LMFDB - Embedded newform 8039.2.a.b.1.19

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:	$0$
Dimension:	$391$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-2.61852 q^{2} +1.44668 q^{3} +4.85663 q^{4} +3.17736 q^{5} -3.78815 q^{6} +3.56525 q^{7} -7.48013 q^{8} -0.907124 q^{9} +O(q^{10})$	\(q-2.61852 q^{2} +1.44668 q^{3} +4.85663 q^{4} +3.17736 q^{5} -3.78815 q^{6} +3.56525 q^{7} -7.48013 q^{8} -0.907124 q^{9} -8.31997 q^{10} -3.91439 q^{11} +7.02598 q^{12} +3.45580 q^{13} -9.33567 q^{14} +4.59661 q^{15} +9.87359 q^{16} -1.16053 q^{17} +2.37532 q^{18} -0.890812 q^{19} +15.4313 q^{20} +5.15777 q^{21} +10.2499 q^{22} -5.16487 q^{23} -10.8213 q^{24} +5.09561 q^{25} -9.04907 q^{26} -5.65235 q^{27} +17.3151 q^{28} +0.344224 q^{29} -12.0363 q^{30} +10.0567 q^{31} -10.8939 q^{32} -5.66286 q^{33} +3.03886 q^{34} +11.3281 q^{35} -4.40557 q^{36} +9.11496 q^{37} +2.33261 q^{38} +4.99943 q^{39} -23.7671 q^{40} -0.0364855 q^{41} -13.5057 q^{42} +11.1006 q^{43} -19.0108 q^{44} -2.88226 q^{45} +13.5243 q^{46} -4.59317 q^{47} +14.2839 q^{48} +5.71102 q^{49} -13.3429 q^{50} -1.67891 q^{51} +16.7835 q^{52} +12.6679 q^{53} +14.8008 q^{54} -12.4374 q^{55} -26.6686 q^{56} -1.28872 q^{57} -0.901356 q^{58} +9.92623 q^{59} +22.3240 q^{60} -3.66724 q^{61} -26.3338 q^{62} -3.23413 q^{63} +8.77868 q^{64} +10.9803 q^{65} +14.8283 q^{66} -2.78608 q^{67} -5.63625 q^{68} -7.47191 q^{69} -29.6628 q^{70} -9.44635 q^{71} +6.78541 q^{72} +2.48467 q^{73} -23.8677 q^{74} +7.37170 q^{75} -4.32634 q^{76} -13.9558 q^{77} -13.0911 q^{78} +12.0183 q^{79} +31.3719 q^{80} -5.45575 q^{81} +0.0955379 q^{82} +12.1553 q^{83} +25.0494 q^{84} -3.68741 q^{85} -29.0670 q^{86} +0.497981 q^{87} +29.2802 q^{88} -5.90611 q^{89} +7.54724 q^{90} +12.3208 q^{91} -25.0839 q^{92} +14.5489 q^{93} +12.0273 q^{94} -2.83043 q^{95} -15.7600 q^{96} -5.93879 q^{97} -14.9544 q^{98} +3.55084 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) $ 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * 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 $

$2$	−2.61852	−1.85157	−0.925785	−	0.378049i	$-0.876595\pi$
$2$	−2.61852	−1.85157	−0.925785	+	0.378049i	$0.876595\pi$
$3$	1.44668	0.835240	0.417620	−	0.908622i	$-0.362864\pi$
$3$	1.44668	0.835240	0.417620	+	0.908622i	$0.362864\pi$
$4$	4.85663	2.42831
$5$	3.17736	1.42096	0.710479	−	0.703719i	$-0.248478\pi$
$5$	3.17736	1.42096	0.710479	+	0.703719i	$0.248478\pi$
$6$	−3.78815	−1.54651
$7$	3.56525	1.34754	0.673769	−	0.738942i	$-0.264674\pi$
$7$	3.56525	1.34754	0.673769	+	0.738942i	$0.264674\pi$
$8$	−7.48013	−2.64463
$9$	−0.907124	−0.302375
$10$	−8.31997	−2.63100
$11$	−3.91439	−1.18023	−0.590117	−	0.807318i	$-0.700918\pi$
$11$	−3.91439	−1.18023	−0.590117	+	0.807318i	$0.700918\pi$
$12$	7.02598	2.02822
$13$	3.45580	0.958467	0.479233	−	0.877687i	$-0.340915\pi$
$13$	3.45580	0.958467	0.479233	+	0.877687i	$0.340915\pi$
$14$	−9.33567	−2.49506
$15$	4.59661	1.18684
$16$	9.87359	2.46840
$17$	−1.16053	−0.281469	−0.140735	−	0.990047i	$-0.544946\pi$
$17$	−1.16053	−0.281469	−0.140735	+	0.990047i	$0.544946\pi$
$18$	2.37532	0.559868
$19$	−0.890812	−0.204366	−0.102183	−	0.994766i	$-0.532583\pi$
$19$	−0.890812	−0.204366	−0.102183	+	0.994766i	$0.532583\pi$
$20$	15.4313	3.45053
$21$	5.15777	1.12552
$22$	10.2499	2.18529
$23$	−5.16487	−1.07695	−0.538475	−	0.842641i	$-0.681000\pi$
$23$	−5.16487	−1.07695	−0.538475	+	0.842641i	$0.681000\pi$
$24$	−10.8213	−2.20890
$25$	5.09561	1.01912
$26$	−9.04907	−1.77467
$27$	−5.65235	−1.08780
$28$	17.3151	3.27225
$29$	0.344224	0.0639208	0.0319604	−	0.999489i	$-0.489825\pi$
$29$	0.344224	0.0639208	0.0319604	+	0.999489i	$0.489825\pi$
$30$	−12.0363	−2.19752
$31$	10.0567	1.80624	0.903122	−	0.429383i	$-0.141269\pi$
$31$	10.0567	1.80624	0.903122	+	0.429383i	$0.141269\pi$
$32$	−10.8939	−1.92579
$33$	−5.66286	−0.985778
$34$	3.03886	0.521160
$35$	11.3281	1.91480
$36$	−4.40557	−0.734261
$37$	9.11496	1.49849	0.749245	−	0.662293i	$-0.230416\pi$
$37$	9.11496	1.49849	0.749245	+	0.662293i	$0.230416\pi$
$38$	2.33261	0.378399
$39$	4.99943	0.800550
$40$	−23.7671	−3.75790
$41$	−0.0364855	−0.00569808	−0.00284904	−	0.999996i	$-0.500907\pi$
$41$	−0.0364855	−0.00569808	−0.00284904	+	0.999996i	$0.500907\pi$
$42$	−13.5057	−2.08398
$43$	11.1006	1.69282	0.846409	−	0.532533i	$-0.178760\pi$
$43$	11.1006	1.69282	0.846409	+	0.532533i	$0.178760\pi$
$44$	−19.0108	−2.86598
$45$	−2.88226	−0.429662
$46$	13.5243	1.99405
$47$	−4.59317	−0.669983	−0.334991	−	0.942221i	$-0.608733\pi$
$47$	−4.59317	−0.669983	−0.334991	+	0.942221i	$0.608733\pi$
$48$	14.2839	2.06170
$49$	5.71102	0.815860
$50$	−13.3429	−1.88697
$51$	−1.67891	−0.235094
$52$	16.7835	2.32746
$53$	12.6679	1.74008	0.870038	−	0.492984i	$-0.164094\pi$
$53$	12.6679	1.74008	0.870038	+	0.492984i	$0.164094\pi$
$54$	14.8008	2.01413
$55$	−12.4374	−1.67706
$56$	−26.6686	−3.56374
$57$	−1.28872	−0.170695
$58$	−0.901356	−0.118354
$59$	9.92623	1.29229	0.646143	−	0.763217i	$-0.276381\pi$
$59$	9.92623	1.29229	0.646143	+	0.763217i	$0.276381\pi$
$60$	22.3240	2.88202
$61$	−3.66724	−0.469543	−0.234771	−	0.972051i	$-0.575434\pi$
$61$	−3.66724	−0.469543	−0.234771	+	0.972051i	$0.575434\pi$
$62$	−26.3338	−3.34439
$63$	−3.23413	−0.407462
$64$	8.77868	1.09734
$65$	10.9803	1.36194
$66$	14.8283	1.82524
$67$	−2.78608	−0.340374	−0.170187	−	0.985412i	$-0.554437\pi$
$67$	−2.78608	−0.340374	−0.170187	+	0.985412i	$0.554437\pi$
$68$	−5.63625	−0.683496
$69$	−7.47191	−0.899512
$70$	−29.6628	−3.54538
$71$	−9.44635	−1.12108	−0.560538	−	0.828129i	$-0.689406\pi$
$71$	−9.44635	−1.12108	−0.560538	+	0.828129i	$0.689406\pi$
$72$	6.78541	0.799668
$73$	2.48467	0.290809	0.145404	−	0.989372i	$-0.453552\pi$
$73$	2.48467	0.290809	0.145404	+	0.989372i	$0.453552\pi$
$74$	−23.8677	−2.77456
$75$	7.37170	0.851210
$76$	−4.32634	−0.496266
$77$	−13.9558	−1.59041
$78$	−13.0911	−1.48227
