LMFDB - Embedded newform 6015.2.a.b.1.4

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:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
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)

$f(q)$	$=$	$q-2.14529 q^{2} +1.00000 q^{3} +2.60225 q^{4} +1.00000 q^{5} -2.14529 q^{6} -2.89107 q^{7} -1.29200 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.14529 q^{2} +1.00000 q^{3} +2.60225 q^{4} +1.00000 q^{5} -2.14529 q^{6} -2.89107 q^{7} -1.29200 q^{8} +1.00000 q^{9} -2.14529 q^{10} -2.09902 q^{11} +2.60225 q^{12} -1.63292 q^{13} +6.20217 q^{14} +1.00000 q^{15} -2.43280 q^{16} +3.96885 q^{17} -2.14529 q^{18} +3.33187 q^{19} +2.60225 q^{20} -2.89107 q^{21} +4.50299 q^{22} -6.77479 q^{23} -1.29200 q^{24} +1.00000 q^{25} +3.50309 q^{26} +1.00000 q^{27} -7.52328 q^{28} -1.74925 q^{29} -2.14529 q^{30} +2.91978 q^{31} +7.80304 q^{32} -2.09902 q^{33} -8.51430 q^{34} -2.89107 q^{35} +2.60225 q^{36} +6.40744 q^{37} -7.14780 q^{38} -1.63292 q^{39} -1.29200 q^{40} -4.81152 q^{41} +6.20217 q^{42} +0.742694 q^{43} -5.46217 q^{44} +1.00000 q^{45} +14.5339 q^{46} -0.257035 q^{47} -2.43280 q^{48} +1.35828 q^{49} -2.14529 q^{50} +3.96885 q^{51} -4.24928 q^{52} +9.77462 q^{53} -2.14529 q^{54} -2.09902 q^{55} +3.73525 q^{56} +3.33187 q^{57} +3.75263 q^{58} -7.42538 q^{59} +2.60225 q^{60} -10.8978 q^{61} -6.26377 q^{62} -2.89107 q^{63} -11.8741 q^{64} -1.63292 q^{65} +4.50299 q^{66} +8.56626 q^{67} +10.3279 q^{68} -6.77479 q^{69} +6.20217 q^{70} +8.68137 q^{71} -1.29200 q^{72} -2.91294 q^{73} -13.7458 q^{74} +1.00000 q^{75} +8.67034 q^{76} +6.06841 q^{77} +3.50309 q^{78} -4.60562 q^{79} -2.43280 q^{80} +1.00000 q^{81} +10.3221 q^{82} +2.11335 q^{83} -7.52328 q^{84} +3.96885 q^{85} -1.59329 q^{86} -1.74925 q^{87} +2.71192 q^{88} -0.741249 q^{89} -2.14529 q^{90} +4.72090 q^{91} -17.6297 q^{92} +2.91978 q^{93} +0.551414 q^{94} +3.33187 q^{95} +7.80304 q^{96} -16.2525 q^{97} -2.91391 q^{98} -2.09902 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * 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 $

$2$	−2.14529	−1.51695	−0.758473	−	0.651705i	$-0.774054\pi$
$2$	−2.14529	−1.51695	−0.758473	+	0.651705i	$0.774054\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.60225	1.30112
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.14529	−0.875809
$7$	−2.89107	−1.09272	−0.546361	−	0.837550i	$-0.683987\pi$
$7$	−2.89107	−1.09272	−0.546361	+	0.837550i	$0.683987\pi$
$8$	−1.29200	−0.456789
$9$	1.00000	0.333333
$10$	−2.14529	−0.678399
$11$	−2.09902	−0.632878	−0.316439	−	0.948613i	$-0.602487\pi$
$11$	−2.09902	−0.632878	−0.316439	+	0.948613i	$0.602487\pi$
$12$	2.60225	0.751205
$13$	−1.63292	−0.452892	−0.226446	−	0.974024i	$-0.572711\pi$
$13$	−1.63292	−0.452892	−0.226446	+	0.974024i	$0.572711\pi$
$14$	6.20217	1.65760
$15$	1.00000	0.258199
$16$	−2.43280	−0.608200
$17$	3.96885	0.962586	0.481293	−	0.876560i	$-0.340167\pi$
$17$	3.96885	0.962586	0.481293	+	0.876560i	$0.340167\pi$
$18$	−2.14529	−0.505649
$19$	3.33187	0.764382	0.382191	−	0.924083i	$-0.375170\pi$
$19$	3.33187	0.764382	0.382191	+	0.924083i	$0.375170\pi$
$20$	2.60225	0.581881
$21$	−2.89107	−0.630883
$22$	4.50299	0.960041
$23$	−6.77479	−1.41264	−0.706321	−	0.707892i	$-0.749647\pi$
$23$	−6.77479	−1.41264	−0.706321	+	0.707892i	$0.749647\pi$
$24$	−1.29200	−0.263728
$25$	1.00000	0.200000
$26$	3.50309	0.687012
$27$	1.00000	0.192450
$28$	−7.52328	−1.42177
$29$	−1.74925	−0.324827	−0.162413	−	0.986723i	$-0.551928\pi$
$29$	−1.74925	−0.324827	−0.162413	+	0.986723i	$0.551928\pi$
$30$	−2.14529	−0.391674
$31$	2.91978	0.524409	0.262204	−	0.965012i	$-0.415551\pi$
$31$	2.91978	0.524409	0.262204	+	0.965012i	$0.415551\pi$
$32$	7.80304	1.37940
$33$	−2.09902	−0.365392
$34$	−8.51430	−1.46019
$35$	−2.89107	−0.488680
$36$	2.60225	0.433708
$37$	6.40744	1.05338	0.526689	−	0.850058i	$-0.323433\pi$
$37$	6.40744	1.05338	0.526689	+	0.850058i	$0.323433\pi$
$38$	−7.14780	−1.15953
$39$	−1.63292	−0.261477
$40$	−1.29200	−0.204282
$41$	−4.81152	−0.751433	−0.375716	−	0.926735i	$-0.622603\pi$
$41$	−4.81152	−0.751433	−0.375716	+	0.926735i	$0.622603\pi$
$42$	6.20217	0.957015
$43$	0.742694	0.113260	0.0566299	−	0.998395i	$-0.481964\pi$
$43$	0.742694	0.113260	0.0566299	+	0.998395i	$0.481964\pi$
$44$	−5.46217	−0.823453
$45$	1.00000	0.149071
$46$	14.5339	2.14290
$47$	−0.257035	−0.0374924	−0.0187462	−	0.999824i	$-0.505967\pi$
$47$	−0.257035	−0.0374924	−0.0187462	+	0.999824i	$0.505967\pi$
$48$	−2.43280	−0.351144
$49$	1.35828	0.194040
$50$	−2.14529	−0.303389
$51$	3.96885	0.555749
$52$	−4.24928	−0.589269
$53$	9.77462	1.34265	0.671324	−	0.741164i	$-0.265726\pi$
$53$	9.77462	1.34265	0.671324	+	0.741164i	$0.265726\pi$
$54$	−2.14529	−0.291936
$55$	−2.09902	−0.283031
$56$	3.73525	0.499144
$57$	3.33187	0.441316
$58$	3.75263	0.492745
$59$	−7.42538	−0.966702	−0.483351	−	0.875427i	$-0.660581\pi$
$59$	−7.42538	−0.966702	−0.483351	+	0.875427i	$0.660581\pi$
$60$	2.60225	0.335949
$61$	−10.8978	−1.39532	−0.697661	−	0.716428i	$-0.745776\pi$
$61$	−10.8978	−1.39532	−0.697661	+	0.716428i	$0.745776\pi$
$62$	−6.26377	−0.795500
$63$	−2.89107	−0.364241
$64$	−11.8741	−1.48427
$65$	−1.63292	−0.202539
$66$	4.50299	0.554280
$67$	8.56626	1.04654	0.523268	−	0.852168i	$-0.324713\pi$
$67$	8.56626	1.04654	0.523268	+	0.852168i	$0.324713\pi$
$68$	10.3279	1.25244
$69$	−6.77479	−0.815589
$70$	6.20217	0.741301
$71$	8.68137	1.03029	0.515145	−	0.857103i	$-0.327738\pi$
$71$	8.68137	1.03029	0.515145	+	0.857103i	$0.327738\pi$
$72$	−1.29200	−0.152263
$73$	−2.91294	−0.340934	−0.170467	−	0.985363i	$-0.554528\pi$
