LMFDB - Embedded newform 6026.2.a.j.1.20

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:	$33$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q-1.00000 q^{2} +0.581698 q^{3} +1.00000 q^{4} -2.21086 q^{5} -0.581698 q^{6} +1.23881 q^{7} -1.00000 q^{8} -2.66163 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} +0.581698 q^{3} +1.00000 q^{4} -2.21086 q^{5} -0.581698 q^{6} +1.23881 q^{7} -1.00000 q^{8} -2.66163 q^{9} +2.21086 q^{10} -2.13653 q^{11} +0.581698 q^{12} -1.70351 q^{13} -1.23881 q^{14} -1.28605 q^{15} +1.00000 q^{16} +3.71601 q^{17} +2.66163 q^{18} +1.68538 q^{19} -2.21086 q^{20} +0.720612 q^{21} +2.13653 q^{22} +1.00000 q^{23} -0.581698 q^{24} -0.112114 q^{25} +1.70351 q^{26} -3.29336 q^{27} +1.23881 q^{28} -3.90780 q^{29} +1.28605 q^{30} +2.91437 q^{31} -1.00000 q^{32} -1.24281 q^{33} -3.71601 q^{34} -2.73883 q^{35} -2.66163 q^{36} +1.60709 q^{37} -1.68538 q^{38} -0.990932 q^{39} +2.21086 q^{40} -7.44415 q^{41} -0.720612 q^{42} +8.65379 q^{43} -2.13653 q^{44} +5.88448 q^{45} -1.00000 q^{46} -5.23024 q^{47} +0.581698 q^{48} -5.46536 q^{49} +0.112114 q^{50} +2.16160 q^{51} -1.70351 q^{52} +9.01190 q^{53} +3.29336 q^{54} +4.72355 q^{55} -1.23881 q^{56} +0.980383 q^{57} +3.90780 q^{58} -13.8356 q^{59} -1.28605 q^{60} -0.596683 q^{61} -2.91437 q^{62} -3.29724 q^{63} +1.00000 q^{64} +3.76623 q^{65} +1.24281 q^{66} +6.56329 q^{67} +3.71601 q^{68} +0.581698 q^{69} +2.73883 q^{70} +3.45803 q^{71} +2.66163 q^{72} -2.66788 q^{73} -1.60709 q^{74} -0.0652162 q^{75} +1.68538 q^{76} -2.64675 q^{77} +0.990932 q^{78} -8.04141 q^{79} -2.21086 q^{80} +6.06914 q^{81} +7.44415 q^{82} -10.6901 q^{83} +0.720612 q^{84} -8.21557 q^{85} -8.65379 q^{86} -2.27316 q^{87} +2.13653 q^{88} -4.63872 q^{89} -5.88448 q^{90} -2.11033 q^{91} +1.00000 q^{92} +1.69528 q^{93} +5.23024 q^{94} -3.72614 q^{95} -0.581698 q^{96} +2.02431 q^{97} +5.46536 q^{98} +5.68664 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) $ 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * 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
$3$	0.581698	0.335844	0.167922	−	0.985800i	$-0.446294\pi$
$3$	0.581698	0.335844	0.167922	+	0.985800i	$0.446294\pi$
$4$	1.00000	0.500000
$5$	−2.21086	−0.988725	−0.494363	−	0.869256i	$-0.664598\pi$
$5$	−2.21086	−0.988725	−0.494363	+	0.869256i	$0.664598\pi$
$6$	−0.581698	−0.237477
$7$	1.23881	0.468225	0.234113	−	0.972209i	$-0.424782\pi$
$7$	1.23881	0.468225	0.234113	+	0.972209i	$0.424782\pi$
$8$	−1.00000	−0.353553
$9$	−2.66163	−0.887209
$10$	2.21086	0.699134
$11$	−2.13653	−0.644187	−0.322094	−	0.946708i	$-0.604387\pi$
$11$	−2.13653	−0.644187	−0.322094	+	0.946708i	$0.604387\pi$
$12$	0.581698	0.167922
$13$	−1.70351	−0.472470	−0.236235	−	0.971696i	$-0.575914\pi$
$13$	−1.70351	−0.472470	−0.236235	+	0.971696i	$0.575914\pi$
$14$	−1.23881	−0.331085
$15$	−1.28605	−0.332057
$16$	1.00000	0.250000
$17$	3.71601	0.901265	0.450633	−	0.892709i	$-0.351198\pi$
$17$	3.71601	0.901265	0.450633	+	0.892709i	$0.351198\pi$
$18$	2.66163	0.627352
$19$	1.68538	0.386653	0.193326	−	0.981134i	$-0.438072\pi$
$19$	1.68538	0.386653	0.193326	+	0.981134i	$0.438072\pi$
$20$	−2.21086	−0.494363
$21$	0.720612	0.157250
$22$	2.13653	0.455509
$23$	1.00000	0.208514
$23$	1.00000	0.208514
$24$	−0.581698	−0.118739
$25$	−0.112114	−0.0224227
$26$	1.70351	0.334087
$27$	−3.29336	−0.633807
$28$	1.23881	0.234113
$29$	−3.90780	−0.725660	−0.362830	−	0.931855i	$-0.618189\pi$
$29$	−3.90780	−0.725660	−0.362830	+	0.931855i	$0.618189\pi$
$30$	1.28605	0.234800
$31$	2.91437	0.523436	0.261718	−	0.965144i	$-0.415711\pi$
$31$	2.91437	0.523436	0.261718	+	0.965144i	$0.415711\pi$
$32$	−1.00000	−0.176777
$33$	−1.24281	−0.216346
$34$	−3.71601	−0.637291
$35$	−2.73883	−0.462946
$36$	−2.66163	−0.443605
$37$	1.60709	0.264204	0.132102	−	0.991236i	$-0.457827\pi$
$37$	1.60709	0.264204	0.132102	+	0.991236i	$0.457827\pi$
$38$	−1.68538	−0.273405
$39$	−0.990932	−0.158676
$40$	2.21086	0.349567
$41$	−7.44415	−1.16258	−0.581290	−	0.813696i	$-0.697452\pi$
$41$	−7.44415	−1.16258	−0.581290	+	0.813696i	$0.697452\pi$
$42$	−0.720612	−0.111193
$43$	8.65379	1.31969	0.659846	−	0.751401i	$-0.270622\pi$
$43$	8.65379	1.31969	0.659846	+	0.751401i	$0.270622\pi$
$44$	−2.13653	−0.322094
$45$	5.88448	0.877206
$46$	−1.00000	−0.147442
$47$	−5.23024	−0.762909	−0.381455	−	0.924388i	$-0.624577\pi$
$47$	−5.23024	−0.762909	−0.381455	+	0.924388i	$0.624577\pi$
$48$	0.581698	0.0839609
$49$	−5.46536	−0.780765
$50$	0.112114	0.0158552
$51$	2.16160	0.302684
$52$	−1.70351	−0.236235
$53$	9.01190	1.23788	0.618940	−	0.785438i	$-0.287562\pi$
$53$	9.01190	1.23788	0.618940	+	0.785438i	$0.287562\pi$
$54$	3.29336	0.448169
$55$	4.72355	0.636924
$56$	−1.23881	−0.165543
$57$	0.980383	0.129855
$58$	3.90780	0.513119
$59$	−13.8356	−1.80125	−0.900623	−	0.434601i	$-0.856889\pi$
$59$	−13.8356	−1.80125	−0.900623	+	0.434601i	$0.856889\pi$
$60$	−1.28605	−0.166028
$61$	−0.596683	−0.0763974	−0.0381987	−	0.999270i	$-0.512162\pi$
$61$	−0.596683	−0.0763974	−0.0381987	+	0.999270i	$0.512162\pi$
$62$	−2.91437	−0.370125
$63$	−3.29724	−0.415414
$64$	1.00000	0.125000
$65$	3.76623	0.467143
$66$	1.24281	0.152980
$67$	6.56329	0.801833	0.400917	−	0.916114i	$-0.368692\pi$
$67$	6.56329	0.801833	0.400917	+	0.916114i	$0.368692\pi$
$68$	3.71601	0.450633
$69$	0.581698	0.0700282
$70$	2.73883	0.327352
$71$	3.45803	0.410393	0.205196	−	0.978721i	$-0.434217\pi$
$71$	3.45803	0.410393	0.205196	+	0.978721i	$0.434217\pi$
$72$	2.66163	0.313676
$73$	−2.66788	−0.312252	−0.156126	−	0.987737i	$-0.549901\pi$
$73$	−2.66788	−0.312252	−0.156126	+	0.987737i	$0.549901\pi$
$74$	−1.60709	−0.186820
$75$	−0.0652162	−0.00753052
$76$	1.68538	0.193326
$77$	−2.64675	−0.301625
$78$	0.990932	0.112201
$79$	−8.04141	−0.904730	−0.452365	−	0.891833i	$-0.649420\pi$
$79$	−8.04141	−0.904730	−0.452365	+	0.891833i	$0.649420\pi$
$80$	−2.21086	−0.247181