$79$	12.0183	1.35216	0.676079	−	0.736829i	$-0.263678\pi$
$79$	12.0183	1.35216	0.676079	+	0.736829i	$0.263678\pi$
$80$	31.3719	3.50749
$81$	−5.45575	−0.606195
$82$	0.0955379	0.0105504
$83$	12.1553	1.33422	0.667109	−	0.744960i	$-0.267532\pi$
$83$	12.1553	1.33422	0.667109	+	0.744960i	$0.267532\pi$
$84$	25.0494	2.73311
$85$	−3.68741	−0.399956
$86$	−29.0670	−3.13437
$87$	0.497981	0.0533891
$88$	29.2802	3.12128
$89$	−5.90611	−0.626046	−0.313023	−	0.949746i	$-0.601342\pi$
$89$	−5.90611	−0.626046	−0.313023	+	0.949746i	$0.601342\pi$
$90$	7.54724	0.795549
$91$	12.3208	1.29157
$92$	−25.0839	−2.61518
$93$	14.5489	1.50865
$94$	12.0273	1.24052
$95$	−2.83043	−0.290396
$96$	−15.7600	−1.60849
$97$	−5.93879	−0.602993	−0.301497	−	0.953467i	$-0.597486\pi$
$97$	−5.93879	−0.602993	−0.301497	+	0.953467i	$0.597486\pi$
$98$	−14.9544	−1.51062
$99$	3.55084	0.356873
$100$	24.7475	2.47475
$101$	−9.72491	−0.967665	−0.483832	−	0.875161i	$-0.660756\pi$
$101$	−9.72491	−0.967665	−0.483832	+	0.875161i	$0.660756\pi$
$102$	4.39625	0.435294
$103$	8.84198	0.871226	0.435613	−	0.900134i	$-0.356532\pi$
$103$	8.84198	0.871226	0.435613	+	0.900134i	$0.356532\pi$
$104$	−25.8499	−2.53479
$105$	16.3881	1.59931
$106$	−33.1712	−3.22188
$107$	−7.74595	−0.748829	−0.374415	−	0.927261i	$-0.622156\pi$
$107$	−7.74595	−0.748829	−0.374415	+	0.927261i	$0.622156\pi$
$108$	−27.4514	−2.64151
$109$	−12.4088	−1.18855	−0.594276	−	0.804262i	$-0.702561\pi$
$109$	−12.4088	−1.18855	−0.594276	+	0.804262i	$0.702561\pi$
$110$	32.5676	3.10520
$111$	13.1864	1.25160
$112$	35.2018	3.32626
$113$	−1.86003	−0.174977	−0.0874886	−	0.996166i	$-0.527884\pi$
$113$	−1.86003	−0.174977	−0.0874886	+	0.996166i	$0.527884\pi$
$114$	3.37453	0.316053
$115$	−16.4107	−1.53030
$116$	1.67177	0.155220
$117$	−3.13484	−0.289816
$118$	−25.9920	−2.39276
$119$	−4.13757	−0.379290
$120$	−34.3833	−3.13875
$121$	4.32247	0.392952
$122$	9.60274	0.869391
$123$	−0.0527828	−0.00475926
$124$	48.8419	4.38613
$125$	0.303772	0.0271702
$126$	8.46861	0.754444
$127$	−22.4447	−1.99165	−0.995824	−	0.0912943i	$-0.970900\pi$
$127$	−22.4447	−1.99165	−0.995824	+	0.0912943i	$0.970900\pi$
$128$	−1.19932	−0.106006
$129$	16.0589	1.41391
$130$	−28.7522	−2.52173
$131$	14.2647	1.24631	0.623157	−	0.782097i	$-0.285850\pi$
$131$	14.2647	1.24631	0.623157	+	0.782097i	$0.285850\pi$
$132$	−27.5024	−2.39378
$133$	−3.17597	−0.275391
$134$	7.29541	0.630227
$135$	−17.9595	−1.54571
$136$	8.68090	0.744381
$137$	0.356634	0.0304693	0.0152346	−	0.999884i	$-0.495150\pi$
$137$	0.356634	0.0304693	0.0152346	+	0.999884i	$0.495150\pi$
$138$	19.5653	1.66551
$139$	−1.72312	−0.146153	−0.0730764	−	0.997326i	$-0.523282\pi$
$139$	−1.72312	−0.146153	−0.0730764	+	0.997326i	$0.523282\pi$
$140$	55.0163	4.64973
$141$	−6.64483	−0.559596
$142$	24.7354	2.07575
$143$	−13.5274	−1.13122
$144$	−8.95658	−0.746381
$145$	1.09372	0.0908287
$146$	−6.50615	−0.538453
$147$	8.26200	0.681438
$148$	44.2680	3.63881
$149$	−10.2178	−0.837077	−0.418539	−	0.908199i	$-0.637458\pi$
$149$	−10.2178	−0.837077	−0.418539	+	0.908199i	$0.637458\pi$
$150$	−19.3029	−1.57608
$151$	−2.12987	−0.173327	−0.0866634	−	0.996238i	$-0.527620\pi$
$151$	−2.12987	−0.173327	−0.0866634	+	0.996238i	$0.527620\pi$
$152$	6.66339	0.540472
$153$	1.05274	0.0851092
$154$	36.5435	2.94476
$155$	31.9539	2.56660
$156$	24.2804	1.94399
$157$	7.73565	0.617372	0.308686	−	0.951164i	$-0.400111\pi$
$157$	7.73565	0.617372	0.308686	+	0.951164i	$0.400111\pi$
$158$	−31.4700	−2.50362
$159$	18.3264	1.45338
$160$	−34.6138	−2.73646
$161$	−18.4141	−1.45123
$162$	14.2860	1.12241
$163$	9.47447	0.742098	0.371049	−	0.928613i	$-0.378998\pi$
$163$	9.47447	0.742098	0.371049	+	0.928613i	$0.378998\pi$
$164$	−0.177197	−0.0138367
$165$	−17.9929	−1.40075
$166$	−31.8289	−2.47040
$167$	6.16995	0.477445	0.238723	−	0.971088i	$-0.423271\pi$
$167$	6.16995	0.477445	0.238723	+	0.971088i	$0.423271\pi$
$168$	−38.5808	−2.97657
$169$	−1.05743	−0.0813411
$170$	9.65554	0.740546
$171$	0.808077	0.0617952
$172$	53.9113	4.11070
$173$	22.4025	1.70323	0.851616	−	0.524167i	$-0.175623\pi$
$173$	22.4025	1.70323	0.851616	+	0.524167i	$0.175623\pi$
$174$	−1.30397	−0.0988538
$175$	18.1671	1.37330
$176$	−38.6491	−2.91329
$177$	14.3601	1.07937
$178$	15.4652	1.15917
$179$	13.6812	1.02258	0.511291	−	0.859408i	$-0.329167\pi$
$179$	13.6812	1.02258	0.511291	+	0.859408i	$0.329167\pi$
$180$	−13.9981	−1.04335
$181$	17.6598	1.31264	0.656320	−	0.754483i	$-0.272112\pi$
$181$	17.6598	1.31264	0.656320	+	0.754483i	$0.272112\pi$
$182$	−32.2622	−2.39144
$183$	−5.30532	−0.392181
$184$	38.6339	2.84813
$185$	28.9615	2.12929
$186$	−38.0964	−2.79337
$187$	4.54276	0.332199
$188$	−22.3073	−1.62693
$189$	−20.1520	−1.46585
$190$	7.41152	0.537688
$191$	6.52308	0.471994	0.235997	−	0.971754i	$-0.424165\pi$
$191$	6.52308	0.471994	0.235997	+	0.971754i	$0.424165\pi$
$192$	12.6999	0.916538
$193$	19.6539	1.41472	0.707359	−	0.706854i	$-0.249886\pi$
$193$	19.6539	1.41472	0.707359	+	0.706854i	$0.249886\pi$
$194$	15.5508	1.11648
$195$	15.8850	1.13755
$196$	27.7363	1.98116
$197$	18.8058	1.33986	0.669928	−	0.742426i	$-0.266325\pi$
$197$	18.8058	1.33986	0.669928	+	0.742426i	$0.266325\pi$
$198$	−9.29794	−0.660776
$199$	−14.9198	−1.05764	−0.528818	−	0.848735i	$-0.677365\pi$
$199$	−14.9198	−1.05764	−0.528818	+	0.848735i	$0.677365\pi$
$200$	−38.1158	−2.69519
$201$	−4.03057	−0.284294
$202$	25.4648	1.79170
$203$	1.22724	0.0861357
$204$	−8.15384	−0.570883
$205$	−0.115928	−0.00809673
$206$	−23.1529	−1.61314
$207$	4.68518	0.325643
$208$	34.1212	2.36588
$209$	3.48699	0.241200
$210$	−42.9125	−2.96124
$211$	−14.8237	−1.02050	−0.510252	−	0.860025i	$-0.670448\pi$
$211$	−14.8237	−1.02050	−0.510252	+	0.860025i	$0.670448\pi$
$212$	61.5235	4.22545
$213$	−13.6658	−0.936367
$214$	20.2829	1.38651
$215$	35.2704	2.40542
$216$	42.2803	2.87681
$217$	35.8548	2.43398
$218$	32.4927	2.20069
$219$	3.59452	0.242895
