LMFDB - Embedded newform 798.2.a.k.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [798,2,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, 2, names="a")

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

chi := DirichletCharacter("798.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 798 = 2 \cdot 3 \cdot 7 \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
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:	$6.37206208130$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{12})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - 3 $ x^2 - 3
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-1.73205$ 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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.46410 q^{10} -5.46410 q^{11} -1.00000 q^{12} -3.46410 q^{13} +1.00000 q^{14} +3.46410 q^{15} +1.00000 q^{16} +7.46410 q^{17} -1.00000 q^{18} +1.00000 q^{19} -3.46410 q^{20} +1.00000 q^{21} +5.46410 q^{22} -5.46410 q^{23} +1.00000 q^{24} +7.00000 q^{25} +3.46410 q^{26} -1.00000 q^{27} -1.00000 q^{28} -6.00000 q^{29} -3.46410 q^{30} +6.92820 q^{31} -1.00000 q^{32} +5.46410 q^{33} -7.46410 q^{34} +3.46410 q^{35} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} +3.46410 q^{39} +3.46410 q^{40} -2.00000 q^{41} -1.00000 q^{42} -6.92820 q^{43} -5.46410 q^{44} -3.46410 q^{45} +5.46410 q^{46} +10.9282 q^{47} -1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} -7.46410 q^{51} -3.46410 q^{52} +2.00000 q^{53} +1.00000 q^{54} +18.9282 q^{55} +1.00000 q^{56} -1.00000 q^{57} +6.00000 q^{58} +4.00000 q^{59} +3.46410 q^{60} -4.92820 q^{61} -6.92820 q^{62} -1.00000 q^{63} +1.00000 q^{64} +12.0000 q^{65} -5.46410 q^{66} +9.46410 q^{67} +7.46410 q^{68} +5.46410 q^{69} -3.46410 q^{70} +2.92820 q^{71} -1.00000 q^{72} +10.0000 q^{73} -10.0000 q^{74} -7.00000 q^{75} +1.00000 q^{76} +5.46410 q^{77} -3.46410 q^{78} -12.3923 q^{79} -3.46410 q^{80} +1.00000 q^{81} +2.00000 q^{82} +8.00000 q^{83} +1.00000 q^{84} -25.8564 q^{85} +6.92820 q^{86} +6.00000 q^{87} +5.46410 q^{88} -2.00000 q^{89} +3.46410 q^{90} +3.46410 q^{91} -5.46410 q^{92} -6.92820 q^{93} -10.9282 q^{94} -3.46410 q^{95} +1.00000 q^{96} +4.53590 q^{97} -1.00000 q^{98} -5.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	$ 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{11} - 2 q^{12} + 2 q^{14} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} + 14 q^{25} - 2 q^{27} - 2 q^{28} - 12 q^{29} - 2 q^{32} + 4 q^{33} - 8 q^{34} + 2 q^{36} + 20 q^{37} - 2 q^{38} - 4 q^{41} - 2 q^{42} - 4 q^{44} + 4 q^{46} + 8 q^{47} - 2 q^{48} + 2 q^{49} - 14 q^{50} - 8 q^{51} + 4 q^{53} + 2 q^{54} + 24 q^{55} + 2 q^{56} - 2 q^{57} + 12 q^{58} + 8 q^{59} + 4 q^{61} - 2 q^{63} + 2 q^{64} + 24 q^{65} - 4 q^{66} + 12 q^{67} + 8 q^{68} + 4 q^{69} - 8 q^{71} - 2 q^{72} + 20 q^{73} - 20 q^{74} - 14 q^{75} + 2 q^{76} + 4 q^{77} - 4 q^{79} + 2 q^{81} + 4 q^{82} + 16 q^{83} + 2 q^{84} - 24 q^{85} + 12 q^{87} + 4 q^{88} - 4 q^{89} - 4 q^{92} - 8 q^{94} + 2 q^{96} + 16 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 4 * q^11 - 2 * q^12 + 2 * q^14 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 + 14 * q^25 - 2 * q^27 - 2 * q^28 - 12 * q^29 - 2 * q^32 + 4 * q^33 - 8 * q^34 + 2 * q^36 + 20 * q^37 - 2 * q^38 - 4 * q^41 - 2 * q^42 - 4 * q^44 + 4 * q^46 + 8 * q^47 - 2 * q^48 + 2 * q^49 - 14 * q^50 - 8 * q^51 + 4 * q^53 + 2 * q^54 + 24 * q^55 + 2 * q^56 - 2 * q^57 + 12 * q^58 + 8 * q^59 + 4 * q^61 - 2 * q^63 + 2 * q^64 + 24 * q^65 - 4 * q^66 + 12 * q^67 + 8 * q^68 + 4 * q^69 - 8 * q^71 - 2 * q^72 + 20 * q^73 - 20 * q^74 - 14 * q^75 + 2 * q^76 + 4 * q^77 - 4 * q^79 + 2 * q^81 + 4 * q^82 + 16 * q^83 + 2 * q^84 - 24 * q^85 + 12 * q^87 + 4 * q^88 - 4 * q^89 - 4 * q^92 - 8 * q^94 + 2 * q^96 + 16 * q^97 - 2 * q^98 - 4 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	−3.46410	−1.54919	−0.774597	−	0.632456i	$-0.782047\pi$
$5$	−3.46410	−1.54919	−0.774597	+	0.632456i	$0.782047\pi$
$6$	1.00000	0.408248
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	1.00000	0.333333
$10$	3.46410	1.09545
$11$	−5.46410	−1.64749	−0.823744	−	0.566961i	$-0.808119\pi$
$11$	−5.46410	−1.64749	−0.823744	+	0.566961i	$0.808119\pi$
$12$	−1.00000	−0.288675
$13$	−3.46410	−0.960769	−0.480384	−	0.877058i	$-0.659503\pi$
$13$	−3.46410	−0.960769	−0.480384	+	0.877058i	$0.659503\pi$
$14$	1.00000	0.267261
$15$	3.46410	0.894427
$16$	1.00000	0.250000
$17$	7.46410	1.81031	0.905155	−	0.425081i	$-0.139754\pi$
$17$	7.46410	1.81031	0.905155	+	0.425081i	$0.139754\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−3.46410	−0.774597
$21$	1.00000	0.218218
$22$	5.46410	1.16495
$23$	−5.46410	−1.13934	−0.569672	−	0.821872i	$-0.692930\pi$
$23$	−5.46410	−1.13934	−0.569672	+	0.821872i	$0.692930\pi$
$24$	1.00000	0.204124
$25$	7.00000	1.40000
$26$	3.46410	0.679366
$27$	−1.00000	−0.192450
$28$	−1.00000	−0.188982
$29$	−6.00000	−1.11417	−0.557086	−	0.830455i	$-0.688081\pi$
$29$	−6.00000	−1.11417	−0.557086	+	0.830455i	$0.688081\pi$
$30$	−3.46410	−0.632456
$31$	6.92820	1.24434	0.622171	−	0.782881i	$-0.286251\pi$
$31$	6.92820	1.24434	0.622171	+	0.782881i	$0.286251\pi$
$32$	−1.00000	−0.176777
$33$	5.46410	0.951178
$34$	−7.46410	−1.28008
$35$	3.46410	0.585540
$36$	1.00000	0.166667
$37$	10.0000	1.64399	0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000	1.64399	0.821995	+	0.569495i	$0.192861\pi$
$38$	−1.00000	−0.162221
$39$	3.46410	0.554700
$40$	3.46410	0.547723
$41$	−2.00000	−0.312348	−0.156174	−	0.987730i	$-0.549916\pi$
$41$	−2.00000	−0.312348	−0.156174	+	0.987730i	$0.549916\pi$
$42$	−1.00000	−0.154303
$43$	−6.92820	−1.05654	−0.528271	−	0.849076i	$-0.677159\pi$
$43$	−6.92820	−1.05654	−0.528271	+	0.849076i	$0.677159\pi$
$44$	−5.46410	−0.823744
$45$	−3.46410	−0.516398
$46$	5.46410	0.805638
$47$	10.9282	1.59404	0.797021	−	0.603951i	$-0.206408\pi$
