LMFDB - Embedded newform 798.4.a.r.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:	$5$
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			1.4
Root			$12.1875$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.9744 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.9744 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +31.9487 q^{10} +49.9762 q^{11} +12.0000 q^{12} +12.6049 q^{13} +14.0000 q^{14} +47.9231 q^{15} +16.0000 q^{16} -97.0478 q^{17} +18.0000 q^{18} +19.0000 q^{19} +63.8974 q^{20} +21.0000 q^{21} +99.9525 q^{22} -14.0138 q^{23} +24.0000 q^{24} +130.180 q^{25} +25.2098 q^{26} +27.0000 q^{27} +28.0000 q^{28} +282.480 q^{29} +95.8461 q^{30} -132.431 q^{31} +32.0000 q^{32} +149.929 q^{33} -194.096 q^{34} +111.820 q^{35} +36.0000 q^{36} -340.696 q^{37} +38.0000 q^{38} +37.8147 q^{39} +127.795 q^{40} -470.641 q^{41} +42.0000 q^{42} +137.939 q^{43} +199.905 q^{44} +143.769 q^{45} -28.0275 q^{46} -489.300 q^{47} +48.0000 q^{48} +49.0000 q^{49} +260.360 q^{50} -291.143 q^{51} +50.4196 q^{52} +156.230 q^{53} +54.0000 q^{54} +798.338 q^{55} +56.0000 q^{56} +57.0000 q^{57} +564.959 q^{58} -262.675 q^{59} +191.692 q^{60} +774.392 q^{61} -264.862 q^{62} +63.0000 q^{63} +64.0000 q^{64} +201.355 q^{65} +299.857 q^{66} -635.570 q^{67} -388.191 q^{68} -42.0413 q^{69} +223.641 q^{70} -218.529 q^{71} +72.0000 q^{72} +1117.95 q^{73} -681.392 q^{74} +390.540 q^{75} +76.0000 q^{76} +349.834 q^{77} +75.6294 q^{78} -298.545 q^{79} +255.590 q^{80} +81.0000 q^{81} -941.281 q^{82} +335.009 q^{83} +84.0000 q^{84} -1550.28 q^{85} +275.877 q^{86} +847.439 q^{87} +399.810 q^{88} +586.432 q^{89} +287.538 q^{90} +88.2342 q^{91} -56.0551 q^{92} -397.293 q^{93} -978.600 q^{94} +303.513 q^{95} +96.0000 q^{96} -758.421 q^{97} +98.0000 q^{98} +449.786 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$5$	15.9744	1.42879	0.714395	−	0.699743i	$-0.246702\pi$
$5$	15.9744	1.42879	0.714395	+	0.699743i	$0.246702\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	31.9487	1.01031
$11$	49.9762	1.36985	0.684927	−	0.728611i	$-0.259834\pi$
$11$	49.9762	1.36985	0.684927	+	0.728611i	$0.259834\pi$
$12$	12.0000	0.288675
$13$	12.6049	0.268921	0.134460	−	0.990919i	$-0.457070\pi$
$13$	12.6049	0.268921	0.134460	+	0.990919i	$0.457070\pi$
$14$	14.0000	0.267261
$15$	47.9231	0.824912
$16$	16.0000	0.250000
$17$	−97.0478	−1.38456	−0.692281	−	0.721628i	$-0.743394\pi$
$17$	−97.0478	−1.38456	−0.692281	+	0.721628i	$0.743394\pi$
$18$	18.0000	0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	63.8974	0.714395
$21$	21.0000	0.218218
$22$	99.9525	0.968634
$23$	−14.0138	−0.127047	−0.0635233	−	0.997980i	$-0.520234\pi$
$23$	−14.0138	−0.127047	−0.0635233	+	0.997980i	$0.520234\pi$
$24$	24.0000	0.204124
$25$	130.180	1.04144
$26$	25.2098	0.190156
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	282.480	1.80880	0.904399	−	0.426688i	$-0.140320\pi$
$29$	282.480	1.80880	0.904399	+	0.426688i	$0.140320\pi$
$30$	95.8461	0.583301
$31$	−132.431	−0.767268	−0.383634	−	0.923485i	$-0.625328\pi$
$31$	−132.431	−0.767268	−0.383634	+	0.923485i	$0.625328\pi$
$32$	32.0000	0.176777
$33$	149.929	0.790886
$34$	−194.096	−0.979033
$35$	111.820	0.540032
$36$	36.0000	0.166667
$37$	−340.696	−1.51378	−0.756892	−	0.653539i	$-0.773283\pi$
$37$	−340.696	−1.51378	−0.756892	+	0.653539i	$0.773283\pi$
$38$	38.0000	0.162221
$39$	37.8147	0.155261
$40$	127.795	0.505153
$41$	−470.641	−1.79272	−0.896362	−	0.443322i	$-0.853800\pi$
$41$	−470.641	−1.79272	−0.896362	+	0.443322i	$0.853800\pi$
$42$	42.0000	0.154303
$43$	137.939	0.489196	0.244598	−	0.969625i	$-0.421344\pi$
$43$	137.939	0.489196	0.244598	+	0.969625i	$0.421344\pi$
$44$	199.905	0.684927
$45$	143.769	0.476263
$46$	−28.0275	−0.0898355
$47$	−489.300	−1.51855	−0.759274	−	0.650771i	$-0.774446\pi$
$47$	−489.300	−1.51855	−0.759274	+	0.650771i	$0.774446\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	260.360	0.736409
$51$	−291.143	−0.799377
$52$	50.4196	0.134460
$53$	156.230	0.404902	0.202451	−	0.979292i	$-0.435109\pi$
$53$	156.230	0.404902	0.202451	+	0.979292i	$0.435109\pi$
$54$	54.0000	0.136083
$55$	798.338	1.95723
$56$	56.0000	0.133631
$57$	57.0000	0.132453
$58$	564.959	1.27901
$59$	−262.675	−0.579617	−0.289809	−	0.957085i	$-0.593592\pi$
$59$	−262.675	−0.579617	−0.289809	+	0.957085i	$0.593592\pi$
$60$	191.692	0.412456
$61$	774.392	1.62542	0.812711	−	0.582668i	$-0.197991\pi$
$61$	774.392	1.62542	0.812711	+	0.582668i	$0.197991\pi$
$62$	−264.862	−0.542541
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	201.355	0.384231
$66$	299.857	0.559241
$67$	−635.570	−1.15891	−0.579457	−	0.815003i	$-0.696735\pi$
$67$	−635.570	−1.15891	−0.579457	+	0.815003i	$0.696735\pi$
$68$	−388.191	−0.692281
$69$	−42.0413	−0.0733504
$70$	223.641	0.381860
$71$	−218.529	−0.365276	−0.182638	−	0.983180i	$-0.558464\pi$
$71$	−218.529	−0.365276	−0.182638	+	0.983180i	$0.558464\pi$
$72$	72.0000	0.117851
$73$	1117.95	1.79241	0.896205	−	0.443640i	$-0.146313\pi$
$73$	1117.95	1.79241	0.896205	+	0.443640i	$0.146313\pi$
$74$	−681.392	−1.07041
$75$	390.540	0.601275
$76$	76.0000	0.114708
$77$	349.834	0.517756
$78$	75.6294	0.109786
$79$	−298.545	−0.425176	−0.212588	−	0.977142i	$-0.568189\pi$
$79$	−298.545	−0.425176	−0.212588	+	0.977142i	$0.568189\pi$
$80$	255.590	0.357197
$81$	81.0000	0.111111
$82$	−941.281	−1.26765
$83$	335.009	0.443037	0.221518	−	0.975156i	$-0.428899\pi$
$83$	335.009	0.443037	0.221518	+	0.975156i	$0.428899\pi$
