LMFDB - Embedded newform 4031.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4031,2,Mod(1,4031)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4031, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("4031.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4031 = 29 \cdot 139 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4031.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:	$32.1876970548$
Analytic rank:	$1$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Character	$\chi$	$=$	4031.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.67397 q^{2} -0.759884 q^{3} +0.802190 q^{4} +2.08858 q^{5} +1.27203 q^{6} -1.20948 q^{7} +2.00510 q^{8} -2.42258 q^{9} +O(q^{10})$	\(q-1.67397 q^{2} -0.759884 q^{3} +0.802190 q^{4} +2.08858 q^{5} +1.27203 q^{6} -1.20948 q^{7} +2.00510 q^{8} -2.42258 q^{9} -3.49623 q^{10} +0.872783 q^{11} -0.609571 q^{12} -1.63350 q^{13} +2.02464 q^{14} -1.58708 q^{15} -4.96087 q^{16} +4.07334 q^{17} +4.05533 q^{18} +0.346683 q^{19} +1.67544 q^{20} +0.919067 q^{21} -1.46102 q^{22} -5.88362 q^{23} -1.52365 q^{24} -0.637840 q^{25} +2.73443 q^{26} +4.12053 q^{27} -0.970236 q^{28} +1.00000 q^{29} +2.65673 q^{30} +6.54222 q^{31} +4.29416 q^{32} -0.663214 q^{33} -6.81867 q^{34} -2.52610 q^{35} -1.94337 q^{36} +2.25609 q^{37} -0.580338 q^{38} +1.24127 q^{39} +4.18782 q^{40} +5.30697 q^{41} -1.53849 q^{42} +6.40472 q^{43} +0.700138 q^{44} -5.05974 q^{45} +9.84902 q^{46} -4.58648 q^{47} +3.76969 q^{48} -5.53715 q^{49} +1.06773 q^{50} -3.09527 q^{51} -1.31037 q^{52} -13.1227 q^{53} -6.89766 q^{54} +1.82288 q^{55} -2.42514 q^{56} -0.263439 q^{57} -1.67397 q^{58} -1.64556 q^{59} -1.27314 q^{60} -12.3423 q^{61} -10.9515 q^{62} +2.93007 q^{63} +2.73342 q^{64} -3.41168 q^{65} +1.11020 q^{66} +2.98614 q^{67} +3.26759 q^{68} +4.47087 q^{69} +4.22863 q^{70} -11.8995 q^{71} -4.85752 q^{72} +7.78542 q^{73} -3.77663 q^{74} +0.484685 q^{75} +0.278106 q^{76} -1.05562 q^{77} -2.07785 q^{78} +9.99150 q^{79} -10.3612 q^{80} +4.13661 q^{81} -8.88374 q^{82} +6.27488 q^{83} +0.737266 q^{84} +8.50750 q^{85} -10.7213 q^{86} -0.759884 q^{87} +1.75002 q^{88} -4.35379 q^{89} +8.46988 q^{90} +1.97569 q^{91} -4.71978 q^{92} -4.97133 q^{93} +7.67765 q^{94} +0.724075 q^{95} -3.26307 q^{96} +10.3985 q^{97} +9.26904 q^{98} -2.11438 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−1.67397	−1.18368	−0.591839	−	0.806056i	$-0.701598\pi$
$2$	−1.67397	−1.18368	−0.591839	+	0.806056i	$0.701598\pi$
$3$	−0.759884	−0.438719	−0.219360	−	0.975644i	$-0.570397\pi$
$3$	−0.759884	−0.438719	−0.219360	+	0.975644i	$0.570397\pi$
$4$	0.802190	0.401095
$5$	2.08858	0.934041	0.467020	−	0.884247i	$-0.345327\pi$
$5$	2.08858	0.934041	0.467020	+	0.884247i	$0.345327\pi$
$6$	1.27203	0.519302
$7$	−1.20948	−0.457142	−0.228571	−	0.973527i	$-0.573405\pi$
$7$	−1.20948	−0.457142	−0.228571	+	0.973527i	$0.573405\pi$
$8$	2.00510	0.708911
$9$	−2.42258	−0.807526
$10$	−3.49623	−1.10560
$11$	0.872783	0.263154	0.131577	−	0.991306i	$-0.457996\pi$
$11$	0.872783	0.263154	0.131577	+	0.991306i	$0.457996\pi$
$12$	−0.609571	−0.175968
$13$	−1.63350	−0.453050	−0.226525	−	0.974005i	$-0.572737\pi$
$13$	−1.63350	−0.453050	−0.226525	+	0.974005i	$0.572737\pi$
$14$	2.02464	0.541109
$15$	−1.58708	−0.409781
$16$	−4.96087	−1.24022
$17$	4.07334	0.987931	0.493965	−	0.869482i	$-0.335547\pi$
$17$	4.07334	0.987931	0.493965	+	0.869482i	$0.335547\pi$
$18$	4.05533	0.955851
$19$	0.346683	0.0795345	0.0397673	−	0.999209i	$-0.487338\pi$
$19$	0.346683	0.0795345	0.0397673	+	0.999209i	$0.487338\pi$
$20$	1.67544	0.374639
$21$	0.919067	0.200557
$22$	−1.46102	−0.311490
$23$	−5.88362	−1.22682	−0.613409	−	0.789765i	$-0.710202\pi$
$23$	−5.88362	−1.22682	−0.613409	+	0.789765i	$0.710202\pi$
$24$	−1.52365	−0.311013
$25$	−0.637840	−0.127568
$26$	2.73443	0.536266
$27$	4.12053	0.792996
$28$	−0.970236	−0.183357
$29$	1.00000	0.185695
$29$	1.00000	0.185695
$30$	2.65673	0.485050
$31$	6.54222	1.17502	0.587509	−	0.809218i	$-0.300109\pi$
$31$	6.54222	1.17502	0.587509	+	0.809218i	$0.300109\pi$
$32$	4.29416	0.759108
$33$	−0.663214	−0.115451
$34$	−6.81867	−1.16939
$35$	−2.52610	−0.426989
$36$	−1.94337	−0.323894
$37$	2.25609	0.370898	0.185449	−	0.982654i	$-0.440626\pi$
$37$	2.25609	0.370898	0.185449	+	0.982654i	$0.440626\pi$
$38$	−0.580338	−0.0941433
$39$	1.24127	0.198762
$40$	4.18782	0.662152
$41$	5.30697	0.828810	0.414405	−	0.910093i	$-0.363990\pi$
$41$	5.30697	0.828810	0.414405	+	0.910093i	$0.363990\pi$
$42$	−1.53849	−0.237395
$43$	6.40472	0.976710	0.488355	−	0.872645i	$-0.337597\pi$
$43$	6.40472	0.976710	0.488355	+	0.872645i	$0.337597\pi$
$44$	0.700138	0.105550
$45$	−5.05974	−0.754262
$46$	9.84902	1.45216
$47$	−4.58648	−0.669007	−0.334503	−	0.942395i	$-0.608569\pi$
$47$	−4.58648	−0.669007	−0.334503	+	0.942395i	$0.608569\pi$
$48$	3.76969	0.544107
$49$	−5.53715	−0.791021
$50$	1.06773	0.151000
$51$	−3.09527	−0.433424
$52$	−1.31037	−0.181716
$53$	−13.1227	−1.80255	−0.901273	−	0.433253i	$-0.857366\pi$
$53$	−13.1227	−1.80255	−0.901273	+	0.433253i	$0.857366\pi$
$54$	−6.89766	−0.938652
$55$	1.82288	0.245796
$56$	−2.42514	−0.324073
$57$	−0.263439	−0.0348933
$58$	−1.67397	−0.219804
$59$	−1.64556	−0.214234	−0.107117	−	0.994246i	$-0.534162\pi$
$59$	−1.64556	−0.214234	−0.107117	+	0.994246i	$0.534162\pi$
$60$	−1.27314	−0.164361
$61$	−12.3423	−1.58028	−0.790138	−	0.612930i	$-0.789991\pi$
$61$	−12.3423	−1.58028	−0.790138	+	0.612930i	$0.789991\pi$
$62$	−10.9515	−1.39084
$63$	2.93007	0.369154
$64$	2.73342	0.341678
$65$	−3.41168	−0.423167
$66$	1.11020	0.136656
$67$	2.98614	0.364815	0.182407	−	0.983223i	$-0.441611\pi$
$67$	2.98614	0.364815	0.182407	+	0.983223i	$0.441611\pi$
$68$	3.26759	0.396254
$69$	4.47087	0.538229
$70$	4.22863	0.505418
$71$	−11.8995	−1.41221	−0.706105	−	0.708107i	$-0.749549\pi$
$71$	−11.8995	−1.41221	−0.706105	+	0.708107i	$0.749549\pi$
$72$	−4.85752	−0.572464
$73$	7.78542	0.911215	0.455607	−	0.890181i	$-0.349422\pi$
