LMFDB - Embedded newform 6026.2.a.l.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -1.53572 q^{3} +1.00000 q^{4} -3.94419 q^{5} +1.53572 q^{6} +4.26764 q^{7} -1.00000 q^{8} -0.641564 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.53572 q^{3} +1.00000 q^{4} -3.94419 q^{5} +1.53572 q^{6} +4.26764 q^{7} -1.00000 q^{8} -0.641564 q^{9} +3.94419 q^{10} +1.05593 q^{11} -1.53572 q^{12} +4.01212 q^{13} -4.26764 q^{14} +6.05717 q^{15} +1.00000 q^{16} +1.88404 q^{17} +0.641564 q^{18} +1.53204 q^{19} -3.94419 q^{20} -6.55390 q^{21} -1.05593 q^{22} -1.00000 q^{23} +1.53572 q^{24} +10.5566 q^{25} -4.01212 q^{26} +5.59242 q^{27} +4.26764 q^{28} -5.71070 q^{29} -6.05717 q^{30} +1.80242 q^{31} -1.00000 q^{32} -1.62162 q^{33} -1.88404 q^{34} -16.8324 q^{35} -0.641564 q^{36} +2.92481 q^{37} -1.53204 q^{38} -6.16149 q^{39} +3.94419 q^{40} -2.93369 q^{41} +6.55390 q^{42} +12.1007 q^{43} +1.05593 q^{44} +2.53045 q^{45} +1.00000 q^{46} +9.76213 q^{47} -1.53572 q^{48} +11.2128 q^{49} -10.5566 q^{50} -2.89336 q^{51} +4.01212 q^{52} +8.87351 q^{53} -5.59242 q^{54} -4.16480 q^{55} -4.26764 q^{56} -2.35278 q^{57} +5.71070 q^{58} +6.05509 q^{59} +6.05717 q^{60} +7.17215 q^{61} -1.80242 q^{62} -2.73797 q^{63} +1.00000 q^{64} -15.8245 q^{65} +1.62162 q^{66} -1.54216 q^{67} +1.88404 q^{68} +1.53572 q^{69} +16.8324 q^{70} -9.68409 q^{71} +0.641564 q^{72} +2.57077 q^{73} -2.92481 q^{74} -16.2120 q^{75} +1.53204 q^{76} +4.50635 q^{77} +6.16149 q^{78} -11.9977 q^{79} -3.94419 q^{80} -6.66370 q^{81} +2.93369 q^{82} -13.1505 q^{83} -6.55390 q^{84} -7.43102 q^{85} -12.1007 q^{86} +8.77004 q^{87} -1.05593 q^{88} -0.977823 q^{89} -2.53045 q^{90} +17.1223 q^{91} -1.00000 q^{92} -2.76801 q^{93} -9.76213 q^{94} -6.04265 q^{95} +1.53572 q^{96} +3.08429 q^{97} -11.2128 q^{98} -0.677449 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) $ 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−1.53572	−0.886648	−0.443324	−	0.896361i	$-0.646201\pi$
$3$	−1.53572	−0.886648	−0.443324	+	0.896361i	$0.646201\pi$
$4$	1.00000	0.500000
$5$	−3.94419	−1.76389	−0.881947	−	0.471349i	$-0.843767\pi$
$5$	−3.94419	−1.76389	−0.881947	+	0.471349i	$0.843767\pi$
$6$	1.53572	0.626955
$7$	4.26764	1.61302	0.806509	−	0.591222i	$-0.201354\pi$
$7$	4.26764	1.61302	0.806509	+	0.591222i	$0.201354\pi$
$8$	−1.00000	−0.353553
$9$	−0.641564	−0.213855
$10$	3.94419	1.24726
$11$	1.05593	0.318376	0.159188	−	0.987248i	$-0.449112\pi$
$11$	1.05593	0.318376	0.159188	+	0.987248i	$0.449112\pi$
$12$	−1.53572	−0.443324
$13$	4.01212	1.11276	0.556380	−	0.830928i	$-0.312190\pi$
$13$	4.01212	1.11276	0.556380	+	0.830928i	$0.312190\pi$
$14$	−4.26764	−1.14058
$15$	6.05717	1.56395
$16$	1.00000	0.250000
$17$	1.88404	0.456948	0.228474	−	0.973550i	$-0.426626\pi$
$17$	1.88404	0.456948	0.228474	+	0.973550i	$0.426626\pi$
$18$	0.641564	0.151218
$19$	1.53204	0.351474	0.175737	−	0.984437i	$-0.443769\pi$
$19$	1.53204	0.351474	0.175737	+	0.984437i	$0.443769\pi$
$20$	−3.94419	−0.881947
$21$	−6.55390	−1.43018
$22$	−1.05593	−0.225126
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	1.53572	0.313478
$25$	10.5566	2.11132
$26$	−4.01212	−0.786841
$27$	5.59242	1.07626
$28$	4.26764	0.806509
$29$	−5.71070	−1.06045	−0.530225	−	0.847857i	$-0.677893\pi$
$29$	−5.71070	−1.06045	−0.530225	+	0.847857i	$0.677893\pi$
$30$	−6.05717	−1.10588
$31$	1.80242	0.323724	0.161862	−	0.986813i	$-0.448250\pi$
$31$	1.80242	0.323724	0.161862	+	0.986813i	$0.448250\pi$
$32$	−1.00000	−0.176777
$33$	−1.62162	−0.282287
$34$	−1.88404	−0.323111
$35$	−16.8324	−2.84519
$36$	−0.641564	−0.106927
$37$	2.92481	0.480835	0.240418	−	0.970670i	$-0.422716\pi$
$37$	2.92481	0.480835	0.240418	+	0.970670i	$0.422716\pi$
$38$	−1.53204	−0.248530
$39$	−6.16149	−0.986627
$40$	3.94419	0.623631
$41$	−2.93369	−0.458165	−0.229083	−	0.973407i	$-0.573573\pi$
$41$	−2.93369	−0.458165	−0.229083	+	0.973407i	$0.573573\pi$
$42$	6.55390	1.01129
$43$	12.1007	1.84534	0.922671	−	0.385589i	$-0.126002\pi$
$43$	12.1007	1.84534	0.922671	+	0.385589i	$0.126002\pi$
$44$	1.05593	0.159188
$45$	2.53045	0.377217
$46$	1.00000	0.147442
$47$	9.76213	1.42395	0.711976	−	0.702204i	$-0.247800\pi$
$47$	9.76213	1.42395	0.711976	+	0.702204i	$0.247800\pi$
$48$	−1.53572	−0.221662
$49$	11.2128	1.60182
$50$	−10.5566	−1.49293
$51$	−2.89336	−0.405152
$52$	4.01212	0.556380
$53$	8.87351	1.21887	0.609435	−	0.792836i	$-0.291396\pi$
$53$	8.87351	1.21887	0.609435	+	0.792836i	$0.291396\pi$
$54$	−5.59242	−0.761032
$55$	−4.16480	−0.561581
$56$	−4.26764	−0.570288
$57$	−2.35278	−0.311634
$58$	5.71070	0.749852
$59$	6.05509	0.788306	0.394153	−	0.919045i	$-0.371038\pi$
$59$	6.05509	0.788306	0.394153	+	0.919045i	$0.371038\pi$
$60$	6.05717	0.781977
$61$	7.17215	0.918300	0.459150	−	0.888359i	$-0.348154\pi$
$61$	7.17215	0.918300	0.459150	+	0.888359i	$0.348154\pi$
$62$	−1.80242	−0.228908
$63$	−2.73797	−0.344951
$64$	1.00000	0.125000
$65$	−15.8245	−1.96279
$66$	1.62162	0.199607
$67$	−1.54216	−0.188405	−0.0942024	−	0.995553i	$-0.530030\pi$
$67$	−1.54216	−0.188405	−0.0942024	+	0.995553i	$0.530030\pi$
$68$	1.88404	0.228474
$69$	1.53572	0.184879
$70$	16.8324	2.01185
$71$	−9.68409	−1.14929	−0.574645	−	0.818403i	$-0.694860\pi$
$71$	−9.68409	−1.14929	−0.574645	+	0.818403i	$0.694860\pi$
$72$	0.641564	0.0756091
$73$	2.57077	0.300886	0.150443	−	0.988619i	$-0.451930\pi$
$73$	2.57077	0.300886	0.150443	+	0.988619i	$0.451930\pi$
$74$	−2.92481	−0.340002
$75$	−16.2120	−1.87200
$76$	1.53204	0.175737
$77$	4.50635	0.513546
$78$	6.16149	0.697651
$79$	−11.9977	−1.34984	−0.674922	−	0.737889i	$-0.735823\pi$
$79$	−11.9977	−1.34984	−0.674922	+	0.737889i	$0.735823\pi$
$80$	−3.94419	−0.440973
$81$	−6.66370	−0.740411
$82$	2.93369	0.323972
$83$	−13.1505	−1.44345	−0.721727	−	0.692178i	$-0.756651\pi$
$83$	−13.1505	−1.44345	−0.721727	+	0.692178i	$0.756651\pi$