$84$	84.0000	0.109109
$85$	−1550.28	−1.97825
$86$	275.877	0.345914
$87$	847.439	1.04431
$88$	399.810	0.484317
$89$	586.432	0.698446	0.349223	−	0.937040i	$-0.386446\pi$
$89$	586.432	0.698446	0.349223	+	0.937040i	$0.386446\pi$
$90$	287.538	0.336769
$91$	88.2342	0.101642
$92$	−56.0551	−0.0635233
$93$	−397.293	−0.442982
$94$	−978.600	−1.07378
$95$	303.513	0.327787
$96$	96.0000	0.102062
$97$	−758.421	−0.793876	−0.396938	−	0.917845i	$-0.629927\pi$
$97$	−758.421	−0.793876	−0.396938	+	0.917845i	$0.629927\pi$
$98$	98.0000	0.101015
$99$	449.786	0.456618
$100$	520.720	0.520720
$101$	−1841.57	−1.81429	−0.907144	−	0.420820i	$-0.861742\pi$
$101$	−1841.57	−1.81429	−0.907144	+	0.420820i	$0.861742\pi$
$102$	−582.287	−0.565245
$103$	41.7272	0.0399175	0.0199588	−	0.999801i	$-0.493647\pi$
$103$	41.7272	0.0399175	0.0199588	+	0.999801i	$0.493647\pi$
$104$	100.839	0.0950778
$105$	335.461	0.311787
$106$	312.460	0.286309
$107$	−598.395	−0.540645	−0.270323	−	0.962770i	$-0.587130\pi$
$107$	−598.395	−0.540645	−0.270323	+	0.962770i	$0.587130\pi$
$108$	108.000	0.0962250
$109$	1143.07	1.00446	0.502231	−	0.864734i	$-0.332513\pi$
$109$	1143.07	1.00446	0.502231	+	0.864734i	$0.332513\pi$
$110$	1596.68	1.38397
$111$	−1022.09	−0.873984
$112$	112.000	0.0944911
$113$	218.622	0.182002	0.0910011	−	0.995851i	$-0.470993\pi$
$113$	218.622	0.182002	0.0910011	+	0.995851i	$0.470993\pi$
$114$	114.000	0.0936586
$115$	−223.861	−0.181523
$116$	1129.92	0.904399
$117$	113.444	0.0896402
$118$	−525.351	−0.409851
$119$	−679.335	−0.523315
$120$	383.384	0.291650
$121$	1166.62	0.876502
$122$	1548.78	1.14935
$123$	−1411.92	−1.03503
$124$	−529.724	−0.383634
$125$	82.7460	0.0592082
$126$	126.000	0.0890871
$127$	808.013	0.564564	0.282282	−	0.959332i	$-0.408909\pi$
$127$	808.013	0.564564	0.282282	+	0.959332i	$0.408909\pi$
$128$	128.000	0.0883883
$129$	413.816	0.282438
$130$	402.710	0.271692
$131$	1420.65	0.947499	0.473750	−	0.880660i	$-0.342900\pi$
$131$	1420.65	0.947499	0.473750	+	0.880660i	$0.342900\pi$
$132$	599.715	0.395443
$133$	133.000	0.0867110
$134$	−1271.14	−0.819476
$135$	431.308	0.274971
$136$	−776.382	−0.489516
$137$	1252.73	0.781227	0.390614	−	0.920555i	$-0.372263\pi$
$137$	1252.73	0.781227	0.390614	+	0.920555i	$0.372263\pi$
$138$	−84.0826	−0.0518666
$139$	−1416.77	−0.864524	−0.432262	−	0.901748i	$-0.642284\pi$
$139$	−1416.77	−0.864524	−0.432262	+	0.901748i	$0.642284\pi$
$140$	447.282	0.270016
$141$	−1467.90	−0.876734
$142$	−437.057	−0.258289
$143$	629.945	0.368382
$144$	144.000	0.0833333
$145$	4512.43	2.58439
$146$	2235.90	1.26743
$147$	147.000	0.0824786
$148$	−1362.78	−0.756892
$149$	−1587.27	−0.872714	−0.436357	−	0.899774i	$-0.643732\pi$
$149$	−1587.27	−0.872714	−0.436357	+	0.899774i	$0.643732\pi$
$150$	781.080	0.425166
$151$	−384.731	−0.207344	−0.103672	−	0.994612i	$-0.533059\pi$
$151$	−384.731	−0.207344	−0.103672	+	0.994612i	$0.533059\pi$
$152$	152.000	0.0811107
$153$	−873.430	−0.461521
$154$	699.667	0.366109
$155$	−2115.50	−1.09626
$156$	151.259	0.0776307
$157$	2250.54	1.14403	0.572014	−	0.820244i	$-0.306162\pi$
$157$	2250.54	1.14403	0.572014	+	0.820244i	$0.306162\pi$
$158$	−597.089	−0.300645
$159$	468.689	0.233770
$160$	511.179	0.252577
$161$	−98.0964	−0.0480191
$162$	162.000	0.0785674
$163$	2984.42	1.43410	0.717049	−	0.697023i	$-0.245492\pi$
$163$	2984.42	1.43410	0.717049	+	0.697023i	$0.245492\pi$
$164$	−1882.56	−0.896362
$165$	2395.01	1.13001
$166$	670.019	0.313274
$167$	3133.07	1.45176	0.725881	−	0.687820i	$-0.241432\pi$
$167$	3133.07	1.45176	0.725881	+	0.687820i	$0.241432\pi$
$168$	168.000	0.0771517
$169$	−2038.12	−0.927682
$170$	−3100.55	−1.39883
$171$	171.000	0.0764719
$172$	551.754	0.244598
$173$	−664.164	−0.291881	−0.145941	−	0.989293i	$-0.546621\pi$
$173$	−664.164	−0.291881	−0.145941	+	0.989293i	$0.546621\pi$
$174$	1694.88	0.738438
$175$	911.260	0.393627
$176$	799.620	0.342464
$177$	−788.026	−0.334642
$178$	1172.86	0.493876
$179$	3565.67	1.48888	0.744442	−	0.667687i	$-0.232715\pi$
$179$	3565.67	1.48888	0.744442	+	0.667687i	$0.232715\pi$
$180$	575.077	0.238132
$181$	−3943.49	−1.61943	−0.809716	−	0.586822i	$-0.800379\pi$
$181$	−3943.49	−1.61943	−0.809716	+	0.586822i	$0.800379\pi$
$182$	176.468	0.0718721
$183$	2323.18	0.938437
$184$	−112.110	−0.0449178
$185$	−5442.39	−2.16288
$186$	−794.586	−0.313236
$187$	−4850.08	−1.89665
$188$	−1957.20	−0.759274
$189$	189.000	0.0727393
$190$	607.025	0.231780
$191$	−1338.13	−0.506930	−0.253465	−	0.967345i	$-0.581570\pi$
$191$	−1338.13	−0.506930	−0.253465	+	0.967345i	$0.581570\pi$
$192$	192.000	0.0721688
$193$	−2232.82	−0.832757	−0.416378	−	0.909191i	$-0.636701\pi$
$193$	−2232.82	−0.832757	−0.416378	+	0.909191i	$0.636701\pi$
$194$	−1516.84	−0.561355
$195$	604.065	0.221836
$196$	196.000	0.0714286
$197$	2428.81	0.878405	0.439203	−	0.898388i	$-0.355261\pi$
$197$	2428.81	0.878405	0.439203	+	0.898388i	$0.355261\pi$
$198$	899.572	0.322878
$199$	3800.08	1.35367	0.676836	−	0.736134i	$-0.263351\pi$
$199$	3800.08	1.35367	0.676836	+	0.736134i	$0.263351\pi$
$200$	1041.44	0.368204
$201$	−1906.71	−0.669099
$202$	−3683.14	−1.28290
$203$	1977.36	0.683661
$204$	−1164.57	−0.399688
$205$	−7518.18	−2.56143
$206$	83.4544	0.0282259
$207$	−126.124	−0.0423489
$208$	201.678	0.0672302
$209$	949.549	0.314266
$210$	670.923	0.220467
$211$	−687.731	−0.224386	−0.112193	−	0.993686i	$-0.535787\pi$
$211$	−687.731	−0.224386	−0.112193	+	0.993686i	$0.535787\pi$
$212$	624.919	0.202451
$213$	−655.586	−0.210892
$214$	−1196.79	−0.382294