$73$	7.78542	0.911215	0.455607	+	0.890181i	$0.349422\pi$
$74$	−3.77663	−0.439024
$75$	0.484685	0.0559665
$76$	0.278106	0.0319009
$77$	−1.05562	−0.120299
$78$	−2.07785	−0.235270
$79$	9.99150	1.12413	0.562066	−	0.827093i	$-0.310007\pi$
$79$	9.99150	1.12413	0.562066	+	0.827093i	$0.310007\pi$
$80$	−10.3612	−1.15841
$81$	4.13661	0.459623
$82$	−8.88374	−0.981044
$83$	6.27488	0.688758	0.344379	−	0.938831i	$-0.388090\pi$
$83$	6.27488	0.688758	0.344379	+	0.938831i	$0.388090\pi$
$84$	0.737266	0.0804424
$85$	8.50750	0.922768
$86$	−10.7213	−1.15611
$87$	−0.759884	−0.0814681
$88$	1.75002	0.186553
$89$	−4.35379	−0.461501	−0.230750	−	0.973013i	$-0.574118\pi$
$89$	−4.35379	−0.461501	−0.230750	+	0.973013i	$0.574118\pi$
$90$	8.46988	0.892803
$91$	1.97569	0.207108
$92$	−4.71978	−0.492071
$93$	−4.97133	−0.515503
$94$	7.67765	0.791889
$95$	0.724075	0.0742885
$96$	−3.26307	−0.333035
$97$	10.3985	1.05580	0.527902	−	0.849306i	$-0.322979\pi$
$97$	10.3985	1.05580	0.527902	+	0.849306i	$0.322979\pi$
$98$	9.26904	0.936315
$99$	−2.11438	−0.212504
$100$	−0.511669	−0.0511669
$101$	10.1672	1.01168	0.505839	−	0.862628i	$-0.331183\pi$
$101$	10.1672	1.01168	0.505839	+	0.862628i	$0.331183\pi$
$102$	5.18140	0.513035
$103$	−14.3815	−1.41706	−0.708528	−	0.705683i	$-0.750640\pi$
$103$	−14.3815	−1.41706	−0.708528	+	0.705683i	$0.750640\pi$
$104$	−3.27533	−0.321172
$105$	1.91954	0.187328
$106$	21.9671	2.13363
$107$	−3.57358	−0.345471	−0.172736	−	0.984968i	$-0.555261\pi$
$107$	−3.57358	−0.345471	−0.172736	+	0.984968i	$0.555261\pi$
$108$	3.30545	0.318067
$109$	5.67750	0.543806	0.271903	−	0.962325i	$-0.412347\pi$
$109$	5.67750	0.543806	0.271903	+	0.962325i	$0.412347\pi$
$110$	−3.05145	−0.290944
$111$	−1.71436	−0.162720
$112$	6.00009	0.566956
$113$	0.177433	0.0166915	0.00834576	−	0.999965i	$-0.497343\pi$
$113$	0.177433	0.0166915	0.00834576	+	0.999965i	$0.497343\pi$
$114$	0.440990	0.0413025
$115$	−12.2884	−1.14590
$116$	0.802190	0.0744815
$117$	3.95727	0.365850
$118$	2.75463	0.253584
$119$	−4.92664	−0.451625
$120$	−3.18225	−0.290499
$121$	−10.2383	−0.930750
$122$	20.6608	1.87054
$123$	−4.03268	−0.363615
$124$	5.24810	0.471294
$125$	−11.7751	−1.05319
$126$	−4.90486	−0.436959
$127$	6.85541	0.608319	0.304159	−	0.952621i	$-0.401624\pi$
$127$	6.85541	0.608319	0.304159	+	0.952621i	$0.401624\pi$
$128$	−13.1640	−1.16354
$129$	−4.86684	−0.428501
$130$	5.71107	0.500894
$131$	−13.3584	−1.16713	−0.583566	−	0.812066i	$-0.698343\pi$
$131$	−13.3584	−1.16713	−0.583566	+	0.812066i	$0.698343\pi$
$132$	−0.532023	−0.0463067
$133$	−0.419307	−0.0363586
$134$	−4.99872	−0.431824
$135$	8.60605	0.740690
$136$	8.16747	0.700355
$137$	−11.3302	−0.968002	−0.484001	−	0.875068i	$-0.660817\pi$
$137$	−11.3302	−0.968002	−0.484001	+	0.875068i	$0.660817\pi$
$138$	−7.48411	−0.637090
$139$	1.00000	0.0848189
$139$	1.00000	0.0848189
$140$	−2.02641	−0.171263
$141$	3.48519	0.293506
$142$	19.9194	1.67160
$143$	−1.42569	−0.119222
$144$	12.0181	1.00151
$145$	2.08858	0.173447
$146$	−13.0326	−1.07859
$147$	4.20759	0.347036
$148$	1.80981	0.148765
$149$	12.4387	1.01902	0.509508	−	0.860466i	$-0.329827\pi$
$149$	12.4387	1.01902	0.509508	+	0.860466i	$0.329827\pi$
$150$	−0.811349	−0.0662464
$151$	−13.8962	−1.13086	−0.565428	−	0.824798i	$-0.691289\pi$
$151$	−13.8962	−1.13086	−0.565428	+	0.824798i	$0.691289\pi$
$152$	0.695135	0.0563829
$153$	−9.86799	−0.797779
$154$	1.76708	0.142395
$155$	13.6639	1.09751
$156$	0.995732	0.0797223
$157$	0.999786	0.0797916	0.0398958	−	0.999204i	$-0.487297\pi$
$157$	0.999786	0.0797916	0.0398958	+	0.999204i	$0.487297\pi$
$158$	−16.7255	−1.33061
$159$	9.97175	0.790811
$160$	8.96870	0.709038
$161$	7.11614	0.560830
$162$	−6.92457	−0.544046
$163$	−9.52993	−0.746441	−0.373221	−	0.927743i	$-0.621747\pi$
$163$	−9.52993	−0.746441	−0.373221	+	0.927743i	$0.621747\pi$
$164$	4.25720	0.332431
$165$	−1.38517	−0.107836
$166$	−10.5040	−0.815268
$167$	13.9715	1.08114	0.540572	−	0.841298i	$-0.318208\pi$
$167$	13.9715	1.08114	0.540572	+	0.841298i	$0.318208\pi$
$168$	1.84282	0.142177
$169$	−10.3317	−0.794746
$170$	−14.2413	−1.09226
$171$	−0.839866	−0.0642262
$172$	5.13780	0.391754
$173$	−2.50021	−0.190088	−0.0950438	−	0.995473i	$-0.530299\pi$
$173$	−2.50021	−0.190088	−0.0950438	+	0.995473i	$0.530299\pi$
$174$	1.27203	0.0964320
$175$	0.771458	0.0583167
$176$	−4.32976	−0.326368
$177$	1.25044	0.0939886
$178$	7.28813	0.546268
$179$	9.25085	0.691441	0.345720	−	0.938338i	$-0.387635\pi$
$179$	9.25085	0.691441	0.345720	+	0.938338i	$0.387635\pi$
$180$	−4.05887	−0.302531
$181$	13.7001	1.01832	0.509160	−	0.860672i	$-0.329956\pi$
$181$	13.7001	1.01832	0.509160	+	0.860672i	$0.329956\pi$
$182$	−3.30725	−0.245150
$183$	9.37875	0.693297
$184$	−11.7973	−0.869706
$185$	4.71201	0.346434
$186$	8.32187	0.610189
$187$	3.55514	0.259978
$188$	−3.67923	−0.268335
$189$	−4.98371	−0.362512
$190$	−1.21208	−0.0879337
$191$	12.1621	0.880019	0.440009	−	0.897993i	$-0.354975\pi$
$191$	12.1621	0.880019	0.440009	+	0.897993i	$0.354975\pi$
$192$	−2.07708	−0.149901
$193$	−16.2564	−1.17016	−0.585080	−	0.810976i	$-0.698937\pi$
$193$	−16.2564	−1.17016	−0.585080	+	0.810976i	$0.698937\pi$
$194$	−17.4067	−1.24973
$195$	2.59248	0.185652
$196$	−4.44184	−0.317275
$197$	15.2507	1.08657	0.543283	−	0.839550i	$-0.317181\pi$
$197$	15.2507	1.08657	0.543283	+	0.839550i	$0.317181\pi$
$198$	3.53942	0.251536
$199$	4.04089	0.286451	0.143225	−	0.989690i	$-0.454253\pi$
$199$	4.04089	0.286451	0.143225	+	0.989690i	$0.454253\pi$
$200$	−1.27894	−0.0904344
$201$	−2.26912	−0.160051
$202$	−17.0197	−1.19750
$203$	−1.20948	−0.0848891
$204$	−2.48299	−0.173844
$205$	11.0840	0.774142
$206$	24.0743	1.67734
$207$	14.2535	0.990688
$208$	8.10356	0.561881
$209$	0.302579	0.0209298
$210$	−3.21327	−0.221736
$211$	−8.10689	−0.558101	−0.279051	−	0.960276i	$-0.590020\pi$
$211$	−8.10689	−0.558101	−0.279051	+	0.960276i	$0.590020\pi$
$212$	−10.5269	−0.722992
$213$	9.04223	0.619563
$214$	5.98209	0.408927
