LMFDB - Embedded newform 798.4.a.f.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,4,Mod(1,798)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(798, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 4, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("798.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$47.0835241846$
Analytic rank:	$1$
Dimension:	$3$
Coefficient field:	3.3.93944.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{3} - x^{2} - 72x + 44 $ x^3 - x^2 - 72*x + 44
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$-8.30610$ of defining polynomial
Character	$\chi$	$=$	798.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +0.328719 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +0.328719 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -0.657438 q^{10} -40.5669 q^{11} -12.0000 q^{12} +0.612191 q^{13} -14.0000 q^{14} -0.986157 q^{15} +16.0000 q^{16} +96.1477 q^{17} -18.0000 q^{18} -19.0000 q^{19} +1.31488 q^{20} -21.0000 q^{21} +81.1339 q^{22} +120.386 q^{23} +24.0000 q^{24} -124.892 q^{25} -1.22438 q^{26} -27.0000 q^{27} +28.0000 q^{28} -76.6039 q^{29} +1.97231 q^{30} -272.021 q^{31} -32.0000 q^{32} +121.701 q^{33} -192.295 q^{34} +2.30103 q^{35} +36.0000 q^{36} -57.9446 q^{37} +38.0000 q^{38} -1.83657 q^{39} -2.62975 q^{40} -197.913 q^{41} +42.0000 q^{42} +371.604 q^{43} -162.268 q^{44} +2.95847 q^{45} -240.772 q^{46} +574.061 q^{47} -48.0000 q^{48} +49.0000 q^{49} +249.784 q^{50} -288.443 q^{51} +2.44876 q^{52} +459.549 q^{53} +54.0000 q^{54} -13.3351 q^{55} -56.0000 q^{56} +57.0000 q^{57} +153.208 q^{58} +553.926 q^{59} -3.94463 q^{60} -551.453 q^{61} +544.043 q^{62} +63.0000 q^{63} +64.0000 q^{64} +0.201239 q^{65} -243.402 q^{66} +292.811 q^{67} +384.591 q^{68} -361.158 q^{69} -4.60207 q^{70} -302.022 q^{71} -72.0000 q^{72} -452.231 q^{73} +115.889 q^{74} +374.676 q^{75} -76.0000 q^{76} -283.969 q^{77} +3.67314 q^{78} +142.290 q^{79} +5.25950 q^{80} +81.0000 q^{81} +395.826 q^{82} -1234.34 q^{83} -84.0000 q^{84} +31.6056 q^{85} -743.208 q^{86} +229.812 q^{87} +324.536 q^{88} -1260.51 q^{89} -5.91694 q^{90} +4.28533 q^{91} +481.544 q^{92} +816.064 q^{93} -1148.12 q^{94} -6.24566 q^{95} +96.0000 q^{96} +211.272 q^{97} -98.0000 q^{98} -365.102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	\( 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} + 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} - 20 q^{10} - 36 q^{12} - 50 q^{13} - 42 q^{14} - 30 q^{15} + 48 q^{16} + 18 q^{17} - 54 q^{18} - 57 q^{19} + 40 q^{20} - 63 q^{21} - 40 q^{23} + 72 q^{24} - 111 q^{25} + 100 q^{26} - 81 q^{27} + 84 q^{28} - 54 q^{29} + 60 q^{30} - 336 q^{31} - 96 q^{32} - 36 q^{34} + 70 q^{35} + 108 q^{36} - 282 q^{37} + 114 q^{38} + 150 q^{39} - 80 q^{40} + 150 q^{41} + 126 q^{42} + 184 q^{43} + 90 q^{45} + 80 q^{46} + 708 q^{47} - 144 q^{48} + 147 q^{49} + 222 q^{50} - 54 q^{51} - 200 q^{52} + 378 q^{53} + 162 q^{54} + 280 q^{55} - 168 q^{56} + 171 q^{57} + 108 q^{58} + 260 q^{59} - 120 q^{60} + 90 q^{61} + 672 q^{62} + 189 q^{63} + 192 q^{64} - 76 q^{65} - 280 q^{67} + 72 q^{68} + 120 q^{69} - 140 q^{70} - 248 q^{71} - 216 q^{72} - 978 q^{73} + 564 q^{74} + 333 q^{75} - 228 q^{76} - 300 q^{78} - 664 q^{79} + 160 q^{80} + 243 q^{81} - 300 q^{82} + 516 q^{83} - 252 q^{84} - 1192 q^{85} - 368 q^{86} + 162 q^{87} - 90 q^{89} - 180 q^{90} - 350 q^{91} - 160 q^{92} + 1008 q^{93} - 1416 q^{94} - 190 q^{95} + 288 q^{96} - 1390 q^{97} - 294 q^{98}+O(q^{100}) \) 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 - 36 * q^12 - 50 * q^13 - 42 * q^14 - 30 * q^15 + 48 * q^16 + 18 * q^17 - 54 * q^18 - 57 * q^19 + 40 * q^20 - 63 * q^21 - 40 * q^23 + 72 * q^24 - 111 * q^25 + 100 * q^26 - 81 * q^27 + 84 * q^28 - 54 * q^29 + 60 * q^30 - 336 * q^31 - 96 * q^32 - 36 * q^34 + 70 * q^35 + 108 * q^36 - 282 * q^37 + 114 * q^38 + 150 * q^39 - 80 * q^40 + 150 * q^41 + 126 * q^42 + 184 * q^43 + 90 * q^45 + 80 * q^46 + 708 * q^47 - 144 * q^48 + 147 * q^49 + 222 * q^50 - 54 * q^51 - 200 * q^52 + 378 * q^53 + 162 * q^54 + 280 * q^55 - 168 * q^56 + 171 * q^57 + 108 * q^58 + 260 * q^59 - 120 * q^60 + 90 * q^61 + 672 * q^62 + 189 * q^63 + 192 * q^64 - 76 * q^65 - 280 * q^67 + 72 * q^68 + 120 * q^69 - 140 * q^70 - 248 * q^71 - 216 * q^72 - 978 * q^73 + 564 * q^74 + 333 * q^75 - 228 * q^76 - 300 * q^78 - 664 * q^79 + 160 * q^80 + 243 * q^81 - 300 * q^82 + 516 * q^83 - 252 * q^84 - 1192 * q^85 - 368 * q^86 + 162 * q^87 - 90 * q^89 - 180 * q^90 - 350 * q^91 - 160 * q^92 + 1008 * q^93 - 1416 * q^94 - 190 * q^95 + 288 * q^96 - 1390 * q^97 - 294 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.00000	−0.707107
$2$	−2.00000	−0.707107
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.00000	0.500000
$5$	0.328719	0.0294015	0.0147008	−	0.999892i	$-0.495320\pi$
$5$	0.328719	0.0294015	0.0147008	+	0.999892i	$0.495320\pi$
$6$	6.00000	0.408248
$7$	7.00000	0.377964
$7$	7.00000	0.377964
$8$	−8.00000	−0.353553
$9$	9.00000	0.333333
$10$	−0.657438	−0.0207900
$11$	−40.5669	−1.11194	−0.555972	−	0.831201i	$-0.687654\pi$
$11$	−40.5669	−1.11194	−0.555972	+	0.831201i	$0.687654\pi$
$12$	−12.0000	−0.288675
$13$	0.612191	0.0130609	0.00653043	−	0.999979i	$-0.497921\pi$
$13$	0.612191	0.0130609	0.00653043	+	0.999979i	$0.497921\pi$
$14$	−14.0000	−0.267261
$15$	−0.986157	−0.0169750
$16$	16.0000	0.250000
$17$	96.1477	1.37172	0.685860	−	0.727733i	$-0.259426\pi$
$17$	96.1477	1.37172	0.685860	+	0.727733i	$0.259426\pi$
$18$	−18.0000	−0.235702
$19$	−19.0000	−0.229416
$19$	−19.0000	−0.229416
$20$	1.31488	0.0147008
$21$	−21.0000	−0.218218
$22$	81.1339	0.786264
$23$	120.386	1.09140	0.545700	−	0.837981i	$-0.316264\pi$
$23$	120.386	1.09140	0.545700	+	0.837981i	$0.316264\pi$
$24$	24.0000	0.204124
$25$	−124.892	−0.999136
$26$	−1.22438	−0.00923542
$27$	−27.0000	−0.192450
$28$	28.0000	0.188982
$29$	−76.6039	−0.490517	−0.245258	−	0.969458i	$-0.578873\pi$
$29$	−76.6039	−0.490517	−0.245258	+	0.969458i	$0.578873\pi$
$30$	1.97231	0.0120031
$31$	−272.021	−1.57602	−0.788008	−	0.615666i	$-0.788887\pi$
$31$	−272.021	−1.57602	−0.788008	+	0.615666i	$0.788887\pi$
$32$	−32.0000	−0.176777
$33$	121.701	0.641982
$34$	−192.295	−0.969953
$35$	2.30103	0.0111127
