LMFDB - Embedded newform 798.2.a.k.1.2

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			1.2
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} +1.46410 q^{11} -1.00000 q^{12} +3.46410 q^{13} +1.00000 q^{14} -3.46410 q^{15} +1.00000 q^{16} +0.535898 q^{17} -1.00000 q^{18} +1.00000 q^{19} +3.46410 q^{20} +1.00000 q^{21} -1.46410 q^{22} +1.46410 q^{23} +1.00000 q^{24} +7.00000 q^{25} -3.46410 q^{26} -1.00000 q^{27} -1.00000 q^{28} -6.00000 q^{29} +3.46410 q^{30} -6.92820 q^{31} -1.00000 q^{32} -1.46410 q^{33} -0.535898 q^{34} -3.46410 q^{35} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} -3.46410 q^{39} -3.46410 q^{40} -2.00000 q^{41} -1.00000 q^{42} +6.92820 q^{43} +1.46410 q^{44} +3.46410 q^{45} -1.46410 q^{46} -2.92820 q^{47} -1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} -0.535898 q^{51} +3.46410 q^{52} +2.00000 q^{53} +1.00000 q^{54} +5.07180 q^{55} +1.00000 q^{56} -1.00000 q^{57} +6.00000 q^{58} +4.00000 q^{59} -3.46410 q^{60} +8.92820 q^{61} +6.92820 q^{62} -1.00000 q^{63} +1.00000 q^{64} +12.0000 q^{65} +1.46410 q^{66} +2.53590 q^{67} +0.535898 q^{68} -1.46410 q^{69} +3.46410 q^{70} -10.9282 q^{71} -1.00000 q^{72} +10.0000 q^{73} -10.0000 q^{74} -7.00000 q^{75} +1.00000 q^{76} -1.46410 q^{77} +3.46410 q^{78} +8.39230 q^{79} +3.46410 q^{80} +1.00000 q^{81} +2.00000 q^{82} +8.00000 q^{83} +1.00000 q^{84} +1.85641 q^{85} -6.92820 q^{86} +6.00000 q^{87} -1.46410 q^{88} -2.00000 q^{89} -3.46410 q^{90} -3.46410 q^{91} +1.46410 q^{92} +6.92820 q^{93} +2.92820 q^{94} +3.46410 q^{95} +1.00000 q^{96} +11.4641 q^{97} -1.00000 q^{98} +1.46410 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.217953\pi$
$5$	3.46410	1.54919	0.774597	+	0.632456i	$0.217953\pi$
$6$	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
$11$	1.46410	0.441443	0.220722	−	0.975337i	$-0.429159\pi$
$11$	1.46410	0.441443	0.220722	+	0.975337i	$0.429159\pi$
$12$	−1.00000	−0.288675
$13$	3.46410	0.960769	0.480384	−	0.877058i	$-0.340497\pi$
$13$	3.46410	0.960769	0.480384	+	0.877058i	$0.340497\pi$
$14$	1.00000	0.267261
$15$	−3.46410	−0.894427
$16$	1.00000	0.250000
$17$	0.535898	0.129974	0.0649872	−	0.997886i	$-0.479299\pi$
$17$	0.535898	0.129974	0.0649872	+	0.997886i	$0.479299\pi$
$18$	−1.00000	−0.235702
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	3.46410	0.774597
$21$	1.00000	0.218218
$22$	−1.46410	−0.312148
$23$	1.46410	0.305286	0.152643	−	0.988281i	$-0.451221\pi$
$23$	1.46410	0.305286	0.152643	+	0.988281i	$0.451221\pi$
$24$	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	$-0.713749\pi$
$31$	−6.92820	−1.24434	−0.622171	+	0.782881i	$0.713749\pi$
$32$	−1.00000	−0.176777
$33$	−1.46410	−0.254867
$34$	−0.535898	−0.0919058
$35$	−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	$-0.322841\pi$
$43$	6.92820	1.05654	0.528271	+	0.849076i	$0.322841\pi$
$44$	1.46410	0.220722
$45$	3.46410	0.516398
$46$	−1.46410	−0.215870
$47$	−2.92820	−0.427122	−0.213561	−	0.976930i	$-0.568506\pi$
$47$	−2.92820	−0.427122	−0.213561	+	0.976930i	$0.568506\pi$
$48$	−1.00000	−0.144338
$49$	1.00000	0.142857
$50$	−7.00000	−0.989949
$51$	−0.535898	−0.0750408
$52$	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
$55$	5.07180	0.683881
$56$	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
$61$	8.92820	1.14314	0.571570	−	0.820554i	$-0.306335\pi$
$61$	8.92820	1.14314	0.571570	+	0.820554i	$0.306335\pi$
$62$	6.92820	0.879883
$63$	−1.00000	−0.125988
$64$	1.00000	0.125000
$65$	12.0000	1.48842
$66$	1.46410	0.180218
$67$	2.53590	0.309809	0.154905	−	0.987929i	$-0.450493\pi$
$67$	2.53590	0.309809	0.154905	+	0.987929i	$0.450493\pi$
$68$	0.535898	0.0649872
$69$	−1.46410	−0.176257
$70$	3.46410	0.414039
$71$	−10.9282	−1.29694	−0.648470	−	0.761241i	$-0.724591\pi$
$71$	−10.9282	−1.29694	−0.648470	+	0.761241i	$0.724591\pi$
$72$	−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
$77$	−1.46410	−0.166850
$78$	3.46410	0.392232
$79$	8.39230	0.944208	0.472104	−	0.881543i	$-0.343495\pi$
$79$	8.39230	0.944208	0.472104	+	0.881543i	$0.343495\pi$
$80$	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
$85$	1.85641	0.201356
$86$	−6.92820	−0.747087
$87$	6.00000	0.643268
$88$	−1.46410	−0.156074
$89$	−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
$92$	1.46410	0.152643
$93$	6.92820	0.718421
$94$	2.92820	0.302021
$95$	3.46410	0.355409
$96$	1.00000	0.102062
$97$	11.4641	1.16400	0.582002	−	0.813188i	$-0.302270\pi$
$97$	11.4641	1.16400	0.582002	+	0.813188i	$0.302270\pi$
$98$	−1.00000	−0.101015
$99$	1.46410	0.147148
$100$	7.00000	0.700000
$101$	11.4641	1.14072	0.570360	−	0.821395i	$-0.306804\pi$
$101$	11.4641	1.14072	0.570360	+	0.821395i	$0.306804\pi$
$102$	0.535898	0.0530618
$103$	6.92820	0.682656	0.341328	−	0.939944i	$-0.389123\pi$
$103$	6.92820	0.682656	0.341328	+	0.939944i	$0.389123\pi$
$104$	−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	$0.469465\pi$
$110$	−5.07180	−0.483577
$111$	−10.0000	−0.949158
$112$	−1.00000	−0.0944911
$113$	−15.8564	−1.49165	−0.745823	−	0.666145i	$-0.767943\pi$
