LMFDB - Embedded newform 798.4.a.l.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,4,Mod(1,798)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("798.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	798.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:	$47.0835241846$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 2x^{3} - 94x^{2} + 2x + 1632 $ x^4 - 2x^3 - 94x^2 + 2*x + 1632
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3}\cdot 3 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$-6.61955$ of defining polynomial
Character	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +17.2391 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +17.2391 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -34.4782 q^{10} -32.9384 q^{11} -12.0000 q^{12} +53.2307 q^{13} -14.0000 q^{14} -51.7173 q^{15} +16.0000 q^{16} +9.19480 q^{17} -18.0000 q^{18} +19.0000 q^{19} +68.9564 q^{20} -21.0000 q^{21} +65.8767 q^{22} +84.8940 q^{23} +24.0000 q^{24} +172.187 q^{25} -106.461 q^{26} -27.0000 q^{27} +28.0000 q^{28} +115.214 q^{29} +103.435 q^{30} +148.311 q^{31} -32.0000 q^{32} +98.8151 q^{33} -18.3896 q^{34} +120.674 q^{35} +36.0000 q^{36} -399.763 q^{37} -38.0000 q^{38} -159.692 q^{39} -137.913 q^{40} +242.551 q^{41} +42.0000 q^{42} +395.453 q^{43} -131.753 q^{44} +155.152 q^{45} -169.788 q^{46} -385.347 q^{47} -48.0000 q^{48} +49.0000 q^{49} -344.373 q^{50} -27.5844 q^{51} +212.923 q^{52} -174.149 q^{53} +54.0000 q^{54} -567.828 q^{55} -56.0000 q^{56} -57.0000 q^{57} -230.429 q^{58} +304.607 q^{59} -206.869 q^{60} -178.921 q^{61} -296.621 q^{62} +63.0000 q^{63} +64.0000 q^{64} +917.649 q^{65} -197.630 q^{66} -625.016 q^{67} +36.7792 q^{68} -254.682 q^{69} -241.347 q^{70} -981.324 q^{71} -72.0000 q^{72} +1185.67 q^{73} +799.526 q^{74} -516.560 q^{75} +76.0000 q^{76} -230.568 q^{77} +319.384 q^{78} -894.655 q^{79} +275.826 q^{80} +81.0000 q^{81} -485.103 q^{82} +197.354 q^{83} -84.0000 q^{84} +158.510 q^{85} -790.907 q^{86} -345.643 q^{87} +263.507 q^{88} +8.42853 q^{89} -310.304 q^{90} +372.615 q^{91} +339.576 q^{92} -444.932 q^{93} +770.694 q^{94} +327.543 q^{95} +96.0000 q^{96} +1215.90 q^{97} -98.0000 q^{98} -296.445 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 24 q^{10} + 54 q^{11} - 48 q^{12} - 46 q^{13} - 56 q^{14} - 36 q^{15} + 64 q^{16} + 100 q^{17} - 72 q^{18} + 76 q^{19} + 48 q^{20} - 84 q^{21} - 108 q^{22} + 274 q^{23} + 96 q^{24} + 300 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} - 214 q^{29} + 72 q^{30} + 228 q^{31} - 128 q^{32} - 162 q^{33} - 200 q^{34} + 84 q^{35} + 144 q^{36} - 124 q^{37} - 152 q^{38} + 138 q^{39} - 96 q^{40} - 484 q^{41} + 168 q^{42} + 276 q^{43} + 216 q^{44} + 108 q^{45} - 548 q^{46} - 506 q^{47} - 192 q^{48} + 196 q^{49} - 600 q^{50} - 300 q^{51} - 184 q^{52} - 1002 q^{53} + 216 q^{54} + 8 q^{55} - 224 q^{56} - 228 q^{57} + 428 q^{58} - 808 q^{59} - 144 q^{60} - 72 q^{61} - 456 q^{62} + 252 q^{63} + 256 q^{64} + 616 q^{65} + 324 q^{66} + 138 q^{67} + 400 q^{68} - 822 q^{69} - 168 q^{70} - 654 q^{71} - 288 q^{72} + 2348 q^{73} + 248 q^{74} - 900 q^{75} + 304 q^{76} + 378 q^{77} - 276 q^{78} + 234 q^{79} + 192 q^{80} + 324 q^{81} + 968 q^{82} - 258 q^{83} - 336 q^{84} + 2696 q^{85} - 552 q^{86} + 642 q^{87} - 432 q^{88} - 1316 q^{89} - 216 q^{90} - 322 q^{91} + 1096 q^{92} - 684 q^{93} + 1012 q^{94} + 228 q^{95} + 384 q^{96} + 1166 q^{97} - 392 q^{98} + 486 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 24 * q^10 + 54 * q^11 - 48 * q^12 - 46 * q^13 - 56 * q^14 - 36 * q^15 + 64 * q^16 + 100 * q^17 - 72 * q^18 + 76 * q^19 + 48 * q^20 - 84 * q^21 - 108 * q^22 + 274 * q^23 + 96 * q^24 + 300 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 - 214 * q^29 + 72 * q^30 + 228 * q^31 - 128 * q^32 - 162 * q^33 - 200 * q^34 + 84 * q^35 + 144 * q^36 - 124 * q^37 - 152 * q^38 + 138 * q^39 - 96 * q^40 - 484 * q^41 + 168 * q^42 + 276 * q^43 + 216 * q^44 + 108 * q^45 - 548 * q^46 - 506 * q^47 - 192 * q^48 + 196 * q^49 - 600 * q^50 - 300 * q^51 - 184 * q^52 - 1002 * q^53 + 216 * q^54 + 8 * q^55 - 224 * q^56 - 228 * q^57 + 428 * q^58 - 808 * q^59 - 144 * q^60 - 72 * q^61 - 456 * q^62 + 252 * q^63 + 256 * q^64 + 616 * q^65 + 324 * q^66 + 138 * q^67 + 400 * q^68 - 822 * q^69 - 168 * q^70 - 654 * q^71 - 288 * q^72 + 2348 * q^73 + 248 * q^74 - 900 * q^75 + 304 * q^76 + 378 * q^77 - 276 * q^78 + 234 * q^79 + 192 * q^80 + 324 * q^81 + 968 * q^82 - 258 * q^83 - 336 * q^84 + 2696 * q^85 - 552 * q^86 + 642 * q^87 - 432 * q^88 - 1316 * q^89 - 216 * q^90 - 322 * q^91 + 1096 * q^92 - 684 * q^93 + 1012 * q^94 + 228 * q^95 + 384 * q^96 + 1166 * q^97 - 392 * q^98 + 486 * 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 $

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	17.2391	1.54191	0.770956	−	0.636888i	$-0.219779\pi$
$5$	17.2391	1.54191	0.770956	+	0.636888i	$0.219779\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−34.4782	−1.09030
$11$	−32.9384	−0.902844	−0.451422	−	0.892311i	$-0.649083\pi$
$11$	−32.9384	−0.902844	−0.451422	+	0.892311i	$0.649083\pi$
$12$	−12.0000	−0.288675
$13$	53.2307	1.13566	0.567828	−	0.823147i	$-0.307784\pi$
$13$	53.2307	1.13566	0.567828	+	0.823147i	$0.307784\pi$
$14$	−14.0000	−0.267261
$15$	−51.7173	−0.890223
$16$	16.0000	0.250000
$17$	9.19480	0.131180	0.0655902	−	0.997847i	$-0.479107\pi$
$17$	9.19480	0.131180	0.0655902	+	0.997847i	$0.479107\pi$
$18$	−18.0000	−0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	68.9564	0.770956
$21$	−21.0000	−0.218218
$22$	65.8767	0.638407
$23$	84.8940	0.769636	0.384818	−	0.922992i	$-0.374264\pi$
$23$	84.8940	0.769636	0.384818	+	0.922992i	$0.374264\pi$
$24$	24.0000	0.204124
$25$	172.187	1.37749
$26$	−106.461	−0.803030
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	115.214	0.737750	0.368875	−	0.929479i	$-0.379743\pi$
$29$	115.214	0.737750	0.368875	+	0.929479i	$0.379743\pi$
$30$	103.435	0.629483
$31$	148.311	0.859270	0.429635	−	0.903003i	$-0.358642\pi$
$31$	148.311	0.859270	0.429635	+	0.903003i	$0.358642\pi$
$32$	−32.0000	−0.176777
$33$	98.8151	0.521257
$34$	−18.3896	−0.0927585
$35$	120.674	0.582788
$36$	36.0000	0.166667