$73$	−2.91294	−0.340934	−0.170467	+	0.985363i	$0.554528\pi$
$74$	−13.7458	−1.59792
$75$	1.00000	0.115470
$76$	8.67034	0.994556
$77$	6.06841	0.691559
$78$	3.50309	0.396647
$79$	−4.60562	−0.518173	−0.259086	−	0.965854i	$-0.583421\pi$
$79$	−4.60562	−0.518173	−0.259086	+	0.965854i	$0.583421\pi$
$80$	−2.43280	−0.271995
$81$	1.00000	0.111111
$82$	10.3221	1.13988
$83$	2.11335	0.231970	0.115985	−	0.993251i	$-0.462998\pi$
$83$	2.11335	0.231970	0.115985	+	0.993251i	$0.462998\pi$
$84$	−7.52328	−0.820857
$85$	3.96885	0.430482
$86$	−1.59329	−0.171809
$87$	−1.74925	−0.187539
$88$	2.71192	0.289092
$89$	−0.741249	−0.0785723	−0.0392861	−	0.999228i	$-0.512508\pi$
$89$	−0.741249	−0.0785723	−0.0392861	+	0.999228i	$0.512508\pi$
$90$	−2.14529	−0.226133
$91$	4.72090	0.494885
$92$	−17.6297	−1.83802
$93$	2.91978	0.302767
$94$	0.551414	0.0568740
$95$	3.33187	0.341842
$96$	7.80304	0.796394
$97$	−16.2525	−1.65019	−0.825096	−	0.564992i	$-0.808879\pi$
$97$	−16.2525	−1.65019	−0.825096	+	0.564992i	$0.808879\pi$
$98$	−2.91391	−0.294349
$99$	−2.09902	−0.210959
$100$	2.60225	0.260225
$101$	15.2164	1.51409	0.757045	−	0.653363i	$-0.226643\pi$
$101$	15.2164	1.51409	0.757045	+	0.653363i	$0.226643\pi$
$102$	−8.51430	−0.843042
$103$	15.1560	1.49337	0.746684	−	0.665179i	$-0.231645\pi$
$103$	15.1560	1.49337	0.746684	+	0.665179i	$0.231645\pi$
$104$	2.10973	0.206876
$105$	−2.89107	−0.282140
$106$	−20.9693	−2.03672
$107$	12.9782	1.25465	0.627324	−	0.778758i	$-0.284150\pi$
$107$	12.9782	1.25465	0.627324	+	0.778758i	$0.284150\pi$
$108$	2.60225	0.250402
$109$	−16.0863	−1.54079	−0.770394	−	0.637569i	$-0.779940\pi$
$109$	−16.0863	−1.54079	−0.770394	+	0.637569i	$0.779940\pi$
$110$	4.50299	0.429343
$111$	6.40744	0.608168
$112$	7.03339	0.664593
$113$	1.90271	0.178992	0.0894960	−	0.995987i	$-0.471474\pi$
$113$	1.90271	0.178992	0.0894960	+	0.995987i	$0.471474\pi$
$114$	−7.14780	−0.669453
$115$	−6.77479	−0.631753
$116$	−4.55197	−0.422640
$117$	−1.63292	−0.150964
$118$	15.9296	1.46643
$119$	−11.4742	−1.05184
$120$	−1.29200	−0.117943
$121$	−6.59413	−0.599466
$122$	23.3789	2.11663
$123$	−4.81152	−0.433840
$124$	7.59800	0.682321
$125$	1.00000	0.0894427
$126$	6.20217	0.552533
$127$	−1.16771	−0.103617	−0.0518086	−	0.998657i	$-0.516499\pi$
$127$	−1.16771	−0.103617	−0.0518086	+	0.998657i	$0.516499\pi$
$128$	9.86735	0.872159
$129$	0.742694	0.0653906
$130$	3.50309	0.307241
$131$	−14.3435	−1.25320	−0.626598	−	0.779343i	$-0.715553\pi$
$131$	−14.3435	−1.25320	−0.626598	+	0.779343i	$0.715553\pi$
$132$	−5.46217	−0.475421
$133$	−9.63265	−0.835257
$134$	−18.3771	−1.58754
$135$	1.00000	0.0860663
$136$	−5.12773	−0.439699
$137$	−10.0480	−0.858460	−0.429230	−	0.903195i	$-0.641215\pi$
$137$	−10.0480	−0.858460	−0.429230	+	0.903195i	$0.641215\pi$
$138$	14.5339	1.23720
$139$	−14.1849	−1.20315	−0.601573	−	0.798818i	$-0.705459\pi$
$139$	−14.1849	−1.20315	−0.601573	+	0.798818i	$0.705459\pi$
$140$	−7.52328	−0.635833
$141$	−0.257035	−0.0216463
$142$	−18.6240	−1.56289
$143$	3.42754	0.286625
$144$	−2.43280	−0.202733
$145$	−1.74925	−0.145267
$146$	6.24909	0.517178
$147$	1.35828	0.112029
$148$	16.6738	1.37057
$149$	12.9154	1.05807	0.529033	−	0.848601i	$-0.322555\pi$
$149$	12.9154	1.05807	0.529033	+	0.848601i	$0.322555\pi$
$150$	−2.14529	−0.175162
$151$	7.91182	0.643855	0.321928	−	0.946764i	$-0.395669\pi$
$151$	7.91182	0.643855	0.321928	+	0.946764i	$0.395669\pi$
$152$	−4.30476	−0.349162
$153$	3.96885	0.320862
$154$	−13.0185	−1.04906
$155$	2.91978	0.234523
$156$	−4.24928	−0.340214
$157$	−16.4502	−1.31287	−0.656433	−	0.754384i	$-0.727936\pi$
$157$	−16.4502	−1.31287	−0.656433	+	0.754384i	$0.727936\pi$
$158$	9.88037	0.786040
$159$	9.77462	0.775178
$160$	7.80304	0.616884
$161$	19.5864	1.54362
$162$	−2.14529	−0.168550
$163$	−14.4815	−1.13428	−0.567140	−	0.823621i	$-0.691950\pi$
$163$	−14.4815	−1.13428	−0.567140	+	0.823621i	$0.691950\pi$
$164$	−12.5208	−0.977707
$165$	−2.09902	−0.163408
$166$	−4.53373	−0.351886
$167$	−25.1098	−1.94305	−0.971527	−	0.236929i	$-0.923859\pi$
$167$	−25.1098	−1.94305	−0.971527	+	0.236929i	$0.923859\pi$
$168$	3.73525	0.288181
$169$	−10.3336	−0.794889
$170$	−8.51430	−0.653017
$171$	3.33187	0.254794
$172$	1.93268	0.147365
$173$	−9.79130	−0.744418	−0.372209	−	0.928149i	$-0.621400\pi$
$173$	−9.79130	−0.744418	−0.372209	+	0.928149i	$0.621400\pi$
$174$	3.75263	0.284486
$175$	−2.89107	−0.218544
$176$	5.10649	0.384916
$177$	−7.42538	−0.558126
$178$	1.59019	0.119190
$179$	16.1886	1.20999	0.604997	−	0.796227i	$-0.293174\pi$
$179$	16.1886	1.20999	0.604997	+	0.796227i	$0.293174\pi$
$180$	2.60225	0.193960
$181$	−25.4790	−1.89384	−0.946921	−	0.321466i	$-0.895824\pi$
$181$	−25.4790	−1.89384	−0.946921	+	0.321466i	$0.895824\pi$
$182$	−10.1277	−0.750713
$183$	−10.8978	−0.805589
$184$	8.75301	0.645280
$185$	6.40744	0.471085
$186$	−6.26377	−0.459282
$187$	−8.33068	−0.609199
$188$	−0.668869	−0.0487823
$189$	−2.89107	−0.210294
$190$	−7.14780	−0.518556
$191$	−1.29423	−0.0936474	−0.0468237	−	0.998903i	$-0.514910\pi$
$191$	−1.29423	−0.0936474	−0.0468237	+	0.998903i	$0.514910\pi$
$192$	−11.8741	−0.856943
$193$	−7.85973	−0.565756	−0.282878	−	0.959156i	$-0.591289\pi$
$193$	−7.85973	−0.565756	−0.282878	+	0.959156i	$0.591289\pi$
$194$	34.8663	2.50325
$195$	−1.63292	−0.116936
$196$	3.53459	0.252471
$197$	−5.05895	−0.360435	−0.180218	−	0.983627i	$-0.557680\pi$
$197$	−5.05895	−0.360435	−0.180218	+	0.983627i	$0.557680\pi$
$198$	4.50299	0.320014
$199$	26.0672	1.84786	0.923928	−	0.382567i	$-0.124960\pi$
$199$	26.0672	1.84786	0.923928	+	0.382567i	$0.124960\pi$
$200$	−1.29200	−0.0913579
