LMFDB - Embedded newform 798.4.a.r.1.2

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:	$5$
Coefficient field:	$\mathbb{Q}[x]/(x^{5} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{5} - 2x^{4} - 382x^{3} + 570x^{2} + 32160x - 9856 $ x^5 - 2x^4 - 382x^3 + 570x^2 + 32160x - 9856
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			1.2
Root			$0.305155$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.885094 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.885094 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -1.77019 q^{10} -20.7572 q^{11} +12.0000 q^{12} +63.4981 q^{13} +14.0000 q^{14} -2.65528 q^{15} +16.0000 q^{16} +24.8244 q^{17} +18.0000 q^{18} +19.0000 q^{19} -3.54038 q^{20} +21.0000 q^{21} -41.5145 q^{22} +25.1065 q^{23} +24.0000 q^{24} -124.217 q^{25} +126.996 q^{26} +27.0000 q^{27} +28.0000 q^{28} +156.821 q^{29} -5.31056 q^{30} +96.3140 q^{31} +32.0000 q^{32} -62.2717 q^{33} +49.6487 q^{34} -6.19566 q^{35} +36.0000 q^{36} -229.860 q^{37} +38.0000 q^{38} +190.494 q^{39} -7.08075 q^{40} +366.729 q^{41} +42.0000 q^{42} +103.439 q^{43} -83.0290 q^{44} -7.96585 q^{45} +50.2130 q^{46} +17.7138 q^{47} +48.0000 q^{48} +49.0000 q^{49} -248.433 q^{50} +74.4731 q^{51} +253.992 q^{52} +391.306 q^{53} +54.0000 q^{54} +18.3721 q^{55} +56.0000 q^{56} +57.0000 q^{57} +313.641 q^{58} +559.900 q^{59} -10.6211 q^{60} -447.068 q^{61} +192.628 q^{62} +63.0000 q^{63} +64.0000 q^{64} -56.2018 q^{65} -124.543 q^{66} +121.194 q^{67} +99.2974 q^{68} +75.3196 q^{69} -12.3913 q^{70} -383.655 q^{71} +72.0000 q^{72} +61.8593 q^{73} -459.720 q^{74} -372.650 q^{75} +76.0000 q^{76} -145.301 q^{77} +380.988 q^{78} +565.582 q^{79} -14.1615 q^{80} +81.0000 q^{81} +733.457 q^{82} +46.7179 q^{83} +84.0000 q^{84} -21.9719 q^{85} +206.879 q^{86} +470.462 q^{87} -166.058 q^{88} -985.047 q^{89} -15.9317 q^{90} +444.487 q^{91} +100.426 q^{92} +288.942 q^{93} +35.4276 q^{94} -16.8168 q^{95} +96.0000 q^{96} +50.1371 q^{97} +98.0000 q^{98} -186.815 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) $ 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9} + 40 q^{10} + 82 q^{11} + 60 q^{12} + 20 q^{13} + 70 q^{14} + 60 q^{15} + 80 q^{16} + 48 q^{17} + 90 q^{18} + 95 q^{19} + 80 q^{20} + 105 q^{21} + 164 q^{22} + 166 q^{23} + 120 q^{24} + 235 q^{25} + 40 q^{26} + 135 q^{27} + 140 q^{28} + 134 q^{29} + 120 q^{30} + 124 q^{31} + 160 q^{32} + 246 q^{33} + 96 q^{34} + 140 q^{35} + 180 q^{36} + 334 q^{37} + 190 q^{38} + 60 q^{39} + 160 q^{40} - 126 q^{41} + 210 q^{42} + 132 q^{43} + 328 q^{44} + 180 q^{45} + 332 q^{46} + 120 q^{47} + 240 q^{48} + 245 q^{49} + 470 q^{50} + 144 q^{51} + 80 q^{52} + 142 q^{53} + 270 q^{54} + 64 q^{55} + 280 q^{56} + 285 q^{57} + 268 q^{58} + 12 q^{59} + 240 q^{60} + 614 q^{61} + 248 q^{62} + 315 q^{63} + 320 q^{64} + 672 q^{65} + 492 q^{66} - 30 q^{67} + 192 q^{68} + 498 q^{69} + 280 q^{70} + 548 q^{71} + 360 q^{72} + 554 q^{73} + 668 q^{74} + 705 q^{75} + 380 q^{76} + 574 q^{77} + 120 q^{78} - 138 q^{79} + 320 q^{80} + 405 q^{81} - 252 q^{82} + 100 q^{83} + 420 q^{84} - 156 q^{85} + 264 q^{86} + 402 q^{87} + 656 q^{88} + 842 q^{89} + 360 q^{90} + 140 q^{91} + 664 q^{92} + 372 q^{93} + 240 q^{94} + 380 q^{95} + 480 q^{96} - 568 q^{97} + 490 q^{98} + 738 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9 + 40 * q^10 + 82 * q^11 + 60 * q^12 + 20 * q^13 + 70 * q^14 + 60 * q^15 + 80 * q^16 + 48 * q^17 + 90 * q^18 + 95 * q^19 + 80 * q^20 + 105 * q^21 + 164 * q^22 + 166 * q^23 + 120 * q^24 + 235 * q^25 + 40 * q^26 + 135 * q^27 + 140 * q^28 + 134 * q^29 + 120 * q^30 + 124 * q^31 + 160 * q^32 + 246 * q^33 + 96 * q^34 + 140 * q^35 + 180 * q^36 + 334 * q^37 + 190 * q^38 + 60 * q^39 + 160 * q^40 - 126 * q^41 + 210 * q^42 + 132 * q^43 + 328 * q^44 + 180 * q^45 + 332 * q^46 + 120 * q^47 + 240 * q^48 + 245 * q^49 + 470 * q^50 + 144 * q^51 + 80 * q^52 + 142 * q^53 + 270 * q^54 + 64 * q^55 + 280 * q^56 + 285 * q^57 + 268 * q^58 + 12 * q^59 + 240 * q^60 + 614 * q^61 + 248 * q^62 + 315 * q^63 + 320 * q^64 + 672 * q^65 + 492 * q^66 - 30 * q^67 + 192 * q^68 + 498 * q^69 + 280 * q^70 + 548 * q^71 + 360 * q^72 + 554 * q^73 + 668 * q^74 + 705 * q^75 + 380 * q^76 + 574 * q^77 + 120 * q^78 - 138 * q^79 + 320 * q^80 + 405 * q^81 - 252 * q^82 + 100 * q^83 + 420 * q^84 - 156 * q^85 + 264 * q^86 + 402 * q^87 + 656 * q^88 + 842 * q^89 + 360 * q^90 + 140 * q^91 + 664 * q^92 + 372 * q^93 + 240 * q^94 + 380 * q^95 + 480 * q^96 - 568 * q^97 + 490 * q^98 + 738 * 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
$5$	−0.885094	−0.0791652	−0.0395826	−	0.999216i	$-0.512603\pi$
$5$	−0.885094	−0.0791652	−0.0395826	+	0.999216i	$0.512603\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−1.77019	−0.0559783
$11$	−20.7572	−0.568959	−0.284479	−	0.958682i	$-0.591821\pi$
$11$	−20.7572	−0.568959	−0.284479	+	0.958682i	$0.591821\pi$
$12$	12.0000	0.288675
$13$	63.4981	1.35471	0.677354	−	0.735657i	$-0.263127\pi$
$13$	63.4981	1.35471	0.677354	+	0.735657i	$0.263127\pi$
$14$	14.0000	0.267261
$15$	−2.65528	−0.0457061
$16$	16.0000	0.250000
$17$	24.8244	0.354164	0.177082	−	0.984196i	$-0.443334\pi$
$17$	24.8244	0.354164	0.177082	+	0.984196i	$0.443334\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	−3.54038	−0.0395826
$21$	21.0000	0.218218
$22$	−41.5145	−0.402315
$23$	25.1065	0.227612	0.113806	−	0.993503i	$-0.463696\pi$
$23$	25.1065	0.227612	0.113806	+	0.993503i	$0.463696\pi$
$24$	24.0000	0.204124
$25$	−124.217	−0.993733
$26$	126.996	0.957923
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	156.821	1.00417	0.502084	−	0.864819i	$-0.332567\pi$
$29$	156.821	1.00417	0.502084	+	0.864819i	$0.332567\pi$
$30$	−5.31056	−0.0323191
$31$	96.3140	0.558017	0.279008	−	0.960289i	$-0.409994\pi$
$31$	96.3140	0.558017	0.279008	+	0.960289i	$0.409994\pi$
$32$	32.0000	0.176777
$33$	−62.2717	−0.328488
$34$	49.6487	0.250432
$35$	−6.19566	−0.0299216
$36$	36.0000	0.166667
$37$	−229.860	−1.02132	−0.510659	−	0.859783i	$-0.670599\pi$
$37$	−229.860	−1.02132	−0.510659	+	0.859783i	$0.670599\pi$
$38$	38.0000	0.162221
$39$	190.494	0.782141
$40$	−7.08075	−0.0279891
$41$	366.729	1.39691	0.698456	−	0.715653i	$-0.253871\pi$
