LMFDB - Embedded newform 619.2.a.b.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [619,2,Mod(1,619)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(619, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("619.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 619 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	619.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:	$4.94273988512$
Analytic rank:	$0$
Dimension:	$30$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	619.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.938541 q^{2} +2.04590 q^{3} -1.11914 q^{4} +3.68832 q^{5} -1.92016 q^{6} -2.71706 q^{7} +2.92744 q^{8} +1.18571 q^{9} +O(q^{10})$	\(q-0.938541 q^{2} +2.04590 q^{3} -1.11914 q^{4} +3.68832 q^{5} -1.92016 q^{6} -2.71706 q^{7} +2.92744 q^{8} +1.18571 q^{9} -3.46164 q^{10} -2.41470 q^{11} -2.28965 q^{12} +5.06418 q^{13} +2.55007 q^{14} +7.54594 q^{15} -0.509241 q^{16} +2.79712 q^{17} -1.11283 q^{18} +4.67066 q^{19} -4.12775 q^{20} -5.55882 q^{21} +2.26630 q^{22} +2.15658 q^{23} +5.98925 q^{24} +8.60372 q^{25} -4.75294 q^{26} -3.71186 q^{27} +3.04077 q^{28} +0.405665 q^{29} -7.08217 q^{30} -2.87253 q^{31} -5.37694 q^{32} -4.94024 q^{33} -2.62521 q^{34} -10.0214 q^{35} -1.32697 q^{36} +4.37362 q^{37} -4.38361 q^{38} +10.3608 q^{39} +10.7973 q^{40} -2.91057 q^{41} +5.21718 q^{42} +4.39958 q^{43} +2.70239 q^{44} +4.37326 q^{45} -2.02404 q^{46} -4.68612 q^{47} -1.04186 q^{48} +0.382395 q^{49} -8.07494 q^{50} +5.72263 q^{51} -5.66753 q^{52} +5.90078 q^{53} +3.48374 q^{54} -8.90619 q^{55} -7.95402 q^{56} +9.55571 q^{57} -0.380734 q^{58} +2.92099 q^{59} -8.44497 q^{60} -8.81228 q^{61} +2.69599 q^{62} -3.22163 q^{63} +6.06496 q^{64} +18.6783 q^{65} +4.63661 q^{66} +6.63389 q^{67} -3.13037 q^{68} +4.41214 q^{69} +9.40547 q^{70} +1.75461 q^{71} +3.47108 q^{72} +11.6980 q^{73} -4.10482 q^{74} +17.6023 q^{75} -5.22713 q^{76} +6.56088 q^{77} -9.72404 q^{78} -17.0954 q^{79} -1.87824 q^{80} -11.1512 q^{81} +2.73169 q^{82} -9.17823 q^{83} +6.22111 q^{84} +10.3167 q^{85} -4.12919 q^{86} +0.829951 q^{87} -7.06889 q^{88} -10.6864 q^{89} -4.10449 q^{90} -13.7597 q^{91} -2.41352 q^{92} -5.87692 q^{93} +4.39811 q^{94} +17.2269 q^{95} -11.0007 q^{96} -6.48573 q^{97} -0.358893 q^{98} -2.86312 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) $ 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * 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 $

$2$	−0.938541	−0.663649	−0.331824	−	0.943341i	$-0.607664\pi$
$2$	−0.938541	−0.663649	−0.331824	+	0.943341i	$0.607664\pi$
$3$	2.04590	1.18120	0.590600	−	0.806964i	$-0.298891\pi$
$3$	2.04590	1.18120	0.590600	+	0.806964i	$0.298891\pi$
$4$	−1.11914	−0.559571
$5$	3.68832	1.64947	0.824734	−	0.565521i	$-0.191325\pi$
$5$	3.68832	1.64947	0.824734	+	0.565521i	$0.191325\pi$
$6$	−1.92016	−0.783902
$7$	−2.71706	−1.02695	−0.513475	−	0.858104i	$-0.671642\pi$
$7$	−2.71706	−1.02695	−0.513475	+	0.858104i	$0.671642\pi$
$8$	2.92744	1.03501
$9$	1.18571	0.395235
$10$	−3.46164	−1.09467
$11$	−2.41470	−0.728060	−0.364030	−	0.931387i	$-0.618599\pi$
$11$	−2.41470	−0.728060	−0.364030	+	0.931387i	$0.618599\pi$
$12$	−2.28965	−0.660965
$13$	5.06418	1.40455	0.702275	−	0.711905i	$-0.252168\pi$
$13$	5.06418	1.40455	0.702275	+	0.711905i	$0.252168\pi$
$14$	2.55007	0.681534
$15$	7.54594	1.94835
$16$	−0.509241	−0.127310
$17$	2.79712	0.678401	0.339201	−	0.940714i	$-0.389843\pi$
$17$	2.79712	0.678401	0.339201	+	0.940714i	$0.389843\pi$
$18$	−1.11283	−0.262297
$19$	4.67066	1.07152	0.535762	−	0.844369i	$-0.320024\pi$
$19$	4.67066	1.07152	0.535762	+	0.844369i	$0.320024\pi$
$20$	−4.12775	−0.922994
$21$	−5.55882	−1.21303
$22$	2.26630	0.483176
$23$	2.15658	0.449678	0.224839	−	0.974396i	$-0.427814\pi$
$23$	2.15658	0.449678	0.224839	+	0.974396i	$0.427814\pi$
$24$	5.98925	1.22255
$25$	8.60372	1.72074
$26$	−4.75294	−0.932128
$27$	−3.71186	−0.714349
$28$	3.04077	0.574651
$29$	0.405665	0.0753302	0.0376651	−	0.999290i	$-0.488008\pi$
$29$	0.405665	0.0753302	0.0376651	+	0.999290i	$0.488008\pi$
$30$	−7.08217	−1.29302
$31$	−2.87253	−0.515922	−0.257961	−	0.966155i	$-0.583051\pi$
$31$	−2.87253	−0.515922	−0.257961	+	0.966155i	$0.583051\pi$
$32$	−5.37694	−0.950518
$33$	−4.94024	−0.859985
$34$	−2.62521	−0.450220
$35$	−10.0214	−1.69392
$36$	−1.32697	−0.221162
$37$	4.37362	0.719019	0.359509	−	0.933141i	$-0.382944\pi$
$37$	4.37362	0.719019	0.359509	+	0.933141i	$0.382944\pi$
$38$	−4.38361	−0.711115
$39$	10.3608	1.65906
$40$	10.7973	1.70721
$41$	−2.91057	−0.454555	−0.227278	−	0.973830i	$-0.572982\pi$
$41$	−2.91057	−0.454555	−0.227278	+	0.973830i	$0.572982\pi$
$42$	5.21718	0.805029
$43$	4.39958	0.670930	0.335465	−	0.942053i	$-0.391107\pi$
$43$	4.39958	0.670930	0.335465	+	0.942053i	$0.391107\pi$
$44$	2.70239	0.407401
$45$	4.37326	0.651928
$46$	−2.02404	−0.298428
$47$	−4.68612	−0.683540	−0.341770	−	0.939784i	$-0.611026\pi$
$47$	−4.68612	−0.683540	−0.341770	+	0.939784i	$0.611026\pi$
$48$	−1.04186	−0.150379
$49$	0.382395	0.0546278
$50$	−8.07494	−1.14197
$51$	5.72263	0.801328
$52$	−5.66753	−0.785945
$53$	5.90078	0.810534	0.405267	−	0.914198i	$-0.367178\pi$
$53$	5.90078	0.810534	0.405267	+	0.914198i	$0.367178\pi$
$54$	3.48374	0.474076
$55$	−8.90619	−1.20091
$56$	−7.95402	−1.06290
$57$	9.55571	1.26568
$58$	−0.380734	−0.0499928
$59$	2.92099	0.380280	0.190140	−	0.981757i	$-0.439106\pi$
$59$	2.92099	0.380280	0.190140	+	0.981757i	$0.439106\pi$
$60$	−8.44497	−1.09024
$61$	−8.81228	−1.12830	−0.564148	−	0.825673i	$-0.690795\pi$
$61$	−8.81228	−1.12830	−0.564148	+	0.825673i	$0.690795\pi$
$62$	2.69599	0.342391
$63$	−3.22163	−0.405887
$64$	6.06496	0.758120
$65$	18.6783	2.31676
$66$	4.63661	0.570728
$67$	6.63389	0.810459	0.405230	−	0.914215i	$-0.367192\pi$
$67$	6.63389	0.810459	0.405230	+	0.914215i	$0.367192\pi$
$68$	−3.13037	−0.379613
$69$	4.41214	0.531160
$70$	9.40547	1.12417
$71$	1.75461	0.208234	0.104117	−	0.994565i	$-0.466798\pi$