$215$	2203.48	0.698958
$216$	216.000	0.0680414
$217$	−927.017	−0.290000
$218$	2286.14	0.710262
$219$	3353.84	1.03485
$220$	3193.35	0.978617
$221$	−1223.28	−0.372337
$222$	−2044.17	−0.618000
$223$	2490.88	0.747989	0.373995	−	0.927431i	$-0.377988\pi$
$223$	2490.88	0.747989	0.373995	+	0.927431i	$0.377988\pi$
$224$	224.000	0.0668153
$225$	1171.62	0.347146
$226$	437.244	0.128695
$227$	4624.56	1.35217	0.676086	−	0.736823i	$-0.263675\pi$
$227$	4624.56	1.35217	0.676086	+	0.736823i	$0.263675\pi$
$228$	228.000	0.0662266
$229$	−2834.76	−0.818019	−0.409010	−	0.912530i	$-0.634126\pi$
$229$	−2834.76	−0.818019	−0.409010	+	0.912530i	$0.634126\pi$
$230$	−447.722	−0.128356
$231$	1049.50	0.298927
$232$	2259.84	0.639506
$233$	−4113.76	−1.15666	−0.578329	−	0.815803i	$-0.696295\pi$
$233$	−4113.76	−1.15666	−0.578329	+	0.815803i	$0.696295\pi$
$234$	226.888	0.0633852
$235$	−7816.25	−2.16969
$236$	−1050.70	−0.289809
$237$	−895.634	−0.245475
$238$	−1358.67	−0.370040
$239$	−2688.04	−0.727510	−0.363755	−	0.931495i	$-0.618505\pi$
$239$	−2688.04	−0.727510	−0.363755	+	0.931495i	$0.618505\pi$
$240$	766.769	0.206228
$241$	−3505.52	−0.936974	−0.468487	−	0.883470i	$-0.655201\pi$
$241$	−3505.52	−0.936974	−0.468487	+	0.883470i	$0.655201\pi$
$242$	2333.25	0.619781
$243$	243.000	0.0641500
$244$	3097.57	0.812711
$245$	782.743	0.204113
$246$	−2823.84	−0.731877
$247$	239.493	0.0616946
$248$	−1059.45	−0.271270
$249$	1005.03	0.255787
$250$	165.492	0.0418665
$251$	−3054.68	−0.768167	−0.384084	−	0.923298i	$-0.625483\pi$
$251$	−3054.68	−0.768167	−0.384084	+	0.923298i	$0.625483\pi$
$252$	252.000	0.0629941
$253$	−700.355	−0.174035
$254$	1616.03	0.399207
$255$	−4650.83	−1.14214
$256$	256.000	0.0625000
$257$	−619.705	−0.150413	−0.0752065	−	0.997168i	$-0.523962\pi$
$257$	−619.705	−0.150413	−0.0752065	+	0.997168i	$0.523962\pi$
$258$	827.631	0.199714
$259$	−2384.87	−0.572157
$260$	805.420	0.192115
$261$	2542.32	0.602932
$262$	2841.29	0.669983
$263$	4327.82	1.01469	0.507347	−	0.861742i	$-0.330626\pi$
$263$	4327.82	1.01469	0.507347	+	0.861742i	$0.330626\pi$
$264$	1199.43	0.279620
$265$	2495.67	0.578520
$266$	266.000	0.0613139
$267$	1759.30	0.403248
$268$	−2542.28	−0.579457
$269$	−4748.36	−1.07625	−0.538127	−	0.842864i	$-0.680868\pi$
$269$	−4748.36	−1.07625	−0.538127	+	0.842864i	$0.680868\pi$
$270$	862.615	0.194434
$271$	−2252.14	−0.504827	−0.252413	−	0.967619i	$-0.581224\pi$
$271$	−2252.14	−0.504827	−0.252413	+	0.967619i	$0.581224\pi$
$272$	−1552.76	−0.346140
$273$	264.703	0.0586833
$274$	2505.46	0.552411
$275$	6505.90	1.42662
$276$	−168.165	−0.0366752
$277$	−2504.76	−0.543308	−0.271654	−	0.962395i	$-0.587571\pi$
$277$	−2504.76	−0.543308	−0.271654	+	0.962395i	$0.587571\pi$
$278$	−2833.54	−0.611311
$279$	−1191.88	−0.255756
$280$	894.564	0.190930
$281$	−6911.97	−1.46738	−0.733690	−	0.679485i	$-0.762203\pi$
$281$	−6911.97	−1.46738	−0.733690	+	0.679485i	$0.762203\pi$
$282$	−2935.80	−0.619945
$283$	−7253.42	−1.52357	−0.761786	−	0.647829i	$-0.775677\pi$
$283$	−7253.42	−1.52357	−0.761786	+	0.647829i	$0.775677\pi$
$284$	−874.115	−0.182638
$285$	910.538	0.189248
$286$	1259.89	0.260486
$287$	−3294.48	−0.677586
$288$	288.000	0.0589256
$289$	4505.27	0.917011
$290$	9024.85	1.82744
$291$	−2275.26	−0.458344
$292$	4471.79	0.896205
$293$	2282.79	0.455160	0.227580	−	0.973759i	$-0.426919\pi$
$293$	2282.79	0.455160	0.227580	+	0.973759i	$0.426919\pi$
$294$	294.000	0.0583212
$295$	−4196.07	−0.828151
$296$	−2725.57	−0.535204
$297$	1349.36	0.263629
$298$	−3174.54	−0.617102
$299$	−176.642	−0.0341655
$300$	1562.16	0.300638
$301$	965.570	0.184899
$302$	−769.463	−0.146615
$303$	−5524.71	−1.04748
$304$	304.000	0.0573539
$305$	12370.4	2.32238
$306$	−1746.86	−0.326344
$307$	−585.585	−0.108863	−0.0544317	−	0.998517i	$-0.517335\pi$
$307$	−585.585	−0.108863	−0.0544317	+	0.998517i	$0.517335\pi$
$308$	1399.33	0.258878
$309$	125.182	0.0230464
$310$	−4231.00	−0.775176
$311$	−8120.94	−1.48070	−0.740348	−	0.672224i	$-0.765339\pi$
$311$	−8120.94	−1.48070	−0.740348	+	0.672224i	$0.765339\pi$
$312$	302.517	0.0548932
$313$	−2025.21	−0.365724	−0.182862	−	0.983139i	$-0.558536\pi$
$313$	−2025.21	−0.365724	−0.182862	+	0.983139i	$0.558536\pi$
$314$	4501.07	0.808949
$315$	1006.38	0.180011
$316$	−1194.18	−0.212588
$317$	1848.43	0.327501	0.163751	−	0.986502i	$-0.447641\pi$
$317$	1848.43	0.327501	0.163751	+	0.986502i	$0.447641\pi$
$318$	937.379	0.165301
$319$	14117.3	2.47779
$320$	1022.36	0.178599
$321$	−1795.19	−0.312142
$322$	−196.193	−0.0339546
$323$	−1843.91	−0.317640
$324$	324.000	0.0555556
$325$	1640.90	0.280065
$326$	5968.84	1.01406
$327$	3429.21	0.579926
$328$	−3765.13	−0.633824
$329$	−3425.10	−0.573957
$330$	4790.03	0.799037
$331$	−1373.46	−0.228074	−0.114037	−	0.993477i	$-0.536378\pi$
$331$	−1373.46	−0.228074	−0.114037	+	0.993477i	$0.536378\pi$
$332$	1340.04	0.221518
$333$	−3066.26	−0.504595
$334$	6266.14	1.02655
$335$	−10152.8	−1.65584
$336$	336.000	0.0545545
$337$	−1492.55	−0.241260	−0.120630	−	0.992698i	$-0.538491\pi$
$337$	−1492.55	−0.241260	−0.120630	+	0.992698i	$0.538491\pi$
$338$	−4076.23	−0.655970
$339$	655.867	0.105079
$340$	−6201.10	−0.989123
$341$	−6618.40	−1.05105
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	1103.51	0.172957
$345$	−671.583	−0.104802
$346$	−1328.33	−0.206391
$347$	8848.16	1.36886	0.684430	−	0.729079i	$-0.260051\pi$
$347$	8848.16	1.36886	0.684430	+	0.729079i	$0.260051\pi$
$348$	3389.75	0.522155
$349$	−9323.77	−1.43006	−0.715029	−	0.699095i	$-0.753587\pi$