$41$	366.729	1.39691	0.698456	+	0.715653i	$0.253871\pi$
$42$	42.0000	0.154303
$43$	103.439	0.366846	0.183423	−	0.983034i	$-0.441282\pi$
$43$	103.439	0.366846	0.183423	+	0.983034i	$0.441282\pi$
$44$	−83.0290	−0.284479
$45$	−7.96585	−0.0263884
$46$	50.2130	0.160946
$47$	17.7138	0.0549749	0.0274875	−	0.999622i	$-0.491249\pi$
$47$	17.7138	0.0549749	0.0274875	+	0.999622i	$0.491249\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−248.433	−0.702675
$51$	74.4731	0.204477
$52$	253.992	0.677354
$53$	391.306	1.01415	0.507075	−	0.861902i	$-0.330727\pi$
$53$	391.306	1.01415	0.507075	+	0.861902i	$0.330727\pi$
$54$	54.0000	0.136083
$55$	18.3721	0.0450417
$56$	56.0000	0.133631
$57$	57.0000	0.132453
$58$	313.641	0.710054
$59$	559.900	1.23547	0.617735	−	0.786386i	$-0.288051\pi$
$59$	559.900	1.23547	0.617735	+	0.786386i	$0.288051\pi$
$60$	−10.6211	−0.0228530
$61$	−447.068	−0.938381	−0.469190	−	0.883097i	$-0.655454\pi$
$61$	−447.068	−0.938381	−0.469190	+	0.883097i	$0.655454\pi$
$62$	192.628	0.394577
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−56.2018	−0.107246
$66$	−124.543	−0.232276
$67$	121.194	0.220988	0.110494	−	0.993877i	$-0.464757\pi$
$67$	121.194	0.220988	0.110494	+	0.993877i	$0.464757\pi$
$68$	99.2974	0.177082
$69$	75.3196	0.131412
$70$	−12.3913	−0.0211578
$71$	−383.655	−0.641288	−0.320644	−	0.947200i	$-0.603899\pi$
$71$	−383.655	−0.641288	−0.320644	+	0.947200i	$0.603899\pi$
$72$	72.0000	0.117851
$73$	61.8593	0.0991792	0.0495896	−	0.998770i	$-0.484209\pi$
$73$	61.8593	0.0991792	0.0495896	+	0.998770i	$0.484209\pi$
$74$	−459.720	−0.722181
$75$	−372.650	−0.573732
$76$	76.0000	0.114708
$77$	−145.301	−0.215046
$78$	380.988	0.553057
$79$	565.582	0.805480	0.402740	−	0.915314i	$-0.368058\pi$
$79$	565.582	0.805480	0.402740	+	0.915314i	$0.368058\pi$
$80$	−14.1615	−0.0197913
$81$	81.0000	0.111111
$82$	733.457	0.987766
$83$	46.7179	0.0617826	0.0308913	−	0.999523i	$-0.490165\pi$
$83$	46.7179	0.0617826	0.0308913	+	0.999523i	$0.490165\pi$
$84$	84.0000	0.109109
$85$	−21.9719	−0.0280375
$86$	206.879	0.259399
$87$	470.462	0.579757
$88$	−166.058	−0.201157
$89$	−985.047	−1.17320	−0.586600	−	0.809877i	$-0.699534\pi$
$89$	−985.047	−1.17320	−0.586600	+	0.809877i	$0.699534\pi$
$90$	−15.9317	−0.0186594
$91$	444.487	0.512031
$92$	100.426	0.113806
$93$	288.942	0.322171
$94$	35.4276	0.0388731
$95$	−16.8168	−0.0181617
$96$	96.0000	0.102062
$97$	50.1371	0.0524809	0.0262405	−	0.999656i	$-0.491646\pi$
$97$	50.1371	0.0524809	0.0262405	+	0.999656i	$0.491646\pi$
$98$	98.0000	0.101015
$99$	−186.815	−0.189653
$100$	−496.866	−0.496866
$101$	−196.800	−0.193884	−0.0969421	−	0.995290i	$-0.530906\pi$
$101$	−196.800	−0.193884	−0.0969421	+	0.995290i	$0.530906\pi$
$102$	148.946	0.144587
$103$	699.380	0.669048	0.334524	−	0.942387i	$-0.391424\pi$
$103$	699.380	0.669048	0.334524	+	0.942387i	$0.391424\pi$
$104$	507.985	0.478961
$105$	−18.5870	−0.0172753
$106$	782.611	0.717113
$107$	1320.25	1.19284	0.596419	−	0.802674i	$-0.296590\pi$
$107$	1320.25	1.19284	0.596419	+	0.802674i	$0.296590\pi$
$108$	108.000	0.0962250
$109$	−1538.59	−1.35202	−0.676009	−	0.736894i	$-0.736292\pi$
$109$	−1538.59	−1.35202	−0.676009	+	0.736894i	$0.736292\pi$
$110$	36.7442	0.0318493
$111$	−689.580	−0.589658
$112$	112.000	0.0944911
$113$	2102.63	1.75043	0.875214	−	0.483736i	$-0.160720\pi$
$113$	2102.63	1.75043	0.875214	+	0.483736i	$0.160720\pi$
$114$	114.000	0.0936586
$115$	−22.2216	−0.0180189
$116$	627.283	0.502084
$117$	571.483	0.451569
$118$	1119.80	0.873609
$119$	173.770	0.133861
$120$	−21.2423	−0.0161595
$121$	−900.137	−0.676286
$122$	−894.136	−0.663535
$123$	1100.19	0.806508
$124$	385.256	0.279008
$125$	220.580	0.157834
$126$	126.000	0.0890871
$127$	−598.685	−0.418305	−0.209152	−	0.977883i	$-0.567070\pi$
$127$	−598.685	−0.418305	−0.209152	+	0.977883i	$0.567070\pi$
$128$	128.000	0.0883883
$129$	310.318	0.211799
$130$	−112.404	−0.0758342
$131$	−1829.64	−1.22028	−0.610139	−	0.792294i	$-0.708886\pi$
$131$	−1829.64	−1.22028	−0.610139	+	0.792294i	$0.708886\pi$
$132$	−249.087	−0.164244
$133$	133.000	0.0867110
$134$	242.388	0.156262
$135$	−23.8975	−0.0152354
$136$	198.595	0.125216
$137$	−1215.97	−0.758305	−0.379152	−	0.925334i	$-0.623784\pi$
$137$	−1215.97	−0.758305	−0.379152	+	0.925334i	$0.623784\pi$
$138$	150.639	0.0929221
$139$	−134.081	−0.0818171	−0.0409086	−	0.999163i	$-0.513025\pi$
$139$	−134.081	−0.0818171	−0.0409086	+	0.999163i	$0.513025\pi$
$140$	−24.7826	−0.0149608
$141$	53.1414	0.0317398
$142$	−767.309	−0.453459
$143$	−1318.05	−0.770773
$144$	144.000	0.0833333
$145$	−138.801	−0.0794952
$146$	123.719	0.0701303
$147$	147.000	0.0824786
$148$	−919.440	−0.510659
$149$	1198.14	0.658759	0.329379	−	0.944198i	$-0.393160\pi$
$149$	1198.14	0.658759	0.329379	+	0.944198i	$0.393160\pi$
$150$	−745.300	−0.405690
$151$	220.095	0.118616	0.0593081	−	0.998240i	$-0.481111\pi$
$151$	220.095	0.118616	0.0593081	+	0.998240i	$0.481111\pi$
$152$	152.000	0.0811107
$153$	223.419	0.118055
$154$	−290.601	−0.152061
$155$	−85.2470	−0.0441755
$156$	761.977	0.391070
$157$	−1223.45	−0.621922	−0.310961	−	0.950423i	$-0.600651\pi$
$157$	−1223.45	−0.621922	−0.310961	+	0.950423i	$0.600651\pi$
$158$	1131.16	0.569560
$159$	1173.92	0.585520
$160$	−28.3230	−0.0139946
$161$	175.746	0.0860292
$162$	162.000	0.0785674
$163$	−1543.01	−0.741459	−0.370729	−	0.928741i	$-0.620892\pi$
$163$	−1543.01	−0.741459	−0.370729	+	0.928741i	$0.620892\pi$
$164$	1466.91	0.698456
$165$	55.1163	0.0260049
$166$	93.4359	0.0436869
$167$	−673.729	−0.312184	−0.156092	−	0.987743i	$-0.549890\pi$
$167$	−673.729	−0.312184	−0.156092	+	0.987743i	$0.549890\pi$
$168$	168.000	0.0771517
$169$	1835.01	0.835232
$170$	−43.9438	−0.0198255
$171$	171.000	0.0764719
$172$	413.758	0.183423
$173$	−1171.04	−0.514638	−0.257319	−	0.966327i	$-0.582839\pi$
$173$	−1171.04	−0.514638	−0.257319	+	0.966327i	$0.582839\pi$
$174$	940.924	0.409950
$175$	−869.516	−0.375596
$176$	−332.116	−0.142240
$177$	1679.70	0.713299
$178$	−1970.09	−0.829578
$179$	271.916	0.113542	0.0567708	−	0.998387i	$-0.481920\pi$
$179$	271.916	0.113542	0.0567708	+	0.998387i	$0.481920\pi$
$180$	−31.8634	−0.0131942
$181$	−349.456	−0.143508	−0.0717538	−	0.997422i	$-0.522860\pi$