$81$	6.06914	0.674349
$82$	7.44415	0.822069
$83$	−10.6901	−1.17339	−0.586695	−	0.809808i	$-0.699571\pi$
$83$	−10.6901	−1.17339	−0.586695	+	0.809808i	$0.699571\pi$
$84$	0.720612	0.0786252
$85$	−8.21557	−0.891104
$86$	−8.65379	−0.933163
$87$	−2.27316	−0.243708
$88$	2.13653	0.227755
$89$	−4.63872	−0.491703	−0.245852	−	0.969307i	$-0.579068\pi$
$89$	−4.63872	−0.491703	−0.245852	+	0.969307i	$0.579068\pi$
$90$	−5.88448	−0.620278
$91$	−2.11033	−0.221222
$92$	1.00000	0.104257
$93$	1.69528	0.175793
$94$	5.23024	0.539458
$95$	−3.72614	−0.382294
$96$	−0.581698	−0.0593693
$97$	2.02431	0.205537	0.102769	−	0.994705i	$-0.467230\pi$
$97$	2.02431	0.205537	0.102769	+	0.994705i	$0.467230\pi$
$98$	5.46536	0.552084
$99$	5.68664	0.571529
$100$	−0.112114	−0.0112114
$101$	0.112073	0.0111517	0.00557583	−	0.999984i	$-0.498225\pi$
$101$	0.112073	0.0111517	0.00557583	+	0.999984i	$0.498225\pi$
$102$	−2.16160	−0.214030
$103$	3.44852	0.339793	0.169897	−	0.985462i	$-0.445657\pi$
$103$	3.44852	0.339793	0.169897	+	0.985462i	$0.445657\pi$
$104$	1.70351	0.167043
$105$	−1.59317	−0.155477
$106$	−9.01190	−0.875313
$107$	−4.62168	−0.446794	−0.223397	−	0.974727i	$-0.571715\pi$
$107$	−4.62168	−0.446794	−0.223397	+	0.974727i	$0.571715\pi$
$108$	−3.29336	−0.316904
$109$	11.7874	1.12902	0.564512	−	0.825425i	$-0.309064\pi$
$109$	11.7874	1.12902	0.564512	+	0.825425i	$0.309064\pi$
$110$	−4.72355	−0.450373
$111$	0.934842	0.0887312
$112$	1.23881	0.117056
$113$	12.1070	1.13893	0.569464	−	0.822016i	$-0.307151\pi$
$113$	12.1070	1.13893	0.569464	+	0.822016i	$0.307151\pi$
$114$	−0.980383	−0.0918213
$115$	−2.21086	−0.206163
$116$	−3.90780	−0.362830
$117$	4.53412	0.419180
$118$	13.8356	1.27367
$119$	4.60343	0.421995
$120$	1.28605	0.117400
$121$	−6.43525	−0.585023
$122$	0.596683	0.0540211
$123$	−4.33025	−0.390445
$124$	2.91437	0.261718
$125$	11.3021	1.01089
$126$	3.29724	0.293742
$127$	1.98412	0.176062	0.0880310	−	0.996118i	$-0.471943\pi$
$127$	1.98412	0.176062	0.0880310	+	0.996118i	$0.471943\pi$
$128$	−1.00000	−0.0883883
$129$	5.03390	0.443210
$130$	−3.76623	−0.330320
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	−1.24281	−0.108173
$133$	2.08786	0.181041
$134$	−6.56329	−0.566982
$135$	7.28114	0.626661
$136$	−3.71601	−0.318645
$137$	10.1090	0.863668	0.431834	−	0.901953i	$-0.357867\pi$
$137$	10.1090	0.863668	0.431834	+	0.901953i	$0.357867\pi$
$138$	−0.581698	−0.0495174
$139$	0.468262	0.0397175	0.0198587	−	0.999803i	$-0.493678\pi$
$139$	0.468262	0.0397175	0.0198587	+	0.999803i	$0.493678\pi$
$140$	−2.73883	−0.231473
$141$	−3.04242	−0.256218
$142$	−3.45803	−0.290192
$143$	3.63961	0.304359
$144$	−2.66163	−0.221802
$145$	8.63958	0.717478
$146$	2.66788	0.220796
$147$	−3.17919	−0.262215
$148$	1.60709	0.132102
$149$	22.2524	1.82299	0.911495	−	0.411311i	$-0.134929\pi$
$149$	22.2524	1.82299	0.911495	+	0.411311i	$0.134929\pi$
$150$	0.0652162	0.00532488
$151$	23.6631	1.92568	0.962840	−	0.270074i	$-0.0870482\pi$
$151$	23.6631	1.92568	0.962840	+	0.270074i	$0.0870482\pi$
$152$	−1.68538	−0.136702
$153$	−9.89064	−0.799611
$154$	2.64675	0.213281
$155$	−6.44325	−0.517535
$156$	−0.990932	−0.0793380
$157$	−7.73343	−0.617195	−0.308598	−	0.951193i	$-0.599860\pi$
$157$	−7.73343	−0.617195	−0.308598	+	0.951193i	$0.599860\pi$
$158$	8.04141	0.639741
$159$	5.24221	0.415734
$160$	2.21086	0.174784
$161$	1.23881	0.0976317
$162$	−6.06914	−0.476837
$163$	21.9634	1.72030	0.860151	−	0.510039i	$-0.170369\pi$
$163$	21.9634	1.72030	0.860151	+	0.510039i	$0.170369\pi$
$164$	−7.44415	−0.581290
$165$	2.74768	0.213907
$166$	10.6901	0.829711
$167$	16.6595	1.28915	0.644577	−	0.764540i	$-0.277034\pi$
$167$	16.6595	1.28915	0.644577	+	0.764540i	$0.277034\pi$
$168$	−0.720612	−0.0555964
$169$	−10.0980	−0.776772
$170$	8.21557	0.630106
$171$	−4.48586	−0.343042
$172$	8.65379	0.659846
$173$	−5.93258	−0.451045	−0.225523	−	0.974238i	$-0.572409\pi$
$173$	−5.93258	−0.451045	−0.225523	+	0.974238i	$0.572409\pi$
$174$	2.27316	0.172328
$175$	−0.138887	−0.0104989
$176$	−2.13653	−0.161047
$177$	−8.04816	−0.604937
$178$	4.63872	0.347687
$179$	2.47324	0.184859	0.0924294	−	0.995719i	$-0.470537\pi$
$179$	2.47324	0.184859	0.0924294	+	0.995719i	$0.470537\pi$
$180$	5.88448	0.438603
$181$	18.9084	1.40545	0.702726	−	0.711461i	$-0.251966\pi$
$181$	18.9084	1.40545	0.702726	+	0.711461i	$0.251966\pi$
$182$	2.11033	0.156428
$183$	−0.347089	−0.0256576
$184$	−1.00000	−0.0737210
$185$	−3.55305	−0.261225
$186$	−1.69528	−0.124304
$187$	−7.93936	−0.580584
$188$	−5.23024	−0.381455
$189$	−4.07984	−0.296765
$190$	3.72614	0.270322
$191$	−26.0213	−1.88284	−0.941418	−	0.337242i	$-0.890506\pi$
$191$	−26.0213	−1.88284	−0.941418	+	0.337242i	$0.890506\pi$
$192$	0.581698	0.0419805
$193$	26.2000	1.88592	0.942958	−	0.332913i	$-0.108032\pi$
$193$	26.2000	1.88592	0.942958	+	0.332913i	$0.108032\pi$
$194$	−2.02431	−0.145337
$195$	2.19081	0.156887
$196$	−5.46536	−0.390383
$197$	−5.14803	−0.366782	−0.183391	−	0.983040i	$-0.558707\pi$
$197$	−5.14803	−0.366782	−0.183391	+	0.983040i	$0.558707\pi$
$198$	−5.68664	−0.404132
$199$	16.0626	1.13865	0.569323	−	0.822114i	$-0.307205\pi$
$199$	16.0626	1.13865	0.569323	+	0.822114i	$0.307205\pi$
$200$	0.112114	0.00792762
$201$	3.81785	0.269291
$202$	−0.112073	−0.00788542
$203$	−4.84101	−0.339772
$204$	2.16160	0.151342
$205$	16.4579	1.14947
$206$	−3.44852	−0.240270
$207$	−2.66163	−0.184996
$208$	−1.70351	−0.118118
$209$	−3.60086	−0.249077
$210$	1.59317	0.109939
$211$	−6.65901	−0.458425	−0.229213	−	0.973376i	$-0.573615\pi$
$211$	−6.65901	−0.458425	−0.229213	+	0.973376i	$0.573615\pi$
$212$	9.01190	0.618940
$213$	2.01153	0.137828
$214$	4.62168	0.315931
$215$	−19.1323	−1.30481
$216$	3.29336	0.224085
$217$	3.61034	0.245086
$218$	−11.7874	−0.798341
$219$	−1.55190	−0.104868
$220$	4.72355	0.318462
$221$	−6.33028	−0.425821
$222$	−0.934842	−0.0627425
$223$	−11.2220	−0.751481	−0.375740	−	0.926725i	$-0.622612\pi$
