995292i	$-0.469100\pi$
$599$	2841.85	0.193848	0.0969240	+	0.995292i	$0.469100\pi$
$600$	16817.5	1.14428
$601$	−12220.8	−0.829445	−0.414722	−	0.909948i	$-0.636121\pi$
$601$	−12220.8	−0.829445	−0.414722	+	0.909948i	$0.636121\pi$
$602$	−56671.9	−3.83684
$603$	50068.3	3.38133
$604$	46994.9	3.16589
$605$	6272.67	0.421521
$606$	49410.1	3.31213
$607$	−21259.2	−1.42156	−0.710779	−	0.703416i	$-0.751657\pi$
$607$	−21259.2	−1.42156	−0.710779	+	0.703416i	$0.751657\pi$
$608$	−43594.4	−2.90787
$609$	−22601.4	−1.50387
$610$	−30704.3	−2.03800
$611$	13344.3	0.883559
$612$	−27482.6	−1.81522
$613$	485.980	0.0320205	0.0160102	−	0.999872i	$-0.494904\pi$
$613$	485.980	0.0320205	0.0160102	+	0.999872i	$0.494904\pi$
$614$	29250.8	1.92259
$615$	27053.3	1.77381
$616$	−113632.	−7.43244
$617$	−17264.5	−1.12649	−0.563243	−	0.826292i	$-0.690446\pi$
$617$	−17264.5	−1.12649	−0.563243	+	0.826292i	$0.690446\pi$
$618$	40362.8	2.62723
$619$	1655.80	0.107516	0.0537579	−	0.998554i	$-0.482880\pi$
$619$	1655.80	0.107516	0.0537579	+	0.998554i	$0.482880\pi$
$620$	−59667.9	−3.86503
$621$	−14111.9	−0.911903
$622$	−9018.18	−0.581344
$623$	−44676.3	−2.87306
$624$	−112118.	−7.19282
$625$	−11940.0	−0.764161
$626$	−51487.9	−3.28733
$627$	24910.7	1.58667
$628$	−15843.1	−1.00670
$629$	1149.28	0.0728535
$630$	−101103.	−6.39369
$631$	4561.98	0.287812	0.143906	−	0.989591i	$-0.454034\pi$
$631$	4561.98	0.287812	0.143906	+	0.989591i	$0.454034\pi$
$632$	−55450.8	−3.49006
$633$	55015.9	3.45448
$634$	−38911.9	−2.43752
$635$	−8948.77	−0.559246
$636$	66642.1	4.15493
$637$	−42116.5	−2.61965
$638$	17837.7	1.10690
$639$	−34371.6	−2.12789
$640$	−48417.8	−2.99044
$641$	−18890.0	−1.16398	−0.581991	−	0.813195i	$-0.697726\pi$
$641$	−18890.0	−1.16398	−0.581991	+	0.813195i	$0.697726\pi$
$642$	−92633.7	−5.69464
$643$	17226.7	1.05654	0.528271	−	0.849076i	$-0.322840\pi$
$643$	17226.7	1.05654	0.528271	+	0.849076i	$0.322840\pi$
$644$	−42302.8	−2.58845
$645$	27627.0	1.68653
$646$	7880.00	0.479929
$647$	15699.4	0.953950	0.476975	−	0.878917i	$-0.341733\pi$
$647$	15699.4	0.953950	0.476975	+	0.878917i	$0.341733\pi$
$648$	−57752.3	−3.50112
$649$	−10626.3	−0.642710
$650$	−7005.21	−0.422718
$651$	−83472.1	−5.02539
$652$	48648.9	2.92215
$653$	−3771.00	−0.225988	−0.112994	−	0.993596i	$-0.536044\pi$
$653$	−3771.00	−0.225988	−0.112994	+	0.993596i	$0.536044\pi$
$654$	74366.1	4.44640
$655$	−23453.0	−1.39906
$656$	71424.6	4.25101
$657$	65066.7	3.86377
$658$	47532.0	2.81610
$659$	−23106.7	−1.36587	−0.682935	−	0.730479i	$-0.739297\pi$
