LMFDB - Embedded newform 8039.2.a.a.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8039,2,Mod(1,8039)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8039, 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("8039.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8039 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8039.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:	$64.1917381849$
Analytic rank:	$1$
Dimension:	$279$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	8039.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.59800 q^{2} -2.63260 q^{3} +4.74962 q^{4} +0.476137 q^{5} +6.83949 q^{6} +1.24122 q^{7} -7.14351 q^{8} +3.93057 q^{9} +O(q^{10})$	\(q-2.59800 q^{2} -2.63260 q^{3} +4.74962 q^{4} +0.476137 q^{5} +6.83949 q^{6} +1.24122 q^{7} -7.14351 q^{8} +3.93057 q^{9} -1.23700 q^{10} -1.02362 q^{11} -12.5038 q^{12} -0.261735 q^{13} -3.22468 q^{14} -1.25348 q^{15} +9.05962 q^{16} -4.44362 q^{17} -10.2116 q^{18} -0.367700 q^{19} +2.26147 q^{20} -3.26762 q^{21} +2.65937 q^{22} +5.88120 q^{23} +18.8060 q^{24} -4.77329 q^{25} +0.679988 q^{26} -2.44982 q^{27} +5.89530 q^{28} -0.473167 q^{29} +3.25653 q^{30} -8.72164 q^{31} -9.24990 q^{32} +2.69479 q^{33} +11.5445 q^{34} +0.590989 q^{35} +18.6687 q^{36} +2.90033 q^{37} +0.955286 q^{38} +0.689043 q^{39} -3.40129 q^{40} +3.68863 q^{41} +8.48930 q^{42} -5.32187 q^{43} -4.86181 q^{44} +1.87149 q^{45} -15.2794 q^{46} +8.42290 q^{47} -23.8503 q^{48} -5.45938 q^{49} +12.4010 q^{50} +11.6983 q^{51} -1.24314 q^{52} +9.03718 q^{53} +6.36463 q^{54} -0.487384 q^{55} -8.86664 q^{56} +0.968007 q^{57} +1.22929 q^{58} -6.91845 q^{59} -5.95353 q^{60} +6.69052 q^{61} +22.6588 q^{62} +4.87869 q^{63} +5.91201 q^{64} -0.124622 q^{65} -7.00106 q^{66} +4.49018 q^{67} -21.1055 q^{68} -15.4828 q^{69} -1.53539 q^{70} +3.31155 q^{71} -28.0781 q^{72} +10.8701 q^{73} -7.53506 q^{74} +12.5662 q^{75} -1.74644 q^{76} -1.27054 q^{77} -1.79014 q^{78} +1.74281 q^{79} +4.31362 q^{80} -5.34233 q^{81} -9.58307 q^{82} +7.53371 q^{83} -15.5200 q^{84} -2.11577 q^{85} +13.8262 q^{86} +1.24566 q^{87} +7.31226 q^{88} +18.0761 q^{89} -4.86213 q^{90} -0.324870 q^{91} +27.9335 q^{92} +22.9606 q^{93} -21.8827 q^{94} -0.175076 q^{95} +24.3513 q^{96} +8.57881 q^{97} +14.1835 q^{98} -4.02342 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) $ 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.59800	−1.83707	−0.918533	−	0.395345i	$-0.870625\pi$
$2$	−2.59800	−1.83707	−0.918533	+	0.395345i	$0.870625\pi$
$3$	−2.63260	−1.51993	−0.759965	−	0.649963i	$-0.774784\pi$
$3$	−2.63260	−1.51993	−0.759965	+	0.649963i	$0.774784\pi$
$4$	4.74962	2.37481
$5$	0.476137	0.212935	0.106467	−	0.994316i	$-0.466046\pi$
$5$	0.476137	0.212935	0.106467	+	0.994316i	$0.466046\pi$
$6$	6.83949	2.79221
$7$	1.24122	0.469136	0.234568	−	0.972100i	$-0.424632\pi$
$7$	1.24122	0.469136	0.234568	+	0.972100i	$0.424632\pi$
$8$	−7.14351	−2.52561
$9$	3.93057	1.31019
$10$	−1.23700	−0.391175
$11$	−1.02362	−0.308634	−0.154317	−	0.988021i	$-0.549318\pi$
$11$	−1.02362	−0.308634	−0.154317	+	0.988021i	$0.549318\pi$
$12$	−12.5038	−3.60954
$13$	−0.261735	−0.0725923	−0.0362961	−	0.999341i	$-0.511556\pi$
$13$	−0.261735	−0.0725923	−0.0362961	+	0.999341i	$0.511556\pi$
$14$	−3.22468	−0.861833
$15$	−1.25348	−0.323646
$16$	9.05962	2.26490
$17$	−4.44362	−1.07774	−0.538868	−	0.842390i	$-0.681148\pi$
$17$	−4.44362	−1.07774	−0.538868	+	0.842390i	$0.681148\pi$
$18$	−10.2116	−2.40690
$19$	−0.367700	−0.0843562	−0.0421781	−	0.999110i	$-0.513430\pi$
$19$	−0.367700	−0.0843562	−0.0421781	+	0.999110i	$0.513430\pi$
$20$	2.26147	0.505679
$21$	−3.26762	−0.713054
$22$	2.65937	0.566980
$23$	5.88120	1.22632	0.613158	−	0.789960i	$-0.289899\pi$
$23$	5.88120	1.22632	0.613158	+	0.789960i	$0.289899\pi$
$24$	18.8060	3.83876
$25$	−4.77329	−0.954659
$26$	0.679988	0.133357
$27$	−2.44982	−0.471468
$28$	5.89530	1.11411
$29$	−0.473167	−0.0878649	−0.0439325	−	0.999035i	$-0.513989\pi$
$29$	−0.473167	−0.0878649	−0.0439325	+	0.999035i	$0.513989\pi$
$30$	3.25653	0.594559
$31$	−8.72164	−1.56645	−0.783226	−	0.621737i	$-0.786427\pi$
$31$	−8.72164	−1.56645	−0.783226	+	0.621737i	$0.786427\pi$
$32$	−9.24990	−1.63517
$33$	2.69479	0.469102
$34$	11.5445	1.97987
$35$	0.590989	0.0998953
$36$	18.6687	3.11145
$37$	2.90033	0.476811	0.238406	−	0.971166i	$-0.423375\pi$
$37$	2.90033	0.476811	0.238406	+	0.971166i	$0.423375\pi$
$38$	0.955286	0.154968
$39$	0.689043	0.110335
$40$	−3.40129	−0.537790
$41$	3.68863	0.576067	0.288034	−	0.957620i	$-0.406999\pi$
$41$	3.68863	0.576067	0.288034	+	0.957620i	$0.406999\pi$
$42$	8.48930	1.30993
$43$	−5.32187	−0.811577	−0.405788	−	0.913967i	$-0.633003\pi$
$43$	−5.32187	−0.811577	−0.405788	+	0.913967i	$0.633003\pi$
$44$	−4.86181	−0.732946
$45$	1.87149	0.278985
$46$	−15.2794	−2.25282
$47$	8.42290	1.22861	0.614303	−	0.789070i	$-0.289437\pi$
$47$	8.42290	1.22861	0.614303	+	0.789070i	$0.289437\pi$
$48$	−23.8503	−3.44250
$49$	−5.45938	−0.779912
$50$	12.4010	1.75377
$51$	11.6983	1.63808
$52$	−1.24314	−0.172393
$53$	9.03718	1.24135	0.620676	−	0.784067i	$-0.286858\pi$
$53$	9.03718	1.24135	0.620676	+	0.784067i	$0.286858\pi$
$54$	6.36463	0.866116
$55$	−0.487384	−0.0657189
$56$	−8.86664	−1.18485
$57$	0.968007	0.128216
$58$	1.22929	0.161414
$59$	−6.91845	−0.900705	−0.450352	−	0.892851i	$-0.648702\pi$
$59$	−6.91845	−0.900705	−0.450352	+	0.892851i	$0.648702\pi$
$60$	−5.95353	−0.768597
$61$	6.69052	0.856633	0.428317	−	0.903629i	$-0.359107\pi$
$61$	6.69052	0.856633	0.428317	+	0.903629i	$0.359107\pi$
$62$	22.6588	2.87768
$63$	4.87869	0.614657
$64$	5.91201	0.739001
$65$	−0.124622	−0.0154574
$66$	−7.00106	−0.861771
$67$	4.49018	0.548563	0.274281	−	0.961649i	$-0.411560\pi$
$67$	4.49018	0.548563	0.274281	+	0.961649i	$0.411560\pi$
$68$	−21.1055	−2.55941
$69$	−15.4828	−1.86392
$70$	−1.53539	−0.183514
$71$	3.31155	0.393008	0.196504	−	0.980503i	$-0.437041\pi$
$71$	3.31155	0.393008	0.196504	+	0.980503i	$0.437041\pi$
