LMFDB - Embedded newform 798.4.a.j.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:	$0$
Dimension:	$3$
Coefficient field:	3.3.57553.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 68x - 92 $ x^3 - x^2 - 68*x - 92
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$9.33757$ 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)

$f(q)$	$=$	$q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -14.6751 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -14.6751 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -29.3503 q^{10} -7.26391 q^{11} +12.0000 q^{12} +26.9089 q^{13} -14.0000 q^{14} -44.0254 q^{15} +16.0000 q^{16} +73.0302 q^{17} +18.0000 q^{18} -19.0000 q^{19} -58.7006 q^{20} -21.0000 q^{21} -14.5278 q^{22} +16.9089 q^{23} +24.0000 q^{24} +90.3598 q^{25} +53.8177 q^{26} +27.0000 q^{27} -28.0000 q^{28} +105.644 q^{29} -88.0509 q^{30} +162.892 q^{31} +32.0000 q^{32} -21.7917 q^{33} +146.060 q^{34} +102.726 q^{35} +36.0000 q^{36} -101.238 q^{37} -38.0000 q^{38} +80.7266 q^{39} -117.401 q^{40} -63.7149 q^{41} -42.0000 q^{42} +199.238 q^{43} -29.0556 q^{44} -132.076 q^{45} +33.8177 q^{46} +414.031 q^{47} +48.0000 q^{48} +49.0000 q^{49} +180.720 q^{50} +219.091 q^{51} +107.635 q^{52} +416.933 q^{53} +54.0000 q^{54} +106.599 q^{55} -56.0000 q^{56} -57.0000 q^{57} +211.289 q^{58} +252.000 q^{59} -176.102 q^{60} +272.317 q^{61} +325.785 q^{62} -63.0000 q^{63} +64.0000 q^{64} -394.891 q^{65} -43.5834 q^{66} +369.652 q^{67} +292.121 q^{68} +50.7266 q^{69} +205.452 q^{70} +597.493 q^{71} +72.0000 q^{72} -239.644 q^{73} -202.476 q^{74} +271.079 q^{75} -76.0000 q^{76} +50.8473 q^{77} +161.453 q^{78} -387.416 q^{79} -234.802 q^{80} +81.0000 q^{81} -127.430 q^{82} +166.773 q^{83} -84.0000 q^{84} -1071.73 q^{85} +398.476 q^{86} +316.933 q^{87} -58.1112 q^{88} +1474.80 q^{89} -264.153 q^{90} -188.362 q^{91} +67.6354 q^{92} +488.677 q^{93} +828.062 q^{94} +278.828 q^{95} +96.0000 q^{96} +65.1801 q^{97} +98.0000 q^{98} -65.3752 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 10 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 + 10 * q^5 + 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 10 q^{5} + 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 20 q^{10} + 54 q^{11} + 36 q^{12} + 92 q^{13} - 42 q^{14} + 30 q^{15} + 48 q^{16} + 78 q^{17} + 54 q^{18} - 57 q^{19} + 40 q^{20} - 63 q^{21} + 108 q^{22} + 62 q^{23} + 72 q^{24} + 205 q^{25} + 184 q^{26} + 81 q^{27} - 84 q^{28} - 8 q^{29} + 60 q^{30} + 292 q^{31} + 96 q^{32} + 162 q^{33} + 156 q^{34} - 70 q^{35} + 108 q^{36} + 22 q^{37} - 114 q^{38} + 276 q^{39} + 80 q^{40} - 38 q^{41} - 126 q^{42} + 272 q^{43} + 216 q^{44} + 90 q^{45} + 124 q^{46} + 422 q^{47} + 144 q^{48} + 147 q^{49} + 410 q^{50} + 234 q^{51} + 368 q^{52} + 276 q^{53} + 162 q^{54} + 752 q^{55} - 168 q^{56} - 171 q^{57} - 16 q^{58} + 756 q^{59} + 120 q^{60} + 562 q^{61} + 584 q^{62} - 189 q^{63} + 192 q^{64} - 164 q^{65} + 324 q^{66} + 1362 q^{67} + 312 q^{68} + 186 q^{69} - 140 q^{70} + 258 q^{71} + 216 q^{72} + 18 q^{73} + 44 q^{74} + 615 q^{75} - 228 q^{76} - 378 q^{77} + 552 q^{78} - 114 q^{79} + 160 q^{80} + 243 q^{81} - 76 q^{82} - 902 q^{83} - 252 q^{84} - 388 q^{85} + 544 q^{86} - 24 q^{87} + 432 q^{88} - 270 q^{89} + 180 q^{90} - 644 q^{91} + 248 q^{92} + 876 q^{93} + 844 q^{94} - 190 q^{95} + 288 q^{96} + 28 q^{97} + 294 q^{98} + 486 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 10 * q^5 + 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 20 * q^10 + 54 * q^11 + 36 * q^12 + 92 * q^13 - 42 * q^14 + 30 * q^15 + 48 * q^16 + 78 * q^17 + 54 * q^18 - 57 * q^19 + 40 * q^20 - 63 * q^21 + 108 * q^22 + 62 * q^23 + 72 * q^24 + 205 * q^25 + 184 * q^26 + 81 * q^27 - 84 * q^28 - 8 * q^29 + 60 * q^30 + 292 * q^31 + 96 * q^32 + 162 * q^33 + 156 * q^34 - 70 * q^35 + 108 * q^36 + 22 * q^37 - 114 * q^38 + 276 * q^39 + 80 * q^40 - 38 * q^41 - 126 * q^42 + 272 * q^43 + 216 * q^44 + 90 * q^45 + 124 * q^46 + 422 * q^47 + 144 * q^48 + 147 * q^49 + 410 * q^50 + 234 * q^51 + 368 * q^52 + 276 * q^53 + 162 * q^54 + 752 * q^55 - 168 * q^56 - 171 * q^57 - 16 * q^58 + 756 * q^59 + 120 * q^60 + 562 * q^61 + 584 * q^62 - 189 * q^63 + 192 * q^64 - 164 * q^65 + 324 * q^66 + 1362 * q^67 + 312 * q^68 + 186 * q^69 - 140 * q^70 + 258 * q^71 + 216 * q^72 + 18 * q^73 + 44 * q^74 + 615 * q^75 - 228 * q^76 - 378 * q^77 + 552 * q^78 - 114 * q^79 + 160 * q^80 + 243 * q^81 - 76 * q^82 - 902 * q^83 - 252 * q^84 - 388 * q^85 + 544 * q^86 - 24 * q^87 + 432 * q^88 - 270 * q^89 + 180 * q^90 - 644 * q^91 + 248 * q^92 + 876 * q^93 + 844 * q^94 - 190 * q^95 + 288 * q^96 + 28 * q^97 + 294 * q^98 + 486 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.00000	0.707107
$2$	2.00000	0.707107
$3$	3.00000	0.577350
$3$	3.00000	0.577350
$4$	4.00000	0.500000
$5$	−14.6751	−1.31258	−0.656292	−	0.754507i	$-0.727876\pi$
$5$	−14.6751	−1.31258	−0.656292	+	0.754507i	$0.727876\pi$
$6$	6.00000	0.408248
$7$	−7.00000	−0.377964
$7$	−7.00000	−0.377964
$8$	8.00000	0.353553
$9$	9.00000	0.333333
$10$	−29.3503	−0.928138
$11$	−7.26391	−0.199105	−0.0995523	−	0.995032i	$-0.531741\pi$
$11$	−7.26391	−0.199105	−0.0995523	+	0.995032i	$0.531741\pi$
$12$	12.0000	0.288675
$13$	26.9089	0.574090	0.287045	−	0.957917i	$-0.407327\pi$
$13$	26.9089	0.574090	0.287045	+	0.957917i	$0.407327\pi$
$14$	−14.0000	−0.267261
$15$	−44.0254	−0.757821
$16$	16.0000	0.250000
$17$	73.0302	1.04191	0.520954	−	0.853585i	$-0.325576\pi$
$17$	73.0302	1.04191	0.520954	+	0.853585i	$0.325576\pi$
$18$	18.0000	0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	−58.7006	−0.656292
$21$	−21.0000	−0.218218
$22$	−14.5278	−0.140788
$23$	16.9089	0.153293	0.0766465	−	0.997058i	$-0.475579\pi$
$23$	16.9089	0.153293	0.0766465	+	0.997058i	$0.475579\pi$
$24$	24.0000	0.204124
$25$	90.3598	0.722879
$26$	53.8177	0.405943
$27$	27.0000	0.192450
$28$	−28.0000	−0.188982
$29$	105.644	0.676471	0.338236	−	0.941061i	$-0.390170\pi$
$29$	105.644	0.676471	0.338236	+	0.941061i	$0.390170\pi$
$30$	−88.0509	−0.535860
$31$	162.892	0.943753	0.471876	−	0.881665i	$-0.343577\pi$
$31$	162.892	0.943753	0.471876	+	0.881665i	$0.343577\pi$
$32$	32.0000	0.176777
$33$	−21.7917	−0.114953
$34$	146.060	0.736740