$37$	−399.763	−1.77623	−0.888117	−	0.459618i	$-0.847986\pi$
$37$	−399.763	−1.77623	−0.888117	+	0.459618i	$0.847986\pi$
$38$	−38.0000	−0.162221
$39$	−159.692	−0.655671
$40$	−137.913	−0.545148
$41$	242.551	0.923906	0.461953	−	0.886904i	$-0.347149\pi$
$41$	242.551	0.923906	0.461953	+	0.886904i	$0.347149\pi$
$42$	42.0000	0.154303
$43$	395.453	1.40247	0.701233	−	0.712932i	$-0.252633\pi$
$43$	395.453	1.40247	0.701233	+	0.712932i	$0.252633\pi$
$44$	−131.753	−0.451422
$45$	155.152	0.513971
$46$	−169.788	−0.544215
$47$	−385.347	−1.19593	−0.597964	−	0.801523i	$-0.704024\pi$
$47$	−385.347	−1.19593	−0.597964	+	0.801523i	$0.704024\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	−344.373	−0.974034
$51$	−27.5844	−0.0757370
$52$	212.923	0.567828
$53$	−174.149	−0.451344	−0.225672	−	0.974203i	$-0.572458\pi$
$53$	−174.149	−0.451344	−0.225672	+	0.974203i	$0.572458\pi$
$54$	54.0000	0.136083
$55$	−567.828	−1.39211
$56$	−56.0000	−0.133631
$57$	−57.0000	−0.132453
$58$	−230.429	−0.521668
$59$	304.607	0.672143	0.336071	−	0.941837i	$-0.390902\pi$
$59$	304.607	0.672143	0.336071	+	0.941837i	$0.390902\pi$
$60$	−206.869	−0.445112
$61$	−178.921	−0.375548	−0.187774	−	0.982212i	$-0.560127\pi$
$61$	−178.921	−0.375548	−0.187774	+	0.982212i	$0.560127\pi$
$62$	−296.621	−0.607596
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	917.649	1.75108
$66$	−197.630	−0.368585
$67$	−625.016	−1.13967	−0.569835	−	0.821759i	$-0.692993\pi$
$67$	−625.016	−1.13967	−0.569835	+	0.821759i	$0.692993\pi$
$68$	36.7792	0.0655902
$69$	−254.682	−0.444350
$70$	−241.347	−0.412093
$71$	−981.324	−1.64031	−0.820153	−	0.572144i	$-0.806112\pi$
$71$	−981.324	−1.64031	−0.820153	+	0.572144i	$0.806112\pi$
$72$	−72.0000	−0.117851
$73$	1185.67	1.90099	0.950493	−	0.310747i	$-0.100579\pi$
$73$	1185.67	1.90099	0.950493	+	0.310747i	$0.100579\pi$
$74$	799.526	1.25599
$75$	−516.560	−0.795296
$76$	76.0000	0.114708
$77$	−230.568	−0.341243
$78$	319.384	0.463630
$79$	−894.655	−1.27413	−0.637067	−	0.770809i	$-0.719852\pi$
$79$	−894.655	−1.27413	−0.637067	+	0.770809i	$0.719852\pi$
$80$	275.826	0.385478
$81$	81.0000	0.111111
$82$	−485.103	−0.653300
$83$	197.354	0.260994	0.130497	−	0.991449i	$-0.458343\pi$
$83$	197.354	0.260994	0.130497	+	0.991449i	$0.458343\pi$
$84$	−84.0000	−0.109109
$85$	158.510	0.202269
$86$	−790.907	−0.991694
$87$	−345.643	−0.425940
$88$	263.507	0.319204
$89$	8.42853	0.0100384	0.00501922	−	0.999987i	$-0.498402\pi$
$89$	8.42853	0.0100384	0.00501922	+	0.999987i	$0.498402\pi$
$90$	−310.304	−0.363432
$91$	372.615	0.429238
$92$	339.576	0.384818
$93$	−444.932	−0.496100
$94$	770.694	0.845650
$95$	327.543	0.353739
$96$	96.0000	0.102062
$97$	1215.90	1.27274	0.636371	−	0.771383i	$-0.280435\pi$
$97$	1215.90	1.27274	0.636371	+	0.771383i	$0.280435\pi$
$98$	−98.0000	−0.101015
$99$	−296.445	−0.300948
$100$	688.746	0.688746
$101$	1291.24	1.27211	0.636054	−	0.771645i	$-0.280566\pi$
$101$	1291.24	1.27211	0.636054	+	0.771645i	$0.280566\pi$
$102$	55.1688	0.0535541
$103$	570.738	0.545985	0.272992	−	0.962016i	$-0.411987\pi$
$103$	570.738	0.545985	0.272992	+	0.962016i	$0.411987\pi$
$104$	−425.845	−0.401515
$105$	−362.021	−0.336473
$106$	348.298	0.319148
$107$	−1767.02	−1.59648	−0.798242	−	0.602336i	$-0.794237\pi$
$107$	−1767.02	−1.59648	−0.798242	+	0.602336i	$0.794237\pi$
$108$	−108.000	−0.0962250
$109$	684.204	0.601237	0.300619	−	0.953744i	$-0.402807\pi$
$109$	684.204	0.601237	0.300619	+	0.953744i	$0.402807\pi$
$110$	1135.66	0.984368
$111$	1199.29	1.02551
$112$	112.000	0.0944911
$113$	1343.30	1.11829	0.559146	−	0.829069i	$-0.311129\pi$
$113$	1343.30	1.11829	0.559146	+	0.829069i	$0.311129\pi$
$114$	114.000	0.0936586
$115$	1463.50	1.18671
$116$	460.857	0.368875
$117$	479.076	0.378552
$118$	−609.213	−0.475277
$119$	64.3636	0.0495815
$120$	413.738	0.314741
$121$	−246.065	−0.184872
$122$	357.841	0.265553
$123$	−727.654	−0.533418
$124$	593.242	0.429635
$125$	813.454	0.582061
$126$	−126.000	−0.0890871
$127$	2286.81	1.59781	0.798904	−	0.601459i	$-0.205413\pi$
$127$	2286.81	1.59781	0.798904	+	0.601459i	$0.205413\pi$
$128$	−128.000	−0.0883883
$129$	−1186.36	−0.809715
$130$	−1835.30	−1.23820
$131$	1724.63	1.15024	0.575122	−	0.818068i	$-0.304955\pi$
$131$	1724.63	1.15024	0.575122	+	0.818068i	$0.304955\pi$
$132$	395.260	0.260629
$133$	133.000	0.0867110
$134$	1250.03	0.805868
$135$	−465.456	−0.296741
$136$	−73.5584	−0.0463792
$137$	1525.29	0.951198	0.475599	−	0.879662i	$-0.342231\pi$
$137$	1525.29	0.951198	0.475599	+	0.879662i	$0.342231\pi$
$138$	509.364	0.314203
$139$	1775.39	1.08336	0.541678	−	0.840586i	$-0.317789\pi$
$139$	1775.39	1.08336	0.541678	+	0.840586i	$0.317789\pi$
$140$	482.695	0.291394
$141$	1156.04	0.690470
$142$	1962.65	1.15987
$143$	−1753.33	−1.02532
$144$	144.000	0.0833333
$145$	1986.19	1.13755
$146$	−2371.34	−1.34420
$147$	−147.000	−0.0824786
$148$	−1599.05	−0.888117
$149$	−856.075	−0.470687	−0.235344	−	0.971912i	$-0.575622\pi$
$149$	−856.075	−0.470687	−0.235344	+	0.971912i	$0.575622\pi$
$150$	1033.12	0.562359
$151$	1018.84	0.549085	0.274543	−	0.961575i	$-0.411474\pi$
$151$	1018.84	0.549085	0.274543	+	0.961575i	$0.411474\pi$
$152$	−152.000	−0.0811107
$153$	82.7532	0.0437268
$154$	461.137	0.241295
$155$	2556.74	1.32492
$156$	−638.768	−0.327836
$157$	3029.42	1.53996	0.769981	−	0.638066i	$-0.220265\pi$
$157$	3029.42	1.53996	0.769981	+	0.638066i	$0.220265\pi$
$158$	1789.31	0.900948
$159$	522.447	0.260583
$160$	−551.651	−0.272574
$161$	594.258	0.290895
$162$	−162.000	−0.0785674
$163$	−585.677	−0.281434	−0.140717	−	0.990050i	$-0.544941\pi$
$163$	−585.677	−0.281434	−0.140717	+	0.990050i	$0.544941\pi$
$164$	970.205	0.461953
$165$	1703.48	0.803733
$166$	−394.709	−0.184550
$167$	−3858.94	−1.78811	−0.894053	−	0.447962i	$-0.852150\pi$
$167$	−3858.94	−1.78811	−0.894053	+	0.447962i	$0.852150\pi$
$168$	168.000	0.0771517
$169$	636.504	0.289715
$170$	−317.020	−0.143025
$171$	171.000	0.0764719
$172$	1581.81	0.701233
$173$	454.152	0.199587	0.0997936	−	0.995008i	$-0.468182\pi$
$173$	454.152	0.199587	0.0997936	+	0.995008i	$0.468182\pi$
$174$	691.286	0.301185
$175$	1205.31	0.520643
$176$	−527.014	−0.225711
$177$	−913.820	−0.388062
$178$	−16.8571	−0.00709826
$179$	−3201.89	−1.33698	−0.668492	−	0.743719i	$-0.733060\pi$
