LMFDB - Embedded newform 6041.2.a.d.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6041,2,Mod(1,6041)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6041, 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("6041.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6041 = 7 \cdot 863 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6041.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:	$48.2376278611$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	6041.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.37665 q^{2} +1.96222 q^{3} +3.64847 q^{4} -3.56190 q^{5} -4.66352 q^{6} -1.00000 q^{7} -3.91784 q^{8} +0.850318 q^{9} +O(q^{10})$	\(q-2.37665 q^{2} +1.96222 q^{3} +3.64847 q^{4} -3.56190 q^{5} -4.66352 q^{6} -1.00000 q^{7} -3.91784 q^{8} +0.850318 q^{9} +8.46540 q^{10} +4.74907 q^{11} +7.15911 q^{12} +2.97414 q^{13} +2.37665 q^{14} -6.98925 q^{15} +2.01439 q^{16} +0.999446 q^{17} -2.02091 q^{18} -8.30256 q^{19} -12.9955 q^{20} -1.96222 q^{21} -11.2869 q^{22} +2.31262 q^{23} -7.68767 q^{24} +7.68715 q^{25} -7.06850 q^{26} -4.21815 q^{27} -3.64847 q^{28} -5.81439 q^{29} +16.6110 q^{30} +2.26683 q^{31} +3.04816 q^{32} +9.31873 q^{33} -2.37533 q^{34} +3.56190 q^{35} +3.10236 q^{36} -0.420073 q^{37} +19.7323 q^{38} +5.83593 q^{39} +13.9550 q^{40} +10.4563 q^{41} +4.66352 q^{42} +3.28011 q^{43} +17.3268 q^{44} -3.02875 q^{45} -5.49630 q^{46} -6.74227 q^{47} +3.95269 q^{48} +1.00000 q^{49} -18.2697 q^{50} +1.96114 q^{51} +10.8511 q^{52} -1.54907 q^{53} +10.0251 q^{54} -16.9157 q^{55} +3.91784 q^{56} -16.2915 q^{57} +13.8188 q^{58} +5.12395 q^{59} -25.5001 q^{60} -3.66541 q^{61} -5.38747 q^{62} -0.850318 q^{63} -11.2732 q^{64} -10.5936 q^{65} -22.1474 q^{66} -3.50746 q^{67} +3.64645 q^{68} +4.53788 q^{69} -8.46540 q^{70} -6.39439 q^{71} -3.33141 q^{72} +2.33893 q^{73} +0.998368 q^{74} +15.0839 q^{75} -30.2917 q^{76} -4.74907 q^{77} -13.8700 q^{78} -1.77715 q^{79} -7.17507 q^{80} -10.8279 q^{81} -24.8509 q^{82} +1.90168 q^{83} -7.15911 q^{84} -3.55993 q^{85} -7.79567 q^{86} -11.4091 q^{87} -18.6061 q^{88} +13.5931 q^{89} +7.19828 q^{90} -2.97414 q^{91} +8.43753 q^{92} +4.44803 q^{93} +16.0240 q^{94} +29.5729 q^{95} +5.98118 q^{96} +7.75304 q^{97} -2.37665 q^{98} +4.03822 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) $ 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * 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 $

$2$	−2.37665	−1.68055	−0.840273	−	0.542163i	$-0.817605\pi$
$2$	−2.37665	−1.68055	−0.840273	+	0.542163i	$0.817605\pi$
$3$	1.96222	1.13289	0.566445	−	0.824100i	$-0.308318\pi$
$3$	1.96222	1.13289	0.566445	+	0.824100i	$0.308318\pi$
$4$	3.64847	1.82424
$5$	−3.56190	−1.59293	−0.796466	−	0.604684i	$-0.793299\pi$
$5$	−3.56190	−1.59293	−0.796466	+	0.604684i	$0.793299\pi$
$6$	−4.66352	−1.90387
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−3.91784	−1.38517
$9$	0.850318	0.283439
$10$	8.46540	2.67699
$11$	4.74907	1.43190	0.715949	−	0.698152i	$-0.245994\pi$
$11$	4.74907	1.43190	0.715949	+	0.698152i	$0.245994\pi$
$12$	7.15911	2.06666
$13$	2.97414	0.824878	0.412439	−	0.910985i	$-0.364677\pi$
$13$	2.97414	0.824878	0.412439	+	0.910985i	$0.364677\pi$
$14$	2.37665	0.635187
$15$	−6.98925	−1.80462
$16$	2.01439	0.503599
$17$	0.999446	0.242401	0.121201	−	0.992628i	$-0.461326\pi$
$17$	0.999446	0.242401	0.121201	+	0.992628i	$0.461326\pi$
$18$	−2.02091	−0.476333
$19$	−8.30256	−1.90474	−0.952369	−	0.304947i	$-0.901361\pi$
$19$	−8.30256	−1.90474	−0.952369	+	0.304947i	$0.901361\pi$
$20$	−12.9955	−2.90588
$21$	−1.96222	−0.428192
$22$	−11.2869	−2.40637
$23$	2.31262	0.482215	0.241108	−	0.970498i	$-0.422489\pi$
$23$	2.31262	0.482215	0.241108	+	0.970498i	$0.422489\pi$
$24$	−7.68767	−1.56924
$25$	7.68715	1.53743
$26$	−7.06850	−1.38625
$27$	−4.21815	−0.811784
$28$	−3.64847	−0.689496
$29$	−5.81439	−1.07970	−0.539852	−	0.841760i	$-0.681520\pi$
$29$	−5.81439	−1.07970	−0.539852	+	0.841760i	$0.681520\pi$
$30$	16.6110	3.03274
$31$	2.26683	0.407135	0.203568	−	0.979061i	$-0.434746\pi$
$31$	2.26683	0.407135	0.203568	+	0.979061i	$0.434746\pi$
$32$	3.04816	0.538844
$33$	9.31873	1.62218
$34$	−2.37533	−0.407367
$35$	3.56190	0.602071
$36$	3.10236	0.517060
$37$	−0.420073	−0.0690596	−0.0345298	−	0.999404i	$-0.510993\pi$
$37$	−0.420073	−0.0690596	−0.0345298	+	0.999404i	$0.510993\pi$
$38$	19.7323	3.20100
$39$	5.83593	0.934496
$40$	13.9550	2.20647
$41$	10.4563	1.63300	0.816499	−	0.577348i	$-0.195912\pi$
$41$	10.4563	1.63300	0.816499	+	0.577348i	$0.195912\pi$
$42$	4.66352	0.719597
$43$	3.28011	0.500212	0.250106	−	0.968218i	$-0.419535\pi$
$43$	3.28011	0.500212	0.250106	+	0.968218i	$0.419535\pi$
$44$	17.3268	2.61212
$45$	−3.02875	−0.451499
$46$	−5.49630	−0.810385
$47$	−6.74227	−0.983460	−0.491730	−	0.870748i	$-0.663635\pi$
$47$	−6.74227	−0.983460	−0.491730	+	0.870748i	$0.663635\pi$
$48$	3.95269	0.570522
$49$	1.00000	0.142857
$50$	−18.2697	−2.58372
$51$	1.96114	0.274614
$52$	10.8511	1.50477
$53$	−1.54907	−0.212781	−0.106390	−	0.994324i	$-0.533929\pi$
$53$	−1.54907	−0.212781	−0.106390	+	0.994324i	$0.533929\pi$
$54$	10.0251	1.36424
$55$	−16.9157	−2.28092
$56$	3.91784	0.523543
$57$	−16.2915	−2.15786
$58$	13.8188	1.81449
$59$	5.12395	0.667082	0.333541	−	0.942736i	$-0.391757\pi$
$59$	5.12395	0.667082	0.333541	+	0.942736i	$0.391757\pi$
$60$	−25.5001	−3.29204
$61$	−3.66541	−0.469307	−0.234654	−	0.972079i	$-0.575396\pi$
