LMFDB - Embedded newform 6046.2.a.e.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6046,2,Mod(1,6046)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6046, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("6046.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6046 = 2 \cdot 3023 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6046.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:	$48.2775530621$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	6046.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.43348 q^{3} +1.00000 q^{4} -1.73446 q^{5} -2.43348 q^{6} -1.67668 q^{7} +1.00000 q^{8} +2.92185 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.43348 q^{3} +1.00000 q^{4} -1.73446 q^{5} -2.43348 q^{6} -1.67668 q^{7} +1.00000 q^{8} +2.92185 q^{9} -1.73446 q^{10} -1.47743 q^{11} -2.43348 q^{12} -2.80106 q^{13} -1.67668 q^{14} +4.22077 q^{15} +1.00000 q^{16} +4.61875 q^{17} +2.92185 q^{18} -3.67566 q^{19} -1.73446 q^{20} +4.08018 q^{21} -1.47743 q^{22} +4.55945 q^{23} -2.43348 q^{24} -1.99166 q^{25} -2.80106 q^{26} +0.190180 q^{27} -1.67668 q^{28} +7.39932 q^{29} +4.22077 q^{30} +8.27128 q^{31} +1.00000 q^{32} +3.59531 q^{33} +4.61875 q^{34} +2.90813 q^{35} +2.92185 q^{36} -7.95068 q^{37} -3.67566 q^{38} +6.81634 q^{39} -1.73446 q^{40} +10.8781 q^{41} +4.08018 q^{42} -8.21581 q^{43} -1.47743 q^{44} -5.06782 q^{45} +4.55945 q^{46} +7.62833 q^{47} -2.43348 q^{48} -4.18874 q^{49} -1.99166 q^{50} -11.2397 q^{51} -2.80106 q^{52} +9.29471 q^{53} +0.190180 q^{54} +2.56254 q^{55} -1.67668 q^{56} +8.94465 q^{57} +7.39932 q^{58} -13.8888 q^{59} +4.22077 q^{60} -9.15887 q^{61} +8.27128 q^{62} -4.89901 q^{63} +1.00000 q^{64} +4.85832 q^{65} +3.59531 q^{66} -2.71897 q^{67} +4.61875 q^{68} -11.0954 q^{69} +2.90813 q^{70} +5.49990 q^{71} +2.92185 q^{72} +0.923118 q^{73} -7.95068 q^{74} +4.84667 q^{75} -3.67566 q^{76} +2.47718 q^{77} +6.81634 q^{78} +5.33352 q^{79} -1.73446 q^{80} -9.22835 q^{81} +10.8781 q^{82} +8.63102 q^{83} +4.08018 q^{84} -8.01103 q^{85} -8.21581 q^{86} -18.0061 q^{87} -1.47743 q^{88} -0.766957 q^{89} -5.06782 q^{90} +4.69649 q^{91} +4.55945 q^{92} -20.1280 q^{93} +7.62833 q^{94} +6.37527 q^{95} -2.43348 q^{96} +3.33078 q^{97} -4.18874 q^{98} -4.31683 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) $ 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * 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
$3$	−2.43348	−1.40497	−0.702487	−	0.711697i	$-0.747927\pi$
$3$	−2.43348	−1.40497	−0.702487	+	0.711697i	$0.747927\pi$
$4$	1.00000	0.500000
$5$	−1.73446	−0.775673	−0.387836	−	0.921728i	$-0.626777\pi$
$5$	−1.73446	−0.775673	−0.387836	+	0.921728i	$0.626777\pi$
$6$	−2.43348	−0.993466
$7$	−1.67668	−0.633726	−0.316863	−	0.948471i	$-0.602630\pi$
$7$	−1.67668	−0.633726	−0.316863	+	0.948471i	$0.602630\pi$
$8$	1.00000	0.353553
$9$	2.92185	0.973950
$10$	−1.73446	−0.548483
$11$	−1.47743	−0.445463	−0.222731	−	0.974880i	$-0.571497\pi$
$11$	−1.47743	−0.445463	−0.222731	+	0.974880i	$0.571497\pi$
$12$	−2.43348	−0.702487
$13$	−2.80106	−0.776874	−0.388437	−	0.921475i	$-0.626985\pi$
$13$	−2.80106	−0.776874	−0.388437	+	0.921475i	$0.626985\pi$
$14$	−1.67668	−0.448112
$15$	4.22077	1.08980
$16$	1.00000	0.250000
$17$	4.61875	1.12021	0.560106	−	0.828421i	$-0.310760\pi$
$17$	4.61875	1.12021	0.560106	+	0.828421i	$0.310760\pi$
$18$	2.92185	0.688686
$19$	−3.67566	−0.843253	−0.421627	−	0.906770i	$-0.638541\pi$
$19$	−3.67566	−0.843253	−0.421627	+	0.906770i	$0.638541\pi$
$20$	−1.73446	−0.387836
$21$	4.08018	0.890368
$22$	−1.47743	−0.314990
$23$	4.55945	0.950711	0.475356	−	0.879794i	$-0.342319\pi$
$23$	4.55945	0.950711	0.475356	+	0.879794i	$0.342319\pi$
$24$	−2.43348	−0.496733
$25$	−1.99166	−0.398332
$26$	−2.80106	−0.549333
$27$	0.190180	0.0366002
$28$	−1.67668	−0.316863
$29$	7.39932	1.37402	0.687009	−	0.726649i	$-0.258923\pi$
$29$	7.39932	1.37402	0.687009	+	0.726649i	$0.258923\pi$
$30$	4.22077	0.770604
$31$	8.27128	1.48557	0.742783	−	0.669532i	$-0.233505\pi$
$31$	8.27128	1.48557	0.742783	+	0.669532i	$0.233505\pi$
$32$	1.00000	0.176777
$33$	3.59531	0.625863
$34$	4.61875	0.792110
$35$	2.90813	0.491564
$36$	2.92185	0.486975
$37$	−7.95068	−1.30708	−0.653542	−	0.756890i	$-0.726718\pi$
$37$	−7.95068	−1.30708	−0.653542	+	0.756890i	$0.726718\pi$
$38$	−3.67566	−0.596270
$39$	6.81634	1.09149
$40$	−1.73446	−0.274242
$41$	10.8781	1.69888	0.849439	−	0.527687i	$-0.176941\pi$
$41$	10.8781	1.69888	0.849439	+	0.527687i	$0.176941\pi$
$42$	4.08018	0.629586
$43$	−8.21581	−1.25290	−0.626450	−	0.779462i	$-0.715493\pi$
$43$	−8.21581	−1.25290	−0.626450	+	0.779462i	$0.715493\pi$
$44$	−1.47743	−0.222731
$45$	−5.06782	−0.755466
$46$	4.55945	0.672254
$47$	7.62833	1.11271	0.556353	−	0.830946i	$-0.312200\pi$
$47$	7.62833	1.11271	0.556353	+	0.830946i	$0.312200\pi$
$48$	−2.43348	−0.351243
$49$	−4.18874	−0.598391
$50$	−1.99166	−0.281663
$51$	−11.2397	−1.57387
$52$	−2.80106	−0.388437
$53$	9.29471	1.27673	0.638363	−	0.769735i	$-0.279612\pi$
$53$	9.29471	1.27673	0.638363	+	0.769735i	$0.279612\pi$
$54$	0.190180	0.0258803
$55$	2.56254	0.345533
$56$	−1.67668	−0.224056
$57$	8.94465	1.18475
$58$	7.39932	0.971578
$59$	−13.8888	−1.80817	−0.904087	−	0.427349i	$-0.859447\pi$
$59$	−13.8888	−1.80817	−0.904087	+	0.427349i	$0.859447\pi$
$60$	4.22077	0.544900
$61$	−9.15887	−1.17267	−0.586337	−	0.810068i	$-0.699430\pi$
$61$	−9.15887	−1.17267	−0.586337	+	0.810068i	$0.699430\pi$
$62$	8.27128	1.05045
$63$	−4.89901	−0.617217
$64$	1.00000	0.125000
$65$	4.85832	0.602600
$66$	3.59531	0.442552
$67$	−2.71897	−0.332175	−0.166087	−	0.986111i	$-0.553113\pi$
$67$	−2.71897	−0.332175	−0.166087	+	0.986111i	$0.553113\pi$
$68$	4.61875	0.560106
$69$	−11.0954	−1.33572
$70$	2.90813	0.347588
$71$	5.49990	0.652718	0.326359	−	0.945246i	$-0.394178\pi$
$71$	5.49990	0.652718	0.326359	+	0.945246i	$0.394178\pi$
$72$	2.92185	0.344343
$73$	0.923118	0.108043	0.0540214	−	0.998540i	$-0.482796\pi$
