LMFDB - Embedded newform 8018.2.a.j.1.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8018,2,Mod(1,8018)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8018, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8018.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8018 = 2 \cdot 19 \cdot 211 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8018.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:	$64.0240523407$
Analytic rank:	$0$
Dimension:	$47$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
Character	$\chi$	$=$	8018.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.14813 q^{3} +1.00000 q^{4} +2.89240 q^{5} -1.14813 q^{6} +3.60462 q^{7} +1.00000 q^{8} -1.68179 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.14813 q^{3} +1.00000 q^{4} +2.89240 q^{5} -1.14813 q^{6} +3.60462 q^{7} +1.00000 q^{8} -1.68179 q^{9} +2.89240 q^{10} +3.08565 q^{11} -1.14813 q^{12} +1.07318 q^{13} +3.60462 q^{14} -3.32087 q^{15} +1.00000 q^{16} +2.58429 q^{17} -1.68179 q^{18} -1.00000 q^{19} +2.89240 q^{20} -4.13859 q^{21} +3.08565 q^{22} -1.16430 q^{23} -1.14813 q^{24} +3.36601 q^{25} +1.07318 q^{26} +5.37532 q^{27} +3.60462 q^{28} +5.13064 q^{29} -3.32087 q^{30} -0.677721 q^{31} +1.00000 q^{32} -3.54274 q^{33} +2.58429 q^{34} +10.4260 q^{35} -1.68179 q^{36} -2.27963 q^{37} -1.00000 q^{38} -1.23216 q^{39} +2.89240 q^{40} -3.80407 q^{41} -4.13859 q^{42} +1.52856 q^{43} +3.08565 q^{44} -4.86441 q^{45} -1.16430 q^{46} +1.09313 q^{47} -1.14813 q^{48} +5.99332 q^{49} +3.36601 q^{50} -2.96711 q^{51} +1.07318 q^{52} +11.0126 q^{53} +5.37532 q^{54} +8.92496 q^{55} +3.60462 q^{56} +1.14813 q^{57} +5.13064 q^{58} +7.21434 q^{59} -3.32087 q^{60} -11.7845 q^{61} -0.677721 q^{62} -6.06222 q^{63} +1.00000 q^{64} +3.10408 q^{65} -3.54274 q^{66} -14.8513 q^{67} +2.58429 q^{68} +1.33677 q^{69} +10.4260 q^{70} +8.91929 q^{71} -1.68179 q^{72} +3.33975 q^{73} -2.27963 q^{74} -3.86463 q^{75} -1.00000 q^{76} +11.1226 q^{77} -1.23216 q^{78} -10.6382 q^{79} +2.89240 q^{80} -1.12622 q^{81} -3.80407 q^{82} -4.72324 q^{83} -4.13859 q^{84} +7.47481 q^{85} +1.52856 q^{86} -5.89066 q^{87} +3.08565 q^{88} -0.242858 q^{89} -4.86441 q^{90} +3.86842 q^{91} -1.16430 q^{92} +0.778115 q^{93} +1.09313 q^{94} -2.89240 q^{95} -1.14813 q^{96} +0.265223 q^{97} +5.99332 q^{98} -5.18942 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) $ 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.14813	−0.662875	−0.331438	−	0.943477i	$-0.607534\pi$
$3$	−1.14813	−0.662875	−0.331438	+	0.943477i	$0.607534\pi$
$4$	1.00000	0.500000
$5$	2.89240	1.29352	0.646761	−	0.762692i	$-0.276123\pi$
$5$	2.89240	1.29352	0.646761	+	0.762692i	$0.276123\pi$
$6$	−1.14813	−0.468724
$7$	3.60462	1.36242	0.681210	−	0.732088i	$-0.261454\pi$
$7$	3.60462	1.36242	0.681210	+	0.732088i	$0.261454\pi$
$8$	1.00000	0.353553
$9$	−1.68179	−0.560596
$10$	2.89240	0.914659
$11$	3.08565	0.930360	0.465180	−	0.885216i	$-0.345990\pi$
$11$	3.08565	0.930360	0.465180	+	0.885216i	$0.345990\pi$
$12$	−1.14813	−0.331438
$13$	1.07318	0.297647	0.148824	−	0.988864i	$-0.452451\pi$
$13$	1.07318	0.297647	0.148824	+	0.988864i	$0.452451\pi$
$14$	3.60462	0.963377
$15$	−3.32087	−0.857444
$16$	1.00000	0.250000
$17$	2.58429	0.626782	0.313391	−	0.949624i	$-0.398535\pi$
$17$	2.58429	0.626782	0.313391	+	0.949624i	$0.398535\pi$
$18$	−1.68179	−0.396401
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	2.89240	0.646761
$21$	−4.13859	−0.903115
$22$	3.08565	0.657864
$23$	−1.16430	−0.242772	−0.121386	−	0.992605i	$-0.538734\pi$
$23$	−1.16430	−0.242772	−0.121386	+	0.992605i	$0.538734\pi$
$24$	−1.14813	−0.234362
$25$	3.36601	0.673201
$26$	1.07318	0.210468
$27$	5.37532	1.03448
$28$	3.60462	0.681210
$29$	5.13064	0.952735	0.476368	−	0.879246i	$-0.341953\pi$
$29$	5.13064	0.952735	0.476368	+	0.879246i	$0.341953\pi$
$30$	−3.32087	−0.606305
$31$	−0.677721	−0.121722	−0.0608612	−	0.998146i	$-0.519385\pi$
$31$	−0.677721	−0.121722	−0.0608612	+	0.998146i	$0.519385\pi$
$32$	1.00000	0.176777
$33$	−3.54274	−0.616712
$34$	2.58429	0.443202
$35$	10.4260	1.76232
$36$	−1.68179	−0.280298
$37$	−2.27963	−0.374768	−0.187384	−	0.982287i	$-0.560001\pi$
$37$	−2.27963	−0.374768	−0.187384	+	0.982287i	$0.560001\pi$
$38$	−1.00000	−0.162221
$39$	−1.23216	−0.197303
$40$	2.89240	0.457329
$41$	−3.80407	−0.594096	−0.297048	−	0.954863i	$-0.596002\pi$
$41$	−3.80407	−0.594096	−0.297048	+	0.954863i	$0.596002\pi$
$42$	−4.13859	−0.638599
$43$	1.52856	0.233103	0.116551	−	0.993185i	$-0.462816\pi$
$43$	1.52856	0.233103	0.116551	+	0.993185i	$0.462816\pi$
$44$	3.08565	0.465180
$45$	−4.86441	−0.725144
$46$	−1.16430	−0.171666
$47$	1.09313	0.159450	0.0797248	−	0.996817i	$-0.474596\pi$
$47$	1.09313	0.159450	0.0797248	+	0.996817i	$0.474596\pi$
$48$	−1.14813	−0.165719
$49$	5.99332	0.856189
$50$	3.36601	0.476025
$51$	−2.96711	−0.415478
$52$	1.07318	0.148824
$53$	11.0126	1.51270	0.756351	−	0.654166i	$-0.226980\pi$
$53$	11.0126	1.51270	0.756351	+	0.654166i	$0.226980\pi$
$54$	5.37532	0.731488
$55$	8.92496	1.20344
$56$	3.60462	0.481688
$57$	1.14813	0.152074
$58$	5.13064	0.673685
$59$	7.21434	0.939228	0.469614	−	0.882872i	$-0.344393\pi$
$59$	7.21434	0.939228	0.469614	+	0.882872i	$0.344393\pi$
$60$	−3.32087	−0.428722
$61$	−11.7845	−1.50885	−0.754426	−	0.656385i	$-0.772085\pi$
$61$	−11.7845	−1.50885	−0.754426	+	0.656385i	$0.772085\pi$
$62$	−0.677721	−0.0860707
$63$	−6.06222	−0.763768
$64$	1.00000	0.125000
$65$	3.10408	0.385013
$66$	−3.54274	−0.436082
$67$	−14.8513	−1.81437	−0.907185	−	0.420732i	$-0.861773\pi$
$67$	−14.8513	−1.81437	−0.907185	+	0.420732i	$0.861773\pi$
$68$	2.58429	0.313391
$69$	1.33677	0.160928
$70$	10.4260	1.24615
$71$	8.91929	1.05852	0.529262	−	0.848458i	$-0.322469\pi$
$71$	8.91929	1.05852	0.529262	+	0.848458i	$0.322469\pi$
$72$	−1.68179	−0.198201
$73$	3.33975	0.390889	0.195444	−	0.980715i	$-0.437385\pi$
$73$	3.33975	0.390889	0.195444	+	0.980715i	$0.437385\pi$
