LMFDB - Embedded newform 6015.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.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:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+0.806575 q^{2} -1.00000 q^{3} -1.34944 q^{4} +1.00000 q^{5} -0.806575 q^{6} +2.45232 q^{7} -2.70157 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.806575 q^{2} -1.00000 q^{3} -1.34944 q^{4} +1.00000 q^{5} -0.806575 q^{6} +2.45232 q^{7} -2.70157 q^{8} +1.00000 q^{9} +0.806575 q^{10} +2.93288 q^{11} +1.34944 q^{12} -1.89110 q^{13} +1.97798 q^{14} -1.00000 q^{15} +0.519854 q^{16} -1.43077 q^{17} +0.806575 q^{18} -2.97412 q^{19} -1.34944 q^{20} -2.45232 q^{21} +2.36558 q^{22} -6.45068 q^{23} +2.70157 q^{24} +1.00000 q^{25} -1.52532 q^{26} -1.00000 q^{27} -3.30925 q^{28} -1.21404 q^{29} -0.806575 q^{30} +3.43286 q^{31} +5.82244 q^{32} -2.93288 q^{33} -1.15402 q^{34} +2.45232 q^{35} -1.34944 q^{36} -0.0402500 q^{37} -2.39885 q^{38} +1.89110 q^{39} -2.70157 q^{40} -2.33640 q^{41} -1.97798 q^{42} +9.77303 q^{43} -3.95773 q^{44} +1.00000 q^{45} -5.20296 q^{46} -8.78014 q^{47} -0.519854 q^{48} -0.986133 q^{49} +0.806575 q^{50} +1.43077 q^{51} +2.55192 q^{52} -2.31150 q^{53} -0.806575 q^{54} +2.93288 q^{55} -6.62511 q^{56} +2.97412 q^{57} -0.979216 q^{58} -14.8320 q^{59} +1.34944 q^{60} -3.11083 q^{61} +2.76886 q^{62} +2.45232 q^{63} +3.65653 q^{64} -1.89110 q^{65} -2.36558 q^{66} +0.311707 q^{67} +1.93073 q^{68} +6.45068 q^{69} +1.97798 q^{70} +12.1689 q^{71} -2.70157 q^{72} -2.72970 q^{73} -0.0324646 q^{74} -1.00000 q^{75} +4.01339 q^{76} +7.19235 q^{77} +1.52532 q^{78} -15.2865 q^{79} +0.519854 q^{80} +1.00000 q^{81} -1.88448 q^{82} +6.48280 q^{83} +3.30925 q^{84} -1.43077 q^{85} +7.88268 q^{86} +1.21404 q^{87} -7.92338 q^{88} -3.96363 q^{89} +0.806575 q^{90} -4.63759 q^{91} +8.70479 q^{92} -3.43286 q^{93} -7.08184 q^{94} -2.97412 q^{95} -5.82244 q^{96} +6.61920 q^{97} -0.795390 q^{98} +2.93288 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	0.806575	0.570335	0.285167	−	0.958478i	$-0.407951\pi$
$2$	0.806575	0.570335	0.285167	+	0.958478i	$0.407951\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.34944	−0.674718
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.806575	−0.329283
$7$	2.45232	0.926889	0.463445	−	0.886126i	$-0.346613\pi$
$7$	2.45232	0.926889	0.463445	+	0.886126i	$0.346613\pi$
$8$	−2.70157	−0.955150
$9$	1.00000	0.333333
$10$	0.806575	0.255061
$11$	2.93288	0.884295	0.442148	−	0.896942i	$-0.354217\pi$
$11$	2.93288	0.884295	0.442148	+	0.896942i	$0.354217\pi$
$12$	1.34944	0.389549
$13$	−1.89110	−0.524498	−0.262249	−	0.965000i	$-0.584464\pi$
$13$	−1.89110	−0.524498	−0.262249	+	0.965000i	$0.584464\pi$
$14$	1.97798	0.528637
$15$	−1.00000	−0.258199
$16$	0.519854	0.129963
$17$	−1.43077	−0.347012	−0.173506	−	0.984833i	$-0.555510\pi$
$17$	−1.43077	−0.347012	−0.173506	+	0.984833i	$0.555510\pi$
$18$	0.806575	0.190112
$19$	−2.97412	−0.682310	−0.341155	−	0.940007i	$-0.610818\pi$
$19$	−2.97412	−0.682310	−0.341155	+	0.940007i	$0.610818\pi$
$20$	−1.34944	−0.301743
$21$	−2.45232	−0.535140
$22$	2.36558	0.504344
$23$	−6.45068	−1.34506	−0.672530	−	0.740070i	$-0.734793\pi$
$23$	−6.45068	−1.34506	−0.672530	+	0.740070i	$0.734793\pi$
$24$	2.70157	0.551456
$25$	1.00000	0.200000
$26$	−1.52532	−0.299139
$27$	−1.00000	−0.192450
$28$	−3.30925	−0.625389
$29$	−1.21404	−0.225442	−0.112721	−	0.993627i	$-0.535957\pi$
$29$	−1.21404	−0.225442	−0.112721	+	0.993627i	$0.535957\pi$
$30$	−0.806575	−0.147260
$31$	3.43286	0.616560	0.308280	−	0.951296i	$-0.400247\pi$
$31$	3.43286	0.616560	0.308280	+	0.951296i	$0.400247\pi$
$32$	5.82244	1.02927
$33$	−2.93288	−0.510548
$34$	−1.15402	−0.197913
$35$	2.45232	0.414518
$36$	−1.34944	−0.224906
$37$	−0.0402500	−0.00661706	−0.00330853	−	0.999995i	$-0.501053\pi$
$37$	−0.0402500	−0.00661706	−0.00330853	+	0.999995i	$0.501053\pi$
$38$	−2.39885	−0.389145
$39$	1.89110	0.302819
$40$	−2.70157	−0.427156
$41$	−2.33640	−0.364885	−0.182443	−	0.983217i	$-0.558400\pi$
$41$	−2.33640	−0.364885	−0.182443	+	0.983217i	$0.558400\pi$
$42$	−1.97798	−0.305209
$43$	9.77303	1.49037	0.745187	−	0.666856i	$-0.232360\pi$
$43$	9.77303	1.49037	0.745187	+	0.666856i	$0.232360\pi$
$44$	−3.95773	−0.596650
$45$	1.00000	0.149071
$46$	−5.20296	−0.767135
$47$	−8.78014	−1.28072	−0.640358	−	0.768077i	$-0.721214\pi$
$47$	−8.78014	−1.28072	−0.640358	+	0.768077i	$0.721214\pi$
$48$	−0.519854	−0.0750344
$49$	−0.986133	−0.140876
$50$	0.806575	0.114067
$51$	1.43077	0.200347
$52$	2.55192	0.353888
$53$	−2.31150	−0.317510	−0.158755	−	0.987318i	$-0.550748\pi$
$53$	−2.31150	−0.317510	−0.158755	+	0.987318i	$0.550748\pi$
$54$	−0.806575	−0.109761
$55$	2.93288	0.395469
$56$	−6.62511	−0.885318
$57$	2.97412	0.393932
$58$	−0.979216	−0.128577
$59$	−14.8320	−1.93097	−0.965484	−	0.260462i	$-0.916125\pi$
$59$	−14.8320	−1.93097	−0.965484	+	0.260462i	$0.916125\pi$
$60$	1.34944	0.174212
$61$	−3.11083	−0.398301	−0.199150	−	0.979969i	$-0.563818\pi$
$61$	−3.11083	−0.398301	−0.199150	+	0.979969i	$0.563818\pi$
$62$	2.76886	0.351645
$63$	2.45232	0.308963
$64$	3.65653	0.457066
$65$	−1.89110	−0.234562
$66$	−2.36558	−0.291183
$67$	0.311707	0.0380811	0.0190405	−	0.999819i	$-0.493939\pi$
$67$	0.311707	0.0380811	0.0190405	+	0.999819i	$0.493939\pi$
$68$	1.93073	0.234135
$69$	6.45068	0.776571
$70$	1.97798	0.236414
$71$	12.1689	1.44418	0.722089	−	0.691800i	$-0.243182\pi$
$71$	12.1689	1.44418	0.722089	+	0.691800i	$0.243182\pi$
$72$	−2.70157	−0.318383
$73$	−2.72970	−0.319487	−0.159743	−	0.987159i	$-0.551067\pi$
$73$	−2.72970	−0.319487	−0.159743	+	0.987159i	$0.551067\pi$