$47$	10.9282	1.59404	0.797021	+	0.603951i	$0.206408\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−7.00000	−0.989949
$51$	−7.46410	−1.04518
$52$	−3.46410	−0.480384
$53$	2.00000	0.274721	0.137361	−	0.990521i	$-0.456138\pi$
$53$	2.00000	0.274721	0.137361	+	0.990521i	$0.456138\pi$
$54$	1.00000	0.136083
$55$	18.9282	2.55228
$56$	1.00000	0.133631
$57$	−1.00000	−0.132453
$58$	6.00000	0.787839
$59$	4.00000	0.520756	0.260378	−	0.965507i	$-0.416153\pi$
$59$	4.00000	0.520756	0.260378	+	0.965507i	$0.416153\pi$
$60$	3.46410	0.447214
$61$	−4.92820	−0.630992	−0.315496	−	0.948927i	$-0.602171\pi$
$61$	−4.92820	−0.630992	−0.315496	+	0.948927i	$0.602171\pi$
$62$	−6.92820	−0.879883
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	12.0000	1.48842
$66$	−5.46410	−0.672584
$67$	9.46410	1.15622	0.578112	−	0.815957i	$-0.303790\pi$
$67$	9.46410	1.15622	0.578112	+	0.815957i	$0.303790\pi$
$68$	7.46410	0.905155
$69$	5.46410	0.657801
$70$	−3.46410	−0.414039
$71$	2.92820	0.347514	0.173757	−	0.984789i	$-0.444409\pi$
$71$	2.92820	0.347514	0.173757	+	0.984789i	$0.444409\pi$
$72$	−1.00000	−0.117851
$73$	10.0000	1.17041	0.585206	−	0.810885i	$-0.301014\pi$
$73$	10.0000	1.17041	0.585206	+	0.810885i	$0.301014\pi$
$74$	−10.0000	−1.16248
$75$	−7.00000	−0.808290
$76$	1.00000	0.114708
$77$	5.46410	0.622692
$78$	−3.46410	−0.392232
$79$	−12.3923	−1.39424	−0.697122	−	0.716953i	$-0.745536\pi$
$79$	−12.3923	−1.39424	−0.697122	+	0.716953i	$0.745536\pi$
$80$	−3.46410	−0.387298
$81$	1.00000	0.111111
$82$	2.00000	0.220863
$83$	8.00000	0.878114	0.439057	−	0.898459i	$-0.355313\pi$
$83$	8.00000	0.878114	0.439057	+	0.898459i	$0.355313\pi$
$84$	1.00000	0.109109
$85$	−25.8564	−2.80452
$86$	6.92820	0.747087
$87$	6.00000	0.643268
$88$	5.46410	0.582475
$89$	−2.00000	−0.212000	−0.106000	−	0.994366i	$-0.533804\pi$
$89$	−2.00000	−0.212000	−0.106000	+	0.994366i	$0.533804\pi$
$90$	3.46410	0.365148
$91$	3.46410	0.363137
$92$	−5.46410	−0.569672
$93$	−6.92820	−0.718421
$94$	−10.9282	−1.12716
$95$	−3.46410	−0.355409
$96$	1.00000	0.102062
$97$	4.53590	0.460551	0.230275	−	0.973126i	$-0.426037\pi$
$97$	4.53590	0.460551	0.230275	+	0.973126i	$0.426037\pi$
$98$	−1.00000	−0.101015
$99$	−5.46410	−0.549163
$100$	7.00000	0.700000
$101$	4.53590	0.451339	0.225669	−	0.974204i	$-0.427543\pi$
$101$	4.53590	0.451339	0.225669	+	0.974204i	$0.427543\pi$
$102$	7.46410	0.739056
$103$	−6.92820	−0.682656	−0.341328	−	0.939944i	$-0.610877\pi$
$103$	−6.92820	−0.682656	−0.341328	+	0.939944i	$0.610877\pi$
$104$	3.46410	0.339683
$105$	−3.46410	−0.338062
$106$	−2.00000	−0.194257
$107$	−4.00000	−0.386695	−0.193347	−	0.981130i	$-0.561934\pi$
$107$	−4.00000	−0.386695	−0.193347	+	0.981130i	$0.561934\pi$
$108$	−1.00000	−0.0962250
$109$	2.00000	0.191565	0.0957826	−	0.995402i	$-0.469465\pi$
$109$	2.00000	0.191565	0.0957826	+	0.995402i	$0.469465\pi$
$110$	−18.9282	−1.80473
$111$	−10.0000	−0.949158
$112$	−1.00000	−0.0944911
$113$	11.8564	1.11536	0.557678	−	0.830057i	$-0.311692\pi$
$113$	11.8564	1.11536	0.557678	+	0.830057i	$0.311692\pi$
$114$	1.00000	0.0936586
$115$	18.9282	1.76506
$116$	−6.00000	−0.557086
$117$	−3.46410	−0.320256
$118$	−4.00000	−0.368230
$119$	−7.46410	−0.684233
$120$	−3.46410	−0.316228
$121$	18.8564	1.71422
$122$	4.92820	0.446179
$123$	2.00000	0.180334
$124$	6.92820	0.622171
$125$	−6.92820	−0.619677
$126$	1.00000	0.0890871
$127$	−17.4641	−1.54969	−0.774844	−	0.632152i	$-0.782172\pi$
$127$	−17.4641	−1.54969	−0.774844	+	0.632152i	$0.782172\pi$
$128$	−1.00000	−0.0883883
$129$	6.92820	0.609994
$130$	−12.0000	−1.05247
$131$	−5.07180	−0.443125	−0.221562	−	0.975146i	$-0.571116\pi$
$131$	−5.07180	−0.443125	−0.221562	+	0.975146i	$0.571116\pi$
$132$	5.46410	0.475589
$133$	−1.00000	−0.0867110
$134$	−9.46410	−0.817574
$135$	3.46410	0.298142
$136$	−7.46410	−0.640041
$137$	−0.928203	−0.0793018	−0.0396509	−	0.999214i	$-0.512625\pi$
$137$	−0.928203	−0.0793018	−0.0396509	+	0.999214i	$0.512625\pi$
$138$	−5.46410	−0.465135
$139$	9.85641	0.836009	0.418005	−	0.908445i	$-0.362730\pi$
$139$	9.85641	0.836009	0.418005	+	0.908445i	$0.362730\pi$
$140$	3.46410	0.292770
$141$	−10.9282	−0.920321
$142$	−2.92820	−0.245729
$143$	18.9282	1.58286
$144$	1.00000	0.0833333
$145$	20.7846	1.72607
$146$	−10.0000	−0.827606
$147$	−1.00000	−0.0824786
$148$	10.0000	0.821995
$149$	−3.07180	−0.251651	−0.125826	−	0.992052i	$-0.540158\pi$
$149$	−3.07180	−0.251651	−0.125826	+	0.992052i	$0.540158\pi$
$150$	7.00000	0.571548
$151$	1.46410	0.119147	0.0595734	−	0.998224i	$-0.481026\pi$
$151$	1.46410	0.119147	0.0595734	+	0.998224i	$0.481026\pi$
$152$	−1.00000	−0.0811107
$153$	7.46410	0.603437
$154$	−5.46410	−0.440310
$155$	−24.0000	−1.92773
$156$	3.46410	0.277350
$157$	19.8564	1.58471	0.792357	−	0.610058i	$-0.208854\pi$
$157$	19.8564	1.58471	0.792357	+	0.610058i	$0.208854\pi$
$158$	12.3923	0.985879
$159$	−2.00000	−0.158610
$160$	3.46410	0.273861
$161$	5.46410	0.430632
$162$	−1.00000	−0.0785674
$163$	1.07180	0.0839496	0.0419748	−	0.999119i	$-0.486635\pi$
$163$	1.07180	0.0839496	0.0419748	+	0.999119i	$0.486635\pi$
$164$	−2.00000	−0.156174
$165$	−18.9282	−1.47356
$166$	−8.00000	−0.620920
$167$	−18.9282	−1.46471	−0.732354	−	0.680924i	$-0.761578\pi$
$167$	−18.9282	−1.46471	−0.732354	+	0.680924i	$0.761578\pi$
$168$	−1.00000	−0.0771517
$169$	−1.00000	−0.0769231
$170$	25.8564	1.98310
$171$	1.00000	0.0764719
$172$	−6.92820	−0.528271
$173$	−0.928203	−0.0705700	−0.0352850	−	0.999377i	$-0.511234\pi$
$173$	−0.928203	−0.0705700	−0.0352850	+	0.999377i	$0.511234\pi$
$174$	−6.00000	−0.454859
$175$	−7.00000	−0.529150
$176$	−5.46410	−0.411872
$177$	−4.00000	−0.300658
$178$	2.00000	0.149906
$179$	−9.85641	−0.736702	−0.368351	−	0.929687i	$-0.620078\pi$
$179$	−9.85641	−0.736702	−0.368351	+	0.929687i	$0.620078\pi$
$180$	−3.46410	−0.258199
$181$	−8.53590	−0.634468	−0.317234	−	0.948347i	$-0.602754\pi$
$181$	−8.53590	−0.634468	−0.317234	+	0.948347i	$0.602754\pi$
$182$	−3.46410	−0.256776
$183$	4.92820	0.364303
$184$	5.46410	0.402819