$215$	13.3768	0.912287
$216$	8.26208	0.562164
$217$	−7.91271	−0.537150
$218$	−9.50399	−0.643692
$219$	−5.91602	−0.399767
$220$	1.46229	0.0985877
$221$	−6.65379	−0.447582
$222$	2.86980	0.192608
$223$	−7.51629	−0.503328	−0.251664	−	0.967815i	$-0.580978\pi$
$223$	−7.51629	−0.503328	−0.251664	+	0.967815i	$0.580978\pi$
$224$	−5.19372	−0.347020
$225$	1.54522	0.103014
$226$	−0.297019	−0.0197574
$227$	8.78542	0.583109	0.291554	−	0.956554i	$-0.405828\pi$
$227$	8.78542	0.583109	0.291554	+	0.956554i	$0.405828\pi$
$228$	−0.211328	−0.0139955
$229$	−11.9938	−0.792570	−0.396285	−	0.918127i	$-0.629701\pi$
$229$	−11.9938	−0.792570	−0.396285	+	0.918127i	$0.629701\pi$
$230$	20.5705	1.35638
$231$	0.802146	0.0527773
$232$	2.00510	0.131641
$233$	16.5917	1.08696	0.543479	−	0.839423i	$-0.317107\pi$
$233$	16.5917	1.08696	0.543479	+	0.839423i	$0.317107\pi$
$234$	−6.62437	−0.433048
$235$	−9.57922	−0.624879
$236$	−1.32005	−0.0859282
$237$	−7.59238	−0.493178
$238$	8.24707	0.534578
$239$	3.32189	0.214875	0.107437	−	0.994212i	$-0.465735\pi$
$239$	3.32189	0.214875	0.107437	+	0.994212i	$0.465735\pi$
$240$	7.87328	0.508218
$241$	−2.65657	−0.171125	−0.0855624	−	0.996333i	$-0.527269\pi$
$241$	−2.65657	−0.171125	−0.0855624	+	0.996333i	$0.527269\pi$
$242$	17.1386	1.10171
$243$	−15.5049	−0.994641
$244$	−9.90090	−0.633840
$245$	−11.5648	−0.738846
$246$	6.75061	0.430403
$247$	−0.566305	−0.0360331
$248$	13.1178	0.832983
$249$	−4.76818	−0.302171
$250$	19.7112	1.24664
$251$	−6.68508	−0.421959	−0.210979	−	0.977491i	$-0.567665\pi$
$251$	−6.68508	−0.421959	−0.210979	+	0.977491i	$0.567665\pi$
$252$	2.35047	0.148066
$253$	−5.13512	−0.322842
$254$	−11.4758	−0.720054
$255$	−6.46471	−0.404836
$256$	16.5694	1.03559
$257$	−17.9037	−1.11680	−0.558402	−	0.829571i	$-0.688585\pi$
$257$	−17.9037	−1.11680	−0.558402	+	0.829571i	$0.688585\pi$
$258$	8.14697	0.507208
$259$	−2.72870	−0.169553
$260$	−2.73682	−0.169730
$261$	−2.42258	−0.149954
$262$	22.3617	1.38151
$263$	10.9077	0.672598	0.336299	−	0.941755i	$-0.390825\pi$
$263$	10.9077	0.672598	0.336299	+	0.941755i	$0.390825\pi$
$264$	−1.32981	−0.0818442
$265$	−27.4078	−1.68365
$266$	0.701910	0.0430369
$267$	3.30837	0.202469
$268$	2.39545	0.146325
$269$	−28.9344	−1.76416	−0.882081	−	0.471098i	$-0.843858\pi$
$269$	−28.9344	−1.76416	−0.882081	+	0.471098i	$0.843858\pi$
$270$	−14.4063	−0.876739
$271$	11.5432	0.701197	0.350599	−	0.936526i	$-0.385978\pi$
$271$	11.5432	0.701197	0.350599	+	0.936526i	$0.385978\pi$
$272$	−20.2073	−1.22525
$273$	−1.50129	−0.0908623
$274$	18.9664	1.14580
$275$	−0.556696	−0.0335700
$276$	3.58648	0.215881
$277$	−17.2086	−1.03396	−0.516982	−	0.855996i	$-0.672945\pi$
$277$	−17.2086	−1.03396	−0.516982	+	0.855996i	$0.672945\pi$
$278$	−1.67397	−0.100398
$279$	−15.8490	−0.948856
$280$	−5.06510	−0.302697
$281$	−29.3962	−1.75363	−0.876814	−	0.480830i	$-0.840336\pi$
$281$	−29.3962	−1.75363	−0.876814	+	0.480830i	$0.840336\pi$
$282$	−5.83412	−0.347417
$283$	−3.53239	−0.209979	−0.104989	−	0.994473i	$-0.533481\pi$
$283$	−3.53239	−0.209979	−0.104989	+	0.994473i	$0.533481\pi$
$284$	−9.54565	−0.566430
$285$	−0.550212	−0.0325918
$286$	2.38656	0.141120
$287$	−6.41870	−0.378884
$288$	−10.4029	−0.612999
$289$	−0.407875	−0.0239927
$290$	−3.49623	−0.205305
$291$	−7.90162	−0.463201
$292$	6.24539	0.365484
$293$	−20.7708	−1.21344	−0.606721	−	0.794915i	$-0.707515\pi$
$293$	−20.7708	−1.21344	−0.606721	+	0.794915i	$0.707515\pi$
$294$	−7.04340	−0.410779
$295$	−3.43689	−0.200103
$296$	4.52369	0.262934
$297$	3.59633	0.208680
$298$	−20.8220	−1.20619
$299$	9.61086	0.555811
$300$	0.388809	0.0224479
$301$	−7.74640	−0.446495
$302$	23.2619	1.33857
$303$	−7.72592	−0.443843
$304$	−1.71985	−0.0986401
$305$	−25.7780	−1.47604
$306$	16.5188	0.944314
$307$	−7.44444	−0.424877	−0.212438	−	0.977174i	$-0.568140\pi$
$307$	−7.44444	−0.424877	−0.212438	+	0.977174i	$0.568140\pi$
$308$	−0.846805	−0.0482512
$309$	10.9283	0.621689
$310$	−22.8731	−1.29910
$311$	4.48859	0.254525	0.127262	−	0.991869i	$-0.459381\pi$
$311$	4.48859	0.254525	0.127262	+	0.991869i	$0.459381\pi$
$312$	2.48887	0.140904
$313$	3.71574	0.210026	0.105013	−	0.994471i	$-0.466512\pi$
$313$	3.71574	0.210026	0.105013	+	0.994471i	$0.466512\pi$
$314$	−1.67362	−0.0944476
$315$	6.11968	0.344805
$316$	8.01508	0.450883
$317$	1.56109	0.0876795	0.0438397	−	0.999039i	$-0.486041\pi$
$317$	1.56109	0.0876795	0.0438397	+	0.999039i	$0.486041\pi$
$318$	−16.6924	−0.936066
$319$	0.872783	0.0488665
$320$	5.70897	0.319141
$321$	2.71551	0.151565
$322$	−11.9122	−0.663843
$323$	1.41216	0.0785746
$324$	3.31834	0.184352
$325$	1.04191	0.0577947
$326$	15.9529	0.883547
$327$	−4.31424	−0.238578
$328$	10.6410	0.587552
$329$	5.54727	0.305831
$330$	2.31874	0.127643
$331$	−28.0632	−1.54249	−0.771246	−	0.636538i	$-0.780366\pi$
$331$	−28.0632	−1.54249	−0.771246	+	0.636538i	$0.780366\pi$
$332$	5.03365	0.276257
$333$	−5.46554	−0.299510
$334$	−23.3879	−1.27973
$335$	6.23678	0.340752
$336$	−4.55937	−0.248734
$337$	−15.6029	−0.849943	−0.424971	−	0.905207i	$-0.639716\pi$
$337$	−15.6029	−0.849943	−0.424971	+	0.905207i	$0.639716\pi$
$338$	17.2950	0.940723
$339$	−0.134829	−0.00732289
$340$	6.82463	0.370117
$341$	5.70994	0.309210
$342$	1.40591	0.0760231
$343$	15.1635	0.818751
$344$	12.8421	0.692401
$345$	9.33775	0.502728
$346$	4.18529	0.225003
$347$	−15.8776	−0.852355	−0.426177	−	0.904640i	$-0.640140\pi$
$347$	−15.8776	−0.852355	−0.426177	+	0.904640i	$0.640140\pi$
$348$	−0.609571	−0.0326764
$349$	−1.14394	−0.0612337	−0.0306168	−	0.999531i	$-0.509747\pi$
$349$	−1.14394	−0.0612337	−0.0306168	+	0.999531i	$0.509747\pi$
$350$	−1.29140	−0.0690282
$351$	−6.73087	−0.359267
$352$	3.74787	0.199762
$353$	−24.5164	−1.30487	−0.652437	−	0.757843i	$-0.726253\pi$
$353$	−24.5164	−1.30487	−0.652437	+	0.757843i	$0.726253\pi$
$354$	−2.09320	−0.111252
$355$	−24.8530	−1.31906
$356$	−3.49257	−0.185106
$357$	3.74368	0.198136
$358$	−15.4857	−0.818443