$349$	−9323.77	−1.43006	−0.715029	+	0.699095i	$0.753587\pi$
$350$	1822.52	0.278336
$351$	340.332	0.0517538
$352$	1599.24	0.242158
$353$	11373.2	1.71482	0.857411	−	0.514632i	$-0.172071\pi$
$353$	11373.2	1.71482	0.857411	+	0.514632i	$0.172071\pi$
$354$	−1576.05	−0.236628
$355$	−3490.85	−0.521902
$356$	2345.73	0.349223
$357$	−2038.00	−0.302136
$358$	7131.33	1.05280
$359$	−3331.78	−0.489818	−0.244909	−	0.969546i	$-0.578758\pi$
$359$	−3331.78	−0.489818	−0.244909	+	0.969546i	$0.578758\pi$
$360$	1150.15	0.168384
$361$	361.000	0.0526316
$362$	−7886.98	−1.14511
$363$	3499.87	0.506049
$364$	352.937	0.0508212
$365$	17858.5	2.56098
$366$	4646.35	0.663575
$367$	−6646.90	−0.945410	−0.472705	−	0.881221i	$-0.656722\pi$
$367$	−6646.90	−0.945410	−0.472705	+	0.881221i	$0.656722\pi$
$368$	−224.220	−0.0317617
$369$	−4235.77	−0.597575
$370$	−10884.8	−1.52939
$371$	1093.61	0.153039
$372$	−1589.17	−0.221491
$373$	−3217.50	−0.446638	−0.223319	−	0.974745i	$-0.571689\pi$
$373$	−3217.50	−0.446638	−0.223319	+	0.974745i	$0.571689\pi$
$374$	−9700.17	−1.34113
$375$	248.238	0.0341839
$376$	−3914.40	−0.536888
$377$	3560.62	0.486423
$378$	378.000	0.0514344
$379$	−12928.1	−1.75217	−0.876083	−	0.482160i	$-0.839852\pi$
$379$	−12928.1	−1.75217	−0.876083	+	0.482160i	$0.839852\pi$
$380$	1214.05	0.163893
$381$	2424.04	0.325951
$382$	−2676.26	−0.358454
$383$	58.1597	0.00775933	0.00387966	−	0.999992i	$-0.498765\pi$
$383$	58.1597	0.00775933	0.00387966	+	0.999992i	$0.498765\pi$
$384$	384.000	0.0510310
$385$	5588.37	0.739765
$386$	−4465.65	−0.588848
$387$	1241.45	0.163065
$388$	−3033.68	−0.396938
$389$	−6506.17	−0.848010	−0.424005	−	0.905660i	$-0.639376\pi$
$389$	−6506.17	−0.848010	−0.424005	+	0.905660i	$0.639376\pi$
$390$	1208.13	0.156862
$391$	1360.01	0.175904
$392$	392.000	0.0505076
$393$	4261.94	0.547039
$394$	4857.63	0.621126
$395$	−4769.06	−0.607487
$396$	1799.14	0.228309
$397$	−10461.4	−1.32252	−0.661261	−	0.750156i	$-0.729978\pi$
$397$	−10461.4	−1.32252	−0.661261	+	0.750156i	$0.729978\pi$
$398$	7600.17	0.957191
$399$	399.000	0.0500626
$400$	2082.88	0.260360
$401$	8971.47	1.11724	0.558621	−	0.829423i	$-0.311331\pi$
$401$	8971.47	1.11724	0.558621	+	0.829423i	$0.311331\pi$
$402$	−3813.42	−0.473125
$403$	−1669.28	−0.206334
$404$	−7366.28	−0.907144
$405$	1293.92	0.158754
$406$	3954.71	0.483421
$407$	−17026.7	−2.07367
$408$	−2329.15	−0.282622
$409$	−11557.5	−1.39727	−0.698635	−	0.715479i	$-0.746209\pi$
$409$	−11557.5	−1.39727	−0.698635	+	0.715479i	$0.746209\pi$
$410$	−15036.4	−1.81120
$411$	3758.20	0.451042
$412$	166.909	0.0199588
$413$	−1838.73	−0.219075
$414$	−252.248	−0.0299452
$415$	5351.56	0.633007
$416$	403.357	0.0475389
$417$	−4250.31	−0.499133
$418$	1899.10	0.222220
$419$	−4853.85	−0.565934	−0.282967	−	0.959130i	$-0.591319\pi$
$419$	−4853.85	−0.565934	−0.282967	+	0.959130i	$0.591319\pi$
$420$	1341.85	0.155894
$421$	−2652.14	−0.307025	−0.153513	−	0.988147i	$-0.549059\pi$
$421$	−2652.14	−0.307025	−0.153513	+	0.988147i	$0.549059\pi$
$422$	−1375.46	−0.158665
$423$	−4403.70	−0.506183
$424$	1249.84	0.143155
$425$	−12633.7	−1.44194
$426$	−1311.17	−0.149123
$427$	5420.74	0.614351
$428$	−2393.58	−0.270323
$429$	1889.84	0.212686
$430$	4406.96	0.494238
$431$	−5208.97	−0.582152	−0.291076	−	0.956700i	$-0.594013\pi$
$431$	−5208.97	−0.582152	−0.291076	+	0.956700i	$0.594013\pi$
$432$	432.000	0.0481125
$433$	3530.60	0.391847	0.195924	−	0.980619i	$-0.437230\pi$
$433$	3530.60	0.391847	0.195924	+	0.980619i	$0.437230\pi$
$434$	−1854.03	−0.205061
$435$	13537.3	1.49210
$436$	4572.28	0.502231
$437$	−266.262	−0.0291465
$438$	6707.69	0.731748
$439$	10992.7	1.19511	0.597555	−	0.801828i	$-0.296139\pi$
$439$	10992.7	1.19511	0.597555	+	0.801828i	$0.296139\pi$
$440$	6386.70	0.691987
$441$	441.000	0.0476190
$442$	−2446.55	−0.263282
$443$	8516.94	0.913436	0.456718	−	0.889612i	$-0.349025\pi$
$443$	8516.94	0.913436	0.456718	+	0.889612i	$0.349025\pi$
$444$	−4088.35	−0.436992
$445$	9367.88	0.997933
$446$	4981.76	0.528908
$447$	−4761.82	−0.503862
$448$	448.000	0.0472456
$449$	5590.74	0.587625	0.293812	−	0.955863i	$-0.405076\pi$
$449$	5590.74	0.587625	0.293812	+	0.955863i	$0.405076\pi$
$450$	2343.24	0.245470
$451$	−23520.8	−2.45577
$452$	874.489	0.0910011
$453$	−1154.19	−0.119710
$454$	9249.12	0.956130
$455$	1409.48	0.145226
$456$	456.000	0.0468293
$457$	11373.5	1.16418	0.582088	−	0.813126i	$-0.302236\pi$
$457$	11373.5	1.16418	0.582088	+	0.813126i	$0.302236\pi$
$458$	−5669.53	−0.578427
$459$	−2620.29	−0.266459
$460$	−895.443	−0.0907614
$461$	11035.0	1.11486	0.557428	−	0.830225i	$-0.311788\pi$
$461$	11035.0	1.11486	0.557428	+	0.830225i	$0.311788\pi$
$462$	2099.00	0.211373
$463$	−12932.9	−1.29815	−0.649076	−	0.760723i	$-0.724844\pi$
$463$	−12932.9	−1.29815	−0.649076	+	0.760723i	$0.724844\pi$
$464$	4519.67	0.452199
$465$	−6346.50	−0.632929
$466$	−8227.52	−0.817881
$467$	−3775.95	−0.374154	−0.187077	−	0.982345i	$-0.559901\pi$
$467$	−3775.95	−0.374154	−0.187077	+	0.982345i	$0.559901\pi$
$468$	453.776	0.0448201
$469$	−4448.99	−0.438028
$470$	−15632.5	−1.53420
$471$	6751.61	0.660504
$472$	−2101.40	−0.204926
$473$	6893.65	0.670128
$474$	−1791.27	−0.173577
$475$	2473.42	0.238923
$476$	−2717.34	−0.261658
$477$	1406.07	0.134967
$478$	−5376.08	−0.514427
$479$	5143.13	0.490596	0.245298	−	0.969448i	$-0.421114\pi$
$479$	5143.13	0.490596	0.245298	+	0.969448i	$0.421114\pi$
$480$	1533.54	0.145825
$481$	−4294.43	−0.407088
$482$	−7011.05	−0.662541
