LMFDB - Embedded newform 798.4.a.g.1.3

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:	$3$
Coefficient field:	3.3.42440.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 40x + 72 $ x^3 - x^2 - 40*x + 72
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2\cdot 3 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-6.64715$ 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)

$f(q)$	$=$	$q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.41586 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.41586 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -10.8317 q^{10} +17.0512 q^{11} +12.0000 q^{12} -49.6634 q^{13} -14.0000 q^{14} +16.2476 q^{15} +16.0000 q^{16} -110.789 q^{17} -18.0000 q^{18} +19.0000 q^{19} +21.6634 q^{20} +21.0000 q^{21} -34.1023 q^{22} -30.9488 q^{23} -24.0000 q^{24} -95.6685 q^{25} +99.3269 q^{26} +27.0000 q^{27} +28.0000 q^{28} -172.626 q^{29} -32.4951 q^{30} -267.807 q^{31} -32.0000 q^{32} +51.1535 q^{33} +221.578 q^{34} +37.9110 q^{35} +36.0000 q^{36} +299.981 q^{37} -38.0000 q^{38} -148.990 q^{39} -43.3269 q^{40} +108.017 q^{41} -42.0000 q^{42} -322.114 q^{43} +68.2047 q^{44} +48.7427 q^{45} +61.8977 q^{46} -426.533 q^{47} +48.0000 q^{48} +49.0000 q^{49} +191.337 q^{50} -332.366 q^{51} -198.654 q^{52} -136.747 q^{53} -54.0000 q^{54} +92.3467 q^{55} -56.0000 q^{56} +57.0000 q^{57} +345.251 q^{58} +303.707 q^{59} +64.9903 q^{60} +419.278 q^{61} +535.614 q^{62} +63.0000 q^{63} +64.0000 q^{64} -268.970 q^{65} -102.307 q^{66} -709.778 q^{67} -443.155 q^{68} -92.8465 q^{69} -75.8220 q^{70} +37.6851 q^{71} -72.0000 q^{72} +836.090 q^{73} -599.961 q^{74} -287.005 q^{75} +76.0000 q^{76} +119.358 q^{77} +297.981 q^{78} -52.3513 q^{79} +86.6537 q^{80} +81.0000 q^{81} -216.033 q^{82} -762.688 q^{83} +84.0000 q^{84} -600.016 q^{85} +644.228 q^{86} -517.877 q^{87} -136.409 q^{88} -406.261 q^{89} -97.4854 q^{90} -347.644 q^{91} -123.795 q^{92} -803.422 q^{93} +853.067 q^{94} +102.901 q^{95} -96.0000 q^{96} +1481.44 q^{97} -98.0000 q^{98} +153.461 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 20 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 20 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 20 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} + 40 q^{10} - 2 q^{11} + 36 q^{12} - 4 q^{13} - 42 q^{14} - 60 q^{15} + 48 q^{16} - 156 q^{17} - 54 q^{18} + 57 q^{19} - 80 q^{20} + 63 q^{21} + 4 q^{22} - 146 q^{23} - 72 q^{24} + 61 q^{25} + 8 q^{26} + 81 q^{27} + 84 q^{28} - 66 q^{29} + 120 q^{30} - 64 q^{31} - 96 q^{32} - 6 q^{33} + 312 q^{34} - 140 q^{35} + 108 q^{36} + 30 q^{37} - 114 q^{38} - 12 q^{39} + 160 q^{40} + 10 q^{41} - 126 q^{42} + 92 q^{43} - 8 q^{44} - 180 q^{45} + 292 q^{46} - 528 q^{47} + 144 q^{48} + 147 q^{49} - 122 q^{50} - 468 q^{51} - 16 q^{52} - 722 q^{53} - 162 q^{54} + 16 q^{55} - 168 q^{56} + 171 q^{57} + 132 q^{58} - 268 q^{59} - 240 q^{60} - 366 q^{61} + 128 q^{62} + 189 q^{63} + 192 q^{64} - 1184 q^{65} + 12 q^{66} - 926 q^{67} - 624 q^{68} - 438 q^{69} + 280 q^{70} - 252 q^{71} - 216 q^{72} - 58 q^{73} - 60 q^{74} + 183 q^{75} + 228 q^{76} - 14 q^{77} + 24 q^{78} - 534 q^{79} - 320 q^{80} + 243 q^{81} - 20 q^{82} - 1672 q^{83} + 252 q^{84} + 1332 q^{85} - 184 q^{86} - 198 q^{87} + 16 q^{88} - 750 q^{89} + 360 q^{90} - 28 q^{91} - 584 q^{92} - 192 q^{93} + 1056 q^{94} - 380 q^{95} - 288 q^{96} + 820 q^{97} - 294 q^{98} - 18 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 20 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9 + 40 * q^10 - 2 * q^11 + 36 * q^12 - 4 * q^13 - 42 * q^14 - 60 * q^15 + 48 * q^16 - 156 * q^17 - 54 * q^18 + 57 * q^19 - 80 * q^20 + 63 * q^21 + 4 * q^22 - 146 * q^23 - 72 * q^24 + 61 * q^25 + 8 * q^26 + 81 * q^27 + 84 * q^28 - 66 * q^29 + 120 * q^30 - 64 * q^31 - 96 * q^32 - 6 * q^33 + 312 * q^34 - 140 * q^35 + 108 * q^36 + 30 * q^37 - 114 * q^38 - 12 * q^39 + 160 * q^40 + 10 * q^41 - 126 * q^42 + 92 * q^43 - 8 * q^44 - 180 * q^45 + 292 * q^46 - 528 * q^47 + 144 * q^48 + 147 * q^49 - 122 * q^50 - 468 * q^51 - 16 * q^52 - 722 * q^53 - 162 * q^54 + 16 * q^55 - 168 * q^56 + 171 * q^57 + 132 * q^58 - 268 * q^59 - 240 * q^60 - 366 * q^61 + 128 * q^62 + 189 * q^63 + 192 * q^64 - 1184 * q^65 + 12 * q^66 - 926 * q^67 - 624 * q^68 - 438 * q^69 + 280 * q^70 - 252 * q^71 - 216 * q^72 - 58 * q^73 - 60 * q^74 + 183 * q^75 + 228 * q^76 - 14 * q^77 + 24 * q^78 - 534 * q^79 - 320 * q^80 + 243 * q^81 - 20 * q^82 - 1672 * q^83 + 252 * q^84 + 1332 * q^85 - 184 * q^86 - 198 * q^87 + 16 * q^88 - 750 * q^89 + 360 * q^90 - 28 * q^91 - 584 * q^92 - 192 * q^93 + 1056 * q^94 - 380 * q^95 - 288 * q^96 + 820 * q^97 - 294 * q^98 - 18 * 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
$5$	5.41586	0.484409	0.242204	−	0.970225i	$-0.422130\pi$
$5$	5.41586	0.484409	0.242204	+	0.970225i	$0.422130\pi$
$6$	−6.00000	−0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−10.8317	−0.342529
$11$	17.0512	0.467375	0.233687	−	0.972312i	$-0.424921\pi$
$11$	17.0512	0.467375	0.233687	+	0.972312i	$0.424921\pi$
$12$	12.0000	0.288675
$13$	−49.6634	−1.05955	−0.529775	−	0.848138i	$-0.677724\pi$
$13$	−49.6634	−1.05955	−0.529775	+	0.848138i	$0.677724\pi$
$14$	−14.0000	−0.267261
$15$	16.2476	0.279674
$16$	16.0000	0.250000
$17$	−110.789	−1.58060	−0.790301	−	0.612719i	$-0.790076\pi$
$17$	−110.789	−1.58060	−0.790301	+	0.612719i	$0.790076\pi$
$18$	−18.0000	−0.235702
$19$	19.0000	0.229416
$19$	19.0000	0.229416
$20$	21.6634	0.242204
$21$	21.0000	0.218218
$22$	−34.1023	−0.330484
$23$	−30.9488	−0.280577	−0.140289	−	0.990111i	$-0.544803\pi$
$23$	−30.9488	−0.280577	−0.140289	+	0.990111i	$0.544803\pi$
$24$	−24.0000	−0.204124
$25$	−95.6685	−0.765348
$26$	99.3269	0.749215
$27$	27.0000	0.192450
$28$	28.0000	0.188982
$29$	−172.626	−1.10537	−0.552686	−	0.833390i	$-0.686397\pi$
$29$	−172.626	−1.10537	−0.552686	+	0.833390i	$0.686397\pi$
$30$	−32.4951	−0.197759
$31$	−267.807	−1.55160	−0.775800	−	0.630979i	$-0.782653\pi$
$31$	−267.807	−1.55160	−0.775800	+	0.630979i	$0.782653\pi$
$32$	−32.0000	−0.176777
$33$	51.1535	0.269839
$34$	221.578	1.11765
$35$	37.9110	0.183089
$36$	36.0000	0.166667
$37$	299.981	1.33288	0.666439	−	0.745559i	$-0.267818\pi$