$181$	−349.456	−0.143508	−0.0717538	+	0.997422i	$0.522860\pi$
$182$	888.973	0.362061
$183$	−1341.20	−0.541774
$184$	200.852	0.0804729
$185$	203.448	0.0808529
$186$	577.884	0.227809
$187$	−515.285	−0.201505
$188$	70.8551	0.0274875
$189$	189.000	0.0727393
$190$	−33.6336	−0.0128423
$191$	−184.476	−0.0698859	−0.0349429	−	0.999389i	$-0.511125\pi$
$191$	−184.476	−0.0698859	−0.0349429	+	0.999389i	$0.511125\pi$
$192$	192.000	0.0721688
$193$	2723.52	1.01577	0.507884	−	0.861425i	$-0.330428\pi$
$193$	2723.52	1.01577	0.507884	+	0.861425i	$0.330428\pi$
$194$	100.274	0.0371096
$195$	−168.605	−0.0619183
$196$	196.000	0.0714286
$197$	−3241.10	−1.17218	−0.586089	−	0.810247i	$-0.699333\pi$
$197$	−3241.10	−1.17218	−0.586089	+	0.810247i	$0.699333\pi$
$198$	−373.630	−0.134105
$199$	−4036.40	−1.43785	−0.718927	−	0.695086i	$-0.755366\pi$
$199$	−4036.40	−1.43785	−0.718927	+	0.695086i	$0.755366\pi$
$200$	−993.733	−0.351338
$201$	363.582	0.127587
$202$	−393.599	−0.137097
$203$	1097.75	0.379540
$204$	297.892	0.102238
$205$	−324.589	−0.110587
$206$	1398.76	0.473089
$207$	225.959	0.0758706
$208$	1015.97	0.338677
$209$	−394.388	−0.130528
$210$	−37.1739	−0.0122155
$211$	−139.669	−0.0455698	−0.0227849	−	0.999740i	$-0.507253\pi$
$211$	−139.669	−0.0455698	−0.0227849	+	0.999740i	$0.507253\pi$
$212$	1565.22	0.507075
$213$	−1150.96	−0.370248
$214$	2640.50	0.843463
$215$	−91.5537	−0.0290414
$216$	216.000	0.0680414
$217$	674.198	0.210910
$218$	−3077.17	−0.956021
$219$	185.578	0.0572611
$220$	73.4885	0.0225209
$221$	1576.30	0.479789
$222$	−1379.16	−0.416951
$223$	−2576.75	−0.773776	−0.386888	−	0.922127i	$-0.626450\pi$
$223$	−2576.75	−0.773776	−0.386888	+	0.922127i	$0.626450\pi$
$224$	224.000	0.0668153
$225$	−1117.95	−0.331244
$226$	4205.25	1.23774
$227$	702.780	0.205485	0.102743	−	0.994708i	$-0.467238\pi$
$227$	702.780	0.205485	0.102743	+	0.994708i	$0.467238\pi$
$228$	228.000	0.0662266
$229$	2676.98	0.772487	0.386244	−	0.922397i	$-0.373772\pi$
$229$	2676.98	0.772487	0.386244	+	0.922397i	$0.373772\pi$
$230$	−44.4433	−0.0127413
$231$	−435.902	−0.124157
$232$	1254.57	0.355027
$233$	1999.59	0.562221	0.281110	−	0.959675i	$-0.409297\pi$
$233$	1999.59	0.562221	0.281110	+	0.959675i	$0.409297\pi$
$234$	1142.97	0.319308
$235$	−15.6784	−0.00435210
$236$	2239.60	0.617735
$237$	1696.75	0.465044
$238$	347.541	0.0946543
$239$	107.224	0.0290199	0.0145099	−	0.999895i	$-0.495381\pi$
$239$	107.224	0.0290199	0.0145099	+	0.999895i	$0.495381\pi$
$240$	−42.4845	−0.0114265
$241$	4595.00	1.22817	0.614087	−	0.789238i	$-0.289524\pi$
$241$	4595.00	1.22817	0.614087	+	0.789238i	$0.289524\pi$
$242$	−1800.27	−0.478206
$243$	243.000	0.0641500
$244$	−1788.27	−0.469190
$245$	−43.3696	−0.0113093
$246$	2200.37	0.570287
$247$	1206.46	0.310791
$248$	770.512	0.197289
$249$	140.154	0.0356702
$250$	441.160	0.111606
$251$	−3567.21	−0.897053	−0.448526	−	0.893770i	$-0.648051\pi$
$251$	−3567.21	−0.897053	−0.448526	+	0.893770i	$0.648051\pi$
$252$	252.000	0.0629941
$253$	−521.142	−0.129502
$254$	−1197.37	−0.295786
$255$	−65.9157	−0.0161874
$256$	256.000	0.0625000
$257$	−3680.43	−0.893303	−0.446652	−	0.894708i	$-0.647384\pi$
$257$	−3680.43	−0.893303	−0.446652	+	0.894708i	$0.647384\pi$
$258$	620.637	0.149764
$259$	−1609.02	−0.386022
$260$	−224.807	−0.0536229
$261$	1411.39	0.334723
$262$	−3659.28	−0.862867
$263$	−1091.50	−0.255912	−0.127956	−	0.991780i	$-0.540842\pi$
$263$	−1091.50	−0.255912	−0.127956	+	0.991780i	$0.540842\pi$
$264$	−498.174	−0.116138
$265$	−346.342	−0.0802854
$266$	266.000	0.0613139
$267$	−2955.14	−0.677347
$268$	484.776	0.110494
$269$	−2225.63	−0.504457	−0.252228	−	0.967668i	$-0.581163\pi$
$269$	−2225.63	−0.504457	−0.252228	+	0.967668i	$0.581163\pi$
$270$	−47.7951	−0.0107730
$271$	−801.325	−0.179620	−0.0898100	−	0.995959i	$-0.528626\pi$
$271$	−801.325	−0.179620	−0.0898100	+	0.995959i	$0.528626\pi$
$272$	397.190	0.0885410
$273$	1333.46	0.295621
$274$	−2431.95	−0.536202
$275$	2578.39	0.565393
$276$	301.278	0.0657059
$277$	−6504.41	−1.41087	−0.705437	−	0.708773i	$-0.749249\pi$
$277$	−6504.41	−1.41087	−0.705437	+	0.708773i	$0.749249\pi$
$278$	−268.161	−0.0578534
$279$	866.826	0.186006
$280$	−49.5653	−0.0105789
$281$	3251.79	0.690341	0.345170	−	0.938540i	$-0.387821\pi$
$281$	3251.79	0.690341	0.345170	+	0.938540i	$0.387821\pi$
$282$	106.283	0.0224434
$283$	−4953.61	−1.04050	−0.520250	−	0.854014i	$-0.674161\pi$
$283$	−4953.61	−1.04050	−0.520250	+	0.854014i	$0.674161\pi$
$284$	−1534.62	−0.320644
$285$	−50.4504	−0.0104857
$286$	−2636.09	−0.545018
$287$	2567.10	0.527983
$288$	288.000	0.0589256
$289$	−4296.75	−0.874568
$290$	−277.602	−0.0562116
$291$	150.411	0.0302999
$292$	247.437	0.0495896
$293$	1364.23	0.272011	0.136005	−	0.990708i	$-0.456574\pi$
$293$	1364.23	0.272011	0.136005	+	0.990708i	$0.456574\pi$
$294$	294.000	0.0583212
$295$	−495.564	−0.0978062
$296$	−1838.88	−0.361090
$297$	−560.446	−0.109496
$298$	2396.27	0.465813
$299$	1594.22	0.308347
$300$	−1490.60	−0.286866
$301$	724.076	0.138655
$302$	440.189	0.0838744
$303$	−590.399	−0.111939
$304$	304.000	0.0573539
$305$	395.697	0.0742871
$306$	446.838	0.0834773
$307$	−4273.60	−0.794486	−0.397243	−	0.917713i	$-0.630033\pi$
$307$	−4273.60	−0.794486	−0.397243	+	0.917713i	$0.630033\pi$
$308$	−581.203	−0.107523
$309$	2098.14	0.386275
$310$	−170.494	−0.0312368
$311$	−802.946	−0.146402	−0.0732008	−	0.997317i	$-0.523321\pi$
$311$	−802.946	−0.146402	−0.0732008	+	0.997317i	$0.523321\pi$
$312$	1523.95	0.276529
$313$	−5373.48	−0.970375	−0.485187	−	0.874410i	$-0.661249\pi$
$313$	−5373.48	−0.970375	−0.485187	+	0.874410i	$0.661249\pi$
$314$	−2446.90	−0.439765
$315$	−55.7609	−0.00997388
$316$	2262.33	0.402740
$317$	−6196.61	−1.09791	−0.548953	−	0.835853i	$-0.684974\pi$
$317$	−6196.61	−1.09791	−0.548953	+	0.835853i	$0.684974\pi$
$318$	2347.83	0.414025
$319$	−3255.17	−0.571330
$320$	−56.6460	−0.00989565
$321$	3960.76	0.688685
$322$	351.491	0.0608318
$323$	471.663	0.0812508
$324$	324.000	0.0555556
$325$	−7887.52	−1.34622
$326$	−3086.02	−0.524290
$327$	−4615.76	−0.780588
$328$	2933.83	0.493883
$329$	123.996	0.0207786
$330$	110.233	0.0183882
$331$	6269.00	1.04101	0.520506	−	0.853858i	$-0.325743\pi$
