LMFDB - Embedded newform 6022.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6022,2,Mod(1,6022)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6022, 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("6022.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6022 = 2 \cdot 3011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6022.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:	$48.0859120972$
Analytic rank:	$1$
Dimension:	$54$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6022.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -3.06406 q^{3} +1.00000 q^{4} +3.64593 q^{5} -3.06406 q^{6} +0.427453 q^{7} +1.00000 q^{8} +6.38849 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -3.06406 q^{3} +1.00000 q^{4} +3.64593 q^{5} -3.06406 q^{6} +0.427453 q^{7} +1.00000 q^{8} +6.38849 q^{9} +3.64593 q^{10} -3.29238 q^{11} -3.06406 q^{12} -5.34209 q^{13} +0.427453 q^{14} -11.1714 q^{15} +1.00000 q^{16} +4.32504 q^{17} +6.38849 q^{18} -1.91344 q^{19} +3.64593 q^{20} -1.30974 q^{21} -3.29238 q^{22} -1.60649 q^{23} -3.06406 q^{24} +8.29280 q^{25} -5.34209 q^{26} -10.3825 q^{27} +0.427453 q^{28} +8.66294 q^{29} -11.1714 q^{30} -9.58136 q^{31} +1.00000 q^{32} +10.0880 q^{33} +4.32504 q^{34} +1.55846 q^{35} +6.38849 q^{36} +1.52221 q^{37} -1.91344 q^{38} +16.3685 q^{39} +3.64593 q^{40} -10.6038 q^{41} -1.30974 q^{42} -2.94589 q^{43} -3.29238 q^{44} +23.2920 q^{45} -1.60649 q^{46} -12.4740 q^{47} -3.06406 q^{48} -6.81728 q^{49} +8.29280 q^{50} -13.2522 q^{51} -5.34209 q^{52} +4.03069 q^{53} -10.3825 q^{54} -12.0038 q^{55} +0.427453 q^{56} +5.86291 q^{57} +8.66294 q^{58} -4.04307 q^{59} -11.1714 q^{60} -5.73991 q^{61} -9.58136 q^{62} +2.73078 q^{63} +1.00000 q^{64} -19.4769 q^{65} +10.0880 q^{66} -1.56619 q^{67} +4.32504 q^{68} +4.92240 q^{69} +1.55846 q^{70} +15.1731 q^{71} +6.38849 q^{72} -10.7547 q^{73} +1.52221 q^{74} -25.4097 q^{75} -1.91344 q^{76} -1.40734 q^{77} +16.3685 q^{78} +5.89048 q^{79} +3.64593 q^{80} +12.6473 q^{81} -10.6038 q^{82} -1.42221 q^{83} -1.30974 q^{84} +15.7688 q^{85} -2.94589 q^{86} -26.5438 q^{87} -3.29238 q^{88} +9.65720 q^{89} +23.2920 q^{90} -2.28349 q^{91} -1.60649 q^{92} +29.3579 q^{93} -12.4740 q^{94} -6.97628 q^{95} -3.06406 q^{96} -3.21631 q^{97} -6.81728 q^{98} -21.0333 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) $ 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * 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
$3$	−3.06406	−1.76904	−0.884519	−	0.466504i	$-0.845513\pi$
$3$	−3.06406	−1.76904	−0.884519	+	0.466504i	$0.845513\pi$
$4$	1.00000	0.500000
$5$	3.64593	1.63051	0.815255	−	0.579103i	$-0.196597\pi$
$5$	3.64593	1.63051	0.815255	+	0.579103i	$0.196597\pi$
$6$	−3.06406	−1.25090
$7$	0.427453	0.161562	0.0807810	−	0.996732i	$-0.474259\pi$
$7$	0.427453	0.161562	0.0807810	+	0.996732i	$0.474259\pi$
$8$	1.00000	0.353553
$9$	6.38849	2.12950
$10$	3.64593	1.15294
$11$	−3.29238	−0.992689	−0.496344	−	0.868126i	$-0.665325\pi$
$11$	−3.29238	−0.992689	−0.496344	+	0.868126i	$0.665325\pi$
$12$	−3.06406	−0.884519
$13$	−5.34209	−1.48163	−0.740815	−	0.671709i	$-0.765560\pi$
$13$	−5.34209	−1.48163	−0.740815	+	0.671709i	$0.765560\pi$
$14$	0.427453	0.114242
$15$	−11.1714	−2.88443
$16$	1.00000	0.250000
$17$	4.32504	1.04898	0.524488	−	0.851418i	$-0.324257\pi$
$17$	4.32504	1.04898	0.524488	+	0.851418i	$0.324257\pi$
$18$	6.38849	1.50578
$19$	−1.91344	−0.438974	−0.219487	−	0.975615i	$-0.570438\pi$
$19$	−1.91344	−0.438974	−0.219487	+	0.975615i	$0.570438\pi$
$20$	3.64593	0.815255
$21$	−1.30974	−0.285809
$22$	−3.29238	−0.701937
$23$	−1.60649	−0.334977	−0.167488	−	0.985874i	$-0.553566\pi$
$23$	−1.60649	−0.334977	−0.167488	+	0.985874i	$0.553566\pi$
$24$	−3.06406	−0.625449
$25$	8.29280	1.65856
$26$	−5.34209	−1.04767
$27$	−10.3825	−1.99812
$28$	0.427453	0.0807810
$29$	8.66294	1.60867	0.804334	−	0.594178i	$-0.202522\pi$
$29$	8.66294	1.60867	0.804334	+	0.594178i	$0.202522\pi$
$30$	−11.1714	−2.03960
$31$	−9.58136	−1.72086	−0.860432	−	0.509566i	$-0.829806\pi$
$31$	−9.58136	−1.72086	−0.860432	+	0.509566i	$0.829806\pi$
$32$	1.00000	0.176777
$33$	10.0880	1.75610
$34$	4.32504	0.741738
$35$	1.55846	0.263428
$36$	6.38849	1.06475
$37$	1.52221	0.250250	0.125125	−	0.992141i	$-0.460067\pi$
$37$	1.52221	0.250250	0.125125	+	0.992141i	$0.460067\pi$
$38$	−1.91344	−0.310401
$39$	16.3685	2.62106
$40$	3.64593	0.576472
$41$	−10.6038	−1.65603	−0.828015	−	0.560706i	$-0.810530\pi$
$41$	−10.6038	−1.65603	−0.828015	+	0.560706i	$0.810530\pi$
$42$	−1.30974	−0.202098
$43$	−2.94589	−0.449244	−0.224622	−	0.974446i	$-0.572115\pi$
$43$	−2.94589	−0.449244	−0.224622	+	0.974446i	$0.572115\pi$
$44$	−3.29238	−0.496344
$45$	23.2920	3.47216
$46$	−1.60649	−0.236864
$47$	−12.4740	−1.81952	−0.909761	−	0.415133i	$-0.863735\pi$
$47$	−12.4740	−1.81952	−0.909761	+	0.415133i	$0.863735\pi$
$48$	−3.06406	−0.442259
$49$	−6.81728	−0.973898
$50$	8.29280	1.17278
$51$	−13.2522	−1.85568
$52$	−5.34209	−0.740815
$53$	4.03069	0.553659	0.276829	−	0.960919i	$-0.410716\pi$
$53$	4.03069	0.553659	0.276829	+	0.960919i	$0.410716\pi$
$54$	−10.3825	−1.41288
$55$	−12.0038	−1.61859
$56$	0.427453	0.0571208
$57$	5.86291	0.776562
$58$	8.66294	1.13750
$59$	−4.04307	−0.526363	−0.263181	−	0.964746i	$-0.584772\pi$
$59$	−4.04307	−0.526363	−0.263181	+	0.964746i	$0.584772\pi$
$60$	−11.1714	−1.44222
$61$	−5.73991	−0.734920	−0.367460	−	0.930039i	$-0.619773\pi$
$61$	−5.73991	−0.734920	−0.367460	+	0.930039i	$0.619773\pi$
$62$	−9.58136	−1.21683
$63$	2.73078	0.344046
$64$	1.00000	0.125000
$65$	−19.4769	−2.41581
$66$	10.0880	1.24175
$67$	−1.56619	−0.191341	−0.0956704	−	0.995413i	$-0.530499\pi$
$67$	−1.56619	−0.191341	−0.0956704	+	0.995413i	$0.530499\pi$
$68$	4.32504	0.524488
$69$	4.92240	0.592587
$70$	1.55846	0.186272
$71$	15.1731	1.80071	0.900357	−	0.435152i	$-0.143305\pi$
$71$	15.1731	1.80071	0.900357	+	0.435152i	$0.143305\pi$
$72$	6.38849	0.752890