$483$	−294.289	−0.0277238
$484$	4666.50	0.438251
$485$	−12115.3	−1.13428
$486$	486.000	0.0453609
$487$	12115.8	1.12735	0.563676	−	0.825996i	$-0.309386\pi$
$487$	12115.8	1.12735	0.563676	+	0.825996i	$0.309386\pi$
$488$	6195.13	0.574673
$489$	8953.27	0.827977
$490$	1565.49	0.144330
$491$	16855.3	1.54922	0.774611	−	0.632438i	$-0.217946\pi$
$491$	16855.3	1.54922	0.774611	+	0.632438i	$0.217946\pi$
$492$	−5647.69	−0.517515
$493$	−27414.0	−2.50439
$494$	478.986	0.0436247
$495$	7185.04	0.652411
$496$	−2118.90	−0.191817
$497$	−1529.70	−0.138061
$498$	2010.06	0.180869
$499$	19424.2	1.74258	0.871289	−	0.490769i	$-0.163284\pi$
$499$	19424.2	1.74258	0.871289	+	0.490769i	$0.163284\pi$
$500$	330.984	0.0296041
$501$	9399.22	0.838176
$502$	−6109.37	−0.543176
$503$	19440.1	1.72325	0.861623	−	0.507549i	$-0.169448\pi$
$503$	19440.1	1.72325	0.861623	+	0.507549i	$0.169448\pi$
$504$	504.000	0.0445435
$505$	−29417.9	−2.59224
$506$	−1400.71	−0.123062
$507$	−6114.35	−0.535597
$508$	3232.05	0.282282
$509$	−19784.7	−1.72287	−0.861437	−	0.507865i	$-0.830435\pi$
$509$	−19784.7	−1.72287	−0.861437	+	0.507865i	$0.830435\pi$
$510$	−9301.65	−0.807616
$511$	7825.64	0.677467
$512$	512.000	0.0441942
$513$	513.000	0.0441511
$514$	−1239.41	−0.106358
$515$	666.565	0.0570337
$516$	1655.26	0.141219
$517$	−24453.4	−2.08019
$518$	−4769.74	−0.404576
$519$	−1992.49	−0.168518
$520$	1610.84	0.135846
$521$	14262.5	1.19933	0.599665	−	0.800251i	$-0.295301\pi$
$521$	14262.5	1.19933	0.599665	+	0.800251i	$0.295301\pi$
$522$	5084.63	0.426338
$523$	−11656.7	−0.974590	−0.487295	−	0.873237i	$-0.662016\pi$
$523$	−11656.7	−0.974590	−0.487295	+	0.873237i	$0.662016\pi$
$524$	5682.58	0.473750
$525$	2733.78	0.227261
$526$	8655.64	0.717498
$527$	12852.1	1.06233
$528$	2398.86	0.197722
$529$	−11970.6	−0.983859
$530$	4991.34	0.409075
$531$	−2364.08	−0.193206
$532$	532.000	0.0433555
$533$	−5932.37	−0.482101
$534$	3518.59	0.285139
$535$	−9558.98	−0.772468
$536$	−5084.56	−0.409738
$537$	10697.0	0.859608
$538$	−9496.72	−0.761027
$539$	2448.84	0.195694
$540$	1725.23	0.137485
$541$	4730.19	0.375909	0.187955	−	0.982178i	$-0.439814\pi$
$541$	4730.19	0.375909	0.187955	+	0.982178i	$0.439814\pi$
$542$	−4504.29	−0.356966
$543$	−11830.5	−0.934980
$544$	−3105.53	−0.244758
$545$	18259.8	1.43516
$546$	529.405	0.0414954
$547$	12442.9	0.972617	0.486308	−	0.873787i	$-0.338343\pi$
$547$	12442.9	0.972617	0.486308	+	0.873787i	$0.338343\pi$
$548$	5010.93	0.390614
$549$	6969.53	0.541807
$550$	13011.8	1.00877
$551$	5367.11	0.414967
$552$	−336.330	−0.0259333
$553$	−2089.81	−0.160701
$554$	−5009.52	−0.384177
$555$	−16327.2	−1.24874
$556$	−5667.08	−0.432262
$557$	6761.69	0.514366	0.257183	−	0.966363i	$-0.417206\pi$
$557$	6761.69	0.514366	0.257183	+	0.966363i	$0.417206\pi$
$558$	−2383.76	−0.180847
$559$	1738.70	0.131555
$560$	1789.13	0.135008
$561$	−14550.3	−1.09503
$562$	−13823.9	−1.03759
$563$	−22673.2	−1.69727	−0.848635	−	0.528979i	$-0.822575\pi$
$563$	−22673.2	−1.69727	−0.848635	+	0.528979i	$0.822575\pi$
$564$	−5871.60	−0.438367
$565$	3492.35	0.260043
$566$	−14506.8	−1.07733
$567$	567.000	0.0419961
$568$	−1748.23	−0.129145
$569$	1905.84	0.140416	0.0702082	−	0.997532i	$-0.477634\pi$
$569$	1905.84	0.140416	0.0702082	+	0.997532i	$0.477634\pi$
$570$	1821.08	0.133818
$571$	−2475.89	−0.181458	−0.0907292	−	0.995876i	$-0.528920\pi$
$571$	−2475.89	−0.181458	−0.0907292	+	0.995876i	$0.528920\pi$
$572$	2519.78	0.184191
$573$	−4014.39	−0.292676
$574$	−6588.97	−0.479126
$575$	−1824.31	−0.132311
$576$	576.000	0.0416667
$577$	12031.0	0.868039	0.434020	−	0.900903i	$-0.357095\pi$
$577$	12031.0	0.868039	0.434020	+	0.900903i	$0.357095\pi$
$578$	9010.55	0.648424
$579$	−6698.47	−0.480792
$580$	18049.7	1.29220
$581$	2345.07	0.167452
$582$	−4550.52	−0.324098
$583$	7807.78	0.554657
$584$	8943.58	0.633713
$585$	1812.19	0.128077
$586$	4565.57	0.321846
$587$	22791.8	1.60259	0.801294	−	0.598271i	$-0.204145\pi$
$587$	22791.8	1.60259	0.801294	+	0.598271i	$0.204145\pi$
$588$	588.000	0.0412393
$589$	−2516.19	−0.176023
$590$	−8392.14	−0.585591
$591$	7286.44	0.507147
$592$	−5451.13	−0.378446
$593$	−3658.97	−0.253383	−0.126691	−	0.991942i	$-0.540436\pi$
$593$	−3658.97	−0.253383	−0.126691	+	0.991942i	$0.540436\pi$
$594$	2698.72	0.186414
$595$	−10851.9	−0.747707
$596$	−6349.09	−0.436357
$597$	11400.2	0.781543
$598$	−353.284	−0.0241586
$599$	16761.0	1.14330	0.571649	−	0.820498i	$-0.306304\pi$
$599$	16761.0	1.14330	0.571649	+	0.820498i	$0.306304\pi$
$600$	3124.32	0.212583
$601$	−3623.37	−0.245924	−0.122962	−	0.992411i	$-0.539239\pi$
$601$	−3623.37	−0.245924	−0.122962	+	0.992411i	$0.539239\pi$
$602$	1931.14	0.130743
$603$	−5720.13	−0.386305
$604$	−1538.93	−0.103672
$605$	18636.1	1.25234
$606$	−11049.4	−0.740680
$607$	−17599.4	−1.17683	−0.588417	−	0.808558i	$-0.700249\pi$
$607$	−17599.4	−1.17683	−0.588417	+	0.808558i	$0.700249\pi$
$608$	608.000	0.0405554
$609$	5932.07	0.394712
$610$	24740.8	1.64217
$611$	−6167.58	−0.408369
$612$	−3493.72	−0.230760
$613$	15313.5	1.00898	0.504491	−	0.863417i	$-0.331680\pi$
$613$	15313.5	1.00898	0.504491	+	0.863417i	$0.331680\pi$
$614$	−1171.17	−0.0769781
$615$	−22554.5	−1.47884
$616$	2798.67	0.183055
$617$	23741.4	1.54910	0.774549	−	0.632514i	$-0.217977\pi$
$617$	23741.4	1.54910	0.774549	+	0.632514i	$0.217977\pi$
$618$	250.363	0.0162963
$619$	−18701.6	−1.21435	−0.607173	−	0.794570i	$-0.707696\pi$
$619$	−18701.6	−1.21435	−0.607173	+	0.794570i	$0.707696\pi$
$620$	−8462.00	−0.548132