$37$	299.981	1.33288	0.666439	+	0.745559i	$0.267818\pi$
$38$	−38.0000	−0.162221
$39$	−148.990	−0.611732
$40$	−43.3269	−0.171264
$41$	108.017	0.411448	0.205724	−	0.978610i	$-0.434045\pi$
$41$	108.017	0.411448	0.205724	+	0.978610i	$0.434045\pi$
$42$	−42.0000	−0.154303
$43$	−322.114	−1.14237	−0.571186	−	0.820821i	$-0.693516\pi$
$43$	−322.114	−1.14237	−0.571186	+	0.820821i	$0.693516\pi$
$44$	68.2047	0.233687
$45$	48.7427	0.161470
$46$	61.8977	0.198398
$47$	−426.533	−1.32375	−0.661875	−	0.749614i	$-0.730239\pi$
$47$	−426.533	−1.32375	−0.661875	+	0.749614i	$0.730239\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	191.337	0.541183
$51$	−332.366	−0.912561
$52$	−198.654	−0.529775
$53$	−136.747	−0.354409	−0.177205	−	0.984174i	$-0.556705\pi$
$53$	−136.747	−0.354409	−0.177205	+	0.984174i	$0.556705\pi$
$54$	−54.0000	−0.136083
$55$	92.3467	0.226400
$56$	−56.0000	−0.133631
$57$	57.0000	0.132453
$58$	345.251	0.781616
$59$	303.707	0.670157	0.335078	−	0.942190i	$-0.391237\pi$
$59$	303.707	0.670157	0.335078	+	0.942190i	$0.391237\pi$
$60$	64.9903	0.139837
$61$	419.278	0.880050	0.440025	−	0.897986i	$-0.354970\pi$
$61$	419.278	0.880050	0.440025	+	0.897986i	$0.354970\pi$
$62$	535.614	1.09715
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	−268.970	−0.513256
$66$	−102.307	−0.190805
$67$	−709.778	−1.29423	−0.647113	−	0.762394i	$-0.724024\pi$
$67$	−709.778	−1.29423	−0.647113	+	0.762394i	$0.724024\pi$
$68$	−443.155	−0.790301
$69$	−92.8465	−0.161991
$70$	−75.8220	−0.129464
$71$	37.6851	0.0629916	0.0314958	−	0.999504i	$-0.489973\pi$
$71$	37.6851	0.0629916	0.0314958	+	0.999504i	$0.489973\pi$
$72$	−72.0000	−0.117851
$73$	836.090	1.34051	0.670253	−	0.742133i	$-0.266186\pi$
$73$	836.090	1.34051	0.670253	+	0.742133i	$0.266186\pi$
$74$	−599.961	−0.942487
$75$	−287.005	−0.441874
$76$	76.0000	0.114708
$77$	119.358	0.176651
$78$	297.981	0.432560
$79$	−52.3513	−0.0745568	−0.0372784	−	0.999305i	$-0.511869\pi$
$79$	−52.3513	−0.0745568	−0.0372784	+	0.999305i	$0.511869\pi$
$80$	86.6537	0.121102
$81$	81.0000	0.111111
$82$	−216.033	−0.290937
$83$	−762.688	−1.00863	−0.504313	−	0.863521i	$-0.668254\pi$
$83$	−762.688	−1.00863	−0.504313	+	0.863521i	$0.668254\pi$
$84$	84.0000	0.109109
$85$	−600.016	−0.765658
$86$	644.228	0.807778
$87$	−517.877	−0.638186
$88$	−136.409	−0.165242
$89$	−406.261	−0.483860	−0.241930	−	0.970294i	$-0.577780\pi$
$89$	−406.261	−0.483860	−0.241930	+	0.970294i	$0.577780\pi$
$90$	−97.4854	−0.114176
$91$	−347.644	−0.400472
$92$	−123.795	−0.140289
$93$	−803.422	−0.895817
$94$	853.067	0.936033
$95$	102.901	0.111131
$96$	−96.0000	−0.102062
$97$	1481.44	1.55070	0.775349	−	0.631534i	$-0.217574\pi$
$97$	1481.44	1.55070	0.775349	+	0.631534i	$0.217574\pi$
$98$	−98.0000	−0.101015
$99$	153.461	0.155792
$100$	−382.674	−0.382674
$101$	699.119	0.688762	0.344381	−	0.938830i	$-0.388089\pi$
$101$	699.119	0.688762	0.344381	+	0.938830i	$0.388089\pi$
$102$	664.733	0.645278
$103$	866.665	0.829078	0.414539	−	0.910032i	$-0.363943\pi$
$103$	866.665	0.829078	0.414539	+	0.910032i	$0.363943\pi$
$104$	397.307	0.374608
$105$	113.733	0.105707
$106$	273.495	0.250605
$107$	−638.664	−0.577028	−0.288514	−	0.957476i	$-0.593161\pi$
$107$	−638.664	−0.577028	−0.288514	+	0.957476i	$0.593161\pi$
$108$	108.000	0.0962250
$109$	815.109	0.716269	0.358134	−	0.933670i	$-0.383413\pi$
$109$	815.109	0.716269	0.358134	+	0.933670i	$0.383413\pi$
$110$	−184.693	−0.160089
$111$	899.942	0.769538
$112$	112.000	0.0944911
$113$	−543.342	−0.452330	−0.226165	−	0.974089i	$-0.572619\pi$
$113$	−543.342	−0.452330	−0.226165	+	0.974089i	$0.572619\pi$
$114$	−114.000	−0.0936586
$115$	−167.614	−0.135914
$116$	−690.502	−0.552686
$117$	−446.971	−0.353184
$118$	−607.413	−0.473872
$119$	−775.522	−0.597411
$120$	−129.981	−0.0988796
$121$	−1040.26	−0.781561
$122$	−838.556	−0.622289
$123$	324.050	0.237549
$124$	−1071.23	−0.775800
$125$	−1195.11	−0.855150
$126$	−126.000	−0.0890871
$127$	592.184	0.413763	0.206881	−	0.978366i	$-0.433669\pi$
$127$	592.184	0.413763	0.206881	+	0.978366i	$0.433669\pi$
$128$	−128.000	−0.0883883
$129$	−966.343	−0.659548
$130$	537.940	0.362927
$131$	−917.758	−0.612098	−0.306049	−	0.952016i	$-0.599007\pi$
$131$	−917.758	−0.612098	−0.306049	+	0.952016i	$0.599007\pi$
$132$	204.614	0.134919
$133$	133.000	0.0867110
$134$	1419.56	0.915156
$135$	146.228	0.0932246
$136$	886.311	0.558827
$137$	−2365.36	−1.47508	−0.737541	−	0.675303i	$-0.764013\pi$
$137$	−2365.36	−1.47508	−0.737541	+	0.675303i	$0.764013\pi$
$138$	185.693	0.114545
$139$	1233.75	0.752847	0.376423	−	0.926448i	$-0.377154\pi$
$139$	1233.75	0.752847	0.376423	+	0.926448i	$0.377154\pi$
$140$	151.644	0.0915447
$141$	−1279.60	−0.764268
$142$	−75.3702	−0.0445418
$143$	−846.820	−0.495207
$144$	144.000	0.0833333
$145$	−934.916	−0.535452
$146$	−1672.18	−0.947881
$147$	147.000	0.0824786
$148$	1199.92	0.666439
$149$	−181.841	−0.0999796	−0.0499898	−	0.998750i	$-0.515919\pi$
$149$	−181.841	−0.0999796	−0.0499898	+	0.998750i	$0.515919\pi$
$150$	574.011	0.312452
$151$	891.581	0.480502	0.240251	−	0.970711i	$-0.422770\pi$
$151$	891.581	0.480502	0.240251	+	0.970711i	$0.422770\pi$
$152$	−152.000	−0.0811107
$153$	−997.099	−0.526867
$154$	−238.716	−0.124911
$155$	−1450.41	−0.751609
$156$	−595.961	−0.305866
$157$	−3455.38	−1.75649	−0.878246	−	0.478208i	$-0.841286\pi$
$157$	−3455.38	−1.75649	−0.878246	+	0.478208i	$0.841286\pi$
$158$	104.703	0.0527196
$159$	−410.242	−0.204618
$160$	−173.307	−0.0856322
$161$	−216.642	−0.106048
$162$	−162.000	−0.0785674
$163$	−1470.08	−0.706416	−0.353208	−	0.935545i	$-0.614909\pi$
$163$	−1470.08	−0.706416	−0.353208	+	0.935545i	$0.614909\pi$
$164$	432.066	0.205724
$165$	277.040	0.130712
$166$	1525.38	0.713206
$167$	336.212	0.155790	0.0778949	−	0.996962i	$-0.475180\pi$
$167$	336.212	0.155790	0.0778949	+	0.996962i	$0.475180\pi$
$168$	−168.000	−0.0771517
$169$	269.456	0.122647
$170$	1200.03	0.541402
$171$	171.000	0.0764719
$172$	−1288.46	−0.571186
$173$	−3037.39	−1.33485	−0.667423	−	0.744679i	$-0.732603\pi$
$173$	−3037.39	−1.33485	−0.667423	+	0.744679i	$0.732603\pi$
$174$	1035.75	0.451266
$175$	−669.679	−0.289274
$176$	272.819	0.116844
$177$	911.120	0.386915
$178$	812.522	0.342141