$73$	−10.7547	−1.25874	−0.629370	−	0.777106i	$-0.716687\pi$
$73$	−10.7547	−1.25874	−0.629370	+	0.777106i	$0.716687\pi$
$74$	1.52221	0.176954
$75$	−25.4097	−2.93406
$76$	−1.91344	−0.219487
$77$	−1.40734	−0.160381
$78$	16.3685	1.85337
$79$	5.89048	0.662730	0.331365	−	0.943503i	$-0.392491\pi$
$79$	5.89048	0.662730	0.331365	+	0.943503i	$0.392491\pi$
$80$	3.64593	0.407627
$81$	12.6473	1.40525
$82$	−10.6038	−1.17099
$83$	−1.42221	−0.156108	−0.0780538	−	0.996949i	$-0.524871\pi$
$83$	−1.42221	−0.156108	−0.0780538	+	0.996949i	$0.524871\pi$
$84$	−1.30974	−0.142905
$85$	15.7688	1.71037
$86$	−2.94589	−0.317663
$87$	−26.5438	−2.84579
$88$	−3.29238	−0.350968
$89$	9.65720	1.02366	0.511830	−	0.859086i	$-0.328968\pi$
$89$	9.65720	1.02366	0.511830	+	0.859086i	$0.328968\pi$
$90$	23.2920	2.45519
$91$	−2.28349	−0.239375
$92$	−1.60649	−0.167488
$93$	29.3579	3.04427
$94$	−12.4740	−1.28660
$95$	−6.97628	−0.715751
$96$	−3.06406	−0.312725
$97$	−3.21631	−0.326567	−0.163284	−	0.986579i	$-0.552209\pi$
$97$	−3.21631	−0.326567	−0.163284	+	0.986579i	$0.552209\pi$
$98$	−6.81728	−0.688650
$99$	−21.0333	−2.11393
$100$	8.29280	0.829280
$101$	−17.3737	−1.72875	−0.864375	−	0.502848i	$-0.832286\pi$
$101$	−17.3737	−1.72875	−0.864375	+	0.502848i	$0.832286\pi$
$102$	−13.2522	−1.31216
$103$	−1.53717	−0.151462	−0.0757311	−	0.997128i	$-0.524129\pi$
$103$	−1.53717	−0.151462	−0.0757311	+	0.997128i	$0.524129\pi$
$104$	−5.34209	−0.523835
$105$	−4.77523	−0.466015
$106$	4.03069	0.391496
$107$	7.52353	0.727327	0.363664	−	0.931530i	$-0.381526\pi$
$107$	7.52353	0.727327	0.363664	+	0.931530i	$0.381526\pi$
$108$	−10.3825	−0.999060
$109$	−12.6818	−1.21469	−0.607347	−	0.794436i	$-0.707766\pi$
$109$	−12.6818	−1.21469	−0.607347	+	0.794436i	$0.707766\pi$
$110$	−12.0038	−1.14451
$111$	−4.66415	−0.442702
$112$	0.427453	0.0403905
$113$	18.3997	1.73090	0.865448	−	0.500998i	$-0.167034\pi$
$113$	18.3997	1.73090	0.865448	+	0.500998i	$0.167034\pi$
$114$	5.86291	0.549112
$115$	−5.85716	−0.546183
$116$	8.66294	0.804334
$117$	−34.1279	−3.15512
$118$	−4.04307	−0.372195
$119$	1.84875	0.169475
$120$	−11.1714	−1.01980
$121$	−0.160260	−0.0145690
$122$	−5.73991	−0.519667
$123$	32.4906	2.92958
$124$	−9.58136	−0.860432
$125$	12.0053	1.07379
$126$	2.73078	0.243277
$127$	−18.4682	−1.63879	−0.819394	−	0.573231i	$-0.805690\pi$
$127$	−18.4682	−1.63879	−0.819394	+	0.573231i	$0.805690\pi$
$128$	1.00000	0.0883883
$129$	9.02639	0.794729
$130$	−19.4769	−1.70824
$131$	22.0936	1.93032	0.965162	−	0.261652i	$-0.0842673\pi$
$131$	22.0936	1.93032	0.965162	+	0.261652i	$0.0842673\pi$
$132$	10.0880	0.878052
$133$	−0.817907	−0.0709215
$134$	−1.56619	−0.135298
$135$	−37.8540	−3.25795
$136$	4.32504	0.370869
$137$	−15.8964	−1.35812	−0.679059	−	0.734084i	$-0.737612\pi$
$137$	−15.8964	−1.35812	−0.679059	+	0.734084i	$0.737612\pi$
$138$	4.92240	0.419022
$139$	2.54780	0.216102	0.108051	−	0.994145i	$-0.465539\pi$
$139$	2.54780	0.216102	0.108051	+	0.994145i	$0.465539\pi$
$140$	1.55846	0.131714
$141$	38.2212	3.21880
$142$	15.1731	1.27330
$143$	17.5882	1.47080
$144$	6.38849	0.532374
$145$	31.5845	2.62295
$146$	−10.7547	−0.890063
$147$	20.8886	1.72286
$148$	1.52221	0.125125
$149$	5.31833	0.435695	0.217847	−	0.975983i	$-0.430097\pi$
$149$	5.31833	0.435695	0.217847	+	0.975983i	$0.430097\pi$
$150$	−25.4097	−2.07469
$151$	8.47845	0.689967	0.344983	−	0.938609i	$-0.387885\pi$
$151$	8.47845	0.689967	0.344983	+	0.938609i	$0.387885\pi$
$152$	−1.91344	−0.155201
$153$	27.6305	2.23379
$154$	−1.40734	−0.113406
$155$	−34.9330	−2.80588
$156$	16.3685	1.31053
$157$	19.2495	1.53628	0.768141	−	0.640281i	$-0.221182\pi$
$157$	19.2495	1.53628	0.768141	+	0.640281i	$0.221182\pi$
$158$	5.89048	0.468621
$159$	−12.3503	−0.979443
$160$	3.64593	0.288236
$161$	−0.686700	−0.0541196
$162$	12.6473	0.993665
$163$	3.96907	0.310882	0.155441	−	0.987845i	$-0.450320\pi$
$163$	3.96907	0.310882	0.155441	+	0.987845i	$0.450320\pi$
$164$	−10.6038	−0.828015
$165$	36.7803	2.86334
$166$	−1.42221	−0.110385
$167$	−18.6386	−1.44230	−0.721151	−	0.692778i	$-0.756387\pi$
$167$	−18.6386	−1.44230	−0.721151	+	0.692778i	$0.756387\pi$
$168$	−1.30974	−0.101049
$169$	15.5380	1.19523
$170$	15.7688	1.20941
$171$	−12.2240	−0.934793
$172$	−2.94589	−0.224622
$173$	−9.29293	−0.706528	−0.353264	−	0.935524i	$-0.614928\pi$
$173$	−9.29293	−0.706528	−0.353264	+	0.935524i	$0.614928\pi$
$174$	−26.5438	−2.01228
$175$	3.54478	0.267960
$176$	−3.29238	−0.248172
$177$	12.3882	0.931156
$178$	9.65720	0.723838
$179$	−2.40565	−0.179807	−0.0899035	−	0.995950i	$-0.528656\pi$
$179$	−2.40565	−0.179807	−0.0899035	+	0.995950i	$0.528656\pi$
$180$	23.2920	1.73608
$181$	−23.7641	−1.76637	−0.883187	−	0.469021i	$-0.844607\pi$
$181$	−23.7641	−1.76637	−0.883187	+	0.469021i	$0.844607\pi$
$182$	−2.28349	−0.169264
$183$	17.5874	1.30010
$184$	−1.60649	−0.118432
$185$	5.54988	0.408035
$186$	29.3579	2.15263
$187$	−14.2397	−1.04131
$188$	−12.4740	−0.909761
$189$	−4.43805	−0.322820
$190$	−6.97628	−0.506112
$191$	11.8252	0.855639	0.427819	−	0.903864i	$-0.359282\pi$
$191$	11.8252	0.855639	0.427819	+	0.903864i	$0.359282\pi$
$192$	−3.06406	−0.221130
$193$	−5.60247	−0.403275	−0.201637	−	0.979460i	$-0.564626\pi$
$193$	−5.60247	−0.403275	−0.201637	+	0.979460i	$0.564626\pi$
$194$	−3.21631	−0.230918
$195$	59.6784	4.27366
$196$	−6.81728	−0.486949
$197$	−3.45943	−0.246474	−0.123237	−	0.992377i	$-0.539328\pi$
$197$	−3.45943	−0.246474	−0.123237	+	0.992377i	$0.539328\pi$
$198$	−21.0333	−1.49477
$199$	−11.8661	−0.841168	−0.420584	−	0.907254i	$-0.638175\pi$
$199$	−11.8661	−0.841168	−0.420584	+	0.907254i	$0.638175\pi$
$200$	8.29280	0.586390
$201$	4.79891	0.338489
$202$	−17.3737	−1.22241
$203$	3.70300	0.259900
$204$	−13.2522	−0.927839
$205$	−38.6606	−2.70017
$206$	−1.53717	−0.107100
$207$	−10.2631	−0.713332
$208$	−5.34209	−0.370407
$209$	6.29977	0.435765
$210$	−4.77523	−0.329522
$211$	−21.1152	−1.45363	−0.726817	−	0.686831i	$-0.759001\pi$