$331$	6269.00	1.04101	0.520506	+	0.853858i	$0.325743\pi$
$332$	186.872	0.0308913
$333$	−2068.74	−0.340439
$334$	−1347.46	−0.220747
$335$	−107.268	−0.0174946
$336$	336.000	0.0545545
$337$	−7816.80	−1.26353	−0.631763	−	0.775162i	$-0.717668\pi$
$337$	−7816.80	−1.26353	−0.631763	+	0.775162i	$0.717668\pi$
$338$	3670.01	0.590598
$339$	6307.88	1.01061
$340$	−87.8875	−0.0140187
$341$	−1999.21	−0.317488
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	827.516	0.129700
$345$	−66.6649	−0.0104032
$346$	−2342.08	−0.363904
$347$	−2334.09	−0.361096	−0.180548	−	0.983566i	$-0.557787\pi$
$347$	−2334.09	−0.361096	−0.180548	+	0.983566i	$0.557787\pi$
$348$	1881.85	0.289878
$349$	6710.01	1.02917	0.514583	−	0.857441i	$-0.327947\pi$
$349$	6710.01	1.02917	0.514583	+	0.857441i	$0.327947\pi$
$350$	−1739.03	−0.265586
$351$	1714.45	0.260714
$352$	−664.232	−0.100579
$353$	−6504.42	−0.980724	−0.490362	−	0.871519i	$-0.663135\pi$
$353$	−6504.42	−0.980724	−0.490362	+	0.871519i	$0.663135\pi$
$354$	3359.40	0.504378
$355$	339.570	0.0507677
$356$	−3940.19	−0.586600
$357$	521.311	0.0772849
$358$	543.832	0.0802861
$359$	3555.91	0.522768	0.261384	−	0.965235i	$-0.415821\pi$
$359$	3555.91	0.522768	0.261384	+	0.965235i	$0.415821\pi$
$360$	−63.7268	−0.00932971
$361$	361.000	0.0526316
$362$	−698.912	−0.101475
$363$	−2700.41	−0.390454
$364$	1777.95	0.256016
$365$	−54.7513	−0.00785154
$366$	−2682.41	−0.383092
$367$	−6841.57	−0.973098	−0.486549	−	0.873653i	$-0.661744\pi$
$367$	−6841.57	−0.973098	−0.486549	+	0.873653i	$0.661744\pi$
$368$	401.704	0.0569030
$369$	3300.56	0.465637
$370$	406.896	0.0571716
$371$	2739.14	0.383313
$372$	1155.77	0.161085
$373$	4592.01	0.637440	0.318720	−	0.947849i	$-0.396747\pi$
$373$	4592.01	0.637440	0.318720	+	0.947849i	$0.396747\pi$
$374$	−1030.57	−0.142485
$375$	661.740	0.0911257
$376$	141.710	0.0194366
$377$	9957.81	1.36035
$378$	378.000	0.0514344
$379$	−9672.15	−1.31088	−0.655442	−	0.755245i	$-0.727518\pi$
$379$	−9672.15	−1.31088	−0.655442	+	0.755245i	$0.727518\pi$
$380$	−67.2671	−0.00908087
$381$	−1796.06	−0.241508
$382$	−368.952	−0.0494168
$383$	−28.1760	−0.00375907	−0.00187954	−	0.999998i	$-0.500598\pi$
$383$	−28.1760	−0.00375907	−0.00187954	+	0.999998i	$0.500598\pi$
$384$	384.000	0.0510310
$385$	128.605	0.0170242
$386$	5447.04	0.718257
$387$	930.955	0.122282
$388$	200.548	0.0262405
$389$	4512.34	0.588136	0.294068	−	0.955785i	$-0.404991\pi$
$389$	4512.34	0.588136	0.294068	+	0.955785i	$0.404991\pi$
$390$	−337.211	−0.0437829
$391$	623.253	0.0806119
$392$	392.000	0.0505076
$393$	−5488.92	−0.704528
$394$	−6482.20	−0.828855
$395$	−500.593	−0.0637660
$396$	−747.261	−0.0948264
$397$	−8471.28	−1.07094	−0.535468	−	0.844556i	$-0.679865\pi$
$397$	−8471.28	−1.07094	−0.535468	+	0.844556i	$0.679865\pi$
$398$	−8072.80	−1.01672
$399$	399.000	0.0500626
$400$	−1987.47	−0.248433
$401$	2397.70	0.298592	0.149296	−	0.988793i	$-0.452299\pi$
$401$	2397.70	0.298592	0.149296	+	0.988793i	$0.452299\pi$
$402$	727.163	0.0902179
$403$	6115.76	0.755949
$404$	−787.199	−0.0969421
$405$	−71.6926	−0.00879613
$406$	2195.49	0.268375
$407$	4771.26	0.581088
$408$	595.784	0.0722934
$409$	−1526.40	−0.184536	−0.0922682	−	0.995734i	$-0.529412\pi$
$409$	−1526.40	−0.184536	−0.0922682	+	0.995734i	$0.529412\pi$
$410$	−649.179	−0.0781967
$411$	−3647.92	−0.437807
$412$	2797.52	0.334524
$413$	3919.30	0.466964
$414$	451.917	0.0536486
$415$	−41.3498	−0.00489104
$416$	2031.94	0.239481
$417$	−402.242	−0.0472371
$418$	−788.775	−0.0922973
$419$	13191.2	1.53802	0.769011	−	0.639236i	$-0.220749\pi$
$419$	13191.2	1.53802	0.769011	+	0.639236i	$0.220749\pi$
$420$	−74.3479	−0.00863763
$421$	−14786.9	−1.71180	−0.855902	−	0.517137i	$-0.826998\pi$
$421$	−14786.9	−1.71180	−0.855902	+	0.517137i	$0.826998\pi$
$422$	−279.338	−0.0322227
$423$	159.424	0.0183250
$424$	3130.45	0.358556
$425$	−3083.60	−0.351944
$426$	−2301.93	−0.261805
$427$	−3129.48	−0.354675
$428$	5281.01	0.596419
$429$	−3954.14	−0.445006
$430$	−183.107	−0.0205354
$431$	10928.0	1.22131	0.610656	−	0.791896i	$-0.290906\pi$
$431$	10928.0	1.22131	0.610656	+	0.791896i	$0.290906\pi$
$432$	432.000	0.0481125
$433$	−13954.2	−1.54872	−0.774362	−	0.632743i	$-0.781929\pi$
$433$	−13954.2	−1.54872	−0.774362	+	0.632743i	$0.781929\pi$
$434$	1348.40	0.149136
$435$	−416.403	−0.0458966
$436$	−6154.35	−0.676009
$437$	477.024	0.0522177
$438$	371.156	0.0404897
$439$	−8064.03	−0.876708	−0.438354	−	0.898802i	$-0.644438\pi$
$439$	−8064.03	−0.876708	−0.438354	+	0.898802i	$0.644438\pi$
$440$	146.977	0.0159247
$441$	441.000	0.0476190
$442$	3152.60	0.339262
$443$	−16917.3	−1.81437	−0.907184	−	0.420733i	$-0.861773\pi$
$443$	−16917.3	−1.81437	−0.907184	+	0.420733i	$0.861773\pi$
$444$	−2758.32	−0.294829
$445$	871.859	0.0928766
$446$	−5153.51	−0.547143
$447$	3594.41	0.380335
$448$	448.000	0.0472456
$449$	−356.512	−0.0374718	−0.0187359	−	0.999824i	$-0.505964\pi$
$449$	−356.512	−0.0374718	−0.0187359	+	0.999824i	$0.505964\pi$
$450$	−2235.90	−0.234225
$451$	−7612.28	−0.794785
$452$	8410.50	0.875214
$453$	660.284	0.0684831
$454$	1405.56	0.145300
$455$	−393.412	−0.0405351
$456$	456.000	0.0468293
$457$	−11351.7	−1.16195	−0.580973	−	0.813923i	$-0.697328\pi$
$457$	−11351.7	−1.16195	−0.580973	+	0.813923i	$0.697328\pi$
$458$	5353.95	0.546231
$459$	670.257	0.0681589
$460$	−88.8865	−0.00900947
$461$	782.178	0.0790231	0.0395116	−	0.999219i	$-0.487420\pi$
$461$	782.178	0.0790231	0.0395116	+	0.999219i	$0.487420\pi$
$462$	−871.804	−0.0877922
$463$	−8383.78	−0.841528	−0.420764	−	0.907170i	$-0.638238\pi$
$463$	−8383.78	−0.841528	−0.420764	+	0.907170i	$0.638238\pi$
$464$	2509.13	0.251042
$465$	−255.741	−0.0255047
$466$	3999.18	0.397550
$467$	259.865	0.0257497	0.0128748	−	0.999917i	$-0.495902\pi$
$467$	259.865	0.0257497	0.0128748	+	0.999917i	$0.495902\pi$
$468$	2285.93	0.225785
$469$	848.357	0.0835256
$470$	−31.3567	−0.00307740
$471$	−3670.34	−0.359067
$472$	4479.20	0.436804
$473$	−2147.12	−0.208720
$474$	3393.49	0.328836
$475$	−2360.12	−0.227978
$476$	695.082	0.0669307
$477$	3521.75	0.338050
$478$	214.448	0.0205202
$479$	3325.36	0.317202	0.158601	−	0.987343i	$-0.449302\pi$
$479$	3325.36	0.317202	0.158601	+	0.987343i	$0.449302\pi$