$659$	−23106.7	−1.36587	−0.682935	+	0.730479i	$0.739297\pi$
$660$	87388.6	5.15394
$661$	−27148.3	−1.59750	−0.798751	−	0.601662i	$-0.794505\pi$
$661$	−27148.3	−1.59750	−0.798751	+	0.601662i	$0.794505\pi$
$662$	9329.89	0.547759
$663$	10856.9	0.635968
$664$	37633.9	2.19951
$665$	21220.0	1.23741
$666$	14785.4	0.860243
$667$	4209.39	0.244360
$668$	−13638.4	−0.789950
$669$	−13519.9	−0.781332
$670$	−50361.7	−2.90394
$671$	24815.2	1.42769
$672$	−213944.	−12.2813
$673$	−10169.0	−0.582446	−0.291223	−	0.956655i	$-0.594062\pi$
$673$	−10169.0	−0.582446	−0.291223	+	0.956655i	$0.594062\pi$
$674$	57246.2	3.27158
$675$	−6093.14	−0.347445
$676$	11218.0	0.638258
$677$	15799.0	0.896903	0.448451	−	0.893807i	$-0.351976\pi$
$677$	15799.0	0.896903	0.448451	+	0.893807i	$0.351976\pi$
$678$	−26668.2	−1.51060
$679$	9344.27	0.528130
$680$	17523.0	0.988199
$681$	8141.36	0.458117
$682$	65878.7	3.69886
$683$	−10979.9	−0.615131	−0.307565	−	0.951527i	$-0.599514\pi$
$683$	−10979.9	−0.615131	−0.307565	+	0.951527i	$0.599514\pi$
$684$	74207.2	4.14822
$685$	−11077.2	−0.617866
$686$	−86411.3	−4.80933
$687$	−50390.1	−2.79840
$688$	72939.3	4.04184
$689$	−17596.4	−0.972958
$690$	28172.2	1.55434
$691$	−9148.86	−0.503674	−0.251837	−	0.967770i	$-0.581035\pi$
$691$	−9148.86	−0.503674	−0.251837	+	0.967770i	$0.581035\pi$
$692$	−54728.3	−3.00644
$693$	81711.0	4.47900
$694$	16525.5	0.903888
$695$	6050.03	0.330202
$696$	50395.0	2.74456
$697$	−6916.36	−0.375862
$698$	−9782.14	−0.530458
$699$	−17585.8	−0.951583
$700$	−18265.2	−0.986228
$701$	9240.33	0.497864	0.248932	−	0.968521i	$-0.419920\pi$
$701$	9240.33	0.497864	0.248932	+	0.968521i	$0.419920\pi$
$702$	70374.2	3.78362
$703$	−3103.24	−0.166488
$704$	84382.3	4.51744
$705$	−23171.4	−1.23785
$706$	−26540.3	−1.41481
$707$	−34016.8	−1.80952
$708$	−47360.5	−2.51401
$709$	31453.8	1.66611	0.833055	−	0.553191i	$-0.186590\pi$
$709$	31453.8	1.66611	0.833055	+	0.553191i	$0.186590\pi$
$710$	34573.0	1.82747
$711$	39873.7	2.10321
$712$	99615.8	5.24334
$713$	15546.2	0.816565
$714$	38671.9	2.02697
$715$	−23074.3	−1.20690
$716$	67962.4	3.54731
$717$	1529.06	0.0796427
$718$	42143.8	2.19052
$719$	−12653.9	−0.656346	−0.328173	−	0.944618i	$-0.606433\pi$
$719$	−12653.9	−0.656346	−0.328173	+	0.944618i	$0.606433\pi$
$720$	130124.	6.73531
$721$	−27788.1	−1.43534
$722$	16197.9	0.834934
$723$	−51408.5	−2.64440
$724$	−93723.8	−4.81108
$725$	1817.50	0.0931039
$726$	−30866.8	−1.57792
$727$	−15649.8	−0.798378	−0.399189	−	0.916869i	$-0.630708\pi$