$223$	−11.2220	−0.751481	−0.375740	+	0.926725i	$0.622612\pi$
$224$	−1.23881	−0.0827713
$225$	0.298404	0.0198936
$226$	−12.1070	−0.805344
$227$	12.5856	0.835334	0.417667	−	0.908600i	$-0.362848\pi$
$227$	12.5856	0.835334	0.417667	+	0.908600i	$0.362848\pi$
$228$	0.980383	0.0649275
$229$	−16.1149	−1.06490	−0.532451	−	0.846461i	$-0.678729\pi$
$229$	−16.1149	−1.06490	−0.532451	+	0.846461i	$0.678729\pi$
$230$	2.21086	0.145780
$231$	−1.53961	−0.101299
$232$	3.90780	0.256559
$233$	25.5132	1.67143	0.835713	−	0.549166i	$-0.185054\pi$
$233$	25.5132	1.67143	0.835713	+	0.549166i	$0.185054\pi$
$234$	−4.53412	−0.296405
$235$	11.5633	0.754307
$236$	−13.8356	−0.900623
$237$	−4.67768	−0.303848
$238$	−4.60343	−0.298396
$239$	−14.1266	−0.913772	−0.456886	−	0.889525i	$-0.651035\pi$
$239$	−14.1266	−0.913772	−0.456886	+	0.889525i	$0.651035\pi$
$240$	−1.28605	−0.0830142
$241$	2.11369	0.136154	0.0680772	−	0.997680i	$-0.478314\pi$
$241$	2.11369	0.136154	0.0680772	+	0.997680i	$0.478314\pi$
$242$	6.43525	0.413674
$243$	13.4105	0.860283
$244$	−0.596683	−0.0381987
$245$	12.0831	0.771962
$246$	4.33025	0.276087
$247$	−2.87107	−0.182682
$248$	−2.91437	−0.185063
$249$	−6.21840	−0.394075
$250$	−11.3021	−0.714811
$251$	18.8829	1.19188	0.595938	−	0.803031i	$-0.296780\pi$
$251$	18.8829	1.19188	0.595938	+	0.803031i	$0.296780\pi$
$252$	−3.29724	−0.207707
$253$	−2.13653	−0.134322
$254$	−1.98412	−0.124495
$255$	−4.77898	−0.299272
$256$	1.00000	0.0625000
$257$	12.0265	0.750194	0.375097	−	0.926985i	$-0.377609\pi$
$257$	12.0265	0.750194	0.375097	+	0.926985i	$0.377609\pi$
$258$	−5.03390	−0.313397
$259$	1.99088	0.123707
$260$	3.76623	0.233571
$261$	10.4011	0.643812
$262$	1.00000	0.0617802
$263$	23.8860	1.47287	0.736435	−	0.676508i	$-0.236508\pi$
$263$	23.8860	1.47287	0.736435	+	0.676508i	$0.236508\pi$
$264$	1.24281	0.0764899
$265$	−19.9240	−1.22392
$266$	−2.08786	−0.128015
$267$	−2.69834	−0.165135
$268$	6.56329	0.400917
$269$	1.19777	0.0730291	0.0365145	−	0.999333i	$-0.488374\pi$
$269$	1.19777	0.0730291	0.0365145	+	0.999333i	$0.488374\pi$
$270$	−7.28114	−0.443116
$271$	−7.54368	−0.458246	−0.229123	−	0.973398i	$-0.573586\pi$
$271$	−7.54368	−0.458246	−0.229123	+	0.973398i	$0.573586\pi$
$272$	3.71601	0.225316
$273$	−1.22757	−0.0742961
$274$	−10.1090	−0.610705
$275$	0.239534	0.0144444
$276$	0.581698	0.0350141
$277$	−19.4996	−1.17162	−0.585810	−	0.810448i	$-0.699224\pi$
$277$	−19.4996	−1.17162	−0.585810	+	0.810448i	$0.699224\pi$
$278$	−0.468262	−0.0280845
$279$	−7.75697	−0.464397
$280$	2.73883	0.163676
$281$	−2.74749	−0.163901	−0.0819507	−	0.996636i	$-0.526115\pi$
$281$	−2.74749	−0.163901	−0.0819507	+	0.996636i	$0.526115\pi$
$282$	3.04242	0.181174
$283$	16.0305	0.952913	0.476457	−	0.879198i	$-0.341921\pi$
$283$	16.0305	0.952913	0.476457	+	0.879198i	$0.341921\pi$
$284$	3.45803	0.205196
$285$	−2.16749	−0.128391
$286$	−3.63961	−0.215214
$287$	−9.22187	−0.544350
$288$	2.66163	0.156838
$289$	−3.19125	−0.187721
$290$	−8.63958	−0.507334
$291$	1.17754	0.0690285
$292$	−2.66788	−0.156126
$293$	22.5039	1.31469	0.657345	−	0.753590i	$-0.271679\pi$
$293$	22.5039	1.31469	0.657345	+	0.753590i	$0.271679\pi$
$294$	3.17919	0.185414
$295$	30.5886	1.78094
$296$	−1.60709	−0.0934102
$297$	7.03635	0.408290
$298$	−22.2524	−1.28905
$299$	−1.70351	−0.0985168
$300$	−0.0652162	−0.00376526
$301$	10.7204	0.617913
$302$	−23.6631	−1.36166
$303$	0.0651926	0.00374522
$304$	1.68538	0.0966632
$305$	1.31918	0.0755360
$306$	9.89064	0.565410
$307$	1.37105	0.0782499	0.0391250	−	0.999234i	$-0.487543\pi$
$307$	1.37105	0.0782499	0.0391250	+	0.999234i	$0.487543\pi$
$308$	−2.64675	−0.150812
$309$	2.00600	0.114117
$310$	6.44325	0.365952
$311$	−6.39566	−0.362664	−0.181332	−	0.983422i	$-0.558041\pi$
$311$	−6.39566	−0.362664	−0.181332	+	0.983422i	$0.558041\pi$
$312$	0.990932	0.0561005
$313$	−15.9472	−0.901391	−0.450695	−	0.892678i	$-0.648824\pi$
$313$	−15.9472	−0.901391	−0.450695	+	0.892678i	$0.648824\pi$
$314$	7.73343	0.436423
$315$	7.28973	0.410730
$316$	−8.04141	−0.452365
$317$	−8.91280	−0.500593	−0.250296	−	0.968169i	$-0.580528\pi$
$317$	−8.91280	−0.500593	−0.250296	+	0.968169i	$0.580528\pi$
$318$	−5.24221	−0.293968
$319$	8.34911	0.467461
$320$	−2.21086	−0.123591
$321$	−2.68842	−0.150053
$322$	−1.23881	−0.0690361
$323$	6.26290	0.348477
$324$	6.06914	0.337175
$325$	0.190987	0.0105941
$326$	−21.9634	−1.21644
$327$	6.85669	0.379176
$328$	7.44415	0.411034
$329$	−6.47926	−0.357213
$330$	−2.74768	−0.151255
$331$	−6.56447	−0.360816	−0.180408	−	0.983592i	$-0.557742\pi$
$331$	−6.56447	−0.360816	−0.180408	+	0.983592i	$0.557742\pi$
$332$	−10.6901	−0.586695
$333$	−4.27748	−0.234404
$334$	−16.6595	−0.911569
$335$	−14.5105	−0.792793
$336$	0.720612	0.0393126
$337$	27.5229	1.49927	0.749635	−	0.661852i	$-0.230229\pi$
$337$	27.5229	1.49927	0.749635	+	0.661852i	$0.230229\pi$
$338$	10.0980	0.549261
$339$	7.04261	0.382502
$340$	−8.21557	−0.445552
$341$	−6.22663	−0.337191
$342$	4.48586	0.242567
$343$	−15.4422	−0.833799
$344$	−8.65379	−0.466581
$345$	−1.28605	−0.0692387
$346$	5.93258	0.318937
$347$	−22.3362	−1.19907	−0.599536	−	0.800348i	$-0.704648\pi$
$347$	−22.3362	−1.19907	−0.599536	+	0.800348i	$0.704648\pi$
$348$	−2.27316	−0.121854
$349$	4.65859	0.249369	0.124684	−	0.992196i	$-0.460208\pi$
$349$	4.65859	0.249369	0.124684	+	0.992196i	$0.460208\pi$
$350$	0.138887	0.00742383
$351$	5.61028	0.299455
$352$	2.13653	0.113877
$353$	13.4180	0.714169	0.357085	−	0.934072i	$-0.383771\pi$
$353$	13.4180	0.714169	0.357085	+	0.934072i	$0.383771\pi$
$354$	8.04816	0.427755
$355$	−7.64521	−0.405766
$356$	−4.63872	−0.245852
$357$	2.67780	0.141724
$358$	−2.47324	−0.130715
$359$	32.3832	1.70912	0.854560	−	0.519353i	$-0.173827\pi$
$359$	32.3832	1.70912	0.854560	+	0.519353i	$0.173827\pi$
$360$	−5.88448	−0.310139
$361$	−16.1595	−0.850499
$362$	−18.9084	−0.993805
$363$	−3.74338	−0.196476