$84$	−6.55390	−0.715089
$85$	−7.43102	−0.806007
$86$	−12.1007	−1.30485
$87$	8.77004	0.940247
$88$	−1.05593	−0.112563
$89$	−0.977823	−0.103649	−0.0518245	−	0.998656i	$-0.516504\pi$
$89$	−0.977823	−0.103649	−0.0518245	+	0.998656i	$0.516504\pi$
$90$	−2.53045	−0.266733
$91$	17.1223	1.79490
$92$	−1.00000	−0.104257
$93$	−2.76801	−0.287030
$94$	−9.76213	−1.00689
$95$	−6.04265	−0.619963
$96$	1.53572	0.156739
$97$	3.08429	0.313162	0.156581	−	0.987665i	$-0.449953\pi$
$97$	3.08429	0.313162	0.156581	+	0.987665i	$0.449953\pi$
$98$	−11.2128	−1.13266
$99$	−0.677449	−0.0680862
$100$	10.5566	1.05566
$101$	−8.65211	−0.860917	−0.430459	−	0.902610i	$-0.641648\pi$
$101$	−8.65211	−0.860917	−0.430459	+	0.902610i	$0.641648\pi$
$102$	2.89336	0.286486
$103$	−7.55045	−0.743968	−0.371984	−	0.928239i	$-0.621322\pi$
$103$	−7.55045	−0.743968	−0.371984	+	0.928239i	$0.621322\pi$
$104$	−4.01212	−0.393420
$105$	25.8498	2.52268
$106$	−8.87351	−0.861872
$107$	4.53633	0.438544	0.219272	−	0.975664i	$-0.429632\pi$
$107$	4.53633	0.438544	0.219272	+	0.975664i	$0.429632\pi$
$108$	5.59242	0.538131
$109$	−14.6416	−1.40241	−0.701207	−	0.712958i	$-0.747355\pi$
$109$	−14.6416	−1.40241	−0.701207	+	0.712958i	$0.747355\pi$
$110$	4.16480	0.397098
$111$	−4.49168	−0.426332
$112$	4.26764	0.403254
$113$	−9.73932	−0.916199	−0.458099	−	0.888901i	$-0.651470\pi$
$113$	−9.73932	−0.916199	−0.458099	+	0.888901i	$0.651470\pi$
$114$	2.35278	0.220358
$115$	3.94419	0.367797
$116$	−5.71070	−0.530225
$117$	−2.57403	−0.237969
$118$	−6.05509	−0.557417
$119$	8.04043	0.737065
$120$	−6.05717	−0.552941
$121$	−9.88500	−0.898637
$122$	−7.17215	−0.649336
$123$	4.50532	0.406231
$124$	1.80242	0.161862
$125$	−21.9163	−1.96025
$126$	2.73797	0.243918
$127$	−14.3694	−1.27508	−0.637540	−	0.770417i	$-0.720048\pi$
$127$	−14.3694	−1.27508	−0.637540	+	0.770417i	$0.720048\pi$
$128$	−1.00000	−0.0883883
$129$	−18.5833	−1.63617
$130$	15.8245	1.38790
$131$	1.00000	0.0873704
$131$	1.00000	0.0873704
$132$	−1.62162	−0.141144
$133$	6.53820	0.566933
$134$	1.54216	0.133222
$135$	−22.0576	−1.89841
$136$	−1.88404	−0.161555
$137$	13.2121	1.12878	0.564391	−	0.825507i	$-0.309111\pi$
$137$	13.2121	1.12878	0.564391	+	0.825507i	$0.309111\pi$
$138$	−1.53572	−0.130729
$139$	15.3119	1.29874	0.649369	−	0.760473i	$-0.275033\pi$
$139$	15.3119	1.29874	0.649369	+	0.760473i	$0.275033\pi$
$140$	−16.8324	−1.42260
$141$	−14.9919	−1.26255
$142$	9.68409	0.812670
$143$	4.23653	0.354276
$144$	−0.641564	−0.0534637
$145$	22.5241	1.87052
$146$	−2.57077	−0.212758
$147$	−17.2197	−1.42025
$148$	2.92481	0.240418
$149$	23.8341	1.95257	0.976283	−	0.216497i	$-0.0694632\pi$
$149$	23.8341	1.95257	0.976283	+	0.216497i	$0.0694632\pi$
$150$	16.2120	1.32370
$151$	−20.3335	−1.65472	−0.827358	−	0.561675i	$-0.810157\pi$
$151$	−20.3335	−1.65472	−0.827358	+	0.561675i	$0.810157\pi$
$152$	−1.53204	−0.124265
$153$	−1.20874	−0.0977205
$154$	−4.50635	−0.363132
$155$	−7.10908	−0.571015
$156$	−6.16149	−0.493314
$157$	4.18124	0.333700	0.166850	−	0.985982i	$-0.446641\pi$
$157$	4.18124	0.333700	0.166850	+	0.985982i	$0.446641\pi$
$158$	11.9977	0.954483
$159$	−13.6272	−1.08071
$160$	3.94419	0.311815
$161$	−4.26764	−0.336337
$162$	6.66370	0.523550
$163$	20.3081	1.59065	0.795327	−	0.606181i	$-0.207299\pi$
$163$	20.3081	1.59065	0.795327	+	0.606181i	$0.207299\pi$
$164$	−2.93369	−0.229083
$165$	6.39596	0.497925
$166$	13.1505	1.02068
$167$	−15.4271	−1.19379	−0.596893	−	0.802321i	$-0.703598\pi$
$167$	−15.4271	−1.19379	−0.596893	+	0.802321i	$0.703598\pi$
$168$	6.55390	0.505645
$169$	3.09707	0.238236
$170$	7.43102	0.569933
$171$	−0.982902	−0.0751644
$172$	12.1007	0.922671
$173$	17.9546	1.36506	0.682530	−	0.730857i	$-0.260880\pi$
$173$	17.9546	1.36506	0.682530	+	0.730857i	$0.260880\pi$
$174$	−8.77004	−0.664855
$175$	45.0518	3.40560
$176$	1.05593	0.0795940
$177$	−9.29893	−0.698950
$178$	0.977823	0.0732910
$179$	17.1261	1.28006	0.640031	−	0.768349i	$-0.278922\pi$
$179$	17.1261	1.28006	0.640031	+	0.768349i	$0.278922\pi$
$180$	2.53045	0.188609
$181$	−10.9168	−0.811439	−0.405720	−	0.913998i	$-0.632979\pi$
$181$	−10.9168	−0.811439	−0.405720	+	0.913998i	$0.632979\pi$
$182$	−17.1223	−1.26919
$183$	−11.0144	−0.814209
$184$	1.00000	0.0737210
$185$	−11.5360	−0.848142
$186$	2.76801	0.202961
$187$	1.98943	0.145481
$188$	9.76213	0.711976
$189$	23.8665	1.73603
$190$	6.04265	0.438380
$191$	8.28782	0.599685	0.299843	−	0.953989i	$-0.403066\pi$
$191$	8.28782	0.599685	0.299843	+	0.953989i	$0.403066\pi$
$192$	−1.53572	−0.110831
$193$	8.87640	0.638937	0.319468	−	0.947597i	$-0.396496\pi$
$193$	8.87640	0.638937	0.319468	+	0.947597i	$0.396496\pi$
$194$	−3.08429	−0.221439
$195$	24.3020	1.74031
$196$	11.2128	0.800912
$197$	3.28678	0.234174	0.117087	−	0.993122i	$-0.462644\pi$
$197$	3.28678	0.234174	0.117087	+	0.993122i	$0.462644\pi$
$198$	0.677449	0.0481442
$199$	−24.1394	−1.71120	−0.855600	−	0.517638i	$-0.826812\pi$
$199$	−24.1394	−1.71120	−0.855600	+	0.517638i	$0.826812\pi$
$200$	−10.5566	−0.746465
$201$	2.36832	0.167049
$202$	8.65211	0.608760
$203$	−24.3712	−1.71053
$204$	−2.89336	−0.202576
$205$	11.5710	0.808155
$206$	7.55045	0.526065
$207$	0.641564	0.0445918
$208$	4.01212	0.278190
$209$	1.61773	0.111901
$210$	−25.8498	−1.78381
$211$	−22.3699	−1.54001	−0.770004	−	0.638039i	$-0.779746\pi$
$211$	−22.3699	−1.54001	−0.770004	+	0.638039i	$0.779746\pi$
$212$	8.87351	0.609435
$213$	14.8720	1.01902
$214$	−4.53633	−0.310097
$215$	−47.7275	−3.25499
$216$	−5.59242	−0.380516
$217$	7.69209	0.522173
$218$	14.6416	0.991656
$219$	−3.94798	−0.266780
$220$	−4.16480	−0.280791
$221$	7.55900	0.508474
$222$	4.49168	0.301462
$223$	−2.65555	−0.177829	−0.0889145	−	0.996039i	$-0.528340\pi$
$223$	−2.65555	−0.177829	−0.0889145	+	0.996039i	$0.528340\pi$
$224$	−4.26764	−0.285144
$225$	−6.77274	−0.451516
$226$	9.73932	0.647850