$71$	1.75461	0.208234	0.104117	+	0.994565i	$0.466798\pi$
$72$	3.47108	0.409071
$73$	11.6980	1.36914	0.684571	−	0.728946i	$-0.259990\pi$
$73$	11.6980	1.36914	0.684571	+	0.728946i	$0.259990\pi$
$74$	−4.10482	−0.477176
$75$	17.6023	2.03254
$76$	−5.22713	−0.599593
$77$	6.56088	0.747681
$78$	−9.72404	−1.10103
$79$	−17.0954	−1.92338	−0.961690	−	0.274141i	$-0.911607\pi$
$79$	−17.0954	−1.92338	−0.961690	+	0.274141i	$0.911607\pi$
$80$	−1.87824	−0.209994
$81$	−11.1512	−1.23902
$82$	2.73169	0.301665
$83$	−9.17823	−1.00744	−0.503721	−	0.863867i	$-0.668036\pi$
$83$	−9.17823	−1.00744	−0.503721	+	0.863867i	$0.668036\pi$
$84$	6.22111	0.678779
$85$	10.3167	1.11900
$86$	−4.12919	−0.445262
$87$	0.829951	0.0889801
$88$	−7.06889	−0.753547
$89$	−10.6864	−1.13276	−0.566378	−	0.824146i	$-0.691656\pi$
$89$	−10.6864	−1.13276	−0.566378	+	0.824146i	$0.691656\pi$
$90$	−4.10449	−0.432651
$91$	−13.7597	−1.44240
$92$	−2.41352	−0.251627
$93$	−5.87692	−0.609408
$94$	4.39811	0.453630
$95$	17.2269	1.76744
$96$	−11.0007	−1.12275
$97$	−6.48573	−0.658526	−0.329263	−	0.944238i	$-0.606800\pi$
$97$	−6.48573	−0.658526	−0.329263	+	0.944238i	$0.606800\pi$
$98$	−0.358893	−0.0362537
$99$	−2.86312	−0.287755
$100$	−9.62877	−0.962877
$101$	13.6998	1.36318	0.681590	−	0.731734i	$-0.261289\pi$
$101$	13.6998	1.36318	0.681590	+	0.731734i	$0.261289\pi$
$102$	−5.37092	−0.531800
$103$	−19.4892	−1.92032	−0.960162	−	0.279444i	$-0.909850\pi$
$103$	−19.4892	−1.92032	−0.960162	+	0.279444i	$0.909850\pi$
$104$	14.8251	1.45372
$105$	−20.5027	−2.00086
$106$	−5.53812	−0.537910
$107$	4.56732	0.441540	0.220770	−	0.975326i	$-0.429143\pi$
$107$	4.56732	0.441540	0.220770	+	0.975326i	$0.429143\pi$
$108$	4.15410	0.399729
$109$	7.39066	0.707897	0.353949	−	0.935265i	$-0.384839\pi$
$109$	7.39066	0.707897	0.353949	+	0.935265i	$0.384839\pi$
$110$	8.35883	0.796983
$111$	8.94799	0.849305
$112$	1.38364	0.130741
$113$	18.9441	1.78211	0.891056	−	0.453894i	$-0.149965\pi$
$113$	18.9441	1.78211	0.891056	+	0.453894i	$0.149965\pi$
$114$	−8.96842	−0.839970
$115$	7.95416	0.741729
$116$	−0.453997	−0.0421526
$117$	6.00463	0.555128
$118$	−2.74147	−0.252373
$119$	−7.59993	−0.696685
$120$	22.0903	2.01656
$121$	−5.16922	−0.469929
$122$	8.27068	0.748793
$123$	−5.95474	−0.536921
$124$	3.21477	0.288695
$125$	13.2917	1.18884
$126$	3.02363	0.269366
$127$	3.05033	0.270673	0.135337	−	0.990800i	$-0.456788\pi$
$127$	3.05033	0.270673	0.135337	+	0.990800i	$0.456788\pi$
$128$	5.06167	0.447393
$129$	9.00110	0.792503
$130$	−17.5304	−1.53752
$131$	−12.7959	−1.11798	−0.558990	−	0.829174i	$-0.688811\pi$
$131$	−12.7959	−1.11798	−0.558990	+	0.829174i	$0.688811\pi$
$132$	5.52882	0.481222
$133$	−12.6905	−1.10040
$134$	−6.22618	−0.537860
$135$	−13.6906	−1.17829
$136$	8.18840	0.702150
$137$	−17.3319	−1.48076	−0.740380	−	0.672188i	$-0.765354\pi$
$137$	−17.3319	−1.48076	−0.740380	+	0.672188i	$0.765354\pi$
$138$	−4.14098	−0.352503
$139$	−12.8884	−1.09318	−0.546590	−	0.837401i	$-0.684074\pi$
$139$	−12.8884	−1.09318	−0.546590	+	0.837401i	$0.684074\pi$
$140$	11.2153	0.947869
$141$	−9.58732	−0.807398
$142$	−1.64677	−0.138194
$143$	−12.2285	−1.02260
$144$	−0.603809	−0.0503174
$145$	1.49622	0.124255
$146$	−10.9790	−0.908629
$147$	0.782341	0.0645264
$148$	−4.89470	−0.402342
$149$	−18.6003	−1.52380	−0.761898	−	0.647697i	$-0.775732\pi$
$149$	−18.6003	−1.52380	−0.761898	+	0.647697i	$0.775732\pi$
$150$	−16.5205	−1.34889
$151$	13.3926	1.08987	0.544936	−	0.838478i	$-0.316554\pi$
$151$	13.3926	1.08987	0.544936	+	0.838478i	$0.316554\pi$
$152$	13.6731	1.10903
$153$	3.31656	0.268128
$154$	−6.15765	−0.496198
$155$	−10.5948	−0.850997
$156$	−11.5952	−0.928359
$157$	−5.06098	−0.403910	−0.201955	−	0.979395i	$-0.564730\pi$
$157$	−5.06098	−0.403910	−0.201955	+	0.979395i	$0.564730\pi$
$158$	16.0447	1.27645
$159$	12.0724	0.957404
$160$	−19.8319	−1.56785
$161$	−5.85955	−0.461797
$162$	10.4659	0.822277
$163$	−10.1216	−0.792782	−0.396391	−	0.918082i	$-0.629738\pi$
$163$	−10.1216	−0.792782	−0.396391	+	0.918082i	$0.629738\pi$
$164$	3.25734	0.254356
$165$	−18.2212	−1.41852
$166$	8.61414	0.668587
$167$	11.3630	0.879299	0.439649	−	0.898169i	$-0.355103\pi$
$167$	11.3630	0.879299	0.439649	+	0.898169i	$0.355103\pi$
$168$	−16.2731	−1.25550
$169$	12.6459	0.972763
$170$	−9.68262	−0.742623
$171$	5.53803	0.423504
$172$	−4.92375	−0.375433
$173$	−18.1125	−1.37707	−0.688533	−	0.725205i	$-0.741745\pi$
$173$	−18.1125	−1.37707	−0.688533	+	0.725205i	$0.741745\pi$
$174$	−0.778943	−0.0590515
$175$	−23.3768	−1.76712
$176$	1.22966	0.0926894
$177$	5.97605	0.449188
$178$	10.0296	0.751751
$179$	9.43259	0.705025	0.352513	−	0.935807i	$-0.385327\pi$
$179$	9.43259	0.705025	0.352513	+	0.935807i	$0.385327\pi$
$180$	−4.89430	−0.364800
$181$	−24.5527	−1.82499	−0.912495	−	0.409089i	$-0.865847\pi$
$181$	−24.5527	−1.82499	−0.912495	+	0.409089i	$0.865847\pi$
$182$	12.9140	0.957250
$183$	−18.0290	−1.33275
$184$	6.31326	0.465420
$185$	16.1313	1.18600
$186$	5.51573	0.404433
$187$	−6.75421	−0.493916
$188$	5.24443	0.382489
$189$	10.0853	0.733601
$190$	−16.1682	−1.17296
$191$	−17.5270	−1.26821	−0.634106	−	0.773246i	$-0.718632\pi$
$191$	−17.5270	−1.26821	−0.634106	+	0.773246i	$0.718632\pi$
$192$	12.4083	0.895492
$193$	−22.6101	−1.62751	−0.813756	−	0.581206i	$-0.802581\pi$
$193$	−22.6101	−1.62751	−0.813756	+	0.581206i	$0.802581\pi$
$194$	6.08712	0.437030
$195$	38.2140	2.73656
$196$	−0.427954	−0.0305681
$197$	17.7717	1.26618	0.633091	−	0.774078i	$-0.281786\pi$
$197$	17.7717	1.26618	0.633091	+	0.774078i	$0.281786\pi$
$198$	2.68716	0.190968
$199$	−10.2870	−0.729228	−0.364614	−	0.931159i	$-0.618799\pi$
$199$	−10.2870	−0.729228	−0.364614	+	0.931159i	$0.618799\pi$
$200$	25.1869	1.78098
$201$	13.5723	0.957315
$202$	−12.8578	−0.904672
$203$	−1.10222	−0.0773604
$204$	−6.40443	−0.448400
$205$	−10.7351	−0.749774
$206$	18.2914	1.27442
$207$	2.55707	0.177729
$208$	−2.57889	−0.178814
$209$	−11.2783	−0.780133