$179$	−3201.89	−1.33698	−0.668492	+	0.743719i	$0.733060\pi$
$180$	620.608	0.256985
$181$	944.454	0.387849	0.193925	−	0.981016i	$-0.437878\pi$
$181$	944.454	0.387849	0.193925	+	0.981016i	$0.437878\pi$
$182$	−745.229	−0.303517
$183$	536.762	0.216823
$184$	−679.152	−0.272107
$185$	−6891.55	−2.73880
$186$	889.864	0.350796
$187$	−302.861	−0.118435
$188$	−1541.39	−0.597964
$189$	−189.000	−0.0727393
$190$	−655.086	−0.250131
$191$	524.564	0.198723	0.0993616	−	0.995051i	$-0.468320\pi$
$191$	524.564	0.198723	0.0993616	+	0.995051i	$0.468320\pi$
$192$	−192.000	−0.0721688
$193$	3125.65	1.16575	0.582873	−	0.812563i	$-0.301928\pi$
$193$	3125.65	1.16575	0.582873	+	0.812563i	$0.301928\pi$
$194$	−2431.80	−0.899965
$195$	−2752.95	−1.01099
$196$	196.000	0.0714286
$197$	−3349.16	−1.21126	−0.605628	−	0.795748i	$-0.707078\pi$
$197$	−3349.16	−1.21126	−0.605628	+	0.795748i	$0.707078\pi$
$198$	592.890	0.212802
$199$	3231.02	1.15096	0.575479	−	0.817816i	$-0.304816\pi$
$199$	3231.02	1.15096	0.575479	+	0.817816i	$0.304816\pi$
$200$	−1377.49	−0.487017
$201$	1875.05	0.657988
$202$	−2582.47	−0.899516
$203$	806.500	0.278843
$204$	−110.338	−0.0378685
$205$	4181.37	1.42458
$206$	−1141.48	−0.386070
$207$	764.046	0.256545
$208$	851.691	0.283914
$209$	−625.829	−0.207127
$210$	724.042	0.237922
$211$	2182.21	0.711990	0.355995	−	0.934488i	$-0.384142\pi$
$211$	2182.21	0.711990	0.355995	+	0.934488i	$0.384142\pi$
$212$	−696.596	−0.225672
$213$	2943.97	0.947032
$214$	3534.03	1.12889
$215$	6817.26	2.16248
$216$	216.000	0.0680414
$217$	1038.17	0.324774
$218$	−1368.41	−0.425139
$219$	−3557.00	−1.09753
$220$	−2271.31	−0.696053
$221$	489.445	0.148976
$222$	−2398.58	−0.725144
$223$	−1227.23	−0.368527	−0.184264	−	0.982877i	$-0.558990\pi$
$223$	−1227.23	−0.368527	−0.184264	+	0.982877i	$0.558990\pi$
$224$	−224.000	−0.0668153
$225$	1549.68	0.459164
$226$	−2686.60	−0.790751
$227$	−2247.20	−0.657058	−0.328529	−	0.944494i	$-0.606553\pi$
$227$	−2247.20	−0.657058	−0.328529	+	0.944494i	$0.606553\pi$
$228$	−228.000	−0.0662266
$229$	2050.32	0.591655	0.295828	−	0.955241i	$-0.404405\pi$
$229$	2050.32	0.591655	0.295828	+	0.955241i	$0.404405\pi$
$230$	−2926.99	−0.839132
$231$	691.705	0.197017
$232$	−921.714	−0.260834
$233$	2704.99	0.760556	0.380278	−	0.924872i	$-0.375828\pi$
$233$	2704.99	0.760556	0.380278	+	0.924872i	$0.375828\pi$
$234$	−958.152	−0.267677
$235$	−6643.04	−1.84402
$236$	1218.43	0.336071
$237$	2683.96	0.735621
$238$	−128.727	−0.0350594
$239$	6199.99	1.67801	0.839004	−	0.544125i	$-0.183138\pi$
$239$	6199.99	1.67801	0.839004	+	0.544125i	$0.183138\pi$
$240$	−827.477	−0.222556
$241$	369.681	0.0988101	0.0494051	−	0.998779i	$-0.484267\pi$
$241$	369.681	0.0988101	0.0494051	+	0.998779i	$0.484267\pi$
$242$	492.130	0.130724
$243$	−243.000	−0.0641500
$244$	−715.683	−0.187774
$245$	844.716	0.220273
$246$	1455.31	0.377183
$247$	1011.38	0.260537
$248$	−1186.48	−0.303798
$249$	−592.063	−0.150685
$250$	−1626.91	−0.411579
$251$	−992.181	−0.249506	−0.124753	−	0.992188i	$-0.539814\pi$
$251$	−992.181	−0.249506	−0.124753	+	0.992188i	$0.539814\pi$
$252$	252.000	0.0629941
$253$	−2796.27	−0.694862
$254$	−4573.62	−1.12982
$255$	−475.530	−0.116780
$256$	256.000	0.0625000
$257$	−5051.98	−1.22620	−0.613101	−	0.790004i	$-0.710078\pi$
$257$	−5051.98	−1.22620	−0.613101	+	0.790004i	$0.710078\pi$
$258$	2372.72	0.572555
$259$	−2798.34	−0.671353
$260$	3670.60	0.875541
$261$	1036.93	0.245917
$262$	−3449.27	−0.813345
$263$	−6480.41	−1.51939	−0.759695	−	0.650280i	$-0.774652\pi$
$263$	−6480.41	−1.51939	−0.759695	+	0.650280i	$0.774652\pi$
$264$	−790.520	−0.184292
$265$	−3002.17	−0.695932
$266$	−266.000	−0.0613139
$267$	−25.2856	−0.00579570
$268$	−2500.06	−0.569835
$269$	−2265.34	−0.513458	−0.256729	−	0.966483i	$-0.582645\pi$
$269$	−2265.34	−0.513458	−0.256729	+	0.966483i	$0.582645\pi$
$270$	930.911	0.209828
$271$	4172.79	0.935346	0.467673	−	0.883901i	$-0.345092\pi$
$271$	4172.79	0.935346	0.467673	+	0.883901i	$0.345092\pi$
$272$	147.117	0.0327951
$273$	−1117.84	−0.247821
$274$	−3050.58	−0.672599
$275$	−5671.54	−1.24366
$276$	−1018.73	−0.222175
$277$	−1137.03	−0.246633	−0.123316	−	0.992367i	$-0.539353\pi$
$277$	−1137.03	−0.246633	−0.123316	+	0.992367i	$0.539353\pi$
$278$	−3550.78	−0.766049
$279$	1334.80	0.286423
$280$	−965.390	−0.206047
$281$	5241.73	1.11279	0.556397	−	0.830916i	$-0.312183\pi$
$281$	5241.73	1.11279	0.556397	+	0.830916i	$0.312183\pi$
$282$	−2312.08	−0.488236
$283$	3736.25	0.784796	0.392398	−	0.919796i	$-0.371646\pi$
$283$	3736.25	0.784796	0.392398	+	0.919796i	$0.371646\pi$
$284$	−3925.30	−0.820153
$285$	−982.629	−0.204231
$286$	3506.66	0.725011
$287$	1697.86	0.349204
$288$	−288.000	−0.0589256
$289$	−4828.46	−0.982792
$290$	−3972.38	−0.804366
$291$	−3647.70	−0.734818
$292$	4742.67	0.950493
$293$	1654.95	0.329977	0.164988	−	0.986295i	$-0.447241\pi$
$293$	1654.95	0.329977	0.164988	+	0.986295i	$0.447241\pi$
$294$	294.000	0.0583212
$295$	5251.15	1.03638
$296$	3198.10	0.627993
$297$	889.335	0.173752
$298$	1712.15	0.332826
$299$	4518.97	0.874042
$300$	−2066.24	−0.397648
$301$	2768.17	0.530083
$302$	−2037.68	−0.388262
$303$	−3873.71	−0.734451
$304$	304.000	0.0573539
$305$	−3084.43	−0.579063
$306$	−165.506	−0.0309195
$307$	7821.40	1.45404	0.727021	−	0.686615i	$-0.240904\pi$
$307$	7821.40	1.45404	0.727021	+	0.686615i	$0.240904\pi$
$308$	−922.274	−0.170622
$309$	−1712.21	−0.315225
$310$	−5113.48	−0.936859
$311$	−9896.39	−1.80441	−0.902207	−	0.431303i	$-0.858054\pi$
$311$	−9896.39	−1.80441	−0.902207	+	0.431303i	$0.858054\pi$
$312$	1277.54	0.231815
$313$	2803.97	0.506357	0.253178	−	0.967420i	$-0.418524\pi$
$313$	2803.97	0.506357	0.253178	+	0.967420i	$0.418524\pi$
$314$	−6058.84	−1.08892
$315$	1086.06	0.194263
$316$	−3578.62	−0.637067
$317$	4230.58	0.749569	0.374784	−	0.927112i	$-0.377717\pi$
$317$	4230.58	0.749569	0.374784	+	0.927112i	$0.377717\pi$
$318$	−1044.89	−0.184260
$319$	−3794.97	−0.666073
$320$	1103.30	0.192739
$321$	5301.05	0.921731
$322$	−1188.52	−0.205694
$323$	174.701	0.0300948
$324$	324.000	0.0555556
$325$	9165.61	1.56436
$326$	1171.35	0.199004
$327$	−2052.61	−0.347124
$328$	−1940.41	−0.326650
$329$	−2697.43	−0.452019