$727$	−15649.8	−0.798378	−0.399189	+	0.916869i	$0.630708\pi$
$728$	133724.	6.80791
$729$	−18747.3	−0.952463
$730$	−65448.0	−3.31827
$731$	−7063.04	−0.357368
$732$	110599.	5.58451
$733$	5489.41	0.276611	0.138306	−	0.990390i	$-0.455834\pi$
$733$	5489.41	0.276611	0.138306	+	0.990390i	$0.455834\pi$
$734$	67532.2	3.39599
$735$	73132.0	3.67009
$736$	39845.9	1.99557
$737$	40702.2	2.03431
$738$	−88978.2	−4.43812
$739$	−708.302	−0.0352575	−0.0176288	−	0.999845i	$-0.505612\pi$
$739$	−708.302	−0.0352575	−0.0176288	+	0.999845i	$0.505612\pi$
$740$	−10886.4	−0.540799
$741$	−29315.3	−1.45334
$742$	−62677.5	−3.10103
$743$	22328.0	1.10247	0.551235	−	0.834350i	$-0.314157\pi$
$743$	22328.0	1.10247	0.551235	+	0.834350i	$0.314157\pi$
$744$	186120.	9.17135
$745$	7118.88	0.350088
$746$	−7334.21	−0.359952
$747$	−27061.8	−1.32549
$748$	−22341.5	−1.09209
$749$	63774.4	3.11117
$750$	73903.3	3.59809
$751$	14613.3	0.710051	0.355026	−	0.934857i	$-0.384472\pi$
$751$	14613.3	0.710051	0.355026	+	0.934857i	$0.384472\pi$
$752$	−61175.8	−2.96656
$753$	46420.5	2.24656
$754$	−20991.7	−1.01389
$755$	21546.7	1.03863
$756$	183492.	8.82743
$757$	21478.4	1.03124	0.515618	−	0.856818i	$-0.327562\pi$
$757$	21478.4	1.03124	0.515618	+	0.856818i	$0.327562\pi$
$758$	−64600.7	−3.09552
$759$	−22768.7	−1.08887
$760$	−47314.8	−2.25827
$761$	15505.1	0.738581	0.369291	−	0.929314i	$-0.379601\pi$
$761$	15505.1	0.738581	0.369291	+	0.929314i	$0.379601\pi$
$762$	44035.4	2.09348
$763$	−51197.9	−2.42921
$764$	−49413.0	−2.33992
$765$	−12600.4	−0.595517
$766$	−4868.63	−0.229648
$767$	12505.2	0.588704
$768$	100567.	4.72513
$769$	−213.853	−0.0100283	−0.00501414	−	0.999987i	$-0.501596\pi$
$769$	−213.853	−0.0100283	−0.00501414	+	0.999987i	$0.501596\pi$
$770$	−82189.8	−3.84664
$771$	−18252.4	−0.852588
$772$	43243.4	2.01602
$773$	−8019.56	−0.373148	−0.186574	−	0.982441i	$-0.559738\pi$
$773$	−8019.56	−0.373148	−0.186574	+	0.982441i	$0.559738\pi$
$774$	−90865.1	−4.21974
$775$	6712.44	0.311120
$776$	−20835.1	−0.963838
$777$	−15229.5	−0.703158
$778$	−49183.2	−2.26646
$779$	18675.3	0.858935
$780$	−102840.	−4.72086
$781$	−27941.9	−1.28020
$782$	−7202.42	−0.329358
$783$	−18258.6	−0.833345
$784$	193079.	8.79551
$785$	−7263.89	−0.330267
$786$	115408.	5.23725
$787$	−9461.58	−0.428550	−0.214275	−	0.976773i	$-0.568739\pi$
$787$	−9461.58	−0.428550	−0.214275	+	0.976773i	$0.568739\pi$
$788$	47437.8	2.14455
$789$	−17970.0	−0.810835
$790$	−40107.3	−1.80627
$791$	18360.0	0.825291