$210$	19.2427	1.32787
$211$	15.1797	1.04502	0.522508	−	0.852634i	$-0.324996\pi$
$211$	15.1797	1.04502	0.522508	+	0.852634i	$0.324996\pi$
$212$	−6.60381	−0.453551
$213$	3.58976	0.245966
$214$	−4.28662	−0.293027
$215$	16.2271	1.10668
$216$	−10.8663	−0.739356
$217$	7.80484	0.529827
$218$	−6.93644	−0.469795
$219$	23.9328	1.61723
$220$	9.96729	0.671994
$221$	14.1651	0.952849
$222$	−8.39805	−0.563640
$223$	−18.6218	−1.24701	−0.623505	−	0.781820i	$-0.714292\pi$
$223$	−18.6218	−1.24701	−0.623505	+	0.781820i	$0.714292\pi$
$224$	14.6094	0.976135
$225$	10.2015	0.680098
$226$	−17.7798	−1.18270
$227$	−24.7238	−1.64098	−0.820488	−	0.571664i	$-0.806298\pi$
$227$	−24.7238	−1.64098	−0.820488	+	0.571664i	$0.806298\pi$
$228$	−10.6942	−0.708240
$229$	4.39930	0.290714	0.145357	−	0.989379i	$-0.453567\pi$
$229$	4.39930	0.290714	0.145357	+	0.989379i	$0.453567\pi$
$230$	−7.46530	−0.492247
$231$	13.4229	0.883162
$232$	1.18756	0.0779673
$233$	23.3827	1.53185	0.765926	−	0.642929i	$-0.222281\pi$
$233$	23.3827	1.53185	0.765926	+	0.642929i	$0.222281\pi$
$234$	−5.63559	−0.368410
$235$	−17.2839	−1.12748
$236$	−3.26900	−0.212794
$237$	−34.9754	−2.27190
$238$	7.13285	0.462354
$239$	19.1315	1.23752	0.618758	−	0.785582i	$-0.287636\pi$
$239$	19.1315	1.23752	0.618758	+	0.785582i	$0.287636\pi$
$240$	−3.84270	−0.248045
$241$	10.0131	0.644998	0.322499	−	0.946570i	$-0.395477\pi$
$241$	10.0131	0.644998	0.322499	+	0.946570i	$0.395477\pi$
$242$	4.85152	0.311868
$243$	−11.6787	−0.749188
$244$	9.86219	0.631362
$245$	1.41040	0.0901068
$246$	5.58877	0.356327
$247$	23.6531	1.50501
$248$	−8.40918	−0.533983
$249$	−18.7777	−1.18999
$250$	−12.4748	−0.788974
$251$	1.41992	0.0896248	0.0448124	−	0.998995i	$-0.485731\pi$
$251$	1.41992	0.0896248	0.0448124	+	0.998995i	$0.485731\pi$
$252$	3.60546	0.227122
$253$	−5.20749	−0.327392
$254$	−2.86286	−0.179632
$255$	21.1069	1.32176
$256$	−16.8805	−1.05503
$257$	24.5756	1.53298	0.766492	−	0.642254i	$-0.222000\pi$
$257$	24.5756	1.53298	0.766492	+	0.642254i	$0.222000\pi$
$258$	−8.44790	−0.525943
$259$	−11.8834	−0.738397
$260$	−20.9037	−1.29639
$261$	0.481000	0.0297731
$262$	12.0094	0.741946
$263$	28.8924	1.78158	0.890789	−	0.454416i	$-0.150152\pi$
$263$	28.8924	1.78158	0.890789	+	0.454416i	$0.150152\pi$
$264$	−14.4622	−0.890090
$265$	21.7640	1.33695
$266$	11.9105	0.730280
$267$	−21.8633	−1.33801
$268$	−7.42426	−0.453509
$269$	−17.2295	−1.05050	−0.525250	−	0.850948i	$-0.676028\pi$
$269$	−17.2295	−1.05050	−0.525250	+	0.850948i	$0.676028\pi$
$270$	12.8491	0.781974
$271$	19.4823	1.18347	0.591734	−	0.806133i	$-0.298444\pi$
$271$	19.4823	1.18347	0.591734	+	0.806133i	$0.298444\pi$
$272$	−1.42441	−0.0863673
$273$	−28.1509	−1.70377
$274$	16.2667	0.982704
$275$	−20.7754	−1.25280
$276$	−4.93781	−0.297221
$277$	11.3433	0.681554	0.340777	−	0.940144i	$-0.389310\pi$
$277$	11.3433	0.681554	0.340777	+	0.940144i	$0.389310\pi$
$278$	12.0963	0.725487
$279$	−3.40598	−0.203911
$280$	−29.3370	−1.75322
$281$	−19.3347	−1.15341	−0.576705	−	0.816952i	$-0.695662\pi$
$281$	−19.3347	−1.15341	−0.576705	+	0.816952i	$0.695662\pi$
$282$	8.99809	0.535829
$283$	10.2100	0.606923	0.303462	−	0.952844i	$-0.401858\pi$
$283$	10.2100	0.606923	0.303462	+	0.952844i	$0.401858\pi$
$284$	−1.96366	−0.116522
$285$	35.2445	2.08771
$286$	11.4769	0.678645
$287$	7.90819	0.466806
$288$	−6.37547	−0.375678
$289$	−9.17612	−0.539772
$290$	−1.40427	−0.0824615
$291$	−13.2692	−0.777852
$292$	−13.0917	−0.766132
$293$	12.0608	0.704600	0.352300	−	0.935887i	$-0.385400\pi$
$293$	12.0608	0.704600	0.352300	+	0.935887i	$0.385400\pi$
$294$	−0.734259	−0.0428229
$295$	10.7736	0.627260
$296$	12.8035	0.744189
$297$	8.96304	0.520088
$298$	17.4571	1.01126
$299$	10.9213	0.631595
$300$	−19.6995	−1.13735
$301$	−11.9539	−0.689012
$302$	−12.5695	−0.723292
$303$	28.0284	1.61019
$304$	−2.37849	−0.136416
$305$	−32.5025	−1.86109
$306$	−3.11273	−0.177943
$307$	−0.550676	−0.0314288	−0.0157144	−	0.999877i	$-0.505002\pi$
$307$	−0.550676	−0.0314288	−0.0157144	+	0.999877i	$0.505002\pi$
$308$	−7.34255	−0.418381
$309$	−39.8729	−2.26829
$310$	9.94368	0.564763
$311$	19.9296	1.13010	0.565051	−	0.825056i	$-0.308857\pi$
$311$	19.9296	1.13010	0.565051	+	0.825056i	$0.308857\pi$
$312$	30.3306	1.71713
$313$	−21.7539	−1.22961	−0.614803	−	0.788681i	$-0.710764\pi$
$313$	−21.7539	−1.22961	−0.614803	+	0.788681i	$0.710764\pi$
$314$	4.74994	0.268055
$315$	−11.8824	−0.669498
$316$	19.1321	1.07627
$317$	−16.7111	−0.938588	−0.469294	−	0.883042i	$-0.655492\pi$
$317$	−16.7111	−0.938588	−0.469294	+	0.883042i	$0.655492\pi$
$318$	−11.3304	−0.635380
$319$	−0.979561	−0.0548449
$320$	22.3695	1.25049
$321$	9.34428	0.521547
$322$	5.49942	0.306471
$323$	13.0644	0.726923
$324$	12.4798	0.693322
$325$	43.5708	2.41687
$326$	9.49950	0.526129
$327$	15.1206	0.836169
$328$	−8.52054	−0.470468
$329$	12.7324	0.701962
$330$	17.1013	0.941397
$331$	−8.57405	−0.471273	−0.235636	−	0.971841i	$-0.575717\pi$
$331$	−8.57405	−0.471273	−0.235636	+	0.971841i	$0.575717\pi$
$332$	10.2717	0.563734
$333$	5.18583	0.284181
$334$	−10.6647	−0.583545
$335$	24.4679	1.33683
$336$	2.83078	0.154432
$337$	6.53912	0.356209	0.178104	−	0.984012i	$-0.443004\pi$
$337$	6.53912	0.356209	0.178104	+	0.984012i	$0.443004\pi$
$338$	−11.8687	−0.645572
$339$	38.7577	2.10503
$340$	−11.5458	−0.626160
$341$	6.93631	0.375622
$342$	−5.19767	−0.281058
$343$	17.9804	0.970851
$344$	12.8795	0.694417
$345$	16.2734	0.876131
$346$	16.9993	0.913888
$347$	−13.6009	−0.730136	−0.365068	−	0.930981i	$-0.618954\pi$
$347$	−13.6009	−0.730136	−0.365068	+	0.930981i	$0.618954\pi$
$348$	−0.928832	−0.0497906
$349$	−8.81304	−0.471751	−0.235876	−	0.971783i	$-0.575796\pi$
$349$	−8.81304	−0.471751	−0.235876	+	0.971783i	$0.575796\pi$
$350$	21.9401	1.17275
$351$	−18.7975	−1.00334
$352$	12.9837	0.692034
$353$	−10.1022	−0.537688	−0.268844	−	0.963184i	$-0.586642\pi$
$353$	−10.1022	−0.537688	−0.268844	+	0.963184i	$0.586642\pi$