$364$	−2.11033	−0.110611
$365$	5.89831	0.308732
$366$	0.347089	0.0181426
$367$	17.1852	0.897062	0.448531	−	0.893767i	$-0.351947\pi$
$367$	17.1852	0.897062	0.448531	+	0.893767i	$0.351947\pi$
$368$	1.00000	0.0521286
$369$	19.8135	1.03145
$370$	3.55305	0.184714
$371$	11.1640	0.579607
$372$	1.69528	0.0878964
$373$	8.67947	0.449406	0.224703	−	0.974427i	$-0.427859\pi$
$373$	8.67947	0.449406	0.224703	+	0.974427i	$0.427859\pi$
$374$	7.93936	0.410535
$375$	6.57444	0.339503
$376$	5.23024	0.269729
$377$	6.65699	0.342852
$378$	4.07984	0.209844
$379$	25.1228	1.29047	0.645237	−	0.763982i	$-0.276759\pi$
$379$	25.1228	1.29047	0.645237	+	0.763982i	$0.276759\pi$
$380$	−3.72614	−0.191147
$381$	1.15416	0.0591293
$382$	26.0213	1.33137
$383$	−9.53841	−0.487390	−0.243695	−	0.969852i	$-0.578360\pi$
$383$	−9.53841	−0.487390	−0.243695	+	0.969852i	$0.578360\pi$
$384$	−0.581698	−0.0296847
$385$	5.85158	0.298224
$386$	−26.2000	−1.33354
$387$	−23.0332	−1.17084
$388$	2.02431	0.102769
$389$	4.53613	0.229991	0.114995	−	0.993366i	$-0.463315\pi$
$389$	4.53613	0.229991	0.114995	+	0.993366i	$0.463315\pi$
$390$	−2.19081	−0.110936
$391$	3.71601	0.187927
$392$	5.46536	0.276042
$393$	−0.581698	−0.0293428
$394$	5.14803	0.259354
$395$	17.7784	0.894529
$396$	5.68664	0.285764
$397$	−10.0214	−0.502959	−0.251480	−	0.967863i	$-0.580917\pi$
$397$	−10.0214	−0.502959	−0.251480	+	0.967863i	$0.580917\pi$
$398$	−16.0626	−0.805144
$399$	1.21451	0.0608014
$400$	−0.112114	−0.00560568
$401$	−10.6034	−0.529509	−0.264754	−	0.964316i	$-0.585291\pi$
$401$	−10.6034	−0.529509	−0.264754	+	0.964316i	$0.585291\pi$
$402$	−3.81785	−0.190417
$403$	−4.96467	−0.247308
$404$	0.112073	0.00557583
$405$	−13.4180	−0.666746
$406$	4.84101	0.240255
$407$	−3.43359	−0.170197
$408$	−2.16160	−0.107015
$409$	17.6499	0.872731	0.436365	−	0.899770i	$-0.356265\pi$
$409$	17.6499	0.872731	0.436365	+	0.899770i	$0.356265\pi$
$410$	−16.4579	−0.812800
$411$	5.88037	0.290057
$412$	3.44852	0.169897
$413$	−17.1397	−0.843389
$414$	2.66163	0.130812
$415$	23.6342	1.16016
$416$	1.70351	0.0835217
$417$	0.272387	0.0133389
$418$	3.60086	0.176124
$419$	−27.3412	−1.33571	−0.667854	−	0.744293i	$-0.732787\pi$
$419$	−27.3412	−1.33571	−0.667854	+	0.744293i	$0.732787\pi$
$420$	−1.59317	−0.0777387
$421$	24.8373	1.21050	0.605248	−	0.796037i	$-0.293074\pi$
$421$	24.8373	1.21050	0.605248	+	0.796037i	$0.293074\pi$
$422$	6.65901	0.324156
$423$	13.9210	0.676860
$424$	−9.01190	−0.437657
$425$	−0.416615	−0.0202088
$426$	−2.01153	−0.0974590
$427$	−0.739175	−0.0357712
$428$	−4.62168	−0.223397
$429$	2.11715	0.102217
$430$	19.1323	0.922641
$431$	−8.99331	−0.433192	−0.216596	−	0.976261i	$-0.569496\pi$
$431$	−8.99331	−0.433192	−0.216596	+	0.976261i	$0.569496\pi$
$432$	−3.29336	−0.158452
$433$	36.4600	1.75216	0.876078	−	0.482170i	$-0.160151\pi$
$433$	36.4600	1.75216	0.876078	+	0.482170i	$0.160151\pi$
$434$	−3.61034	−0.173302
$435$	5.02563	0.240960
$436$	11.7874	0.564512
$437$	1.68538	0.0806227
$438$	1.55190	0.0741528
$439$	−18.2799	−0.872454	−0.436227	−	0.899837i	$-0.643686\pi$
$439$	−18.2799	−0.872454	−0.436227	+	0.899837i	$0.643686\pi$
$440$	−4.72355	−0.225187
$441$	14.5467	0.692702
$442$	6.33028	0.301101
$443$	22.9333	1.08960	0.544798	−	0.838567i	$-0.316606\pi$
$443$	22.9333	1.08960	0.544798	+	0.838567i	$0.316606\pi$
$444$	0.934842	0.0443656
$445$	10.2555	0.486160
$446$	11.2220	0.531377
$447$	12.9442	0.612240
$448$	1.23881	0.0585282
$449$	4.38520	0.206950	0.103475	−	0.994632i	$-0.467004\pi$
$449$	4.38520	0.206950	0.103475	+	0.994632i	$0.467004\pi$
$450$	−0.298404	−0.0140669
$451$	15.9046	0.748919
$452$	12.1070	0.569464
$453$	13.7648	0.646727
$454$	−12.5856	−0.590670
$455$	4.66563	0.218728
$456$	−0.980383	−0.0459107
$457$	32.2628	1.50919	0.754596	−	0.656190i	$-0.227833\pi$
$457$	32.2628	1.50919	0.754596	+	0.656190i	$0.227833\pi$
$458$	16.1149	0.753000
$459$	−12.2382	−0.571228
$460$	−2.21086	−0.103082
$461$	−19.2650	−0.897258	−0.448629	−	0.893718i	$-0.648088\pi$
$461$	−19.2650	−0.897258	−0.448629	+	0.893718i	$0.648088\pi$
$462$	1.53961	0.0716290
$463$	−24.5255	−1.13980	−0.569898	−	0.821716i	$-0.693017\pi$
$463$	−24.5255	−1.13980	−0.569898	+	0.821716i	$0.693017\pi$
$464$	−3.90780	−0.181415
$465$	−3.74803	−0.173811
$466$	−25.5132	−1.18188
$467$	−35.2519	−1.63126	−0.815631	−	0.578572i	$-0.803610\pi$
$467$	−35.2519	−1.63126	−0.815631	+	0.578572i	$0.803610\pi$
$468$	4.53412	0.209590
$469$	8.13065	0.375439
$470$	−11.5633	−0.533376
$471$	−4.49852	−0.207281
$472$	13.8356	0.636837
$473$	−18.4891	−0.850128
$474$	4.67768	0.214853
$475$	−0.188954	−0.00866981
$476$	4.60343	0.210998
$477$	−23.9863	−1.09826
$478$	14.1266	0.646134
$479$	−42.0142	−1.91968	−0.959839	−	0.280551i	$-0.909483\pi$
$479$	−42.0142	−1.91968	−0.959839	+	0.280551i	$0.909483\pi$
$480$	1.28605	0.0586999
$481$	−2.73770	−0.124828
$482$	−2.11369	−0.0962757
$483$	0.720612	0.0327890
$484$	−6.43525	−0.292512
$485$	−4.47546	−0.203220
$486$	−13.4105	−0.608312
$487$	28.8097	1.30549	0.652746	−	0.757577i	$-0.273617\pi$
$487$	28.8097	1.30549	0.652746	+	0.757577i	$0.273617\pi$
$488$	0.596683	0.0270106
$489$	12.7760	0.577753
$490$	−12.0831	−0.545860
$491$	−5.11017	−0.230619	−0.115309	−	0.993330i	$-0.536786\pi$
$491$	−5.11017	−0.230619	−0.115309	+	0.993330i	$0.536786\pi$
$492$	−4.33025	−0.195223
$493$	−14.5214	−0.654012
$494$	2.87107	0.129176
$495$	−12.5723	−0.565085
$496$	2.91437	0.130859
$497$	4.28384	0.192156
$498$	6.21840	0.278653
$499$	41.2747	1.84771	0.923854	−	0.382744i	$-0.125021\pi$
$499$	41.2747	1.84771	0.923854	+	0.382744i	$0.125021\pi$
$500$	11.3021	0.505447
$501$	9.69082	0.432954
$502$	−18.8829	−0.842783
$503$	−36.7661	−1.63932	−0.819659	−	0.572851i	$-0.805837\pi$
$503$	−36.7661	−1.63932	−0.819659	+	0.572851i	$0.805837\pi$
$504$	3.29724	0.146871
$505$	−0.247777	−0.0110259
$506$	2.13653	0.0949802
$507$	−5.87401	−0.260874
$508$	1.98412	0.0880310