$35$	102.726	0.496110
$36$	36.0000	0.166667
$37$	−101.238	−0.449822	−0.224911	−	0.974379i	$-0.572209\pi$
$37$	−101.238	−0.449822	−0.224911	+	0.974379i	$0.572209\pi$
$38$	−38.0000	−0.162221
$39$	80.7266	0.331451
$40$	−117.401	−0.464069
$41$	−63.7149	−0.242697	−0.121349	−	0.992610i	$-0.538722\pi$
$41$	−63.7149	−0.242697	−0.121349	+	0.992610i	$0.538722\pi$
$42$	−42.0000	−0.154303
$43$	199.238	0.706593	0.353296	−	0.935511i	$-0.385061\pi$
$43$	199.238	0.706593	0.353296	+	0.935511i	$0.385061\pi$
$44$	−29.0556	−0.0995523
$45$	−132.076	−0.437528
$46$	33.8177	0.108395
$47$	414.031	1.28495	0.642475	−	0.766307i	$-0.277908\pi$
$47$	414.031	1.28495	0.642475	+	0.766307i	$0.277908\pi$
$48$	48.0000	0.144338
$49$	49.0000	0.142857
$50$	180.720	0.511152
$51$	219.091	0.601545
$52$	107.635	0.287045
$53$	416.933	1.08057	0.540285	−	0.841482i	$-0.318317\pi$
$53$	416.933	1.08057	0.540285	+	0.841482i	$0.318317\pi$
$54$	54.0000	0.136083
$55$	106.599	0.261342
$56$	−56.0000	−0.133631
$57$	−57.0000	−0.132453
$58$	211.289	0.478338
$59$	252.000	0.556061	0.278031	−	0.960572i	$-0.410318\pi$
$59$	252.000	0.556061	0.278031	+	0.960572i	$0.410318\pi$
$60$	−176.102	−0.378911
$61$	272.317	0.571584	0.285792	−	0.958292i	$-0.407743\pi$
$61$	272.317	0.571584	0.285792	+	0.958292i	$0.407743\pi$
$62$	325.785	0.667334
$63$	−63.0000	−0.125988
$64$	64.0000	0.125000
$65$	−394.891	−0.753542
$66$	−43.5834	−0.0812841
$67$	369.652	0.674032	0.337016	−	0.941499i	$-0.390582\pi$
$67$	369.652	0.674032	0.337016	+	0.941499i	$0.390582\pi$
$68$	292.121	0.520954
$69$	50.7266	0.0885038
$70$	205.452	0.350803
$71$	597.493	0.998723	0.499362	−	0.866394i	$-0.333568\pi$
$71$	597.493	0.998723	0.499362	+	0.866394i	$0.333568\pi$
$72$	72.0000	0.117851
$73$	−239.644	−0.384222	−0.192111	−	0.981373i	$-0.561533\pi$
$73$	−239.644	−0.384222	−0.192111	+	0.981373i	$0.561533\pi$
$74$	−202.476	−0.318072
$75$	271.079	0.417354
$76$	−76.0000	−0.114708
$77$	50.8473	0.0752544
$78$	161.453	0.234371
$79$	−387.416	−0.551744	−0.275872	−	0.961194i	$-0.588967\pi$
$79$	−387.416	−0.551744	−0.275872	+	0.961194i	$0.588967\pi$
$80$	−234.802	−0.328146
$81$	81.0000	0.111111
$82$	−127.430	−0.171613
$83$	166.773	0.220551	0.110275	−	0.993901i	$-0.464827\pi$
$83$	166.773	0.220551	0.110275	+	0.993901i	$0.464827\pi$
$84$	−84.0000	−0.109109
$85$	−1071.73	−1.36759
$86$	398.476	0.499637
$87$	316.933	0.390561
$88$	−58.1112	−0.0703941
$89$	1474.80	1.75650	0.878251	−	0.478201i	$-0.158711\pi$
$89$	1474.80	1.75650	0.878251	+	0.478201i	$0.158711\pi$
$90$	−264.153	−0.309379
$91$	−188.362	−0.216986
$92$	67.6354	0.0766465
$93$	488.677	0.544876
$94$	828.062	0.908597
$95$	278.828	0.301128
$96$	96.0000	0.102062
$97$	65.1801	0.0682272	0.0341136	−	0.999418i	$-0.489139\pi$
$97$	65.1801	0.0682272	0.0341136	+	0.999418i	$0.489139\pi$
$98$	98.0000	0.101015
$99$	−65.3752	−0.0663682
$100$	361.439	0.361439
$101$	−403.451	−0.397474	−0.198737	−	0.980053i	$-0.563684\pi$
$101$	−403.451	−0.397474	−0.198737	+	0.980053i	$0.563684\pi$
$102$	438.181	0.425357
$103$	413.936	0.395984	0.197992	−	0.980204i	$-0.436558\pi$
$103$	413.936	0.395984	0.197992	+	0.980204i	$0.436558\pi$
$104$	215.271	0.202972
$105$	308.178	0.286429
$106$	833.866	0.764078
$107$	−709.645	−0.641159	−0.320579	−	0.947222i	$-0.603878\pi$
$107$	−709.645	−0.641159	−0.320579	+	0.947222i	$0.603878\pi$
$108$	108.000	0.0962250
$109$	143.863	0.126418	0.0632092	−	0.998000i	$-0.479866\pi$
$109$	143.863	0.126418	0.0632092	+	0.998000i	$0.479866\pi$
$110$	213.198	0.184796
$111$	−303.714	−0.259705
$112$	−112.000	−0.0944911
$113$	−1276.17	−1.06241	−0.531203	−	0.847245i	$-0.678260\pi$
$113$	−1276.17	−1.06241	−0.531203	+	0.847245i	$0.678260\pi$
$114$	−114.000	−0.0936586
$115$	−248.140	−0.201210
$116$	422.578	0.338236
$117$	242.180	0.191363
$118$	504.000	0.393195
$119$	−511.211	−0.393804
$120$	−352.203	−0.267930
$121$	−1278.24	−0.960357
$122$	544.634	0.404171
$123$	−191.145	−0.140121
$124$	651.570	0.471876
$125$	508.350	0.363745
$126$	−126.000	−0.0890871
$127$	−1996.23	−1.39478	−0.697388	−	0.716694i	$-0.745655\pi$
$127$	−1996.23	−1.39478	−0.697388	+	0.716694i	$0.745655\pi$
$128$	128.000	0.0883883
$129$	597.714	0.407952
$130$	−789.783	−0.532835
$131$	1157.59	0.772055	0.386027	−	0.922487i	$-0.373847\pi$
$131$	1157.59	0.772055	0.386027	+	0.922487i	$0.373847\pi$
$132$	−87.1669	−0.0574765
$133$	133.000	0.0867110
$134$	739.304	0.476613
$135$	−396.229	−0.252607
$136$	584.242	0.368370
$137$	1064.69	0.663960	0.331980	−	0.943286i	$-0.392283\pi$
$137$	1064.69	0.663960	0.331980	+	0.943286i	$0.392283\pi$
$138$	101.453	0.0625816
$139$	−3070.59	−1.87370	−0.936850	−	0.349732i	$-0.886273\pi$
$139$	−3070.59	−1.87370	−0.936850	+	0.349732i	$0.886273\pi$
$140$	410.904	0.248055
$141$	1242.09	0.741866
$142$	1194.99	0.706204
$143$	−195.463	−0.114304
$144$	144.000	0.0833333
$145$	−1550.35	−0.887926
$146$	−479.288	−0.271686
$147$	147.000	0.0824786
$148$	−404.952	−0.224911
$149$	−1402.41	−0.771073	−0.385537	−	0.922693i	$-0.625984\pi$
$149$	−1402.41	−0.771073	−0.385537	+	0.922693i	$0.625984\pi$
$150$	542.159	0.295114
$151$	−1036.50	−0.558603	−0.279302	−	0.960203i	$-0.590103\pi$
$151$	−1036.50	−0.558603	−0.279302	+	0.960203i	$0.590103\pi$
$152$	−152.000	−0.0811107
$153$	657.272	0.347302
$154$	101.695	0.0532129
$155$	−2390.47	−1.23876
$156$	322.906	0.165726
$157$	2006.94	1.02020	0.510099	−	0.860116i	$-0.329609\pi$
$157$	2006.94	1.02020	0.510099	+	0.860116i	$0.329609\pi$
$158$	−774.833	−0.390142
$159$	1250.80	0.623867
$160$	−469.605	−0.232034
$161$	−118.362	−0.0579393
$162$	162.000	0.0785674
$163$	−691.732	−0.332396	−0.166198	−	0.986092i	$-0.553149\pi$
$163$	−691.732	−0.332396	−0.166198	+	0.986092i	$0.553149\pi$
$164$	−254.859	−0.121349
$165$	319.797	0.150886
$166$	333.546	0.155953
$167$	−1611.47	−0.746701	−0.373350	−	0.927690i	$-0.621791\pi$
$167$	−1611.47	−0.746701	−0.373350	+	0.927690i	$0.621791\pi$
$168$	−168.000	−0.0771517
$169$	−1472.91	−0.670420
$170$	−2143.46	−0.967033
$171$	−171.000	−0.0764719
$172$	796.952	0.353296
$173$	626.642	0.275391	0.137696	−	0.990475i	$-0.456030\pi$
$173$	626.642	0.275391	0.137696	+	0.990475i	$0.456030\pi$
$174$	633.866	0.276168
$175$	−632.519	−0.273222
$176$	−116.222	−0.0497761