$354$	−5.60877	−0.298103
$355$	6.47157	0.343475
$356$	11.9596	0.633857
$357$	−15.5487	−0.822924
$358$	−8.85287	−0.467889
$359$	21.5410	1.13689	0.568445	−	0.822721i	$-0.307545\pi$
$359$	21.5410	1.13689	0.568445	+	0.822721i	$0.307545\pi$
$360$	12.8025	0.674750
$361$	2.81510	0.148163
$362$	23.0437	1.21115
$363$	−10.5757	−0.555081
$364$	15.3990	0.807127
$365$	43.1458	2.25836
$366$	16.9210	0.884474
$367$	7.76452	0.405305	0.202652	−	0.979251i	$-0.435044\pi$
$367$	7.76452	0.405305	0.202652	+	0.979251i	$0.435044\pi$
$368$	−1.09822	−0.0572486
$369$	−3.45108	−0.179656
$370$	−15.1399	−0.787086
$371$	−16.0328	−0.832379
$372$	6.57710	0.341007
$373$	29.4708	1.52594	0.762970	−	0.646434i	$-0.223740\pi$
$373$	29.4708	1.52594	0.762970	+	0.646434i	$0.223740\pi$
$374$	6.33910	0.327787
$375$	27.1934	1.40426
$376$	−13.7183	−0.707469
$377$	2.05436	0.105805
$378$	−9.46551	−0.486853
$379$	8.31615	0.427172	0.213586	−	0.976924i	$-0.431486\pi$
$379$	8.31615	0.427172	0.213586	+	0.976924i	$0.431486\pi$
$380$	−19.2793	−0.989009
$381$	6.24068	0.319720
$382$	16.4498	0.841647
$383$	5.60989	0.286652	0.143326	−	0.989676i	$-0.454220\pi$
$383$	5.60989	0.286652	0.143326	+	0.989676i	$0.454220\pi$
$384$	10.3557	0.528460
$385$	24.1986	1.23328
$386$	21.2205	1.08010
$387$	5.21661	0.265175
$388$	7.25845	0.368492
$389$	−0.563342	−0.0285626	−0.0142813	−	0.999898i	$-0.504546\pi$
$389$	−0.563342	−0.0285626	−0.0142813	+	0.999898i	$0.504546\pi$
$390$	−35.8654	−1.81611
$391$	6.03221	0.305062
$392$	1.11944	0.0565402
$393$	−26.1791	−1.32056
$394$	−16.6795	−0.840299
$395$	−63.0532	−3.17255
$396$	3.20424	0.161019
$397$	−7.43322	−0.373063	−0.186531	−	0.982449i	$-0.559725\pi$
$397$	−7.43322	−0.373063	−0.186531	+	0.982449i	$0.559725\pi$
$398$	9.65480	0.483951
$399$	−25.9634	−1.29980
$400$	−4.38136	−0.219068
$401$	15.9423	0.796119	0.398059	−	0.917360i	$-0.369684\pi$
$401$	15.9423	0.796119	0.398059	+	0.917360i	$0.369684\pi$
$402$	−12.7381	−0.635321
$403$	−14.5470	−0.724639
$404$	−15.3320	−0.762795
$405$	−41.1293	−2.04373
$406$	1.03447	0.0513401
$407$	−10.5610	−0.523488
$408$	16.7527	0.829380
$409$	−28.5003	−1.40925	−0.704624	−	0.709581i	$-0.748884\pi$
$409$	−28.5003	−1.40925	−0.704624	+	0.709581i	$0.748884\pi$
$410$	10.0754	0.497587
$411$	−35.4592	−1.74908
$412$	21.8111	1.07456
$413$	−7.93649	−0.390529
$414$	−2.39991	−0.117949
$415$	−33.8522	−1.66174
$416$	−27.2298	−1.33505
$417$	−26.3684	−1.29126
$418$	10.5851	0.517734
$419$	4.52331	0.220978	0.110489	−	0.993877i	$-0.464758\pi$
$419$	4.52331	0.220978	0.110489	+	0.993877i	$0.464758\pi$
$420$	22.9455	1.11962
$421$	16.3341	0.796074	0.398037	−	0.917369i	$-0.369692\pi$
$421$	16.3341	0.796074	0.398037	+	0.917369i	$0.369692\pi$
$422$	−14.2468	−0.693523
$423$	−5.55635	−0.270159
$424$	17.2742	0.838909
$425$	24.0656	1.16735
$426$	−3.36913	−0.163235
$427$	23.9435	1.15871
$428$	−5.11148	−0.247073
$429$	−25.0182	−1.20789
$430$	−15.2298	−0.734445
$431$	−3.98556	−0.191978	−0.0959889	−	0.995382i	$-0.530601\pi$
$431$	−3.98556	−0.191978	−0.0959889	+	0.995382i	$0.530601\pi$
$432$	1.89023	0.0909438
$433$	26.3837	1.26792	0.633959	−	0.773366i	$-0.281429\pi$
$433$	26.3837	1.26792	0.633959	+	0.773366i	$0.281429\pi$
$434$	−7.32516	−0.351619
$435$	3.06113	0.146770
$436$	−8.27120	−0.396118
$437$	10.0727	0.481840
$438$	−22.4620	−1.07327
$439$	32.3911	1.54595	0.772973	−	0.634439i	$-0.218769\pi$
$439$	32.3911	1.54595	0.772973	+	0.634439i	$0.218769\pi$
$440$	−26.0724	−1.24295
$441$	0.453408	0.0215908
$442$	−13.2945	−0.632357
$443$	−2.29328	−0.108957	−0.0544785	−	0.998515i	$-0.517350\pi$
$443$	−2.29328	−0.108957	−0.0544785	+	0.998515i	$0.517350\pi$
$444$	−10.0141	−0.475246
$445$	−39.4149	−1.86844
$446$	17.4773	0.827576
$447$	−38.0543	−1.79991
$448$	−16.4788	−0.778552
$449$	19.5422	0.922254	0.461127	−	0.887334i	$-0.347445\pi$
$449$	19.5422	0.922254	0.461127	+	0.887334i	$0.347445\pi$
$450$	−9.57450	−0.451346
$451$	7.02817	0.330943
$452$	−21.2011	−0.997217
$453$	27.3998	1.28736
$454$	23.2043	1.08903
$455$	−50.7501	−2.37920
$456$	27.9738	1.30999
$457$	−4.68139	−0.218986	−0.109493	−	0.993988i	$-0.534923\pi$
$457$	−4.68139	−0.218986	−0.109493	+	0.993988i	$0.534923\pi$
$458$	−4.12892	−0.192932
$459$	−10.3825	−0.484615
$460$	−8.90183	−0.415050
$461$	8.93426	0.416110	0.208055	−	0.978117i	$-0.433287\pi$
$461$	8.93426	0.416110	0.208055	+	0.978117i	$0.433287\pi$
$462$	−12.5979	−0.586109
$463$	−30.6401	−1.42397	−0.711983	−	0.702197i	$-0.752203\pi$
$463$	−30.6401	−1.42397	−0.711983	+	0.702197i	$0.752203\pi$
$464$	−0.206581	−0.00959030
$465$	−21.6760	−1.00520
$466$	−21.9456	−1.01661
$467$	−26.9036	−1.24495	−0.622475	−	0.782640i	$-0.713873\pi$
$467$	−26.9036	−1.24495	−0.622475	+	0.782640i	$0.713873\pi$
$468$	−6.72002	−0.310633
$469$	−18.0247	−0.832301
$470$	16.2216	0.748249
$471$	−10.3543	−0.477099
$472$	8.55103	0.393593
$473$	−10.6237	−0.488477
$474$	32.8258	1.50774
$475$	40.1851	1.84382
$476$	8.50540	0.389844
$477$	6.99659	0.320352
$478$	−17.9557	−0.821276
$479$	33.0101	1.50827	0.754135	−	0.656719i	$-0.228056\pi$
$479$	33.0101	1.50827	0.754135	+	0.656719i	$0.228056\pi$
$480$	−40.5740	−1.85194
$481$	22.1488	1.00990
$482$	−9.39766	−0.428052
$483$	−11.9880	−0.545475
$484$	5.78509	0.262959
$485$	−23.9215	−1.08622
$486$	10.9609	0.497197
$487$	−22.0103	−0.997383	−0.498691	−	0.866780i	$-0.666186\pi$
$487$	−22.0103	−0.997383	−0.498691	+	0.866780i	$0.666186\pi$
$488$	−25.7974	−1.16779
$489$	−20.7077	−0.936435
$490$	−1.32371	−0.0597993
$491$	−23.2875	−1.05095	−0.525474	−	0.850809i	$-0.676112\pi$
$491$	−23.2875	−1.05095	−0.525474	+	0.850809i	$0.676112\pi$
$492$	6.66420	0.300445
$493$	1.13469	0.0511041
$494$	−22.1994	−0.998797
$495$	−10.5601	−0.474642
$496$	1.46281	0.0656822
$497$	−4.76737	−0.213846
$498$	17.6237	0.789735
$499$	20.0711	0.898507	0.449254	−	0.893404i	$-0.351690\pi$
$499$	20.0711	0.898507	0.449254	+	0.893404i	$0.351690\pi$
$500$	−14.8753	−0.665242
$501$	23.2476	1.03863