$74$	−2.27963	−0.265001
$75$	−3.86463	−0.446248
$76$	−1.00000	−0.114708
$77$	11.1226	1.26754
$78$	−1.23216	−0.139514
$79$	−10.6382	−1.19689	−0.598447	−	0.801162i	$-0.704215\pi$
$79$	−10.6382	−1.19689	−0.598447	+	0.801162i	$0.704215\pi$
$80$	2.89240	0.323381
$81$	−1.12622	−0.125136
$82$	−3.80407	−0.420089
$83$	−4.72324	−0.518443	−0.259221	−	0.965818i	$-0.583466\pi$
$83$	−4.72324	−0.518443	−0.259221	+	0.965818i	$0.583466\pi$
$84$	−4.13859	−0.451557
$85$	7.47481	0.810757
$86$	1.52856	0.164829
$87$	−5.89066	−0.631545
$88$	3.08565	0.328932
$89$	−0.242858	−0.0257429	−0.0128715	−	0.999917i	$-0.504097\pi$
$89$	−0.242858	−0.0257429	−0.0128715	+	0.999917i	$0.504097\pi$
$90$	−4.86441	−0.512754
$91$	3.86842	0.405520
$92$	−1.16430	−0.121386
$93$	0.778115	0.0806868
$94$	1.09313	0.112748
$95$	−2.89240	−0.296754
$96$	−1.14813	−0.117181
$97$	0.265223	0.0269294	0.0134647	−	0.999909i	$-0.495714\pi$
$97$	0.265223	0.0269294	0.0134647	+	0.999909i	$0.495714\pi$
$98$	5.99332	0.605417
$99$	−5.18942	−0.521556
$100$	3.36601	0.336601
$101$	9.48072	0.943367	0.471683	−	0.881768i	$-0.343647\pi$
$101$	9.48072	0.943367	0.471683	+	0.881768i	$0.343647\pi$
$102$	−2.96711	−0.293788
$103$	15.5020	1.52746	0.763728	−	0.645539i	$-0.223367\pi$
$103$	15.5020	1.52746	0.763728	+	0.645539i	$0.223367\pi$
$104$	1.07318	0.105234
$105$	−11.9705	−1.16820
$106$	11.0126	1.06964
$107$	18.6332	1.80134	0.900670	−	0.434505i	$-0.143077\pi$
$107$	18.6332	1.80134	0.900670	+	0.434505i	$0.143077\pi$
$108$	5.37532	0.517240
$109$	3.82871	0.366724	0.183362	−	0.983045i	$-0.441302\pi$
$109$	3.82871	0.366724	0.183362	+	0.983045i	$0.441302\pi$
$110$	8.92496	0.850961
$111$	2.61732	0.248425
$112$	3.60462	0.340605
$113$	9.80817	0.922675	0.461337	−	0.887225i	$-0.347370\pi$
$113$	9.80817	0.922675	0.461337	+	0.887225i	$0.347370\pi$
$114$	1.14813	0.107533
$115$	−3.36761	−0.314032
$116$	5.13064	0.476368
$117$	−1.80486	−0.166860
$118$	7.21434	0.664134
$119$	9.31539	0.853940
$120$	−3.32087	−0.303152
$121$	−1.47874	−0.134431
$122$	−11.7845	−1.06692
$123$	4.36758	0.393811
$124$	−0.677721	−0.0608612
$125$	−4.72617	−0.422722
$126$	−6.06222	−0.540065
$127$	−17.2883	−1.53409	−0.767043	−	0.641596i	$-0.778273\pi$
$127$	−17.2883	−1.53409	−0.767043	+	0.641596i	$0.778273\pi$
$128$	1.00000	0.0883883
$129$	−1.75499	−0.154518
$130$	3.10408	0.272245
$131$	−12.1046	−1.05759	−0.528794	−	0.848750i	$-0.677356\pi$
$131$	−12.1046	−1.05759	−0.528794	+	0.848750i	$0.677356\pi$
$132$	−3.54274	−0.308356
$133$	−3.60462	−0.312561
$134$	−14.8513	−1.28295
$135$	15.5476	1.33812
$136$	2.58429	0.221601
$137$	0.462454	0.0395101	0.0197551	−	0.999805i	$-0.493711\pi$
$137$	0.462454	0.0395101	0.0197551	+	0.999805i	$0.493711\pi$
$138$	1.33677	0.113793
$139$	−8.83197	−0.749118	−0.374559	−	0.927203i	$-0.622206\pi$
$139$	−8.83197	−0.749118	−0.374559	+	0.927203i	$0.622206\pi$
$140$	10.4260	0.881161
$141$	−1.25506	−0.105695
$142$	8.91929	0.748490
$143$	3.31147	0.276919
$144$	−1.68179	−0.140149
$145$	14.8399	1.23238
$146$	3.33975	0.276400
$147$	−6.88113	−0.567546
$148$	−2.27963	−0.187384
$149$	−4.05865	−0.332498	−0.166249	−	0.986084i	$-0.553166\pi$
$149$	−4.05865	−0.332498	−0.166249	+	0.986084i	$0.553166\pi$
$150$	−3.86463	−0.315545
$151$	16.1335	1.31293	0.656465	−	0.754357i	$-0.272051\pi$
$151$	16.1335	1.31293	0.656465	+	0.754357i	$0.272051\pi$
$152$	−1.00000	−0.0811107
$153$	−4.34623	−0.351372
$154$	11.1226	0.896287
$155$	−1.96024	−0.157451
$156$	−1.23216	−0.0986514
$157$	−17.7036	−1.41290	−0.706451	−	0.707762i	$-0.749705\pi$
$157$	−17.7036	−1.41290	−0.706451	+	0.707762i	$0.749705\pi$
$158$	−10.6382	−0.846332
$159$	−12.6440	−1.00273
$160$	2.89240	0.228665
$161$	−4.19685	−0.330758
$162$	−1.12622	−0.0884843
$163$	−1.50056	−0.117533	−0.0587665	−	0.998272i	$-0.518717\pi$
$163$	−1.50056	−0.117533	−0.0587665	+	0.998272i	$0.518717\pi$
$164$	−3.80407	−0.297048
$165$	−10.2470	−0.797732
$166$	−4.72324	−0.366594
$167$	−12.3838	−0.958286	−0.479143	−	0.877737i	$-0.659053\pi$
$167$	−12.3838	−0.958286	−0.479143	+	0.877737i	$0.659053\pi$
$168$	−4.13859	−0.319299
$169$	−11.8483	−0.911406
$170$	7.47481	0.573292
$171$	1.68179	0.128610
$172$	1.52856	0.116551
$173$	−13.4040	−1.01908	−0.509542	−	0.860446i	$-0.670185\pi$
$173$	−13.4040	−1.01908	−0.509542	+	0.860446i	$0.670185\pi$
$174$	−5.89066	−0.446570
$175$	12.1332	0.917183
$176$	3.08565	0.232590
$177$	−8.28303	−0.622591
$178$	−0.242858	−0.0182030
$179$	11.7540	0.878535	0.439268	−	0.898356i	$-0.355238\pi$
$179$	11.7540	0.878535	0.439268	+	0.898356i	$0.355238\pi$
$180$	−4.86441	−0.362572
$181$	15.2678	1.13485	0.567423	−	0.823426i	$-0.307940\pi$
$181$	15.2678	1.13485	0.567423	+	0.823426i	$0.307940\pi$
$182$	3.86842	0.286746
$183$	13.5302	1.00018
$184$	−1.16430	−0.0858330
$185$	−6.59360	−0.484771
$186$	0.778115	0.0570542
$187$	7.97422	0.583133
$188$	1.09313	0.0797248
$189$	19.3760	1.40940
$190$	−2.89240	−0.209837
$191$	6.05520	0.438139	0.219070	−	0.975709i	$-0.429698\pi$
$191$	6.05520	0.438139	0.219070	+	0.975709i	$0.429698\pi$
$192$	−1.14813	−0.0828594
$193$	−8.50248	−0.612022	−0.306011	−	0.952028i	$-0.598994\pi$
$193$	−8.50248	−0.612022	−0.306011	+	0.952028i	$0.598994\pi$
$194$	0.265223	0.0190419
$195$	−3.56389	−0.255216
$196$	5.99332	0.428094
$197$	−1.75387	−0.124958	−0.0624791	−	0.998046i	$-0.519901\pi$
$197$	−1.75387	−0.124958	−0.0624791	+	0.998046i	$0.519901\pi$
$198$	−5.18942	−0.368796
$199$	7.86507	0.557540	0.278770	−	0.960358i	$-0.410073\pi$
$199$	7.86507	0.557540	0.278770	+	0.960358i	$0.410073\pi$
$200$	3.36601	0.238013
$201$	17.0512	1.20270
$202$	9.48072	0.667061
$203$	18.4940	1.29803
$204$	−2.96711	−0.207739
$205$	−11.0029	−0.768476
$206$	15.5020	1.08007
$207$	1.95810	0.136097
$208$	1.07318	0.0744118
$209$	−3.08565	−0.213439
$210$	−11.9705	−0.826042
$211$	−1.00000	−0.0688428
$211$	−1.00000	−0.0688428
$212$	11.0126	0.756351
$213$	−10.2405	−0.701670
$214$	18.6332	1.27374
$215$	4.42121	0.301524
$216$	5.37532	0.365744