$72$	−28.0781	−3.30903
$73$	10.8701	1.27225	0.636126	−	0.771585i	$-0.280536\pi$
$73$	10.8701	1.27225	0.636126	+	0.771585i	$0.280536\pi$
$74$	−7.53506	−0.875933
$75$	12.5662	1.45102
$76$	−1.74644	−0.200330
$77$	−1.27054	−0.144791
$78$	−1.79014	−0.202693
$79$	1.74281	0.196081	0.0980406	−	0.995182i	$-0.468742\pi$
$79$	1.74281	0.196081	0.0980406	+	0.995182i	$0.468742\pi$
$80$	4.31362	0.482277
$81$	−5.34233	−0.593592
$82$	−9.58307	−1.05827
$83$	7.53371	0.826932	0.413466	−	0.910520i	$-0.364318\pi$
$83$	7.53371	0.826932	0.413466	+	0.910520i	$0.364318\pi$
$84$	−15.5200	−1.69337
$85$	−2.11577	−0.229487
$86$	13.8262	1.49092
$87$	1.24566	0.133549
$88$	7.31226	0.779489
$89$	18.0761	1.91607	0.958033	−	0.286657i	$-0.0925441\pi$
$89$	18.0761	1.91607	0.958033	+	0.286657i	$0.0925441\pi$
$90$	−4.86213	−0.512514
$91$	−0.324870	−0.0340556
$92$	27.9335	2.91226
$93$	22.9606	2.38090
$94$	−21.8827	−2.25703
$95$	−0.175076	−0.0179624
$96$	24.3513	2.48534
$97$	8.57881	0.871046	0.435523	−	0.900178i	$-0.356563\pi$
$97$	8.57881	0.871046	0.435523	+	0.900178i	$0.356563\pi$
$98$	14.1835	1.43275
$99$	−4.02342	−0.404369
$100$	−22.6713	−2.26713
$101$	−12.4753	−1.24134	−0.620669	−	0.784072i	$-0.713139\pi$
$101$	−12.4753	−1.24134	−0.620669	+	0.784072i	$0.713139\pi$
$102$	−30.3921	−3.00927
$103$	−13.6570	−1.34566	−0.672830	−	0.739797i	$-0.734921\pi$
$103$	−13.6570	−1.34566	−0.672830	+	0.739797i	$0.734921\pi$
$104$	1.86971	0.183340
$105$	−1.55584	−0.151834
$106$	−23.4786	−2.28044
$107$	−14.1096	−1.36403	−0.682015	−	0.731338i	$-0.738896\pi$
$107$	−14.1096	−1.36403	−0.682015	+	0.731338i	$0.738896\pi$
$108$	−11.6357	−1.11964
$109$	−11.1728	−1.07016	−0.535080	−	0.844801i	$-0.679719\pi$
$109$	−11.1728	−1.07016	−0.535080	+	0.844801i	$0.679719\pi$
$110$	1.26623	0.120730
$111$	−7.63540	−0.724720
$112$	11.2450	1.06255
$113$	−5.64548	−0.531082	−0.265541	−	0.964100i	$-0.585551\pi$
$113$	−5.64548	−0.531082	−0.265541	+	0.964100i	$0.585551\pi$
$114$	−2.51488	−0.235540
$115$	2.80026	0.261125
$116$	−2.24736	−0.208662
$117$	−1.02877	−0.0951096
$118$	17.9741	1.65465
$119$	−5.51549	−0.505604
$120$	8.95422	0.817404
$121$	−9.95220	−0.904745
$122$	−17.3820	−1.57369
$123$	−9.71068	−0.875582
$124$	−41.4244	−3.72002
$125$	−4.65342	−0.416215
$126$	−12.6748	−1.12917
$127$	−3.35000	−0.297264	−0.148632	−	0.988893i	$-0.547487\pi$
$127$	−3.35000	−0.297264	−0.148632	+	0.988893i	$0.547487\pi$
$128$	3.14037	0.277572
$129$	14.0103	1.23354
$130$	0.323767	0.0283963
$131$	11.1144	0.971067	0.485533	−	0.874218i	$-0.338625\pi$
$131$	11.1144	0.971067	0.485533	+	0.874218i	$0.338625\pi$
$132$	12.7992	1.11403
$133$	−0.456396	−0.0395745
$134$	−11.6655	−1.00775
$135$	−1.16645	−0.100392
$136$	31.7430	2.72194
$137$	−8.87266	−0.758042	−0.379021	−	0.925388i	$-0.623739\pi$
$137$	−8.87266	−0.758042	−0.379021	+	0.925388i	$0.623739\pi$
$138$	40.2245	3.42413
$139$	−18.2379	−1.54692	−0.773459	−	0.633847i	$-0.781475\pi$
$139$	−18.2379	−1.54692	−0.773459	+	0.633847i	$0.781475\pi$
$140$	2.80697	0.237232
$141$	−22.1741	−1.86740
$142$	−8.60341	−0.721982
$143$	0.267918	0.0224044
$144$	35.6095	2.96746
$145$	−0.225292	−0.0187095
$146$	−28.2406	−2.33721
$147$	14.3724	1.18541
$148$	13.7754	1.13233
$149$	−0.894150	−0.0732516	−0.0366258	−	0.999329i	$-0.511661\pi$
$149$	−0.894150	−0.0732516	−0.0366258	+	0.999329i	$0.511661\pi$
$150$	−32.6469	−2.66561
$151$	5.65590	0.460270	0.230135	−	0.973159i	$-0.426083\pi$
$151$	5.65590	0.460270	0.230135	+	0.973159i	$0.426083\pi$
$152$	2.62667	0.213051
$153$	−17.4659	−1.41204
$154$	3.30086	0.265991
$155$	−4.15269	−0.333552
$156$	3.27269	0.262025
$157$	−15.1387	−1.20820	−0.604100	−	0.796909i	$-0.706467\pi$
$157$	−15.1387	−1.20820	−0.604100	+	0.796909i	$0.706467\pi$
$158$	−4.52782	−0.360214
$159$	−23.7913	−1.88677
$160$	−4.40421	−0.348184
$161$	7.29985	0.575309
$162$	13.8794	1.09047
$163$	19.5628	1.53228	0.766138	−	0.642676i	$-0.222176\pi$
$163$	19.5628	1.53228	0.766138	+	0.642676i	$0.222176\pi$
$164$	17.5196	1.36805
$165$	1.28309	0.0998881
$166$	−19.5726	−1.51913
$167$	7.40593	0.573088	0.286544	−	0.958067i	$-0.407494\pi$
$167$	7.40593	0.573088	0.286544	+	0.958067i	$0.407494\pi$
$168$	23.3423	1.80090
$169$	−12.9315	−0.994730
$170$	5.49677	0.421583
$171$	−1.44527	−0.110523
$172$	−25.2768	−1.92734
$173$	−9.08380	−0.690628	−0.345314	−	0.938487i	$-0.612228\pi$
$173$	−9.08380	−0.690628	−0.345314	+	0.938487i	$0.612228\pi$
$174$	−3.23622	−0.245337
$175$	−5.92469	−0.447865
$176$	−9.27363	−0.699026
$177$	18.2135	1.36901
$178$	−46.9618	−3.51994
$179$	15.3816	1.14968	0.574839	−	0.818266i	$-0.305065\pi$
$179$	15.3816	1.14968	0.574839	+	0.818266i	$0.305065\pi$
$180$	8.88885	0.662536
$181$	3.96328	0.294589	0.147294	−	0.989093i	$-0.452944\pi$
$181$	3.96328	0.294589	0.147294	+	0.989093i	$0.452944\pi$
$182$	0.844013	0.0625624
$183$	−17.6134	−1.30202
$184$	−42.0124	−3.09720
$185$	1.38095	0.101530
$186$	−59.6516	−4.37387
$187$	4.54859	0.332626
$188$	40.0056	2.91771
$189$	−3.04075	−0.221182
$190$	0.454847	0.0329980
$191$	26.2407	1.89871	0.949357	−	0.314200i	$-0.101736\pi$
$191$	26.2407	1.89871	0.949357	+	0.314200i	$0.101736\pi$
$192$	−15.5639	−1.12323
$193$	−0.318816	−0.0229488	−0.0114744	−	0.999934i	$-0.503653\pi$
$193$	−0.318816	−0.0229488	−0.0114744	+	0.999934i	$0.503653\pi$
$194$	−22.2878	−1.60017
$195$	0.328079	0.0234942
$196$	−25.9300	−1.85214
$197$	13.6620	0.973378	0.486689	−	0.873575i	$-0.338204\pi$
$197$	13.6620	0.973378	0.486689	+	0.873575i	$0.338204\pi$
$198$	10.4529	0.742852
$199$	−2.01265	−0.142673	−0.0713366	−	0.997452i	$-0.522726\pi$
$199$	−2.01265	−0.142673	−0.0713366	+	0.997452i	$0.522726\pi$
$200$	34.0981	2.41110
$201$	−11.8208	−0.833778
$202$	32.4109	2.28042
$203$	−0.587303	−0.0412206
$204$	55.5622	3.89013
$205$	1.75629	0.122665
$206$	35.4808	2.47206
$207$	23.1165	1.60671
$208$	−2.37122	−0.164415
$209$	0.376386	0.0260352
$210$	4.04206	0.278929
$211$	−23.5966	−1.62446	−0.812230	−	0.583338i	$-0.801746\pi$