$201$	8.56626	0.604218
$202$	−32.6435	−2.29679
$203$	5.05719	0.354945
$204$	10.3279	0.723099
$205$	−4.81152	−0.336051
$206$	−32.5140	−2.26536
$207$	−6.77479	−0.470881
$208$	3.97258	0.275449
$209$	−6.99364	−0.483760
$210$	6.20217	0.427990
$211$	−6.81659	−0.469274	−0.234637	−	0.972083i	$-0.575390\pi$
$211$	−6.81659	−0.469274	−0.234637	+	0.972083i	$0.575390\pi$
$212$	25.4360	1.74695
$213$	8.68137	0.594838
$214$	−27.8419	−1.90323
$215$	0.742694	0.0506513
$216$	−1.29200	−0.0879092
$217$	−8.44130	−0.573033
$218$	34.5097	2.33729
$219$	−2.91294	−0.196838
$220$	−5.46217	−0.368259
$221$	−6.48082	−0.435947
$222$	−13.7458	−0.922557
$223$	9.76525	0.653929	0.326965	−	0.945037i	$-0.393974\pi$
$223$	9.76525	0.653929	0.326965	+	0.945037i	$0.393974\pi$
$224$	−22.5591	−1.50730
$225$	1.00000	0.0666667
$226$	−4.08186	−0.271521
$227$	24.3745	1.61779	0.808896	−	0.587951i	$-0.200065\pi$
$227$	24.3745	1.61779	0.808896	+	0.587951i	$0.200065\pi$
$228$	8.67034	0.574207
$229$	−20.9198	−1.38242	−0.691210	−	0.722654i	$-0.742922\pi$
$229$	−20.9198	−1.38242	−0.691210	+	0.722654i	$0.742922\pi$
$230$	14.5339	0.958335
$231$	6.06841	0.399272
$232$	2.26002	0.148377
$233$	−18.1642	−1.18998	−0.594989	−	0.803734i	$-0.702844\pi$
$233$	−18.1642	−1.18998	−0.594989	+	0.803734i	$0.702844\pi$
$234$	3.50309	0.229004
$235$	−0.257035	−0.0167671
$236$	−19.3227	−1.25780
$237$	−4.60562	−0.299167
$238$	24.6154	1.59558
$239$	−8.19325	−0.529978	−0.264989	−	0.964252i	$-0.585368\pi$
$239$	−8.19325	−0.529978	−0.264989	+	0.964252i	$0.585368\pi$
$240$	−2.43280	−0.157036
$241$	−16.4056	−1.05678	−0.528388	−	0.849003i	$-0.677203\pi$
$241$	−16.4056	−1.05678	−0.528388	+	0.849003i	$0.677203\pi$
$242$	14.1463	0.909357
$243$	1.00000	0.0641500
$244$	−28.3588	−1.81549
$245$	1.35828	0.0867775
$246$	10.3221	0.658112
$247$	−5.44068	−0.346182
$248$	−3.77235	−0.239544
$249$	2.11335	0.133928
$250$	−2.14529	−0.135680
$251$	−8.55795	−0.540173	−0.270086	−	0.962836i	$-0.587052\pi$
$251$	−8.55795	−0.540173	−0.270086	+	0.962836i	$0.587052\pi$
$252$	−7.52328	−0.473922
$253$	14.2204	0.894030
$254$	2.50506	0.157182
$255$	3.96885	0.248539
$256$	2.58000	0.161250
$257$	0.0540866	0.00337383	0.00168691	−	0.999999i	$-0.499463\pi$
$257$	0.0540866	0.00337383	0.00168691	+	0.999999i	$0.499463\pi$
$258$	−1.59329	−0.0991940
$259$	−18.5244	−1.15105
$260$	−4.24928	−0.263529
$261$	−1.74925	−0.108276
$262$	30.7709	1.90103
$263$	23.8798	1.47249	0.736246	−	0.676714i	$-0.236597\pi$
$263$	23.8798	1.47249	0.736246	+	0.676714i	$0.236597\pi$
$264$	2.71192	0.166907
$265$	9.77462	0.600450
$266$	20.6648	1.26704
$267$	−0.741249	−0.0453637
$268$	22.2916	1.36167
$269$	10.6182	0.647404	0.323702	−	0.946159i	$-0.395072\pi$
$269$	10.6182	0.647404	0.323702	+	0.946159i	$0.395072\pi$
$270$	−2.14529	−0.130558
$271$	−29.0887	−1.76702	−0.883508	−	0.468416i	$-0.844825\pi$
$271$	−29.0887	−1.76702	−0.883508	+	0.468416i	$0.844825\pi$
$272$	−9.65540	−0.585445
$273$	4.72090	0.285722
$274$	21.5559	1.30224
$275$	−2.09902	−0.126576
$276$	−17.6297	−1.06118
$277$	−19.0936	−1.14722	−0.573611	−	0.819128i	$-0.694458\pi$
$277$	−19.0936	−1.14722	−0.573611	+	0.819128i	$0.694458\pi$
$278$	30.4306	1.82511
$279$	2.91978	0.174803
$280$	3.73525	0.223224
$281$	24.5581	1.46501	0.732506	−	0.680761i	$-0.238351\pi$
$281$	24.5581	1.46501	0.732506	+	0.680761i	$0.238351\pi$
$282$	0.551414	0.0328362
$283$	4.04729	0.240587	0.120293	−	0.992738i	$-0.461616\pi$
$283$	4.04729	0.240587	0.120293	+	0.992738i	$0.461616\pi$
$284$	22.5911	1.34053
$285$	3.33187	0.197363
$286$	−7.35304	−0.434795
$287$	13.9104	0.821107
$288$	7.80304	0.459798
$289$	−1.24827	−0.0734276
$290$	3.75263	0.220362
$291$	−16.2525	−0.952739
$292$	−7.58020	−0.443597
$293$	4.87738	0.284939	0.142470	−	0.989799i	$-0.454496\pi$
$293$	4.87738	0.284939	0.142470	+	0.989799i	$0.454496\pi$
$294$	−2.91391	−0.169942
$295$	−7.42538	−0.432322
$296$	−8.27839	−0.481172
$297$	−2.09902	−0.121797
$298$	−27.7071	−1.60503
$299$	11.0627	0.639774
$300$	2.60225	0.150241
$301$	−2.14718	−0.123761
$302$	−16.9731	−0.976693
$303$	15.2164	0.874160
$304$	−8.10576	−0.464897
$305$	−10.8978	−0.624007
$306$	−8.51430	−0.486730
$307$	20.9424	1.19525	0.597623	−	0.801777i	$-0.296112\pi$
$307$	20.9424	1.19525	0.597623	+	0.801777i	$0.296112\pi$
$308$	15.7915	0.899804
$309$	15.1560	0.862196
$310$	−6.26377	−0.355758
$311$	−25.1591	−1.42664	−0.713322	−	0.700837i	$-0.752810\pi$
$311$	−25.1591	−1.42664	−0.713322	+	0.700837i	$0.752810\pi$
$312$	2.10973	0.119440
$313$	22.3888	1.26549	0.632745	−	0.774360i	$-0.281928\pi$
$313$	22.3888	1.26549	0.632745	+	0.774360i	$0.281928\pi$
$314$	35.2903	1.99155
$315$	−2.89107	−0.162893
$316$	−11.9850	−0.674207
$317$	−1.38351	−0.0777058	−0.0388529	−	0.999245i	$-0.512370\pi$
$317$	−1.38351	−0.0777058	−0.0388529	+	0.999245i	$0.512370\pi$
$318$	−20.9693	−1.17590
$319$	3.67170	0.205576
$320$	−11.8741	−0.663785
$321$	12.9782	0.724371
$322$	−42.0184	−2.34159
$323$	13.2237	0.735784
$324$	2.60225	0.144569
$325$	−1.63292	−0.0905784
$326$	31.0670	1.72064
$327$	−16.0863	−0.889574
$328$	6.21646	0.343247
$329$	0.743106	0.0409688
$330$	4.50299	0.247882
$331$	−0.323425	−0.0177770	−0.00888852	−	0.999960i	$-0.502829\pi$
$331$	−0.323425	−0.0177770	−0.00888852	+	0.999960i	$0.502829\pi$
$332$	5.49945	0.301822
$333$	6.40744	0.351126
$334$	53.8677	2.94751
$335$	8.56626	0.468025
$336$	7.03339	0.383703
$337$	0.953590	0.0519453	0.0259727	−	0.999663i	$-0.491732\pi$
$337$	0.953590	0.0519453	0.0259727	+	0.999663i	$0.491732\pi$
$338$	22.1684	1.20580
$339$	1.90271	0.103341
$340$	10.3279	0.560110