$73$	0.923118	0.108043	0.0540214	+	0.998540i	$0.482796\pi$
$74$	−7.95068	−0.924248
$75$	4.84667	0.559646
$76$	−3.67566	−0.421627
$77$	2.47718	0.282301
$78$	6.81634	0.771798
$79$	5.33352	0.600068	0.300034	−	0.953929i	$-0.403002\pi$
$79$	5.33352	0.600068	0.300034	+	0.953929i	$0.403002\pi$
$80$	−1.73446	−0.193918
$81$	−9.22835	−1.02537
$82$	10.8781	1.20129
$83$	8.63102	0.947377	0.473689	−	0.880692i	$-0.342922\pi$
$83$	8.63102	0.947377	0.473689	+	0.880692i	$0.342922\pi$
$84$	4.08018	0.445184
$85$	−8.01103	−0.868918
$86$	−8.21581	−0.885934
$87$	−18.0061	−1.93046
$88$	−1.47743	−0.157495
$89$	−0.766957	−0.0812973	−0.0406486	−	0.999174i	$-0.512942\pi$
$89$	−0.766957	−0.0812973	−0.0406486	+	0.999174i	$0.512942\pi$
$90$	−5.06782	−0.534195
$91$	4.69649	0.492326
$92$	4.55945	0.475356
$93$	−20.1280	−2.08718
$94$	7.62833	0.786803
$95$	6.37527	0.654089
$96$	−2.43348	−0.248367
$97$	3.33078	0.338189	0.169095	−	0.985600i	$-0.445916\pi$
$97$	3.33078	0.338189	0.169095	+	0.985600i	$0.445916\pi$
$98$	−4.18874	−0.423126
$99$	−4.31683	−0.433858
$100$	−1.99166	−0.199166
$101$	4.48831	0.446604	0.223302	−	0.974749i	$-0.428316\pi$
$101$	4.48831	0.446604	0.223302	+	0.974749i	$0.428316\pi$
$102$	−11.2397	−1.11289
$103$	2.05394	0.202381	0.101190	−	0.994867i	$-0.467735\pi$
$103$	2.05394	0.202381	0.101190	+	0.994867i	$0.467735\pi$
$104$	−2.80106	−0.274667
$105$	−7.07690	−0.690634
$106$	9.29471	0.902782
$107$	−15.2769	−1.47687	−0.738436	−	0.674323i	$-0.764435\pi$
$107$	−15.2769	−1.47687	−0.738436	+	0.674323i	$0.764435\pi$
$108$	0.190180	0.0183001
$109$	−15.1271	−1.44891	−0.724455	−	0.689322i	$-0.757909\pi$
$109$	−15.1271	−1.44891	−0.724455	+	0.689322i	$0.757909\pi$
$110$	2.56254	0.244329
$111$	19.3479	1.83642
$112$	−1.67668	−0.158432
$113$	7.89675	0.742864	0.371432	−	0.928460i	$-0.378867\pi$
$113$	7.89675	0.742864	0.371432	+	0.928460i	$0.378867\pi$
$114$	8.94465	0.837744
$115$	−7.90817	−0.737441
$116$	7.39932	0.687009
$117$	−8.18427	−0.756636
$118$	−13.8888	−1.27857
$119$	−7.74418	−0.709908
$120$	4.22077	0.385302
$121$	−8.81719	−0.801563
$122$	−9.15887	−0.829205
$123$	−26.4718	−2.38688
$124$	8.27128	0.742783
$125$	12.1267	1.08465
$126$	−4.89901	−0.436439
$127$	−11.2577	−0.998959	−0.499479	−	0.866326i	$-0.666475\pi$
$127$	−11.2577	−0.998959	−0.499479	+	0.866326i	$0.666475\pi$
$128$	1.00000	0.0883883
$129$	19.9930	1.76029
$130$	4.85832	0.426103
$131$	−11.8547	−1.03575	−0.517875	−	0.855456i	$-0.673277\pi$
$131$	−11.8547	−1.03575	−0.517875	+	0.855456i	$0.673277\pi$
$132$	3.59531	0.312931
$133$	6.16291	0.534392
$134$	−2.71897	−0.234883
$135$	−0.329860	−0.0283898
$136$	4.61875	0.396055
$137$	5.49625	0.469576	0.234788	−	0.972047i	$-0.424560\pi$
$137$	5.49625	0.469576	0.234788	+	0.972047i	$0.424560\pi$
$138$	−11.0954	−0.944499
$139$	−15.2731	−1.29545	−0.647723	−	0.761876i	$-0.724279\pi$
$139$	−15.2731	−1.29545	−0.647723	+	0.761876i	$0.724279\pi$
$140$	2.90813	0.245782
$141$	−18.5634	−1.56332
$142$	5.49990	0.461541
$143$	4.13838	0.346068
$144$	2.92185	0.243487
$145$	−12.8338	−1.06579
$146$	0.923118	0.0763978
$147$	10.1932	0.840723
$148$	−7.95068	−0.653542
$149$	6.17203	0.505633	0.252816	−	0.967514i	$-0.418643\pi$
$149$	6.17203	0.505633	0.252816	+	0.967514i	$0.418643\pi$
$150$	4.84667	0.395729
$151$	8.95488	0.728738	0.364369	−	0.931255i	$-0.381285\pi$
$151$	8.95488	0.728738	0.364369	+	0.931255i	$0.381285\pi$
$152$	−3.67566	−0.298135
$153$	13.4953	1.09103
$154$	2.47718	0.199617
$155$	−14.3462	−1.15231
$156$	6.81634	0.545744
$157$	13.6153	1.08662	0.543312	−	0.839531i	$-0.317170\pi$
$157$	13.6153	1.08662	0.543312	+	0.839531i	$0.317170\pi$
$158$	5.33352	0.424312
$159$	−22.6185	−1.79377
$160$	−1.73446	−0.137121
$161$	−7.64475	−0.602491
$162$	−9.22835	−0.725047
$163$	−20.1208	−1.57598	−0.787992	−	0.615685i	$-0.788879\pi$
$163$	−20.1208	−1.57598	−0.787992	+	0.615685i	$0.788879\pi$
$164$	10.8781	0.849439
$165$	−6.23591	−0.485465
$166$	8.63102	0.669897
$167$	−18.9475	−1.46620	−0.733100	−	0.680120i	$-0.761927\pi$
$167$	−18.9475	−1.46620	−0.733100	+	0.680120i	$0.761927\pi$
$168$	4.08018	0.314793
$169$	−5.15406	−0.396466
$170$	−8.01103	−0.614418
$171$	−10.7397	−0.821286
$172$	−8.21581	−0.626450
$173$	6.80237	0.517175	0.258587	−	0.965988i	$-0.416743\pi$
$173$	6.80237	0.517175	0.258587	+	0.965988i	$0.416743\pi$
$174$	−18.0061	−1.36504
$175$	3.33938	0.252433
$176$	−1.47743	−0.111366
$177$	33.7983	2.54043
$178$	−0.766957	−0.0574859
$179$	17.9187	1.33931	0.669654	−	0.742673i	$-0.266442\pi$
$179$	17.9187	1.33931	0.669654	+	0.742673i	$0.266442\pi$
$180$	−5.06782	−0.377733
$181$	11.1532	0.829012	0.414506	−	0.910046i	$-0.363954\pi$
$181$	11.1532	0.829012	0.414506	+	0.910046i	$0.363954\pi$
$182$	4.69649	0.348127
$183$	22.2880	1.64757
$184$	4.55945	0.336127
$185$	13.7901	1.01387
$186$	−20.1280	−1.47586
$187$	−6.82390	−0.499013
$188$	7.62833	0.556353
$189$	−0.318872	−0.0231945
$190$	6.37527	0.462510
$191$	−24.6453	−1.78327	−0.891636	−	0.452753i	$-0.850442\pi$
$191$	−24.6453	−1.78327	−0.891636	+	0.452753i	$0.850442\pi$
$192$	−2.43348	−0.175622
$193$	5.02429	0.361656	0.180828	−	0.983515i	$-0.442122\pi$
$193$	5.02429	0.361656	0.180828	+	0.983515i	$0.442122\pi$
$194$	3.33078	0.239136
$195$	−11.8226	−0.846637
$196$	−4.18874	−0.299195
$197$	11.9986	0.854863	0.427432	−	0.904048i	$-0.359418\pi$
$197$	11.9986	0.854863	0.427432	+	0.904048i	$0.359418\pi$
$198$	−4.31683	−0.306784
$199$	15.6396	1.10867	0.554333	−	0.832295i	$-0.312974\pi$
$199$	15.6396	1.10867	0.554333	+	0.832295i	$0.312974\pi$
$200$	−1.99166	−0.140832
$201$	6.61656	0.466696
$202$	4.48831	0.315796
$203$	−12.4063	−0.870752
$204$	−11.2397	−0.786934
$205$	−18.8676	−1.31777
$206$	2.05394	0.143105
$207$	13.3220	0.925945
$208$	−2.80106	−0.194219
$209$	5.43053	0.375638
$210$	−7.07690	−0.488352
$211$	−1.48562	−0.102274	−0.0511372	−	0.998692i	$-0.516285\pi$
$211$	−1.48562	−0.102274	−0.0511372	+	0.998692i	$0.516285\pi$
$212$	9.29471	0.638363