$227$	−19.3937	−1.28721	−0.643603	−	0.765360i	$-0.722561\pi$
$227$	−19.3937	−1.28721	−0.643603	+	0.765360i	$0.722561\pi$
$228$	−2.35278	−0.155817
$229$	3.67251	0.242686	0.121343	−	0.992611i	$-0.461280\pi$
$229$	3.67251	0.242686	0.121343	+	0.992611i	$0.461280\pi$
$230$	−3.94419	−0.260072
$231$	−6.92049	−0.455335
$232$	5.71070	0.374926
$233$	26.4524	1.73295	0.866477	−	0.499217i	$-0.166379\pi$
$233$	26.4524	1.73295	0.866477	+	0.499217i	$0.166379\pi$
$234$	2.57403	0.168270
$235$	−38.5036	−2.51170
$236$	6.05509	0.394153
$237$	18.4251	1.19684
$238$	−8.04043	−0.521184
$239$	12.8606	0.831885	0.415942	−	0.909391i	$-0.363452\pi$
$239$	12.8606	0.831885	0.415942	+	0.909391i	$0.363452\pi$
$240$	6.05717	0.390988
$241$	−0.611379	−0.0393824	−0.0196912	−	0.999806i	$-0.506268\pi$
$241$	−0.611379	−0.0393824	−0.0196912	+	0.999806i	$0.506268\pi$
$242$	9.88500	0.635432
$243$	−6.54369	−0.419778
$244$	7.17215	0.459150
$245$	−44.2253	−2.82545
$246$	−4.50532	−0.287249
$247$	6.14672	0.391106
$248$	−1.80242	−0.114454
$249$	20.1955	1.27984
$250$	21.9163	1.38611
$251$	−3.45464	−0.218055	−0.109027	−	0.994039i	$-0.534774\pi$
$251$	−3.45464	−0.218055	−0.109027	+	0.994039i	$0.534774\pi$
$252$	−2.73797	−0.172476
$253$	−1.05593	−0.0663860
$254$	14.3694	0.901618
$255$	11.4120	0.714645
$256$	1.00000	0.0625000
$257$	11.2143	0.699530	0.349765	−	0.936837i	$-0.386261\pi$
$257$	11.2143	0.699530	0.349765	+	0.936837i	$0.386261\pi$
$258$	18.5833	1.15695
$259$	12.4820	0.775595
$260$	−15.8245	−0.981396
$261$	3.66378	0.226782
$262$	−1.00000	−0.0617802
$263$	23.8224	1.46895	0.734477	−	0.678633i	$-0.237427\pi$
$263$	23.8224	1.46895	0.734477	+	0.678633i	$0.237427\pi$
$264$	1.62162	0.0998037
$265$	−34.9988	−2.14996
$266$	−6.53820	−0.400883
$267$	1.50166	0.0919003
$268$	−1.54216	−0.0942024
$269$	14.2133	0.866600	0.433300	−	0.901250i	$-0.357349\pi$
$269$	14.2133	0.866600	0.433300	+	0.901250i	$0.357349\pi$
$270$	22.0576	1.34238
$271$	22.6830	1.37790	0.688948	−	0.724811i	$-0.258073\pi$
$271$	22.6830	1.37790	0.688948	+	0.724811i	$0.258073\pi$
$272$	1.88404	0.114237
$273$	−26.2950	−1.59145
$274$	−13.2121	−0.798170
$275$	11.1471	0.672194
$276$	1.53572	0.0924395
$277$	−15.7885	−0.948639	−0.474320	−	0.880353i	$-0.657306\pi$
$277$	−15.7885	−0.948639	−0.474320	+	0.880353i	$0.657306\pi$
$278$	−15.3119	−0.918347
$279$	−1.15637	−0.0692300
$280$	16.8324	1.00593
$281$	18.9856	1.13258	0.566292	−	0.824205i	$-0.308378\pi$
$281$	18.9856	1.13258	0.566292	+	0.824205i	$0.308378\pi$
$282$	14.9919	0.892754
$283$	−1.88838	−0.112252	−0.0561262	−	0.998424i	$-0.517875\pi$
$283$	−1.88838	−0.112252	−0.0561262	+	0.998424i	$0.517875\pi$
$284$	−9.68409	−0.574645
$285$	9.27982	0.549689
$286$	−4.23653	−0.250511
$287$	−12.5199	−0.739028
$288$	0.641564	0.0378045
$289$	−13.4504	−0.791199
$290$	−22.5241	−1.32266
$291$	−4.73660	−0.277665
$292$	2.57077	0.150443
$293$	−6.94975	−0.406009	−0.203004	−	0.979178i	$-0.565071\pi$
$293$	−6.94975	−0.406009	−0.203004	+	0.979178i	$0.565071\pi$
$294$	17.2197	1.00427
$295$	−23.8824	−1.39049
$296$	−2.92481	−0.170001
$297$	5.90523	0.342656
$298$	−23.8341	−1.38067
$299$	−4.01212	−0.232027
$300$	−16.2120	−0.936000
$301$	51.6415	2.97657
$302$	20.3335	1.17006
$303$	13.2872	0.763331
$304$	1.53204	0.0878685
$305$	−28.2883	−1.61978
$306$	1.20874	0.0690988
$307$	8.15630	0.465505	0.232752	−	0.972536i	$-0.425227\pi$
$307$	8.15630	0.465505	0.232752	+	0.972536i	$0.425227\pi$
$308$	4.50635	0.256773
$309$	11.5954	0.659638
$310$	7.10908	0.403769
$311$	26.3468	1.49399	0.746996	−	0.664828i	$-0.231495\pi$
$311$	26.3468	1.49399	0.746996	+	0.664828i	$0.231495\pi$
$312$	6.16149	0.348825
$313$	−0.491300	−0.0277699	−0.0138849	−	0.999904i	$-0.504420\pi$
$313$	−0.491300	−0.0277699	−0.0138849	+	0.999904i	$0.504420\pi$
$314$	−4.18124	−0.235961
$315$	10.7991	0.608458
$316$	−11.9977	−0.674922
$317$	9.12653	0.512597	0.256299	−	0.966598i	$-0.417497\pi$
$317$	9.12653	0.512597	0.256299	+	0.966598i	$0.417497\pi$
$318$	13.6272	0.764177
$319$	−6.03012	−0.337622
$320$	−3.94419	−0.220487
$321$	−6.96654	−0.388834
$322$	4.26764	0.237826
$323$	2.88643	0.160605
$324$	−6.66370	−0.370206
$325$	42.3543	2.34939
$326$	−20.3081	−1.12476
$327$	22.4854	1.24345
$328$	2.93369	0.161986
$329$	41.6613	2.29686
$330$	−6.39596	−0.352086
$331$	−9.26062	−0.509010	−0.254505	−	0.967071i	$-0.581913\pi$
$331$	−9.26062	−0.509010	−0.254505	+	0.967071i	$0.581913\pi$
$332$	−13.1505	−0.721727
$333$	−1.87645	−0.102829
$334$	15.4271	0.844134
$335$	6.08256	0.332326
$336$	−6.55390	−0.357545
$337$	11.7363	0.639317	0.319659	−	0.947533i	$-0.396432\pi$
$337$	11.7363	0.639317	0.319659	+	0.947533i	$0.396432\pi$
$338$	−3.09707	−0.168458
$339$	14.9569	0.812346
$340$	−7.43102	−0.403004
$341$	1.90324	0.103066
$342$	0.982902	0.0531492
$343$	17.9786	0.970753
$344$	−12.1007	−0.652427
$345$	−6.05717	−0.326107
$346$	−17.9546	−0.965244
$347$	21.4354	1.15071	0.575355	−	0.817904i	$-0.304864\pi$
$347$	21.4354	1.15071	0.575355	+	0.817904i	$0.304864\pi$
$348$	8.77004	0.470123
$349$	28.3261	1.51626	0.758130	−	0.652104i	$-0.226113\pi$
$349$	28.3261	1.51626	0.758130	+	0.652104i	$0.226113\pi$
$350$	−45.0518	−2.40812
$351$	22.4374	1.19762
$352$	−1.05593	−0.0562814
$353$	−9.36182	−0.498279	−0.249140	−	0.968468i	$-0.580148\pi$
$353$	−9.36182	−0.498279	−0.249140	+	0.968468i	$0.580148\pi$
$354$	9.29893	0.494232
$355$	38.1958	2.02722
$356$	−0.977823	−0.0518245
$357$	−12.3478	−0.653517
$358$	−17.1261	−0.905140
$359$	−13.8509	−0.731020	−0.365510	−	0.930807i	$-0.619105\pi$
$359$	−13.8509	−0.731020	−0.365510	+	0.930807i	$0.619105\pi$
$360$	−2.53045	−0.133366
$361$	−16.6529	−0.876466
$362$	10.9168	0.573774
$363$	15.1806	0.796775
$364$	17.1223	0.897451
$365$	−10.1396	−0.530731
$366$	11.0144	0.575733
$367$	−36.5835	−1.90964	−0.954822	−	0.297179i	$-0.903954\pi$