$113$	−15.8564	−1.49165	−0.745823	+	0.666145i	$0.767943\pi$
$114$	1.00000	0.0936586
$115$	5.07180	0.472947
$116$	−6.00000	−0.557086
$117$	3.46410	0.320256
$118$	−4.00000	−0.368230
$119$	−0.535898	−0.0491257
$120$	3.46410	0.316228
$121$	−8.85641	−0.805128
$122$	−8.92820	−0.808322
$123$	2.00000	0.180334
$124$	−6.92820	−0.622171
$125$	6.92820	0.619677
$126$	1.00000	0.0890871
$127$	−10.5359	−0.934910	−0.467455	−	0.884017i	$-0.654829\pi$
$127$	−10.5359	−0.934910	−0.467455	+	0.884017i	$0.654829\pi$
$128$	−1.00000	−0.0883883
$129$	−6.92820	−0.609994
$130$	−12.0000	−1.05247
$131$	−18.9282	−1.65376	−0.826882	−	0.562375i	$-0.809888\pi$
$131$	−18.9282	−1.65376	−0.826882	+	0.562375i	$0.809888\pi$
$132$	−1.46410	−0.127434
$133$	−1.00000	−0.0867110
$134$	−2.53590	−0.219068
$135$	−3.46410	−0.298142
$136$	−0.535898	−0.0459529
$137$	12.9282	1.10453	0.552265	−	0.833668i	$-0.313763\pi$
$137$	12.9282	1.10453	0.552265	+	0.833668i	$0.313763\pi$
$138$	1.46410	0.124633
$139$	−17.8564	−1.51456	−0.757280	−	0.653090i	$-0.773472\pi$
$139$	−17.8564	−1.51456	−0.757280	+	0.653090i	$0.773472\pi$
$140$	−3.46410	−0.292770
$141$	2.92820	0.246599
$142$	10.9282	0.917074
$143$	5.07180	0.424125
$144$	1.00000	0.0833333
$145$	−20.7846	−1.72607
$146$	−10.0000	−0.827606
$147$	−1.00000	−0.0824786
$148$	10.0000	0.821995
$149$	−16.9282	−1.38681	−0.693406	−	0.720547i	$-0.743891\pi$
$149$	−16.9282	−1.38681	−0.693406	+	0.720547i	$0.743891\pi$
$150$	7.00000	0.571548
$151$	−5.46410	−0.444662	−0.222331	−	0.974971i	$-0.571367\pi$
$151$	−5.46410	−0.444662	−0.222331	+	0.974971i	$0.571367\pi$
$152$	−1.00000	−0.0811107
$153$	0.535898	0.0433248
$154$	1.46410	0.117981
$155$	−24.0000	−1.92773
$156$	−3.46410	−0.277350
$157$	−7.85641	−0.627009	−0.313505	−	0.949587i	$-0.601503\pi$
$157$	−7.85641	−0.627009	−0.313505	+	0.949587i	$0.601503\pi$
$158$	−8.39230	−0.667656
$159$	−2.00000	−0.158610
$160$	−3.46410	−0.273861
$161$	−1.46410	−0.115387
$162$	−1.00000	−0.0785674
$163$	14.9282	1.16927	0.584634	−	0.811297i	$-0.301238\pi$
$163$	14.9282	1.16927	0.584634	+	0.811297i	$0.301238\pi$
$164$	−2.00000	−0.156174
$165$	−5.07180	−0.394839
$166$	−8.00000	−0.620920
$167$	−5.07180	−0.392467	−0.196234	−	0.980557i	$-0.562871\pi$
$167$	−5.07180	−0.392467	−0.196234	+	0.980557i	$0.562871\pi$
$168$	−1.00000	−0.0771517
$169$	−1.00000	−0.0769231
$170$	−1.85641	−0.142380
$171$	1.00000	0.0764719
$172$	6.92820	0.528271
$173$	12.9282	0.982913	0.491457	−	0.870902i	$-0.336465\pi$
$173$	12.9282	0.982913	0.491457	+	0.870902i	$0.336465\pi$
$174$	−6.00000	−0.454859
$175$	−7.00000	−0.529150
$176$	1.46410	0.110361
$177$	−4.00000	−0.300658
$178$	2.00000	0.149906
$179$	17.8564	1.33465	0.667325	−	0.744766i	$-0.267439\pi$
$179$	17.8564	1.33465	0.667325	+	0.744766i	$0.267439\pi$
$180$	3.46410	0.258199
$181$	−15.4641	−1.14944	−0.574719	−	0.818351i	$-0.694889\pi$
$181$	−15.4641	−1.14944	−0.574719	+	0.818351i	$0.694889\pi$
$182$	3.46410	0.256776
$183$	−8.92820	−0.659992
$184$	−1.46410	−0.107935
$185$	34.6410	2.54686
$186$	−6.92820	−0.508001
$187$	0.784610	0.0573763
$188$	−2.92820	−0.213561
$189$	1.00000	0.0727393
$190$	−3.46410	−0.251312
$191$	1.46410	0.105939	0.0529693	−	0.998596i	$-0.483131\pi$
$191$	1.46410	0.105939	0.0529693	+	0.998596i	$0.483131\pi$
$192$	−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	$0.790854\pi$
$194$	−11.4641	−0.823075
$195$	−12.0000	−0.859338
$196$	1.00000	0.0714286
$197$	−8.92820	−0.636108	−0.318054	−	0.948073i	$-0.603029\pi$
$197$	−8.92820	−0.636108	−0.318054	+	0.948073i	$0.603029\pi$
$198$	−1.46410	−0.104049
$199$	16.7846	1.18983	0.594915	−	0.803789i	$-0.297186\pi$
$199$	16.7846	1.18983	0.594915	+	0.803789i	$0.297186\pi$
$200$	−7.00000	−0.494975
$201$	−2.53590	−0.178868
$202$	−11.4641	−0.806611
$203$	6.00000	0.421117
$204$	−0.535898	−0.0375204
$205$	−6.92820	−0.483887
$206$	−6.92820	−0.482711
$207$	1.46410	0.101762
$208$	3.46410	0.240192
$209$	1.46410	0.101274
$210$	−3.46410	−0.239046
$211$	−5.46410	−0.376164	−0.188082	−	0.982153i	$-0.560227\pi$
$211$	−5.46410	−0.376164	−0.188082	+	0.982153i	$0.560227\pi$
$212$	2.00000	0.137361
$213$	10.9282	0.748788
$214$	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
$220$	5.07180	0.341940
$221$	1.85641	0.124875
$222$	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
$226$	15.8564	1.05475
$227$	1.07180	0.0711377	0.0355688	−	0.999367i	$-0.488676\pi$
$227$	1.07180	0.0711377	0.0355688	+	0.999367i	$0.488676\pi$
$228$	−1.00000	−0.0662266
$229$	16.9282	1.11865	0.559324	−	0.828949i	$-0.311061\pi$
$229$	16.9282	1.11865	0.559324	+	0.828949i	$0.311061\pi$
$230$	−5.07180	−0.334424
$231$	1.46410	0.0963308
$232$	6.00000	0.393919
$233$	−14.7846	−0.968572	−0.484286	−	0.874910i	$-0.660921\pi$
$233$	−14.7846	−0.968572	−0.484286	+	0.874910i	$0.660921\pi$
$234$	−3.46410	−0.226455
$235$	−10.1436	−0.661695
$236$	4.00000	0.260378
$237$	−8.39230	−0.545139
$238$	0.535898	0.0347371
$239$	−18.2487	−1.18041	−0.590206	−	0.807253i	$-0.700953\pi$
$239$	−18.2487	−1.18041	−0.590206	+	0.807253i	$0.700953\pi$
$240$	−3.46410	−0.223607