$211$	−21.1152	−1.45363	−0.726817	+	0.686831i	$0.759001\pi$
$212$	4.03069	0.276829
$213$	−46.4913	−3.18553
$214$	7.52353	0.514298
$215$	−10.7405	−0.732496
$216$	−10.3825	−0.706442
$217$	−4.09558	−0.278026
$218$	−12.6818	−0.858919
$219$	32.9530	2.22676
$220$	−12.0038	−0.809294
$221$	−23.1048	−1.55419
$222$	−4.66415	−0.313038
$223$	−14.1020	−0.944341	−0.472171	−	0.881507i	$-0.656529\pi$
$223$	−14.1020	−0.944341	−0.472171	+	0.881507i	$0.656529\pi$
$224$	0.427453	0.0285604
$225$	52.9784	3.53190
$226$	18.3997	1.22393
$227$	16.5441	1.09807	0.549035	−	0.835799i	$-0.314995\pi$
$227$	16.5441	1.09807	0.549035	+	0.835799i	$0.314995\pi$
$228$	5.86291	0.388281
$229$	18.8483	1.24553	0.622765	−	0.782409i	$-0.286009\pi$
$229$	18.8483	1.24553	0.622765	+	0.782409i	$0.286009\pi$
$230$	−5.85716	−0.386210
$231$	4.31217	0.283720
$232$	8.66294	0.568750
$233$	−0.139630	−0.00914747	−0.00457374	−	0.999990i	$-0.501456\pi$
$233$	−0.139630	−0.00914747	−0.00457374	+	0.999990i	$0.501456\pi$
$234$	−34.1279	−2.23101
$235$	−45.4794	−2.96675
$236$	−4.04307	−0.263181
$237$	−18.0488	−1.17240
$238$	1.84875	0.119837
$239$	12.7550	0.825051	0.412526	−	0.910946i	$-0.364647\pi$
$239$	12.7550	0.825051	0.412526	+	0.910946i	$0.364647\pi$
$240$	−11.1714	−0.721108
$241$	2.38148	0.153405	0.0767024	−	0.997054i	$-0.475561\pi$
$241$	2.38148	0.153405	0.0767024	+	0.997054i	$0.475561\pi$
$242$	−0.160260	−0.0103019
$243$	−7.60449	−0.487828
$244$	−5.73991	−0.367460
$245$	−24.8553	−1.58795
$246$	32.4906	2.07153
$247$	10.2218	0.650397
$248$	−9.58136	−0.608417
$249$	4.35773	0.276160
$250$	12.0053	0.759283
$251$	11.2533	0.710304	0.355152	−	0.934808i	$-0.384429\pi$
$251$	11.2533	0.710304	0.355152	+	0.934808i	$0.384429\pi$
$252$	2.73078	0.172023
$253$	5.28918	0.332528
$254$	−18.4682	−1.15880
$255$	−48.3166	−3.02570
$256$	1.00000	0.0625000
$257$	28.1024	1.75298	0.876489	−	0.481421i	$-0.159879\pi$
$257$	28.1024	1.75298	0.876489	+	0.481421i	$0.159879\pi$
$258$	9.02639	0.561958
$259$	0.650674	0.0404309
$260$	−19.4769	−1.20791
$261$	55.3431	3.42565
$262$	22.0936	1.36495
$263$	−2.89804	−0.178701	−0.0893505	−	0.996000i	$-0.528479\pi$
$263$	−2.89804	−0.178701	−0.0893505	+	0.996000i	$0.528479\pi$
$264$	10.0880	0.620877
$265$	14.6956	0.902745
$266$	−0.817907	−0.0501491
$267$	−29.5903	−1.81089
$268$	−1.56619	−0.0956704
$269$	−7.89923	−0.481625	−0.240812	−	0.970572i	$-0.577414\pi$
$269$	−7.89923	−0.481625	−0.240812	+	0.970572i	$0.577414\pi$
$270$	−37.8540	−2.30372
$271$	17.5855	1.06824	0.534122	−	0.845408i	$-0.320642\pi$
$271$	17.5855	1.06824	0.534122	+	0.845408i	$0.320642\pi$
$272$	4.32504	0.262244
$273$	6.99677	0.423464
$274$	−15.8964	−0.960335
$275$	−27.3030	−1.64643
$276$	4.92240	0.296293
$277$	−16.9097	−1.01601	−0.508003	−	0.861356i	$-0.669616\pi$
$277$	−16.9097	−1.01601	−0.508003	+	0.861356i	$0.669616\pi$
$278$	2.54780	0.152807
$279$	−61.2104	−3.66457
$280$	1.55846	0.0931360
$281$	−12.2586	−0.731284	−0.365642	−	0.930756i	$-0.619151\pi$
$281$	−12.2586	−0.731284	−0.365642	+	0.930756i	$0.619151\pi$
$282$	38.2212	2.27604
$283$	−27.5748	−1.63915	−0.819576	−	0.572970i	$-0.805791\pi$
$283$	−27.5748	−1.63915	−0.819576	+	0.572970i	$0.805791\pi$
$284$	15.1731	0.900357
$285$	21.3758	1.26619
$286$	17.5882	1.04001
$287$	−4.53261	−0.267552
$288$	6.38849	0.376445
$289$	1.70597	0.100351
$290$	31.5845	1.85470
$291$	9.85498	0.577709
$292$	−10.7547	−0.629370
$293$	28.4537	1.66228	0.831140	−	0.556063i	$-0.187689\pi$
$293$	28.4537	1.66228	0.831140	+	0.556063i	$0.187689\pi$
$294$	20.8886	1.21825
$295$	−14.7407	−0.858240
$296$	1.52221	0.0884768
$297$	34.1832	1.98351
$298$	5.31833	0.308083
$299$	8.58203	0.496312
$300$	−25.4097	−1.46703
$301$	−1.25923	−0.0725808
$302$	8.47845	0.487880
$303$	53.2342	3.05822
$304$	−1.91344	−0.109743
$305$	−20.9273	−1.19829
$306$	27.6305	1.57953
$307$	6.47632	0.369623	0.184812	−	0.982774i	$-0.440832\pi$
$307$	6.47632	0.369623	0.184812	+	0.982774i	$0.440832\pi$
$308$	−1.40734	−0.0801904
$309$	4.71000	0.267942
$310$	−34.9330	−1.98406
$311$	−20.3783	−1.15555	−0.577775	−	0.816196i	$-0.696079\pi$
$311$	−20.3783	−1.15555	−0.577775	+	0.816196i	$0.696079\pi$
$312$	16.3685	0.926684
$313$	−31.1640	−1.76150	−0.880748	−	0.473585i	$-0.842960\pi$
$313$	−31.1640	−1.76150	−0.880748	+	0.473585i	$0.842960\pi$
$314$	19.2495	1.08631
$315$	9.95622	0.560970
$316$	5.89048	0.331365
$317$	1.50721	0.0846534	0.0423267	−	0.999104i	$-0.486523\pi$
$317$	1.50721	0.0846534	0.0423267	+	0.999104i	$0.486523\pi$
$318$	−12.3503	−0.692571
$319$	−28.5217	−1.59691
$320$	3.64593	0.203814
$321$	−23.0526	−1.28667
$322$	−0.686700	−0.0382683
$323$	−8.27572	−0.460473
$324$	12.6473	0.702627
$325$	−44.3009	−2.45737
$326$	3.96907	0.219827
$327$	38.8578	2.14884
$328$	−10.6038	−0.585495
$329$	−5.33205	−0.293966
$330$	36.7803	2.02469
$331$	−7.14775	−0.392876	−0.196438	−	0.980516i	$-0.562937\pi$
$331$	−7.14775	−0.392876	−0.196438	+	0.980516i	$0.562937\pi$
$332$	−1.42221	−0.0780538
$333$	9.72463	0.532906
$334$	−18.6386	−1.01986
$335$	−5.71023	−0.311983
$336$	−1.30974	−0.0714523
$337$	−25.5725	−1.39302	−0.696510	−	0.717547i	$-0.745265\pi$
$337$	−25.5725	−1.39302	−0.696510	+	0.717547i	$0.745265\pi$
$338$	15.5380	0.845153
$339$	−56.3778	−3.06202
$340$	15.7688	0.855183
$341$	31.5454	1.70828
$342$	−12.2240	−0.660998
$343$	−5.90624	−0.318907
$344$	−2.94589	−0.158832
$345$	17.9467	0.966218
$346$	−9.29293	−0.499591
$347$	−16.3406	−0.877212	−0.438606	−	0.898679i	$-0.644528\pi$
$347$	−16.3406	−0.877212	−0.438606	+	0.898679i	$0.644528\pi$
$348$	−26.5438	−1.42290
$349$	7.97244	0.426755	0.213377	−	0.976970i	$-0.431554\pi$
$349$	7.97244	0.426755	0.213377	+	0.976970i	$0.431554\pi$
$350$	3.54478	0.189477
$351$	55.4645	2.96047
$352$	−3.29238	−0.175484
$353$	−25.6068	−1.36291	−0.681456	−	0.731860i	$-0.738653\pi$
$353$	−25.6068	−1.36291	−0.681456	+	0.731860i	$0.738653\pi$
$354$	12.3882	0.658427
$355$	55.3200	2.93608
$356$	9.65720	0.511830
$357$	−5.66469	−0.299807
$358$	−2.40565	−0.127143