$341$	−6.12868	−0.331886
$342$	−7.14780	−0.386509
$343$	16.3106	0.880689
$344$	−0.959558	−0.0517359
$345$	−6.77479	−0.364743
$346$	21.0051	1.12924
$347$	1.76692	0.0948535	0.0474267	−	0.998875i	$-0.484898\pi$
$347$	1.76692	0.0948535	0.0474267	+	0.998875i	$0.484898\pi$
$348$	−4.55197	−0.244011
$349$	−19.5581	−1.04692	−0.523460	−	0.852050i	$-0.675359\pi$
$349$	−19.5581	−1.04692	−0.523460	+	0.852050i	$0.675359\pi$
$350$	6.20217	0.331520
$351$	−1.63292	−0.0871591
$352$	−16.3787	−0.872988
$353$	−26.1086	−1.38962	−0.694810	−	0.719193i	$-0.744512\pi$
$353$	−26.1086	−1.38962	−0.694810	+	0.719193i	$0.744512\pi$
$354$	15.9296	0.846646
$355$	8.68137	0.460759
$356$	−1.92891	−0.102232
$357$	−11.4742	−0.607279
$358$	−34.7292	−1.83550
$359$	13.9574	0.736645	0.368322	−	0.929698i	$-0.379932\pi$
$359$	13.9574	0.736645	0.368322	+	0.929698i	$0.379932\pi$
$360$	−1.29200	−0.0680942
$361$	−7.89867	−0.415720
$362$	54.6598	2.87286
$363$	−6.59413	−0.346102
$364$	12.2850	0.643906
$365$	−2.91294	−0.152470
$366$	23.3789	1.22204
$367$	−8.49849	−0.443617	−0.221809	−	0.975090i	$-0.571196\pi$
$367$	−8.49849	−0.443617	−0.221809	+	0.975090i	$0.571196\pi$
$368$	16.4817	0.859168
$369$	−4.81152	−0.250478
$370$	−13.7458	−0.714610
$371$	−28.2591	−1.46714
$372$	7.59800	0.393938
$373$	−7.19414	−0.372498	−0.186249	−	0.982503i	$-0.559633\pi$
$373$	−7.19414	−0.372498	−0.186249	+	0.982503i	$0.559633\pi$
$374$	17.8717	0.924122
$375$	1.00000	0.0516398
$376$	0.332088	0.0171261
$377$	2.85639	0.147111
$378$	6.20217	0.319005
$379$	−24.5437	−1.26072	−0.630361	−	0.776302i	$-0.717093\pi$
$379$	−24.5437	−1.26072	−0.630361	+	0.776302i	$0.717093\pi$
$380$	8.67034	0.444779
$381$	−1.16771	−0.0598234
$382$	2.77650	0.142058
$383$	14.1062	0.720793	0.360396	−	0.932799i	$-0.382641\pi$
$383$	14.1062	0.720793	0.360396	+	0.932799i	$0.382641\pi$
$384$	9.86735	0.503541
$385$	6.06841	0.309275
$386$	16.8614	0.858221
$387$	0.742694	0.0377533
$388$	−42.2931	−2.14711
$389$	−35.6219	−1.80610	−0.903052	−	0.429531i	$-0.858679\pi$
$389$	−35.6219	−1.80610	−0.903052	+	0.429531i	$0.858679\pi$
$390$	3.50309	0.177386
$391$	−26.8881	−1.35979
$392$	−1.75490	−0.0886356
$393$	−14.3435	−0.723533
$394$	10.8529	0.546761
$395$	−4.60562	−0.231734
$396$	−5.46217	−0.274484
$397$	10.1835	0.511097	0.255549	−	0.966796i	$-0.417744\pi$
$397$	10.1835	0.511097	0.255549	+	0.966796i	$0.417744\pi$
$398$	−55.9216	−2.80310
$399$	−9.63265	−0.482236
$400$	−2.43280	−0.121640
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	−18.3771	−0.916566
$403$	−4.76779	−0.237500
$404$	39.5969	1.97002
$405$	1.00000	0.0496904
$406$	−10.8491	−0.538433
$407$	−13.4493	−0.666659
$408$	−5.12773	−0.253860
$409$	−13.2505	−0.655197	−0.327599	−	0.944817i	$-0.606239\pi$
$409$	−13.2505	−0.655197	−0.327599	+	0.944817i	$0.606239\pi$
$410$	10.3221	0.509771
$411$	−10.0480	−0.495632
$412$	39.4398	1.94306
$413$	21.4673	1.05634
$414$	14.5339	0.714301
$415$	2.11335	0.103740
$416$	−12.7418	−0.624717
$417$	−14.1849	−0.694637
$418$	15.0034	0.733838
$419$	−35.2728	−1.72319	−0.861595	−	0.507596i	$-0.830534\pi$
$419$	−35.2728	−1.72319	−0.861595	+	0.507596i	$0.830534\pi$
$420$	−7.52328	−0.367099
$421$	37.5036	1.82781	0.913907	−	0.405924i	$-0.133050\pi$
$421$	37.5036	1.82781	0.913907	+	0.405924i	$0.133050\pi$
$422$	14.6235	0.711862
$423$	−0.257035	−0.0124975
$424$	−12.6288	−0.613307
$425$	3.96885	0.192517
$426$	−18.6240	−0.902337
$427$	31.5063	1.52470
$428$	33.7725	1.63245
$429$	3.42754	0.165483
$430$	−1.59329	−0.0768353
$431$	7.39697	0.356300	0.178150	−	0.984003i	$-0.442989\pi$
$431$	7.39697	0.356300	0.178150	+	0.984003i	$0.442989\pi$
$432$	−2.43280	−0.117048
$433$	−3.92803	−0.188769	−0.0943846	−	0.995536i	$-0.530088\pi$
$433$	−3.92803	−0.188769	−0.0943846	+	0.995536i	$0.530088\pi$
$434$	18.1090	0.869260
$435$	−1.74925	−0.0838699
$436$	−41.8605	−2.00476
$437$	−22.5727	−1.07980
$438$	6.24909	0.298593
$439$	26.8437	1.28118	0.640591	−	0.767882i	$-0.278689\pi$
$439$	26.8437	1.28118	0.640591	+	0.767882i	$0.278689\pi$
$440$	2.71192	0.129286
$441$	1.35828	0.0646802
$442$	13.9032	0.661309
$443$	−2.14861	−0.102083	−0.0510417	−	0.998697i	$-0.516254\pi$
$443$	−2.14861	−0.102083	−0.0510417	+	0.998697i	$0.516254\pi$
$444$	16.6738	0.791302
$445$	−0.741249	−0.0351386
$446$	−20.9492	−0.991976
$447$	12.9154	0.610875
$448$	34.3290	1.62189
$449$	12.4295	0.586586	0.293293	−	0.956023i	$-0.405249\pi$
$449$	12.4295	0.586586	0.293293	+	0.956023i	$0.405249\pi$
$450$	−2.14529	−0.101130
$451$	10.0995	0.475565
$452$	4.95133	0.232891
$453$	7.91182	0.371730
$454$	−52.2903	−2.45410
$455$	4.72090	0.221319
$456$	−4.30476	−0.201589
$457$	−25.7906	−1.20643	−0.603217	−	0.797577i	$-0.706115\pi$
$457$	−25.7906	−1.20643	−0.603217	+	0.797577i	$0.706115\pi$
$458$	44.8790	2.09706
$459$	3.96885	0.185250
$460$	−17.6297	−0.821989
$461$	−5.49278	−0.255824	−0.127912	−	0.991785i	$-0.540828\pi$
$461$	−5.49278	−0.255824	−0.127912	+	0.991785i	$0.540828\pi$
$462$	−13.0185	−0.605674
$463$	37.9178	1.76219	0.881095	−	0.472938i	$-0.156807\pi$
$463$	37.9178	1.76219	0.881095	+	0.472938i	$0.156807\pi$
$464$	4.25556	0.197560
$465$	2.91978	0.135402
$466$	38.9674	1.80513
$467$	2.36111	0.109259	0.0546296	−	0.998507i	$-0.482602\pi$
$467$	2.36111	0.109259	0.0546296	+	0.998507i	$0.482602\pi$
$468$	−4.24928	−0.196423
$469$	−24.7657	−1.14357
$470$	0.551414	0.0254348
$471$	−16.4502	−0.757984
$472$	9.59356	0.441579
$473$	−1.55893	−0.0716796
$474$	9.88037	0.453820
$475$	3.33187	0.152876
$476$	−29.8587	−1.36857
$477$	9.77462	0.447549
$478$	17.5769	0.803947
$479$	0.507292	0.0231788	0.0115894	−	0.999933i	$-0.496311\pi$