$61$	−3.66541	−0.469307	−0.234654	+	0.972079i	$0.575396\pi$
$62$	−5.38747	−0.684210
$63$	−0.850318	−0.107130
$64$	−11.2732	−1.40915
$65$	−10.5936	−1.31397
$66$	−22.1474	−2.72615
$67$	−3.50746	−0.428504	−0.214252	−	0.976778i	$-0.568731\pi$
$67$	−3.50746	−0.428504	−0.214252	+	0.976778i	$0.568731\pi$
$68$	3.64645	0.442197
$69$	4.53788	0.546297
$70$	−8.46540	−1.01181
$71$	−6.39439	−0.758875	−0.379437	−	0.925217i	$-0.623882\pi$
$71$	−6.39439	−0.758875	−0.379437	+	0.925217i	$0.623882\pi$
$72$	−3.33141	−0.392610
$73$	2.33893	0.273751	0.136875	−	0.990588i	$-0.456294\pi$
$73$	2.33893	0.273751	0.136875	+	0.990588i	$0.456294\pi$
$74$	0.998368	0.116058
$75$	15.0839	1.74174
$76$	−30.2917	−3.47469
$77$	−4.74907	−0.541207
$78$	−13.8700	−1.57046
$79$	−1.77715	−0.199945	−0.0999726	−	0.994990i	$-0.531876\pi$
$79$	−1.77715	−0.199945	−0.0999726	+	0.994990i	$0.531876\pi$
$80$	−7.17507	−0.802198
$81$	−10.8279	−1.20310
$82$	−24.8509	−2.74433
$83$	1.90168	0.208737	0.104368	−	0.994539i	$-0.466718\pi$
$83$	1.90168	0.208737	0.104368	+	0.994539i	$0.466718\pi$
$84$	−7.15911	−0.781123
$85$	−3.55993	−0.386129
$86$	−7.79567	−0.840629
$87$	−11.4091	−1.22319
$88$	−18.6061	−1.98342
$89$	13.5931	1.44086	0.720432	−	0.693526i	$-0.243944\pi$
$89$	13.5931	1.44086	0.720432	+	0.693526i	$0.243944\pi$
$90$	7.19828	0.758765
$91$	−2.97414	−0.311775
$92$	8.43753	0.879674
$93$	4.44803	0.461240
$94$	16.0240	1.65275
$95$	29.5729	3.03412
$96$	5.98118	0.610451
$97$	7.75304	0.787202	0.393601	−	0.919281i	$-0.371229\pi$
$97$	7.75304	0.787202	0.393601	+	0.919281i	$0.371229\pi$
$98$	−2.37665	−0.240078
$99$	4.03822	0.405856
$100$	28.0463	2.80463
$101$	−1.08304	−0.107767	−0.0538833	−	0.998547i	$-0.517160\pi$
$101$	−1.08304	−0.107767	−0.0538833	+	0.998547i	$0.517160\pi$
$102$	−4.66094	−0.461501
$103$	−17.0850	−1.68344	−0.841719	−	0.539915i	$-0.818456\pi$
$103$	−17.0850	−1.68344	−0.841719	+	0.539915i	$0.818456\pi$
$104$	−11.6522	−1.14259
$105$	6.98925	0.682080
$106$	3.68159	0.357588
$107$	−16.5667	−1.60157	−0.800783	−	0.598954i	$-0.795583\pi$
$107$	−16.5667	−1.60157	−0.800783	+	0.598954i	$0.795583\pi$
$108$	−15.3898	−1.48089
$109$	−0.245439	−0.0235087	−0.0117544	−	0.999931i	$-0.503742\pi$
$109$	−0.245439	−0.0235087	−0.0117544	+	0.999931i	$0.503742\pi$
$110$	40.2028	3.83318
$111$	−0.824277	−0.0782370
$112$	−2.01439	−0.190342
$113$	15.9003	1.49577	0.747887	−	0.663826i	$-0.231068\pi$
$113$	15.9003	1.49577	0.747887	+	0.663826i	$0.231068\pi$
$114$	38.7192	3.62638
$115$	−8.23733	−0.768135
$116$	−21.2136	−1.96964
$117$	2.52897	0.233803
$118$	−12.1778	−1.12106
$119$	−0.999446	−0.0916191
$120$	27.3827	2.49969
$121$	11.5537	1.05033
$122$	8.71139	0.788692
$123$	20.5176	1.85001
$124$	8.27048	0.742711
$125$	−9.57135	−0.856088
$126$	2.02091	0.180037
$127$	−6.15283	−0.545975	−0.272988	−	0.962018i	$-0.588012\pi$
$127$	−6.15283	−0.545975	−0.272988	+	0.962018i	$0.588012\pi$
$128$	20.6962	1.82930
$129$	6.43630	0.566685
$130$	25.1773	2.20819
$131$	9.76372	0.853060	0.426530	−	0.904473i	$-0.359736\pi$
$131$	9.76372	0.853060	0.426530	+	0.904473i	$0.359736\pi$
$132$	33.9991	2.95924
$133$	8.30256	0.719924
$134$	8.33600	0.720121
$135$	15.0247	1.29312
$136$	−3.91567	−0.335766
$137$	−8.55980	−0.731313	−0.365657	−	0.930750i	$-0.619156\pi$
$137$	−8.55980	−0.731313	−0.365657	+	0.930750i	$0.619156\pi$
$138$	−10.7850	−0.918077
$139$	−7.25435	−0.615306	−0.307653	−	0.951499i	$-0.599544\pi$
$139$	−7.25435	−0.615306	−0.307653	+	0.951499i	$0.599544\pi$
$140$	12.9955	1.09832
$141$	−13.2298	−1.11415
$142$	15.1972	1.27532
$143$	14.1244	1.18114
$144$	1.71288	0.142740
$145$	20.7103	1.71990
$146$	−5.55882	−0.460051
$147$	1.96222	0.161841
$148$	−1.53263	−0.125981
$149$	3.63764	0.298007	0.149004	−	0.988837i	$-0.452393\pi$
$149$	3.63764	0.298007	0.149004	+	0.988837i	$0.452393\pi$
$150$	−35.8491	−2.92707
$151$	−4.62641	−0.376492	−0.188246	−	0.982122i	$-0.560280\pi$
$151$	−4.62641	−0.376492	−0.188246	+	0.982122i	$0.560280\pi$
$152$	32.5281	2.63838
$153$	0.849847	0.0687061
$154$	11.2869	0.909523
$155$	−8.07424	−0.648539
$156$	21.2922	1.70474
$157$	4.10074	0.327275	0.163637	−	0.986521i	$-0.447677\pi$
$157$	4.10074	0.327275	0.163637	+	0.986521i	$0.447677\pi$
$158$	4.22367	0.336017
$159$	−3.03961	−0.241057
$160$	−10.8573	−0.858342
$161$	−2.31262	−0.182260
$162$	25.7342	2.02187
$163$	−9.47510	−0.742147	−0.371074	−	0.928603i	$-0.621010\pi$
$163$	−9.47510	−0.742147	−0.371074	+	0.928603i	$0.621010\pi$
$164$	38.1494	2.97897
$165$	−33.1924	−2.58403
$166$	−4.51963	−0.350791
$167$	−16.8114	−1.30090	−0.650452	−	0.759547i	$-0.725420\pi$
$167$	−16.8114	−1.30090	−0.650452	+	0.759547i	$0.725420\pi$
$168$	7.68767	0.593117
$169$	−4.15448	−0.319576
$170$	8.46071	0.648907
$171$	−7.05982	−0.539878
$172$	11.9674	0.912504
$173$	−1.24363	−0.0945513	−0.0472756	−	0.998882i	$-0.515054\pi$
$173$	−1.24363	−0.0945513	−0.0472756	+	0.998882i	$0.515054\pi$
$174$	27.1155	2.05562
$175$	−7.68715	−0.581094
$176$	9.56650	0.721102
$177$	10.0543	0.755730
$178$	−32.3060	−2.42144
$179$	14.9337	1.11619	0.558097	−	0.829775i	$-0.311532\pi$
$179$	14.9337	1.11619	0.558097	+	0.829775i	$0.311532\pi$
$180$	−11.0503	−0.823641
$181$	15.9252	1.18371	0.591855	−	0.806044i	$-0.298396\pi$
$181$	15.9252	1.18371	0.591855	+	0.806044i	$0.298396\pi$
$182$	7.06850	0.523952
$183$	−7.19234	−0.531673
$184$	−9.06048	−0.667948
$185$	1.49626	0.110007