$359$	−20.4867	−1.08125	−0.540623	−	0.841265i	$-0.681811\pi$
$359$	−20.4867	−1.08125	−0.540623	+	0.841265i	$0.681811\pi$
$360$	23.2920	1.22759
$361$	−15.3387	−0.807302
$362$	−23.7641	−1.24901
$363$	0.491045	0.0257732
$364$	−2.28349	−0.119688
$365$	−39.2108	−2.05239
$366$	17.5874	0.919310
$367$	−23.4282	−1.22294	−0.611471	−	0.791267i	$-0.709422\pi$
$367$	−23.4282	−1.22294	−0.611471	+	0.791267i	$0.709422\pi$
$368$	−1.60649	−0.0837442
$369$	−67.7420	−3.52651
$370$	5.54988	0.288524
$371$	1.72293	0.0894502
$372$	29.3579	1.52214
$373$	8.62709	0.446694	0.223347	−	0.974739i	$-0.428302\pi$
$373$	8.62709	0.446694	0.223347	+	0.974739i	$0.428302\pi$
$374$	−14.2397	−0.736315
$375$	−36.7851	−1.89957
$376$	−12.4740	−0.643298
$377$	−46.2782	−2.38345
$378$	−4.43805	−0.228268
$379$	11.5306	0.592290	0.296145	−	0.955143i	$-0.404299\pi$
$379$	11.5306	0.592290	0.296145	+	0.955143i	$0.404299\pi$
$380$	−6.97628	−0.357876
$381$	56.5877	2.89908
$382$	11.8252	0.605028
$383$	29.3435	1.49938	0.749691	−	0.661788i	$-0.230202\pi$
$383$	29.3435	1.49938	0.749691	+	0.661788i	$0.230202\pi$
$384$	−3.06406	−0.156362
$385$	−5.13105	−0.261502
$386$	−5.60247	−0.285158
$387$	−18.8198	−0.956662
$388$	−3.21631	−0.163284
$389$	−13.9766	−0.708641	−0.354321	−	0.935124i	$-0.615288\pi$
$389$	−13.9766	−0.708641	−0.354321	+	0.935124i	$0.615288\pi$
$390$	59.6784	3.02194
$391$	−6.94815	−0.351383
$392$	−6.81728	−0.344325
$393$	−67.6961	−3.41482
$394$	−3.45943	−0.174284
$395$	21.4763	1.08059
$396$	−21.0333	−1.05696
$397$	−18.3041	−0.918657	−0.459329	−	0.888266i	$-0.651910\pi$
$397$	−18.3041	−0.918657	−0.459329	+	0.888266i	$0.651910\pi$
$398$	−11.8661	−0.594796
$399$	2.50612	0.125463
$400$	8.29280	0.414640
$401$	26.3455	1.31563	0.657816	−	0.753179i	$-0.271480\pi$
$401$	26.3455	1.31563	0.657816	+	0.753179i	$0.271480\pi$
$402$	4.79891	0.239348
$403$	51.1845	2.54968
$404$	−17.3737	−0.864375
$405$	46.1111	2.29128
$406$	3.70300	0.183777
$407$	−5.01169	−0.248420
$408$	−13.2522	−0.656082
$409$	−20.6661	−1.02187	−0.510937	−	0.859618i	$-0.670701\pi$
$409$	−20.6661	−1.02187	−0.510937	+	0.859618i	$0.670701\pi$
$410$	−38.6606	−1.90931
$411$	48.7075	2.40256
$412$	−1.53717	−0.0757311
$413$	−1.72822	−0.0850403
$414$	−10.2631	−0.504402
$415$	−5.18527	−0.254535
$416$	−5.34209	−0.261918
$417$	−7.80664	−0.382293
$418$	6.29977	0.308132
$419$	32.7769	1.60126	0.800628	−	0.599162i	$-0.204500\pi$
$419$	32.7769	1.60126	0.800628	+	0.599162i	$0.204500\pi$
$420$	−4.77523	−0.233007
$421$	9.02226	0.439718	0.219859	−	0.975532i	$-0.429440\pi$
$421$	9.02226	0.439718	0.219859	+	0.975532i	$0.429440\pi$
$422$	−21.1152	−1.02787
$423$	−79.6900	−3.87466
$424$	4.03069	0.195748
$425$	35.8667	1.73979
$426$	−46.4913	−2.25251
$427$	−2.45354	−0.118735
$428$	7.52353	0.363664
$429$	−53.8913	−2.60190
$430$	−10.7405	−0.517953
$431$	−1.15016	−0.0554014	−0.0277007	−	0.999616i	$-0.508819\pi$
$431$	−1.15016	−0.0554014	−0.0277007	+	0.999616i	$0.508819\pi$
$432$	−10.3825	−0.499530
$433$	−34.8008	−1.67242	−0.836210	−	0.548409i	$-0.815234\pi$
$433$	−34.8008	−1.67242	−0.836210	+	0.548409i	$0.815234\pi$
$434$	−4.09558	−0.196594
$435$	−96.7768	−4.64009
$436$	−12.6818	−0.607347
$437$	3.07393	0.147046
$438$	32.9530	1.57456
$439$	23.5405	1.12353	0.561763	−	0.827298i	$-0.310123\pi$
$439$	23.5405	1.12353	0.561763	+	0.827298i	$0.310123\pi$
$440$	−12.0038	−0.572257
$441$	−43.5521	−2.07391
$442$	−23.1048	−1.09898
$443$	−32.5922	−1.54850	−0.774250	−	0.632880i	$-0.781873\pi$
$443$	−32.5922	−1.54850	−0.774250	+	0.632880i	$0.781873\pi$
$444$	−4.66415	−0.221351
$445$	35.2095	1.66909
$446$	−14.1020	−0.667750
$447$	−16.2957	−0.770760
$448$	0.427453	0.0201953
$449$	−22.5919	−1.06618	−0.533088	−	0.846060i	$-0.678969\pi$
$449$	−22.5919	−1.06618	−0.533088	+	0.846060i	$0.678969\pi$
$450$	52.9784	2.49743
$451$	34.9116	1.64392
$452$	18.3997	0.865448
$453$	−25.9785	−1.22058
$454$	16.5441	0.776453
$455$	−8.32546	−0.390303
$456$	5.86291	0.274556
$457$	−12.8700	−0.602033	−0.301016	−	0.953619i	$-0.597326\pi$
$457$	−12.8700	−0.602033	−0.301016	+	0.953619i	$0.597326\pi$
$458$	18.8483	0.880723
$459$	−44.9049	−2.09598
$460$	−5.85716	−0.273091
$461$	−5.10292	−0.237667	−0.118833	−	0.992914i	$-0.537915\pi$
$461$	−5.10292	−0.237667	−0.118833	+	0.992914i	$0.537915\pi$
$462$	4.31217	0.200620
$463$	−13.5557	−0.629986	−0.314993	−	0.949094i	$-0.602002\pi$
$463$	−13.5557	−0.629986	−0.314993	+	0.949094i	$0.602002\pi$
$464$	8.66294	0.402167
$465$	107.037	4.96371
$466$	−0.139630	−0.00646824
$467$	−7.82045	−0.361887	−0.180944	−	0.983493i	$-0.557915\pi$
$467$	−7.82045	−0.361887	−0.180944	+	0.983493i	$0.557915\pi$
$468$	−34.1279	−1.57756
$469$	−0.669474	−0.0309134
$470$	−45.4794	−2.09781
$471$	−58.9818	−2.71774
$472$	−4.04307	−0.186097
$473$	9.69897	0.445959
$474$	−18.0488	−0.829009
$475$	−15.8678	−0.728065
$476$	1.84875	0.0847374
$477$	25.7500	1.17901
$478$	12.7550	0.583399
$479$	−41.9173	−1.91525	−0.957625	−	0.288017i	$-0.907004\pi$
$479$	−41.9173	−1.91525	−0.957625	+	0.288017i	$0.907004\pi$
$480$	−11.1714	−0.509900
$481$	−8.13180	−0.370778
$482$	2.38148	0.108474
$483$	2.10409	0.0957396
$484$	−0.160260	−0.00728452
$485$	−11.7264	−0.532471
$486$	−7.60449	−0.344947
$487$	16.1800	0.733184	0.366592	−	0.930382i	$-0.380525\pi$
$487$	16.1800	0.733184	0.366592	+	0.930382i	$0.380525\pi$
$488$	−5.73991	−0.259833
$489$	−12.1615	−0.549961
$490$	−24.8553	−1.12285
$491$	8.66285	0.390949	0.195474	−	0.980709i	$-0.437375\pi$
$491$	8.66285	0.390949	0.195474	+	0.980709i	$0.437375\pi$
$492$	32.4906	1.46479
$493$	37.4676	1.68745
$494$	10.2218	0.459900
$495$	−76.6859	−3.44678
$496$	−9.58136	−0.430216
$497$	6.48578	0.290927
$498$	4.35773	0.195275
$499$	−27.2797	−1.22121	−0.610603	−	0.791937i	$-0.709073\pi$
$499$	−27.2797	−1.22121	−0.610603	+	0.791937i	$0.709073\pi$
$500$	12.0053	0.536894
$501$	57.1100	2.55149
$502$	11.2533	0.502261
$503$	27.4578	1.22428	0.612142	−	0.790748i	$-0.290308\pi$