$367$	−36.5835	−1.90964	−0.954822	+	0.297179i	$0.903954\pi$
$368$	−1.00000	−0.0521286
$369$	1.88215	0.0979808
$370$	11.5360	0.599727
$371$	37.8690	1.96606
$372$	−2.76801	−0.143515
$373$	−4.54189	−0.235170	−0.117585	−	0.993063i	$-0.537515\pi$
$373$	−4.54189	−0.235170	−0.117585	+	0.993063i	$0.537515\pi$
$374$	−1.98943	−0.102871
$375$	33.6573	1.73805
$376$	−9.76213	−0.503443
$377$	−22.9120	−1.18003
$378$	−23.8665	−1.22756
$379$	−9.75389	−0.501024	−0.250512	−	0.968114i	$-0.580599\pi$
$379$	−9.75389	−0.501024	−0.250512	+	0.968114i	$0.580599\pi$
$380$	−6.04265	−0.309981
$381$	22.0674	1.13055
$382$	−8.28782	−0.424042
$383$	27.0445	1.38191	0.690954	−	0.722898i	$-0.257190\pi$
$383$	27.0445	1.38191	0.690954	+	0.722898i	$0.257190\pi$
$384$	1.53572	0.0783694
$385$	−17.7739	−0.905840
$386$	−8.87640	−0.451797
$387$	−7.76339	−0.394635
$388$	3.08429	0.156581
$389$	1.00436	0.0509231	0.0254616	−	0.999676i	$-0.491894\pi$
$389$	1.00436	0.0509231	0.0254616	+	0.999676i	$0.491894\pi$
$390$	−24.3020	−1.23058
$391$	−1.88404	−0.0952802
$392$	−11.2128	−0.566330
$393$	−1.53572	−0.0774668
$394$	−3.28678	−0.165586
$395$	47.3211	2.38098
$396$	−0.677449	−0.0340431
$397$	37.8138	1.89782	0.948910	−	0.315547i	$-0.102188\pi$
$397$	37.8138	1.89782	0.948910	+	0.315547i	$0.102188\pi$
$398$	24.1394	1.21000
$399$	−10.0408	−0.502671
$400$	10.5566	0.527830
$401$	4.39512	0.219482	0.109741	−	0.993960i	$-0.464998\pi$
$401$	4.39512	0.219482	0.109741	+	0.993960i	$0.464998\pi$
$402$	−2.36832	−0.118121
$403$	7.23152	0.360228
$404$	−8.65211	−0.430459
$405$	26.2829	1.30601
$406$	24.3712	1.20952
$407$	3.08840	0.153086
$408$	2.89336	0.143243
$409$	−26.6019	−1.31538	−0.657690	−	0.753288i	$-0.728466\pi$
$409$	−26.6019	−1.31538	−0.657690	+	0.753288i	$0.728466\pi$
$410$	−11.5710	−0.571452
$411$	−20.2900	−1.00083
$412$	−7.55045	−0.371984
$413$	25.8410	1.27155
$414$	−0.641564	−0.0315312
$415$	51.8680	2.54610
$416$	−4.01212	−0.196710
$417$	−23.5148	−1.15152
$418$	−1.61773	−0.0791258
$419$	−1.22341	−0.0597677	−0.0298838	−	0.999553i	$-0.509514\pi$
$419$	−1.22341	−0.0597677	−0.0298838	+	0.999553i	$0.509514\pi$
$420$	25.8498	1.26134
$421$	25.4108	1.23845	0.619223	−	0.785215i	$-0.287448\pi$
$421$	25.4108	1.23845	0.619223	+	0.785215i	$0.287448\pi$
$422$	22.3699	1.08895
$423$	−6.26303	−0.304519
$424$	−8.87351	−0.430936
$425$	19.8891	0.964764
$426$	−14.8720	−0.720553
$427$	30.6082	1.48123
$428$	4.53633	0.219272
$429$	−6.50612	−0.314118
$430$	47.7275	2.30162
$431$	−5.10880	−0.246082	−0.123041	−	0.992402i	$-0.539265\pi$
$431$	−5.10880	−0.246082	−0.123041	+	0.992402i	$0.539265\pi$
$432$	5.59242	0.269066
$433$	29.6474	1.42476	0.712382	−	0.701792i	$-0.247616\pi$
$433$	29.6474	1.42476	0.712382	+	0.701792i	$0.247616\pi$
$434$	−7.69209	−0.369232
$435$	−34.5907	−1.65850
$436$	−14.6416	−0.701207
$437$	−1.53204	−0.0732874
$438$	3.94798	0.188642
$439$	18.5103	0.883447	0.441723	−	0.897151i	$-0.354367\pi$
$439$	18.5103	0.883447	0.441723	+	0.897151i	$0.354367\pi$
$440$	4.16480	0.198549
$441$	−7.19371	−0.342558
$442$	−7.55900	−0.359545
$443$	−9.58676	−0.455481	−0.227740	−	0.973722i	$-0.573134\pi$
$443$	−9.58676	−0.455481	−0.227740	+	0.973722i	$0.573134\pi$
$444$	−4.49168	−0.213166
$445$	3.85672	0.182826
$446$	2.65555	0.125744
$447$	−36.6025	−1.73124
$448$	4.26764	0.201627
$449$	−17.7496	−0.837657	−0.418828	−	0.908065i	$-0.637559\pi$
$449$	−17.7496	−0.837657	−0.418828	+	0.908065i	$0.637559\pi$
$450$	6.77274	0.319270
$451$	−3.09778	−0.145869
$452$	−9.73932	−0.458099
$453$	31.2265	1.46715
$454$	19.3937	0.910192
$455$	−67.5334	−3.16602
$456$	2.35278	0.110179
$457$	20.4353	0.955923	0.477962	−	0.878381i	$-0.341376\pi$
$457$	20.4353	0.955923	0.477962	+	0.878381i	$0.341376\pi$
$458$	−3.67251	−0.171605
$459$	10.5364	0.491796
$460$	3.94419	0.183899
$461$	7.67582	0.357499	0.178749	−	0.983895i	$-0.442795\pi$
$461$	7.67582	0.357499	0.178749	+	0.983895i	$0.442795\pi$
$462$	6.92049	0.321970
$463$	−14.4998	−0.673864	−0.336932	−	0.941529i	$-0.609389\pi$
$463$	−14.4998	−0.673864	−0.336932	+	0.941529i	$0.609389\pi$
$464$	−5.71070	−0.265113
$465$	10.9176	0.506290
$466$	−26.4524	−1.22538
$467$	5.73522	0.265394	0.132697	−	0.991157i	$-0.457636\pi$
$467$	5.73522	0.265394	0.132697	+	0.991157i	$0.457636\pi$
$468$	−2.57403	−0.118985
$469$	−6.58139	−0.303900
$470$	38.5036	1.77604
$471$	−6.42122	−0.295874
$472$	−6.05509	−0.278708
$473$	12.7775	0.587512
$474$	−18.4251	−0.846291
$475$	16.1731	0.742074
$476$	8.04043	0.368532
$477$	−5.69293	−0.260661
$478$	−12.8606	−0.588231
$479$	−13.6973	−0.625848	−0.312924	−	0.949778i	$-0.601308\pi$
$479$	−13.6973	−0.625848	−0.312924	+	0.949778i	$0.601308\pi$
$480$	−6.05717	−0.276471
$481$	11.7347	0.535054
$482$	0.611379	0.0278476
$483$	6.55390	0.298213
$484$	−9.88500	−0.449318
$485$	−12.1650	−0.552385
$486$	6.54369	0.296828
$487$	−30.4848	−1.38140	−0.690700	−	0.723142i	$-0.742697\pi$
$487$	−30.4848	−1.38140	−0.690700	+	0.723142i	$0.742697\pi$
$488$	−7.17215	−0.324668
$489$	−31.1876	−1.41035
$490$	44.2253	1.99789
$491$	14.7987	0.667856	0.333928	−	0.942599i	$-0.391626\pi$
$491$	14.7987	0.667856	0.333928	+	0.942599i	$0.391626\pi$
$492$	4.50532	0.203116
$493$	−10.7592	−0.484571
$494$	−6.14672	−0.276554
$495$	2.67199	0.120097
$496$	1.80242	0.0809311
$497$	−41.3282	−1.85382
$498$	−20.1955	−0.904980
$499$	21.3673	0.956532	0.478266	−	0.878215i	$-0.341265\pi$
$499$	21.3673	0.956532	0.478266	+	0.878215i	$0.341265\pi$
$500$	−21.9163	−0.980126
$501$	23.6917	1.05847
$502$	3.45464	0.154188
$503$	9.87082	0.440118	0.220059	−	0.975487i	$-0.429375\pi$
$503$	9.87082	0.440118	0.220059	+	0.975487i	$0.429375\pi$
$504$	2.73797	0.121959
$505$	34.1255	1.51857
$506$	1.05593	0.0469420
$507$	−4.75623	−0.211232
$508$	−14.3694	−0.637540
$509$	−32.3139	−1.43229	−0.716145	−	0.697952i	$-0.754095\pi$
$509$	−32.3139	−1.43229	−0.716145	+	0.697952i	$0.754095\pi$