$186$	−10.5714	−0.775134
$187$	4.74644	0.347094
$188$	−24.5990	−1.79406
$189$	4.21815	0.306826
$190$	−70.2845	−5.09897
$191$	8.64436	0.625484	0.312742	−	0.949838i	$-0.398752\pi$
$191$	8.64436	0.625484	0.312742	+	0.949838i	$0.398752\pi$
$192$	−22.1206	−1.59641
$193$	9.80212	0.705572	0.352786	−	0.935704i	$-0.385234\pi$
$193$	9.80212	0.705572	0.352786	+	0.935704i	$0.385234\pi$
$194$	−18.4263	−1.32293
$195$	−20.7870	−1.48859
$196$	3.64847	0.260605
$197$	23.0685	1.64356	0.821782	−	0.569803i	$-0.192980\pi$
$197$	23.0685	1.64356	0.821782	+	0.569803i	$0.192980\pi$
$198$	−9.59744	−0.682060
$199$	−23.3131	−1.65262	−0.826310	−	0.563216i	$-0.809564\pi$
$199$	−23.3131	−1.65262	−0.826310	+	0.563216i	$0.809564\pi$
$200$	−30.1170	−2.12959
$201$	−6.88241	−0.485448
$202$	2.57401	0.181107
$203$	5.81439	0.408090
$204$	7.15515	0.500960
$205$	−37.2443	−2.60125
$206$	40.6052	2.82910
$207$	1.96646	0.136679
$208$	5.99109	0.415408
$209$	−39.4295	−2.72739
$210$	−16.6110	−1.14627
$211$	−1.92066	−0.132224	−0.0661119	−	0.997812i	$-0.521059\pi$
$211$	−1.92066	−0.132224	−0.0661119	+	0.997812i	$0.521059\pi$
$212$	−5.65172	−0.388162
$213$	−12.5472	−0.859722
$214$	39.3733	2.69151
$215$	−11.6834	−0.796803
$216$	16.5260	1.12446
$217$	−2.26683	−0.153883
$218$	0.583322	0.0395075
$219$	4.58950	0.310129
$220$	−61.7165	−4.16093
$221$	2.97249	0.199952
$222$	1.95902	0.131481
$223$	−15.9447	−1.06774	−0.533869	−	0.845567i	$-0.679262\pi$
$223$	−15.9447	−1.06774	−0.533869	+	0.845567i	$0.679262\pi$
$224$	−3.04816	−0.203664
$225$	6.53652	0.435768
$226$	−37.7895	−2.51372
$227$	−4.08019	−0.270811	−0.135406	−	0.990790i	$-0.543234\pi$
$227$	−4.08019	−0.270811	−0.135406	+	0.990790i	$0.543234\pi$
$228$	−59.4390	−3.93644
$229$	1.12412	0.0742837	0.0371418	−	0.999310i	$-0.488175\pi$
$229$	1.12412	0.0742837	0.0371418	+	0.999310i	$0.488175\pi$
$230$	19.5773	1.29089
$231$	−9.31873	−0.613128
$232$	22.7798	1.49557
$233$	−22.3662	−1.46526	−0.732629	−	0.680629i	$-0.761707\pi$
$233$	−22.3662	−1.46526	−0.732629	+	0.680629i	$0.761707\pi$
$234$	−6.01047	−0.392917
$235$	24.0153	1.56658
$236$	18.6946	1.21691
$237$	−3.48717	−0.226516
$238$	2.37533	0.153970
$239$	25.4895	1.64878	0.824388	−	0.566025i	$-0.191519\pi$
$239$	25.4895	1.64878	0.824388	+	0.566025i	$0.191519\pi$
$240$	−14.0791	−0.908802
$241$	−4.21203	−0.271320	−0.135660	−	0.990755i	$-0.543316\pi$
$241$	−4.21203	−0.271320	−0.135660	+	0.990755i	$0.543316\pi$
$242$	−27.4590	−1.76513
$243$	−8.59231	−0.551197
$244$	−13.3731	−0.856127
$245$	−3.56190	−0.227562
$246$	−48.7631	−3.10902
$247$	−24.6930	−1.57118
$248$	−8.88109	−0.563950
$249$	3.73152	0.236476
$250$	22.7478	1.43869
$251$	−11.5458	−0.728766	−0.364383	−	0.931249i	$-0.618720\pi$
$251$	−11.5458	−0.728766	−0.364383	+	0.931249i	$0.618720\pi$
$252$	−3.10236	−0.195430
$253$	10.9828	0.690483
$254$	14.6231	0.917537
$255$	−6.98537	−0.437441
$256$	−26.6411	−1.66507
$257$	5.40995	0.337464	0.168732	−	0.985662i	$-0.446033\pi$
$257$	5.40995	0.337464	0.168732	+	0.985662i	$0.446033\pi$
$258$	−15.2968	−0.952340
$259$	0.420073	0.0261021
$260$	−38.6504	−2.39700
$261$	−4.94408	−0.306031
$262$	−23.2050	−1.43361
$263$	8.39209	0.517478	0.258739	−	0.965947i	$-0.416693\pi$
$263$	8.39209	0.517478	0.258739	+	0.965947i	$0.416693\pi$
$264$	−36.5093	−2.24699
$265$	5.51762	0.338945
$266$	−19.7323	−1.20986
$267$	26.6726	1.63234
$268$	−12.7968	−0.781692
$269$	−14.4665	−0.882037	−0.441019	−	0.897498i	$-0.645383\pi$
$269$	−14.4665	−0.882037	−0.441019	+	0.897498i	$0.645383\pi$
$270$	−35.7084	−2.17314
$271$	−22.6813	−1.37779	−0.688896	−	0.724860i	$-0.741904\pi$
$271$	−22.6813	−1.37779	−0.688896	+	0.724860i	$0.741904\pi$
$272$	2.01328	0.122073
$273$	−5.83593	−0.353206
$274$	20.3437	1.22901
$275$	36.5068	2.20144
$276$	16.5563	0.996573
$277$	−19.8653	−1.19359	−0.596794	−	0.802394i	$-0.703559\pi$
$277$	−19.8653	−1.19359	−0.596794	+	0.802394i	$0.703559\pi$
$278$	17.2411	1.03405
$279$	1.92753	0.115398
$280$	−13.9550	−0.833968
$281$	−26.7619	−1.59648	−0.798242	−	0.602337i	$-0.794236\pi$
$281$	−26.7619	−1.59648	−0.798242	+	0.602337i	$0.794236\pi$
$282$	31.4427	1.87238
$283$	−28.7606	−1.70964	−0.854820	−	0.518924i	$-0.826333\pi$
$283$	−28.7606	−1.70964	−0.854820	+	0.518924i	$0.826333\pi$
$284$	−23.3298	−1.38437
$285$	58.0287	3.43732
$286$	−33.5688	−1.98496
$287$	−10.4563	−0.617215
$288$	2.59191	0.152730
$289$	−16.0011	−0.941242
$290$	−49.2211	−2.89036
$291$	15.2132	0.891813
$292$	8.53351	0.499386
$293$	25.6891	1.50077	0.750385	−	0.661001i	$-0.229868\pi$
$293$	25.6891	1.50077	0.750385	+	0.661001i	$0.229868\pi$
$294$	−4.66352	−0.271982
$295$	−18.2510	−1.06261
$296$	1.64578	0.0956590
$297$	−20.0323	−1.16239
$298$	−8.64540	−0.500815
$299$	6.87807	0.397769
$300$	55.0331	3.17734
$301$	−3.28011	−0.189062
$302$	10.9954	0.632712
$303$	−2.12517	−0.122088
$304$	−16.7246	−0.959224
$305$	13.0558	0.747574
$306$	−2.01979	−0.115464
$307$	−9.55218	−0.545171	−0.272586	−	0.962131i	$-0.587879\pi$
$307$	−9.55218	−0.545171	−0.272586	+	0.962131i	$0.587879\pi$
$308$	−17.3268	−0.987288
$309$	−33.5246	−1.90715
$310$	19.1897	1.08990
$311$	16.3151	0.925142	0.462571	−	0.886582i	$-0.346927\pi$
$311$	16.3151	0.925142	0.462571	+	0.886582i	$0.346927\pi$
$312$	−22.8642	−1.29443
$313$	18.5654	1.04938	0.524690	−	0.851293i	$-0.324181\pi$
$313$	18.5654	1.04938	0.524690	+	0.851293i	$0.324181\pi$
$314$	−9.74603	−0.550000