$185$	−34.6410	−2.54686
$186$	6.92820	0.508001
$187$	−40.7846	−2.98247
$188$	10.9282	0.797021
$189$	1.00000	0.0727393
$190$	3.46410	0.251312
$191$	−5.46410	−0.395369	−0.197684	−	0.980266i	$-0.563342\pi$
$191$	−5.46410	−0.395369	−0.197684	+	0.980266i	$0.563342\pi$
$192$	−1.00000	−0.0721688
$193$	−22.0000	−1.58359	−0.791797	−	0.610784i	$-0.790854\pi$
$193$	−22.0000	−1.58359	−0.791797	+	0.610784i	$0.790854\pi$
$194$	−4.53590	−0.325659
$195$	−12.0000	−0.859338
$196$	1.00000	0.0714286
$197$	4.92820	0.351120	0.175560	−	0.984469i	$-0.443826\pi$
$197$	4.92820	0.351120	0.175560	+	0.984469i	$0.443826\pi$
$198$	5.46410	0.388317
$199$	−24.7846	−1.75693	−0.878467	−	0.477803i	$-0.841433\pi$
$199$	−24.7846	−1.75693	−0.878467	+	0.477803i	$0.841433\pi$
$200$	−7.00000	−0.494975
$201$	−9.46410	−0.667546
$202$	−4.53590	−0.319145
$203$	6.00000	0.421117
$204$	−7.46410	−0.522592
$205$	6.92820	0.483887
$206$	6.92820	0.482711
$207$	−5.46410	−0.379781
$208$	−3.46410	−0.240192
$209$	−5.46410	−0.377960
$210$	3.46410	0.239046
$211$	1.46410	0.100793	0.0503965	−	0.998729i	$-0.483952\pi$
$211$	1.46410	0.100793	0.0503965	+	0.998729i	$0.483952\pi$
$212$	2.00000	0.137361
$213$	−2.92820	−0.200637
$214$	4.00000	0.273434
$215$	24.0000	1.63679
$216$	1.00000	0.0680414
$217$	−6.92820	−0.470317
$218$	−2.00000	−0.135457
$219$	−10.0000	−0.675737
$220$	18.9282	1.27614
$221$	−25.8564	−1.73929
$222$	10.0000	0.671156
$223$	−12.0000	−0.803579	−0.401790	−	0.915732i	$-0.631612\pi$
$223$	−12.0000	−0.803579	−0.401790	+	0.915732i	$0.631612\pi$
$224$	1.00000	0.0668153
$225$	7.00000	0.466667
$226$	−11.8564	−0.788676
$227$	14.9282	0.990820	0.495410	−	0.868659i	$-0.335018\pi$
$227$	14.9282	0.990820	0.495410	+	0.868659i	$0.335018\pi$
$228$	−1.00000	−0.0662266
$229$	3.07180	0.202990	0.101495	−	0.994836i	$-0.467637\pi$
$229$	3.07180	0.202990	0.101495	+	0.994836i	$0.467637\pi$
$230$	−18.9282	−1.24809
$231$	−5.46410	−0.359511
$232$	6.00000	0.393919
$233$	26.7846	1.75472	0.877359	−	0.479834i	$-0.159303\pi$
$233$	26.7846	1.75472	0.877359	+	0.479834i	$0.159303\pi$
$234$	3.46410	0.226455
$235$	−37.8564	−2.46948
$236$	4.00000	0.260378
$237$	12.3923	0.804967
$238$	7.46410	0.483826
$239$	30.2487	1.95663	0.978313	−	0.207131i	$-0.0664126\pi$
$239$	30.2487	1.95663	0.978313	+	0.207131i	$0.0664126\pi$
$240$	3.46410	0.223607
$241$	21.3205	1.37337	0.686687	−	0.726953i	$-0.259064\pi$
$241$	21.3205	1.37337	0.686687	+	0.726953i	$0.259064\pi$
$242$	−18.8564	−1.21214
$243$	−1.00000	−0.0641500
$244$	−4.92820	−0.315496
$245$	−3.46410	−0.221313
$246$	−2.00000	−0.127515
$247$	−3.46410	−0.220416
$248$	−6.92820	−0.439941
$249$	−8.00000	−0.506979
$250$	6.92820	0.438178
$251$	5.07180	0.320129	0.160064	−	0.987107i	$-0.448830\pi$
$251$	5.07180	0.320129	0.160064	+	0.987107i	$0.448830\pi$
$252$	−1.00000	−0.0629941
$253$	29.8564	1.87706
$254$	17.4641	1.09580
$255$	25.8564	1.61919
$256$	1.00000	0.0625000
$257$	24.9282	1.55498	0.777489	−	0.628896i	$-0.216493\pi$
$257$	24.9282	1.55498	0.777489	+	0.628896i	$0.216493\pi$
$258$	−6.92820	−0.431331
$259$	−10.0000	−0.621370
$260$	12.0000	0.744208
$261$	−6.00000	−0.371391
$262$	5.07180	0.313337
$263$	11.3205	0.698052	0.349026	−	0.937113i	$-0.386512\pi$
$263$	11.3205	0.698052	0.349026	+	0.937113i	$0.386512\pi$
$264$	−5.46410	−0.336292
$265$	−6.92820	−0.425596
$266$	1.00000	0.0613139
$267$	2.00000	0.122398
$268$	9.46410	0.578112
$269$	−16.9282	−1.03213	−0.516065	−	0.856549i	$-0.672604\pi$
$269$	−16.9282	−1.03213	−0.516065	+	0.856549i	$0.672604\pi$
$270$	−3.46410	−0.210819
$271$	−29.8564	−1.81365	−0.906824	−	0.421510i	$-0.861500\pi$
$271$	−29.8564	−1.81365	−0.906824	+	0.421510i	$0.861500\pi$
$272$	7.46410	0.452578
$273$	−3.46410	−0.209657
$274$	0.928203	0.0560748
$275$	−38.2487	−2.30648
$276$	5.46410	0.328900
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	−9.85641	−0.591148
$279$	6.92820	0.414781
$280$	−3.46410	−0.207020
$281$	−26.0000	−1.55103	−0.775515	−	0.631329i	$-0.782510\pi$
$281$	−26.0000	−1.55103	−0.775515	+	0.631329i	$0.782510\pi$
$282$	10.9282	0.650765
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	2.92820	0.173757
$285$	3.46410	0.205196
$286$	−18.9282	−1.11925
$287$	2.00000	0.118056
$288$	−1.00000	−0.0589256
$289$	38.7128	2.27722
$290$	−20.7846	−1.22051
$291$	−4.53590	−0.265899
$292$	10.0000	0.585206
$293$	7.07180	0.413139	0.206569	−	0.978432i	$-0.433770\pi$
$293$	7.07180	0.413139	0.206569	+	0.978432i	$0.433770\pi$
$294$	1.00000	0.0583212
$295$	−13.8564	−0.806751
$296$	−10.0000	−0.581238
$297$	5.46410	0.317059
$298$	3.07180	0.177944
$299$	18.9282	1.09465
$300$	−7.00000	−0.404145
$301$	6.92820	0.399335
$302$	−1.46410	−0.0842496
$303$	−4.53590	−0.260581
$304$	1.00000	0.0573539
$305$	17.0718	0.977528
$306$	−7.46410	−0.426694
$307$	20.7846	1.18624	0.593120	−	0.805114i	$-0.297896\pi$
$307$	20.7846	1.18624	0.593120	+	0.805114i	$0.297896\pi$
$308$	5.46410	0.311346
$309$	6.92820	0.394132
$310$	24.0000	1.36311
$311$	2.14359	0.121552	0.0607760	−	0.998151i	$-0.480642\pi$
$311$	2.14359	0.121552	0.0607760	+	0.998151i	$0.480642\pi$
$312$	−3.46410	−0.196116
$313$	−6.00000	−0.339140	−0.169570	−	0.985518i	$-0.554238\pi$
$313$	−6.00000	−0.339140	−0.169570	+	0.985518i	$0.554238\pi$
$314$	−19.8564	−1.12056
$315$	3.46410	0.195180
$316$	−12.3923	−0.697122
$317$	7.85641	0.441260	0.220630	−	0.975358i	$-0.429189\pi$
$317$	7.85641	0.441260	0.220630	+	0.975358i	$0.429189\pi$
$318$	2.00000	0.112154
$319$	32.7846	1.83559
$320$	−3.46410	−0.193649
$321$	4.00000	0.223258
$322$	−5.46410	−0.304502
$323$	7.46410	0.415314
$324$	1.00000	0.0555556
$325$	−24.2487	−1.34508
$326$	−1.07180	−0.0593613
$327$	−2.00000	−0.110600
$328$	2.00000	0.110432
$329$	−10.9282	−0.602491
$330$	18.9282	1.04196
$331$	14.5359	0.798965	0.399483	−	0.916741i	$-0.369190\pi$
$331$	14.5359	0.798965	0.399483	+	0.916741i	$0.369190\pi$
$332$	8.00000	0.439057
$333$	10.0000	0.547997
$334$	18.9282	1.03571
