LMFDB - Embedded newform 798.4.a.m.1.1

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:	$1$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 84x^{2} - 9x + 1321 $ x^4 - x^3 - 84x^2 - 9x + 1321
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$8.74702$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -19.4940 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -19.4940 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +38.9881 q^{10} -13.8745 q^{11} +12.0000 q^{12} +50.1985 q^{13} +14.0000 q^{14} -58.4821 q^{15} +16.0000 q^{16} +50.6145 q^{17} -18.0000 q^{18} -19.0000 q^{19} -77.9761 q^{20} -21.0000 q^{21} +27.7489 q^{22} +203.619 q^{23} -24.0000 q^{24} +255.017 q^{25} -100.397 q^{26} +27.0000 q^{27} -28.0000 q^{28} -171.261 q^{29} +116.964 q^{30} -82.6182 q^{31} -32.0000 q^{32} -41.6234 q^{33} -101.229 q^{34} +136.458 q^{35} +36.0000 q^{36} +347.533 q^{37} +38.0000 q^{38} +150.595 q^{39} +155.952 q^{40} -454.830 q^{41} +42.0000 q^{42} +105.059 q^{43} -55.4978 q^{44} -175.446 q^{45} -407.238 q^{46} -116.102 q^{47} +48.0000 q^{48} +49.0000 q^{49} -510.035 q^{50} +151.843 q^{51} +200.794 q^{52} -385.204 q^{53} -54.0000 q^{54} +270.469 q^{55} +56.0000 q^{56} -57.0000 q^{57} +342.523 q^{58} -265.292 q^{59} -233.928 q^{60} -629.575 q^{61} +165.236 q^{62} -63.0000 q^{63} +64.0000 q^{64} -978.571 q^{65} +83.2467 q^{66} -767.200 q^{67} +202.458 q^{68} +610.857 q^{69} -272.916 q^{70} -819.687 q^{71} -72.0000 q^{72} -117.962 q^{73} -695.065 q^{74} +765.052 q^{75} -76.0000 q^{76} +97.1212 q^{77} -301.191 q^{78} -37.8794 q^{79} -311.905 q^{80} +81.0000 q^{81} +909.659 q^{82} +565.412 q^{83} -84.0000 q^{84} -986.680 q^{85} -210.117 q^{86} -513.784 q^{87} +110.996 q^{88} -1457.03 q^{89} +350.893 q^{90} -351.389 q^{91} +814.476 q^{92} -247.855 q^{93} +232.204 q^{94} +370.387 q^{95} -96.0000 q^{96} +1557.79 q^{97} -98.0000 q^{98} -124.870 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) $ 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} + 20 q^{10} + 4 q^{11} + 48 q^{12} + 16 q^{13} + 56 q^{14} - 30 q^{15} + 64 q^{16} - 66 q^{17} - 72 q^{18} - 76 q^{19} - 40 q^{20} - 84 q^{21} - 8 q^{22} + 32 q^{23} - 96 q^{24} + 200 q^{25} - 32 q^{26} + 108 q^{27} - 112 q^{28} - 10 q^{29} + 60 q^{30} + 108 q^{31} - 128 q^{32} + 12 q^{33} + 132 q^{34} + 70 q^{35} + 144 q^{36} - 116 q^{37} + 152 q^{38} + 48 q^{39} + 80 q^{40} - 988 q^{41} + 168 q^{42} - 448 q^{43} + 16 q^{44} - 90 q^{45} - 64 q^{46} - 850 q^{47} + 192 q^{48} + 196 q^{49} - 400 q^{50} - 198 q^{51} + 64 q^{52} - 998 q^{53} - 216 q^{54} - 904 q^{55} + 224 q^{56} - 228 q^{57} + 20 q^{58} - 680 q^{59} - 120 q^{60} - 208 q^{61} - 216 q^{62} - 252 q^{63} + 256 q^{64} - 676 q^{65} - 24 q^{66} + 108 q^{67} - 264 q^{68} + 96 q^{69} - 140 q^{70} - 1050 q^{71} - 288 q^{72} + 100 q^{73} + 232 q^{74} + 600 q^{75} - 304 q^{76} - 28 q^{77} - 96 q^{78} + 1540 q^{79} - 160 q^{80} + 324 q^{81} + 1976 q^{82} + 94 q^{83} - 336 q^{84} - 844 q^{85} + 896 q^{86} - 30 q^{87} - 32 q^{88} - 2284 q^{89} + 180 q^{90} - 112 q^{91} + 128 q^{92} + 324 q^{93} + 1700 q^{94} + 190 q^{95} - 384 q^{96} - 136 q^{97} - 392 q^{98} + 36 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9 + 20 * q^10 + 4 * q^11 + 48 * q^12 + 16 * q^13 + 56 * q^14 - 30 * q^15 + 64 * q^16 - 66 * q^17 - 72 * q^18 - 76 * q^19 - 40 * q^20 - 84 * q^21 - 8 * q^22 + 32 * q^23 - 96 * q^24 + 200 * q^25 - 32 * q^26 + 108 * q^27 - 112 * q^28 - 10 * q^29 + 60 * q^30 + 108 * q^31 - 128 * q^32 + 12 * q^33 + 132 * q^34 + 70 * q^35 + 144 * q^36 - 116 * q^37 + 152 * q^38 + 48 * q^39 + 80 * q^40 - 988 * q^41 + 168 * q^42 - 448 * q^43 + 16 * q^44 - 90 * q^45 - 64 * q^46 - 850 * q^47 + 192 * q^48 + 196 * q^49 - 400 * q^50 - 198 * q^51 + 64 * q^52 - 998 * q^53 - 216 * q^54 - 904 * q^55 + 224 * q^56 - 228 * q^57 + 20 * q^58 - 680 * q^59 - 120 * q^60 - 208 * q^61 - 216 * q^62 - 252 * q^63 + 256 * q^64 - 676 * q^65 - 24 * q^66 + 108 * q^67 - 264 * q^68 + 96 * q^69 - 140 * q^70 - 1050 * q^71 - 288 * q^72 + 100 * q^73 + 232 * q^74 + 600 * q^75 - 304 * q^76 - 28 * q^77 - 96 * q^78 + 1540 * q^79 - 160 * q^80 + 324 * q^81 + 1976 * q^82 + 94 * q^83 - 336 * q^84 - 844 * q^85 + 896 * q^86 - 30 * q^87 - 32 * q^88 - 2284 * q^89 + 180 * q^90 - 112 * q^91 + 128 * q^92 + 324 * q^93 + 1700 * q^94 + 190 * q^95 - 384 * q^96 - 136 * q^97 - 392 * q^98 + 36 * 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
$5$	−19.4940	−1.74360	−0.871800	−	0.489863i	$-0.837047\pi$
$5$	−19.4940	−1.74360	−0.871800	+	0.489863i	$0.837047\pi$
$6$	−6.00000	−0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	38.9881	1.23291
$11$	−13.8745	−0.380300	−0.190150	−	0.981755i	$-0.560898\pi$
$11$	−13.8745	−0.380300	−0.190150	+	0.981755i	$0.560898\pi$
$12$	12.0000	0.288675
$13$	50.1985	1.07097	0.535483	−	0.844546i	$-0.320130\pi$
$13$	50.1985	1.07097	0.535483	+	0.844546i	$0.320130\pi$
$14$	14.0000	0.267261
$15$	−58.4821	−1.00667
$16$	16.0000	0.250000
$17$	50.6145	0.722106	0.361053	−	0.932545i	$-0.382417\pi$
$17$	50.6145	0.722106	0.361053	+	0.932545i	$0.382417\pi$
$18$	−18.0000	−0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−77.9761	−0.871800
$21$	−21.0000	−0.218218
$22$	27.7489	0.268913
$23$	203.619	1.84598	0.922989	−	0.384825i	$-0.125738\pi$
$23$	203.619	1.84598	0.922989	+	0.384825i	$0.125738\pi$
$24$	−24.0000	−0.204124
$25$	255.017	2.04014
$26$	−100.397	−0.757287
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	−171.261	−1.09664	−0.548318	−	0.836270i	$-0.684732\pi$
$29$	−171.261	−1.09664	−0.548318	+	0.836270i	$0.684732\pi$
$30$	116.964	0.711821
$31$	−82.6182	−0.478667	−0.239333	−	0.970937i	$-0.576929\pi$
$31$	−82.6182	−0.478667	−0.239333	+	0.970937i	$0.576929\pi$
$32$	−32.0000	−0.176777
$33$	−41.6234	−0.219567
$34$	−101.229	−0.510606
$35$	136.458	0.659019
$36$	36.0000	0.166667
$37$	347.533	1.54416	0.772081	−	0.635524i	$-0.219216\pi$
$37$	347.533	1.54416	0.772081	+	0.635524i	$0.219216\pi$
$38$	38.0000	0.162221
$39$	150.595	0.618322
$40$	155.952	0.616455
$41$	−454.830	−1.73250	−0.866249	−	0.499612i	$-0.833476\pi$
$41$	−454.830	−1.73250	−0.866249	+	0.499612i	$0.833476\pi$