$330$	−3406.97	−0.568325
$331$	2241.31	0.372185	0.186093	−	0.982532i	$-0.440418\pi$
$331$	2241.31	0.372185	0.186093	+	0.982532i	$0.440418\pi$
$332$	789.418	0.130497
$333$	−3597.87	−0.592078
$334$	7717.88	1.26438
$335$	−10774.7	−1.75727
$336$	−336.000	−0.0545545
$337$	−5188.33	−0.838654	−0.419327	−	0.907835i	$-0.637734\pi$
$337$	−5188.33	−0.838654	−0.419327	+	0.907835i	$0.637734\pi$
$338$	−1273.01	−0.204860
$339$	−4029.90	−0.645646
$340$	634.040	0.101134
$341$	−4885.11	−0.775787
$342$	−342.000	−0.0540738
$343$	343.000	0.0539949
$344$	−3163.63	−0.495847
$345$	−4390.49	−0.685148
$346$	−908.305	−0.141129
$347$	8920.34	1.38003	0.690013	−	0.723797i	$-0.257605\pi$
$347$	8920.34	1.38003	0.690013	+	0.723797i	$0.257605\pi$
$348$	−1382.57	−0.212970
$349$	−372.556	−0.0571417	−0.0285709	−	0.999592i	$-0.509096\pi$
$349$	−372.556	−0.0571417	−0.0285709	+	0.999592i	$0.509096\pi$
$350$	−2410.61	−0.368150
$351$	−1437.23	−0.218557
$352$	1054.03	0.159602
$353$	9289.51	1.40065	0.700327	−	0.713822i	$-0.253038\pi$
$353$	9289.51	1.40065	0.700327	+	0.713822i	$0.253038\pi$
$354$	1827.64	0.274401
$355$	−16917.2	−2.52921
$356$	33.7141	0.00501922
$357$	−193.091	−0.0286259
$358$	6403.77	0.945391
$359$	−6039.30	−0.887861	−0.443930	−	0.896061i	$-0.646416\pi$
$359$	−6039.30	−0.887861	−0.443930	+	0.896061i	$0.646416\pi$
$360$	−1241.22	−0.181716
$361$	361.000	0.0526316
$362$	−1888.91	−0.274251
$363$	738.195	0.106736
$364$	1490.46	0.214619
$365$	20439.9	2.93115
$366$	−1073.52	−0.153317
$367$	1729.66	0.246015	0.123007	−	0.992406i	$-0.460746\pi$
$367$	1729.66	0.246015	0.123007	+	0.992406i	$0.460746\pi$
$368$	1358.30	0.192409
$369$	2182.96	0.307969
$370$	13783.1	1.93662
$371$	−1219.04	−0.170592
$372$	−1779.73	−0.248050
$373$	−9748.22	−1.35320	−0.676600	−	0.736351i	$-0.736547\pi$
$373$	−9748.22	−1.35320	−0.676600	+	0.736351i	$0.736547\pi$
$374$	605.723	0.0837465
$375$	−2440.36	−0.336053
$376$	3082.78	0.422825
$377$	6132.93	0.837830
$378$	378.000	0.0514344
$379$	7054.64	0.956128	0.478064	−	0.878325i	$-0.341339\pi$
$379$	7054.64	0.956128	0.478064	+	0.878325i	$0.341339\pi$
$380$	1310.17	0.176869
$381$	−6860.43	−0.922495
$382$	−1049.13	−0.140518
$383$	3655.46	0.487689	0.243845	−	0.969814i	$-0.421591\pi$
$383$	3655.46	0.487689	0.243845	+	0.969814i	$0.421591\pi$
$384$	384.000	0.0510310
$385$	−3974.79	−0.526167
$386$	−6251.30	−0.824308
$387$	3559.08	0.467489
$388$	4863.60	0.636371
$389$	8655.08	1.12810	0.564049	−	0.825741i	$-0.309243\pi$
$389$	8655.08	1.12810	0.564049	+	0.825741i	$0.309243\pi$
$390$	5505.89	0.714876
$391$	780.583	0.100961
$392$	−392.000	−0.0505076
$393$	−5173.90	−0.664093
$394$	6698.31	0.856488
$395$	−15423.0	−1.96460
$396$	−1185.78	−0.150474
$397$	−1058.29	−0.133789	−0.0668943	−	0.997760i	$-0.521309\pi$
$397$	−1058.29	−0.133789	−0.0668943	+	0.997760i	$0.521309\pi$
$398$	−6462.03	−0.813851
$399$	−399.000	−0.0500626
$400$	2754.99	0.344373
$401$	−931.428	−0.115993	−0.0579966	−	0.998317i	$-0.518471\pi$
$401$	−931.428	−0.115993	−0.0579966	+	0.998317i	$0.518471\pi$
$402$	−3750.09	−0.465268
$403$	7894.67	0.975835
$404$	5164.95	0.636054
$405$	1396.37	0.171324
$406$	−1613.00	−0.197172
$407$	13167.5	1.60366
$408$	220.675	0.0267771
$409$	−11492.2	−1.38938	−0.694688	−	0.719311i	$-0.744458\pi$
$409$	−11492.2	−1.38938	−0.694688	+	0.719311i	$0.744458\pi$
$410$	−8362.73	−1.00733
$411$	−4575.86	−0.549175
$412$	2282.95	0.272992
$413$	2132.25	0.254046
$414$	−1528.09	−0.181405
$415$	3402.21	0.402429
$416$	−1703.38	−0.200758
$417$	−5326.17	−0.625476
$418$	1251.66	0.146461
$419$	−5507.95	−0.642198	−0.321099	−	0.947046i	$-0.604052\pi$
$419$	−5507.95	−0.642198	−0.321099	+	0.947046i	$0.604052\pi$
$420$	−1448.08	−0.168236
$421$	−4768.29	−0.552001	−0.276001	−	0.961157i	$-0.589009\pi$
$421$	−4768.29	−0.552001	−0.276001	+	0.961157i	$0.589009\pi$
$422$	−4364.43	−0.503453
$423$	−3468.12	−0.398643
$424$	1393.19	0.159574
$425$	1583.22	0.180700
$426$	−5887.95	−0.669652
$427$	−1252.45	−0.141944
$428$	−7068.06	−0.798242
$429$	5259.99	0.591969
$430$	−13634.5	−1.52910
$431$	−17739.0	−1.98250	−0.991250	−	0.131995i	$-0.957862\pi$
$431$	−17739.0	−1.98250	−0.991250	+	0.131995i	$0.957862\pi$
$432$	−432.000	−0.0481125
$433$	−6281.49	−0.697158	−0.348579	−	0.937279i	$-0.613336\pi$
$433$	−6281.49	−0.697158	−0.348579	+	0.937279i	$0.613336\pi$
$434$	−2076.35	−0.229650
$435$	−5958.57	−0.656762
$436$	2736.82	0.300619
$437$	1612.99	0.176567
$438$	7114.01	0.776074
$439$	−14319.2	−1.55676	−0.778379	−	0.627794i	$-0.783958\pi$
$439$	−14319.2	−1.55676	−0.778379	+	0.627794i	$0.783958\pi$
$440$	4542.62	0.492184
$441$	441.000	0.0476190
$442$	−978.890	−0.105342
$443$	13616.3	1.46034	0.730172	−	0.683264i	$-0.239440\pi$
$443$	13616.3	1.46034	0.730172	+	0.683264i	$0.239440\pi$
$444$	4797.16	0.512754
$445$	145.300	0.0154784
$446$	2454.46	0.260588
$447$	2568.22	0.271751
$448$	448.000	0.0472456
$449$	9440.26	0.992235	0.496118	−	0.868255i	$-0.334758\pi$
$449$	9440.26	0.992235	0.496118	+	0.868255i	$0.334758\pi$
$450$	−3099.36	−0.324678
$451$	−7989.24	−0.834143
$452$	5373.19	0.559146
$453$	−3056.51	−0.317014
$454$	4494.41	0.464610
$455$	6423.54	0.661847
$456$	456.000	0.0468293
$457$	8254.68	0.844940	0.422470	−	0.906377i	$-0.361163\pi$
$457$	8254.68	0.844940	0.422470	+	0.906377i	$0.361163\pi$
$458$	−4100.64	−0.418364
$459$	−248.259	−0.0252457
$460$	5853.99	0.593356
$461$	−510.133	−0.0515385	−0.0257693	−	0.999668i	$-0.508204\pi$
$461$	−510.133	−0.0515385	−0.0257693	+	0.999668i	$0.508204\pi$
$462$	−1383.41	−0.139312
$463$	9098.06	0.913224	0.456612	−	0.889666i	$-0.349063\pi$
$463$	9098.06	0.913224	0.456612	+	0.889666i	$0.349063\pi$
$464$	1843.43	0.184438
$465$	−7670.22	−0.764942
$466$	−5409.98	−0.537795
$467$	−15915.0	−1.57700	−0.788500	−	0.615035i	$-0.789142\pi$
$467$	−15915.0	−1.57700	−0.788500	+	0.615035i	$0.789142\pi$
$468$	1916.30	0.189276
$469$	−4375.11	−0.430754
$470$	13286.1	1.30392
$471$	−9088.26	−0.889098
$472$	−2436.85	−0.237638
$473$	−13025.6	−1.26621
$474$	−5367.93	−0.520163
$475$	3271.55	0.316019
$476$	257.454	0.0247907
$477$	−1567.34	−0.150448
$478$	−12400.0	−1.18653
$479$	−9283.35	−0.885526	−0.442763	−	0.896639i	$-0.646002\pi$