$36$	36.0000	0.166667
$37$	−57.9446	−0.257460	−0.128730	−	0.991680i	$-0.541090\pi$
$37$	−57.9446	−0.257460	−0.128730	+	0.991680i	$0.541090\pi$
$38$	38.0000	0.162221
$39$	−1.83657	−0.00754069
$40$	−2.62975	−0.0103950
$41$	−197.913	−0.753874	−0.376937	−	0.926239i	$-0.623023\pi$
$41$	−197.913	−0.753874	−0.376937	+	0.926239i	$0.623023\pi$
$42$	42.0000	0.154303
$43$	371.604	1.31789	0.658943	−	0.752193i	$-0.271004\pi$
$43$	371.604	1.31789	0.658943	+	0.752193i	$0.271004\pi$
$44$	−162.268	−0.555972
$45$	2.95847	0.00980051
$46$	−240.772	−0.771737
$47$	574.061	1.78160	0.890802	−	0.454391i	$-0.150143\pi$
$47$	574.061	1.78160	0.890802	+	0.454391i	$0.150143\pi$
$48$	−48.0000	−0.144338
$49$	49.0000	0.142857
$50$	249.784	0.706496
$51$	−288.443	−0.791963
$52$	2.44876	0.00653043
$53$	459.549	1.19102	0.595509	−	0.803349i	$-0.296950\pi$
$53$	459.549	1.19102	0.595509	+	0.803349i	$0.296950\pi$
$54$	54.0000	0.136083
$55$	−13.3351	−0.0326929
$56$	−56.0000	−0.133631
$57$	57.0000	0.132453
$58$	153.208	0.346848
$59$	553.926	1.22229	0.611144	−	0.791519i	$-0.290710\pi$
$59$	553.926	1.22229	0.611144	+	0.791519i	$0.290710\pi$
$60$	−3.94463	−0.00848749
$61$	−551.453	−1.15748	−0.578741	−	0.815512i	$-0.696456\pi$
$61$	−551.453	−1.15748	−0.578741	+	0.815512i	$0.696456\pi$
$62$	544.043	1.11441
$63$	63.0000	0.125988
$64$	64.0000	0.125000
$65$	0.201239	0.000384009 0
$66$	−243.402	−0.453950
$67$	292.811	0.533918	0.266959	−	0.963708i	$-0.413981\pi$
$67$	292.811	0.533918	0.266959	+	0.963708i	$0.413981\pi$
$68$	384.591	0.685860
$69$	−361.158	−0.630120
$70$	−4.60207	−0.00785789
$71$	−302.022	−0.504837	−0.252419	−	0.967618i	$-0.581226\pi$
$71$	−302.022	−0.504837	−0.252419	+	0.967618i	$0.581226\pi$
$72$	−72.0000	−0.117851
$73$	−452.231	−0.725063	−0.362532	−	0.931971i	$-0.618088\pi$
$73$	−452.231	−0.725063	−0.362532	+	0.931971i	$0.618088\pi$
$74$	115.889	0.182052
$75$	374.676	0.576851
$76$	−76.0000	−0.114708
$77$	−283.969	−0.420276
$78$	3.67314	0.00533207
$79$	142.290	0.202644	0.101322	−	0.994854i	$-0.467693\pi$
$79$	142.290	0.202644	0.101322	+	0.994854i	$0.467693\pi$
$80$	5.25950	0.00735038
$81$	81.0000	0.111111
$82$	395.826	0.533070
$83$	−1234.34	−1.63236	−0.816181	−	0.577797i	$-0.803913\pi$
$83$	−1234.34	−1.63236	−0.816181	+	0.577797i	$0.803913\pi$
$84$	−84.0000	−0.109109
$85$	31.6056	0.0403307
$86$	−743.208	−0.931886
$87$	229.812	0.283200
$88$	324.536	0.393132
$89$	−1260.51	−1.50127	−0.750637	−	0.660715i	$-0.770253\pi$
$89$	−1260.51	−1.50127	−0.750637	+	0.660715i	$0.770253\pi$
$90$	−5.91694	−0.00693001
$91$	4.28533	0.00493654
$92$	481.544	0.545700
$93$	816.064	0.909913
$94$	−1148.12	−1.25978
$95$	−6.24566	−0.00674517
$96$	96.0000	0.102062
$97$	211.272	0.221149	0.110575	−	0.993868i	$-0.464731\pi$
$97$	211.272	0.221149	0.110575	+	0.993868i	$0.464731\pi$
$98$	−98.0000	−0.101015
$99$	−365.102	−0.370648
$100$	−499.568	−0.499568
$101$	337.343	0.332345	0.166173	−	0.986097i	$-0.446859\pi$
$101$	337.343	0.332345	0.166173	+	0.986097i	$0.446859\pi$
$102$	576.886	0.560003
$103$	−1280.32	−1.22479	−0.612396	−	0.790551i	$-0.709794\pi$
$103$	−1280.32	−1.22479	−0.612396	+	0.790551i	$0.709794\pi$
$104$	−4.89752	−0.00461771
$105$	−6.90310	−0.00641594
$106$	−919.099	−0.842177
$107$	−13.5382	−0.0122317	−0.00611583	−	0.999981i	$-0.501947\pi$
$107$	−13.5382	−0.0122317	−0.00611583	+	0.999981i	$0.501947\pi$
$108$	−108.000	−0.0962250
$109$	−1126.25	−0.989680	−0.494840	−	0.868984i	$-0.664773\pi$
$109$	−1126.25	−0.989680	−0.494840	+	0.868984i	$0.664773\pi$
$110$	26.6703	0.0231174
$111$	173.834	0.148645
$112$	112.000	0.0944911
$113$	−1075.74	−0.895549	−0.447775	−	0.894146i	$-0.647783\pi$
$113$	−1075.74	−0.895549	−0.447775	+	0.894146i	$0.647783\pi$
$114$	−114.000	−0.0936586
$115$	39.5732	0.0320888
$116$	−306.416	−0.245258
$117$	5.50972	0.00435362
$118$	−1107.85	−0.864289
$119$	673.034	0.518462
$120$	7.88926	0.00600156
$121$	314.677	0.236421
$122$	1102.91	0.818463
$123$	593.740	0.435250
$124$	−1088.09	−0.788008
$125$	−82.1442	−0.0587776
$126$	−126.000	−0.0890871
$127$	−1997.03	−1.39534	−0.697668	−	0.716421i	$-0.745779\pi$
$127$	−1997.03	−1.39534	−0.697668	+	0.716421i	$0.745779\pi$
$128$	−128.000	−0.0883883
$129$	−1114.81	−0.760881
$130$	−0.402477	−0.000271535 0
$131$	−697.723	−0.465346	−0.232673	−	0.972555i	$-0.574747\pi$
$131$	−697.723	−0.465346	−0.232673	+	0.972555i	$0.574747\pi$
$132$	486.803	0.320991
$133$	−133.000	−0.0867110
$134$	−585.622	−0.377537
$135$	−8.87541	−0.00565833
$136$	−769.182	−0.484976
$137$	−3096.64	−1.93112	−0.965560	−	0.260179i	$-0.916219\pi$
$137$	−3096.64	−1.93112	−0.965560	+	0.260179i	$0.916219\pi$
$138$	722.316	0.445562
$139$	2340.40	1.42813	0.714065	−	0.700080i	$-0.246852\pi$
$139$	2340.40	1.42813	0.714065	+	0.700080i	$0.246852\pi$
$140$	9.20413	0.00555637
$141$	−1722.18	−1.02861
$142$	604.044	0.356974
$143$	−24.8347	−0.0145230
$144$	144.000	0.0833333
$145$	−25.1812	−0.0144219
$146$	904.462	0.512697
$147$	−147.000	−0.0824786
$148$	−231.779	−0.128730
$149$	2689.66	1.47883	0.739416	−	0.673249i	$-0.235102\pi$
$149$	2689.66	1.47883	0.739416	+	0.673249i	$0.235102\pi$
$150$	−749.352	−0.407895
$151$	−138.209	−0.0744852	−0.0372426	−	0.999306i	$-0.511857\pi$
$151$	−138.209	−0.0744852	−0.0372426	+	0.999306i	$0.511857\pi$
$152$	152.000	0.0811107
$153$	865.330	0.457240
$154$	567.937	0.297180
$155$	−89.4186	−0.0463372
$156$	−7.34629	−0.00377034
$157$	−3720.36	−1.89119	−0.945595	−	0.325347i	$-0.894519\pi$
$157$	−3720.36	−1.89119	−0.945595	+	0.325347i	$0.894519\pi$
$158$	−284.580	−0.143291
$159$	−1378.65	−0.687635
$160$	−10.5190	−0.00519750
$161$	842.702	0.412511
$162$	−162.000	−0.0785674
$163$	−2698.81	−1.29685	−0.648426	−	0.761278i	$-0.724572\pi$
$163$	−2698.81	−1.29685	−0.648426	+	0.761278i	$0.724572\pi$
$164$	−791.653	−0.376937
$165$	40.0054	0.0188752
$166$	2468.67	1.15425
$167$	−830.989	−0.385053	−0.192527	−	0.981292i	$-0.561668\pi$
$167$	−830.989	−0.385053	−0.192527	+	0.981292i	$0.561668\pi$
$168$	168.000	0.0771517
$169$	−2196.63	−0.999829
$170$	−63.2112	−0.0285181
$171$	−171.000	−0.0764719
$172$	1486.42	0.658943
$173$	1992.62	0.875701	0.437851	−	0.899048i	$-0.355740\pi$
$173$	1992.62	0.875701	0.437851	+	0.899048i	$0.355740\pi$
$174$	−459.624	−0.200253
$175$	−874.244	−0.377638