$179$	−2696.27	−1.12586	−0.562929	−	0.826505i	$-0.690325\pi$
$179$	−2696.27	−1.12586	−0.562929	+	0.826505i	$0.690325\pi$
$180$	194.971	0.0807348
$181$	−3365.77	−1.38219	−0.691093	−	0.722766i	$-0.742871\pi$
$181$	−3365.77	−1.38219	−0.691093	+	0.722766i	$0.742871\pi$
$182$	695.288	0.283177
$183$	1257.83	0.508097
$184$	247.591	0.0991990
$185$	1624.65	0.645658
$186$	1606.84	0.633438
$187$	−1889.08	−0.738733
$188$	−1706.13	−0.661875
$189$	189.000	0.0727393
$190$	−205.803	−0.0785815
$191$	3210.75	1.21635	0.608173	−	0.793805i	$-0.291903\pi$
$191$	3210.75	1.21635	0.608173	+	0.793805i	$0.291903\pi$
$192$	192.000	0.0721688
$193$	1996.75	0.744712	0.372356	−	0.928090i	$-0.378550\pi$
$193$	1996.75	0.744712	0.372356	+	0.928090i	$0.378550\pi$
$194$	−2962.88	−1.09651
$195$	−806.910	−0.296328
$196$	196.000	0.0714286
$197$	−2391.45	−0.864891	−0.432446	−	0.901660i	$-0.642349\pi$
$197$	−2391.45	−0.864891	−0.432446	+	0.901660i	$0.642349\pi$
$198$	−306.921	−0.110161
$199$	−3118.09	−1.11073	−0.555366	−	0.831606i	$-0.687422\pi$
$199$	−3118.09	−1.11073	−0.555366	+	0.831606i	$0.687422\pi$
$200$	765.348	0.270591
$201$	−2129.33	−0.747222
$202$	−1398.24	−0.487028
$203$	−1208.38	−0.417791
$204$	−1329.47	−0.456281
$205$	585.002	0.199309
$206$	−1733.33	−0.586246
$207$	−278.539	−0.0935258
$208$	−794.615	−0.264888
$209$	323.972	0.107223
$210$	−227.466	−0.0747459
$211$	1196.10	0.390250	0.195125	−	0.980778i	$-0.437489\pi$
$211$	1196.10	0.390250	0.195125	+	0.980778i	$0.437489\pi$
$212$	−546.989	−0.177205
$213$	113.055	0.0363682
$214$	1277.33	0.408021
$215$	−1744.52	−0.553375
$216$	−216.000	−0.0680414
$217$	−1874.65	−0.586450
$218$	−1630.22	−0.506479
$219$	2508.27	0.773942
$220$	369.387	0.113200
$221$	5502.15	1.67473
$222$	−1799.88	−0.544145
$223$	2874.33	0.863137	0.431569	−	0.902080i	$-0.357960\pi$
$223$	2874.33	0.863137	0.431569	+	0.902080i	$0.357960\pi$
$224$	−224.000	−0.0668153
$225$	−861.016	−0.255116
$226$	1086.68	0.319846
$227$	3091.11	0.903806	0.451903	−	0.892067i	$-0.350745\pi$
$227$	3091.11	0.903806	0.451903	+	0.892067i	$0.350745\pi$
$228$	228.000	0.0662266
$229$	419.406	0.121027	0.0605134	−	0.998167i	$-0.480726\pi$
$229$	419.406	0.121027	0.0605134	+	0.998167i	$0.480726\pi$
$230$	335.229	0.0961058
$231$	358.075	0.101990
$232$	1381.00	0.390808
$233$	−1290.12	−0.362741	−0.181370	−	0.983415i	$-0.558053\pi$
$233$	−1290.12	−0.362741	−0.181370	+	0.983415i	$0.558053\pi$
$234$	893.942	0.249738
$235$	−2310.04	−0.641237
$236$	1214.83	0.335078
$237$	−157.054	−0.0430454
$238$	1551.04	0.422434
$239$	68.9574	0.0186631	0.00933156	−	0.999956i	$-0.497030\pi$
$239$	68.9574	0.0186631	0.00933156	+	0.999956i	$0.497030\pi$
$240$	259.961	0.0699184
$241$	5019.19	1.34155	0.670776	−	0.741660i	$-0.265961\pi$
$241$	5019.19	1.34155	0.670776	+	0.741660i	$0.265961\pi$
$242$	2080.52	0.552647
$243$	243.000	0.0641500
$244$	1677.11	0.440025
$245$	265.377	0.0692013
$246$	−648.099	−0.167973
$247$	−943.605	−0.243078
$248$	2142.46	0.548573
$249$	−2288.06	−0.582330
$250$	2390.22	0.604683
$251$	−5148.12	−1.29461	−0.647303	−	0.762232i	$-0.724103\pi$
$251$	−5148.12	−1.29461	−0.647303	+	0.762232i	$0.724103\pi$
$252$	252.000	0.0629941
$253$	−527.714	−0.131135
$254$	−1184.37	−0.292574
$255$	−1800.05	−0.442053
$256$	256.000	0.0625000
$257$	−4417.55	−1.07221	−0.536107	−	0.844150i	$-0.680106\pi$
$257$	−4417.55	−1.07221	−0.536107	+	0.844150i	$0.680106\pi$
$258$	1932.69	0.466371
$259$	2099.86	0.503781
$260$	−1075.88	−0.256628
$261$	−1553.63	−0.368457
$262$	1835.52	0.432819
$263$	−7286.88	−1.70847	−0.854236	−	0.519885i	$-0.825975\pi$
$263$	−7286.88	−1.70847	−0.854236	+	0.519885i	$0.825975\pi$
$264$	−409.228	−0.0954024
$265$	−740.604	−0.171679
$266$	−266.000	−0.0613139
$267$	−1218.78	−0.279357
$268$	−2839.11	−0.647113
$269$	2804.62	0.635690	0.317845	−	0.948143i	$-0.397041\pi$
$269$	2804.62	0.635690	0.317845	+	0.948143i	$0.397041\pi$
$270$	−292.456	−0.0659197
$271$	3841.35	0.861053	0.430527	−	0.902578i	$-0.358328\pi$
$271$	3841.35	0.861053	0.430527	+	0.902578i	$0.358328\pi$
$272$	−1772.62	−0.395151
$273$	−1042.93	−0.231213
$274$	4730.72	1.04304
$275$	−1631.26	−0.357704
$276$	−371.386	−0.0809957
$277$	2702.65	0.586233	0.293116	−	0.956077i	$-0.405308\pi$
$277$	2702.65	0.586233	0.293116	+	0.956077i	$0.405308\pi$
$278$	−2467.51	−0.532343
$279$	−2410.27	−0.517200
$280$	−303.288	−0.0647319
$281$	−264.948	−0.0562473	−0.0281236	−	0.999604i	$-0.508953\pi$
$281$	−264.948	−0.0562473	−0.0281236	+	0.999604i	$0.508953\pi$
$282$	2559.20	0.540419
$283$	7686.64	1.61457	0.807285	−	0.590162i	$-0.200936\pi$
$283$	7686.64	1.61457	0.807285	+	0.590162i	$0.200936\pi$
$284$	150.740	0.0314958
$285$	308.704	0.0641615
$286$	1693.64	0.350164
$287$	756.116	0.155513
$288$	−288.000	−0.0589256
$289$	7361.16	1.49830
$290$	1869.83	0.378622
$291$	4444.33	0.895295
$292$	3344.36	0.670253
$293$	−2606.64	−0.519732	−0.259866	−	0.965645i	$-0.583678\pi$
$293$	−2606.64	−0.519732	−0.259866	+	0.965645i	$0.583678\pi$
$294$	−294.000	−0.0583212
$295$	1644.83	0.324630
$296$	−2399.84	−0.471244
$297$	460.382	0.0899463
$298$	363.681	0.0706963
$299$	1537.03	0.297286
$300$	−1148.02	−0.220937
$301$	−2254.80	−0.431776
$302$	−1783.16	−0.339766
$303$	2097.36	0.397657
$304$	304.000	0.0573539
$305$	2270.75	0.426304
$306$	1994.20	0.372551
$307$	5946.98	1.10558	0.552788	−	0.833322i	$-0.313564\pi$
$307$	5946.98	1.10558	0.552788	+	0.833322i	$0.313564\pi$
$308$	477.433	0.0883255
$309$	2599.99	0.478668
$310$	2900.81	0.531468
$311$	1478.50	0.269575	0.134788	−	0.990874i	$-0.456965\pi$
$311$	1478.50	0.269575	0.134788	+	0.990874i	$0.456965\pi$
$312$	1191.92	0.216280
$313$	−808.101	−0.145931	−0.0729657	−	0.997334i	$-0.523246\pi$
$313$	−808.101	−0.145931	−0.0729657	+	0.997334i	$0.523246\pi$
$314$	6910.76	1.24203
$315$	341.199	0.0610298
$316$	−209.405	−0.0372784
$317$	4204.29	0.744910	0.372455	−	0.928050i	$-0.378516\pi$
$317$	4204.29	0.744910	0.372455	+	0.928050i	$0.378516\pi$
$318$	820.484	0.144687
$319$	−2943.47	−0.516623
$320$	346.615	0.0605511
$321$	−1915.99	−0.333147
$322$	433.284	0.0749874
$323$	−2104.99	−0.362615
$324$	324.000	0.0555556
$325$	4751.23	0.810925
$326$	2940.17	0.499511
$327$	2445.33	0.413538
$328$	−864.132	−0.145469