$792$	−182193.	−8.17418
$793$	−29202.9	−1.30772
$794$	44693.8	1.99764
$795$	30554.7	1.36310
$796$	−3883.24	−0.172912
$797$	26286.6	1.16828	0.584139	−	0.811654i	$-0.301432\pi$
$797$	26286.6	1.16828	0.584139	+	0.811654i	$0.301432\pi$
$798$	−104420.	−4.63212
$799$	5923.93	0.262295
$800$	17204.4	0.760333
$801$	−71631.9	−3.15979
$802$	31564.1	1.38973
$803$	52894.9	2.32456
$804$	181406.	7.95735
$805$	−19395.4	−0.849189
$806$	−77527.0	−3.38805
$807$	−48901.8	−2.13312
$808$	75848.0	3.30238
$809$	−23460.5	−1.01956	−0.509781	−	0.860304i	$-0.670274\pi$
$809$	−23460.5	−1.01956	−0.509781	+	0.860304i	$0.670274\pi$
$810$	−41771.9	−1.81199
$811$	5426.61	0.234962	0.117481	−	0.993075i	$-0.462518\pi$
$811$	5426.61	0.234962	0.117481	+	0.993075i	$0.462518\pi$
$812$	−54733.2	−2.36547
$813$	−5845.87	−0.252182
$814$	12019.5	0.517548
$815$	22305.0	0.958663
$816$	−49772.4	−2.13527
$817$	19071.3	0.816671
$818$	−46337.9	−1.98064
$819$	−96158.8	−4.10264
$820$	65514.1	2.79006
$821$	42269.7	1.79686	0.898431	−	0.439114i	$-0.144708\pi$
$821$	42269.7	1.79686	0.898431	+	0.439114i	$0.144708\pi$
$822$	54509.1	2.31292
$823$	26126.2	1.10656	0.553282	−	0.832994i	$-0.313375\pi$
$823$	26126.2	1.10656	0.553282	+	0.832994i	$0.313375\pi$
$824$	61959.8	2.61950
$825$	−9830.93	−0.414871
$826$	44543.0	1.87633
$827$	18497.2	0.777765	0.388883	−	0.921287i	$-0.372861\pi$
$827$	18497.2	0.777765	0.388883	+	0.921287i	$0.372861\pi$
$828$	−67826.4	−2.84677
$829$	−22797.6	−0.955119	−0.477560	−	0.878599i	$-0.658479\pi$
$829$	−22797.6	−0.955119	−0.477560	+	0.878599i	$0.658479\pi$
$830$	27220.4	1.13835
$831$	60232.7	2.51438
$832$	−99302.4	−4.13785
$833$	−18696.7	−0.777674
$834$	−29771.2	−1.23608
$835$	−6253.07	−0.259157
$836$	60325.6	2.49570
$837$	−67433.1	−2.78474
$838$	−59031.7	−2.43343
$839$	2559.61	0.105325	0.0526624	−	0.998612i	$-0.483229\pi$
$839$	2559.61	0.105325	0.0526624	+	0.998612i	$0.483229\pi$
$840$	−232202.	−9.53777
$841$	−18942.7	−0.776691
$842$	−19686.7	−0.805759
$843$	−56462.5	−2.30685
$844$	133230.	5.43362
$845$	5143.34	0.209392
$846$	76210.6	3.09713
$847$	21250.5	0.862071
$848$	80668.8	3.26672
$849$	−6942.99	−0.280663
$850$	−3109.81	−0.125489
$851$	2836.40	0.114255
$852$	−124534.	−5.00761
$853$	−7204.29	−0.289180	−0.144590	−	0.989492i	$-0.546186\pi$
$853$	−7204.29	−0.289180	−0.144590	+	0.989492i	$0.546186\pi$
$854$	−104019.	−4.16800
$855$	34023.2	1.36090
$856$	−142199.	−5.67788
$857$	−2429.54	−0.0968395	−0.0484198	−	0.998827i	$-0.515419\pi$