$359$	20.4331	1.07842	0.539210	−	0.842171i	$-0.318723\pi$
$359$	20.4331	1.07842	0.539210	+	0.842171i	$0.318723\pi$
$360$	−10.1453	−0.534704
$361$	−18.8798	−0.993674
$362$	−22.9336	−1.20536
$363$	7.77988	0.408338
$364$	1.58488	0.0830701
$365$	16.2605	0.851112
$366$	−15.6998	−0.820641
$367$	5.93878	0.310002	0.155001	−	0.987914i	$-0.450462\pi$
$367$	5.93878	0.310002	0.155001	+	0.987914i	$0.450462\pi$
$368$	29.1879	1.52152
$369$	−12.8565	−0.669285
$370$	−7.88779	−0.410067
$371$	15.8717	0.824019
$372$	−3.98795	−0.206765
$373$	−15.4008	−0.797425	−0.398713	−	0.917076i	$-0.630543\pi$
$373$	−15.4008	−0.797425	−0.398713	+	0.917076i	$0.630543\pi$
$374$	−5.95122	−0.307730
$375$	8.94769	0.462057
$376$	−9.19636	−0.474266
$377$	−1.63350	−0.0841293
$378$	8.34261	0.429097
$379$	6.48943	0.333340	0.166670	−	0.986013i	$-0.446699\pi$
$379$	6.48943	0.333340	0.166670	+	0.986013i	$0.446699\pi$
$380$	0.580845	0.0297967
$381$	−5.20931	−0.266881
$382$	−20.3590	−1.04166
$383$	−0.835621	−0.0426982	−0.0213491	−	0.999772i	$-0.506796\pi$
$383$	−0.835621	−0.0426982	−0.0213491	+	0.999772i	$0.506796\pi$
$384$	10.0031	0.510469
$385$	−2.20474	−0.112364
$386$	27.2128	1.38509
$387$	−15.5159	−0.788718
$388$	8.34153	0.423477
$389$	−12.0363	−0.610264	−0.305132	−	0.952310i	$-0.598701\pi$
$389$	−12.0363	−0.610264	−0.305132	+	0.952310i	$0.598701\pi$
$390$	−4.33975	−0.219752
$391$	−23.9660	−1.21201
$392$	−11.1026	−0.560764
$393$	10.1509	0.512043
$394$	−25.5292	−1.28614
$395$	20.8680	1.04998
$396$	−1.69614	−0.0852341
$397$	−20.2501	−1.01632	−0.508162	−	0.861262i	$-0.669675\pi$
$397$	−20.2501	−1.01632	−0.508162	+	0.861262i	$0.669675\pi$
$398$	−6.76434	−0.339066
$399$	0.318625	0.0159512
$400$	3.16424	0.158212
$401$	−30.3838	−1.51729	−0.758646	−	0.651503i	$-0.774139\pi$
$401$	−30.3838	−1.51729	−0.758646	+	0.651503i	$0.774139\pi$
$402$	3.79845	0.189449
$403$	−10.6867	−0.532342
$404$	8.15606	0.405779
$405$	8.63963	0.429307
$406$	2.02464	0.100481
$407$	1.96907	0.0976034
$408$	−6.20633	−0.307259
$409$	−12.4439	−0.615310	−0.307655	−	0.951498i	$-0.599544\pi$
$409$	−12.4439	−0.615310	−0.307655	+	0.951498i	$0.599544\pi$
$410$	−18.5544	−0.916335
$411$	8.60961	0.424681
$412$	−11.5367	−0.568374
$413$	1.99028	0.0979354
$414$	−23.8600	−1.17266
$415$	13.1056	0.643328
$416$	−7.01450	−0.343914
$417$	−0.759884	−0.0372117
$418$	−0.506509	−0.0247742
$419$	−33.7887	−1.65069	−0.825344	−	0.564630i	$-0.809019\pi$
$419$	−33.7887	−1.65069	−0.825344	+	0.564630i	$0.809019\pi$
$420$	1.53984	0.0751364
$421$	2.15341	0.104951	0.0524755	−	0.998622i	$-0.483289\pi$
$421$	2.15341	0.104951	0.0524755	+	0.998622i	$0.483289\pi$
$422$	13.5707	0.660613
$423$	11.1111	0.540240
$424$	−26.3124	−1.27784
$425$	−2.59814	−0.126028
$426$	−15.1365	−0.733364
$427$	14.9279	0.722410
$428$	−2.86669	−0.138567
$429$	1.08336	0.0523049
$430$	−22.3923	−1.07985
$431$	−4.77353	−0.229933	−0.114966	−	0.993369i	$-0.536676\pi$
$431$	−4.77353	−0.229933	−0.114966	+	0.993369i	$0.536676\pi$
$432$	−20.4414	−0.983488
$433$	−15.3770	−0.738972	−0.369486	−	0.929236i	$-0.620466\pi$
$433$	−15.3770	−0.738972	−0.369486	+	0.929236i	$0.620466\pi$
$434$	13.2457	0.635813
$435$	−1.58708	−0.0760945
$436$	4.55443	0.218118
$437$	−2.03975	−0.0975745
$438$	9.90326	0.473196
$439$	−15.7132	−0.749951	−0.374975	−	0.927035i	$-0.622349\pi$
$439$	−15.7132	−0.749951	−0.374975	+	0.927035i	$0.622349\pi$
$440$	3.65505	0.174248
$441$	13.4142	0.638770
$442$	11.1383	0.529794
$443$	13.8342	0.657281	0.328640	−	0.944455i	$-0.393410\pi$
$443$	13.8342	0.657281	0.328640	+	0.944455i	$0.393410\pi$
$444$	−1.37525	−0.0652662
$445$	−9.09323	−0.431060
$446$	12.5821	0.595779
$447$	−9.45195	−0.447062
$448$	−3.30603	−0.156195
$449$	−8.41440	−0.397100	−0.198550	−	0.980091i	$-0.563623\pi$
$449$	−8.41440	−0.397100	−0.198550	+	0.980091i	$0.563623\pi$
$450$	−2.58665	−0.121936
$451$	4.63183	0.218105
$452$	0.142335	0.00669489
$453$	10.5595	0.496128
$454$	−14.7066	−0.690213
$455$	4.12638	0.193448
$456$	−0.528222	−0.0247363
$457$	17.7081	0.828350	0.414175	−	0.910197i	$-0.364070\pi$
$457$	17.7081	0.828350	0.414175	+	0.910197i	$0.364070\pi$
$458$	20.0773	0.938149
$459$	16.7843	0.783425
$460$	−9.85763	−0.459614
$461$	−24.6462	−1.14789	−0.573945	−	0.818894i	$-0.694588\pi$
$461$	−24.6462	−1.14789	−0.573945	+	0.818894i	$0.694588\pi$
$462$	−1.34277	−0.0624714
$463$	4.02078	0.186862	0.0934308	−	0.995626i	$-0.470217\pi$
$463$	4.02078	0.186862	0.0934308	+	0.995626i	$0.470217\pi$
$464$	−4.96087	−0.230303
$465$	−10.3830	−0.481500
$466$	−27.7741	−1.28661
$467$	−21.2936	−0.985349	−0.492675	−	0.870214i	$-0.663981\pi$
$467$	−21.2936	−0.985349	−0.492675	+	0.870214i	$0.663981\pi$
$468$	3.17448	0.146740
$469$	−3.61169	−0.166772
$470$	16.0354	0.739656
$471$	−0.759721	−0.0350061
$472$	−3.29953	−0.151873
$473$	5.58993	0.257025
$474$	12.7094	0.583764
$475$	−0.221128	−0.0101461
$476$	−3.95210	−0.181144
$477$	31.7908	1.45560
$478$	−5.56075	−0.254343
$479$	−8.63347	−0.394473	−0.197237	−	0.980356i	$-0.563197\pi$
$479$	−8.63347	−0.394473	−0.197237	+	0.980356i	$0.563197\pi$
$480$	−6.81517	−0.311068
$481$	−3.68531	−0.168036
$482$	4.44703	0.202557
$483$	−5.40744	−0.246047
$484$	−8.21302	−0.373319
$485$	21.7180	0.986163
$486$	25.9548	1.17734
$487$	−40.5928	−1.83944	−0.919718	−	0.392579i	$-0.871583\pi$
$487$	−40.5928	−1.83944	−0.919718	+	0.392579i	$0.871583\pi$
$488$	−24.7477	−1.12027
$489$	7.24164	0.327478
$490$	19.3591	0.874556
$491$	8.35307	0.376969	0.188484	−	0.982076i	$-0.439643\pi$
$491$	8.35307	0.376969	0.188484	+	0.982076i	$0.439643\pi$
$492$	−3.23498	−0.145844
$493$	4.07334	0.183454
$494$	0.947980	0.0426516
$495$	−4.41606	−0.198487
$496$	−32.4551	−1.45728
$497$	14.3922	0.645580
$498$	7.98181	0.357673
$499$	21.2676	0.952067	0.476033	−	0.879427i	$-0.342074\pi$
$499$	21.2676	0.952067	0.476033	+	0.879427i	$0.342074\pi$
$500$	−9.44584	−0.422431
$501$	−10.6167	−0.474319
$502$	11.1907	0.499463
$503$	11.3840	0.507586	0.253793	−	0.967259i	$-0.418322\pi$