$217$	−2.44293	−0.165837
$218$	3.82871	0.259313
$219$	−3.83448	−0.259110
$220$	8.92496	0.601721
$221$	2.77341	0.186560
$222$	2.61732	0.175663
$223$	−5.48270	−0.367149	−0.183574	−	0.983006i	$-0.558767\pi$
$223$	−5.48270	−0.367149	−0.183574	+	0.983006i	$0.558767\pi$
$224$	3.60462	0.240844
$225$	−5.66091	−0.377394
$226$	9.80817	0.652430
$227$	−3.85510	−0.255872	−0.127936	−	0.991782i	$-0.540835\pi$
$227$	−3.85510	−0.255872	−0.127936	+	0.991782i	$0.540835\pi$
$228$	1.14813	0.0760370
$229$	−21.4613	−1.41821	−0.709103	−	0.705105i	$-0.750900\pi$
$229$	−21.4613	−1.41821	−0.709103	+	0.705105i	$0.750900\pi$
$230$	−3.36761	−0.222054
$231$	−12.7703	−0.840222
$232$	5.13064	0.336843
$233$	−12.9795	−0.850315	−0.425157	−	0.905119i	$-0.639781\pi$
$233$	−12.9795	−0.850315	−0.425157	+	0.905119i	$0.639781\pi$
$234$	−1.80486	−0.117988
$235$	3.16178	0.206252
$236$	7.21434	0.469614
$237$	12.2141	0.793392
$238$	9.31539	0.603827
$239$	−7.42290	−0.480148	−0.240074	−	0.970755i	$-0.577172\pi$
$239$	−7.42290	−0.480148	−0.240074	+	0.970755i	$0.577172\pi$
$240$	−3.32087	−0.214361
$241$	26.4390	1.70308	0.851542	−	0.524286i	$-0.175668\pi$
$241$	26.4390	1.70308	0.851542	+	0.524286i	$0.175668\pi$
$242$	−1.47874	−0.0950571
$243$	−14.8329	−0.951531
$244$	−11.7845	−0.754426
$245$	17.3351	1.10750
$246$	4.36758	0.278467
$247$	−1.07318	−0.0682849
$248$	−0.677721	−0.0430354
$249$	5.42291	0.343663
$250$	−4.72617	−0.298909
$251$	−18.0281	−1.13792	−0.568962	−	0.822364i	$-0.692655\pi$
$251$	−18.0281	−1.13792	−0.568962	+	0.822364i	$0.692655\pi$
$252$	−6.06222	−0.381884
$253$	−3.59261	−0.225866
$254$	−17.2883	−1.08476
$255$	−8.58208	−0.537431
$256$	1.00000	0.0625000
$257$	−7.48343	−0.466804	−0.233402	−	0.972380i	$-0.574986\pi$
$257$	−7.48343	−0.466804	−0.233402	+	0.972380i	$0.574986\pi$
$258$	−1.75499	−0.109261
$259$	−8.21720	−0.510592
$260$	3.10408	0.192507
$261$	−8.62864	−0.534100
$262$	−12.1046	−0.747828
$263$	−15.8610	−0.978030	−0.489015	−	0.872275i	$-0.662644\pi$
$263$	−15.8610	−0.978030	−0.489015	+	0.872275i	$0.662644\pi$
$264$	−3.54274	−0.218041
$265$	31.8530	1.95671
$266$	−3.60462	−0.221014
$267$	0.278834	0.0170644
$268$	−14.8513	−0.907185
$269$	15.8287	0.965094	0.482547	−	0.875870i	$-0.339712\pi$
$269$	15.8287	0.965094	0.482547	+	0.875870i	$0.339712\pi$
$270$	15.5476	0.946197
$271$	−3.22902	−0.196149	−0.0980744	−	0.995179i	$-0.531268\pi$
$271$	−3.22902	−0.196149	−0.0980744	+	0.995179i	$0.531268\pi$
$272$	2.58429	0.156696
$273$	−4.44146	−0.268809
$274$	0.462454	0.0279379
$275$	10.3863	0.626319
$276$	1.33677	0.0804639
$277$	−23.7207	−1.42524	−0.712620	−	0.701550i	$-0.752492\pi$
$277$	−23.7207	−1.42524	−0.712620	+	0.701550i	$0.752492\pi$
$278$	−8.83197	−0.529706
$279$	1.13978	0.0682371
$280$	10.4260	0.623075
$281$	−3.25297	−0.194056	−0.0970280	−	0.995282i	$-0.530934\pi$
$281$	−3.25297	−0.194056	−0.0970280	+	0.995282i	$0.530934\pi$
$282$	−1.25506	−0.0747378
$283$	−20.4911	−1.21807	−0.609034	−	0.793144i	$-0.708443\pi$
$283$	−20.4911	−1.21807	−0.609034	+	0.793144i	$0.708443\pi$
$284$	8.91929	0.529262
$285$	3.32087	0.196711
$286$	3.31147	0.195811
$287$	−13.7122	−0.809408
$288$	−1.68179	−0.0991003
$289$	−10.3215	−0.607144
$290$	14.8399	0.871427
$291$	−0.304512	−0.0178508
$292$	3.33975	0.195444
$293$	24.1342	1.40994	0.704969	−	0.709238i	$-0.250961\pi$
$293$	24.1342	1.40994	0.704969	+	0.709238i	$0.250961\pi$
$294$	−6.88113	−0.401316
$295$	20.8668	1.21491
$296$	−2.27963	−0.132501
$297$	16.5864	0.962439
$298$	−4.05865	−0.235112
$299$	−1.24950	−0.0722605
$300$	−3.86463	−0.223124
$301$	5.50987	0.317584
$302$	16.1335	0.928381
$303$	−10.8851	−0.625335
$304$	−1.00000	−0.0573539
$305$	−34.0856	−1.95173
$306$	−4.34623	−0.248457
$307$	28.9899	1.65454	0.827272	−	0.561802i	$-0.189892\pi$
$307$	28.9899	1.65454	0.827272	+	0.561802i	$0.189892\pi$
$308$	11.1226	0.633770
$309$	−17.7983	−1.01251
$310$	−1.96024	−0.111334
$311$	20.6627	1.17168	0.585838	−	0.810428i	$-0.300765\pi$
$311$	20.6627	1.17168	0.585838	+	0.810428i	$0.300765\pi$
$312$	−1.23216	−0.0697571
$313$	28.1894	1.59336	0.796678	−	0.604404i	$-0.206589\pi$
$313$	28.1894	1.59336	0.796678	+	0.604404i	$0.206589\pi$
$314$	−17.7036	−0.999072
$315$	−17.5344	−0.987951
$316$	−10.6382	−0.598447
$317$	−19.1312	−1.07452	−0.537258	−	0.843418i	$-0.680540\pi$
$317$	−19.1312	−1.07452	−0.537258	+	0.843418i	$0.680540\pi$
$318$	−12.6440	−0.709039
$319$	15.8314	0.886386
$320$	2.89240	0.161690
$321$	−21.3934	−1.19406
$322$	−4.19685	−0.233881
$323$	−2.58429	−0.143794
$324$	−1.12622	−0.0625679
$325$	3.61234	0.200376
$326$	−1.50056	−0.0831083
$327$	−4.39587	−0.243092
$328$	−3.80407	−0.210045
$329$	3.94033	0.217237
$330$	−10.2470	−0.564081
$331$	11.9430	0.656446	0.328223	−	0.944600i	$-0.393550\pi$
$331$	11.9430	0.656446	0.328223	+	0.944600i	$0.393550\pi$
$332$	−4.72324	−0.259221
$333$	3.83385	0.210094
$334$	−12.3838	−0.677611
$335$	−42.9558	−2.34693
$336$	−4.13859	−0.225779
$337$	22.3523	1.21761	0.608804	−	0.793320i	$-0.291649\pi$
$337$	22.3523	1.21761	0.608804	+	0.793320i	$0.291649\pi$
$338$	−11.8483	−0.644462
$339$	−11.2611	−0.611618
$340$	7.47481	0.405378
$341$	−2.09121	−0.113246
$342$	1.68179	0.0909407
$343$	−3.62870	−0.195931
$344$	1.52856	0.0824143
$345$	3.86647	0.208164
$346$	−13.4040	−0.720601
$347$	9.09589	0.488293	0.244146	−	0.969738i	$-0.421492\pi$
$347$	9.09589	0.488293	0.244146	+	0.969738i	$0.421492\pi$
$348$	−5.89066	−0.315772
$349$	−3.38526	−0.181209	−0.0906045	−	0.995887i	$-0.528880\pi$
$349$	−3.38526	−0.181209	−0.0906045	+	0.995887i	$0.528880\pi$
$350$	12.1332	0.648546
$351$	5.76869	0.307910
$352$	3.08565	0.164466
$353$	22.5913	1.20241	0.601207	−	0.799093i	$-0.294687\pi$
$353$	22.5913	1.20241	0.601207	+	0.799093i	$0.294687\pi$
$354$	−8.28303	−0.440238
$355$	25.7982	1.36923
$356$	−0.242858	−0.0128715
$357$	−10.6953	−0.566056
$358$	11.7540	0.621218
$359$	−2.77138	−0.146268	−0.0731338	−	0.997322i	$-0.523300\pi$