$510$	−11.4120	−0.505330
$511$	10.9711	0.485334
$512$	−1.00000	−0.0441942
$513$	8.56781	0.378278
$514$	−11.2143	−0.494643
$515$	29.7804	1.31228
$516$	−18.5833	−0.818084
$517$	10.3082	0.453352
$518$	−12.4820	−0.548429
$519$	−27.5732	−1.21033
$520$	15.8245	0.693952
$521$	−24.9412	−1.09269	−0.546347	−	0.837559i	$-0.683982\pi$
$521$	−24.9412	−1.09269	−0.546347	+	0.837559i	$0.683982\pi$
$522$	−3.66378	−0.160359
$523$	−35.0176	−1.53121	−0.765607	−	0.643309i	$-0.777561\pi$
$523$	−35.0176	−1.53121	−0.765607	+	0.643309i	$0.777561\pi$
$524$	1.00000	0.0436852
$525$	−69.1870	−3.01957
$526$	−23.8224	−1.03871
$527$	3.39584	0.147925
$528$	−1.62162	−0.0705719
$529$	1.00000	0.0434783
$530$	34.9988	1.52025
$531$	−3.88473	−0.168583
$532$	6.53820	0.283467
$533$	−11.7703	−0.509828
$534$	−1.50166	−0.0649833
$535$	−17.8921	−0.773545
$536$	1.54216	0.0666111
$537$	−26.3008	−1.13496
$538$	−14.2133	−0.612778
$539$	11.8399	0.509982
$540$	−22.0576	−0.949206
$541$	−3.68348	−0.158365	−0.0791825	−	0.996860i	$-0.525231\pi$
$541$	−3.68348	−0.158365	−0.0791825	+	0.996860i	$0.525231\pi$
$542$	−22.6830	−0.974320
$543$	16.7651	0.719461
$544$	−1.88404	−0.0807777
$545$	57.7493	2.47371
$546$	26.2950	1.12532
$547$	18.0809	0.773082	0.386541	−	0.922272i	$-0.373670\pi$
$547$	18.0809	0.773082	0.386541	+	0.922272i	$0.373670\pi$
$548$	13.2121	0.564391
$549$	−4.60140	−0.196383
$550$	−11.1471	−0.475313
$551$	−8.74902	−0.372721
$552$	−1.53572	−0.0653646
$553$	−51.2018	−2.17732
$554$	15.7885	0.670789
$555$	17.7160	0.752004
$556$	15.3119	0.649369
$557$	−10.2055	−0.432422	−0.216211	−	0.976347i	$-0.569370\pi$
$557$	−10.2055	−0.432422	−0.216211	+	0.976347i	$0.569370\pi$
$558$	1.15637	0.0489530
$559$	48.5495	2.05342
$560$	−16.8324	−0.711298
$561$	−3.05520	−0.128991
$562$	−18.9856	−0.800857
$563$	43.0478	1.81425	0.907125	−	0.420862i	$-0.138272\pi$
$563$	43.0478	1.81425	0.907125	+	0.420862i	$0.138272\pi$
$564$	−14.9919	−0.631273
$565$	38.4137	1.61608
$566$	1.88838	0.0793744
$567$	−28.4383	−1.19430
$568$	9.68409	0.406335
$569$	−1.30011	−0.0545033	−0.0272517	−	0.999629i	$-0.508676\pi$
$569$	−1.30011	−0.0545033	−0.0272517	+	0.999629i	$0.508676\pi$
$570$	−9.27982	−0.388689
$571$	21.8455	0.914205	0.457102	−	0.889414i	$-0.348887\pi$
$571$	21.8455	0.914205	0.457102	+	0.889414i	$0.348887\pi$
$572$	4.23653	0.177138
$573$	−12.7278	−0.531710
$574$	12.5199	0.522572
$575$	−10.5566	−0.440241
$576$	−0.641564	−0.0267318
$577$	24.7169	1.02898	0.514490	−	0.857497i	$-0.327981\pi$
$577$	24.7169	1.02898	0.514490	+	0.857497i	$0.327981\pi$
$578$	13.4504	0.559462
$579$	−13.6317	−0.566512
$580$	22.5241	0.935261
$581$	−56.1216	−2.32831
$582$	4.73660	0.196339
$583$	9.36984	0.388059
$584$	−2.57077	−0.106379
$585$	10.1525	0.419752
$586$	6.94975	0.287091
$587$	−42.8698	−1.76943	−0.884714	−	0.466134i	$-0.845646\pi$
$587$	−42.8698	−1.76943	−0.884714	+	0.466134i	$0.845646\pi$
$588$	−17.2197	−0.710127
$589$	2.76138	0.113781
$590$	23.8824	0.983224
$591$	−5.04758	−0.207630
$592$	2.92481	0.120209
$593$	−27.9172	−1.14642	−0.573210	−	0.819408i	$-0.694302\pi$
$593$	−27.9172	−1.14642	−0.573210	+	0.819408i	$0.694302\pi$
$594$	−5.90523	−0.242294
$595$	−31.7129	−1.30010
$596$	23.8341	0.976283
$597$	37.0714	1.51723
$598$	4.01212	0.164068
$599$	25.0993	1.02553	0.512765	−	0.858529i	$-0.328621\pi$
$599$	25.0993	1.02553	0.512765	+	0.858529i	$0.328621\pi$
$600$	16.2120	0.661852
$601$	−45.1063	−1.83993	−0.919963	−	0.392006i	$-0.871781\pi$
$601$	−45.1063	−1.83993	−0.919963	+	0.392006i	$0.871781\pi$
$602$	−51.6415	−2.10475
$603$	0.989395	0.0402913
$604$	−20.3335	−0.827358
$605$	38.9883	1.58510
$606$	−13.2872	−0.539756
$607$	42.9599	1.74369	0.871844	−	0.489784i	$-0.162924\pi$
$607$	42.9599	1.74369	0.871844	+	0.489784i	$0.162924\pi$
$608$	−1.53204	−0.0621324
$609$	37.4274	1.51663
$610$	28.2883	1.14536
$611$	39.1668	1.58452
$612$	−1.20874	−0.0488602
$613$	−3.40957	−0.137711	−0.0688557	−	0.997627i	$-0.521935\pi$
$613$	−3.40957	−0.137711	−0.0688557	+	0.997627i	$0.521935\pi$
$614$	−8.15630	−0.329162
$615$	−17.7698	−0.716549
$616$	−4.50635	−0.181566
$617$	49.5589	1.99517	0.997583	−	0.0694812i	$-0.0221344\pi$
$617$	49.5589	1.99517	0.997583	+	0.0694812i	$0.0221344\pi$
$618$	−11.5954	−0.466434
$619$	−17.8285	−0.716588	−0.358294	−	0.933609i	$-0.616641\pi$
$619$	−17.8285	−0.716588	−0.358294	+	0.933609i	$0.616641\pi$
$620$	−7.10908	−0.285508
$621$	−5.59242	−0.224416
$622$	−26.3468	−1.05641
$623$	−4.17300	−0.167188
$624$	−6.16149	−0.246657
$625$	33.6589	1.34636
$626$	0.491300	0.0196363
$627$	−2.48438	−0.0992167
$628$	4.18124	0.166850
$629$	5.51046	0.219717
$630$	−10.7991	−0.430245
$631$	16.7933	0.668532	0.334266	−	0.942479i	$-0.391512\pi$
$631$	16.7933	0.668532	0.334266	+	0.942479i	$0.391512\pi$
$632$	11.9977	0.477242
$633$	34.3539	1.36545
$634$	−9.12653	−0.362461
$635$	56.6757	2.24911
$636$	−13.6272	−0.540355
$637$	44.9869	1.78245
$638$	6.03012	0.238735
$639$	6.21296	0.245781
$640$	3.94419	0.155908
$641$	−9.65298	−0.381270	−0.190635	−	0.981661i	$-0.561055\pi$
$641$	−9.65298	−0.381270	−0.190635	+	0.981661i	$0.561055\pi$
$642$	6.96654	0.274947
$643$	10.0598	0.396720	0.198360	−	0.980129i	$-0.436439\pi$
$643$	10.0598	0.396720	0.198360	+	0.980129i	$0.436439\pi$
$644$	−4.26764	−0.168169
$645$	73.2960	2.88603
$646$	−2.88643	−0.113565
$647$	−24.8408	−0.976591	−0.488295	−	0.872678i	$-0.662381\pi$
$647$	−24.8408	−0.976591	−0.488295	+	0.872678i	$0.662381\pi$
$648$	6.66370	0.261775
$649$	6.39378	0.250978
$650$	−42.3543	−1.66127
$651$	−11.8129	−0.462984
$652$	20.3081	0.795327
$653$	1.50131	0.0587509	0.0293754	−	0.999568i	$-0.490648\pi$
$653$	1.50131	0.0587509	0.0293754	+	0.999568i	$0.490648\pi$
$654$	−22.4854	−0.879250
$655$	−3.94419	−0.154112
$656$	−2.93369	−0.114541
$657$	−1.64931	−0.0643459
$658$	−41.6613	−1.62413