$176$	−649.071	−0.277986
$177$	−1661.78	−0.705689
$178$	2521.01	1.06156
$179$	1721.98	0.719032	0.359516	−	0.933139i	$-0.382942\pi$
$179$	1721.98	0.719032	0.359516	+	0.933139i	$0.382942\pi$
$180$	11.8339	0.00490025
$181$	−1174.35	−0.482256	−0.241128	−	0.970493i	$-0.577517\pi$
$181$	−1174.35	−0.482256	−0.241128	+	0.970493i	$0.577517\pi$
$182$	−8.57067	−0.00349066
$183$	1654.36	0.668272
$184$	−963.088	−0.385868
$185$	−19.0475	−0.00756973
$186$	−1632.13	−0.643405
$187$	−3900.42	−1.52528
$188$	2296.24	0.890802
$189$	−189.000	−0.0727393
$190$	12.4913	0.00476956
$191$	−1831.49	−0.693831	−0.346915	−	0.937896i	$-0.612771\pi$
$191$	−1831.49	−0.693831	−0.346915	+	0.937896i	$0.612771\pi$
$192$	−192.000	−0.0721688
$193$	502.078	0.187256	0.0936278	−	0.995607i	$-0.470154\pi$
$193$	502.078	0.187256	0.0936278	+	0.995607i	$0.470154\pi$
$194$	−422.545	−0.156376
$195$	−0.603716	−0.000221708 0
$196$	196.000	0.0714286
$197$	−3723.03	−1.34647	−0.673235	−	0.739429i	$-0.735096\pi$
$197$	−3723.03	−1.34647	−0.673235	+	0.739429i	$0.735096\pi$
$198$	730.205	0.262088
$199$	−4207.07	−1.49865	−0.749325	−	0.662203i	$-0.769622\pi$
$199$	−4207.07	−1.49865	−0.749325	+	0.662203i	$0.769622\pi$
$200$	999.136	0.353248
$201$	−878.432	−0.308258
$202$	−674.686	−0.235004
$203$	−536.228	−0.185398
$204$	−1153.77	−0.395982
$205$	−65.0578	−0.0221651
$206$	2560.64	0.866059
$207$	1083.47	0.363800
$208$	9.79505	0.00326521
$209$	770.772	0.255098
$210$	13.8062	0.00453675
$211$	−4365.74	−1.42441	−0.712204	−	0.701973i	$-0.752303\pi$
$211$	−4365.74	−1.42441	−0.712204	+	0.701973i	$0.752303\pi$
$212$	1838.20	0.595509
$213$	906.066	0.291468
$214$	27.0764	0.00864909
$215$	122.153	0.0387478
$216$	216.000	0.0680414
$217$	−1904.15	−0.595678
$218$	2252.50	0.699810
$219$	1356.69	0.418616
$220$	−53.3405	−0.0163464
$221$	58.8607	0.0179158
$222$	−347.668	−0.105108
$223$	−2761.44	−0.829237	−0.414618	−	0.909995i	$-0.636085\pi$
$223$	−2761.44	−0.829237	−0.414618	+	0.909995i	$0.636085\pi$
$224$	−224.000	−0.0668153
$225$	−1124.03	−0.333045
$226$	2151.48	0.633249
$227$	3645.00	1.06576	0.532879	−	0.846191i	$-0.321110\pi$
$227$	3645.00	1.06576	0.532879	+	0.846191i	$0.321110\pi$
$228$	228.000	0.0662266
$229$	4379.48	1.26377	0.631887	−	0.775061i	$-0.282281\pi$
$229$	4379.48	1.26377	0.631887	+	0.775061i	$0.282281\pi$
$230$	−79.1463	−0.0226902
$231$	851.906	0.242646
$232$	612.831	0.173424
$233$	−3358.08	−0.944186	−0.472093	−	0.881549i	$-0.656501\pi$
$233$	−3358.08	−0.944186	−0.472093	+	0.881549i	$0.656501\pi$
$234$	−11.0194	−0.00307847
$235$	188.705	0.0523819
$236$	2215.70	0.611144
$237$	−426.870	−0.116997
$238$	−1346.07	−0.366608
$239$	2458.54	0.665398	0.332699	−	0.943033i	$-0.392041\pi$
$239$	2458.54	0.665398	0.332699	+	0.943033i	$0.392041\pi$
$240$	−15.7785	−0.00424374
$241$	4498.79	1.20246	0.601229	−	0.799077i	$-0.294678\pi$
$241$	4498.79	1.20246	0.601229	+	0.799077i	$0.294678\pi$
$242$	−629.354	−0.167175
$243$	−243.000	−0.0641500
$244$	−2205.81	−0.578741
$245$	16.1072	0.00420022
$246$	−1187.48	−0.307768
$247$	−11.6316	−0.00299637
$248$	2176.17	0.557205
$249$	3703.01	0.942444
$250$	164.288	0.0415621
$251$	4906.35	1.23381	0.616904	−	0.787038i	$-0.288387\pi$
$251$	4906.35	1.23381	0.616904	+	0.787038i	$0.288387\pi$
$252$	252.000	0.0629941
$253$	−4883.69	−1.21358
$254$	3994.06	0.986652
$255$	−94.8168	−0.0232849
$256$	256.000	0.0625000
$257$	−2600.98	−0.631302	−0.315651	−	0.948875i	$-0.602223\pi$
$257$	−2600.98	−0.631302	−0.315651	+	0.948875i	$0.602223\pi$
$258$	2229.62	0.538024
$259$	−405.612	−0.0973109
$260$	0.804955	0.000192005 0
$261$	−689.435	−0.163506
$262$	1395.45	0.329050
$263$	−2556.10	−0.599301	−0.299650	−	0.954049i	$-0.596870\pi$
$263$	−2556.10	−0.599301	−0.299650	+	0.954049i	$0.596870\pi$
$264$	−973.607	−0.226975
$265$	151.063	0.0350177
$266$	266.000	0.0613139
$267$	3781.52	0.866761
$268$	1171.24	0.266959
$269$	5727.95	1.29829	0.649144	−	0.760665i	$-0.275127\pi$
$269$	5727.95	1.29829	0.649144	+	0.760665i	$0.275127\pi$
$270$	17.7508	0.00400104
$271$	−6540.81	−1.46615	−0.733074	−	0.680149i	$-0.761915\pi$
$271$	−6540.81	−1.46615	−0.733074	+	0.680149i	$0.761915\pi$
$272$	1538.36	0.342930
$273$	−12.8560	−0.00285011
$274$	6193.27	1.36551
$275$	5066.48	1.11098
$276$	−1444.63	−0.315060
$277$	3236.49	0.702028	0.351014	−	0.936370i	$-0.385837\pi$
$277$	3236.49	0.702028	0.351014	+	0.936370i	$0.385837\pi$
$278$	−4680.80	−1.00984
$279$	−2448.19	−0.525338
$280$	−18.4083	−0.00392894
$281$	−8659.79	−1.83843	−0.919217	−	0.393751i	$-0.871177\pi$
$281$	−8659.79	−1.83843	−0.919217	+	0.393751i	$0.871177\pi$
$282$	3444.37	0.727337
$283$	8546.03	1.79508	0.897542	−	0.440928i	$-0.145351\pi$
$283$	8546.03	1.79508	0.897542	+	0.440928i	$0.145351\pi$
$284$	−1208.09	−0.252419
$285$	18.7370	0.00389433
$286$	49.6694	0.0102693
$287$	−1385.39	−0.284938
$288$	−288.000	−0.0589256
$289$	4331.39	0.881617
$290$	50.3623	0.0101979
$291$	−633.817	−0.127680
$292$	−1808.92	−0.362532
$293$	3926.88	0.782972	0.391486	−	0.920184i	$-0.371961\pi$
$293$	3926.88	0.782972	0.391486	+	0.920184i	$0.371961\pi$
$294$	294.000	0.0583212
$295$	182.086	0.0359371
$296$	463.557	0.0910260
$297$	1095.31	0.213994
$298$	−5379.33	−1.04569
$299$	73.6992	0.0142546
$300$	1498.70	0.288426
$301$	2601.23	0.498114
$302$	276.417	0.0526690
$303$	−1012.03	−0.191880
$304$	−304.000	−0.0573539
$305$	−181.273	−0.0340317
$306$	−1730.66	−0.323318
$307$	−4734.29	−0.880131	−0.440065	−	0.897966i	$-0.645045\pi$
$307$	−4734.29	−0.880131	−0.440065	+	0.897966i	$0.645045\pi$
$308$	−1135.87	−0.210138
$309$	3840.96	0.707134
$310$	178.837	0.0327654
$311$	71.2844	0.0129973	0.00649866	−	0.999979i	$-0.497931\pi$
$311$	71.2844	0.0129973	0.00649866	+	0.999979i	$0.497931\pi$
$312$	14.6926	0.00266604
$313$	1101.05	0.198834	0.0994169	−	0.995046i	$-0.468302\pi$
$313$	1101.05	0.198834	0.0994169	+	0.995046i	$0.468302\pi$
$314$	7440.71	1.33727
$315$	20.7093	0.00370424
$316$	569.160	0.101322
$317$	−7909.15	−1.40133	−0.700666	−	0.713490i	$-0.747114\pi$
$317$	−7909.15	−1.40133	−0.700666	+	0.713490i	$0.747114\pi$
$318$	2757.30	0.486231
$319$	3107.59	0.545428
$320$	21.0380	0.00367519
$321$	40.6146	0.00706196
$322$	−1685.40	−0.291689
$323$	−1826.81	−0.314694
$324$	324.000	0.0555556
$325$	−76.4577	−0.0130496