$359$	−2.77138	−0.146268	−0.0731338	+	0.997322i	$0.523300\pi$
$360$	−4.86441	−0.256377
$361$	1.00000	0.0526316
$362$	15.2678	0.802457
$363$	1.69779	0.0891110
$364$	3.86842	0.202760
$365$	9.65992	0.505623
$366$	13.5302	0.707235
$367$	−4.57543	−0.238836	−0.119418	−	0.992844i	$-0.538103\pi$
$367$	−4.57543	−0.238836	−0.119418	+	0.992844i	$0.538103\pi$
$368$	−1.16430	−0.0606931
$369$	6.39764	0.333048
$370$	−6.59360	−0.342785
$371$	39.6964	2.06094
$372$	0.778115	0.0403434
$373$	−23.4072	−1.21198	−0.605990	−	0.795472i	$-0.707223\pi$
$373$	−23.4072	−1.21198	−0.605990	+	0.795472i	$0.707223\pi$
$374$	7.97422	0.412337
$375$	5.42628	0.280212
$376$	1.09313	0.0563739
$377$	5.50610	0.283579
$378$	19.3760	0.996595
$379$	6.81075	0.349845	0.174922	−	0.984582i	$-0.444033\pi$
$379$	6.81075	0.349845	0.174922	+	0.984582i	$0.444033\pi$
$380$	−2.89240	−0.148377
$381$	19.8493	1.01691
$382$	6.05520	0.309811
$383$	−31.2900	−1.59884	−0.799422	−	0.600769i	$-0.794861\pi$
$383$	−31.2900	−1.59884	−0.799422	+	0.600769i	$0.794861\pi$
$384$	−1.14813	−0.0585905
$385$	32.1711	1.63959
$386$	−8.50248	−0.432765
$387$	−2.57071	−0.130677
$388$	0.265223	0.0134647
$389$	18.2539	0.925511	0.462755	−	0.886486i	$-0.346861\pi$
$389$	18.2539	0.925511	0.462755	+	0.886486i	$0.346861\pi$
$390$	−3.56389	−0.180465
$391$	−3.00887	−0.152165
$392$	5.99332	0.302708
$393$	13.8978	0.701049
$394$	−1.75387	−0.0883587
$395$	−30.7701	−1.54821
$396$	−5.18942	−0.260778
$397$	38.3890	1.92669	0.963343	−	0.268272i	$-0.0864526\pi$
$397$	38.3890	1.92669	0.963343	+	0.268272i	$0.0864526\pi$
$398$	7.86507	0.394241
$399$	4.13859	0.207189
$400$	3.36601	0.168300
$401$	24.7296	1.23494	0.617468	−	0.786596i	$-0.288159\pi$
$401$	24.7296	1.23494	0.617468	+	0.786596i	$0.288159\pi$
$402$	17.0512	0.850438
$403$	−0.727318	−0.0362303
$404$	9.48072	0.471683
$405$	−3.25749	−0.161866
$406$	18.4940	0.917843
$407$	−7.03414	−0.348669
$408$	−2.96711	−0.146894
$409$	−21.3875	−1.05754	−0.528772	−	0.848764i	$-0.677347\pi$
$409$	−21.3875	−1.05754	−0.528772	+	0.848764i	$0.677347\pi$
$410$	−11.0029	−0.543395
$411$	−0.530959	−0.0261903
$412$	15.5020	0.763728
$413$	26.0050	1.27962
$414$	1.95810	0.0962353
$415$	−13.6615	−0.670617
$416$	1.07318	0.0526171
$417$	10.1403	0.496572
$418$	−3.08565	−0.150924
$419$	−16.4139	−0.801870	−0.400935	−	0.916107i	$-0.631315\pi$
$419$	−16.4139	−0.801870	−0.400935	+	0.916107i	$0.631315\pi$
$420$	−11.9705	−0.584100
$421$	28.9547	1.41116	0.705582	−	0.708629i	$-0.250686\pi$
$421$	28.9547	1.41116	0.705582	+	0.708629i	$0.250686\pi$
$422$	−1.00000	−0.0486792
$423$	−1.83841	−0.0893868
$424$	11.0126	0.534821
$425$	8.69873	0.421950
$426$	−10.2405	−0.496156
$427$	−42.4788	−2.05569
$428$	18.6332	0.900670
$429$	−3.80201	−0.183563
$430$	4.42121	0.213209
$431$	25.4238	1.22462	0.612311	−	0.790617i	$-0.290240\pi$
$431$	25.4238	1.22462	0.612311	+	0.790617i	$0.290240\pi$
$432$	5.37532	0.258620
$433$	14.1481	0.679916	0.339958	−	0.940441i	$-0.389587\pi$
$433$	14.1481	0.679916	0.339958	+	0.940441i	$0.389587\pi$
$434$	−2.44293	−0.117264
$435$	−17.0382	−0.816917
$436$	3.82871	0.183362
$437$	1.16430	0.0556958
$438$	−3.83448	−0.183219
$439$	−0.514582	−0.0245597	−0.0122798	−	0.999925i	$-0.503909\pi$
$439$	−0.514582	−0.0245597	−0.0122798	+	0.999925i	$0.503909\pi$
$440$	8.92496	0.425481
$441$	−10.0795	−0.479976
$442$	2.77341	0.131918
$443$	31.2539	1.48492	0.742459	−	0.669891i	$-0.233659\pi$
$443$	31.2539	1.48492	0.742459	+	0.669891i	$0.233659\pi$
$444$	2.61732	0.124212
$445$	−0.702445	−0.0332991
$446$	−5.48270	−0.259613
$447$	4.65988	0.220405
$448$	3.60462	0.170303
$449$	27.1541	1.28148	0.640740	−	0.767758i	$-0.278628\pi$
$449$	27.1541	1.28148	0.640740	+	0.767758i	$0.278628\pi$
$450$	−5.66091	−0.266858
$451$	−11.7380	−0.552723
$452$	9.80817	0.461337
$453$	−18.5235	−0.870309
$454$	−3.85510	−0.180929
$455$	11.1890	0.524550
$456$	1.14813	0.0537663
$457$	14.4320	0.675101	0.337551	−	0.941307i	$-0.390402\pi$
$457$	14.4320	0.675101	0.337551	+	0.941307i	$0.390402\pi$
$458$	−21.4613	−1.00282
$459$	13.8914	0.648394
$460$	−3.36761	−0.157016
$461$	21.3289	0.993386	0.496693	−	0.867926i	$-0.334548\pi$
$461$	21.3289	0.993386	0.496693	+	0.867926i	$0.334548\pi$
$462$	−12.7703	−0.594126
$463$	−33.5908	−1.56110	−0.780549	−	0.625094i	$-0.785061\pi$
$463$	−33.5908	−1.56110	−0.780549	+	0.625094i	$0.785061\pi$
$464$	5.13064	0.238184
$465$	2.25062	0.104370
$466$	−12.9795	−0.601263
$467$	−1.87156	−0.0866053	−0.0433027	−	0.999062i	$-0.513788\pi$
$467$	−1.87156	−0.0866053	−0.0433027	+	0.999062i	$0.513788\pi$
$468$	−1.80486	−0.0834299
$469$	−53.5332	−2.47193
$470$	3.16178	0.145842
$471$	20.3261	0.936578
$472$	7.21434	0.332067
$473$	4.71660	0.216869
$474$	12.2141	0.561013
$475$	−3.36601	−0.154443
$476$	9.31539	0.426970
$477$	−18.5209	−0.848015
$478$	−7.42290	−0.339516
$479$	−12.3853	−0.565900	−0.282950	−	0.959135i	$-0.591313\pi$
$479$	−12.3853	−0.565900	−0.282950	+	0.959135i	$0.591313\pi$
$480$	−3.32087	−0.151576
$481$	−2.44645	−0.111549
$482$	26.4390	1.20426
$483$	4.81854	0.219251
$484$	−1.47874	−0.0672155
$485$	0.767134	0.0348337
$486$	−14.8329	−0.672834
$487$	29.3283	1.32899	0.664496	−	0.747292i	$-0.268646\pi$
$487$	29.3283	1.32899	0.664496	+	0.747292i	$0.268646\pi$
$488$	−11.7845	−0.533460
$489$	1.72284	0.0779097
$490$	17.3351	0.783120
$491$	−16.1721	−0.729834	−0.364917	−	0.931040i	$-0.618903\pi$
$491$	−16.1721	−0.729834	−0.364917	+	0.931040i	$0.618903\pi$
$492$	4.36758	0.196906
$493$	13.2590	0.597157
$494$	−1.07318	−0.0482847
$495$	−15.0099	−0.674645
$496$	−0.677721	−0.0304306
$497$	32.1507	1.44216
$498$	5.42291	0.243006
$499$	−9.16856	−0.410441	−0.205220	−	0.978716i	$-0.565791\pi$
$499$	−9.16856	−0.410441	−0.205220	+	0.978716i	$0.565791\pi$
$500$	−4.72617	−0.211361
$501$	14.2182	0.635224
$502$	−18.0281	−0.804634
$503$	9.02603	0.402451	0.201225	−	0.979545i	$-0.435508\pi$
$503$	9.02603	0.402451	0.201225	+	0.979545i	$0.435508\pi$
$504$	−6.06222	−0.270033