$315$	3.02875	0.170651
$316$	−6.48389	−0.364747
$317$	−2.66543	−0.149705	−0.0748527	−	0.997195i	$-0.523849\pi$
$317$	−2.66543	−0.149705	−0.0748527	+	0.997195i	$0.523849\pi$
$318$	7.22410	0.405107
$319$	−27.6129	−1.54603
$320$	40.1541	2.24468
$321$	−32.5076	−1.81440
$322$	5.49630	0.306297
$323$	−8.29797	−0.461711
$324$	−39.5053	−2.19474
$325$	22.8627	1.26819
$326$	22.5190	1.24721
$327$	−0.481605	−0.0266328
$328$	−40.9660	−2.26197
$329$	6.74227	0.371713
$330$	78.8868	4.34257
$331$	−25.5238	−1.40292	−0.701458	−	0.712710i	$-0.747467\pi$
$331$	−25.5238	−1.40292	−0.701458	+	0.712710i	$0.747467\pi$
$332$	6.93823	0.380785
$333$	−0.357196	−0.0195742
$334$	39.9548	2.18623
$335$	12.4932	0.682577
$336$	−3.95269	−0.215637
$337$	14.0604	0.765917	0.382958	−	0.923766i	$-0.374905\pi$
$337$	14.0604	0.765917	0.382958	+	0.923766i	$0.374905\pi$
$338$	9.87376	0.537062
$339$	31.1999	1.69455
$340$	−12.9883	−0.704389
$341$	10.7654	0.582977
$342$	16.7787	0.907290
$343$	−1.00000	−0.0539949
$344$	−12.8509	−0.692876
$345$	−16.1635	−0.870213
$346$	2.95567	0.158898
$347$	−16.7973	−0.901725	−0.450863	−	0.892593i	$-0.648884\pi$
$347$	−16.7973	−0.901725	−0.450863	+	0.892593i	$0.648884\pi$
$348$	−41.6258	−2.23138
$349$	32.3519	1.73176	0.865880	−	0.500252i	$-0.166759\pi$
$349$	32.3519	1.73176	0.865880	+	0.500252i	$0.166759\pi$
$350$	18.2697	0.976555
$351$	−12.5454	−0.669623
$352$	14.4759	0.771571
$353$	12.0083	0.639135	0.319568	−	0.947563i	$-0.396462\pi$
$353$	12.0083	0.639135	0.319568	+	0.947563i	$0.396462\pi$
$354$	−23.8956	−1.27004
$355$	22.7762	1.20884
$356$	49.5939	2.62847
$357$	−1.96114	−0.103794
$358$	−35.4921	−1.87582
$359$	−0.169811	−0.00896230	−0.00448115	−	0.999990i	$-0.501426\pi$
$359$	−0.169811	−0.00896230	−0.00448115	+	0.999990i	$0.501426\pi$
$360$	11.8662	0.625401
$361$	49.9326	2.62803
$362$	−37.8486	−1.98928
$363$	22.6709	1.18991
$364$	−10.8511	−0.568750
$365$	−8.33103	−0.436066
$366$	17.0937	0.893501
$367$	−35.7439	−1.86582	−0.932908	−	0.360115i	$-0.882737\pi$
$367$	−35.7439	−1.86582	−0.932908	+	0.360115i	$0.882737\pi$
$368$	4.65853	0.242843
$369$	8.89117	0.462856
$370$	−3.55609	−0.184872
$371$	1.54907	0.0804235
$372$	16.2285	0.841410
$373$	−23.7939	−1.23200	−0.616000	−	0.787746i	$-0.711248\pi$
$373$	−23.7939	−1.23200	−0.616000	+	0.787746i	$0.711248\pi$
$374$	−11.2806	−0.583308
$375$	−18.7811	−0.969853
$376$	26.4151	1.36226
$377$	−17.2928	−0.890625
$378$	−10.0251	−0.515635
$379$	−3.64832	−0.187402	−0.0937009	−	0.995600i	$-0.529870\pi$
$379$	−3.64832	−0.187402	−0.0937009	+	0.995600i	$0.529870\pi$
$380$	107.896	5.53494
$381$	−12.0732	−0.618530
$382$	−20.5446	−1.05115
$383$	−18.1986	−0.929906	−0.464953	−	0.885335i	$-0.653929\pi$
$383$	−18.1986	−0.929906	−0.464953	+	0.885335i	$0.653929\pi$
$384$	40.6105	2.07239
$385$	16.9157	0.862105
$386$	−23.2962	−1.18575
$387$	2.78914	0.141780
$388$	28.2867	1.43604
$389$	−7.21165	−0.365645	−0.182823	−	0.983146i	$-0.558523\pi$
$389$	−7.21165	−0.365645	−0.182823	+	0.983146i	$0.558523\pi$
$390$	49.4035	2.50164
$391$	2.31134	0.116890
$392$	−3.91784	−0.197881
$393$	19.1586	0.966423
$394$	−54.8258	−2.76208
$395$	6.33004	0.318499
$396$	14.7333	0.740377
$397$	15.5720	0.781537	0.390769	−	0.920489i	$-0.372209\pi$
$397$	15.5720	0.781537	0.390769	+	0.920489i	$0.372209\pi$
$398$	55.4070	2.77730
$399$	16.2915	0.815594
$400$	15.4849	0.774247
$401$	22.9707	1.14710	0.573552	−	0.819169i	$-0.305565\pi$
$401$	22.9707	1.14710	0.573552	+	0.819169i	$0.305565\pi$
$402$	16.3571	0.815817
$403$	6.74189	0.335837
$404$	−3.95144	−0.196591
$405$	38.5680	1.91646
$406$	−13.8188	−0.685814
$407$	−1.99496	−0.0988864
$408$	−7.68341	−0.380386
$409$	−14.5624	−0.720065	−0.360032	−	0.932940i	$-0.617234\pi$
$409$	−14.5624	−0.720065	−0.360032	+	0.932940i	$0.617234\pi$
$410$	88.5166	4.37152
$411$	−16.7962	−0.828497
$412$	−62.3342	−3.07099
$413$	−5.12395	−0.252133
$414$	−4.67360	−0.229695
$415$	−6.77360	−0.332503
$416$	9.06567	0.444481
$417$	−14.2347	−0.697074
$418$	93.7101	4.58351
$419$	−35.6059	−1.73946	−0.869732	−	0.493524i	$-0.835708\pi$
$419$	−35.6059	−1.73946	−0.869732	+	0.493524i	$0.835708\pi$
$420$	25.5001	1.24428
$421$	8.40757	0.409760	0.204880	−	0.978787i	$-0.434320\pi$
$421$	8.40757	0.409760	0.204880	+	0.978787i	$0.434320\pi$
$422$	4.56474	0.222208
$423$	−5.73307	−0.278751
$424$	6.06899	0.294736
$425$	7.68289	0.372675
$426$	29.8204	1.44480
$427$	3.66541	0.177381
$428$	−60.4432	−2.92163
$429$	27.7152	1.33810
$430$	27.7674	1.33906
$431$	−27.3866	−1.31917	−0.659583	−	0.751631i	$-0.729267\pi$
$431$	−27.3866	−1.31917	−0.659583	+	0.751631i	$0.729267\pi$
$432$	−8.49703	−0.408813
$433$	−19.8133	−0.952167	−0.476084	−	0.879400i	$-0.657944\pi$
$433$	−19.8133	−0.952167	−0.476084	+	0.879400i	$0.657944\pi$
$434$	5.38747	0.258607
$435$	40.6382	1.94845
$436$	−0.895475	−0.0428855
$437$	−19.2007	−0.918494
$438$	−10.9076	−0.521187
$439$	−35.4777	−1.69326	−0.846629	−	0.532184i	$-0.821371\pi$
$439$	−35.4777	−1.69326	−0.846629	+	0.532184i	$0.821371\pi$
$440$	66.2731	3.15944
$441$	0.850318	0.0404913
$442$	−7.06458	−0.336028
$443$	4.08137	0.193912	0.0969559	−	0.995289i	$-0.469089\pi$
$443$	4.08137	0.193912	0.0969559	+	0.995289i	$0.469089\pi$
$444$	−3.00735	−0.142723
$445$	−48.4172	−2.29520
$446$	37.8950	1.79438
$447$	7.13786	0.337609
$448$	11.2732	0.532609
$449$	−37.4161	−1.76578	−0.882888	−	0.469584i	$-0.844404\pi$