$857$	−2429.54	−0.0968395	−0.0484198	+	0.998827i	$0.515419\pi$
$858$	113545.	4.51789
$859$	−21102.3	−0.838185	−0.419092	−	0.907944i	$-0.637652\pi$
$859$	−21102.3	−0.838185	−0.419092	+	0.907944i	$0.637652\pi$
$860$	66903.5	2.65278
$861$	91650.7	3.62770
$862$	−20080.2	−0.793428
$863$	45055.4	1.77718	0.888589	−	0.458704i	$-0.151686\pi$
$863$	45055.4	1.77718	0.888589	+	0.458704i	$0.151686\pi$
$864$	−172835.	−6.80551
$865$	−25092.3	−0.986317
$866$	62606.5	2.45665
$867$	−39511.6	−1.54773
$868$	−202142.	−7.90454
$869$	32414.7	1.26535
$870$	36450.4	1.42044
$871$	−47899.0	−1.86337
$872$	114157.	4.43332
$873$	14982.2	0.580836
$874$	19447.7	0.752662
$875$	−50879.3	−1.96575
$876$	235748.	9.09269
$877$	17437.7	0.671414	0.335707	−	0.941967i	$-0.391025\pi$
$877$	17437.7	0.671414	0.335707	+	0.941967i	$0.391025\pi$
$878$	55398.7	2.12940
$879$	−6744.64	−0.258807
$880$	105782.	4.05217
$881$	−24428.7	−0.934194	−0.467097	−	0.884206i	$-0.654700\pi$
$881$	−24428.7	−0.934194	−0.467097	+	0.884206i	$0.654700\pi$
$882$	−240531.	−9.18265
$883$	3733.73	0.142299	0.0711495	−	0.997466i	$-0.477333\pi$
$883$	3733.73	0.142299	0.0711495	+	0.997466i	$0.477333\pi$
$884$	26291.8	1.00033
$885$	−21714.3	−0.824765
$886$	13440.2	0.509630
$887$	−36448.7	−1.37974	−0.689869	−	0.723934i	$-0.742332\pi$
$887$	−36448.7	−1.37974	−0.689869	+	0.723934i	$0.742332\pi$
$888$	33957.5	1.28326
$889$	−30316.5	−1.14374
$890$	72051.6	2.71368
$891$	33760.0	1.26936
$892$	−32740.8	−1.22897
$893$	−15995.5	−0.599406
$894$	−35030.8	−1.31052
$895$	31160.0	1.16376
$896$	−164029.	−6.11587
$897$	26794.6	0.997375
$898$	65649.8	2.43960
$899$	20114.4	0.746220
$900$	−29285.6	−1.08465
$901$	−7811.52	−0.288834
$902$	−72333.4	−2.67011
$903$	93594.3	3.44920
$904$	−40937.6	−1.50616
$905$	−42971.4	−1.57836
$906$	−106027.	−3.88800
$907$	−16523.1	−0.604897	−0.302448	−	0.953166i	$-0.597804\pi$
$907$	−16523.1	−0.604897	−0.302448	+	0.953166i	$0.597804\pi$
$908$	19715.7	0.720581
$909$	−54540.9	−1.99011
$910$	96722.2	3.52342
$911$	23465.7	0.853408	0.426704	−	0.904391i	$-0.359675\pi$
$911$	23465.7	0.853408	0.426704	+	0.904391i	$0.359675\pi$
$912$	134393.	4.87961
$913$	−21999.5	−0.797455
$914$	−76812.3	−2.77979
$915$	50708.5	1.83210
$916$	−122028.	−4.40166
$917$	−79453.8	−2.86128
$918$	31241.1	1.12321
$919$	18086.3	0.649198	0.324599	−	0.945852i	$-0.394771\pi$
$919$	18086.3	0.649198	0.324599	+	0.945852i	$0.394771\pi$
$920$	43246.3	1.54977
$921$	−48308.1	−1.72834
$922$	34454.1	1.23068
$923$	32882.4	1.17263
$924$	296054.	10.5405