$505$	27.4221	1.22027
$506$	−3.59261	−0.159711
$507$	13.6034	0.604149
$508$	−17.2883	−0.767043
$509$	−39.3273	−1.74315	−0.871577	−	0.490259i	$-0.836902\pi$
$509$	−39.3273	−1.74315	−0.871577	+	0.490259i	$0.836902\pi$
$510$	−8.58208	−0.380021
$511$	12.0386	0.532555
$512$	1.00000	0.0441942
$513$	−5.37532	−0.237326
$514$	−7.48343	−0.330080
$515$	44.8380	1.97580
$516$	−1.75499	−0.0772590
$517$	3.37302	0.148345
$518$	−8.21720	−0.361043
$519$	15.3895	0.675526
$520$	3.10408	0.136123
$521$	34.7695	1.52328	0.761640	−	0.648001i	$-0.224395\pi$
$521$	34.7695	1.52328	0.761640	+	0.648001i	$0.224395\pi$
$522$	−8.62864	−0.377666
$523$	−36.3544	−1.58967	−0.794834	−	0.606827i	$-0.792442\pi$
$523$	−36.3544	−1.58967	−0.794834	+	0.606827i	$0.792442\pi$
$524$	−12.1046	−0.528794
$525$	−13.9305	−0.607978
$526$	−15.8610	−0.691572
$527$	−1.75143	−0.0762934
$528$	−3.54274	−0.154178
$529$	−21.6444	−0.941062
$530$	31.8530	1.38361
$531$	−12.1330	−0.526527
$532$	−3.60462	−0.156280
$533$	−4.08246	−0.176831
$534$	0.278834	0.0120663
$535$	53.8947	2.33007
$536$	−14.8513	−0.641477
$537$	−13.4952	−0.582360
$538$	15.8287	0.682424
$539$	18.4933	0.796563
$540$	15.5476	0.669062
$541$	−5.54859	−0.238553	−0.119276	−	0.992861i	$-0.538057\pi$
$541$	−5.54859	−0.238553	−0.119276	+	0.992861i	$0.538057\pi$
$542$	−3.22902	−0.138698
$543$	−17.5295	−0.752262
$544$	2.58429	0.110800
$545$	11.0742	0.474366
$546$	−4.44146	−0.190077
$547$	5.05168	0.215994	0.107997	−	0.994151i	$-0.465556\pi$
$547$	5.05168	0.215994	0.107997	+	0.994151i	$0.465556\pi$
$548$	0.462454	0.0197551
$549$	19.8191	0.845857
$550$	10.3863	0.442875
$551$	−5.13064	−0.218572
$552$	1.33677	0.0568966
$553$	−38.3468	−1.63067
$554$	−23.7207	−1.00780
$555$	7.57034	0.321343
$556$	−8.83197	−0.374559
$557$	6.42784	0.272356	0.136178	−	0.990684i	$-0.456518\pi$
$557$	6.42784	0.272356	0.136178	+	0.990684i	$0.456518\pi$
$558$	1.13978	0.0482509
$559$	1.64042	0.0693823
$560$	10.4260	0.440580
$561$	−9.15547	−0.386544
$562$	−3.25297	−0.137218
$563$	−32.5159	−1.37038	−0.685190	−	0.728364i	$-0.740281\pi$
$563$	−32.5159	−1.37038	−0.685190	+	0.728364i	$0.740281\pi$
$564$	−1.25506	−0.0528476
$565$	28.3692	1.19350
$566$	−20.4911	−0.861304
$567$	−4.05961	−0.170487
$568$	8.91929	0.374245
$569$	5.47372	0.229470	0.114735	−	0.993396i	$-0.463398\pi$
$569$	5.47372	0.229470	0.114735	+	0.993396i	$0.463398\pi$
$570$	3.32087	0.139096
$571$	−17.7775	−0.743966	−0.371983	−	0.928240i	$-0.621322\pi$
$571$	−17.7775	−0.743966	−0.371983	+	0.928240i	$0.621322\pi$
$572$	3.31147	0.138459
$573$	−6.95218	−0.290432
$574$	−13.7122	−0.572338
$575$	−3.91902	−0.163435
$576$	−1.68179	−0.0700745
$577$	47.0623	1.95923	0.979614	−	0.200888i	$-0.0643827\pi$
$577$	47.0623	1.95923	0.979614	+	0.200888i	$0.0643827\pi$
$578$	−10.3215	−0.429316
$579$	9.76199	0.405694
$580$	14.8399	0.616192
$581$	−17.0255	−0.706337
$582$	−0.304512	−0.0126224
$583$	33.9812	1.40736
$584$	3.33975	0.138200
$585$	−5.22040	−0.215837
$586$	24.1342	0.996976
$587$	13.6260	0.562405	0.281203	−	0.959648i	$-0.409267\pi$
$587$	13.6260	0.562405	0.281203	+	0.959648i	$0.409267\pi$
$588$	−6.88113	−0.283773
$589$	0.677721	0.0279250
$590$	20.8668	0.859073
$591$	2.01368	0.0828317
$592$	−2.27963	−0.0936920
$593$	−24.2196	−0.994580	−0.497290	−	0.867584i	$-0.665671\pi$
$593$	−24.2196	−0.994580	−0.497290	+	0.867584i	$0.665671\pi$
$594$	16.5864	0.680547
$595$	26.9439	1.10459
$596$	−4.05865	−0.166249
$597$	−9.03016	−0.369580
$598$	−1.24950	−0.0510959
$599$	−37.9391	−1.55015	−0.775074	−	0.631870i	$-0.782287\pi$
$599$	−37.9391	−1.55015	−0.775074	+	0.631870i	$0.782287\pi$
$600$	−3.86463	−0.157773
$601$	23.0960	0.942104	0.471052	−	0.882106i	$-0.343874\pi$
$601$	23.0960	0.942104	0.471052	+	0.882106i	$0.343874\pi$
$602$	5.50987	0.224566
$603$	24.9767	1.01713
$604$	16.1335	0.656465
$605$	−4.27712	−0.173890
$606$	−10.8851	−0.442178
$607$	16.7339	0.679209	0.339604	−	0.940568i	$-0.389707\pi$
$607$	16.7339	0.679209	0.339604	+	0.940568i	$0.389707\pi$
$608$	−1.00000	−0.0405554
$609$	−21.2336	−0.860429
$610$	−34.0856	−1.38008
$611$	1.17313	0.0474597
$612$	−4.34623	−0.175686
$613$	−25.7889	−1.04160	−0.520802	−	0.853678i	$-0.674367\pi$
$613$	−25.7889	−1.04160	−0.520802	+	0.853678i	$0.674367\pi$
$614$	28.9899	1.16994
$615$	12.6328	0.509404
$616$	11.1226	0.448143
$617$	9.86843	0.397288	0.198644	−	0.980072i	$-0.436346\pi$
$617$	9.86843	0.397288	0.198644	+	0.980072i	$0.436346\pi$
$618$	−17.7983	−0.715955
$619$	−8.02685	−0.322626	−0.161313	−	0.986903i	$-0.551573\pi$
$619$	−8.02685	−0.322626	−0.161313	+	0.986903i	$0.551573\pi$
$620$	−1.96024	−0.0787253
$621$	−6.25846	−0.251143
$622$	20.6627	0.828500
$623$	−0.875414	−0.0350727
$624$	−1.23216	−0.0493257
$625$	−30.5000	−1.22000
$626$	28.1894	1.12667
$627$	3.54274	0.141484
$628$	−17.7036	−0.706451
$629$	−5.89121	−0.234898
$630$	−17.5344	−0.698587
$631$	4.70063	0.187129	0.0935646	−	0.995613i	$-0.470174\pi$
$631$	4.70063	0.187129	0.0935646	+	0.995613i	$0.470174\pi$
$632$	−10.6382	−0.423166
$633$	1.14813	0.0456342
$634$	−19.1312	−0.759798
$635$	−50.0047	−1.98438
$636$	−12.6440	−0.501367
$637$	6.43192	0.254842
$638$	15.8314	0.626770
$639$	−15.0004	−0.593405
$640$	2.89240	0.114332
$641$	−43.4498	−1.71617	−0.858083	−	0.513511i	$-0.828344\pi$
$641$	−43.4498	−1.71617	−0.858083	+	0.513511i	$0.828344\pi$
$642$	−21.3934	−0.844330
$643$	−7.19718	−0.283829	−0.141914	−	0.989879i	$-0.545326\pi$
$643$	−7.19718	−0.283829	−0.141914	+	0.989879i	$0.545326\pi$
$644$	−4.19685	−0.165379
$645$	−5.07614	−0.199873
$646$	−2.58429	−0.101677
$647$	13.0129	0.511589	0.255794	−	0.966731i	$-0.417663\pi$
$647$	13.0129	0.511589	0.255794	+	0.966731i	$0.417663\pi$
$648$	−1.12622	−0.0442422
$649$	22.2610	0.873819
$650$	3.61234	0.141687
$651$	2.80481	0.109929
$652$	−1.50056	−0.0587665
$653$	22.9873	0.899564	0.449782	−	0.893138i	$-0.351502\pi$
$653$	22.9873	0.899564	0.449782	+	0.893138i	$0.351502\pi$
$654$	−4.39587	−0.171892