$449$	−37.4161	−1.76578	−0.882888	+	0.469584i	$0.844404\pi$
$450$	−15.5350	−0.732328
$451$	49.6576	2.33829
$452$	58.0118	2.72864
$453$	−9.07805	−0.426524
$454$	9.69718	0.455111
$455$	10.5936	0.496636
$456$	63.8274	2.98899
$457$	34.3726	1.60788	0.803942	−	0.594707i	$-0.202732\pi$
$457$	34.3726	1.60788	0.803942	+	0.594707i	$0.202732\pi$
$458$	−2.67163	−0.124837
$459$	−4.21582	−0.196778
$460$	−30.0537	−1.40126
$461$	−8.15098	−0.379629	−0.189814	−	0.981820i	$-0.560789\pi$
$461$	−8.15098	−0.379629	−0.189814	+	0.981820i	$0.560789\pi$
$462$	22.1474	1.03039
$463$	0.553706	0.0257329	0.0128665	−	0.999917i	$-0.495904\pi$
$463$	0.553706	0.0257329	0.0128665	+	0.999917i	$0.495904\pi$
$464$	−11.7125	−0.543738
$465$	−15.8435	−0.734723
$466$	53.1566	2.46243
$467$	−19.7349	−0.913222	−0.456611	−	0.889667i	$-0.650937\pi$
$467$	−19.7349	−0.913222	−0.456611	+	0.889667i	$0.650937\pi$
$468$	9.22686	0.426512
$469$	3.50746	0.161959
$470$	−57.0760	−2.63272
$471$	8.04657	0.370766
$472$	−20.0748	−0.924018
$473$	15.5775	0.716253
$474$	8.28778	0.380671
$475$	−63.8230	−2.92840
$476$	−3.64645	−0.167135
$477$	−1.31720	−0.0603104
$478$	−60.5796	−2.77084
$479$	−39.4810	−1.80393	−0.901967	−	0.431805i	$-0.857877\pi$
$479$	−39.4810	−1.80393	−0.901967	+	0.431805i	$0.857877\pi$
$480$	−21.3044	−0.972407
$481$	−1.24936	−0.0569658
$482$	10.0105	0.455967
$483$	−4.53788	−0.206481
$484$	42.1532	1.91606
$485$	−27.6156	−1.25396
$486$	20.4209	0.926312
$487$	2.13269	0.0966416	0.0483208	−	0.998832i	$-0.484613\pi$
$487$	2.13269	0.0966416	0.0483208	+	0.998832i	$0.484613\pi$
$488$	14.3605	0.650068
$489$	−18.5923	−0.840771
$490$	8.46540	0.382428
$491$	−7.95588	−0.359044	−0.179522	−	0.983754i	$-0.557455\pi$
$491$	−7.95588	−0.359044	−0.179522	+	0.983754i	$0.557455\pi$
$492$	74.8577	3.37485
$493$	−5.81117	−0.261722
$494$	58.6866	2.64044
$495$	−14.3837	−0.646501
$496$	4.56630	0.205033
$497$	6.39439	0.286828
$498$	−8.86852	−0.397408
$499$	−17.3536	−0.776853	−0.388427	−	0.921480i	$-0.626981\pi$
$499$	−17.3536	−0.776853	−0.388427	+	0.921480i	$0.626981\pi$
$500$	−34.9208	−1.56171
$501$	−32.9877	−1.47378
$502$	27.4404	1.22472
$503$	−22.5875	−1.00713	−0.503563	−	0.863958i	$-0.667978\pi$
$503$	−22.5875	−1.00713	−0.503563	+	0.863958i	$0.667978\pi$
$504$	3.33141	0.148393
$505$	3.85768	0.171665
$506$	−26.1023	−1.16039
$507$	−8.15202	−0.362044
$508$	−22.4484	−0.995987
$509$	−27.0186	−1.19758	−0.598789	−	0.800907i	$-0.704351\pi$
$509$	−27.0186	−1.19758	−0.598789	+	0.800907i	$0.704351\pi$
$510$	16.6018	0.735140
$511$	−2.33893	−0.103468
$512$	21.9243	0.968928
$513$	35.0215	1.54624
$514$	−12.8576	−0.567123
$515$	60.8552	2.68160
$516$	23.4827	1.03377
$517$	−32.0195	−1.40822
$518$	−0.998368	−0.0438658
$519$	−2.44027	−0.107116
$520$	41.5040	1.82007
$521$	−18.8515	−0.825899	−0.412950	−	0.910754i	$-0.635501\pi$
$521$	−18.8515	−0.825899	−0.412950	+	0.910754i	$0.635501\pi$
$522$	11.7503	0.514299
$523$	−9.09659	−0.397766	−0.198883	−	0.980023i	$-0.563731\pi$
$523$	−9.09659	−0.397766	−0.198883	+	0.980023i	$0.563731\pi$
$524$	35.6226	1.55618
$525$	−15.0839	−0.658315
$526$	−19.9451	−0.869646
$527$	2.26558	0.0986902
$528$	18.7716	0.816929
$529$	−17.6518	−0.767469
$530$	−13.1135	−0.569613
$531$	4.35699	0.189077
$532$	30.2917	1.31331
$533$	31.0985	1.34702
$534$	−63.3916	−2.74322
$535$	59.0091	2.55118
$536$	13.7416	0.593549
$537$	29.3032	1.26453
$538$	34.3818	1.48230
$539$	4.74907	0.204557
$540$	54.8170	2.35895
$541$	−20.1506	−0.866342	−0.433171	−	0.901312i	$-0.642605\pi$
$541$	−20.1506	−0.866342	−0.433171	+	0.901312i	$0.642605\pi$
$542$	53.9056	2.31544
$543$	31.2488	1.34101
$544$	3.04648	0.130617
$545$	0.874228	0.0374478
$546$	13.8700	0.593580
$547$	37.4201	1.59997	0.799983	−	0.600023i	$-0.204842\pi$
$547$	37.4201	1.59997	0.799983	+	0.600023i	$0.204842\pi$
$548$	−31.2302	−1.33409
$549$	−3.11676	−0.133020
$550$	−86.7639	−3.69963
$551$	48.2743	2.05656
$552$	−17.7787	−0.756711
$553$	1.77715	0.0755722
$554$	47.2128	2.00588
$555$	2.93600	0.124626
$556$	−26.4673	−1.12246
$557$	13.5016	0.572080	0.286040	−	0.958218i	$-0.407661\pi$
$557$	13.5016	0.572080	0.286040	+	0.958218i	$0.407661\pi$
$558$	−4.58107	−0.193932
$559$	9.75551	0.412614
$560$	7.17507	0.303202
$561$	9.31357	0.393219
$562$	63.6038	2.68296
$563$	1.79765	0.0757618	0.0378809	−	0.999282i	$-0.487939\pi$
$563$	1.79765	0.0757618	0.0378809	+	0.999282i	$0.487939\pi$
$564$	−48.2686	−2.03248
$565$	−56.6353	−2.38267
$566$	68.3539	2.87313
$567$	10.8279	0.454730
$568$	25.0522	1.05117
$569$	26.7992	1.12348	0.561741	−	0.827313i	$-0.310132\pi$
$569$	26.7992	1.12348	0.561741	+	0.827313i	$0.310132\pi$
$570$	−137.914	−5.77658
$571$	−16.4325	−0.687680	−0.343840	−	0.939028i	$-0.611728\pi$
$571$	−16.4325	−0.687680	−0.343840	+	0.939028i	$0.611728\pi$
$572$	51.5325	2.15468
$573$	16.9622	0.708605
$574$	24.8509	1.03726
$575$	17.7775	0.741372
$576$	−9.58581	−0.399409
$577$	−41.4404	−1.72519	−0.862593	−	0.505898i	$-0.831161\pi$
$577$	−41.4404	−1.72519	−0.862593	+	0.505898i	$0.831161\pi$
$578$	38.0290	1.58180
$579$	19.2339	0.799335
$580$	75.5608	3.13749
$581$	−1.90168	−0.0788950
$582$	−36.1565	−1.49873
$583$	−7.35663	−0.304680
$584$	−9.16354	−0.379190
$585$	−9.00793	−0.372432
$586$	−61.0539	−2.52211
$587$	21.7054	0.895878	0.447939	−	0.894064i	$-0.352158\pi$
$587$	21.7054	0.895878	0.447939	+	0.894064i	$0.352158\pi$
$588$	7.15911	0.295237
$589$	−18.8205	−0.775487
$590$	43.3763	1.78577