$213$	−13.3839	−0.917051
$214$	−15.2769	−1.04431
$215$	14.2500	0.971840
$216$	0.190180	0.0129401
$217$	−13.8683	−0.941442
$218$	−15.1271	−1.02453
$219$	−2.24639	−0.151797
$220$	2.56254	0.172767
$221$	−12.9374	−0.870264
$222$	19.3479	1.29854
$223$	−13.5411	−0.906780	−0.453390	−	0.891312i	$-0.649786\pi$
$223$	−13.5411	−0.906780	−0.453390	+	0.891312i	$0.649786\pi$
$224$	−1.67668	−0.112028
$225$	−5.81933	−0.387955
$226$	7.89675	0.525284
$227$	−4.86914	−0.323176	−0.161588	−	0.986858i	$-0.551662\pi$
$227$	−4.86914	−0.323176	−0.161588	+	0.986858i	$0.551662\pi$
$228$	8.94465	0.592374
$229$	−6.93924	−0.458558	−0.229279	−	0.973361i	$-0.573637\pi$
$229$	−6.93924	−0.458558	−0.229279	+	0.973361i	$0.573637\pi$
$230$	−7.90817	−0.521449
$231$	−6.02819	−0.396626
$232$	7.39932	0.485789
$233$	12.6118	0.826224	0.413112	−	0.910680i	$-0.364442\pi$
$233$	12.6118	0.826224	0.413112	+	0.910680i	$0.364442\pi$
$234$	−8.18427	−0.535023
$235$	−13.2310	−0.863096
$236$	−13.8888	−0.904087
$237$	−12.9790	−0.843079
$238$	−7.74418	−0.501981
$239$	−25.2641	−1.63420	−0.817099	−	0.576497i	$-0.804419\pi$
$239$	−25.2641	−1.63420	−0.817099	+	0.576497i	$0.804419\pi$
$240$	4.22077	0.272450
$241$	1.81987	0.117228	0.0586141	−	0.998281i	$-0.481332\pi$
$241$	1.81987	0.117228	0.0586141	+	0.998281i	$0.481332\pi$
$242$	−8.81719	−0.566791
$243$	21.8865	1.40402
$244$	−9.15887	−0.586337
$245$	7.26518	0.464156
$246$	−26.4718	−1.68778
$247$	10.2957	0.655102
$248$	8.27128	0.525227
$249$	−21.0035	−1.33104
$250$	12.1267	0.766962
$251$	3.84973	0.242993	0.121496	−	0.992592i	$-0.461231\pi$
$251$	3.84973	0.242993	0.121496	+	0.992592i	$0.461231\pi$
$252$	−4.89901	−0.308609
$253$	−6.73628	−0.423506
$254$	−11.2577	−0.706371
$255$	19.4947	1.22081
$256$	1.00000	0.0625000
$257$	−24.0592	−1.50077	−0.750385	−	0.661001i	$-0.770132\pi$
$257$	−24.0592	−1.50077	−0.750385	+	0.661001i	$0.770132\pi$
$258$	19.9930	1.24471
$259$	13.3308	0.828334
$260$	4.85832	0.301300
$261$	21.6197	1.33822
$262$	−11.8547	−0.732386
$263$	−23.0108	−1.41890	−0.709452	−	0.704753i	$-0.751058\pi$
$263$	−23.0108	−1.41890	−0.709452	+	0.704753i	$0.751058\pi$
$264$	3.59531	0.221276
$265$	−16.1213	−0.990321
$266$	6.16291	0.377872
$267$	1.86638	0.114220
$268$	−2.71897	−0.166087
$269$	−23.4563	−1.43016	−0.715079	−	0.699043i	$-0.753609\pi$
$269$	−23.4563	−1.43016	−0.715079	+	0.699043i	$0.753609\pi$
$270$	−0.329860	−0.0200746
$271$	17.8028	1.08144	0.540722	−	0.841201i	$-0.318151\pi$
$271$	17.8028	1.08144	0.540722	+	0.841201i	$0.318151\pi$
$272$	4.61875	0.280053
$273$	−11.4288	−0.691704
$274$	5.49625	0.332041
$275$	2.94254	0.177442
$276$	−11.0954	−0.667862
$277$	−17.0890	−1.02678	−0.513390	−	0.858156i	$-0.671610\pi$
$277$	−17.0890	−1.02678	−0.513390	+	0.858156i	$0.671610\pi$
$278$	−15.2731	−0.916019
$279$	24.1674	1.44687
$280$	2.90813	0.173794
$281$	−18.1072	−1.08019	−0.540094	−	0.841605i	$-0.681611\pi$
$281$	−18.1072	−1.08019	−0.540094	+	0.841605i	$0.681611\pi$
$282$	−18.5634	−1.10544
$283$	−16.6038	−0.986995	−0.493497	−	0.869747i	$-0.664282\pi$
$283$	−16.6038	−0.986995	−0.493497	+	0.869747i	$0.664282\pi$
$284$	5.49990	0.326359
$285$	−15.5141	−0.918977
$286$	4.13838	0.244707
$287$	−18.2392	−1.07662
$288$	2.92185	0.172172
$289$	4.33290	0.254876
$290$	−12.8338	−0.753626
$291$	−8.10540	−0.475147
$292$	0.923118	0.0540214
$293$	15.9968	0.934541	0.467270	−	0.884114i	$-0.345237\pi$
$293$	15.9968	0.934541	0.467270	+	0.884114i	$0.345237\pi$
$294$	10.1932	0.594481
$295$	24.0896	1.40255
$296$	−7.95068	−0.462124
$297$	−0.280979	−0.0163040
$298$	6.17203	0.357536
$299$	−12.7713	−0.738583
$300$	4.84667	0.279823
$301$	13.7753	0.793995
$302$	8.95488	0.515295
$303$	−10.9222	−0.627466
$304$	−3.67566	−0.210813
$305$	15.8857	0.909610
$306$	13.4953	0.771475
$307$	5.76038	0.328762	0.164381	−	0.986397i	$-0.447437\pi$
$307$	5.76038	0.328762	0.164381	+	0.986397i	$0.447437\pi$
$308$	2.47718	0.141151
$309$	−4.99824	−0.284340
$310$	−14.3462	−0.814808
$311$	−1.95681	−0.110961	−0.0554804	−	0.998460i	$-0.517669\pi$
$311$	−1.95681	−0.110961	−0.0554804	+	0.998460i	$0.517669\pi$
$312$	6.81634	0.385899
$313$	3.37010	0.190490	0.0952448	−	0.995454i	$-0.469637\pi$
$313$	3.37010	0.190490	0.0952448	+	0.995454i	$0.469637\pi$
$314$	13.6153	0.768359
$315$	8.49712	0.478759
$316$	5.33352	0.300034
$317$	−15.8004	−0.887436	−0.443718	−	0.896166i	$-0.646341\pi$
$317$	−15.8004	−0.887436	−0.443718	+	0.896166i	$0.646341\pi$
$318$	−22.6185	−1.26838
$319$	−10.9320	−0.612074
$320$	−1.73446	−0.0969591
$321$	37.1761	2.07497
$322$	−7.64475	−0.426025
$323$	−16.9770	−0.944623
$324$	−9.22835	−0.512686
$325$	5.57876	0.309454
$326$	−20.1208	−1.11439
$327$	36.8115	2.03568
$328$	10.8781	0.600644
$329$	−12.7903	−0.705152
$330$	−6.23591	−0.343275
$331$	−27.2807	−1.49948	−0.749741	−	0.661731i	$-0.769822\pi$
$331$	−27.2807	−1.49948	−0.749741	+	0.661731i	$0.769822\pi$
$332$	8.63102	0.473689
$333$	−23.2307	−1.27303
$334$	−18.9475	−1.03676
$335$	4.71593	0.257659
$336$	4.08018	0.222592
$337$	−5.86743	−0.319619	−0.159810	−	0.987148i	$-0.551088\pi$
$337$	−5.86743	−0.319619	−0.159810	+	0.987148i	$0.551088\pi$
$338$	−5.15406	−0.280344
$339$	−19.2166	−1.04370
$340$	−8.01103	−0.434459
$341$	−12.2203	−0.661764
$342$	−10.7397	−0.580737
$343$	18.7600	1.01294
$344$	−8.21581	−0.442967
$345$	19.2444	1.03608
$346$	6.80237	0.365698
$347$	15.7387	0.844899	0.422449	−	0.906387i	$-0.361170\pi$
$347$	15.7387	0.844899	0.422449	+	0.906387i	$0.361170\pi$
$348$	−18.0061	−0.965230
$349$	20.3168	1.08754	0.543768	−	0.839236i	$-0.316997\pi$
$349$	20.3168	1.08754	0.543768	+	0.839236i	$0.316997\pi$
$350$	3.33938	0.178497
$351$	−0.532707	−0.0284338
$352$	−1.47743	−0.0787474
$353$	−19.7115	−1.04914	−0.524568	−	0.851368i	$-0.675773\pi$
$353$	−19.7115	−1.04914	−0.524568	+	0.851368i	$0.675773\pi$
$354$	33.7983	1.79636
$355$	−9.53933	−0.506295
$356$	−0.766957	−0.0406486
$357$	18.8454	0.997402
$358$	17.9187	0.947034
$359$	−9.58105	−0.505669	−0.252834	−	0.967510i	$-0.581363\pi$