$479$	0.507292	0.0231788	0.0115894	+	0.999933i	$0.496311\pi$
$480$	7.80304	0.356158
$481$	−10.4629	−0.477066
$482$	35.1946	1.60307
$483$	19.5864	0.891212
$484$	−17.1596	−0.779980
$485$	−16.2525	−0.737988
$486$	−2.14529	−0.0973121
$487$	32.4324	1.46965	0.734827	−	0.678255i	$-0.237263\pi$
$487$	32.4324	1.46965	0.734827	+	0.678255i	$0.237263\pi$
$488$	14.0799	0.637368
$489$	−14.4815	−0.654877
$490$	−2.91391	−0.131637
$491$	30.3373	1.36910	0.684551	−	0.728965i	$-0.259998\pi$
$491$	30.3373	1.36910	0.684551	+	0.728965i	$0.259998\pi$
$492$	−12.5208	−0.564480
$493$	−6.94249	−0.312674
$494$	11.6718	0.525140
$495$	−2.09902	−0.0943438
$496$	−7.10325	−0.318945
$497$	−25.0985	−1.12582
$498$	−4.53373	−0.203161
$499$	−14.7620	−0.660838	−0.330419	−	0.943834i	$-0.607190\pi$
$499$	−14.7620	−0.660838	−0.330419	+	0.943834i	$0.607190\pi$
$500$	2.60225	0.116376
$501$	−25.1098	−1.12182
$502$	18.3592	0.819413
$503$	1.12535	0.0501770	0.0250885	−	0.999685i	$-0.492013\pi$
$503$	1.12535	0.0501770	0.0250885	+	0.999685i	$0.492013\pi$
$504$	3.73525	0.166381
$505$	15.2164	0.677121
$506$	−30.5068	−1.35619
$507$	−10.3336	−0.458929
$508$	−3.03866	−0.134819
$509$	−25.2154	−1.11765	−0.558827	−	0.829285i	$-0.688748\pi$
$509$	−25.2154	−1.11765	−0.558827	+	0.829285i	$0.688748\pi$
$510$	−8.51430	−0.377020
$511$	8.42151	0.372546
$512$	−25.2695	−1.11677
$513$	3.33187	0.147105
$514$	−0.116031	−0.00511791
$515$	15.1560	0.667854
$516$	1.93268	0.0850813
$517$	0.539521	0.0237281
$518$	39.7400	1.74608
$519$	−9.79130	−0.429790
$520$	2.10973	0.0925178
$521$	14.9347	0.654301	0.327150	−	0.944972i	$-0.393912\pi$
$521$	14.9347	0.654301	0.327150	+	0.944972i	$0.393912\pi$
$522$	3.75263	0.164248
$523$	−30.5457	−1.33567	−0.667836	−	0.744308i	$-0.732779\pi$
$523$	−30.5457	−1.33567	−0.667836	+	0.744308i	$0.732779\pi$
$524$	−37.3253	−1.63056
$525$	−2.89107	−0.126177
$526$	−51.2290	−2.23369
$527$	11.5882	0.504789
$528$	5.10649	0.222231
$529$	22.8978	0.995558
$530$	−20.9693	−0.910850
$531$	−7.42538	−0.322234
$532$	−25.0666	−1.08677
$533$	7.85684	0.340318
$534$	1.59019	0.0688143
$535$	12.9782	0.561096
$536$	−11.0676	−0.478047
$537$	16.1886	0.698591
$538$	−22.7791	−0.982077
$539$	−2.85106	−0.122804
$540$	2.60225	0.111983
$541$	12.0274	0.517099	0.258550	−	0.965998i	$-0.416755\pi$
$541$	12.0274	0.517099	0.258550	+	0.965998i	$0.416755\pi$
$542$	62.4037	2.68047
$543$	−25.4790	−1.09341
$544$	30.9690	1.32779
$545$	−16.0863	−0.689061
$546$	−10.1277	−0.433424
$547$	−7.29336	−0.311842	−0.155921	−	0.987770i	$-0.549834\pi$
$547$	−7.29336	−0.311842	−0.155921	+	0.987770i	$0.549834\pi$
$548$	−26.1474	−1.11696
$549$	−10.8978	−0.465107
$550$	4.50299	0.192008
$551$	−5.82825	−0.248292
$552$	8.75301	0.372553
$553$	13.3152	0.566218
$554$	40.9611	1.74027
$555$	6.40744	0.271981
$556$	−36.9126	−1.56544
$557$	0.254146	0.0107685	0.00538426	−	0.999986i	$-0.498286\pi$
$557$	0.254146	0.0107685	0.00538426	+	0.999986i	$0.498286\pi$
$558$	−6.26377	−0.265167
$559$	−1.21276	−0.0512945
$560$	7.03339	0.297215
$561$	−8.33068	−0.351721
$562$	−52.6841	−2.22234
$563$	−36.5800	−1.54166	−0.770832	−	0.637039i	$-0.780159\pi$
$563$	−36.5800	−1.54166	−0.770832	+	0.637039i	$0.780159\pi$
$564$	−0.668869	−0.0281645
$565$	1.90271	0.0800476
$566$	−8.68260	−0.364957
$567$	−2.89107	−0.121414
$568$	−11.2163	−0.470625
$569$	−8.59806	−0.360449	−0.180225	−	0.983625i	$-0.557682\pi$
$569$	−8.59806	−0.360449	−0.180225	+	0.983625i	$0.557682\pi$
$570$	−7.14780	−0.299388
$571$	−25.4010	−1.06300	−0.531500	−	0.847058i	$-0.678371\pi$
$571$	−25.4010	−1.06300	−0.531500	+	0.847058i	$0.678371\pi$
$572$	8.91930	0.372935
$573$	−1.29423	−0.0540673
$574$	−29.8418	−1.24557
$575$	−6.77479	−0.282528
$576$	−11.8741	−0.494756
$577$	1.10960	0.0461935	0.0230967	−	0.999733i	$-0.492647\pi$
$577$	1.10960	0.0461935	0.0230967	+	0.999733i	$0.492647\pi$
$578$	2.67789	0.111386
$579$	−7.85973	−0.326639
$580$	−4.55197	−0.189010
$581$	−6.10983	−0.253478
$582$	34.8663	1.44525
$583$	−20.5171	−0.849731
$584$	3.76351	0.155735
$585$	−1.63292	−0.0675131
$586$	−10.4634	−0.432238
$587$	−1.35273	−0.0558330	−0.0279165	−	0.999610i	$-0.508887\pi$
$587$	−1.35273	−0.0558330	−0.0279165	+	0.999610i	$0.508887\pi$
$588$	3.53459	0.145764
$589$	9.72833	0.400849
$590$	15.9296	0.655810
$591$	−5.05895	−0.208097
$592$	−15.5880	−0.640664
$593$	−33.5846	−1.37916	−0.689578	−	0.724212i	$-0.742204\pi$
$593$	−33.5846	−1.37916	−0.689578	+	0.724212i	$0.742204\pi$
$594$	4.50299	0.184760
$595$	−11.4742	−0.470397
$596$	33.6090	1.37668
$597$	26.0672	1.06686
$598$	−23.7327	−0.970503
$599$	4.77591	0.195138	0.0975692	−	0.995229i	$-0.468893\pi$
$599$	4.77591	0.195138	0.0975692	+	0.995229i	$0.468893\pi$
$600$	−1.29200	−0.0527455
$601$	−16.2918	−0.664556	−0.332278	−	0.943182i	$-0.607817\pi$
$601$	−16.2918	−0.664556	−0.332278	+	0.943182i	$0.607817\pi$
$602$	4.60632	0.187739
$603$	8.56626	0.348845
$604$	20.5885	0.837736
$605$	−6.59413	−0.268089
$606$	−32.6435	−1.32605
$607$	−47.6760	−1.93511	−0.967554	−	0.252664i	$-0.918693\pi$
$607$	−47.6760	−1.93511	−0.967554	+	0.252664i	$0.918693\pi$
$608$	25.9987	1.05439
$609$	5.05719	0.204928
$610$	23.3789	0.946584
$611$	0.419719	0.0169800
$612$	10.3279	0.417482
$613$	−2.61520	−0.105627	−0.0528135	−	0.998604i	$-0.516819\pi$
$613$	−2.61520	−0.105627	−0.0528135	+	0.998604i	$0.516819\pi$
$614$	−44.9274	−1.81312
$615$	−4.81152	−0.194019
$616$	−7.84035	−0.315897
$617$	4.04299	0.162765	0.0813823	−	0.996683i	$-0.474067\pi$
$617$	4.04299	0.162765	0.0813823	+	0.996683i	$0.474067\pi$
$618$	−32.5140	−1.30790