$479$	−9283.35	−0.885526	−0.442763	+	0.896639i	$0.646002\pi$
$480$	1654.95	0.157371
$481$	−21279.7	−2.01719
$482$	−739.362	−0.0698693
$483$	−1782.77	−0.167948
$484$	−984.260	−0.0924362
$485$	20961.0	1.96246
$486$	486.000	0.0453609
$487$	322.642	0.0300212	0.0150106	−	0.999887i	$-0.495222\pi$
$487$	322.642	0.0300212	0.0150106	+	0.999887i	$0.495222\pi$
$488$	1431.37	0.132776
$489$	1757.03	0.162486
$490$	−1689.43	−0.155757
$491$	−7905.47	−0.726617	−0.363308	−	0.931669i	$-0.618353\pi$
$491$	−7905.47	−0.726617	−0.363308	+	0.931669i	$0.618353\pi$
$492$	−2910.62	−0.266709
$493$	1059.37	0.0967783
$494$	−2022.77	−0.184228
$495$	−5110.45	−0.464035
$496$	2372.97	0.214817
$497$	−6869.27	−0.619978
$498$	1184.13	0.106550
$499$	−21428.1	−1.92235	−0.961176	−	0.275936i	$-0.911012\pi$
$499$	−21428.1	−1.92235	−0.961176	+	0.275936i	$0.911012\pi$
$500$	3253.82	0.291030
$501$	11576.8	1.03236
$502$	1984.36	0.176427
$503$	−3916.95	−0.347213	−0.173606	−	0.984815i	$-0.555542\pi$
$503$	−3916.95	−0.347213	−0.173606	+	0.984815i	$0.555542\pi$
$504$	−504.000	−0.0445435
$505$	22259.8	1.96148
$506$	5592.54	0.491341
$507$	−1909.51	−0.167267
$508$	9147.24	0.798904
$509$	−5416.23	−0.471651	−0.235826	−	0.971795i	$-0.575779\pi$
$509$	−5416.23	−0.471651	−0.235826	+	0.971795i	$0.575779\pi$
$510$	951.060	0.0825758
$511$	8299.68	0.718505
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	10104.0	0.867056
$515$	9839.00	0.841861
$516$	−4745.44	−0.404857
$517$	12692.7	1.07974
$518$	5596.68	0.474718
$519$	−1362.46	−0.115232
$520$	−7341.19	−0.619101
$521$	1772.03	0.149010	0.0745048	−	0.997221i	$-0.476262\pi$
$521$	1772.03	0.149010	0.0745048	+	0.997221i	$0.476262\pi$
$522$	−2073.86	−0.173889
$523$	−10436.7	−0.872595	−0.436297	−	0.899803i	$-0.643710\pi$
$523$	−10436.7	−0.872595	−0.436297	+	0.899803i	$0.643710\pi$
$524$	6898.53	0.575122
$525$	−3615.92	−0.300594
$526$	12960.8	1.07437
$527$	1363.69	0.112719
$528$	1581.04	0.130314
$529$	−4960.00	−0.407660
$530$	6004.35	0.492098
$531$	2741.46	0.224048
$532$	532.000	0.0433555
$533$	12911.2	1.04924
$534$	50.5712	0.00409818
$535$	−30461.8	−2.46164
$536$	5000.13	0.402934
$537$	9605.66	0.771908
$538$	4530.68	0.363070
$539$	−1613.98	−0.128978
$540$	−1861.82	−0.148371
$541$	565.507	0.0449409	0.0224705	−	0.999748i	$-0.492847\pi$
$541$	565.507	0.0449409	0.0224705	+	0.999748i	$0.492847\pi$
$542$	−8345.58	−0.661390
$543$	−2833.36	−0.223925
$544$	−294.233	−0.0231896
$545$	11795.1	0.927055
$546$	2235.69	0.175236
$547$	−841.325	−0.0657632	−0.0328816	−	0.999459i	$-0.510468\pi$
$547$	−841.325	−0.0657632	−0.0328816	+	0.999459i	$0.510468\pi$
$548$	6101.15	0.475599
$549$	−1610.29	−0.125183
$550$	11343.1	0.879401
$551$	2189.07	0.169251
$552$	2037.46	0.157101
$553$	−6262.58	−0.481577
$554$	2274.05	0.174396
$555$	20674.7	1.58124
$556$	7101.56	0.541678
$557$	12874.9	0.979402	0.489701	−	0.871890i	$-0.337106\pi$
$557$	12874.9	0.979402	0.489701	+	0.871890i	$0.337106\pi$
$558$	−2669.59	−0.202532
$559$	21050.2	1.59272
$560$	1930.78	0.145697
$561$	908.584	0.0683787
$562$	−10483.5	−0.786865
$563$	−4717.12	−0.353113	−0.176557	−	0.984290i	$-0.556496\pi$
$563$	−4717.12	−0.353113	−0.176557	+	0.984290i	$0.556496\pi$
$564$	4624.17	0.345235
$565$	23157.3	1.72431
$566$	−7472.51	−0.554934
$567$	567.000	0.0419961
$568$	7850.60	0.579936
$569$	−13903.9	−1.02440	−0.512200	−	0.858866i	$-0.671169\pi$
$569$	−13903.9	−1.02440	−0.512200	+	0.858866i	$0.671169\pi$
$570$	1965.26	0.144413
$571$	1435.47	0.105206	0.0526028	−	0.998616i	$-0.483248\pi$
$571$	1435.47	0.105206	0.0526028	+	0.998616i	$0.483248\pi$
$572$	−7013.32	−0.512660
$573$	−1573.69	−0.114733
$574$	−3395.72	−0.246924
$575$	14617.6	1.06017
$576$	576.000	0.0416667
$577$	−9978.20	−0.719927	−0.359964	−	0.932966i	$-0.617211\pi$
$577$	−9978.20	−0.719927	−0.359964	+	0.932966i	$0.617211\pi$
$578$	9656.91	0.694939
$579$	−9376.95	−0.673044
$580$	7944.76	0.568773
$581$	1381.48	0.0986463
$582$	7295.41	0.519595
$583$	5736.18	0.407493
$584$	−9485.34	−0.672100
$585$	8258.84	0.583694
$586$	−3309.90	−0.233329
$587$	3268.26	0.229805	0.114902	−	0.993377i	$-0.463344\pi$
$587$	3268.26	0.229805	0.114902	+	0.993377i	$0.463344\pi$
$588$	−588.000	−0.0412393
$589$	2817.90	0.197130
$590$	−10502.3	−0.732835
$591$	10047.5	0.699319
$592$	−6396.21	−0.444058
$593$	21648.3	1.49914	0.749568	−	0.661928i	$-0.230261\pi$
$593$	21648.3	1.49914	0.749568	+	0.661928i	$0.230261\pi$
$594$	−1778.67	−0.122862
$595$	1109.57	0.0764503
$596$	−3424.30	−0.235344
$597$	−9693.05	−0.664506
$598$	−9037.93	−0.618041
$599$	−3168.59	−0.216135	−0.108068	−	0.994144i	$-0.534466\pi$
$599$	−3168.59	−0.216135	−0.108068	+	0.994144i	$0.534466\pi$
$600$	4132.48	0.281180
$601$	−11048.2	−0.749859	−0.374929	−	0.927053i	$-0.622333\pi$
$601$	−11048.2	−0.749859	−0.374929	+	0.927053i	$0.622333\pi$
$602$	−5536.35	−0.374825
$603$	−5625.14	−0.379890
$604$	4075.35	0.274543
$605$	−4241.94	−0.285057
$606$	7747.42	0.519336
$607$	16734.2	1.11898	0.559489	−	0.828838i	$-0.310997\pi$
$607$	16734.2	1.11898	0.559489	+	0.828838i	$0.310997\pi$
$608$	−608.000	−0.0405554
$609$	−2419.50	−0.160990
$610$	6168.87	0.409459
$611$	−20512.3	−1.35816
$612$	331.013	0.0218634
$613$	−21075.7	−1.38864	−0.694321	−	0.719665i	$-0.744295\pi$
$613$	−21075.7	−1.38864	−0.694321	+	0.719665i	$0.744295\pi$
$614$	−15642.8	−1.02816
$615$	−12544.1	−0.822483
$616$	1844.55	0.120648
$617$	4697.28	0.306492	0.153246	−	0.988188i	$-0.451027\pi$
$617$	4697.28	0.306492	0.153246	+	0.988188i	$0.451027\pi$
$618$	3424.43	0.222897
$619$	17397.9	1.12970	0.564849	−	0.825195i	$-0.308935\pi$
$619$	17397.9	1.12970	0.564849	+	0.825195i	$0.308935\pi$
$620$	10227.0	0.662459
$621$	−2292.14	−0.148117
$622$	19792.8	1.27591
$623$	58.9997	0.00379418
$624$	−2555.07	−0.163918
$625$	−7500.10	−0.480007
$626$	−5607.94	−0.358048
$627$	1877.49	0.119585
$628$	12117.7	0.769981
$629$	−3675.74	−0.233007
$630$	−2172.13	−0.137364
$631$	−6459.89	−0.407550	−0.203775	−	0.979018i	$-0.565321\pi$
$631$	−6459.89	−0.407550	−0.203775	+	0.979018i	$0.565321\pi$
$632$	7157.24	0.450474
$633$	−6546.64	−0.411067
$634$	−8461.17	−0.530025
$635$	39422.6	2.46368
$636$	2089.79	0.130292
$637$	2608.30	0.162237
$638$	7589.94	0.470985
$639$	−8831.92	−0.546769