$621$	−378.372	−0.0244501
$622$	−16241.9	−1.04701
$623$	4105.03	0.263988
$624$	605.035	0.0388153
$625$	−14950.7	−0.956843
$626$	−4050.42	−0.258606
$627$	2848.65	0.181442
$628$	9002.14	0.572014
$629$	33063.8	2.09593
$630$	2012.77	0.127287
$631$	30357.5	1.91524	0.957618	−	0.288042i	$-0.0930043\pi$
$631$	30357.5	1.91524	0.957618	+	0.288042i	$0.0930043\pi$
$632$	−2388.36	−0.150322
$633$	−2063.19	−0.129549
$634$	3696.85	0.231578
$635$	12907.5	0.806643
$636$	1874.76	0.116885
$637$	617.640	0.0384172
$638$	28234.5	1.75206
$639$	−1966.76	−0.121759
$640$	2044.72	0.126288
$641$	−4450.98	−0.274264	−0.137132	−	0.990553i	$-0.543788\pi$
$641$	−4450.98	−0.274264	−0.137132	+	0.990553i	$0.543788\pi$
$642$	−3590.37	−0.220718
$643$	8469.36	0.519439	0.259719	−	0.965684i	$-0.416370\pi$
$643$	8469.36	0.519439	0.259719	+	0.965684i	$0.416370\pi$
$644$	−392.385	−0.0240096
$645$	6610.44	0.403544
$646$	−3687.82	−0.224606
$647$	9441.50	0.573699	0.286850	−	0.957976i	$-0.407392\pi$
$647$	9441.50	0.573699	0.286850	+	0.957976i	$0.407392\pi$
$648$	648.000	0.0392837
$649$	−13127.5	−0.793992
$650$	3281.81	0.198036
$651$	−2781.05	−0.167432
$652$	11937.7	0.717049
$653$	−10182.6	−0.610224	−0.305112	−	0.952316i	$-0.598694\pi$
$653$	−10182.6	−0.610224	−0.305112	+	0.952316i	$0.598694\pi$
$654$	6858.42	0.410070
$655$	22693.9	1.35378
$656$	−7530.25	−0.448181
$657$	10061.5	0.597470
$658$	−6850.20	−0.405849
$659$	22514.1	1.33084	0.665421	−	0.746469i	$-0.268252\pi$
$659$	22514.1	1.33084	0.665421	+	0.746469i	$0.268252\pi$
$660$	9580.06	0.565005
$661$	−1851.11	−0.108926	−0.0544629	−	0.998516i	$-0.517345\pi$
$661$	−1851.11	−0.108926	−0.0544629	+	0.998516i	$0.517345\pi$
$662$	−2746.93	−0.161273
$663$	−3669.83	−0.214969
$664$	2680.08	0.156637
$665$	2124.59	0.123892
$666$	−6132.52	−0.356803
$667$	−3958.60	−0.229802
$668$	12532.3	0.725881
$669$	7472.64	0.431852
$670$	−20305.6	−1.17086
$671$	38701.2	2.22659
$672$	672.000	0.0385758
$673$	−16555.8	−0.948263	−0.474131	−	0.880454i	$-0.657238\pi$
$673$	−16555.8	−0.948263	−0.474131	+	0.880454i	$0.657238\pi$
$674$	−2985.11	−0.170597
$675$	3514.86	0.200425
$676$	−8152.47	−0.463841
$677$	386.923	0.0219655	0.0109828	−	0.999940i	$-0.496504\pi$
$677$	386.923	0.0219655	0.0109828	+	0.999940i	$0.496504\pi$
$678$	1311.73	0.0743021
$679$	−5308.94	−0.300057
$680$	−12402.2	−0.699416
$681$	13873.7	0.780676
$682$	−13236.8	−0.743202
$683$	4283.21	0.239960	0.119980	−	0.992776i	$-0.461717\pi$
$683$	4283.21	0.239960	0.119980	+	0.992776i	$0.461717\pi$
$684$	684.000	0.0382360
$685$	20011.6	1.11621
$686$	686.000	0.0381802
$687$	−8504.29	−0.472284
$688$	2207.02	0.122299
$689$	1969.26	0.108887
$690$	−1343.17	−0.0741064
$691$	−19159.2	−1.05477	−0.527387	−	0.849625i	$-0.676828\pi$
$691$	−19159.2	−1.05477	−0.527387	+	0.849625i	$0.676828\pi$
$692$	−2656.66	−0.145941
$693$	3148.50	0.172585
$694$	17696.3	0.967930
$695$	−22632.0	−1.23522
$696$	6779.51	0.369219
$697$	45674.6	2.48214
$698$	−18647.5	−1.01120
$699$	−12341.3	−0.667797
$700$	3645.04	0.196814
$701$	17531.5	0.944586	0.472293	−	0.881441i	$-0.343426\pi$
$701$	17531.5	0.944586	0.472293	+	0.881441i	$0.343426\pi$
$702$	680.664	0.0365955
$703$	−6473.22	−0.347286
$704$	3198.48	0.171232
$705$	−23448.8	−1.25267
$706$	22746.3	1.21256
$707$	−12891.0	−0.685737
$708$	−3152.11	−0.167321
$709$	−32529.2	−1.72308	−0.861538	−	0.507693i	$-0.830499\pi$
$709$	−32529.2	−1.72308	−0.861538	+	0.507693i	$0.830499\pi$
$710$	−6981.71	−0.369041
$711$	−2686.90	−0.141725
$712$	4691.46	0.246938
$713$	1855.86	0.0974788
$714$	−4076.01	−0.213642
$715$	10063.0	0.526341
$716$	14262.7	0.744442
$717$	−8064.12	−0.420028
$718$	−6663.57	−0.346354
$719$	−33208.5	−1.72248	−0.861242	−	0.508195i	$-0.830313\pi$
$719$	−33208.5	−1.72248	−0.861242	+	0.508195i	$0.830313\pi$
$720$	2300.31	0.119066
$721$	292.090	0.0150874
$722$	722.000	0.0372161
$723$	−10516.6	−0.540962
$724$	−15774.0	−0.809716
$725$	36773.2	1.88375
$726$	6999.75	0.357831
$727$	35038.0	1.78746	0.893732	−	0.448602i	$-0.148078\pi$
$727$	35038.0	1.78746	0.893732	+	0.448602i	$0.148078\pi$
$728$	705.874	0.0359360
$729$	729.000	0.0370370
$730$	35717.0	1.81088
$731$	−13386.6	−0.677322
$732$	9292.70	0.469219
$733$	9109.10	0.459007	0.229504	−	0.973308i	$-0.426290\pi$
$733$	9109.10	0.459007	0.229504	+	0.973308i	$0.426290\pi$
$734$	−13293.8	−0.668506
$735$	2348.23	0.117845
$736$	−448.441	−0.0224589
$737$	−31763.4	−1.58754
$738$	−8471.53	−0.422549
$739$	31202.8	1.55320	0.776599	−	0.629996i	$-0.216943\pi$
$739$	31202.8	1.55320	0.776599	+	0.629996i	$0.216943\pi$
$740$	−21769.6	−1.08144
$741$	718.479	0.0356194
$742$	2187.22	0.108215
$743$	14203.9	0.701333	0.350667	−	0.936500i	$-0.385955\pi$
$743$	14203.9	0.701333	0.350667	+	0.936500i	$0.385955\pi$
$744$	−3178.34	−0.156618
$745$	−25355.6	−1.24692
$746$	−6435.00	−0.315821
$747$	3015.09	0.147679
$748$	−19400.3	−0.948324
$749$	−4188.77	−0.204345
$750$	496.476	0.0241717
$751$	36039.6	1.75114	0.875568	−	0.483095i	$-0.160487\pi$
$751$	36039.6	1.75114	0.875568	+	0.483095i	$0.160487\pi$
$752$	−7828.80	−0.379637
$753$	−9164.05	−0.443501
$754$	7121.25	0.343953
$755$	−6145.83	−0.296251
$756$	756.000	0.0363696
$757$	−14157.9	−0.679761	−0.339881	−	0.940469i	$-0.610387\pi$
$757$	−14157.9	−0.679761	−0.339881	+	0.940469i	$0.610387\pi$
$758$	−25856.2	−1.23897
$759$	−2101.07	−0.100479
$760$	2428.10	0.115890
$761$	−34476.1	−1.64226	−0.821128	−	0.570744i	$-0.806655\pi$
$761$	−34476.1	−1.64226	−0.821128	+	0.570744i	$0.806655\pi$