$326$	5397.61	0.917013
$327$	3378.75	0.571392
$328$	1583.31	0.266535
$329$	4018.43	0.673383
$330$	−80.0108	−0.0133468
$331$	31.2350	0.00518681	0.00259340	−	0.999997i	$-0.499174\pi$
$331$	31.2350	0.00518681	0.00259340	+	0.999997i	$0.499174\pi$
$332$	−4937.34	−0.816181
$333$	−521.502	−0.0858202
$334$	1661.98	0.272274
$335$	96.2525	0.0156980
$336$	−336.000	−0.0545545
$337$	−9392.89	−1.51829	−0.759145	−	0.650922i	$-0.774383\pi$
$337$	−9392.89	−1.51829	−0.759145	+	0.650922i	$0.774383\pi$
$338$	4393.25	0.706986
$339$	3227.22	0.517046
$340$	126.422	0.0201653
$341$	11035.1	1.75244
$342$	342.000	0.0540738
$343$	343.000	0.0539949
$344$	−2972.83	−0.465943
$345$	−118.719	−0.0185265
$346$	−3985.25	−0.619214
$347$	10389.1	1.60725	0.803626	−	0.595134i	$-0.202901\pi$
$347$	10389.1	1.60725	0.803626	+	0.595134i	$0.202901\pi$
$348$	919.247	0.141600
$349$	−4681.49	−0.718036	−0.359018	−	0.933331i	$-0.616888\pi$
$349$	−4681.49	−0.718036	−0.359018	+	0.933331i	$0.616888\pi$
$350$	1748.49	0.267030
$351$	−16.5291	−0.00251356
$352$	1298.14	0.196566
$353$	3027.97	0.456552	0.228276	−	0.973597i	$-0.426691\pi$
$353$	3027.97	0.456552	0.228276	+	0.973597i	$0.426691\pi$
$354$	3323.56	0.498997
$355$	−99.2804	−0.0148430
$356$	−5042.02	−0.750637
$357$	−2019.10	−0.299334
$358$	−3443.96	−0.508432
$359$	5240.12	0.770370	0.385185	−	0.922839i	$-0.374138\pi$
$359$	5240.12	0.770370	0.385185	+	0.922839i	$0.374138\pi$
$360$	−23.6678	−0.00346500
$361$	361.000	0.0526316
$362$	2348.69	0.341007
$363$	−944.031	−0.136498
$364$	17.1413	0.00246827
$365$	−148.657	−0.0213180
$366$	−3308.72	−0.472540
$367$	9511.02	1.35278	0.676391	−	0.736543i	$-0.263543\pi$
$367$	9511.02	1.35278	0.676391	+	0.736543i	$0.263543\pi$
$368$	1926.18	0.272850
$369$	−1781.22	−0.251291
$370$	38.0950	0.00535261
$371$	3216.85	0.450163
$372$	3264.26	0.454956
$373$	−1590.79	−0.220825	−0.110413	−	0.993886i	$-0.535217\pi$
$373$	−1590.79	−0.220825	−0.110413	+	0.993886i	$0.535217\pi$
$374$	7800.84	1.07853
$375$	246.433	0.0339353
$376$	−4592.49	−0.629892
$377$	−46.8962	−0.00640657
$378$	378.000	0.0514344
$379$	2872.35	0.389295	0.194647	−	0.980873i	$-0.437644\pi$
$379$	2872.35	0.389295	0.194647	+	0.980873i	$0.437644\pi$
$380$	−24.9826	−0.00337259
$381$	5991.09	0.805598
$382$	3662.97	0.490613
$383$	−12031.4	−1.60516	−0.802579	−	0.596546i	$-0.796539\pi$
$383$	−12031.4	−1.60516	−0.802579	+	0.596546i	$0.796539\pi$
$384$	384.000	0.0510310
$385$	−93.3459	−0.0123567
$386$	−1004.16	−0.132410
$387$	3344.44	0.439295
$388$	845.089	0.110575
$389$	−13260.7	−1.72839	−0.864193	−	0.503161i	$-0.832170\pi$
$389$	−13260.7	−1.72839	−0.864193	+	0.503161i	$0.832170\pi$
$390$	1.20743	0.000156771 0
$391$	11574.8	1.49710
$392$	−392.000	−0.0505076
$393$	2093.17	0.268668
$394$	7446.05	0.952098
$395$	46.7735	0.00595805
$396$	−1460.41	−0.185324
$397$	3492.66	0.441540	0.220770	−	0.975326i	$-0.429143\pi$
$397$	3492.66	0.441540	0.220770	+	0.975326i	$0.429143\pi$
$398$	8414.14	1.05971
$399$	399.000	0.0500626
$400$	−1998.27	−0.249784
$401$	−1361.03	−0.169492	−0.0847462	−	0.996403i	$-0.527008\pi$
$401$	−1361.03	−0.169492	−0.0847462	+	0.996403i	$0.527008\pi$
$402$	1756.86	0.217971
$403$	−166.529	−0.0205841
$404$	1349.37	0.166173
$405$	26.6262	0.00326684
$406$	1072.46	0.131096
$407$	2350.64	0.286282
$408$	2307.55	0.280001
$409$	−14265.2	−1.72462	−0.862311	−	0.506379i	$-0.830984\pi$
$409$	−14265.2	−1.72462	−0.862311	+	0.506379i	$0.830984\pi$
$410$	130.116	0.0156731
$411$	9289.91	1.11493
$412$	−5121.28	−0.612396
$413$	3877.48	0.461982
$414$	−2166.95	−0.257246
$415$	−405.750	−0.0479939
$416$	−19.5901	−0.00230885
$417$	−7021.20	−0.824531
$418$	−1541.54	−0.180381
$419$	−4868.08	−0.567592	−0.283796	−	0.958885i	$-0.591594\pi$
$419$	−4868.08	−0.567592	−0.283796	+	0.958885i	$0.591594\pi$
$420$	−27.6124	−0.00320797
$421$	−14593.2	−1.68938	−0.844689	−	0.535257i	$-0.820215\pi$
$421$	−14593.2	−1.68938	−0.844689	+	0.535257i	$0.820215\pi$
$422$	8731.48	1.00721
$423$	5166.55	0.593868
$424$	−3676.40	−0.421089
$425$	−12008.1	−1.37053
$426$	−1812.13	−0.206099
$427$	−3860.17	−0.437487
$428$	−54.1529	−0.00611583
$429$	74.5041	0.00838483
$430$	−244.307	−0.0273989
$431$	1993.13	0.222751	0.111376	−	0.993778i	$-0.464474\pi$
$431$	1993.13	0.222751	0.111376	+	0.993778i	$0.464474\pi$
$432$	−432.000	−0.0481125
$433$	6251.03	0.693777	0.346888	−	0.937906i	$-0.387238\pi$
$433$	6251.03	0.693777	0.346888	+	0.937906i	$0.387238\pi$
$434$	3808.30	0.421208
$435$	75.5435	0.00832651
$436$	−4505.00	−0.494840
$437$	−2287.33	−0.250384
$438$	−2713.39	−0.296006
$439$	7.82630	0.000850863 0	0.000425432	−	1.00000i	$-0.499865\pi$
$439$	7.82630	0.000850863 0	0.000425432		1.00000i	$0.499865\pi$
$440$	106.681	0.0115587
$441$	441.000	0.0476190
$442$	−117.721	−0.0126684
$443$	15635.6	1.67690	0.838451	−	0.544976i	$-0.183461\pi$
$443$	15635.6	1.67690	0.838451	+	0.544976i	$0.183461\pi$
$444$	695.336	0.0743224
$445$	−414.352	−0.0441397
$446$	5522.88	0.586359
$447$	−8068.99	−0.853804
$448$	448.000	0.0472456
$449$	−3408.96	−0.358304	−0.179152	−	0.983821i	$-0.557335\pi$
$449$	−3408.96	−0.358304	−0.179152	+	0.983821i	$0.557335\pi$
$450$	2248.05	0.235499
$451$	8028.73	0.838267
$452$	−4302.96	−0.447775
$453$	414.626	0.0430040
$454$	−7290.00	−0.753605
$455$	1.40867	0.000145142 0
$456$	−456.000	−0.0468293
$457$	11319.4	1.15864	0.579322	−	0.815098i	$-0.303317\pi$
$457$	11319.4	1.15864	0.579322	+	0.815098i	$0.303317\pi$
$458$	−8758.96	−0.893623
$459$	−2595.99	−0.263988
$460$	158.293	0.0160444
$461$	−6012.77	−0.607468	−0.303734	−	0.952757i	$-0.598233\pi$
$461$	−6012.77	−0.607468	−0.303734	+	0.952757i	$0.598233\pi$
$462$	−1703.81	−0.171577
$463$	2141.60	0.214964	0.107482	−	0.994207i	$-0.465721\pi$
$463$	2141.60	0.214964	0.107482	+	0.994207i	$0.465721\pi$
$464$	−1225.66	−0.122629
$465$	268.256	0.0267528
$466$	6716.17	0.667641
$467$	9338.18	0.925309	0.462655	−	0.886539i	$-0.346897\pi$
$467$	9338.18	0.925309	0.462655	+	0.886539i	$0.346897\pi$
$468$	22.0389	0.00217681
$469$	2049.68	0.201802
$470$	−377.409	−0.0370396
$471$	11161.1	1.09188
$472$	−4431.41	−0.432144
$473$	−15074.8	−1.46542
$474$	853.741	0.0827291
$475$	2372.95	0.229217
$476$	2692.14	0.259231
$477$	4135.94	0.397006
$478$	−4917.09	−0.470507