$42$	42.0000	0.154303
$43$	105.059	0.372588	0.186294	−	0.982494i	$-0.440352\pi$
$43$	105.059	0.372588	0.186294	+	0.982494i	$0.440352\pi$
$44$	−55.4978	−0.190150
$45$	−175.446	−0.581200
$46$	−407.238	−1.30530
$47$	−116.102	−0.360324	−0.180162	−	0.983637i	$-0.557662\pi$
$47$	−116.102	−0.360324	−0.180162	+	0.983637i	$0.557662\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	−510.035	−1.44260
$51$	151.843	0.416908
$52$	200.794	0.535483
$53$	−385.204	−0.998337	−0.499169	−	0.866505i	$-0.666361\pi$
$53$	−385.204	−0.998337	−0.499169	+	0.866505i	$0.666361\pi$
$54$	−54.0000	−0.136083
$55$	270.469	0.663092
$56$	56.0000	0.133631
$57$	−57.0000	−0.132453
$58$	342.523	0.775439
$59$	−265.292	−0.585392	−0.292696	−	0.956206i	$-0.594552\pi$
$59$	−265.292	−0.585392	−0.292696	+	0.956206i	$0.594552\pi$
$60$	−233.928	−0.503334
$61$	−629.575	−1.32146	−0.660728	−	0.750625i	$-0.729753\pi$
$61$	−629.575	−1.32146	−0.660728	+	0.750625i	$0.729753\pi$
$62$	165.236	0.338469
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−978.571	−1.86734
$66$	83.2467	0.155257
$67$	−767.200	−1.39893	−0.699466	−	0.714666i	$-0.746579\pi$
$67$	−767.200	−1.39893	−0.699466	+	0.714666i	$0.746579\pi$
$68$	202.458	0.361053
$69$	610.857	1.06578
$70$	−272.916	−0.465996
$71$	−819.687	−1.37013	−0.685063	−	0.728484i	$-0.740225\pi$
$71$	−819.687	−1.37013	−0.685063	+	0.728484i	$0.740225\pi$
$72$	−72.0000	−0.117851
$73$	−117.962	−0.189129	−0.0945645	−	0.995519i	$-0.530146\pi$
$73$	−117.962	−0.189129	−0.0945645	+	0.995519i	$0.530146\pi$
$74$	−695.065	−1.09189
$75$	765.052	1.17787
$76$	−76.0000	−0.114708
$77$	97.1212	0.143740
$78$	−301.191	−0.437220
$79$	−37.8794	−0.0539464	−0.0269732	−	0.999636i	$-0.508587\pi$
$79$	−37.8794	−0.0539464	−0.0269732	+	0.999636i	$0.508587\pi$
$80$	−311.905	−0.435900
$81$	81.0000	0.111111
$82$	909.659	1.22506
$83$	565.412	0.747736	0.373868	−	0.927482i	$-0.378031\pi$
$83$	565.412	0.747736	0.373868	+	0.927482i	$0.378031\pi$
$84$	−84.0000	−0.109109
$85$	−986.680	−1.25906
$86$	−210.117	−0.263460
$87$	−513.784	−0.633143
$88$	110.996	0.134457
$89$	−1457.03	−1.73533	−0.867665	−	0.497149i	$-0.834380\pi$
$89$	−1457.03	−1.73533	−0.867665	+	0.497149i	$0.834380\pi$
$90$	350.893	0.410970
$91$	−351.389	−0.404787
$92$	814.476	0.922989
$93$	−247.855	−0.276358
$94$	232.204	0.254788
$95$	370.387	0.400009
$96$	−96.0000	−0.102062
$97$	1557.79	1.63061	0.815305	−	0.579032i	$-0.196569\pi$
$97$	1557.79	1.63061	0.815305	+	0.579032i	$0.196569\pi$
$98$	−98.0000	−0.101015
$99$	−124.870	−0.126767
$100$	1020.07	1.02007
$101$	657.278	0.647540	0.323770	−	0.946136i	$-0.395050\pi$
$101$	657.278	0.647540	0.323770	+	0.946136i	$0.395050\pi$
$102$	−303.687	−0.294799
$103$	1431.16	1.36909	0.684546	−	0.728970i	$-0.260001\pi$
$103$	1431.16	1.36909	0.684546	+	0.728970i	$0.260001\pi$
$104$	−401.588	−0.378644
$105$	409.375	0.380485
$106$	770.408	0.705931
$107$	1978.52	1.78757	0.893787	−	0.448491i	$-0.148039\pi$
$107$	1978.52	1.78757	0.893787	+	0.448491i	$0.148039\pi$
$108$	108.000	0.0962250
$109$	1458.40	1.28155	0.640776	−	0.767728i	$-0.278613\pi$
$109$	1458.40	1.28155	0.640776	+	0.767728i	$0.278613\pi$
$110$	−540.938	−0.468877
$111$	1042.60	0.891523
$112$	−112.000	−0.0944911
$113$	−651.206	−0.542126	−0.271063	−	0.962562i	$-0.587375\pi$
$113$	−651.206	−0.542126	−0.271063	+	0.962562i	$0.587375\pi$
$114$	114.000	0.0936586
$115$	−3969.36	−3.21865
$116$	−685.046	−0.548318
$117$	451.786	0.356989
$118$	530.585	0.413935
$119$	−354.301	−0.272931
$120$	467.857	0.355911
$121$	−1138.50	−0.855372
$122$	1259.15	0.934411
$123$	−1364.49	−1.00026
$124$	−330.473	−0.239333
$125$	−2534.56	−1.81358
$126$	126.000	0.0890871
$127$	−2284.99	−1.59654	−0.798270	−	0.602300i	$-0.794251\pi$
$127$	−2284.99	−1.59654	−0.798270	+	0.602300i	$0.794251\pi$
$128$	−128.000	−0.0883883
$129$	315.176	0.215114
$130$	1957.14	1.32041
$131$	−956.667	−0.638049	−0.319024	−	0.947747i	$-0.603355\pi$
$131$	−956.667	−0.638049	−0.319024	+	0.947747i	$0.603355\pi$
$132$	−166.493	−0.109783
$133$	133.000	0.0867110
$134$	1534.40	0.989194
$135$	−526.339	−0.335556
$136$	−404.916	−0.255303
$137$	−1610.76	−1.00450	−0.502251	−	0.864722i	$-0.667495\pi$
$137$	−1610.76	−1.00450	−0.502251	+	0.864722i	$0.667495\pi$
$138$	−1221.71	−0.753618
$139$	−1477.78	−0.901755	−0.450877	−	0.892586i	$-0.648889\pi$
$139$	−1477.78	−0.901755	−0.450877	+	0.892586i	$0.648889\pi$
$140$	545.833	0.329509
$141$	−348.306	−0.208033
$142$	1639.37	0.968826
$143$	−696.477	−0.407289
$144$	144.000	0.0833333
$145$	3338.58	1.91209
$146$	235.924	0.133734
$147$	147.000	0.0824786
$148$	1390.13	0.772081
$149$	951.048	0.522905	0.261453	−	0.965216i	$-0.415798\pi$
$149$	951.048	0.522905	0.261453	+	0.965216i	$0.415798\pi$
$150$	−1530.10	−0.832883
$151$	−592.542	−0.319340	−0.159670	−	0.987170i	$-0.551043\pi$
$151$	−592.542	−0.319340	−0.159670	+	0.987170i	$0.551043\pi$
$152$	152.000	0.0811107
$153$	455.530	0.240702
$154$	−194.242	−0.101640
$155$	1610.56	0.834603
$156$	602.382	0.309161
$157$	−1446.71	−0.735415	−0.367708	−	0.929941i	$-0.619857\pi$
$157$	−1446.71	−0.735415	−0.367708	+	0.929941i	$0.619857\pi$
$158$	75.7589	0.0381459
$159$	−1155.61	−0.576390
$160$	623.809	0.308228
$161$	−1425.33	−0.697714
$162$	−162.000	−0.0785674
$163$	779.949	0.374787	0.187394	−	0.982285i	$-0.439996\pi$
$163$	779.949	0.374787	0.187394	+	0.982285i	$0.439996\pi$
$164$	−1819.32	−0.866249
$165$	811.407	0.382836
$166$	−1130.82	−0.528729
$167$	−3478.98	−1.61205	−0.806024	−	0.591883i	$-0.798385\pi$
$167$	−3478.98	−1.61205	−0.806024	+	0.591883i	$0.798385\pi$
$168$	168.000	0.0771517
$169$	322.889	0.146968
$170$	1973.36	0.890293
$171$	−171.000	−0.0764719
$172$	420.235	0.186294
$173$	1454.89	0.639384	0.319692	−	0.947522i	$-0.396421\pi$
$173$	1454.89	0.639384	0.319692	+	0.947522i	$0.396421\pi$
$174$	1027.57	0.447700
$175$	−1785.12	−0.771100
$176$	−221.991	−0.0950751
$177$	−795.877	−0.337976
$178$	2914.05	1.22706
$179$	−2942.27	−1.22858	−0.614290	−	0.789080i	$-0.710558\pi$
$179$	−2942.27	−1.22858	−0.614290	+	0.789080i	$0.710558\pi$
$180$	−701.785	−0.290600
$181$	897.415	0.368532	0.184266	−	0.982876i	$-0.441009\pi$