$762$	4848.08	0.230482
$763$	8001.49	0.379651
$764$	−5352.52	−0.253465
$765$	−13952.5	−0.659416
$766$	116.319	0.00548667
$767$	−3311.00	−0.155871
$768$	768.000	0.0360844
$769$	−19805.1	−0.928725	−0.464362	−	0.885645i	$-0.653716\pi$
$769$	−19805.1	−0.928725	−0.464362	+	0.885645i	$0.653716\pi$
$770$	11176.7	0.523093
$771$	−1859.11	−0.0868410
$772$	−8931.29	−0.416378
$773$	41500.3	1.93100	0.965499	−	0.260407i	$-0.0838566\pi$
$773$	41500.3	1.93100	0.965499	+	0.260407i	$0.0838566\pi$
$774$	2482.89	0.115305
$775$	−17239.9	−0.799063
$776$	−6067.37	−0.280677
$777$	−7154.61	−0.330335
$778$	−13012.3	−0.599634
$779$	−8942.17	−0.411279
$780$	2416.26	0.110918
$781$	−10921.2	−0.500375
$782$	2720.01	0.124383
$783$	7626.95	0.348103
$784$	784.000	0.0357143
$785$	35950.8	1.63457
$786$	8523.88	0.386815
$787$	15535.1	0.703643	0.351822	−	0.936067i	$-0.385562\pi$
$787$	15535.1	0.703643	0.351822	+	0.936067i	$0.385562\pi$
$788$	9715.25	0.439203
$789$	12983.5	0.585834
$790$	−9538.11	−0.429558
$791$	1530.36	0.0687904
$792$	3598.29	0.161439
$793$	9761.12	0.437109
$794$	−20922.8	−0.935165
$795$	7487.01	0.334009
$796$	15200.3	0.676836
$797$	−24160.5	−1.07379	−0.536893	−	0.843650i	$-0.680402\pi$
$797$	−24160.5	−1.07379	−0.536893	+	0.843650i	$0.680402\pi$
$798$	798.000	0.0353996
$799$	47485.5	2.10252
$800$	4165.76	0.184102
$801$	5277.89	0.232815
$802$	17942.9	0.790009
$803$	55870.8	2.45534
$804$	−7626.84	−0.334550
$805$	−1567.03	−0.0686092
$806$	−3338.56	−0.145900
$807$	−14245.1	−0.621376
$808$	−14732.6	−0.641448
$809$	14411.4	0.626301	0.313150	−	0.949704i	$-0.398616\pi$
$809$	14411.4	0.626301	0.313150	+	0.949704i	$0.398616\pi$
$810$	2587.85	0.112256
$811$	−7038.51	−0.304754	−0.152377	−	0.988322i	$-0.548693\pi$
$811$	−7038.51	−0.304754	−0.152377	+	0.988322i	$0.548693\pi$
$812$	7909.43	0.341831
$813$	−6756.43	−0.291462
$814$	−34053.4	−1.46630
$815$	47674.2	2.04902
$816$	−4658.29	−0.199844
$817$	2620.83	0.112229
$818$	−23115.1	−0.988018
$819$	794.108	0.0338808
$820$	−30072.7	−1.28071
$821$	−36608.2	−1.55620	−0.778098	−	0.628143i	$-0.783815\pi$
$821$	−36608.2	−1.55620	−0.778098	+	0.628143i	$0.783815\pi$
$822$	7516.39	0.318935
$823$	−9311.87	−0.394400	−0.197200	−	0.980363i	$-0.563185\pi$
$823$	−9311.87	−0.394400	−0.197200	+	0.980363i	$0.563185\pi$
$824$	333.818	0.0141130
$825$	19517.7	0.823660
$826$	−3677.46	−0.154909
$827$	19689.4	0.827894	0.413947	−	0.910301i	$-0.364150\pi$
$827$	19689.4	0.827894	0.413947	+	0.910301i	$0.364150\pi$
$828$	−504.496	−0.0211744
$829$	20931.8	0.876948	0.438474	−	0.898744i	$-0.355519\pi$
$829$	20931.8	0.876948	0.438474	+	0.898744i	$0.355519\pi$
$830$	10703.1	0.447603
$831$	−7514.28	−0.313679
$832$	806.713	0.0336151
$833$	−4755.34	−0.197795
$834$	−8500.62	−0.352940
$835$	50048.8	2.07426
$836$	3798.19	0.157133
$837$	−3575.64	−0.147661
$838$	−9707.70	−0.400175
$839$	17388.9	0.715531	0.357765	−	0.933811i	$-0.383539\pi$
$839$	17388.9	0.715531	0.357765	+	0.933811i	$0.383539\pi$
$840$	2683.69	0.110234
$841$	55405.7	2.27175
$842$	−5304.29	−0.217100
$843$	−20735.9	−0.847192
$844$	−2750.92	−0.112193
$845$	−32557.6	−1.32546
$846$	−8807.40	−0.357925
$847$	8166.37	0.331287
$848$	2499.68	0.101226
$849$	−21760.3	−0.879635
$850$	−25267.3	−1.01960
$851$	4774.43	0.192321
$852$	−2622.34	−0.105446
$853$	−1621.64	−0.0650926	−0.0325463	−	0.999470i	$-0.510362\pi$
$853$	−1621.64	−0.0650926	−0.0325463	+	0.999470i	$0.510362\pi$
$854$	10841.5	0.434412
$855$	2731.61	0.109262
$856$	−4787.16	−0.191147
$857$	−19137.2	−0.762796	−0.381398	−	0.924411i	$-0.624557\pi$
$857$	−19137.2	−0.762796	−0.381398	+	0.924411i	$0.624557\pi$
$858$	3779.67	0.150391
$859$	35793.3	1.42171	0.710856	−	0.703337i	$-0.248308\pi$
$859$	35793.3	1.42171	0.710856	+	0.703337i	$0.248308\pi$
$860$	8813.92	0.349479
$861$	−9883.45	−0.391205
$862$	−10417.9	−0.411643
$863$	−23972.4	−0.945573	−0.472787	−	0.881177i	$-0.656752\pi$
$863$	−23972.4	−0.945573	−0.472787	+	0.881177i	$0.656752\pi$
$864$	864.000	0.0340207
$865$	−10609.6	−0.417037
$866$	7061.20	0.277078
$867$	13515.8	0.529436
$868$	−3708.07	−0.145000
$869$	−14920.1	−0.582429
$870$	27074.6	1.05507
$871$	−8011.29	−0.311656
$872$	9144.57	0.355131
$873$	−6825.79	−0.264625
$874$	−532.523	−0.0206097
$875$	579.222	0.0223786
$876$	13415.4	0.517424
$877$	−9508.86	−0.366125	−0.183062	−	0.983101i	$-0.558601\pi$
$877$	−9508.86	−0.366125	−0.183062	+	0.983101i	$0.558601\pi$
$878$	21985.4	0.845071
$879$	6848.36	0.262786
$880$	12773.4	0.489309
$881$	48176.4	1.84234	0.921172	−	0.389155i	$-0.127233\pi$
$881$	48176.4	1.84234	0.921172	+	0.389155i	$0.127233\pi$
$882$	882.000	0.0336718
$883$	35388.1	1.34870	0.674352	−	0.738410i	$-0.264423\pi$
$883$	35388.1	1.34870	0.674352	+	0.738410i	$0.264423\pi$
$884$	−4893.11	−0.186169
$885$	−12588.2	−0.478133
$886$	17033.9	0.645897
$887$	−15778.7	−0.597292	−0.298646	−	0.954364i	$-0.596535\pi$
$887$	−15778.7	−0.597292	−0.298646	+	0.954364i	$0.596535\pi$
$888$	−8176.70	−0.309000
$889$	5656.09	0.213385
$890$	18735.8	0.705645
$891$	4048.08	0.152206
$892$	9963.52	0.373995
$893$	−9296.70	−0.348379
$894$	−9523.63	−0.356284
$895$	56959.2	2.12730
$896$	896.000	0.0334077
$897$	−529.926	−0.0197254
$898$	11181.5	0.415513
$899$	−37409.0	−1.38783
$900$	4686.48	0.173573
$901$	−15161.8	−0.560612
$902$	−47041.7	−1.73649
$903$	2896.71	0.106751
$904$	1748.98	0.0643475
$905$	−62994.7	−2.31383
$906$	−2308.39	−0.0846480
$907$	−27262.5	−0.998055	−0.499027	−	0.866586i	$-0.666309\pi$