$480$	−84.9690	−0.00807977
$481$	−14595.7	−1.38359
$482$	9190.00	0.868450
$483$	527.237	0.0496690
$484$	−3600.55	−0.338143
$485$	−44.3760	−0.00415466
$486$	486.000	0.0453609
$487$	15571.7	1.44892	0.724459	−	0.689318i	$-0.242090\pi$
$487$	15571.7	1.44892	0.724459	+	0.689318i	$0.242090\pi$
$488$	−3576.55	−0.331768
$489$	−4629.03	−0.428081
$490$	−86.7392	−0.00799689
$491$	1081.21	0.0993778	0.0496889	−	0.998765i	$-0.484177\pi$
$491$	1081.21	0.0993778	0.0496889	+	0.998765i	$0.484177\pi$
$492$	4400.74	0.403254
$493$	3892.97	0.355640
$494$	2412.93	0.219763
$495$	165.349	0.0150139
$496$	1541.02	0.139504
$497$	−2685.58	−0.242384
$498$	280.308	0.0252227
$499$	−1251.47	−0.112272	−0.0561359	−	0.998423i	$-0.517878\pi$
$499$	−1251.47	−0.112272	−0.0561359	+	0.998423i	$0.517878\pi$
$500$	882.321	0.0789171
$501$	−2021.19	−0.180239
$502$	−7134.42	−0.634312
$503$	16779.1	1.48736	0.743681	−	0.668535i	$-0.233078\pi$
$503$	16779.1	1.48736	0.743681	+	0.668535i	$0.233078\pi$
$504$	504.000	0.0445435
$505$	174.186	0.0153489
$506$	−1042.28	−0.0915715
$507$	5505.02	0.482222
$508$	−2394.74	−0.209152
$509$	−10469.6	−0.911700	−0.455850	−	0.890057i	$-0.650665\pi$
$509$	−10469.6	−0.911700	−0.455850	+	0.890057i	$0.650665\pi$
$510$	−131.831	−0.0114463
$511$	433.015	0.0374862
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	−7360.86	−0.631661
$515$	−619.017	−0.0529654
$516$	1241.27	0.105899
$517$	−367.689	−0.0312785
$518$	−3218.04	−0.272959
$519$	−3513.11	−0.297126
$520$	−449.614	−0.0379171
$521$	−11881.8	−0.999141	−0.499570	−	0.866273i	$-0.666509\pi$
$521$	−11881.8	−0.999141	−0.499570	+	0.866273i	$0.666509\pi$
$522$	2822.77	0.236685
$523$	16416.4	1.37254	0.686270	−	0.727347i	$-0.259247\pi$
$523$	16416.4	1.37254	0.686270	+	0.727347i	$0.259247\pi$
$524$	−7318.56	−0.610139
$525$	−2608.55	−0.216850
$526$	−2183.00	−0.180957
$527$	2390.93	0.197629
$528$	−996.348	−0.0821221
$529$	−11536.7	−0.948193
$530$	−692.685	−0.0567704
$531$	5039.10	0.411823
$532$	532.000	0.0433555
$533$	23286.6	1.89241
$534$	−5910.28	−0.478957
$535$	−1168.55	−0.0944312
$536$	969.551	0.0781310
$537$	815.748	0.0655533
$538$	−4451.25	−0.356705
$539$	−1017.11	−0.0812798
$540$	−95.5902	−0.00761768
$541$	10403.4	0.826757	0.413378	−	0.910559i	$-0.364349\pi$
$541$	10403.4	0.826757	0.413378	+	0.910559i	$0.364349\pi$
$542$	−1602.65	−0.127010
$543$	−1048.37	−0.0828541
$544$	794.379	0.0626080
$545$	1361.79	0.107033
$546$	2666.92	0.209036
$547$	21738.9	1.69925	0.849623	−	0.527391i	$-0.176830\pi$
$547$	21738.9	1.69925	0.849623	+	0.527391i	$0.176830\pi$
$548$	−4863.90	−0.379152
$549$	−4023.61	−0.312794
$550$	5156.79	0.399793
$551$	2979.59	0.230372
$552$	602.557	0.0464611
$553$	3959.07	0.304443
$554$	−13008.8	−0.997638
$555$	610.343	0.0466804
$556$	−536.323	−0.0409086
$557$	21459.0	1.63240	0.816200	−	0.577770i	$-0.196077\pi$
$557$	21459.0	1.63240	0.816200	+	0.577770i	$0.196077\pi$
$558$	1733.65	0.131526
$559$	6568.21	0.496969
$560$	−99.1305	−0.00748041
$561$	−1545.86	−0.116339
$562$	6503.59	0.488145
$563$	−465.196	−0.0348236	−0.0174118	−	0.999848i	$-0.505543\pi$
$563$	−465.196	−0.0348236	−0.0174118	+	0.999848i	$0.505543\pi$
$564$	212.565	0.0158699
$565$	−1861.02	−0.138573
$566$	−9907.23	−0.735745
$567$	567.000	0.0419961
$568$	−3069.24	−0.226729
$569$	12172.2	0.896811	0.448405	−	0.893830i	$-0.351992\pi$
$569$	12172.2	0.896811	0.448405	+	0.893830i	$0.351992\pi$
$570$	−100.901	−0.00741450
$571$	7478.49	0.548100	0.274050	−	0.961715i	$-0.411637\pi$
$571$	7478.49	0.548100	0.274050	+	0.961715i	$0.411637\pi$
$572$	−5272.18	−0.385386
$573$	−553.428	−0.0403486
$574$	5134.20	0.373340
$575$	−3118.65	−0.226185
$576$	576.000	0.0416667
$577$	−15302.8	−1.10410	−0.552049	−	0.833812i	$-0.686154\pi$
$577$	−15302.8	−1.10410	−0.552049	+	0.833812i	$0.686154\pi$
$578$	−8593.50	−0.618413
$579$	8170.57	0.586454
$580$	−555.204	−0.0397476
$581$	327.026	0.0233516
$582$	300.823	0.0214253
$583$	−8122.43	−0.577010
$584$	494.874	0.0350651
$585$	−505.816	−0.0357486
$586$	2728.46	0.192341
$587$	7480.56	0.525989	0.262995	−	0.964797i	$-0.415290\pi$
$587$	7480.56	0.525989	0.262995	+	0.964797i	$0.415290\pi$
$588$	588.000	0.0412393
$589$	1829.97	0.128018
$590$	−991.127	−0.0691594
$591$	−9723.31	−0.676757
$592$	−3677.76	−0.255330
$593$	−1405.37	−0.0973213	−0.0486607	−	0.998815i	$-0.515495\pi$
$593$	−1405.37	−0.0973213	−0.0486607	+	0.998815i	$0.515495\pi$
$594$	−1120.89	−0.0774255
$595$	−153.803	−0.0105972
$596$	4792.54	0.329379
$597$	−12109.2	−0.830145
$598$	3188.43	0.218035
$599$	28223.9	1.92520	0.962602	−	0.270919i	$-0.0873275\pi$
$599$	28223.9	1.92520	0.962602	+	0.270919i	$0.0873275\pi$
$600$	−2981.20	−0.202845
$601$	−1066.73	−0.0724007	−0.0362003	−	0.999345i	$-0.511525\pi$
$601$	−1066.73	−0.0724007	−0.0362003	+	0.999345i	$0.511525\pi$
$602$	1448.15	0.0980437
$603$	1090.75	0.0736626
$604$	880.379	0.0593081
$605$	796.706	0.0535383
$606$	−1180.80	−0.0791529
$607$	−26463.1	−1.76953	−0.884763	−	0.466040i	$-0.845680\pi$
$607$	−26463.1	−1.76953	−0.884763	+	0.466040i	$0.845680\pi$
$608$	608.000	0.0405554
$609$	3293.24	0.219127
$610$	791.395	0.0525289
$611$	1124.79	0.0744749
$612$	893.677	0.0590273
$613$	15765.0	1.03873	0.519365	−	0.854552i	$-0.326168\pi$
$613$	15765.0	1.03873	0.519365	+	0.854552i	$0.326168\pi$
$614$	−8547.20	−0.561787
$615$	−973.768	−0.0638474
$616$	−1162.41	−0.0760303
$617$	−7925.20	−0.517109	−0.258555	−	0.965997i	$-0.583246\pi$
$617$	−7925.20	−0.517109	−0.258555	+	0.965997i	$0.583246\pi$
$618$	4196.28	0.273138
$619$	−3749.86	−0.243489	−0.121744	−	0.992561i	$-0.538849\pi$
$619$	−3749.86	−0.243489	−0.121744	+	0.992561i	$0.538849\pi$
$620$	−340.988	−0.0220877
$621$	677.876	0.0438039
$622$	−1605.89	−0.103522
$623$	−6895.33	−0.443428
$624$	3047.91	0.195535
$625$	15331.8	0.981238
$626$	−10747.0	−0.686159
$627$	−1183.16	−0.0753604
$628$	−4893.79	−0.310961
$629$	−5706.13	−0.361714
$630$	−111.522	−0.00705260
$631$	315.583	0.0199099	0.00995497	−	0.999950i	$-0.496831\pi$
$631$	315.583	0.0199099	0.00995497	+	0.999950i	$0.496831\pi$
$632$	4524.65	0.284780
$633$	−419.008	−0.0263097
$634$	−12393.2	−0.776337
$635$	529.893	0.0331152
$636$	4695.67	0.292760
$637$	3111.41	0.193530
$638$	−6510.33	−0.403991