$503$	11.3840	0.507586	0.253793	+	0.967259i	$0.418322\pi$
$504$	5.87509	0.261697
$505$	21.2351	0.944949
$506$	8.59606	0.382141
$507$	7.85089	0.348670
$508$	5.49934	0.243994
$509$	−15.4472	−0.684684	−0.342342	−	0.939575i	$-0.611220\pi$
$509$	−15.4472	−0.684684	−0.342342	+	0.939575i	$0.611220\pi$
$510$	10.8218	0.479195
$511$	−9.41634	−0.416555
$512$	−1.40868	−0.0622553
$513$	1.42852	0.0630706
$514$	29.9704	1.32194
$515$	−30.0370	−1.32359
$516$	−3.90413	−0.171870
$517$	−4.00300	−0.176052
$518$	4.56777	0.200696
$519$	1.89987	0.0833950
$520$	−6.84078	−0.299988
$521$	−14.0644	−0.616172	−0.308086	−	0.951359i	$-0.599688\pi$
$521$	−14.0644	−0.616172	−0.308086	+	0.951359i	$0.599688\pi$
$522$	4.05533	0.177497
$523$	25.5680	1.11801	0.559006	−	0.829164i	$-0.311183\pi$
$523$	25.5680	1.11801	0.559006	+	0.829164i	$0.311183\pi$
$524$	−10.7160	−0.468131
$525$	−0.586218	−0.0255847
$526$	−18.2592	−0.796140
$527$	26.6487	1.16084
$528$	3.29012	0.143184
$529$	11.6169	0.505085
$530$	45.8800	1.99290
$531$	3.98650	0.173000
$532$	−0.336364	−0.0145832
$533$	−8.66892	−0.375492
$534$	−5.53813	−0.239658
$535$	−7.46371	−0.322684
$536$	5.98752	0.258621
$537$	−7.02957	−0.303348
$538$	48.4354	2.08820
$539$	−4.83273	−0.208160
$540$	6.90368	0.297087
$541$	−11.4275	−0.491308	−0.245654	−	0.969358i	$-0.579003\pi$
$541$	−11.4275	−0.491308	−0.245654	+	0.969358i	$0.579003\pi$
$542$	−19.3230	−0.829992
$543$	−10.4105	−0.446756
$544$	17.4916	0.749946
$545$	11.8579	0.507937
$546$	2.51312	0.107552
$547$	−38.3109	−1.63806	−0.819028	−	0.573754i	$-0.805487\pi$
$547$	−38.3109	−1.63806	−0.819028	+	0.573754i	$0.805487\pi$
$548$	−9.08895	−0.388261
$549$	29.9003	1.27611
$550$	0.931895	0.0397361
$551$	0.346683	0.0147692
$552$	8.96455	0.381556
$553$	−12.0846	−0.513888
$554$	28.8068	1.22388
$555$	−3.58058	−0.151987
$556$	0.802190	0.0340204
$557$	25.2205	1.06863	0.534314	−	0.845286i	$-0.320570\pi$
$557$	25.2205	1.06863	0.534314	+	0.845286i	$0.320570\pi$
$558$	26.5309	1.12314
$559$	−10.4621	−0.442499
$560$	12.5317	0.529560
$561$	−2.70150	−0.114057
$562$	49.2084	2.07573
$563$	3.33057	0.140367	0.0701835	−	0.997534i	$-0.477642\pi$
$563$	3.33057	0.140367	0.0701835	+	0.997534i	$0.477642\pi$
$564$	2.79578	0.117724
$565$	0.370583	0.0155906
$566$	5.91313	0.248547
$567$	−5.00316	−0.210113
$568$	−23.8597	−1.00113
$569$	−10.4526	−0.438197	−0.219099	−	0.975703i	$-0.570312\pi$
$569$	−10.4526	−0.438197	−0.219099	+	0.975703i	$0.570312\pi$
$570$	0.921042	0.0385782
$571$	16.7258	0.699953	0.349977	−	0.936758i	$-0.386190\pi$
$571$	16.7258	0.699953	0.349977	+	0.936758i	$0.386190\pi$
$572$	−1.14367	−0.0478193
$573$	−9.24178	−0.386081
$574$	10.7447	0.448477
$575$	3.75281	0.156503
$576$	−6.62192	−0.275914
$577$	23.3282	0.971164	0.485582	−	0.874191i	$-0.338608\pi$
$577$	23.3282	0.971164	0.485582	+	0.874191i	$0.338608\pi$
$578$	0.682773	0.0283996
$579$	12.3530	0.513371
$580$	1.67544	0.0695687
$581$	−7.58937	−0.314860
$582$	13.2271	0.548281
$583$	−11.4533	−0.474347
$584$	15.6106	0.645970
$585$	8.26507	0.341718
$586$	34.7697	1.43632
$587$	−16.7347	−0.690715	−0.345358	−	0.938471i	$-0.612242\pi$
$587$	−16.7347	−0.690715	−0.345358	+	0.938471i	$0.612242\pi$
$588$	3.37529	0.139194
$589$	2.26808	0.0934544
$590$	5.75326	0.236858
$591$	−11.5887	−0.476697
$592$	−11.1922	−0.459995
$593$	−30.1399	−1.23770	−0.618849	−	0.785510i	$-0.712401\pi$
$593$	−30.1399	−1.23770	−0.618849	+	0.785510i	$0.712401\pi$
$594$	−6.02016	−0.247010
$595$	−10.2897	−0.421836
$596$	9.97818	0.408722
$597$	−3.07060	−0.125671
$598$	−16.0883	−0.657901
$599$	32.7389	1.33768	0.668838	−	0.743409i	$-0.266792\pi$
$599$	32.7389	1.33768	0.668838	+	0.743409i	$0.266792\pi$
$600$	0.971843	0.0396753
$601$	−6.47379	−0.264071	−0.132036	−	0.991245i	$-0.542151\pi$
$601$	−6.47379	−0.264071	−0.132036	+	0.991245i	$0.542151\pi$
$602$	12.9673	0.528507
$603$	−7.23415	−0.294597
$604$	−11.1474	−0.453580
$605$	−21.3834	−0.869358
$606$	12.9330	0.525367
$607$	−11.3125	−0.459161	−0.229580	−	0.973290i	$-0.573735\pi$
$607$	−11.3125	−0.459161	−0.229580	+	0.973290i	$0.573735\pi$
$608$	1.48871	0.0603753
$609$	0.919067	0.0372425
$610$	43.1516	1.74716
$611$	7.49199	0.303094
$612$	−7.91600	−0.319985
$613$	−10.2075	−0.412276	−0.206138	−	0.978523i	$-0.566090\pi$
$613$	−10.2075	−0.412276	−0.206138	+	0.978523i	$0.566090\pi$
$614$	12.4618	0.502917
$615$	−8.42257	−0.339631
$616$	−2.11662	−0.0852811
$617$	37.7087	1.51810	0.759049	−	0.651034i	$-0.225664\pi$
$617$	37.7087	1.51810	0.759049	+	0.651034i	$0.225664\pi$
$618$	−18.2937	−0.735880
$619$	−43.1665	−1.73501	−0.867505	−	0.497429i	$-0.834278\pi$
$619$	−43.1665	−1.73501	−0.867505	+	0.497429i	$0.834278\pi$
$620$	10.9611	0.440207
$621$	−24.2436	−0.972862
$622$	−7.51379	−0.301275
$623$	5.26584	0.210971
$624$	−6.15777	−0.246508
$625$	−21.4040	−0.856158
$626$	−6.22005	−0.248603
$627$	−0.229925	−0.00918231
$628$	0.802018	0.0320040
$629$	9.18982	0.366422
$630$	−10.2442	−0.408138
$631$	−23.0180	−0.916331	−0.458166	−	0.888867i	$-0.651493\pi$
$631$	−23.0180	−0.916331	−0.458166	+	0.888867i	$0.651493\pi$
$632$	20.0340	0.796909
$633$	6.16030	0.244850
$634$	−2.61322	−0.103784
$635$	14.3181	0.568195
$636$	7.99923	0.317190
$637$	9.04491	0.358372
$638$	−1.46102	−0.0578422
$639$	28.8274	1.14040
$640$	−27.4941	−1.08680
$641$	−13.2100	−0.521765	−0.260883	−	0.965371i	$-0.584014\pi$
$641$	−13.2100	−0.521765	−0.260883	+	0.965371i	$0.584014\pi$
$642$	−4.54569	−0.179404
$643$	3.88059	0.153036	0.0765178	−	0.997068i	$-0.475620\pi$
$643$	3.88059	0.153036	0.0765178	+	0.997068i	$0.475620\pi$
$644$	5.70850	0.224946
$645$	−10.1648	−0.400238
$646$	−2.36392	−0.0930071
$647$	−6.45540	−0.253788	−0.126894	−	0.991916i	$-0.540501\pi$
$647$	−6.45540	−0.253788	−0.126894	+	0.991916i	$0.540501\pi$
$648$	8.29433	0.325832
$649$	−1.43622	−0.0563766
$650$	−1.74413	−0.0684104
$651$	6.01274	0.235658
$652$	−7.64481	−0.299394
$653$	−11.8397	−0.463325	−0.231662	−	0.972796i	$-0.574416\pi$