$220$	−60.4040	−4.07244
$221$	−4.01055	−0.269779
$222$	−34.5288	−2.31742
$223$	−11.2824	−0.755528	−0.377764	−	0.925902i	$-0.623307\pi$
$223$	−11.2824	−0.755528	−0.377764	+	0.925902i	$0.623307\pi$
$224$	−38.8395	−2.59507
$225$	−4.62235	−0.308157
$226$	4.87053	0.323983
$227$	−22.9752	−1.52492	−0.762459	−	0.647037i	$-0.776008\pi$
$227$	−22.9752	−1.52492	−0.762459	+	0.647037i	$0.776008\pi$
$228$	−6.25882	−0.414501
$229$	−17.7965	−1.17603	−0.588014	−	0.808851i	$-0.700090\pi$
$229$	−17.7965	−1.17603	−0.588014	+	0.808851i	$0.700090\pi$
$230$	42.9716	2.83346
$231$	−20.1895	−1.32837
$232$	−2.57484	−0.169047
$233$	6.14157	0.402348	0.201174	−	0.979556i	$-0.435524\pi$
$233$	6.14157	0.402348	0.201174	+	0.979556i	$0.435524\pi$
$234$	8.20864	0.536615
$235$	−14.5941	−0.952017
$236$	48.2080	3.13808
$237$	17.3865	1.12938
$238$	10.8343	0.702283
$239$	−0.261418	−0.0169097	−0.00845485	−	0.999964i	$-0.502691\pi$
$239$	−0.261418	−0.0169097	−0.00845485	+	0.999964i	$0.502691\pi$
$240$	45.3851	2.92959
$241$	9.57180	0.616574	0.308287	−	0.951293i	$-0.400244\pi$
$241$	9.57180	0.616574	0.308287	+	0.951293i	$0.400244\pi$
$242$	−11.3185	−0.727579
$243$	9.06433	0.581477
$244$	−17.8104	−1.14020
$245$	18.1460	1.15930
$246$	0.138213	0.00881211
$247$	−3.07847	−0.195878
$248$	−75.2258	−4.77684
$249$	17.5848	1.11439
$250$	−0.795432	−0.0503076
$251$	7.51899	0.474594	0.237297	−	0.971437i	$-0.423739\pi$
$251$	7.51899	0.474594	0.237297	+	0.971437i	$0.423739\pi$
$252$	−15.7070	−0.989445
$253$	20.2173	1.27105
$254$	58.7719	3.68768
$255$	−5.33449	−0.334059
$256$	−14.4169	−0.901058
$257$	18.3704	1.14591	0.572957	−	0.819585i	$-0.305796\pi$
$257$	18.3704	1.14591	0.572957	+	0.819585i	$0.305796\pi$
$258$	−42.0506	−2.61795
$259$	32.4971	2.01927
$260$	53.3273	3.30722
$261$	−0.312254	−0.0193280
$262$	−37.3524	−2.30764
$263$	−15.3515	−0.946613	−0.473307	−	0.880898i	$-0.656940\pi$
$263$	−15.3515	−0.946613	−0.473307	+	0.880898i	$0.656940\pi$
$264$	42.3590	2.60701
$265$	40.2506	2.47258
$266$	8.31632	0.509907
$267$	−8.54423	−0.522898
$268$	−13.5310	−0.826536
$269$	−3.11332	−0.189823	−0.0949114	−	0.995486i	$-0.530257\pi$
$269$	−3.11332	−0.189823	−0.0949114	+	0.995486i	$0.530257\pi$
$270$	47.0273	2.86199
$271$	9.81320	0.596109	0.298055	−	0.954549i	$-0.403662\pi$
$271$	9.81320	0.596109	0.298055	+	0.954549i	$0.403662\pi$
$272$	−11.4586	−0.694778
$273$	17.8242	1.07877
$274$	−0.933852	−0.0564161
$275$	−19.9462	−1.20280
$276$	−36.2883	−2.18430
$277$	26.4101	1.58683	0.793414	−	0.608682i	$-0.208301\pi$
$277$	26.4101	1.58683	0.793414	+	0.608682i	$0.208301\pi$
$278$	4.51201	0.270612
$279$	−9.12272	−0.546163
$280$	−84.7356	−5.06392
$281$	20.5349	1.22501	0.612506	−	0.790466i	$-0.290161\pi$
$281$	20.5349	1.22501	0.612506	+	0.790466i	$0.290161\pi$
$282$	17.3996	1.03613
$283$	−5.97229	−0.355015	−0.177508	−	0.984119i	$-0.556803\pi$
$283$	−5.97229	−0.355015	−0.177508	+	0.984119i	$0.556803\pi$
$284$	−45.8774	−2.72232
$285$	−4.09472	−0.242550
$286$	35.4216	2.09453
$287$	−0.130080	−0.00767838
$288$	9.88213	0.582310
$289$	−15.6532	−0.920775
$290$	−2.86393	−0.168176
$291$	−8.59152	−0.503644
$292$	12.0671	0.706175
$293$	20.2945	1.18562	0.592808	−	0.805344i	$-0.298019\pi$
$293$	20.2945	1.18562	0.592808	+	0.805344i	$0.298019\pi$
$294$	−21.6342	−1.26173
$295$	31.5392	1.83628
$296$	−68.1811	−3.96295
$297$	22.1255	1.28385
$298$	26.7556	1.54991
$299$	−17.8488	−1.03222
$300$	35.8016	2.06701
$301$	39.5763	2.28114
$302$	5.57711	0.320927
$303$	−14.0688	−0.808232
$304$	−8.79551	−0.504457
$305$	−11.6521	−0.667200
$306$	−2.75662	−0.157586
$307$	17.4199	0.994204	0.497102	−	0.867692i	$-0.334398\pi$
$307$	17.4199	0.994204	0.497102	+	0.867692i	$0.334398\pi$
$308$	−67.7781	−3.86202
$309$	12.7915	0.727683
$310$	−83.6718	−4.75224
$311$	23.8246	1.35097	0.675484	−	0.737375i	$-0.263935\pi$
$311$	23.8246	1.35097	0.675484	+	0.737375i	$0.263935\pi$
$312$	−37.3964	−2.11715
$313$	−21.8323	−1.23403	−0.617017	−	0.786950i	$-0.711659\pi$
$313$	−21.8323	−1.23403	−0.617017	+	0.786950i	$0.711659\pi$
$314$	−20.2559	−1.14311
$315$	−10.2760	−0.578986
$316$	58.3682	3.28347
$317$	12.5215	0.703276	0.351638	−	0.936136i	$-0.385625\pi$
$317$	12.5215	0.703276	0.351638	+	0.936136i	$0.385625\pi$
$318$	−47.9881	−2.69104
$319$	−1.34743	−0.0754414
$320$	27.8930	1.55927
$321$	−11.2059	−0.625452
$322$	48.2176	2.68706
$323$	1.03381	0.0575228
$324$	−26.4966	−1.47203
$325$	17.6094	0.976794
$326$	−24.8091	−1.37405
$327$	−17.9516	−0.992725
$328$	0.272916	0.0150693
$329$	−16.3758	−0.902827
$330$	47.1148	2.59359
$331$	−23.1192	−1.27075	−0.635373	−	0.772205i	$-0.719154\pi$
$331$	−23.1192	−1.27075	−0.635373	+	0.772205i	$0.719154\pi$
$332$	59.0338	3.23990
$333$	−8.26840	−0.453106
$334$	−16.1561	−0.884024
$335$	−8.85239	−0.483658
$336$	50.9257	2.77823
$337$	−27.1141	−1.47700	−0.738500	−	0.674253i	$-0.764466\pi$
$337$	−27.1141	−1.47700	−0.738500	+	0.674253i	$0.764466\pi$
$338$	2.76891	0.150609
$339$	−2.69087	−0.146148
$340$	−17.9084	−0.971219
$341$	−39.3661	−2.13179
$342$	−2.11596	−0.114418
$343$	−4.59554	−0.248136
$344$	−83.0336	−4.47687
$345$	−23.7409	−1.27817
$346$	−58.6614	−3.15365
$347$	6.04363	0.324439	0.162219	−	0.986755i	$-0.448135\pi$
$347$	6.04363	0.324439	0.162219	+	0.986755i	$0.448135\pi$
$348$	2.41851	0.129646
$349$	16.9954	0.909744	0.454872	−	0.890557i	$-0.349685\pi$
$349$	16.9954	0.909744	0.454872	+	0.890557i	$0.349685\pi$
$350$	−47.5709	−2.54277
$351$	−19.5334	−1.04262
$352$	42.6430	2.27288
$353$	1.28684	0.0684916	0.0342458	−	0.999413i	$-0.489097\pi$
$353$	1.28684	0.0684916	0.0342458	+	0.999413i	$0.489097\pi$
$354$	−37.6020	−1.99853
$355$	−30.0144	−1.59300
$356$	−28.6838	−1.52024
$357$	−5.98573	−0.316798
$358$	−35.8245	−1.89338
$359$	−30.3952	−1.60420	−0.802098	−	0.597193i	$-0.796283\pi$
$359$	−30.3952	−1.60420	−0.802098	+	0.597193i	$0.796283\pi$
$360$	21.5597	1.13630
$361$	−18.2065	−0.958234