$502$	−1.33266	−0.0594794
$503$	10.8823	0.485218	0.242609	−	0.970124i	$-0.421997\pi$
$503$	10.8823	0.485218	0.242609	+	0.970124i	$0.421997\pi$
$504$	−9.43113	−0.420096
$505$	50.5292	2.24852
$506$	4.88745	0.217273
$507$	25.8723	1.14903
$508$	−3.41375	−0.151461
$509$	3.58455	0.158883	0.0794413	−	0.996840i	$-0.474686\pi$
$509$	3.58455	0.158883	0.0794413	+	0.996840i	$0.474686\pi$
$510$	−19.8097	−0.877187
$511$	−31.7840	−1.40604
$512$	5.71970	0.252777
$513$	−17.3369	−0.765441
$514$	−23.0652	−1.01736
$515$	−71.8823	−3.16751
$516$	−10.0735	−0.443461
$517$	11.3156	0.497658
$518$	11.1530	0.490036
$519$	−37.0563	−1.62659
$520$	54.6797	2.39786
$521$	5.42122	0.237508	0.118754	−	0.992924i	$-0.462110\pi$
$521$	5.42122	0.237508	0.118754	+	0.992924i	$0.462110\pi$
$522$	−0.451438	−0.0197589
$523$	−42.6840	−1.86644	−0.933220	−	0.359306i	$-0.883013\pi$
$523$	−42.6840	−1.86644	−0.933220	+	0.359306i	$0.883013\pi$
$524$	14.3204	0.625589
$525$	−47.8266	−2.08732
$526$	−27.1167	−1.18234
$527$	−8.03482	−0.350002
$528$	2.51577	0.109485
$529$	−18.3492	−0.797790
$530$	−20.4264	−0.887265
$531$	3.46343	0.150300
$532$	14.2024	0.615753
$533$	−14.7397	−0.638446
$534$	20.5196	0.887969
$535$	16.8458	0.728305
$536$	19.4203	0.838831
$537$	19.2981	0.832776
$538$	16.1706	0.697163
$539$	−0.923369	−0.0397723
$540$	15.3217	0.659339
$541$	−12.2836	−0.528113	−0.264057	−	0.964507i	$-0.585061\pi$
$541$	−12.2836	−0.528113	−0.264057	+	0.964507i	$0.585061\pi$
$542$	−18.2850	−0.785407
$543$	−50.2324	−2.15568
$544$	−15.0399	−0.644832
$545$	27.2591	1.16765
$546$	26.4208	1.13070
$547$	−19.4082	−0.829836	−0.414918	−	0.909859i	$-0.636190\pi$
$547$	−19.4082	−0.829836	−0.414918	+	0.909859i	$0.636190\pi$
$548$	19.3968	0.828590
$549$	−10.4488	−0.445943
$550$	19.4986	0.831422
$551$	1.89473	0.0807181
$552$	12.9163	0.549754
$553$	46.4491	1.97522
$554$	−10.6462	−0.452312
$555$	33.0031	1.40090
$556$	14.4239	0.611711
$557$	−12.9922	−0.550498	−0.275249	−	0.961373i	$-0.588760\pi$
$557$	−12.9922	−0.550498	−0.275249	+	0.961373i	$0.588760\pi$
$558$	3.19665	0.135325
$559$	22.2803	0.942355
$560$	5.10329	0.215653
$561$	−13.8184	−0.583415
$562$	18.1464	0.765459
$563$	−32.6802	−1.37731	−0.688653	−	0.725091i	$-0.741798\pi$
$563$	−32.6802	−1.37731	−0.688653	+	0.725091i	$0.741798\pi$
$564$	10.7296	0.451796
$565$	69.8720	2.93954
$566$	−9.58253	−0.402784
$567$	30.2985	1.27242
$568$	5.13652	0.215524
$569$	28.2125	1.18273	0.591365	−	0.806404i	$-0.298589\pi$
$569$	28.2125	1.18273	0.591365	+	0.806404i	$0.298589\pi$
$570$	−33.0784	−1.38550
$571$	6.12528	0.256335	0.128168	−	0.991753i	$-0.459090\pi$
$571$	6.12528	0.256335	0.128168	+	0.991753i	$0.459090\pi$
$572$	13.6854	0.572215
$573$	−35.8586	−1.49801
$574$	−7.42216	−0.309795
$575$	18.5546	0.773780
$576$	7.19125	0.299636
$577$	6.27920	0.261406	0.130703	−	0.991422i	$-0.458277\pi$
$577$	6.27920	0.261406	0.130703	+	0.991422i	$0.458277\pi$
$578$	8.61217	0.358219
$579$	−46.2580	−1.92242
$580$	−1.67449	−0.0695293
$581$	24.9378	1.03459
$582$	12.4536	0.516220
$583$	−14.2486	−0.590117
$584$	34.2451	1.41707
$585$	22.1470	0.915665
$586$	−11.3196	−0.467606
$587$	11.0713	0.456961	0.228481	−	0.973548i	$-0.426624\pi$
$587$	11.0713	0.456961	0.228481	+	0.973548i	$0.426624\pi$
$588$	−0.875551	−0.0361071
$589$	−13.4166	−0.552823
$590$	−10.1114	−0.416280
$591$	36.3591	1.49561
$592$	−2.22722	−0.0915384
$593$	5.98380	0.245725	0.122863	−	0.992424i	$-0.460793\pi$
$593$	5.98380	0.245725	0.122863	+	0.992424i	$0.460793\pi$
$594$	−8.41218	−0.345156
$595$	−28.0310	−1.14916
$596$	20.8164	0.852671
$597$	−21.0462	−0.861365
$598$	−10.2501	−0.419157
$599$	−17.4424	−0.712679	−0.356339	−	0.934357i	$-0.615975\pi$
$599$	−17.4424	−0.712679	−0.356339	+	0.934357i	$0.615975\pi$
$600$	51.5298	2.10370
$601$	44.5375	1.81672	0.908362	−	0.418185i	$-0.137334\pi$
$601$	44.5375	1.81672	0.908362	+	0.418185i	$0.137334\pi$
$602$	11.2192	0.457262
$603$	7.86584	0.320322
$604$	−14.9882	−0.609860
$605$	−19.0657	−0.775133
$606$	−26.3058	−1.06860
$607$	16.9812	0.689244	0.344622	−	0.938742i	$-0.388007\pi$
$607$	16.9812	0.689244	0.344622	+	0.938742i	$0.388007\pi$
$608$	−25.1139	−1.01850
$609$	−2.25502	−0.0913781
$610$	30.5049	1.23511
$611$	−23.7313	−0.960067
$612$	−3.71170	−0.150037
$613$	39.8340	1.60888	0.804439	−	0.594035i	$-0.202466\pi$
$613$	39.8340	1.60888	0.804439	+	0.594035i	$0.202466\pi$
$614$	0.516832	0.0208577
$615$	−21.9630	−0.885634
$616$	19.2066	0.773855
$617$	8.08667	0.325557	0.162779	−	0.986663i	$-0.447954\pi$
$617$	8.08667	0.325557	0.162779	+	0.986663i	$0.447954\pi$
$618$	37.4223	1.50535
$619$	1.00000	0.0401934
$619$	1.00000	0.0401934
$620$	11.8571	0.476193
$621$	−8.00493	−0.321227
$622$	−18.7047	−0.749990
$623$	29.0355	1.16328
$624$	−5.27614	−0.211215
$625$	6.00537	0.240215
$626$	20.4170	0.816026
$627$	−23.0742	−0.921494
$628$	5.66395	0.226016
$629$	12.2335	0.487783
$630$	11.1521	0.444311
$631$	13.6691	0.544158	0.272079	−	0.962275i	$-0.412289\pi$
$631$	13.6691	0.544158	0.272079	+	0.962275i	$0.412289\pi$
$632$	−50.0457	−1.99071
$633$	31.0562	1.23437
$634$	15.6840	0.622893
$635$	11.2506	0.446467
$636$	−13.5107	−0.535735
$637$	1.93652	0.0767276
$638$	0.919358	0.0363977
$639$	2.08045	0.0823014
$640$	18.6691	0.737959
$641$	26.9643	1.06503	0.532513	−	0.846422i	$-0.321248\pi$
$641$	26.9643	1.06503	0.532513	+	0.846422i	$0.321248\pi$
$642$	−8.76999	−0.346124
$643$	−36.6704	−1.44614	−0.723069	−	0.690775i	$-0.757269\pi$
$643$	−36.6704	−1.44614	−0.723069	+	0.690775i	$0.757269\pi$
$644$	6.55766	0.258408
$645$	33.1990	1.30721
$646$	−12.2615	−0.482421
$647$	−10.7513	−0.422676	−0.211338	−	0.977413i	$-0.567782\pi$
$647$	−10.7513	−0.422676	−0.211338	+	0.977413i	$0.567782\pi$
$648$	−32.6445	−1.28240
$649$	−7.05332	−0.276867
$650$	−40.8929	−1.60395
$651$	15.9679	0.625832
$652$	11.3275	0.443618
$653$	−29.5031	−1.15455	−0.577273	−	0.816552i	$-0.695883\pi$
$653$	−29.5031	−1.15455	−0.577273	+	0.816552i	$0.695883\pi$