$640$	−2206.60	−0.136287
$641$	−20393.4	−1.25662	−0.628309	−	0.777964i	$-0.716253\pi$
$641$	−20393.4	−1.25662	−0.628309	+	0.777964i	$0.716253\pi$
$642$	−10602.1	−0.651762
$643$	14774.7	0.906152	0.453076	−	0.891472i	$-0.350327\pi$
$643$	14774.7	0.906152	0.453076	+	0.891472i	$0.350327\pi$
$644$	2377.03	0.145448
$645$	−20451.8	−1.24851
$646$	−349.402	−0.0212803
$647$	10730.8	0.652045	0.326022	−	0.945362i	$-0.394291\pi$
$647$	10730.8	0.652045	0.326022	+	0.945362i	$0.394291\pi$
$648$	−648.000	−0.0392837
$649$	−10033.2	−0.606840
$650$	−18331.2	−1.10617
$651$	−3114.52	−0.187508
$652$	−2342.71	−0.140717
$653$	−8470.22	−0.507604	−0.253802	−	0.967256i	$-0.581681\pi$
$653$	−8470.22	−0.507604	−0.253802	+	0.967256i	$0.581681\pi$
$654$	4105.22	0.245454
$655$	29731.1	1.77357
$656$	3880.82	0.230977
$657$	10671.0	0.633662
$658$	5394.86	0.319625
$659$	−5512.65	−0.325861	−0.162930	−	0.986638i	$-0.552095\pi$
$659$	−5512.65	−0.325861	−0.162930	+	0.986638i	$0.552095\pi$
$660$	6813.93	0.401866
$661$	−248.418	−0.0146177	−0.00730887	−	0.999973i	$-0.502327\pi$
$661$	−248.418	−0.0146177	−0.00730887	+	0.999973i	$0.502327\pi$
$662$	−4482.61	−0.263175
$663$	−1468.34	−0.0860112
$664$	−1578.84	−0.0922752
$665$	2292.80	0.133701
$666$	7195.73	0.418662
$667$	9781.00	0.567799
$668$	−15435.8	−0.894053
$669$	3681.70	0.212769
$670$	21549.4	1.24258
$671$	5893.35	0.339062
$672$	672.000	0.0385758
$673$	−761.537	−0.0436183	−0.0218091	−	0.999762i	$-0.506943\pi$
$673$	−761.537	−0.0436183	−0.0218091	+	0.999762i	$0.506943\pi$
$674$	10376.7	0.593018
$675$	−4649.04	−0.265099
$676$	2546.02	0.144858
$677$	−22992.3	−1.30527	−0.652634	−	0.757674i	$-0.726336\pi$
$677$	−22992.3	−1.30527	−0.652634	+	0.757674i	$0.726336\pi$
$678$	8059.79	0.456540
$679$	8511.31	0.481051
$680$	−1268.08	−0.0715127
$681$	6741.61	0.379353
$682$	9770.21	0.548564
$683$	12789.9	0.716534	0.358267	−	0.933619i	$-0.383368\pi$
$683$	12789.9	0.716534	0.358267	+	0.933619i	$0.383368\pi$
$684$	684.000	0.0382360
$685$	26294.6	1.46666
$686$	−686.000	−0.0381802
$687$	−6150.97	−0.341592
$688$	6327.25	0.350617
$689$	−9270.07	−0.512571
$690$	8780.98	0.484473
$691$	27002.6	1.48658	0.743292	−	0.668968i	$-0.233264\pi$
$691$	27002.6	1.48658	0.743292	+	0.668968i	$0.233264\pi$
$692$	1816.61	0.0997936
$693$	−2075.12	−0.113748
$694$	−17840.7	−0.975825
$695$	30606.1	1.67044
$696$	2765.14	0.150593
$697$	2230.21	0.121198
$698$	745.112	0.0404053
$699$	−8114.96	−0.439107
$700$	4821.22	0.260322
$701$	−29295.4	−1.57842	−0.789210	−	0.614123i	$-0.789510\pi$
$701$	−29295.4	−1.57842	−0.789210	+	0.614123i	$0.789510\pi$
$702$	2874.46	0.154543
$703$	−7595.50	−0.407496
$704$	−2108.05	−0.112856
$705$	19929.1	1.06464
$706$	−18579.0	−0.990412
$707$	9038.65	0.480811
$708$	−3655.28	−0.194031
$709$	17307.3	0.916770	0.458385	−	0.888754i	$-0.348428\pi$
$709$	17307.3	0.916770	0.458385	+	0.888754i	$0.348428\pi$
$710$	33834.3	1.78842
$711$	−8051.89	−0.424711
$712$	−67.4282	−0.00354913
$713$	12590.7	0.661325
$714$	386.181	0.0202416
$715$	−30225.8	−1.58095
$716$	−12807.5	−0.668492
$717$	−18600.0	−0.968799
$718$	12078.6	0.627812
$719$	−30816.2	−1.59840	−0.799201	−	0.601064i	$-0.794744\pi$
$719$	−30816.2	−1.59840	−0.799201	+	0.601064i	$0.794744\pi$
$720$	2482.43	0.128493
$721$	3995.16	0.206363
$722$	−722.000	−0.0372161
$723$	−1109.04	−0.0570481
$724$	3777.82	0.193925
$725$	19838.4	1.01625
$726$	−1476.39	−0.0754738
$727$	18073.9	0.922043	0.461021	−	0.887389i	$-0.347483\pi$
$727$	18073.9	0.922043	0.461021	+	0.887389i	$0.347483\pi$
$728$	−2980.92	−0.151758
$729$	729.000	0.0370370
$730$	−40879.7	−2.07264
$731$	3636.11	0.183976
$732$	2147.05	0.108411
$733$	−5457.36	−0.274996	−0.137498	−	0.990502i	$-0.543906\pi$
$733$	−5457.36	−0.274996	−0.137498	+	0.990502i	$0.543906\pi$
$734$	−3459.31	−0.173959
$735$	−2534.15	−0.127175
$736$	−2716.61	−0.136054
$737$	20587.0	1.02894
$738$	−4365.92	−0.217767
$739$	−36422.7	−1.81303	−0.906515	−	0.422173i	$-0.861267\pi$
$739$	−36422.7	−1.81303	−0.906515	+	0.422173i	$0.861267\pi$
$740$	−27566.2	−1.36940
$741$	−3034.15	−0.150421
$742$	2438.09	0.120627
$743$	26939.8	1.33018	0.665090	−	0.746763i	$-0.268393\pi$
$743$	26939.8	1.33018	0.665090	+	0.746763i	$0.268393\pi$
$744$	3559.45	0.175398
$745$	−14758.0	−0.725758
$746$	19496.4	0.956857
$747$	1776.19	0.0869979
$748$	−1211.45	−0.0592177
$749$	−12369.1	−0.603415
$750$	4880.73	0.237625
$751$	3773.23	0.183338	0.0916692	−	0.995790i	$-0.470780\pi$
$751$	3773.23	0.183338	0.0916692	+	0.995790i	$0.470780\pi$
$752$	−6165.55	−0.298982
$753$	2976.54	0.144052
$754$	−12265.9	−0.592436
$755$	17563.8	0.846641
$756$	−756.000	−0.0363696
$757$	34964.1	1.67872	0.839361	−	0.543574i	$-0.182929\pi$
$757$	34964.1	1.67872	0.839361	+	0.543574i	$0.182929\pi$
$758$	−14109.3	−0.676085
$759$	8388.81	0.401179
$760$	−2620.34	−0.125066
$761$	10245.4	0.488036	0.244018	−	0.969771i	$-0.421534\pi$
$761$	10245.4	0.488036	0.244018	+	0.969771i	$0.421534\pi$
$762$	13720.9	0.652302
$763$	4789.43	0.227246
$764$	2098.26	0.0993616
$765$	1426.59	0.0674228
$766$	−7310.91	−0.344849
$767$	16214.4	0.763323
$768$	−768.000	−0.0360844
$769$	−888.305	−0.0416555	−0.0208278	−	0.999783i	$-0.506630\pi$
$769$	−888.305	−0.0416555	−0.0208278	+	0.999783i	$0.506630\pi$
$770$	7949.59	0.372056
$771$	15156.0	0.707948
$772$	12502.6	0.582873
$773$	−5451.77	−0.253670	−0.126835	−	0.991924i	$-0.540482\pi$
$773$	−5451.77	−0.253670	−0.126835	+	0.991924i	$0.540482\pi$
$774$	−7118.16	−0.330565
$775$	25537.1	1.18364
$776$	−9727.21	−0.449982
$777$	8395.02	0.387606
$778$	−17310.2	−0.797686
$779$	4608.48	0.211959
$780$	−11011.8	−0.505494
$781$	32323.2	1.48094
$782$	−1561.17	−0.0713903
$783$	−3110.79	−0.141980
$784$	784.000	0.0357143
$785$	52224.5	2.37449
$786$	10347.8	0.469585
$787$	12923.9	0.585372	0.292686	−	0.956209i	$-0.405451\pi$
$787$	12923.9	0.585372	0.292686	+	0.956209i	$0.405451\pi$
$788$	−13396.6	−0.605628
$789$	19441.2	0.877220
$790$	30846.1	1.38918
$791$	9403.09	0.422674
$792$	2371.56	0.106401
$793$	−9524.07	−0.426494
$794$	2116.58	0.0946029
$795$	9006.52	0.401797
$796$	12924.1	0.575479
$797$	−33813.0	−1.50278	−0.751391	−	0.659858i	$-0.770617\pi$
$797$	−33813.0	−1.50278	−0.751391	+	0.659858i	$0.770617\pi$