$241$	−13.3205	−0.858049	−0.429025	−	0.903293i	$-0.641143\pi$
$241$	−13.3205	−0.858049	−0.429025	+	0.903293i	$0.641143\pi$
$242$	8.85641	0.569311
$243$	−1.00000	−0.0641500
$244$	8.92820	0.571570
$245$	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
$251$	18.9282	1.19474	0.597369	−	0.801967i	$-0.296213\pi$
$251$	18.9282	1.19474	0.597369	+	0.801967i	$0.296213\pi$
$252$	−1.00000	−0.0629941
$253$	2.14359	0.134767
$254$	10.5359	0.661081
$255$	−1.85641	−0.116253
$256$	1.00000	0.0625000
$257$	11.0718	0.690640	0.345320	−	0.938485i	$-0.387770\pi$
$257$	11.0718	0.690640	0.345320	+	0.938485i	$0.387770\pi$
$258$	6.92820	0.431331
$259$	−10.0000	−0.621370
$260$	12.0000	0.744208
$261$	−6.00000	−0.371391
$262$	18.9282	1.16939
$263$	−23.3205	−1.43800	−0.719002	−	0.695008i	$-0.755401\pi$
$263$	−23.3205	−1.43800	−0.719002	+	0.695008i	$0.755401\pi$
$264$	1.46410	0.0901092
$265$	6.92820	0.425596
$266$	1.00000	0.0613139
$267$	2.00000	0.122398
$268$	2.53590	0.154905
$269$	−3.07180	−0.187291	−0.0936454	−	0.995606i	$-0.529852\pi$
$269$	−3.07180	−0.187291	−0.0936454	+	0.995606i	$0.529852\pi$
$270$	3.46410	0.210819
$271$	−2.14359	−0.130214	−0.0651070	−	0.997878i	$-0.520739\pi$
$271$	−2.14359	−0.130214	−0.0651070	+	0.997878i	$0.520739\pi$
$272$	0.535898	0.0324936
$273$	3.46410	0.209657
$274$	−12.9282	−0.781021
$275$	10.2487	0.618021
$276$	−1.46410	−0.0881286
$277$	22.0000	1.32185	0.660926	−	0.750451i	$-0.270164\pi$
$277$	22.0000	1.32185	0.660926	+	0.750451i	$0.270164\pi$
$278$	17.8564	1.07096
$279$	−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	$0.782510\pi$
$282$	−2.92820	−0.174372
$283$	−20.0000	−1.18888	−0.594438	−	0.804141i	$-0.702626\pi$
$283$	−20.0000	−1.18888	−0.594438	+	0.804141i	$0.702626\pi$
$284$	−10.9282	−0.648470
$285$	−3.46410	−0.205196
$286$	−5.07180	−0.299902
$287$	2.00000	0.118056
$288$	−1.00000	−0.0589256
$289$	−16.7128	−0.983107
$290$	20.7846	1.22051
$291$	−11.4641	−0.672038
$292$	10.0000	0.585206
$293$	20.9282	1.22264	0.611319	−	0.791384i	$-0.290639\pi$
$293$	20.9282	1.22264	0.611319	+	0.791384i	$0.290639\pi$
$294$	1.00000	0.0583212
$295$	13.8564	0.806751
$296$	−10.0000	−0.581238
$297$	−1.46410	−0.0849558
$298$	16.9282	0.980624
$299$	5.07180	0.293310
$300$	−7.00000	−0.404145
$301$	−6.92820	−0.399335
$302$	5.46410	0.314424
$303$	−11.4641	−0.658595
$304$	1.00000	0.0573539
$305$	30.9282	1.77094
$306$	−0.535898	−0.0306353
$307$	−20.7846	−1.18624	−0.593120	−	0.805114i	$-0.702104\pi$
$307$	−20.7846	−1.18624	−0.593120	+	0.805114i	$0.702104\pi$
$308$	−1.46410	−0.0834249
$309$	−6.92820	−0.394132
$310$	24.0000	1.36311
$311$	29.8564	1.69300	0.846501	−	0.532388i	$-0.178705\pi$
$311$	29.8564	1.69300	0.846501	+	0.532388i	$0.178705\pi$
$312$	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	$0.554238\pi$
$314$	7.85641	0.443363
$315$	−3.46410	−0.195180
$316$	8.39230	0.472104
$317$	−19.8564	−1.11525	−0.557623	−	0.830094i	$-0.688287\pi$
$317$	−19.8564	−1.11525	−0.557623	+	0.830094i	$0.688287\pi$
$318$	2.00000	0.112154
$319$	−8.78461	−0.491844
$320$	3.46410	0.193649
$321$	4.00000	0.223258
$322$	1.46410	0.0815912
$323$	0.535898	0.0298182
$324$	1.00000	0.0555556
$325$	24.2487	1.34508
$326$	−14.9282	−0.826797
$327$	−2.00000	−0.110600
$328$	2.00000	0.110432
$329$	2.92820	0.161437
$330$	5.07180	0.279193
$331$	21.4641	1.17977	0.589887	−	0.807486i	$-0.299172\pi$
$331$	21.4641	1.17977	0.589887	+	0.807486i	$0.299172\pi$
$332$	8.00000	0.439057
$333$	10.0000	0.547997
$334$	5.07180	0.277516
$335$	8.78461	0.479954
$336$	1.00000	0.0545545
$337$	−30.7846	−1.67694	−0.838472	−	0.544944i	$-0.816551\pi$
$337$	−30.7846	−1.67694	−0.838472	+	0.544944i	$0.816551\pi$
$338$	1.00000	0.0543928
$339$	15.8564	0.861202
$340$	1.85641	0.100678
$341$	−10.1436	−0.549306
$342$	−1.00000	−0.0540738
$343$	−1.00000	−0.0539949
$344$	−6.92820	−0.373544
$345$	−5.07180	−0.273056
$346$	−12.9282	−0.695025
$347$	−7.32051	−0.392985	−0.196493	−	0.980505i	$-0.562955\pi$
$347$	−7.32051	−0.392985	−0.196493	+	0.980505i	$0.562955\pi$
$348$	6.00000	0.321634
$349$	8.14359	0.435917	0.217958	−	0.975958i	$-0.430060\pi$
$349$	8.14359	0.435917	0.217958	+	0.975958i	$0.430060\pi$
$350$	7.00000	0.374166
$351$	−3.46410	−0.184900
$352$	−1.46410	−0.0780369
$353$	−29.3205	−1.56057	−0.780287	−	0.625422i	$-0.784927\pi$
$353$	−29.3205	−1.56057	−0.780287	+	0.625422i	$0.784927\pi$
$354$	4.00000	0.212598
$355$	−37.8564	−2.00921
$356$	−2.00000	−0.106000
$357$	0.535898	0.0283628
$358$	−17.8564	−0.943740
$359$	0.679492	0.0358622	0.0179311	−	0.999839i	$-0.494292\pi$
$359$	0.679492	0.0358622	0.0179311	+	0.999839i	$0.494292\pi$
$360$	−3.46410	−0.182574
$361$	1.00000	0.0526316
$362$	15.4641	0.812775
$363$	8.85641	0.464841
$364$	−3.46410	−0.181568
$365$	34.6410	1.81319
$366$	8.92820	0.466685
$367$	8.00000	0.417597	0.208798	−	0.977959i	$-0.433045\pi$
$367$	8.00000	0.417597	0.208798	+	0.977959i	$0.433045\pi$
$368$	1.46410	0.0763216
$369$	−2.00000	−0.104116
$370$	−34.6410	−1.80090
$371$	−2.00000	−0.103835
$372$	6.92820	0.359211
$373$	−30.7846	−1.59397	−0.796983	−	0.604001i	$-0.793572\pi$