$639$	−3452.89	−0.213763
$640$	−113.292	−0.00699728
$641$	21685.9	1.33626	0.668129	−	0.744046i	$-0.267096\pi$
$641$	21685.9	1.33626	0.668129	+	0.744046i	$0.267096\pi$
$642$	7921.51	0.486974
$643$	−6054.21	−0.371314	−0.185657	−	0.982615i	$-0.559441\pi$
$643$	−6054.21	−0.371314	−0.185657	+	0.982615i	$0.559441\pi$
$644$	702.983	0.0430146
$645$	−274.661	−0.0167671
$646$	943.325	0.0574530
$647$	−22556.9	−1.37064	−0.685318	−	0.728244i	$-0.740337\pi$
$647$	−22556.9	−1.37064	−0.685318	+	0.728244i	$0.740337\pi$
$648$	648.000	0.0392837
$649$	−11622.0	−0.702931
$650$	−15775.0	−0.951919
$651$	2022.59	0.121769
$652$	−6172.03	−0.370729
$653$	−4406.19	−0.264055	−0.132027	−	0.991246i	$-0.542149\pi$
$653$	−4406.19	−0.264055	−0.132027	+	0.991246i	$0.542149\pi$
$654$	−9231.52	−0.551959
$655$	1619.40	0.0966036
$656$	5867.66	0.349228
$657$	556.733	0.0330597
$658$	247.993	0.0146927
$659$	18181.1	1.07471	0.537356	−	0.843355i	$-0.319423\pi$
$659$	18181.1	1.07471	0.537356	+	0.843355i	$0.319423\pi$
$660$	220.465	0.0130024
$661$	−14624.8	−0.860575	−0.430287	−	0.902692i	$-0.641588\pi$
$661$	−14624.8	−0.860575	−0.430287	+	0.902692i	$0.641588\pi$
$662$	12538.0	0.736107
$663$	4728.90	0.277006
$664$	373.743	0.0218435
$665$	−117.718	−0.00686449
$666$	−4137.48	−0.240727
$667$	3937.22	0.228561
$668$	−2694.92	−0.156092
$669$	−7730.26	−0.446740
$670$	−214.536	−0.0123705
$671$	9279.91	0.533900
$672$	672.000	0.0385758
$673$	7188.63	0.411741	0.205870	−	0.978579i	$-0.433997\pi$
$673$	7188.63	0.411741	0.205870	+	0.978579i	$0.433997\pi$
$674$	−15633.6	−0.893447
$675$	−3353.85	−0.191244
$676$	7340.02	0.417616
$677$	7535.53	0.427790	0.213895	−	0.976857i	$-0.431385\pi$
$677$	7535.53	0.427790	0.213895	+	0.976857i	$0.431385\pi$
$678$	12615.8	0.714609
$679$	350.960	0.0198359
$680$	−175.775	−0.00991274
$681$	2108.34	0.118637
$682$	−3998.43	−0.224498
$683$	−1605.58	−0.0899500	−0.0449750	−	0.998988i	$-0.514321\pi$
$683$	−1605.58	−0.0899500	−0.0449750	+	0.998988i	$0.514321\pi$
$684$	684.000	0.0382360
$685$	1076.25	0.0600313
$686$	686.000	0.0381802
$687$	8030.93	0.445996
$688$	1655.03	0.0917115
$689$	24847.2	1.37388
$690$	−133.330	−0.00735620
$691$	11052.0	0.608446	0.304223	−	0.952601i	$-0.401603\pi$
$691$	11052.0	0.608446	0.304223	+	0.952601i	$0.401603\pi$
$692$	−4684.15	−0.257319
$693$	−1307.71	−0.0716821
$694$	−4668.17	−0.255333
$695$	118.674	0.00647707
$696$	3763.70	0.204975
$697$	9103.80	0.494736
$698$	13420.0	0.727730
$699$	5998.76	0.324598
$700$	−3478.07	−0.187798
$701$	27168.9	1.46384	0.731922	−	0.681389i	$-0.238624\pi$
$701$	27168.9	1.46384	0.731922	+	0.681389i	$0.238624\pi$
$702$	3428.90	0.184352
$703$	−4367.34	−0.234306
$704$	−1328.46	−0.0711198
$705$	−47.0351	−0.00251269
$706$	−13008.8	−0.693476
$707$	−1377.60	−0.0732813
$708$	6718.79	0.356649
$709$	694.660	0.0367962	0.0183981	−	0.999831i	$-0.494143\pi$
$709$	694.660	0.0367962	0.0183981	+	0.999831i	$0.494143\pi$
$710$	679.141	0.0358982
$711$	5090.24	0.268493
$712$	−7880.38	−0.414789
$713$	2418.11	0.127011
$714$	1042.62	0.0546487
$715$	1166.59	0.0610184
$716$	1087.66	0.0567708
$717$	321.672	0.0167546
$718$	7111.82	0.369653
$719$	1114.82	0.0578243	0.0289121	−	0.999582i	$-0.490796\pi$
$719$	1114.82	0.0578243	0.0289121	+	0.999582i	$0.490796\pi$
$720$	−127.454	−0.00659710
$721$	4895.66	0.252877
$722$	722.000	0.0372161
$723$	13785.0	0.709087
$724$	−1397.82	−0.0717538
$725$	−19479.7	−0.997875
$726$	−5400.82	−0.276093
$727$	32952.8	1.68109	0.840546	−	0.541741i	$-0.182234\pi$
$727$	32952.8	1.68109	0.840546	+	0.541741i	$0.182234\pi$
$728$	3555.89	0.181030
$729$	729.000	0.0370370
$730$	−109.503	−0.00555188
$731$	2567.82	0.129924
$732$	−5364.82	−0.270887
$733$	−20527.9	−1.03440	−0.517201	−	0.855864i	$-0.673026\pi$
$733$	−20527.9	−1.03440	−0.517201	+	0.855864i	$0.673026\pi$
$734$	−13683.1	−0.688084
$735$	−130.109	−0.00652944
$736$	803.409	0.0402365
$737$	−2515.65	−0.125733
$738$	6601.12	0.329255
$739$	21383.0	1.06439	0.532196	−	0.846621i	$-0.321367\pi$
$739$	21383.0	1.06439	0.532196	+	0.846621i	$0.321367\pi$
$740$	813.791	0.0404264
$741$	3619.39	0.179435
$742$	5478.28	0.271043
$743$	35960.7	1.77560	0.887799	−	0.460232i	$-0.152234\pi$
$743$	35960.7	1.77560	0.887799	+	0.460232i	$0.152234\pi$
$744$	2311.54	0.113905
$745$	−1060.46	−0.0521508
$746$	9184.01	0.450738
$747$	420.461	0.0205942
$748$	−2061.14	−0.100752
$749$	9241.76	0.450850
$750$	1323.48	0.0644356
$751$	−3622.27	−0.176003	−0.0880017	−	0.996120i	$-0.528048\pi$
$751$	−3622.27	−0.176003	−0.0880017	+	0.996120i	$0.528048\pi$
$752$	283.421	0.0137437
$753$	−10701.6	−0.517914
$754$	19915.6	0.961916
$755$	−194.805	−0.00939028
$756$	756.000	0.0363696
$757$	39999.1	1.92046	0.960232	−	0.279202i	$-0.0900700\pi$
$757$	39999.1	1.92046	0.960232	+	0.279202i	$0.0900700\pi$
$758$	−19344.3	−0.926935
$759$	−1563.43	−0.0747678
$760$	−134.534	−0.00642115
$761$	−13452.4	−0.640799	−0.320400	−	0.947282i	$-0.603817\pi$
$761$	−13452.4	−0.640799	−0.320400	+	0.947282i	$0.603817\pi$
$762$	−3592.11	−0.170772
$763$	−10770.1	−0.511015
$764$	−737.903	−0.0349429
$765$	−197.747	−0.00934583
$766$	−56.3520	−0.00265807
$767$	35552.5	1.67370
$768$	768.000	0.0360844
$769$	28067.1	1.31616	0.658078	−	0.752950i	$-0.271370\pi$
$769$	28067.1	1.31616	0.658078	+	0.752950i	$0.271370\pi$
$770$	257.210	0.0120379
$771$	−11041.3	−0.515749
$772$	10894.1	0.507884
$773$	−8301.46	−0.386265	−0.193132	−	0.981173i	$-0.561865\pi$
$773$	−8301.46	−0.386265	−0.193132	+	0.981173i	$0.561865\pi$
$774$	1861.91	0.0864664
$775$	−11963.8	−0.554519
$776$	401.097	0.0185548
$777$	−4827.06	−0.222870
$778$	9024.68	0.415875
$779$	6967.85	0.320474
$780$	−674.421	−0.0309592
$781$	7963.61	0.364866
$782$	1246.51	0.0570012
$783$	4234.16	0.193252
$784$	784.000	0.0357143
$785$	1082.87	0.0492346
$786$	−10977.8	−0.498176
$787$	−4770.64	−0.216080	−0.108040	−	0.994147i	$-0.534457\pi$
$787$	−4770.64	−0.216080	−0.108040	+	0.994147i	$0.534457\pi$
$788$	−12964.4	−0.586089
$789$	−3274.50	−0.147751
$790$	−1001.19	−0.0450894
$791$	14718.4	0.661600
$792$	−1494.52	−0.0670524
$793$	−28388.0	−1.27123
$794$	−16942.6	−0.757266
$795$	−1039.03	−0.0463528
$796$	−16145.6	−0.718927