$362$	−46.2424	−2.43044
$363$	6.25322	0.328209
$364$	59.8376	3.13634
$365$	7.89469	0.413227
$366$	13.8921	0.726150
$367$	−9.91723	−0.517675	−0.258838	−	0.965921i	$-0.583339\pi$
$367$	−9.91723	−0.517675	−0.258838	+	0.965921i	$0.583339\pi$
$368$	−50.9959	−2.65834
$369$	0.0330969	0.00172296
$370$	−75.8362	−3.94253
$371$	45.1644	2.34482
$372$	70.6585	3.66347
$373$	23.0519	1.19358	0.596790	−	0.802397i	$-0.296443\pi$
$373$	23.0519	1.19358	0.596790	+	0.802397i	$0.296443\pi$
$374$	−11.8953	−0.615091
$375$	0.439460	0.0226936
$376$	34.3575	1.77185
$377$	1.18957	0.0612659
$378$	52.7685	2.71412
$379$	−27.5537	−1.41534	−0.707670	−	0.706543i	$-0.750254\pi$
$379$	−27.5537	−1.41534	−0.707670	+	0.706543i	$0.750254\pi$
$380$	−13.7463	−0.705172
$381$	−32.4703	−1.66350
$382$	−17.0808	−0.873930
$383$	23.8420	1.21827	0.609135	−	0.793067i	$-0.291517\pi$
$383$	23.8420	1.21827	0.609135	+	0.793067i	$0.291517\pi$
$384$	−1.73503	−0.0885403
$385$	−44.3426	−2.25991
$386$	−51.4640	−2.61945
$387$	−10.0696	−0.511866
$388$	−28.8425	−1.46426
$389$	−2.59070	−0.131354	−0.0656770	−	0.997841i	$-0.520921\pi$
$389$	−2.59070	−0.131354	−0.0656770	+	0.997841i	$0.520921\pi$
$390$	−41.5951	−2.10625
$391$	5.99398	0.303128
$392$	−42.7192	−2.15764
$393$	20.6364	1.04097
$394$	−49.2432	−2.48084
$395$	38.1863	1.92136
$396$	17.2451	0.866600
$397$	−6.66332	−0.334423	−0.167211	−	0.985921i	$-0.553476\pi$
$397$	−6.66332	−0.334423	−0.167211	+	0.985921i	$0.553476\pi$
$398$	39.0677	1.95829
$399$	−4.59460	−0.230018
$400$	50.3119	2.51560
$401$	−0.0606807	−0.00303025	−0.00151512	−	0.999999i	$-0.500482\pi$
$401$	−0.0606807	−0.00303025	−0.00151512	+	0.999999i	$0.500482\pi$
$402$	10.5541	0.526391
$403$	34.7541	1.73123
$404$	−47.2303	−2.34979
$405$	−17.3349	−0.861377
$406$	−3.21356	−0.159486
$407$	−35.6795	−1.76857
$408$	12.5585	0.621736
$409$	−17.0824	−0.844668	−0.422334	−	0.906440i	$-0.638789\pi$
$409$	−17.0824	−0.844668	−0.422334	+	0.906440i	$0.638789\pi$
$410$	0.303558	0.0149917
$411$	0.515934	0.0254492
$412$	42.9422	2.11561
$413$	35.3895	1.74140
$414$	−12.2682	−0.602951
$415$	38.6217	1.89587
$416$	−37.6472	−1.84580
$417$	−2.49279	−0.122073
$418$	−9.13073	−0.446599
$419$	25.9107	1.26582	0.632911	−	0.774225i	$-0.281860\pi$
$419$	25.9107	1.26582	0.632911	+	0.774225i	$0.281860\pi$
$420$	79.5908	3.88364
$421$	26.4130	1.28729	0.643645	−	0.765324i	$-0.277421\pi$
$421$	26.4130	1.28729	0.643645	+	0.765324i	$0.277421\pi$
$422$	38.8160	1.88953
$423$	4.16658	0.202586
$424$	−94.7579	−4.60185
$425$	−5.91359	−0.286851
$426$	35.7842	1.73375
$427$	−13.0746	−0.632727
$428$	−37.6192	−1.81839
$429$	−19.5697	−0.944836
$430$	−92.3562	−4.45381
$431$	−2.40265	−0.115732	−0.0578659	−	0.998324i	$-0.518430\pi$
$431$	−2.40265	−0.115732	−0.0578659	+	0.998324i	$0.518430\pi$
$432$	−55.8090	−2.68511
$433$	−6.35488	−0.305396	−0.152698	−	0.988273i	$-0.548796\pi$
$433$	−6.35488	−0.305396	−0.152698	+	0.988273i	$0.548796\pi$
$434$	−93.8865	−4.50669
$435$	1.58226	0.0758637
$436$	−60.2651	−2.88618
$437$	4.60093	0.220092
$438$	−9.41230	−0.449737
$439$	32.4437	1.54845	0.774227	−	0.632908i	$-0.218139\pi$
$439$	32.4437	1.54845	0.774227	+	0.632908i	$0.218139\pi$
$440$	93.0336	4.43520
$441$	−5.18060	−0.246695
$442$	10.5017	0.499515
$443$	16.9696	0.806250	0.403125	−	0.915145i	$-0.367924\pi$
$443$	16.9696	0.806250	0.403125	+	0.915145i	$0.367924\pi$
$444$	64.0415	3.03928
$445$	−18.7658	−0.889585
$446$	29.5433	1.39891
$447$	−14.7819	−0.699160
$448$	31.2982	1.47870
$449$	−4.05489	−0.191362	−0.0956810	−	0.995412i	$-0.530503\pi$
$449$	−4.05489	−0.191362	−0.0956810	+	0.995412i	$0.530503\pi$
$450$	12.1037	0.570574
$451$	0.142819	0.00672507
$452$	−9.03349	−0.424900
$453$	−3.08124	−0.144769
$454$	60.1610	2.82349
$455$	39.1476	1.83527
$456$	9.63978	0.451424
$457$	24.8433	1.16212	0.581060	−	0.813861i	$-0.302638\pi$
$457$	24.8433	1.16212	0.581060	+	0.813861i	$0.302638\pi$
$458$	46.6005	2.17750
$459$	6.55970	0.306181
$460$	−79.7005	−3.71605
$461$	−28.4478	−1.32494	−0.662472	−	0.749086i	$-0.730493\pi$
$461$	−28.4478	−1.32494	−0.662472	+	0.749086i	$0.730493\pi$
$462$	52.8666	2.45958
$463$	−24.9732	−1.16060	−0.580300	−	0.814402i	$-0.697065\pi$
$463$	−24.9732	−1.16060	−0.580300	+	0.814402i	$0.697065\pi$
$464$	3.39873	0.157782
$465$	46.2270	2.14372
$466$	−16.0818	−0.744975
$467$	−2.62834	−0.121625	−0.0608125	−	0.998149i	$-0.519369\pi$
$467$	−2.62834	−0.121625	−0.0608125	+	0.998149i	$0.519369\pi$
$468$	−15.2248	−0.703765
$469$	−9.93309	−0.458668
$470$	38.2150	1.76273
$471$	11.1910	0.515654
$472$	−74.2495	−3.41761
$473$	−43.4519	−1.99792
$474$	−45.5269	−2.09112
$475$	−4.53922	−0.208274
$476$	−20.0946	−0.921037
$477$	−11.4914	−0.526155
$478$	0.684526	0.0313095
$479$	−3.25943	−0.148927	−0.0744636	−	0.997224i	$-0.523724\pi$
$479$	−3.25943	−0.148927	−0.0744636	+	0.997224i	$0.523724\pi$
$480$	−50.0751	−2.28560
$481$	31.4995	1.43625
$482$	−25.0639	−1.14163
$483$	−26.6392	−1.21213
$484$	20.9927	0.954211
$485$	−18.8697	−0.856828
$486$	−23.7351	−1.07665
$487$	33.8681	1.53471	0.767354	−	0.641223i	$-0.221573\pi$
$487$	33.8681	1.53471	0.767354	+	0.641223i	$0.221573\pi$
$488$	27.4315	1.24176
$489$	13.7065	0.619829
$490$	−47.5155	−2.14653
$491$	−28.4073	−1.28200	−0.641001	−	0.767540i	$-0.721481\pi$
$491$	−28.4073	−1.28200	−0.641001	+	0.767540i	$0.721481\pi$
$492$	−0.256346	−0.0115570
$493$	−0.399481	−0.0179917
$494$	8.06102	0.362682
$495$	11.2823	0.507101
$496$	99.2962	4.45853
$497$	−33.6786	−1.51069
$498$	−46.0461	−2.06337
$499$	15.8677	0.710335	0.355167	−	0.934803i	$-0.384424\pi$
$499$	15.8677	0.710335	0.355167	+	0.934803i	$0.384424\pi$
$500$	1.47531	0.0659778
$501$	8.92593	0.398781
$502$	−19.6886	−0.878745
$503$	−16.0505	−0.715654	−0.357827	−	0.933788i	$-0.616482\pi$
$503$	−16.0505	−0.715654	−0.357827	+	0.933788i	$0.616482\pi$
$504$	24.1917	1.07758
$505$	−30.8995	−1.37501
$506$	−52.9395	−2.35345