$373$	−30.7846	−1.59397	−0.796983	+	0.604001i	$0.793572\pi$
$374$	−0.784610	−0.0405712
$375$	−6.92820	−0.357771
$376$	2.92820	0.151011
$377$	−20.7846	−1.07046
$378$	−1.00000	−0.0514344
$379$	5.46410	0.280672	0.140336	−	0.990104i	$-0.455182\pi$
$379$	5.46410	0.280672	0.140336	+	0.990104i	$0.455182\pi$
$380$	3.46410	0.177705
$381$	10.5359	0.539770
$382$	−1.46410	−0.0749100
$383$	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
$385$	−5.07180	−0.258483
$386$	22.0000	1.11977
$387$	6.92820	0.352180
$388$	11.4641	0.582002
$389$	−25.7128	−1.30369	−0.651846	−	0.758352i	$-0.726005\pi$
$389$	−25.7128	−1.30369	−0.651846	+	0.758352i	$0.726005\pi$
$390$	12.0000	0.607644
$391$	0.784610	0.0396794
$392$	−1.00000	−0.0505076
$393$	18.9282	0.954802
$394$	8.92820	0.449796
$395$	29.0718	1.46276
$396$	1.46410	0.0735739
$397$	−7.85641	−0.394302	−0.197151	−	0.980373i	$-0.563169\pi$
$397$	−7.85641	−0.394302	−0.197151	+	0.980373i	$0.563169\pi$
$398$	−16.7846	−0.841336
$399$	1.00000	0.0500626
$400$	7.00000	0.350000
$401$	−7.85641	−0.392330	−0.196165	−	0.980571i	$-0.562849\pi$
$401$	−7.85641	−0.392330	−0.196165	+	0.980571i	$0.562849\pi$
$402$	2.53590	0.126479
$403$	−24.0000	−1.19553
$404$	11.4641	0.570360
$405$	3.46410	0.172133
$406$	−6.00000	−0.297775
$407$	14.6410	0.725728
$408$	0.535898	0.0265309
$409$	31.1769	1.54160	0.770800	−	0.637078i	$-0.219857\pi$
$409$	31.1769	1.54160	0.770800	+	0.637078i	$0.219857\pi$
$410$	6.92820	0.342160
$411$	−12.9282	−0.637701
$412$	6.92820	0.341328
$413$	−4.00000	−0.196827
$414$	−1.46410	−0.0719567
$415$	27.7128	1.36037
$416$	−3.46410	−0.169842
$417$	17.8564	0.874432
$418$	−1.46410	−0.0716116
$419$	5.07180	0.247773	0.123887	−	0.992296i	$-0.460464\pi$
$419$	5.07180	0.247773	0.123887	+	0.992296i	$0.460464\pi$
$420$	3.46410	0.169031
$421$	−22.7846	−1.11045	−0.555227	−	0.831699i	$-0.687369\pi$
$421$	−22.7846	−1.11045	−0.555227	+	0.831699i	$0.687369\pi$
$422$	5.46410	0.265988
$423$	−2.92820	−0.142374
$424$	−2.00000	−0.0971286
$425$	3.75129	0.181964
$426$	−10.9282	−0.529473
$427$	−8.92820	−0.432066
$428$	−4.00000	−0.193347
$429$	−5.07180	−0.244869
$430$	−24.0000	−1.15738
$431$	−21.0718	−1.01499	−0.507496	−	0.861654i	$-0.669429\pi$
$431$	−21.0718	−1.01499	−0.507496	+	0.861654i	$0.669429\pi$
$432$	−1.00000	−0.0481125
$433$	41.3205	1.98574	0.992868	−	0.119215i	$-0.0380378\pi$
$433$	41.3205	1.98574	0.992868	+	0.119215i	$0.0380378\pi$
$434$	−6.92820	−0.332564
$435$	20.7846	0.996546
$436$	2.00000	0.0957826
$437$	1.46410	0.0700375
$438$	10.0000	0.477818
$439$	36.7846	1.75563	0.877817	−	0.478996i	$-0.158999\pi$
$439$	36.7846	1.75563	0.877817	+	0.478996i	$0.158999\pi$
$440$	−5.07180	−0.241788
$441$	1.00000	0.0476190
$442$	−1.85641	−0.0883003
$443$	23.3205	1.10799	0.553995	−	0.832520i	$-0.313103\pi$
$443$	23.3205	1.10799	0.553995	+	0.832520i	$0.313103\pi$
$444$	−10.0000	−0.474579
$445$	−6.92820	−0.328428
$446$	12.0000	0.568216
$447$	16.9282	0.800677
$448$	−1.00000	−0.0472456
$449$	19.8564	0.937082	0.468541	−	0.883442i	$-0.344780\pi$
$449$	19.8564	0.937082	0.468541	+	0.883442i	$0.344780\pi$
$450$	−7.00000	−0.329983
$451$	−2.92820	−0.137884
$452$	−15.8564	−0.745823
$453$	5.46410	0.256726
$454$	−1.07180	−0.0503019
$455$	−12.0000	−0.562569
$456$	1.00000	0.0468293
$457$	39.8564	1.86440	0.932202	−	0.361938i	$-0.117885\pi$
$457$	39.8564	1.86440	0.932202	+	0.361938i	$0.117885\pi$
$458$	−16.9282	−0.791003
$459$	−0.535898	−0.0250136
$460$	5.07180	0.236474
$461$	−38.1051	−1.77473	−0.887366	−	0.461065i	$-0.847467\pi$
$461$	−38.1051	−1.77473	−0.887366	+	0.461065i	$0.847467\pi$
$462$	−1.46410	−0.0681162
$463$	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
$466$	14.7846	0.684884
$467$	−19.7128	−0.912200	−0.456100	−	0.889928i	$-0.650754\pi$
$467$	−19.7128	−0.912200	−0.456100	+	0.889928i	$0.650754\pi$
$468$	3.46410	0.160128
$469$	−2.53590	−0.117097
$470$	10.1436	0.467889
$471$	7.85641	0.362004
$472$	−4.00000	−0.184115
$473$	10.1436	0.466403
$474$	8.39230	0.385471
$475$	7.00000	0.321182
$476$	−0.535898	−0.0245629
$477$	2.00000	0.0915737
$478$	18.2487	0.834677
$479$	−27.7128	−1.26623	−0.633115	−	0.774057i	$-0.718224\pi$
$479$	−27.7128	−1.26623	−0.633115	+	0.774057i	$0.718224\pi$
$480$	3.46410	0.158114
$481$	34.6410	1.57949
$482$	13.3205	0.606733
$483$	1.46410	0.0666189
$484$	−8.85641	−0.402564
$485$	39.7128	1.80327
$486$	1.00000	0.0453609
$487$	−4.67949	−0.212048	−0.106024	−	0.994364i	$-0.533812\pi$
$487$	−4.67949	−0.212048	−0.106024	+	0.994364i	$0.533812\pi$
$488$	−8.92820	−0.404161
$489$	−14.9282	−0.675077
$490$	−3.46410	−0.156492
$491$	−19.6077	−0.884883	−0.442441	−	0.896797i	$-0.645888\pi$
$491$	−19.6077	−0.884883	−0.442441	+	0.896797i	$0.645888\pi$
$492$	2.00000	0.0901670
$493$	−3.21539	−0.144814
$494$	−3.46410	−0.155857
$495$	5.07180	0.227960
$496$	−6.92820	−0.311086
$497$	10.9282	0.490197
$498$	8.00000	0.358489
$499$	−9.07180	−0.406109	−0.203055	−	0.979167i	$-0.565087\pi$
$499$	−9.07180	−0.406109	−0.203055	+	0.979167i	$0.565087\pi$
$500$	6.92820	0.309839
$501$	5.07180	0.226591