$177$	756.000	0.321042
$178$	2949.60	1.24203
$179$	2889.08	1.20637	0.603185	−	0.797602i	$-0.293898\pi$
$179$	2889.08	1.20637	0.603185	+	0.797602i	$0.293898\pi$
$180$	−528.305	−0.218764
$181$	433.467	0.178008	0.0890038	−	0.996031i	$-0.471632\pi$
$181$	433.467	0.178008	0.0890038	+	0.996031i	$0.471632\pi$
$182$	−376.724	−0.153432
$183$	816.951	0.330004
$184$	135.271	0.0541973
$185$	1485.68	0.590429
$186$	977.354	0.385285
$187$	−530.484	−0.207448
$188$	1656.12	0.642475
$189$	−189.000	−0.0727393
$190$	557.655	0.212929
$191$	−3569.71	−1.35233	−0.676165	−	0.736751i	$-0.736359\pi$
$191$	−3569.71	−1.35233	−0.676165	+	0.736751i	$0.736359\pi$
$192$	192.000	0.0721688
$193$	−155.032	−0.0578211	−0.0289106	−	0.999582i	$-0.509204\pi$
$193$	−155.032	−0.0578211	−0.0289106	+	0.999582i	$0.509204\pi$
$194$	130.360	0.0482439
$195$	−1184.67	−0.435058
$196$	196.000	0.0714286
$197$	759.799	0.274789	0.137395	−	0.990516i	$-0.456127\pi$
$197$	759.799	0.274789	0.137395	+	0.990516i	$0.456127\pi$
$198$	−130.750	−0.0469294
$199$	810.494	0.288716	0.144358	−	0.989526i	$-0.453888\pi$
$199$	810.494	0.288716	0.144358	+	0.989526i	$0.453888\pi$
$200$	722.879	0.255576
$201$	1108.96	0.389153
$202$	−806.902	−0.281057
$203$	−739.511	−0.255682
$204$	876.362	0.300773
$205$	935.025	0.318561
$206$	827.872	0.280003
$207$	152.180	0.0510977
$208$	430.542	0.143523
$209$	138.014	0.0456777
$210$	616.356	0.202536
$211$	2179.44	0.711084	0.355542	−	0.934660i	$-0.384296\pi$
$211$	2179.44	0.711084	0.355542	+	0.934660i	$0.384296\pi$
$212$	1667.73	0.540285
$213$	1792.48	0.576613
$214$	−1419.29	−0.453368
$215$	−2923.84	−0.927463
$216$	216.000	0.0680414
$217$	−1140.25	−0.356705
$218$	287.727	0.0893913
$219$	−718.931	−0.221831
$220$	426.395	0.130671
$221$	1965.16	0.598149
$222$	−607.427	−0.183639
$223$	3711.66	1.11458	0.557290	−	0.830318i	$-0.311841\pi$
$223$	3711.66	1.11458	0.557290	+	0.830318i	$0.311841\pi$
$224$	−224.000	−0.0668153
$225$	813.238	0.240960
$226$	−2552.34	−0.751234
$227$	−2293.92	−0.670718	−0.335359	−	0.942090i	$-0.608858\pi$
$227$	−2293.92	−0.670718	−0.335359	+	0.942090i	$0.608858\pi$
$228$	−228.000	−0.0662266
$229$	4464.72	1.28837	0.644185	−	0.764870i	$-0.277197\pi$
$229$	4464.72	1.28837	0.644185	+	0.764870i	$0.277197\pi$
$230$	−496.280	−0.142277
$231$	152.542	0.0434482
$232$	845.155	0.239169
$233$	−7062.99	−1.98589	−0.992944	−	0.118583i	$-0.962165\pi$
$233$	−7062.99	−1.98589	−0.992944	+	0.118583i	$0.962165\pi$
$234$	484.359	0.135314
$235$	−6075.97	−1.68661
$236$	1008.00	0.278031
$237$	−1162.25	−0.318549
$238$	−1022.42	−0.278461
$239$	5110.97	1.38327	0.691635	−	0.722247i	$-0.256891\pi$
$239$	5110.97	1.38327	0.691635	+	0.722247i	$0.256891\pi$
$240$	−704.407	−0.189455
$241$	4843.29	1.29454	0.647269	−	0.762262i	$-0.275911\pi$
$241$	4843.29	1.29454	0.647269	+	0.762262i	$0.275911\pi$
$242$	−2556.47	−0.679075
$243$	243.000	0.0641500
$244$	1089.27	0.285792
$245$	−719.082	−0.187512
$246$	−382.289	−0.0990808
$247$	−511.268	−0.131705
$248$	1303.14	0.333667
$249$	500.319	0.127335
$250$	1016.70	0.257207
$251$	4175.94	1.05013	0.525065	−	0.851062i	$-0.324041\pi$
$251$	4175.94	1.05013	0.525065	+	0.851062i	$0.324041\pi$
$252$	−252.000	−0.0629941
$253$	−122.824	−0.0305213
$254$	−3992.46	−0.986256
$255$	−3215.19	−0.789579
$256$	256.000	0.0625000
$257$	−1266.43	−0.307383	−0.153692	−	0.988119i	$-0.549116\pi$
$257$	−1266.43	−0.307383	−0.153692	+	0.988119i	$0.549116\pi$
$258$	1195.43	0.288465
$259$	708.665	0.170017
$260$	−1579.57	−0.376771
$261$	950.799	0.225490
$262$	2315.18	0.545925
$263$	595.688	0.139664	0.0698321	−	0.997559i	$-0.477754\pi$
$263$	595.688	0.139664	0.0698321	+	0.997559i	$0.477754\pi$
$264$	−174.334	−0.0406420
$265$	−6118.55	−1.41834
$266$	266.000	0.0613139
$267$	4424.40	1.01412
$268$	1478.61	0.337016
$269$	2868.33	0.650131	0.325065	−	0.945692i	$-0.394614\pi$
$269$	2868.33	0.650131	0.325065	+	0.945692i	$0.394614\pi$
$270$	−792.458	−0.178620
$271$	−639.023	−0.143239	−0.0716197	−	0.997432i	$-0.522817\pi$
$271$	−639.023	−0.143239	−0.0716197	+	0.997432i	$0.522817\pi$
$272$	1168.48	0.260477
$273$	−565.086	−0.125277
$274$	2129.38	0.469490
$275$	−656.365	−0.143928
$276$	202.906	0.0442519
$277$	4242.22	0.920183	0.460091	−	0.887872i	$-0.347817\pi$
$277$	4242.22	0.920183	0.460091	+	0.887872i	$0.347817\pi$
$278$	−6141.19	−1.32491
$279$	1466.03	0.314584
$280$	821.808	0.175402
$281$	−1192.88	−0.253242	−0.126621	−	0.991951i	$-0.540413\pi$
$281$	−1192.88	−0.253242	−0.126621	+	0.991951i	$0.540413\pi$
$282$	2484.19	0.524579
$283$	−1193.12	−0.250614	−0.125307	−	0.992118i	$-0.539992\pi$
$283$	−1193.12	−0.250614	−0.125307	+	0.992118i	$0.539992\pi$
$284$	2389.97	0.499362
$285$	836.483	0.173856
$286$	−390.927	−0.0808251
$287$	446.004	0.0917310
$288$	288.000	0.0589256
$289$	420.409	0.0855708
$290$	−3100.69	−0.627858
$291$	195.540	0.0393910
$292$	−958.575	−0.192111
$293$	−2455.06	−0.489508	−0.244754	−	0.969585i	$-0.578707\pi$
$293$	−2455.06	−0.489508	−0.244754	+	0.969585i	$0.578707\pi$
$294$	294.000	0.0583212
$295$	−3698.14	−0.729877
$296$	−809.903	−0.159036
$297$	−196.125	−0.0383177
$298$	−2804.82	−0.545231
$299$	454.998	0.0880040
$300$	1084.32	0.208677
$301$	−1394.67	−0.267067
$302$	−2073.00	−0.394992
$303$	−1210.35	−0.229482
$304$	−304.000	−0.0573539
$305$	−3996.29	−0.750252
$306$	1314.54	0.245580
$307$	−10333.1	−1.92099	−0.960495	−	0.278297i	$-0.910230\pi$
$307$	−10333.1	−1.92099	−0.960495	+	0.278297i	$0.910230\pi$
$308$	203.389	0.0376272
$309$	1241.81	0.228621
$310$	−4780.94	−0.875932
$311$	−999.379	−0.182217	−0.0911086	−	0.995841i	$-0.529041\pi$
$311$	−999.379	−0.182217	−0.0911086	+	0.995841i	$0.529041\pi$
$312$	645.812	0.117186
$313$	2103.79	0.379915	0.189958	−	0.981792i	$-0.439165\pi$
$313$	2103.79	0.379915	0.189958	+	0.981792i	$0.439165\pi$
$314$	4013.87	0.721389
$315$	924.534	0.165370
$316$	−1549.67	−0.275872
$317$	−2162.31	−0.383116	−0.191558	−	0.981481i	$-0.561354\pi$
$317$	−2162.31	−0.383116	−0.191558	+	0.981481i	$0.561354\pi$
$318$	2501.60	0.441141
$319$	−767.391	−0.134689
$320$	−939.209	−0.164073
$321$	−2128.94	−0.370173
$322$	−236.724	−0.0409693
$323$	−1387.57	−0.239030
$324$	324.000	0.0555556
$325$	2431.48	0.414998
$326$	−1383.46	−0.235040
$327$	431.590	0.0729877