$654$	−14.1913	−0.554922
$655$	−47.1953	−1.84407
$656$	1.48218	0.0578695
$657$	13.8703	0.541133
$658$	−11.9499	−0.465856
$659$	33.1605	1.29175	0.645874	−	0.763444i	$-0.276493\pi$
$659$	33.1605	1.29175	0.645874	+	0.763444i	$0.276493\pi$
$660$	20.3921	0.793760
$661$	−9.47927	−0.368701	−0.184350	−	0.982861i	$-0.559018\pi$
$661$	−9.47927	−0.368701	−0.184350	+	0.982861i	$0.559018\pi$
$662$	8.04710	0.312759
$663$	28.9804	1.12551
$664$	−26.8687	−1.04271
$665$	−46.8065	−1.81508
$666$	−4.86711	−0.188597
$667$	0.874850	0.0338743
$668$	−12.7169	−0.492030
$669$	−38.0984	−1.47297
$670$	−22.9642	−0.887183
$671$	21.2790	0.821467
$672$	29.8895	1.15301
$673$	−35.0763	−1.35209	−0.676046	−	0.736859i	$-0.736308\pi$
$673$	−35.0763	−1.35209	−0.676046	+	0.736859i	$0.736308\pi$
$674$	−6.13723	−0.236397
$675$	−31.9358	−1.22921
$676$	−14.1526	−0.544329
$677$	45.3854	1.74430	0.872152	−	0.489235i	$-0.162724\pi$
$677$	45.3854	1.74430	0.872152	+	0.489235i	$0.162724\pi$
$678$	−36.3757	−1.39700
$679$	17.6221	0.676274
$680$	30.2015	1.15817
$681$	−50.5824	−1.93832
$682$	−6.51001	−0.249281
$683$	38.5031	1.47328	0.736640	−	0.676285i	$-0.236411\pi$
$683$	38.5031	1.47328	0.736640	+	0.676285i	$0.236411\pi$
$684$	−6.19784	−0.236980
$685$	−63.9255	−2.44247
$686$	−16.8753	−0.644304
$687$	9.00052	0.343391
$688$	−2.24045	−0.0854162
$689$	29.8826	1.13844
$690$	−15.2733	−0.581443
$691$	45.9369	1.74752	0.873761	−	0.486356i	$-0.161674\pi$
$691$	45.9369	1.74752	0.873761	+	0.486356i	$0.161674\pi$
$692$	20.2704	0.770566
$693$	7.77927	0.295510
$694$	12.7650	0.484554
$695$	−47.5365	−1.80316
$696$	2.42963	0.0920950
$697$	−8.14122	−0.308371
$698$	8.27140	0.313077
$699$	47.8387	1.80942
$700$	26.1619	0.988828
$701$	45.3751	1.71380	0.856898	−	0.515486i	$-0.172389\pi$
$701$	45.3751	1.71380	0.856898	+	0.515486i	$0.172389\pi$
$702$	17.6423	0.665864
$703$	20.4277	0.770446
$704$	−14.6451	−0.551956
$705$	−35.3611	−1.33178
$706$	9.48137	0.356836
$707$	−37.2231	−1.39992
$708$	−6.68805	−0.251352
$709$	46.4351	1.74391	0.871954	−	0.489589i	$-0.162853\pi$
$709$	46.4351	1.74391	0.871954	+	0.489589i	$0.162853\pi$
$710$	−6.07383	−0.227947
$711$	−20.2701	−0.760187
$712$	−31.2838	−1.17241
$713$	−6.19485	−0.231999
$714$	14.5931	0.546133
$715$	−45.1026	−1.68674
$716$	−10.5564	−0.394511
$717$	39.1412	1.46176
$718$	−20.2171	−0.754495
$719$	27.1580	1.01282	0.506410	−	0.862293i	$-0.330972\pi$
$719$	27.1580	1.01282	0.506410	+	0.862293i	$0.330972\pi$
$720$	−2.22704	−0.0829970
$721$	52.9532	1.97208
$722$	−2.64208	−0.0983281
$723$	20.4857	0.761872
$724$	27.4780	1.02121
$725$	3.49023	0.129624
$726$	9.92573	0.368378
$727$	−5.60126	−0.207739	−0.103870	−	0.994591i	$-0.533122\pi$
$727$	−5.60126	−0.207739	−0.103870	+	0.994591i	$0.533122\pi$
$728$	−40.2806	−1.49290
$729$	9.56024	0.354083
$730$	−40.4941	−1.49875
$731$	12.3062	0.455160
$732$	20.1770	0.745765
$733$	11.3772	0.420225	0.210113	−	0.977677i	$-0.432617\pi$
$733$	11.3772	0.420225	0.210113	+	0.977677i	$0.432617\pi$
$734$	−7.28732	−0.268980
$735$	2.88553	0.106434
$736$	−11.5958	−0.427427
$737$	−16.0189	−0.590063
$738$	3.23898	0.119229
$739$	17.4817	0.643076	0.321538	−	0.946897i	$-0.395800\pi$
$739$	17.4817	0.643076	0.321538	+	0.946897i	$0.395800\pi$
$740$	−18.0532	−0.663650
$741$	48.3918	1.77772
$742$	15.0474	0.552407
$743$	0.403961	0.0148199	0.00740994	−	0.999973i	$-0.497641\pi$
$743$	0.403961	0.0148199	0.00740994	+	0.999973i	$0.497641\pi$
$744$	−17.2043	−0.630741
$745$	−68.6039	−2.51345
$746$	−27.6596	−1.01269
$747$	−10.8827	−0.398176
$748$	7.55891	0.276381
$749$	−12.4097	−0.453439
$750$	−25.5221	−0.931937
$751$	−32.7479	−1.19499	−0.597494	−	0.801874i	$-0.703837\pi$
$751$	−32.7479	−1.19499	−0.597494	+	0.801874i	$0.703837\pi$
$752$	2.38636	0.0870216
$753$	2.90502	0.105865
$754$	−1.92810	−0.0702174
$755$	49.3961	1.79771
$756$	−11.2869	−0.410501
$757$	−26.3257	−0.956823	−0.478411	−	0.878136i	$-0.658787\pi$
$757$	−26.3257	−0.956823	−0.478411	+	0.878136i	$0.658787\pi$
$758$	−7.80505	−0.283492
$759$	−10.6540	−0.386716
$760$	50.4308	1.82932
$761$	−22.9125	−0.830578	−0.415289	−	0.909689i	$-0.636320\pi$
$761$	−22.9125	−0.830578	−0.415289	+	0.909689i	$0.636320\pi$
$762$	−5.85713	−0.212181
$763$	−20.0809	−0.726976
$764$	19.6152	0.709654
$765$	12.2325	0.442268
$766$	−5.26511	−0.190236
$767$	14.7924	0.534123
$768$	−34.5358	−1.24620
$769$	9.94215	0.358523	0.179262	−	0.983801i	$-0.442629\pi$
$769$	9.94215	0.358523	0.179262	+	0.983801i	$0.442629\pi$
$770$	−22.7114	−0.818462
$771$	50.2792	1.81076
$772$	25.3039	0.910708
$773$	−33.5600	−1.20707	−0.603535	−	0.797337i	$-0.706242\pi$
$773$	−33.5600	−1.20707	−0.603535	+	0.797337i	$0.706242\pi$
$774$	−4.89600	−0.175983
$775$	−24.7145	−0.887770
$776$	−18.9866	−0.681579
$777$	−24.3122	−0.872195
$778$	0.528719	0.0189555
$779$	−13.5943	−0.487067
$780$	−42.7668	−1.53130
$781$	−4.23686	−0.151607
$782$	−5.66148	−0.202454
$783$	−1.50578	−0.0538120
$784$	−0.194731	−0.00695468
$785$	−18.6665	−0.666237
$786$	24.5701	0.876387
$787$	−22.0758	−0.786916	−0.393458	−	0.919343i	$-0.628721\pi$
$787$	−22.0758	−0.786916	−0.393458	+	0.919343i	$0.628721\pi$
$788$	−19.8890	−0.708518
$789$	59.1109	2.10440
$790$	59.1780	2.10546
$791$	−51.4722	−1.83014
$792$	−8.38163	−0.297828
$793$	−44.6270	−1.58475
$794$	6.97638	0.247582
$795$	44.5269	1.57921
$796$	11.5126	0.408055
$797$	10.0663	0.356567	0.178283	−	0.983979i	$-0.442946\pi$
$797$	10.0663	0.356567	0.178283	+	0.983979i	$0.442946\pi$
$798$	24.3677	0.862608
$799$	−13.1076	−0.463714
$800$	−46.2617	−1.63560
$801$	−12.6709	−0.447705
$802$	−14.9625	−0.528343
$803$	−28.2471	−0.996817
$804$	−15.1893	−0.535685
$805$	−21.6119	−0.761719
$806$	13.6530	0.480906
$807$	−35.2498	−1.24085
$808$	40.1053	1.41090
$809$	28.9342	1.01727	0.508635	−	0.860982i	$-0.330150\pi$
$809$	28.9342	1.01727	0.508635	+	0.860982i	$0.330150\pi$
$810$	38.6015	1.35632
$811$	−43.6513	−1.53280	−0.766402	−	0.642362i	$-0.777955\pi$