$74$	−0.0324646	−0.00377394
$75$	−1.00000	−0.115470
$76$	4.01339	0.460367
$77$	7.19235	0.819644
$78$	1.52532	0.172708
$79$	−15.2865	−1.71986	−0.859931	−	0.510410i	$-0.829494\pi$
$79$	−15.2865	−1.71986	−0.859931	+	0.510410i	$0.829494\pi$
$80$	0.519854	0.0581214
$81$	1.00000	0.111111
$82$	−1.88448	−0.208107
$83$	6.48280	0.711579	0.355790	−	0.934566i	$-0.384212\pi$
$83$	6.48280	0.711579	0.355790	+	0.934566i	$0.384212\pi$
$84$	3.30925	0.361069
$85$	−1.43077	−0.155188
$86$	7.88268	0.850012
$87$	1.21404	0.130159
$88$	−7.92338	−0.844635
$89$	−3.96363	−0.420144	−0.210072	−	0.977686i	$-0.567370\pi$
$89$	−3.96363	−0.420144	−0.210072	+	0.977686i	$0.567370\pi$
$90$	0.806575	0.0850205
$91$	−4.63759	−0.486151
$92$	8.70479	0.907537
$93$	−3.43286	−0.355971
$94$	−7.08184	−0.730436
$95$	−2.97412	−0.305138
$96$	−5.82244	−0.594251
$97$	6.61920	0.672078	0.336039	−	0.941848i	$-0.390913\pi$
$97$	6.61920	0.672078	0.336039	+	0.941848i	$0.390913\pi$
$98$	−0.795390	−0.0803465
$99$	2.93288	0.294765
$100$	−1.34944	−0.134944
$101$	11.7155	1.16574	0.582868	−	0.812567i	$-0.301931\pi$
$101$	11.7155	1.16574	0.582868	+	0.812567i	$0.301931\pi$
$102$	1.15402	0.114265
$103$	−15.2978	−1.50733	−0.753666	−	0.657257i	$-0.771716\pi$
$103$	−15.2978	−1.50733	−0.753666	+	0.657257i	$0.771716\pi$
$104$	5.10895	0.500974
$105$	−2.45232	−0.239322
$106$	−1.86440	−0.181087
$107$	2.55181	0.246693	0.123346	−	0.992364i	$-0.460637\pi$
$107$	2.55181	0.246693	0.123346	+	0.992364i	$0.460637\pi$
$108$	1.34944	0.129850
$109$	−7.62111	−0.729970	−0.364985	−	0.931013i	$-0.618926\pi$
$109$	−7.62111	−0.729970	−0.364985	+	0.931013i	$0.618926\pi$
$110$	2.36558	0.225550
$111$	0.0402500	0.00382036
$112$	1.27485	0.120462
$113$	−2.18576	−0.205619	−0.102809	−	0.994701i	$-0.532783\pi$
$113$	−2.18576	−0.205619	−0.102809	+	0.994701i	$0.532783\pi$
$114$	2.39885	0.224673
$115$	−6.45068	−0.601529
$116$	1.63827	0.152110
$117$	−1.89110	−0.174833
$118$	−11.9632	−1.10130
$119$	−3.50870	−0.321642
$120$	2.70157	0.246619
$121$	−2.39824	−0.218022
$122$	−2.50912	−0.227165
$123$	2.33640	0.210666
$124$	−4.63243	−0.416004
$125$	1.00000	0.0894427
$126$	1.97798	0.176212
$127$	15.9850	1.41844	0.709218	−	0.704989i	$-0.249048\pi$
$127$	15.9850	1.41844	0.709218	+	0.704989i	$0.249048\pi$
$128$	−8.69562	−0.768592
$129$	−9.77303	−0.860468
$130$	−1.52532	−0.133779
$131$	−12.4886	−1.09114	−0.545568	−	0.838066i	$-0.683686\pi$
$131$	−12.4886	−1.09114	−0.545568	+	0.838066i	$0.683686\pi$
$132$	3.95773	0.344476
$133$	−7.29349	−0.632425
$134$	0.251415	0.0217190
$135$	−1.00000	−0.0860663
$136$	3.86532	0.331448
$137$	10.9767	0.937803	0.468901	−	0.883251i	$-0.344650\pi$
$137$	10.9767	0.937803	0.468901	+	0.883251i	$0.344650\pi$
$138$	5.20296	0.442905
$139$	11.3033	0.958736	0.479368	−	0.877614i	$-0.340866\pi$
$139$	11.3033	0.958736	0.479368	+	0.877614i	$0.340866\pi$
$140$	−3.30925	−0.279683
$141$	8.78014	0.739421
$142$	9.81510	0.823665
$143$	−5.54637	−0.463811
$144$	0.519854	0.0433211
$145$	−1.21404	−0.100821
$146$	−2.20170	−0.182214
$147$	0.986133	0.0813349
$148$	0.0543148	0.00446465
$149$	3.22900	0.264530	0.132265	−	0.991214i	$-0.457775\pi$
$149$	3.22900	0.264530	0.132265	+	0.991214i	$0.457775\pi$
$150$	−0.806575	−0.0658566
$151$	−9.56598	−0.778469	−0.389234	−	0.921139i	$-0.627260\pi$
$151$	−9.56598	−0.778469	−0.389234	+	0.921139i	$0.627260\pi$
$152$	8.03479	0.651708
$153$	−1.43077	−0.115671
$154$	5.80117	0.467471
$155$	3.43286	0.275734
$156$	−2.55192	−0.204317
$157$	20.1697	1.60972	0.804860	−	0.593465i	$-0.202241\pi$
$157$	20.1697	1.60972	0.804860	+	0.593465i	$0.202241\pi$
$158$	−12.3297	−0.980897
$159$	2.31150	0.183314
$160$	5.82244	0.460305
$161$	−15.8191	−1.24672
$162$	0.806575	0.0633705
$163$	13.4630	1.05451	0.527253	−	0.849708i	$-0.323222\pi$
$163$	13.4630	1.05451	0.527253	+	0.849708i	$0.323222\pi$
$164$	3.15283	0.246195
$165$	−2.93288	−0.228324
$166$	5.22886	0.405838
$167$	3.13533	0.242619	0.121310	−	0.992615i	$-0.461291\pi$
$167$	3.13533	0.242619	0.121310	+	0.992615i	$0.461291\pi$
$168$	6.62511	0.511139
$169$	−9.42373	−0.724902
$170$	−1.15402	−0.0885093
$171$	−2.97412	−0.227437
$172$	−13.1881	−1.00558
$173$	−24.8880	−1.89220	−0.946099	−	0.323877i	$-0.895014\pi$
$173$	−24.8880	−1.89220	−0.946099	+	0.323877i	$0.895014\pi$
$174$	0.979216	0.0742342
$175$	2.45232	0.185378
$176$	1.52467	0.114926
$177$	14.8320	1.11485
$178$	−3.19696	−0.239623
$179$	−15.5813	−1.16460	−0.582299	−	0.812975i	$-0.697847\pi$
$179$	−15.5813	−1.16460	−0.582299	+	0.812975i	$0.697847\pi$
$180$	−1.34944	−0.100581
$181$	10.9502	0.813922	0.406961	−	0.913446i	$-0.366589\pi$
$181$	10.9502	0.813922	0.406961	+	0.913446i	$0.366589\pi$
$182$	−3.74056	−0.277269
$183$	3.11083	0.229959
$184$	17.4270	1.28473
$185$	−0.0402500	−0.00295924
$186$	−2.76886	−0.203023
$187$	−4.19626	−0.306861
$188$	11.8482	0.864122
$189$	−2.45232	−0.178380
$190$	−2.39885	−0.174031
$191$	3.53267	0.255615	0.127808	−	0.991799i	$-0.459206\pi$
$191$	3.53267	0.255615	0.127808	+	0.991799i	$0.459206\pi$
$192$	−3.65653	−0.263887
$193$	26.6432	1.91782	0.958910	−	0.283710i	$-0.0915652\pi$
$193$	26.6432	1.91782	0.958910	+	0.283710i	$0.0915652\pi$
$194$	5.33888	0.383309
$195$	1.89110	0.135425
$196$	1.33072	0.0950517
$197$	−27.8250	−1.98245	−0.991224	−	0.132192i	$-0.957798\pi$
$197$	−27.8250	−1.98245	−0.991224	+	0.132192i	$0.957798\pi$
$198$	2.36558	0.168115
$199$	−12.6342	−0.895613	−0.447806	−	0.894131i	$-0.647795\pi$
$199$	−12.6342	−0.895613	−0.447806	+	0.894131i	$0.647795\pi$
$200$	−2.70157	−0.191030
$201$	−0.311707	−0.0219861
$202$	9.44943	0.664859