$181$	897.415	0.368532	0.184266	+	0.982876i	$0.441009\pi$
$182$	702.779	0.286228
$183$	−1888.73	−0.762944
$184$	−1628.95	−0.652652
$185$	−6774.81	−2.69240
$186$	495.709	0.195415
$187$	−702.248	−0.274617
$188$	−464.408	−0.180162
$189$	−189.000	−0.0727393
$190$	−740.773	−0.282849
$191$	−1083.18	−0.410346	−0.205173	−	0.978726i	$-0.565776\pi$
$191$	−1083.18	−0.410346	−0.205173	+	0.978726i	$0.565776\pi$
$192$	192.000	0.0721688
$193$	−5034.29	−1.87760	−0.938798	−	0.344468i	$-0.888059\pi$
$193$	−5034.29	−1.87760	−0.938798	+	0.344468i	$0.888059\pi$
$194$	−3115.57	−1.15302
$195$	−2935.71	−1.07811
$196$	196.000	0.0714286
$197$	2849.99	1.03073	0.515365	−	0.856971i	$-0.327656\pi$
$197$	2849.99	1.03073	0.515365	+	0.856971i	$0.327656\pi$
$198$	249.740	0.0896377
$199$	−1187.06	−0.422856	−0.211428	−	0.977394i	$-0.567811\pi$
$199$	−1187.06	−0.422856	−0.211428	+	0.977394i	$0.567811\pi$
$200$	−2040.14	−0.721298
$201$	−2301.60	−0.807674
$202$	−1314.56	−0.457880
$203$	1198.83	0.414489
$204$	607.373	0.208454
$205$	8866.46	3.02078
$206$	−2862.32	−0.968094
$207$	1832.57	0.615326
$208$	803.176	0.267741
$209$	263.615	0.0872469
$210$	−818.749	−0.269043
$211$	3062.79	0.999295	0.499648	−	0.866229i	$-0.333463\pi$
$211$	3062.79	0.999295	0.499648	+	0.866229i	$0.333463\pi$
$212$	−1540.82	−0.499169
$213$	−2459.06	−0.791043
$214$	−3957.03	−1.26401
$215$	−2048.02	−0.649645
$216$	−216.000	−0.0680414
$217$	578.328	0.180919
$218$	−2916.80	−0.906194
$219$	−353.886	−0.109194
$220$	1081.88	0.331546
$221$	2540.77	0.773351
$222$	−2085.20	−0.630402
$223$	−2837.31	−0.852019	−0.426010	−	0.904719i	$-0.640081\pi$
$223$	−2837.31	−0.852019	−0.426010	+	0.904719i	$0.640081\pi$
$224$	224.000	0.0668153
$225$	2295.16	0.680046
$226$	1302.41	0.383341
$227$	−3979.17	−1.16347	−0.581733	−	0.813380i	$-0.697625\pi$
$227$	−3979.17	−1.16347	−0.581733	+	0.813380i	$0.697625\pi$
$228$	−228.000	−0.0662266
$229$	−784.720	−0.226444	−0.113222	−	0.993570i	$-0.536117\pi$
$229$	−784.720	−0.226444	−0.113222	+	0.993570i	$0.536117\pi$
$230$	7938.71	2.27593
$231$	291.364	0.0829884
$232$	1370.09	0.387719
$233$	2274.82	0.639608	0.319804	−	0.947484i	$-0.396383\pi$
$233$	2274.82	0.639608	0.319804	+	0.947484i	$0.396383\pi$
$234$	−903.573	−0.252429
$235$	2263.30	0.628261
$236$	−1061.17	−0.292696
$237$	−113.638	−0.0311460
$238$	708.602	0.192991
$239$	1420.99	0.384588	0.192294	−	0.981337i	$-0.438407\pi$
$239$	1420.99	0.384588	0.192294	+	0.981337i	$0.438407\pi$
$240$	−935.714	−0.251667
$241$	−4456.02	−1.19103	−0.595514	−	0.803345i	$-0.703052\pi$
$241$	−4456.02	−1.19103	−0.595514	+	0.803345i	$0.703052\pi$
$242$	2277.00	0.604839
$243$	243.000	0.0641500
$244$	−2518.30	−0.660728
$245$	−955.208	−0.249086
$246$	2728.98	0.707290
$247$	−953.771	−0.245696
$248$	660.946	0.169234
$249$	1696.24	0.431706
$250$	5069.12	1.28240
$251$	−3666.30	−0.921973	−0.460986	−	0.887407i	$-0.652504\pi$
$251$	−3666.30	−0.921973	−0.460986	+	0.887407i	$0.652504\pi$
$252$	−252.000	−0.0629941
$253$	−2825.10	−0.702027
$254$	4569.99	1.12892
$255$	−2960.04	−0.726921
$256$	256.000	0.0625000
$257$	7027.68	1.70574	0.852869	−	0.522125i	$-0.174861\pi$
$257$	7027.68	1.70574	0.852869	+	0.522125i	$0.174861\pi$
$258$	−630.352	−0.152109
$259$	−2432.73	−0.583639
$260$	−3914.28	−0.933668
$261$	−1541.35	−0.365545
$262$	1913.33	0.451169
$263$	−3426.81	−0.803445	−0.401723	−	0.915761i	$-0.631588\pi$
$263$	−3426.81	−0.803445	−0.401723	+	0.915761i	$0.631588\pi$
$264$	332.987	0.0776285
$265$	7509.18	1.74070
$266$	−266.000	−0.0613139
$267$	−4371.08	−1.00189
$268$	−3068.80	−0.699466
$269$	5289.82	1.19898	0.599490	−	0.800382i	$-0.295370\pi$
$269$	5289.82	1.19898	0.599490	+	0.800382i	$0.295370\pi$
$270$	1052.68	0.237274
$271$	2628.14	0.589106	0.294553	−	0.955635i	$-0.404829\pi$
$271$	2628.14	0.589106	0.294553	+	0.955635i	$0.404829\pi$
$272$	809.831	0.180527
$273$	−1054.17	−0.233704
$274$	3221.53	0.710290
$275$	−3538.23	−0.775865
$276$	2443.43	0.532888
$277$	1036.68	0.224866	0.112433	−	0.993659i	$-0.464136\pi$
$277$	1036.68	0.224866	0.112433	+	0.993659i	$0.464136\pi$
$278$	2955.57	0.637637
$279$	−743.564	−0.159556
$280$	−1091.67	−0.232998
$281$	3688.73	0.783100	0.391550	−	0.920157i	$-0.371939\pi$
$281$	3688.73	0.783100	0.391550	+	0.920157i	$0.371939\pi$
$282$	696.613	0.147102
$283$	−2477.91	−0.520482	−0.260241	−	0.965544i	$-0.583802\pi$
$283$	−2477.91	−0.520482	−0.260241	+	0.965544i	$0.583802\pi$
$284$	−3278.75	−0.685063
$285$	1111.16	0.230945
$286$	1392.95	0.287997
$287$	3183.81	0.654823
$288$	−288.000	−0.0589256
$289$	−2351.18	−0.478562
$290$	−6677.15	−1.35205
$291$	4673.36	0.941433
$292$	−471.848	−0.0945645
$293$	−8109.08	−1.61685	−0.808425	−	0.588599i	$-0.799680\pi$
$293$	−8109.08	−1.61685	−0.808425	+	0.588599i	$0.799680\pi$
$294$	−294.000	−0.0583212
$295$	5171.62	1.02069
$296$	−2780.26	−0.545944
$297$	−374.610	−0.0731889
$298$	−1902.10	−0.369750
$299$	10221.4	1.97698
$300$	3060.21	0.588937
$301$	−735.411	−0.140825
$302$	1185.08	0.225808
$303$	1971.83	0.373858
$304$	−304.000	−0.0573539
$305$	12273.0	2.30409
$306$	−911.060	−0.170202
$307$	−1802.27	−0.335052	−0.167526	−	0.985868i	$-0.553578\pi$
$307$	−1802.27	−0.335052	−0.167526	+	0.985868i	$0.553578\pi$
$308$	388.485	0.0718700
$309$	4293.48	0.790445
$310$	−3221.12	−0.590154
$311$	−2386.30	−0.435096	−0.217548	−	0.976050i	$-0.569806\pi$
$311$	−2386.30	−0.435096	−0.217548	+	0.976050i	$0.569806\pi$
$312$	−1204.76	−0.218610
$313$	−7738.69	−1.39750	−0.698748	−	0.715367i	$-0.746259\pi$
$313$	−7738.69	−1.39750	−0.698748	+	0.715367i	$0.746259\pi$
$314$	2893.42	0.520017
$315$	1228.12	0.219673
$316$	−151.518	−0.0269732
$317$	−190.930	−0.0338287	−0.0169143	−	0.999857i	$-0.505384\pi$
$317$	−190.930	−0.0338287	−0.0169143	+	0.999857i	$0.505384\pi$
$318$	2311.23	0.407569
$319$	2376.16	0.417051
$320$	−1247.62	−0.217950
$321$	5935.55	1.03206
$322$	2850.67	0.493359
$323$	−961.675	−0.165663
$324$	324.000	0.0555556
$325$	12801.5	2.18492
$326$	−1559.90	−0.265014
$327$	4375.19	0.739905
$328$	3638.64	0.612531
$329$	812.715	0.136190
$330$	−1622.81	−0.270706
$331$	−436.740	−0.0725239	−0.0362620	−	0.999342i	$-0.511545\pi$