$619$	−27.4053	−1.10151	−0.550756	−	0.834666i	$-0.685660\pi$
$619$	−27.4053	−1.10151	−0.550756	+	0.834666i	$0.685660\pi$
$620$	7.59800	0.305143
$621$	−6.77479	−0.271863
$622$	53.9735	2.16414
$623$	2.14300	0.0858576
$624$	3.97258	0.159030
$625$	1.00000	0.0400000
$626$	−48.0304	−1.91968
$627$	−6.99364	−0.279299
$628$	−42.8074	−1.70820
$629$	25.4302	1.01397
$630$	6.20217	0.247100
$631$	−12.6088	−0.501947	−0.250974	−	0.967994i	$-0.580751\pi$
$631$	−12.6088	−0.501947	−0.250974	+	0.967994i	$0.580751\pi$
$632$	5.95044	0.236696
$633$	−6.81659	−0.270935
$634$	2.96803	0.117876
$635$	−1.16771	−0.0463390
$636$	25.4360	1.00860
$637$	−2.21797	−0.0878793
$638$	−7.87684	−0.311847
$639$	8.68137	0.343430
$640$	9.86735	0.390041
$641$	5.93257	0.234322	0.117161	−	0.993113i	$-0.462621\pi$
$641$	5.93257	0.234322	0.117161	+	0.993113i	$0.462621\pi$
$642$	−27.8419	−1.09883
$643$	8.33963	0.328883	0.164441	−	0.986387i	$-0.447418\pi$
$643$	8.33963	0.328883	0.164441	+	0.986387i	$0.447418\pi$
$644$	50.9687	2.00845
$645$	0.742694	0.0292436
$646$	−28.3685	−1.11614
$647$	−33.6896	−1.32447	−0.662237	−	0.749294i	$-0.730393\pi$
$647$	−33.6896	−1.32447	−0.662237	+	0.749294i	$0.730393\pi$
$648$	−1.29200	−0.0507544
$649$	15.5860	0.611804
$650$	3.50309	0.137402
$651$	−8.44130	−0.330841
$652$	−37.6845	−1.47584
$653$	29.4341	1.15184	0.575922	−	0.817505i	$-0.304643\pi$
$653$	29.4341	1.15184	0.575922	+	0.817505i	$0.304643\pi$
$654$	34.5097	1.34944
$655$	−14.3435	−0.560446
$656$	11.7055	0.457021
$657$	−2.91294	−0.113645
$658$	−1.59417	−0.0621474
$659$	−19.0962	−0.743884	−0.371942	−	0.928256i	$-0.621308\pi$
$659$	−19.0962	−0.743884	−0.371942	+	0.928256i	$0.621308\pi$
$660$	−5.46217	−0.212615
$661$	2.26965	0.0882791	0.0441396	−	0.999025i	$-0.485945\pi$
$661$	2.26965	0.0882791	0.0441396	+	0.999025i	$0.485945\pi$
$662$	0.693838	0.0269668
$663$	−6.48082	−0.251694
$664$	−2.73043	−0.105961
$665$	−9.63265	−0.373538
$666$	−13.7458	−0.532639
$667$	11.8508	0.458864
$668$	−65.3419	−2.52815
$669$	9.76525	0.377546
$670$	−18.3771	−0.709969
$671$	22.8747	0.883068
$672$	−22.5591	−0.870237
$673$	−4.78157	−0.184316	−0.0921580	−	0.995744i	$-0.529376\pi$
$673$	−4.78157	−0.184316	−0.0921580	+	0.995744i	$0.529376\pi$
$674$	−2.04572	−0.0787983
$675$	1.00000	0.0384900
$676$	−26.8905	−1.03425
$677$	−22.8760	−0.879195	−0.439597	−	0.898195i	$-0.644879\pi$
$677$	−22.8760	−0.879195	−0.439597	+	0.898195i	$0.644879\pi$
$678$	−4.08186	−0.156763
$679$	46.9871	1.80320
$680$	−5.12773	−0.196639
$681$	24.3745	0.934033
$682$	13.1478	0.503454
$683$	49.0547	1.87702	0.938512	−	0.345246i	$-0.112205\pi$
$683$	49.0547	1.87702	0.938512	+	0.345246i	$0.112205\pi$
$684$	8.67034	0.331519
$685$	−10.0480	−0.383915
$686$	−34.9909	−1.33596
$687$	−20.9198	−0.798141
$688$	−1.80683	−0.0688846
$689$	−15.9612	−0.608074
$690$	14.5339	0.553295
$691$	−23.0432	−0.876605	−0.438302	−	0.898828i	$-0.644420\pi$
$691$	−23.0432	−0.876605	−0.438302	+	0.898828i	$0.644420\pi$
$692$	−25.4794	−0.968581
$693$	6.06841	0.230520
$694$	−3.79056	−0.143888
$695$	−14.1849	−0.538063
$696$	2.26002	0.0856658
$697$	−19.0962	−0.723319
$698$	41.9577	1.58812
$699$	−18.1642	−0.687034
$700$	−7.52328	−0.284353
$701$	23.9774	0.905613	0.452807	−	0.891609i	$-0.350423\pi$
$701$	23.9774	0.905613	0.452807	+	0.891609i	$0.350423\pi$
$702$	3.50309	0.132216
$703$	21.3487	0.805183
$704$	24.9240	0.939360
$705$	−0.257035	−0.00968050
$706$	56.0104	2.10798
$707$	−43.9917	−1.65448
$708$	−19.3227	−0.726191
$709$	−7.31636	−0.274772	−0.137386	−	0.990518i	$-0.543870\pi$
$709$	−7.31636	−0.274772	−0.137386	+	0.990518i	$0.543870\pi$
$710$	−18.6240	−0.698947
$711$	−4.60562	−0.172724
$712$	0.957691	0.0358910
$713$	−19.7809	−0.740802
$714$	24.6154	0.921210
$715$	3.42754	0.128183
$716$	42.1268	1.57435
$717$	−8.19325	−0.305983
$718$	−29.9427	−1.11745
$719$	−32.8604	−1.22549	−0.612743	−	0.790282i	$-0.709934\pi$
$719$	−32.8604	−1.22549	−0.612743	+	0.790282i	$0.709934\pi$
$720$	−2.43280	−0.0906650
$721$	−43.8171	−1.63183
$722$	16.9449	0.630624
$723$	−16.4056	−0.610130
$724$	−66.3028	−2.46412
$725$	−1.74925	−0.0649654
$726$	14.1463	0.525018
$727$	26.2970	0.975301	0.487650	−	0.873039i	$-0.337854\pi$
$727$	26.2970	0.975301	0.487650	+	0.873039i	$0.337854\pi$
$728$	−6.09938	−0.226058
$729$	1.00000	0.0370370
$730$	6.24909	0.231289
$731$	2.94764	0.109022
$732$	−28.3588	−1.04817
$733$	−1.78270	−0.0658454	−0.0329227	−	0.999458i	$-0.510482\pi$
$733$	−1.78270	−0.0658454	−0.0329227	+	0.999458i	$0.510482\pi$
$734$	18.2317	0.672943
$735$	1.35828	0.0501010
$736$	−52.8640	−1.94859
$737$	−17.9807	−0.662329
$738$	10.3221	0.379961
$739$	−43.6867	−1.60704	−0.803520	−	0.595278i	$-0.797042\pi$
$739$	−43.6867	−1.60704	−0.803520	+	0.595278i	$0.797042\pi$
$740$	16.6738	0.612940
$741$	−5.44068	−0.199869
$742$	60.6238	2.22557
$743$	4.42770	0.162437	0.0812183	−	0.996696i	$-0.474119\pi$
$743$	4.42770	0.162437	0.0812183	+	0.996696i	$0.474119\pi$
$744$	−3.77235	−0.138301
$745$	12.9154	0.473182
$746$	15.4335	0.565060
$747$	2.11335	0.0773233
$748$	−21.6785	−0.792644
$749$	−37.5208	−1.37098
$750$	−2.14529	−0.0783347
$751$	39.8469	1.45403	0.727017	−	0.686619i	$-0.240906\pi$
$751$	39.8469	1.45403	0.727017	+	0.686619i	$0.240906\pi$
$752$	0.625315	0.0228029
$753$	−8.55795	−0.311869
$754$	−6.12776	−0.223160
$755$	7.91182	0.287941
$756$	−7.52328	−0.273619
$757$	18.2240	0.662364	0.331182	−	0.943567i	$-0.392553\pi$
$757$	18.2240	0.662364	0.331182	+	0.943567i	$0.392553\pi$
$758$	52.6531	1.91245
$759$	14.2204	0.516168
$760$	−4.30476	−0.156150
$761$	17.2202	0.624232	0.312116	−	0.950044i	$-0.398962\pi$