$328$	−509.719	−0.0858065
$329$	−2898.22	−0.485666
$330$	639.593	0.106692
$331$	−7417.28	−1.23169	−0.615847	−	0.787866i	$-0.711186\pi$
$331$	−7417.28	−1.23169	−0.615847	+	0.787866i	$0.711186\pi$
$332$	667.093	0.110275
$333$	−911.141	−0.149941
$334$	−3222.93	−0.527997
$335$	−5424.69	−0.884724
$336$	−336.000	−0.0545545
$337$	−3299.14	−0.533281	−0.266641	−	0.963796i	$-0.585914\pi$
$337$	−3299.14	−0.533281	−0.266641	+	0.963796i	$0.585914\pi$
$338$	−2945.83	−0.474059
$339$	−3828.51	−0.613380
$340$	−4286.91	−0.683796
$341$	−1183.24	−0.187905
$342$	−342.000	−0.0540738
$343$	−343.000	−0.0539949
$344$	1593.90	0.249818
$345$	−744.420	−0.116169
$346$	1253.28	0.194731
$347$	−263.470	−0.0407602	−0.0203801	−	0.999792i	$-0.506488\pi$
$347$	−263.470	−0.0407602	−0.0203801	+	0.999792i	$0.506488\pi$
$348$	1267.73	0.195280
$349$	−10071.8	−1.54479	−0.772396	−	0.635141i	$-0.780942\pi$
$349$	−10071.8	−1.54479	−0.772396	+	0.635141i	$0.780942\pi$
$350$	−1265.04	−0.193197
$351$	726.539	0.110484
$352$	−232.445	−0.0351970
$353$	4092.82	0.617108	0.308554	−	0.951207i	$-0.400155\pi$
$353$	4092.82	0.617108	0.308554	+	0.951207i	$0.400155\pi$
$354$	1512.00	0.227011
$355$	−8768.29	−1.31091
$356$	5899.20	0.878251
$357$	−1533.63	−0.227363
$358$	5778.16	0.853032
$359$	10410.0	1.53042	0.765210	−	0.643781i	$-0.222635\pi$
$359$	10410.0	1.53042	0.765210	+	0.643781i	$0.222635\pi$
$360$	−1056.61	−0.154690
$361$	361.000	0.0526316
$362$	866.935	0.125870
$363$	−3834.71	−0.554463
$364$	−753.448	−0.108493
$365$	3516.81	0.504324
$366$	1633.90	0.233348
$367$	−7444.41	−1.05884	−0.529421	−	0.848359i	$-0.677591\pi$
$367$	−7444.41	−1.05884	−0.529421	+	0.848359i	$0.677591\pi$
$368$	270.542	0.0383233
$369$	−573.434	−0.0808991
$370$	2971.36	0.417497
$371$	−2918.53	−0.408417
$372$	1954.71	0.272438
$373$	−2856.88	−0.396578	−0.198289	−	0.980144i	$-0.563538\pi$
$373$	−2856.88	−0.396578	−0.198289	+	0.980144i	$0.563538\pi$
$374$	−1060.97	−0.146688
$375$	1525.05	0.210008
$376$	3312.25	0.454299
$377$	2842.77	0.388356
$378$	−378.000	−0.0514344
$379$	1437.40	0.194814	0.0974070	−	0.995245i	$-0.468945\pi$
$379$	1437.40	0.194814	0.0974070	+	0.995245i	$0.468945\pi$
$380$	1115.31	0.150564
$381$	−5988.69	−0.805275
$382$	−7139.41	−0.956241
$383$	12054.5	1.60823	0.804117	−	0.594471i	$-0.202638\pi$
$383$	12054.5	1.60823	0.804117	+	0.594471i	$0.202638\pi$
$384$	384.000	0.0510310
$385$	−746.192	−0.0987778
$386$	−310.065	−0.0408857
$387$	1793.14	0.235531
$388$	260.721	0.0341136
$389$	5883.32	0.766828	0.383414	−	0.923577i	$-0.374748\pi$
$389$	5883.32	0.766828	0.383414	+	0.923577i	$0.374748\pi$
$390$	−2369.35	−0.307632
$391$	1234.86	0.159717
$392$	392.000	0.0505076
$393$	3472.77	0.445746
$394$	1519.60	0.194305
$395$	5685.39	0.724210
$396$	−261.501	−0.0331841
$397$	−5316.67	−0.672131	−0.336065	−	0.941839i	$-0.609096\pi$
$397$	−5316.67	−0.672131	−0.336065	+	0.941839i	$0.609096\pi$
$398$	1620.99	0.204153
$399$	399.000	0.0500626
$400$	1445.76	0.180720
$401$	6280.73	0.782157	0.391078	−	0.920357i	$-0.372102\pi$
$401$	6280.73	0.782157	0.391078	+	0.920357i	$0.372102\pi$
$402$	2217.91	0.275173
$403$	4383.25	0.541799
$404$	−1613.80	−0.198737
$405$	−1188.69	−0.145843
$406$	−1479.02	−0.180795
$407$	735.383	0.0895616
$408$	1752.72	0.212678
$409$	−13195.6	−1.59531	−0.797653	−	0.603116i	$-0.793926\pi$
$409$	−13195.6	−1.59531	−0.797653	+	0.603116i	$0.793926\pi$
$410$	1870.05	0.225257
$411$	3194.07	0.383337
$412$	1655.74	0.197992
$413$	−1764.00	−0.210171
$414$	304.359	0.0361315
$415$	−2447.42	−0.289492
$416$	861.083	0.101486
$417$	−9211.78	−1.08178
$418$	276.028	0.0322990
$419$	2546.32	0.296887	0.148444	−	0.988921i	$-0.452574\pi$
$419$	2546.32	0.296887	0.148444	+	0.988921i	$0.452574\pi$
$420$	1232.71	0.143215
$421$	729.255	0.0844221	0.0422110	−	0.999109i	$-0.486560\pi$
$421$	729.255	0.0844221	0.0422110	+	0.999109i	$0.486560\pi$
$422$	4358.88	0.502813
$423$	3726.28	0.428317
$424$	3335.47	0.382039
$425$	6599.00	0.753172
$426$	3584.96	0.407727
$427$	−1906.22	−0.216038
$428$	−2838.58	−0.320579
$429$	−586.390	−0.0659934
$430$	−5847.69	−0.655815
$431$	−3518.06	−0.393177	−0.196588	−	0.980486i	$-0.562986\pi$
$431$	−3518.06	−0.393177	−0.196588	+	0.980486i	$0.562986\pi$
$432$	432.000	0.0481125
$433$	−815.289	−0.0904856	−0.0452428	−	0.998976i	$-0.514406\pi$
$433$	−815.289	−0.0904856	−0.0452428	+	0.998976i	$0.514406\pi$
$434$	−2280.49	−0.252229
$435$	−4651.04	−0.512644
$436$	575.453	0.0632092
$437$	−321.268	−0.0351678
$438$	−1437.86	−0.156858
$439$	−2713.15	−0.294969	−0.147484	−	0.989064i	$-0.547118\pi$
$439$	−2713.15	−0.294969	−0.147484	+	0.989064i	$0.547118\pi$
$440$	852.791	0.0923982
$441$	441.000	0.0476190
$442$	3930.32	0.422955
$443$	9943.62	1.06645	0.533223	−	0.845975i	$-0.320981\pi$
$443$	9943.62	1.06645	0.533223	+	0.845975i	$0.320981\pi$
$444$	−1214.85	−0.129852
$445$	−21642.9	−2.30556
$446$	7423.32	0.788127
$447$	−4207.23	−0.445179
$448$	−448.000	−0.0472456
$449$	−13786.2	−1.44902	−0.724510	−	0.689264i	$-0.757934\pi$
$449$	−13786.2	−1.44902	−0.724510	+	0.689264i	$0.757934\pi$
$450$	1626.48	0.170384
$451$	462.819	0.0483221
$452$	−5104.68	−0.531203
$453$	−3109.50	−0.322510
$454$	−4587.85	−0.474269
$455$	2764.24	0.284812
$456$	−456.000	−0.0468293
$457$	7646.57	0.782695	0.391347	−	0.920243i	$-0.372009\pi$
$457$	7646.57	0.782695	0.391347	+	0.920243i	$0.372009\pi$
$458$	8929.43	0.911015
$459$	1971.82	0.200515
$460$	−992.559	−0.100605
$461$	4832.49	0.488225	0.244112	−	0.969747i	$-0.421503\pi$
$461$	4832.49	0.488225	0.244112	+	0.969747i	$0.421503\pi$
$462$	305.084	0.0307225
$463$	−10672.2	−1.07123	−0.535614	−	0.844463i	$-0.679920\pi$
$463$	−10672.2	−1.07123	−0.535614	+	0.844463i	$0.679920\pi$
$464$	1690.31	0.169118
$465$	−7171.41	−0.715196
$466$	−14126.0	−1.40423
$467$	7977.45	0.790476	0.395238	−	0.918579i	$-0.370662\pi$
$467$	7977.45	0.790476	0.395238	+	0.918579i	$0.370662\pi$
$468$	968.719	0.0956817
$469$	−2587.56	−0.254760
$470$	−12151.9	−1.19261
$471$	6020.81	0.589011
$472$	2016.00	0.196597
$473$	−1447.25	−0.140686
$474$	−2324.50	−0.225248
$475$	−1716.84	−0.165840
$476$	−2044.85	−0.196902
$477$	3752.40	0.360190
$478$	10221.9	0.978119
$479$	16007.0	1.52689	0.763445	−	0.645873i	$-0.223506\pi$