$503$	27.4578	1.22428	0.612142	+	0.790748i	$0.290308\pi$
$504$	2.73078	0.121638
$505$	−63.3434	−2.81874
$506$	5.28918	0.235133
$507$	−47.6093	−2.11440
$508$	−18.4682	−0.819394
$509$	29.7658	1.31935	0.659673	−	0.751553i	$-0.270695\pi$
$509$	29.7658	1.31935	0.659673	+	0.751553i	$0.270695\pi$
$510$	−48.3166	−2.13949
$511$	−4.59712	−0.203365
$512$	1.00000	0.0441942
$513$	19.8664	0.877123
$514$	28.1024	1.23954
$515$	−5.60442	−0.246960
$516$	9.02639	0.397365
$517$	41.0691	1.80622
$518$	0.650674	0.0285890
$519$	28.4741	1.24988
$520$	−19.4769	−0.854118
$521$	23.0911	1.01164	0.505821	−	0.862639i	$-0.331190\pi$
$521$	23.0911	1.01164	0.505821	+	0.862639i	$0.331190\pi$
$522$	55.3431	2.42230
$523$	−10.1225	−0.442624	−0.221312	−	0.975203i	$-0.571034\pi$
$523$	−10.1225	−0.442624	−0.221312	+	0.975203i	$0.571034\pi$
$524$	22.0936	0.965162
$525$	−10.8614	−0.474032
$526$	−2.89804	−0.126361
$527$	−41.4398	−1.80514
$528$	10.0880	0.439026
$529$	−20.4192	−0.887790
$530$	14.6956	0.638337
$531$	−25.8291	−1.12089
$532$	−0.817907	−0.0354608
$533$	56.6463	2.45362
$534$	−29.5903	−1.28050
$535$	27.4303	1.18591
$536$	−1.56619	−0.0676492
$537$	7.37108	0.318085
$538$	−7.89923	−0.340560
$539$	22.4451	0.966777
$540$	−37.8540	−1.62898
$541$	−34.0838	−1.46538	−0.732688	−	0.680564i	$-0.761735\pi$
$541$	−34.0838	−1.46538	−0.732688	+	0.680564i	$0.761735\pi$
$542$	17.5855	0.755362
$543$	72.8148	3.12478
$544$	4.32504	0.185435
$545$	−46.2369	−1.98057
$546$	6.99677	0.299434
$547$	34.9718	1.49529	0.747643	−	0.664101i	$-0.231186\pi$
$547$	34.9718	1.49529	0.747643	+	0.664101i	$0.231186\pi$
$548$	−15.8964	−0.679059
$549$	−36.6693	−1.56501
$550$	−27.3030	−1.16420
$551$	−16.5760	−0.706163
$552$	4.92240	0.209511
$553$	2.51790	0.107072
$554$	−16.9097	−0.718424
$555$	−17.0052	−0.721830
$556$	2.54780	0.108051
$557$	−10.2759	−0.435405	−0.217703	−	0.976015i	$-0.569856\pi$
$557$	−10.2759	−0.435405	−0.217703	+	0.976015i	$0.569856\pi$
$558$	−61.2104	−2.59124
$559$	15.7372	0.665613
$560$	1.55846	0.0658571
$561$	43.6312	1.84211
$562$	−12.2586	−0.517096
$563$	−33.6082	−1.41642	−0.708208	−	0.706004i	$-0.750496\pi$
$563$	−33.6082	−1.41642	−0.708208	+	0.706004i	$0.750496\pi$
$564$	38.2212	1.60940
$565$	67.0840	2.82224
$566$	−27.5748	−1.15906
$567$	5.40612	0.227036
$568$	15.1731	0.636649
$569$	28.7828	1.20664	0.603319	−	0.797500i	$-0.293844\pi$
$569$	28.7828	1.20664	0.603319	+	0.797500i	$0.293844\pi$
$570$	21.3758	0.895332
$571$	−17.2119	−0.720294	−0.360147	−	0.932896i	$-0.617273\pi$
$571$	−17.2119	−0.720294	−0.360147	+	0.932896i	$0.617273\pi$
$572$	17.5882	0.735399
$573$	−36.2330	−1.51366
$574$	−4.53261	−0.189188
$575$	−13.3223	−0.555579
$576$	6.38849	0.266187
$577$	−7.57466	−0.315337	−0.157669	−	0.987492i	$-0.550398\pi$
$577$	−7.57466	−0.315337	−0.157669	+	0.987492i	$0.550398\pi$
$578$	1.70597	0.0709592
$579$	17.1663	0.713408
$580$	31.5845	1.31147
$581$	−0.607927	−0.0252211
$582$	9.85498	0.408502
$583$	−13.2706	−0.549611
$584$	−10.7547	−0.445032
$585$	−124.428	−5.14446
$586$	28.4537	1.17541
$587$	13.8535	0.571795	0.285897	−	0.958260i	$-0.407708\pi$
$587$	13.8535	0.571795	0.285897	+	0.958260i	$0.407708\pi$
$588$	20.8886	0.861431
$589$	18.3334	0.755414
$590$	−14.7407	−0.606867
$591$	10.5999	0.436023
$592$	1.52221	0.0625625
$593$	5.97744	0.245464	0.122732	−	0.992440i	$-0.460834\pi$
$593$	5.97744	0.245464	0.122732	+	0.992440i	$0.460834\pi$
$594$	34.1832	1.40255
$595$	6.74042	0.276330
$596$	5.31833	0.217847
$597$	36.3586	1.48806
$598$	8.58203	0.350945
$599$	28.8526	1.17888	0.589442	−	0.807811i	$-0.299348\pi$
$599$	28.8526	1.17888	0.589442	+	0.807811i	$0.299348\pi$
$600$	−25.4097	−1.03735
$601$	−26.8549	−1.09544	−0.547718	−	0.836663i	$-0.684503\pi$
$601$	−26.8549	−1.09544	−0.547718	+	0.836663i	$0.684503\pi$
$602$	−1.25923	−0.0513223
$603$	−10.0056	−0.407459
$604$	8.47845	0.344983
$605$	−0.584295	−0.0237550
$606$	53.2342	2.16249
$607$	8.88663	0.360697	0.180348	−	0.983603i	$-0.442277\pi$
$607$	8.88663	0.360697	0.180348	+	0.983603i	$0.442277\pi$
$608$	−1.91344	−0.0776004
$609$	−11.3462	−0.459772
$610$	−20.9273	−0.847322
$611$	66.6373	2.69586
$612$	27.6305	1.11690
$613$	39.6775	1.60256	0.801280	−	0.598290i	$-0.204153\pi$
$613$	39.6775	1.60256	0.801280	+	0.598290i	$0.204153\pi$
$614$	6.47632	0.261363
$615$	118.458	4.77671
$616$	−1.40734	−0.0567032
$617$	0.774124	0.0311651	0.0155825	−	0.999879i	$-0.495040\pi$
$617$	0.774124	0.0311651	0.0155825	+	0.999879i	$0.495040\pi$
$618$	4.71000	0.189464
$619$	16.0232	0.644027	0.322013	−	0.946735i	$-0.395640\pi$
$619$	16.0232	0.644027	0.322013	+	0.946735i	$0.395640\pi$
$620$	−34.9330	−1.40294
$621$	16.6795	0.669324
$622$	−20.3783	−0.817097
$623$	4.12800	0.165385
$624$	16.3685	0.655265
$625$	2.30655	0.0922619
$626$	−31.1640	−1.24557
$627$	−19.3029	−0.770884
$628$	19.2495	0.768141
$629$	6.58363	0.262506
$630$	9.95622	0.396665
$631$	−8.28353	−0.329762	−0.164881	−	0.986313i	$-0.552724\pi$
$631$	−8.28353	−0.329762	−0.164881	+	0.986313i	$0.552724\pi$
$632$	5.89048	0.234311
$633$	64.6985	2.57153
$634$	1.50721	0.0598590
$635$	−67.3338	−2.67206
$636$	−12.3503	−0.489721
$637$	36.4186	1.44296
$638$	−28.5217	−1.12918
$639$	96.9331	3.83461
$640$	3.64593	0.144118
$641$	28.7015	1.13364	0.566821	−	0.823841i	$-0.308173\pi$
$641$	28.7015	1.13364	0.566821	+	0.823841i	$0.308173\pi$
$642$	−23.0526	−0.909813
$643$	14.3209	0.564763	0.282382	−	0.959302i	$-0.408876\pi$
$643$	14.3209	0.564763	0.282382	+	0.959302i	$0.408876\pi$
$644$	−0.686700	−0.0270598
$645$	32.9096	1.29581
$646$	−8.27572	−0.325604
$647$	−10.6264	−0.417767	−0.208884	−	0.977941i	$-0.566983\pi$
$647$	−10.6264	−0.417767	−0.208884	+	0.977941i	$0.566983\pi$
$648$	12.6473	0.496832
$649$	13.3113	0.522515
$650$	−44.3009	−1.73762
$651$	12.5491	0.491839
$652$	3.96907	0.155441
$653$	35.0340	1.37099	0.685493	−	0.728080i	$-0.259587\pi$
$653$	35.0340	1.37099	0.685493	+	0.728080i	$0.259587\pi$
$654$	38.8578	1.51946
$655$	80.5516	3.14741