$203$	−2.97722	−0.208960
$204$	−1.93073	−0.135178
$205$	−2.33640	−0.163182
$206$	−12.3388	−0.859684
$207$	−6.45068	−0.448354
$208$	−0.983097	−0.0681655
$209$	−8.72272	−0.603363
$210$	−1.97798	−0.136494
$211$	−22.2005	−1.52834	−0.764172	−	0.645013i	$-0.776852\pi$
$211$	−22.2005	−1.52834	−0.764172	+	0.645013i	$0.776852\pi$
$212$	3.11923	0.214230
$213$	−12.1689	−0.833797
$214$	2.05822	0.140697
$215$	9.77303	0.666515
$216$	2.70157	0.183819
$217$	8.41846	0.571483
$218$	−6.14700	−0.416327
$219$	2.72970	0.184456
$220$	−3.95773	−0.266830
$221$	2.70573	0.182007
$222$	0.0324646	0.00217888
$223$	−26.9944	−1.80768	−0.903840	−	0.427871i	$-0.859264\pi$
$223$	−26.9944	−1.80768	−0.903840	+	0.427871i	$0.859264\pi$
$224$	14.2785	0.954022
$225$	1.00000	0.0666667
$226$	−1.76298	−0.117272
$227$	−28.7480	−1.90807	−0.954035	−	0.299694i	$-0.903115\pi$
$227$	−28.7480	−1.90807	−0.954035	+	0.299694i	$0.903115\pi$
$228$	−4.01339	−0.265793
$229$	−15.3719	−1.01581	−0.507903	−	0.861414i	$-0.669579\pi$
$229$	−15.3719	−1.01581	−0.507903	+	0.861414i	$0.669579\pi$
$230$	−5.20296	−0.343073
$231$	−7.19235	−0.473222
$232$	3.27982	0.215331
$233$	1.55634	0.101959	0.0509796	−	0.998700i	$-0.483766\pi$
$233$	1.55634	0.101959	0.0509796	+	0.998700i	$0.483766\pi$
$234$	−1.52532	−0.0997130
$235$	−8.78014	−0.572753
$236$	20.0149	1.30286
$237$	15.2865	0.992963
$238$	−2.83003	−0.183443
$239$	25.6358	1.65824	0.829122	−	0.559068i	$-0.188841\pi$
$239$	25.6358	1.65824	0.829122	+	0.559068i	$0.188841\pi$
$240$	−0.519854	−0.0335564
$241$	−17.9970	−1.15929	−0.579645	−	0.814869i	$-0.696809\pi$
$241$	−17.9970	−1.15929	−0.579645	+	0.814869i	$0.696809\pi$
$242$	−1.93436	−0.124345
$243$	−1.00000	−0.0641500
$244$	4.19787	0.268741
$245$	−0.986133	−0.0630017
$246$	1.88448	0.120150
$247$	5.62436	0.357870
$248$	−9.27412	−0.588907
$249$	−6.48280	−0.410830
$250$	0.806575	0.0510123
$251$	−16.6366	−1.05010	−0.525048	−	0.851073i	$-0.675952\pi$
$251$	−16.6366	−1.05010	−0.525048	+	0.851073i	$0.675952\pi$
$252$	−3.30925	−0.208463
$253$	−18.9191	−1.18943
$254$	12.8931	0.808983
$255$	1.43077	0.0895981
$256$	−14.3267	−0.895421
$257$	−20.2640	−1.26404	−0.632018	−	0.774954i	$-0.717773\pi$
$257$	−20.2640	−1.26404	−0.632018	+	0.774954i	$0.717773\pi$
$258$	−7.88268	−0.490754
$259$	−0.0987058	−0.00613328
$260$	2.55192	0.158264
$261$	−1.21404	−0.0751473
$262$	−10.0730	−0.622313
$263$	3.07616	0.189684	0.0948420	−	0.995492i	$-0.469765\pi$
$263$	3.07616	0.189684	0.0948420	+	0.995492i	$0.469765\pi$
$264$	7.92338	0.487650
$265$	−2.31150	−0.141995
$266$	−5.88274	−0.360694
$267$	3.96363	0.242570
$268$	−0.420629	−0.0256940
$269$	−22.0222	−1.34272	−0.671359	−	0.741132i	$-0.734289\pi$
$269$	−22.0222	−1.34272	−0.671359	+	0.741132i	$0.734289\pi$
$270$	−0.806575	−0.0490866
$271$	0.466785	0.0283552	0.0141776	−	0.999899i	$-0.495487\pi$
$271$	0.466785	0.0283552	0.0141776	+	0.999899i	$0.495487\pi$
$272$	−0.743789	−0.0450989
$273$	4.63759	0.280680
$274$	8.85353	0.534861
$275$	2.93288	0.176859
$276$	−8.70479	−0.523967
$277$	−5.53573	−0.332610	−0.166305	−	0.986074i	$-0.553184\pi$
$277$	−5.53573	−0.332610	−0.166305	+	0.986074i	$0.553184\pi$
$278$	9.11698	0.546800
$279$	3.43286	0.205520
$280$	−6.62511	−0.395926
$281$	4.97037	0.296508	0.148254	−	0.988949i	$-0.452635\pi$
$281$	4.97037	0.296508	0.148254	+	0.988949i	$0.452635\pi$
$282$	7.08184	0.421718
$283$	−24.0340	−1.42867	−0.714336	−	0.699803i	$-0.753271\pi$
$283$	−24.0340	−1.42867	−0.714336	+	0.699803i	$0.753271\pi$
$284$	−16.4211	−0.974414
$285$	2.97412	0.176172
$286$	−4.47356	−0.264527
$287$	−5.72961	−0.338208
$288$	5.82244	0.343091
$289$	−14.9529	−0.879583
$290$	−0.979216	−0.0575015
$291$	−6.61920	−0.388024
$292$	3.68355	0.215564
$293$	−0.0516212	−0.00301574	−0.00150787	−	0.999999i	$-0.500480\pi$
$293$	−0.0516212	−0.00301574	−0.00150787	+	0.999999i	$0.500480\pi$
$294$	0.795390	0.0463881
$295$	−14.8320	−0.863555
$296$	0.108738	0.00632028
$297$	−2.93288	−0.170183
$298$	2.60443	0.150871
$299$	12.1989	0.705481
$300$	1.34944	0.0779098
$301$	23.9666	1.38141
$302$	−7.71568	−0.443988
$303$	−11.7155	−0.673038
$304$	−1.54611	−0.0886753
$305$	−3.11083	−0.178126
$306$	−1.15402	−0.0659710
$307$	−30.3984	−1.73493	−0.867464	−	0.497500i	$-0.834251\pi$
$307$	−30.3984	−1.73493	−0.867464	+	0.497500i	$0.834251\pi$
$308$	−9.70562	−0.553029
$309$	15.2978	0.870259
$310$	2.76886	0.157261
$311$	−3.30812	−0.187586	−0.0937931	−	0.995592i	$-0.529899\pi$
$311$	−3.30812	−0.187586	−0.0937931	+	0.995592i	$0.529899\pi$
$312$	−5.10895	−0.289237
$313$	18.6456	1.05391	0.526957	−	0.849892i	$-0.323333\pi$
$313$	18.6456	1.05391	0.526957	+	0.849892i	$0.323333\pi$
$314$	16.2684	0.918079
$315$	2.45232	0.138173
$316$	20.6281	1.16042
$317$	−23.3027	−1.30881	−0.654405	−	0.756145i	$-0.727081\pi$
$317$	−23.3027	−1.30881	−0.654405	+	0.756145i	$0.727081\pi$
$318$	1.86440	0.104550
$319$	−3.56064	−0.199357
$320$	3.65653	0.204406
$321$	−2.55181	−0.142428
$322$	−12.7593	−0.711049
$323$	4.25527	0.236770
$324$	−1.34944	−0.0749687
$325$	−1.89110	−0.104900
$326$	10.8590	0.601422
$327$	7.62111	0.421448
$328$	6.31196	0.348520
$329$	−21.5317	−1.18708
$330$	−2.36558	−0.130221
$331$	−11.9246	−0.655437	−0.327719	−	0.944775i	$-0.606280\pi$
$331$	−11.9246	−0.655437	−0.327719	+	0.944775i	$0.606280\pi$
$332$	−8.74812	−0.480116
$333$	−0.0402500	−0.00220569
$334$	2.52888	0.138374
$335$	0.311707	0.0170304
$336$	−1.27485	−0.0695486
$337$	9.06384	0.493739	0.246869	−	0.969049i	$-0.420598\pi$
$337$	9.06384	0.493739	0.246869	+	0.969049i	$0.420598\pi$
$338$	−7.60094	−0.413437
$339$	2.18576	0.118714