$329$	−2985.73	−0.500331
$330$	−554.080	−0.0924276
$331$	3358.50	0.557704	0.278852	−	0.960334i	$-0.410046\pi$
$331$	3358.50	0.557704	0.278852	+	0.960334i	$0.410046\pi$
$332$	−3050.75	−0.504313
$333$	2699.83	0.444293
$334$	−672.425	−0.110160
$335$	−3844.05	−0.626935
$336$	336.000	0.0545545
$337$	−9194.01	−1.48614	−0.743071	−	0.669213i	$-0.766632\pi$
$337$	−9194.01	−1.48614	−0.743071	+	0.669213i	$0.766632\pi$
$338$	−538.912	−0.0867247
$339$	−1630.03	−0.261153
$340$	−2400.07	−0.382829
$341$	−4566.43	−0.725178
$342$	−342.000	−0.0540738
$343$	343.000	0.0539949
$344$	2576.91	0.403889
$345$	−502.843	−0.0784701
$346$	6074.77	0.943878
$347$	5904.30	0.913428	0.456714	−	0.889614i	$-0.349026\pi$
$347$	5904.30	0.913428	0.456714	+	0.889614i	$0.349026\pi$
$348$	−2071.51	−0.319093
$349$	3244.92	0.497697	0.248849	−	0.968542i	$-0.419948\pi$
$349$	3244.92	0.497697	0.248849	+	0.968542i	$0.419948\pi$
$350$	1339.36	0.204548
$351$	−1340.91	−0.203911
$352$	−545.637	−0.0826209
$353$	−613.549	−0.0925097	−0.0462548	−	0.998930i	$-0.514729\pi$
$353$	−613.549	−0.0925097	−0.0462548	+	0.998930i	$0.514729\pi$
$354$	−1822.24	−0.273590
$355$	204.097	0.0305137
$356$	−1625.04	−0.241930
$357$	−2326.57	−0.344916
$358$	5392.54	0.796101
$359$	9178.00	1.34929	0.674646	−	0.738141i	$-0.264296\pi$
$359$	9178.00	1.34929	0.674646	+	0.738141i	$0.264296\pi$
$360$	−389.942	−0.0570881
$361$	361.000	0.0526316
$362$	6731.54	0.977353
$363$	−3120.77	−0.451234
$364$	−1390.58	−0.200236
$365$	4528.14	0.649353
$366$	−2515.67	−0.359279
$367$	3990.14	0.567530	0.283765	−	0.958894i	$-0.408416\pi$
$367$	3990.14	0.567530	0.283765	+	0.958894i	$0.408416\pi$
$368$	−495.181	−0.0701443
$369$	972.149	0.137149
$370$	−3249.30	−0.456549
$371$	−957.232	−0.133954
$372$	−3213.69	−0.447908
$373$	7372.75	1.02345	0.511725	−	0.859149i	$-0.329007\pi$
$373$	7372.75	1.02345	0.511725	+	0.859149i	$0.329007\pi$
$374$	3778.16	0.522363
$375$	−3585.33	−0.493721
$376$	3412.27	0.468017
$377$	8573.18	1.17120
$378$	−378.000	−0.0514344
$379$	−1457.69	−0.197563	−0.0987816	−	0.995109i	$-0.531495\pi$
$379$	−1457.69	−0.197563	−0.0987816	+	0.995109i	$0.531495\pi$
$380$	411.605	0.0555655
$381$	1776.55	0.238886
$382$	−6421.51	−0.860086
$383$	−490.016	−0.0653751	−0.0326875	−	0.999466i	$-0.510407\pi$
$383$	−490.016	−0.0653751	−0.0326875	+	0.999466i	$0.510407\pi$
$384$	−384.000	−0.0510310
$385$	646.427	0.0855713
$386$	−3993.51	−0.526591
$387$	−2899.03	−0.380790
$388$	5925.77	0.775349
$389$	−847.457	−0.110457	−0.0552285	−	0.998474i	$-0.517589\pi$
$389$	−847.457	−0.110457	−0.0552285	+	0.998474i	$0.517589\pi$
$390$	1613.82	0.209536
$391$	3428.78	0.443481
$392$	−392.000	−0.0505076
$393$	−2753.27	−0.353395
$394$	4782.90	0.611570
$395$	−283.527	−0.0361160
$396$	613.842	0.0778958
$397$	−9120.07	−1.15296	−0.576478	−	0.817113i	$-0.695573\pi$
$397$	−9120.07	−1.15296	−0.576478	+	0.817113i	$0.695573\pi$
$398$	6236.19	0.785406
$399$	399.000	0.0500626
$400$	−1530.70	−0.191337
$401$	2801.55	0.348885	0.174442	−	0.984667i	$-0.444188\pi$
$401$	2801.55	0.348885	0.174442	+	0.984667i	$0.444188\pi$
$402$	4258.67	0.528366
$403$	13300.2	1.64400
$404$	2796.48	0.344381
$405$	438.684	0.0538232
$406$	2416.76	0.295423
$407$	5115.02	0.622954
$408$	2658.93	0.322639
$409$	14166.3	1.71267	0.856334	−	0.516423i	$-0.172737\pi$
$409$	14166.3	1.71267	0.856334	+	0.516423i	$0.172737\pi$
$410$	−1170.00	−0.140933
$411$	−7096.07	−0.851639
$412$	3466.66	0.414539
$413$	2125.95	0.253295
$414$	557.079	0.0661327
$415$	−4130.61	−0.488587
$416$	1589.23	0.187304
$417$	3701.26	0.434656
$418$	−647.944	−0.0758182
$419$	1319.09	0.153799	0.0768995	−	0.997039i	$-0.475498\pi$
$419$	1319.09	0.153799	0.0768995	+	0.997039i	$0.475498\pi$
$420$	454.932	0.0528534
$421$	−4653.55	−0.538717	−0.269359	−	0.963040i	$-0.586812\pi$
$421$	−4653.55	−0.538717	−0.269359	+	0.963040i	$0.586812\pi$
$422$	−2392.20	−0.275949
$423$	−3838.80	−0.441250
$424$	1093.98	0.125303
$425$	10599.0	1.20971
$426$	−226.111	−0.0257162
$427$	2934.95	0.332628
$428$	−2554.66	−0.288514
$429$	−2540.46	−0.285908
$430$	3489.05	0.391295
$431$	1328.68	0.148492	0.0742462	−	0.997240i	$-0.476345\pi$
$431$	1328.68	0.148492	0.0742462	+	0.997240i	$0.476345\pi$
$432$	432.000	0.0481125
$433$	1912.17	0.212224	0.106112	−	0.994354i	$-0.466160\pi$
$433$	1912.17	0.212224	0.106112	+	0.994354i	$0.466160\pi$
$434$	3749.30	0.414683
$435$	−2804.75	−0.309143
$436$	3260.44	0.358134
$437$	−588.028	−0.0643688
$438$	−5016.54	−0.547259
$439$	−15056.5	−1.63692	−0.818459	−	0.574565i	$-0.805171\pi$
$439$	−15056.5	−1.63692	−0.818459	+	0.574565i	$0.805171\pi$
$440$	−738.774	−0.0800447
$441$	441.000	0.0476190
$442$	−11004.3	−1.18421
$443$	2815.83	0.301996	0.150998	−	0.988534i	$-0.451751\pi$
$443$	2815.83	0.301996	0.150998	+	0.988534i	$0.451751\pi$
$444$	3599.77	0.384769
$445$	−2200.25	−0.234386
$446$	−5748.67	−0.610330
$447$	−545.522	−0.0577233
$448$	448.000	0.0472456
$449$	17361.3	1.82479	0.912394	−	0.409314i	$-0.134232\pi$
$449$	17361.3	1.82479	0.912394	+	0.409314i	$0.134232\pi$
$450$	1722.03	0.180394
$451$	1841.81	0.192300
$452$	−2173.37	−0.226165
$453$	2674.74	0.277418
$454$	−6182.22	−0.639088
$455$	−1882.79	−0.193992
$456$	−456.000	−0.0468293
$457$	−2575.90	−0.263667	−0.131833	−	0.991272i	$-0.542086\pi$
$457$	−2575.90	−0.263667	−0.131833	+	0.991272i	$0.542086\pi$
$458$	−838.812	−0.0855789
$459$	−2991.30	−0.304187
$460$	−670.458	−0.0679571
$461$	−14639.1	−1.47899	−0.739493	−	0.673165i	$-0.764934\pi$
$461$	−14639.1	−1.47899	−0.739493	+	0.673165i	$0.764934\pi$
$462$	−716.149	−0.0721175
$463$	−5734.50	−0.575604	−0.287802	−	0.957690i	$-0.592925\pi$
$463$	−5734.50	−0.575604	−0.287802	+	0.957690i	$0.592925\pi$
$464$	−2762.01	−0.276343
$465$	−4351.22	−0.433942
$466$	2580.24	0.256496
$467$	−13301.0	−1.31798	−0.658991	−	0.752151i	$-0.729016\pi$
$467$	−13301.0	−1.31798	−0.658991	+	0.752151i	$0.729016\pi$
$468$	−1787.88	−0.176592
$469$	−4968.44	−0.489171
$470$	4620.09	0.453423
$471$	−10366.1	−1.01411
$472$	−2429.65	−0.236936
$473$	−5492.42	−0.533915
$474$	314.108	0.0304377
$475$	−1817.70	−0.175583
$476$	−3102.09	−0.298706
$477$	−1230.73	−0.118136
$478$	−137.915	−0.0131968
$479$	16360.7	1.56063	0.780314	−	0.625388i	$-0.215059\pi$