$479$	16007.0	1.52689	0.763445	+	0.645873i	$0.223506\pi$
$480$	−1408.81	−0.133965
$481$	−2724.20	−0.258238
$482$	9686.58	0.915377
$483$	−355.086	−0.0334513
$484$	−5112.94	−0.480179
$485$	−956.528	−0.0895540
$486$	486.000	0.0453609
$487$	−12108.8	−1.12670	−0.563349	−	0.826219i	$-0.690487\pi$
$487$	−12108.8	−1.12670	−0.563349	+	0.826219i	$0.690487\pi$
$488$	2178.54	0.202085
$489$	−2075.20	−0.191909
$490$	−1438.16	−0.132591
$491$	−14691.8	−1.35037	−0.675186	−	0.737647i	$-0.735937\pi$
$491$	−14691.8	−1.35037	−0.675186	+	0.737647i	$0.735937\pi$
$492$	−764.578	−0.0700607
$493$	7715.23	0.704820
$494$	−1022.54	−0.0931297
$495$	959.390	0.0871139
$496$	2606.28	0.235938
$497$	−4182.45	−0.377482
$498$	1000.64	0.0900395
$499$	−2916.65	−0.261657	−0.130829	−	0.991405i	$-0.541764\pi$
$499$	−2916.65	−0.261657	−0.130829	+	0.991405i	$0.541764\pi$
$500$	2033.40	0.181873
$501$	−4834.40	−0.431108
$502$	8351.88	0.742555
$503$	12514.2	1.10930	0.554651	−	0.832083i	$-0.312852\pi$
$503$	12514.2	1.10930	0.554651	+	0.832083i	$0.312852\pi$
$504$	−504.000	−0.0445435
$505$	5920.70	0.521718
$506$	−245.649	−0.0215818
$507$	−4418.74	−0.387067
$508$	−7984.91	−0.697388
$509$	7232.89	0.629847	0.314924	−	0.949117i	$-0.398021\pi$
$509$	7232.89	0.629847	0.314924	+	0.949117i	$0.398021\pi$
$510$	−6430.37	−0.558317
$511$	1677.51	0.145222
$512$	512.000	0.0441942
$513$	−513.000	−0.0441511
$514$	−2532.85	−0.217353
$515$	−6074.57	−0.519763
$516$	2390.85	0.203976
$517$	−3007.48	−0.255839
$518$	1417.33	0.120220
$519$	1879.93	0.158997
$520$	−3159.13	−0.266417
$521$	−9725.43	−0.817810	−0.408905	−	0.912577i	$-0.634089\pi$
$521$	−9725.43	−0.817810	−0.408905	+	0.912577i	$0.634089\pi$
$522$	1901.60	0.159446
$523$	887.405	0.0741941	0.0370971	−	0.999312i	$-0.488189\pi$
$523$	887.405	0.0741941	0.0370971	+	0.999312i	$0.488189\pi$
$524$	4630.36	0.386027
$525$	−1897.56	−0.157745
$526$	1191.38	0.0987575
$527$	11896.1	0.983303
$528$	−348.667	−0.0287383
$529$	−11881.1	−0.976501
$530$	−12237.1	−1.00292
$531$	2268.00	0.185354
$532$	532.000	0.0433555
$533$	−1714.49	−0.139330
$534$	8848.81	0.717089
$535$	10414.1	0.841575
$536$	2957.21	0.238306
$537$	8667.24	0.696497
$538$	5736.66	0.459712
$539$	−355.931	−0.0284435
$540$	−1584.92	−0.126304
$541$	17709.1	1.40734	0.703671	−	0.710526i	$-0.251543\pi$
$541$	17709.1	1.40734	0.703671	+	0.710526i	$0.251543\pi$
$542$	−1278.05	−0.101286
$543$	1300.40	0.102773
$544$	2336.97	0.184185
$545$	−2111.22	−0.165935
$546$	−1130.17	−0.0885840
$547$	15980.7	1.24915	0.624574	−	0.780966i	$-0.285273\pi$
$547$	15980.7	1.24915	0.624574	+	0.780966i	$0.285273\pi$
$548$	4258.75	0.331980
$549$	2450.85	0.190528
$550$	−1312.73	−0.101773
$551$	−2007.24	−0.155193
$552$	405.812	0.0312908
$553$	2711.92	0.208540
$554$	8484.45	0.650667
$555$	4457.04	0.340885
$556$	−12282.4	−0.936850
$557$	6198.76	0.471544	0.235772	−	0.971808i	$-0.424238\pi$
$557$	6198.76	0.471544	0.235772	+	0.971808i	$0.424238\pi$
$558$	2932.06	0.222445
$559$	5361.26	0.405648
$560$	1643.62	0.124028
$561$	−1591.45	−0.119770
$562$	−2385.75	−0.179069
$563$	−90.3624	−0.00676433	−0.00338217	−	0.999994i	$-0.501077\pi$
$563$	−90.3624	−0.00676433	−0.00338217	+	0.999994i	$0.501077\pi$
$564$	4968.37	0.370933
$565$	18728.0	1.39450
$566$	−2386.25	−0.177211
$567$	−567.000	−0.0419961
$568$	4779.94	0.353102
$569$	−10774.2	−0.793814	−0.396907	−	0.917859i	$-0.629916\pi$
$569$	−10774.2	−0.793814	−0.396907	+	0.917859i	$0.629916\pi$
$570$	1672.97	0.122935
$571$	−8299.59	−0.608279	−0.304139	−	0.952628i	$-0.598369\pi$
$571$	−8299.59	−0.608279	−0.304139	+	0.952628i	$0.598369\pi$
$572$	−781.854	−0.0571520
$573$	−10709.1	−0.780768
$574$	892.008	0.0648636
$575$	1527.88	0.110812
$576$	576.000	0.0416667
$577$	7389.30	0.533138	0.266569	−	0.963816i	$-0.414110\pi$
$577$	7389.30	0.533138	0.266569	+	0.963816i	$0.414110\pi$
$578$	840.819	0.0605077
$579$	−465.097	−0.0333830
$580$	−6201.39	−0.443963
$581$	−1167.41	−0.0833604
$582$	391.081	0.0278536
$583$	−3028.56	−0.215146
$584$	−1917.15	−0.135843
$585$	−3554.02	−0.251181
$586$	−4910.11	−0.346135
$587$	10586.8	0.744404	0.372202	−	0.928152i	$-0.378603\pi$
$587$	10586.8	0.744404	0.372202	+	0.928152i	$0.378603\pi$
$588$	588.000	0.0412393
$589$	−3094.96	−0.216512
$590$	−7396.27	−0.516101
$591$	2279.40	0.158650
$592$	−1619.81	−0.112455
$593$	10323.2	0.714876	0.357438	−	0.933937i	$-0.383650\pi$
$593$	10323.2	0.714876	0.357438	+	0.933937i	$0.383650\pi$
$594$	−392.251	−0.0270947
$595$	7502.10	0.516901
$596$	−5609.64	−0.385537
$597$	2431.48	0.166690
$598$	909.996	0.0622282
$599$	−3352.55	−0.228684	−0.114342	−	0.993441i	$-0.536476\pi$
$599$	−3352.55	−0.228684	−0.114342	+	0.993441i	$0.536476\pi$
$600$	2168.64	0.147557
$601$	−17060.5	−1.15792	−0.578961	−	0.815355i	$-0.696542\pi$
$601$	−17060.5	−1.15792	−0.578961	+	0.815355i	$0.696542\pi$
$602$	−2789.33	−0.188845
$603$	3326.87	0.224677
$604$	−4145.99	−0.279302
$605$	18758.3	1.26055
$606$	−2420.71	−0.162268
$607$	−2603.86	−0.174115	−0.0870573	−	0.996203i	$-0.527746\pi$
$607$	−2603.86	−0.174115	−0.0870573	+	0.996203i	$0.527746\pi$
$608$	−608.000	−0.0405554
$609$	−2218.53	−0.147618
$610$	−7992.58	−0.530508
$611$	11141.1	0.737677
$612$	2629.09	0.173651
$613$	2779.41	0.183131	0.0915656	−	0.995799i	$-0.470813\pi$
$613$	2779.41	0.183131	0.0915656	+	0.995799i	$0.470813\pi$
$614$	−20666.3	−1.35835
$615$	2805.07	0.183921
$616$	406.779	0.0266065
$617$	−16951.3	−1.10605	−0.553027	−	0.833164i	$-0.686527\pi$
$617$	−16951.3	−1.10605	−0.553027	+	0.833164i	$0.686527\pi$
$618$	2483.62	0.161660
$619$	1053.35	0.0683972	0.0341986	−	0.999415i	$-0.489112\pi$
$619$	1053.35	0.0683972	0.0341986	+	0.999415i	$0.489112\pi$
$620$	−9561.88	−0.619378
$621$	456.539	0.0295013
$622$	−1998.76	−0.128847
$623$	−10323.6	−0.663895
$624$	1291.62	0.0828628
$625$	−18755.1	−1.20033
$626$	4207.59	0.268641
$627$	414.043	0.0263720
$628$	8027.75	0.510099
$629$	−7393.42	−0.468673
$630$	1849.07	0.116934
$631$	−4165.00	−0.262767	−0.131383	−	0.991332i	$-0.541942\pi$
$631$	−4165.00	−0.262767	−0.131383	+	0.991332i	$0.541942\pi$
$632$	−3099.33	−0.195071
$633$	6538.32	0.410545
$634$	−4324.63	−0.270904
$635$	29294.9	1.83076
$636$	5003.20	0.311933
$637$	1318.53	0.0820129
$638$	−1534.78	−0.0952392