$655$	−35.0115	−1.36801
$656$	−3.80407	−0.148524
$657$	−5.61676	−0.219131
$658$	3.94033	0.153610
$659$	3.50503	0.136537	0.0682684	−	0.997667i	$-0.478253\pi$
$659$	3.50503	0.136537	0.0682684	+	0.997667i	$0.478253\pi$
$660$	−10.2470	−0.398866
$661$	−28.9152	−1.12467	−0.562336	−	0.826909i	$-0.690097\pi$
$661$	−28.9152	−1.12467	−0.562336	+	0.826909i	$0.690097\pi$
$662$	11.9430	0.464178
$663$	−3.18425	−0.123666
$664$	−4.72324	−0.183297
$665$	−10.4260	−0.404304
$666$	3.83385	0.148559
$667$	−5.97357	−0.231298
$668$	−12.3838	−0.479143
$669$	6.29488	0.243374
$670$	−42.9558	−1.65953
$671$	−36.3629	−1.40378
$672$	−4.13859	−0.159650
$673$	−3.99305	−0.153921	−0.0769603	−	0.997034i	$-0.524521\pi$
$673$	−3.99305	−0.153921	−0.0769603	+	0.997034i	$0.524521\pi$
$674$	22.3523	0.860979
$675$	18.0934	0.696414
$676$	−11.8483	−0.455703
$677$	−39.0687	−1.50153	−0.750766	−	0.660568i	$-0.770315\pi$
$677$	−39.0687	−1.50153	−0.750766	+	0.660568i	$0.770315\pi$
$678$	−11.2611	−0.432480
$679$	0.956031	0.0366891
$680$	7.47481	0.286646
$681$	4.42618	0.169611
$682$	−2.09121	−0.0800767
$683$	−9.58891	−0.366909	−0.183455	−	0.983028i	$-0.558728\pi$
$683$	−9.58891	−0.366909	−0.183455	+	0.983028i	$0.558728\pi$
$684$	1.68179	0.0643048
$685$	1.33760	0.0511072
$686$	−3.62870	−0.138544
$687$	24.6405	0.940093
$688$	1.52856	0.0582757
$689$	11.8186	0.450251
$690$	3.86647	0.147194
$691$	−13.1465	−0.500116	−0.250058	−	0.968231i	$-0.580450\pi$
$691$	−13.1465	−0.500116	−0.250058	+	0.968231i	$0.580450\pi$
$692$	−13.4040	−0.509542
$693$	−18.7059	−0.710578
$694$	9.09589	0.345275
$695$	−25.5456	−0.969001
$696$	−5.89066	−0.223285
$697$	−9.83081	−0.372369
$698$	−3.38526	−0.128134
$699$	14.9022	0.563653
$700$	12.1332	0.458591
$701$	5.51304	0.208225	0.104112	−	0.994566i	$-0.466800\pi$
$701$	5.51304	0.208225	0.104112	+	0.994566i	$0.466800\pi$
$702$	5.76869	0.217725
$703$	2.27963	0.0859777
$704$	3.08565	0.116295
$705$	−3.63014	−0.136719
$706$	22.5913	0.850236
$707$	34.1744	1.28526
$708$	−8.28303	−0.311295
$709$	42.9535	1.61315	0.806575	−	0.591131i	$-0.201318\pi$
$709$	42.9535	1.61315	0.806575	+	0.591131i	$0.201318\pi$
$710$	25.7982	0.968189
$711$	17.8913	0.670975
$712$	−0.242858	−0.00910151
$713$	0.789068	0.0295508
$714$	−10.6953	−0.400262
$715$	9.57810	0.358201
$716$	11.7540	0.439268
$717$	8.52248	0.318278
$718$	−2.77138	−0.103427
$719$	−17.5295	−0.653741	−0.326871	−	0.945069i	$-0.605994\pi$
$719$	−17.5295	−0.653741	−0.326871	+	0.945069i	$0.605994\pi$
$720$	−4.86441	−0.181286
$721$	55.8788	2.08104
$722$	1.00000	0.0372161
$723$	−30.3555	−1.12893
$724$	15.2678	0.567423
$725$	17.2697	0.641382
$726$	1.69779	0.0630110
$727$	−0.524755	−0.0194621	−0.00973105	−	0.999953i	$-0.503098\pi$
$727$	−0.524755	−0.0194621	−0.00973105	+	0.999953i	$0.503098\pi$
$728$	3.86842	0.143373
$729$	20.4088	0.755883
$730$	9.65992	0.357530
$731$	3.95023	0.146105
$732$	13.5302	0.500091
$733$	37.6584	1.39095	0.695473	−	0.718552i	$-0.255195\pi$
$733$	37.6584	1.39095	0.695473	+	0.718552i	$0.255195\pi$
$734$	−4.57543	−0.168882
$735$	−19.9030	−0.734134
$736$	−1.16430	−0.0429165
$737$	−45.8258	−1.68802
$738$	6.39764	0.235500
$739$	−17.3819	−0.639402	−0.319701	−	0.947518i	$-0.603583\pi$
$739$	−17.3819	−0.639402	−0.319701	+	0.947518i	$0.603583\pi$
$740$	−6.59360	−0.242386
$741$	1.23216	0.0452644
$742$	39.6964	1.45730
$743$	33.2555	1.22003	0.610013	−	0.792391i	$-0.291164\pi$
$743$	33.2555	1.22003	0.610013	+	0.792391i	$0.291164\pi$
$744$	0.778115	0.0285271
$745$	−11.7393	−0.430094
$746$	−23.4072	−0.857000
$747$	7.94349	0.290637
$748$	7.97422	0.291566
$749$	67.1657	2.45418
$750$	5.42628	0.198140
$751$	−31.0890	−1.13446	−0.567228	−	0.823561i	$-0.691984\pi$
$751$	−31.0890	−1.13446	−0.567228	+	0.823561i	$0.691984\pi$
$752$	1.09313	0.0398624
$753$	20.6987	0.754302
$754$	5.50610	0.200520
$755$	46.6647	1.69830
$756$	19.3760	0.704699
$757$	6.61706	0.240501	0.120251	−	0.992744i	$-0.461630\pi$
$757$	6.61706	0.240501	0.120251	+	0.992744i	$0.461630\pi$
$758$	6.81075	0.247378
$759$	4.12480	0.149721
$760$	−2.89240	−0.104919
$761$	−32.5345	−1.17937	−0.589687	−	0.807632i	$-0.700749\pi$
$761$	−32.5345	−1.17937	−0.589687	+	0.807632i	$0.700749\pi$
$762$	19.8493	0.719063
$763$	13.8011	0.499632
$764$	6.05520	0.219070
$765$	−12.5710	−0.454507
$766$	−31.2900	−1.13055
$767$	7.74230	0.279558
$768$	−1.14813	−0.0414297
$769$	31.8448	1.14835	0.574177	−	0.818731i	$-0.305322\pi$
$769$	31.8448	1.14835	0.574177	+	0.818731i	$0.305322\pi$
$770$	32.1711	1.15937
$771$	8.59198	0.309433
$772$	−8.50248	−0.306011
$773$	50.4131	1.81323	0.906616	−	0.421957i	$-0.138657\pi$
$773$	50.4131	1.81323	0.906616	+	0.421957i	$0.138657\pi$
$774$	−2.57071	−0.0924023
$775$	−2.28121	−0.0819436
$776$	0.265223	0.00952097
$777$	9.43444	0.338459
$778$	18.2539	0.654435
$779$	3.80407	0.136295
$780$	−3.56389	−0.127608
$781$	27.5218	0.984808
$782$	−3.00887	−0.107597
$783$	27.5788	0.985586
$784$	5.99332	0.214047
$785$	−51.2060	−1.82762
$786$	13.8978	0.495717
$787$	−35.4413	−1.26335	−0.631673	−	0.775235i	$-0.717631\pi$
$787$	−35.4413	−1.26335	−0.631673	+	0.775235i	$0.717631\pi$
$788$	−1.75387	−0.0624791
$789$	18.2105	0.648312
$790$	−30.7701	−1.09475
$791$	35.3548	1.25707
$792$	−5.18942	−0.184398
$793$	−12.6469	−0.449105
$794$	38.3890	1.36237
$795$	−36.5715	−1.29706
$796$	7.86507	0.278770
$797$	22.0512	0.781095	0.390547	−	0.920583i	$-0.372286\pi$
$797$	22.0512	0.781095	0.390547	+	0.920583i	$0.372286\pi$
$798$	4.13859	0.146505
$799$	2.82497	0.0999401
$800$	3.36601	0.119006
$801$	0.408437	0.0144314
$802$	24.7296	0.873231
$803$	10.3053	0.363667
$804$	17.0512	0.601351
$805$	−12.1390	−0.427843
$806$	−0.727318	−0.0256187
$807$	−18.1735	−0.639737
$808$	9.48072	0.333530
$809$	−9.18925	−0.323077	−0.161538	−	0.986866i	$-0.551646\pi$
$809$	−9.18925	−0.323077	−0.161538	+	0.986866i	$0.551646\pi$
$810$	−3.25749	−0.114456
$811$	9.37174	0.329086	0.164543	−	0.986370i	$-0.447385\pi$
$811$	9.37174	0.329086	0.164543	+	0.986370i	$0.447385\pi$