$659$	39.2069	1.52729	0.763643	−	0.645639i	$-0.223409\pi$
$659$	39.2069	1.52729	0.763643	+	0.645639i	$0.223409\pi$
$660$	6.39596	0.248963
$661$	31.3966	1.22119	0.610593	−	0.791944i	$-0.290931\pi$
$661$	31.3966	1.22119	0.610593	+	0.791944i	$0.290931\pi$
$662$	9.26062	0.359924
$663$	−11.6085	−0.450837
$664$	13.1505	0.510338
$665$	−25.7879	−1.00001
$666$	1.87645	0.0727110
$667$	5.71070	0.221119
$668$	−15.4271	−0.596893
$669$	4.07819	0.157672
$670$	−6.08256	−0.234990
$671$	7.57332	0.292365
$672$	6.55390	0.252822
$673$	5.28130	0.203579	0.101790	−	0.994806i	$-0.467543\pi$
$673$	5.28130	0.203579	0.101790	+	0.994806i	$0.467543\pi$
$674$	−11.7363	−0.452066
$675$	59.0370	2.27234
$676$	3.09707	0.119118
$677$	−26.4044	−1.01480	−0.507401	−	0.861710i	$-0.669394\pi$
$677$	−26.4044	−1.01480	−0.507401	+	0.861710i	$0.669394\pi$
$678$	−14.9569	−0.574415
$679$	13.1626	0.505136
$680$	7.43102	0.284967
$681$	29.7833	1.14130
$682$	−1.90324	−0.0728787
$683$	28.6845	1.09758	0.548792	−	0.835959i	$-0.315088\pi$
$683$	28.6845	1.09758	0.548792	+	0.835959i	$0.315088\pi$
$684$	−0.982902	−0.0375822
$685$	−52.1108	−1.99105
$686$	−17.9786	−0.686426
$687$	−5.63995	−0.215177
$688$	12.1007	0.461335
$689$	35.6016	1.35631
$690$	6.05717	0.230592
$691$	−19.7951	−0.753041	−0.376520	−	0.926408i	$-0.622879\pi$
$691$	−19.7951	−0.753041	−0.376520	+	0.926408i	$0.622879\pi$
$692$	17.9546	0.682530
$693$	−2.89111	−0.109824
$694$	−21.4354	−0.813675
$695$	−60.3930	−2.29084
$696$	−8.77004	−0.332427
$697$	−5.52720	−0.209358
$698$	−28.3261	−1.07216
$699$	−40.6235	−1.53652
$700$	45.0518	1.70280
$701$	36.8269	1.39093	0.695467	−	0.718558i	$-0.255197\pi$
$701$	36.8269	1.39093	0.695467	+	0.718558i	$0.255197\pi$
$702$	−22.4374	−0.846847
$703$	4.48092	0.169001
$704$	1.05593	0.0397970
$705$	59.1308	2.22700
$706$	9.36182	0.352337
$707$	−36.9241	−1.38867
$708$	−9.29893	−0.349475
$709$	27.5164	1.03340	0.516701	−	0.856166i	$-0.327160\pi$
$709$	27.5164	1.03340	0.516701	+	0.856166i	$0.327160\pi$
$710$	−38.1958	−1.43346
$711$	7.69728	0.288670
$712$	0.977823	0.0366455
$713$	−1.80242	−0.0675012
$714$	12.3478	0.462106
$715$	−16.7097	−0.624905
$716$	17.1261	0.640031
$717$	−19.7503	−0.737589
$718$	13.8509	0.516909
$719$	41.5225	1.54853	0.774264	−	0.632863i	$-0.218120\pi$
$719$	41.5225	1.54853	0.774264	+	0.632863i	$0.218120\pi$
$720$	2.53045	0.0943043
$721$	−32.2226	−1.20003
$722$	16.6529	0.619755
$723$	0.938907	0.0349183
$724$	−10.9168	−0.405720
$725$	−60.2856	−2.23895
$726$	−15.1806	−0.563405
$727$	27.9312	1.03591	0.517955	−	0.855408i	$-0.326693\pi$
$727$	27.9312	1.03591	0.517955	+	0.855408i	$0.326693\pi$
$728$	−17.1223	−0.634594
$729$	30.0404	1.11261
$730$	10.1396	0.375283
$731$	22.7983	0.843225
$732$	−11.0144	−0.407105
$733$	0.789110	0.0291464	0.0145732	−	0.999894i	$-0.495361\pi$
$733$	0.789110	0.0291464	0.0145732	+	0.999894i	$0.495361\pi$
$734$	36.5835	1.35032
$735$	67.9176	2.50518
$736$	1.00000	0.0368605
$737$	−1.62842	−0.0599835
$738$	−1.88215	−0.0692829
$739$	46.3142	1.70370	0.851848	−	0.523789i	$-0.175482\pi$
$739$	46.3142	1.70370	0.851848	+	0.523789i	$0.175482\pi$
$740$	−11.5360	−0.424071
$741$	−9.43964	−0.346774
$742$	−37.8690	−1.39021
$743$	−2.08772	−0.0765909	−0.0382955	−	0.999266i	$-0.512193\pi$
$743$	−2.08772	−0.0765909	−0.0382955	+	0.999266i	$0.512193\pi$
$744$	2.76801	0.101480
$745$	−94.0062	−3.44412
$746$	4.54189	0.166290
$747$	8.43688	0.308689
$748$	1.98943	0.0727406
$749$	19.3594	0.707379
$750$	−33.6573	−1.22899
$751$	−38.3657	−1.39998	−0.699991	−	0.714151i	$-0.746813\pi$
$751$	−38.3657	−1.39998	−0.699991	+	0.714151i	$0.746813\pi$
$752$	9.76213	0.355988
$753$	5.30536	0.193338
$754$	22.9120	0.834406
$755$	80.1990	2.91874
$756$	23.8665	0.868015
$757$	−22.7585	−0.827173	−0.413587	−	0.910465i	$-0.635724\pi$
$757$	−22.7585	−0.827173	−0.413587	+	0.910465i	$0.635724\pi$
$758$	9.75389	0.354277
$759$	1.62162	0.0588610
$760$	6.04265	0.219190
$761$	−34.8077	−1.26178	−0.630889	−	0.775873i	$-0.717310\pi$
$761$	−34.8077	−1.26178	−0.630889	+	0.775873i	$0.717310\pi$
$762$	−22.0674	−0.799418
$763$	−62.4852	−2.26212
$764$	8.28782	0.299843
$765$	4.76748	0.172369
$766$	−27.0445	−0.977157
$767$	24.2937	0.877196
$768$	−1.53572	−0.0554155
$769$	27.7678	1.00133	0.500666	−	0.865641i	$-0.333089\pi$
$769$	27.7678	1.00133	0.500666	+	0.865641i	$0.333089\pi$
$770$	17.7739	0.640526
$771$	−17.2221	−0.620237
$772$	8.87640	0.319468
$773$	−52.3082	−1.88140	−0.940698	−	0.339244i	$-0.889829\pi$
$773$	−52.3082	−1.88140	−0.940698	+	0.339244i	$0.889829\pi$
$774$	7.76339	0.279049
$775$	19.0274	0.683486
$776$	−3.08429	−0.110720
$777$	−19.1689	−0.687680
$778$	−1.00436	−0.0360081
$779$	−4.49453	−0.161033
$780$	24.3020	0.870153
$781$	−10.2257	−0.365906
$782$	1.88404	0.0673733
$783$	−31.9367	−1.14132
$784$	11.2128	0.400456
$785$	−16.4916	−0.588611
$786$	1.53572	0.0547773
$787$	12.8495	0.458035	0.229018	−	0.973422i	$-0.426449\pi$
$787$	12.8495	0.458035	0.229018	+	0.973422i	$0.426449\pi$
$788$	3.28678	0.117087
$789$	−36.5846	−1.30245
$790$	−47.3211	−1.68361
$791$	−41.5640	−1.47784
$792$	0.677449	0.0240721
$793$	28.7755	1.02185
$794$	−37.8138	−1.34196
$795$	53.7483	1.90626
$796$	−24.1394	−0.855600
$797$	−51.3256	−1.81805	−0.909024	−	0.416745i	$-0.863171\pi$
$797$	−51.3256	−1.81805	−0.909024	+	0.416745i	$0.863171\pi$
$798$	10.0408	0.355442
$799$	18.3923	0.650672
$800$	−10.5566	−0.373232
$801$	0.627337	0.0221659
$802$	−4.39512	−0.155197
$803$	2.71456	0.0957948
$804$	2.36832	0.0835244
$805$	16.8324	0.593263
$806$	−7.23152	−0.254719
$807$	−21.8276	−0.768369
$808$	8.65211	0.304380
$809$	−5.57984	−0.196177	−0.0980884	−	0.995178i	$-0.531273\pi$
$809$	−5.57984	−0.196177	−0.0980884	+	0.995178i	$0.531273\pi$
$810$	−26.2829	−0.923486
$811$	−4.41301	−0.154962	−0.0774808	−	0.996994i	$-0.524688\pi$
$811$	−4.41301	−0.154962	−0.0774808	+	0.996994i	$0.524688\pi$