$656$	−10.6038	−0.414007
$657$	−68.7061	−2.68048
$658$	−5.33205	−0.207865
$659$	49.7090	1.93639	0.968193	−	0.250204i	$-0.0804978\pi$
$659$	49.7090	1.93639	0.968193	+	0.250204i	$0.0804978\pi$
$660$	36.7803	1.43167
$661$	21.7804	0.847161	0.423580	−	0.905858i	$-0.360773\pi$
$661$	21.7804	0.847161	0.423580	+	0.905858i	$0.360773\pi$
$662$	−7.14775	−0.277805
$663$	70.7945	2.74943
$664$	−1.42221	−0.0551924
$665$	−2.98203	−0.115638
$666$	9.72463	0.376822
$667$	−13.9169	−0.538866
$668$	−18.6386	−0.721151
$669$	43.2095	1.67058
$670$	−5.71023	−0.220605
$671$	18.8979	0.729547
$672$	−1.30974	−0.0505244
$673$	−37.6032	−1.44950	−0.724748	−	0.689014i	$-0.758044\pi$
$673$	−37.6032	−1.44950	−0.724748	+	0.689014i	$0.758044\pi$
$674$	−25.5725	−0.985014
$675$	−86.1003	−3.31400
$676$	15.5380	0.597614
$677$	3.50568	0.134734	0.0673671	−	0.997728i	$-0.478540\pi$
$677$	3.50568	0.134734	0.0673671	+	0.997728i	$0.478540\pi$
$678$	−56.3778	−2.16518
$679$	−1.37482	−0.0527608
$680$	15.7688	0.604706
$681$	−50.6922	−1.94253
$682$	31.5454	1.20794
$683$	12.1203	0.463771	0.231885	−	0.972743i	$-0.425511\pi$
$683$	12.1203	0.463771	0.231885	+	0.972743i	$0.425511\pi$
$684$	−12.2240	−0.467396
$685$	−57.9570	−2.21442
$686$	−5.90624	−0.225501
$687$	−57.7524	−2.20339
$688$	−2.94589	−0.112311
$689$	−21.5323	−0.820317
$690$	17.9467	0.683220
$691$	35.5149	1.35105	0.675526	−	0.737336i	$-0.263917\pi$
$691$	35.5149	1.35105	0.675526	+	0.737336i	$0.263917\pi$
$692$	−9.29293	−0.353264
$693$	−8.99075	−0.341530
$694$	−16.3406	−0.620283
$695$	9.28912	0.352356
$696$	−26.5438	−1.00614
$697$	−45.8617	−1.73714
$698$	7.97244	0.301761
$699$	0.427835	0.0161822
$700$	3.54478	0.133980
$701$	−19.3387	−0.730411	−0.365205	−	0.930927i	$-0.619001\pi$
$701$	−19.3387	−0.730411	−0.365205	+	0.930927i	$0.619001\pi$
$702$	55.4645	2.09337
$703$	−2.91267	−0.109853
$704$	−3.29238	−0.124086
$705$	139.352	5.24829
$706$	−25.6068	−0.963724
$707$	−7.42645	−0.279300
$708$	12.3882	0.465578
$709$	22.9082	0.860334	0.430167	−	0.902749i	$-0.358455\pi$
$709$	22.9082	0.860334	0.430167	+	0.902749i	$0.358455\pi$
$710$	55.3200	2.07612
$711$	37.6312	1.41128
$712$	9.65720	0.361919
$713$	15.3924	0.576449
$714$	−5.66469	−0.211996
$715$	64.1253	2.39815
$716$	−2.40565	−0.0899035
$717$	−39.0821	−1.45955
$718$	−20.4867	−0.764556
$719$	−26.7945	−0.999268	−0.499634	−	0.866237i	$-0.666532\pi$
$719$	−26.7945	−0.999268	−0.499634	+	0.866237i	$0.666532\pi$
$720$	23.2920	0.868040
$721$	−0.657069	−0.0244705
$722$	−15.3387	−0.570849
$723$	−7.29701	−0.271379
$724$	−23.7641	−0.883187
$725$	71.8400	2.66807
$726$	0.491045	0.0182244
$727$	−26.5448	−0.984491	−0.492245	−	0.870456i	$-0.663824\pi$
$727$	−26.5448	−0.984491	−0.492245	+	0.870456i	$0.663824\pi$
$728$	−2.28349	−0.0846319
$729$	−14.6412	−0.542267
$730$	−39.2108	−1.45126
$731$	−12.7411	−0.471246
$732$	17.5874	0.650051
$733$	33.6463	1.24276	0.621378	−	0.783511i	$-0.286573\pi$
$733$	33.6463	1.24276	0.621378	+	0.783511i	$0.286573\pi$
$734$	−23.4282	−0.864750
$735$	76.1583	2.80914
$736$	−1.60649	−0.0592161
$737$	5.15650	0.189942
$738$	−67.7420	−2.49362
$739$	−7.20246	−0.264947	−0.132473	−	0.991187i	$-0.542292\pi$
$739$	−7.20246	−0.264947	−0.132473	+	0.991187i	$0.542292\pi$
$740$	5.54988	0.204018
$741$	−31.3202	−1.15058
$742$	1.72293	0.0632508
$743$	22.4972	0.825343	0.412672	−	0.910880i	$-0.364596\pi$
$743$	22.4972	0.825343	0.412672	+	0.910880i	$0.364596\pi$
$744$	29.3579	1.07631
$745$	19.3903	0.710404
$746$	8.62709	0.315860
$747$	−9.08575	−0.332430
$748$	−14.2397	−0.520654
$749$	3.21596	0.117509
$750$	−36.7851	−1.34320
$751$	31.1247	1.13576	0.567879	−	0.823112i	$-0.307764\pi$
$751$	31.1247	1.13576	0.567879	+	0.823112i	$0.307764\pi$
$752$	−12.4740	−0.454880
$753$	−34.4809	−1.25656
$754$	−46.2782	−1.68535
$755$	30.9118	1.12500
$756$	−4.43805	−0.161410
$757$	−5.97855	−0.217294	−0.108647	−	0.994080i	$-0.534652\pi$
$757$	−5.97855	−0.217294	−0.108647	+	0.994080i	$0.534652\pi$
$758$	11.5306	0.418812
$759$	−16.2064	−0.588254
$760$	−6.97628	−0.253056
$761$	−3.74245	−0.135664	−0.0678318	−	0.997697i	$-0.521608\pi$
$761$	−3.74245	−0.135664	−0.0678318	+	0.997697i	$0.521608\pi$
$762$	56.5877	2.04996
$763$	−5.42087	−0.196249
$764$	11.8252	0.427819
$765$	100.739	3.64222
$766$	29.3435	1.06022
$767$	21.5985	0.779875
$768$	−3.06406	−0.110565
$769$	34.4471	1.24219	0.621097	−	0.783734i	$-0.286687\pi$
$769$	34.4471	1.24219	0.621097	+	0.783734i	$0.286687\pi$
$770$	−5.13105	−0.184910
$771$	−86.1075	−3.10109
$772$	−5.60247	−0.201637
$773$	−3.40024	−0.122298	−0.0611491	−	0.998129i	$-0.519477\pi$
$773$	−3.40024	−0.122298	−0.0611491	+	0.998129i	$0.519477\pi$
$774$	−18.8198	−0.676463
$775$	−79.4563	−2.85416
$776$	−3.21631	−0.115459
$777$	−1.99371	−0.0715238
$778$	−13.9766	−0.501085
$779$	20.2897	0.726954
$780$	59.6784	2.13683
$781$	−49.9555	−1.78755
$782$	−6.94815	−0.248465
$783$	−89.9433	−3.21431
$784$	−6.81728	−0.243474
$785$	70.1825	2.50492
$786$	−67.6961	−2.41464
$787$	12.6171	0.449751	0.224876	−	0.974387i	$-0.427802\pi$
$787$	12.6171	0.449751	0.224876	+	0.974387i	$0.427802\pi$
$788$	−3.45943	−0.123237
$789$	8.87979	0.316129
$790$	21.4763	0.764091
$791$	7.86500	0.279647
$792$	−21.0333	−0.747386
$793$	30.6631	1.08888
$794$	−18.3041	−0.649589
$795$	−45.0283	−1.59699
$796$	−11.8661	−0.420584
$797$	−30.5035	−1.08049	−0.540245	−	0.841508i	$-0.681668\pi$
$797$	−30.5035	−1.08049	−0.540245	+	0.841508i	$0.681668\pi$
$798$	2.50612	0.0887157
$799$	−53.9506	−1.90864
$800$	8.29280	0.293195
$801$	61.6949	2.17988
$802$	26.3455	0.930292
$803$	35.4084	1.24954
$804$	4.79891	0.169245
$805$	−2.50366	−0.0882424
$806$	51.1845	1.80290
$807$	24.2037	0.852012
$808$	−17.3737	−0.611206
$809$	−23.2162	−0.816238	−0.408119	−	0.912929i	$-0.633815\pi$
$809$	−23.2162	−0.816238	−0.408119	+	0.912929i	$0.633815\pi$
$810$	46.1111	1.62018
$811$	12.0573	0.423390	0.211695	−	0.977336i	$-0.432102\pi$
$811$	12.0573	0.423390	0.211695	+	0.977336i	$0.432102\pi$