$761$	17.2202	0.624232	0.312116	+	0.950044i	$0.398962\pi$
$762$	2.50506	0.0907489
$763$	46.5066	1.68365
$764$	−3.36792	−0.121847
$765$	3.96885	0.143494
$766$	−30.2618	−1.09340
$767$	12.1251	0.437811
$768$	2.58000	0.0930978
$769$	−27.0303	−0.974739	−0.487370	−	0.873196i	$-0.662044\pi$
$769$	−27.0303	−0.974739	−0.487370	+	0.873196i	$0.662044\pi$
$770$	−13.0185	−0.469153
$771$	0.0540866	0.00194788
$772$	−20.4530	−0.736119
$773$	−40.0091	−1.43903	−0.719514	−	0.694478i	$-0.755635\pi$
$773$	−40.0091	−1.43903	−0.719514	+	0.694478i	$0.755635\pi$
$774$	−1.59329	−0.0572697
$775$	2.91978	0.104882
$776$	20.9982	0.753791
$777$	−18.5244	−0.664558
$778$	76.4192	2.73976
$779$	−16.0313	−0.574382
$780$	−4.24928	−0.152148
$781$	−18.2224	−0.652047
$782$	57.6827	2.06273
$783$	−1.74925	−0.0625129
$784$	−3.30443	−0.118015
$785$	−16.4502	−0.587132
$786$	30.7709	1.09756
$787$	−41.7208	−1.48719	−0.743593	−	0.668633i	$-0.766880\pi$
$787$	−41.7208	−1.48719	−0.743593	+	0.668633i	$0.766880\pi$
$788$	−13.1646	−0.468971
$789$	23.8798	0.850144
$790$	9.88037	0.351528
$791$	−5.50087	−0.195588
$792$	2.71192	0.0963639
$793$	17.7953	0.631930
$794$	−21.8466	−0.775306
$795$	9.77462	0.346670
$796$	67.8334	2.40429
$797$	−30.5314	−1.08148	−0.540739	−	0.841191i	$-0.681855\pi$
$797$	−30.5314	−1.08148	−0.540739	+	0.841191i	$0.681855\pi$
$798$	20.6648	0.731526
$799$	−1.02013	−0.0360897
$800$	7.80304	0.275879
$801$	−0.741249	−0.0261908
$802$	2.14529	0.0757527
$803$	6.11431	0.215769
$804$	22.2916	0.786162
$805$	19.5864	0.690330
$806$	10.2283	0.360275
$807$	10.6182	0.373779
$808$	−19.6595	−0.691620
$809$	−31.3471	−1.10211	−0.551053	−	0.834470i	$-0.685774\pi$
$809$	−31.3471	−1.10211	−0.551053	+	0.834470i	$0.685774\pi$
$810$	−2.14529	−0.0753776
$811$	−1.13948	−0.0400126	−0.0200063	−	0.999800i	$-0.506369\pi$
$811$	−1.13948	−0.0400126	−0.0200063	+	0.999800i	$0.506369\pi$
$812$	13.1601	0.461828
$813$	−29.0887	−1.02019
$814$	28.8527	1.01129
$815$	−14.4815	−0.507266
$816$	−9.65540	−0.338007
$817$	2.47456	0.0865738
$818$	28.4262	0.993899
$819$	4.72090	0.164962
$820$	−12.5208	−0.437244
$821$	−16.6555	−0.581281	−0.290640	−	0.956832i	$-0.593868\pi$
$821$	−16.6555	−0.581281	−0.290640	+	0.956832i	$0.593868\pi$
$822$	21.5559	0.751847
$823$	−1.52038	−0.0529972	−0.0264986	−	0.999649i	$-0.508436\pi$
$823$	−1.52038	−0.0529972	−0.0264986	+	0.999649i	$0.508436\pi$
$824$	−19.5815	−0.682155
$825$	−2.09902	−0.0730784
$826$	−46.0535	−1.60240
$827$	−23.9257	−0.831978	−0.415989	−	0.909370i	$-0.636565\pi$
$827$	−23.9257	−0.831978	−0.415989	+	0.909370i	$0.636565\pi$
$828$	−17.6297	−0.612674
$829$	−51.9666	−1.80488	−0.902438	−	0.430820i	$-0.858224\pi$
$829$	−51.9666	−1.80488	−0.902438	+	0.430820i	$0.858224\pi$
$830$	−4.53373	−0.157368
$831$	−19.0936	−0.662348
$832$	19.3896	0.672213
$833$	5.39082	0.186781
$834$	30.4306	1.05373
$835$	−25.1098	−0.868960
$836$	−18.1992	−0.629433
$837$	2.91978	0.100922
$838$	75.6703	2.61399
$839$	−39.9895	−1.38059	−0.690295	−	0.723528i	$-0.742519\pi$
$839$	−39.9895	−1.38059	−0.690295	+	0.723528i	$0.742519\pi$
$840$	3.73525	0.128878
$841$	−25.9401	−0.894488
$842$	−80.4559	−2.77269
$843$	24.5581	0.845825
$844$	−17.7385	−0.610583
$845$	−10.3336	−0.355485
$846$	0.551414	0.0189580
$847$	19.0641	0.655049
$848$	−23.7797	−0.816598
$849$	4.04729	0.138903
$850$	−8.51430	−0.292038
$851$	−43.4091	−1.48805
$852$	22.5911	0.773958
$853$	2.07483	0.0710408	0.0355204	−	0.999369i	$-0.488691\pi$
$853$	2.07483	0.0710408	0.0355204	+	0.999369i	$0.488691\pi$
$854$	−67.5901	−2.31288
$855$	3.33187	0.113947
$856$	−16.7678	−0.573110
$857$	−35.8929	−1.22608	−0.613039	−	0.790052i	$-0.710053\pi$
$857$	−35.8929	−1.22608	−0.613039	+	0.790052i	$0.710053\pi$
$858$	−7.35304	−0.251029
$859$	6.96415	0.237614	0.118807	−	0.992917i	$-0.462093\pi$
$859$	6.96415	0.237614	0.118807	+	0.992917i	$0.462093\pi$
$860$	1.93268	0.0659037
$861$	13.9104	0.474066
$862$	−15.8686	−0.540487
$863$	23.2181	0.790353	0.395177	−	0.918605i	$-0.370683\pi$
$863$	23.2181	0.790353	0.395177	+	0.918605i	$0.370683\pi$
$864$	7.80304	0.265465
$865$	−9.79130	−0.332914
$866$	8.42675	0.286352
$867$	−1.24827	−0.0423934
$868$	−21.9664	−0.745587
$869$	9.66727	0.327940
$870$	3.75263	0.127226
$871$	−13.9881	−0.473967
$872$	20.7834	0.703815
$873$	−16.2525	−0.550064
$874$	48.4249	1.63800
$875$	−2.89107	−0.0977360
$876$	−7.58020	−0.256111
$877$	28.6584	0.967726	0.483863	−	0.875144i	$-0.339233\pi$
$877$	28.6584	0.967726	0.483863	+	0.875144i	$0.339233\pi$
$878$	−57.5875	−1.94348
$879$	4.87738	0.164510
$880$	5.10649	0.172140
$881$	−51.4717	−1.73413	−0.867063	−	0.498199i	$-0.833995\pi$
$881$	−51.4717	−1.73413	−0.867063	+	0.498199i	$0.833995\pi$
$882$	−2.91391	−0.0981163
$883$	33.0173	1.11112	0.555560	−	0.831476i	$-0.312504\pi$
$883$	33.0173	1.11112	0.555560	+	0.831476i	$0.312504\pi$
$884$	−16.8647	−0.567222
$885$	−7.42538	−0.249601
$886$	4.60938	0.154855
$887$	−31.0149	−1.04138	−0.520690	−	0.853746i	$-0.674325\pi$
$887$	−31.0149	−1.04138	−0.520690	+	0.853746i	$0.674325\pi$
$888$	−8.27839	−0.277805
$889$	3.37592	0.113225
$890$	1.59019	0.0533033
$891$	−2.09902	−0.0703197
$892$	25.4116	0.850844
$893$	−0.856406	−0.0286585
$894$	−27.7071	−0.926664
$895$	16.1886	0.541126
$896$	−28.5272	−0.953027
$897$	11.0627	0.369374
$898$	−26.6649	−0.889819
$899$	−5.10742	−0.170342
$900$	2.60225	0.0867416
$901$	38.7940	1.29241
$902$	−21.6662	−0.721406
$903$	−2.14718	−0.0714537
$904$	−2.45829	−0.0817616
$905$	−25.4790	−0.846952
$906$	−16.9731	−0.563894
$907$	37.7675	1.25405	0.627025	−	0.778999i	$-0.284272\pi$