$502$	−18.9282	−0.844807
$503$	5.85641	0.261124	0.130562	−	0.991440i	$-0.458322\pi$
$503$	5.85641	0.261124	0.130562	+	0.991440i	$0.458322\pi$
$504$	1.00000	0.0445435
$505$	39.7128	1.76720
$506$	−2.14359	−0.0952944
$507$	1.00000	0.0444116
$508$	−10.5359	−0.467455
$509$	24.6410	1.09219	0.546097	−	0.837722i	$-0.316113\pi$
$509$	24.6410	1.09219	0.546097	+	0.837722i	$0.316113\pi$
$510$	1.85641	0.0822031
$511$	−10.0000	−0.442374
$512$	−1.00000	−0.0441942
$513$	−1.00000	−0.0441511
$514$	−11.0718	−0.488356
$515$	24.0000	1.05757
$516$	−6.92820	−0.304997
$517$	−4.28719	−0.188550
$518$	10.0000	0.439375
$519$	−12.9282	−0.567485
$520$	−12.0000	−0.526235
$521$	−29.7128	−1.30174	−0.650871	−	0.759188i	$-0.725596\pi$
$521$	−29.7128	−1.30174	−0.650871	+	0.759188i	$0.725596\pi$
$522$	6.00000	0.262613
$523$	−42.6410	−1.86456	−0.932281	−	0.361736i	$-0.882184\pi$
$523$	−42.6410	−1.86456	−0.932281	+	0.361736i	$0.882184\pi$
$524$	−18.9282	−0.826882
$525$	7.00000	0.305505
$526$	23.3205	1.01682
$527$	−3.71281	−0.161733
$528$	−1.46410	−0.0637168
$529$	−20.8564	−0.906800
$530$	−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
$536$	−2.53590	−0.109534
$537$	−17.8564	−0.770561
$538$	3.07180	0.132435
$539$	1.46410	0.0630633
$540$	−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	$0.760893\pi$
$542$	2.14359	0.0920752
$543$	15.4641	0.663628
$544$	−0.535898	−0.0229765
$545$	6.92820	0.296772
$546$	−3.46410	−0.148250
$547$	38.2487	1.63540	0.817698	−	0.575647i	$-0.195250\pi$
$547$	38.2487	1.63540	0.817698	+	0.575647i	$0.195250\pi$
$548$	12.9282	0.552265
$549$	8.92820	0.381046
$550$	−10.2487	−0.437007
$551$	−6.00000	−0.255609
$552$	1.46410	0.0623163
$553$	−8.39230	−0.356877
$554$	−22.0000	−0.934690
$555$	−34.6410	−1.47043
$556$	−17.8564	−0.757280
$557$	−8.92820	−0.378300	−0.189150	−	0.981948i	$-0.560573\pi$
$557$	−8.92820	−0.378300	−0.189150	+	0.981948i	$0.560573\pi$
$558$	6.92820	0.293294
$559$	24.0000	1.01509
$560$	−3.46410	−0.146385
$561$	−0.784610	−0.0331262
$562$	26.0000	1.09674
$563$	−1.85641	−0.0782382	−0.0391191	−	0.999235i	$-0.512455\pi$
$563$	−1.85641	−0.0782382	−0.0391191	+	0.999235i	$0.512455\pi$
$564$	2.92820	0.123300
$565$	−54.9282	−2.31085
$566$	20.0000	0.840663
$567$	−1.00000	−0.0419961
$568$	10.9282	0.458537
$569$	9.71281	0.407182	0.203591	−	0.979056i	$-0.434739\pi$
$569$	9.71281	0.407182	0.203591	+	0.979056i	$0.434739\pi$
$570$	3.46410	0.145095
$571$	−45.5692	−1.90701	−0.953506	−	0.301373i	$-0.902555\pi$
$571$	−45.5692	−1.90701	−0.953506	+	0.301373i	$0.902555\pi$
$572$	5.07180	0.212062
$573$	−1.46410	−0.0611637
$574$	−2.00000	−0.0834784
$575$	10.2487	0.427401
$576$	1.00000	0.0416667
$577$	23.8564	0.993155	0.496578	−	0.867992i	$-0.334590\pi$
$577$	23.8564	0.993155	0.496578	+	0.867992i	$0.334590\pi$
$578$	16.7128	0.695161
$579$	22.0000	0.914289
$580$	−20.7846	−0.863034
$581$	−8.00000	−0.331896
$582$	11.4641	0.475202
$583$	2.92820	0.121274
$584$	−10.0000	−0.413803
$585$	12.0000	0.496139
$586$	−20.9282	−0.864536
$587$	−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
$591$	8.92820	0.367257
$592$	10.0000	0.410997
$593$	19.4641	0.799295	0.399647	−	0.916669i	$-0.369133\pi$
$593$	19.4641	0.799295	0.399647	+	0.916669i	$0.369133\pi$
$594$	1.46410	0.0600728
$595$	−1.85641	−0.0761052
$596$	−16.9282	−0.693406
$597$	−16.7846	−0.686948
$598$	−5.07180	−0.207401
$599$	26.9282	1.10026	0.550128	−	0.835080i	$-0.314579\pi$
$599$	26.9282	1.10026	0.550128	+	0.835080i	$0.314579\pi$
$600$	7.00000	0.285774
$601$	41.3205	1.68550	0.842749	−	0.538306i	$-0.180936\pi$
$601$	41.3205	1.68550	0.842749	+	0.538306i	$0.180936\pi$
$602$	6.92820	0.282372
$603$	2.53590	0.103270
$604$	−5.46410	−0.222331
$605$	−30.6795	−1.24730
$606$	11.4641	0.465697
$607$	9.85641	0.400059	0.200030	−	0.979790i	$-0.435896\pi$
$607$	9.85641	0.400059	0.200030	+	0.979790i	$0.435896\pi$
$608$	−1.00000	−0.0405554
$609$	−6.00000	−0.243132
$610$	−30.9282	−1.25225
$611$	−10.1436	−0.410366
$612$	0.535898	0.0216624
$613$	3.85641	0.155759	0.0778794	−	0.996963i	$-0.475185\pi$
$613$	3.85641	0.155759	0.0778794	+	0.996963i	$0.475185\pi$
$614$	20.7846	0.838799
$615$	6.92820	0.279372
$616$	1.46410	0.0589903
$617$	−0.928203	−0.0373681	−0.0186840	−	0.999825i	$-0.505948\pi$
$617$	−0.928203	−0.0373681	−0.0186840	+	0.999825i	$0.505948\pi$
$618$	6.92820	0.278693
$619$	−42.6410	−1.71389	−0.856944	−	0.515410i	$-0.827640\pi$
$619$	−42.6410	−1.71389	−0.856944	+	0.515410i	$0.827640\pi$
$620$	−24.0000	−0.963863
$621$	−1.46410	−0.0587524
$622$	−29.8564	−1.19713
$623$	2.00000	0.0801283
$624$	−3.46410	−0.138675
$625$	−11.0000	−0.440000
$626$	6.00000	0.239808
$627$	−1.46410	−0.0584706
$628$	−7.85641	−0.313505
$629$	5.35898	0.213677
$630$	3.46410	0.138013
$631$	−24.7846	−0.986660	−0.493330	−	0.869842i	$-0.664220\pi$
$631$	−24.7846	−0.986660	−0.493330	+	0.869842i	$0.664220\pi$
$632$	−8.39230	−0.333828
$633$	5.46410	0.217179
$634$	19.8564	0.788599
$635$	−36.4974	−1.44836
$636$	−2.00000	−0.0793052
$637$	3.46410	0.137253
$638$	8.78461	0.347786
$639$	−10.9282	−0.432313