$479$	16360.7	1.56063	0.780314	+	0.625388i	$0.215059\pi$
$480$	−519.922	−0.0494398
$481$	−14898.1	−1.41225
$482$	−10038.4	−0.948621
$483$	−649.925	−0.0612270
$484$	−4161.03	−0.390780
$485$	8023.28	0.751172
$486$	−486.000	−0.0453609
$487$	18156.8	1.68945	0.844725	−	0.535200i	$-0.179764\pi$
$487$	18156.8	1.68945	0.844725	+	0.535200i	$0.179764\pi$
$488$	−3354.22	−0.311145
$489$	−4410.25	−0.407849
$490$	−530.754	−0.0489327
$491$	11629.7	1.06892	0.534462	−	0.845193i	$-0.320514\pi$
$491$	11629.7	1.06892	0.534462	+	0.845193i	$0.320514\pi$
$492$	1296.20	0.118775
$493$	19125.0	1.74715
$494$	1887.21	0.171882
$495$	831.120	0.0754668
$496$	−4284.92	−0.387900
$497$	263.796	0.0238086
$498$	4576.13	0.411770
$499$	−12530.6	−1.12414	−0.562072	−	0.827088i	$-0.689996\pi$
$499$	−12530.6	−1.12414	−0.562072	+	0.827088i	$0.689996\pi$
$500$	−4780.44	−0.427575
$501$	1008.64	0.0899453
$502$	10296.2	0.915425
$503$	−13060.9	−1.15777	−0.578885	−	0.815409i	$-0.696512\pi$
$503$	−13060.9	−1.15777	−0.578885	+	0.815409i	$0.696512\pi$
$504$	−504.000	−0.0445435
$505$	3786.33	0.333642
$506$	1055.43	0.0927262
$507$	808.368	0.0708105
$508$	2368.74	0.206881
$509$	7380.31	0.642685	0.321342	−	0.946963i	$-0.395866\pi$
$509$	7380.31	0.642685	0.321342	+	0.946963i	$0.395866\pi$
$510$	3600.10	0.312579
$511$	5852.63	0.506664
$512$	−512.000	−0.0441942
$513$	513.000	0.0441511
$514$	8835.10	0.758170
$515$	4693.73	0.401613
$516$	−3865.37	−0.329774
$517$	−7272.89	−0.618688
$518$	−4199.73	−0.356227
$519$	−9112.16	−0.770673
$520$	2151.76	0.181463
$521$	−17260.4	−1.45142	−0.725712	−	0.687999i	$-0.758490\pi$
$521$	−17260.4	−1.45142	−0.725712	+	0.687999i	$0.758490\pi$
$522$	3107.26	0.260539
$523$	21454.2	1.79374	0.896870	−	0.442294i	$-0.145835\pi$
$523$	21454.2	1.79374	0.896870	+	0.442294i	$0.145835\pi$
$524$	−3671.03	−0.306049
$525$	−2009.04	−0.167013
$526$	14573.8	1.20807
$527$	29670.0	2.45246
$528$	818.456	0.0674597
$529$	−11209.2	−0.921276
$530$	1481.21	0.121395
$531$	2733.36	0.223386
$532$	532.000	0.0433555
$533$	−5364.47	−0.435950
$534$	2437.57	0.197535
$535$	−3458.92	−0.279518
$536$	5678.22	0.457578
$537$	−8088.80	−0.650014
$538$	−5609.23	−0.449501
$539$	835.507	0.0667678
$540$	584.913	0.0466123
$541$	3647.48	0.289866	0.144933	−	0.989441i	$-0.453703\pi$
$541$	3647.48	0.289866	0.144933	+	0.989441i	$0.453703\pi$
$542$	−7682.70	−0.608857
$543$	−10097.3	−0.798006
$544$	3545.24	0.279414
$545$	4414.51	0.346967
$546$	2085.86	0.163492
$547$	−15004.8	−1.17287	−0.586435	−	0.809997i	$-0.699469\pi$
$547$	−15004.8	−1.17287	−0.586435	+	0.809997i	$0.699469\pi$
$548$	−9461.43	−0.737541
$549$	3773.50	0.293350
$550$	3262.52	0.252935
$551$	−3279.89	−0.253590
$552$	742.772	0.0572726
$553$	−366.459	−0.0281798
$554$	−5405.30	−0.414529
$555$	4873.96	0.372771
$556$	4935.02	0.376423
$557$	22045.6	1.67702	0.838512	−	0.544882i	$-0.183426\pi$
$557$	22045.6	1.67702	0.838512	+	0.544882i	$0.183426\pi$
$558$	4820.53	0.365716
$559$	15997.3	1.21040
$560$	606.576	0.0457723
$561$	−5667.24	−0.426508
$562$	529.896	0.0397728
$563$	4469.39	0.334569	0.167285	−	0.985909i	$-0.446500\pi$
$563$	4469.39	0.334569	0.167285	+	0.985909i	$0.446500\pi$
$564$	−5118.40	−0.382134
$565$	−2942.66	−0.219113
$566$	−15373.3	−1.14167
$567$	567.000	0.0419961
$568$	−301.481	−0.0222709
$569$	−24334.6	−1.79290	−0.896450	−	0.443145i	$-0.853863\pi$
$569$	−24334.6	−1.79290	−0.896450	+	0.443145i	$0.853863\pi$
$570$	−617.408	−0.0453691
$571$	−19232.8	−1.40958	−0.704788	−	0.709418i	$-0.748958\pi$
$571$	−19232.8	−1.40958	−0.704788	+	0.709418i	$0.748958\pi$
$572$	−3387.28	−0.247604
$573$	9632.26	0.702257
$574$	−1512.23	−0.109964
$575$	2960.83	0.214739
$576$	576.000	0.0416667
$577$	1645.78	0.118743	0.0593714	−	0.998236i	$-0.481090\pi$
$577$	1645.78	0.118743	0.0593714	+	0.998236i	$0.481090\pi$
$578$	−14722.3	−1.05946
$579$	5990.26	0.429960
$580$	−3739.66	−0.267726
$581$	−5338.82	−0.381225
$582$	−8888.65	−0.633069
$583$	−2331.70	−0.165642
$584$	−6688.72	−0.473941
$585$	−2420.73	−0.171085
$586$	5213.28	0.367506
$587$	13841.2	0.973231	0.486615	−	0.873616i	$-0.338231\pi$
$587$	13841.2	0.973231	0.486615	+	0.873616i	$0.338231\pi$
$588$	588.000	0.0412393
$589$	−5088.34	−0.355961
$590$	−3289.66	−0.229548
$591$	−7174.34	−0.499345
$592$	4799.69	0.333220
$593$	−1880.71	−0.130239	−0.0651193	−	0.997877i	$-0.520743\pi$
$593$	−1880.71	−0.130239	−0.0651193	+	0.997877i	$0.520743\pi$
$594$	−920.763	−0.0636016
$595$	−4200.11	−0.289391
$596$	−727.362	−0.0499898
$597$	−9354.28	−0.641282
$598$	−3074.05	−0.210213
$599$	−25826.8	−1.76169	−0.880847	−	0.473401i	$-0.843026\pi$
$599$	−25826.8	−1.76169	−0.880847	+	0.473401i	$0.843026\pi$
$600$	2296.04	0.156226
$601$	−26077.5	−1.76993	−0.884963	−	0.465662i	$-0.845816\pi$
$601$	−26077.5	−1.76993	−0.884963	+	0.465662i	$0.845816\pi$
$602$	4509.60	0.305312
$603$	−6388.00	−0.431409
$604$	3566.32	0.240251
$605$	−5633.89	−0.378595
$606$	−4194.71	−0.281186
$607$	20611.1	1.37822	0.689109	−	0.724658i	$-0.258002\pi$
$607$	20611.1	1.37822	0.689109	+	0.724658i	$0.258002\pi$
$608$	−608.000	−0.0405554
$609$	−3625.14	−0.241212
$610$	−4541.50	−0.301442
$611$	21183.1	1.40258
$612$	−3988.40	−0.263434
$613$	9744.93	0.642078	0.321039	−	0.947066i	$-0.395968\pi$
$613$	9744.93	0.642078	0.321039	+	0.947066i	$0.395968\pi$
$614$	−11894.0	−0.781760
$615$	1755.01	0.115071
$616$	−954.865	−0.0624556
$617$	−8815.84	−0.575223	−0.287611	−	0.957747i	$-0.592861\pi$
$617$	−8815.84	−0.575223	−0.287611	+	0.957747i	$0.592861\pi$
$618$	−5199.99	−0.338470
$619$	5962.26	0.387146	0.193573	−	0.981086i	$-0.437992\pi$
$619$	5962.26	0.387146	0.193573	+	0.981086i	$0.437992\pi$
$620$	−5801.62	−0.375804
$621$	−835.618	−0.0539971
$622$	−2957.00	−0.190619
$623$	−2843.83	−0.182882
$624$	−2383.84	−0.152933
$625$	5486.02	0.351105
$626$	1616.20	0.103189
$627$	971.917	0.0619053
$628$	−13821.5	−0.878246
$629$	−33234.5	−2.10675
$630$	−682.398	−0.0431546
$631$	−17994.3	−1.13525	−0.567625	−	0.823288i	$-0.692137\pi$
$631$	−17994.3	−1.13525	−0.567625	+	0.823288i	$0.692137\pi$
$632$	418.811	0.0263598
$633$	3588.29	0.225311
$634$	−8408.58	−0.526731
$635$	3207.19	0.200430
$636$	−1640.97	−0.102309
$637$	−2433.51	−0.151364
$638$	5886.94	0.365307
$639$	339.166	0.0209972