$211$	−23.5966	−1.62446	−0.812230	+	0.583338i	$0.801746\pi$
$212$	42.9231	2.94797
$213$	−8.71797	−0.597346
$214$	36.6569	2.50581
$215$	−2.53394	−0.172813
$216$	17.5003	1.19074
$217$	−10.8254	−0.734879
$218$	29.0270	1.96595
$219$	−28.6167	−1.93374
$220$	−2.31489	−0.156070
$221$	1.16305	0.0782352
$222$	19.8368	1.33136
$223$	24.5387	1.64323	0.821617	−	0.570040i	$-0.193072\pi$
$223$	24.5387	1.64323	0.821617	+	0.570040i	$0.193072\pi$
$224$	−11.4811	−0.767115
$225$	−18.7618	−1.25078
$226$	14.6670	0.975631
$227$	29.2724	1.94288	0.971439	−	0.237291i	$-0.0762596\pi$
$227$	29.2724	1.94288	0.971439	+	0.237291i	$0.0762596\pi$
$228$	4.59766	0.304488
$229$	4.03313	0.266517	0.133258	−	0.991081i	$-0.457456\pi$
$229$	4.03313	0.266517	0.133258	+	0.991081i	$0.457456\pi$
$230$	−7.27507	−0.479704
$231$	3.34481	0.220073
$232$	3.38007	0.221913
$233$	−0.629225	−0.0412219	−0.0206110	−	0.999788i	$-0.506561\pi$
$233$	−0.629225	−0.0412219	−0.0206110	+	0.999788i	$0.506561\pi$
$234$	2.67274	0.174723
$235$	4.01045	0.261613
$236$	−32.8600	−2.13900
$237$	−4.58811	−0.298030
$238$	14.3293	0.928828
$239$	−4.81440	−0.311418	−0.155709	−	0.987803i	$-0.549766\pi$
$239$	−4.81440	−0.311418	−0.155709	+	0.987803i	$0.549766\pi$
$240$	−11.3560	−0.733028
$241$	−19.5673	−1.26044	−0.630220	−	0.776417i	$-0.717035\pi$
$241$	−19.5673	−1.26044	−0.630220	+	0.776417i	$0.717035\pi$
$242$	25.8558	1.66208
$243$	21.4137	1.37369
$244$	31.7774	2.03434
$245$	−2.59941	−0.166070
$246$	25.2284	1.60850
$247$	0.0962401	0.00612361
$248$	62.3031	3.95625
$249$	−19.8332	−1.25688
$250$	12.0896	0.764614
$251$	−30.4295	−1.92069	−0.960346	−	0.278813i	$-0.910059\pi$
$251$	−30.4295	−1.92069	−0.960346	+	0.278813i	$0.910059\pi$
$252$	23.1719	1.45969
$253$	−6.02013	−0.378482
$254$	8.70330	0.546094
$255$	5.56997	0.348805
$256$	−19.9827	−1.24892
$257$	−8.09798	−0.505138	−0.252569	−	0.967579i	$-0.581275\pi$
$257$	−8.09798	−0.505138	−0.252569	+	0.967579i	$0.581275\pi$
$258$	−36.3989	−2.26609
$259$	3.59994	0.223689
$260$	−0.591905	−0.0367084
$261$	−1.85982	−0.115120
$262$	−28.8751	−1.78391
$263$	−19.6602	−1.21230	−0.606149	−	0.795351i	$-0.707286\pi$
$263$	−19.6602	−1.21230	−0.606149	+	0.795351i	$0.707286\pi$
$264$	−19.2502	−1.18477
$265$	4.30293	0.264327
$266$	1.18572	0.0727010
$267$	−47.5872	−2.91229
$268$	21.3266	1.30273
$269$	14.3358	0.874068	0.437034	−	0.899445i	$-0.356029\pi$
$269$	14.3358	0.874068	0.437034	+	0.899445i	$0.356029\pi$
$270$	3.03043	0.184426
$271$	25.4425	1.54552	0.772761	−	0.634697i	$-0.218875\pi$
$271$	25.4425	1.54552	0.772761	+	0.634697i	$0.218875\pi$
$272$	−40.2575	−2.44097
$273$	0.855252	0.0517622
$274$	23.0512	1.39257
$275$	4.88605	0.294640
$276$	−73.5375	−4.42644
$277$	17.4660	1.04943	0.524715	−	0.851278i	$-0.324172\pi$
$277$	17.4660	1.04943	0.524715	+	0.851278i	$0.324172\pi$
$278$	47.3821	2.84179
$279$	−34.2810	−2.05235
$280$	−4.22173	−0.252297
$281$	−11.5975	−0.691850	−0.345925	−	0.938262i	$-0.612435\pi$
$281$	−11.5975	−0.691850	−0.345925	+	0.938262i	$0.612435\pi$
$282$	57.6084	3.43053
$283$	−16.9050	−1.00490	−0.502450	−	0.864606i	$-0.667568\pi$
$283$	−16.9050	−1.00490	−0.502450	+	0.864606i	$0.667568\pi$
$284$	15.7286	0.933319
$285$	0.460903	0.0273016
$286$	−0.696051	−0.0411584
$287$	4.57839	0.270254
$288$	−36.3574	−2.14238
$289$	2.74573	0.161513
$290$	0.585309	0.0343706
$291$	−22.5845	−1.32393
$292$	51.6289	3.02135
$293$	28.0930	1.64121	0.820606	−	0.571494i	$-0.193636\pi$
$293$	28.0930	1.64121	0.820606	+	0.571494i	$0.193636\pi$
$294$	−37.3394	−2.17768
$295$	−3.29413	−0.191791
$296$	−20.7185	−1.20424
$297$	2.50769	0.145511
$298$	2.32300	0.134568
$299$	−1.53932	−0.0890210
$300$	59.6844	3.44588
$301$	−6.60559	−0.380740
$302$	−14.6940	−0.845547
$303$	32.8424	1.88675
$304$	−3.33122	−0.191059
$305$	3.18560	0.182407
$306$	45.3766	2.59401
$307$	9.93985	0.567297	0.283649	−	0.958928i	$-0.408455\pi$
$307$	9.93985	0.567297	0.283649	+	0.958928i	$0.408455\pi$
$308$	−6.03457	−0.343851
$309$	35.9533	2.04531
$310$	10.7887	0.612757
$311$	−6.67625	−0.378576	−0.189288	−	0.981922i	$-0.560618\pi$
$311$	−6.67625	−0.378576	−0.189288	+	0.981922i	$0.560618\pi$
$312$	−4.92219	−0.278664
$313$	−17.5719	−0.993225	−0.496613	−	0.867972i	$-0.665423\pi$
$313$	−17.5719	−0.993225	−0.496613	+	0.867972i	$0.665423\pi$
$314$	39.3304	2.21954
$315$	2.32292	0.130882
$316$	8.27767	0.465655
$317$	22.1448	1.24378	0.621889	−	0.783105i	$-0.286365\pi$
$317$	22.1448	1.24378	0.621889	+	0.783105i	$0.286365\pi$
$318$	61.8097	3.46612
$319$	0.484344	0.0271181
$320$	2.81492	0.157359
$321$	37.1450	2.07323
$322$	−18.9650	−1.05688
$323$	1.63392	0.0909137
$324$	−25.3740	−1.40967
$325$	1.24934	0.0693008
$326$	−50.8242	−2.81489
$327$	29.4135	1.62657
$328$	−26.3498	−1.45492
$329$	10.4547	0.576384
$330$	−3.33346	−0.183501
$331$	35.2867	1.93953	0.969766	−	0.244037i	$-0.0784718\pi$
$331$	35.2867	1.93953	0.969766	+	0.244037i	$0.0784718\pi$
$332$	35.7822	1.96380
$333$	11.3999	0.624713
$334$	−19.2406	−1.05280
$335$	2.13794	0.116808
$336$	−29.6034	−1.61500
$337$	32.2833	1.75858	0.879291	−	0.476285i	$-0.158017\pi$
$337$	32.2833	1.75858	0.879291	+	0.476285i	$0.158017\pi$
$338$	33.5961	1.82738
$339$	14.8623	0.807207
$340$	−10.0491	−0.544988
$341$	8.92767	0.483460
$342$	3.75482	0.203037
$343$	−15.4648	−0.835020
$344$	38.0168	2.04973
$345$	−7.37195	−0.396892
$346$	23.5997	1.26873
$347$	11.4358	0.613904	0.306952	−	0.951725i	$-0.400691\pi$
$347$	11.4358	0.613904	0.306952	+	0.951725i	$0.400691\pi$
$348$	5.91640	0.317152
$349$	3.88558	0.207990	0.103995	−	0.994578i	$-0.466837\pi$
$349$	3.88558	0.207990	0.103995	+	0.994578i	$0.466837\pi$
$350$	15.3924	0.822756
$351$	0.641203	0.0342249
$352$	9.46840	0.504668
$353$	−22.7841	−1.21268	−0.606339	−	0.795206i	$-0.707362\pi$
$353$	−22.7841	−1.21268	−0.606339	+	0.795206i	$0.707362\pi$
$354$	−47.3187	−2.51496
$355$	1.57675	0.0836851
$356$	85.8547	4.55029
$357$	14.5201	0.768484
$358$	−39.9616	−2.11203