$797$	14739.5	0.655084	0.327542	−	0.944837i	$-0.393780\pi$
$797$	14739.5	0.655084	0.327542	+	0.944837i	$0.393780\pi$
$798$	798.000	0.0353996
$799$	439.733	0.0194701
$800$	−3974.93	−0.175669
$801$	−8865.42	−0.391067
$802$	4795.40	0.211137
$803$	−1284.03	−0.0564289
$804$	1454.33	0.0637937
$805$	−155.551	−0.00681052
$806$	12231.5	0.534537
$807$	−6676.88	−0.291248
$808$	−1574.40	−0.0685484
$809$	−16154.4	−0.702051	−0.351025	−	0.936366i	$-0.614167\pi$
$809$	−16154.4	−0.702051	−0.351025	+	0.936366i	$0.614167\pi$
$810$	−143.385	−0.00621981
$811$	41387.8	1.79201	0.896007	−	0.444040i	$-0.146455\pi$
$811$	41387.8	1.79201	0.896007	+	0.444040i	$0.146455\pi$
$812$	4390.98	0.189770
$813$	−2403.97	−0.103704
$814$	9542.53	0.410891
$815$	1365.71	0.0586977
$816$	1191.57	0.0511192
$817$	1965.35	0.0841602
$818$	−3052.79	−0.130487
$819$	4000.38	0.170677
$820$	−1298.36	−0.0552934
$821$	−18131.6	−0.770762	−0.385381	−	0.922757i	$-0.625930\pi$
$821$	−18131.6	−0.770762	−0.385381	+	0.922757i	$0.625930\pi$
$822$	−7295.85	−0.309577
$823$	31884.2	1.35044	0.675222	−	0.737615i	$-0.264048\pi$
$823$	31884.2	1.35044	0.675222	+	0.737615i	$0.264048\pi$
$824$	5595.04	0.236544
$825$	7735.18	0.326430
$826$	7838.59	0.330193
$827$	16655.0	0.700305	0.350153	−	0.936693i	$-0.386130\pi$
$827$	16655.0	0.700305	0.350153	+	0.936693i	$0.386130\pi$
$828$	903.835	0.0379353
$829$	−4463.20	−0.186989	−0.0934943	−	0.995620i	$-0.529804\pi$
$829$	−4463.20	−0.186989	−0.0934943	+	0.995620i	$0.529804\pi$
$830$	−82.6995	−0.00345848
$831$	−19513.2	−0.814568
$832$	4063.88	0.169338
$833$	1216.39	0.0505949
$834$	−804.484	−0.0334017
$835$	596.313	0.0247141
$836$	−1577.55	−0.0652640
$837$	2600.48	0.107390
$838$	26382.3	1.08755
$839$	42573.9	1.75186	0.875932	−	0.482435i	$-0.160248\pi$
$839$	42573.9	1.75186	0.875932	+	0.482435i	$0.160248\pi$
$840$	−148.696	−0.00610773
$841$	203.737	0.00835366
$842$	−29573.8	−1.21043
$843$	9755.38	0.398568
$844$	−558.677	−0.0227849
$845$	−1624.15	−0.0661213
$846$	318.848	0.0129577
$847$	−6300.96	−0.255612
$848$	6260.89	0.253538
$849$	−14860.8	−0.600733
$850$	−6167.19	−0.248862
$851$	−5770.99	−0.232464
$852$	−4603.86	−0.185124
$853$	3843.73	0.154287	0.0771436	−	0.997020i	$-0.475420\pi$
$853$	3843.73	0.154287	0.0771436	+	0.997020i	$0.475420\pi$
$854$	−6258.96	−0.250793
$855$	−151.351	−0.00605392
$856$	10562.0	0.421732
$857$	41386.2	1.64962	0.824811	−	0.565408i	$-0.191281\pi$
$857$	41386.2	1.64962	0.824811	+	0.565408i	$0.191281\pi$
$858$	−7908.27	−0.314667
$859$	−8211.88	−0.326177	−0.163088	−	0.986611i	$-0.552146\pi$
$859$	−8211.88	−0.326177	−0.163088	+	0.986611i	$0.552146\pi$
$860$	−366.215	−0.0145207
$861$	7701.30	0.304831
$862$	21856.1	0.863597
$863$	−30034.1	−1.18467	−0.592336	−	0.805691i	$-0.701794\pi$
$863$	−30034.1	−1.18467	−0.592336	+	0.805691i	$0.701794\pi$
$864$	864.000	0.0340207
$865$	1036.48	0.0407414
$866$	−27908.5	−1.09511
$867$	−12890.3	−0.504932
$868$	2696.79	0.105455
$869$	−11739.9	−0.458285
$870$	−832.806	−0.0324538
$871$	7695.58	0.299374
$872$	−12308.7	−0.478010
$873$	451.234	0.0174936
$874$	954.048	0.0369235
$875$	1544.06	0.0596558
$876$	742.311	0.0286306
$877$	3821.61	0.147146	0.0735728	−	0.997290i	$-0.476560\pi$
$877$	3821.61	0.147146	0.0735728	+	0.997290i	$0.476560\pi$
$878$	−16128.1	−0.619926
$879$	4092.69	0.157046
$880$	293.954	0.0112604
$881$	−41942.0	−1.60393	−0.801965	−	0.597371i	$-0.796212\pi$
$881$	−41942.0	−1.60393	−0.801965	+	0.597371i	$0.796212\pi$
$882$	882.000	0.0336718
$883$	−15094.4	−0.575272	−0.287636	−	0.957740i	$-0.592869\pi$
$883$	−15094.4	−0.575272	−0.287636	+	0.957740i	$0.592869\pi$
$884$	6305.19	0.239894
$885$	−1486.69	−0.0564684
$886$	−33834.6	−1.28295
$887$	20973.4	0.793932	0.396966	−	0.917833i	$-0.370063\pi$
$887$	20973.4	0.793932	0.396966	+	0.917833i	$0.370063\pi$
$888$	−5516.64	−0.208476
$889$	−4190.80	−0.158104
$890$	1743.72	0.0656737
$891$	−1681.34	−0.0632176
$892$	−10307.0	−0.386888
$893$	336.562	0.0126121
$894$	7188.81	0.268937
$895$	−240.671	−0.00898855
$896$	896.000	0.0334077
$897$	4782.65	0.178024
$898$	−713.025	−0.0264966
$899$	15104.0	0.560342
$900$	−4471.80	−0.165622
$901$	9713.91	0.359176
$902$	−15224.6	−0.561998
$903$	2172.23	0.0800523
$904$	16821.0	0.618870
$905$	309.301	0.0113608
$906$	1320.57	0.0484249
$907$	−16803.1	−0.615146	−0.307573	−	0.951524i	$-0.599517\pi$
$907$	−16803.1	−0.615146	−0.307573	+	0.951524i	$0.599517\pi$
$908$	2811.12	0.102743
$909$	−1771.20	−0.0646281
$910$	−786.825	−0.0286626
$911$	21214.4	0.771532	0.385766	−	0.922597i	$-0.373937\pi$
$911$	21214.4	0.771532	0.385766	+	0.922597i	$0.373937\pi$
$912$	912.000	0.0331133
$913$	−969.736	−0.0351518
$914$	−22703.4	−0.821620
$915$	1187.09	0.0428897
$916$	10707.9	0.386244
$917$	−12807.5	−0.461222
$918$	1340.51	0.0481956
$919$	45782.2	1.64333	0.821663	−	0.569974i	$-0.193047\pi$
$919$	45782.2	1.64333	0.821663	+	0.569974i	$0.193047\pi$
$920$	−177.773	−0.00637066
$921$	−12820.8	−0.458697
$922$	1564.36	0.0558778
$923$	−24361.3	−0.868757
$924$	−1743.61	−0.0620785
$925$	28552.4	1.01492
$926$	−16767.6	−0.595050
$927$	6294.42	0.223016
$928$	5018.26	0.177514
$929$	−17234.4	−0.608656	−0.304328	−	0.952567i	$-0.598432\pi$
$929$	−17234.4	−0.608656	−0.304328	+	0.952567i	$0.598432\pi$
$930$	−511.482	−0.0180346
$931$	931.000	0.0327737
$932$	7998.35	0.281110
$933$	−2408.84	−0.0845250
$934$	519.729	0.0182078
$935$	456.076	0.0159522
$936$	4571.86	0.159654
$937$	35151.7	1.22557	0.612783	−	0.790251i	$-0.290050\pi$
$937$	35151.7	1.22557	0.612783	+	0.790251i	$0.290050\pi$
$938$	1696.71	0.0590615
$939$	−16120.5	−0.560246
$940$	−62.7135	−0.00217605
$941$	16184.0	0.560662	0.280331	−	0.959903i	$-0.409556\pi$
$941$	16184.0	0.560662	0.280331	+	0.959903i	$0.409556\pi$
$942$	−7340.69	−0.253899
$943$	9207.28	0.317954
$944$	8958.39	0.308867
$945$	−167.283	−0.00575842
$946$	−4294.24	−0.147587
$947$	−33832.7	−1.16095	−0.580473	−	0.814280i	$-0.697132\pi$
$947$	−33832.7	−1.16095	−0.580473	+	0.814280i	$0.697132\pi$
$948$	6786.98	0.232522
$949$	3927.94	0.134359
$950$	−4720.23	−0.161205
$951$	−18589.8	−0.633877
$952$	1390.16	0.0473272
$953$	−1919.15	−0.0652332	−0.0326166	−	0.999468i	$-0.510384\pi$
$953$	−1919.15	−0.0652332	−0.0326166	+	0.999468i	$0.510384\pi$