$509$	27.8384	1.23392	0.616958	−	0.786996i	$-0.288365\pi$
$509$	27.8384	1.23392	0.616958	+	0.786996i	$0.288365\pi$
$510$	4.77898	0.211617
$511$	−3.30500	−0.146204
$512$	−1.00000	−0.0441942
$513$	−5.55056	−0.245063
$514$	−12.0265	−0.530468
$515$	−7.62419	−0.335962
$516$	5.03390	0.221605
$517$	11.1745	0.491456
$518$	−1.99088	−0.0874741
$519$	−3.45097	−0.151481
$520$	−3.76623	−0.165160
$521$	27.1705	1.19036	0.595181	−	0.803592i	$-0.297081\pi$
$521$	27.1705	1.19036	0.595181	+	0.803592i	$0.297081\pi$
$522$	−10.4011	−0.455244
$523$	−6.37998	−0.278977	−0.139489	−	0.990224i	$-0.544546\pi$
$523$	−6.37998	−0.278977	−0.139489	+	0.990224i	$0.544546\pi$
$524$	−1.00000	−0.0436852
$525$	−0.0807904	−0.00352598
$526$	−23.8860	−1.04148
$527$	10.8298	0.471755
$528$	−1.24281	−0.0540865
$529$	1.00000	0.0434783
$530$	19.9240	0.865444
$531$	36.8253	1.59808
$532$	2.08786	0.0905204
$533$	12.6812	0.549285
$534$	2.69834	0.116768
$535$	10.2179	0.441757
$536$	−6.56329	−0.283491
$537$	1.43868	0.0620836
$538$	−1.19777	−0.0516394
$539$	11.6769	0.502959
$540$	7.28114	0.313330
$541$	12.5227	0.538393	0.269197	−	0.963085i	$-0.413242\pi$
$541$	12.5227	0.538393	0.269197	+	0.963085i	$0.413242\pi$
$542$	7.54368	0.324029
$543$	10.9990	0.472012
$544$	−3.71601	−0.159323
$545$	−26.0602	−1.11629
$546$	1.22757	0.0525353
$547$	−35.2563	−1.50745	−0.753725	−	0.657190i	$-0.771745\pi$
$547$	−35.2563	−1.50745	−0.753725	+	0.657190i	$0.771745\pi$
$548$	10.1090	0.431834
$549$	1.58815	0.0677805
$550$	−0.239534	−0.0102137
$551$	−6.58613	−0.280578
$552$	−0.581698	−0.0247587
$553$	−9.96177	−0.423617
$554$	19.4996	0.828461
$555$	−2.06680	−0.0877308
$556$	0.468262	0.0198587
$557$	13.2799	0.562685	0.281343	−	0.959607i	$-0.409220\pi$
$557$	13.2799	0.562685	0.281343	+	0.959607i	$0.409220\pi$
$558$	7.75697	0.328379
$559$	−14.7419	−0.623515
$560$	−2.73883	−0.115737
$561$	−4.61831	−0.194985
$562$	2.74749	0.115896
$563$	5.22320	0.220132	0.110066	−	0.993924i	$-0.464894\pi$
$563$	5.22320	0.220132	0.110066	+	0.993924i	$0.464894\pi$
$564$	−3.04242	−0.128109
$565$	−26.7668	−1.12609
$566$	−16.0305	−0.673812
$567$	7.51850	0.315747
$568$	−3.45803	−0.145096
$569$	−18.6495	−0.781829	−0.390915	−	0.920427i	$-0.627841\pi$
$569$	−18.6495	−0.781829	−0.390915	+	0.920427i	$0.627841\pi$
$570$	2.16749	0.0907860
$571$	21.7990	0.912260	0.456130	−	0.889913i	$-0.349235\pi$
$571$	21.7990	0.912260	0.456130	+	0.889913i	$0.349235\pi$
$572$	3.63961	0.152180
$573$	−15.1365	−0.632338
$574$	9.22187	0.384913
$575$	−0.112114	−0.00467546
$576$	−2.66163	−0.110901
$577$	2.80723	0.116866	0.0584332	−	0.998291i	$-0.481390\pi$
$577$	2.80723	0.116866	0.0584332	+	0.998291i	$0.481390\pi$
$578$	3.19125	0.132738
$579$	15.2405	0.633373
$580$	8.63958	0.358739
$581$	−13.2430	−0.549410
$582$	−1.17754	−0.0488105
$583$	−19.2542	−0.797426
$584$	2.66788	0.110398
$585$	−10.0243	−0.414453
$586$	−22.5039	−0.929627
$587$	30.1782	1.24559	0.622794	−	0.782386i	$-0.285997\pi$
$587$	30.1782	1.24559	0.622794	+	0.782386i	$0.285997\pi$
$588$	−3.17919	−0.131107
$589$	4.91182	0.202388
$590$	−30.5886	−1.25931
$591$	−2.99460	−0.123181
$592$	1.60709	0.0660510
$593$	−33.9019	−1.39218	−0.696092	−	0.717953i	$-0.745079\pi$
$593$	−33.9019	−1.39218	−0.696092	+	0.717953i	$0.745079\pi$
$594$	−7.03635	−0.288705
$595$	−10.1775	−0.417237
$596$	22.2524	0.911495
$597$	9.34357	0.382407
$598$	1.70351	0.0696619
$599$	−30.6293	−1.25148	−0.625740	−	0.780031i	$-0.715203\pi$
$599$	−30.6293	−1.25148	−0.625740	+	0.780031i	$0.715203\pi$
$600$	0.0652162	0.00266244
$601$	25.3209	1.03286	0.516431	−	0.856329i	$-0.327260\pi$
$601$	25.3209	1.03286	0.516431	+	0.856329i	$0.327260\pi$
$602$	−10.7204	−0.436930
$603$	−17.4690	−0.711394
$604$	23.6631	0.962840
$605$	14.2274	0.578427
$606$	−0.0651926	−0.00264827
$607$	37.4434	1.51978	0.759889	−	0.650052i	$-0.225253\pi$
$607$	37.4434	1.51978	0.759889	+	0.650052i	$0.225253\pi$
$608$	−1.68538	−0.0683512
$609$	−2.81601	−0.114110
$610$	−1.31918	−0.0534120
$611$	8.90979	0.360452
$612$	−9.89064	−0.399805
$613$	28.0675	1.13364	0.566818	−	0.823843i	$-0.308174\pi$
$613$	28.0675	1.13364	0.566818	+	0.823843i	$0.308174\pi$
$614$	−1.37105	−0.0553311
$615$	9.57356	0.386043
$616$	2.64675	0.106640
$617$	4.28859	0.172652	0.0863261	−	0.996267i	$-0.472487\pi$
$617$	4.28859	0.172652	0.0863261	+	0.996267i	$0.472487\pi$
$618$	−2.00600	−0.0806932
$619$	27.0372	1.08672	0.543359	−	0.839500i	$-0.317152\pi$
$619$	27.0372	1.08672	0.543359	+	0.839500i	$0.317152\pi$
$620$	−6.44325	−0.258767
$621$	−3.29336	−0.132158
$622$	6.39566	0.256443
$623$	−5.74648	−0.230228
$624$	−0.990932	−0.0396690
$625$	−24.4269	−0.977075
$626$	15.9472	0.637379
$627$	−2.09462	−0.0836509
$628$	−7.73343	−0.308598
$629$	5.97197	0.238118
$630$	−7.28973	−0.290430
$631$	−11.6752	−0.464782	−0.232391	−	0.972622i	$-0.574655\pi$
$631$	−11.6752	−0.464782	−0.232391	+	0.972622i	$0.574655\pi$
$632$	8.04141	0.319870
$633$	−3.87354	−0.153959
$634$	8.91280	0.353972
$635$	−4.38660	−0.174077
$636$	5.24221	0.207867
$637$	9.31031	0.368888
$638$	−8.34911	−0.330545
$639$	−9.20399	−0.364104
$640$	2.21086	0.0873918
$641$	36.0465	1.42375	0.711875	−	0.702306i	$-0.247846\pi$
$641$	36.0465	1.42375	0.711875	+	0.702306i	$0.247846\pi$
$642$	2.68842	0.106104
$643$	−15.7118	−0.619612	−0.309806	−	0.950800i	$-0.600264\pi$
$643$	−15.7118	−0.619612	−0.309806	+	0.950800i	$0.600264\pi$
$644$	1.23881	0.0488159
$645$	−11.1292	−0.438213
$646$	−6.26290	−0.246410
$647$	−9.72469	−0.382317	−0.191158	−	0.981559i	$-0.561224\pi$
$647$	−9.72469	−0.382317	−0.191158	+	0.981559i	$0.561224\pi$
$648$	−6.06914	−0.238418
$649$	29.5602	1.16034
$650$	−0.190987	−0.00749113
$651$	2.10013	0.0823106
$652$	21.9634	0.860151
$653$	37.2833	1.45901	0.729504	−	0.683976i	$-0.239751\pi$
$653$	37.2833	1.45901	0.729504	+	0.683976i	$0.239751\pi$
$654$	−6.85669	−0.268118
$655$	2.21086	0.0863853
$656$	−7.44415	−0.290645