$359$	−25.2651	−1.33344	−0.666722	−	0.745307i	$-0.732303\pi$
$359$	−25.2651	−1.33344	−0.666722	+	0.745307i	$0.732303\pi$
$360$	−13.3690	−0.704608
$361$	−18.8648	−0.992884
$362$	−10.2966	−0.541178
$363$	26.2001	1.37515
$364$	−1.54301	−0.0808756
$365$	5.17567	0.270907
$366$	45.7598	2.39190
$367$	−32.4388	−1.69329	−0.846646	−	0.532157i	$-0.821382\pi$
$367$	−32.4388	−1.69329	−0.846646	+	0.532157i	$0.821382\pi$
$368$	53.2815	2.77749
$369$	14.4984	0.754757
$370$	−3.58772	−0.186517
$371$	11.2171	0.582363
$372$	109.054	5.65418
$373$	−22.7951	−1.18028	−0.590142	−	0.807299i	$-0.700928\pi$
$373$	−22.7951	−1.18028	−0.590142	+	0.807299i	$0.700928\pi$
$374$	−11.8172	−0.611055
$375$	12.2506	0.632618
$376$	−60.1691	−3.10298
$377$	0.123844	0.00637831
$378$	7.89989	0.406326
$379$	13.2892	0.682619	0.341310	−	0.939951i	$-0.389130\pi$
$379$	13.2892	0.682619	0.341310	+	0.939951i	$0.389130\pi$
$380$	−0.831542	−0.0426572
$381$	8.81919	0.451821
$382$	−68.1735	−3.48806
$383$	9.39248	0.479933	0.239967	−	0.970781i	$-0.422863\pi$
$383$	9.39248	0.479933	0.239967	+	0.970781i	$0.422863\pi$
$384$	−8.26734	−0.421891
$385$	−0.604949	−0.0308311
$386$	0.828284	0.0421585
$387$	−20.9180	−1.06332
$388$	40.7460	2.06857
$389$	19.8736	1.00763	0.503817	−	0.863810i	$-0.331929\pi$
$389$	19.8736	1.00763	0.503817	+	0.863810i	$0.331929\pi$
$390$	−0.852349	−0.0431604
$391$	−26.1338	−1.32164
$392$	38.9991	1.96975
$393$	−29.2597	−1.47595
$394$	−35.4939	−1.78816
$395$	0.829815	0.0417525
$396$	−19.1097	−0.960299
$397$	0.118178	0.00593116	0.00296558	−	0.999996i	$-0.499056\pi$
$397$	0.118178	0.00593116	0.00296558	+	0.999996i	$0.499056\pi$
$398$	5.22888	0.262100
$399$	1.20151	0.0601506
$400$	−43.2442	−2.16221
$401$	10.0190	0.500325	0.250163	−	0.968204i	$-0.419516\pi$
$401$	10.0190	0.500325	0.250163	+	0.968204i	$0.419516\pi$
$402$	30.7106	1.53170
$403$	2.28276	0.113712
$404$	−59.2529	−2.94794
$405$	−2.54368	−0.126396
$406$	1.52581	0.0757249
$407$	−2.96884	−0.147160
$408$	−83.5666	−4.13716
$409$	−31.5627	−1.56067	−0.780337	−	0.625359i	$-0.784953\pi$
$409$	−31.5627	−1.56067	−0.780337	+	0.625359i	$0.784953\pi$
$410$	−4.56285	−0.225343
$411$	23.3581	1.15217
$412$	−64.8653	−3.19568
$413$	−8.58729	−0.422553
$414$	−60.0567	−2.95162
$415$	3.58707	0.176083
$416$	2.42102	0.118700
$417$	48.0130	2.35121
$418$	−0.977852	−0.0478283
$419$	22.1841	1.08376	0.541882	−	0.840454i	$-0.317712\pi$
$419$	22.1841	1.08376	0.541882	+	0.840454i	$0.317712\pi$
$420$	−7.38962	−0.360577
$421$	11.0311	0.537625	0.268813	−	0.963193i	$-0.413369\pi$
$421$	11.0311	0.537625	0.268813	+	0.963193i	$0.413369\pi$
$422$	61.3041	2.98424
$423$	33.1068	1.60971
$424$	−64.5572	−3.13517
$425$	21.2107	1.02887
$426$	22.6493	1.09736
$427$	8.30438	0.401877
$428$	−67.0154	−3.23931
$429$	−0.705320	−0.0340532
$430$	6.58317	0.317469
$431$	−9.03815	−0.435352	−0.217676	−	0.976021i	$-0.569848\pi$
$431$	−9.03815	−0.435352	−0.217676	+	0.976021i	$0.569848\pi$
$432$	−22.1944	−1.06783
$433$	25.6531	1.23281	0.616404	−	0.787430i	$-0.288589\pi$
$433$	25.6531	1.23281	0.616404	+	0.787430i	$0.288589\pi$
$434$	28.1245	1.35002
$435$	0.593104	0.0284371
$436$	−53.0665	−2.54143
$437$	−2.16252	−0.103447
$438$	74.3462	3.55240
$439$	33.4433	1.59616	0.798081	−	0.602550i	$-0.205848\pi$
$439$	33.4433	1.59616	0.798081	+	0.602550i	$0.205848\pi$
$440$	3.48163	0.165980
$441$	−21.4585	−1.02183
$442$	−3.02161	−0.143723
$443$	23.7383	1.12784	0.563919	−	0.825830i	$-0.309293\pi$
$443$	23.7383	1.12784	0.563919	+	0.825830i	$0.309293\pi$
$444$	−36.2652	−1.72107
$445$	8.60671	0.407997
$446$	−63.7516	−3.01873
$447$	2.35394	0.111337
$448$	7.33809	0.346692
$449$	−26.7078	−1.26042	−0.630210	−	0.776425i	$-0.717031\pi$
$449$	−26.7078	−1.26042	−0.630210	+	0.776425i	$0.717031\pi$
$450$	48.7431	2.29777
$451$	−3.77576	−0.177794
$452$	−26.8138	−1.26122
$453$	−14.8897	−0.699579
$454$	−76.0497	−3.56919
$455$	−0.154682	−0.00725163
$456$	−6.91497	−0.323823
$457$	22.3061	1.04344	0.521719	−	0.853118i	$-0.325291\pi$
$457$	22.3061	1.04344	0.521719	+	0.853118i	$0.325291\pi$
$458$	−10.4781	−0.489608
$459$	10.8860	0.508117
$460$	13.3001	0.620122
$461$	28.7090	1.33711	0.668557	−	0.743661i	$-0.266912\pi$
$461$	28.7090	1.33711	0.668557	+	0.743661i	$0.266912\pi$
$462$	−8.68983	−0.404288
$463$	3.74177	0.173895	0.0869474	−	0.996213i	$-0.472289\pi$
$463$	3.74177	0.173895	0.0869474	+	0.996213i	$0.472289\pi$
$464$	−4.28671	−0.199006
$465$	10.9324	0.506976
$466$	1.63473	0.0757274
$467$	−42.4347	−1.96365	−0.981823	−	0.189799i	$-0.939216\pi$
$467$	−42.4347	−1.96365	−0.981823	+	0.189799i	$0.939216\pi$
$468$	−4.88625	−0.225867
$469$	5.57329	0.257351
$470$	−10.4192	−0.480600
$471$	39.8541	1.83638
$472$	49.4220	2.27483
$473$	5.44758	0.250480
$474$	11.9199	0.547500
$475$	1.75514	0.0805314
$476$	−26.1965	−1.20071
$477$	35.5213	1.62641
$478$	12.5078	0.572094
$479$	−5.09980	−0.233016	−0.116508	−	0.993190i	$-0.537170\pi$
$479$	−5.09980	−0.233016	−0.116508	+	0.993190i	$0.537170\pi$
$480$	11.5945	0.529215
$481$	−0.759118	−0.0346128
$482$	50.8359	2.31551
$483$	−19.2176	−0.874429
$484$	−47.2691	−2.14860
$485$	4.08468	0.185476
$486$	−55.6327	−2.52355
$487$	−23.5483	−1.06707	−0.533537	−	0.845777i	$-0.679137\pi$
$487$	−23.5483	−1.06707	−0.533537	+	0.845777i	$0.679137\pi$
$488$	−47.7938	−2.16352
$489$	−51.5010	−2.32895
$490$	6.75328	0.305082
$491$	−23.5394	−1.06232	−0.531158	−	0.847273i	$-0.678243\pi$
$491$	−23.5394	−1.06232	−0.531158	+	0.847273i	$0.678243\pi$
$492$	−46.1220	−2.07934
$493$	2.10257	0.0946951
$494$	−0.250032	−0.0112495
$495$	−1.91570	−0.0861042
$496$	−79.0147	−3.54787
$497$	4.11035	0.184374
$498$	51.5268	2.30897
$499$	−4.89502	−0.219131	−0.109566	−	0.993980i	$-0.534946\pi$
$499$	−4.89502	−0.219131	−0.109566	+	0.993980i	$0.534946\pi$
$500$	−22.1020	−0.988430
$501$	−19.4968	−0.871054
$502$	79.0558	3.52843
$503$	−14.3380	−0.639300	−0.319650	−	0.947536i	$-0.603565\pi$
$503$	−14.3380	−0.639300	−0.319650	+	0.947536i	$0.603565\pi$