$335$	−32.7846	−1.79121
$336$	1.00000	0.0545545
$337$	10.7846	0.587475	0.293738	−	0.955886i	$-0.405101\pi$
$337$	10.7846	0.587475	0.293738	+	0.955886i	$0.405101\pi$
$338$	1.00000	0.0543928
$339$	−11.8564	−0.643952
$340$	−25.8564	−1.40226
$341$	−37.8564	−2.05004
$342$	−1.00000	−0.0540738
$343$	−1.00000	−0.0539949
$344$	6.92820	0.373544
$345$	−18.9282	−1.01906
$346$	0.928203	0.0499005
$347$	27.3205	1.46664	0.733321	−	0.679883i	$-0.237969\pi$
$347$	27.3205	1.46664	0.733321	+	0.679883i	$0.237969\pi$
$348$	6.00000	0.321634
$349$	35.8564	1.91935	0.959675	−	0.281113i	$-0.0907035\pi$
$349$	35.8564	1.91935	0.959675	+	0.281113i	$0.0907035\pi$
$350$	7.00000	0.374166
$351$	3.46410	0.184900
$352$	5.46410	0.291238
$353$	5.32051	0.283182	0.141591	−	0.989925i	$-0.454778\pi$
$353$	5.32051	0.283182	0.141591	+	0.989925i	$0.454778\pi$
$354$	4.00000	0.212598
$355$	−10.1436	−0.538366
$356$	−2.00000	−0.106000
$357$	7.46410	0.395042
$358$	9.85641	0.520927
$359$	35.3205	1.86415	0.932073	−	0.362272i	$-0.117999\pi$
$359$	35.3205	1.86415	0.932073	+	0.362272i	$0.117999\pi$
$360$	3.46410	0.182574
$361$	1.00000	0.0526316
$362$	8.53590	0.448637
$363$	−18.8564	−0.989705
$364$	3.46410	0.181568
$365$	−34.6410	−1.81319
$366$	−4.92820	−0.257601
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	−5.46410	−0.284836
$369$	−2.00000	−0.104116
$370$	34.6410	1.80090
$371$	−2.00000	−0.103835
$372$	−6.92820	−0.359211
$373$	10.7846	0.558406	0.279203	−	0.960232i	$-0.409930\pi$
$373$	10.7846	0.558406	0.279203	+	0.960232i	$0.409930\pi$
$374$	40.7846	2.10892
$375$	6.92820	0.357771
$376$	−10.9282	−0.563579
$377$	20.7846	1.07046
$378$	−1.00000	−0.0514344
$379$	−1.46410	−0.0752058	−0.0376029	−	0.999293i	$-0.511972\pi$
$379$	−1.46410	−0.0752058	−0.0376029	+	0.999293i	$0.511972\pi$
$380$	−3.46410	−0.177705
$381$	17.4641	0.894713
$382$	5.46410	0.279568
$383$	8.00000	0.408781	0.204390	−	0.978889i	$-0.434479\pi$
$383$	8.00000	0.408781	0.204390	+	0.978889i	$0.434479\pi$
$384$	1.00000	0.0510310
$385$	−18.9282	−0.964671
$386$	22.0000	1.11977
$387$	−6.92820	−0.352180
$388$	4.53590	0.230275
$389$	29.7128	1.50650	0.753250	−	0.657735i	$-0.228485\pi$
$389$	29.7128	1.50650	0.753250	+	0.657735i	$0.228485\pi$
$390$	12.0000	0.607644
$391$	−40.7846	−2.06257
$392$	−1.00000	−0.0505076
$393$	5.07180	0.255838
$394$	−4.92820	−0.248279
$395$	42.9282	2.15995
$396$	−5.46410	−0.274581
$397$	19.8564	0.996564	0.498282	−	0.867015i	$-0.333964\pi$
$397$	19.8564	0.996564	0.498282	+	0.867015i	$0.333964\pi$
$398$	24.7846	1.24234
$399$	1.00000	0.0500626
$400$	7.00000	0.350000
$401$	19.8564	0.991582	0.495791	−	0.868442i	$-0.334878\pi$
$401$	19.8564	0.991582	0.495791	+	0.868442i	$0.334878\pi$
$402$	9.46410	0.472026
$403$	−24.0000	−1.19553
$404$	4.53590	0.225669
$405$	−3.46410	−0.172133
$406$	−6.00000	−0.297775
$407$	−54.6410	−2.70845
$408$	7.46410	0.369528
$409$	−31.1769	−1.54160	−0.770800	−	0.637078i	$-0.780143\pi$
$409$	−31.1769	−1.54160	−0.770800	+	0.637078i	$0.780143\pi$
$410$	−6.92820	−0.342160
$411$	0.928203	0.0457849
$412$	−6.92820	−0.341328
$413$	−4.00000	−0.196827
$414$	5.46410	0.268546
$415$	−27.7128	−1.36037
$416$	3.46410	0.169842
$417$	−9.85641	−0.482670
$418$	5.46410	0.267258
$419$	18.9282	0.924703	0.462352	−	0.886697i	$-0.347006\pi$
$419$	18.9282	0.924703	0.462352	+	0.886697i	$0.347006\pi$
$420$	−3.46410	−0.169031
$421$	18.7846	0.915506	0.457753	−	0.889079i	$-0.348654\pi$
$421$	18.7846	0.915506	0.457753	+	0.889079i	$0.348654\pi$
$422$	−1.46410	−0.0712714
$423$	10.9282	0.531347
$424$	−2.00000	−0.0971286
$425$	52.2487	2.53443
$426$	2.92820	0.141872
$427$	4.92820	0.238492
$428$	−4.00000	−0.193347
$429$	−18.9282	−0.913862
$430$	−24.0000	−1.15738
$431$	−34.9282	−1.68243	−0.841216	−	0.540699i	$-0.818160\pi$
$431$	−34.9282	−1.68243	−0.841216	+	0.540699i	$0.818160\pi$
$432$	−1.00000	−0.0481125
$433$	6.67949	0.320996	0.160498	−	0.987036i	$-0.448690\pi$
$433$	6.67949	0.320996	0.160498	+	0.987036i	$0.448690\pi$
$434$	6.92820	0.332564
$435$	−20.7846	−0.996546
$436$	2.00000	0.0957826
$437$	−5.46410	−0.261383
$438$	10.0000	0.477818
$439$	−4.78461	−0.228357	−0.114178	−	0.993460i	$-0.536424\pi$
$439$	−4.78461	−0.228357	−0.114178	+	0.993460i	$0.536424\pi$
$440$	−18.9282	−0.902367
$441$	1.00000	0.0476190
$442$	25.8564	1.22986
$443$	−11.3205	−0.537854	−0.268927	−	0.963161i	$-0.586669\pi$
$443$	−11.3205	−0.537854	−0.268927	+	0.963161i	$0.586669\pi$
$444$	−10.0000	−0.474579
$445$	6.92820	0.328428
$446$	12.0000	0.568216
$447$	3.07180	0.145291
$448$	−1.00000	−0.0472456
$449$	−7.85641	−0.370767	−0.185383	−	0.982666i	$-0.559353\pi$
$449$	−7.85641	−0.370767	−0.185383	+	0.982666i	$0.559353\pi$
$450$	−7.00000	−0.329983
$451$	10.9282	0.514589
$452$	11.8564	0.557678
$453$	−1.46410	−0.0687895
$454$	−14.9282	−0.700615
$455$	−12.0000	−0.562569
$456$	1.00000	0.0468293
$457$	12.1436	0.568053	0.284027	−	0.958816i	$-0.408330\pi$
$457$	12.1436	0.568053	0.284027	+	0.958816i	$0.408330\pi$
$458$	−3.07180	−0.143536
$459$	−7.46410	−0.348394
$460$	18.9282	0.882532
$461$	38.1051	1.77473	0.887366	−	0.461065i	$-0.152533\pi$
$461$	38.1051	1.77473	0.887366	+	0.461065i	$0.152533\pi$
$462$	5.46410	0.254213
$463$	24.0000	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$463$	24.0000	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$464$	−6.00000	−0.278543
$465$	24.0000	1.11297
$466$	−26.7846	−1.24077
$467$	35.7128	1.65259	0.826296	−	0.563236i	$-0.190444\pi$
$467$	35.7128	1.65259	0.826296	+	0.563236i	$0.190444\pi$
$468$	−3.46410	−0.160128
$469$	−9.46410	−0.437012
$470$	37.8564	1.74619
$471$	−19.8564	−0.914935
$472$	−4.00000	−0.184115
$473$	37.8564	1.74064
$474$	−12.3923	−0.569197
$475$	7.00000	0.321182
$476$	−7.46410	−0.342117
$477$	2.00000	0.0915737
$478$	−30.2487	−1.38354
$479$	27.7128	1.26623	0.633115	−	0.774057i	$-0.281776\pi$
$479$	27.7128	1.26623	0.633115	+	0.774057i	$0.281776\pi$
$480$	−3.46410	−0.158114
$481$	−34.6410	−1.57949