$812$	−24.3712	−0.855263
$813$	−34.8348	−1.22171
$814$	−3.08840	−0.108248
$815$	−80.0989	−2.80574
$816$	−2.89336	−0.101288
$817$	18.5388	0.648589
$818$	26.6019	0.930115
$819$	−10.9850	−0.383848
$820$	11.5710	0.404077
$821$	−7.89427	−0.275512	−0.137756	−	0.990466i	$-0.543989\pi$
$821$	−7.89427	−0.275512	−0.137756	+	0.990466i	$0.543989\pi$
$822$	20.2900	0.707696
$823$	−25.0629	−0.873639	−0.436819	−	0.899549i	$-0.643895\pi$
$823$	−25.0629	−0.873639	−0.436819	+	0.899549i	$0.643895\pi$
$824$	7.55045	0.263032
$825$	−17.1188	−0.595999
$826$	−25.8410	−0.899123
$827$	−34.0097	−1.18263	−0.591316	−	0.806440i	$-0.701391\pi$
$827$	−34.0097	−1.18263	−0.591316	+	0.806440i	$0.701391\pi$
$828$	0.641564	0.0222959
$829$	44.1902	1.53479	0.767395	−	0.641174i	$-0.221552\pi$
$829$	44.1902	1.53479	0.767395	+	0.641174i	$0.221552\pi$
$830$	−51.8680	−1.80036
$831$	24.2467	0.841109
$832$	4.01212	0.139095
$833$	21.1254	0.731950
$834$	23.5148	0.814251
$835$	60.8474	2.10571
$836$	1.61773	0.0559504
$837$	10.0799	0.348412
$838$	1.22341	0.0422621
$839$	−0.272983	−0.00942444	−0.00471222	−	0.999989i	$-0.501500\pi$
$839$	−0.272983	−0.00942444	−0.00471222	+	0.999989i	$0.501500\pi$
$840$	−25.8498	−0.891903
$841$	3.61212	0.124556
$842$	−25.4108	−0.875714
$843$	−29.1565	−1.00420
$844$	−22.3699	−0.770004
$845$	−12.2154	−0.420223
$846$	6.26303	0.215327
$847$	−42.1857	−1.44952
$848$	8.87351	0.304718
$849$	2.90002	0.0995283
$850$	−19.8891	−0.682191
$851$	−2.92481	−0.100261
$852$	14.8720	0.509508
$853$	−28.6498	−0.980950	−0.490475	−	0.871455i	$-0.663177\pi$
$853$	−28.6498	−0.980950	−0.490475	+	0.871455i	$0.663177\pi$
$854$	−30.6082	−1.04739
$855$	3.87675	0.132582
$856$	−4.53633	−0.155049
$857$	−24.3028	−0.830167	−0.415084	−	0.909783i	$-0.636248\pi$
$857$	−24.3028	−0.830167	−0.415084	+	0.909783i	$0.636248\pi$
$858$	6.50612	0.222115
$859$	54.6538	1.86476	0.932381	−	0.361476i	$-0.117727\pi$
$859$	54.6538	1.86476	0.932381	+	0.361476i	$0.117727\pi$
$860$	−47.7275	−1.62749
$861$	19.2271	0.655258
$862$	5.10880	0.174006
$863$	23.6967	0.806644	0.403322	−	0.915058i	$-0.367856\pi$
$863$	23.6967	0.806644	0.403322	+	0.915058i	$0.367856\pi$
$864$	−5.59242	−0.190258
$865$	−70.8162	−2.40782
$866$	−29.6474	−1.00746
$867$	20.6560	0.701515
$868$	7.69209	0.261086
$869$	−12.6687	−0.429758
$870$	34.5907	1.17273
$871$	−6.18732	−0.209649
$872$	14.6416	0.495828
$873$	−1.97877	−0.0669712
$874$	1.53204	0.0518220
$875$	−93.5309	−3.16192
$876$	−3.94798	−0.133390
$877$	−16.8849	−0.570161	−0.285081	−	0.958504i	$-0.592020\pi$
$877$	−16.8849	−0.570161	−0.285081	+	0.958504i	$0.592020\pi$
$878$	−18.5103	−0.624691
$879$	10.6729	0.359987
$880$	−4.16480	−0.140395
$881$	−54.4217	−1.83351	−0.916757	−	0.399445i	$-0.869203\pi$
$881$	−54.4217	−1.83351	−0.916757	+	0.399445i	$0.869203\pi$
$882$	7.19371	0.242225
$883$	25.7780	0.867497	0.433749	−	0.901034i	$-0.357191\pi$
$883$	25.7780	0.867497	0.433749	+	0.901034i	$0.357191\pi$
$884$	7.55900	0.254237
$885$	36.6767	1.23287
$886$	9.58676	0.322074
$887$	−18.7544	−0.629710	−0.314855	−	0.949140i	$-0.601956\pi$
$887$	−18.7544	−0.629710	−0.314855	+	0.949140i	$0.601956\pi$
$888$	4.49168	0.150731
$889$	−61.3235	−2.05673
$890$	−3.85672	−0.129277
$891$	−7.03643	−0.235729
$892$	−2.65555	−0.0889145
$893$	14.9560	0.500482
$894$	36.6025	1.22417
$895$	−67.5483	−2.25789
$896$	−4.26764	−0.142572
$897$	6.16149	0.205726
$898$	17.7496	0.592313
$899$	−10.2931	−0.343294
$900$	−6.77274	−0.225758
$901$	16.7181	0.556960
$902$	3.09778	0.103145
$903$	−79.3069	−2.63917
$904$	9.73932	0.323925
$905$	43.0579	1.43129
$906$	−31.2265	−1.03743
$907$	−0.0269077	−0.000893456 0	−0.000446728	−	1.00000i	$-0.500142\pi$
$907$	−0.0269077	−0.000893456 0	−0.000446728		1.00000i	$0.500142\pi$
$908$	−19.3937	−0.643603
$909$	5.55089	0.184111
$910$	67.5334	2.23871
$911$	−0.646491	−0.0214192	−0.0107096	−	0.999943i	$-0.503409\pi$
$911$	−0.646491	−0.0214192	−0.0107096	+	0.999943i	$0.503409\pi$
$912$	−2.35278	−0.0779084
$913$	−13.8860	−0.459561
$914$	−20.4353	−0.675940
$915$	43.4429	1.43618
$916$	3.67251	0.121343
$917$	4.26764	0.140930
$918$	−10.5364	−0.347752
$919$	4.18106	0.137920	0.0689601	−	0.997619i	$-0.478032\pi$
$919$	4.18106	0.137920	0.0689601	+	0.997619i	$0.478032\pi$
$920$	−3.94419	−0.130036
$921$	−12.5258	−0.412739
$922$	−7.67582	−0.252790
$923$	−38.8537	−1.27888
$924$	−6.92049	−0.227667
$925$	30.8760	1.01520
$926$	14.4998	0.476494
$927$	4.84410	0.159101
$928$	5.71070	0.187463
$929$	48.0063	1.57504	0.787519	−	0.616291i	$-0.211365\pi$
$929$	48.0063	1.57504	0.787519	+	0.616291i	$0.211365\pi$
$930$	−10.9176	−0.358001
$931$	17.1784	0.563000
$932$	26.4524	0.866477
$933$	−40.4614	−1.32465
$934$	−5.73522	−0.187662
$935$	−7.84666	−0.256613
$936$	2.57403	0.0841348
$937$	31.2474	1.02081	0.510403	−	0.859935i	$-0.329496\pi$
$937$	31.2474	1.02081	0.510403	+	0.859935i	$0.329496\pi$
$938$	6.58139	0.214890
$939$	0.754498	0.0246221
$940$	−38.5036	−1.25585
$941$	7.09331	0.231235	0.115618	−	0.993294i	$-0.463115\pi$
$941$	7.09331	0.231235	0.115618	+	0.993294i	$0.463115\pi$
$942$	6.42122	0.209215
$943$	2.93369	0.0955341
$944$	6.05509	0.197077
$945$	−94.1338	−3.06217
$946$	−12.7775	−0.415434
$947$	−50.4541	−1.63954	−0.819769	−	0.572694i	$-0.805898\pi$
$947$	−50.4541	−1.63954	−0.819769	+	0.572694i	$0.805898\pi$
$948$	18.4251	0.598418
$949$	10.3142	0.334814
$950$	−16.1731	−0.524726
$951$	−14.0158	−0.454493
$952$	−8.04043	−0.260592
$953$	−9.67904	−0.313535	−0.156767	−	0.987636i	$-0.550107\pi$
$953$	−9.67904	−0.313535	−0.156767	+	0.987636i	$0.550107\pi$
$954$	5.69293	0.184315
$955$	−32.6887	−1.05778
$956$	12.8606	0.415942
$957$	9.26058	0.299352
$958$	13.6973	0.442541
$959$	56.3844	1.82075
$960$	6.05717	0.195494
$961$	−27.7513	−0.895203
$962$	−11.7347	−0.378341
$963$	−2.91035	−0.0937847
$964$	−0.611379	−0.0196912