$504$	−34.8510	−1.55239
$505$	−5.93995	−0.264324
$506$	15.6403	0.695297
$507$	34.0434	1.51192
$508$	−15.9112	−0.705945
$509$	−38.6535	−1.71329	−0.856643	−	0.515909i	$-0.827454\pi$
$509$	−38.6535	−1.71329	−0.856643	+	0.515909i	$0.827454\pi$
$510$	−14.4708	−0.640777
$511$	13.4922	0.596859
$512$	45.6344	2.01677
$513$	0.900798	0.0397712
$514$	21.0386	0.927971
$515$	−6.50258	−0.286538
$516$	66.5437	2.92942
$517$	−8.62188	−0.379190
$518$	−9.35264	−0.410932
$519$	23.9140	1.04971
$520$	0.890236	0.0390394
$521$	−24.6307	−1.07909	−0.539545	−	0.841957i	$-0.681404\pi$
$521$	−24.6307	−1.07909	−0.539545	+	0.841957i	$0.681404\pi$
$522$	4.83181	0.211482
$523$	−11.5995	−0.507211	−0.253605	−	0.967308i	$-0.581616\pi$
$523$	−11.5995	−0.507211	−0.253605	+	0.967308i	$0.581616\pi$
$524$	52.7890	2.30610
$525$	15.5973	0.680723
$526$	51.0771	2.22707
$527$	38.7556	1.68822
$528$	24.4137	1.06247
$529$	11.5885	0.503850
$530$	−11.1790	−0.485586
$531$	−27.1934	−1.18009
$532$	−2.16770	−0.0939819
$533$	−0.965444	−0.0418180
$534$	123.632	5.35006
$535$	−6.71811	−0.290449
$536$	−32.0756	−1.38546
$537$	−40.4937	−1.74743
$538$	−37.2444	−1.60572
$539$	5.58835	0.240707
$540$	−5.54018	−0.238411
$541$	6.85541	0.294737	0.147369	−	0.989082i	$-0.452920\pi$
$541$	6.85541	0.294737	0.147369	+	0.989082i	$0.452920\pi$
$542$	−66.0997	−2.83922
$543$	−10.4337	−0.447754
$544$	41.1030	1.76228
$545$	−5.31978	−0.227874
$546$	−2.22195	−0.0950905
$547$	−10.4701	−0.447670	−0.223835	−	0.974627i	$-0.571858\pi$
$547$	−10.4701	−0.447670	−0.223835	+	0.974627i	$0.571858\pi$
$548$	−42.1417	−1.80021
$549$	26.2976	1.12235
$550$	−12.6940	−0.541273
$551$	0.173984	0.00741195
$552$	110.602	4.70753
$553$	2.16320	0.0919887
$554$	−45.3767	−1.92787
$555$	−3.63549	−0.154318
$556$	−86.6229	−3.67363
$557$	−36.7408	−1.55676	−0.778378	−	0.627796i	$-0.783957\pi$
$557$	−36.7408	−1.55676	−0.778378	+	0.627796i	$0.783957\pi$
$558$	89.0621	3.77030
$559$	1.39292	0.0589142
$560$	5.35413	0.226253
$561$	−11.9746	−0.505568
$562$	30.1304	1.27097
$563$	21.4326	0.903278	0.451639	−	0.892201i	$-0.350840\pi$
$563$	21.4326	0.903278	0.451639	+	0.892201i	$0.350840\pi$
$564$	−105.319	−4.43471
$565$	−2.68802	−0.113086
$566$	43.9193	1.84607
$567$	−6.63099	−0.278475
$568$	−23.6561	−0.992587
$569$	7.43646	0.311753	0.155876	−	0.987777i	$-0.450180\pi$
$569$	7.43646	0.311753	0.155876	+	0.987777i	$0.450180\pi$
$570$	−1.19743	−0.0501548
$571$	19.4090	0.812241	0.406121	−	0.913819i	$-0.366881\pi$
$571$	19.4090	0.812241	0.406121	+	0.913819i	$0.366881\pi$
$572$	1.27251	0.0532062
$573$	−69.0813	−2.88591
$574$	−11.8947	−0.496474
$575$	−28.0727	−1.17071
$576$	23.2376	0.968232
$577$	−16.4730	−0.685779	−0.342889	−	0.939376i	$-0.611406\pi$
$577$	−16.4730	−0.685779	−0.342889	+	0.939376i	$0.611406\pi$
$578$	−7.13341	−0.296711
$579$	0.839313	0.0348807
$580$	−1.07005	−0.0444315
$581$	9.35097	0.387943
$582$	58.6747	2.43214
$583$	−9.25066	−0.383123
$584$	−77.6508	−3.21321
$585$	−0.489834	−0.0202521
$586$	−72.9857	−3.01501
$587$	35.6331	1.47074	0.735369	−	0.677667i	$-0.237009\pi$
$587$	35.6331	1.47074	0.735369	+	0.677667i	$0.237009\pi$
$588$	68.2632	2.81513
$589$	3.20695	0.132140
$590$	8.55815	0.352333
$591$	−35.9666	−1.47947
$592$	26.2759	1.07993
$593$	−15.7709	−0.647635	−0.323817	−	0.946120i	$-0.604966\pi$
$593$	−15.7709	−0.647635	−0.323817	+	0.946120i	$0.604966\pi$
$594$	−6.51498	−0.267313
$595$	−2.62613	−0.107661
$596$	−4.24687	−0.173959
$597$	5.29850	0.216853
$598$	3.99915	0.163537
$599$	6.16712	0.251982	0.125991	−	0.992031i	$-0.459789\pi$
$599$	6.16712	0.251982	0.125991	+	0.992031i	$0.459789\pi$
$600$	−89.7665	−3.66470
$601$	5.16064	0.210507	0.105253	−	0.994445i	$-0.466435\pi$
$601$	5.16064	0.210507	0.105253	+	0.994445i	$0.466435\pi$
$602$	17.1613	0.699444
$603$	17.6490	0.718722
$604$	26.8633	1.09305
$605$	−4.73861	−0.192652
$606$	−85.3248	−3.46608
$607$	3.70805	0.150505	0.0752526	−	0.997165i	$-0.476024\pi$
$607$	3.70805	0.150505	0.0752526	+	0.997165i	$0.476024\pi$
$608$	3.40119	0.137936
$609$	1.54613	0.0626524
$610$	−8.27620	−0.335093
$611$	−2.20457	−0.0891873
$612$	−82.9565	−3.35332
$613$	−15.0288	−0.607009	−0.303504	−	0.952830i	$-0.598157\pi$
$613$	−15.0288	−0.607009	−0.303504	+	0.952830i	$0.598157\pi$
$614$	−25.8238	−1.04216
$615$	−4.62361	−0.186442
$616$	9.07610	0.365686
$617$	−9.48566	−0.381878	−0.190939	−	0.981602i	$-0.561153\pi$
$617$	−9.48566	−0.381878	−0.190939	+	0.981602i	$0.561153\pi$
$618$	−93.4067	−3.75737
$619$	19.4770	0.782845	0.391422	−	0.920211i	$-0.371983\pi$
$619$	19.4770	0.782845	0.391422	+	0.920211i	$0.371983\pi$
$620$	−19.7237	−0.792122
$621$	−14.4079	−0.578168
$622$	17.3449	0.695468
$623$	22.4364	0.898895
$624$	6.24247	0.249899
$625$	21.6508	0.866032
$626$	45.6520	1.82462
$627$	−0.990874	−0.0395717
$628$	−71.9030	−2.86924
$629$	−12.8879	−0.513876
$630$	−6.03496	−0.240438
$631$	18.1137	0.721093	0.360547	−	0.932741i	$-0.382590\pi$
$631$	18.1137	0.721093	0.360547	+	0.932741i	$0.382590\pi$
$632$	−12.4498	−0.495225
$633$	62.1204	2.46907
$634$	−57.5323	−2.28490
$635$	−1.59506	−0.0632979
$636$	−112.999	−4.48072
$637$	1.42891	0.0566155
$638$	−1.25833	−0.0498177
$639$	13.0163	0.514916
$640$	1.49525	0.0591048
$641$	48.5548	1.91780	0.958900	−	0.283745i	$-0.0915769\pi$
$641$	48.5548	1.91780	0.958900	+	0.283745i	$0.0915769\pi$
$642$	−96.5028	−3.80866
$643$	1.00514	0.0396388	0.0198194	−	0.999804i	$-0.493691\pi$
$643$	1.00514	0.0396388	0.0198194	+	0.999804i	$0.493691\pi$
$644$	34.6715	1.36625
$645$	6.67083	0.262664
$646$	−4.24493	−0.167014
$647$	−7.89146	−0.310245	−0.155123	−	0.987895i	$-0.549577\pi$
$647$	−7.89146	−0.310245	−0.155123	+	0.987895i	$0.549577\pi$
$648$	38.1630	1.49918
$649$	7.08188	0.277988
$650$	−3.24578	−0.127310
$651$	28.4990	1.11697
$652$	92.9158	3.63886
$653$	−17.2527	−0.675152	−0.337576	−	0.941298i	$-0.609607\pi$
$653$	−17.2527	−0.675152	−0.337576	+	0.941298i	$0.609607\pi$
$654$	−76.4163	−2.98811
$655$	5.29196	0.206774
$656$	33.4176	1.30474