$340$	1.93073	0.104709
$341$	10.0682	0.545221
$342$	−2.39885	−0.129715
$343$	−19.5845	−1.05747
$344$	−26.4026	−1.42353
$345$	6.45068	0.347293
$346$	−20.0740	−1.07919
$347$	14.0594	0.754750	0.377375	−	0.926061i	$-0.376827\pi$
$347$	14.0594	0.754750	0.377375	+	0.926061i	$0.376827\pi$
$348$	−1.63827	−0.0878207
$349$	−29.9464	−1.60299	−0.801496	−	0.598000i	$-0.795962\pi$
$349$	−29.9464	−1.60299	−0.801496	+	0.598000i	$0.795962\pi$
$350$	1.97798	0.105727
$351$	1.89110	0.100940
$352$	17.0765	0.910181
$353$	7.29345	0.388191	0.194096	−	0.980983i	$-0.437823\pi$
$353$	7.29345	0.388191	0.194096	+	0.980983i	$0.437823\pi$
$354$	11.9632	0.635835
$355$	12.1689	0.645856
$356$	5.34867	0.283479
$357$	3.50870	0.185700
$358$	−12.5675	−0.664211
$359$	3.32641	0.175561	0.0877805	−	0.996140i	$-0.472023\pi$
$359$	3.32641	0.175561	0.0877805	+	0.996140i	$0.472023\pi$
$360$	−2.70157	−0.142385
$361$	−10.1546	−0.534454
$362$	8.83215	0.464208
$363$	2.39824	0.125875
$364$	6.25813	0.328015
$365$	−2.72970	−0.142879
$366$	2.50912	0.131154
$367$	25.2234	1.31665	0.658325	−	0.752734i	$-0.271265\pi$
$367$	25.2234	1.31665	0.658325	+	0.752734i	$0.271265\pi$
$368$	−3.35341	−0.174809
$369$	−2.33640	−0.121628
$370$	−0.0324646	−0.00168776
$371$	−5.66854	−0.294296
$372$	4.63243	0.240180
$373$	−29.2887	−1.51651	−0.758256	−	0.651957i	$-0.773948\pi$
$373$	−29.2887	−1.51651	−0.758256	+	0.651957i	$0.773948\pi$
$374$	−3.38460	−0.175013
$375$	−1.00000	−0.0516398
$376$	23.7202	1.22327
$377$	2.29588	0.118244
$378$	−1.97798	−0.101736
$379$	−16.0994	−0.826970	−0.413485	−	0.910511i	$-0.635689\pi$
$379$	−16.0994	−0.826970	−0.413485	+	0.910511i	$0.635689\pi$
$380$	4.01339	0.205882
$381$	−15.9850	−0.818934
$382$	2.84936	0.145786
$383$	20.7246	1.05898	0.529489	−	0.848317i	$-0.322384\pi$
$383$	20.7246	1.05898	0.529489	+	0.848317i	$0.322384\pi$
$384$	8.69562	0.443747
$385$	7.19235	0.366556
$386$	21.4897	1.09380
$387$	9.77303	0.496791
$388$	−8.93219	−0.453463
$389$	31.6429	1.60436	0.802179	−	0.597083i	$-0.203674\pi$
$389$	31.6429	1.60436	0.802179	+	0.597083i	$0.203674\pi$
$390$	1.52532	0.0772374
$391$	9.22943	0.466752
$392$	2.66411	0.134558
$393$	12.4886	0.629968
$394$	−22.4429	−1.13066
$395$	−15.2865	−0.769146
$396$	−3.95773	−0.198883
$397$	−6.48711	−0.325579	−0.162789	−	0.986661i	$-0.552049\pi$
$397$	−6.48711	−0.325579	−0.162789	+	0.986661i	$0.552049\pi$
$398$	−10.1904	−0.510799
$399$	7.29349	0.365131
$400$	0.519854	0.0259927
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−0.251415	−0.0125394
$403$	−6.49189	−0.323384
$404$	−15.8093	−0.786543
$405$	1.00000	0.0496904
$406$	−2.40135	−0.119177
$407$	−0.118048	−0.00585143
$408$	−3.86532	−0.191362
$409$	8.93869	0.441990	0.220995	−	0.975275i	$-0.429070\pi$
$409$	8.93869	0.441990	0.220995	+	0.975275i	$0.429070\pi$
$410$	−1.88448	−0.0930681
$411$	−10.9767	−0.541441
$412$	20.6433	1.01702
$413$	−36.3729	−1.78979
$414$	−5.20296	−0.255712
$415$	6.48280	0.318228
$416$	−11.0108	−0.539851
$417$	−11.3033	−0.553526
$418$	−7.03553	−0.344119
$419$	12.4780	0.609591	0.304795	−	0.952418i	$-0.401412\pi$
$419$	12.4780	0.609591	0.304795	+	0.952418i	$0.401412\pi$
$420$	3.30925	0.161475
$421$	17.5623	0.855932	0.427966	−	0.903795i	$-0.359230\pi$
$421$	17.5623	0.855932	0.427966	+	0.903795i	$0.359230\pi$
$422$	−17.9063	−0.871667
$423$	−8.78014	−0.426905
$424$	6.24469	0.303269
$425$	−1.43077	−0.0694024
$426$	−9.81510	−0.475543
$427$	−7.62874	−0.369181
$428$	−3.44350	−0.166448
$429$	5.54637	0.267781
$430$	7.88268	0.380137
$431$	−20.5256	−0.988681	−0.494340	−	0.869268i	$-0.664590\pi$
$431$	−20.5256	−0.988681	−0.494340	+	0.869268i	$0.664590\pi$
$432$	−0.519854	−0.0250115
$433$	21.0894	1.01349	0.506747	−	0.862095i	$-0.330848\pi$
$433$	21.0894	1.01349	0.506747	+	0.862095i	$0.330848\pi$
$434$	6.79012	0.325936
$435$	1.21404	0.0582089
$436$	10.2842	0.492524
$437$	19.1851	0.917748
$438$	2.20170	0.105201
$439$	15.1430	0.722738	0.361369	−	0.932423i	$-0.382309\pi$
$439$	15.1430	0.722738	0.361369	+	0.932423i	$0.382309\pi$
$440$	−7.92338	−0.377732
$441$	−0.986133	−0.0469587
$442$	2.18237	0.103805
$443$	−24.2736	−1.15327	−0.576637	−	0.817000i	$-0.695635\pi$
$443$	−24.2736	−1.15327	−0.576637	+	0.817000i	$0.695635\pi$
$444$	−0.0543148	−0.00257767
$445$	−3.96363	−0.187894
$446$	−21.7730	−1.03098
$447$	−3.22900	−0.152727
$448$	8.96698	0.423650
$449$	−25.5531	−1.20592	−0.602962	−	0.797770i	$-0.706013\pi$
$449$	−25.5531	−1.20592	−0.602962	+	0.797770i	$0.706013\pi$
$450$	0.806575	0.0380223
$451$	−6.85238	−0.322666
$452$	2.94954	0.138735
$453$	9.56598	0.449449
$454$	−23.1874	−1.08824
$455$	−4.63759	−0.217413
$456$	−8.03479	−0.376264
$457$	−35.7050	−1.67021	−0.835105	−	0.550090i	$-0.814593\pi$
$457$	−35.7050	−1.67021	−0.835105	+	0.550090i	$0.814593\pi$
$458$	−12.3986	−0.579349
$459$	1.43077	0.0667825
$460$	8.70479	0.405863
$461$	−9.47400	−0.441248	−0.220624	−	0.975359i	$-0.570809\pi$
$461$	−9.47400	−0.441248	−0.220624	+	0.975359i	$0.570809\pi$
$462$	−5.80117	−0.269895
$463$	21.6175	1.00465	0.502325	−	0.864679i	$-0.332478\pi$
$463$	21.6175	1.00465	0.502325	+	0.864679i	$0.332478\pi$
$464$	−0.631124	−0.0292992
$465$	−3.43286	−0.159195
$466$	1.25530	0.0581509
$467$	4.66089	0.215680	0.107840	−	0.994168i	$-0.465607\pi$
$467$	4.66089	0.215680	0.107840	+	0.994168i	$0.465607\pi$
$468$	2.55192	0.117963
$469$	0.764405	0.0352969
$470$	−7.08184	−0.326661
$471$	−20.1697	−0.929372
$472$	40.0698	1.84436
$473$	28.6631	1.31793
$474$	12.3297	0.566321
$475$	−2.97412	−0.136462
$476$	4.73476	0.217018
$477$	−2.31150	−0.105837
$478$	20.6772	0.945754