$591$	45.2656	1.86198
$592$	−0.846193	−0.0347783
$593$	11.4719	0.471094	0.235547	−	0.971863i	$-0.424312\pi$
$593$	11.4719	0.471094	0.235547	+	0.971863i	$0.424312\pi$
$594$	47.6098	1.95345
$595$	3.55993	0.145943
$596$	13.2718	0.543635
$597$	−45.7454	−1.87224
$598$	−16.3468	−0.668469
$599$	−0.900843	−0.0368075	−0.0184037	−	0.999831i	$-0.505858\pi$
$599$	−0.900843	−0.0368075	−0.0184037	+	0.999831i	$0.505858\pi$
$600$	−59.0963	−2.41259
$601$	−38.5048	−1.57064	−0.785322	−	0.619087i	$-0.787503\pi$
$601$	−38.5048	−1.57064	−0.785322	+	0.619087i	$0.787503\pi$
$602$	7.79567	0.317728
$603$	−2.98245	−0.121455
$604$	−16.8793	−0.686810
$605$	−41.1530	−1.67311
$606$	5.05078	0.205174
$607$	2.83901	0.115232	0.0576160	−	0.998339i	$-0.481650\pi$
$607$	2.83901	0.115232	0.0576160	+	0.998339i	$0.481650\pi$
$608$	−25.3076	−1.02636
$609$	11.4091	0.462321
$610$	−31.0291	−1.25633
$611$	−20.0524	−0.811235
$612$	3.10064	0.125336
$613$	35.5112	1.43428	0.717142	−	0.696927i	$-0.245450\pi$
$613$	35.5112	1.43428	0.717142	+	0.696927i	$0.245450\pi$
$614$	22.7022	0.916186
$615$	−73.0815	−2.94693
$616$	18.6061	0.749661
$617$	7.53124	0.303196	0.151598	−	0.988442i	$-0.451558\pi$
$617$	7.53124	0.303196	0.151598	+	0.988442i	$0.451558\pi$
$618$	79.6764	3.20505
$619$	−29.5746	−1.18870	−0.594352	−	0.804205i	$-0.702591\pi$
$619$	−29.5746	−1.18870	−0.594352	+	0.804205i	$0.702591\pi$
$620$	−29.4586	−1.18309
$621$	−9.75500	−0.391455
$622$	−38.7752	−1.55474
$623$	−13.5931	−0.544595
$624$	11.7559	0.470611
$625$	−4.34351	−0.173741
$626$	−44.1236	−1.76353
$627$	−77.3694	−3.08984
$628$	14.9614	0.597026
$629$	−0.419841	−0.0167401
$630$	−7.19828	−0.286786
$631$	16.2292	0.646073	0.323036	−	0.946387i	$-0.395296\pi$
$631$	16.2292	0.646073	0.323036	+	0.946387i	$0.395296\pi$
$632$	6.96260	0.276957
$633$	−3.76876	−0.149795
$634$	6.33480	0.251587
$635$	21.9158	0.869701
$636$	−11.0899	−0.439745
$637$	2.97414	0.117840
$638$	65.6263	2.59817
$639$	−5.43727	−0.215095
$640$	−73.7177	−2.91395
$641$	−33.6552	−1.32930	−0.664651	−	0.747154i	$-0.731420\pi$
$641$	−33.6552	−1.32930	−0.664651	+	0.747154i	$0.731420\pi$
$642$	77.2593	3.04918
$643$	20.9227	0.825109	0.412555	−	0.910933i	$-0.364637\pi$
$643$	20.9227	0.825109	0.412555	+	0.910933i	$0.364637\pi$
$644$	−8.43753	−0.332485
$645$	−22.9255	−0.902690
$646$	19.7214	0.775927
$647$	−17.9145	−0.704290	−0.352145	−	0.935945i	$-0.614548\pi$
$647$	−17.9145	−0.704290	−0.352145	+	0.935945i	$0.614548\pi$
$648$	42.4220	1.66649
$649$	24.3340	0.955193
$650$	−54.3366	−2.13126
$651$	−4.44803	−0.174332
$652$	−34.5696	−1.35385
$653$	29.9471	1.17192	0.585960	−	0.810340i	$-0.300717\pi$
$653$	29.9471	1.17192	0.585960	+	0.810340i	$0.300717\pi$
$654$	1.14461	0.0447577
$655$	−34.7774	−1.35887
$656$	21.0631	0.822375
$657$	1.98883	0.0775917
$658$	−16.0240	−0.624681
$659$	33.3354	1.29856	0.649281	−	0.760549i	$-0.275070\pi$
$659$	33.3354	1.29856	0.649281	+	0.760549i	$0.275070\pi$
$660$	−121.102	−4.71387
$661$	−25.0816	−0.975561	−0.487781	−	0.872966i	$-0.662193\pi$
$661$	−25.0816	−0.975561	−0.487781	+	0.872966i	$0.662193\pi$
$662$	60.6612	2.35767
$663$	5.83269	0.226523
$664$	−7.45048	−0.289135
$665$	−29.5729	−1.14679
$666$	0.848930	0.0328954
$667$	−13.4465	−0.520650
$668$	−61.3358	−2.37315
$669$	−31.2871	−1.20963
$670$	−29.6920	−1.14710
$671$	−17.4073	−0.672000
$672$	−5.98118	−0.230729
$673$	−28.4841	−1.09798	−0.548991	−	0.835828i	$-0.684988\pi$
$673$	−28.4841	−1.09798	−0.548991	+	0.835828i	$0.684988\pi$
$674$	−33.4166	−1.28716
$675$	−32.4256	−1.24806
$676$	−15.1575	−0.582981
$677$	−38.4677	−1.47843	−0.739216	−	0.673468i	$-0.764804\pi$
$677$	−38.4677	−1.47843	−0.739216	+	0.673468i	$0.764804\pi$
$678$	−74.1514	−2.84777
$679$	−7.75304	−0.297534
$680$	13.9472	0.534852
$681$	−8.00623	−0.306800
$682$	−25.5855	−0.979719
$683$	33.7337	1.29079	0.645393	−	0.763851i	$-0.276694\pi$
$683$	33.7337	1.29079	0.645393	+	0.763851i	$0.276694\pi$
$684$	−25.7575	−0.984864
$685$	30.4892	1.16493
$686$	2.37665	0.0907410
$687$	2.20577	0.0841552
$688$	6.60743	0.251906
$689$	−4.60714	−0.175518
$690$	38.4150	1.46243
$691$	7.80096	0.296763	0.148381	−	0.988930i	$-0.452594\pi$
$691$	7.80096	0.296763	0.148381	+	0.988930i	$0.452594\pi$
$692$	−4.53734	−0.172484
$693$	−4.03822	−0.153399
$694$	39.9213	1.51539
$695$	25.8393	0.980141
$696$	44.6991	1.69432
$697$	10.4505	0.395841
$698$	−76.8893	−2.91030
$699$	−43.8874	−1.65998
$700$	−28.0463	−1.06005
$701$	50.4573	1.90575	0.952873	−	0.303370i	$-0.0981118\pi$
$701$	50.4573	1.90575	0.952873	+	0.303370i	$0.0981118\pi$
$702$	29.8160	1.12533
$703$	3.48769	0.131541
$704$	−53.5373	−2.01776
$705$	47.1233	1.77477
$706$	−28.5394	−1.07410
$707$	1.08304	0.0407319
$708$	36.6829	1.37863
$709$	−49.6604	−1.86504	−0.932518	−	0.361124i	$-0.882393\pi$
$709$	−49.6604	−1.86504	−0.932518	+	0.361124i	$0.882393\pi$
$710$	−54.1311	−2.03150
$711$	−1.51114	−0.0566724
$712$	−53.2555	−1.99583
$713$	5.24233	0.196327
$714$	4.66094	0.174431
$715$	−50.3098	−1.88148
$716$	54.4850	2.03620
$717$	50.0160	1.86788
$718$	0.403582	0.0150616
$719$	23.5128	0.876878	0.438439	−	0.898761i	$-0.355531\pi$
$719$	23.5128	0.876878	0.438439	+	0.898761i	$0.355531\pi$
$720$	−6.10110	−0.227374
$721$	17.0850	0.636280
$722$	−118.672	−4.41653
$723$	−8.26493	−0.307376
$724$	58.1026	2.15937
$725$	−44.6961	−1.65997
$726$	−53.8807	−1.99970
$727$	−24.1106	−0.894213	−0.447107	−	0.894481i	$-0.647546\pi$