$507$	−1.52977	−0.0679393
$508$	−109.006	−4.83635
$509$	4.62446	0.204976	0.102488	−	0.994734i	$-0.467320\pi$
$509$	4.62446	0.204976	0.102488	+	0.994734i	$0.467320\pi$
$510$	13.9685	0.618534
$511$	8.85847	0.391876
$512$	40.1496	1.77438
$513$	5.03518	0.222309
$514$	−48.1032	−2.12174
$515$	28.0941	1.23798
$516$	77.9922	3.43342
$517$	17.9795	0.790736
$518$	−85.0943	−3.73883
$519$	32.4092	1.42261
$520$	−82.1343	−3.60183
$521$	8.48440	0.371708	0.185854	−	0.982577i	$-0.440495\pi$
$521$	8.48440	0.371708	0.185854	+	0.982577i	$0.440495\pi$
$522$	0.817642	0.0357872
$523$	−32.1838	−1.40730	−0.703649	−	0.710548i	$-0.748447\pi$
$523$	−32.1838	−1.40730	−0.703649	+	0.710548i	$0.748447\pi$
$524$	69.2784	3.02644
$525$	26.2820	1.14704
$526$	40.1981	1.75272
$527$	−11.6711	−0.508402
$528$	−55.9128	−2.43329
$529$	3.67593	0.159823
$530$	−105.397	−4.57815
$531$	−9.00433	−0.390755
$532$	−15.4245	−0.668737
$533$	−0.126087	−0.00546142
$534$	22.3732	0.968183
$535$	−24.6117	−1.06405
$536$	20.8403	0.900163
$537$	19.7923	0.854101
$538$	8.15229	0.351470
$539$	−22.3552	−0.962905
$540$	−87.2228	−3.75347
$541$	27.9119	1.20003	0.600013	−	0.799990i	$-0.295162\pi$
$541$	27.9119	1.20003	0.600013	+	0.799990i	$0.295162\pi$
$542$	−25.6960	−1.10374
$543$	25.5480	1.09637
$544$	12.6427	0.542050
$545$	−39.4273	−1.68888
$546$	−46.6730	−1.99742
$547$	25.8459	1.10509	0.552546	−	0.833483i	$-0.313657\pi$
$547$	25.8459	1.10509	0.552546	+	0.833483i	$0.313657\pi$
$548$	1.73204	0.0739890
$549$	3.32665	0.141978
$550$	52.2295	2.22707
$551$	−0.306639	−0.0130632
$552$	55.8909	2.37887
$553$	42.8481	1.82209
$554$	−69.1553	−2.93813
$555$	41.8979	1.77847
$556$	−8.36854	−0.354905
$557$	−1.88175	−0.0797321	−0.0398660	−	0.999205i	$-0.512693\pi$
$557$	−1.88175	−0.0797321	−0.0398660	+	0.999205i	$0.512693\pi$
$558$	23.8880	1.01126
$559$	38.3613	1.62251
$560$	111.849	4.72648
$561$	6.57191	0.277466
$562$	−53.7711	−2.26820
$563$	24.3317	1.02546	0.512729	−	0.858551i	$-0.328635\pi$
$563$	24.3317	1.02546	0.512729	+	0.858551i	$0.328635\pi$
$564$	−32.2715	−1.35888
$565$	−5.90999	−0.248635
$566$	15.6385	0.657336
$567$	−19.4511	−0.816871
$568$	70.6600	2.96483
$569$	26.6170	1.11584	0.557921	−	0.829894i	$-0.311599\pi$
$569$	26.6170	1.11584	0.557921	+	0.829894i	$0.311599\pi$
$570$	10.7221	0.449099
$571$	37.7228	1.57865	0.789324	−	0.613977i	$-0.210431\pi$
$571$	37.7228	1.57865	0.789324	+	0.613977i	$0.210431\pi$
$572$	−65.6974	−2.74695
$573$	9.43679	0.394228
$574$	0.340617	0.0142171
$575$	−26.3182	−1.09754
$576$	−7.96336	−0.331807
$577$	−34.7635	−1.44722	−0.723612	−	0.690207i	$-0.757520\pi$
$577$	−34.7635	−1.44722	−0.723612	+	0.690207i	$0.757520\pi$
$578$	40.9881	1.70488
$579$	28.4328	1.18163
$580$	5.31180	0.220561
$581$	43.3367	1.79791
$582$	22.4970	0.932532
$583$	−49.5873	−2.05370
$584$	−18.5857	−0.769080
$585$	−9.96052	−0.411817
$586$	−53.1414	−2.19525
$587$	−1.89976	−0.0784116	−0.0392058	−	0.999231i	$-0.512483\pi$
$587$	−1.89976	−0.0784116	−0.0392058	+	0.999231i	$0.512483\pi$
$588$	40.1255	1.65475
$589$	−8.95867	−0.369135
$590$	−82.5859	−3.40001
$591$	27.2059	1.11910
$592$	89.9974	3.69887
$593$	−30.2926	−1.24397	−0.621984	−	0.783030i	$-0.713673\pi$
$593$	−30.2926	−1.24397	−0.621984	+	0.783030i	$0.713673\pi$
$594$	−57.9360	−2.37714
$595$	−13.1465	−0.538956
$596$	−49.6242	−2.03269
$597$	−21.5841	−0.883380
$598$	46.7373	1.91123
$599$	−29.1197	−1.18980	−0.594899	−	0.803801i	$-0.702808\pi$
$599$	−29.1197	−1.18980	−0.594899	+	0.803801i	$0.702808\pi$
$600$	−55.1413	−2.25113
$601$	22.4828	0.917093	0.458546	−	0.888670i	$-0.348370\pi$
$601$	22.4828	0.917093	0.458546	+	0.888670i	$0.348370\pi$
$602$	−103.631	−4.22369
$603$	2.52733	0.102921
$604$	−10.3440	−0.420892
$605$	13.7340	0.558368
$606$	36.8394	1.49650
$607$	−6.02546	−0.244566	−0.122283	−	0.992495i	$-0.539022\pi$
$607$	−6.02546	−0.244566	−0.122283	+	0.992495i	$0.539022\pi$
$608$	9.70442	0.393566
$609$	1.77543	0.0719439
$610$	30.5113	1.23537
$611$	−15.8731	−0.642156
$612$	5.11278	0.206672
$613$	30.0538	1.21386	0.606932	−	0.794754i	$-0.292400\pi$
$613$	30.0538	1.21386	0.606932	+	0.794754i	$0.292400\pi$
$614$	−45.6142	−1.84084
$615$	−0.167710	−0.00676271
$616$	104.391	4.20604
$617$	10.2204	0.411456	0.205728	−	0.978609i	$-0.434044\pi$
$617$	10.2204	0.411456	0.205728	+	0.978609i	$0.434044\pi$
$618$	−33.4947	−1.34736
$619$	5.78392	0.232475	0.116238	−	0.993221i	$-0.462917\pi$
$619$	5.78392	0.232475	0.116238	+	0.993221i	$0.462917\pi$
$620$	155.188	6.23251
$621$	29.1937	1.17150
$622$	−62.3851	−2.50141
$623$	−21.0568	−0.843621
$624$	49.3623	1.97608
$625$	−24.5128	−0.980513
$626$	57.1682	2.28490
$627$	5.04455	0.201460
$628$	37.5692	1.49917
$629$	−10.5782	−0.421779
$630$	26.9078	1.07203
$631$	−17.8982	−0.712517	−0.356258	−	0.934387i	$-0.615948\pi$
$631$	−17.8982	−0.712517	−0.356258	+	0.934387i	$0.615948\pi$
$632$	−89.8981	−3.57596
$633$	−21.4451	−0.852365
$634$	−32.7877	−1.30217
$635$	−71.3150	−2.83005
$636$	89.0047	3.52927
$637$	19.7361	0.781975
$638$	3.52826	0.139685
$639$	8.56901	0.338985
$640$	−3.81067	−0.150630
$641$	−42.3984	−1.67464	−0.837318	−	0.546717i	$-0.815877\pi$
$641$	−42.3984	−1.67464	−0.837318	+	0.546717i	$0.815877\pi$
$642$	29.3428	1.15807
$643$	−30.6341	−1.20809	−0.604045	−	0.796950i	$-0.706445\pi$
$643$	−30.6341	−1.20809	−0.604045	+	0.796950i	$0.706445\pi$
$644$	−89.4304	−3.52405
$645$	51.0250	2.00911
$646$	−2.70705	−0.106508
$647$	−20.2891	−0.797647	−0.398824	−	0.917028i	$-0.630581\pi$
$647$	−20.2891	−0.797647	−0.398824	+	0.917028i	$0.630581\pi$
$648$	40.8098	1.60316
$649$	−38.8552	−1.52520
$650$	−46.1105	−1.80860
$651$	51.8704	2.03296
$652$	46.0140	1.80205
$653$	36.6936	1.43593	0.717966	−	0.696078i	$-0.245073\pi$
$653$	36.6936	1.43593	0.717966	+	0.696078i	$0.245073\pi$
$654$	47.0065	1.83810
$655$	45.3241	1.77096
$656$	−0.360243	−0.0140651
$657$	−2.25390	−0.0879332
$658$	42.8803	1.67165