$479$	9897.81	0.944139	0.472070	−	0.881561i	$-0.343507\pi$
$479$	9897.81	0.944139	0.472070	+	0.881561i	$0.343507\pi$
$480$	31.5570	0.00300078
$481$	−35.4732	−0.00336265
$482$	−8997.57	−0.850266
$483$	−2528.11	−0.238163
$484$	1258.71	0.118211
$485$	69.4492	0.00650212
$486$	486.000	0.0453609
$487$	−1025.02	−0.0953758	−0.0476879	−	0.998862i	$-0.515185\pi$
$487$	−1025.02	−0.0953758	−0.0476879	+	0.998862i	$0.515185\pi$
$488$	4411.63	0.409231
$489$	8096.42	0.748738
$490$	−32.2145	−0.00297000
$491$	711.136	0.0653627	0.0326814	−	0.999466i	$-0.489595\pi$
$491$	711.136	0.0653627	0.0326814	+	0.999466i	$0.489595\pi$
$492$	2374.96	0.217625
$493$	−7365.29	−0.672852
$494$	23.2632	0.00211875
$495$	−120.016	−0.0108976
$496$	−4352.34	−0.394004
$497$	−2114.15	−0.190810
$498$	−7406.02	−0.666409
$499$	14863.8	1.33345	0.666727	−	0.745302i	$-0.267695\pi$
$499$	14863.8	1.33345	0.666727	+	0.745302i	$0.267695\pi$
$500$	−328.577	−0.0293888
$501$	2492.97	0.222311
$502$	−9812.69	−0.872434
$503$	−2309.46	−0.204719	−0.102359	−	0.994747i	$-0.532639\pi$
$503$	−2309.46	−0.204719	−0.102359	+	0.994747i	$0.532639\pi$
$504$	−504.000	−0.0445435
$505$	110.891	0.00977145
$506$	9767.38	0.858128
$507$	6589.88	0.577252
$508$	−7988.12	−0.697668
$509$	17282.5	1.50498	0.752489	−	0.658605i	$-0.228853\pi$
$509$	17282.5	1.50498	0.752489	+	0.658605i	$0.228853\pi$
$510$	189.634	0.0164649
$511$	−3165.62	−0.274048
$512$	−512.000	−0.0441942
$513$	513.000	0.0441511
$514$	5201.96	0.446398
$515$	−420.865	−0.0360108
$516$	−4459.25	−0.380441
$517$	−23287.9	−1.98105
$518$	811.225	0.0688092
$519$	−5977.87	−0.505586
$520$	−1.60991	−0.000135768 0
$521$	19412.8	1.63242	0.816208	−	0.577758i	$-0.196072\pi$
$521$	19412.8	1.63242	0.816208	+	0.577758i	$0.196072\pi$
$522$	1378.87	0.115616
$523$	5400.36	0.451513	0.225756	−	0.974184i	$-0.427515\pi$
$523$	5400.36	0.451513	0.225756	+	0.974184i	$0.427515\pi$
$524$	−2790.89	−0.232673
$525$	2622.73	0.218029
$526$	5112.21	0.423770
$527$	−26154.2	−2.16185
$528$	1947.21	0.160495
$529$	2325.78	0.191155
$530$	−302.125	−0.0247613
$531$	4985.33	0.407430
$532$	−532.000	−0.0433555
$533$	−121.161	−0.00984625
$534$	−7563.03	−0.612892
$535$	−4.45027	−0.000359630 0
$536$	−2342.49	−0.188769
$537$	−5165.94	−0.415133
$538$	−11455.9	−0.918028
$539$	−1987.78	−0.158849
$540$	−35.5017	−0.00282916
$541$	−1649.23	−0.131064	−0.0655322	−	0.997850i	$-0.520875\pi$
$541$	−1649.23	−0.131064	−0.0655322	+	0.997850i	$0.520875\pi$
$542$	13081.6	1.03672
$543$	3523.04	0.278431
$544$	−3076.73	−0.242488
$545$	−370.220	−0.0290981
$546$	25.7120	0.00201533
$547$	−19908.9	−1.55620	−0.778100	−	0.628141i	$-0.783816\pi$
$547$	−19908.9	−1.55620	−0.778100	+	0.628141i	$0.783816\pi$
$548$	−12386.5	−0.965560
$549$	−4963.08	−0.385827
$550$	−10133.0	−0.785584
$551$	1455.47	0.112532
$552$	2889.26	0.222781
$553$	996.031	0.0765923
$554$	−6472.98	−0.496409
$555$	57.1425	0.00437039
$556$	9361.60	0.714065
$557$	6077.99	0.462357	0.231178	−	0.972911i	$-0.425742\pi$
$557$	6077.99	0.462357	0.231178	+	0.972911i	$0.425742\pi$
$558$	4896.38	0.371470
$559$	227.492	0.0172127
$560$	36.8165	0.00277818
$561$	11701.3	0.880619
$562$	17319.6	1.29997
$563$	−17335.7	−1.29772	−0.648858	−	0.760910i	$-0.724753\pi$
$563$	−17335.7	−1.29772	−0.648858	+	0.760910i	$0.724753\pi$
$564$	−6888.73	−0.514305
$565$	−353.616	−0.0263305
$566$	−17092.1	−1.26932
$567$	567.000	0.0419961
$568$	2416.18	0.178487
$569$	−12373.3	−0.911628	−0.455814	−	0.890075i	$-0.650652\pi$
$569$	−12373.3	−0.911628	−0.455814	+	0.890075i	$0.650652\pi$
$570$	−37.4740	−0.00275370
$571$	−12247.5	−0.897623	−0.448812	−	0.893626i	$-0.648153\pi$
$571$	−12247.5	−0.897623	−0.448812	+	0.893626i	$0.648153\pi$
$572$	−99.3388	−0.00726148
$573$	5494.46	0.400583
$574$	2770.79	0.201481
$575$	−15035.2	−1.09046
$576$	576.000	0.0416667
$577$	16707.1	1.20542	0.602709	−	0.797961i	$-0.294088\pi$
$577$	16707.1	1.20542	0.602709	+	0.797961i	$0.294088\pi$
$578$	−8662.77	−0.623398
$579$	−1506.23	−0.108112
$580$	−100.725	−0.00721097
$581$	−8640.35	−0.616975
$582$	1267.63	0.0902837
$583$	−18642.5	−1.32435
$584$	3617.85	0.256349
$585$	1.81115	0.000128003 0
$586$	−7853.76	−0.553645
$587$	−4820.51	−0.338950	−0.169475	−	0.985534i	$-0.554207\pi$
$587$	−4820.51	−0.338950	−0.169475	+	0.985534i	$0.554207\pi$
$588$	−588.000	−0.0412393
$589$	5168.40	0.361563
$590$	−364.172	−0.0254114
$591$	11169.1	0.777385
$592$	−927.114	−0.0643651
$593$	−16287.1	−1.12788	−0.563940	−	0.825816i	$-0.690715\pi$
$593$	−16287.1	−1.12788	−0.563940	+	0.825816i	$0.690715\pi$
$594$	−2190.61	−0.151317
$595$	221.239	0.0152436
$596$	10758.7	0.739416
$597$	12621.2	0.865246
$598$	−147.398	−0.0100795
$599$	12650.8	0.862936	0.431468	−	0.902128i	$-0.357996\pi$
$599$	12650.8	0.862936	0.431468	+	0.902128i	$0.357996\pi$
$600$	−2997.41	−0.203948
$601$	−6908.98	−0.468924	−0.234462	−	0.972125i	$-0.575333\pi$
$601$	−6908.98	−0.468924	−0.234462	+	0.972125i	$0.575333\pi$
$602$	−5202.46	−0.352220
$603$	2635.30	0.177973
$604$	−552.835	−0.0372426
$605$	103.440	0.00695115
$606$	2024.06	0.135679
$607$	19518.4	1.30515	0.652575	−	0.757724i	$-0.273689\pi$
$607$	19518.4	1.30515	0.652575	+	0.757724i	$0.273689\pi$
$608$	608.000	0.0405554
$609$	1608.68	0.107040
$610$	362.546	0.0240641
$611$	351.435	0.0232693
$612$	3461.32	0.228620
$613$	−4050.72	−0.266896	−0.133448	−	0.991056i	$-0.542605\pi$
$613$	−4050.72	−0.266896	−0.133448	+	0.991056i	$0.542605\pi$
$614$	9468.58	0.622346
$615$	195.174	0.0127970
$616$	2271.75	0.148590
$617$	9689.91	0.632254	0.316127	−	0.948717i	$-0.397617\pi$
$617$	9689.91	0.632254	0.316127	+	0.948717i	$0.397617\pi$
$618$	−7681.92	−0.500019
$619$	22782.4	1.47932	0.739662	−	0.672978i	$-0.234985\pi$
$619$	22782.4	1.47932	0.739662	+	0.672978i	$0.234985\pi$
$620$	−357.674	−0.0231686
$621$	−3250.42	−0.210040
$622$	−142.569	−0.00919050
$623$	−8823.54	−0.567428
$624$	−29.3851	−0.00188517
$625$	15584.5	0.997407
$626$	−2202.10	−0.140597
$627$	−2312.32	−0.147281
$628$	−14881.4	−0.945595
$629$	−5571.24	−0.353164
$630$	−41.4186	−0.00261930
$631$	12521.4	0.789966	0.394983	−	0.918688i	$-0.370750\pi$
$631$	12521.4	0.789966	0.394983	+	0.918688i	$0.370750\pi$
$632$	−1138.32	−0.0716455
$633$	13097.2	0.822382
$634$	15818.3	0.990891
$635$	−656.462	−0.0410250