$331$	−436.740	−0.0725239	−0.0362620	+	0.999342i	$0.511545\pi$
$332$	2261.65	0.373868
$333$	3127.79	0.514721
$334$	6957.97	1.13989
$335$	14955.8	2.43918
$336$	−336.000	−0.0545545
$337$	2715.02	0.438862	0.219431	−	0.975628i	$-0.429580\pi$
$337$	2715.02	0.438862	0.219431	+	0.975628i	$0.429580\pi$
$338$	−645.777	−0.103922
$339$	−1953.62	−0.312997
$340$	−3946.72	−0.629532
$341$	1146.28	0.182037
$342$	342.000	0.0540738
$343$	−343.000	−0.0539949
$344$	−840.469	−0.131730
$345$	−11908.1	−1.85829
$346$	−2909.78	−0.452112
$347$	−6993.98	−1.08201	−0.541004	−	0.841020i	$-0.681955\pi$
$347$	−6993.98	−1.08201	−0.541004	+	0.841020i	$0.681955\pi$
$348$	−2055.14	−0.316572
$349$	11307.8	1.73436	0.867180	−	0.497994i	$-0.165930\pi$
$349$	11307.8	1.73436	0.867180	+	0.497994i	$0.165930\pi$
$350$	3570.24	0.545250
$351$	1355.36	0.206107
$352$	443.982	0.0672283
$353$	−6402.03	−0.965285	−0.482642	−	0.875818i	$-0.660323\pi$
$353$	−6402.03	−0.965285	−0.482642	+	0.875818i	$0.660323\pi$
$354$	1591.75	0.238985
$355$	15979.0	2.38895
$356$	−5828.10	−0.867665
$357$	−1062.90	−0.157577
$358$	5884.55	0.868738
$359$	11106.0	1.63273	0.816366	−	0.577534i	$-0.195985\pi$
$359$	11106.0	1.63273	0.816366	+	0.577534i	$0.195985\pi$
$360$	1403.57	0.205485
$361$	361.000	0.0526316
$362$	−1794.83	−0.260592
$363$	−3415.50	−0.493849
$364$	−1405.56	−0.202394
$365$	2299.56	0.329765
$366$	3777.45	0.539483
$367$	2595.33	0.369143	0.184571	−	0.982819i	$-0.440910\pi$
$367$	2595.33	0.369143	0.184571	+	0.982819i	$0.440910\pi$
$368$	3257.91	0.461495
$369$	−4093.47	−0.577499
$370$	13549.6	1.90382
$371$	2696.43	0.377336
$372$	−991.419	−0.138179
$373$	6589.34	0.914700	0.457350	−	0.889287i	$-0.348799\pi$
$373$	6589.34	0.914700	0.457350	+	0.889287i	$0.348799\pi$
$374$	1404.50	0.194184
$375$	−7603.68	−1.04707
$376$	928.817	0.127394
$377$	−8597.06	−1.17446
$378$	378.000	0.0514344
$379$	2622.33	0.355409	0.177704	−	0.984084i	$-0.443133\pi$
$379$	2622.33	0.355409	0.177704	+	0.984084i	$0.443133\pi$
$380$	1481.55	0.200005
$381$	−6854.98	−0.921762
$382$	2166.36	0.290159
$383$	606.266	0.0808844	0.0404422	−	0.999182i	$-0.487123\pi$
$383$	606.266	0.0808844	0.0404422	+	0.999182i	$0.487123\pi$
$384$	−384.000	−0.0510310
$385$	−1893.28	−0.250625
$386$	10068.6	1.32766
$387$	945.528	0.124196
$388$	6231.14	0.815305
$389$	−7610.96	−0.992008	−0.496004	−	0.868320i	$-0.665200\pi$
$389$	−7610.96	−0.992008	−0.496004	+	0.868320i	$0.665200\pi$
$390$	5871.43	0.762336
$391$	10306.1	1.33299
$392$	−392.000	−0.0505076
$393$	−2870.00	−0.368378
$394$	−5699.99	−0.728836
$395$	738.423	0.0940610
$396$	−499.480	−0.0633834
$397$	66.5466	0.00841280	0.00420640	−	0.999991i	$-0.498661\pi$
$397$	66.5466	0.00841280	0.00420640	+	0.999991i	$0.498661\pi$
$398$	2374.12	0.299005
$399$	399.000	0.0500626
$400$	4080.28	0.510035
$401$	−8940.26	−1.11335	−0.556677	−	0.830729i	$-0.687924\pi$
$401$	−8940.26	−1.11335	−0.556677	+	0.830729i	$0.687924\pi$
$402$	4603.20	0.571112
$403$	−4147.31	−0.512636
$404$	2629.11	0.323770
$405$	−1579.02	−0.193733
$406$	−2397.66	−0.293088
$407$	−4821.83	−0.587246
$408$	−1214.75	−0.147399
$409$	12369.9	1.49548	0.747741	−	0.663990i	$-0.231138\pi$
$409$	12369.9	1.49548	0.747741	+	0.663990i	$0.231138\pi$
$410$	−17732.9	−2.13602
$411$	−4832.29	−0.579950
$412$	5724.64	0.684546
$413$	1857.05	0.221257
$414$	−3665.14	−0.435101
$415$	−11022.2	−1.30375
$416$	−1606.35	−0.189322
$417$	−4433.35	−0.520628
$418$	−527.229	−0.0616929
$419$	−3866.79	−0.450848	−0.225424	−	0.974261i	$-0.572377\pi$
$419$	−3866.79	−0.450848	−0.225424	+	0.974261i	$0.572377\pi$
$420$	1637.50	0.190242
$421$	−16969.8	−1.96451	−0.982254	−	0.187554i	$-0.939944\pi$
$421$	−16969.8	−1.96451	−0.982254	+	0.187554i	$0.939944\pi$
$422$	−6125.58	−0.706608
$423$	−1044.92	−0.120108
$424$	3081.63	0.352965
$425$	12907.6	1.47320
$426$	4918.12	0.559352
$427$	4407.03	0.499464
$428$	7914.07	0.893787
$429$	−2089.43	−0.235148
$430$	4096.03	0.459368
$431$	1611.72	0.180125	0.0900627	−	0.995936i	$-0.471293\pi$
$431$	1611.72	0.180125	0.0900627	+	0.995936i	$0.471293\pi$
$432$	432.000	0.0481125
$433$	−15579.7	−1.72913	−0.864563	−	0.502525i	$-0.832404\pi$
$433$	−15579.7	−1.72913	−0.864563	+	0.502525i	$0.832404\pi$
$434$	−1156.66	−0.127929
$435$	10015.7	1.10395
$436$	5833.59	0.640776
$437$	−3868.76	−0.423497
$438$	707.772	0.0772116
$439$	−17268.3	−1.87738	−0.938691	−	0.344760i	$-0.887960\pi$
$439$	−17268.3	−1.87738	−0.938691	+	0.344760i	$0.887960\pi$
$440$	−2163.75	−0.234438
$441$	441.000	0.0476190
$442$	−5081.54	−0.546842
$443$	2914.80	0.312610	0.156305	−	0.987709i	$-0.450042\pi$
$443$	2914.80	0.312610	0.156305	+	0.987709i	$0.450042\pi$
$444$	4170.39	0.445761
$445$	28403.3	3.02572
$446$	5674.62	0.602469
$447$	2853.14	0.301899
$448$	−448.000	−0.0472456
$449$	2495.47	0.262290	0.131145	−	0.991363i	$-0.458135\pi$
$449$	2495.47	0.262290	0.131145	+	0.991363i	$0.458135\pi$
$450$	−4590.31	−0.480865
$451$	6310.51	0.658870
$452$	−2604.82	−0.271063
$453$	−1777.62	−0.184371
$454$	7958.34	0.822695
$455$	6850.00	0.705786
$456$	456.000	0.0468293
$457$	−11906.1	−1.21869	−0.609347	−	0.792904i	$-0.708568\pi$
$457$	−11906.1	−1.21869	−0.609347	+	0.792904i	$0.708568\pi$
$458$	1569.44	0.160120
$459$	1366.59	0.138969
$460$	−15877.4	−1.60932
$461$	−12866.3	−1.29987	−0.649937	−	0.759989i	$-0.725205\pi$
$461$	−12866.3	−1.29987	−0.649937	+	0.759989i	$0.725205\pi$
$462$	−582.727	−0.0586816
$463$	17656.6	1.77230	0.886148	−	0.463402i	$-0.153371\pi$
$463$	17656.6	1.77230	0.886148	+	0.463402i	$0.153371\pi$
$464$	−2740.18	−0.274159
$465$	4831.69	0.481858
$466$	−4549.65	−0.452271
$467$	15890.2	1.57454	0.787272	−	0.616606i	$-0.211493\pi$
$467$	15890.2	1.57454	0.787272	+	0.616606i	$0.211493\pi$
$468$	1807.15	0.178494
$469$	5370.40	0.528747
$470$	−4526.60	−0.444247
$471$	−4340.14	−0.424592
$472$	2122.34	0.206967
$473$	−1457.63	−0.141696
$474$	227.277	0.0220235
$475$	−4845.33	−0.468040
$476$	−1417.20	−0.136465
$477$	−3466.84	−0.332779
$478$	−2841.99	−0.271945
$479$	−15521.2	−1.48054	−0.740271	−	0.672309i	$-0.765303\pi$
$479$	−15521.2	−1.48054	−0.740271	+	0.672309i	$0.765303\pi$