$659$	34.2962	1.33599	0.667995	−	0.744166i	$-0.267153\pi$
$659$	34.2962	1.33599	0.667995	+	0.744166i	$0.267153\pi$
$660$	−87.3851	−3.40146
$661$	−7.64058	−0.297184	−0.148592	−	0.988899i	$-0.547474\pi$
$661$	−7.64058	−0.297184	−0.148592	+	0.988899i	$0.547474\pi$
$662$	60.5380	2.35288
$663$	−5.80197	−0.225330
$664$	−90.9233	−3.52851
$665$	−10.0912	−0.391319
$666$	21.6510	0.838957
$667$	−1.77787	−0.0688395
$668$	29.9652	1.15939
$669$	−16.3221	−0.631047
$670$	23.1801	0.895526
$671$	14.3550	0.554170
$672$	−56.1882	−2.16751
$673$	4.68367	0.180542	0.0902711	−	0.995917i	$-0.471227\pi$
$673$	4.68367	0.180542	0.0902711	+	0.995917i	$0.471227\pi$
$674$	70.9988	2.73477
$675$	−28.8021	−1.10859
$676$	−5.13557	−0.197522
$677$	36.2761	1.39420	0.697102	−	0.716972i	$-0.254472\pi$
$677$	36.2761	1.39420	0.697102	+	0.716972i	$0.254472\pi$
$678$	7.04608	0.270603
$679$	−21.1733	−0.812556
$680$	27.5823	1.05773
$681$	−33.2377	−1.27367
$682$	103.081	3.94716
$683$	−18.4688	−0.706690	−0.353345	−	0.935493i	$-0.614956\pi$
$683$	−18.4688	−0.706690	−0.353345	+	0.935493i	$0.614956\pi$
$684$	3.92453	0.150058
$685$	1.13315	0.0432956
$686$	12.0335	0.459441
$687$	−25.7458	−0.982265
$688$	109.602	4.17855
$689$	43.7779	1.66781
$690$	62.1660	2.36662
$691$	−31.9657	−1.21603	−0.608016	−	0.793925i	$-0.708034\pi$
$691$	−31.9657	−1.21603	−0.608016	+	0.793925i	$0.708034\pi$
$692$	108.801	4.13598
$693$	12.6596	0.480900
$694$	−15.8253	−0.600721
$695$	−5.47496	−0.207677
$696$	−3.72496	−0.141194
$697$	0.0423424	0.00160383
$698$	−44.5028	−1.68446
$699$	8.88487	0.336057
$700$	88.2310	3.33482
$701$	21.6657	0.818302	0.409151	−	0.912467i	$-0.365825\pi$
$701$	21.6657	0.818302	0.409151	+	0.912467i	$0.365825\pi$
$702$	51.1485	1.93048
$703$	−8.11971	−0.306241
$704$	−34.3632	−1.29511
$705$	−21.1130	−0.795162
$706$	−3.36961	−0.126817
$707$	−34.6718	−1.30397
$708$	69.7415	2.62105
$709$	44.9945	1.68981	0.844903	−	0.534920i	$-0.179658\pi$
$709$	44.9945	1.68981	0.844903	+	0.534920i	$0.179658\pi$
$710$	78.5933	2.94955
$711$	−10.9020	−0.408859
$712$	44.1785	1.65566
$713$	−51.9418	−1.94524
$714$	15.6737	0.586575
$715$	−42.9813	−1.60741
$716$	66.4446	2.48315
$717$	−0.378187	−0.0141236
$718$	79.5903	2.97028
$719$	−41.4558	−1.54604	−0.773021	−	0.634380i	$-0.781255\pi$
$719$	−41.4558	−1.54604	−0.773021	+	0.634380i	$0.781255\pi$
$720$	−28.4583	−1.06058
$721$	31.5239	1.17401
$722$	47.6739	1.77424
$723$	13.8473	0.514987
$724$	85.7669	3.18750
$725$	1.75403	0.0651430
$726$	−16.3742	−0.607703
$727$	1.02136	0.0378800	0.0189400	−	0.999821i	$-0.493971\pi$
$727$	1.02136	0.0378800	0.0189400	+	0.999821i	$0.493971\pi$
$728$	−92.1612	−3.41572
$729$	29.4804	1.09187
$730$	−20.6724	−0.765119
$731$	−12.8825	−0.476476
$732$	−25.7660	−0.952338
$733$	−53.2591	−1.96717	−0.983584	−	0.180450i	$-0.942244\pi$
$733$	−53.2591	−1.96717	−0.983584	+	0.180450i	$0.942244\pi$
$734$	25.9684	0.958512
$735$	26.2513	0.968295
$736$	56.2656	2.07398
$737$	10.9058	0.401721
$738$	−0.0866648	−0.00319017
$739$	−34.8159	−1.28072	−0.640362	−	0.768073i	$-0.721216\pi$
$739$	−34.8159	−1.28072	−0.640362	+	0.768073i	$0.721216\pi$
$740$	140.655	5.17059
$741$	−4.45355	−0.163605
$742$	−118.264	−4.34160
$743$	3.89189	0.142780	0.0713898	−	0.997448i	$-0.477257\pi$
$743$	3.89189	0.142780	0.0713898	+	0.997448i	$0.477257\pi$
$744$	−108.827	−3.98981
$745$	−32.4657	−1.18945
$746$	−60.3617	−2.21000
$747$	−11.0264	−0.403434
$748$	22.0625	0.806685
$749$	−27.6163	−1.00908
$750$	−1.15073	−0.0420189
$751$	14.0726	0.513515	0.256757	−	0.966476i	$-0.417346\pi$
$751$	14.0726	0.513515	0.256757	+	0.966476i	$0.417346\pi$
$752$	−45.3511	−1.65378
$753$	10.8775	0.396400
$754$	−3.11491	−0.113438
$755$	−6.76737	−0.246290
$756$	−97.8710	−3.55953
$757$	5.67917	0.206413	0.103206	−	0.994660i	$-0.467090\pi$
$757$	5.67917	0.206413	0.103206	+	0.994660i	$0.467090\pi$
$758$	72.1499	2.62060
$759$	29.2480	1.06163
$760$	21.1720	0.767988
$761$	14.4597	0.524165	0.262082	−	0.965046i	$-0.415591\pi$
$761$	14.4597	0.524165	0.262082	+	0.965046i	$0.415591\pi$
$762$	85.0240	3.08009
$763$	−44.2406	−1.60162
$764$	31.6802	1.14615
$765$	3.34494	0.120937
$766$	−62.4307	−2.25571
$767$	34.3031	1.23861
$768$	−20.8566	−0.752599
$769$	−34.9860	−1.26163	−0.630814	−	0.775934i	$-0.717279\pi$
$769$	−34.9860	−1.26163	−0.630814	+	0.775934i	$0.717279\pi$
$770$	116.112	4.18438
$771$	26.5760	0.957113
$772$	95.4517	3.43538
$773$	44.7003	1.60776	0.803879	−	0.594792i	$-0.202766\pi$
$773$	44.7003	1.60776	0.803879	+	0.594792i	$0.202766\pi$
$774$	26.3674	0.947756
$775$	51.2452	1.84078
$776$	44.4230	1.59469
$777$	47.0129	1.68658
$778$	6.78380	0.243211
$779$	0.0325017	0.00116449
$780$	77.1475	2.76232
$781$	36.9767	1.32313
$782$	−15.6953	−0.561264
$783$	−1.94567	−0.0695327
$784$	56.3883	2.01387
$785$	24.5789	0.877260
$786$	−54.0369	−1.92743
$787$	−5.97963	−0.213151	−0.106575	−	0.994305i	$-0.533989\pi$
$787$	−5.97963	−0.213151	−0.106575	+	0.994305i	$0.533989\pi$
$788$	91.3326	3.25359
$789$	−22.2087	−0.790649
$790$	−99.9914	−3.55754
$791$	−6.63149	−0.235789
$792$	−26.5608	−0.943796
$793$	−12.6733	−0.450041
$794$	17.4480	0.619207
$795$	58.2297	2.06519
$796$	−72.4599	−2.56827
$797$	−2.27640	−0.0806343	−0.0403172	−	0.999187i	$-0.512837\pi$
$797$	−2.27640	−0.0806343	−0.0403172	+	0.999187i	$0.512837\pi$
$798$	12.0310	0.425894
$799$	5.33050	0.188579
$800$	−55.5110	−1.96261
$801$	5.35757	0.189301
$802$	0.158893	0.00561072
$803$	−9.72598	−0.343222
$804$	−19.5750	−0.690356
$805$	−58.5081	−2.06214
$806$	−91.0042	−3.20549
$807$	−4.50398	−0.158547
$808$	72.7436	2.55911
$809$	13.5151	0.475167	0.237583	−	0.971367i	$-0.423645\pi$
$809$	13.5151	0.475167	0.237583	+	0.971367i	$0.423645\pi$
$810$	45.3917	1.59490
$811$	21.7085	0.762288	0.381144	−	0.924516i	$-0.375530\pi$
$811$	21.7085	0.762288	0.381144	+	0.924516i	$0.375530\pi$
$812$	5.96027	0.209165
$813$	14.1965	0.497894
$814$	93.4275	3.27463