$359$	−9.58105	−0.505669	−0.252834	+	0.967510i	$0.581363\pi$
$360$	−5.06782	−0.267098
$361$	−5.48955	−0.288924
$362$	11.1532	0.586200
$363$	21.4565	1.12617
$364$	4.69649	0.246163
$365$	−1.60111	−0.0838058
$366$	22.2880	1.16501
$367$	−9.51485	−0.496671	−0.248335	−	0.968674i	$-0.579884\pi$
$367$	−9.51485	−0.496671	−0.248335	+	0.968674i	$0.579884\pi$
$368$	4.55945	0.237678
$369$	31.7842	1.65462
$370$	13.7901	0.716914
$371$	−15.5843	−0.809095
$372$	−20.1280	−1.04359
$373$	3.17222	0.164252	0.0821258	−	0.996622i	$-0.473829\pi$
$373$	3.17222	0.164252	0.0821258	+	0.996622i	$0.473829\pi$
$374$	−6.82390	−0.352855
$375$	−29.5102	−1.52390
$376$	7.62833	0.393401
$377$	−20.7259	−1.06744
$378$	−0.318872	−0.0164010
$379$	−12.2390	−0.628675	−0.314338	−	0.949311i	$-0.601782\pi$
$379$	−12.2390	−0.628675	−0.314338	+	0.949311i	$0.601782\pi$
$380$	6.37527	0.327044
$381$	27.3954	1.40351
$382$	−24.6453	−1.26096
$383$	31.0014	1.58410	0.792048	−	0.610458i	$-0.209015\pi$
$383$	31.0014	1.58410	0.792048	+	0.610458i	$0.209015\pi$
$384$	−2.43348	−0.124183
$385$	−4.29657	−0.218973
$386$	5.02429	0.255729
$387$	−24.0054	−1.22026
$388$	3.33078	0.169095
$389$	14.4603	0.733165	0.366583	−	0.930385i	$-0.380528\pi$
$389$	14.4603	0.733165	0.366583	+	0.930385i	$0.380528\pi$
$390$	−11.8226	−0.598663
$391$	21.0590	1.06500
$392$	−4.18874	−0.211563
$393$	28.8483	1.45520
$394$	11.9986	0.604480
$395$	−9.25076	−0.465456
$396$	−4.31683	−0.216929
$397$	−4.02599	−0.202058	−0.101029	−	0.994883i	$-0.532214\pi$
$397$	−4.02599	−0.202058	−0.101029	+	0.994883i	$0.532214\pi$
$398$	15.6396	0.783945
$399$	−14.9973	−0.750806
$400$	−1.99166	−0.0995830
$401$	1.76890	0.0883348	0.0441674	−	0.999024i	$-0.485937\pi$
$401$	1.76890	0.0883348	0.0441674	+	0.999024i	$0.485937\pi$
$402$	6.61656	0.330004
$403$	−23.1684	−1.15410
$404$	4.48831	0.223302
$405$	16.0062	0.795353
$406$	−12.4063	−0.615714
$407$	11.7466	0.582257
$408$	−11.2397	−0.556447
$409$	−4.45546	−0.220308	−0.110154	−	0.993915i	$-0.535134\pi$
$409$	−4.45546	−0.220308	−0.110154	+	0.993915i	$0.535134\pi$
$410$	−18.8676	−0.931806
$411$	−13.3750	−0.659742
$412$	2.05394	0.101190
$413$	23.2872	1.14589
$414$	13.3220	0.654742
$415$	−14.9701	−0.734855
$416$	−2.80106	−0.137333
$417$	37.1668	1.82007
$418$	5.43053	0.265616
$419$	−5.29702	−0.258776	−0.129388	−	0.991594i	$-0.541301\pi$
$419$	−5.29702	−0.258776	−0.129388	+	0.991594i	$0.541301\pi$
$420$	−7.07690	−0.345317
$421$	−2.01222	−0.0980696	−0.0490348	−	0.998797i	$-0.515615\pi$
$421$	−2.01222	−0.0980696	−0.0490348	+	0.998797i	$0.515615\pi$
$422$	−1.48562	−0.0723189
$423$	22.2888	1.08372
$424$	9.29471	0.451391
$425$	−9.19899	−0.446216
$426$	−13.3839	−0.648453
$427$	15.3565	0.743154
$428$	−15.2769	−0.738436
$429$	−10.0707	−0.486217
$430$	14.2500	0.687194
$431$	−33.3323	−1.60556	−0.802781	−	0.596274i	$-0.796647\pi$
$431$	−33.3323	−1.60556	−0.802781	+	0.596274i	$0.796647\pi$
$432$	0.190180	0.00915006
$433$	−23.8617	−1.14672	−0.573360	−	0.819303i	$-0.694360\pi$
$433$	−23.8617	−1.14672	−0.573360	+	0.819303i	$0.694360\pi$
$434$	−13.8683	−0.665700
$435$	31.2308	1.49740
$436$	−15.1271	−0.724455
$437$	−16.7590	−0.801690
$438$	−2.24639	−0.107337
$439$	−28.6508	−1.36743	−0.683714	−	0.729750i	$-0.739636\pi$
$439$	−28.6508	−1.36743	−0.683714	+	0.729750i	$0.739636\pi$
$440$	2.56254	0.122164
$441$	−12.2389	−0.582803
$442$	−12.9374	−0.615370
$443$	12.4509	0.591560	0.295780	−	0.955256i	$-0.404420\pi$
$443$	12.4509	0.591560	0.295780	+	0.955256i	$0.404420\pi$
$444$	19.3479	0.918209
$445$	1.33025	0.0630601
$446$	−13.5411	−0.641191
$447$	−15.0196	−0.710400
$448$	−1.67668	−0.0792158
$449$	19.1697	0.904674	0.452337	−	0.891847i	$-0.350590\pi$
$449$	19.1697	0.904674	0.452337	+	0.891847i	$0.350590\pi$
$450$	−5.81933	−0.274326
$451$	−16.0717	−0.756786
$452$	7.89675	0.371432
$453$	−21.7916	−1.02386
$454$	−4.86914	−0.228520
$455$	−8.14586	−0.381884
$456$	8.94465	0.418872
$457$	−11.1950	−0.523679	−0.261839	−	0.965111i	$-0.584329\pi$
$457$	−11.1950	−0.523679	−0.261839	+	0.965111i	$0.584329\pi$
$458$	−6.93924	−0.324249
$459$	0.878397	0.0410001
$460$	−7.90817	−0.368720
$461$	24.9647	1.16272	0.581362	−	0.813645i	$-0.302520\pi$
$461$	24.9647	1.16272	0.581362	+	0.813645i	$0.302520\pi$
$462$	−6.02819	−0.280457
$463$	33.4913	1.55647	0.778236	−	0.627972i	$-0.216115\pi$
$463$	33.4913	1.55647	0.778236	+	0.627972i	$0.216115\pi$
$464$	7.39932	0.343505
$465$	34.9112	1.61897
$466$	12.6118	0.584229
$467$	−36.8368	−1.70460	−0.852301	−	0.523051i	$-0.824794\pi$
$467$	−36.8368	−1.70460	−0.852301	+	0.523051i	$0.824794\pi$
$468$	−8.18427	−0.378318
$469$	4.55884	0.210508
$470$	−13.2310	−0.610301
$471$	−33.1327	−1.52668
$472$	−13.8888	−0.639286
$473$	12.1383	0.558120
$474$	−12.9790	−0.596147
$475$	7.32066	0.335895
$476$	−7.74418	−0.354954
$477$	27.1577	1.24347
$478$	−25.2641	−1.15555
$479$	−15.0474	−0.687535	−0.343768	−	0.939055i	$-0.611703\pi$
$479$	−15.0474	−0.687535	−0.343768	+	0.939055i	$0.611703\pi$
$480$	4.22077	0.192651
$481$	22.2703	1.01544
$482$	1.81987	0.0828929
$483$	18.6034	0.846483
$484$	−8.81719	−0.400782
$485$	−5.77709	−0.262324
$486$	21.8865	0.992792
$487$	−8.18508	−0.370901	−0.185451	−	0.982654i	$-0.559374\pi$
$487$	−8.18508	−0.370901	−0.185451	+	0.982654i	$0.559374\pi$
$488$	−9.15887	−0.414603
$489$	48.9637	2.21422
$490$	7.26518	0.328208
$491$	−32.6516	−1.47355	−0.736773	−	0.676140i	$-0.763651\pi$
$491$	−32.6516	−1.47355	−0.736773	+	0.676140i	$0.763651\pi$
$492$	−26.4718	−1.19344
$493$	34.1756	1.53919
$494$	10.2957	0.463227
$495$	7.48736	0.336532
$496$	8.27128	0.371392
$497$	−9.22158	−0.413644
$498$	−21.0035	−0.941187
$499$	−8.22805	−0.368338	−0.184169	−	0.982895i	$-0.558959\pi$
$499$	−8.22805	−0.368338	−0.184169	+	0.982895i	$0.558959\pi$
$500$	12.1267	0.542324
$501$	46.1084	2.05997
$502$	3.84973	0.171822
$503$	−9.87075	−0.440115	−0.220057	−	0.975487i	$-0.570624\pi$
$503$	−9.87075	−0.440115	−0.220057	+	0.975487i	$0.570624\pi$