$657$	7.10091	0.277033
$658$	6.47926	0.252588
$659$	22.5832	0.879716	0.439858	−	0.898067i	$-0.355029\pi$
$659$	22.5832	0.879716	0.439858	+	0.898067i	$0.355029\pi$
$660$	2.74768	0.106953
$661$	9.03938	0.351591	0.175796	−	0.984427i	$-0.443750\pi$
$661$	9.03938	0.351591	0.175796	+	0.984427i	$0.443750\pi$
$662$	6.56447	0.255135
$663$	−3.68231	−0.143009
$664$	10.6901	0.414856
$665$	−4.61597	−0.179000
$666$	4.27748	0.165749
$667$	−3.90780	−0.151311
$668$	16.6595	0.644577
$669$	−6.52782	−0.252380
$670$	14.5105	0.560589
$671$	1.27483	0.0492142
$672$	−0.720612	−0.0277982
$673$	−39.3452	−1.51665	−0.758323	−	0.651879i	$-0.773981\pi$
$673$	−39.3452	−1.51665	−0.758323	+	0.651879i	$0.773981\pi$
$674$	−27.5229	−1.06014
$675$	0.369230	0.0142117
$676$	−10.0980	−0.388386
$677$	−34.8188	−1.33820	−0.669098	−	0.743174i	$-0.733320\pi$
$677$	−34.8188	−1.33820	−0.669098	+	0.743174i	$0.733320\pi$
$678$	−7.04261	−0.270470
$679$	2.50773	0.0962379
$680$	8.21557	0.315053
$681$	7.32101	0.280542
$682$	6.22663	0.238430
$683$	−50.8010	−1.94384	−0.971922	−	0.235302i	$-0.924392\pi$
$683$	−50.8010	−1.94384	−0.971922	+	0.235302i	$0.924392\pi$
$684$	−4.48586	−0.171521
$685$	−22.3495	−0.853930
$686$	15.4422	0.589585
$687$	−9.37401	−0.357641
$688$	8.65379	0.329923
$689$	−15.3519	−0.584861
$690$	1.28605	0.0489591
$691$	5.38335	0.204792	0.102396	−	0.994744i	$-0.467349\pi$
$691$	5.38335	0.204792	0.102396	+	0.994744i	$0.467349\pi$
$692$	−5.93258	−0.225523
$693$	7.04465	0.267604
$694$	22.3362	0.847872
$695$	−1.03526	−0.0392697
$696$	2.27316	0.0861638
$697$	−27.6626	−1.04779
$698$	−4.65859	−0.176330
$699$	14.8410	0.561338
$700$	−0.138887	−0.00524944
$701$	−27.4116	−1.03532	−0.517661	−	0.855586i	$-0.673197\pi$
$701$	−27.4116	−1.03532	−0.517661	+	0.855586i	$0.673197\pi$
$702$	−5.61028	−0.211747
$703$	2.70856	0.102155
$704$	−2.13653	−0.0805234
$705$	6.72636	0.253329
$706$	−13.4180	−0.504994
$707$	0.138837	0.00522149
$708$	−8.04816	−0.302468
$709$	34.3158	1.28876	0.644378	−	0.764707i	$-0.277116\pi$
$709$	34.3158	1.28876	0.644378	+	0.764707i	$0.277116\pi$
$710$	7.64521	0.286920
$711$	21.4032	0.802684
$712$	4.63872	0.173843
$713$	2.91437	0.109144
$714$	−2.67780	−0.100214
$715$	−8.04664	−0.300927
$716$	2.47324	0.0924294
$717$	−8.21740	−0.306884
$718$	−32.3832	−1.20853
$719$	44.0431	1.64253	0.821265	−	0.570547i	$-0.193269\pi$
$719$	44.0431	1.64253	0.821265	+	0.570547i	$0.193269\pi$
$720$	5.88448	0.219301
$721$	4.27206	0.159100
$722$	16.1595	0.601394
$723$	1.22953	0.0457266
$724$	18.9084	0.702726
$725$	0.438117	0.0162713
$726$	3.74338	0.138930
$727$	−51.6494	−1.91557	−0.957785	−	0.287486i	$-0.907181\pi$
$727$	−51.6494	−1.91557	−0.957785	+	0.287486i	$0.907181\pi$
$728$	2.11033	0.0782139
$729$	−10.4066	−0.385428
$730$	−5.89831	−0.218306
$731$	32.1576	1.18939
$732$	−0.347089	−0.0128288
$733$	19.1849	0.708609	0.354305	−	0.935130i	$-0.384718\pi$
$733$	19.1849	0.708609	0.354305	+	0.935130i	$0.384718\pi$
$734$	−17.1852	−0.634319
$735$	7.02873	0.259258
$736$	−1.00000	−0.0368605
$737$	−14.0226	−0.516531
$738$	−19.8135	−0.729347
$739$	24.2755	0.892989	0.446494	−	0.894786i	$-0.352672\pi$
$739$	24.2755	0.892989	0.446494	+	0.894786i	$0.352672\pi$
$740$	−3.55305	−0.130613
$741$	−1.67010	−0.0613526
$742$	−11.1640	−0.409844
$743$	−25.7225	−0.943665	−0.471833	−	0.881688i	$-0.656407\pi$
$743$	−25.7225	−0.943665	−0.471833	+	0.881688i	$0.656407\pi$
$744$	−1.69528	−0.0621521
$745$	−49.1969	−1.80244
$746$	−8.67947	−0.317778
$747$	28.4530	1.04104
$748$	−7.93936	−0.290292
$749$	−5.72537	−0.209200
$750$	−6.57444	−0.240065
$751$	−16.9494	−0.618492	−0.309246	−	0.950982i	$-0.600077\pi$
$751$	−16.9494	−0.618492	−0.309246	+	0.950982i	$0.600077\pi$
$752$	−5.23024	−0.190727
$753$	10.9841	0.400284
$754$	−6.65699	−0.242433
$755$	−52.3158	−1.90397
$756$	−4.07984	−0.148382
$757$	25.1938	0.915683	0.457841	−	0.889034i	$-0.348623\pi$
$757$	25.1938	0.915683	0.457841	+	0.889034i	$0.348623\pi$
$758$	−25.1228	−0.912503
$759$	−1.24281	−0.0451113
$760$	3.72614	0.135161
$761$	−45.8119	−1.66068	−0.830341	−	0.557256i	$-0.811854\pi$
$761$	−45.8119	−1.66068	−0.830341	+	0.557256i	$0.811854\pi$
$762$	−1.15416	−0.0418107
$763$	14.6023	0.528638
$764$	−26.0213	−0.941418
$765$	21.8668	0.790595
$766$	9.53841	0.344637
$767$	23.5692	0.851035
$768$	0.581698	0.0209902
$769$	−51.9097	−1.87191	−0.935957	−	0.352115i	$-0.885463\pi$
$769$	−51.9097	−1.87191	−0.935957	+	0.352115i	$0.885463\pi$
$770$	−5.85158	−0.210876
$771$	6.99581	0.251948
$772$	26.2000	0.942958
$773$	−29.9485	−1.07717	−0.538586	−	0.842571i	$-0.681041\pi$
$773$	−29.9485	−1.07717	−0.538586	+	0.842571i	$0.681041\pi$
$774$	23.0332	0.827910
$775$	−0.326740	−0.0117369
$776$	−2.02431	−0.0726685
$777$	1.15809	0.0415462
$778$	−4.53613	−0.162628
$779$	−12.5462	−0.449515
$780$	2.19081	0.0784435
$781$	−7.38818	−0.264370
$782$	−3.71601	−0.132884
$783$	12.8698	0.459928
$784$	−5.46536	−0.195191
$785$	17.0975	0.610236
$786$	0.581698	0.0207485
$787$	15.8164	0.563795	0.281898	−	0.959444i	$-0.409036\pi$
$787$	15.8164	0.563795	0.281898	+	0.959444i	$0.409036\pi$
$788$	−5.14803	−0.183391
$789$	13.8944	0.494654
$790$	−17.7784	−0.632527
$791$	14.9982	0.533275
$792$	−5.68664	−0.202066
$793$	1.01646	0.0360955
$794$	10.0214	0.355646
$795$	−11.5898	−0.411047
$796$	16.0626	0.569323
$797$	41.8017	1.48069	0.740346	−	0.672225i	$-0.234661\pi$
$797$	41.8017	1.48069	0.740346	+	0.672225i	$0.234661\pi$
$798$	−1.21451	−0.0429931
$799$	−19.4356	−0.687584
$800$	0.112114	0.00396381
$801$	12.3465	0.436244
$802$	10.6034	0.374419
$803$	5.70001	0.201149
$804$	3.81785	0.134645
$805$	−2.73883	−0.0965309
$806$	4.96467	0.174873
$807$	0.696738	0.0245264
$808$	−0.112073	−0.00394271
$809$	6.31779	0.222122	0.111061	−	0.993814i	$-0.464575\pi$
$809$	6.31779	0.222122	0.111061	+	0.993814i	$0.464575\pi$
$810$	13.4180	0.471460
$811$	19.9487	0.700493	0.350247	−	0.936658i	$-0.386098\pi$