$815$	30.1038	1.05449
$816$	−16.5769	−0.580306
$817$	−9.88850	−0.345955
$818$	44.7304	1.56396
$819$	−11.1765	−0.390539
$820$	−0.563017	−0.0196614
$821$	30.3225	1.05826	0.529131	−	0.848540i	$-0.322518\pi$
$821$	30.3225	1.05826	0.529131	+	0.848540i	$0.322518\pi$
$822$	−1.35098	−0.0471209
$823$	1.05422	0.0367477	0.0183739	−	0.999831i	$-0.494151\pi$
$823$	1.05422	0.0367477	0.0183739	+	0.999831i	$0.494151\pi$
$824$	−66.1392	−2.30407
$825$	−28.8557	−1.00463
$826$	−92.6680	−3.22433
$827$	−25.9132	−0.901091	−0.450546	−	0.892753i	$-0.648771\pi$
$827$	−25.9132	−0.901091	−0.450546	+	0.892753i	$0.648771\pi$
$828$	22.7542	0.790763
$829$	−26.5327	−0.921520	−0.460760	−	0.887525i	$-0.652423\pi$
$829$	−26.5327	−0.921520	−0.460760	+	0.887525i	$0.652423\pi$
$830$	−101.132	−3.51033
$831$	38.2069	1.32538
$832$	30.3374	1.05176
$833$	−6.62779	−0.229639
$834$	6.52742	0.226026
$835$	19.6041	0.678429
$836$	16.9350	0.585709
$837$	−56.8442	−1.96482
$838$	−67.8477	−2.34376
$839$	−29.4329	−1.01613	−0.508067	−	0.861317i	$-0.669640\pi$
$839$	−29.4329	−1.01613	−0.508067	+	0.861317i	$0.669640\pi$
$840$	−122.585	−4.22958
$841$	−28.8815	−0.995914
$842$	−69.1628	−2.38351
$843$	29.7074	1.02318
$844$	−71.9931	−2.47810
$845$	−3.35985	−0.115582
$846$	−10.9102	−0.375102
$847$	15.4107	0.529518
$848$	125.078	4.29520
$849$	−8.63997	−0.296523
$850$	15.4848	0.531125
$851$	−47.0776	−1.61380
$852$	−66.3698	−2.27379
$853$	12.6775	0.434069	0.217035	−	0.976164i	$-0.430362\pi$
$853$	12.6775	0.434069	0.217035	+	0.976164i	$0.430362\pi$
$854$	34.2362	1.17154
$855$	2.56755	0.0878084
$856$	57.9407	1.98037
$857$	−2.37905	−0.0812669	−0.0406334	−	0.999174i	$-0.512938\pi$
$857$	−2.37905	−0.0812669	−0.0406334	+	0.999174i	$0.512938\pi$
$858$	51.2437	1.74943
$859$	12.8242	0.437556	0.218778	−	0.975775i	$-0.429793\pi$
$859$	12.8242	0.437556	0.218778	+	0.975775i	$0.429793\pi$
$860$	171.295	5.84113
$861$	−0.188184	−0.00641329
$862$	6.29139	0.214286
$863$	−22.7728	−0.775195	−0.387597	−	0.921829i	$-0.626695\pi$
$863$	−22.7728	−0.775195	−0.387597	+	0.921829i	$0.626695\pi$
$864$	61.5761	2.09486
$865$	71.1808	2.42022
$866$	16.6404	0.565463
$867$	−22.6451	−0.769068
$868$	174.134	5.91048
$869$	−47.0442	−1.59586
$870$	−4.14318	−0.140467
$871$	−9.62816	−0.326238
$872$	92.8198	3.14327
$873$	5.38722	0.182330
$874$	−12.0476	−0.407517
$875$	1.08302	0.0366129
$876$	17.4572	0.589825
$877$	10.4615	0.353261	0.176631	−	0.984277i	$-0.443480\pi$
$877$	10.4615	0.353261	0.176631	+	0.984277i	$0.443480\pi$
$878$	−84.9544	−2.86707
$879$	29.3596	0.990274
$880$	−122.802	−4.13966
$881$	48.0911	1.62023	0.810115	−	0.586271i	$-0.199405\pi$
$881$	48.0911	1.62023	0.810115	+	0.586271i	$0.199405\pi$
$882$	13.5655	0.456774
$883$	−44.6164	−1.50146	−0.750731	−	0.660608i	$-0.770299\pi$
$883$	−44.6164	−1.50146	−0.750731	+	0.660608i	$0.770299\pi$
$884$	−19.4778	−0.655108
$885$	45.6270	1.53374
$886$	−44.4352	−1.49283
$887$	−36.8271	−1.23653	−0.618267	−	0.785968i	$-0.712165\pi$
$887$	−36.8271	−1.23653	−0.618267	+	0.785968i	$0.712165\pi$
$888$	−98.6361	−3.31001
$889$	−80.0211	−2.68382
$890$	49.1386	1.64713
$891$	21.3560	0.715452
$892$	−54.7947	−1.83466
$893$	4.09165	0.136922
$894$	38.7067	1.29454
$895$	43.4701	1.45305
$896$	−4.27588	−0.142847
$897$	−25.8214	−0.862152
$898$	10.6178	0.354320
$899$	3.46177	0.115457
$900$	−22.4490	−0.748301
$901$	−14.7015	−0.489778
$902$	−0.373973	−0.0124519
$903$	57.2541	1.90530
$904$	13.9133	0.462749
$905$	56.1114	1.86520
$906$	8.06828	0.268051
$907$	−21.5551	−0.715726	−0.357863	−	0.933774i	$-0.616494\pi$
$907$	−21.5551	−0.715726	−0.357863	+	0.933774i	$0.616494\pi$
$908$	−111.582	−3.70298
$909$	8.82170	0.292597
$910$	−102.509	−3.39813
$911$	8.56281	0.283699	0.141849	−	0.989888i	$-0.454695\pi$
$911$	8.56281	0.283699	0.141849	+	0.989888i	$0.454695\pi$
$912$	−12.7243	−0.421343
$913$	−47.5806	−1.57469
$914$	−65.0526	−2.15175
$915$	−16.8569	−0.557272
$916$	−86.4311	−2.85577
$917$	50.8573	1.67946
$918$	−17.1767	−0.566915
$919$	21.5890	0.712155	0.356077	−	0.934456i	$-0.384114\pi$
$919$	21.5890	0.712155	0.356077	+	0.934456i	$0.384114\pi$
$920$	122.754	4.04708
$921$	25.2009	0.830398
$922$	74.4910	2.45323
$923$	−32.6447	−1.07451
$924$	−98.0531	−3.22571
$925$	46.4462	1.52714
$926$	65.3926	2.14893
$927$	−8.02077	−0.263437
$928$	−3.74994	−0.123098
$929$	−36.2908	−1.19066	−0.595331	−	0.803480i	$-0.702979\pi$
$929$	−36.2908	−1.19066	−0.595331	+	0.803480i	$0.702979\pi$
$930$	−121.046	−3.96926
$931$	−5.08744	−0.166734
$932$	29.8273	0.977026
$933$	34.4665	1.12838
$934$	6.88235	0.225197
$935$	14.4340	0.472041
$936$	23.4490	0.766456
$937$	−27.0281	−0.882970	−0.441485	−	0.897269i	$-0.645548\pi$
$937$	−27.0281	−0.882970	−0.441485	+	0.897269i	$0.645548\pi$
$938$	26.0100	0.849256
$939$	−31.5843	−1.03071
$940$	−70.8784	−2.31180
$941$	−2.17878	−0.0710263	−0.0355132	−	0.999369i	$-0.511307\pi$
$941$	−2.17878	−0.0710263	−0.0355132	+	0.999369i	$0.511307\pi$
$942$	−29.3038	−0.954769
$943$	0.188443	0.00613655
$944$	98.0076	3.18987
$945$	−64.0303	−2.08290
$946$	113.780	3.69929
$947$	1.69732	0.0551556	0.0275778	−	0.999620i	$-0.491221\pi$
$947$	1.69732	0.0551556	0.0275778	+	0.999620i	$0.491221\pi$
$948$	84.4400	2.74248
$949$	8.58653	0.278730
$950$	11.8860	0.385634
$951$	18.1145	0.587404
$952$	30.9496	1.00308
$953$	−42.5572	−1.37856	−0.689281	−	0.724494i	$-0.742074\pi$
$953$	−42.5572	−1.37856	−0.689281	+	0.724494i	$0.742074\pi$
$954$	30.0904	0.974214
$955$	20.7262	0.670683
$956$	−1.26961	−0.0410621
$957$	−1.94929	−0.0630117
$958$	8.53488	0.275749
$959$	1.27149	0.0410585
$960$	40.3522	1.30236
$961$	70.1381	2.26252
$962$	−82.4820	−2.65933
$963$	7.02654	0.226427
$964$	46.4867	1.49724
$965$	62.4475	2.01025
$966$	69.7553	2.24434
$967$	58.2636	1.87363	0.936815	−	0.349826i	$-0.113759\pi$
$967$	58.2636	1.87363	0.936815	+	0.349826i	$0.113759\pi$
$968$	−32.3327	−1.03921