$482$	−21.3205	−0.971123
$483$	−5.46410	−0.248625
$484$	18.8564	0.857109
$485$	−15.7128	−0.713482
$486$	1.00000	0.0453609
$487$	−39.3205	−1.78178	−0.890891	−	0.454217i	$-0.849919\pi$
$487$	−39.3205	−1.78178	−0.890891	+	0.454217i	$0.849919\pi$
$488$	4.92820	0.223089
$489$	−1.07180	−0.0484683
$490$	3.46410	0.156492
$491$	−40.3923	−1.82288	−0.911440	−	0.411434i	$-0.865028\pi$
$491$	−40.3923	−1.82288	−0.911440	+	0.411434i	$0.865028\pi$
$492$	2.00000	0.0901670
$493$	−44.7846	−2.01700
$494$	3.46410	0.155857
$495$	18.9282	0.850759
$496$	6.92820	0.311086
$497$	−2.92820	−0.131348
$498$	8.00000	0.358489
$499$	−22.9282	−1.02641	−0.513204	−	0.858267i	$-0.671541\pi$
$499$	−22.9282	−1.02641	−0.513204	+	0.858267i	$0.671541\pi$
$500$	−6.92820	−0.309839
$501$	18.9282	0.845650
$502$	−5.07180	−0.226365
$503$	−21.8564	−0.974529	−0.487264	−	0.873254i	$-0.662005\pi$
$503$	−21.8564	−0.974529	−0.487264	+	0.873254i	$0.662005\pi$
$504$	1.00000	0.0445435
$505$	−15.7128	−0.699211
$506$	−29.8564	−1.32728
$507$	1.00000	0.0444116
$508$	−17.4641	−0.774844
$509$	−44.6410	−1.97868	−0.989339	−	0.145630i	$-0.953479\pi$
$509$	−44.6410	−1.97868	−0.989339	+	0.145630i	$0.953479\pi$
$510$	−25.8564	−1.14494
$511$	−10.0000	−0.442374
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−24.9282	−1.09954
$515$	24.0000	1.05757
$516$	6.92820	0.304997
$517$	−59.7128	−2.62617
$518$	10.0000	0.439375
$519$	0.928203	0.0407436
$520$	−12.0000	−0.526235
$521$	25.7128	1.12650	0.563249	−	0.826287i	$-0.309551\pi$
$521$	25.7128	1.12650	0.563249	+	0.826287i	$0.309551\pi$
$522$	6.00000	0.262613
$523$	26.6410	1.16493	0.582465	−	0.812856i	$-0.302088\pi$
$523$	26.6410	1.16493	0.582465	+	0.812856i	$0.302088\pi$
$524$	−5.07180	−0.221562
$525$	7.00000	0.305505
$526$	−11.3205	−0.493598
$527$	51.7128	2.25265
$528$	5.46410	0.237795
$529$	6.85641	0.298105
$530$	6.92820	0.300942
$531$	4.00000	0.173585
$532$	−1.00000	−0.0433555
$533$	6.92820	0.300094
$534$	−2.00000	−0.0865485
$535$	13.8564	0.599065
$536$	−9.46410	−0.408787
$537$	9.85641	0.425335
$538$	16.9282	0.729827
$539$	−5.46410	−0.235356
$540$	3.46410	0.149071
$541$	−34.0000	−1.46177	−0.730887	−	0.682498i	$-0.760893\pi$
$541$	−34.0000	−1.46177	−0.730887	+	0.682498i	$0.760893\pi$
$542$	29.8564	1.28244
$543$	8.53590	0.366310
$544$	−7.46410	−0.320021
$545$	−6.92820	−0.296772
$546$	3.46410	0.148250
$547$	−10.2487	−0.438203	−0.219102	−	0.975702i	$-0.570313\pi$
$547$	−10.2487	−0.438203	−0.219102	+	0.975702i	$0.570313\pi$
$548$	−0.928203	−0.0396509
$549$	−4.92820	−0.210331
$550$	38.2487	1.63093
$551$	−6.00000	−0.255609
$552$	−5.46410	−0.232568
$553$	12.3923	0.526974
$554$	−22.0000	−0.934690
$555$	34.6410	1.47043
$556$	9.85641	0.418005
$557$	4.92820	0.208815	0.104407	−	0.994535i	$-0.466705\pi$
$557$	4.92820	0.208815	0.104407	+	0.994535i	$0.466705\pi$
$558$	−6.92820	−0.293294
$559$	24.0000	1.01509
$560$	3.46410	0.146385
$561$	40.7846	1.72193
$562$	26.0000	1.09674
$563$	25.8564	1.08972	0.544859	−	0.838528i	$-0.316583\pi$
$563$	25.8564	1.08972	0.544859	+	0.838528i	$0.316583\pi$
$564$	−10.9282	−0.460160
$565$	−41.0718	−1.72790
$566$	20.0000	0.840663
$567$	−1.00000	−0.0419961
$568$	−2.92820	−0.122865
$569$	−45.7128	−1.91638	−0.958190	−	0.286131i	$-0.907631\pi$
$569$	−45.7128	−1.91638	−0.958190	+	0.286131i	$0.907631\pi$
$570$	−3.46410	−0.145095
$571$	37.5692	1.57222	0.786111	−	0.618085i	$-0.212091\pi$
$571$	37.5692	1.57222	0.786111	+	0.618085i	$0.212091\pi$
$572$	18.9282	0.791428
$573$	5.46410	0.228266
$574$	−2.00000	−0.0834784
$575$	−38.2487	−1.59508
$576$	1.00000	0.0416667
$577$	−3.85641	−0.160544	−0.0802722	−	0.996773i	$-0.525579\pi$
$577$	−3.85641	−0.160544	−0.0802722	+	0.996773i	$0.525579\pi$
$578$	−38.7128	−1.61024
$579$	22.0000	0.914289
$580$	20.7846	0.863034
$581$	−8.00000	−0.331896
$582$	4.53590	0.188019
$583$	−10.9282	−0.452600
$584$	−10.0000	−0.413803
$585$	12.0000	0.496139
$586$	−7.07180	−0.292133
$587$	−8.00000	−0.330195	−0.165098	−	0.986277i	$-0.552794\pi$
$587$	−8.00000	−0.330195	−0.165098	+	0.986277i	$0.552794\pi$
$588$	−1.00000	−0.0412393
$589$	6.92820	0.285472
$590$	13.8564	0.570459
$591$	−4.92820	−0.202719
$592$	10.0000	0.410997
$593$	12.5359	0.514788	0.257394	−	0.966307i	$-0.417136\pi$
$593$	12.5359	0.514788	0.257394	+	0.966307i	$0.417136\pi$
$594$	−5.46410	−0.224195
$595$	25.8564	1.06001
$596$	−3.07180	−0.125826
$597$	24.7846	1.01437
$598$	−18.9282	−0.774032
$599$	13.0718	0.534099	0.267050	−	0.963683i	$-0.413951\pi$
$599$	13.0718	0.534099	0.267050	+	0.963683i	$0.413951\pi$
$600$	7.00000	0.285774
$601$	6.67949	0.272462	0.136231	−	0.990677i	$-0.456501\pi$
$601$	6.67949	0.272462	0.136231	+	0.990677i	$0.456501\pi$
$602$	−6.92820	−0.282372
$603$	9.46410	0.385408
$604$	1.46410	0.0595734
$605$	−65.3205	−2.65566
$606$	4.53590	0.184258
$607$	−17.8564	−0.724769	−0.362385	−	0.932029i	$-0.618037\pi$
$607$	−17.8564	−0.724769	−0.362385	+	0.932029i	$0.618037\pi$
$608$	−1.00000	−0.0405554
$609$	−6.00000	−0.243132
$610$	−17.0718	−0.691217
$611$	−37.8564	−1.53151
$612$	7.46410	0.301718
$613$	−23.8564	−0.963551	−0.481776	−	0.876295i	$-0.660008\pi$
$613$	−23.8564	−0.963551	−0.481776	+	0.876295i	$0.660008\pi$
$614$	−20.7846	−0.838799
$615$	−6.92820	−0.279372
$616$	−5.46410	−0.220155
$617$	12.9282	0.520470	0.260235	−	0.965545i	$-0.416200\pi$
$617$	12.9282	0.520470	0.260235	+	0.965545i	$0.416200\pi$
$618$	−6.92820	−0.278693
$619$	26.6410	1.07079	0.535396	−	0.844601i	$-0.320162\pi$
$619$	26.6410	1.07079	0.535396	+	0.844601i	$0.320162\pi$
$620$	−24.0000	−0.963863
$621$	5.46410	0.219267
$622$	−2.14359	−0.0859503
$623$	2.00000	0.0801283
$624$	3.46410	0.138675
$625$	−11.0000	−0.440000
$626$	6.00000	0.239808
$627$	5.46410	0.218215
$628$	19.8564	0.792357
$629$	74.6410	2.97613
$630$	−3.46410	−0.138013
$631$	16.7846	0.668185	0.334092	−	0.942540i	$-0.391570\pi$
$631$	16.7846	0.668185	0.334092	+	0.942540i	$0.391570\pi$
$632$	12.3923	0.492939