$480$	1871.43	0.177955
$481$	17445.6	1.65375
$482$	8912.05	0.842184
$483$	−4276.00	−0.402826
$484$	−4554.00	−0.427686
$485$	−30367.5	−2.84313
$486$	−486.000	−0.0453609
$487$	14590.9	1.35765	0.678827	−	0.734298i	$-0.262488\pi$
$487$	14590.9	1.35765	0.678827	+	0.734298i	$0.262488\pi$
$488$	5036.60	0.467206
$489$	2339.85	0.216383
$490$	1910.42	0.176130
$491$	−48.4269	−0.00445107	−0.00222553	−	0.999998i	$-0.500708\pi$
$491$	−48.4269	−0.00445107	−0.00222553	+	0.999998i	$0.500708\pi$
$492$	−5457.95	−0.500129
$493$	−8668.30	−0.791888
$494$	1907.54	0.173734
$495$	2434.22	0.221031
$496$	−1321.89	−0.119667
$497$	5737.81	0.517859
$498$	−3392.47	−0.305262
$499$	5100.11	0.457540	0.228770	−	0.973481i	$-0.426530\pi$
$499$	5100.11	0.457540	0.228770	+	0.973481i	$0.426530\pi$
$500$	−10138.2	−0.906792
$501$	−10437.0	−0.930716
$502$	7332.61	0.651933
$503$	8418.68	0.746263	0.373131	−	0.927778i	$-0.378284\pi$
$503$	8418.68	0.746263	0.373131	+	0.927778i	$0.378284\pi$
$504$	504.000	0.0445435
$505$	−12813.0	−1.12905
$506$	5650.21	0.496408
$507$	968.666	0.0848520
$508$	−9139.98	−0.798270
$509$	728.287	0.0634200	0.0317100	−	0.999497i	$-0.489905\pi$
$509$	728.287	0.0634200	0.0317100	+	0.999497i	$0.489905\pi$
$510$	5920.08	0.514011
$511$	825.734	0.0714840
$512$	−512.000	−0.0441942
$513$	−513.000	−0.0441511
$514$	−14055.4	−1.20614
$515$	−27899.1	−2.38715
$516$	1260.70	0.107557
$517$	1610.85	0.137031
$518$	4865.46	0.412695
$519$	4364.67	0.369148
$520$	7828.57	0.660203
$521$	−15014.4	−1.26256	−0.631278	−	0.775556i	$-0.717469\pi$
$521$	−15014.4	−1.26256	−0.631278	+	0.775556i	$0.717469\pi$
$522$	3082.71	0.258480
$523$	−4963.70	−0.415005	−0.207502	−	0.978235i	$-0.566533\pi$
$523$	−4963.70	−0.415005	−0.207502	+	0.978235i	$0.566533\pi$
$524$	−3826.67	−0.319024
$525$	−5355.36	−0.445195
$526$	6853.62	0.568122
$527$	−4181.68	−0.345648
$528$	−665.974	−0.0548916
$529$	29293.7	2.40764
$530$	−15018.4	−1.23086
$531$	−2387.63	−0.195131
$532$	532.000	0.0433555
$533$	−22831.8	−1.85545
$534$	8742.15	0.708446
$535$	−38569.3	−3.11681
$536$	6137.60	0.494597
$537$	−8826.82	−0.709321
$538$	−10579.6	−0.847807
$539$	−679.848	−0.0543286
$540$	−2105.36	−0.167778
$541$	−5424.60	−0.431094	−0.215547	−	0.976493i	$-0.569153\pi$
$541$	−5424.60	−0.431094	−0.215547	+	0.976493i	$0.569153\pi$
$542$	−5256.27	−0.416561
$543$	2692.24	0.212772
$544$	−1619.66	−0.127652
$545$	−28430.1	−2.23451
$546$	2108.34	0.165254
$547$	9964.36	0.778876	0.389438	−	0.921053i	$-0.372669\pi$
$547$	9964.36	0.778876	0.389438	+	0.921053i	$0.372669\pi$
$548$	−6443.05	−0.502251
$549$	−5666.18	−0.440486
$550$	7076.45	0.548620
$551$	3253.97	0.251586
$552$	−4886.86	−0.376809
$553$	265.156	0.0203898
$554$	−2073.35	−0.159004
$555$	−20324.4	−1.55446
$556$	−5911.13	−0.450877
$557$	17956.5	1.36597	0.682983	−	0.730434i	$-0.260682\pi$
$557$	17956.5	1.36597	0.682983	+	0.730434i	$0.260682\pi$
$558$	1487.13	0.112823
$559$	5273.79	0.399029
$560$	2183.33	0.164755
$561$	−2106.74	−0.158550
$562$	−7377.45	−0.553735
$563$	12658.0	0.947554	0.473777	−	0.880645i	$-0.342890\pi$
$563$	12658.0	0.947554	0.473777	+	0.880645i	$0.342890\pi$
$564$	−1393.23	−0.104017
$565$	12694.6	0.945251
$566$	4955.82	0.368037
$567$	−567.000	−0.0419961
$568$	6557.50	0.484413
$569$	−4324.46	−0.318613	−0.159307	−	0.987229i	$-0.550926\pi$
$569$	−4324.46	−0.318613	−0.159307	+	0.987229i	$0.550926\pi$
$570$	−2222.32	−0.163303
$571$	13614.9	0.997839	0.498920	−	0.866648i	$-0.333730\pi$
$571$	13614.9	0.997839	0.498920	+	0.866648i	$0.333730\pi$
$572$	−2785.91	−0.203644
$573$	−3249.54	−0.236914
$574$	−6367.61	−0.463030
$575$	51926.4	3.76605
$576$	576.000	0.0416667
$577$	−10167.4	−0.733577	−0.366789	−	0.930304i	$-0.619543\pi$
$577$	−10167.4	−0.733577	−0.366789	+	0.930304i	$0.619543\pi$
$578$	4702.35	0.338395
$579$	−15102.9	−1.08403
$580$	13354.3	0.956047
$581$	−3957.89	−0.282618
$582$	−9346.71	−0.665694
$583$	5344.50	0.379668
$584$	943.696	0.0668672
$585$	−8807.14	−0.622445
$586$	16218.2	1.14329
$587$	1801.02	0.126638	0.0633188	−	0.997993i	$-0.479832\pi$
$587$	1801.02	0.126638	0.0633188	+	0.997993i	$0.479832\pi$
$588$	588.000	0.0412393
$589$	1569.75	0.109814
$590$	−10343.2	−0.721736
$591$	8549.98	0.595092
$592$	5560.52	0.386041
$593$	−9778.36	−0.677148	−0.338574	−	0.940940i	$-0.609945\pi$
$593$	−9778.36	−0.677148	−0.338574	+	0.940940i	$0.609945\pi$
$594$	749.220	0.0517523
$595$	6906.76	0.475881
$596$	3804.19	0.261453
$597$	−3561.18	−0.244136
$598$	−20442.7	−1.39794
$599$	20828.4	1.42074	0.710371	−	0.703827i	$-0.248527\pi$
$599$	20828.4	1.42074	0.710371	+	0.703827i	$0.248527\pi$
$600$	−6120.41	−0.416441
$601$	−12965.3	−0.879978	−0.439989	−	0.898003i	$-0.645018\pi$
$601$	−12965.3	−0.879978	−0.439989	+	0.898003i	$0.645018\pi$
$602$	1470.82	0.0995784
$603$	−6904.80	−0.466311
$604$	−2370.17	−0.159670
$605$	22193.9	1.49143
$606$	−3943.67	−0.264357
$607$	−17535.8	−1.17258	−0.586290	−	0.810101i	$-0.699412\pi$
$607$	−17535.8	−1.17258	−0.586290	+	0.810101i	$0.699412\pi$
$608$	608.000	0.0405554
$609$	3596.49	0.239306
$610$	−24545.9	−1.62924
$611$	−5828.15	−0.385895
$612$	1822.12	0.120351
$613$	5841.45	0.384884	0.192442	−	0.981308i	$-0.438359\pi$
$613$	5841.45	0.384884	0.192442	+	0.981308i	$0.438359\pi$
$614$	3604.54	0.236918
$615$	26599.4	1.74405
$616$	−776.969	−0.0508198
$617$	10284.0	0.671016	0.335508	−	0.942037i	$-0.391092\pi$
$617$	10284.0	0.671016	0.335508	+	0.942037i	$0.391092\pi$
$618$	−8586.96	−0.558929
$619$	1574.19	0.102217	0.0511083	−	0.998693i	$-0.483725\pi$
$619$	1574.19	0.102217	0.0511083	+	0.998693i	$0.483725\pi$
$620$	6442.25	0.417302
$621$	5497.72	0.355259
$622$	4772.60	0.307659
$623$	10199.2	0.655893
$624$	2409.53	0.154581
$625$	17531.6	1.12203
$626$	15477.4	0.988180
$627$	790.844	0.0503720
$628$	−5786.85	−0.367708
$629$	17590.2	1.11505
$630$	−2456.25	−0.155332
$631$	−20538.4	−1.29576	−0.647878	−	0.761744i	$-0.724343\pi$
$631$	−20538.4	−1.29576	−0.647878	+	0.761744i	$0.724343\pi$
$632$	303.035	0.0190729
$633$	9188.37	0.576943
$634$	381.860	0.0239205
$635$	44543.8	2.78372
$636$	−4622.45	−0.288195
$637$	2459.73	0.152995
$638$	−4752.32	−0.294900