$479$	37.9785	1.73528	0.867642	−	0.497190i	$-0.165635\pi$
$479$	37.9785	1.73528	0.867642	+	0.497190i	$0.165635\pi$
$480$	−5.82244	−0.265757
$481$	0.0761169	0.00347063
$482$	−14.5160	−0.661184
$483$	15.8191	0.719796
$484$	3.23627	0.147103
$485$	6.61920	0.300562
$486$	−0.806575	−0.0365870
$487$	0.606842	0.0274986	0.0137493	−	0.999905i	$-0.495623\pi$
$487$	0.606842	0.0274986	0.0137493	+	0.999905i	$0.495623\pi$
$488$	8.40413	0.380437
$489$	−13.4630	−0.608820
$490$	−0.795390	−0.0359321
$491$	23.6714	1.06828	0.534139	−	0.845397i	$-0.320636\pi$
$491$	23.6714	1.06828	0.534139	+	0.845397i	$0.320636\pi$
$492$	−3.15283	−0.142141
$493$	1.73701	0.0782311
$494$	4.53647	0.204105
$495$	2.93288	0.131823
$496$	1.78458	0.0801302
$497$	29.8419	1.33859
$498$	−5.22886	−0.234311
$499$	20.7881	0.930603	0.465301	−	0.885152i	$-0.345946\pi$
$499$	20.7881	0.930603	0.465301	+	0.885152i	$0.345946\pi$
$500$	−1.34944	−0.0603487
$501$	−3.13533	−0.140076
$502$	−13.4187	−0.598906
$503$	−25.5229	−1.13801	−0.569004	−	0.822335i	$-0.692671\pi$
$503$	−25.5229	−1.13801	−0.569004	+	0.822335i	$0.692671\pi$
$504$	−6.62511	−0.295106
$505$	11.7155	0.521333
$506$	−15.2596	−0.678374
$507$	9.42373	0.418523
$508$	−21.5707	−0.957045
$509$	19.8077	0.877961	0.438980	−	0.898497i	$-0.355340\pi$
$509$	19.8077	0.877961	0.438980	+	0.898497i	$0.355340\pi$
$510$	1.15402	0.0511009
$511$	−6.69408	−0.296129
$512$	5.83566	0.257902
$513$	2.97412	0.131311
$514$	−16.3445	−0.720923
$515$	−15.2978	−0.674099
$516$	13.1881	0.580573
$517$	−25.7511	−1.13253
$518$	−0.0796136	−0.00349802
$519$	24.8880	1.09246
$520$	5.10895	0.224042
$521$	−22.5403	−0.987510	−0.493755	−	0.869601i	$-0.664376\pi$
$521$	−22.5403	−0.987510	−0.493755	+	0.869601i	$0.664376\pi$
$522$	−0.979216	−0.0428591
$523$	37.6286	1.64538	0.822692	−	0.568487i	$-0.192471\pi$
$523$	37.6286	1.64538	0.822692	+	0.568487i	$0.192471\pi$
$524$	16.8526	0.736210
$525$	−2.45232	−0.107028
$526$	2.48115	0.108183
$527$	−4.91162	−0.213954
$528$	−1.52467	−0.0663526
$529$	18.6113	0.809188
$530$	−1.86440	−0.0809844
$531$	−14.8320	−0.643656
$532$	9.84210	0.426709
$533$	4.41838	0.191381
$534$	3.19696	0.138346
$535$	2.55181	0.110324
$536$	−0.842099	−0.0363731
$537$	15.5813	0.672381
$538$	−17.7626	−0.765799
$539$	−2.89221	−0.124576
$540$	1.34944	0.0580705
$541$	24.9216	1.07146	0.535732	−	0.844388i	$-0.320036\pi$
$541$	24.9216	1.07146	0.535732	+	0.844388i	$0.320036\pi$
$542$	0.376497	0.0161719
$543$	−10.9502	−0.469918
$544$	−8.33056	−0.357170
$545$	−7.62111	−0.326453
$546$	3.74056	0.160081
$547$	29.1211	1.24513	0.622565	−	0.782568i	$-0.286091\pi$
$547$	29.1211	1.24513	0.622565	+	0.782568i	$0.286091\pi$
$548$	−14.8124	−0.632753
$549$	−3.11083	−0.132767
$550$	2.36558	0.100869
$551$	3.61071	0.153821
$552$	−17.4270	−0.741742
$553$	−37.4873	−1.59412
$554$	−4.46498	−0.189699
$555$	0.0402500	0.00170852
$556$	−15.2531	−0.646877
$557$	38.7711	1.64279	0.821393	−	0.570363i	$-0.193197\pi$
$557$	38.7711	1.64279	0.821393	+	0.570363i	$0.193197\pi$
$558$	2.76886	0.117215
$559$	−18.4818	−0.781697
$560$	1.27485	0.0538721
$561$	4.19626	0.177166
$562$	4.00898	0.169109
$563$	35.9541	1.51528	0.757642	−	0.652670i	$-0.226351\pi$
$563$	35.9541	1.51528	0.757642	+	0.652670i	$0.226351\pi$
$564$	−11.8482	−0.498901
$565$	−2.18576	−0.0919556
$566$	−19.3852	−0.814821
$567$	2.45232	0.102988
$568$	−32.8751	−1.37941
$569$	−41.1665	−1.72579	−0.862896	−	0.505382i	$-0.831352\pi$
$569$	−41.1665	−1.72579	−0.862896	+	0.505382i	$0.831352\pi$
$570$	2.39885	0.100477
$571$	17.3911	0.727795	0.363898	−	0.931439i	$-0.381446\pi$
$571$	17.3911	0.727795	0.363898	+	0.931439i	$0.381446\pi$
$572$	7.48448	0.312942
$573$	−3.53267	−0.147579
$574$	−4.62136	−0.192892
$575$	−6.45068	−0.269012
$576$	3.65653	0.152355
$577$	33.2030	1.38226	0.691130	−	0.722730i	$-0.257113\pi$
$577$	33.2030	1.38226	0.691130	+	0.722730i	$0.257113\pi$
$578$	−12.0606	−0.501656
$579$	−26.6432	−1.10725
$580$	1.63827	0.0680256
$581$	15.8979	0.659555
$582$	−5.33888	−0.221304
$583$	−6.77936	−0.280772
$584$	7.37447	0.305158
$585$	−1.89110	−0.0781875
$586$	−0.0416364	−0.00171998
$587$	−22.2555	−0.918584	−0.459292	−	0.888285i	$-0.651897\pi$
$587$	−22.2555	−0.918584	−0.459292	+	0.888285i	$0.651897\pi$
$588$	−1.33072	−0.0548782
$589$	−10.2097	−0.420685
$590$	−11.9632	−0.492515
$591$	27.8250	1.14457
$592$	−0.0209241	−0.000859975 0
$593$	−30.3483	−1.24625	−0.623127	−	0.782121i	$-0.714138\pi$
$593$	−30.3483	−1.24625	−0.623127	+	0.782121i	$0.714138\pi$
$594$	−2.36558	−0.0970611
$595$	−3.50870	−0.143843
$596$	−4.35734	−0.178483
$597$	12.6342	0.517082
$598$	9.83933	0.402360
$599$	31.6909	1.29486	0.647428	−	0.762126i	$-0.275845\pi$
$599$	31.6909	1.29486	0.647428	+	0.762126i	$0.275845\pi$
$600$	2.70157	0.110291
$601$	−11.3153	−0.461560	−0.230780	−	0.973006i	$-0.574128\pi$
$601$	−11.3153	−0.461560	−0.230780	+	0.973006i	$0.574128\pi$
$602$	19.3309	0.787867
$603$	0.311707	0.0126937
$604$	12.9087	0.525247
$605$	−2.39824	−0.0975022
$606$	−9.44943	−0.383857
$607$	12.5085	0.507703	0.253852	−	0.967243i	$-0.418303\pi$
$607$	12.5085	0.507703	0.253852	+	0.967243i	$0.418303\pi$
$608$	−17.3166	−0.702283
$609$	2.97722	0.120643
$610$	−2.50912	−0.101591
$611$	16.6042	0.671732
$612$	1.93073	0.0780451
$613$	−9.12436	−0.368529	−0.184265	−	0.982877i	$-0.558990\pi$
$613$	−9.12436	−0.368529	−0.184265	+	0.982877i	$0.558990\pi$
$614$	−24.5186	−0.989489
$615$	2.33640	0.0942129
$616$	−19.4306	−0.782883
$617$	−28.1318	−1.13254	−0.566272	−	0.824218i	$-0.691615\pi$
$617$	−28.1318	−1.13254	−0.566272	+	0.824218i	$0.691615\pi$
$618$	12.3388	0.496339