$954$	7043.50	0.239038
$955$	163.278	0.00553253
$956$	428.897	0.0145099
$957$	−9765.50	−0.329858
$958$	6650.72	0.224296
$959$	−8511.82	−0.286612
$960$	−169.938	−0.00571326
$961$	−20514.6	−0.688618
$962$	−29191.3	−0.978344
$963$	11882.3	0.397612
$964$	18380.0	0.614087
$965$	−2410.57	−0.0804136
$966$	1054.47	0.0351213
$967$	8938.25	0.297244	0.148622	−	0.988894i	$-0.452516\pi$
$967$	8938.25	0.297244	0.148622	+	0.988894i	$0.452516\pi$
$968$	−7201.09	−0.239103
$969$	1414.99	0.0469102
$970$	−88.7521	−0.00293779
$971$	3657.02	0.120865	0.0604323	−	0.998172i	$-0.480752\pi$
$971$	3657.02	0.120865	0.0604323	+	0.998172i	$0.480752\pi$
$972$	972.000	0.0320750
$973$	−938.565	−0.0309240
$974$	31143.5	1.02454
$975$	−23662.5	−0.777239
$976$	−7153.09	−0.234595
$977$	−6308.64	−0.206583	−0.103291	−	0.994651i	$-0.532937\pi$
$977$	−6308.64	−0.206583	−0.103291	+	0.994651i	$0.532937\pi$
$978$	−9258.05	−0.302699
$979$	20446.9	0.667502
$980$	−173.478	−0.00565466
$981$	−13847.3	−0.450672
$982$	2162.43	0.0702707
$983$	46986.3	1.52455	0.762273	−	0.647256i	$-0.224083\pi$
$983$	46986.3	1.52455	0.762273	+	0.647256i	$0.224083\pi$
$984$	8801.49	0.285144
$985$	2868.68	0.0927957
$986$	7785.95	0.251476
$987$	371.989	0.0119965
$988$	4825.85	0.155396
$989$	2597.01	0.0834984
$990$	330.698	0.0106164
$991$	26138.4	0.837853	0.418927	−	0.908020i	$-0.362406\pi$
$991$	26138.4	0.837853	0.418927	+	0.908020i	$0.362406\pi$
$992$	3082.05	0.0986443
$993$	18807.0	0.601029
$994$	−5371.16	−0.171391
$995$	3572.59	0.113828
$996$	560.615	0.0178351
$997$	−41678.3	−1.32394	−0.661969	−	0.749531i	$-0.730279\pi$
$997$	−41678.3	−1.32394	−0.661969	+	0.749531i	$0.730279\pi$
$998$	−2502.95	−0.0793881
$999$	−6206.22	−0.196553

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.r.1.2	✓	5
3.2	odd	2		2394.4.a.bb.1.4		5

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.r.1.2	✓	5	1.1	even	1	trivial
2394.4.a.bb.1.4		5	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)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.885094 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -0.885094 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -1.77019 q^{10} -20.7572 q^{11} +12.0000 q^{12} +63.4981 q^{13} +14.0000 q^{14} -2.65528 q^{15} +16.0000 q^{16} +24.8244 q^{17} +18.0000 q^{18} +19.0000 q^{19} -3.54038 q^{20} +21.0000 q^{21} -41.5145 q^{22} +25.1065 q^{23} +24.0000 q^{24} -124.217 q^{25} +126.996 q^{26} +27.0000 q^{27} +28.0000 q^{28} +156.821 q^{29} -5.31056 q^{30} +96.3140 q^{31} +32.0000 q^{32} -62.2717 q^{33} +49.6487 q^{34} -6.19566 q^{35} +36.0000 q^{36} -229.860 q^{37} +38.0000 q^{38} +190.494 q^{39} -7.08075 q^{40} +366.729 q^{41} +42.0000 q^{42} +103.439 q^{43} -83.0290 q^{44} -7.96585 q^{45} +50.2130 q^{46} +17.7138 q^{47} +48.0000 q^{48} +49.0000 q^{49} -248.433 q^{50} +74.4731 q^{51} +253.992 q^{52} +391.306 q^{53} +54.0000 q^{54} +18.3721 q^{55} +56.0000 q^{56} +57.0000 q^{57} +313.641 q^{58} +559.900 q^{59} -10.6211 q^{60} -447.068 q^{61} +192.628 q^{62} +63.0000 q^{63} +64.0000 q^{64} -56.2018 q^{65} -124.543 q^{66} +121.194 q^{67} +99.2974 q^{68} +75.3196 q^{69} -12.3913 q^{70} -383.655 q^{71} +72.0000 q^{72} +61.8593 q^{73} -459.720 q^{74} -372.650 q^{75} +76.0000 q^{76} -145.301 q^{77} +380.988 q^{78} +565.582 q^{79} -14.1615 q^{80} +81.0000 q^{81} +733.457 q^{82} +46.7179 q^{83} +84.0000 q^{84} -21.9719 q^{85} +206.879 q^{86} +470.462 q^{87} -166.058 q^{88} -985.047 q^{89} -15.9317 q^{90} +444.487 q^{91} +100.426 q^{92} +288.942 q^{93} +35.4276 q^{94} -16.8168 q^{95} +96.0000 q^{96} +50.1371 q^{97} +98.0000 q^{98} -186.815 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9} + 40 q^{10} + 82 q^{11} + 60 q^{12} + 20 q^{13} + 70 q^{14} + 60 q^{15} + 80 q^{16} + 48 q^{17} + 90 q^{18} + 95 q^{19} + 80 q^{20} + 105 q^{21} + 164 q^{22} + 166 q^{23} + 120 q^{24} + 235 q^{25} + 40 q^{26} + 135 q^{27} + 140 q^{28} + 134 q^{29} + 120 q^{30} + 124 q^{31} + 160 q^{32} + 246 q^{33} + 96 q^{34} + 140 q^{35} + 180 q^{36} + 334 q^{37} + 190 q^{38} + 60 q^{39} + 160 q^{40} - 126 q^{41} + 210 q^{42} + 132 q^{43} + 328 q^{44} + 180 q^{45} + 332 q^{46} + 120 q^{47} + 240 q^{48} + 245 q^{49} + 470 q^{50} + 144 q^{51} + 80 q^{52} + 142 q^{53} + 270 q^{54} + 64 q^{55} + 280 q^{56} + 285 q^{57} + 268 q^{58} + 12 q^{59} + 240 q^{60} + 614 q^{61} + 248 q^{62} + 315 q^{63} + 320 q^{64} + 672 q^{65} + 492 q^{66} - 30 q^{67} + 192 q^{68} + 498 q^{69} + 280 q^{70} + 548 q^{71} + 360 q^{72} + 554 q^{73} + 668 q^{74} + 705 q^{75} + 380 q^{76} + 574 q^{77} + 120 q^{78} - 138 q^{79} + 320 q^{80} + 405 q^{81} - 252 q^{82} + 100 q^{83} + 420 q^{84} - 156 q^{85} + 264 q^{86} + 402 q^{87} + 656 q^{88} + 842 q^{89} + 360 q^{90} + 140 q^{91} + 664 q^{92} + 372 q^{93} + 240 q^{94} + 380 q^{95} + 480 q^{96} - 568 q^{97} + 490 q^{98} + 738 q^{99}+O(q^{100}) \) 5 * q + 10 * q^2 + 15 * q^3 + 20 * q^4 + 20 * q^5 + 30 * q^6 + 35 * q^7 + 40 * q^8 + 45 * q^9 + 40 * q^10 + 82 * q^11 + 60 * q^12 + 20 * q^13 + 70 * q^14 + 60 * q^15 + 80 * q^16 + 48 * q^17 + 90 * q^18 + 95 * q^19 + 80 * q^20 + 105 * q^21 + 164 * q^22 + 166 * q^23 + 120 * q^24 + 235 * q^25 + 40 * q^26 + 135 * q^27 + 140 * q^28 + 134 * q^29 + 120 * q^30 + 124 * q^31 + 160 * q^32 + 246 * q^33 + 96 * q^34 + 140 * q^35 + 180 * q^36 + 334 * q^37 + 190 * q^38 + 60 * q^39 + 160 * q^40 - 126 * q^41 + 210 * q^42 + 132 * q^43 + 328 * q^44 + 180 * q^45 + 332 * q^46 + 120 * q^47 + 240 * q^48 + 245 * q^49 + 470 * q^50 + 144 * q^51 + 80 * q^52 + 142 * q^53 + 270 * q^54 + 64 * q^55 + 280 * q^56 + 285 * q^57 + 268 * q^58 + 12 * q^59 + 240 * q^60 + 614 * q^61 + 248 * q^62 + 315 * q^63 + 320 * q^64 + 672 * q^65 + 492 * q^66 - 30 * q^67 + 192 * q^68 + 498 * q^69 + 280 * q^70 + 548 * q^71 + 360 * q^72 + 554 * q^73 + 668 * q^74 + 705 * q^75 + 380 * q^76 + 574 * q^77 + 120 * q^78 - 138 * q^79 + 320 * q^80 + 405 * q^81 - 252 * q^82 + 100 * q^83 + 420 * q^84 - 156 * q^85 + 264 * q^86 + 402 * q^87 + 656 * q^88 + 842 * q^89 + 360 * q^90 + 140 * q^91 + 664 * q^92 + 372 * q^93 + 240 * q^94 + 380 * q^95 + 480 * q^96 - 568 * q^97 + 490 * q^98 + 738 * q^99

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