$798$	798.000	0.0353996
$799$	−3543.19	−0.156882
$800$	−5509.97	−0.243509
$801$	75.8567	0.00334615
$802$	1862.86	0.0820196
$803$	−39054.0	−1.71629
$804$	7500.19	0.328994
$805$	10244.5	0.448535
$806$	−15789.3	−0.690020
$807$	6796.02	0.296445
$808$	−10329.9	−0.449758
$809$	−35578.3	−1.54619	−0.773095	−	0.634290i	$-0.781292\pi$
$809$	−35578.3	−1.54619	−0.773095	+	0.634290i	$0.781292\pi$
$810$	−2792.73	−0.121144
$811$	−35677.9	−1.54479	−0.772393	−	0.635145i	$-0.780941\pi$
$811$	−35677.9	−1.54479	−0.772393	+	0.635145i	$0.780941\pi$
$812$	3226.00	0.139422
$813$	−12518.4	−0.540022
$814$	−26335.1	−1.13396
$815$	−10096.5	−0.433947
$816$	−441.350	−0.0189342
$817$	7513.61	0.321748
$818$	22984.5	0.982438
$819$	3353.53	0.143079
$820$	16725.5	0.712291
$821$	30982.2	1.31703	0.658517	−	0.752566i	$-0.271184\pi$
$821$	30982.2	1.31703	0.658517	+	0.752566i	$0.271184\pi$
$822$	9151.73	0.388325
$823$	18765.8	0.794817	0.397409	−	0.917642i	$-0.369910\pi$
$823$	18765.8	0.794817	0.397409	+	0.917642i	$0.369910\pi$
$824$	−4565.90	−0.193035
$825$	17014.6	0.718028
$826$	−4264.49	−0.179638
$827$	−31215.5	−1.31254	−0.656269	−	0.754527i	$-0.727866\pi$
$827$	−31215.5	−1.31254	−0.656269	+	0.754527i	$0.727866\pi$
$828$	3056.19	0.128273
$829$	−36528.6	−1.53039	−0.765193	−	0.643801i	$-0.777357\pi$
$829$	−36528.6	−1.53039	−0.765193	+	0.643801i	$0.777357\pi$
$830$	−6804.43	−0.284560
$831$	3411.08	0.142393
$832$	3406.76	0.141957
$833$	450.545	0.0187400
$834$	10652.3	0.442279
$835$	−66524.6	−2.75710
$836$	−2503.31	−0.103563
$837$	−4004.39	−0.165367
$838$	11015.9	0.454102
$839$	8707.37	0.358298	0.179149	−	0.983822i	$-0.442666\pi$
$839$	8707.37	0.358298	0.179149	+	0.983822i	$0.442666\pi$
$840$	2896.17	0.118961
$841$	−11114.7	−0.455725
$842$	9536.59	0.390324
$843$	−15725.2	−0.642472
$844$	8728.86	0.355995
$845$	10972.8	0.446715
$846$	6936.25	0.281883
$847$	−1722.46	−0.0698752
$848$	−2786.39	−0.112836
$849$	−11208.8	−0.453102
$850$	−3166.44	−0.127774
$851$	−33937.5	−1.36705
$852$	11775.9	0.473516
$853$	−9385.08	−0.376716	−0.188358	−	0.982100i	$-0.560317\pi$
$853$	−9385.08	−0.376716	−0.188358	+	0.982100i	$0.560317\pi$
$854$	2504.89	0.100370
$855$	2947.89	0.117913
$856$	14136.1	0.564443
$857$	−46282.8	−1.84480	−0.922399	−	0.386238i	$-0.873774\pi$
$857$	−46282.8	−1.84480	−0.922399	+	0.386238i	$0.873774\pi$
$858$	−10520.0	−0.418585
$859$	−36548.9	−1.45172	−0.725862	−	0.687840i	$-0.758559\pi$
$859$	−36548.9	−1.45172	−0.725862	+	0.687840i	$0.758559\pi$
$860$	27269.0	1.08124
$861$	−5093.58	−0.201613
$862$	35478.0	1.40184
$863$	−10348.3	−0.408179	−0.204090	−	0.978952i	$-0.565423\pi$
$863$	−10348.3	−0.408179	−0.204090	+	0.978952i	$0.565423\pi$
$864$	864.000	0.0340207
$865$	7829.18	0.307746
$866$	12563.0	0.492965
$867$	14485.4	0.567415
$868$	4152.70	0.162387
$869$	29468.5	1.15034
$870$	11917.1	0.464401
$871$	−33270.0	−1.29427
$872$	−5473.63	−0.212569
$873$	10943.1	0.424248
$874$	−3225.97	−0.124851
$875$	5694.18	0.219998
$876$	−14228.0	−0.548767
$877$	−24785.4	−0.954327	−0.477163	−	0.878815i	$-0.658335\pi$
$877$	−24785.4	−0.954327	−0.477163	+	0.878815i	$0.658335\pi$
$878$	28638.4	1.10079
$879$	−4964.85	−0.190512
$880$	−9085.24	−0.348027
$881$	−25830.3	−0.987794	−0.493897	−	0.869521i	$-0.664428\pi$
$881$	−25830.3	−0.987794	−0.493897	+	0.869521i	$0.664428\pi$
$882$	−882.000	−0.0336718
$883$	−13850.4	−0.527862	−0.263931	−	0.964542i	$-0.585019\pi$
$883$	−13850.4	−0.527862	−0.263931	+	0.964542i	$0.585019\pi$
$884$	1957.78	0.0744879
$885$	−15753.4	−0.598357
$886$	−27232.7	−1.03262
$887$	40635.2	1.53822	0.769108	−	0.639119i	$-0.220701\pi$
$887$	40635.2	1.53822	0.769108	+	0.639119i	$0.220701\pi$
$888$	−9594.31	−0.362572
$889$	16007.7	0.603915
$890$	−290.600	−0.0109449
$891$	−2668.01	−0.100316
$892$	−4908.93	−0.184264
$893$	−7321.60	−0.274365
$894$	−5136.45	−0.192157
$895$	−55197.6	−2.06151
$896$	−896.000	−0.0334077
$897$	−13556.9	−0.504628
$898$	−18880.5	−0.701616
$899$	17087.5	0.633926
$900$	6198.72	0.229582
$901$	−1601.27	−0.0592074
$902$	15978.5	0.589829
$903$	−8304.52	−0.306043
$904$	−10746.4	−0.395376
$905$	16281.5	0.598029
$906$	6113.03	0.224163
$907$	−9481.35	−0.347104	−0.173552	−	0.984825i	$-0.555524\pi$
$907$	−9481.35	−0.347104	−0.173552	+	0.984825i	$0.555524\pi$
$908$	−8988.81	−0.328529
$909$	11621.1	0.424036
$910$	−12847.1	−0.467996
$911$	12969.1	0.471665	0.235833	−	0.971794i	$-0.424218\pi$
$911$	12969.1	0.471665	0.235833	+	0.971794i	$0.424218\pi$
$912$	−912.000	−0.0331133
$913$	−6500.53	−0.235637
$914$	−16509.4	−0.597463
$915$	9253.30	0.334322
$916$	8201.29	0.295828
$917$	12072.4	0.434751
$918$	496.519	0.0178514
$919$	−2277.89	−0.0817634	−0.0408817	−	0.999164i	$-0.513017\pi$
$919$	−2277.89	−0.0817634	−0.0408817	+	0.999164i	$0.513017\pi$
$920$	−11708.0	−0.419566
$921$	−23464.2	−0.839491
$922$	1020.27	0.0364432
$923$	−52236.6	−1.86282
$924$	2766.82	0.0985084
$925$	−68833.8	−2.44675
$926$	−18196.1	−0.645747
$927$	5136.64	0.181995
$928$	−3686.86	−0.130417
$929$	−10005.1	−0.353345	−0.176673	−	0.984270i	$-0.556533\pi$
$929$	−10005.1	−0.353345	−0.176673	+	0.984270i	$0.556533\pi$
$930$	15340.4	0.540896
$931$	931.000	0.0327737
$932$	10820.0	0.380278
$933$	29689.2	1.04178
$934$	31830.0	1.11511
$935$	−5221.06	−0.182617
$936$	−3832.61	−0.133838
$937$	10787.9	0.376122	0.188061	−	0.982157i	$-0.439780\pi$
$937$	10787.9	0.376122	0.188061	+	0.982157i	$0.439780\pi$
$938$	8750.22	0.304589
$939$	−8411.91	−0.292345
$940$	−26572.2	−0.922009
$941$	−885.733	−0.0306845	−0.0153422	−	0.999882i	$-0.504884\pi$
$941$	−885.733	−0.0306845	−0.0153422	+	0.999882i	$0.504884\pi$
$942$	18176.5	0.628687
$943$	20591.2	0.711072
$944$	4873.71	0.168036
$945$	−3258.19	−0.112158
$946$	26051.2	0.895345
$947$	−46099.4	−1.58187	−0.790934	−	0.611901i	$-0.790405\pi$
$947$	−46099.4	−1.58187	−0.790934	+	0.611901i	$0.790405\pi$
$948$	10735.9	0.367811
$949$	63113.9	2.15887
$950$	−6543.09	−0.223459
$951$	−12691.8	−0.432764
$952$	−514.909	−0.0175297
$953$	19066.6	0.648087	0.324044	−	0.946042i	$-0.394958\pi$
$953$	19066.6	0.648087	0.324044	+	0.946042i	$0.394958\pi$
$954$	3134.68	0.106383
$955$	9043.01	0.306414
$956$	24800.0	0.839004
$957$	11384.9	0.384558
$958$	18566.7	0.626162