$504$	−4.89901	−0.218219
$505$	−7.78478	−0.346418
$506$	−6.73628	−0.299464
$507$	12.5423	0.557024
$508$	−11.2577	−0.499479
$509$	−23.0106	−1.01993	−0.509964	−	0.860196i	$-0.670341\pi$
$509$	−23.0106	−1.01993	−0.509964	+	0.860196i	$0.670341\pi$
$510$	19.4947	0.863241
$511$	−1.54778	−0.0684696
$512$	1.00000	0.0441942
$513$	−0.699038	−0.0308633
$514$	−24.0592	−1.06121
$515$	−3.56247	−0.156981
$516$	19.9930	0.880145
$517$	−11.2703	−0.495669
$518$	13.3308	0.585720
$519$	−16.5535	−0.726617
$520$	4.85832	0.213051
$521$	2.21300	0.0969534	0.0484767	−	0.998824i	$-0.484563\pi$
$521$	2.21300	0.0969534	0.0484767	+	0.998824i	$0.484563\pi$
$522$	21.6197	0.946268
$523$	43.6544	1.90887	0.954436	−	0.298415i	$-0.0964579\pi$
$523$	43.6544	1.90887	0.954436	+	0.298415i	$0.0964579\pi$
$524$	−11.8547	−0.517875
$525$	−8.12633	−0.354662
$526$	−23.0108	−1.00332
$527$	38.2030	1.66415
$528$	3.59531	0.156466
$529$	−2.21141	−0.0961481
$530$	−16.1213	−0.700263
$531$	−40.5811	−1.76107
$532$	6.16291	0.267196
$533$	−30.4703	−1.31981
$534$	1.86638	0.0807661
$535$	26.4971	1.14557
$536$	−2.71897	−0.117441
$537$	−43.6049	−1.88169
$538$	−23.4563	−1.01127
$539$	6.18857	0.266561
$540$	−0.329860	−0.0141949
$541$	1.22422	0.0526332	0.0263166	−	0.999654i	$-0.491622\pi$
$541$	1.22422	0.0526332	0.0263166	+	0.999654i	$0.491622\pi$
$542$	17.8028	0.764697
$543$	−27.1412	−1.16474
$544$	4.61875	0.198027
$545$	26.2373	1.12388
$546$	−11.4288	−0.489109
$547$	5.84038	0.249717	0.124858	−	0.992175i	$-0.460152\pi$
$547$	5.84038	0.249717	0.124858	+	0.992175i	$0.460152\pi$
$548$	5.49625	0.234788
$549$	−26.7608	−1.14212
$550$	2.94254	0.125470
$551$	−27.1973	−1.15865
$552$	−11.0954	−0.472250
$553$	−8.94261	−0.380279
$554$	−17.0890	−0.726043
$555$	−33.5580	−1.42446
$556$	−15.2731	−0.647723
$557$	4.54052	0.192388	0.0961941	−	0.995363i	$-0.469333\pi$
$557$	4.54052	0.192388	0.0961941	+	0.995363i	$0.469333\pi$
$558$	24.1674	1.02309
$559$	23.0130	0.973345
$560$	2.90813	0.122891
$561$	16.6059	0.701100
$562$	−18.1072	−0.763808
$563$	37.0810	1.56278	0.781389	−	0.624044i	$-0.214511\pi$
$563$	37.0810	1.56278	0.781389	+	0.624044i	$0.214511\pi$
$564$	−18.5634	−0.781662
$565$	−13.6966	−0.576219
$566$	−16.6038	−0.697911
$567$	15.4730	0.649805
$568$	5.49990	0.230771
$569$	−2.99845	−0.125702	−0.0628508	−	0.998023i	$-0.520019\pi$
$569$	−2.99845	−0.125702	−0.0628508	+	0.998023i	$0.520019\pi$
$570$	−15.5141	−0.649815
$571$	−28.6353	−1.19835	−0.599175	−	0.800618i	$-0.704505\pi$
$571$	−28.6353	−1.19835	−0.599175	+	0.800618i	$0.704505\pi$
$572$	4.13838	0.173034
$573$	59.9740	2.50545
$574$	−18.2392	−0.761288
$575$	−9.08087	−0.378699
$576$	2.92185	0.121744
$577$	30.4725	1.26859	0.634294	−	0.773092i	$-0.281291\pi$
$577$	30.4725	1.26859	0.634294	+	0.773092i	$0.281291\pi$
$578$	4.33290	0.180225
$579$	−12.2265	−0.508117
$580$	−12.8338	−0.532894
$581$	−14.4715	−0.600378
$582$	−8.10540	−0.335980
$583$	−13.7323	−0.568734
$584$	0.923118	0.0381989
$585$	14.1953	0.586902
$586$	15.9968	0.660820
$587$	−10.6453	−0.439378	−0.219689	−	0.975570i	$-0.570504\pi$
$587$	−10.6453	−0.439378	−0.219689	+	0.975570i	$0.570504\pi$
$588$	10.1932	0.420362
$589$	−30.4024	−1.25271
$590$	24.0896	0.991753
$591$	−29.1984	−1.20106
$592$	−7.95068	−0.326771
$593$	−2.33558	−0.0959107	−0.0479553	−	0.998849i	$-0.515271\pi$
$593$	−2.33558	−0.0959107	−0.0479553	+	0.998849i	$0.515271\pi$
$594$	−0.280979	−0.0115287
$595$	13.4320	0.550656
$596$	6.17203	0.252816
$597$	−38.0588	−1.55765
$598$	−12.7713	−0.522257
$599$	−13.6993	−0.559738	−0.279869	−	0.960038i	$-0.590291\pi$
$599$	−13.6993	−0.559738	−0.279869	+	0.960038i	$0.590291\pi$
$600$	4.84667	0.197865
$601$	18.2452	0.744237	0.372119	−	0.928185i	$-0.378631\pi$
$601$	18.2452	0.744237	0.372119	+	0.928185i	$0.378631\pi$
$602$	13.7753	0.561439
$603$	−7.94441	−0.323521
$604$	8.95488	0.364369
$605$	15.2930	0.621751
$606$	−10.9222	−0.443685
$607$	35.9030	1.45726	0.728629	−	0.684909i	$-0.240158\pi$
$607$	35.9030	1.45726	0.728629	+	0.684909i	$0.240158\pi$
$608$	−3.67566	−0.149068
$609$	30.1905	1.22338
$610$	15.8857	0.643192
$611$	−21.3674	−0.864433
$612$	13.4953	0.545515
$613$	19.0023	0.767497	0.383749	−	0.923438i	$-0.374633\pi$
$613$	19.0023	0.767497	0.383749	+	0.923438i	$0.374633\pi$
$614$	5.76038	0.232470
$615$	45.9141	1.85144
$616$	2.47718	0.0998086
$617$	−11.4829	−0.462285	−0.231142	−	0.972920i	$-0.574246\pi$
$617$	−11.4829	−0.462285	−0.231142	+	0.972920i	$0.574246\pi$
$618$	−4.99824	−0.201059
$619$	34.8866	1.40221	0.701105	−	0.713058i	$-0.252690\pi$
$619$	34.8866	1.40221	0.701105	+	0.713058i	$0.252690\pi$
$620$	−14.3462	−0.576157
$621$	0.867119	0.0347963
$622$	−1.95681	−0.0784611
$623$	1.28594	0.0515202
$624$	6.81634	0.272872
$625$	−11.0750	−0.443000
$626$	3.37010	0.134696
$627$	−13.2151	−0.527761
$628$	13.6153	0.543312
$629$	−36.7222	−1.46421
$630$	8.49712	0.338534
$631$	−43.6184	−1.73642	−0.868211	−	0.496194i	$-0.834730\pi$
$631$	−43.6184	−1.73642	−0.868211	+	0.496194i	$0.834730\pi$
$632$	5.33352	0.212156
$633$	3.61524	0.143693
$634$	−15.8004	−0.627512
$635$	19.5260	0.774865
$636$	−22.6185	−0.896883
$637$	11.7329	0.464875
$638$	−10.9320	−0.432802
$639$	16.0699	0.635714
$640$	−1.73446	−0.0685604
$641$	7.10126	0.280483	0.140241	−	0.990117i	$-0.455212\pi$
$641$	7.10126	0.280483	0.140241	+	0.990117i	$0.455212\pi$
$642$	37.1761	1.46722
$643$	−7.52088	−0.296595	−0.148297	−	0.988943i	$-0.547379\pi$
$643$	−7.52088	−0.296595	−0.148297	+	0.988943i	$0.547379\pi$
$644$	−7.64475	−0.301245
$645$	−34.6771	−1.36541
$646$	−16.9770	−0.667949
$647$	5.84769	0.229896	0.114948	−	0.993371i	$-0.463330\pi$
$647$	5.84769	0.229896	0.114948	+	0.993371i	$0.463330\pi$
$648$	−9.22835	−0.362524
$649$	20.5198	0.805474
$650$	5.57876	0.218817
$651$	33.7483	1.32270
$652$	−20.1208	−0.787992
$653$	16.4418	0.643417	0.321708	−	0.946839i	$-0.395743\pi$
$653$	16.4418	0.643417	0.321708	+	0.946839i	$0.395743\pi$
$654$	36.8115	1.43944