$811$	19.9487	0.700493	0.350247	+	0.936658i	$0.386098\pi$
$812$	−4.84101	−0.169886
$813$	−4.38814	−0.153899
$814$	3.43359	0.120347
$815$	−48.5578	−1.70091
$816$	2.16160	0.0756711
$817$	14.5849	0.510263
$818$	−17.6499	−0.617114
$819$	5.61691	0.196271
$820$	16.4579	0.574736
$821$	−1.39467	−0.0486743	−0.0243372	−	0.999704i	$-0.507748\pi$
$821$	−1.39467	−0.0486743	−0.0243372	+	0.999704i	$0.507748\pi$
$822$	−5.88037	−0.205101
$823$	46.8612	1.63348	0.816740	−	0.577006i	$-0.195779\pi$
$823$	46.8612	1.63348	0.816740	+	0.577006i	$0.195779\pi$
$824$	−3.44852	−0.120135
$825$	0.139336	0.00485107
$826$	17.1397	0.596366
$827$	−11.9052	−0.413985	−0.206993	−	0.978343i	$-0.566368\pi$
$827$	−11.9052	−0.413985	−0.206993	+	0.978343i	$0.566368\pi$
$828$	−2.66163	−0.0924979
$829$	41.6515	1.44662	0.723308	−	0.690526i	$-0.242621\pi$
$829$	41.6515	1.44662	0.723308	+	0.690526i	$0.242621\pi$
$830$	−23.6342	−0.820356
$831$	−11.3429	−0.393481
$832$	−1.70351	−0.0590588
$833$	−20.3093	−0.703677
$834$	−0.272387	−0.00943200
$835$	−36.8318	−1.27462
$836$	−3.60086	−0.124538
$837$	−9.59806	−0.331758
$838$	27.3412	0.944488
$839$	−56.5408	−1.95201	−0.976003	−	0.217759i	$-0.930125\pi$
$839$	−56.5408	−1.95201	−0.976003	+	0.217759i	$0.930125\pi$
$840$	1.59317	0.0549696
$841$	−13.7291	−0.473418
$842$	−24.8373	−0.855950
$843$	−1.59821	−0.0550452
$844$	−6.65901	−0.229213
$845$	22.3253	0.768014
$846$	−13.9210	−0.478612
$847$	−7.97204	−0.273923
$848$	9.01190	0.309470
$849$	9.32490	0.320030
$850$	0.416615	0.0142898
$851$	1.60709	0.0550904
$852$	2.01153	0.0689139
$853$	45.5901	1.56098	0.780488	−	0.625170i	$-0.214971\pi$
$853$	45.5901	1.56098	0.780488	+	0.625170i	$0.214971\pi$
$854$	0.739175	0.0252941
$855$	9.91759	0.339174
$856$	4.62168	0.157966
$857$	23.0057	0.785860	0.392930	−	0.919568i	$-0.371462\pi$
$857$	23.0057	0.785860	0.392930	+	0.919568i	$0.371462\pi$
$858$	−2.11715	−0.0722784
$859$	12.4438	0.424578	0.212289	−	0.977207i	$-0.431908\pi$
$859$	12.4438	0.424578	0.212289	+	0.977207i	$0.431908\pi$
$860$	−19.1323	−0.652406
$861$	−5.36434	−0.182816
$862$	8.99331	0.306313
$863$	35.6975	1.21516	0.607579	−	0.794259i	$-0.292141\pi$
$863$	35.6975	1.21516	0.607579	+	0.794259i	$0.292141\pi$
$864$	3.29336	0.112042
$865$	13.1161	0.445960
$866$	−36.4600	−1.23896
$867$	−1.85634	−0.0630447
$868$	3.61034	0.122543
$869$	17.1807	0.582815
$870$	−5.02563	−0.170385
$871$	−11.1807	−0.378842
$872$	−11.7874	−0.399170
$873$	−5.38796	−0.182355
$874$	−1.68538	−0.0570089
$875$	14.0012	0.473327
$876$	−1.55190	−0.0524340
$877$	27.6255	0.932847	0.466424	−	0.884561i	$-0.345542\pi$
$877$	27.6255	0.932847	0.466424	+	0.884561i	$0.345542\pi$
$878$	18.2799	0.616918
$879$	13.0905	0.441530
$880$	4.72355	0.159231
$881$	42.8991	1.44531	0.722654	−	0.691210i	$-0.242922\pi$
$881$	42.8991	1.44531	0.722654	+	0.691210i	$0.242922\pi$
$882$	−14.5467	−0.489814
$883$	51.8824	1.74598	0.872991	−	0.487737i	$-0.162178\pi$
$883$	51.8824	1.74598	0.872991	+	0.487737i	$0.162178\pi$
$884$	−6.33028	−0.212910
$885$	17.7933	0.598116
$886$	−22.9333	−0.770461
$887$	28.3889	0.953205	0.476602	−	0.879119i	$-0.341868\pi$
$887$	28.3889	0.953205	0.476602	+	0.879119i	$0.341868\pi$
$888$	−0.934842	−0.0313712
$889$	2.45794	0.0824367
$890$	−10.2555	−0.343767
$891$	−12.9669	−0.434407
$892$	−11.2220	−0.375740
$893$	−8.81495	−0.294981
$894$	−12.9442	−0.432919
$895$	−5.46798	−0.182775
$896$	−1.23881	−0.0413857
$897$	−0.990932	−0.0330862
$898$	−4.38520	−0.146336
$899$	−11.3888	−0.379837
$900$	0.298404	0.00994681
$901$	33.4883	1.11566
$902$	−15.9046	−0.529566
$903$	6.23603	0.207522
$904$	−12.1070	−0.402672
$905$	−41.8038	−1.38961
$906$	−13.7648	−0.457305
$907$	38.6141	1.28216	0.641079	−	0.767475i	$-0.278487\pi$
$907$	38.6141	1.28216	0.641079	+	0.767475i	$0.278487\pi$
$908$	12.5856	0.417667
$909$	−0.298296	−0.00989386
$910$	−4.66563	−0.154664
$911$	−58.5869	−1.94107	−0.970535	−	0.240960i	$-0.922538\pi$
$911$	−58.5869	−1.94107	−0.970535	+	0.240960i	$0.922538\pi$
$912$	0.980383	0.0324637
$913$	22.8396	0.755882
$914$	−32.2628	−1.06716
$915$	0.767364	0.0253683
$916$	−16.1149	−0.532451
$917$	−1.23881	−0.0409090
$918$	12.2382	0.403920
$919$	−30.1771	−0.995450	−0.497725	−	0.867335i	$-0.665831\pi$
$919$	−30.1771	−0.995450	−0.497725	+	0.867335i	$0.665831\pi$
$920$	2.21086	0.0728898
$921$	0.797537	0.0262797
$922$	19.2650	0.634457
$923$	−5.89081	−0.193898
$924$	−1.53961	−0.0506494
$925$	−0.180177	−0.00592417
$926$	24.5255	0.805957
$927$	−9.17869	−0.301468
$928$	3.90780	0.128280
$929$	44.9379	1.47437	0.737183	−	0.675693i	$-0.236156\pi$
$929$	44.9379	1.47437	0.737183	+	0.675693i	$0.236156\pi$
$930$	3.74803	0.122903
$931$	−9.21121	−0.301885
$932$	25.5132	0.835713
$933$	−3.72034	−0.121799
$934$	35.2519	1.15348
$935$	17.5528	0.574038
$936$	−4.53412	−0.148202
$937$	−26.5885	−0.868609	−0.434305	−	0.900766i	$-0.643006\pi$
$937$	−26.5885	−0.868609	−0.434305	+	0.900766i	$0.643006\pi$
$938$	−8.13065	−0.265475
$939$	−9.27647	−0.302726
$940$	11.5633	0.377154
$941$	27.5435	0.897892	0.448946	−	0.893559i	$-0.351800\pi$
$941$	27.5435	0.897892	0.448946	+	0.893559i	$0.351800\pi$
$942$	4.49852	0.146570
$943$	−7.44415	−0.242415
$944$	−13.8356	−0.450311
$945$	9.01994	0.293419
$946$	18.4891	0.601131
$947$	5.53875	0.179985	0.0899926	−	0.995942i	$-0.471316\pi$
$947$	5.53875	0.179985	0.0899926	+	0.995942i	$0.471316\pi$
$948$	−4.67768	−0.151924
$949$	4.54478	0.147530
$950$	0.188954	0.00613048
$951$	−5.18456	−0.168121
$952$	−4.60343	−0.149198
$953$	28.0320	0.908047	0.454023	−	0.890990i	$-0.349988\pi$
$953$	28.0320	0.908047	0.454023	+	0.890990i	$0.349988\pi$
$954$	23.9863	0.776586
$955$	57.5294	1.86161
$956$	−14.1266	−0.456886
$957$	4.85666	0.156994
$958$	42.0142	1.35742
$959$	12.5231	0.404391
$960$	−1.28605	−0.0415071
$961$	−22.5064	−0.726014
$962$	2.73770	0.0882671
$963$	12.3012	0.396400
$964$	2.11369	0.0680772