$965$	−35.0102	−1.12702
$966$	−6.55390	−0.210868
$967$	35.8087	1.15153	0.575765	−	0.817615i	$-0.304704\pi$
$967$	35.8087	1.15153	0.575765	+	0.817615i	$0.304704\pi$
$968$	9.88500	0.317716
$969$	−4.43275	−0.142400
$970$	12.1650	0.390595
$971$	28.0880	0.901388	0.450694	−	0.892678i	$-0.351177\pi$
$971$	28.0880	0.901388	0.450694	+	0.892678i	$0.351177\pi$
$972$	−6.54369	−0.209889
$973$	65.3457	2.09489
$974$	30.4848	0.976797
$975$	−65.0444	−2.08309
$976$	7.17215	0.229575
$977$	−10.0441	−0.321338	−0.160669	−	0.987008i	$-0.551365\pi$
$977$	−10.0441	−0.321338	−0.160669	+	0.987008i	$0.551365\pi$
$978$	31.1876	0.997268
$979$	−1.03252	−0.0329994
$980$	−44.2253	−1.41272
$981$	9.39354	0.299913
$982$	−14.7987	−0.472246
$983$	46.3629	1.47875	0.739373	−	0.673296i	$-0.235122\pi$
$983$	46.3629	1.47875	0.739373	+	0.673296i	$0.235122\pi$
$984$	−4.50532	−0.143624
$985$	−12.9637	−0.413057
$986$	10.7592	0.342643
$987$	−63.9800	−2.03651
$988$	6.14672	0.195553
$989$	−12.1007	−0.384780
$990$	−2.67199	−0.0849213
$991$	54.9761	1.74637	0.873187	−	0.487386i	$-0.162050\pi$
$991$	54.9761	1.74637	0.873187	+	0.487386i	$0.162050\pi$
$992$	−1.80242	−0.0572269
$993$	14.2217	0.451313
$994$	41.3282	1.31085
$995$	95.2105	3.01837
$996$	20.1955	0.639918
$997$	23.4372	0.742265	0.371132	−	0.928580i	$-0.378970\pi$
$997$	23.4372	0.742265	0.371132	+	0.928580i	$0.378970\pi$
$998$	−21.3673	−0.676370
$999$	16.3568	0.517505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.l.1.11	✓	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.l.1.11	✓	36	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.53572 q^{3} +1.00000 q^{4} -3.94419 q^{5} +1.53572 q^{6} +4.26764 q^{7} -1.00000 q^{8} -0.641564 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.53572 q^{3} +1.00000 q^{4} -3.94419 q^{5} +1.53572 q^{6} +4.26764 q^{7} -1.00000 q^{8} -0.641564 q^{9} +3.94419 q^{10} +1.05593 q^{11} -1.53572 q^{12} +4.01212 q^{13} -4.26764 q^{14} +6.05717 q^{15} +1.00000 q^{16} +1.88404 q^{17} +0.641564 q^{18} +1.53204 q^{19} -3.94419 q^{20} -6.55390 q^{21} -1.05593 q^{22} -1.00000 q^{23} +1.53572 q^{24} +10.5566 q^{25} -4.01212 q^{26} +5.59242 q^{27} +4.26764 q^{28} -5.71070 q^{29} -6.05717 q^{30} +1.80242 q^{31} -1.00000 q^{32} -1.62162 q^{33} -1.88404 q^{34} -16.8324 q^{35} -0.641564 q^{36} +2.92481 q^{37} -1.53204 q^{38} -6.16149 q^{39} +3.94419 q^{40} -2.93369 q^{41} +6.55390 q^{42} +12.1007 q^{43} +1.05593 q^{44} +2.53045 q^{45} +1.00000 q^{46} +9.76213 q^{47} -1.53572 q^{48} +11.2128 q^{49} -10.5566 q^{50} -2.89336 q^{51} +4.01212 q^{52} +8.87351 q^{53} -5.59242 q^{54} -4.16480 q^{55} -4.26764 q^{56} -2.35278 q^{57} +5.71070 q^{58} +6.05509 q^{59} +6.05717 q^{60} +7.17215 q^{61} -1.80242 q^{62} -2.73797 q^{63} +1.00000 q^{64} -15.8245 q^{65} +1.62162 q^{66} -1.54216 q^{67} +1.88404 q^{68} +1.53572 q^{69} +16.8324 q^{70} -9.68409 q^{71} +0.641564 q^{72} +2.57077 q^{73} -2.92481 q^{74} -16.2120 q^{75} +1.53204 q^{76} +4.50635 q^{77} +6.16149 q^{78} -11.9977 q^{79} -3.94419 q^{80} -6.66370 q^{81} +2.93369 q^{82} -13.1505 q^{83} -6.55390 q^{84} -7.43102 q^{85} -12.1007 q^{86} +8.77004 q^{87} -1.05593 q^{88} -0.977823 q^{89} -2.53045 q^{90} +17.1223 q^{91} -1.00000 q^{92} -2.76801 q^{93} -9.76213 q^{94} -6.04265 q^{95} +1.53572 q^{96} +3.08429 q^{97} -11.2128 q^{98} -0.677449 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9}+O(q^{10}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9	\( 36 q - 36 q^{2} + 4 q^{3} + 36 q^{4} + q^{5} - 4 q^{6} + 13 q^{7} - 36 q^{8} + 46 q^{9} - q^{10} + 14 q^{11} + 4 q^{12} + 4 q^{13} - 13 q^{14} + 10 q^{15} + 36 q^{16} - 4 q^{17} - 46 q^{18} + 29 q^{19} + q^{20} + 24 q^{21} - 14 q^{22} - 36 q^{23} - 4 q^{24} + 49 q^{25} - 4 q^{26} + 19 q^{27} + 13 q^{28} - 13 q^{29} - 10 q^{30} + 21 q^{31} - 36 q^{32} - 5 q^{33} + 4 q^{34} + 30 q^{35} + 46 q^{36} + 13 q^{37} - 29 q^{38} + 30 q^{39} - q^{40} - 8 q^{41} - 24 q^{42} + 42 q^{43} + 14 q^{44} + 30 q^{45} + 36 q^{46} - 14 q^{47} + 4 q^{48} + 61 q^{49} - 49 q^{50} + 46 q^{51} + 4 q^{52} - 3 q^{53} - 19 q^{54} + 26 q^{55} - 13 q^{56} + 26 q^{57} + 13 q^{58} + 45 q^{59} + 10 q^{60} + 34 q^{61} - 21 q^{62} + 63 q^{63} + 36 q^{64} - 25 q^{65} + 5 q^{66} + 42 q^{67} - 4 q^{68} - 4 q^{69} - 30 q^{70} - 2 q^{71} - 46 q^{72} + 16 q^{73} - 13 q^{74} + 72 q^{75} + 29 q^{76} - 36 q^{77} - 30 q^{78} + 33 q^{79} + q^{80} + 96 q^{81} + 8 q^{82} + 8 q^{83} + 24 q^{84} + 18 q^{85} - 42 q^{86} + 11 q^{87} - 14 q^{88} + 21 q^{89} - 30 q^{90} + 60 q^{91} - 36 q^{92} - 27 q^{93} + 14 q^{94} - 44 q^{95} - 4 q^{96} + 20 q^{97} - 61 q^{98} + 76 q^{99}+O(q^{100}) \) 36 * q - 36 * q^2 + 4 * q^3 + 36 * q^4 + q^5 - 4 * q^6 + 13 * q^7 - 36 * q^8 + 46 * q^9 - q^10 + 14 * q^11 + 4 * q^12 + 4 * q^13 - 13 * q^14 + 10 * q^15 + 36 * q^16 - 4 * q^17 - 46 * q^18 + 29 * q^19 + q^20 + 24 * q^21 - 14 * q^22 - 36 * q^23 - 4 * q^24 + 49 * q^25 - 4 * q^26 + 19 * q^27 + 13 * q^28 - 13 * q^29 - 10 * q^30 + 21 * q^31 - 36 * q^32 - 5 * q^33 + 4 * q^34 + 30 * q^35 + 46 * q^36 + 13 * q^37 - 29 * q^38 + 30 * q^39 - q^40 - 8 * q^41 - 24 * q^42 + 42 * q^43 + 14 * q^44 + 30 * q^45 + 36 * q^46 - 14 * q^47 + 4 * q^48 + 61 * q^49 - 49 * q^50 + 46 * q^51 + 4 * q^52 - 3 * q^53 - 19 * q^54 + 26 * q^55 - 13 * q^56 + 26 * q^57 + 13 * q^58 + 45 * q^59 + 10 * q^60 + 34 * q^61 - 21 * q^62 + 63 * q^63 + 36 * q^64 - 25 * q^65 + 5 * q^66 + 42 * q^67 - 4 * q^68 - 4 * q^69 - 30 * q^70 - 2 * q^71 - 46 * q^72 + 16 * q^73 - 13 * q^74 + 72 * q^75 + 29 * q^76 - 36 * q^77 - 30 * q^78 + 33 * q^79 + q^80 + 96 * q^81 + 8 * q^82 + 8 * q^83 + 24 * q^84 + 18 * q^85 - 42 * q^86 + 11 * q^87 - 14 * q^88 + 21 * q^89 - 30 * q^90 + 60 * q^91 - 36 * q^92 - 27 * q^93 + 14 * q^94 - 44 * q^95 - 4 * q^96 + 20 * q^97 - 61 * q^98 + 76 * q^99

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