$639$	5377.43	0.332908
$640$	−1878.42	−0.116017
$641$	−13467.8	−0.829867	−0.414934	−	0.909852i	$-0.636195\pi$
$641$	−13467.8	−0.829867	−0.414934	+	0.909852i	$0.636195\pi$
$642$	−4257.87	−0.261752
$643$	−5498.95	−0.337259	−0.168629	−	0.985680i	$-0.553934\pi$
$643$	−5498.95	−0.337259	−0.168629	+	0.985680i	$0.553934\pi$
$644$	−473.448	−0.0289697
$645$	−8771.53	−0.535471
$646$	−2775.15	−0.169020
$647$	11063.8	0.672274	0.336137	−	0.941813i	$-0.390879\pi$
$647$	11063.8	0.672274	0.336137	+	0.941813i	$0.390879\pi$
$648$	648.000	0.0392837
$649$	−1830.50	−0.110714
$650$	4862.96	0.293448
$651$	−3420.74	−0.205944
$652$	−2766.93	−0.166198
$653$	−5838.81	−0.349909	−0.174954	−	0.984577i	$-0.555978\pi$
$653$	−5838.81	−0.349909	−0.174954	+	0.984577i	$0.555978\pi$
$654$	863.180	0.0516101
$655$	−16987.8	−1.01339
$656$	−1019.44	−0.0606743
$657$	−2156.79	−0.128074
$658$	−5796.44	−0.343417
$659$	6410.58	0.378939	0.189469	−	0.981887i	$-0.439323\pi$
$659$	6410.58	0.378939	0.189469	+	0.981887i	$0.439323\pi$
$660$	1279.19	0.0754428
$661$	16628.7	0.978488	0.489244	−	0.872147i	$-0.337273\pi$
$661$	16628.7	0.978488	0.489244	+	0.872147i	$0.337273\pi$
$662$	−14834.6	−0.870939
$663$	5895.48	0.345341
$664$	1334.19	0.0779765
$665$	−1951.79	−0.113816
$666$	−1822.28	−0.106024
$667$	1786.33	0.103698
$668$	−6445.87	−0.373350
$669$	11135.0	0.643503
$670$	−10849.4	−0.625595
$671$	−1978.08	−0.113805
$672$	−672.000	−0.0385758
$673$	8874.78	0.508318	0.254159	−	0.967163i	$-0.418201\pi$
$673$	8874.78	0.508318	0.254159	+	0.967163i	$0.418201\pi$
$674$	−6598.29	−0.377087
$675$	2439.72	0.139118
$676$	−5891.65	−0.335210
$677$	2899.41	0.164599	0.0822993	−	0.996608i	$-0.473774\pi$
$677$	2899.41	0.164599	0.0822993	+	0.996608i	$0.473774\pi$
$678$	−7657.01	−0.433725
$679$	−456.261	−0.0257875
$680$	−8573.83	−0.483517
$681$	−6881.77	−0.387239
$682$	−2366.47	−0.132869
$683$	−3395.37	−0.190220	−0.0951099	−	0.995467i	$-0.530320\pi$
$683$	−3395.37	−0.190220	−0.0951099	+	0.995467i	$0.530320\pi$
$684$	−684.000	−0.0382360
$685$	−15624.5	−0.871503
$686$	−686.000	−0.0381802
$687$	13394.1	0.743841
$688$	3187.81	0.176648
$689$	11219.2	0.620344
$690$	−1488.84	−0.0821437
$691$	15350.4	0.845090	0.422545	−	0.906342i	$-0.361137\pi$
$691$	15350.4	0.845090	0.422545	+	0.906342i	$0.361137\pi$
$692$	2506.57	0.137696
$693$	457.626	0.0250848
$694$	−526.940	−0.0288218
$695$	45061.4	2.45939
$696$	2535.47	0.138084
$697$	−4653.11	−0.252868
$698$	−20143.6	−1.09233
$699$	−21189.0	−1.14655
$700$	−2530.07	−0.136611
$701$	−5746.27	−0.309606	−0.154803	−	0.987945i	$-0.549474\pi$
$701$	−5746.27	−0.309606	−0.154803	+	0.987945i	$0.549474\pi$
$702$	1453.08	0.0781238
$703$	1923.52	0.103196
$704$	−464.890	−0.0248881
$705$	−18227.9	−0.973762
$706$	8185.65	0.436361
$707$	2824.16	0.150231
$708$	3024.00	0.160521
$709$	12371.4	0.655313	0.327656	−	0.944797i	$-0.393741\pi$
$709$	12371.4	0.655313	0.327656	+	0.944797i	$0.393741\pi$
$710$	−17536.6	−0.926952
$711$	−3486.75	−0.183915
$712$	11798.4	0.621017
$713$	2754.32	0.144671
$714$	−3067.27	−0.160770
$715$	2868.45	0.150034
$716$	11556.3	0.603185
$717$	15332.9	0.798631
$718$	20820.1	1.08217
$719$	11164.6	0.579097	0.289549	−	0.957163i	$-0.406495\pi$
$719$	11164.6	0.579097	0.289549	+	0.957163i	$0.406495\pi$
$720$	−2113.22	−0.109382
$721$	−2897.55	−0.149668
$722$	722.000	0.0372161
$723$	14529.9	0.747402
$724$	1733.87	0.0890038
$725$	9546.01	0.489007
$726$	−7669.41	−0.392064
$727$	14151.6	0.721943	0.360971	−	0.932577i	$-0.382445\pi$
$727$	14151.6	0.721943	0.360971	+	0.932577i	$0.382445\pi$
$728$	−1506.90	−0.0767160
$729$	729.000	0.0370370
$730$	7033.61	0.356611
$731$	14550.4	0.736204
$732$	3267.80	0.165002
$733$	4923.27	0.248083	0.124042	−	0.992277i	$-0.460414\pi$
$733$	4923.27	0.248083	0.124042	+	0.992277i	$0.460414\pi$
$734$	−14888.8	−0.748714
$735$	−2157.25	−0.108260
$736$	541.083	0.0270986
$737$	−2685.12	−0.134203
$738$	−1146.87	−0.0572043
$739$	23898.5	1.18961	0.594805	−	0.803870i	$-0.297229\pi$
$739$	23898.5	1.18961	0.594805	+	0.803870i	$0.297229\pi$
$740$	5942.72	0.295215
$741$	−1533.80	−0.0760401
$742$	−5837.06	−0.288794
$743$	27053.8	1.33581	0.667905	−	0.744246i	$-0.267191\pi$
$743$	27053.8	1.33581	0.667905	+	0.744246i	$0.267191\pi$
$744$	3909.42	0.192643
$745$	20580.6	1.01210
$746$	−5713.75	−0.280423
$747$	1500.96	0.0735170
$748$	−2121.94	−0.103724
$749$	4967.52	0.242335
$750$	3050.10	0.148498
$751$	−7326.28	−0.355978	−0.177989	−	0.984032i	$-0.556959\pi$
$751$	−7326.28	−0.355978	−0.177989	+	0.984032i	$0.556959\pi$
$752$	6624.50	0.321238
$753$	12527.8	0.606293
$754$	5685.54	0.274609
$755$	15210.8	0.733214
$756$	−756.000	−0.0363696
$757$	1057.93	0.0507943	0.0253971	−	0.999677i	$-0.491915\pi$
$757$	1057.93	0.0507943	0.0253971	+	0.999677i	$0.491915\pi$
$758$	2874.81	0.137754
$759$	−368.473	−0.0176215
$760$	2230.62	0.106465
$761$	16000.9	0.762199	0.381100	−	0.924534i	$-0.375546\pi$
$761$	16000.9	0.762199	0.381100	+	0.924534i	$0.375546\pi$
$762$	−11977.4	−0.569415
$763$	−1007.04	−0.0477817
$764$	−14278.8	−0.676165
$765$	−9645.56	−0.455864
$766$	24108.9	1.13719
$767$	6781.03	0.319229
$768$	768.000	0.0360844
$769$	9149.69	0.429059	0.214529	−	0.976718i	$-0.431178\pi$
$769$	9149.69	0.429059	0.214529	+	0.976718i	$0.431178\pi$
$770$	−1492.38	−0.0698465
$771$	−3799.28	−0.177468
$772$	−620.130	−0.0289106
$773$	−7374.46	−0.343132	−0.171566	−	0.985173i	$-0.554883\pi$
$773$	−7374.46	−0.343132	−0.171566	+	0.985173i	$0.554883\pi$
$774$	3586.28	0.166546
$775$	14718.9	0.682219
$776$	521.441	0.0241220
$777$	2126.00	0.0981592
$778$	11766.6	0.542229
$779$	1210.58	0.0556786
$780$	−4738.70	−0.217529
$781$	−4340.13	−0.198850
$782$	2469.71	0.112937
$783$	2852.40	0.130187
$784$	784.000	0.0357143
$785$	−29452.1	−1.33910
$786$	6945.54	0.315190
$787$	17457.6	0.790719	0.395359	−	0.918527i	$-0.370620\pi$
$787$	17457.6	0.790719	0.395359	+	0.918527i	$0.370620\pi$
$788$	3039.20	0.137395
$789$	1787.06	0.0806351
$790$	11370.8	0.512094
$791$	8933.18	0.401552
$792$	−523.001	−0.0234647
$793$	7327.74	0.328141
$794$	−10633.3	−0.475268
$795$	−18355.7	−0.818878
$796$	3241.98	0.144358
$797$	−1667.52	−0.0741113	−0.0370556	−	0.999313i	$-0.511798\pi$
$797$	−1667.52	−0.0741113	−0.0370556	+	0.999313i	$0.511798\pi$