$633$	−1.46410	−0.0581928
$634$	−7.85641	−0.312018
$635$	60.4974	2.40077
$636$	−2.00000	−0.0793052
$637$	−3.46410	−0.137253
$638$	−32.7846	−1.29796
$639$	2.92820	0.115838
$640$	3.46410	0.136931
$641$	−15.8564	−0.626290	−0.313145	−	0.949705i	$-0.601383\pi$
$641$	−15.8564	−0.626290	−0.313145	+	0.949705i	$0.601383\pi$
$642$	−4.00000	−0.157867
$643$	−14.9282	−0.588711	−0.294355	−	0.955696i	$-0.595105\pi$
$643$	−14.9282	−0.588711	−0.294355	+	0.955696i	$0.595105\pi$
$644$	5.46410	0.215316
$645$	−24.0000	−0.944999
$646$	−7.46410	−0.293671
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−1.00000	−0.0392837
$649$	−21.8564	−0.857939
$650$	24.2487	0.951113
$651$	6.92820	0.271538
$652$	1.07180	0.0419748
$653$	−33.7128	−1.31928	−0.659642	−	0.751580i	$-0.729292\pi$
$653$	−33.7128	−1.31928	−0.659642	+	0.751580i	$0.729292\pi$
$654$	2.00000	0.0782062
$655$	17.5692	0.686486
$656$	−2.00000	−0.0780869
$657$	10.0000	0.390137
$658$	10.9282	0.426026
$659$	14.1436	0.550956	0.275478	−	0.961307i	$-0.411164\pi$
$659$	14.1436	0.550956	0.275478	+	0.961307i	$0.411164\pi$
$660$	−18.9282	−0.736779
$661$	45.3205	1.76276	0.881382	−	0.472405i	$-0.156614\pi$
$661$	45.3205	1.76276	0.881382	+	0.472405i	$0.156614\pi$
$662$	−14.5359	−0.564954
$663$	25.8564	1.00418
$664$	−8.00000	−0.310460
$665$	3.46410	0.134332
$666$	−10.0000	−0.387492
$667$	32.7846	1.26943
$668$	−18.9282	−0.732354
$669$	12.0000	0.463947
$670$	32.7846	1.26658
$671$	26.9282	1.03955
$672$	−1.00000	−0.0385758
$673$	−16.9282	−0.652534	−0.326267	−	0.945278i	$-0.605791\pi$
$673$	−16.9282	−0.652534	−0.326267	+	0.945278i	$0.605791\pi$
$674$	−10.7846	−0.415408
$675$	−7.00000	−0.269430
$676$	−1.00000	−0.0384615
$677$	−19.8564	−0.763144	−0.381572	−	0.924339i	$-0.624617\pi$
$677$	−19.8564	−0.763144	−0.381572	+	0.924339i	$0.624617\pi$
$678$	11.8564	0.455343
$679$	−4.53590	−0.174072
$680$	25.8564	0.991548
$681$	−14.9282	−0.572050
$682$	37.8564	1.44960
$683$	30.9282	1.18343	0.591717	−	0.806145i	$-0.298450\pi$
$683$	30.9282	1.18343	0.591717	+	0.806145i	$0.298450\pi$
$684$	1.00000	0.0382360
$685$	3.21539	0.122854
$686$	1.00000	0.0381802
$687$	−3.07180	−0.117196
$688$	−6.92820	−0.264135
$689$	−6.92820	−0.263944
$690$	18.9282	0.720584
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	−0.928203	−0.0352850
$693$	5.46410	0.207564
$694$	−27.3205	−1.03707
$695$	−34.1436	−1.29514
$696$	−6.00000	−0.227429
$697$	−14.9282	−0.565446
$698$	−35.8564	−1.35718
$699$	−26.7846	−1.01309
$700$	−7.00000	−0.264575
$701$	13.7128	0.517926	0.258963	−	0.965887i	$-0.416619\pi$
$701$	13.7128	0.517926	0.258963	+	0.965887i	$0.416619\pi$
$702$	−3.46410	−0.130744
$703$	10.0000	0.377157
$704$	−5.46410	−0.205936
$705$	37.8564	1.42575
$706$	−5.32051	−0.200240
$707$	−4.53590	−0.170590
$708$	−4.00000	−0.150329
$709$	14.0000	0.525781	0.262891	−	0.964826i	$-0.415324\pi$
$709$	14.0000	0.525781	0.262891	+	0.964826i	$0.415324\pi$
$710$	10.1436	0.380682
$711$	−12.3923	−0.464748
$712$	2.00000	0.0749532
$713$	−37.8564	−1.41773
$714$	−7.46410	−0.279337
$715$	−65.5692	−2.45215
$716$	−9.85641	−0.368351
$717$	−30.2487	−1.12966
$718$	−35.3205	−1.31815
$719$	16.0000	0.596699	0.298350	−	0.954457i	$-0.403564\pi$
$719$	16.0000	0.596699	0.298350	+	0.954457i	$0.403564\pi$
$720$	−3.46410	−0.129099
$721$	6.92820	0.258020
$722$	−1.00000	−0.0372161
$723$	−21.3205	−0.792918
$724$	−8.53590	−0.317234
$725$	−42.0000	−1.55984
$726$	18.8564	0.699827
$727$	8.00000	0.296704	0.148352	−	0.988935i	$-0.452603\pi$
$727$	8.00000	0.296704	0.148352	+	0.988935i	$0.452603\pi$
$728$	−3.46410	−0.128388
$729$	1.00000	0.0370370
$730$	34.6410	1.28212
$731$	−51.7128	−1.91267
$732$	4.92820	0.182152
$733$	−2.00000	−0.0738717	−0.0369358	−	0.999318i	$-0.511760\pi$
$733$	−2.00000	−0.0738717	−0.0369358	+	0.999318i	$0.511760\pi$
$734$	−8.00000	−0.295285
$735$	3.46410	0.127775
$736$	5.46410	0.201409
$737$	−51.7128	−1.90487
$738$	2.00000	0.0736210
$739$	−9.85641	−0.362574	−0.181287	−	0.983430i	$-0.558026\pi$
$739$	−9.85641	−0.362574	−0.181287	+	0.983430i	$0.558026\pi$
$740$	−34.6410	−1.27343
$741$	3.46410	0.127257
$742$	2.00000	0.0734223
$743$	27.7128	1.01668	0.508342	−	0.861155i	$-0.330258\pi$
$743$	27.7128	1.01668	0.508342	+	0.861155i	$0.330258\pi$
$744$	6.92820	0.254000
$745$	10.6410	0.389857
$746$	−10.7846	−0.394853
$747$	8.00000	0.292705
$748$	−40.7846	−1.49123
$749$	4.00000	0.146157
$750$	−6.92820	−0.252982
$751$	20.3923	0.744126	0.372063	−	0.928208i	$-0.378651\pi$
$751$	20.3923	0.744126	0.372063	+	0.928208i	$0.378651\pi$
$752$	10.9282	0.398511
$753$	−5.07180	−0.184827
$754$	−20.7846	−0.756931
$755$	−5.07180	−0.184582
$756$	1.00000	0.0363696
$757$	3.85641	0.140163	0.0700817	−	0.997541i	$-0.477674\pi$
$757$	3.85641	0.140163	0.0700817	+	0.997541i	$0.477674\pi$
$758$	1.46410	0.0531786
$759$	−29.8564	−1.08372
$760$	3.46410	0.125656
$761$	4.53590	0.164426	0.0822131	−	0.996615i	$-0.473801\pi$
$761$	4.53590	0.164426	0.0822131	+	0.996615i	$0.473801\pi$
$762$	−17.4641	−0.632658
$763$	−2.00000	−0.0724049
$764$	−5.46410	−0.197684
$765$	−25.8564	−0.934840
$766$	−8.00000	−0.289052
$767$	−13.8564	−0.500326
$768$	−1.00000	−0.0360844
$769$	−19.8564	−0.716040	−0.358020	−	0.933714i	$-0.616548\pi$
$769$	−19.8564	−0.716040	−0.358020	+	0.933714i	$0.616548\pi$
$770$	18.9282	0.682125
$771$	−24.9282	−0.897767
$772$	−22.0000	−0.791797
$773$	2.78461	0.100155	0.0500777	−	0.998745i	$-0.484053\pi$
$773$	2.78461	0.100155	0.0500777	+	0.998745i	$0.484053\pi$
$774$	6.92820	0.249029
$775$	48.4974	1.74208
$776$	−4.53590	−0.162829
$777$	10.0000	0.358748
$778$	−29.7128	−1.06526
$779$	−2.00000	−0.0716574
$780$	−12.0000	−0.429669
$781$	−16.0000	−0.572525
$782$	40.7846	1.45845
$783$	6.00000	0.214423
$784$	1.00000	0.0357143
$785$	−68.7846	−2.45503
$786$	−5.07180	−0.180905
$787$	−11.2154	−0.399785	−0.199893	−	0.979818i	$-0.564059\pi$
$787$	−11.2154	−0.399785	−0.199893	+	0.979818i	$0.564059\pi$
$788$	4.92820	0.175560