$811$	−43.6513	−1.53280	−0.766402	+	0.642362i	$0.777955\pi$
$812$	1.23354	0.0432886
$813$	39.8589	1.39791
$814$	9.91191	0.347412
$815$	−37.3316	−1.30767
$816$	−2.91419	−0.102017
$817$	20.5490	0.718917
$818$	26.7487	0.935246
$819$	−16.3149	−0.570089
$820$	12.0141	0.419552
$821$	23.3643	0.815420	0.407710	−	0.913112i	$-0.366328\pi$
$821$	23.3643	0.815420	0.407710	+	0.913112i	$0.366328\pi$
$822$	33.2799	1.16077
$823$	−12.8335	−0.447346	−0.223673	−	0.974664i	$-0.571805\pi$
$823$	−12.8335	−0.447346	−0.223673	+	0.974664i	$0.571805\pi$
$824$	−57.0534	−1.98755
$825$	−42.5044	−1.47981
$826$	7.44872	0.259174
$827$	39.1758	1.36227	0.681137	−	0.732156i	$-0.261486\pi$
$827$	39.1758	1.36227	0.681137	+	0.732156i	$0.261486\pi$
$828$	−2.86172	−0.0994517
$829$	−1.61275	−0.0560133	−0.0280066	−	0.999608i	$-0.508916\pi$
$829$	−1.61275	−0.0560133	−0.0280066	+	0.999608i	$0.508916\pi$
$830$	31.7717	1.10281
$831$	23.2073	0.805052
$832$	30.7140	1.06482
$833$	1.06960	0.0370596
$834$	24.7478	0.856945
$835$	41.9106	1.45037
$836$	12.6220	0.436540
$837$	10.6625	0.368549
$838$	−4.24531	−0.146652
$839$	36.9833	1.27680	0.638402	−	0.769703i	$-0.279596\pi$
$839$	36.9833	1.27680	0.638402	+	0.769703i	$0.279596\pi$
$840$	−60.0205	−2.07091
$841$	−28.8354	−0.994325
$842$	−15.3302	−0.528313
$843$	−39.5568	−1.36241
$844$	−16.9883	−0.584760
$845$	46.6422	1.60454
$846$	5.21486	0.179291
$847$	14.0451	0.482594
$848$	−3.00492	−0.103189
$849$	20.8887	0.716898
$850$	−22.5866	−0.774713
$851$	9.43206	0.323327
$852$	−4.01744	−0.137635
$853$	34.2323	1.17209	0.586046	−	0.810278i	$-0.300684\pi$
$853$	34.2323	1.17209	0.586046	+	0.810278i	$0.300684\pi$
$854$	−22.4719	−0.768973
$855$	20.4260	0.698556
$856$	13.3706	0.456996
$857$	−15.6699	−0.535275	−0.267637	−	0.963520i	$-0.586243\pi$
$857$	−15.6699	−0.535275	−0.267637	+	0.963520i	$0.586243\pi$
$858$	23.4806	0.801616
$859$	−52.0826	−1.77703	−0.888517	−	0.458844i	$-0.848264\pi$
$859$	−52.0826	−1.77703	−0.888517	+	0.458844i	$0.848264\pi$
$860$	−18.1604	−0.619264
$861$	16.1794	0.551392
$862$	3.74061	0.127406
$863$	48.0878	1.63693	0.818463	−	0.574559i	$-0.194826\pi$
$863$	48.0878	1.63693	0.818463	+	0.574559i	$0.194826\pi$
$864$	19.9585	0.679001
$865$	−66.8046	−2.27143
$866$	−24.7622	−0.841452
$867$	−18.7734	−0.637579
$868$	−8.73472	−0.296476
$869$	41.2802	1.40033
$870$	−2.87299	−0.0974035
$871$	33.5952	1.13833
$872$	21.6357	0.732678
$873$	−7.69017	−0.260273
$874$	−9.45360	−0.319773
$875$	−36.1142	−1.22088
$876$	−26.7842	−0.904955
$877$	−53.0077	−1.78994	−0.894971	−	0.446125i	$-0.852804\pi$
$877$	−53.0077	−1.78994	−0.894971	+	0.446125i	$0.852804\pi$
$878$	−30.4004	−1.02596
$879$	24.6752	0.832273
$880$	4.53539	0.152888
$881$	16.0327	0.540156	0.270078	−	0.962838i	$-0.412950\pi$
$881$	16.0327	0.540156	0.270078	+	0.962838i	$0.412950\pi$
$882$	−0.425542	−0.0143287
$883$	9.79720	0.329702	0.164851	−	0.986318i	$-0.447286\pi$
$883$	9.79720	0.329702	0.164851	+	0.986318i	$0.447286\pi$
$884$	−15.8528	−0.533186
$885$	22.0416	0.740920
$886$	2.15234	0.0723092
$887$	18.9336	0.635727	0.317863	−	0.948137i	$-0.397035\pi$
$887$	18.9336	0.635727	0.317863	+	0.948137i	$0.397035\pi$
$888$	26.1947	0.879037
$889$	−8.28793	−0.277968
$890$	36.9924	1.23999
$891$	26.9269	0.902084
$892$	20.8404	0.697790
$893$	−21.8873	−0.732430
$894$	35.7155	1.19451
$895$	34.7904	1.16292
$896$	−13.7528	−0.459450
$897$	22.3439	0.746041
$898$	−18.3412	−0.612053
$899$	−1.16529	−0.0388645
$900$	−11.4169	−0.380563
$901$	16.5052	0.549867
$902$	−6.59622	−0.219630
$903$	−24.4565	−0.813861
$904$	55.4578	1.84450
$905$	−90.5583	−3.01026
$906$	−25.7159	−0.854353
$907$	−4.06639	−0.135022	−0.0675111	−	0.997719i	$-0.521506\pi$
$907$	−4.06639	−0.135022	−0.0675111	+	0.997719i	$0.521506\pi$
$908$	27.6694	0.918242
$909$	16.2439	0.538777
$910$	47.6310	1.57895
$911$	9.87329	0.327117	0.163558	−	0.986534i	$-0.447703\pi$
$911$	9.87329	0.327117	0.163558	+	0.986534i	$0.447703\pi$
$912$	−4.86615	−0.161134
$913$	22.1627	0.733477
$914$	4.39368	0.145330
$915$	−66.4969	−2.19832
$916$	−4.92344	−0.162675
$917$	34.7671	1.14811
$918$	9.74443	0.321614
$919$	5.98000	0.197262	0.0986311	−	0.995124i	$-0.468554\pi$
$919$	5.98000	0.197262	0.0986311	+	0.995124i	$0.468554\pi$
$920$	23.2853	0.767695
$921$	−1.12663	−0.0371237
$922$	−8.38517	−0.276151
$923$	8.88566	0.292475
$924$	−15.0221	−0.494191
$925$	37.6294	1.23725
$926$	28.7570	0.945013
$927$	−23.1084	−0.758980
$928$	−2.18124	−0.0716027
$929$	2.88995	0.0948162	0.0474081	−	0.998876i	$-0.484904\pi$
$929$	2.88995	0.0948162	0.0474081	+	0.998876i	$0.484904\pi$
$930$	20.3438	0.667099
$931$	1.78604	0.0585350
$932$	−26.1685	−0.857179
$933$	40.7739	1.33488
$934$	25.2501	0.826209
$935$	−24.9117	−0.814699
$936$	17.5782	0.574561
$937$	6.34674	0.207339	0.103670	−	0.994612i	$-0.466942\pi$
$937$	6.34674	0.207339	0.103670	+	0.994612i	$0.466942\pi$
$938$	16.9169	0.552356
$939$	−44.5064	−1.45241
$940$	19.3431	0.630903
$941$	12.1993	0.397685	0.198843	−	0.980031i	$-0.436282\pi$
$941$	12.1993	0.397685	0.198843	+	0.980031i	$0.436282\pi$
$942$	9.71790	0.316626
$943$	−6.27688	−0.204403
$944$	−1.48749	−0.0484136
$945$	37.1980	1.21005
$946$	9.97075	0.324177
$947$	−37.1970	−1.20874	−0.604370	−	0.796704i	$-0.706575\pi$
$947$	−37.1970	−1.20874	−0.604370	+	0.796704i	$0.706575\pi$
$948$	39.1424	1.27129
$949$	59.2406	1.92303
$950$	−37.7153	−1.22365
$951$	−34.1892	−1.10866
$952$	−22.2484	−0.721073
$953$	−56.1815	−1.81990	−0.909948	−	0.414722i	$-0.863879\pi$
$953$	−56.1815	−1.81990	−0.909948	+	0.414722i	$0.863879\pi$
$954$	−6.56658	−0.212601
$955$	−64.6454	−2.09187
$956$	−21.4109	−0.692478
$957$	−2.00408	−0.0647828
$958$	−30.9813	−1.00096
$959$	47.0916	1.52067
$960$	45.7658	1.47708
$961$	−22.7485	−0.733824
$962$	−20.7875	−0.670217
$963$	5.41550	0.174512
$964$	−11.2060	−0.360922
$965$	−83.3934	−2.68453
$966$	11.2513	0.362004
$967$	32.7394	1.05283	0.526414	−	0.850229i	$-0.323536\pi$