$657$	42.7258	1.66689
$658$	−27.1612	−1.05885
$659$	10.8342	0.422041	0.211020	−	0.977482i	$-0.432321\pi$
$659$	10.8342	0.422041	0.211020	+	0.977482i	$0.432321\pi$
$660$	6.09417	0.237215
$661$	25.9017	1.00746	0.503730	−	0.863861i	$-0.331961\pi$
$661$	25.9017	1.00746	0.503730	+	0.863861i	$0.331961\pi$
$662$	−91.6749	−3.56305
$663$	−3.06184	−0.118912
$664$	−53.8171	−2.08851
$665$	−0.217307	−0.00842679
$666$	−29.6171	−1.14764
$667$	−2.78279	−0.107750
$668$	35.1753	1.36097
$669$	−64.6006	−2.49760
$670$	−5.55437	−0.214584
$671$	−6.84857	−0.264386
$672$	30.2252	1.16596
$673$	−12.0462	−0.464348	−0.232174	−	0.972674i	$-0.574584\pi$
$673$	−12.0462	−0.464348	−0.232174	+	0.972674i	$0.574584\pi$
$674$	−83.8720	−3.23063
$675$	11.6937	0.450091
$676$	−61.4196	−2.36229
$677$	−36.7146	−1.41106	−0.705528	−	0.708682i	$-0.749290\pi$
$677$	−36.7146	−1.41106	−0.705528	+	0.708682i	$0.749290\pi$
$678$	−38.6122	−1.48289
$679$	10.6482	0.408639
$680$	15.1140	0.579596
$681$	−77.0624	−2.95304
$682$	−23.1941	−0.888148
$683$	−42.8995	−1.64150	−0.820752	−	0.571285i	$-0.806445\pi$
$683$	−42.8995	−1.64150	−0.820752	+	0.571285i	$0.806445\pi$
$684$	−6.86449	−0.262470
$685$	−4.22460	−0.161414
$686$	40.1776	1.53399
$687$	−10.6176	−0.405087
$688$	−48.2141	−1.83814
$689$	−2.36535	−0.0901125
$690$	19.1523	0.729117
$691$	−44.1754	−1.68051	−0.840256	−	0.542189i	$-0.817595\pi$
$691$	−44.1754	−1.68051	−0.840256	+	0.542189i	$0.817595\pi$
$692$	−43.1446	−1.64011
$693$	−4.99394	−0.189704
$694$	−29.7101	−1.12778
$695$	−8.68372	−0.329392
$696$	−8.89837	−0.337292
$697$	−16.3909	−0.620848
$698$	−10.0948	−0.382092
$699$	1.65650	0.0626545
$700$	−28.1400	−1.06359
$701$	−48.0109	−1.81335	−0.906674	−	0.421832i	$-0.861387\pi$
$701$	−48.0109	−1.81335	−0.906674	+	0.421832i	$0.861387\pi$
$702$	−1.66585	−0.0628733
$703$	−1.06645	−0.0402220
$704$	−6.05167	−0.228081
$705$	−10.5579	−0.397634
$706$	59.1933	2.22777
$707$	−15.4846	−0.582357
$708$	86.5071	3.25113
$709$	−39.0921	−1.46813	−0.734067	−	0.679077i	$-0.762380\pi$
$709$	−39.0921	−1.46813	−0.734067	+	0.679077i	$0.762380\pi$
$710$	−4.09640	−0.153735
$711$	6.85023	0.256904
$712$	−129.127	−4.83924
$713$	−51.2937	−1.92097
$714$	−37.7232	−1.41175
$715$	0.127566	0.00477068
$716$	73.0569	2.73027
$717$	12.6744	0.473333
$718$	65.6389	2.44962
$719$	18.1758	0.677842	0.338921	−	0.940815i	$-0.389938\pi$
$719$	18.1758	0.677842	0.338921	+	0.940815i	$0.389938\pi$
$720$	16.9550	0.631875
$721$	−16.9512	−0.631297
$722$	49.0108	1.82399
$723$	51.5128	1.91578
$724$	18.8241	0.699591
$725$	2.25857	0.0838810
$726$	−68.0680	−2.52624
$727$	32.7985	1.21643	0.608214	−	0.793773i	$-0.291886\pi$
$727$	32.7985	1.21643	0.608214	+	0.793773i	$0.291886\pi$
$728$	2.32071	0.0860113
$729$	−40.3465	−1.49432
$730$	−13.4464	−0.497673
$731$	23.6483	0.874665
$732$	−83.6571	−3.09206
$733$	19.3317	0.714031	0.357015	−	0.934098i	$-0.383794\pi$
$733$	19.3317	0.714031	0.357015	+	0.934098i	$0.383794\pi$
$734$	84.2761	3.11069
$735$	6.84320	0.252415
$736$	−54.4005	−2.00523
$737$	−4.59625	−0.169305
$738$	−37.6669	−1.38654
$739$	13.4719	0.495571	0.247785	−	0.968815i	$-0.420297\pi$
$739$	13.4719	0.495571	0.247785	+	0.968815i	$0.420297\pi$
$740$	6.55899	0.241113
$741$	−0.253361	−0.00930746
$742$	−29.1420	−1.06984
$743$	31.2352	1.14591	0.572954	−	0.819587i	$-0.305797\pi$
$743$	31.2352	1.14591	0.572954	+	0.819587i	$0.305797\pi$
$744$	−164.019	−6.01323
$745$	−0.425738	−0.0155978
$746$	59.2217	2.16826
$747$	29.6118	1.08344
$748$	21.6040	0.789922
$749$	−17.5131	−0.639915
$750$	−31.8271	−1.16216
$751$	−32.4187	−1.18298	−0.591488	−	0.806314i	$-0.701459\pi$
$751$	−32.4187	−1.18298	−0.591488	+	0.806314i	$0.701459\pi$
$752$	76.3083	2.78268
$753$	80.1085	2.91932
$754$	−0.321748	−0.0117174
$755$	2.69298	0.0980076
$756$	−14.4424	−0.525266
$757$	−16.8631	−0.612899	−0.306449	−	0.951887i	$-0.599141\pi$
$757$	−16.8631	−0.612899	−0.306449	+	0.951887i	$0.599141\pi$
$758$	−34.5253	−1.25402
$759$	15.8486	0.575267
$760$	1.25065	0.0453660
$761$	34.6595	1.25641	0.628203	−	0.778049i	$-0.283791\pi$
$761$	34.6595	1.25641	0.628203	+	0.778049i	$0.283791\pi$
$762$	−22.9123	−0.830025
$763$	−13.8679	−0.502051
$764$	124.633	4.50908
$765$	−8.31618	−0.300672
$766$	−24.4017	−0.881669
$767$	1.81080	0.0653842
$768$	52.6065	1.89827
$769$	−22.5295	−0.812436	−0.406218	−	0.913776i	$-0.633153\pi$
$769$	−22.5295	−0.812436	−0.406218	+	0.913776i	$0.633153\pi$
$770$	1.57166	0.0566387
$771$	21.3187	0.767775
$772$	−1.51425	−0.0544991
$773$	20.0599	0.721504	0.360752	−	0.932662i	$-0.382520\pi$
$773$	20.0599	0.721504	0.360752	+	0.932662i	$0.382520\pi$
$774$	54.3449	1.95339
$775$	41.6309	1.49543
$776$	−61.2828	−2.19992
$777$	−9.47718	−0.339992
$778$	−51.6318	−1.85109
$779$	−1.35631	−0.0485948
$780$	1.55825	0.0557942
$781$	−3.38977	−0.121296
$782$	67.8957	2.42795
$783$	1.15917	0.0414254
$784$	−49.4599	−1.76643
$785$	−7.20809	−0.257268
$786$	76.0166	2.71142
$787$	25.2484	0.900008	0.450004	−	0.893027i	$-0.351423\pi$
$787$	25.2484	0.900008	0.450004	+	0.893027i	$0.351423\pi$
$788$	64.8893	2.31159
$789$	51.7573	1.84261
$790$	−2.15586	−0.0767021
$791$	−7.00726	−0.249149
$792$	28.7413	1.02128
$793$	−1.75114	−0.0621849
$794$	−0.307026	−0.0108959
$795$	−11.3279	−0.401759
$796$	−9.55933	−0.338821
$797$	24.7238	0.875761	0.437881	−	0.899033i	$-0.355729\pi$
$797$	24.7238	0.875761	0.437881	+	0.899033i	$0.355729\pi$
$798$	−3.12152	−0.110500
$799$	−37.4282	−1.32411
$800$	44.1525	1.56103
$801$	71.0495	2.51041
$802$	−26.0294	−0.919130
$803$	−11.1269	−0.392660
$804$	−56.1445	−1.98006
$805$	3.47572	0.122503
$806$	−5.93061	−0.208897
$807$	−37.7404	−1.32852
$808$	89.1174	3.13514
$809$	−23.6103	−0.830096	−0.415048	−	0.909800i	$-0.636235\pi$
$809$	−23.6103	−0.830096	−0.415048	+	0.909800i	$0.636235\pi$
$810$	6.60848	0.232198
$811$	−30.3234	−1.06480	−0.532400	−	0.846493i	$-0.678710\pi$
$811$	−30.3234	−1.06480	−0.532400	+	0.846493i	$0.678710\pi$
$812$	−2.78946	−0.0978910