$636$	−5514.59	−0.343817
$637$	29.9973	0.00186584
$638$	−6215.17	−0.385676
$639$	−2718.20	−0.168279
$640$	−42.0760	−0.00259875
$641$	4512.33	0.278044	0.139022	−	0.990289i	$-0.455604\pi$
$641$	4512.33	0.278044	0.139022	+	0.990289i	$0.455604\pi$
$642$	−81.2293	−0.00499356
$643$	24205.4	1.48455	0.742276	−	0.670094i	$-0.233746\pi$
$643$	24205.4	1.48455	0.742276	+	0.670094i	$0.233746\pi$
$644$	3370.81	0.206255
$645$	−366.460	−0.0223711
$646$	3653.61	0.222522
$647$	−12069.1	−0.733362	−0.366681	−	0.930347i	$-0.619506\pi$
$647$	−12069.1	−0.733362	−0.366681	+	0.930347i	$0.619506\pi$
$648$	−648.000	−0.0392837
$649$	−22471.1	−1.35912
$650$	152.915	0.00922744
$651$	5712.45	0.343915
$652$	−10795.2	−0.648426
$653$	28766.5	1.72392	0.861960	−	0.506976i	$-0.169237\pi$
$653$	28766.5	1.72392	0.861960	+	0.506976i	$0.169237\pi$
$654$	−6757.50	−0.404035
$655$	−229.355	−0.0136819
$656$	−3166.61	−0.188469
$657$	−4070.08	−0.241688
$658$	−8036.85	−0.476154
$659$	−10509.5	−0.621229	−0.310615	−	0.950536i	$-0.600535\pi$
$659$	−10509.5	−0.621229	−0.310615	+	0.950536i	$0.600535\pi$
$660$	160.022	0.00943762
$661$	−20523.8	−1.20769	−0.603846	−	0.797101i	$-0.706366\pi$
$661$	−20523.8	−1.20769	−0.603846	+	0.797101i	$0.706366\pi$
$662$	−62.4701	−0.00366763
$663$	−176.582	−0.0103437
$664$	9874.69	0.577127
$665$	−43.7196	−0.00254944
$666$	1043.00	0.0606840
$667$	−9222.04	−0.535350
$668$	−3323.96	−0.192527
$669$	8284.32	0.478760
$670$	−192.505	−0.0111002
$671$	22370.8	1.28706
$672$	672.000	0.0385758
$673$	12446.5	0.712896	0.356448	−	0.934315i	$-0.383988\pi$
$673$	12446.5	0.712896	0.356448	+	0.934315i	$0.383988\pi$
$674$	18785.8	1.07359
$675$	3372.08	0.192284
$676$	−8786.50	−0.499915
$677$	−14501.3	−0.823235	−0.411617	−	0.911357i	$-0.635036\pi$
$677$	−14501.3	−0.823235	−0.411617	+	0.911357i	$0.635036\pi$
$678$	−6454.44	−0.365606
$679$	1478.91	0.0835865
$680$	−252.845	−0.0142590
$681$	−10935.0	−0.615316
$682$	−22070.1	−1.23916
$683$	−1466.44	−0.0821551	−0.0410775	−	0.999156i	$-0.513079\pi$
$683$	−1466.44	−0.0821551	−0.0410775	+	0.999156i	$0.513079\pi$
$684$	−684.000	−0.0382360
$685$	−1017.92	−0.0567779
$686$	−686.000	−0.0381802
$687$	−13138.4	−0.729640
$688$	5945.66	0.329471
$689$	281.332	0.0155557
$690$	237.439	0.0131002
$691$	−11804.8	−0.649890	−0.324945	−	0.945733i	$-0.605346\pi$
$691$	−11804.8	−0.649890	−0.324945	+	0.945733i	$0.605346\pi$
$692$	7970.49	0.437851
$693$	−2555.72	−0.140092
$694$	−20778.2	−1.13650
$695$	769.334	0.0419892
$696$	−1838.49	−0.100126
$697$	−19028.9	−1.03411
$698$	9362.99	0.507728
$699$	10074.3	0.545126
$700$	−3496.97	−0.188819
$701$	−31095.3	−1.67540	−0.837698	−	0.546134i	$-0.816099\pi$
$701$	−31095.3	−1.67540	−0.837698	+	0.546134i	$0.816099\pi$
$702$	33.0583	0.00177736
$703$	1100.95	0.0590655
$704$	−2596.28	−0.138993
$705$	−566.114	−0.0302427
$706$	−6055.94	−0.322831
$707$	2361.40	0.125615
$708$	−6647.11	−0.352844
$709$	−15340.8	−0.812604	−0.406302	−	0.913739i	$-0.633182\pi$
$709$	−15340.8	−0.812604	−0.406302	+	0.913739i	$0.633182\pi$
$710$	198.561	0.0104956
$711$	1280.61	0.0675480
$712$	10084.0	0.530780
$713$	−32747.5	−1.72006
$714$	4038.20	0.211661
$715$	−8.16364	−0.000426997 0
$716$	6887.92	0.359516
$717$	−7375.63	−0.384167
$718$	−10480.2	−0.544734
$719$	−17640.2	−0.914978	−0.457489	−	0.889215i	$-0.651251\pi$
$719$	−17640.2	−0.914978	−0.457489	+	0.889215i	$0.651251\pi$
$720$	47.3355	0.00245013
$721$	−8962.24	−0.462928
$722$	−722.000	−0.0372161
$723$	−13496.4	−0.694239
$724$	−4697.38	−0.241128
$725$	9567.21	0.490093
$726$	1888.06	0.0965186
$727$	−5152.94	−0.262877	−0.131439	−	0.991324i	$-0.541960\pi$
$727$	−5152.94	−0.262877	−0.131439	+	0.991324i	$0.541960\pi$
$728$	−34.2827	−0.00174533
$729$	729.000	0.0370370
$730$	297.314	0.0150741
$731$	35728.9	1.80777
$732$	6617.44	0.334136
$733$	−12022.3	−0.605802	−0.302901	−	0.953022i	$-0.597955\pi$
$733$	−12022.3	−0.605802	−0.302901	+	0.953022i	$0.597955\pi$
$734$	−19022.0	−0.956561
$735$	−48.3217	−0.00242500
$736$	−3852.35	−0.192934
$737$	−11878.4	−0.593688
$738$	3562.44	0.177690
$739$	−26212.8	−1.30481	−0.652403	−	0.757872i	$-0.726239\pi$
$739$	−26212.8	−1.30481	−0.652403	+	0.757872i	$0.726239\pi$
$740$	−76.1900	−0.00378487
$741$	34.8949	0.00172995
$742$	−6433.69	−0.318313
$743$	−10086.5	−0.498032	−0.249016	−	0.968499i	$-0.580107\pi$
$743$	−10086.5	−0.498032	−0.249016	+	0.968499i	$0.580107\pi$
$744$	−6528.51	−0.321703
$745$	884.144	0.0434799
$746$	3181.57	0.156147
$747$	−11109.0	−0.544120
$748$	−15601.7	−0.762639
$749$	−94.7675	−0.00462314
$750$	−492.865	−0.0239959
$751$	28599.3	1.38962	0.694809	−	0.719195i	$-0.255489\pi$
$751$	28599.3	1.38962	0.694809	+	0.719195i	$0.255489\pi$
$752$	9184.98	0.445401
$753$	−14719.0	−0.712340
$754$	93.7924	0.00453013
$755$	−45.4318	−0.00218998
$756$	−756.000	−0.0363696
$757$	−18762.7	−0.900847	−0.450423	−	0.892815i	$-0.648727\pi$
$757$	−18762.7	−0.900847	−0.450423	+	0.892815i	$0.648727\pi$
$758$	−5744.70	−0.275273
$759$	14651.1	0.700659
$760$	49.9653	0.00238478
$761$	−864.831	−0.0411959	−0.0205980	−	0.999788i	$-0.506557\pi$
$761$	−864.831	−0.0411959	−0.0205980	+	0.999788i	$0.506557\pi$
$762$	−11982.2	−0.569644
$763$	−7883.75	−0.374064
$764$	−7325.95	−0.346915
$765$	284.450	0.0134436
$766$	24062.8	1.13502
$767$	339.108	0.0159641
$768$	−768.000	−0.0360844
$769$	−11505.1	−0.539510	−0.269755	−	0.962929i	$-0.586943\pi$
$769$	−11505.1	−0.539510	−0.269755	+	0.962929i	$0.586943\pi$
$770$	186.692	0.00873754
$771$	7802.94	0.364482
$772$	2008.31	0.0936278
$773$	−34452.0	−1.60304	−0.801522	−	0.597965i	$-0.795976\pi$
$773$	−34452.0	−1.60304	−0.801522	+	0.597965i	$0.795976\pi$
$774$	−6688.87	−0.310629
$775$	33973.3	1.57465
$776$	−1690.18	−0.0781880
$777$	1216.84	0.0561825
$778$	26521.3	1.22215
$779$	3760.35	0.172951
$780$	−2.41486	−0.000110854 0
$781$	12252.1	0.561351
$782$	−23149.7	−1.05861
$783$	2068.31	0.0944000
$784$	784.000	0.0357143
$785$	−1222.95	−0.0556038
$786$	−4186.34	−0.189977
$787$	10144.1	0.459462	0.229731	−	0.973254i	$-0.426215\pi$
$787$	10144.1	0.459462	0.229731	+	0.973254i	$0.426215\pi$
$788$	−14892.1	−0.673235
$789$	7668.31	0.346007
$790$	−93.5469	−0.00421297
$791$	−7530.18	−0.338486
$792$	2920.82	0.131044
$793$	−337.595	−0.0151177
$794$	−6985.32	−0.312216