$655$	20.5615	0.803404
$656$	10.8781	0.424719
$657$	2.69721	0.105228
$658$	−12.7903	−0.498617
$659$	39.4782	1.53785	0.768926	−	0.639337i	$-0.220791\pi$
$659$	39.4782	1.53785	0.768926	+	0.639337i	$0.220791\pi$
$660$	−6.23591	−0.242732
$661$	16.2491	0.632018	0.316009	−	0.948756i	$-0.397657\pi$
$661$	16.2491	0.632018	0.316009	+	0.948756i	$0.397657\pi$
$662$	−27.2807	−1.06029
$663$	31.4830	1.22270
$664$	8.63102	0.334948
$665$	−10.6893	−0.414513
$666$	−23.2307	−0.900171
$667$	33.7368	1.30629
$668$	−18.9475	−0.733100
$669$	32.9521	1.27400
$670$	4.71593	0.182192
$671$	13.5316	0.522382
$672$	4.08018	0.157396
$673$	−9.44875	−0.364223	−0.182111	−	0.983278i	$-0.558293\pi$
$673$	−9.44875	−0.364223	−0.182111	+	0.983278i	$0.558293\pi$
$674$	−5.86743	−0.226005
$675$	−0.378775	−0.0145790
$676$	−5.15406	−0.198233
$677$	0.357955	0.0137573	0.00687866	−	0.999976i	$-0.497810\pi$
$677$	0.357955	0.0137573	0.00687866	+	0.999976i	$0.497810\pi$
$678$	−19.2166	−0.738010
$679$	−5.58466	−0.214320
$680$	−8.01103	−0.307209
$681$	11.8490	0.454054
$682$	−12.2203	−0.467938
$683$	28.0063	1.07163	0.535815	−	0.844335i	$-0.320004\pi$
$683$	28.0063	1.07163	0.535815	+	0.844335i	$0.320004\pi$
$684$	−10.7397	−0.410643
$685$	−9.53301	−0.364237
$686$	18.7600	0.716258
$687$	16.8865	0.644261
$688$	−8.21581	−0.313225
$689$	−26.0350	−0.991856
$690$	19.2444	0.732622
$691$	13.4425	0.511377	0.255688	−	0.966759i	$-0.417698\pi$
$691$	13.4425	0.511377	0.255688	+	0.966759i	$0.417698\pi$
$692$	6.80237	0.258587
$693$	7.23796	0.274947
$694$	15.7387	0.597434
$695$	26.4905	1.00484
$696$	−18.0061	−0.682520
$697$	50.2434	1.90310
$698$	20.3168	0.769004
$699$	−30.6905	−1.16082
$700$	3.33938	0.126217
$701$	52.0604	1.96630	0.983148	−	0.182812i	$-0.0585199\pi$
$701$	52.0604	1.96630	0.983148	+	0.182812i	$0.0585199\pi$
$702$	−0.532707	−0.0201057
$703$	29.2240	1.10220
$704$	−1.47743	−0.0556828
$705$	32.1975	1.21263
$706$	−19.7115	−0.741852
$707$	−7.52547	−0.283024
$708$	33.7983	1.27022
$709$	17.6982	0.664669	0.332334	−	0.943162i	$-0.392164\pi$
$709$	17.6982	0.664669	0.332334	+	0.943162i	$0.392164\pi$
$710$	−9.53933	−0.358005
$711$	15.5837	0.584436
$712$	−0.766957	−0.0287429
$713$	37.7125	1.41234
$714$	18.8454	0.705270
$715$	−7.17784	−0.268436
$716$	17.9187	0.669654
$717$	61.4798	2.29601
$718$	−9.58105	−0.357562
$719$	−5.77878	−0.215512	−0.107756	−	0.994177i	$-0.534367\pi$
$719$	−5.77878	−0.215512	−0.107756	+	0.994177i	$0.534367\pi$
$720$	−5.06782	−0.188867
$721$	−3.44381	−0.128254
$722$	−5.48955	−0.204300
$723$	−4.42863	−0.164703
$724$	11.1532	0.414506
$725$	−14.7369	−0.547315
$726$	21.4565	0.796326
$727$	−43.5348	−1.61462	−0.807309	−	0.590129i	$-0.799077\pi$
$727$	−43.5348	−1.61462	−0.807309	+	0.590129i	$0.799077\pi$
$728$	4.69649	0.174063
$729$	−25.5754	−0.947238
$730$	−1.60111	−0.0592597
$731$	−37.9468	−1.40351
$732$	22.2880	0.823787
$733$	28.4660	1.05142	0.525708	−	0.850665i	$-0.323800\pi$
$733$	28.4660	1.05142	0.525708	+	0.850665i	$0.323800\pi$
$734$	−9.51485	−0.351199
$735$	−17.6797	−0.652126
$736$	4.55945	0.168064
$737$	4.01709	0.147971
$738$	31.7842	1.16999
$739$	−30.4590	−1.12045	−0.560227	−	0.828339i	$-0.689286\pi$
$739$	−30.4590	−1.12045	−0.560227	+	0.828339i	$0.689286\pi$
$740$	13.7901	0.506935
$741$	−25.0545	−0.920401
$742$	−15.5843	−0.572116
$743$	15.5518	0.570539	0.285270	−	0.958447i	$-0.407917\pi$
$743$	15.5518	0.570539	0.285270	+	0.958447i	$0.407917\pi$
$744$	−20.1280	−0.737930
$745$	−10.7051	−0.392205
$746$	3.17222	0.116143
$747$	25.2185	0.922698
$748$	−6.82390	−0.249506
$749$	25.6145	0.935933
$750$	−29.5102	−1.07756
$751$	−21.7185	−0.792519	−0.396259	−	0.918139i	$-0.629692\pi$
$751$	−21.7185	−0.792519	−0.396259	+	0.918139i	$0.629692\pi$
$752$	7.62833	0.278177
$753$	−9.36826	−0.341399
$754$	−20.7259	−0.754794
$755$	−15.5318	−0.565262
$756$	−0.318872	−0.0115973
$757$	−25.3717	−0.922149	−0.461075	−	0.887361i	$-0.652536\pi$
$757$	−25.3717	−0.922149	−0.461075	+	0.887361i	$0.652536\pi$
$758$	−12.2390	−0.444541
$759$	16.3926	0.595015
$760$	6.37527	0.231255
$761$	−22.9568	−0.832185	−0.416092	−	0.909322i	$-0.636601\pi$
$761$	−22.9568	−0.832185	−0.416092	+	0.909322i	$0.636601\pi$
$762$	27.3954	0.992432
$763$	25.3633	0.918213
$764$	−24.6453	−0.891636
$765$	−23.4070	−0.846283
$766$	31.0014	1.12013
$767$	38.9035	1.40472
$768$	−2.43348	−0.0878108
$769$	3.48148	0.125545	0.0627727	−	0.998028i	$-0.480006\pi$
$769$	3.48148	0.125545	0.0627727	+	0.998028i	$0.480006\pi$
$770$	−4.29657	−0.154838
$771$	58.5477	2.10854
$772$	5.02429	0.180828
$773$	42.1369	1.51556	0.757780	−	0.652511i	$-0.226284\pi$
$773$	42.1369	1.51556	0.757780	+	0.652511i	$0.226284\pi$
$774$	−24.0054	−0.862855
$775$	−16.4736	−0.591748
$776$	3.33078	0.119568
$777$	−32.4402	−1.16379
$778$	14.4603	0.518426
$779$	−39.9842	−1.43258
$780$	−11.8226	−0.423319
$781$	−8.12572	−0.290761
$782$	21.0590	0.753068
$783$	1.40721	0.0502894
$784$	−4.18874	−0.149598
$785$	−23.6152	−0.842864
$786$	28.8483	1.02898
$787$	−34.7902	−1.24014	−0.620068	−	0.784548i	$-0.712895\pi$
$787$	−34.7902	−1.24014	−0.620068	+	0.784548i	$0.712895\pi$
$788$	11.9986	0.427432
$789$	55.9964	1.99352
$790$	−9.25076	−0.329127
$791$	−13.2403	−0.470773
$792$	−4.31683	−0.153392
$793$	25.6545	0.911020
$794$	−4.02599	−0.142877
$795$	39.2309	1.39138
$796$	15.6396	0.554333
$797$	−8.19266	−0.290199	−0.145099	−	0.989417i	$-0.546350\pi$
$797$	−8.19266	−0.290199	−0.145099	+	0.989417i	$0.546350\pi$
$798$	−14.9973	−0.530900
$799$	35.2334	1.24647
$800$	−1.99166	−0.0704158
$801$	−2.24093	−0.0791794
$802$	1.76890	0.0624621
$803$	−1.36384	−0.0481290
$804$	6.61656	0.233348
$805$	13.2595	0.467336
$806$	−23.1684	−0.816071
$807$	57.0807	2.00933
$808$	4.48831	0.157898
$809$	−23.4461	−0.824322	−0.412161	−	0.911111i	$-0.635226\pi$
$809$	−23.4461	−0.824322	−0.412161	+	0.911111i	$0.635226\pi$
$810$	16.0062	0.562399
$811$	−34.2710	−1.20342	−0.601709	−	0.798715i	$-0.705513\pi$
$811$	−34.2710	−1.20342	−0.601709	+	0.798715i	$0.705513\pi$