$653$	−11.8397	−0.463325	−0.231662	+	0.972796i	$0.574416\pi$
$654$	7.22193	0.282400
$655$	−27.9001	−1.09015
$656$	−26.3272	−1.02790
$657$	−18.8608	−0.735829
$658$	−9.28599	−0.362006
$659$	31.9996	1.24653	0.623263	−	0.782012i	$-0.285806\pi$
$659$	31.9996	1.24653	0.623263	+	0.782012i	$0.285806\pi$
$660$	−1.11117	−0.0432523
$661$	9.86037	0.383524	0.191762	−	0.981441i	$-0.438580\pi$
$661$	9.86037	0.383524	0.191762	+	0.981441i	$0.438580\pi$
$662$	46.9770	1.82581
$663$	5.05611	0.196363
$664$	12.5818	0.488268
$665$	−0.875756	−0.0339604
$666$	9.14918	0.354523
$667$	−5.88362	−0.227815
$668$	11.2078	0.433642
$669$	5.71151	0.220820
$670$	−10.4402	−0.403341
$671$	−10.7722	−0.415856
$672$	3.94663	0.152244
$673$	15.1686	0.584707	0.292353	−	0.956310i	$-0.405562\pi$
$673$	15.1686	0.584707	0.292353	+	0.956310i	$0.405562\pi$
$674$	26.1188	1.00606
$675$	−2.62824	−0.101161
$676$	−8.28798	−0.318768
$677$	51.5127	1.97979	0.989897	−	0.141787i	$-0.0452849\pi$
$677$	51.5127	1.97979	0.989897	+	0.141787i	$0.0452849\pi$
$678$	0.225700	0.00866795
$679$	−12.5768	−0.482652
$680$	17.0584	0.654160
$681$	−6.67590	−0.255821
$682$	−9.55829	−0.366006
$683$	6.90419	0.264182	0.132091	−	0.991238i	$-0.457831\pi$
$683$	6.90419	0.264182	0.132091	+	0.991238i	$0.457831\pi$
$684$	−0.673732	−0.0257608
$685$	−23.6639	−0.904153
$686$	−25.3833	−0.969138
$687$	9.11387	0.347716
$688$	−31.7730	−1.21133
$689$	21.4359	0.816643
$690$	−15.6312	−0.595068
$691$	−39.5370	−1.50406	−0.752029	−	0.659130i	$-0.770925\pi$
$691$	−39.5370	−1.50406	−0.752029	+	0.659130i	$0.770925\pi$
$692$	−2.00564	−0.0762432
$693$	2.55731	0.0971443
$694$	26.5787	1.00891
$695$	2.08858	0.0792243
$696$	−1.52365	−0.0577536
$697$	21.6171	0.818807
$698$	1.91492	0.0724810
$699$	−12.6078	−0.476869
$700$	0.618855	0.0233905
$701$	−36.3238	−1.37193	−0.685966	−	0.727634i	$-0.740620\pi$
$701$	−36.3238	−1.37193	−0.685966	+	0.727634i	$0.740620\pi$
$702$	11.2673	0.425257
$703$	0.782147	0.0294992
$704$	2.38568	0.0899138
$705$	7.27909	0.274147
$706$	41.0398	1.54455
$707$	−12.2971	−0.462481
$708$	1.00309	0.0376984
$709$	−21.1318	−0.793622	−0.396811	−	0.917900i	$-0.629883\pi$
$709$	−21.1318	−0.793622	−0.396811	+	0.917900i	$0.629883\pi$
$710$	41.6033	1.56134
$711$	−24.2052	−0.907765
$712$	−8.72980	−0.327163
$713$	−38.4919	−1.44153
$714$	−6.26682	−0.234530
$715$	−2.97766	−0.111358
$716$	7.42093	0.277333
$717$	−2.52425	−0.0942697
$718$	−34.2046	−1.27650
$719$	36.4633	1.35985	0.679925	−	0.733281i	$-0.262012\pi$
$719$	36.4633	1.35985	0.679925	+	0.733281i	$0.262012\pi$
$720$	25.1007	0.935449
$721$	17.3942	0.647795
$722$	31.6043	1.17619
$723$	2.01869	0.0750758
$724$	10.9901	0.408443
$725$	−0.637840	−0.0236888
$726$	−13.0233	−0.483341
$727$	29.3420	1.08823	0.544117	−	0.839009i	$-0.316865\pi$
$727$	29.3420	1.08823	0.544117	+	0.839009i	$0.316865\pi$
$728$	3.96146	0.146821
$729$	−0.627881	−0.0232548
$730$	−27.2196	−1.00744
$731$	26.0886	0.964922
$732$	7.52354	0.278078
$733$	7.76498	0.286806	0.143403	−	0.989664i	$-0.454196\pi$
$733$	7.76498	0.286806	0.143403	+	0.989664i	$0.454196\pi$
$734$	−9.94136	−0.366942
$735$	8.78788	0.324146
$736$	−25.2652	−0.931288
$737$	2.60625	0.0960025
$738$	21.5215	0.792218
$739$	−1.63864	−0.0602782	−0.0301391	−	0.999546i	$-0.509595\pi$
$739$	−1.63864	−0.0602782	−0.0301391	+	0.999546i	$0.509595\pi$
$740$	3.77993	0.138953
$741$	0.430326	0.0158084
$742$	−26.5689	−0.975374
$743$	5.50482	0.201952	0.100976	−	0.994889i	$-0.467803\pi$
$743$	5.50482	0.201952	0.100976	+	0.994889i	$0.467803\pi$
$744$	−9.96802	−0.365445
$745$	25.9791	0.951802
$746$	25.7806	0.943895
$747$	−15.2014	−0.556189
$748$	2.85190	0.104276
$749$	4.32219	0.157929
$750$	−14.9782	−0.546926
$751$	3.06691	0.111913	0.0559566	−	0.998433i	$-0.482179\pi$
$751$	3.06691	0.111913	0.0559566	+	0.998433i	$0.482179\pi$
$752$	22.7529	0.829714
$753$	5.07989	0.185121
$754$	2.73443	0.0995821
$755$	−29.0233	−1.05626
$756$	−3.99788	−0.145402
$757$	17.6180	0.640338	0.320169	−	0.947360i	$-0.396260\pi$
$757$	17.6180	0.640338	0.320169	+	0.947360i	$0.396260\pi$
$758$	−10.8631	−0.394567
$759$	3.90209	0.141637
$760$	1.45184	0.0526639
$761$	−30.6175	−1.10988	−0.554942	−	0.831889i	$-0.687260\pi$
$761$	−30.6175	−1.10988	−0.554942	+	0.831889i	$0.687260\pi$
$762$	8.72025	0.315901
$763$	−6.86685	−0.248597
$764$	9.75632	0.352971
$765$	−20.6101	−0.745158
$766$	1.39881	0.0505410
$767$	2.68802	0.0970588
$768$	−12.5908	−0.454331
$769$	43.9852	1.58615	0.793074	−	0.609125i	$-0.208479\pi$
$769$	43.9852	1.58615	0.793074	+	0.609125i	$0.208479\pi$
$770$	3.69068	0.133003
$771$	13.6048	0.489963
$772$	−13.0407	−0.469345
$773$	16.9500	0.609650	0.304825	−	0.952408i	$-0.401402\pi$
$773$	16.9500	0.609650	0.304825	+	0.952408i	$0.401402\pi$
$774$	25.9732	0.933589
$775$	−4.17289	−0.149895
$776$	20.8500	0.748470
$777$	2.07350	0.0743862
$778$	20.1484	0.722357
$779$	1.83984	0.0659190
$780$	2.07966	0.0744639
$781$	−10.3857	−0.371629
$782$	40.1185	1.43463
$783$	4.12053	0.147256
$784$	27.4691	0.981039
$785$	2.08813	0.0745286
$786$	−16.9923	−0.606094
$787$	−3.40678	−0.121439	−0.0607193	−	0.998155i	$-0.519339\pi$
$787$	−3.40678	−0.121439	−0.0607193	+	0.998155i	$0.519339\pi$
$788$	12.2339	0.435816
$789$	−8.28859	−0.295082
$790$	−34.9325	−1.24284
$791$	−0.214603	−0.00763040
$792$	−4.23956	−0.150646
$793$	20.1612	0.715944
$794$	33.8981	1.20300
$795$	20.8268	0.738650
$796$	3.24156	0.114894
$797$	5.19269	0.183935	0.0919673	−	0.995762i	$-0.470684\pi$
$797$	5.19269	0.183935	0.0919673	+	0.995762i	$0.470684\pi$
$798$	−0.533370	−0.0188811
$799$	−18.6823	−0.660932
$800$	−2.73899	−0.0968380
$801$	10.5474	0.372674
$802$	50.8616	1.79599
$803$	6.79498	0.239790
$804$	−1.82026	−0.0641958
$805$	14.8626	0.523838
$806$	17.8892	0.630122
$807$	21.9868	0.773971
$808$	20.3864	0.717190
$809$	45.4054	1.59637	0.798184	−	0.602414i	$-0.205794\pi$
$809$	45.4054	1.59637	0.798184	+	0.602414i	$0.205794\pi$
$810$	−14.4625	−0.508161