$795$	−453.188	−0.0202175
$796$	−16828.3	−0.749325
$797$	−33184.0	−1.47483	−0.737414	−	0.675441i	$-0.763953\pi$
$797$	−33184.0	−1.47483	−0.737414	+	0.675441i	$0.763953\pi$
$798$	−798.000	−0.0353996
$799$	55194.7	2.44386
$800$	3996.54	0.176624
$801$	−11344.6	−0.500425
$802$	2722.06	0.119849
$803$	18345.6	0.806231
$804$	−3513.73	−0.154129
$805$	277.012	0.0121284
$806$	333.058	0.0145552
$807$	−17183.9	−0.749567
$808$	−2698.74	−0.117502
$809$	14208.4	0.617477	0.308739	−	0.951147i	$-0.400093\pi$
$809$	14208.4	0.617477	0.308739	+	0.951147i	$0.400093\pi$
$810$	−53.2525	−0.00231000
$811$	−12106.1	−0.524171	−0.262085	−	0.965045i	$-0.584410\pi$
$811$	−12106.1	−0.524171	−0.262085	+	0.965045i	$0.584410\pi$
$812$	−2144.91	−0.0926990
$813$	19622.4	0.846481
$814$	−4701.27	−0.202432
$815$	−887.149	−0.0381294
$816$	−4615.09	−0.197991
$817$	−7060.47	−0.302344
$818$	28530.5	1.21949
$819$	38.5680	0.00164551
$820$	−260.231	−0.0110825
$821$	4248.91	0.180619	0.0903094	−	0.995914i	$-0.471214\pi$
$821$	4248.91	0.180619	0.0903094	+	0.995914i	$0.471214\pi$
$822$	−18579.8	−0.788377
$823$	45714.3	1.93621	0.968104	−	0.250547i	$-0.0806106\pi$
$823$	45714.3	1.93621	0.968104	+	0.250547i	$0.0806106\pi$
$824$	10242.6	0.433030
$825$	−15199.5	−0.641427
$826$	−7754.96	−0.326670
$827$	−38084.6	−1.60137	−0.800684	−	0.599087i	$-0.795530\pi$
$827$	−38084.6	−1.60137	−0.800684	+	0.599087i	$0.795530\pi$
$828$	4333.89	0.181900
$829$	38660.1	1.61969	0.809843	−	0.586646i	$-0.199552\pi$
$829$	38660.1	1.61969	0.809843	+	0.586646i	$0.199552\pi$
$830$	811.500	0.0339368
$831$	−9709.47	−0.405316
$832$	39.1802	0.00163261
$833$	4711.24	0.195960
$834$	14042.4	0.583032
$835$	−273.162	−0.0113211
$836$	3083.09	0.127549
$837$	7344.57	0.303304
$838$	9736.15	0.401348
$839$	−14121.6	−0.581087	−0.290543	−	0.956862i	$-0.593836\pi$
$839$	−14121.6	−0.581087	−0.290543	+	0.956862i	$0.593836\pi$
$840$	55.2248	0.00226838
$841$	−18520.8	−0.759393
$842$	29186.4	1.19457
$843$	25979.4	1.06142
$844$	−17463.0	−0.712204
$845$	−722.072	−0.0293965
$846$	−10333.1	−0.419928
$847$	2202.74	0.0893589
$848$	7352.79	0.297755
$849$	−25638.1	−1.03639
$850$	24016.2	0.969114
$851$	−6975.72	−0.280992
$852$	3624.27	0.145734
$853$	−6782.33	−0.272242	−0.136121	−	0.990692i	$-0.543464\pi$
$853$	−6782.33	−0.272242	−0.136121	+	0.990692i	$0.543464\pi$
$854$	7720.35	0.309350
$855$	−56.2109	−0.00224839
$856$	108.306	0.00432455
$857$	39360.7	1.56889	0.784443	−	0.620200i	$-0.212949\pi$
$857$	39360.7	1.56889	0.784443	+	0.620200i	$0.212949\pi$
$858$	−149.008	−0.00592897
$859$	−16537.7	−0.656878	−0.328439	−	0.944525i	$-0.606523\pi$
$859$	−16537.7	−0.656878	−0.328439	+	0.944525i	$0.606523\pi$
$860$	488.613	0.0193739
$861$	4156.18	0.164509
$862$	−3986.26	−0.157509
$863$	−43422.3	−1.71276	−0.856379	−	0.516347i	$-0.827291\pi$
$863$	−43422.3	−1.71276	−0.856379	+	0.516347i	$0.827291\pi$
$864$	864.000	0.0340207
$865$	655.013	0.0257469
$866$	−12502.1	−0.490574
$867$	−12994.2	−0.509002
$868$	−7616.60	−0.297839
$869$	−5772.27	−0.225329
$870$	−151.087	−0.00588773
$871$	179.256	0.00697343
$872$	9010.00	0.349905
$873$	1901.45	0.0737163
$874$	4574.67	0.177049
$875$	−575.010	−0.0222159
$876$	5426.77	0.209308
$877$	49850.5	1.91942	0.959710	−	0.280994i	$-0.0906640\pi$
$877$	49850.5	1.91942	0.959710	+	0.280994i	$0.0906640\pi$
$878$	−15.6526	−0.000601651 0
$879$	−11780.6	−0.452049
$880$	−213.362	−0.00817322
$881$	34587.0	1.32266	0.661332	−	0.750094i	$-0.269992\pi$
$881$	34587.0	1.32266	0.661332	+	0.750094i	$0.269992\pi$
$882$	−882.000	−0.0336718
$883$	−18662.2	−0.711250	−0.355625	−	0.934629i	$-0.615732\pi$
$883$	−18662.2	−0.711250	−0.355625	+	0.934629i	$0.615732\pi$
$884$	235.443	0.00895792
$885$	−546.258	−0.0207483
$886$	−31271.1	−1.18575
$887$	48448.3	1.83397	0.916986	−	0.398919i	$-0.130615\pi$
$887$	48448.3	1.83397	0.916986	+	0.398919i	$0.130615\pi$
$888$	−1390.67	−0.0525539
$889$	−13979.2	−0.527388
$890$	828.704	0.0312115
$891$	−3285.92	−0.123549
$892$	−11045.8	−0.414618
$893$	−10907.2	−0.408728
$894$	16138.0	0.603730
$895$	566.047	0.0211406
$896$	−896.000	−0.0334077
$897$	−221.097	−0.00822991
$898$	6817.91	0.253359
$899$	20837.9	0.773062
$900$	−4496.11	−0.166523
$901$	44184.6	1.63374
$902$	−16057.5	−0.592744
$903$	−7803.68	−0.287586
$904$	8605.92	0.316624
$905$	−386.030	−0.0141791
$906$	−829.252	−0.0304084
$907$	43077.9	1.57704	0.788521	−	0.615008i	$-0.210847\pi$
$907$	43077.9	1.57704	0.788521	+	0.615008i	$0.210847\pi$
$908$	14580.0	0.532879
$909$	3036.09	0.110782
$910$	−2.81734	−0.000102631 0
$911$	−20072.5	−0.730000	−0.365000	−	0.931008i	$-0.618931\pi$
$911$	−20072.5	−0.730000	−0.365000	+	0.931008i	$0.618931\pi$
$912$	912.000	0.0331133
$913$	50073.2	1.81510
$914$	−22638.9	−0.819286
$915$	543.820	0.0196482
$916$	17517.9	0.631887
$917$	−4884.06	−0.175884
$918$	5191.98	0.186668
$919$	−20001.9	−0.717958	−0.358979	−	0.933346i	$-0.616875\pi$
$919$	−20001.9	−0.717958	−0.358979	+	0.933346i	$0.616875\pi$
$920$	−316.585	−0.0113451
$921$	14202.9	0.508144
$922$	12025.5	0.429545
$923$	−184.895	−0.00659360
$924$	3407.62	0.121323
$925$	7236.82	0.257238
$926$	−4283.19	−0.152003
$927$	−11522.9	−0.408264
$928$	2451.33	0.0867120
$929$	2338.74	0.0825959	0.0412979	−	0.999147i	$-0.486851\pi$
$929$	2338.74	0.0825959	0.0412979	+	0.999147i	$0.486851\pi$
$930$	−536.511	−0.0189171
$931$	−931.000	−0.0327737
$932$	−13432.3	−0.472093
$933$	−213.853	−0.00750401
$934$	−18676.4	−0.654292
$935$	−1282.14	−0.0448455
$936$	−44.0777	−0.00153924
$937$	1371.20	0.0478070	0.0239035	−	0.999714i	$-0.492391\pi$
$937$	1371.20	0.0478070	0.0239035	+	0.999714i	$0.492391\pi$
$938$	−4099.35	−0.142696
$939$	−3303.15	−0.114797
$940$	754.819	0.0261909
$941$	37083.4	1.28468	0.642340	−	0.766420i	$-0.277964\pi$
$941$	37083.4	1.28468	0.642340	+	0.766420i	$0.277964\pi$
$942$	−22322.1	−0.772075
$943$	−23826.0	−0.822779
$944$	8862.82	0.305572
$945$	−62.1279	−0.00213865
$946$	30149.7	1.03621
$947$	2956.29	0.101443	0.0507214	−	0.998713i	$-0.483848\pi$
$947$	2956.29	0.101443	0.0507214	+	0.998713i	$0.483848\pi$
$948$	−1707.48	−0.0584983
$949$	−276.852	−0.00946995
$950$	−4745.89	−0.162081
$951$	23727.5	0.809059
$952$	−5384.27	−0.183304
$953$	2074.64	0.0705185	0.0352593	−	0.999378i	$-0.488774\pi$