$619$	28.5663	1.14818	0.574088	−	0.818793i	$-0.305357\pi$
$619$	28.5663	1.14818	0.574088	+	0.818793i	$0.305357\pi$
$620$	−4.63243	−0.186043
$621$	6.45068	0.258857
$622$	−2.66825	−0.106987
$623$	−9.72008	−0.389427
$624$	0.983097	0.0393554
$625$	1.00000	0.0400000
$626$	15.0391	0.601083
$627$	8.72272	0.348352
$628$	−27.2178	−1.08611
$629$	0.0575883	0.00229620
$630$	1.97798	0.0788046
$631$	−4.38275	−0.174474	−0.0872372	−	0.996188i	$-0.527804\pi$
$631$	−4.38275	−0.174474	−0.0872372	+	0.996188i	$0.527804\pi$
$632$	41.2975	1.64273
$633$	22.2005	0.882389
$634$	−18.7954	−0.746459
$635$	15.9850	0.634344
$636$	−3.11923	−0.123685
$637$	1.86488	0.0738892
$638$	−2.87192	−0.113700
$639$	12.1689	0.481393
$640$	−8.69562	−0.343725
$641$	42.0329	1.66020	0.830101	−	0.557614i	$-0.188283\pi$
$641$	42.0329	1.66020	0.830101	+	0.557614i	$0.188283\pi$
$642$	−2.05822	−0.0812316
$643$	35.8594	1.41416	0.707078	−	0.707136i	$-0.250013\pi$
$643$	35.8594	1.41416	0.707078	+	0.707136i	$0.250013\pi$
$644$	21.3469	0.841187
$645$	−9.77303	−0.384813
$646$	3.43219	0.135038
$647$	−22.0182	−0.865624	−0.432812	−	0.901484i	$-0.642479\pi$
$647$	−22.0182	−0.865624	−0.432812	+	0.901484i	$0.642479\pi$
$648$	−2.70157	−0.106128
$649$	−43.5006	−1.70755
$650$	−1.52532	−0.0598278
$651$	−8.41846	−0.329946
$652$	−18.1675	−0.711495
$653$	15.8606	0.620673	0.310336	−	0.950627i	$-0.399558\pi$
$653$	15.8606	0.620673	0.310336	+	0.950627i	$0.399558\pi$
$654$	6.14700	0.240367
$655$	−12.4886	−0.487971
$656$	−1.21459	−0.0474217
$657$	−2.72970	−0.106496
$658$	−17.3669	−0.677033
$659$	4.52047	0.176092	0.0880462	−	0.996116i	$-0.471938\pi$
$659$	4.52047	0.176092	0.0880462	+	0.996116i	$0.471938\pi$
$660$	3.95773	0.154054
$661$	−12.1255	−0.471625	−0.235813	−	0.971799i	$-0.575775\pi$
$661$	−12.1255	−0.471625	−0.235813	+	0.971799i	$0.575775\pi$
$662$	−9.61811	−0.373818
$663$	−2.70573	−0.105082
$664$	−17.5137	−0.679665
$665$	−7.29349	−0.282829
$666$	−0.0324646	−0.00125798
$667$	7.83140	0.303233
$668$	−4.23093	−0.163700
$669$	26.9944	1.04366
$670$	0.251415	0.00971301
$671$	−9.12367	−0.352216
$672$	−14.2785	−0.550805
$673$	20.6487	0.795947	0.397974	−	0.917397i	$-0.369714\pi$
$673$	20.6487	0.795947	0.397974	+	0.917397i	$0.369714\pi$
$674$	7.31067	0.281596
$675$	−1.00000	−0.0384900
$676$	12.7167	0.489105
$677$	−20.5369	−0.789298	−0.394649	−	0.918832i	$-0.629134\pi$
$677$	−20.5369	−0.789298	−0.394649	+	0.918832i	$0.629134\pi$
$678$	1.76298	0.0677068
$679$	16.2324	0.622942
$680$	3.86532	0.148228
$681$	28.7480	1.10163
$682$	8.12072	0.310958
$683$	16.0491	0.614100	0.307050	−	0.951693i	$-0.400658\pi$
$683$	16.0491	0.614100	0.307050	+	0.951693i	$0.400658\pi$
$684$	4.01339	0.153456
$685$	10.9767	0.419398
$686$	−15.7964	−0.603109
$687$	15.3719	0.586475
$688$	5.08055	0.193694
$689$	4.37129	0.166533
$690$	5.20296	0.198073
$691$	−29.1177	−1.10769	−0.553844	−	0.832620i	$-0.686840\pi$
$691$	−29.1177	−1.10769	−0.553844	+	0.832620i	$0.686840\pi$
$692$	33.5848	1.27670
$693$	7.19235	0.273215
$694$	11.3400	0.430460
$695$	11.3033	0.428760
$696$	−3.27982	−0.124321
$697$	3.34285	0.126619
$698$	−24.1540	−0.914242
$699$	−1.55634	−0.0588662
$700$	−3.30925	−0.125078
$701$	−18.7643	−0.708717	−0.354358	−	0.935110i	$-0.615301\pi$
$701$	−18.7643	−0.708717	−0.354358	+	0.935110i	$0.615301\pi$
$702$	1.52532	0.0575694
$703$	0.119708	0.00451488
$704$	10.7242	0.404182
$705$	8.78014	0.330679
$706$	5.88272	0.221399
$707$	28.7301	1.08051
$708$	−20.0149	−0.752207
$709$	20.3985	0.766081	0.383041	−	0.923731i	$-0.374877\pi$
$709$	20.3985	0.766081	0.383041	+	0.923731i	$0.374877\pi$
$710$	9.81510	0.368354
$711$	−15.2865	−0.573287
$712$	10.7080	0.401300
$713$	−22.1443	−0.829310
$714$	2.83003	0.105911
$715$	−5.54637	−0.207423
$716$	21.0259	0.785776
$717$	−25.6358	−0.957388
$718$	2.68300	0.100129
$719$	−42.2281	−1.57484	−0.787422	−	0.616414i	$-0.788585\pi$
$719$	−42.2281	−1.57484	−0.787422	+	0.616414i	$0.788585\pi$
$720$	0.519854	0.0193738
$721$	−37.5150	−1.39713
$722$	−8.19046	−0.304817
$723$	17.9970	0.669317
$724$	−14.7766	−0.549168
$725$	−1.21404	−0.0450884
$726$	1.93436	0.0717908
$727$	27.2521	1.01072	0.505362	−	0.862907i	$-0.331359\pi$
$727$	27.2521	1.01072	0.505362	+	0.862907i	$0.331359\pi$
$728$	12.5288	0.464347
$729$	1.00000	0.0370370
$730$	−2.20170	−0.0814887
$731$	−13.9829	−0.517177
$732$	−4.19787	−0.155158
$733$	32.2132	1.18982	0.594912	−	0.803791i	$-0.297187\pi$
$733$	32.2132	1.18982	0.594912	+	0.803791i	$0.297187\pi$
$734$	20.3445	0.750931
$735$	0.986133	0.0363741
$736$	−37.5588	−1.38443
$737$	0.914198	0.0336749
$738$	−1.88448	−0.0693688
$739$	22.8531	0.840664	0.420332	−	0.907370i	$-0.361914\pi$
$739$	22.8531	0.840664	0.420332	+	0.907370i	$0.361914\pi$
$740$	0.0543148	0.00199665
$741$	−5.62436	−0.206616
$742$	−4.57211	−0.167847
$743$	−12.1611	−0.446146	−0.223073	−	0.974802i	$-0.571609\pi$
$743$	−12.1611	−0.446146	−0.223073	+	0.974802i	$0.571609\pi$
$744$	9.27412	0.340006
$745$	3.22900	0.118302
$746$	−23.6235	−0.864919
$747$	6.48280	0.237193
$748$	5.66259	0.207045
$749$	6.25785	0.228657
$750$	−0.806575	−0.0294520
$751$	−3.08035	−0.112403	−0.0562017	−	0.998419i	$-0.517899\pi$
$751$	−3.08035	−0.112403	−0.0562017	+	0.998419i	$0.517899\pi$
$752$	−4.56439	−0.166446
$753$	16.6366	0.606273
$754$	1.85180	0.0674385
$755$	−9.56598	−0.348142
$756$	3.30925	0.120356
$757$	−19.2881	−0.701037	−0.350519	−	0.936556i	$-0.613995\pi$
$757$	−19.2881	−0.701037	−0.350519	+	0.936556i	$0.613995\pi$
$758$	−12.9854	−0.471650
$759$	18.9191	0.686718
$760$	8.03479	0.291453
$761$	29.2283	1.05953	0.529763	−	0.848146i	$-0.322281\pi$