$789$	−11.3205	−0.403021
$790$	−42.9282	−1.52732
$791$	−11.8564	−0.421565
$792$	5.46410	0.194158
$793$	17.0718	0.606237
$794$	−19.8564	−0.704677
$795$	6.92820	0.245718
$796$	−24.7846	−0.878467
$797$	−44.6410	−1.58127	−0.790633	−	0.612290i	$-0.790248\pi$
$797$	−44.6410	−1.58127	−0.790633	+	0.612290i	$0.790248\pi$
$798$	−1.00000	−0.0353996
$799$	81.5692	2.88571
$800$	−7.00000	−0.247487
$801$	−2.00000	−0.0706665
$802$	−19.8564	−0.701154
$803$	−54.6410	−1.92824
$804$	−9.46410	−0.333773
$805$	−18.9282	−0.667132
$806$	24.0000	0.845364
$807$	16.9282	0.595901
$808$	−4.53590	−0.159572
$809$	18.0000	0.632846	0.316423	−	0.948618i	$-0.397518\pi$
$809$	18.0000	0.632846	0.316423	+	0.948618i	$0.397518\pi$
$810$	3.46410	0.121716
$811$	33.0718	1.16131	0.580654	−	0.814150i	$-0.302797\pi$
$811$	33.0718	1.16131	0.580654	+	0.814150i	$0.302797\pi$
$812$	6.00000	0.210559
$813$	29.8564	1.04711
$814$	54.6410	1.91517
$815$	−3.71281	−0.130054
$816$	−7.46410	−0.261296
$817$	−6.92820	−0.242387
$818$	31.1769	1.09008
$819$	3.46410	0.121046
$820$	6.92820	0.241943
$821$	−48.9282	−1.70761	−0.853803	−	0.520596i	$-0.825710\pi$
$821$	−48.9282	−1.70761	−0.853803	+	0.520596i	$0.825710\pi$
$822$	−0.928203	−0.0323748
$823$	−21.8564	−0.761866	−0.380933	−	0.924603i	$-0.624397\pi$
$823$	−21.8564	−0.761866	−0.380933	+	0.924603i	$0.624397\pi$
$824$	6.92820	0.241355
$825$	38.2487	1.33165
$826$	4.00000	0.139178
$827$	−12.0000	−0.417281	−0.208640	−	0.977992i	$-0.566904\pi$
$827$	−12.0000	−0.417281	−0.208640	+	0.977992i	$0.566904\pi$
$828$	−5.46410	−0.189891
$829$	−5.60770	−0.194763	−0.0973817	−	0.995247i	$-0.531047\pi$
$829$	−5.60770	−0.194763	−0.0973817	+	0.995247i	$0.531047\pi$
$830$	27.7128	0.961926
$831$	−22.0000	−0.763172
$832$	−3.46410	−0.120096
$833$	7.46410	0.258616
$834$	9.85641	0.341299
$835$	65.5692	2.26912
$836$	−5.46410	−0.188980
$837$	−6.92820	−0.239474
$838$	−18.9282	−0.653864
$839$	−5.07180	−0.175098	−0.0875489	−	0.996160i	$-0.527903\pi$
$839$	−5.07180	−0.175098	−0.0875489	+	0.996160i	$0.527903\pi$
$840$	3.46410	0.119523
$841$	7.00000	0.241379
$842$	−18.7846	−0.647360
$843$	26.0000	0.895488
$844$	1.46410	0.0503965
$845$	3.46410	0.119169
$846$	−10.9282	−0.375719
$847$	−18.8564	−0.647914
$848$	2.00000	0.0686803
$849$	20.0000	0.686398
$850$	−52.2487	−1.79212
$851$	−54.6410	−1.87307
$852$	−2.92820	−0.100319
$853$	35.0718	1.20084	0.600418	−	0.799687i	$-0.295001\pi$
$853$	35.0718	1.20084	0.600418	+	0.799687i	$0.295001\pi$
$854$	−4.92820	−0.168640
$855$	−3.46410	−0.118470
$856$	4.00000	0.136717
$857$	47.5692	1.62493	0.812467	−	0.583007i	$-0.198124\pi$
$857$	47.5692	1.62493	0.812467	+	0.583007i	$0.198124\pi$
$858$	18.9282	0.646198
$859$	−28.7846	−0.982118	−0.491059	−	0.871126i	$-0.663390\pi$
$859$	−28.7846	−0.982118	−0.491059	+	0.871126i	$0.663390\pi$
$860$	24.0000	0.818393
$861$	−2.00000	−0.0681598
$862$	34.9282	1.18966
$863$	18.1436	0.617615	0.308808	−	0.951125i	$-0.400070\pi$
$863$	18.1436	0.617615	0.308808	+	0.951125i	$0.400070\pi$
$864$	1.00000	0.0340207
$865$	3.21539	0.109327
$866$	−6.67949	−0.226978
$867$	−38.7128	−1.31476
$868$	−6.92820	−0.235159
$869$	67.7128	2.29700
$870$	20.7846	0.704664
$871$	−32.7846	−1.11086
$872$	−2.00000	−0.0677285
$873$	4.53590	0.153517
$874$	5.46410	0.184826
$875$	6.92820	0.234216
$876$	−10.0000	−0.337869
$877$	2.00000	0.0675352	0.0337676	−	0.999430i	$-0.489249\pi$
$877$	2.00000	0.0675352	0.0337676	+	0.999430i	$0.489249\pi$
$878$	4.78461	0.161473
$879$	−7.07180	−0.238526
$880$	18.9282	0.638070
$881$	43.1769	1.45467	0.727334	−	0.686284i	$-0.240759\pi$
$881$	43.1769	1.45467	0.727334	+	0.686284i	$0.240759\pi$
$882$	−1.00000	−0.0336718
$883$	48.4974	1.63207	0.816034	−	0.578004i	$-0.196168\pi$
$883$	48.4974	1.63207	0.816034	+	0.578004i	$0.196168\pi$
$884$	−25.8564	−0.869645
$885$	13.8564	0.465778
$886$	11.3205	0.380320
$887$	−27.7128	−0.930505	−0.465253	−	0.885178i	$-0.654037\pi$
$887$	−27.7128	−0.930505	−0.465253	+	0.885178i	$0.654037\pi$
$888$	10.0000	0.335578
$889$	17.4641	0.585727
$890$	−6.92820	−0.232234
$891$	−5.46410	−0.183054
$892$	−12.0000	−0.401790
$893$	10.9282	0.365698
$894$	−3.07180	−0.102736
$895$	34.1436	1.14129
$896$	1.00000	0.0334077
$897$	−18.9282	−0.631994
$898$	7.85641	0.262172
$899$	−41.5692	−1.38641
$900$	7.00000	0.233333
$901$	14.9282	0.497331
$902$	−10.9282	−0.363869
$903$	−6.92820	−0.230556
$904$	−11.8564	−0.394338
$905$	29.5692	0.982914
$906$	1.46410	0.0486415
$907$	−41.4641	−1.37679	−0.688396	−	0.725335i	$-0.741685\pi$
$907$	−41.4641	−1.37679	−0.688396	+	0.725335i	$0.741685\pi$
$908$	14.9282	0.495410
$909$	4.53590	0.150446
$910$	12.0000	0.397796
$911$	22.6410	0.750130	0.375065	−	0.926998i	$-0.377620\pi$
$911$	22.6410	0.750130	0.375065	+	0.926998i	$0.377620\pi$
$912$	−1.00000	−0.0331133
$913$	−43.7128	−1.44668
$914$	−12.1436	−0.401674
$915$	−17.0718	−0.564376
$916$	3.07180	0.101495
$917$	5.07180	0.167485
$918$	7.46410	0.246352
$919$	−49.5692	−1.63514	−0.817569	−	0.575831i	$-0.804679\pi$
$919$	−49.5692	−1.63514	−0.817569	+	0.575831i	$0.804679\pi$
$920$	−18.9282	−0.624044
$921$	−20.7846	−0.684876
$922$	−38.1051	−1.25493
$923$	−10.1436	−0.333880
$924$	−5.46410	−0.179756
$925$	70.0000	2.30159
$926$	−24.0000	−0.788689
$927$	−6.92820	−0.227552
$928$	6.00000	0.196960
$929$	25.6077	0.840161	0.420081	−	0.907487i	$-0.362002\pi$
$929$	25.6077	0.840161	0.420081	+	0.907487i	$0.362002\pi$
$930$	−24.0000	−0.786991
$931$	1.00000	0.0327737
$932$	26.7846	0.877359
$933$	−2.14359	−0.0701781
$934$	−35.7128	−1.16856
$935$	141.282	4.62042
$936$	3.46410	0.113228
$937$	20.9282	0.683695	0.341847	−	0.939756i	$-0.388947\pi$
$937$	20.9282	0.683695	0.341847	+	0.939756i	$0.388947\pi$
$938$	9.46410	0.309014
$939$	6.00000	0.195803
$940$	−37.8564	−1.23474
$941$	−5.21539	−0.170017	−0.0850084	−	0.996380i	$-0.527092\pi$
$941$	−5.21539	−0.170017	−0.0850084	+	0.996380i	$0.527092\pi$
$942$	19.8564	0.646957
$943$	10.9282	0.355871