$812$	18.4940	0.649013
$813$	3.70734	0.130022
$814$	−7.03414	−0.246546
$815$	−4.34023	−0.152032
$816$	−2.96711	−0.103870
$817$	−1.52856	−0.0534774
$818$	−21.3875	−0.747796
$819$	−6.50586	−0.227333
$820$	−11.0029	−0.384238
$821$	−47.5802	−1.66056	−0.830280	−	0.557347i	$-0.811819\pi$
$821$	−47.5802	−1.66056	−0.830280	+	0.557347i	$0.811819\pi$
$822$	−0.530959	−0.0185193
$823$	−37.1208	−1.29395	−0.646975	−	0.762511i	$-0.723966\pi$
$823$	−37.1208	−1.29395	−0.646975	+	0.762511i	$0.723966\pi$
$824$	15.5020	0.540037
$825$	−11.9249	−0.415172
$826$	26.0050	0.904830
$827$	14.2641	0.496011	0.248005	−	0.968759i	$-0.420225\pi$
$827$	14.2641	0.496011	0.248005	+	0.968759i	$0.420225\pi$
$828$	1.95810	0.0680486
$829$	40.2831	1.39909	0.699546	−	0.714588i	$-0.253386\pi$
$829$	40.2831	1.39909	0.699546	+	0.714588i	$0.253386\pi$
$830$	−13.6615	−0.474198
$831$	27.2346	0.944757
$832$	1.07318	0.0372059
$833$	15.4885	0.536644
$834$	10.1403	0.351129
$835$	−35.8189	−1.23957
$836$	−3.08565	−0.106720
$837$	−3.64297	−0.125919
$838$	−16.4139	−0.567007
$839$	−35.2303	−1.21629	−0.608143	−	0.793828i	$-0.708085\pi$
$839$	−35.2303	−1.21629	−0.608143	+	0.793828i	$0.708085\pi$
$840$	−11.9705	−0.413021
$841$	−2.67658	−0.0922958
$842$	28.9547	0.997843
$843$	3.73485	0.128635
$844$	−1.00000	−0.0344214
$845$	−34.2700	−1.17892
$846$	−1.83841	−0.0632060
$847$	−5.33031	−0.183152
$848$	11.0126	0.378176
$849$	23.5265	0.807427
$850$	8.69873	0.298364
$851$	2.65416	0.0909833
$852$	−10.2405	−0.350835
$853$	1.99140	0.0681841	0.0340920	−	0.999419i	$-0.489146\pi$
$853$	1.99140	0.0681841	0.0340920	+	0.999419i	$0.489146\pi$
$854$	−42.4788	−1.45359
$855$	4.86441	0.166359
$856$	18.6332	0.636870
$857$	−15.6461	−0.534462	−0.267231	−	0.963632i	$-0.586109\pi$
$857$	−15.6461	−0.534462	−0.267231	+	0.963632i	$0.586109\pi$
$858$	−3.80201	−0.129798
$859$	28.4105	0.969355	0.484678	−	0.874693i	$-0.338937\pi$
$859$	28.4105	0.969355	0.484678	+	0.874693i	$0.338937\pi$
$860$	4.42121	0.150762
$861$	15.7435	0.536537
$862$	25.4238	0.865939
$863$	−45.9406	−1.56384	−0.781919	−	0.623380i	$-0.785759\pi$
$863$	−45.9406	−1.56384	−0.781919	+	0.623380i	$0.785759\pi$
$864$	5.37532	0.182872
$865$	−38.7697	−1.31821
$866$	14.1481	0.480773
$867$	11.8504	0.402461
$868$	−2.44293	−0.0829185
$869$	−32.8259	−1.11354
$870$	−17.0382	−0.577648
$871$	−15.9381	−0.540042
$872$	3.82871	0.129657
$873$	−0.446050	−0.0150965
$874$	1.16430	0.0393829
$875$	−17.0361	−0.575925
$876$	−3.83448	−0.129555
$877$	−50.8605	−1.71744	−0.858719	−	0.512447i	$-0.828739\pi$
$877$	−50.8605	−1.71744	−0.858719	+	0.512447i	$0.828739\pi$
$878$	−0.514582	−0.0173663
$879$	−27.7093	−0.934613
$880$	8.92496	0.300860
$881$	24.2179	0.815922	0.407961	−	0.912999i	$-0.366240\pi$
$881$	24.2179	0.815922	0.407961	+	0.912999i	$0.366240\pi$
$882$	−10.0795	−0.339394
$883$	−45.4004	−1.52784	−0.763922	−	0.645308i	$-0.776729\pi$
$883$	−45.4004	−1.52784	−0.763922	+	0.645308i	$0.776729\pi$
$884$	2.77341	0.0932799
$885$	−23.9579	−0.805335
$886$	31.2539	1.05000
$887$	−37.2388	−1.25036	−0.625179	−	0.780482i	$-0.714974\pi$
$887$	−37.2388	−1.25036	−0.625179	+	0.780482i	$0.714974\pi$
$888$	2.61732	0.0878314
$889$	−62.3177	−2.09007
$890$	−0.702445	−0.0235460
$891$	−3.47513	−0.116421
$892$	−5.48270	−0.183574
$893$	−1.09313	−0.0365802
$894$	4.65988	0.155850
$895$	33.9973	1.13641
$896$	3.60462	0.120422
$897$	1.43459	0.0478997
$898$	27.1541	0.906143
$899$	−3.47714	−0.115969
$900$	−5.66091	−0.188697
$901$	28.4598	0.948135
$902$	−11.7380	−0.390834
$903$	−6.32607	−0.210519
$904$	9.80817	0.326215
$905$	44.1606	1.46795
$906$	−18.5235	−0.615401
$907$	−10.2174	−0.339263	−0.169632	−	0.985508i	$-0.554258\pi$
$907$	−10.2174	−0.339263	−0.169632	+	0.985508i	$0.554258\pi$
$908$	−3.85510	−0.127936
$909$	−15.9446	−0.528848
$910$	11.1890	0.370913
$911$	−20.4904	−0.678876	−0.339438	−	0.940628i	$-0.610237\pi$
$911$	−20.4904	−0.678876	−0.339438	+	0.940628i	$0.610237\pi$
$912$	1.14813	0.0380185
$913$	−14.5743	−0.482338
$914$	14.4320	0.477369
$915$	39.1348	1.29376
$916$	−21.4613	−0.709103
$917$	−43.6327	−1.44088
$918$	13.8914	0.458484
$919$	22.3104	0.735953	0.367977	−	0.929835i	$-0.380051\pi$
$919$	22.3104	0.735953	0.367977	+	0.929835i	$0.380051\pi$
$920$	−3.36761	−0.111027
$921$	−33.2843	−1.09676
$922$	21.3289	0.702430
$923$	9.57201	0.315067
$924$	−12.7703	−0.420111
$925$	−7.67323	−0.252294
$926$	−33.5908	−1.10386
$927$	−26.0711	−0.856286
$928$	5.13064	0.168421
$929$	−3.86980	−0.126964	−0.0634820	−	0.997983i	$-0.520221\pi$
$929$	−3.86980	−0.126964	−0.0634820	+	0.997983i	$0.520221\pi$
$930$	2.25062	0.0738009
$931$	−5.99332	−0.196423
$932$	−12.9795	−0.425157
$933$	−23.7236	−0.776675
$934$	−1.87156	−0.0612392
$935$	23.0647	0.754295
$936$	−1.80486	−0.0589938
$937$	−24.6326	−0.804712	−0.402356	−	0.915483i	$-0.631809\pi$
$937$	−24.6326	−0.804712	−0.402356	+	0.915483i	$0.631809\pi$
$938$	−53.5332	−1.74792
$939$	−32.3652	−1.05620
$940$	3.16178	0.103126
$941$	−41.7786	−1.36195	−0.680973	−	0.732309i	$-0.738443\pi$
$941$	−41.7786	−1.36195	−0.680973	+	0.732309i	$0.738443\pi$
$942$	20.3261	0.662260
$943$	4.42906	0.144230
$944$	7.21434	0.234807
$945$	56.0433	1.82309
$946$	4.71660	0.153350
$947$	46.1205	1.49872	0.749358	−	0.662165i	$-0.230362\pi$
$947$	46.1205	1.49872	0.749358	+	0.662165i	$0.230362\pi$
$948$	12.2141	0.396696
$949$	3.58416	0.116347
$950$	−3.36601	−0.109208
$951$	21.9652	0.712271
$952$	9.31539	0.301914
$953$	24.6958	0.799975	0.399987	−	0.916521i	$-0.369014\pi$
$953$	24.6958	0.799975	0.399987	+	0.916521i	$0.369014\pi$
$954$	−18.5209	−0.599637
$955$	17.5141	0.566743
$956$	−7.42290	−0.240074
$957$	−18.1765	−0.587564
$958$	−12.3853	−0.400152
$959$	1.66697	0.0538294
$960$	−3.32087	−0.107181
$961$	−30.5407	−0.985184
$962$	−2.44645	−0.0788768
$963$	−31.3371	−1.00982
$964$	26.4390	0.851542
$965$	−24.5926	−0.791664
$966$	4.81854	0.155034
$967$	44.0588	1.41683	0.708417	−	0.705794i	$-0.249410\pi$