$727$	−24.1106	−0.894213	−0.447107	+	0.894481i	$0.647546\pi$
$728$	11.6522	0.431859
$729$	15.6237	0.578656
$730$	19.8000	0.732829
$731$	3.27829	0.121252
$732$	−26.2410	−0.969897
$733$	−9.59428	−0.354373	−0.177186	−	0.984177i	$-0.556700\pi$
$733$	−9.59428	−0.354373	−0.177186	+	0.984177i	$0.556700\pi$
$734$	84.9508	3.13559
$735$	−6.98925	−0.257802
$736$	7.04925	0.259839
$737$	−16.6572	−0.613574
$738$	−21.1312	−0.777850
$739$	29.6972	1.09243	0.546215	−	0.837645i	$-0.316068\pi$
$739$	29.6972	1.09243	0.546215	+	0.837645i	$0.316068\pi$
$740$	5.45906	0.200679
$741$	−48.4532	−1.77997
$742$	−3.68159	−0.135155
$743$	31.9611	1.17254	0.586270	−	0.810116i	$-0.300596\pi$
$743$	31.9611	1.17254	0.586270	+	0.810116i	$0.300596\pi$
$744$	−17.4267	−0.638893
$745$	−12.9569	−0.474705
$746$	56.5497	2.07043
$747$	1.61703	0.0591642
$748$	17.3172	0.633181
$749$	16.5667	0.605335
$750$	44.6362	1.62988
$751$	−2.73933	−0.0999595	−0.0499797	−	0.998750i	$-0.515916\pi$
$751$	−2.73933	−0.0999595	−0.0499797	+	0.998750i	$0.515916\pi$
$752$	−13.5816	−0.495269
$753$	−22.6555	−0.825611
$754$	41.0990	1.49674
$755$	16.4788	0.599726
$756$	15.3898	0.559722
$757$	26.6291	0.967850	0.483925	−	0.875109i	$-0.339211\pi$
$757$	26.6291	0.967850	0.483925	+	0.875109i	$0.339211\pi$
$758$	8.67079	0.314937
$759$	21.5507	0.782241
$760$	−115.862	−4.20275
$761$	−27.1061	−0.982595	−0.491298	−	0.870992i	$-0.663477\pi$
$761$	−27.1061	−0.982595	−0.491298	+	0.870992i	$0.663477\pi$
$762$	28.6938	1.03947
$763$	0.245439	0.00888547
$764$	31.5387	1.14103
$765$	−3.02707	−0.109444
$766$	43.2518	1.56275
$767$	15.2394	0.550261
$768$	−52.2758	−1.88634
$769$	18.3459	0.661569	0.330784	−	0.943706i	$-0.392687\pi$
$769$	18.3459	0.661569	0.330784	+	0.943706i	$0.392687\pi$
$770$	−40.2028	−1.44881
$771$	10.6155	0.382309
$772$	35.7627	1.28713
$773$	−5.77193	−0.207602	−0.103801	−	0.994598i	$-0.533101\pi$
$773$	−5.77193	−0.207602	−0.103801	+	0.994598i	$0.533101\pi$
$774$	−6.62880	−0.238267
$775$	17.4255	0.625942
$776$	−30.3752	−1.09040
$777$	0.824277	0.0295708
$778$	17.1396	0.614483
$779$	−86.8140	−3.11043
$780$	−75.8408	−2.71553
$781$	−30.3674	−1.08663
$782$	−5.49325	−0.196438
$783$	24.5260	0.876487
$784$	2.01439	0.0719427
$785$	−14.6064	−0.521326
$786$	−45.5333	−1.62412
$787$	15.3910	0.548629	0.274314	−	0.961640i	$-0.411549\pi$
$787$	15.3910	0.548629	0.274314	+	0.961640i	$0.411549\pi$
$788$	84.1648	2.99825
$789$	16.4672	0.586246
$790$	−15.0443	−0.535252
$791$	−15.9003	−0.565350
$792$	−15.8211	−0.562178
$793$	−10.9014	−0.387121
$794$	−37.0093	−1.31341
$795$	10.8268	0.383987
$796$	−85.0570	−3.01477
$797$	−18.0960	−0.640995	−0.320497	−	0.947249i	$-0.603850\pi$
$797$	−18.0960	−0.640995	−0.320497	+	0.947249i	$0.603850\pi$
$798$	−38.7192	−1.37064
$799$	−6.73853	−0.238392
$800$	23.4317	0.828435
$801$	11.5584	0.408397
$802$	−54.5934	−1.92776
$803$	11.1077	0.391983
$804$	−25.1103	−0.885571
$805$	8.23733	0.290328
$806$	−16.0231	−0.564390
$807$	−28.3865	−0.999251
$808$	4.24318	0.149274
$809$	−50.1295	−1.76246	−0.881230	−	0.472688i	$-0.843284\pi$
$809$	−50.1295	−1.76246	−0.881230	+	0.472688i	$0.843284\pi$
$810$	−91.6626	−3.22070
$811$	−13.0808	−0.459327	−0.229664	−	0.973270i	$-0.573763\pi$
$811$	−13.0808	−0.459327	−0.229664	+	0.973270i	$0.573763\pi$
$812$	21.2136	0.744452
$813$	−44.5058	−1.56089
$814$	4.74132	0.166183
$815$	33.7494	1.18219
$816$	3.95050	0.138295
$817$	−27.2333	−0.952773
$818$	34.6098	1.21010
$819$	−2.52897	−0.0883692
$820$	−135.885	−4.74529
$821$	45.7888	1.59804	0.799020	−	0.601304i	$-0.205352\pi$
$821$	45.7888	1.59804	0.799020	+	0.601304i	$0.205352\pi$
$822$	39.9188	1.39233
$823$	−0.235027	−0.00819251	−0.00409626	−	0.999992i	$-0.501304\pi$
$823$	−0.235027	−0.00819251	−0.00409626	+	0.999992i	$0.501304\pi$
$824$	66.9364	2.33184
$825$	71.6345	2.49399
$826$	12.1778	0.423721
$827$	42.0577	1.46249	0.731245	−	0.682115i	$-0.238940\pi$
$827$	42.0577	1.46249	0.731245	+	0.682115i	$0.238940\pi$
$828$	7.17459	0.249334
$829$	−46.5086	−1.61531	−0.807655	−	0.589656i	$-0.799263\pi$
$829$	−46.5086	−1.61531	−0.807655	+	0.589656i	$0.799263\pi$
$830$	16.0985	0.558787
$831$	−38.9801	−1.35220
$832$	−33.5281	−1.16238
$833$	0.999446	0.0346288
$834$	33.8308	1.17147
$835$	59.8805	2.07225
$836$	−143.857	−4.97541
$837$	−9.56186	−0.330506
$838$	84.6229	2.92325
$839$	−14.2588	−0.492267	−0.246133	−	0.969236i	$-0.579160\pi$
$839$	−14.2588	−0.492267	−0.246133	+	0.969236i	$0.579160\pi$
$840$	−27.3827	−0.944794
$841$	4.80711	0.165762
$842$	−19.9819	−0.688620
$843$	−52.5129	−1.80864
$844$	−7.00747	−0.241207
$845$	14.7979	0.509062
$846$	13.6255	0.468455
$847$	−11.5537	−0.396989
$848$	−3.12043	−0.107156
$849$	−56.4347	−1.93683
$850$	−18.2595	−0.626297
$851$	−0.971471	−0.0333016
$852$	−45.7782	−1.56833
$853$	−20.1652	−0.690443	−0.345222	−	0.938521i	$-0.612196\pi$
$853$	−20.1652	−0.690443	−0.345222	+	0.938521i	$0.612196\pi$
$854$	−8.71139	−0.298098
$855$	25.1464	0.859988
$856$	64.9058	2.21843
$857$	−30.7265	−1.04960	−0.524799	−	0.851226i	$-0.675860\pi$
$857$	−30.7265	−1.04960	−0.524799	+	0.851226i	$0.675860\pi$
$858$	−65.8694	−2.24875
$859$	47.4580	1.61925	0.809623	−	0.586950i	$-0.199672\pi$
$859$	47.4580	1.61925	0.809623	+	0.586950i	$0.199672\pi$
$860$	−42.6266	−1.45356
$861$	−20.5176	−0.699236
$862$	65.0884	2.21692
$863$	−1.00000	−0.0340404
$863$	−1.00000	−0.0340404
$864$	−12.8576	−0.437425