$812$	−12.4063	−0.435376
$813$	−43.3229	−1.51940
$814$	11.7466	0.411718
$815$	34.8987	1.22245
$816$	−11.2397	−0.393467
$817$	30.1985	1.05651
$818$	−4.45546	−0.155781
$819$	13.7224	0.479500
$820$	−18.8676	−0.658886
$821$	−13.3332	−0.465331	−0.232666	−	0.972557i	$-0.574745\pi$
$821$	−13.3332	−0.465331	−0.232666	+	0.972557i	$0.574745\pi$
$822$	−13.3750	−0.466508
$823$	15.3048	0.533491	0.266745	−	0.963767i	$-0.414052\pi$
$823$	15.3048	0.533491	0.266745	+	0.963767i	$0.414052\pi$
$824$	2.05394	0.0715525
$825$	−7.16063	−0.249301
$826$	23.2872	0.810264
$827$	45.4487	1.58041	0.790203	−	0.612846i	$-0.209975\pi$
$827$	45.4487	1.58041	0.790203	+	0.612846i	$0.209975\pi$
$828$	13.3220	0.462972
$829$	−36.1121	−1.25423	−0.627113	−	0.778928i	$-0.715764\pi$
$829$	−36.1121	−1.25423	−0.627113	+	0.778928i	$0.715764\pi$
$830$	−14.9701	−0.519621
$831$	41.5859	1.44260
$832$	−2.80106	−0.0971093
$833$	−19.3467	−0.670325
$834$	37.1668	1.28698
$835$	32.8636	1.13729
$836$	5.43053	0.187819
$837$	1.57304	0.0543721
$838$	−5.29702	−0.182982
$839$	−22.0689	−0.761903	−0.380951	−	0.924595i	$-0.624403\pi$
$839$	−22.0689	−0.761903	−0.380951	+	0.924595i	$0.624403\pi$
$840$	−7.07690	−0.244176
$841$	25.7499	0.887927
$842$	−2.01222	−0.0693457
$843$	44.0637	1.51763
$844$	−1.48562	−0.0511372
$845$	8.93950	0.307528
$846$	22.2888	0.766306
$847$	14.7836	0.507972
$848$	9.29471	0.319181
$849$	40.4052	1.38670
$850$	−9.19899	−0.315523
$851$	−36.2507	−1.24266
$852$	−13.3839	−0.458525
$853$	−24.9379	−0.853857	−0.426928	−	0.904285i	$-0.640404\pi$
$853$	−24.9379	−0.853857	−0.426928	+	0.904285i	$0.640404\pi$
$854$	15.3565	0.525489
$855$	18.6276	0.637049
$856$	−15.2769	−0.522153
$857$	44.4456	1.51823	0.759116	−	0.650955i	$-0.225632\pi$
$857$	44.4456	1.51823	0.759116	+	0.650955i	$0.225632\pi$
$858$	−10.0707	−0.343807
$859$	54.4801	1.85884	0.929418	−	0.369029i	$-0.120310\pi$
$859$	54.4801	1.85884	0.929418	+	0.369029i	$0.120310\pi$
$860$	14.2500	0.485920
$861$	44.3847	1.51263
$862$	−33.3323	−1.13530
$863$	−21.5393	−0.733207	−0.366604	−	0.930377i	$-0.619479\pi$
$863$	−21.5393	−0.733207	−0.366604	+	0.930377i	$0.619479\pi$
$864$	0.190180	0.00647007
$865$	−11.7984	−0.401158
$866$	−23.8617	−0.810854
$867$	−10.5440	−0.358094
$868$	−13.8683	−0.470721
$869$	−7.87991	−0.267308
$870$	31.2308	1.05882
$871$	7.61599	0.258058
$872$	−15.1271	−0.512267
$873$	9.73203	0.329379
$874$	−16.7590	−0.566881
$875$	−20.3327	−0.687370
$876$	−2.24639	−0.0758986
$877$	−15.1288	−0.510862	−0.255431	−	0.966827i	$-0.582217\pi$
$877$	−15.1288	−0.510862	−0.255431	+	0.966827i	$0.582217\pi$
$878$	−28.6508	−0.966917
$879$	−38.9279	−1.31300
$880$	2.56254	0.0863833
$881$	−42.9661	−1.44757	−0.723783	−	0.690027i	$-0.757598\pi$
$881$	−42.9661	−1.44757	−0.723783	+	0.690027i	$0.757598\pi$
$882$	−12.2389	−0.412104
$883$	−15.5357	−0.522818	−0.261409	−	0.965228i	$-0.584187\pi$
$883$	−15.5357	−0.522818	−0.261409	+	0.965228i	$0.584187\pi$
$884$	−12.9374	−0.435132
$885$	−58.6217	−1.97055
$886$	12.4509	0.418296
$887$	−52.4803	−1.76211	−0.881057	−	0.473009i	$-0.843168\pi$
$887$	−52.4803	−1.76211	−0.881057	+	0.473009i	$0.843168\pi$
$888$	19.3479	0.649272
$889$	18.8756	0.633067
$890$	1.33025	0.0445902
$891$	13.6343	0.456765
$892$	−13.5411	−0.453390
$893$	−28.0391	−0.938294
$894$	−15.0196	−0.502329
$895$	−31.0792	−1.03886
$896$	−1.67668	−0.0560140
$897$	31.0788	1.03769
$898$	19.1697	0.639701
$899$	61.2018	2.04120
$900$	−5.81933	−0.193978
$901$	42.9300	1.43020
$902$	−16.0717	−0.535129
$903$	−33.5220	−1.11554
$904$	7.89675	0.262642
$905$	−19.3448	−0.643042
$906$	−21.7916	−0.723976
$907$	−14.1199	−0.468842	−0.234421	−	0.972135i	$-0.575319\pi$
$907$	−14.1199	−0.468842	−0.234421	+	0.972135i	$0.575319\pi$
$908$	−4.86914	−0.161588
$909$	13.1142	0.434969
$910$	−8.14586	−0.270033
$911$	12.4258	0.411684	0.205842	−	0.978585i	$-0.434007\pi$
$911$	12.4258	0.411684	0.205842	+	0.978585i	$0.434007\pi$
$912$	8.94465	0.296187
$913$	−12.7517	−0.422021
$914$	−11.1950	−0.370297
$915$	−38.6575	−1.27798
$916$	−6.93924	−0.229279
$917$	19.8766	0.656383
$918$	0.878397	0.0289914
$919$	−27.9939	−0.923434	−0.461717	−	0.887027i	$-0.652767\pi$
$919$	−27.9939	−0.923434	−0.461717	+	0.887027i	$0.652767\pi$
$920$	−7.90817	−0.260725
$921$	−14.0178	−0.461902
$922$	24.9647	0.822170
$923$	−15.4055	−0.507080
$924$	−6.02819	−0.198313
$925$	15.8350	0.520653
$926$	33.4913	1.10059
$927$	6.00131	0.197109
$928$	7.39932	0.242894
$929$	56.2352	1.84502	0.922509	−	0.385975i	$-0.126135\pi$
$929$	56.2352	1.84502	0.922509	+	0.385975i	$0.126135\pi$
$930$	34.9112	1.14478
$931$	15.3964	0.504595
$932$	12.6118	0.413112
$933$	4.76188	0.155897
$934$	−36.8368	−1.20534
$935$	11.8358	0.387071
$936$	−8.18427	−0.267511
$937$	−19.1665	−0.626141	−0.313071	−	0.949730i	$-0.601358\pi$
$937$	−19.1665	−0.626141	−0.313071	+	0.949730i	$0.601358\pi$
$938$	4.55884	0.148851
$939$	−8.20110	−0.267633
$940$	−13.2310	−0.431548
$941$	−35.3778	−1.15328	−0.576642	−	0.816997i	$-0.695637\pi$
$941$	−35.3778	−1.15328	−0.576642	+	0.816997i	$0.695637\pi$
$942$	−33.1327	−1.07952
$943$	49.5983	1.61514
$944$	−13.8888	−0.452043
$945$	0.553070	0.0179914
$946$	12.1383	0.394650
$947$	−52.3783	−1.70207	−0.851033	−	0.525112i	$-0.824023\pi$
$947$	−52.3783	−1.70207	−0.851033	+	0.525112i	$0.824023\pi$
$948$	−12.9790	−0.421539
$949$	−2.58571	−0.0839357
$950$	7.32066	0.237513
$951$	38.4499	1.24682
$952$	−7.74418	−0.250990
$953$	0.881783	0.0285638	0.0142819	−	0.999898i	$-0.495454\pi$
$953$	0.881783	0.0285638	0.0142819	+	0.999898i	$0.495454\pi$
$954$	27.1577	0.879264
$955$	42.7462	1.38324
$956$	−25.2641	−0.817099
$957$	26.6028	0.859947
$958$	−15.0474	−0.486161
$959$	−9.21546	−0.297583
$960$	4.22077	0.136225
$961$	37.4141	1.20691
$962$	22.2703	0.718025
$963$	−44.6367	−1.43840
$964$	1.81987	0.0586141
$965$	−8.71441	−0.280527
$966$	18.6034	0.598554
$967$	37.8751	1.21798	0.608990	−	0.793178i	$-0.291575\pi$