$967$	44.0588	1.41683	0.708417	+	0.705794i	$0.249410\pi$
$968$	−1.47874	−0.0475286
$969$	2.96711	0.0953173
$970$	0.767134	0.0246312
$971$	26.9373	0.864460	0.432230	−	0.901764i	$-0.357727\pi$
$971$	26.9373	0.864460	0.432230	+	0.901764i	$0.357727\pi$
$972$	−14.8329	−0.475766
$973$	−31.8359	−1.02061
$974$	29.3283	0.939739
$975$	−4.14744	−0.132825
$976$	−11.7845	−0.377213
$977$	32.3232	1.03411	0.517055	−	0.855952i	$-0.327028\pi$
$977$	32.3232	1.03411	0.517055	+	0.855952i	$0.327028\pi$
$978$	1.72284	0.0550905
$979$	−0.749377	−0.0239502
$980$	17.3351	0.553750
$981$	−6.43908	−0.205584
$982$	−16.1721	−0.516071
$983$	−28.6064	−0.912402	−0.456201	−	0.889877i	$-0.650790\pi$
$983$	−28.6064	−0.912402	−0.456201	+	0.889877i	$0.650790\pi$
$984$	4.36758	0.139233
$985$	−5.07290	−0.161636
$986$	13.2590	0.422254
$987$	−4.52402	−0.144001
$988$	−1.07318	−0.0341425
$989$	−1.77969	−0.0565909
$990$	−15.0099	−0.477046
$991$	−0.869027	−0.0276056	−0.0138028	−	0.999905i	$-0.504394\pi$
$991$	−0.869027	−0.0276056	−0.0138028	+	0.999905i	$0.504394\pi$
$992$	−0.677721	−0.0215177
$993$	−13.7122	−0.435142
$994$	32.1507	1.01976
$995$	22.7490	0.721191
$996$	5.42291	0.171831
$997$	6.73255	0.213222	0.106611	−	0.994301i	$-0.466000\pi$
$997$	6.73255	0.213222	0.106611	+	0.994301i	$0.466000\pi$
$998$	−9.16856	−0.290226
$999$	−12.2537	−0.387691

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8018.2.a.j.1.15	✓	47

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8018.2.a.j.1.15	✓	47	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:	\( N \)	\(=\)	\( 8018 = 2 \cdot 19 \cdot 211 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8018.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.14813 q^{3} +1.00000 q^{4} +2.89240 q^{5} -1.14813 q^{6} +3.60462 q^{7} +1.00000 q^{8} -1.68179 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.14813 q^{3} +1.00000 q^{4} +2.89240 q^{5} -1.14813 q^{6} +3.60462 q^{7} +1.00000 q^{8} -1.68179 q^{9} +2.89240 q^{10} +3.08565 q^{11} -1.14813 q^{12} +1.07318 q^{13} +3.60462 q^{14} -3.32087 q^{15} +1.00000 q^{16} +2.58429 q^{17} -1.68179 q^{18} -1.00000 q^{19} +2.89240 q^{20} -4.13859 q^{21} +3.08565 q^{22} -1.16430 q^{23} -1.14813 q^{24} +3.36601 q^{25} +1.07318 q^{26} +5.37532 q^{27} +3.60462 q^{28} +5.13064 q^{29} -3.32087 q^{30} -0.677721 q^{31} +1.00000 q^{32} -3.54274 q^{33} +2.58429 q^{34} +10.4260 q^{35} -1.68179 q^{36} -2.27963 q^{37} -1.00000 q^{38} -1.23216 q^{39} +2.89240 q^{40} -3.80407 q^{41} -4.13859 q^{42} +1.52856 q^{43} +3.08565 q^{44} -4.86441 q^{45} -1.16430 q^{46} +1.09313 q^{47} -1.14813 q^{48} +5.99332 q^{49} +3.36601 q^{50} -2.96711 q^{51} +1.07318 q^{52} +11.0126 q^{53} +5.37532 q^{54} +8.92496 q^{55} +3.60462 q^{56} +1.14813 q^{57} +5.13064 q^{58} +7.21434 q^{59} -3.32087 q^{60} -11.7845 q^{61} -0.677721 q^{62} -6.06222 q^{63} +1.00000 q^{64} +3.10408 q^{65} -3.54274 q^{66} -14.8513 q^{67} +2.58429 q^{68} +1.33677 q^{69} +10.4260 q^{70} +8.91929 q^{71} -1.68179 q^{72} +3.33975 q^{73} -2.27963 q^{74} -3.86463 q^{75} -1.00000 q^{76} +11.1226 q^{77} -1.23216 q^{78} -10.6382 q^{79} +2.89240 q^{80} -1.12622 q^{81} -3.80407 q^{82} -4.72324 q^{83} -4.13859 q^{84} +7.47481 q^{85} +1.52856 q^{86} -5.89066 q^{87} +3.08565 q^{88} -0.242858 q^{89} -4.86441 q^{90} +3.86842 q^{91} -1.16430 q^{92} +0.778115 q^{93} +1.09313 q^{94} -2.89240 q^{95} -1.14813 q^{96} +0.265223 q^{97} +5.99332 q^{98} -5.18942 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9}+O(q^{10}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9	\( 47 q + 47 q^{2} + 10 q^{3} + 47 q^{4} + 15 q^{5} + 10 q^{6} + 47 q^{8} + 69 q^{9} + 15 q^{10} + 17 q^{11} + 10 q^{12} + 27 q^{13} + 10 q^{15} + 47 q^{16} + 16 q^{17} + 69 q^{18} - 47 q^{19} + 15 q^{20} + 26 q^{21} + 17 q^{22} + 24 q^{23} + 10 q^{24} + 86 q^{25} + 27 q^{26} + 43 q^{27} + 58 q^{29} + 10 q^{30} + 21 q^{31} + 47 q^{32} + 18 q^{33} + 16 q^{34} + 24 q^{35} + 69 q^{36} + 78 q^{37} - 47 q^{38} - 4 q^{39} + 15 q^{40} + 53 q^{41} + 26 q^{42} + 47 q^{43} + 17 q^{44} + 23 q^{45} + 24 q^{46} + 16 q^{47} + 10 q^{48} + 93 q^{49} + 86 q^{50} + 28 q^{51} + 27 q^{52} + 43 q^{53} + 43 q^{54} + 23 q^{55} - 10 q^{57} + 58 q^{58} + 3 q^{59} + 10 q^{60} + 12 q^{61} + 21 q^{62} - 5 q^{63} + 47 q^{64} + 62 q^{65} + 18 q^{66} + 68 q^{67} + 16 q^{68} + 12 q^{69} + 24 q^{70} - 13 q^{71} + 69 q^{72} + 35 q^{73} + 78 q^{74} + 22 q^{75} - 47 q^{76} + 26 q^{77} - 4 q^{78} + 21 q^{79} + 15 q^{80} + 123 q^{81} + 53 q^{82} + 23 q^{83} + 26 q^{84} + 38 q^{85} + 47 q^{86} + 39 q^{87} + 17 q^{88} + 24 q^{89} + 23 q^{90} + 49 q^{91} + 24 q^{92} + 91 q^{93} + 16 q^{94} - 15 q^{95} + 10 q^{96} + 88 q^{97} + 93 q^{98} + 26 q^{99}+O(q^{100}) \) 47 * q + 47 * q^2 + 10 * q^3 + 47 * q^4 + 15 * q^5 + 10 * q^6 + 47 * q^8 + 69 * q^9 + 15 * q^10 + 17 * q^11 + 10 * q^12 + 27 * q^13 + 10 * q^15 + 47 * q^16 + 16 * q^17 + 69 * q^18 - 47 * q^19 + 15 * q^20 + 26 * q^21 + 17 * q^22 + 24 * q^23 + 10 * q^24 + 86 * q^25 + 27 * q^26 + 43 * q^27 + 58 * q^29 + 10 * q^30 + 21 * q^31 + 47 * q^32 + 18 * q^33 + 16 * q^34 + 24 * q^35 + 69 * q^36 + 78 * q^37 - 47 * q^38 - 4 * q^39 + 15 * q^40 + 53 * q^41 + 26 * q^42 + 47 * q^43 + 17 * q^44 + 23 * q^45 + 24 * q^46 + 16 * q^47 + 10 * q^48 + 93 * q^49 + 86 * q^50 + 28 * q^51 + 27 * q^52 + 43 * q^53 + 43 * q^54 + 23 * q^55 - 10 * q^57 + 58 * q^58 + 3 * q^59 + 10 * q^60 + 12 * q^61 + 21 * q^62 - 5 * q^63 + 47 * q^64 + 62 * q^65 + 18 * q^66 + 68 * q^67 + 16 * q^68 + 12 * q^69 + 24 * q^70 - 13 * q^71 + 69 * q^72 + 35 * q^73 + 78 * q^74 + 22 * q^75 - 47 * q^76 + 26 * q^77 - 4 * q^78 + 21 * q^79 + 15 * q^80 + 123 * q^81 + 53 * q^82 + 23 * q^83 + 26 * q^84 + 38 * q^85 + 47 * q^86 + 39 * q^87 + 17 * q^88 + 24 * q^89 + 23 * q^90 + 49 * q^91 + 24 * q^92 + 91 * q^93 + 16 * q^94 - 15 * q^95 + 10 * q^96 + 88 * q^97 + 93 * q^98 + 26 * q^99

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