$813$	−66.9799	−2.34909
$814$	7.71306	0.270343
$815$	9.31457	0.326275
$816$	105.982	3.71010
$817$	1.95685	0.0684616
$818$	81.9999	2.86706
$819$	−1.27692	−0.0446193
$820$	8.34171	0.291305
$821$	−49.9545	−1.74342	−0.871712	−	0.490019i	$-0.836990\pi$
$821$	−49.9545	−1.74342	−0.871712	+	0.490019i	$0.836990\pi$
$822$	−60.6845	−2.11662
$823$	25.0400	0.872840	0.436420	−	0.899743i	$-0.356246\pi$
$823$	25.0400	0.872840	0.436420	+	0.899743i	$0.356246\pi$
$824$	97.5586	3.39861
$825$	−12.8630	−0.447832
$826$	22.3098	0.776257
$827$	−46.2423	−1.60800	−0.804001	−	0.594628i	$-0.797299\pi$
$827$	−46.2423	−1.60800	−0.804001	+	0.594628i	$0.797299\pi$
$828$	109.794	3.81562
$829$	−7.23047	−0.251125	−0.125562	−	0.992086i	$-0.540073\pi$
$829$	−7.23047	−0.251125	−0.125562	+	0.992086i	$0.540073\pi$
$830$	−9.31923	−0.323475
$831$	−45.9809	−1.59506
$832$	−1.54738	−0.0536458
$833$	24.2594	0.840538
$834$	−124.738	−4.31932
$835$	3.52623	0.122030
$836$	1.78769	0.0618286
$837$	21.3664	0.738531
$838$	−57.6344	−1.99095
$839$	−41.4793	−1.43202	−0.716012	−	0.698088i	$-0.754035\pi$
$839$	−41.4793	−1.43202	−0.716012	+	0.698088i	$0.754035\pi$
$840$	11.1141	0.383474
$841$	−28.7761	−0.992280
$842$	−28.6589	−0.987652
$843$	30.5316	1.05156
$844$	−112.075	−3.85778
$845$	−6.15716	−0.211813
$846$	−86.0116	−2.95714
$847$	−12.3528	−0.424448
$848$	81.8734	2.81154
$849$	44.5041	1.52738
$850$	−55.1054	−1.89010
$851$	17.0574	0.584721
$852$	−41.4070	−1.41858
$853$	−35.0524	−1.20017	−0.600085	−	0.799936i	$-0.704867\pi$
$853$	−35.0524	−1.20017	−0.600085	+	0.799936i	$0.704867\pi$
$854$	−21.5748	−0.738275
$855$	−0.688147	−0.0235341
$856$	100.792	3.44501
$857$	34.0417	1.16284	0.581421	−	0.813603i	$-0.302497\pi$
$857$	34.0417	1.16284	0.581421	+	0.813603i	$0.302497\pi$
$858$	1.83242	0.0625579
$859$	45.5450	1.55397	0.776987	−	0.629516i	$-0.216747\pi$
$859$	45.5450	1.55397	0.776987	+	0.629516i	$0.216747\pi$
$860$	−12.0352	−0.410398
$861$	−12.0531	−0.410767
$862$	23.4811	0.799770
$863$	−17.2615	−0.587587	−0.293793	−	0.955869i	$-0.594918\pi$
$863$	−17.2615	−0.587587	−0.293793	+	0.955869i	$0.594918\pi$
$864$	22.6606	0.770928
$865$	−4.32513	−0.147059
$866$	−66.6468	−2.26475
$867$	−7.22840	−0.245489
$868$	−51.4167	−1.74520
$869$	−1.78398	−0.0605173
$870$	−1.54088	−0.0522409
$871$	−1.17524	−0.0398214
$872$	79.8130	2.70281
$873$	33.7196	1.14124
$874$	5.61823	0.190040
$875$	−5.77591	−0.195261
$876$	−135.918	−4.59225
$877$	−11.9947	−0.405032	−0.202516	−	0.979279i	$-0.564912\pi$
$877$	−11.9947	−0.405032	−0.202516	+	0.979279i	$0.564912\pi$
$878$	−86.8858	−2.93225
$879$	−73.9576	−2.49453
$880$	−4.41552	−0.148847
$881$	1.21625	0.0409766	0.0204883	−	0.999790i	$-0.493478\pi$
$881$	1.21625	0.0409766	0.0204883	+	0.999790i	$0.493478\pi$
$882$	55.7492	1.87717
$883$	10.2779	0.345879	0.172939	−	0.984932i	$-0.444674\pi$
$883$	10.2779	0.345879	0.172939	+	0.984932i	$0.444674\pi$
$884$	5.52404	0.185794
$885$	8.67211	0.291510
$886$	−61.6721	−2.07191
$887$	−35.5800	−1.19466	−0.597330	−	0.801996i	$-0.703772\pi$
$887$	−35.5800	−1.19466	−0.597330	+	0.801996i	$0.703772\pi$
$888$	54.5435	1.83036
$889$	−4.15807	−0.139457
$890$	−22.3602	−0.749517
$891$	5.46853	0.183203
$892$	116.549	3.90237
$893$	−3.09710	−0.103641
$894$	−6.11553	−0.204534
$895$	7.32377	0.244806
$896$	3.89788	0.130219
$897$	4.05240	0.135306
$898$	69.3869	2.31547
$899$	4.12679	0.137636
$900$	−89.1112	−2.97037
$901$	−40.1578	−1.33785
$902$	9.80944	0.326619
$903$	17.3899	0.578698
$904$	40.3285	1.34131
$905$	1.88706	0.0627281
$906$	38.6835	1.28517
$907$	−28.0903	−0.932725	−0.466362	−	0.884594i	$-0.654436\pi$
$907$	−28.0903	−0.932725	−0.466362	+	0.884594i	$0.654436\pi$
$908$	139.033	4.61396
$909$	−49.0350	−1.62639
$910$	0.401865	0.0133217
$911$	−40.7058	−1.34864	−0.674322	−	0.738438i	$-0.735564\pi$
$911$	−40.7058	−1.34864	−0.674322	+	0.738438i	$0.735564\pi$
$912$	8.76977	0.290396
$913$	−7.71167	−0.255219
$914$	−57.9514	−1.91686
$915$	−8.38641	−0.277246
$916$	19.1558	0.632926
$917$	13.7953	0.455562
$918$	−28.2820	−0.933444
$919$	39.7079	1.30984	0.654921	−	0.755697i	$-0.272702\pi$
$919$	39.7079	1.30984	0.654921	+	0.755697i	$0.272702\pi$
$920$	−20.0037	−0.659501
$921$	−26.1676	−0.862253
$922$	−74.5861	−2.45636
$923$	−0.866748	−0.0285294
$924$	15.8866	0.522630
$925$	−13.8441	−0.455192
$926$	−9.72113	−0.319456
$927$	−53.6796	−1.76307
$928$	4.37675	0.143674
$929$	−33.4313	−1.09684	−0.548422	−	0.836201i	$-0.684771\pi$
$929$	−33.4313	−1.09684	−0.548422	+	0.836201i	$0.684771\pi$
$930$	−28.4023	−0.931348
$931$	2.00742	0.0657904
$932$	−2.98858	−0.0978942
$933$	17.5759	0.575409
$934$	110.246	3.60735
$935$	2.16575	0.0708275
$936$	7.34901	0.240210
$937$	−49.4016	−1.61388	−0.806939	−	0.590634i	$-0.798878\pi$
$937$	−49.4016	−1.61388	−0.806939	+	0.590634i	$0.798878\pi$
$938$	−14.4794	−0.472770
$939$	46.2599	1.50963
$940$	19.0481	0.621281
$941$	−0.378747	−0.0123468	−0.00617340	−	0.999981i	$-0.501965\pi$
$941$	−0.378747	−0.0123468	−0.00617340	+	0.999981i	$0.501965\pi$
$942$	−103.541	−3.37355
$943$	21.6936	0.706440
$944$	−62.6785	−2.04001
$945$	−1.44781	−0.0470974
$946$	−14.1528	−0.460148
$947$	−47.9035	−1.55666	−0.778328	−	0.627858i	$-0.783932\pi$
$947$	−47.9035	−1.55666	−0.778328	+	0.627858i	$0.783932\pi$
$948$	−21.7918	−0.707764
$949$	−2.84509	−0.0923556
$950$	−4.55986	−0.147941
$951$	−58.2985	−1.89046
$952$	39.4000	1.27696
$953$	−6.59047	−0.213486	−0.106743	−	0.994287i	$-0.534042\pi$
$953$	−6.59047	−0.213486	−0.106743	+	0.994287i	$0.534042\pi$
$954$	−92.2843	−2.98782
$955$	12.4942	0.404302
$956$	−22.8665	−0.739557
$957$	−1.27508	−0.0412176
$958$	13.2493	0.428065
$959$	−11.0129	−0.355625
$960$	−7.41056	−0.239175
$961$	45.0670	1.45377
$962$	1.97219	0.0635859
$963$	−55.4589	−1.78714
$964$	−92.9371	−2.99330
$965$	−0.151800	−0.00488661
$966$	49.9273	1.60638
$967$	26.8571	0.863666	0.431833	−	0.901953i	$-0.357867\pi$
$967$	26.8571	0.863666	0.431833	+	0.901953i	$0.357867\pi$
$968$	71.0936	2.28503