$953$	2074.64	0.0705185	0.0352593	+	0.999378i	$0.488774\pi$
$954$	−8271.89	−0.280726
$955$	−602.044	−0.0203997
$956$	9834.18	0.332699
$957$	−9322.76	−0.314903
$958$	−19795.6	−0.667607
$959$	−21676.5	−0.729895
$960$	−63.1140	−0.00212187
$961$	44204.6	1.48382
$962$	70.9463	0.00237776
$963$	−121.844	−0.00407722
$964$	17995.1	0.601229
$965$	165.042	0.00550560
$966$	5056.21	0.168407
$967$	11704.2	0.389228	0.194614	−	0.980880i	$-0.437655\pi$
$967$	11704.2	0.389228	0.194614	+	0.980880i	$0.437655\pi$
$968$	−2517.42	−0.0835876
$969$	5480.42	0.181689
$970$	−138.898	−0.00459769
$971$	7575.66	0.250375	0.125188	−	0.992133i	$-0.460047\pi$
$971$	7575.66	0.250375	0.125188	+	0.992133i	$0.460047\pi$
$972$	−972.000	−0.0320750
$973$	16382.8	0.539782
$974$	2050.04	0.0674409
$975$	229.373	0.00753417
$976$	−8823.25	−0.289370
$977$	−31044.5	−1.01658	−0.508291	−	0.861185i	$-0.669723\pi$
$977$	−31044.5	−1.01658	−0.508291	+	0.861185i	$0.669723\pi$
$978$	−16192.8	−0.529438
$979$	51134.9	1.66933
$980$	64.4289	0.00210011
$981$	−10136.2	−0.329893
$982$	−1422.27	−0.0462184
$983$	13620.2	0.441929	0.220965	−	0.975282i	$-0.429079\pi$
$983$	13620.2	0.441929	0.220965	+	0.975282i	$0.429079\pi$
$984$	−4749.92	−0.153884
$985$	−1223.83	−0.0395883
$986$	14730.6	0.475778
$987$	−12055.3	−0.388778
$988$	−46.5265	−0.00149818
$989$	44735.9	1.43834
$990$	240.032	0.00770578
$991$	−2170.29	−0.0695677	−0.0347839	−	0.999395i	$-0.511074\pi$
$991$	−2170.29	−0.0695677	−0.0347839	+	0.999395i	$0.511074\pi$
$992$	8704.68	0.278603
$993$	−93.7051	−0.00299460
$994$	4228.31	0.134923
$995$	−1382.94	−0.0440626
$996$	14812.0	0.471222
$997$	−20585.6	−0.653913	−0.326957	−	0.945039i	$-0.606023\pi$
$997$	−20585.6	−0.653913	−0.326957	+	0.945039i	$0.606023\pi$
$998$	−29727.6	−0.942895
$999$	1564.50	0.0495483

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.4.a.f.1.2	✓	3
3.2	odd	2		2394.4.a.n.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.4.a.f.1.2	✓	3	1.1	even	1	trivial
2394.4.a.n.1.2		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)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +0.328719 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-2.00000 q^{2} -3.00000 q^{3} +4.00000 q^{4} +0.328719 q^{5} +6.00000 q^{6} +7.00000 q^{7} -8.00000 q^{8} +9.00000 q^{9} -0.657438 q^{10} -40.5669 q^{11} -12.0000 q^{12} +0.612191 q^{13} -14.0000 q^{14} -0.986157 q^{15} +16.0000 q^{16} +96.1477 q^{17} -18.0000 q^{18} -19.0000 q^{19} +1.31488 q^{20} -21.0000 q^{21} +81.1339 q^{22} +120.386 q^{23} +24.0000 q^{24} -124.892 q^{25} -1.22438 q^{26} -27.0000 q^{27} +28.0000 q^{28} -76.6039 q^{29} +1.97231 q^{30} -272.021 q^{31} -32.0000 q^{32} +121.701 q^{33} -192.295 q^{34} +2.30103 q^{35} +36.0000 q^{36} -57.9446 q^{37} +38.0000 q^{38} -1.83657 q^{39} -2.62975 q^{40} -197.913 q^{41} +42.0000 q^{42} +371.604 q^{43} -162.268 q^{44} +2.95847 q^{45} -240.772 q^{46} +574.061 q^{47} -48.0000 q^{48} +49.0000 q^{49} +249.784 q^{50} -288.443 q^{51} +2.44876 q^{52} +459.549 q^{53} +54.0000 q^{54} -13.3351 q^{55} -56.0000 q^{56} +57.0000 q^{57} +153.208 q^{58} +553.926 q^{59} -3.94463 q^{60} -551.453 q^{61} +544.043 q^{62} +63.0000 q^{63} +64.0000 q^{64} +0.201239 q^{65} -243.402 q^{66} +292.811 q^{67} +384.591 q^{68} -361.158 q^{69} -4.60207 q^{70} -302.022 q^{71} -72.0000 q^{72} -452.231 q^{73} +115.889 q^{74} +374.676 q^{75} -76.0000 q^{76} -283.969 q^{77} +3.67314 q^{78} +142.290 q^{79} +5.25950 q^{80} +81.0000 q^{81} +395.826 q^{82} -1234.34 q^{83} -84.0000 q^{84} +31.6056 q^{85} -743.208 q^{86} +229.812 q^{87} +324.536 q^{88} -1260.51 q^{89} -5.91694 q^{90} +4.28533 q^{91} +481.544 q^{92} +816.064 q^{93} -1148.12 q^{94} -6.24566 q^{95} +96.0000 q^{96} +211.272 q^{97} -98.0000 q^{98} -365.102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} + 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 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	\( 3 q - 6 q^{2} - 9 q^{3} + 12 q^{4} + 10 q^{5} + 18 q^{6} + 21 q^{7} - 24 q^{8} + 27 q^{9} - 20 q^{10} - 36 q^{12} - 50 q^{13} - 42 q^{14} - 30 q^{15} + 48 q^{16} + 18 q^{17} - 54 q^{18} - 57 q^{19} + 40 q^{20} - 63 q^{21} - 40 q^{23} + 72 q^{24} - 111 q^{25} + 100 q^{26} - 81 q^{27} + 84 q^{28} - 54 q^{29} + 60 q^{30} - 336 q^{31} - 96 q^{32} - 36 q^{34} + 70 q^{35} + 108 q^{36} - 282 q^{37} + 114 q^{38} + 150 q^{39} - 80 q^{40} + 150 q^{41} + 126 q^{42} + 184 q^{43} + 90 q^{45} + 80 q^{46} + 708 q^{47} - 144 q^{48} + 147 q^{49} + 222 q^{50} - 54 q^{51} - 200 q^{52} + 378 q^{53} + 162 q^{54} + 280 q^{55} - 168 q^{56} + 171 q^{57} + 108 q^{58} + 260 q^{59} - 120 q^{60} + 90 q^{61} + 672 q^{62} + 189 q^{63} + 192 q^{64} - 76 q^{65} - 280 q^{67} + 72 q^{68} + 120 q^{69} - 140 q^{70} - 248 q^{71} - 216 q^{72} - 978 q^{73} + 564 q^{74} + 333 q^{75} - 228 q^{76} - 300 q^{78} - 664 q^{79} + 160 q^{80} + 243 q^{81} - 300 q^{82} + 516 q^{83} - 252 q^{84} - 1192 q^{85} - 368 q^{86} + 162 q^{87} - 90 q^{89} - 180 q^{90} - 350 q^{91} - 160 q^{92} + 1008 q^{93} - 1416 q^{94} - 190 q^{95} + 288 q^{96} - 1390 q^{97} - 294 q^{98}+O(q^{100}) \) 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 - 36 * q^12 - 50 * q^13 - 42 * q^14 - 30 * q^15 + 48 * q^16 + 18 * q^17 - 54 * q^18 - 57 * q^19 + 40 * q^20 - 63 * q^21 - 40 * q^23 + 72 * q^24 - 111 * q^25 + 100 * q^26 - 81 * q^27 + 84 * q^28 - 54 * q^29 + 60 * q^30 - 336 * q^31 - 96 * q^32 - 36 * q^34 + 70 * q^35 + 108 * q^36 - 282 * q^37 + 114 * q^38 + 150 * q^39 - 80 * q^40 + 150 * q^41 + 126 * q^42 + 184 * q^43 + 90 * q^45 + 80 * q^46 + 708 * q^47 - 144 * q^48 + 147 * q^49 + 222 * q^50 - 54 * q^51 - 200 * q^52 + 378 * q^53 + 162 * q^54 + 280 * q^55 - 168 * q^56 + 171 * q^57 + 108 * q^58 + 260 * q^59 - 120 * q^60 + 90 * q^61 + 672 * q^62 + 189 * q^63 + 192 * q^64 - 76 * q^65 - 280 * q^67 + 72 * q^68 + 120 * q^69 - 140 * q^70 - 248 * q^71 - 216 * q^72 - 978 * q^73 + 564 * q^74 + 333 * q^75 - 228 * q^76 - 300 * q^78 - 664 * q^79 + 160 * q^80 + 243 * q^81 - 300 * q^82 + 516 * q^83 - 252 * q^84 - 1192 * q^85 - 368 * q^86 + 162 * q^87 - 90 * q^89 - 180 * q^90 - 350 * q^91 - 160 * q^92 + 1008 * q^93 - 1416 * q^94 - 190 * q^95 + 288 * q^96 - 1390 * q^97 - 294 * q^98

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