$907$	−27262.5	−0.998055	−0.499027	+	0.866586i	$0.666309\pi$
$908$	18498.2	0.676086
$909$	−16574.1	−0.604763
$910$	2818.97	0.102690
$911$	26454.4	0.962100	0.481050	−	0.876693i	$-0.340256\pi$
$911$	26454.4	0.962100	0.481050	+	0.876693i	$0.340256\pi$
$912$	912.000	0.0331133
$913$	16742.5	0.606896
$914$	22746.9	0.823197
$915$	37111.2	1.34083
$916$	−11339.1	−0.409010
$917$	9944.52	0.358121
$918$	−5240.58	−0.188415
$919$	−3609.76	−0.129570	−0.0647852	−	0.997899i	$-0.520636\pi$
$919$	−3609.76	−0.129570	−0.0647852	+	0.997899i	$0.520636\pi$
$920$	−1790.89	−0.0641780
$921$	−1756.75	−0.0628523
$922$	22069.9	0.788323
$923$	−2754.53	−0.0982302
$924$	4198.00	0.149463
$925$	−44351.8	−1.57652
$926$	−25865.9	−0.917933
$927$	375.545	0.0133058
$928$	9039.34	0.319753
$929$	53272.9	1.88141	0.940704	−	0.339229i	$-0.110166\pi$
$929$	53272.9	1.88141	0.940704	+	0.339229i	$0.110166\pi$
$930$	−12693.0	−0.447548
$931$	931.000	0.0327737
$932$	−16455.0	−0.578329
$933$	−24362.8	−0.854880
$934$	−7551.90	−0.264567
$935$	−77476.9	−2.70991
$936$	907.552	0.0316926
$937$	38183.4	1.33127	0.665633	−	0.746279i	$-0.268162\pi$
$937$	38183.4	1.33127	0.665633	+	0.746279i	$0.268162\pi$
$938$	−8897.98	−0.309733
$939$	−6075.63	−0.211151
$940$	−31265.0	−1.08484
$941$	11813.2	0.409244	0.204622	−	0.978841i	$-0.434403\pi$
$941$	11813.2	0.409244	0.204622	+	0.978841i	$0.434403\pi$
$942$	13503.2	0.467047
$943$	6595.45	0.227760
$944$	−4202.81	−0.144904
$945$	3019.15	0.103929
$946$	13787.3	0.473852
$947$	−3057.87	−0.104929	−0.0524643	−	0.998623i	$-0.516708\pi$
$947$	−3057.87	−0.104929	−0.0524643	+	0.998623i	$0.516708\pi$
$948$	−3582.53	−0.122738
$949$	14091.6	0.482016
$950$	4946.84	0.168944
$951$	5545.28	0.189083
$952$	−5434.68	−0.185020
$953$	−8275.80	−0.281301	−0.140650	−	0.990059i	$-0.544919\pi$
$953$	−8275.80	−0.281301	−0.140650	+	0.990059i	$0.544919\pi$
$954$	2812.14	0.0954363
$955$	−21375.8	−0.724297
$956$	−10752.2	−0.363755
$957$	42351.8	1.43055
$958$	10286.3	0.346904
$959$	8769.12	0.295276
$960$	3067.08	0.103114
$961$	−12253.0	−0.411300
$962$	−8588.87	−0.287855
$963$	−5385.56	−0.180215
$964$	−14022.1	−0.468487
$965$	−35667.9	−1.18983
$966$	−588.578	−0.0196037
$967$	−34378.3	−1.14326	−0.571630	−	0.820512i	$-0.693689\pi$
$967$	−34378.3	−1.14326	−0.571630	+	0.820512i	$0.693689\pi$
$968$	9332.99	0.309890
$969$	−5531.72	−0.183390
$970$	−24230.6	−0.802058
$971$	10323.3	0.341186	0.170593	−	0.985342i	$-0.445432\pi$
$971$	10323.3	0.341186	0.170593	+	0.985342i	$0.445432\pi$
$972$	972.000	0.0320750
$973$	−9917.38	−0.326759
$974$	24231.7	0.797159
$975$	4922.71	0.161695
$976$	12390.3	0.406355
$977$	−20105.5	−0.658375	−0.329188	−	0.944264i	$-0.606775\pi$
$977$	−20105.5	−0.658375	−0.329188	+	0.944264i	$0.606775\pi$
$978$	17906.5	0.585468
$979$	29307.7	0.956770
$980$	3130.97	0.102056
$981$	10287.6	0.334821
$982$	33710.6	1.09547
$983$	17920.3	0.581453	0.290726	−	0.956806i	$-0.406103\pi$
$983$	17920.3	0.581453	0.290726	+	0.956806i	$0.406103\pi$
$984$	−11295.4	−0.365938
$985$	38798.7	1.25506
$986$	−54828.0	−1.77087
$987$	−10275.3	−0.331374
$988$	957.972	0.0308473
$989$	−1933.04	−0.0621507
$990$	14370.1	0.461325
$991$	−25901.6	−0.830262	−0.415131	−	0.909762i	$-0.636264\pi$
$991$	−25901.6	−0.830262	−0.415131	+	0.909762i	$0.636264\pi$
$992$	−4237.79	−0.135635
$993$	−4120.39	−0.131678
$994$	−3059.40	−0.0976241
$995$	60703.9	1.93411
$996$	4020.11	0.127894
$997$	40251.6	1.27862	0.639309	−	0.768950i	$-0.279220\pi$
$997$	40251.6	1.27862	0.639309	+	0.768950i	$0.279220\pi$
$998$	38848.4	1.23219
$999$	−9198.79	−0.291328

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.9744 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +15.9744 q^{5} +6.00000 q^{6} +7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +31.9487 q^{10} +49.9762 q^{11} +12.0000 q^{12} +12.6049 q^{13} +14.0000 q^{14} +47.9231 q^{15} +16.0000 q^{16} -97.0478 q^{17} +18.0000 q^{18} +19.0000 q^{19} +63.8974 q^{20} +21.0000 q^{21} +99.9525 q^{22} -14.0138 q^{23} +24.0000 q^{24} +130.180 q^{25} +25.2098 q^{26} +27.0000 q^{27} +28.0000 q^{28} +282.480 q^{29} +95.8461 q^{30} -132.431 q^{31} +32.0000 q^{32} +149.929 q^{33} -194.096 q^{34} +111.820 q^{35} +36.0000 q^{36} -340.696 q^{37} +38.0000 q^{38} +37.8147 q^{39} +127.795 q^{40} -470.641 q^{41} +42.0000 q^{42} +137.939 q^{43} +199.905 q^{44} +143.769 q^{45} -28.0275 q^{46} -489.300 q^{47} +48.0000 q^{48} +49.0000 q^{49} +260.360 q^{50} -291.143 q^{51} +50.4196 q^{52} +156.230 q^{53} +54.0000 q^{54} +798.338 q^{55} +56.0000 q^{56} +57.0000 q^{57} +564.959 q^{58} -262.675 q^{59} +191.692 q^{60} +774.392 q^{61} -264.862 q^{62} +63.0000 q^{63} +64.0000 q^{64} +201.355 q^{65} +299.857 q^{66} -635.570 q^{67} -388.191 q^{68} -42.0413 q^{69} +223.641 q^{70} -218.529 q^{71} +72.0000 q^{72} +1117.95 q^{73} -681.392 q^{74} +390.540 q^{75} +76.0000 q^{76} +349.834 q^{77} +75.6294 q^{78} -298.545 q^{79} +255.590 q^{80} +81.0000 q^{81} -941.281 q^{82} +335.009 q^{83} +84.0000 q^{84} -1550.28 q^{85} +275.877 q^{86} +847.439 q^{87} +399.810 q^{88} +586.432 q^{89} +287.538 q^{90} +88.2342 q^{91} -56.0551 q^{92} -397.293 q^{93} -978.600 q^{94} +303.513 q^{95} +96.0000 q^{96} -758.421 q^{97} +98.0000 q^{98} +449.786 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 5 q + 10 q^{2} + 15 q^{3} + 20 q^{4} + 20 q^{5} + 30 q^{6} + 35 q^{7} + 40 q^{8} + 45 q^{9}+O(q^{10}) \) 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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