$812$	3.70300	0.129950
$813$	−53.8831	−1.88976
$814$	−5.01169	−0.175660
$815$	14.4710	0.506895
$816$	−13.2522	−0.463920
$817$	5.63679	0.197206
$818$	−20.6661	−0.722574
$819$	−14.5881	−0.509748
$820$	−38.6606	−1.35009
$821$	6.66005	0.232437	0.116219	−	0.993224i	$-0.462923\pi$
$821$	6.66005	0.232437	0.116219	+	0.993224i	$0.462923\pi$
$822$	48.7075	1.69887
$823$	24.8897	0.867601	0.433800	−	0.901009i	$-0.357172\pi$
$823$	24.8897	0.867601	0.433800	+	0.901009i	$0.357172\pi$
$824$	−1.53717	−0.0535500
$825$	83.6582	2.91260
$826$	−1.72822	−0.0601326
$827$	8.33765	0.289928	0.144964	−	0.989437i	$-0.453693\pi$
$827$	8.33765	0.289928	0.144964	+	0.989437i	$0.453693\pi$
$828$	−10.2631	−0.356666
$829$	46.0747	1.60024	0.800120	−	0.599840i	$-0.204769\pi$
$829$	46.0747	1.60024	0.800120	+	0.599840i	$0.204769\pi$
$830$	−5.18527	−0.179983
$831$	51.8124	1.79735
$832$	−5.34209	−0.185204
$833$	−29.4850	−1.02160
$834$	−7.80664	−0.270322
$835$	−67.9552	−2.35169
$836$	6.29977	0.217882
$837$	99.4788	3.43849
$838$	32.7769	1.13226
$839$	0.844533	0.0291565	0.0145783	−	0.999894i	$-0.495359\pi$
$839$	0.844533	0.0291565	0.0145783	+	0.999894i	$0.495359\pi$
$840$	−4.77523	−0.164761
$841$	46.0465	1.58781
$842$	9.02226	0.310928
$843$	37.5610	1.29367
$844$	−21.1152	−0.726817
$845$	56.6503	1.94883
$846$	−79.6900	−2.73980
$847$	−0.0685034	−0.00235381
$848$	4.03069	0.138415
$849$	84.4910	2.89972
$850$	35.8667	1.23022
$851$	−2.44542	−0.0838280
$852$	−46.4913	−1.59277
$853$	−16.5767	−0.567574	−0.283787	−	0.958887i	$-0.591591\pi$
$853$	−16.5767	−0.567574	−0.283787	+	0.958887i	$0.591591\pi$
$854$	−2.45354	−0.0839585
$855$	−44.5679	−1.52419
$856$	7.52353	0.257149
$857$	22.8912	0.781947	0.390974	−	0.920402i	$-0.372138\pi$
$857$	22.8912	0.781947	0.390974	+	0.920402i	$0.372138\pi$
$858$	−53.8913	−1.83982
$859$	37.5173	1.28007	0.640037	−	0.768344i	$-0.278919\pi$
$859$	37.5173	1.28007	0.640037	+	0.768344i	$0.278919\pi$
$860$	−10.7405	−0.366248
$861$	13.8882	0.473309
$862$	−1.15016	−0.0391747
$863$	−8.14990	−0.277426	−0.138713	−	0.990333i	$-0.544297\pi$
$863$	−8.14990	−0.277426	−0.138713	+	0.990333i	$0.544297\pi$
$864$	−10.3825	−0.353221
$865$	−33.8814	−1.15200
$866$	−34.8008	−1.18258
$867$	−5.22721	−0.177525
$868$	−4.09558	−0.139013
$869$	−19.3937	−0.657885
$870$	−96.7768	−3.28104
$871$	8.36675	0.283496
$872$	−12.6818	−0.429459
$873$	−20.5474	−0.695423
$874$	3.07393	0.103977
$875$	5.13171	0.173483
$876$	32.9530	1.11338
$877$	−21.3046	−0.719404	−0.359702	−	0.933067i	$-0.617122\pi$
$877$	−21.3046	−0.719404	−0.359702	+	0.933067i	$0.617122\pi$
$878$	23.5405	0.794452
$879$	−87.1838	−2.94064
$880$	−12.0038	−0.404647
$881$	22.4000	0.754674	0.377337	−	0.926076i	$-0.376840\pi$
$881$	22.4000	0.754674	0.377337	+	0.926076i	$0.376840\pi$
$882$	−43.5521	−1.46648
$883$	−35.3656	−1.19015	−0.595074	−	0.803671i	$-0.702877\pi$
$883$	−35.3656	−1.19015	−0.595074	+	0.803671i	$0.702877\pi$
$884$	−23.1048	−0.777097
$885$	45.1666	1.51826
$886$	−32.5922	−1.09496
$887$	−43.9936	−1.47716	−0.738580	−	0.674166i	$-0.764503\pi$
$887$	−43.9936	−1.47716	−0.738580	+	0.674166i	$0.764503\pi$
$888$	−4.66415	−0.156519
$889$	−7.89429	−0.264766
$890$	35.2095	1.18022
$891$	−41.6396	−1.39498
$892$	−14.1020	−0.472171
$893$	23.8683	0.798723
$894$	−16.2957	−0.545010
$895$	−8.77085	−0.293177
$896$	0.427453	0.0142802
$897$	−26.2959	−0.877994
$898$	−22.5919	−0.753901
$899$	−83.0027	−2.76830
$900$	52.9784	1.76595
$901$	17.4329	0.580775
$902$	34.9116	1.16243
$903$	3.85836	0.128398
$904$	18.3997	0.611964
$905$	−86.6423	−2.88009
$906$	−25.9785	−0.863078
$907$	−8.73097	−0.289907	−0.144954	−	0.989438i	$-0.546303\pi$
$907$	−8.73097	−0.289907	−0.144954	+	0.989438i	$0.546303\pi$
$908$	16.5441	0.549035
$909$	−110.992	−3.68137
$910$	−8.32546	−0.275986
$911$	35.4963	1.17605	0.588023	−	0.808844i	$-0.299906\pi$
$911$	35.4963	1.17605	0.588023	+	0.808844i	$0.299906\pi$
$912$	5.86291	0.194140
$913$	4.68244	0.154966
$914$	−12.8700	−0.425701
$915$	64.1226	2.11983
$916$	18.8483	0.622765
$917$	9.44397	0.311867
$918$	−44.9049	−1.48208
$919$	−48.3241	−1.59407	−0.797033	−	0.603935i	$-0.793598\pi$
$919$	−48.3241	−1.59407	−0.797033	+	0.603935i	$0.793598\pi$
$920$	−5.85716	−0.193105
$921$	−19.8439	−0.653878
$922$	−5.10292	−0.168056
$923$	−81.0561	−2.66799
$924$	4.31217	0.141860
$925$	12.6234	0.415055
$926$	−13.5557	−0.445467
$927$	−9.82021	−0.322538
$928$	8.66294	0.284375
$929$	21.6293	0.709635	0.354817	−	0.934936i	$-0.384543\pi$
$929$	21.6293	0.709635	0.354817	+	0.934936i	$0.384543\pi$
$930$	107.037	3.50988
$931$	13.0445	0.427516
$932$	−0.139630	−0.00457374
$933$	62.4405	2.04421
$934$	−7.82045	−0.255893
$935$	−51.9168	−1.69786
$936$	−34.1279	−1.11550
$937$	20.4911	0.669416	0.334708	−	0.942322i	$-0.391362\pi$
$937$	20.4911	0.669416	0.334708	+	0.942322i	$0.391362\pi$
$938$	−0.669474	−0.0218591
$939$	95.4886	3.11615
$940$	−45.4794	−1.48337
$941$	−13.3731	−0.435952	−0.217976	−	0.975954i	$-0.569945\pi$
$941$	−13.3731	−0.435952	−0.217976	+	0.975954i	$0.569945\pi$
$942$	−58.9818	−1.92173
$943$	17.0349	0.554732
$944$	−4.04307	−0.131591
$945$	−16.1808	−0.526361
$946$	9.69897	0.315341
$947$	−23.9056	−0.776827	−0.388413	−	0.921485i	$-0.626977\pi$
$947$	−23.9056	−0.776827	−0.388413	+	0.921485i	$0.626977\pi$
$948$	−18.0488	−0.586198
$949$	57.4525	1.86499
$950$	−15.8678	−0.514820
$951$	−4.61819	−0.149755
$952$	1.84875	0.0599184
$953$	−3.01136	−0.0975474	−0.0487737	−	0.998810i	$-0.515531\pi$
$953$	−3.01136	−0.0975474	−0.0487737	+	0.998810i	$0.515531\pi$
$954$	25.7500	0.833688
$955$	43.1137	1.39513
$956$	12.7550	0.412526
$957$	87.3922	2.82499
$958$	−41.9173	−1.35429
$959$	−6.79495	−0.219420
$960$	−11.1714	−0.360554
$961$	60.8025	1.96137
$962$	−8.13180	−0.262180
$963$	48.0640	1.54884
$964$	2.38148	0.0767024
$965$	−20.4262	−0.657543
$966$	2.10409	0.0676981
$967$	−16.3940	−0.527196	−0.263598	−	0.964633i	$-0.584909\pi$
$967$	−16.3940	−0.527196	−0.263598	+	0.964633i	$0.584909\pi$