$969$	1.49559	0.0480453
$970$	49.4106	1.58648
$971$	27.7114	0.889302	0.444651	−	0.895704i	$-0.353328\pi$
$971$	27.7114	0.889302	0.444651	+	0.895704i	$0.353328\pi$
$972$	44.0221	1.41201
$973$	−6.14335	−0.196947
$974$	−88.6841	−2.84162
$975$	25.4751	0.815857
$976$	−36.2089	−1.15902
$977$	−0.218839	−0.00700127	−0.00350063	−	0.999994i	$-0.501114\pi$
$977$	−0.218839	−0.00700127	−0.00350063	+	0.999994i	$0.501114\pi$
$978$	−35.8907	−1.14766
$979$	23.1188	0.738881
$980$	88.1282	2.81515
$981$	11.2564	0.359388
$982$	74.3849	2.37372
$983$	1.19980	0.0382678	0.0191339	−	0.999817i	$-0.493909\pi$
$983$	1.19980	0.0382678	0.0191339	+	0.999817i	$0.493909\pi$
$984$	0.394822	0.0125865
$985$	59.7527	1.90388
$986$	1.04605	0.0333129
$987$	−23.6905	−0.754077
$988$	−14.9510	−0.475654
$989$	−57.3330	−1.82308
$990$	−29.5429	−0.938934
$991$	28.3340	0.900059	0.450029	−	0.893014i	$-0.351414\pi$
$991$	28.3340	0.900059	0.450029	+	0.893014i	$0.351414\pi$
$992$	−109.557	−3.47845
$993$	−33.4460	−1.06138
$994$	88.1880	2.79715
$995$	−47.4055	−1.50286
$996$	85.4028	2.70609
$997$	37.1591	1.17684	0.588420	−	0.808555i	$-0.299750\pi$
$997$	37.1591	1.17684	0.588420	+	0.808555i	$0.299750\pi$
$998$	−41.5498	−1.31524
$999$	−51.5209	−1.63005

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8039.2.a.b.1.19	✓	391

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8039.2.a.b.1.19	✓	391	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)

\(f(q)\)	\(=\)	\(q-2.61852 q^{2} +1.44668 q^{3} +4.85663 q^{4} +3.17736 q^{5} -3.78815 q^{6} +3.56525 q^{7} -7.48013 q^{8} -0.907124 q^{9} +O(q^{10})\)	\(q-2.61852 q^{2} +1.44668 q^{3} +4.85663 q^{4} +3.17736 q^{5} -3.78815 q^{6} +3.56525 q^{7} -7.48013 q^{8} -0.907124 q^{9} -8.31997 q^{10} -3.91439 q^{11} +7.02598 q^{12} +3.45580 q^{13} -9.33567 q^{14} +4.59661 q^{15} +9.87359 q^{16} -1.16053 q^{17} +2.37532 q^{18} -0.890812 q^{19} +15.4313 q^{20} +5.15777 q^{21} +10.2499 q^{22} -5.16487 q^{23} -10.8213 q^{24} +5.09561 q^{25} -9.04907 q^{26} -5.65235 q^{27} +17.3151 q^{28} +0.344224 q^{29} -12.0363 q^{30} +10.0567 q^{31} -10.8939 q^{32} -5.66286 q^{33} +3.03886 q^{34} +11.3281 q^{35} -4.40557 q^{36} +9.11496 q^{37} +2.33261 q^{38} +4.99943 q^{39} -23.7671 q^{40} -0.0364855 q^{41} -13.5057 q^{42} +11.1006 q^{43} -19.0108 q^{44} -2.88226 q^{45} +13.5243 q^{46} -4.59317 q^{47} +14.2839 q^{48} +5.71102 q^{49} -13.3429 q^{50} -1.67891 q^{51} +16.7835 q^{52} +12.6679 q^{53} +14.8008 q^{54} -12.4374 q^{55} -26.6686 q^{56} -1.28872 q^{57} -0.901356 q^{58} +9.92623 q^{59} +22.3240 q^{60} -3.66724 q^{61} -26.3338 q^{62} -3.23413 q^{63} +8.77868 q^{64} +10.9803 q^{65} +14.8283 q^{66} -2.78608 q^{67} -5.63625 q^{68} -7.47191 q^{69} -29.6628 q^{70} -9.44635 q^{71} +6.78541 q^{72} +2.48467 q^{73} -23.8677 q^{74} +7.37170 q^{75} -4.32634 q^{76} -13.9558 q^{77} -13.0911 q^{78} +12.0183 q^{79} +31.3719 q^{80} -5.45575 q^{81} +0.0955379 q^{82} +12.1553 q^{83} +25.0494 q^{84} -3.68741 q^{85} -29.0670 q^{86} +0.497981 q^{87} +29.2802 q^{88} -5.90611 q^{89} +7.54724 q^{90} +12.3208 q^{91} -25.0839 q^{92} +14.5489 q^{93} +12.0273 q^{94} -2.83043 q^{95} -15.7600 q^{96} -5.93879 q^{97} -14.9544 q^{98} +3.55084 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9}+O(q^{10}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9	\( 391 q + 14 q^{2} + 12 q^{3} + 446 q^{4} + 22 q^{5} + 40 q^{6} + 63 q^{7} + 36 q^{8} + 501 q^{9} + 40 q^{10} + 57 q^{11} + 20 q^{12} + 83 q^{13} + 21 q^{14} + 60 q^{15} + 548 q^{16} + 59 q^{17} + 54 q^{18} + 131 q^{19} + 35 q^{20} + 121 q^{21} + 89 q^{22} + 34 q^{23} + 110 q^{24} + 609 q^{25} + 54 q^{26} + 27 q^{27} + 182 q^{28} + 102 q^{29} + 92 q^{30} + 88 q^{31} + 76 q^{32} + 131 q^{33} + 128 q^{34} + 31 q^{35} + 654 q^{36} + 135 q^{37} + 23 q^{38} + 96 q^{39} + 113 q^{40} + 128 q^{41} + 45 q^{42} + 140 q^{43} + 151 q^{44} + 77 q^{45} + 245 q^{46} + 22 q^{47} + 25 q^{48} + 712 q^{49} + 53 q^{50} + 102 q^{51} + 174 q^{52} + 54 q^{53} + 131 q^{54} + 101 q^{55} + 43 q^{56} + 226 q^{57} + 109 q^{58} + 40 q^{59} + 123 q^{60} + 249 q^{61} + 28 q^{62} + 139 q^{63} + 730 q^{64} + 227 q^{65} + 55 q^{66} + 169 q^{67} + 48 q^{68} + 89 q^{69} + 98 q^{70} + 66 q^{71} + 120 q^{72} + 324 q^{73} + 60 q^{74} + 19 q^{75} + 356 q^{76} + 83 q^{77} - 11 q^{78} + 195 q^{79} + 26 q^{80} + 807 q^{81} + 49 q^{82} + 74 q^{83} + 252 q^{84} + 373 q^{85} + 100 q^{86} + 43 q^{87} + 211 q^{88} + 207 q^{89} + 10 q^{90} + 189 q^{91} + 30 q^{92} + 172 q^{93} + 130 q^{94} + 43 q^{95} + 203 q^{96} + 254 q^{97} + 26 q^{98} + 273 q^{99}+O(q^{100}) \) 391 * q + 14 * q^2 + 12 * q^3 + 446 * q^4 + 22 * q^5 + 40 * q^6 + 63 * q^7 + 36 * q^8 + 501 * q^9 + 40 * q^10 + 57 * q^11 + 20 * q^12 + 83 * q^13 + 21 * q^14 + 60 * q^15 + 548 * q^16 + 59 * q^17 + 54 * q^18 + 131 * q^19 + 35 * q^20 + 121 * q^21 + 89 * q^22 + 34 * q^23 + 110 * q^24 + 609 * q^25 + 54 * q^26 + 27 * q^27 + 182 * q^28 + 102 * q^29 + 92 * q^30 + 88 * q^31 + 76 * q^32 + 131 * q^33 + 128 * q^34 + 31 * q^35 + 654 * q^36 + 135 * q^37 + 23 * q^38 + 96 * q^39 + 113 * q^40 + 128 * q^41 + 45 * q^42 + 140 * q^43 + 151 * q^44 + 77 * q^45 + 245 * q^46 + 22 * q^47 + 25 * q^48 + 712 * q^49 + 53 * q^50 + 102 * q^51 + 174 * q^52 + 54 * q^53 + 131 * q^54 + 101 * q^55 + 43 * q^56 + 226 * q^57 + 109 * q^58 + 40 * q^59 + 123 * q^60 + 249 * q^61 + 28 * q^62 + 139 * q^63 + 730 * q^64 + 227 * q^65 + 55 * q^66 + 169 * q^67 + 48 * q^68 + 89 * q^69 + 98 * q^70 + 66 * q^71 + 120 * q^72 + 324 * q^73 + 60 * q^74 + 19 * q^75 + 356 * q^76 + 83 * q^77 - 11 * q^78 + 195 * q^79 + 26 * q^80 + 807 * q^81 + 49 * q^82 + 74 * q^83 + 252 * q^84 + 373 * q^85 + 100 * q^86 + 43 * q^87 + 211 * q^88 + 207 * q^89 + 10 * q^90 + 189 * q^91 + 30 * q^92 + 172 * q^93 + 130 * q^94 + 43 * q^95 + 203 * q^96 + 254 * q^97 + 26 * q^98 + 273 * q^99

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