$640$	−3.46410	−0.136931
$641$	11.8564	0.468300	0.234150	−	0.972200i	$-0.424769\pi$
$641$	11.8564	0.468300	0.234150	+	0.972200i	$0.424769\pi$
$642$	−4.00000	−0.157867
$643$	−1.07180	−0.0422675	−0.0211338	−	0.999777i	$-0.506728\pi$
$643$	−1.07180	−0.0422675	−0.0211338	+	0.999777i	$0.506728\pi$
$644$	−1.46410	−0.0576937
$645$	−24.0000	−0.944999
$646$	−0.535898	−0.0210846
$647$	0	0		−	1.00000i	$-0.5\pi$
$647$	0	0			1.00000i	$0.5\pi$
$648$	−1.00000	−0.0392837
$649$	5.85641	0.229884
$650$	−24.2487	−0.951113
$651$	−6.92820	−0.271538
$652$	14.9282	0.584634
$653$	21.7128	0.849688	0.424844	−	0.905267i	$-0.360329\pi$
$653$	21.7128	0.849688	0.424844	+	0.905267i	$0.360329\pi$
$654$	2.00000	0.0782062
$655$	−65.5692	−2.56200
$656$	−2.00000	−0.0780869
$657$	10.0000	0.390137
$658$	−2.92820	−0.114153
$659$	41.8564	1.63049	0.815247	−	0.579113i	$-0.196601\pi$
$659$	41.8564	1.63049	0.815247	+	0.579113i	$0.196601\pi$
$660$	−5.07180	−0.197419
$661$	10.6795	0.415384	0.207692	−	0.978194i	$-0.433405\pi$
$661$	10.6795	0.415384	0.207692	+	0.978194i	$0.433405\pi$
$662$	−21.4641	−0.834226
$663$	−1.85641	−0.0720969
$664$	−8.00000	−0.310460
$665$	−3.46410	−0.134332
$666$	−10.0000	−0.387492
$667$	−8.78461	−0.340141
$668$	−5.07180	−0.196234
$669$	12.0000	0.463947
$670$	−8.78461	−0.339379
$671$	13.0718	0.504631
$672$	−1.00000	−0.0385758
$673$	−3.07180	−0.118409	−0.0592045	−	0.998246i	$-0.518856\pi$
$673$	−3.07180	−0.118409	−0.0592045	+	0.998246i	$0.518856\pi$
$674$	30.7846	1.18578
$675$	−7.00000	−0.269430
$676$	−1.00000	−0.0384615
$677$	7.85641	0.301946	0.150973	−	0.988538i	$-0.451759\pi$
$677$	7.85641	0.301946	0.150973	+	0.988538i	$0.451759\pi$
$678$	−15.8564	−0.608962
$679$	−11.4641	−0.439952
$680$	−1.85641	−0.0711899
$681$	−1.07180	−0.0410713
$682$	10.1436	0.388418
$683$	17.0718	0.653234	0.326617	−	0.945157i	$-0.394091\pi$
$683$	17.0718	0.653234	0.326617	+	0.945157i	$0.394091\pi$
$684$	1.00000	0.0382360
$685$	44.7846	1.71113
$686$	1.00000	0.0381802
$687$	−16.9282	−0.645851
$688$	6.92820	0.264135
$689$	6.92820	0.263944
$690$	5.07180	0.193080
$691$	−20.0000	−0.760836	−0.380418	−	0.924815i	$-0.624220\pi$
$691$	−20.0000	−0.760836	−0.380418	+	0.924815i	$0.624220\pi$
$692$	12.9282	0.491457
$693$	−1.46410	−0.0556166
$694$	7.32051	0.277883
$695$	−61.8564	−2.34635
$696$	−6.00000	−0.227429
$697$	−1.07180	−0.0405972
$698$	−8.14359	−0.308240
$699$	14.7846	0.559205
$700$	−7.00000	−0.264575
$701$	−41.7128	−1.57547	−0.787736	−	0.616013i	$-0.788747\pi$
$701$	−41.7128	−1.57547	−0.787736	+	0.616013i	$0.788747\pi$
$702$	3.46410	0.130744
$703$	10.0000	0.377157
$704$	1.46410	0.0551804
$705$	10.1436	0.382030
$706$	29.3205	1.10349
$707$	−11.4641	−0.431152
$708$	−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	$0.415324\pi$
$710$	37.8564	1.42073
$711$	8.39230	0.314736
$712$	2.00000	0.0749532
$713$	−10.1436	−0.379881
$714$	−0.535898	−0.0200555
$715$	17.5692	0.657052
$716$	17.8564	0.667325
$717$	18.2487	0.681511
$718$	−0.679492	−0.0253584
$719$	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
$723$	13.3205	0.495395
$724$	−15.4641	−0.574719
$725$	−42.0000	−1.55984
$726$	−8.85641	−0.328692
$727$	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
$731$	3.71281	0.137323
$732$	−8.92820	−0.329996
$733$	−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
$736$	−1.46410	−0.0539675
$737$	3.71281	0.136763
$738$	2.00000	0.0736210
$739$	17.8564	0.656859	0.328429	−	0.944529i	$-0.393481\pi$
$739$	17.8564	0.656859	0.328429	+	0.944529i	$0.393481\pi$
$740$	34.6410	1.27343
$741$	−3.46410	−0.127257
$742$	2.00000	0.0734223
$743$	−27.7128	−1.01668	−0.508342	−	0.861155i	$-0.669742\pi$
$743$	−27.7128	−1.01668	−0.508342	+	0.861155i	$0.669742\pi$
$744$	−6.92820	−0.254000
$745$	−58.6410	−2.14844
$746$	30.7846	1.12710
$747$	8.00000	0.292705
$748$	0.784610	0.0286882
$749$	4.00000	0.146157
$750$	6.92820	0.252982
$751$	−0.392305	−0.0143154	−0.00715770	−	0.999974i	$-0.502278\pi$
$751$	−0.392305	−0.0143154	−0.00715770	+	0.999974i	$0.502278\pi$
$752$	−2.92820	−0.106781
$753$	−18.9282	−0.689782
$754$	20.7846	0.756931
$755$	−18.9282	−0.688868
$756$	1.00000	0.0363696
$757$	−23.8564	−0.867076	−0.433538	−	0.901135i	$-0.642735\pi$
$757$	−23.8564	−0.867076	−0.433538	+	0.901135i	$0.642735\pi$
$758$	−5.46410	−0.198465
$759$	−2.14359	−0.0778075
$760$	−3.46410	−0.125656
$761$	11.4641	0.415573	0.207787	−	0.978174i	$-0.433374\pi$
$761$	11.4641	0.415573	0.207787	+	0.978174i	$0.433374\pi$
$762$	−10.5359	−0.381675
$763$	−2.00000	−0.0724049
$764$	1.46410	0.0529693
$765$	1.85641	0.0671185
$766$	−8.00000	−0.289052
$767$	13.8564	0.500326
$768$	−1.00000	−0.0360844
$769$	7.85641	0.283309	0.141655	−	0.989916i	$-0.454758\pi$
$769$	7.85641	0.283309	0.141655	+	0.989916i	$0.454758\pi$
$770$	5.07180	0.182775
$771$	−11.0718	−0.398741
$772$	−22.0000	−0.791797
$773$	−38.7846	−1.39499	−0.697493	−	0.716592i	$-0.745701\pi$
$773$	−38.7846	−1.39499	−0.697493	+	0.716592i	$0.745701\pi$
$774$	−6.92820	−0.249029
$775$	−48.4974	−1.74208
$776$	−11.4641	−0.411537
$777$	10.0000	0.358748