$967$	37.8751	1.21798	0.608990	+	0.793178i	$0.291575\pi$
$968$	−8.81719	−0.283395
$969$	41.3132	1.32717
$970$	−5.77709	−0.185491
$971$	14.4797	0.464677	0.232338	−	0.972635i	$-0.425362\pi$
$971$	14.4797	0.464677	0.232338	+	0.972635i	$0.425362\pi$
$972$	21.8865	0.702010
$973$	25.6081	0.820958
$974$	−8.18508	−0.262267
$975$	−13.5758	−0.434774
$976$	−9.15887	−0.293168
$977$	−48.7592	−1.55994	−0.779972	−	0.625815i	$-0.784767\pi$
$977$	−48.7592	−1.55994	−0.779972	+	0.625815i	$0.784767\pi$
$978$	48.9637	1.56569
$979$	1.13313	0.0362149
$980$	7.26518	0.232078
$981$	−44.1990	−1.41117
$982$	−32.6516	−1.04195
$983$	−6.90072	−0.220099	−0.110049	−	0.993926i	$-0.535101\pi$
$983$	−6.90072	−0.220099	−0.110049	+	0.993926i	$0.535101\pi$
$984$	−26.4718	−0.843889
$985$	−20.8110	−0.663094
$986$	34.1756	1.08837
$987$	31.1250	0.990719
$988$	10.2957	0.327551
$989$	−37.4596	−1.19115
$990$	7.48736	0.237964
$991$	−27.7575	−0.881747	−0.440874	−	0.897569i	$-0.645331\pi$
$991$	−27.7575	−0.881747	−0.440874	+	0.897569i	$0.645331\pi$
$992$	8.27128	0.262613
$993$	66.3871	2.10673
$994$	−9.22158	−0.292491
$995$	−27.1263	−0.859961
$996$	−21.0035	−0.665520
$997$	−43.4855	−1.37720	−0.688600	−	0.725142i	$-0.741774\pi$
$997$	−43.4855	−1.37720	−0.688600	+	0.725142i	$0.741774\pi$
$998$	−8.22805	−0.260454
$999$	−1.51206	−0.0478396

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6046.2.a.e.1.10	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6046.2.a.e.1.10	✓	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 6046 = 2 \cdot 3023 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6046.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.43348 q^{3} +1.00000 q^{4} -1.73446 q^{5} -2.43348 q^{6} -1.67668 q^{7} +1.00000 q^{8} +2.92185 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.43348 q^{3} +1.00000 q^{4} -1.73446 q^{5} -2.43348 q^{6} -1.67668 q^{7} +1.00000 q^{8} +2.92185 q^{9} -1.73446 q^{10} -1.47743 q^{11} -2.43348 q^{12} -2.80106 q^{13} -1.67668 q^{14} +4.22077 q^{15} +1.00000 q^{16} +4.61875 q^{17} +2.92185 q^{18} -3.67566 q^{19} -1.73446 q^{20} +4.08018 q^{21} -1.47743 q^{22} +4.55945 q^{23} -2.43348 q^{24} -1.99166 q^{25} -2.80106 q^{26} +0.190180 q^{27} -1.67668 q^{28} +7.39932 q^{29} +4.22077 q^{30} +8.27128 q^{31} +1.00000 q^{32} +3.59531 q^{33} +4.61875 q^{34} +2.90813 q^{35} +2.92185 q^{36} -7.95068 q^{37} -3.67566 q^{38} +6.81634 q^{39} -1.73446 q^{40} +10.8781 q^{41} +4.08018 q^{42} -8.21581 q^{43} -1.47743 q^{44} -5.06782 q^{45} +4.55945 q^{46} +7.62833 q^{47} -2.43348 q^{48} -4.18874 q^{49} -1.99166 q^{50} -11.2397 q^{51} -2.80106 q^{52} +9.29471 q^{53} +0.190180 q^{54} +2.56254 q^{55} -1.67668 q^{56} +8.94465 q^{57} +7.39932 q^{58} -13.8888 q^{59} +4.22077 q^{60} -9.15887 q^{61} +8.27128 q^{62} -4.89901 q^{63} +1.00000 q^{64} +4.85832 q^{65} +3.59531 q^{66} -2.71897 q^{67} +4.61875 q^{68} -11.0954 q^{69} +2.90813 q^{70} +5.49990 q^{71} +2.92185 q^{72} +0.923118 q^{73} -7.95068 q^{74} +4.84667 q^{75} -3.67566 q^{76} +2.47718 q^{77} +6.81634 q^{78} +5.33352 q^{79} -1.73446 q^{80} -9.22835 q^{81} +10.8781 q^{82} +8.63102 q^{83} +4.08018 q^{84} -8.01103 q^{85} -8.21581 q^{86} -18.0061 q^{87} -1.47743 q^{88} -0.766957 q^{89} -5.06782 q^{90} +4.69649 q^{91} +4.55945 q^{92} -20.1280 q^{93} +7.62833 q^{94} +6.37527 q^{95} -2.43348 q^{96} +3.33078 q^{97} -4.18874 q^{98} -4.31683 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9}+O(q^{10}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9	\( 56 q + 56 q^{2} - 18 q^{3} + 56 q^{4} - 17 q^{5} - 18 q^{6} - 35 q^{7} + 56 q^{8} + 34 q^{9} - 17 q^{10} - 53 q^{11} - 18 q^{12} - 21 q^{13} - 35 q^{14} - 36 q^{15} + 56 q^{16} - 22 q^{17} + 34 q^{18} - 31 q^{19} - 17 q^{20} - 23 q^{21} - 53 q^{22} - 59 q^{23} - 18 q^{24} + 41 q^{25} - 21 q^{26} - 63 q^{27} - 35 q^{28} - 88 q^{29} - 36 q^{30} - 44 q^{31} + 56 q^{32} + 4 q^{33} - 22 q^{34} - 51 q^{35} + 34 q^{36} - 60 q^{37} - 31 q^{38} - 62 q^{39} - 17 q^{40} - 39 q^{41} - 23 q^{42} - 66 q^{43} - 53 q^{44} - 34 q^{45} - 59 q^{46} - 51 q^{47} - 18 q^{48} + 41 q^{49} + 41 q^{50} - 48 q^{51} - 21 q^{52} - 75 q^{53} - 63 q^{54} - 41 q^{55} - 35 q^{56} - 12 q^{57} - 88 q^{58} - 77 q^{59} - 36 q^{60} - 43 q^{61} - 44 q^{62} - 88 q^{63} + 56 q^{64} - 54 q^{65} + 4 q^{66} - 62 q^{67} - 22 q^{68} - 48 q^{69} - 51 q^{70} - 122 q^{71} + 34 q^{72} - 7 q^{73} - 60 q^{74} - 63 q^{75} - 31 q^{76} - 39 q^{77} - 62 q^{78} - 91 q^{79} - 17 q^{80} + 8 q^{81} - 39 q^{82} - 51 q^{83} - 23 q^{84} - 72 q^{85} - 66 q^{86} - 19 q^{87} - 53 q^{88} - 62 q^{89} - 34 q^{90} - 48 q^{91} - 59 q^{92} - 41 q^{93} - 51 q^{94} - 120 q^{95} - 18 q^{96} + 6 q^{97} + 41 q^{98} - 128 q^{99}+O(q^{100}) \) 56 * q + 56 * q^2 - 18 * q^3 + 56 * q^4 - 17 * q^5 - 18 * q^6 - 35 * q^7 + 56 * q^8 + 34 * q^9 - 17 * q^10 - 53 * q^11 - 18 * q^12 - 21 * q^13 - 35 * q^14 - 36 * q^15 + 56 * q^16 - 22 * q^17 + 34 * q^18 - 31 * q^19 - 17 * q^20 - 23 * q^21 - 53 * q^22 - 59 * q^23 - 18 * q^24 + 41 * q^25 - 21 * q^26 - 63 * q^27 - 35 * q^28 - 88 * q^29 - 36 * q^30 - 44 * q^31 + 56 * q^32 + 4 * q^33 - 22 * q^34 - 51 * q^35 + 34 * q^36 - 60 * q^37 - 31 * q^38 - 62 * q^39 - 17 * q^40 - 39 * q^41 - 23 * q^42 - 66 * q^43 - 53 * q^44 - 34 * q^45 - 59 * q^46 - 51 * q^47 - 18 * q^48 + 41 * q^49 + 41 * q^50 - 48 * q^51 - 21 * q^52 - 75 * q^53 - 63 * q^54 - 41 * q^55 - 35 * q^56 - 12 * q^57 - 88 * q^58 - 77 * q^59 - 36 * q^60 - 43 * q^61 - 44 * q^62 - 88 * q^63 + 56 * q^64 - 54 * q^65 + 4 * q^66 - 62 * q^67 - 22 * q^68 - 48 * q^69 - 51 * q^70 - 122 * q^71 + 34 * q^72 - 7 * q^73 - 60 * q^74 - 63 * q^75 - 31 * q^76 - 39 * q^77 - 62 * q^78 - 91 * q^79 - 17 * q^80 + 8 * q^81 - 39 * q^82 - 51 * q^83 - 23 * q^84 - 72 * q^85 - 66 * q^86 - 19 * q^87 - 53 * q^88 - 62 * q^89 - 34 * q^90 - 48 * q^91 - 59 * q^92 - 41 * q^93 - 51 * q^94 - 120 * q^95 - 18 * q^96 + 6 * q^97 + 41 * q^98 - 128 * q^99

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