$907$	37.7675	1.25405	0.627025	+	0.778999i	$0.284272\pi$
$908$	63.4285	2.10495
$909$	15.2164	0.504696
$910$	−10.1277	−0.335729
$911$	27.5478	0.912699	0.456349	−	0.889801i	$-0.349157\pi$
$911$	27.5478	0.912699	0.456349	+	0.889801i	$0.349157\pi$
$912$	−8.10576	−0.268408
$913$	−4.43595	−0.146808
$914$	55.3282	1.83009
$915$	−10.8978	−0.360270
$916$	−54.4386	−1.79870
$917$	41.4680	1.36939
$918$	−8.51430	−0.281014
$919$	20.5437	0.677673	0.338836	−	0.940845i	$-0.389967\pi$
$919$	20.5437	0.677673	0.338836	+	0.940845i	$0.389967\pi$
$920$	8.75301	0.288578
$921$	20.9424	0.690075
$922$	11.7836	0.388072
$923$	−14.1760	−0.466610
$924$	15.7915	0.519502
$925$	6.40744	0.210675
$926$	−81.3446	−2.67315
$927$	15.1560	0.497789
$928$	−13.6494	−0.448065
$929$	15.4287	0.506200	0.253100	−	0.967440i	$-0.418550\pi$
$929$	15.4287	0.506200	0.253100	+	0.967440i	$0.418550\pi$
$930$	−6.26377	−0.205397
$931$	4.52562	0.148321
$932$	−47.2678	−1.54831
$933$	−25.1591	−0.823673
$934$	−5.06526	−0.165740
$935$	−8.33068	−0.272442
$936$	2.10973	0.0689587
$937$	−34.1078	−1.11425	−0.557127	−	0.830427i	$-0.688096\pi$
$937$	−34.1078	−1.11425	−0.557127	+	0.830427i	$0.688096\pi$
$938$	53.1294	1.73474
$939$	22.3888	0.730631
$940$	−0.668869	−0.0218161
$941$	26.7646	0.872502	0.436251	−	0.899825i	$-0.356306\pi$
$941$	26.7646	0.872502	0.436251	+	0.899825i	$0.356306\pi$
$942$	35.2903	1.14982
$943$	32.5970	1.06151
$944$	18.0645	0.587948
$945$	−2.89107	−0.0940465
$946$	3.34435	0.108734
$947$	−50.0155	−1.62529	−0.812643	−	0.582761i	$-0.801972\pi$
$947$	−50.0155	−1.62529	−0.812643	+	0.582761i	$0.801972\pi$
$948$	−11.9850	−0.389254
$949$	4.75661	0.154406
$950$	−7.14780	−0.231905
$951$	−1.38351	−0.0448635
$952$	14.8246	0.480469
$953$	24.3044	0.787296	0.393648	−	0.919261i	$-0.371213\pi$
$953$	24.3044	0.787296	0.393648	+	0.919261i	$0.371213\pi$
$954$	−20.9693	−0.678908
$955$	−1.29423	−0.0418804
$956$	−21.3209	−0.689567
$957$	3.67170	0.118689
$958$	−1.08829	−0.0351609
$959$	29.0495	0.938058
$960$	−11.8741	−0.383236
$961$	−22.4749	−0.724996
$962$	22.4458	0.723683
$963$	12.9782	0.418216
$964$	−42.6914	−1.37500
$965$	−7.85973	−0.253014
$966$	−42.0184	−1.35192
$967$	−29.7691	−0.957310	−0.478655	−	0.878003i	$-0.658876\pi$
$967$	−29.7691	−0.957310	−0.478655	+	0.878003i	$0.658876\pi$
$968$	8.51958	0.273830
$969$	13.2237	0.424805
$970$	34.8663	1.11949
$971$	56.0709	1.79940	0.899701	−	0.436506i	$-0.143784\pi$
$971$	56.0709	1.79940	0.899701	+	0.436506i	$0.143784\pi$
$972$	2.60225	0.0834672
$973$	41.0095	1.31470
$974$	−69.5768	−2.22939
$975$	−1.63292	−0.0522954
$976$	26.5122	0.848634
$977$	45.8418	1.46661	0.733304	−	0.679901i	$-0.237977\pi$
$977$	45.8418	1.46661	0.733304	+	0.679901i	$0.237977\pi$
$978$	31.0670	0.993413
$979$	1.55590	0.0497266
$980$	3.53459	0.112908
$981$	−16.0863	−0.513596
$982$	−65.0822	−2.07685
$983$	27.5039	0.877238	0.438619	−	0.898673i	$-0.355468\pi$
$983$	27.5039	0.877238	0.438619	+	0.898673i	$0.355468\pi$
$984$	6.21646	0.198173
$985$	−5.05895	−0.161192
$986$	14.8936	0.474309
$987$	0.743106	0.0236533
$988$	−14.1580	−0.450426
$989$	−5.03160	−0.159996
$990$	4.50299	0.143114
$991$	−35.3695	−1.12355	−0.561774	−	0.827291i	$-0.689881\pi$
$991$	−35.3695	−1.12355	−0.561774	+	0.827291i	$0.689881\pi$
$992$	22.7832	0.723367
$993$	−0.323425	−0.0102636
$994$	53.8433	1.70781
$995$	26.0672	0.826386
$996$	5.49945	0.174257
$997$	−41.1135	−1.30208	−0.651039	−	0.759044i	$-0.725667\pi$
$997$	−41.1135	−1.30208	−0.651039	+	0.759044i	$0.725667\pi$
$998$	31.6687	1.00246
$999$	6.40744	0.202723

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.4	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.4	✓	23	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)

\(f(q)\)	\(=\)	\(q-2.14529 q^{2} +1.00000 q^{3} +2.60225 q^{4} +1.00000 q^{5} -2.14529 q^{6} -2.89107 q^{7} -1.29200 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.14529 q^{2} +1.00000 q^{3} +2.60225 q^{4} +1.00000 q^{5} -2.14529 q^{6} -2.89107 q^{7} -1.29200 q^{8} +1.00000 q^{9} -2.14529 q^{10} -2.09902 q^{11} +2.60225 q^{12} -1.63292 q^{13} +6.20217 q^{14} +1.00000 q^{15} -2.43280 q^{16} +3.96885 q^{17} -2.14529 q^{18} +3.33187 q^{19} +2.60225 q^{20} -2.89107 q^{21} +4.50299 q^{22} -6.77479 q^{23} -1.29200 q^{24} +1.00000 q^{25} +3.50309 q^{26} +1.00000 q^{27} -7.52328 q^{28} -1.74925 q^{29} -2.14529 q^{30} +2.91978 q^{31} +7.80304 q^{32} -2.09902 q^{33} -8.51430 q^{34} -2.89107 q^{35} +2.60225 q^{36} +6.40744 q^{37} -7.14780 q^{38} -1.63292 q^{39} -1.29200 q^{40} -4.81152 q^{41} +6.20217 q^{42} +0.742694 q^{43} -5.46217 q^{44} +1.00000 q^{45} +14.5339 q^{46} -0.257035 q^{47} -2.43280 q^{48} +1.35828 q^{49} -2.14529 q^{50} +3.96885 q^{51} -4.24928 q^{52} +9.77462 q^{53} -2.14529 q^{54} -2.09902 q^{55} +3.73525 q^{56} +3.33187 q^{57} +3.75263 q^{58} -7.42538 q^{59} +2.60225 q^{60} -10.8978 q^{61} -6.26377 q^{62} -2.89107 q^{63} -11.8741 q^{64} -1.63292 q^{65} +4.50299 q^{66} +8.56626 q^{67} +10.3279 q^{68} -6.77479 q^{69} +6.20217 q^{70} +8.68137 q^{71} -1.29200 q^{72} -2.91294 q^{73} -13.7458 q^{74} +1.00000 q^{75} +8.67034 q^{76} +6.06841 q^{77} +3.50309 q^{78} -4.60562 q^{79} -2.43280 q^{80} +1.00000 q^{81} +10.3221 q^{82} +2.11335 q^{83} -7.52328 q^{84} +3.96885 q^{85} -1.59329 q^{86} -1.74925 q^{87} +2.71192 q^{88} -0.741249 q^{89} -2.14529 q^{90} +4.72090 q^{91} -17.6297 q^{92} +2.91978 q^{93} +0.551414 q^{94} +3.33187 q^{95} +7.80304 q^{96} -16.2525 q^{97} -2.91391 q^{98} -2.09902 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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