$967$	32.7394	1.05283	0.526414	+	0.850229i	$0.323536\pi$
$968$	−15.1326	−0.486380
$969$	26.7285	0.858642
$970$	22.4513	0.720867
$971$	−34.8206	−1.11744	−0.558722	−	0.829355i	$-0.688708\pi$
$971$	−34.8206	−1.11744	−0.558722	+	0.829355i	$0.688708\pi$
$972$	13.0701	0.419223
$973$	35.0185	1.12264
$974$	20.6576	0.661912
$975$	89.1414	2.85481
$976$	4.48757	0.143644
$977$	21.5209	0.688515	0.344258	−	0.938875i	$-0.388131\pi$
$977$	21.5209	0.688515	0.344258	+	0.938875i	$0.388131\pi$
$978$	19.4350	0.621464
$979$	25.8044	0.824713
$980$	−1.57843	−0.0504211
$981$	8.76315	0.279786
$982$	21.8562	0.697461
$983$	18.7063	0.596638	0.298319	−	0.954466i	$-0.403574\pi$
$983$	18.7063	0.596638	0.298319	+	0.954466i	$0.403574\pi$
$984$	−17.4322	−0.555717
$985$	65.5478	2.08853
$986$	−1.06496	−0.0339151
$987$	26.0493	0.829158
$988$	−26.4711	−0.842159
$989$	9.48805	0.301702
$990$	9.91111	0.314996
$991$	−45.2879	−1.43862	−0.719308	−	0.694691i	$-0.755541\pi$
$991$	−45.2879	−1.43862	−0.719308	+	0.694691i	$0.755541\pi$
$992$	15.4454	0.490393
$993$	−17.5416	−0.556667
$994$	4.47438	0.141919
$995$	−37.9419	−1.20284
$996$	21.0149	0.665884
$997$	43.1794	1.36751	0.683753	−	0.729713i	$-0.260346\pi$
$997$	43.1794	1.36751	0.683753	+	0.729713i	$0.260346\pi$
$998$	−18.8376	−0.596293
$999$	−16.2343	−0.513630

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	619.2.a.b.1.10	✓	30
3.2	odd	2		5571.2.a.g.1.21		30
4.3	odd	2		9904.2.a.n.1.9		30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
619.2.a.b.1.10	✓	30	1.1	even	1	trivial
5571.2.a.g.1.21		30	3.2	odd	2
9904.2.a.n.1.9		30	4.3	odd	2

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:	\( N \)	\(=\)	\( 619 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	619.a (trivial)

\(f(q)\)	\(=\)	\(q-0.938541 q^{2} +2.04590 q^{3} -1.11914 q^{4} +3.68832 q^{5} -1.92016 q^{6} -2.71706 q^{7} +2.92744 q^{8} +1.18571 q^{9} +O(q^{10})\)	\(q-0.938541 q^{2} +2.04590 q^{3} -1.11914 q^{4} +3.68832 q^{5} -1.92016 q^{6} -2.71706 q^{7} +2.92744 q^{8} +1.18571 q^{9} -3.46164 q^{10} -2.41470 q^{11} -2.28965 q^{12} +5.06418 q^{13} +2.55007 q^{14} +7.54594 q^{15} -0.509241 q^{16} +2.79712 q^{17} -1.11283 q^{18} +4.67066 q^{19} -4.12775 q^{20} -5.55882 q^{21} +2.26630 q^{22} +2.15658 q^{23} +5.98925 q^{24} +8.60372 q^{25} -4.75294 q^{26} -3.71186 q^{27} +3.04077 q^{28} +0.405665 q^{29} -7.08217 q^{30} -2.87253 q^{31} -5.37694 q^{32} -4.94024 q^{33} -2.62521 q^{34} -10.0214 q^{35} -1.32697 q^{36} +4.37362 q^{37} -4.38361 q^{38} +10.3608 q^{39} +10.7973 q^{40} -2.91057 q^{41} +5.21718 q^{42} +4.39958 q^{43} +2.70239 q^{44} +4.37326 q^{45} -2.02404 q^{46} -4.68612 q^{47} -1.04186 q^{48} +0.382395 q^{49} -8.07494 q^{50} +5.72263 q^{51} -5.66753 q^{52} +5.90078 q^{53} +3.48374 q^{54} -8.90619 q^{55} -7.95402 q^{56} +9.55571 q^{57} -0.380734 q^{58} +2.92099 q^{59} -8.44497 q^{60} -8.81228 q^{61} +2.69599 q^{62} -3.22163 q^{63} +6.06496 q^{64} +18.6783 q^{65} +4.63661 q^{66} +6.63389 q^{67} -3.13037 q^{68} +4.41214 q^{69} +9.40547 q^{70} +1.75461 q^{71} +3.47108 q^{72} +11.6980 q^{73} -4.10482 q^{74} +17.6023 q^{75} -5.22713 q^{76} +6.56088 q^{77} -9.72404 q^{78} -17.0954 q^{79} -1.87824 q^{80} -11.1512 q^{81} +2.73169 q^{82} -9.17823 q^{83} +6.22111 q^{84} +10.3167 q^{85} -4.12919 q^{86} +0.829951 q^{87} -7.06889 q^{88} -10.6864 q^{89} -4.10449 q^{90} -13.7597 q^{91} -2.41352 q^{92} -5.87692 q^{93} +4.39811 q^{94} +17.2269 q^{95} -11.0007 q^{96} -6.48573 q^{97} -0.358893 q^{98} -2.86312 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9}+O(q^{10}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9	\( 30 q + 9 q^{2} + q^{3} + 33 q^{4} + 21 q^{5} + 6 q^{6} + 2 q^{7} + 27 q^{8} + 43 q^{9} + 5 q^{10} + 23 q^{11} - 6 q^{12} + 9 q^{13} + 7 q^{14} - 2 q^{15} + 35 q^{16} + 4 q^{17} + 10 q^{18} - q^{19} + 29 q^{20} + 30 q^{21} + 4 q^{23} + 4 q^{24} + 35 q^{25} + q^{26} - 5 q^{27} - 13 q^{28} + 90 q^{29} - 31 q^{30} + 2 q^{31} + 43 q^{32} - 6 q^{33} - 9 q^{34} + 9 q^{35} + 33 q^{36} + 19 q^{37} + 5 q^{38} + 32 q^{39} - 12 q^{40} + 59 q^{41} - 25 q^{42} - 4 q^{43} + 52 q^{44} + 30 q^{45} - q^{46} + 4 q^{47} - 44 q^{48} + 30 q^{49} + 31 q^{50} - 12 q^{52} + 34 q^{53} - 28 q^{54} - 17 q^{55} + 2 q^{56} - 8 q^{57} + 6 q^{58} + 13 q^{59} - 64 q^{60} + 16 q^{61} + 28 q^{62} - 40 q^{63} + 37 q^{64} + 31 q^{65} - 59 q^{66} - 11 q^{67} - 52 q^{68} + 6 q^{69} - 40 q^{70} + 42 q^{71} + 6 q^{72} - 4 q^{73} + 16 q^{74} - 52 q^{75} - 42 q^{76} + 29 q^{77} - 56 q^{78} + 3 q^{79} + 21 q^{80} + 30 q^{81} - 43 q^{82} - 11 q^{83} - 36 q^{84} + 19 q^{85} - 11 q^{86} - 20 q^{87} - 47 q^{88} + 58 q^{89} - 33 q^{90} - 39 q^{91} - 7 q^{92} - 15 q^{93} - 46 q^{94} + 23 q^{95} - 70 q^{96} - 9 q^{97} - 8 q^{99}+O(q^{100}) \) 30 * q + 9 * q^2 + q^3 + 33 * q^4 + 21 * q^5 + 6 * q^6 + 2 * q^7 + 27 * q^8 + 43 * q^9 + 5 * q^10 + 23 * q^11 - 6 * q^12 + 9 * q^13 + 7 * q^14 - 2 * q^15 + 35 * q^16 + 4 * q^17 + 10 * q^18 - q^19 + 29 * q^20 + 30 * q^21 + 4 * q^23 + 4 * q^24 + 35 * q^25 + q^26 - 5 * q^27 - 13 * q^28 + 90 * q^29 - 31 * q^30 + 2 * q^31 + 43 * q^32 - 6 * q^33 - 9 * q^34 + 9 * q^35 + 33 * q^36 + 19 * q^37 + 5 * q^38 + 32 * q^39 - 12 * q^40 + 59 * q^41 - 25 * q^42 - 4 * q^43 + 52 * q^44 + 30 * q^45 - q^46 + 4 * q^47 - 44 * q^48 + 30 * q^49 + 31 * q^50 - 12 * q^52 + 34 * q^53 - 28 * q^54 - 17 * q^55 + 2 * q^56 - 8 * q^57 + 6 * q^58 + 13 * q^59 - 64 * q^60 + 16 * q^61 + 28 * q^62 - 40 * q^63 + 37 * q^64 + 31 * q^65 - 59 * q^66 - 11 * q^67 - 52 * q^68 + 6 * q^69 - 40 * q^70 + 42 * q^71 + 6 * q^72 - 4 * q^73 + 16 * q^74 - 52 * q^75 - 42 * q^76 + 29 * q^77 - 56 * q^78 + 3 * q^79 + 21 * q^80 + 30 * q^81 - 43 * q^82 - 11 * q^83 - 36 * q^84 + 19 * q^85 - 11 * q^86 - 20 * q^87 - 47 * q^88 + 58 * q^89 - 33 * q^90 - 39 * q^91 - 7 * q^92 - 15 * q^93 - 46 * q^94 + 23 * q^95 - 70 * q^96 - 9 * q^97 - 8 * q^99

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