$761$	29.2283	1.05953	0.529763	+	0.848146i	$0.322281\pi$
$762$	−12.8931	−0.467067
$763$	−18.6894	−0.676602
$764$	−4.76712	−0.172468
$765$	−1.43077	−0.0517295
$766$	16.7160	0.603972
$767$	28.0489	1.01279
$768$	14.3267	0.516971
$769$	−10.7744	−0.388535	−0.194268	−	0.980949i	$-0.562233\pi$
$769$	−10.7744	−0.388535	−0.194268	+	0.980949i	$0.562233\pi$
$770$	5.80117	0.209060
$771$	20.2640	0.729791
$772$	−35.9533	−1.29399
$773$	34.1419	1.22800	0.613999	−	0.789307i	$-0.289560\pi$
$773$	34.1419	1.22800	0.613999	+	0.789307i	$0.289560\pi$
$774$	7.88268	0.283337
$775$	3.43286	0.123312
$776$	−17.8822	−0.641935
$777$	0.0987058	0.00354105
$778$	25.5224	0.915021
$779$	6.94874	0.248965
$780$	−2.55192	−0.0913735
$781$	35.6898	1.27708
$782$	7.44422	0.266205
$783$	1.21404	0.0433863
$784$	−0.512645	−0.0183087
$785$	20.1697	0.719888
$786$	10.0730	0.359293
$787$	25.4430	0.906945	0.453472	−	0.891270i	$-0.350185\pi$
$787$	25.4430	0.906945	0.453472	+	0.891270i	$0.350185\pi$
$788$	37.5481	1.33759
$789$	−3.07616	−0.109514
$790$	−12.3297	−0.438670
$791$	−5.36018	−0.190586
$792$	−7.92338	−0.281545
$793$	5.88290	0.208908
$794$	−5.23234	−0.185689
$795$	2.31150	0.0819806
$796$	17.0490	0.604287
$797$	−5.90806	−0.209274	−0.104637	−	0.994510i	$-0.533368\pi$
$797$	−5.90806	−0.209274	−0.104637	+	0.994510i	$0.533368\pi$
$798$	5.88274	0.208247
$799$	12.5623	0.444423
$800$	5.82244	0.205855
$801$	−3.96363	−0.140048
$802$	0.806575	0.0284812
$803$	−8.00586	−0.282521
$804$	0.420629	0.0148344
$805$	−15.8191	−0.557551
$806$	−5.23620	−0.184437
$807$	22.0222	0.775219
$808$	−31.6503	−1.11345
$809$	−5.27156	−0.185338	−0.0926691	−	0.995697i	$-0.529540\pi$
$809$	−5.27156	−0.185338	−0.0926691	+	0.995697i	$0.529540\pi$
$810$	0.806575	0.0283402
$811$	19.3790	0.680489	0.340244	−	0.940337i	$-0.389490\pi$
$811$	19.3790	0.680489	0.340244	+	0.940337i	$0.389490\pi$
$812$	4.01757	0.140989
$813$	−0.466785	−0.0163709
$814$	−0.0952147	−0.00333727
$815$	13.4630	0.471590
$816$	0.743789	0.0260378
$817$	−29.0662	−1.01690
$818$	7.20972	0.252082
$819$	−4.63759	−0.162050
$820$	3.15283	0.110102
$821$	−38.3898	−1.33981	−0.669907	−	0.742445i	$-0.733666\pi$
$821$	−38.3898	−1.33981	−0.669907	+	0.742445i	$0.733666\pi$
$822$	−8.85353	−0.308802
$823$	−41.7555	−1.45550	−0.727752	−	0.685841i	$-0.759435\pi$
$823$	−41.7555	−1.45550	−0.727752	+	0.685841i	$0.759435\pi$
$824$	41.3280	1.43973
$825$	−2.93288	−0.102110
$826$	−29.3375	−1.02078
$827$	−7.10959	−0.247225	−0.123612	−	0.992331i	$-0.539448\pi$
$827$	−7.10959	−0.247225	−0.123612	+	0.992331i	$0.539448\pi$
$828$	8.70479	0.302512
$829$	48.7969	1.69479	0.847393	−	0.530965i	$-0.178171\pi$
$829$	48.7969	1.69479	0.847393	+	0.530965i	$0.178171\pi$
$830$	5.22886	0.181496
$831$	5.53573	0.192032
$832$	−6.91488	−0.239730
$833$	1.41093	0.0488857
$834$	−9.11698	−0.315695
$835$	3.13533	0.108503
$836$	11.7708	0.407100
$837$	−3.43286	−0.118657
$838$	10.0644	0.347671
$839$	−50.8123	−1.75423	−0.877117	−	0.480276i	$-0.840536\pi$
$839$	−50.8123	−1.75423	−0.877117	+	0.480276i	$0.840536\pi$
$840$	6.62511	0.228588
$841$	−27.5261	−0.949176
$842$	14.1653	0.488168
$843$	−4.97037	−0.171189
$844$	29.9581	1.03120
$845$	−9.42373	−0.324186
$846$	−7.08184	−0.243479
$847$	−5.88124	−0.202082
$848$	−1.20164	−0.0412646
$849$	24.0340	0.824844
$850$	−1.15402	−0.0395826
$851$	0.259640	0.00890034
$852$	16.4211	0.562578
$853$	−0.356255	−0.0121980	−0.00609898	−	0.999981i	$-0.501941\pi$
$853$	−0.356255	−0.0121980	−0.00609898	+	0.999981i	$0.501941\pi$
$854$	−6.15315	−0.210557
$855$	−2.97412	−0.101713
$856$	−6.89389	−0.235628
$857$	−52.3804	−1.78928	−0.894641	−	0.446787i	$-0.852568\pi$
$857$	−52.3804	−1.78928	−0.894641	+	0.446787i	$0.852568\pi$
$858$	4.47356	0.152725
$859$	−25.5763	−0.872652	−0.436326	−	0.899789i	$-0.643720\pi$
$859$	−25.5763	−0.872652	−0.436326	+	0.899789i	$0.643720\pi$
$860$	−13.1881	−0.449710
$861$	5.72961	0.195264
$862$	−16.5554	−0.563879
$863$	26.5279	0.903019	0.451510	−	0.892266i	$-0.350886\pi$
$863$	26.5279	0.903019	0.451510	+	0.892266i	$0.350886\pi$
$864$	−5.82244	−0.198084
$865$	−24.8880	−0.846217
$866$	17.0102	0.578031
$867$	14.9529	0.507827
$868$	−11.3602	−0.385590
$869$	−44.8333	−1.52087
$870$	0.979216	0.0331985
$871$	−0.589470	−0.0199734
$872$	20.5890	0.697231
$873$	6.61920	0.224026
$874$	15.4742	0.523423
$875$	2.45232	0.0829035
$876$	−3.68355	−0.124456
$877$	43.0181	1.45262	0.726309	−	0.687368i	$-0.241234\pi$
$877$	43.0181	1.45262	0.726309	+	0.687368i	$0.241234\pi$
$878$	12.2140	0.412203
$879$	0.0516212	0.00174114
$880$	1.52467	0.0513965
$881$	−7.49821	−0.252621	−0.126311	−	0.991991i	$-0.540314\pi$
$881$	−7.49821	−0.252621	−0.126311	+	0.991991i	$0.540314\pi$
$882$	−0.795390	−0.0267822
$883$	7.77055	0.261500	0.130750	−	0.991415i	$-0.458262\pi$
$883$	7.77055	0.261500	0.130750	+	0.991415i	$0.458262\pi$
$884$	−3.65121	−0.122803
$885$	14.8320	0.498574
$886$	−19.5785	−0.657752
$887$	35.2421	1.18332	0.591658	−	0.806189i	$-0.298474\pi$
$887$	35.2421	1.18332	0.591658	+	0.806189i	$0.298474\pi$
$888$	−0.108738	−0.00364902
$889$	39.2002	1.31473
$890$	−3.19696	−0.107162
$891$	2.93288	0.0982550
$892$	36.4273	1.21968
$893$	26.1132	0.873844
$894$	−2.60443	−0.0871053
$895$	−15.5813	−0.520824
$896$	−21.3244	−0.712400
$897$	−12.1989	−0.407310
$898$	−20.6105	−0.687780
$899$	−4.16764	−0.138998
$900$	−1.34944	−0.0449812
$901$	3.30722	0.110180
$902$	−5.52696	−0.184028
$903$	−23.9666	−0.797558
$904$	5.90499	0.196397
$905$	10.9502	0.363997
$906$	7.71568	0.256336
$907$	−21.8046	−0.724011	−0.362006	−	0.932176i	$-0.617908\pi$