$639$	−7377.19	−0.456709
$640$	2495.24	0.154114
$641$	14692.7	0.905344	0.452672	−	0.891677i	$-0.350471\pi$
$641$	14692.7	0.905344	0.452672	+	0.891677i	$0.350471\pi$
$642$	−11871.1	−0.729774
$643$	−20336.9	−1.24729	−0.623645	−	0.781708i	$-0.714349\pi$
$643$	−20336.9	−1.24729	−0.623645	+	0.781708i	$0.714349\pi$
$644$	−5701.33	−0.348857
$645$	−6144.05	−0.375073
$646$	1923.35	0.117141
$647$	6750.17	0.410165	0.205082	−	0.978745i	$-0.434254\pi$
$647$	6750.17	0.410165	0.205082	+	0.978745i	$0.434254\pi$
$648$	−648.000	−0.0392837
$649$	3680.79	0.222625
$650$	−25603.0	−1.54497
$651$	1734.98	0.104454
$652$	3119.79	0.187394
$653$	5681.81	0.340500	0.170250	−	0.985401i	$-0.445543\pi$
$653$	5681.81	0.340500	0.170250	+	0.985401i	$0.445543\pi$
$654$	−8750.39	−0.523192
$655$	18649.3	1.11250
$656$	−7277.27	−0.433125
$657$	−1061.66	−0.0630430
$658$	−1625.43	−0.0963006
$659$	−22306.3	−1.31856	−0.659280	−	0.751898i	$-0.729139\pi$
$659$	−22306.3	−1.31856	−0.659280	+	0.751898i	$0.729139\pi$
$660$	3245.63	0.191418
$661$	−1729.19	−0.101752	−0.0508758	−	0.998705i	$-0.516201\pi$
$661$	−1729.19	−0.101752	−0.0508758	+	0.998705i	$0.516201\pi$
$662$	873.480	0.0512821
$663$	7622.31	0.446495
$664$	−4523.30	−0.264365
$665$	−2592.71	−0.151189
$666$	−6255.59	−0.363963
$667$	−34872.1	−2.02437
$668$	−13915.9	−0.806024
$669$	−8511.93	−0.491914
$670$	−29911.7	−1.72476
$671$	8735.01	0.502551
$672$	672.000	0.0385758
$673$	−21103.4	−1.20873	−0.604365	−	0.796707i	$-0.706573\pi$
$673$	−21103.4	−1.20873	−0.604365	+	0.796707i	$0.706573\pi$
$674$	−5430.04	−0.310323
$675$	6885.47	0.392625
$676$	1291.55	0.0734840
$677$	24724.0	1.40358	0.701788	−	0.712386i	$-0.252385\pi$
$677$	24724.0	1.40358	0.701788	+	0.712386i	$0.252385\pi$
$678$	3907.23	0.221322
$679$	−10904.5	−0.616313
$680$	7893.44	0.445146
$681$	−11937.5	−0.671728
$682$	−2292.57	−0.128720
$683$	−1775.25	−0.0994556	−0.0497278	−	0.998763i	$-0.515835\pi$
$683$	−1775.25	−0.0994556	−0.0497278	+	0.998763i	$0.515835\pi$
$684$	−684.000	−0.0382360
$685$	31400.3	1.75145
$686$	686.000	0.0381802
$687$	−2354.16	−0.130738
$688$	1680.94	0.0931471
$689$	−19336.7	−1.06919
$690$	23816.1	1.31401
$691$	−5148.33	−0.283432	−0.141716	−	0.989907i	$-0.545262\pi$
$691$	−5148.33	−0.283432	−0.141716	+	0.989907i	$0.545262\pi$
$692$	5819.57	0.319692
$693$	874.091	0.0479134
$694$	13988.0	0.765095
$695$	28807.9	1.57230
$696$	4110.27	0.223850
$697$	−23020.9	−1.25105
$698$	−22615.6	−1.22638
$699$	6824.47	0.369278
$700$	−7140.48	−0.385550
$701$	10566.6	0.569324	0.284662	−	0.958628i	$-0.408119\pi$
$701$	10566.6	0.569324	0.284662	+	0.958628i	$0.408119\pi$
$702$	−2710.72	−0.145740
$703$	−6603.12	−0.354255
$704$	−887.965	−0.0475376
$705$	6789.89	0.362726
$706$	12804.1	0.682559
$707$	−4600.94	−0.244747
$708$	−3183.51	−0.168988
$709$	−32546.2	−1.72397	−0.861986	−	0.506931i	$-0.830780\pi$
$709$	−32546.2	−1.72397	−0.861986	+	0.506931i	$0.830780\pi$
$710$	−31958.0	−1.68924
$711$	−340.915	−0.0179821
$712$	11656.2	0.613532
$713$	−16822.6	−0.883609
$714$	2125.81	0.111423
$715$	13577.1	0.710148
$716$	−11769.1	−0.614290
$717$	4262.98	0.222042
$718$	−22212.0	−1.15452
$719$	−1694.06	−0.0878689	−0.0439344	−	0.999034i	$-0.513989\pi$
$719$	−1694.06	−0.0878689	−0.0439344	+	0.999034i	$0.513989\pi$
$720$	−2807.14	−0.145300
$721$	−10018.1	−0.517468
$722$	−722.000	−0.0372161
$723$	−13368.1	−0.687640
$724$	3589.66	0.184266
$725$	−43674.6	−2.23729
$726$	6831.00	0.349204
$727$	25608.7	1.30643	0.653215	−	0.757173i	$-0.273420\pi$
$727$	25608.7	1.30643	0.653215	+	0.757173i	$0.273420\pi$
$728$	2811.12	0.143114
$729$	729.000	0.0370370
$730$	−4599.11	−0.233179
$731$	5317.49	0.269048
$732$	−7554.91	−0.381472
$733$	−19137.6	−0.964342	−0.482171	−	0.876077i	$-0.660152\pi$
$733$	−19137.6	−0.964342	−0.482171	+	0.876077i	$0.660152\pi$
$734$	−5190.67	−0.261023
$735$	−2865.62	−0.143810
$736$	−6515.81	−0.326326
$737$	10644.5	0.532015
$738$	8186.93	0.408354
$739$	−7483.15	−0.372493	−0.186246	−	0.982503i	$-0.559632\pi$
$739$	−7483.15	−0.372493	−0.186246	+	0.982503i	$0.559632\pi$
$740$	−27099.3	−1.34620
$741$	−2861.31	−0.141853
$742$	−5392.86	−0.266817
$743$	21857.2	1.07922	0.539611	−	0.841914i	$-0.318571\pi$
$743$	21857.2	1.07922	0.539611	+	0.841914i	$0.318571\pi$
$744$	1982.84	0.0977075
$745$	−18539.8	−0.911737
$746$	−13178.7	−0.646791
$747$	5088.71	0.249245
$748$	−2808.99	−0.137309
$749$	−13849.6	−0.675640
$750$	15207.4	0.740393
$751$	−5393.03	−0.262043	−0.131022	−	0.991380i	$-0.541826\pi$
$751$	−5393.03	−0.262043	−0.131022	+	0.991380i	$0.541826\pi$
$752$	−1857.63	−0.0900810
$753$	−10998.9	−0.532301
$754$	17194.1	0.830469
$755$	11551.0	0.556801
$756$	−756.000	−0.0363696
$757$	2529.43	0.121445	0.0607223	−	0.998155i	$-0.480660\pi$
$757$	2529.43	0.121445	0.0607223	+	0.998155i	$0.480660\pi$
$758$	−5244.65	−0.251312
$759$	−8475.31	−0.405315
$760$	−2963.09	−0.141425
$761$	5681.06	0.270616	0.135308	−	0.990804i	$-0.456798\pi$
$761$	5681.06	0.270616	0.135308	+	0.990804i	$0.456798\pi$
$762$	13710.0	0.651784
$763$	−10208.8	−0.484381
$764$	−4332.72	−0.205173
$765$	−8880.12	−0.419688
$766$	−1212.53	−0.0571939
$767$	−13317.3	−0.626935
$768$	768.000	0.0360844
$769$	−26911.8	−1.26198	−0.630991	−	0.775790i	$-0.717351\pi$
$769$	−26911.8	−1.26198	−0.630991	+	0.775790i	$0.717351\pi$
$770$	3786.57	0.177219
$771$	21083.0	0.984808
$772$	−20137.2	−0.938798
$773$	24266.8	1.12913	0.564563	−	0.825390i	$-0.309045\pi$
$773$	24266.8	1.12913	0.564563	+	0.825390i	$0.309045\pi$
$774$	−1891.06	−0.0878199
$775$	−21069.1	−0.976547
$776$	−12462.3	−0.576508
$777$	−7298.19	−0.336964
$778$	15221.9	0.701455
$779$	8641.76	0.397462
$780$	−11742.9	−0.539053
$781$	11372.7	0.521060
$782$	−20612.1	−0.942568
$783$	−4624.06	−0.211048
$784$	784.000	0.0357143
$785$	28202.3	1.28227
$786$	5740.00	0.260482
$787$	−16145.8	−0.731304	−0.365652	−	0.930752i	$-0.619154\pi$
$787$	−16145.8	−0.731304	−0.365652	+	0.930752i	$0.619154\pi$
$788$	11400.0	0.515365
$789$	−10280.4	−0.463869
$790$	−1476.85	−0.0665111
$791$	4558.44	0.204905
$792$	998.961	0.0448188
$793$	−31603.7	−1.41524
$794$	−133.093	−0.00594875
$795$	22527.6	1.00499