$778$	25.7128	0.921849
$779$	−2.00000	−0.0716574
$780$	−12.0000	−0.429669
$781$	−16.0000	−0.572525
$782$	−0.784610	−0.0280576
$783$	6.00000	0.214423
$784$	1.00000	0.0357143
$785$	−27.2154	−0.971359
$786$	−18.9282	−0.675147
$787$	−52.7846	−1.88157	−0.940784	−	0.339006i	$-0.889909\pi$
$787$	−52.7846	−1.88157	−0.940784	+	0.339006i	$0.889909\pi$
$788$	−8.92820	−0.318054
$789$	23.3205	0.830232
$790$	−29.0718	−1.03433
$791$	15.8564	0.563789
$792$	−1.46410	−0.0520246
$793$	30.9282	1.09829
$794$	7.85641	0.278813
$795$	−6.92820	−0.245718
$796$	16.7846	0.594915
$797$	24.6410	0.872830	0.436415	−	0.899746i	$-0.356248\pi$
$797$	24.6410	0.872830	0.436415	+	0.899746i	$0.356248\pi$
$798$	−1.00000	−0.0353996
$799$	−1.56922	−0.0555150
$800$	−7.00000	−0.247487
$801$	−2.00000	−0.0706665
$802$	7.85641	0.277419
$803$	14.6410	0.516670
$804$	−2.53590	−0.0894342
$805$	−5.07180	−0.178757
$806$	24.0000	0.845364
$807$	3.07180	0.108132
$808$	−11.4641	−0.403306
$809$	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
$811$	46.9282	1.64787	0.823936	−	0.566683i	$-0.191773\pi$
$811$	46.9282	1.64787	0.823936	+	0.566683i	$0.191773\pi$
$812$	6.00000	0.210559
$813$	2.14359	0.0751791
$814$	−14.6410	−0.513167
$815$	51.7128	1.81142
$816$	−0.535898	−0.0187602
$817$	6.92820	0.242387
$818$	−31.1769	−1.09008
$819$	−3.46410	−0.121046
$820$	−6.92820	−0.241943
$821$	−35.0718	−1.22401	−0.612007	−	0.790852i	$-0.709638\pi$
$821$	−35.0718	−1.22401	−0.612007	+	0.790852i	$0.709638\pi$
$822$	12.9282	0.450923
$823$	5.85641	0.204141	0.102071	−	0.994777i	$-0.467453\pi$
$823$	5.85641	0.204141	0.102071	+	0.994777i	$0.467453\pi$
$824$	−6.92820	−0.241355
$825$	−10.2487	−0.356814
$826$	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	$0.566904\pi$
$828$	1.46410	0.0508810
$829$	−26.3923	−0.916643	−0.458321	−	0.888787i	$-0.651549\pi$
$829$	−26.3923	−0.916643	−0.458321	+	0.888787i	$0.651549\pi$
$830$	−27.7128	−0.961926
$831$	−22.0000	−0.763172
$832$	3.46410	0.120096
$833$	0.535898	0.0185678
$834$	−17.8564	−0.618317
$835$	−17.5692	−0.608008
$836$	1.46410	0.0506370
$837$	6.92820	0.239474
$838$	−5.07180	−0.175202
$839$	−18.9282	−0.653474	−0.326737	−	0.945115i	$-0.605949\pi$
$839$	−18.9282	−0.653474	−0.326737	+	0.945115i	$0.605949\pi$
$840$	−3.46410	−0.119523
$841$	7.00000	0.241379
$842$	22.7846	0.785210
$843$	26.0000	0.895488
$844$	−5.46410	−0.188082
$845$	−3.46410	−0.119169
$846$	2.92820	0.100674
$847$	8.85641	0.304310
$848$	2.00000	0.0686803
$849$	20.0000	0.686398
$850$	−3.75129	−0.128668
$851$	14.6410	0.501888
$852$	10.9282	0.374394
$853$	48.9282	1.67527	0.837635	−	0.546231i	$-0.183938\pi$
$853$	48.9282	1.67527	0.837635	+	0.546231i	$0.183938\pi$
$854$	8.92820	0.305517
$855$	3.46410	0.118470
$856$	4.00000	0.136717
$857$	−35.5692	−1.21502	−0.607511	−	0.794311i	$-0.707832\pi$
$857$	−35.5692	−1.21502	−0.607511	+	0.794311i	$0.707832\pi$
$858$	5.07180	0.173148
$859$	12.7846	0.436205	0.218103	−	0.975926i	$-0.430013\pi$
$859$	12.7846	0.436205	0.218103	+	0.975926i	$0.430013\pi$
$860$	24.0000	0.818393
$861$	−2.00000	−0.0681598
$862$	21.0718	0.717708
$863$	45.8564	1.56097	0.780485	−	0.625174i	$-0.214972\pi$
$863$	45.8564	1.56097	0.780485	+	0.625174i	$0.214972\pi$
$864$	1.00000	0.0340207
$865$	44.7846	1.52272
$866$	−41.3205	−1.40413
$867$	16.7128	0.567597
$868$	6.92820	0.235159
$869$	12.2872	0.416814
$870$	−20.7846	−0.704664
$871$	8.78461	0.297655
$872$	−2.00000	−0.0677285
$873$	11.4641	0.388001
$874$	−1.46410	−0.0495240
$875$	−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	$0.489249\pi$
$878$	−36.7846	−1.24142
$879$	−20.9282	−0.705891
$880$	5.07180	0.170970
$881$	−19.1769	−0.646087	−0.323043	−	0.946384i	$-0.604706\pi$
$881$	−19.1769	−0.646087	−0.323043	+	0.946384i	$0.604706\pi$
$882$	−1.00000	−0.0336718
$883$	−48.4974	−1.63207	−0.816034	−	0.578004i	$-0.803832\pi$
$883$	−48.4974	−1.63207	−0.816034	+	0.578004i	$0.803832\pi$
$884$	1.85641	0.0624377
$885$	−13.8564	−0.465778
$886$	−23.3205	−0.783468
$887$	27.7128	0.930505	0.465253	−	0.885178i	$-0.345963\pi$
$887$	27.7128	0.930505	0.465253	+	0.885178i	$0.345963\pi$
$888$	10.0000	0.335578
$889$	10.5359	0.353363
$890$	6.92820	0.232234
$891$	1.46410	0.0490492
$892$	−12.0000	−0.401790
$893$	−2.92820	−0.0979886
$894$	−16.9282	−0.566164
$895$	61.8564	2.06763
$896$	1.00000	0.0334077
$897$	−5.07180	−0.169342
$898$	−19.8564	−0.662617
$899$	41.5692	1.38641
$900$	7.00000	0.233333
$901$	1.07180	0.0357067
$902$	2.92820	0.0974985
$903$	6.92820	0.230556
$904$	15.8564	0.527376
$905$	−53.5692	−1.78070
$906$	−5.46410	−0.181533
$907$	−34.5359	−1.14675	−0.573373	−	0.819295i	$-0.694365\pi$
$907$	−34.5359	−1.14675	−0.573373	+	0.819295i	$0.694365\pi$
$908$	1.07180	0.0355688
$909$	11.4641	0.380240
$910$	12.0000	0.397796
$911$	−46.6410	−1.54529	−0.772643	−	0.634841i	$-0.781066\pi$
$911$	−46.6410	−1.54529	−0.772643	+	0.634841i	$0.781066\pi$
$912$	−1.00000	−0.0331133
$913$	11.7128	0.387638
$914$	−39.8564	−1.31833
$915$	−30.9282	−1.02245
$916$	16.9282	0.559324
$917$	18.9282	0.625064
$918$	0.535898	0.0176873