$640$	−693.230	−0.0428161
$641$	2867.60	0.176698	0.0883489	−	0.996090i	$-0.471841\pi$
$641$	2867.60	0.176698	0.0883489	+	0.996090i	$0.471841\pi$
$642$	3831.99	0.235571
$643$	−20075.3	−1.23125	−0.615623	−	0.788041i	$-0.711096\pi$
$643$	−20075.3	−1.23125	−0.615623	+	0.788041i	$0.711096\pi$
$644$	−866.567	−0.0530241
$645$	−5233.57	−0.319491
$646$	4209.98	0.256408
$647$	9786.39	0.594656	0.297328	−	0.954775i	$-0.403904\pi$
$647$	9786.39	0.594656	0.297328	+	0.954775i	$0.403904\pi$
$648$	−648.000	−0.0392837
$649$	5178.55	0.313214
$650$	−9502.45	−0.573410
$651$	−5623.95	−0.338587
$652$	−5880.33	−0.353208
$653$	−6032.62	−0.361523	−0.180762	−	0.983527i	$-0.557856\pi$
$653$	−6032.62	−0.361523	−0.180762	+	0.983527i	$0.557856\pi$
$654$	−4890.66	−0.292416
$655$	−4970.45	−0.296506
$656$	1728.26	0.102862
$657$	7524.81	0.446835
$658$	5971.47	0.353787
$659$	−27873.9	−1.64767	−0.823835	−	0.566829i	$-0.808170\pi$
$659$	−27873.9	−1.64767	−0.823835	+	0.566829i	$0.808170\pi$
$660$	1108.16	0.0653562
$661$	−1447.36	−0.0851674	−0.0425837	−	0.999093i	$-0.513559\pi$
$661$	−1447.36	−0.0851674	−0.0425837	+	0.999093i	$0.513559\pi$
$662$	−6717.01	−0.394356
$663$	16506.5	0.966905
$664$	6101.51	0.356603
$665$	720.309	0.0420036
$666$	−5399.65	−0.314162
$667$	5342.56	0.310142
$668$	1344.85	0.0778949
$669$	8623.00	0.498333
$670$	7688.11	0.443310
$671$	7149.18	0.411313
$672$	−672.000	−0.0385758
$673$	−28895.2	−1.65502	−0.827511	−	0.561450i	$-0.810244\pi$
$673$	−28895.2	−1.65502	−0.827511	+	0.561450i	$0.810244\pi$
$674$	18388.0	1.05086
$675$	−2583.05	−0.147291
$676$	1077.82	0.0613237
$677$	7557.33	0.429028	0.214514	−	0.976721i	$-0.431183\pi$
$677$	7557.33	0.429028	0.214514	+	0.976721i	$0.431183\pi$
$678$	3260.05	0.184663
$679$	10370.1	0.586108
$680$	4800.13	0.270701
$681$	9273.32	0.521813
$682$	9132.85	0.512779
$683$	6352.18	0.355871	0.177935	−	0.984042i	$-0.443058\pi$
$683$	6352.18	0.355871	0.177935	+	0.984042i	$0.443058\pi$
$684$	684.000	0.0382360
$685$	−12810.4	−0.714543
$686$	−686.000	−0.0381802
$687$	1258.22	0.0698748
$688$	−5153.83	−0.285593
$689$	6791.34	0.375515
$690$	1005.69	0.0554867
$691$	−29053.0	−1.59946	−0.799731	−	0.600359i	$-0.795025\pi$
$691$	−29053.0	−1.59946	−0.799731	+	0.600359i	$0.795025\pi$
$692$	−12149.5	−0.667423
$693$	1074.22	0.0588837
$694$	−11808.6	−0.645891
$695$	6681.84	0.364686
$696$	4143.01	0.225633
$697$	−11967.0	−0.650335
$698$	−6489.83	−0.351925
$699$	−3870.36	−0.209428
$700$	−2678.72	−0.144637
$701$	−8876.42	−0.478257	−0.239128	−	0.970988i	$-0.576862\pi$
$701$	−8876.42	−0.478257	−0.239128	+	0.970988i	$0.576862\pi$
$702$	2681.83	0.144187
$703$	5699.63	0.305783
$704$	1091.27	0.0584218
$705$	−6930.13	−0.370218
$706$	1227.10	0.0654142
$707$	4893.83	0.260327
$708$	3644.48	0.193458
$709$	−12522.7	−0.663326	−0.331663	−	0.943398i	$-0.607610\pi$
$709$	−12522.7	−0.663326	−0.331663	+	0.943398i	$0.607610\pi$
$710$	−408.194	−0.0215764
$711$	−471.162	−0.0248523
$712$	3250.09	0.171070
$713$	8288.32	0.435344
$714$	4653.13	0.243892
$715$	−4586.25	−0.239883
$716$	−10785.1	−0.562929
$717$	206.872	0.0107752
$718$	−18356.0	−0.954094
$719$	23407.9	1.21414	0.607070	−	0.794649i	$-0.292345\pi$
$719$	23407.9	1.21414	0.607070	+	0.794649i	$0.292345\pi$
$720$	779.883	0.0403674
$721$	6066.65	0.313362
$722$	−722.000	−0.0372161
$723$	15057.6	0.774546
$724$	−13463.1	−0.691093
$725$	16514.8	0.845994
$726$	6241.55	0.319071
$727$	29661.1	1.51316	0.756582	−	0.653899i	$-0.226868\pi$
$727$	29661.1	1.51316	0.756582	+	0.653899i	$0.226868\pi$
$728$	2781.15	0.141588
$729$	729.000	0.0370370
$730$	−9056.29	−0.459162
$731$	35686.7	1.80563
$732$	5031.33	0.254048
$733$	−11890.9	−0.599182	−0.299591	−	0.954068i	$-0.596850\pi$
$733$	−11890.9	−0.599182	−0.299591	+	0.954068i	$0.596850\pi$
$734$	−7980.27	−0.401304
$735$	796.131	0.0399534
$736$	990.363	0.0495995
$737$	−12102.5	−0.604888
$738$	−1944.30	−0.0969791
$739$	2155.39	0.107290	0.0536451	−	0.998560i	$-0.482916\pi$
$739$	2155.39	0.107290	0.0536451	+	0.998560i	$0.482916\pi$
$740$	6498.61	0.322829
$741$	−2830.82	−0.140341
$742$	1914.46	0.0947199
$743$	−27229.1	−1.34447	−0.672234	−	0.740339i	$-0.734665\pi$
$743$	−27229.1	−1.34447	−0.672234	+	0.740339i	$0.734665\pi$
$744$	6427.37	0.316719
$745$	−984.823	−0.0484310
$746$	−14745.5	−0.723688
$747$	−6864.19	−0.336208
$748$	−7556.32	−0.369367
$749$	−4470.65	−0.218096
$750$	7170.65	0.349114
$751$	30051.0	1.46015	0.730077	−	0.683365i	$-0.239484\pi$
$751$	30051.0	1.46015	0.730077	+	0.683365i	$0.239484\pi$
$752$	−6824.53	−0.330938
$753$	−15444.4	−0.747442
$754$	−17146.4	−0.828161
$755$	4828.67	0.232760
$756$	756.000	0.0363696
$757$	22234.6	1.06755	0.533773	−	0.845628i	$-0.320774\pi$
$757$	22234.6	1.06755	0.533773	+	0.845628i	$0.320774\pi$
$758$	2915.38	0.139698
$759$	−1583.14	−0.0757107
$760$	−823.210	−0.0392908
$761$	40094.6	1.90989	0.954946	−	0.296781i	$-0.0959132\pi$
$761$	40094.6	1.90989	0.954946	+	0.296781i	$0.0959132\pi$
$762$	−3553.11	−0.168918
$763$	5705.76	0.270724
$764$	12843.0	0.608173
$765$	−5400.15	−0.255219
$766$	980.032	0.0462272
$767$	−15083.1	−0.710065
$768$	768.000	0.0360844
$769$	23861.5	1.11894	0.559472	−	0.828849i	$-0.311004\pi$
$769$	23861.5	1.11894	0.559472	+	0.828849i	$0.311004\pi$
$770$	−1292.85	−0.0605081
$771$	−13252.6	−0.619043
$772$	7987.01	0.372356
$773$	12865.2	0.598613	0.299307	−	0.954157i	$-0.403245\pi$
$773$	12865.2	0.598613	0.299307	+	0.954157i	$0.403245\pi$
$774$	5798.06	0.269259
$775$	25620.7	1.18751
$776$	−11851.5	−0.548254
$777$	6299.59	0.290858
$778$	1694.91	0.0781049
$779$	2052.31	0.0943926
$780$	−3227.64	−0.148164
$781$	642.575	0.0294407
$782$	−6857.57	−0.313588
$783$	−4660.89	−0.212729
$784$	784.000	0.0357143
$785$	−18713.8	−0.850861
$786$	5506.55	0.249888
$787$	−16787.6	−0.760373	−0.380186	−	0.924910i	$-0.624140\pi$
$787$	−16787.6	−0.760373	−0.380186	+	0.924910i	$0.624140\pi$
$788$	−9565.79	−0.432446
$789$	−21860.6	−0.986387
$790$	567.055	0.0255379
$791$	−3803.39	−0.170965
$792$	−1227.68	−0.0550806
$793$	−20822.8	−0.932457
$794$	18240.1	0.815263
$795$	−2221.81	−0.0991190
$796$	−12472.4	−0.555366
$797$	2406.88	0.106971	0.0534857	−	0.998569i	$-0.482967\pi$
$797$	2406.88	0.106971	0.0534857	+	0.998569i	$0.482967\pi$