$907$	−21.8046	−0.724011	−0.362006	+	0.932176i	$0.617908\pi$
$908$	38.7936	1.28741
$909$	11.7155	0.388578
$910$	−3.74056	−0.123998
$911$	17.7398	0.587745	0.293873	−	0.955845i	$-0.405056\pi$
$911$	17.7398	0.587745	0.293873	+	0.955845i	$0.405056\pi$
$912$	1.54611	0.0511967
$913$	19.0132	0.629246
$914$	−28.7988	−0.952579
$915$	3.11083	0.102841
$916$	20.7434	0.685383
$917$	−30.6261	−1.01136
$918$	1.15402	0.0380884
$919$	39.3115	1.29677	0.648383	−	0.761314i	$-0.275446\pi$
$919$	39.3115	1.29677	0.648383	+	0.761314i	$0.275446\pi$
$920$	17.4270	0.574551
$921$	30.3984	1.00166
$922$	−7.64149	−0.251659
$923$	−23.0126	−0.757468
$924$	9.70562	0.319291
$925$	−0.0402500	−0.00132341
$926$	17.4361	0.572987
$927$	−15.2978	−0.502444
$928$	−7.06869	−0.232041
$929$	12.3969	0.406730	0.203365	−	0.979103i	$-0.434812\pi$
$929$	12.3969	0.406730	0.203365	+	0.979103i	$0.434812\pi$
$930$	−2.76886	−0.0907944
$931$	2.93288	0.0961212
$932$	−2.10018	−0.0687937
$933$	3.30812	0.108303
$934$	3.75936	0.123010
$935$	−4.19626	−0.137232
$936$	5.10895	0.166991
$937$	29.6252	0.967814	0.483907	−	0.875119i	$-0.339217\pi$
$937$	29.6252	0.967814	0.483907	+	0.875119i	$0.339217\pi$
$938$	0.616550	0.0201311
$939$	−18.6456	−0.608477
$940$	11.8482	0.386447
$941$	−6.25655	−0.203958	−0.101979	−	0.994787i	$-0.532517\pi$
$941$	−6.25655	−0.203958	−0.101979	+	0.994787i	$0.532517\pi$
$942$	−16.2684	−0.530053
$943$	15.0714	0.490793
$944$	−7.71050	−0.250955
$945$	−2.45232	−0.0797739
$946$	23.1189	0.751661
$947$	−59.1054	−1.92067	−0.960334	−	0.278854i	$-0.910045\pi$
$947$	−59.1054	−1.92067	−0.960334	+	0.278854i	$0.910045\pi$
$948$	−20.6281	−0.669970
$949$	5.16213	0.167570
$950$	−2.39885	−0.0778290
$951$	23.3027	0.755641
$952$	9.47899	0.307216
$953$	−43.1325	−1.39720	−0.698600	−	0.715513i	$-0.746193\pi$
$953$	−43.1325	−1.39720	−0.698600	+	0.715513i	$0.746193\pi$
$954$	−1.86440	−0.0603622
$955$	3.53267	0.114315
$956$	−34.5939	−1.11885
$957$	3.56064	0.115099
$958$	30.6325	0.989692
$959$	26.9184	0.869239
$960$	−3.65653	−0.118014
$961$	−19.2155	−0.619854
$962$	0.0613940	0.00197942
$963$	2.55181	0.0822309
$964$	24.2859	0.782195
$965$	26.6432	0.857675
$966$	12.7593	0.410524
$967$	37.0944	1.19288	0.596438	−	0.802659i	$-0.296582\pi$
$967$	37.0944	1.19288	0.596438	+	0.802659i	$0.296582\pi$
$968$	6.47901	0.208243
$969$	−4.25527	−0.136699
$970$	5.33888	0.171421
$971$	21.8579	0.701454	0.350727	−	0.936478i	$-0.385934\pi$
$971$	21.8579	0.701454	0.350727	+	0.936478i	$0.385934\pi$
$972$	1.34944	0.0432832
$973$	27.7194	0.888642
$974$	0.489463	0.0156834
$975$	1.89110	0.0605638
$976$	−1.61718	−0.0517645
$977$	−31.7759	−1.01660	−0.508300	−	0.861180i	$-0.669726\pi$
$977$	−31.7759	−1.01660	−0.508300	+	0.861180i	$0.669726\pi$
$978$	−10.8590	−0.347231
$979$	−11.6248	−0.371531
$980$	1.33072	0.0425084
$981$	−7.62111	−0.243323
$982$	19.0928	0.609276
$983$	−38.6853	−1.23387	−0.616935	−	0.787014i	$-0.711626\pi$
$983$	−38.6853	−1.23387	−0.616935	+	0.787014i	$0.711626\pi$
$984$	−6.31196	−0.201218
$985$	−27.8250	−0.886578
$986$	1.40103	0.0446179
$987$	21.5317	0.685362
$988$	−7.58972	−0.241461
$989$	−63.0428	−2.00464
$990$	2.36558	0.0751832
$991$	22.3342	0.709468	0.354734	−	0.934967i	$-0.384571\pi$
$991$	22.3342	0.709468	0.354734	+	0.934967i	$0.384571\pi$
$992$	19.9876	0.634608
$993$	11.9246	0.378417
$994$	24.0698	0.763446
$995$	−12.6342	−0.400530
$996$	8.74812	0.277195
$997$	26.8044	0.848903	0.424451	−	0.905451i	$-0.360467\pi$
$997$	26.8044	0.848903	0.424451	+	0.905451i	$0.360467\pi$
$998$	16.7672	0.530755
$999$	0.0402500	0.00127345

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.18	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.18	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q+0.806575 q^{2} -1.00000 q^{3} -1.34944 q^{4} +1.00000 q^{5} -0.806575 q^{6} +2.45232 q^{7} -2.70157 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.806575 q^{2} -1.00000 q^{3} -1.34944 q^{4} +1.00000 q^{5} -0.806575 q^{6} +2.45232 q^{7} -2.70157 q^{8} +1.00000 q^{9} +0.806575 q^{10} +2.93288 q^{11} +1.34944 q^{12} -1.89110 q^{13} +1.97798 q^{14} -1.00000 q^{15} +0.519854 q^{16} -1.43077 q^{17} +0.806575 q^{18} -2.97412 q^{19} -1.34944 q^{20} -2.45232 q^{21} +2.36558 q^{22} -6.45068 q^{23} +2.70157 q^{24} +1.00000 q^{25} -1.52532 q^{26} -1.00000 q^{27} -3.30925 q^{28} -1.21404 q^{29} -0.806575 q^{30} +3.43286 q^{31} +5.82244 q^{32} -2.93288 q^{33} -1.15402 q^{34} +2.45232 q^{35} -1.34944 q^{36} -0.0402500 q^{37} -2.39885 q^{38} +1.89110 q^{39} -2.70157 q^{40} -2.33640 q^{41} -1.97798 q^{42} +9.77303 q^{43} -3.95773 q^{44} +1.00000 q^{45} -5.20296 q^{46} -8.78014 q^{47} -0.519854 q^{48} -0.986133 q^{49} +0.806575 q^{50} +1.43077 q^{51} +2.55192 q^{52} -2.31150 q^{53} -0.806575 q^{54} +2.93288 q^{55} -6.62511 q^{56} +2.97412 q^{57} -0.979216 q^{58} -14.8320 q^{59} +1.34944 q^{60} -3.11083 q^{61} +2.76886 q^{62} +2.45232 q^{63} +3.65653 q^{64} -1.89110 q^{65} -2.36558 q^{66} +0.311707 q^{67} +1.93073 q^{68} +6.45068 q^{69} +1.97798 q^{70} +12.1689 q^{71} -2.70157 q^{72} -2.72970 q^{73} -0.0324646 q^{74} -1.00000 q^{75} +4.01339 q^{76} +7.19235 q^{77} +1.52532 q^{78} -15.2865 q^{79} +0.519854 q^{80} +1.00000 q^{81} -1.88448 q^{82} +6.48280 q^{83} +3.30925 q^{84} -1.43077 q^{85} +7.88268 q^{86} +1.21404 q^{87} -7.92338 q^{88} -3.96363 q^{89} +0.806575 q^{90} -4.63759 q^{91} +8.70479 q^{92} -3.43286 q^{93} -7.08184 q^{94} -2.97412 q^{95} -5.82244 q^{96} +6.61920 q^{97} -0.795390 q^{98} +2.93288 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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