$798$	798.000	0.0353996
$799$	30236.8	1.33880
$800$	2891.51	0.127788
$801$	13273.2	0.585500
$802$	12561.5	0.553068
$803$	1740.75	0.0765003
$804$	4435.82	0.194576
$805$	1736.98	0.0760503
$806$	8766.50	0.383110
$807$	8604.99	0.375353
$808$	−3227.61	−0.140528
$809$	8655.13	0.376141	0.188071	−	0.982156i	$-0.439777\pi$
$809$	8655.13	0.376141	0.188071	+	0.982156i	$0.439777\pi$
$810$	−2377.37	−0.103126
$811$	15312.3	0.662994	0.331497	−	0.943456i	$-0.392446\pi$
$811$	15312.3	0.662994	0.331497	+	0.943456i	$0.392446\pi$
$812$	−2958.04	−0.127841
$813$	−1917.07	−0.0826994
$814$	1470.77	0.0633296
$815$	10151.3	0.436299
$816$	3505.45	0.150386
$817$	−3785.52	−0.162104
$818$	−26391.2	−1.12805
$819$	−1695.26	−0.0723286
$820$	3740.10	0.159280
$821$	−6136.96	−0.260879	−0.130439	−	0.991456i	$-0.541639\pi$
$821$	−6136.96	−0.260879	−0.130439	+	0.991456i	$0.541639\pi$
$822$	6388.13	0.271060
$823$	13497.2	0.571669	0.285835	−	0.958279i	$-0.407729\pi$
$823$	13497.2	0.571669	0.285835	+	0.958279i	$0.407729\pi$
$824$	3311.49	0.140001
$825$	−1969.10	−0.0830971
$826$	−3528.00	−0.148614
$827$	−27596.2	−1.16036	−0.580178	−	0.814490i	$-0.697017\pi$
$827$	−27596.2	−1.16036	−0.580178	+	0.814490i	$0.697017\pi$
$828$	608.719	0.0255488
$829$	28083.7	1.17658	0.588292	−	0.808649i	$-0.299801\pi$
$829$	28083.7	1.17658	0.588292	+	0.808649i	$0.299801\pi$
$830$	−4894.84	−0.204702
$831$	12726.7	0.531268
$832$	1722.17	0.0717613
$833$	3578.48	0.148844
$834$	−18423.6	−0.764935
$835$	23648.5	0.980108
$836$	552.057	0.0228389
$837$	4398.09	0.181625
$838$	5092.64	0.209931
$839$	18303.6	0.753171	0.376586	−	0.926382i	$-0.377098\pi$
$839$	18303.6	0.753171	0.376586	+	0.926382i	$0.377098\pi$
$840$	2465.42	0.101268
$841$	−13228.3	−0.542386
$842$	1458.51	0.0596954
$843$	−3578.63	−0.146209
$844$	8717.76	0.355542
$845$	21615.2	0.879984
$846$	7452.56	0.302866
$847$	8947.65	0.362981
$848$	6670.93	0.270142
$849$	−3579.37	−0.144692
$850$	13198.0	0.532573
$851$	−1711.82	−0.0689546
$852$	7169.91	0.288307
$853$	−42386.3	−1.70138	−0.850691	−	0.525666i	$-0.823816\pi$
$853$	−42386.3	−1.70138	−0.850691	+	0.525666i	$0.823816\pi$
$854$	−3812.44	−0.152762
$855$	2509.45	0.100376
$856$	−5677.16	−0.226684
$857$	−28545.5	−1.13780	−0.568900	−	0.822407i	$-0.692631\pi$
$857$	−28545.5	−1.13780	−0.568900	+	0.822407i	$0.692631\pi$
$858$	−1172.78	−0.0466644
$859$	−16563.9	−0.657921	−0.328960	−	0.944344i	$-0.606698\pi$
$859$	−16563.9	−0.657921	−0.328960	+	0.944344i	$0.606698\pi$
$860$	−11695.4	−0.463732
$861$	1338.01	0.0529609
$862$	−7036.13	−0.278018
$863$	9444.61	0.372536	0.186268	−	0.982499i	$-0.440361\pi$
$863$	9444.61	0.372536	0.186268	+	0.982499i	$0.440361\pi$
$864$	864.000	0.0340207
$865$	−9196.06	−0.361475
$866$	−1630.58	−0.0639830
$867$	1261.23	0.0494043
$868$	−4560.99	−0.178353
$869$	2814.16	0.109855
$870$	−9302.08	−0.362494
$871$	9946.91	0.386955
$872$	1150.91	0.0446957
$873$	586.621	0.0227424
$874$	−642.536	−0.0248674
$875$	−3558.45	−0.137483
$876$	−2875.73	−0.110915
$877$	1423.04	0.0547922	0.0273961	−	0.999625i	$-0.491278\pi$
$877$	1423.04	0.0547922	0.0273961	+	0.999625i	$0.491278\pi$
$878$	−5426.29	−0.208575
$879$	−7365.17	−0.282618
$880$	1705.58	0.0653354
$881$	15683.0	0.599743	0.299872	−	0.953980i	$-0.403056\pi$
$881$	15683.0	0.599743	0.299872	+	0.953980i	$0.403056\pi$
$882$	882.000	0.0336718
$883$	−22952.7	−0.874766	−0.437383	−	0.899275i	$-0.644095\pi$
$883$	−22952.7	−0.874766	−0.437383	+	0.899275i	$0.644095\pi$
$884$	7860.64	0.299074
$885$	−11094.4	−0.421395
$886$	19887.2	0.754091
$887$	−4291.90	−0.162467	−0.0812333	−	0.996695i	$-0.525886\pi$
$887$	−4291.90	−0.162467	−0.0812333	+	0.996695i	$0.525886\pi$
$888$	−2429.71	−0.0918195
$889$	13973.6	0.527176
$890$	−43285.8	−1.63027
$891$	−588.376	−0.0221227
$892$	14846.6	0.557290
$893$	−7866.59	−0.294788
$894$	−8414.46	−0.314789
$895$	−42397.7	−1.58346
$896$	−896.000	−0.0334077
$897$	1364.99	0.0508092
$898$	−27572.4	−1.02461
$899$	17208.7	0.638422
$900$	3252.95	0.120480
$901$	30448.7	1.12585
$902$	925.638	0.0341689
$903$	−4184.00	−0.154191
$904$	−10209.4	−0.375617
$905$	−6361.19	−0.233650
$906$	−6218.99	−0.228049
$907$	40858.2	1.49578	0.747891	−	0.663822i	$-0.231067\pi$
$907$	40858.2	1.49578	0.747891	+	0.663822i	$0.231067\pi$
$908$	−9175.69	−0.335359
$909$	−3631.06	−0.132491
$910$	5528.48	0.201393
$911$	24164.5	0.878821	0.439410	−	0.898286i	$-0.355187\pi$
$911$	24164.5	0.878821	0.439410	+	0.898286i	$0.355187\pi$
$912$	−912.000	−0.0331133
$913$	−1211.42	−0.0439127
$914$	15293.1	0.553449
$915$	−11988.9	−0.433158
$916$	17858.9	0.644185
$917$	−8103.13	−0.291809
$918$	3943.63	0.141786
$919$	−3650.84	−0.131045	−0.0655223	−	0.997851i	$-0.520871\pi$
$919$	−3650.84	−0.131045	−0.0655223	+	0.997851i	$0.520871\pi$
$920$	−1985.12	−0.0711385
$921$	−30999.4	−1.10908
$922$	9664.98	0.345227
$923$	16077.8	0.573357
$924$	610.168	0.0217241
$925$	−9147.84	−0.325167
$926$	−21344.4	−0.757473
$927$	3725.43	0.131995
$928$	3380.62	0.119584
$929$	51154.3	1.80658	0.903292	−	0.429025i	$-0.141143\pi$
$929$	51154.3	1.80658	0.903292	+	0.429025i	$0.141143\pi$
$930$	−14342.8	−0.505720
$931$	−931.000	−0.0327737
$932$	−28252.0	−0.992944
$933$	−2998.14	−0.105203
$934$	15954.9	0.558951
$935$	7784.94	0.272294
$936$	1937.44	0.0676572
$937$	−31440.8	−1.09619	−0.548093	−	0.836417i	$-0.684646\pi$
$937$	−31440.8	−1.09619	−0.548093	+	0.836417i	$0.684646\pi$
$938$	−5175.13	−0.180143
$939$	6311.38	0.219344
$940$	−24303.9	−0.843303
$941$	−52200.5	−1.80838	−0.904191	−	0.427128i	$-0.859525\pi$
$941$	−52200.5	−1.80838	−0.904191	+	0.427128i	$0.859525\pi$
$942$	12041.6	0.416494
$943$	−1077.35	−0.0372038
$944$	4032.00	0.139015
$945$	2773.60	0.0954765
$946$	−2894.49	−0.0994799
$947$	26706.3	0.916407	0.458203	−	0.888847i	$-0.348493\pi$
$947$	26706.3	0.916407	0.458203	+	0.888847i	$0.348493\pi$
$948$	−4649.00	−0.159275
$949$	−6448.54	−0.220578
$950$	−3433.67	−0.117266
$951$	−6486.94	−0.221192
$952$	−4089.69	−0.139231
$953$	−30102.3	−1.02320	−0.511600	−	0.859224i	$-0.670947\pi$
$953$	−30102.3	−1.02320	−0.511600	+	0.859224i	$0.670947\pi$
$954$	7504.80	0.254693
$955$	52386.0	1.77505
$956$	20443.9	0.691635
$957$	−2302.17	−0.0777625
$958$	32014.1	1.07967
$959$	−7452.82	−0.250953