$798$	−798.000	−0.0353996
$799$	47255.1	2.09232
$800$	3061.39	0.135296
$801$	−3656.35	−0.161287
$802$	−5603.10	−0.246699
$803$	14256.3	0.626519
$804$	−8517.33	−0.373611
$805$	−1173.30	−0.0513707
$806$	−26600.4	−1.16248
$807$	8413.85	0.367016
$808$	−5592.95	−0.243514
$809$	−7862.25	−0.341684	−0.170842	−	0.985298i	$-0.554649\pi$
$809$	−7862.25	−0.341684	−0.170842	+	0.985298i	$0.554649\pi$
$810$	−877.369	−0.0380588
$811$	38039.8	1.64705	0.823526	−	0.567279i	$-0.192004\pi$
$811$	38039.8	1.64705	0.823526	+	0.567279i	$0.192004\pi$
$812$	−4833.52	−0.208896
$813$	11524.1	0.497129
$814$	−10230.0	−0.440495
$815$	−7961.76	−0.342194
$816$	−5317.86	−0.228140
$817$	−6120.17	−0.262078
$818$	−28332.7	−1.21104
$819$	−3128.80	−0.133491
$820$	2340.01	0.0996545
$821$	16107.0	0.684701	0.342351	−	0.939572i	$-0.388777\pi$
$821$	16107.0	0.684701	0.342351	+	0.939572i	$0.388777\pi$
$822$	14192.1	0.602199
$823$	−42368.3	−1.79449	−0.897245	−	0.441534i	$-0.854435\pi$
$823$	−42368.3	−1.79449	−0.897245	+	0.441534i	$0.854435\pi$
$824$	−6933.32	−0.293123
$825$	−4893.78	−0.206521
$826$	−4251.89	−0.179107
$827$	21907.1	0.921143	0.460571	−	0.887623i	$-0.347645\pi$
$827$	21907.1	0.921143	0.460571	+	0.887623i	$0.347645\pi$
$828$	−1114.16	−0.0467629
$829$	−21619.1	−0.905746	−0.452873	−	0.891575i	$-0.649601\pi$
$829$	−21619.1	−0.905746	−0.452873	+	0.891575i	$0.649601\pi$
$830$	8261.22	0.345483
$831$	8107.95	0.338462
$832$	−3178.46	−0.132444
$833$	−5428.65	−0.225800
$834$	−7402.53	−0.307348
$835$	1820.88	0.0754660
$836$	1295.89	0.0536115
$837$	−7230.80	−0.298606
$838$	−2638.18	−0.108752
$839$	14418.3	0.593297	0.296649	−	0.954987i	$-0.404131\pi$
$839$	14418.3	0.593297	0.296649	+	0.954987i	$0.404131\pi$
$840$	−909.864	−0.0373730
$841$	5410.60	0.221846
$842$	9307.09	0.380931
$843$	−794.844	−0.0324744
$844$	4784.39	0.195125
$845$	1459.34	0.0594115
$846$	7677.60	0.312011
$847$	−7281.80	−0.295402
$848$	−2187.96	−0.0886023
$849$	23059.9	0.932173
$850$	−21198.0	−0.855395
$851$	−9284.05	−0.373975
$852$	452.221	0.0181841
$853$	−8429.70	−0.338367	−0.169184	−	0.985585i	$-0.554113\pi$
$853$	−8429.70	−0.338367	−0.169184	+	0.985585i	$0.554113\pi$
$854$	−5869.89	−0.235203
$855$	926.112	0.0370437
$856$	5109.32	0.204010
$857$	44059.3	1.75617	0.878084	−	0.478507i	$-0.158822\pi$
$857$	44059.3	1.75617	0.878084	+	0.478507i	$0.158822\pi$
$858$	5080.92	0.202167
$859$	−5162.10	−0.205039	−0.102520	−	0.994731i	$-0.532690\pi$
$859$	−5162.10	−0.205039	−0.102520	+	0.994731i	$0.532690\pi$
$860$	−6978.10	−0.276687
$861$	2268.35	0.0897852
$862$	−2657.36	−0.105000
$863$	−2719.86	−0.107283	−0.0536415	−	0.998560i	$-0.517083\pi$
$863$	−2719.86	−0.107283	−0.0536415	+	0.998560i	$0.517083\pi$
$864$	−864.000	−0.0340207
$865$	−16450.1	−0.646611
$866$	−3824.34	−0.150065
$867$	22083.5	0.865046
$868$	−7498.60	−0.293225
$869$	−892.652	−0.0348460
$870$	5609.49	0.218597
$871$	35250.0	1.37130
$872$	−6520.87	−0.253239
$873$	13333.0	0.516899
$874$	1176.06	0.0455156
$875$	−8365.76	−0.323216
$876$	10033.1	0.386971
$877$	15589.9	0.600265	0.300132	−	0.953898i	$-0.402969\pi$
$877$	15589.9	0.600265	0.300132	+	0.953898i	$0.402969\pi$
$878$	30113.0	1.15748
$879$	−7819.91	−0.300067
$880$	1477.55	0.0566001
$881$	2043.39	0.0781424	0.0390712	−	0.999236i	$-0.487560\pi$
$881$	2043.39	0.0781424	0.0390712	+	0.999236i	$0.487560\pi$
$882$	−882.000	−0.0336718
$883$	−37058.5	−1.41236	−0.706182	−	0.708031i	$-0.749584\pi$
$883$	−37058.5	−1.41236	−0.706182	+	0.708031i	$0.749584\pi$
$884$	22008.6	0.837364
$885$	4934.50	0.187425
$886$	−5631.66	−0.213543
$887$	−47484.0	−1.79747	−0.898735	−	0.438492i	$-0.855513\pi$
$887$	−47484.0	−1.79747	−0.898735	+	0.438492i	$0.855513\pi$
$888$	−7199.53	−0.272073
$889$	4145.29	0.156388
$890$	4400.50	0.165736
$891$	1381.14	0.0519305
$892$	11497.3	0.431569
$893$	−8104.13	−0.303689
$894$	1091.04	0.0408165
$895$	−14602.6	−0.545376
$896$	−896.000	−0.0334077
$897$	4611.08	0.171638
$898$	−34722.6	−1.29032
$899$	46230.4	1.71509
$900$	−3444.07	−0.127558
$901$	15150.1	0.560180
$902$	−3683.62	−0.135977
$903$	−6764.40	−0.249286
$904$	4346.74	0.159923
$905$	−18228.5	−0.669543
$906$	−5349.49	−0.196164
$907$	−18541.1	−0.678772	−0.339386	−	0.940647i	$-0.610219\pi$
$907$	−18541.1	−0.678772	−0.339386	+	0.940647i	$0.610219\pi$
$908$	12364.4	0.451903
$909$	6292.07	0.229587
$910$	3765.58	0.137173
$911$	44888.3	1.63251	0.816255	−	0.577692i	$-0.196047\pi$
$911$	44888.3	1.63251	0.816255	+	0.577692i	$0.196047\pi$
$912$	912.000	0.0331133
$913$	−13004.7	−0.471406
$914$	5151.81	0.186441
$915$	6812.25	0.246127
$916$	1677.62	0.0605134
$917$	−6424.31	−0.231351
$918$	5982.60	0.215093
$919$	3377.59	0.121237	0.0606183	−	0.998161i	$-0.480693\pi$
$919$	3377.59	0.121237	0.0606183	+	0.998161i	$0.480693\pi$
$920$	1340.92	0.0480529
$921$	17840.9	0.638305
$922$	29278.3	1.04580
$923$	−1871.57	−0.0667427
$924$	1432.30	0.0509948
$925$	−28698.7	−1.02012
$926$	11469.0	0.407014
$927$	7799.98	0.276359
$928$	5524.02	0.195404
$929$	−34912.8	−1.23299	−0.616497	−	0.787357i	$-0.711449\pi$
$929$	−34912.8	−1.23299	−0.616497	+	0.787357i	$0.711449\pi$
$930$	8702.43	0.306843
$931$	931.000	0.0327737
$932$	−5160.48	−0.181370
$933$	4435.50	0.155639
$934$	26602.0	0.931954
$935$	−10231.0	−0.357849
$936$	3575.77	0.124869
$937$	−9643.41	−0.336218	−0.168109	−	0.985768i	$-0.553766\pi$
$937$	−9643.41	−0.336218	−0.168109	+	0.985768i	$0.553766\pi$
$938$	9936.89	0.345896
$939$	−2424.30	−0.0842536
$940$	−9240.18	−0.320618
$941$	19400.7	0.672099	0.336050	−	0.941844i	$-0.390909\pi$
$941$	19400.7	0.672099	0.336050	+	0.941844i	$0.390909\pi$
$942$	20732.3	0.717085
$943$	−3342.99	−0.115443
$944$	4859.31	0.167539
$945$	1023.60	0.0352356
$946$	10984.8	0.377535
$947$	35290.1	1.21095	0.605477	−	0.795863i	$-0.292983\pi$
$947$	35290.1	1.21095	0.605477	+	0.795863i	$0.292983\pi$
$948$	−628.216	−0.0215227
$949$	−41523.1	−1.42033
$950$	3635.40	0.124156
$951$	12612.9	0.430074
$952$	6204.17	0.211217
$953$	42711.6	1.45180	0.725900	−	0.687800i	$-0.241423\pi$
$953$	42711.6	1.45180	0.725900	+	0.687800i	$0.241423\pi$
$954$	2461.45	0.0835351
$955$	17389.0	0.589209
$956$	275.830	0.00933156
$957$	−8830.40	−0.298272
$958$	−32721.5	−1.10353