$968$	−0.160260	−0.00515094
$969$	25.3573	0.814595
$970$	−11.7264	−0.376514
$971$	−17.1090	−0.549054	−0.274527	−	0.961579i	$-0.588521\pi$
$971$	−17.1090	−0.549054	−0.274527	+	0.961579i	$0.588521\pi$
$972$	−7.60449	−0.243914
$973$	1.08907	0.0349139
$974$	16.1800	0.518439
$975$	135.741	4.34719
$976$	−5.73991	−0.183730
$977$	29.7119	0.950568	0.475284	−	0.879832i	$-0.342345\pi$
$977$	29.7119	0.950568	0.475284	+	0.879832i	$0.342345\pi$
$978$	−12.1615	−0.388881
$979$	−31.7951	−1.01618
$980$	−24.8553	−0.793975
$981$	−81.0174	−2.58669
$982$	8.66285	0.276443
$983$	−33.2825	−1.06155	−0.530774	−	0.847514i	$-0.678099\pi$
$983$	−33.2825	−1.06155	−0.530774	+	0.847514i	$0.678099\pi$
$984$	32.4906	1.03576
$985$	−12.6128	−0.401879
$986$	37.4676	1.19321
$987$	16.3378	0.520036
$988$	10.2218	0.325198
$989$	4.73255	0.150486
$990$	−76.6859	−2.43724
$991$	−21.0690	−0.669279	−0.334639	−	0.942346i	$-0.608615\pi$
$991$	−21.0690	−0.669279	−0.334639	+	0.942346i	$0.608615\pi$
$992$	−9.58136	−0.304208
$993$	21.9011	0.695012
$994$	6.48578	0.205717
$995$	−43.2631	−1.37153
$996$	4.35773	0.138080
$997$	12.3031	0.389642	0.194821	−	0.980839i	$-0.437587\pi$
$997$	12.3031	0.389642	0.194821	+	0.980839i	$0.437587\pi$
$998$	−27.2797	−0.863524
$999$	−15.8044	−0.500030

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6022.2.a.b.1.5	✓	54

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6022.2.a.b.1.5	✓	54	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:	\( N \)	\(=\)	\( 6022 = 2 \cdot 3011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6022.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -3.06406 q^{3} +1.00000 q^{4} +3.64593 q^{5} -3.06406 q^{6} +0.427453 q^{7} +1.00000 q^{8} +6.38849 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -3.06406 q^{3} +1.00000 q^{4} +3.64593 q^{5} -3.06406 q^{6} +0.427453 q^{7} +1.00000 q^{8} +6.38849 q^{9} +3.64593 q^{10} -3.29238 q^{11} -3.06406 q^{12} -5.34209 q^{13} +0.427453 q^{14} -11.1714 q^{15} +1.00000 q^{16} +4.32504 q^{17} +6.38849 q^{18} -1.91344 q^{19} +3.64593 q^{20} -1.30974 q^{21} -3.29238 q^{22} -1.60649 q^{23} -3.06406 q^{24} +8.29280 q^{25} -5.34209 q^{26} -10.3825 q^{27} +0.427453 q^{28} +8.66294 q^{29} -11.1714 q^{30} -9.58136 q^{31} +1.00000 q^{32} +10.0880 q^{33} +4.32504 q^{34} +1.55846 q^{35} +6.38849 q^{36} +1.52221 q^{37} -1.91344 q^{38} +16.3685 q^{39} +3.64593 q^{40} -10.6038 q^{41} -1.30974 q^{42} -2.94589 q^{43} -3.29238 q^{44} +23.2920 q^{45} -1.60649 q^{46} -12.4740 q^{47} -3.06406 q^{48} -6.81728 q^{49} +8.29280 q^{50} -13.2522 q^{51} -5.34209 q^{52} +4.03069 q^{53} -10.3825 q^{54} -12.0038 q^{55} +0.427453 q^{56} +5.86291 q^{57} +8.66294 q^{58} -4.04307 q^{59} -11.1714 q^{60} -5.73991 q^{61} -9.58136 q^{62} +2.73078 q^{63} +1.00000 q^{64} -19.4769 q^{65} +10.0880 q^{66} -1.56619 q^{67} +4.32504 q^{68} +4.92240 q^{69} +1.55846 q^{70} +15.1731 q^{71} +6.38849 q^{72} -10.7547 q^{73} +1.52221 q^{74} -25.4097 q^{75} -1.91344 q^{76} -1.40734 q^{77} +16.3685 q^{78} +5.89048 q^{79} +3.64593 q^{80} +12.6473 q^{81} -10.6038 q^{82} -1.42221 q^{83} -1.30974 q^{84} +15.7688 q^{85} -2.94589 q^{86} -26.5438 q^{87} -3.29238 q^{88} +9.65720 q^{89} +23.2920 q^{90} -2.28349 q^{91} -1.60649 q^{92} +29.3579 q^{93} -12.4740 q^{94} -6.97628 q^{95} -3.06406 q^{96} -3.21631 q^{97} -6.81728 q^{98} -21.0333 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9}+O(q^{10}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9	\( 54 q + 54 q^{2} - 22 q^{3} + 54 q^{4} - 14 q^{5} - 22 q^{6} - 20 q^{7} + 54 q^{8} + 32 q^{9} - 14 q^{10} - 22 q^{11} - 22 q^{12} - 24 q^{13} - 20 q^{14} - 32 q^{15} + 54 q^{16} - 67 q^{17} + 32 q^{18} - 54 q^{19} - 14 q^{20} - 18 q^{21} - 22 q^{22} - 52 q^{23} - 22 q^{24} + 20 q^{25} - 24 q^{26} - 82 q^{27} - 20 q^{28} - 30 q^{29} - 32 q^{30} - 78 q^{31} + 54 q^{32} - 48 q^{33} - 67 q^{34} - 71 q^{35} + 32 q^{36} - 15 q^{37} - 54 q^{38} - 39 q^{39} - 14 q^{40} - 61 q^{41} - 18 q^{42} - 53 q^{43} - 22 q^{44} - 14 q^{45} - 52 q^{46} - 96 q^{47} - 22 q^{48} + 6 q^{49} + 20 q^{50} - 13 q^{51} - 24 q^{52} - 39 q^{53} - 82 q^{54} - 75 q^{55} - 20 q^{56} - 17 q^{57} - 30 q^{58} - 78 q^{59} - 32 q^{60} - 23 q^{61} - 78 q^{62} - 52 q^{63} + 54 q^{64} - 43 q^{65} - 48 q^{66} - 54 q^{67} - 67 q^{68} + 7 q^{69} - 71 q^{70} - 41 q^{71} + 32 q^{72} - 62 q^{73} - 15 q^{74} - 81 q^{75} - 54 q^{76} - 85 q^{77} - 39 q^{78} - 45 q^{79} - 14 q^{80} + 22 q^{81} - 61 q^{82} - 117 q^{83} - 18 q^{84} - 53 q^{86} - 84 q^{87} - 22 q^{88} - 60 q^{89} - 14 q^{90} - 60 q^{91} - 52 q^{92} + 26 q^{93} - 96 q^{94} - 44 q^{95} - 22 q^{96} - 48 q^{97} + 6 q^{98} + 7 q^{99}+O(q^{100}) \) 54 * q + 54 * q^2 - 22 * q^3 + 54 * q^4 - 14 * q^5 - 22 * q^6 - 20 * q^7 + 54 * q^8 + 32 * q^9 - 14 * q^10 - 22 * q^11 - 22 * q^12 - 24 * q^13 - 20 * q^14 - 32 * q^15 + 54 * q^16 - 67 * q^17 + 32 * q^18 - 54 * q^19 - 14 * q^20 - 18 * q^21 - 22 * q^22 - 52 * q^23 - 22 * q^24 + 20 * q^25 - 24 * q^26 - 82 * q^27 - 20 * q^28 - 30 * q^29 - 32 * q^30 - 78 * q^31 + 54 * q^32 - 48 * q^33 - 67 * q^34 - 71 * q^35 + 32 * q^36 - 15 * q^37 - 54 * q^38 - 39 * q^39 - 14 * q^40 - 61 * q^41 - 18 * q^42 - 53 * q^43 - 22 * q^44 - 14 * q^45 - 52 * q^46 - 96 * q^47 - 22 * q^48 + 6 * q^49 + 20 * q^50 - 13 * q^51 - 24 * q^52 - 39 * q^53 - 82 * q^54 - 75 * q^55 - 20 * q^56 - 17 * q^57 - 30 * q^58 - 78 * q^59 - 32 * q^60 - 23 * q^61 - 78 * q^62 - 52 * q^63 + 54 * q^64 - 43 * q^65 - 48 * q^66 - 54 * q^67 - 67 * q^68 + 7 * q^69 - 71 * q^70 - 41 * q^71 + 32 * q^72 - 62 * q^73 - 15 * q^74 - 81 * q^75 - 54 * q^76 - 85 * q^77 - 39 * q^78 - 45 * q^79 - 14 * q^80 + 22 * q^81 - 61 * q^82 - 117 * q^83 - 18 * q^84 - 53 * q^86 - 84 * q^87 - 22 * q^88 - 60 * q^89 - 14 * q^90 - 60 * q^91 - 52 * q^92 + 26 * q^93 - 96 * q^94 - 44 * q^95 - 22 * q^96 - 48 * q^97 + 6 * q^98 + 7 * q^99

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