$796$	−4748.24	−0.211428
$797$	−20133.7	−0.894820	−0.447410	−	0.894329i	$-0.647653\pi$
$797$	−20133.7	−0.894820	−0.447410	+	0.894329i	$0.647653\pi$
$798$	−798.000	−0.0353996
$799$	−5876.44	−0.260192
$800$	−8160.55	−0.360649
$801$	−13113.2	−0.578443
$802$	17880.5	0.787261
$803$	1636.66	0.0719258
$804$	−9206.41	−0.403837
$805$	27785.5	1.21653
$806$	8294.62	0.362488
$807$	15869.4	0.692232
$808$	−5258.22	−0.228940
$809$	−22330.3	−0.970447	−0.485224	−	0.874390i	$-0.661262\pi$
$809$	−22330.3	−0.970447	−0.485224	+	0.874390i	$0.661262\pi$
$810$	3158.03	0.136990
$811$	−15572.9	−0.674275	−0.337138	−	0.941455i	$-0.609459\pi$
$811$	−15572.9	−0.674275	−0.337138	+	0.941455i	$0.609459\pi$
$812$	4795.32	0.207245
$813$	7884.41	0.340121
$814$	9643.65	0.415246
$815$	−15204.3	−0.653478
$816$	2429.49	0.104227
$817$	−1996.11	−0.0854776
$818$	−24739.8	−1.05747
$819$	−3162.50	−0.134929
$820$	35465.8	1.51039
$821$	33286.6	1.41500	0.707498	−	0.706716i	$-0.249824\pi$
$821$	33286.6	1.41500	0.707498	+	0.706716i	$0.249824\pi$
$822$	9664.58	0.410086
$823$	5748.37	0.243470	0.121735	−	0.992563i	$-0.461154\pi$
$823$	5748.37	0.243470	0.121735	+	0.992563i	$0.461154\pi$
$824$	−11449.3	−0.484047
$825$	−10614.7	−0.447946
$826$	−3714.09	−0.156453
$827$	26327.6	1.10701	0.553506	−	0.832845i	$-0.313289\pi$
$827$	26327.6	1.10701	0.553506	+	0.832845i	$0.313289\pi$
$828$	7330.29	0.307663
$829$	12026.2	0.503843	0.251921	−	0.967748i	$-0.418938\pi$
$829$	12026.2	0.503843	0.251921	+	0.967748i	$0.418938\pi$
$830$	22044.3	0.921892
$831$	3110.03	0.129826
$832$	3212.70	0.133871
$833$	2480.11	0.103158
$834$	8866.70	0.368140
$835$	67819.4	2.81076
$836$	1054.46	0.0436235
$837$	−2230.69	−0.0921195
$838$	7733.58	0.318797
$839$	39917.3	1.64255	0.821274	−	0.570534i	$-0.193264\pi$
$839$	39917.3	1.64255	0.821274	+	0.570534i	$0.193264\pi$
$840$	−3275.00	−0.134522
$841$	4941.47	0.202611
$842$	33939.6	1.38912
$843$	11066.2	0.452123
$844$	12251.2	0.499648
$845$	−6294.40	−0.256253
$846$	2089.84	0.0849292
$847$	7969.50	0.323300
$848$	−6163.27	−0.249584
$849$	−7433.73	−0.300501
$850$	−25815.1	−1.04171
$851$	70764.3	2.85049
$852$	−9836.25	−0.395521
$853$	−28473.1	−1.14291	−0.571453	−	0.820635i	$-0.693620\pi$
$853$	−28473.1	−1.14291	−0.571453	+	0.820635i	$0.693620\pi$
$854$	−8814.06	−0.353174
$855$	3333.48	0.133336
$856$	−15828.1	−0.632003
$857$	−30540.7	−1.21733	−0.608664	−	0.793428i	$-0.708294\pi$
$857$	−30540.7	−1.21733	−0.608664	+	0.793428i	$0.708294\pi$
$858$	4178.86	0.166275
$859$	−47768.7	−1.89738	−0.948689	−	0.316210i	$-0.897589\pi$
$859$	−47768.7	−1.89738	−0.948689	+	0.316210i	$0.897589\pi$
$860$	−8192.07	−0.324822
$861$	9551.42	0.378062
$862$	−3223.45	−0.127368
$863$	22191.5	0.875326	0.437663	−	0.899139i	$-0.355806\pi$
$863$	22191.5	0.875326	0.437663	+	0.899139i	$0.355806\pi$
$864$	−864.000	−0.0340207
$865$	−28361.7	−1.11483
$866$	31159.3	1.22268
$867$	−7053.53	−0.276298
$868$	2313.31	0.0904595
$869$	525.556	0.0205159
$870$	−20031.5	−0.780609
$871$	−38512.3	−1.49821
$872$	−11667.2	−0.453097
$873$	14020.1	0.543537
$874$	7737.52	0.299457
$875$	17741.9	0.685470
$876$	−1415.54	−0.0545968
$877$	11264.1	0.433707	0.216853	−	0.976204i	$-0.430421\pi$
$877$	11264.1	0.433707	0.216853	+	0.976204i	$0.430421\pi$
$878$	34536.6	1.32751
$879$	−24327.2	−0.933489
$880$	4327.50	0.165773
$881$	23170.2	0.886066	0.443033	−	0.896505i	$-0.353902\pi$
$881$	23170.2	0.886066	0.443033	+	0.896505i	$0.353902\pi$
$882$	−882.000	−0.0336718
$883$	48645.6	1.85397	0.926985	−	0.375100i	$-0.122392\pi$
$883$	48645.6	1.85397	0.926985	+	0.375100i	$0.122392\pi$
$884$	10163.1	0.386676
$885$	15514.9	0.589295
$886$	−5829.60	−0.221049
$887$	−37889.6	−1.43428	−0.717141	−	0.696928i	$-0.754550\pi$
$887$	−37889.6	−1.43428	−0.717141	+	0.696928i	$0.754550\pi$
$888$	−8340.79	−0.315201
$889$	15995.0	0.603435
$890$	−56806.6	−2.13951
$891$	−1123.83	−0.0422556
$892$	−11349.2	−0.426010
$893$	2205.94	0.0826640
$894$	−5706.29	−0.213475
$895$	57356.8	2.14215
$896$	896.000	0.0334077
$897$	30664.1	1.14141
$898$	−4990.93	−0.185467
$899$	14149.3	0.524923
$900$	9180.62	0.340023
$901$	−19496.9	−0.720906
$902$	−12621.0	−0.465891
$903$	−2206.23	−0.0813054
$904$	5209.65	0.191671
$905$	−17494.2	−0.642572
$906$	3555.25	0.130370
$907$	−8927.34	−0.326822	−0.163411	−	0.986558i	$-0.552250\pi$
$907$	−8927.34	−0.326822	−0.163411	+	0.986558i	$0.552250\pi$
$908$	−15916.7	−0.581733
$909$	5915.50	0.215847
$910$	−13700.0	−0.499066
$911$	−29895.1	−1.08723	−0.543617	−	0.839333i	$-0.682946\pi$
$911$	−29895.1	−1.08723	−0.543617	+	0.839333i	$0.682946\pi$
$912$	−912.000	−0.0331133
$913$	−7844.79	−0.284364
$914$	23812.2	0.861747
$915$	36818.9	1.33027
$916$	−3138.88	−0.113222
$917$	6696.67	0.241160
$918$	−2733.18	−0.0982662
$919$	15251.1	0.547429	0.273715	−	0.961811i	$-0.411748\pi$
$919$	15251.1	0.547429	0.273715	+	0.961811i	$0.411748\pi$
$920$	31754.9	1.13796
$921$	−5406.82	−0.193443
$922$	25732.5	0.919149
$923$	−41147.1	−1.46736
$924$	1165.45	0.0414942
$925$	88626.8	3.15031
$926$	−35313.3	−1.25320
$927$	12880.4	0.456364
$928$	5480.37	0.193860
$929$	12792.5	0.451783	0.225892	−	0.974152i	$-0.427470\pi$
$929$	12792.5	0.451783	0.225892	+	0.974152i	$0.427470\pi$
$930$	−9663.37	−0.340725
$931$	−931.000	−0.0327737
$932$	9099.29	0.319804
$933$	−7158.90	−0.251203
$934$	−31780.5	−1.11337
$935$	13689.6	0.478823
$936$	−3614.29	−0.126215
$937$	−35225.5	−1.22814	−0.614069	−	0.789252i	$-0.710468\pi$
$937$	−35225.5	−1.22814	−0.614069	+	0.789252i	$0.710468\pi$
$938$	−10740.8	−0.373880
$939$	−23216.1	−0.806845
$940$	9053.19	0.314130
$941$	−15032.2	−0.520759	−0.260380	−	0.965506i	$-0.583848\pi$
$941$	−15032.2	−0.520759	−0.260380	+	0.965506i	$0.583848\pi$
$942$	8680.27	0.300232
$943$	−92612.0	−3.19816
$944$	−4244.68	−0.146348
$945$	3684.37	0.126828
$946$	2915.26	0.100194
$947$	−2132.31	−0.0731686	−0.0365843	−	0.999331i	$-0.511648\pi$
$947$	−2132.31	−0.0731686	−0.0365843	+	0.999331i	$0.511648\pi$
$948$	−454.553	−0.0155730
$949$	−5921.52	−0.202551
$950$	9690.66	0.330954
$951$	−572.789	−0.0195310
$952$	2834.41	0.0964955
$953$	−36667.2	−1.24635	−0.623173	−	0.782084i	$-0.714157\pi$