$959$	−16557.5	−0.557528
$960$	1039.84	0.0349592
$961$	41929.7	1.40746
$962$	29796.1	0.998613
$963$	−5747.98	−0.192343
$964$	20076.7	0.670776
$965$	10814.1	0.360745
$966$	1299.85	0.0432940
$967$	4100.75	0.136371	0.0681857	−	0.997673i	$-0.478279\pi$
$967$	4100.75	0.136371	0.0681857	+	0.997673i	$0.478279\pi$
$968$	8322.06	0.276324
$969$	−6314.96	−0.209356
$970$	−16046.6	−0.531159
$971$	25361.1	0.838182	0.419091	−	0.907944i	$-0.362349\pi$
$971$	25361.1	0.838182	0.419091	+	0.907944i	$0.362349\pi$
$972$	972.000	0.0320750
$973$	8636.28	0.284549
$974$	−36313.6	−1.19462
$975$	14253.7	0.468188
$976$	6708.45	0.220012
$977$	−28928.1	−0.947280	−0.473640	−	0.880719i	$-0.657060\pi$
$977$	−28928.1	−0.947280	−0.473640	+	0.880719i	$0.657060\pi$
$978$	8820.50	0.288393
$979$	−6927.22	−0.226144
$980$	1061.51	0.0346006
$981$	7335.98	0.238756
$982$	−23259.4	−0.755843
$983$	15186.9	0.492765	0.246382	−	0.969173i	$-0.420758\pi$
$983$	15186.9	0.492765	0.246382	+	0.969173i	$0.420758\pi$
$984$	−2592.40	−0.0839864
$985$	−12951.7	−0.418961
$986$	−38250.0	−1.23542
$987$	−8957.20	−0.288866
$988$	−3774.42	−0.121539
$989$	9969.06	0.320523
$990$	−1662.24	−0.0533631
$991$	33820.3	1.08410	0.542048	−	0.840348i	$-0.317649\pi$
$991$	33820.3	1.08410	0.542048	+	0.840348i	$0.317649\pi$
$992$	8569.83	0.274287
$993$	10075.5	0.321991
$994$	−527.592	−0.0168352
$995$	−16887.1	−0.538049
$996$	−9152.26	−0.291165
$997$	24228.9	0.769647	0.384823	−	0.922990i	$-0.374262\pi$
$997$	24228.9	0.769647	0.384823	+	0.922990i	$0.374262\pi$
$998$	25061.2	0.794890
$999$	8099.48	0.256513

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.g.1.3	✓	3
3.2	odd	2		2394.4.a.p.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.g.1.3	✓	3	1.1	even	1	trivial
2394.4.a.p.1.1		3	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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.41586 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} +5.41586 q^{5} -6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -10.8317 q^{10} +17.0512 q^{11} +12.0000 q^{12} -49.6634 q^{13} -14.0000 q^{14} +16.2476 q^{15} +16.0000 q^{16} -110.789 q^{17} -18.0000 q^{18} +19.0000 q^{19} +21.6634 q^{20} +21.0000 q^{21} -34.1023 q^{22} -30.9488 q^{23} -24.0000 q^{24} -95.6685 q^{25} +99.3269 q^{26} +27.0000 q^{27} +28.0000 q^{28} -172.626 q^{29} -32.4951 q^{30} -267.807 q^{31} -32.0000 q^{32} +51.1535 q^{33} +221.578 q^{34} +37.9110 q^{35} +36.0000 q^{36} +299.981 q^{37} -38.0000 q^{38} -148.990 q^{39} -43.3269 q^{40} +108.017 q^{41} -42.0000 q^{42} -322.114 q^{43} +68.2047 q^{44} +48.7427 q^{45} +61.8977 q^{46} -426.533 q^{47} +48.0000 q^{48} +49.0000 q^{49} +191.337 q^{50} -332.366 q^{51} -198.654 q^{52} -136.747 q^{53} -54.0000 q^{54} +92.3467 q^{55} -56.0000 q^{56} +57.0000 q^{57} +345.251 q^{58} +303.707 q^{59} +64.9903 q^{60} +419.278 q^{61} +535.614 q^{62} +63.0000 q^{63} +64.0000 q^{64} -268.970 q^{65} -102.307 q^{66} -709.778 q^{67} -443.155 q^{68} -92.8465 q^{69} -75.8220 q^{70} +37.6851 q^{71} -72.0000 q^{72} +836.090 q^{73} -599.961 q^{74} -287.005 q^{75} +76.0000 q^{76} +119.358 q^{77} +297.981 q^{78} -52.3513 q^{79} +86.6537 q^{80} +81.0000 q^{81} -216.033 q^{82} -762.688 q^{83} +84.0000 q^{84} -600.016 q^{85} +644.228 q^{86} -517.877 q^{87} -136.409 q^{88} -406.261 q^{89} -97.4854 q^{90} -347.644 q^{91} -123.795 q^{92} -803.422 q^{93} +853.067 q^{94} +102.901 q^{95} -96.0000 q^{96} +1481.44 q^{97} -98.0000 q^{98} +153.461 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 20 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 20 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9	\( 3 q - 6 q^{2} + 9 q^{3} + 12 q^{4} - 20 q^{5} - 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} + 40 q^{10} - 2 q^{11} + 36 q^{12} - 4 q^{13} - 42 q^{14} - 60 q^{15} + 48 q^{16} - 156 q^{17} - 54 q^{18} + 57 q^{19} - 80 q^{20} + 63 q^{21} + 4 q^{22} - 146 q^{23} - 72 q^{24} + 61 q^{25} + 8 q^{26} + 81 q^{27} + 84 q^{28} - 66 q^{29} + 120 q^{30} - 64 q^{31} - 96 q^{32} - 6 q^{33} + 312 q^{34} - 140 q^{35} + 108 q^{36} + 30 q^{37} - 114 q^{38} - 12 q^{39} + 160 q^{40} + 10 q^{41} - 126 q^{42} + 92 q^{43} - 8 q^{44} - 180 q^{45} + 292 q^{46} - 528 q^{47} + 144 q^{48} + 147 q^{49} - 122 q^{50} - 468 q^{51} - 16 q^{52} - 722 q^{53} - 162 q^{54} + 16 q^{55} - 168 q^{56} + 171 q^{57} + 132 q^{58} - 268 q^{59} - 240 q^{60} - 366 q^{61} + 128 q^{62} + 189 q^{63} + 192 q^{64} - 1184 q^{65} + 12 q^{66} - 926 q^{67} - 624 q^{68} - 438 q^{69} + 280 q^{70} - 252 q^{71} - 216 q^{72} - 58 q^{73} - 60 q^{74} + 183 q^{75} + 228 q^{76} - 14 q^{77} + 24 q^{78} - 534 q^{79} - 320 q^{80} + 243 q^{81} - 20 q^{82} - 1672 q^{83} + 252 q^{84} + 1332 q^{85} - 184 q^{86} - 198 q^{87} + 16 q^{88} - 750 q^{89} + 360 q^{90} - 28 q^{91} - 584 q^{92} - 192 q^{93} + 1056 q^{94} - 380 q^{95} - 288 q^{96} + 820 q^{97} - 294 q^{98} - 18 q^{99}+O(q^{100}) \) 3 * q - 6 * q^2 + 9 * q^3 + 12 * q^4 - 20 * q^5 - 18 * q^6 + 21 * q^7 - 24 * q^8 + 27 * q^9 + 40 * q^10 - 2 * q^11 + 36 * q^12 - 4 * q^13 - 42 * q^14 - 60 * q^15 + 48 * q^16 - 156 * q^17 - 54 * q^18 + 57 * q^19 - 80 * q^20 + 63 * q^21 + 4 * q^22 - 146 * q^23 - 72 * q^24 + 61 * q^25 + 8 * q^26 + 81 * q^27 + 84 * q^28 - 66 * q^29 + 120 * q^30 - 64 * q^31 - 96 * q^32 - 6 * q^33 + 312 * q^34 - 140 * q^35 + 108 * q^36 + 30 * q^37 - 114 * q^38 - 12 * q^39 + 160 * q^40 + 10 * q^41 - 126 * q^42 + 92 * q^43 - 8 * q^44 - 180 * q^45 + 292 * q^46 - 528 * q^47 + 144 * q^48 + 147 * q^49 - 122 * q^50 - 468 * q^51 - 16 * q^52 - 722 * q^53 - 162 * q^54 + 16 * q^55 - 168 * q^56 + 171 * q^57 + 132 * q^58 - 268 * q^59 - 240 * q^60 - 366 * q^61 + 128 * q^62 + 189 * q^63 + 192 * q^64 - 1184 * q^65 + 12 * q^66 - 926 * q^67 - 624 * q^68 - 438 * q^69 + 280 * q^70 - 252 * q^71 - 216 * q^72 - 58 * q^73 - 60 * q^74 + 183 * q^75 + 228 * q^76 - 14 * q^77 + 24 * q^78 - 534 * q^79 - 320 * q^80 + 243 * q^81 - 20 * q^82 - 1672 * q^83 + 252 * q^84 + 1332 * q^85 - 184 * q^86 - 198 * q^87 + 16 * q^88 - 750 * q^89 + 360 * q^90 - 28 * q^91 - 584 * q^92 - 192 * q^93 + 1056 * q^94 - 380 * q^95 - 288 * q^96 + 820 * q^97 - 294 * q^98 - 18 * q^99

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