$811$	−13.2067	−0.463749	−0.231875	−	0.972746i	$-0.574486\pi$
$811$	−13.2067	−0.463749	−0.231875	+	0.972746i	$0.574486\pi$
$812$	−0.970236	−0.0340486
$813$	−8.77146	−0.307629
$814$	−3.29618	−0.115531
$815$	−19.9040	−0.697207
$816$	15.3552	0.537540
$817$	2.22041	0.0776822
$818$	20.8307	0.728329
$819$	−4.78625	−0.167245
$820$	8.89150	0.310504
$821$	3.31312	0.115629	0.0578144	−	0.998327i	$-0.481587\pi$
$821$	3.31312	0.115629	0.0578144	+	0.998327i	$0.481587\pi$
$822$	−14.4123	−0.502686
$823$	−12.8389	−0.447537	−0.223768	−	0.974642i	$-0.571836\pi$
$823$	−12.8389	−0.447537	−0.223768	+	0.974642i	$0.571836\pi$
$824$	−28.8365	−1.00457
$825$	0.423024	0.0147278
$826$	−3.33168	−0.115924
$827$	29.4914	1.02552	0.512758	−	0.858533i	$-0.328624\pi$
$827$	29.4914	1.02552	0.512758	+	0.858533i	$0.328624\pi$
$828$	11.4340	0.397360
$829$	24.8497	0.863065	0.431533	−	0.902097i	$-0.357973\pi$
$829$	24.8497	0.863065	0.431533	+	0.902097i	$0.357973\pi$
$830$	−21.9384	−0.761493
$831$	13.0765	0.453620
$832$	−4.46503	−0.154797
$833$	−22.5547	−0.781474
$834$	1.27203	0.0440467
$835$	29.1805	1.00983
$836$	0.242726	0.00839485
$837$	26.9574	0.931784
$838$	56.5615	1.95388
$839$	28.8276	0.995240	0.497620	−	0.867395i	$-0.334207\pi$
$839$	28.8276	0.995240	0.497620	+	0.867395i	$0.334207\pi$
$840$	3.84888	0.132799
$841$	1.00000	0.0344828
$842$	−3.60476	−0.124228
$843$	22.3377	0.769350
$844$	−6.50327	−0.223852
$845$	−21.5785	−0.742325
$846$	−18.5997	−0.639470
$847$	12.3830	0.425485
$848$	65.1002	2.23555
$849$	2.68420	0.0921217
$850$	4.34922	0.149177
$851$	−13.2739	−0.455025
$852$	7.25359	0.248504
$853$	−33.1368	−1.13458	−0.567291	−	0.823517i	$-0.692009\pi$
$853$	−33.1368	−1.13458	−0.567291	+	0.823517i	$0.692009\pi$
$854$	−24.9889	−0.855101
$855$	−1.75413	−0.0599898
$856$	−7.16540	−0.244908
$857$	6.64178	0.226879	0.113439	−	0.993545i	$-0.463813\pi$
$857$	6.64178	0.226879	0.113439	+	0.993545i	$0.463813\pi$
$858$	−1.81351	−0.0619122
$859$	21.1222	0.720681	0.360341	−	0.932821i	$-0.382660\pi$
$859$	21.1222	0.720681	0.360341	+	0.932821i	$0.382660\pi$
$860$	10.7307	0.365914
$861$	4.87746	0.166224
$862$	7.99077	0.272167
$863$	52.1404	1.77488	0.887440	−	0.460924i	$-0.152482\pi$
$863$	52.1404	1.77488	0.887440	+	0.460924i	$0.152482\pi$
$864$	17.6942	0.601970
$865$	−5.22189	−0.177550
$866$	25.7407	0.874705
$867$	0.309938	0.0105260
$868$	−6.34749	−0.215448
$869$	8.72041	0.295820
$870$	2.65673	0.0900714
$871$	−4.87784	−0.165279
$872$	11.3840	0.385510
$873$	−25.1911	−0.852588
$874$	3.41449	0.115497
$875$	14.2418	0.481459
$876$	−4.74577	−0.160345
$877$	−16.9905	−0.573729	−0.286864	−	0.957971i	$-0.592613\pi$
$877$	−16.9905	−0.573729	−0.286864	+	0.957971i	$0.592613\pi$
$878$	26.3035	0.887701
$879$	15.7834	0.532360
$880$	−9.04305	−0.304841
$881$	−26.8442	−0.904404	−0.452202	−	0.891915i	$-0.649361\pi$
$881$	−26.8442	−0.904404	−0.452202	+	0.891915i	$0.649361\pi$
$882$	−22.4550	−0.756098
$883$	20.0172	0.673631	0.336815	−	0.941571i	$-0.390650\pi$
$883$	20.0172	0.673631	0.336815	+	0.941571i	$0.390650\pi$
$884$	−5.33760	−0.179523
$885$	2.61164	0.0877892
$886$	−23.1580	−0.778009
$887$	13.8251	0.464202	0.232101	−	0.972692i	$-0.425440\pi$
$887$	13.8251	0.464202	0.232101	+	0.972692i	$0.425440\pi$
$888$	−3.43748	−0.115354
$889$	−8.29150	−0.278088
$890$	15.2218	0.510237
$891$	3.61036	0.120952
$892$	−6.02949	−0.201882
$893$	−1.59005	−0.0532091
$894$	15.8223	0.529177
$895$	19.3211	0.645834
$896$	15.9217	0.531905
$897$	−7.30314	−0.243845
$898$	14.0855	0.470039
$899$	6.54222	0.218195
$900$	1.23956	0.0413186
$901$	−53.4534	−1.78079
$902$	−7.75357	−0.258166
$903$	5.88637	0.195886
$904$	0.355772	0.0118328
$905$	28.6137	0.951152
$906$	−17.6763	−0.587256
$907$	22.4747	0.746261	0.373131	−	0.927779i	$-0.378284\pi$
$907$	22.4747	0.746261	0.373131	+	0.927779i	$0.378284\pi$
$908$	7.04757	0.233882
$909$	−24.6309	−0.816956
$910$	−6.90745	−0.228980
$911$	−23.7277	−0.786133	−0.393067	−	0.919510i	$-0.628586\pi$
$911$	−23.7277	−0.786133	−0.393067	+	0.919510i	$0.628586\pi$
$912$	1.30689	0.0432753
$913$	5.47661	0.181249
$914$	−29.6429	−0.980500
$915$	19.5882	0.647567
$916$	−9.62128	−0.317896
$917$	16.1568	0.533545
$918$	−28.0965	−0.927324
$919$	−6.97296	−0.230017	−0.115008	−	0.993365i	$-0.536690\pi$
$919$	−6.97296	−0.230017	−0.115008	+	0.993365i	$0.536690\pi$
$920$	−24.6395	−0.812340
$921$	5.65691	0.186402
$922$	41.2572	1.35873
$923$	19.4378	0.639802
$924$	0.643473	0.0211687
$925$	−1.43902	−0.0473148
$926$	−6.73069	−0.221184
$927$	34.8404	1.14431
$928$	4.29416	0.140963
$929$	−5.95024	−0.195221	−0.0976106	−	0.995225i	$-0.531120\pi$
$929$	−5.95024	−0.195221	−0.0976106	+	0.995225i	$0.531120\pi$
$930$	17.3809	0.569942
$931$	−1.91964	−0.0629135
$932$	13.3097	0.435973
$933$	−3.41081	−0.111665
$934$	35.6449	1.16634
$935$	7.42520	0.242830
$936$	7.93473	0.259355
$937$	−17.5059	−0.571891	−0.285946	−	0.958246i	$-0.592308\pi$
$937$	−17.5059	−0.571891	−0.285946	+	0.958246i	$0.592308\pi$
$938$	6.04587	0.197405
$939$	−2.82353	−0.0921423
$940$	−7.68435	−0.250636
$941$	12.7580	0.415900	0.207950	−	0.978139i	$-0.433321\pi$
$941$	12.7580	0.415900	0.207950	+	0.978139i	$0.433321\pi$
$942$	1.27175	0.0414360
$943$	−31.2242	−1.01680
$944$	8.16343	0.265697
$945$	−10.4089	−0.338601
$946$	−9.35739	−0.304235
$947$	38.5393	1.25236	0.626179	−	0.779680i	$-0.284618\pi$
$947$	38.5393	1.25236	0.626179	+	0.779680i	$0.284618\pi$
$948$	−6.09053	−0.197811
$949$	−12.7175	−0.412826
$950$	0.370163	0.0120097
$951$	−1.18625	−0.0384667
$952$	−9.87843	−0.320162
$953$	47.9766	1.55411	0.777057	−	0.629430i	$-0.216711\pi$
$953$	47.9766	1.55411	0.777057	+	0.629430i	$0.216711\pi$
$954$	−53.2170	−1.72296
$955$	25.4015	0.821973
$956$	2.66478	0.0861852
$957$	−0.663214	−0.0214386
$958$	14.4522	0.466930
$959$	13.7037	0.442514
$960$	−4.33815	−0.140013
$961$	11.8006	0.380666
$962$	6.16911	0.198900
$963$	8.65728	0.278977
$964$	−2.13108	−0.0686373
$965$	−33.9527	−1.09298
$966$	9.05191	0.291241