$953$	−36667.2	−1.24635	−0.623173	+	0.782084i	$0.714157\pi$
$954$	6933.68	0.235310
$955$	21115.5	0.715480
$956$	5683.98	0.192294
$957$	7128.48	0.240785
$958$	31042.3	1.04690
$959$	11275.3	0.379666
$960$	−3742.85	−0.125833
$961$	−22965.2	−0.770878
$962$	−34891.2	−1.16937
$963$	17806.7	0.595858
$964$	−17824.1	−0.595514
$965$	98138.6	3.27378
$966$	8552.00	0.284841
$967$	58116.8	1.93269	0.966344	−	0.257253i	$-0.0828175\pi$
$967$	58116.8	1.93269	0.966344	+	0.257253i	$0.0828175\pi$
$968$	9108.00	0.302420
$969$	−2885.02	−0.0956453
$970$	60735.0	2.01040
$971$	−44479.3	−1.47004	−0.735020	−	0.678045i	$-0.762827\pi$
$971$	−44479.3	−1.47004	−0.735020	+	0.678045i	$0.762827\pi$
$972$	972.000	0.0320750
$973$	10344.5	0.340831
$974$	−29181.8	−0.960007
$975$	38404.4	1.26146
$976$	−10073.2	−0.330364
$977$	−49804.2	−1.63089	−0.815444	−	0.578837i	$-0.803507\pi$
$977$	−49804.2	−1.63089	−0.815444	+	0.578837i	$0.803507\pi$
$978$	−4679.69	−0.153006
$979$	20215.4	0.659947
$980$	−3820.83	−0.124543
$981$	13125.6	0.427184
$982$	96.8538	0.00314738
$983$	−5090.00	−0.165153	−0.0825767	−	0.996585i	$-0.526315\pi$
$983$	−5090.00	−0.165153	−0.0825767	+	0.996585i	$0.526315\pi$
$984$	10915.9	0.353645
$985$	−55557.9	−1.79718
$986$	17336.6	0.559949
$987$	2438.14	0.0786292
$988$	−3815.09	−0.122848
$989$	21392.0	0.687790
$990$	−4868.44	−0.156292
$991$	−32072.7	−1.02807	−0.514037	−	0.857768i	$-0.671851\pi$
$991$	−32072.7	−1.02807	−0.514037	+	0.857768i	$0.671851\pi$
$992$	2643.78	0.0846171
$993$	−1310.22	−0.0418717
$994$	−11475.6	−0.366182
$995$	23140.6	0.737292
$996$	6784.95	0.215853
$997$	12158.5	0.386222	0.193111	−	0.981177i	$-0.438142\pi$
$997$	12158.5	0.386222	0.193111	+	0.981177i	$0.438142\pi$
$998$	−10200.2	−0.323530
$999$	9383.38	0.297174

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -19.4940 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -19.4940 q^{5} -6.00000 q^{6} -7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +38.9881 q^{10} -13.8745 q^{11} +12.0000 q^{12} +50.1985 q^{13} +14.0000 q^{14} -58.4821 q^{15} +16.0000 q^{16} +50.6145 q^{17} -18.0000 q^{18} -19.0000 q^{19} -77.9761 q^{20} -21.0000 q^{21} +27.7489 q^{22} +203.619 q^{23} -24.0000 q^{24} +255.017 q^{25} -100.397 q^{26} +27.0000 q^{27} -28.0000 q^{28} -171.261 q^{29} +116.964 q^{30} -82.6182 q^{31} -32.0000 q^{32} -41.6234 q^{33} -101.229 q^{34} +136.458 q^{35} +36.0000 q^{36} +347.533 q^{37} +38.0000 q^{38} +150.595 q^{39} +155.952 q^{40} -454.830 q^{41} +42.0000 q^{42} +105.059 q^{43} -55.4978 q^{44} -175.446 q^{45} -407.238 q^{46} -116.102 q^{47} +48.0000 q^{48} +49.0000 q^{49} -510.035 q^{50} +151.843 q^{51} +200.794 q^{52} -385.204 q^{53} -54.0000 q^{54} +270.469 q^{55} +56.0000 q^{56} -57.0000 q^{57} +342.523 q^{58} -265.292 q^{59} -233.928 q^{60} -629.575 q^{61} +165.236 q^{62} -63.0000 q^{63} +64.0000 q^{64} -978.571 q^{65} +83.2467 q^{66} -767.200 q^{67} +202.458 q^{68} +610.857 q^{69} -272.916 q^{70} -819.687 q^{71} -72.0000 q^{72} -117.962 q^{73} -695.065 q^{74} +765.052 q^{75} -76.0000 q^{76} +97.1212 q^{77} -301.191 q^{78} -37.8794 q^{79} -311.905 q^{80} +81.0000 q^{81} +909.659 q^{82} +565.412 q^{83} -84.0000 q^{84} -986.680 q^{85} -210.117 q^{86} -513.784 q^{87} +110.996 q^{88} -1457.03 q^{89} +350.893 q^{90} -351.389 q^{91} +814.476 q^{92} -247.855 q^{93} +232.204 q^{94} +370.387 q^{95} -96.0000 q^{96} +1557.79 q^{97} -98.0000 q^{98} -124.870 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9}+O(q^{10}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9	\( 4 q - 8 q^{2} + 12 q^{3} + 16 q^{4} - 10 q^{5} - 24 q^{6} - 28 q^{7} - 32 q^{8} + 36 q^{9} + 20 q^{10} + 4 q^{11} + 48 q^{12} + 16 q^{13} + 56 q^{14} - 30 q^{15} + 64 q^{16} - 66 q^{17} - 72 q^{18} - 76 q^{19} - 40 q^{20} - 84 q^{21} - 8 q^{22} + 32 q^{23} - 96 q^{24} + 200 q^{25} - 32 q^{26} + 108 q^{27} - 112 q^{28} - 10 q^{29} + 60 q^{30} + 108 q^{31} - 128 q^{32} + 12 q^{33} + 132 q^{34} + 70 q^{35} + 144 q^{36} - 116 q^{37} + 152 q^{38} + 48 q^{39} + 80 q^{40} - 988 q^{41} + 168 q^{42} - 448 q^{43} + 16 q^{44} - 90 q^{45} - 64 q^{46} - 850 q^{47} + 192 q^{48} + 196 q^{49} - 400 q^{50} - 198 q^{51} + 64 q^{52} - 998 q^{53} - 216 q^{54} - 904 q^{55} + 224 q^{56} - 228 q^{57} + 20 q^{58} - 680 q^{59} - 120 q^{60} - 208 q^{61} - 216 q^{62} - 252 q^{63} + 256 q^{64} - 676 q^{65} - 24 q^{66} + 108 q^{67} - 264 q^{68} + 96 q^{69} - 140 q^{70} - 1050 q^{71} - 288 q^{72} + 100 q^{73} + 232 q^{74} + 600 q^{75} - 304 q^{76} - 28 q^{77} - 96 q^{78} + 1540 q^{79} - 160 q^{80} + 324 q^{81} + 1976 q^{82} + 94 q^{83} - 336 q^{84} - 844 q^{85} + 896 q^{86} - 30 q^{87} - 32 q^{88} - 2284 q^{89} + 180 q^{90} - 112 q^{91} + 128 q^{92} + 324 q^{93} + 1700 q^{94} + 190 q^{95} - 384 q^{96} - 136 q^{97} - 392 q^{98} + 36 q^{99}+O(q^{100}) \) 4 * q - 8 * q^2 + 12 * q^3 + 16 * q^4 - 10 * q^5 - 24 * q^6 - 28 * q^7 - 32 * q^8 + 36 * q^9 + 20 * q^10 + 4 * q^11 + 48 * q^12 + 16 * q^13 + 56 * q^14 - 30 * q^15 + 64 * q^16 - 66 * q^17 - 72 * q^18 - 76 * q^19 - 40 * q^20 - 84 * q^21 - 8 * q^22 + 32 * q^23 - 96 * q^24 + 200 * q^25 - 32 * q^26 + 108 * q^27 - 112 * q^28 - 10 * q^29 + 60 * q^30 + 108 * q^31 - 128 * q^32 + 12 * q^33 + 132 * q^34 + 70 * q^35 + 144 * q^36 - 116 * q^37 + 152 * q^38 + 48 * q^39 + 80 * q^40 - 988 * q^41 + 168 * q^42 - 448 * q^43 + 16 * q^44 - 90 * q^45 - 64 * q^46 - 850 * q^47 + 192 * q^48 + 196 * q^49 - 400 * q^50 - 198 * q^51 + 64 * q^52 - 998 * q^53 - 216 * q^54 - 904 * q^55 + 224 * q^56 - 228 * q^57 + 20 * q^58 - 680 * q^59 - 120 * q^60 - 208 * q^61 - 216 * q^62 - 252 * q^63 + 256 * q^64 - 676 * q^65 - 24 * q^66 + 108 * q^67 - 264 * q^68 + 96 * q^69 - 140 * q^70 - 1050 * q^71 - 288 * q^72 + 100 * q^73 + 232 * q^74 + 600 * q^75 - 304 * q^76 - 28 * q^77 - 96 * q^78 + 1540 * q^79 - 160 * q^80 + 324 * q^81 + 1976 * q^82 + 94 * q^83 - 336 * q^84 - 844 * q^85 + 896 * q^86 - 30 * q^87 - 32 * q^88 - 2284 * q^89 + 180 * q^90 - 112 * q^91 + 128 * q^92 + 324 * q^93 + 1700 * q^94 + 190 * q^95 - 384 * q^96 - 136 * q^97 - 392 * q^98 + 36 * q^99

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