$925$	1224.68	0.0435322
$926$	−45934.2	−1.63012
$927$	−44554.1	−1.57859
$928$	51554.3	1.82366
$929$	−33881.4	−1.19657	−0.598284	−	0.801284i	$-0.704151\pi$
$929$	−33881.4	−1.19657	−0.598284	+	0.801284i	$0.704151\pi$
$930$	134620.	4.74661
$931$	50484.0	1.77717
$932$	−42587.0	−1.49676
$933$	14893.6	0.522610
$934$	38084.7	1.33423
$935$	−10243.3	−0.358281
$936$	214408.	7.48732
$937$	40504.9	1.41221	0.706103	−	0.708109i	$-0.250451\pi$
$937$	40504.9	1.41221	0.706103	+	0.708109i	$0.250451\pi$
$938$	−170614.	−5.93897
$939$	85032.8	2.95521
$940$	−56113.4	−1.94704
$941$	21947.1	0.760312	0.380156	−	0.924922i	$-0.375870\pi$
$941$	21947.1	0.760312	0.380156	+	0.924922i	$0.375870\pi$
$942$	35744.4	1.23632
$943$	−17069.4	−0.589456
$944$	−57328.8	−1.97658
$945$	84129.1	2.89600
$946$	−73867.4	−2.53873
$947$	−26290.2	−0.902129	−0.451064	−	0.892491i	$-0.648956\pi$
$947$	−26290.2	−0.902129	−0.451064	+	0.892491i	$0.648956\pi$
$948$	144469.	4.94952
$949$	−62247.6	−2.12923
$950$	8396.97	0.286772
$951$	64263.4	2.19125
$952$	59364.0	2.02101
$953$	−49370.1	−1.67813	−0.839063	−	0.544035i	$-0.816896\pi$
$953$	−49370.1	−1.67813	−0.839063	+	0.544035i	$0.816896\pi$
$954$	−100494.	−3.41050
$955$	−22655.3	−0.767654
$956$	3702.88	0.125272
$957$	−29459.2	−0.995068
$958$	−30642.5	−1.03342
$959$	−37527.2	−1.26362
$960$	172431.	5.79706
$961$	44495.9	1.49360
$962$	−14144.8	−0.474060
$963$	102253.	3.42165
$964$	−124494.	−4.15943
$965$	19826.6	0.661391
$966$	95441.3	3.17885
$967$	13634.3	0.453411	0.226706	−	0.973963i	$-0.427204\pi$
$967$	13634.3	0.453411	0.226706	+	0.973963i	$0.427204\pi$
$968$	−47382.6	−1.57328
$969$	−13013.9	−0.431441
$970$	−15070.0	−0.498832
$971$	24346.5	0.804650	0.402325	−	0.915497i	$-0.368202\pi$
$971$	24346.5	0.804650	0.402325	+	0.915497i	$0.368202\pi$
$972$	4497.14	0.148401
$973$	20496.2	0.675311
$974$	−68060.9	−2.23903
$975$	11569.2	0.380011
$976$	133878.	4.39070
$977$	4794.03	0.156985	0.0784927	−	0.996915i	$-0.474989\pi$
$977$	4794.03	0.156985	0.0784927	+	0.996915i	$0.474989\pi$
$978$	−109759.	−3.58866
$979$	−58232.0	−1.90102
$980$	177101.	5.77275
$981$	−82088.4	−2.67164
$982$	−54099.3	−1.75802
$983$	−983.000	−0.0318950
$983$	−983.000	−0.0318950
$984$	−204356.	−6.62055
$985$	21749.7	0.703557
$986$	−9318.80	−0.300985
$987$	−78499.6	−2.53158
$988$	−70992.0	−2.28599
$989$	−17431.4	−0.560452
$990$	−131779.	−4.23053
$991$	24623.3	0.789288	0.394644	−	0.918834i	$-0.370868\pi$
$991$	24623.3	0.789288	0.394644	+	0.918834i	$0.370868\pi$