$967$	−27.2849	−0.877422	−0.438711	−	0.898628i	$-0.644565\pi$
$967$	−27.2849	−0.877422	−0.438711	+	0.898628i	$0.644565\pi$
$968$	−20.5287	−0.659819
$969$	−1.07308	−0.0344722
$970$	−36.3554	−1.16730
$971$	−43.8382	−1.40683	−0.703417	−	0.710777i	$-0.748343\pi$
$971$	−43.8382	−1.40683	−0.703417	+	0.710777i	$0.748343\pi$
$972$	−12.4379	−0.398946
$973$	−1.20948	−0.0387743
$974$	67.9514	2.17730
$975$	−0.791730	−0.0253557
$976$	61.2288	1.95989
$977$	−4.66520	−0.149253	−0.0746264	−	0.997212i	$-0.523776\pi$
$977$	−4.66520	−0.149253	−0.0746264	+	0.997212i	$0.523776\pi$
$978$	−12.1223	−0.387629
$979$	−3.79991	−0.121446
$980$	−9.27714	−0.296347
$981$	−13.7542	−0.439137
$982$	−13.9828	−0.446210
$983$	36.8388	1.17498	0.587488	−	0.809233i	$-0.300117\pi$
$983$	36.8388	1.17498	0.587488	+	0.809233i	$0.300117\pi$
$984$	−8.08594	−0.257771
$985$	31.8522	1.01490
$986$	−6.81867	−0.217151
$987$	−4.21528	−0.134174
$988$	−0.454284	−0.0144527
$989$	−37.6829	−1.19825
$990$	7.39236	0.234945
$991$	5.51410	0.175161	0.0875806	−	0.996157i	$-0.472086\pi$
$991$	5.51410	0.175161	0.0875806	+	0.996157i	$0.472086\pi$
$992$	28.0934	0.891965
$993$	21.3248	0.676720
$994$	−24.0922	−0.764160
$995$	8.43971	0.267557
$996$	−3.82499	−0.121199
$997$	−57.9820	−1.83631	−0.918155	−	0.396222i	$-0.870321\pi$
$997$	−57.9820	−1.83631	−0.918155	+	0.396222i	$0.870321\pi$
$998$	−35.6013	−1.12694
$999$	9.29627	0.294121

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4031.2.a.b.1.14	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4031.2.a.b.1.14	✓	59	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:	\( N \)	\(=\)	\( 4031 = 29 \cdot 139 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4031.a (trivial)

\(f(q)\)	\(=\)	\(q-1.67397 q^{2} -0.759884 q^{3} +0.802190 q^{4} +2.08858 q^{5} +1.27203 q^{6} -1.20948 q^{7} +2.00510 q^{8} -2.42258 q^{9} +O(q^{10})\)	\(q-1.67397 q^{2} -0.759884 q^{3} +0.802190 q^{4} +2.08858 q^{5} +1.27203 q^{6} -1.20948 q^{7} +2.00510 q^{8} -2.42258 q^{9} -3.49623 q^{10} +0.872783 q^{11} -0.609571 q^{12} -1.63350 q^{13} +2.02464 q^{14} -1.58708 q^{15} -4.96087 q^{16} +4.07334 q^{17} +4.05533 q^{18} +0.346683 q^{19} +1.67544 q^{20} +0.919067 q^{21} -1.46102 q^{22} -5.88362 q^{23} -1.52365 q^{24} -0.637840 q^{25} +2.73443 q^{26} +4.12053 q^{27} -0.970236 q^{28} +1.00000 q^{29} +2.65673 q^{30} +6.54222 q^{31} +4.29416 q^{32} -0.663214 q^{33} -6.81867 q^{34} -2.52610 q^{35} -1.94337 q^{36} +2.25609 q^{37} -0.580338 q^{38} +1.24127 q^{39} +4.18782 q^{40} +5.30697 q^{41} -1.53849 q^{42} +6.40472 q^{43} +0.700138 q^{44} -5.05974 q^{45} +9.84902 q^{46} -4.58648 q^{47} +3.76969 q^{48} -5.53715 q^{49} +1.06773 q^{50} -3.09527 q^{51} -1.31037 q^{52} -13.1227 q^{53} -6.89766 q^{54} +1.82288 q^{55} -2.42514 q^{56} -0.263439 q^{57} -1.67397 q^{58} -1.64556 q^{59} -1.27314 q^{60} -12.3423 q^{61} -10.9515 q^{62} +2.93007 q^{63} +2.73342 q^{64} -3.41168 q^{65} +1.11020 q^{66} +2.98614 q^{67} +3.26759 q^{68} +4.47087 q^{69} +4.22863 q^{70} -11.8995 q^{71} -4.85752 q^{72} +7.78542 q^{73} -3.77663 q^{74} +0.484685 q^{75} +0.278106 q^{76} -1.05562 q^{77} -2.07785 q^{78} +9.99150 q^{79} -10.3612 q^{80} +4.13661 q^{81} -8.88374 q^{82} +6.27488 q^{83} +0.737266 q^{84} +8.50750 q^{85} -10.7213 q^{86} -0.759884 q^{87} +1.75002 q^{88} -4.35379 q^{89} +8.46988 q^{90} +1.97569 q^{91} -4.71978 q^{92} -4.97133 q^{93} +7.67765 q^{94} +0.724075 q^{95} -3.26307 q^{96} +10.3985 q^{97} +9.26904 q^{98} -2.11438 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9	\( 59 q - 5 q^{2} - 6 q^{3} + 41 q^{4} - 5 q^{5} - 7 q^{6} - 10 q^{7} - 12 q^{8} + 23 q^{9} - 18 q^{10} - 27 q^{11} - 8 q^{12} - 22 q^{13} - 24 q^{14} - 18 q^{15} + 5 q^{16} - 23 q^{17} + q^{18} - 32 q^{19} - 14 q^{20} - 36 q^{21} - 6 q^{22} - 3 q^{23} - 18 q^{24} - 8 q^{25} - q^{26} - 12 q^{27} - 9 q^{28} + 59 q^{29} - 18 q^{30} - 32 q^{31} - 39 q^{32} - 12 q^{33} - 18 q^{34} - 9 q^{35} + 10 q^{36} - 44 q^{37} + 5 q^{38} - 27 q^{39} - 68 q^{40} - 44 q^{41} - 25 q^{42} - 40 q^{43} - 56 q^{44} - 39 q^{45} - 40 q^{46} - 20 q^{47} - 9 q^{48} - 39 q^{49} - 21 q^{50} - 28 q^{51} - 49 q^{52} - 31 q^{53} - 32 q^{54} - 32 q^{55} - 48 q^{56} - 58 q^{57} - 5 q^{58} + 6 q^{59} - 44 q^{60} - 88 q^{61} + 35 q^{62} - 22 q^{63} - 10 q^{64} - 43 q^{65} - 31 q^{66} - 45 q^{67} - 29 q^{68} - 60 q^{69} - 14 q^{70} - 20 q^{71} - 4 q^{72} - 90 q^{73} - 25 q^{74} + 15 q^{75} - 64 q^{76} - 39 q^{77} - 28 q^{78} - 120 q^{79} + 24 q^{80} - 77 q^{81} - 71 q^{82} - 33 q^{83} - 14 q^{84} - 71 q^{85} - 61 q^{86} - 6 q^{87} - 34 q^{88} - 78 q^{89} - 88 q^{90} - 28 q^{91} - 31 q^{92} - 36 q^{93} - 4 q^{94} - 12 q^{95} - 29 q^{96} - 48 q^{97} - 4 q^{98} - 43 q^{99}+O(q^{100}) \) 59 * q - 5 * q^2 - 6 * q^3 + 41 * q^4 - 5 * q^5 - 7 * q^6 - 10 * q^7 - 12 * q^8 + 23 * q^9 - 18 * q^10 - 27 * q^11 - 8 * q^12 - 22 * q^13 - 24 * q^14 - 18 * q^15 + 5 * q^16 - 23 * q^17 + q^18 - 32 * q^19 - 14 * q^20 - 36 * q^21 - 6 * q^22 - 3 * q^23 - 18 * q^24 - 8 * q^25 - q^26 - 12 * q^27 - 9 * q^28 + 59 * q^29 - 18 * q^30 - 32 * q^31 - 39 * q^32 - 12 * q^33 - 18 * q^34 - 9 * q^35 + 10 * q^36 - 44 * q^37 + 5 * q^38 - 27 * q^39 - 68 * q^40 - 44 * q^41 - 25 * q^42 - 40 * q^43 - 56 * q^44 - 39 * q^45 - 40 * q^46 - 20 * q^47 - 9 * q^48 - 39 * q^49 - 21 * q^50 - 28 * q^51 - 49 * q^52 - 31 * q^53 - 32 * q^54 - 32 * q^55 - 48 * q^56 - 58 * q^57 - 5 * q^58 + 6 * q^59 - 44 * q^60 - 88 * q^61 + 35 * q^62 - 22 * q^63 - 10 * q^64 - 43 * q^65 - 31 * q^66 - 45 * q^67 - 29 * q^68 - 60 * q^69 - 14 * q^70 - 20 * q^71 - 4 * q^72 - 90 * q^73 - 25 * q^74 + 15 * q^75 - 64 * q^76 - 39 * q^77 - 28 * q^78 - 120 * q^79 + 24 * q^80 - 77 * q^81 - 71 * q^82 - 33 * q^83 - 14 * q^84 - 71 * q^85 - 61 * q^86 - 6 * q^87 - 34 * q^88 - 78 * q^89 - 88 * q^90 - 28 * q^91 - 31 * q^92 - 36 * q^93 - 4 * q^94 - 12 * q^95 - 29 * q^96 - 48 * q^97 - 4 * q^98 - 43 * q^99

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