$944$	4.00000	0.130189
$945$	−3.46410	−0.112687
$946$	−37.8564	−1.23082
$947$	−28.1051	−0.913294	−0.456647	−	0.889648i	$-0.650950\pi$
$947$	−28.1051	−0.913294	−0.456647	+	0.889648i	$0.650950\pi$
$948$	12.3923	0.402483
$949$	−34.6410	−1.12449
$950$	−7.00000	−0.227110
$951$	−7.85641	−0.254761
$952$	7.46410	0.241913
$953$	−31.8564	−1.03193	−0.515965	−	0.856610i	$-0.672567\pi$
$953$	−31.8564	−1.03193	−0.515965	+	0.856610i	$0.672567\pi$
$954$	−2.00000	−0.0647524
$955$	18.9282	0.612502
$956$	30.2487	0.978313
$957$	−32.7846	−1.05978
$958$	−27.7128	−0.895360
$959$	0.928203	0.0299732
$960$	3.46410	0.111803
$961$	17.0000	0.548387
$962$	34.6410	1.11687
$963$	−4.00000	−0.128898
$964$	21.3205	0.686687
$965$	76.2102	2.45329
$966$	5.46410	0.175805
$967$	−18.9282	−0.608690	−0.304345	−	0.952562i	$-0.598438\pi$
$967$	−18.9282	−0.608690	−0.304345	+	0.952562i	$0.598438\pi$
$968$	−18.8564	−0.606068
$969$	−7.46410	−0.239781
$970$	15.7128	0.504508
$971$	−10.6410	−0.341486	−0.170743	−	0.985316i	$-0.554617\pi$
$971$	−10.6410	−0.341486	−0.170743	+	0.985316i	$0.554617\pi$
$972$	−1.00000	−0.0320750
$973$	−9.85641	−0.315982
$974$	39.3205	1.25991
$975$	24.2487	0.776580
$976$	−4.92820	−0.157748
$977$	−7.85641	−0.251349	−0.125674	−	0.992072i	$-0.540109\pi$
$977$	−7.85641	−0.251349	−0.125674	+	0.992072i	$0.540109\pi$
$978$	1.07180	0.0342723
$979$	10.9282	0.349267
$980$	−3.46410	−0.110657
$981$	2.00000	0.0638551
$982$	40.3923	1.28897
$983$	−32.7846	−1.04567	−0.522833	−	0.852435i	$-0.675125\pi$
$983$	−32.7846	−1.04567	−0.522833	+	0.852435i	$0.675125\pi$
$984$	−2.00000	−0.0637577
$985$	−17.0718	−0.543953
$986$	44.7846	1.42623
$987$	10.9282	0.347849
$988$	−3.46410	−0.110208
$989$	37.8564	1.20376
$990$	−18.9282	−0.601578
$991$	35.6077	1.13112	0.565558	−	0.824709i	$-0.308661\pi$
$991$	35.6077	1.13112	0.565558	+	0.824709i	$0.308661\pi$
$992$	−6.92820	−0.219971
$993$	−14.5359	−0.461283
$994$	2.92820	0.0928770
$995$	85.8564	2.72183
$996$	−8.00000	−0.253490
$997$	−47.8564	−1.51563	−0.757814	−	0.652471i	$-0.773732\pi$
$997$	−47.8564	−1.51563	−0.757814	+	0.652471i	$0.773732\pi$
$998$	22.9282	0.725780
$999$	−10.0000	−0.316386

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	798.2.a.k.1.1	✓	2
3.2	odd	2		2394.2.a.x.1.2		2
4.3	odd	2		6384.2.a.br.1.1		2
7.6	odd	2		5586.2.a.bd.1.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
798.2.a.k.1.1	✓	2	1.1	even	1	trivial
2394.2.a.x.1.2		2	3.2	odd	2
5586.2.a.bd.1.2		2	7.6	odd	2
6384.2.a.br.1.1		2	4.3	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:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	798.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} -3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +3.46410 q^{10} -5.46410 q^{11} -1.00000 q^{12} -3.46410 q^{13} +1.00000 q^{14} +3.46410 q^{15} +1.00000 q^{16} +7.46410 q^{17} -1.00000 q^{18} +1.00000 q^{19} -3.46410 q^{20} +1.00000 q^{21} +5.46410 q^{22} -5.46410 q^{23} +1.00000 q^{24} +7.00000 q^{25} +3.46410 q^{26} -1.00000 q^{27} -1.00000 q^{28} -6.00000 q^{29} -3.46410 q^{30} +6.92820 q^{31} -1.00000 q^{32} +5.46410 q^{33} -7.46410 q^{34} +3.46410 q^{35} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} +3.46410 q^{39} +3.46410 q^{40} -2.00000 q^{41} -1.00000 q^{42} -6.92820 q^{43} -5.46410 q^{44} -3.46410 q^{45} +5.46410 q^{46} +10.9282 q^{47} -1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} -7.46410 q^{51} -3.46410 q^{52} +2.00000 q^{53} +1.00000 q^{54} +18.9282 q^{55} +1.00000 q^{56} -1.00000 q^{57} +6.00000 q^{58} +4.00000 q^{59} +3.46410 q^{60} -4.92820 q^{61} -6.92820 q^{62} -1.00000 q^{63} +1.00000 q^{64} +12.0000 q^{65} -5.46410 q^{66} +9.46410 q^{67} +7.46410 q^{68} +5.46410 q^{69} -3.46410 q^{70} +2.92820 q^{71} -1.00000 q^{72} +10.0000 q^{73} -10.0000 q^{74} -7.00000 q^{75} +1.00000 q^{76} +5.46410 q^{77} -3.46410 q^{78} -12.3923 q^{79} -3.46410 q^{80} +1.00000 q^{81} +2.00000 q^{82} +8.00000 q^{83} +1.00000 q^{84} -25.8564 q^{85} +6.92820 q^{86} +6.00000 q^{87} +5.46410 q^{88} -2.00000 q^{89} +3.46410 q^{90} +3.46410 q^{91} -5.46410 q^{92} -6.92820 q^{93} -10.9282 q^{94} -3.46410 q^{95} +1.00000 q^{96} +4.53590 q^{97} -1.00000 q^{98} -5.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9} - 4 q^{11} - 2 q^{12} + 2 q^{14} + 2 q^{16} + 8 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{21} + 4 q^{22} - 4 q^{23} + 2 q^{24} + 14 q^{25} - 2 q^{27} - 2 q^{28} - 12 q^{29} - 2 q^{32} + 4 q^{33} - 8 q^{34} + 2 q^{36} + 20 q^{37} - 2 q^{38} - 4 q^{41} - 2 q^{42} - 4 q^{44} + 4 q^{46} + 8 q^{47} - 2 q^{48} + 2 q^{49} - 14 q^{50} - 8 q^{51} + 4 q^{53} + 2 q^{54} + 24 q^{55} + 2 q^{56} - 2 q^{57} + 12 q^{58} + 8 q^{59} + 4 q^{61} - 2 q^{63} + 2 q^{64} + 24 q^{65} - 4 q^{66} + 12 q^{67} + 8 q^{68} + 4 q^{69} - 8 q^{71} - 2 q^{72} + 20 q^{73} - 20 q^{74} - 14 q^{75} + 2 q^{76} + 4 q^{77} - 4 q^{79} + 2 q^{81} + 4 q^{82} + 16 q^{83} + 2 q^{84} - 24 q^{85} + 12 q^{87} + 4 q^{88} - 4 q^{89} - 4 q^{92} - 8 q^{94} + 2 q^{96} + 16 q^{97} - 2 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^6 - 2 * q^7 - 2 * q^8 + 2 * q^9 - 4 * q^11 - 2 * q^12 + 2 * q^14 + 2 * q^16 + 8 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^21 + 4 * q^22 - 4 * q^23 + 2 * q^24 + 14 * q^25 - 2 * q^27 - 2 * q^28 - 12 * q^29 - 2 * q^32 + 4 * q^33 - 8 * q^34 + 2 * q^36 + 20 * q^37 - 2 * q^38 - 4 * q^41 - 2 * q^42 - 4 * q^44 + 4 * q^46 + 8 * q^47 - 2 * q^48 + 2 * q^49 - 14 * q^50 - 8 * q^51 + 4 * q^53 + 2 * q^54 + 24 * q^55 + 2 * q^56 - 2 * q^57 + 12 * q^58 + 8 * q^59 + 4 * q^61 - 2 * q^63 + 2 * q^64 + 24 * q^65 - 4 * q^66 + 12 * q^67 + 8 * q^68 + 4 * q^69 - 8 * q^71 - 2 * q^72 + 20 * q^73 - 20 * q^74 - 14 * q^75 + 2 * q^76 + 4 * q^77 - 4 * q^79 + 2 * q^81 + 4 * q^82 + 16 * q^83 + 2 * q^84 - 24 * q^85 + 12 * q^87 + 4 * q^88 - 4 * q^89 - 4 * q^92 - 8 * q^94 + 2 * q^96 + 16 * q^97 - 2 * q^98 - 4 * q^99

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