$969$	−4.30145	−0.138183
$970$	−10.6120	−0.340731
$971$	−12.9146	−0.414450	−0.207225	−	0.978293i	$-0.566443\pi$
$971$	−12.9146	−0.414450	−0.207225	+	0.978293i	$0.566443\pi$
$972$	101.707	3.26224
$973$	−22.6372	−0.725714
$974$	61.1784	1.96028
$975$	−3.28901	−0.105332
$976$	60.6136	1.94019
$977$	22.7498	0.727829	0.363915	−	0.931432i	$-0.381440\pi$
$977$	22.7498	0.727829	0.363915	+	0.931432i	$0.381440\pi$
$978$	133.800	4.27844
$979$	−18.5031	−0.591363
$980$	−12.3462	−0.394385
$981$	−43.9155	−1.40211
$982$	61.1553	1.95154
$983$	−38.2439	−1.21979	−0.609896	−	0.792482i	$-0.708789\pi$
$983$	−38.2439	−1.21979	−0.609896	+	0.792482i	$0.708789\pi$
$984$	69.3683	2.21138
$985$	6.50498	0.207266
$986$	−5.46249	−0.173961
$987$	−27.5229	−0.876063
$988$	0.457103	0.0145424
$989$	−31.2990	−0.995249
$990$	4.97699	0.158179
$991$	16.5121	0.524523	0.262261	−	0.964997i	$-0.415532\pi$
$991$	16.5121	0.524523	0.262261	+	0.964997i	$0.415532\pi$
$992$	80.6742	2.56141
$993$	−92.8957	−2.94795
$994$	−10.6787	−0.338708
$995$	−0.958298	−0.0303801
$996$	−94.2002	−2.98485
$997$	35.2056	1.11497	0.557486	−	0.830186i	$-0.311766\pi$
$997$	35.2056	1.11497	0.557486	+	0.830186i	$0.311766\pi$
$998$	12.7173	0.402558
$999$	−7.10527	−0.224801

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.a.1.14	✓	279

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.a.1.14	✓	279	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:	\( N \)	\(=\)	\( 8039 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8039.a (trivial)

\(f(q)\)	\(=\)	\(q-2.59800 q^{2} -2.63260 q^{3} +4.74962 q^{4} +0.476137 q^{5} +6.83949 q^{6} +1.24122 q^{7} -7.14351 q^{8} +3.93057 q^{9} +O(q^{10})\)	\(q-2.59800 q^{2} -2.63260 q^{3} +4.74962 q^{4} +0.476137 q^{5} +6.83949 q^{6} +1.24122 q^{7} -7.14351 q^{8} +3.93057 q^{9} -1.23700 q^{10} -1.02362 q^{11} -12.5038 q^{12} -0.261735 q^{13} -3.22468 q^{14} -1.25348 q^{15} +9.05962 q^{16} -4.44362 q^{17} -10.2116 q^{18} -0.367700 q^{19} +2.26147 q^{20} -3.26762 q^{21} +2.65937 q^{22} +5.88120 q^{23} +18.8060 q^{24} -4.77329 q^{25} +0.679988 q^{26} -2.44982 q^{27} +5.89530 q^{28} -0.473167 q^{29} +3.25653 q^{30} -8.72164 q^{31} -9.24990 q^{32} +2.69479 q^{33} +11.5445 q^{34} +0.590989 q^{35} +18.6687 q^{36} +2.90033 q^{37} +0.955286 q^{38} +0.689043 q^{39} -3.40129 q^{40} +3.68863 q^{41} +8.48930 q^{42} -5.32187 q^{43} -4.86181 q^{44} +1.87149 q^{45} -15.2794 q^{46} +8.42290 q^{47} -23.8503 q^{48} -5.45938 q^{49} +12.4010 q^{50} +11.6983 q^{51} -1.24314 q^{52} +9.03718 q^{53} +6.36463 q^{54} -0.487384 q^{55} -8.86664 q^{56} +0.968007 q^{57} +1.22929 q^{58} -6.91845 q^{59} -5.95353 q^{60} +6.69052 q^{61} +22.6588 q^{62} +4.87869 q^{63} +5.91201 q^{64} -0.124622 q^{65} -7.00106 q^{66} +4.49018 q^{67} -21.1055 q^{68} -15.4828 q^{69} -1.53539 q^{70} +3.31155 q^{71} -28.0781 q^{72} +10.8701 q^{73} -7.53506 q^{74} +12.5662 q^{75} -1.74644 q^{76} -1.27054 q^{77} -1.79014 q^{78} +1.74281 q^{79} +4.31362 q^{80} -5.34233 q^{81} -9.58307 q^{82} +7.53371 q^{83} -15.5200 q^{84} -2.11577 q^{85} +13.8262 q^{86} +1.24566 q^{87} +7.31226 q^{88} +18.0761 q^{89} -4.86213 q^{90} -0.324870 q^{91} +27.9335 q^{92} +22.9606 q^{93} -21.8827 q^{94} -0.175076 q^{95} +24.3513 q^{96} +8.57881 q^{97} +14.1835 q^{98} -4.02342 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9}+O(q^{10}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9	\( 279 q - 13 q^{2} - 12 q^{3} + 227 q^{4} - 20 q^{5} - 40 q^{6} - 57 q^{7} - 39 q^{8} + 175 q^{9} - 42 q^{10} - 53 q^{11} - 36 q^{12} - 75 q^{13} - 31 q^{14} - 60 q^{15} + 127 q^{16} - 55 q^{17} - 57 q^{18} - 113 q^{19} - 43 q^{20} - 103 q^{21} - 73 q^{22} - 30 q^{23} - 106 q^{24} + 75 q^{25} - 42 q^{26} - 45 q^{27} - 146 q^{28} - 92 q^{29} - 76 q^{30} - 84 q^{31} - 71 q^{32} - 117 q^{33} - 106 q^{34} - 49 q^{35} + 67 q^{36} - 123 q^{37} - 21 q^{38} - 92 q^{39} - 97 q^{40} - 116 q^{41} - 19 q^{42} - 126 q^{43} - 131 q^{44} - 85 q^{45} - 183 q^{46} - 42 q^{47} - 47 q^{48} - 22 q^{49} - 64 q^{50} - 90 q^{51} - 158 q^{52} - 60 q^{53} - 117 q^{54} - 99 q^{55} - 65 q^{56} - 182 q^{57} - 93 q^{58} - 58 q^{59} - 141 q^{60} - 217 q^{61} - 16 q^{62} - 141 q^{63} - 47 q^{64} - 197 q^{65} - 53 q^{66} - 147 q^{67} - 90 q^{68} - 103 q^{69} - 118 q^{70} - 78 q^{71} - 135 q^{72} - 282 q^{73} - 98 q^{74} - 53 q^{75} - 296 q^{76} - 53 q^{77} - 27 q^{78} - 153 q^{79} - 52 q^{80} - 89 q^{81} - 81 q^{82} - 54 q^{83} - 164 q^{84} - 303 q^{85} - 82 q^{86} - 29 q^{87} - 203 q^{88} - 185 q^{89} - 56 q^{90} - 163 q^{91} - 66 q^{92} - 156 q^{93} - 134 q^{94} - 69 q^{95} - 189 q^{96} - 212 q^{97} - 13 q^{98} - 181 q^{99}+O(q^{100}) \) 279 * q - 13 * q^2 - 12 * q^3 + 227 * q^4 - 20 * q^5 - 40 * q^6 - 57 * q^7 - 39 * q^8 + 175 * q^9 - 42 * q^10 - 53 * q^11 - 36 * q^12 - 75 * q^13 - 31 * q^14 - 60 * q^15 + 127 * q^16 - 55 * q^17 - 57 * q^18 - 113 * q^19 - 43 * q^20 - 103 * q^21 - 73 * q^22 - 30 * q^23 - 106 * q^24 + 75 * q^25 - 42 * q^26 - 45 * q^27 - 146 * q^28 - 92 * q^29 - 76 * q^30 - 84 * q^31 - 71 * q^32 - 117 * q^33 - 106 * q^34 - 49 * q^35 + 67 * q^36 - 123 * q^37 - 21 * q^38 - 92 * q^39 - 97 * q^40 - 116 * q^41 - 19 * q^42 - 126 * q^43 - 131 * q^44 - 85 * q^45 - 183 * q^46 - 42 * q^47 - 47 * q^48 - 22 * q^49 - 64 * q^50 - 90 * q^51 - 158 * q^52 - 60 * q^53 - 117 * q^54 - 99 * q^55 - 65 * q^56 - 182 * q^57 - 93 * q^58 - 58 * q^59 - 141 * q^60 - 217 * q^61 - 16 * q^62 - 141 * q^63 - 47 * q^64 - 197 * q^65 - 53 * q^66 - 147 * q^67 - 90 * q^68 - 103 * q^69 - 118 * q^70 - 78 * q^71 - 135 * q^72 - 282 * q^73 - 98 * q^74 - 53 * q^75 - 296 * q^76 - 53 * q^77 - 27 * q^78 - 153 * q^79 - 52 * q^80 - 89 * q^81 - 81 * q^82 - 54 * q^83 - 164 * q^84 - 303 * q^85 - 82 * q^86 - 29 * q^87 - 203 * q^88 - 185 * q^89 - 56 * q^90 - 163 * q^91 - 66 * q^92 - 156 * q^93 - 134 * q^94 - 69 * q^95 - 189 * q^96 - 212 * q^97 - 13 * q^98 - 181 * q^99

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