$965$	−57.9244	−1.86465
$966$	−0.720612	−0.0231853
$967$	−23.3400	−0.750565	−0.375283	−	0.926910i	$-0.622454\pi$
$967$	−23.3400	−0.750565	−0.375283	+	0.926910i	$0.622454\pi$
$968$	6.43525	0.206837
$969$	3.64312	0.117034
$970$	4.47546	0.143698
$971$	−40.6783	−1.30543	−0.652714	−	0.757604i	$-0.726370\pi$
$971$	−40.6783	−1.30543	−0.652714	+	0.757604i	$0.726370\pi$
$972$	13.4105	0.430141
$973$	0.580087	0.0185967
$974$	−28.8097	−0.923122
$975$	0.111097	0.00355795
$976$	−0.596683	−0.0190993
$977$	−3.17963	−0.101725	−0.0508627	−	0.998706i	$-0.516197\pi$
$977$	−3.17963	−0.101725	−0.0508627	+	0.998706i	$0.516197\pi$
$978$	−12.7760	−0.408533
$979$	9.91075	0.316749
$980$	12.0831	0.385981
$981$	−31.3736	−1.00168
$982$	5.11017	0.163072
$983$	−9.80392	−0.312696	−0.156348	−	0.987702i	$-0.549972\pi$
$983$	−9.80392	−0.312696	−0.156348	+	0.987702i	$0.549972\pi$
$984$	4.33025	0.138043
$985$	11.3816	0.362647
$986$	14.5214	0.462456
$987$	−3.76898	−0.119968
$988$	−2.87107	−0.0913410
$989$	8.65379	0.275175
$990$	12.5723	0.399575
$991$	−33.4334	−1.06205	−0.531023	−	0.847357i	$-0.678192\pi$
$991$	−33.4334	−1.06205	−0.531023	+	0.847357i	$0.678192\pi$
$992$	−2.91437	−0.0925313
$993$	−3.81854	−0.121178
$994$	−4.28384	−0.135875
$995$	−35.5120	−1.12581
$996$	−6.21840	−0.197038
$997$	−53.6909	−1.70041	−0.850204	−	0.526453i	$-0.823522\pi$
$997$	−53.6909	−1.70041	−0.850204	+	0.526453i	$0.823522\pi$
$998$	−41.2747	−1.30653
$999$	−5.29272	−0.167454

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.j.1.20	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.j.1.20	✓	33	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} +0.581698 q^{3} +1.00000 q^{4} -2.21086 q^{5} -0.581698 q^{6} +1.23881 q^{7} -1.00000 q^{8} -2.66163 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} +0.581698 q^{3} +1.00000 q^{4} -2.21086 q^{5} -0.581698 q^{6} +1.23881 q^{7} -1.00000 q^{8} -2.66163 q^{9} +2.21086 q^{10} -2.13653 q^{11} +0.581698 q^{12} -1.70351 q^{13} -1.23881 q^{14} -1.28605 q^{15} +1.00000 q^{16} +3.71601 q^{17} +2.66163 q^{18} +1.68538 q^{19} -2.21086 q^{20} +0.720612 q^{21} +2.13653 q^{22} +1.00000 q^{23} -0.581698 q^{24} -0.112114 q^{25} +1.70351 q^{26} -3.29336 q^{27} +1.23881 q^{28} -3.90780 q^{29} +1.28605 q^{30} +2.91437 q^{31} -1.00000 q^{32} -1.24281 q^{33} -3.71601 q^{34} -2.73883 q^{35} -2.66163 q^{36} +1.60709 q^{37} -1.68538 q^{38} -0.990932 q^{39} +2.21086 q^{40} -7.44415 q^{41} -0.720612 q^{42} +8.65379 q^{43} -2.13653 q^{44} +5.88448 q^{45} -1.00000 q^{46} -5.23024 q^{47} +0.581698 q^{48} -5.46536 q^{49} +0.112114 q^{50} +2.16160 q^{51} -1.70351 q^{52} +9.01190 q^{53} +3.29336 q^{54} +4.72355 q^{55} -1.23881 q^{56} +0.980383 q^{57} +3.90780 q^{58} -13.8356 q^{59} -1.28605 q^{60} -0.596683 q^{61} -2.91437 q^{62} -3.29724 q^{63} +1.00000 q^{64} +3.76623 q^{65} +1.24281 q^{66} +6.56329 q^{67} +3.71601 q^{68} +0.581698 q^{69} +2.73883 q^{70} +3.45803 q^{71} +2.66163 q^{72} -2.66788 q^{73} -1.60709 q^{74} -0.0652162 q^{75} +1.68538 q^{76} -2.64675 q^{77} +0.990932 q^{78} -8.04141 q^{79} -2.21086 q^{80} +6.06914 q^{81} +7.44415 q^{82} -10.6901 q^{83} +0.720612 q^{84} -8.21557 q^{85} -8.65379 q^{86} -2.27316 q^{87} +2.13653 q^{88} -4.63872 q^{89} -5.88448 q^{90} -2.11033 q^{91} +1.00000 q^{92} +1.69528 q^{93} +5.23024 q^{94} -3.72614 q^{95} -0.581698 q^{96} +2.02431 q^{97} +5.46536 q^{98} +5.68664 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9}+O(q^{10}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9	\( 33 q - 33 q^{2} + 3 q^{3} + 33 q^{4} - 4 q^{5} - 3 q^{6} + 11 q^{7} - 33 q^{8} + 44 q^{9} + 4 q^{10} + 5 q^{11} + 3 q^{12} + 15 q^{13} - 11 q^{14} + 16 q^{15} + 33 q^{16} + 2 q^{17} - 44 q^{18} + 32 q^{19} - 4 q^{20} + 8 q^{21} - 5 q^{22} + 33 q^{23} - 3 q^{24} + 49 q^{25} - 15 q^{26} + 15 q^{27} + 11 q^{28} + 20 q^{29} - 16 q^{30} + 25 q^{31} - 33 q^{32} - 6 q^{33} - 2 q^{34} + 15 q^{35} + 44 q^{36} + 6 q^{37} - 32 q^{38} + 25 q^{39} + 4 q^{40} + 2 q^{41} - 8 q^{42} + 31 q^{43} + 5 q^{44} + 2 q^{45} - 33 q^{46} + 4 q^{47} + 3 q^{48} + 72 q^{49} - 49 q^{50} + 26 q^{51} + 15 q^{52} - 65 q^{53} - 15 q^{54} - 4 q^{55} - 11 q^{56} + 12 q^{57} - 20 q^{58} + 8 q^{59} + 16 q^{60} + 23 q^{61} - 25 q^{62} - 14 q^{63} + 33 q^{64} + 5 q^{65} + 6 q^{66} + 31 q^{67} + 2 q^{68} + 3 q^{69} - 15 q^{70} + 20 q^{71} - 44 q^{72} + 22 q^{73} - 6 q^{74} - 32 q^{75} + 32 q^{76} + 2 q^{77} - 25 q^{78} + 53 q^{79} - 4 q^{80} + 17 q^{81} - 2 q^{82} + 45 q^{83} + 8 q^{84} + 60 q^{85} - 31 q^{86} + 11 q^{87} - 5 q^{88} - 54 q^{89} - 2 q^{90} + 38 q^{91} + 33 q^{92} + 63 q^{93} - 4 q^{94} + 44 q^{95} - 3 q^{96} - 72 q^{98} + 43 q^{99}+O(q^{100}) \) 33 * q - 33 * q^2 + 3 * q^3 + 33 * q^4 - 4 * q^5 - 3 * q^6 + 11 * q^7 - 33 * q^8 + 44 * q^9 + 4 * q^10 + 5 * q^11 + 3 * q^12 + 15 * q^13 - 11 * q^14 + 16 * q^15 + 33 * q^16 + 2 * q^17 - 44 * q^18 + 32 * q^19 - 4 * q^20 + 8 * q^21 - 5 * q^22 + 33 * q^23 - 3 * q^24 + 49 * q^25 - 15 * q^26 + 15 * q^27 + 11 * q^28 + 20 * q^29 - 16 * q^30 + 25 * q^31 - 33 * q^32 - 6 * q^33 - 2 * q^34 + 15 * q^35 + 44 * q^36 + 6 * q^37 - 32 * q^38 + 25 * q^39 + 4 * q^40 + 2 * q^41 - 8 * q^42 + 31 * q^43 + 5 * q^44 + 2 * q^45 - 33 * q^46 + 4 * q^47 + 3 * q^48 + 72 * q^49 - 49 * q^50 + 26 * q^51 + 15 * q^52 - 65 * q^53 - 15 * q^54 - 4 * q^55 - 11 * q^56 + 12 * q^57 - 20 * q^58 + 8 * q^59 + 16 * q^60 + 23 * q^61 - 25 * q^62 - 14 * q^63 + 33 * q^64 + 5 * q^65 + 6 * q^66 + 31 * q^67 + 2 * q^68 + 3 * q^69 - 15 * q^70 + 20 * q^71 - 44 * q^72 + 22 * q^73 - 6 * q^74 - 32 * q^75 + 32 * q^76 + 2 * q^77 - 25 * q^78 + 53 * q^79 - 4 * q^80 + 17 * q^81 - 2 * q^82 + 45 * q^83 + 8 * q^84 + 60 * q^85 - 31 * q^86 + 11 * q^87 - 5 * q^88 - 54 * q^89 - 2 * q^90 + 38 * q^91 + 33 * q^92 + 63 * q^93 - 4 * q^94 + 44 * q^95 - 3 * q^96 - 72 * q^98 + 43 * q^99

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