$992$	190402.	6.09401
$993$	−15408.4	−0.492418
$994$	117126.	3.73743
$995$	−1780.42	−0.0567269
$996$	−98049.8	−3.11930
$997$	14010.4	0.445050	0.222525	−	0.974927i	$-0.428570\pi$
$997$	14010.4	0.445050	0.222525	+	0.974927i	$0.428570\pi$
$998$	49864.1	1.58158
$999$	−12303.1	−0.389644

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	983.4.a.b.1.2	✓	136

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
983.4.a.b.1.2	✓	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)

\(f(q)\)	\(=\)	\(q-5.46364 q^{2} +9.02325 q^{3} +21.8513 q^{4} +10.0186 q^{5} -49.2998 q^{6} +33.9408 q^{7} -75.6787 q^{8} +54.4191 q^{9} +O(q^{10})\)	\(q-5.46364 q^{2} +9.02325 q^{3} +21.8513 q^{4} +10.0186 q^{5} -49.2998 q^{6} +33.9408 q^{7} -75.6787 q^{8} +54.4191 q^{9} -54.7380 q^{10} +44.2392 q^{11} +197.170 q^{12} -52.0613 q^{13} -185.440 q^{14} +90.4003 q^{15} +238.670 q^{16} -23.1115 q^{17} -297.326 q^{18} +62.4046 q^{19} +218.920 q^{20} +306.257 q^{21} -241.707 q^{22} -57.0386 q^{23} -682.868 q^{24} -24.6277 q^{25} +284.444 q^{26} +247.410 q^{27} +741.652 q^{28} -73.7990 q^{29} -493.915 q^{30} -272.556 q^{31} -698.577 q^{32} +399.181 q^{33} +126.273 q^{34} +340.039 q^{35} +1189.13 q^{36} -49.7278 q^{37} -340.956 q^{38} -469.762 q^{39} -758.194 q^{40} +299.261 q^{41} -1673.28 q^{42} +305.607 q^{43} +966.685 q^{44} +545.203 q^{45} +311.638 q^{46} -256.320 q^{47} +2153.58 q^{48} +808.979 q^{49} +134.557 q^{50} -208.541 q^{51} -1137.61 q^{52} +337.993 q^{53} -1351.76 q^{54} +443.214 q^{55} -2568.60 q^{56} +563.093 q^{57} +403.211 q^{58} -240.201 q^{59} +1975.37 q^{60} +560.932 q^{61} +1489.15 q^{62} +1847.03 q^{63} +1907.41 q^{64} -521.581 q^{65} -2180.98 q^{66} +920.050 q^{67} -505.016 q^{68} -514.674 q^{69} -1857.85 q^{70} -631.609 q^{71} -4118.37 q^{72} +1195.66 q^{73} +271.694 q^{74} -222.222 q^{75} +1363.62 q^{76} +1501.51 q^{77} +2566.61 q^{78} +732.714 q^{79} +2391.14 q^{80} +763.125 q^{81} -1635.05 q^{82} -497.285 q^{83} +6692.12 q^{84} -231.545 q^{85} -1669.73 q^{86} -665.907 q^{87} -3347.96 q^{88} -1316.30 q^{89} -2978.79 q^{90} -1767.00 q^{91} -1246.37 q^{92} -2459.34 q^{93} +1400.44 q^{94} +625.206 q^{95} -6303.44 q^{96} +275.311 q^{97} -4419.97 q^{98} +2407.46 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 136 q + 17 q^{2} + 25 q^{3} + 601 q^{4} + 50 q^{5} + 61 q^{6} + 223 q^{7} + 207 q^{8} + 1443 q^{9}+O(q^{10}) \) 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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