$960$	−2817.63	−0.0947276
$961$	−3257.07	−0.109331
$962$	−5448.39	−0.182602
$963$	−6386.81	−0.213720
$964$	19373.2	0.647269
$965$	2275.12	0.0758951
$966$	−710.172	−0.0236536
$967$	−19993.5	−0.664888	−0.332444	−	0.943123i	$-0.607873\pi$
$967$	−19993.5	−0.664888	−0.332444	+	0.943123i	$0.607873\pi$
$968$	−10225.9	−0.339538
$969$	−4162.72	−0.138004
$970$	−1913.06	−0.0633242
$971$	−46004.3	−1.52044	−0.760220	−	0.649666i	$-0.774909\pi$
$971$	−46004.3	−1.52044	−0.760220	+	0.649666i	$0.774909\pi$
$972$	972.000	0.0320750
$973$	21494.2	0.708192
$974$	−24217.6	−0.796696
$975$	7294.44	0.239599
$976$	4357.07	0.142896
$977$	−54661.0	−1.78993	−0.894964	−	0.446138i	$-0.852799\pi$
$977$	−54661.0	−1.78993	−0.894964	+	0.446138i	$0.852799\pi$
$978$	−4150.39	−0.135700
$979$	−10712.8	−0.349727
$980$	−2876.33	−0.0937560
$981$	1294.77	0.0421395
$982$	−29383.7	−0.954858
$983$	9529.47	0.309199	0.154600	−	0.987977i	$-0.450591\pi$
$983$	9529.47	0.309199	0.154600	+	0.987977i	$0.450591\pi$
$984$	−1529.16	−0.0495404
$985$	−11150.2	−0.360684
$986$	15430.5	0.498383
$987$	−8694.66	−0.280399
$988$	−2045.07	−0.0658527
$989$	3368.88	0.108316
$990$	1918.78	0.0615988
$991$	−38266.5	−1.22661	−0.613307	−	0.789844i	$-0.710161\pi$
$991$	−38266.5	−1.22661	−0.613307	+	0.789844i	$0.710161\pi$
$992$	5212.56	0.166834
$993$	−22251.8	−0.711119
$994$	−8364.90	−0.266920
$995$	−11894.1	−0.378964
$996$	2001.28	0.0636676
$997$	23735.5	0.753972	0.376986	−	0.926219i	$-0.376960\pi$
$997$	23735.5	0.753972	0.376986	+	0.926219i	$0.376960\pi$
$998$	−5833.29	−0.185020
$999$	−2733.42	−0.0865683

Twists

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

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

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -14.6751 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +3.00000 q^{3} +4.00000 q^{4} -14.6751 q^{5} +6.00000 q^{6} -7.00000 q^{7} +8.00000 q^{8} +9.00000 q^{9} -29.3503 q^{10} -7.26391 q^{11} +12.0000 q^{12} +26.9089 q^{13} -14.0000 q^{14} -44.0254 q^{15} +16.0000 q^{16} +73.0302 q^{17} +18.0000 q^{18} -19.0000 q^{19} -58.7006 q^{20} -21.0000 q^{21} -14.5278 q^{22} +16.9089 q^{23} +24.0000 q^{24} +90.3598 q^{25} +53.8177 q^{26} +27.0000 q^{27} -28.0000 q^{28} +105.644 q^{29} -88.0509 q^{30} +162.892 q^{31} +32.0000 q^{32} -21.7917 q^{33} +146.060 q^{34} +102.726 q^{35} +36.0000 q^{36} -101.238 q^{37} -38.0000 q^{38} +80.7266 q^{39} -117.401 q^{40} -63.7149 q^{41} -42.0000 q^{42} +199.238 q^{43} -29.0556 q^{44} -132.076 q^{45} +33.8177 q^{46} +414.031 q^{47} +48.0000 q^{48} +49.0000 q^{49} +180.720 q^{50} +219.091 q^{51} +107.635 q^{52} +416.933 q^{53} +54.0000 q^{54} +106.599 q^{55} -56.0000 q^{56} -57.0000 q^{57} +211.289 q^{58} +252.000 q^{59} -176.102 q^{60} +272.317 q^{61} +325.785 q^{62} -63.0000 q^{63} +64.0000 q^{64} -394.891 q^{65} -43.5834 q^{66} +369.652 q^{67} +292.121 q^{68} +50.7266 q^{69} +205.452 q^{70} +597.493 q^{71} +72.0000 q^{72} -239.644 q^{73} -202.476 q^{74} +271.079 q^{75} -76.0000 q^{76} +50.8473 q^{77} +161.453 q^{78} -387.416 q^{79} -234.802 q^{80} +81.0000 q^{81} -127.430 q^{82} +166.773 q^{83} -84.0000 q^{84} -1071.73 q^{85} +398.476 q^{86} +316.933 q^{87} -58.1112 q^{88} +1474.80 q^{89} -264.153 q^{90} -188.362 q^{91} +67.6354 q^{92} +488.677 q^{93} +828.062 q^{94} +278.828 q^{95} +96.0000 q^{96} +65.1801 q^{97} +98.0000 q^{98} -65.3752 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 10 q^{5} + 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9}+O(q^{10}) \) 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 10 * q^5 + 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9	\( 3 q + 6 q^{2} + 9 q^{3} + 12 q^{4} + 10 q^{5} + 18 q^{6} - 21 q^{7} + 24 q^{8} + 27 q^{9} + 20 q^{10} + 54 q^{11} + 36 q^{12} + 92 q^{13} - 42 q^{14} + 30 q^{15} + 48 q^{16} + 78 q^{17} + 54 q^{18} - 57 q^{19} + 40 q^{20} - 63 q^{21} + 108 q^{22} + 62 q^{23} + 72 q^{24} + 205 q^{25} + 184 q^{26} + 81 q^{27} - 84 q^{28} - 8 q^{29} + 60 q^{30} + 292 q^{31} + 96 q^{32} + 162 q^{33} + 156 q^{34} - 70 q^{35} + 108 q^{36} + 22 q^{37} - 114 q^{38} + 276 q^{39} + 80 q^{40} - 38 q^{41} - 126 q^{42} + 272 q^{43} + 216 q^{44} + 90 q^{45} + 124 q^{46} + 422 q^{47} + 144 q^{48} + 147 q^{49} + 410 q^{50} + 234 q^{51} + 368 q^{52} + 276 q^{53} + 162 q^{54} + 752 q^{55} - 168 q^{56} - 171 q^{57} - 16 q^{58} + 756 q^{59} + 120 q^{60} + 562 q^{61} + 584 q^{62} - 189 q^{63} + 192 q^{64} - 164 q^{65} + 324 q^{66} + 1362 q^{67} + 312 q^{68} + 186 q^{69} - 140 q^{70} + 258 q^{71} + 216 q^{72} + 18 q^{73} + 44 q^{74} + 615 q^{75} - 228 q^{76} - 378 q^{77} + 552 q^{78} - 114 q^{79} + 160 q^{80} + 243 q^{81} - 76 q^{82} - 902 q^{83} - 252 q^{84} - 388 q^{85} + 544 q^{86} - 24 q^{87} + 432 q^{88} - 270 q^{89} + 180 q^{90} - 644 q^{91} + 248 q^{92} + 876 q^{93} + 844 q^{94} - 190 q^{95} + 288 q^{96} + 28 q^{97} + 294 q^{98} + 486 q^{99}+O(q^{100}) \) 3 * q + 6 * q^2 + 9 * q^3 + 12 * q^4 + 10 * q^5 + 18 * q^6 - 21 * q^7 + 24 * q^8 + 27 * q^9 + 20 * q^10 + 54 * q^11 + 36 * q^12 + 92 * q^13 - 42 * q^14 + 30 * q^15 + 48 * q^16 + 78 * q^17 + 54 * q^18 - 57 * q^19 + 40 * q^20 - 63 * q^21 + 108 * q^22 + 62 * q^23 + 72 * q^24 + 205 * q^25 + 184 * q^26 + 81 * q^27 - 84 * q^28 - 8 * q^29 + 60 * q^30 + 292 * q^31 + 96 * q^32 + 162 * q^33 + 156 * q^34 - 70 * q^35 + 108 * q^36 + 22 * q^37 - 114 * q^38 + 276 * q^39 + 80 * q^40 - 38 * q^41 - 126 * q^42 + 272 * q^43 + 216 * q^44 + 90 * q^45 + 124 * q^46 + 422 * q^47 + 144 * q^48 + 147 * q^49 + 410 * q^50 + 234 * q^51 + 368 * q^52 + 276 * q^53 + 162 * q^54 + 752 * q^55 - 168 * q^56 - 171 * q^57 - 16 * q^58 + 756 * q^59 + 120 * q^60 + 562 * q^61 + 584 * q^62 - 189 * q^63 + 192 * q^64 - 164 * q^65 + 324 * q^66 + 1362 * q^67 + 312 * q^68 + 186 * q^69 - 140 * q^70 + 258 * q^71 + 216 * q^72 + 18 * q^73 + 44 * q^74 + 615 * q^75 - 228 * q^76 - 378 * q^77 + 552 * q^78 - 114 * q^79 + 160 * q^80 + 243 * q^81 - 76 * q^82 - 902 * q^83 - 252 * q^84 - 388 * q^85 + 544 * q^86 - 24 * q^87 + 432 * q^88 - 270 * q^89 + 180 * q^90 - 644 * q^91 + 248 * q^92 + 876 * q^93 + 844 * q^94 - 190 * q^95 + 288 * q^96 + 28 * q^97 + 294 * q^98 + 486 * q^99

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