$959$	10677.0	0.359519
$960$	−3309.91	−0.111278
$961$	−7794.97	−0.261655
$962$	42559.3	1.42637
$963$	−15903.1	−0.532162
$964$	1478.72	0.0494051
$965$	53883.4	1.79748
$966$	3565.55	0.118757
$967$	−46332.1	−1.54079	−0.770394	−	0.637569i	$-0.779940\pi$
$967$	−46332.1	−1.54079	−0.770394	+	0.637569i	$0.779940\pi$
$968$	1968.52	0.0653622
$969$	−524.103	−0.0173753
$970$	−41922.1	−1.38767
$971$	19968.6	0.659963	0.329982	−	0.943987i	$-0.392957\pi$
$971$	19968.6	0.659963	0.329982	+	0.943987i	$0.392957\pi$
$972$	−972.000	−0.0320750
$973$	12427.7	0.409470
$974$	−645.285	−0.0212282
$975$	−27496.8	−0.903183
$976$	−2862.73	−0.0938871
$977$	41189.0	1.34877	0.674387	−	0.738378i	$-0.264408\pi$
$977$	41189.0	1.34877	0.674387	+	0.738378i	$0.264408\pi$
$978$	−3514.06	−0.114895
$979$	−277.622	−0.00906316
$980$	3378.86	0.110137
$981$	6157.83	0.200412
$982$	15810.9	0.513796
$983$	−22552.8	−0.731764	−0.365882	−	0.930661i	$-0.619233\pi$
$983$	−22552.8	−0.731764	−0.365882	+	0.930661i	$0.619233\pi$
$984$	5821.23	0.188592
$985$	−57736.4	−1.86765
$986$	−2118.74	−0.0684326
$987$	8092.29	0.260973
$988$	4045.53	0.130269
$989$	33571.6	1.07939
$990$	10220.9	0.328123
$991$	2518.69	0.0807353	0.0403676	−	0.999185i	$-0.487147\pi$
$991$	2518.69	0.0807353	0.0403676	+	0.999185i	$0.487147\pi$
$992$	−4745.94	−0.151899
$993$	−6723.92	−0.214881
$994$	13738.5	0.438390
$995$	55699.8	1.77468
$996$	−2368.25	−0.0753424
$997$	−50757.6	−1.61235	−0.806174	−	0.591679i	$-0.798465\pi$
$997$	−50757.6	−1.61235	−0.806174	+	0.591679i	$0.798465\pi$
$998$	42856.2	1.35931
$999$	10793.6	0.341836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.l.1.4	✓	4
3.2	odd	2		2394.4.a.s.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.l.1.4	✓	4	1.1	even	1	trivial
2394.4.a.s.1.1		4	3.2	odd	2

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:	\( N \)	\(=\)	\( 798 = 2 \cdot 3 \cdot 7 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +17.2391 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +17.2391 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -34.4782 q^{10} -32.9384 q^{11} -12.0000 q^{12} +53.2307 q^{13} -14.0000 q^{14} -51.7173 q^{15} +16.0000 q^{16} +9.19480 q^{17} -18.0000 q^{18} +19.0000 q^{19} +68.9564 q^{20} -21.0000 q^{21} +65.8767 q^{22} +84.8940 q^{23} +24.0000 q^{24} +172.187 q^{25} -106.461 q^{26} -27.0000 q^{27} +28.0000 q^{28} +115.214 q^{29} +103.435 q^{30} +148.311 q^{31} -32.0000 q^{32} +98.8151 q^{33} -18.3896 q^{34} +120.674 q^{35} +36.0000 q^{36} -399.763 q^{37} -38.0000 q^{38} -159.692 q^{39} -137.913 q^{40} +242.551 q^{41} +42.0000 q^{42} +395.453 q^{43} -131.753 q^{44} +155.152 q^{45} -169.788 q^{46} -385.347 q^{47} -48.0000 q^{48} +49.0000 q^{49} -344.373 q^{50} -27.5844 q^{51} +212.923 q^{52} -174.149 q^{53} +54.0000 q^{54} -567.828 q^{55} -56.0000 q^{56} -57.0000 q^{57} -230.429 q^{58} +304.607 q^{59} -206.869 q^{60} -178.921 q^{61} -296.621 q^{62} +63.0000 q^{63} +64.0000 q^{64} +917.649 q^{65} -197.630 q^{66} -625.016 q^{67} +36.7792 q^{68} -254.682 q^{69} -241.347 q^{70} -981.324 q^{71} -72.0000 q^{72} +1185.67 q^{73} +799.526 q^{74} -516.560 q^{75} +76.0000 q^{76} -230.568 q^{77} +319.384 q^{78} -894.655 q^{79} +275.826 q^{80} +81.0000 q^{81} -485.103 q^{82} +197.354 q^{83} -84.0000 q^{84} +158.510 q^{85} -790.907 q^{86} -345.643 q^{87} +263.507 q^{88} +8.42853 q^{89} -310.304 q^{90} +372.615 q^{91} +339.576 q^{92} -444.932 q^{93} +770.694 q^{94} +327.543 q^{95} +96.0000 q^{96} +1215.90 q^{97} -98.0000 q^{98} -296.445 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} - 12 q^{3} + 16 q^{4} + 12 q^{5} + 24 q^{6} + 28 q^{7} - 32 q^{8} + 36 q^{9} - 24 q^{10} + 54 q^{11} - 48 q^{12} - 46 q^{13} - 56 q^{14} - 36 q^{15} + 64 q^{16} + 100 q^{17} - 72 q^{18} + 76 q^{19} + 48 q^{20} - 84 q^{21} - 108 q^{22} + 274 q^{23} + 96 q^{24} + 300 q^{25} + 92 q^{26} - 108 q^{27} + 112 q^{28} - 214 q^{29} + 72 q^{30} + 228 q^{31} - 128 q^{32} - 162 q^{33} - 200 q^{34} + 84 q^{35} + 144 q^{36} - 124 q^{37} - 152 q^{38} + 138 q^{39} - 96 q^{40} - 484 q^{41} + 168 q^{42} + 276 q^{43} + 216 q^{44} + 108 q^{45} - 548 q^{46} - 506 q^{47} - 192 q^{48} + 196 q^{49} - 600 q^{50} - 300 q^{51} - 184 q^{52} - 1002 q^{53} + 216 q^{54} + 8 q^{55} - 224 q^{56} - 228 q^{57} + 428 q^{58} - 808 q^{59} - 144 q^{60} - 72 q^{61} - 456 q^{62} + 252 q^{63} + 256 q^{64} + 616 q^{65} + 324 q^{66} + 138 q^{67} + 400 q^{68} - 822 q^{69} - 168 q^{70} - 654 q^{71} - 288 q^{72} + 2348 q^{73} + 248 q^{74} - 900 q^{75} + 304 q^{76} + 378 q^{77} - 276 q^{78} + 234 q^{79} + 192 q^{80} + 324 q^{81} + 968 q^{82} - 258 q^{83} - 336 q^{84} + 2696 q^{85} - 552 q^{86} + 642 q^{87} - 432 q^{88} - 1316 q^{89} - 216 q^{90} - 322 q^{91} + 1096 q^{92} - 684 q^{93} + 1012 q^{94} + 228 q^{95} + 384 q^{96} + 1166 q^{97} - 392 q^{98} + 486 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 - 12 * q^3 + 16 * q^4 + 12 * q^5 + 24 * q^6 + 28 * q^7 - 32 * q^8 + 36 * q^9 - 24 * q^10 + 54 * q^11 - 48 * q^12 - 46 * q^13 - 56 * q^14 - 36 * q^15 + 64 * q^16 + 100 * q^17 - 72 * q^18 + 76 * q^19 + 48 * q^20 - 84 * q^21 - 108 * q^22 + 274 * q^23 + 96 * q^24 + 300 * q^25 + 92 * q^26 - 108 * q^27 + 112 * q^28 - 214 * q^29 + 72 * q^30 + 228 * q^31 - 128 * q^32 - 162 * q^33 - 200 * q^34 + 84 * q^35 + 144 * q^36 - 124 * q^37 - 152 * q^38 + 138 * q^39 - 96 * q^40 - 484 * q^41 + 168 * q^42 + 276 * q^43 + 216 * q^44 + 108 * q^45 - 548 * q^46 - 506 * q^47 - 192 * q^48 + 196 * q^49 - 600 * q^50 - 300 * q^51 - 184 * q^52 - 1002 * q^53 + 216 * q^54 + 8 * q^55 - 224 * q^56 - 228 * q^57 + 428 * q^58 - 808 * q^59 - 144 * q^60 - 72 * q^61 - 456 * q^62 + 252 * q^63 + 256 * q^64 + 616 * q^65 + 324 * q^66 + 138 * q^67 + 400 * q^68 - 822 * q^69 - 168 * q^70 - 654 * q^71 - 288 * q^72 + 2348 * q^73 + 248 * q^74 - 900 * q^75 + 304 * q^76 + 378 * q^77 - 276 * q^78 + 234 * q^79 + 192 * q^80 + 324 * q^81 + 968 * q^82 - 258 * q^83 - 336 * q^84 + 2696 * q^85 - 552 * q^86 + 642 * q^87 - 432 * q^88 - 1316 * q^89 - 216 * q^90 - 322 * q^91 + 1096 * q^92 - 684 * q^93 + 1012 * q^94 + 228 * q^95 + 384 * q^96 + 1166 * q^97 - 392 * q^98 + 486 * q^99

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