$919$	33.5692	1.10735	0.553673	−	0.832734i	$-0.313226\pi$
$919$	33.5692	1.10735	0.553673	+	0.832734i	$0.313226\pi$
$920$	−5.07180	−0.167212
$921$	20.7846	0.684876
$922$	38.1051	1.25493
$923$	−37.8564	−1.24606
$924$	1.46410	0.0481654
$925$	70.0000	2.30159
$926$	−24.0000	−0.788689
$927$	6.92820	0.227552
$928$	6.00000	0.196960
$929$	46.3923	1.52208	0.761041	−	0.648704i	$-0.224689\pi$
$929$	46.3923	1.52208	0.761041	+	0.648704i	$0.224689\pi$
$930$	−24.0000	−0.786991
$931$	1.00000	0.0327737
$932$	−14.7846	−0.484286
$933$	−29.8564	−0.977455
$934$	19.7128	0.645023
$935$	2.71797	0.0888870
$936$	−3.46410	−0.113228
$937$	7.07180	0.231026	0.115513	−	0.993306i	$-0.463149\pi$
$937$	7.07180	0.231026	0.115513	+	0.993306i	$0.463149\pi$
$938$	2.53590	0.0828000
$939$	6.00000	0.195803
$940$	−10.1436	−0.330848
$941$	−46.7846	−1.52513	−0.762567	−	0.646909i	$-0.776061\pi$
$941$	−46.7846	−1.52513	−0.762567	+	0.646909i	$0.776061\pi$
$942$	−7.85641	−0.255976
$943$	−2.92820	−0.0953554
$944$	4.00000	0.130189
$945$	3.46410	0.112687
$946$	−10.1436	−0.329797
$947$	48.1051	1.56321	0.781603	−	0.623776i	$-0.214402\pi$
$947$	48.1051	1.56321	0.781603	+	0.623776i	$0.214402\pi$
$948$	−8.39230	−0.272569
$949$	34.6410	1.12449
$950$	−7.00000	−0.227110
$951$	19.8564	0.643888
$952$	0.535898	0.0173686
$953$	−4.14359	−0.134224	−0.0671121	−	0.997745i	$-0.521379\pi$
$953$	−4.14359	−0.134224	−0.0671121	+	0.997745i	$0.521379\pi$
$954$	−2.00000	−0.0647524
$955$	5.07180	0.164119
$956$	−18.2487	−0.590206
$957$	8.78461	0.283966
$958$	27.7128	0.895360
$959$	−12.9282	−0.417473
$960$	−3.46410	−0.111803
$961$	17.0000	0.548387
$962$	−34.6410	−1.11687
$963$	−4.00000	−0.128898
$964$	−13.3205	−0.429025
$965$	−76.2102	−2.45329
$966$	−1.46410	−0.0471067
$967$	−5.07180	−0.163098	−0.0815490	−	0.996669i	$-0.525987\pi$
$967$	−5.07180	−0.163098	−0.0815490	+	0.996669i	$0.525987\pi$
$968$	8.85641	0.284656
$969$	−0.535898	−0.0172155
$970$	−39.7128	−1.27510
$971$	58.6410	1.88188	0.940940	−	0.338574i	$-0.109944\pi$
$971$	58.6410	1.88188	0.940940	+	0.338574i	$0.109944\pi$
$972$	−1.00000	−0.0320750
$973$	17.8564	0.572450
$974$	4.67949	0.149941
$975$	−24.2487	−0.776580
$976$	8.92820	0.285785
$977$	19.8564	0.635263	0.317631	−	0.948214i	$-0.397113\pi$
$977$	19.8564	0.635263	0.317631	+	0.948214i	$0.397113\pi$
$978$	14.9282	0.477351
$979$	−2.92820	−0.0935858
$980$	3.46410	0.110657
$981$	2.00000	0.0638551
$982$	19.6077	0.625707
$983$	8.78461	0.280186	0.140093	−	0.990138i	$-0.455260\pi$
$983$	8.78461	0.280186	0.140093	+	0.990138i	$0.455260\pi$
$984$	−2.00000	−0.0637577
$985$	−30.9282	−0.985454
$986$	3.21539	0.102399
$987$	−2.92820	−0.0932057
$988$	3.46410	0.110208
$989$	10.1436	0.322548
$990$	−5.07180	−0.161192
$991$	56.3923	1.79136	0.895680	−	0.444699i	$-0.146689\pi$
$991$	56.3923	1.79136	0.895680	+	0.444699i	$0.146689\pi$
$992$	6.92820	0.219971
$993$	−21.4641	−0.681143
$994$	−10.9282	−0.346622
$995$	58.1436	1.84328
$996$	−8.00000	−0.253490
$997$	−20.1436	−0.637954	−0.318977	−	0.947762i	$-0.603339\pi$
$997$	−20.1436	−0.637954	−0.318977	+	0.947762i	$0.603339\pi$
$998$	9.07180	0.287163
$999$	−10.0000	−0.316386

Twists

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

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

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +3.46410 q^{5} +1.00000 q^{6} -1.00000 q^{7} -1.00000 q^{8} +1.00000 q^{9} -3.46410 q^{10} +1.46410 q^{11} -1.00000 q^{12} +3.46410 q^{13} +1.00000 q^{14} -3.46410 q^{15} +1.00000 q^{16} +0.535898 q^{17} -1.00000 q^{18} +1.00000 q^{19} +3.46410 q^{20} +1.00000 q^{21} -1.46410 q^{22} +1.46410 q^{23} +1.00000 q^{24} +7.00000 q^{25} -3.46410 q^{26} -1.00000 q^{27} -1.00000 q^{28} -6.00000 q^{29} +3.46410 q^{30} -6.92820 q^{31} -1.00000 q^{32} -1.46410 q^{33} -0.535898 q^{34} -3.46410 q^{35} +1.00000 q^{36} +10.0000 q^{37} -1.00000 q^{38} -3.46410 q^{39} -3.46410 q^{40} -2.00000 q^{41} -1.00000 q^{42} +6.92820 q^{43} +1.46410 q^{44} +3.46410 q^{45} -1.46410 q^{46} -2.92820 q^{47} -1.00000 q^{48} +1.00000 q^{49} -7.00000 q^{50} -0.535898 q^{51} +3.46410 q^{52} +2.00000 q^{53} +1.00000 q^{54} +5.07180 q^{55} +1.00000 q^{56} -1.00000 q^{57} +6.00000 q^{58} +4.00000 q^{59} -3.46410 q^{60} +8.92820 q^{61} +6.92820 q^{62} -1.00000 q^{63} +1.00000 q^{64} +12.0000 q^{65} +1.46410 q^{66} +2.53590 q^{67} +0.535898 q^{68} -1.46410 q^{69} +3.46410 q^{70} -10.9282 q^{71} -1.00000 q^{72} +10.0000 q^{73} -10.0000 q^{74} -7.00000 q^{75} +1.00000 q^{76} -1.46410 q^{77} +3.46410 q^{78} +8.39230 q^{79} +3.46410 q^{80} +1.00000 q^{81} +2.00000 q^{82} +8.00000 q^{83} +1.00000 q^{84} +1.85641 q^{85} -6.92820 q^{86} +6.00000 q^{87} -1.46410 q^{88} -2.00000 q^{89} -3.46410 q^{90} -3.46410 q^{91} +1.46410 q^{92} +6.92820 q^{93} +2.92820 q^{94} +3.46410 q^{95} +1.00000 q^{96} +11.4641 q^{97} -1.00000 q^{98} +1.46410 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{6} - 2 q^{7} - 2 q^{8} + 2 q^{9}+O(q^{10}) \) 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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