$865$	4.42968	0.150614
$866$	47.0893	1.60016
$867$	−31.3977	−1.06632
$868$	−8.27048	−0.280718
$869$	−8.43982	−0.286301
$870$	−96.5828	−3.27446
$871$	−10.4317	−0.353464
$872$	0.961589	0.0325635
$873$	6.59255	0.223124
$874$	45.6334	1.54357
$875$	9.57135	0.323571
$876$	16.7446	0.565749
$877$	−39.1764	−1.32289	−0.661447	−	0.749992i	$-0.730057\pi$
$877$	−39.1764	−1.32289	−0.661447	+	0.749992i	$0.730057\pi$
$878$	84.3181	2.84560
$879$	50.4076	1.70021
$880$	−34.0749	−1.14867
$881$	−44.8448	−1.51086	−0.755430	−	0.655230i	$-0.772572\pi$
$881$	−44.8448	−1.51086	−0.755430	+	0.655230i	$0.772572\pi$
$882$	−2.02091	−0.0680475
$883$	18.6720	0.628361	0.314181	−	0.949363i	$-0.398270\pi$
$883$	18.6720	0.628361	0.314181	+	0.949363i	$0.398270\pi$
$884$	10.8451	0.364759
$885$	−35.8125	−1.20383
$886$	−9.69999	−0.325878
$887$	−17.5292	−0.588573	−0.294287	−	0.955717i	$-0.595082\pi$
$887$	−17.5292	−0.588573	−0.294287	+	0.955717i	$0.595082\pi$
$888$	3.22939	0.108371
$889$	6.15283	0.206359
$890$	115.071	3.85718
$891$	−51.4225	−1.72272
$892$	−58.1738	−1.94780
$893$	55.9781	1.87324
$894$	−16.9642	−0.567368
$895$	−53.1923	−1.77802
$896$	−20.6962	−0.691410
$897$	13.4963	0.450628
$898$	88.9250	2.96747
$899$	−13.1803	−0.439586
$900$	23.8483	0.794943
$901$	−1.54821	−0.0515783
$902$	−118.019	−3.92960
$903$	−6.43630	−0.214187
$904$	−62.2948	−2.07189
$905$	−56.7240	−1.88557
$906$	21.5754	0.716793
$907$	57.7381	1.91716	0.958581	−	0.284820i	$-0.0919339\pi$
$907$	57.7381	1.91716	0.958581	+	0.284820i	$0.0919339\pi$
$908$	−14.8864	−0.494024
$909$	−0.920929	−0.0305453
$910$	−25.1773	−0.834619
$911$	15.3836	0.509681	0.254840	−	0.966983i	$-0.417977\pi$
$911$	15.3836	0.509681	0.254840	+	0.966983i	$0.417977\pi$
$912$	−32.8175	−1.08669
$913$	9.03122	0.298890
$914$	−81.6918	−2.70212
$915$	25.6184	0.846919
$916$	4.10130	0.135511
$917$	−9.76372	−0.322426
$918$	10.0195	0.330694
$919$	−20.6106	−0.679879	−0.339940	−	0.940447i	$-0.610407\pi$
$919$	−20.6106	−0.679879	−0.339940	+	0.940447i	$0.610407\pi$
$920$	32.2725	1.06399
$921$	−18.7435	−0.617619
$922$	19.3720	0.637984
$923$	−19.0178	−0.625979
$924$	−33.9991	−1.11849
$925$	−3.22917	−0.106174
$926$	−1.31597	−0.0432453
$927$	−14.5277	−0.477153
$928$	−17.7232	−0.581793
$929$	−36.8430	−1.20878	−0.604390	−	0.796688i	$-0.706583\pi$
$929$	−36.8430	−1.20878	−0.604390	+	0.796688i	$0.706583\pi$
$930$	37.6544	1.23474
$931$	−8.30256	−0.272106
$932$	−81.6023	−2.67297
$933$	32.0138	1.04808
$934$	46.9029	1.53471
$935$	−16.9064	−0.552897
$936$	−9.90808	−0.323856
$937$	1.91548	0.0625760	0.0312880	−	0.999510i	$-0.490039\pi$
$937$	1.91548	0.0625760	0.0312880	+	0.999510i	$0.490039\pi$
$938$	−8.33600	−0.272180
$939$	36.4295	1.18883
$940$	87.6191	2.85782
$941$	−8.97840	−0.292688	−0.146344	−	0.989234i	$-0.546751\pi$
$941$	−8.97840	−0.292688	−0.146344	+	0.989234i	$0.546751\pi$
$942$	−19.1239	−0.623090
$943$	24.1814	0.787456
$944$	10.3217	0.335941
$945$	−15.0247	−0.488752
$946$	−37.0222	−1.20370
$947$	−40.2523	−1.30802	−0.654012	−	0.756485i	$-0.726915\pi$
$947$	−40.2523	−1.30802	−0.654012	+	0.756485i	$0.726915\pi$
$948$	−12.7228	−0.413218
$949$	6.95630	0.225811
$950$	151.685	4.92131
$951$	−5.23017	−0.169600
$952$	3.91567	0.126908
$953$	8.79258	0.284820	0.142410	−	0.989808i	$-0.454515\pi$
$953$	8.79258	0.284820	0.142410	+	0.989808i	$0.454515\pi$
$954$	3.13052	0.101354
$955$	−30.7904	−0.996353
$956$	92.9975	3.00776
$957$	−54.1827	−1.75148
$958$	93.8326	3.03159
$959$	8.55980	0.276410
$960$	78.7912	2.54298
$961$	−25.8615	−0.834241
$962$	2.96929	0.0957337
$963$	−14.0870	−0.453947
$964$	−15.3675	−0.494952
$965$	−34.9142	−1.12393
$966$	10.7850	0.347000
$967$	−1.44190	−0.0463684	−0.0231842	−	0.999731i	$-0.507380\pi$
$967$	−1.44190	−0.0463684	−0.0231842	+	0.999731i	$0.507380\pi$
$968$	−45.2654	−1.45489
$969$	−16.2825	−0.523068
$970$	65.6326	2.10734
$971$	9.06792	0.291003	0.145502	−	0.989358i	$-0.453520\pi$
$971$	9.06792	0.291003	0.145502	+	0.989358i	$0.453520\pi$
$972$	−31.3488	−1.00551
$973$	7.25435	0.232564
$974$	−5.06867	−0.162411
$975$	44.8616	1.43672
$976$	−7.38357	−0.236342
$977$	38.2763	1.22457	0.612284	−	0.790638i	$-0.290251\pi$
$977$	38.2763	1.22457	0.612284	+	0.790638i	$0.290251\pi$
$978$	44.1873	1.41295
$979$	64.5545	2.06317
$980$	−12.9955	−0.415126
$981$	−0.208701	−0.00666330
$982$	18.9084	0.603390
$983$	−39.3137	−1.25391	−0.626956	−	0.779055i	$-0.715699\pi$
$983$	−39.3137	−1.25391	−0.626956	+	0.779055i	$0.715699\pi$
$984$	−80.3845	−2.56256
$985$	−82.1678	−2.61808
$986$	13.8111	0.439836
$987$	13.2298	0.421110
$988$	−90.0917	−2.86620
$989$	7.58565	0.241210
$990$	34.1851	1.08648
$991$	−57.5329	−1.82759	−0.913796	−	0.406174i	$-0.866863\pi$
$991$	−57.5329	−1.82759	−0.913796	+	0.406174i	$0.866863\pi$
$992$	6.90968	0.219383
$993$	−50.0834	−1.58935
$994$	−15.1972	−0.482027
$995$	83.0389	2.63251
$996$	13.6143	0.431387
$997$	23.8742	0.756102	0.378051	−	0.925785i	$-0.376594\pi$
$997$	23.8742	0.756102	0.378051	+	0.925785i	$0.376594\pi$
$998$	41.2434	1.30554
$999$	1.77193	0.0560615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6041.2.a.d.1.11	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6041.2.a.d.1.11	✓	101	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:	\( N \)	\(=\)	\( 6041 = 7 \cdot 863 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6041.a (trivial)

\(f(q)\)	\(=\)	\(q-2.37665 q^{2} +1.96222 q^{3} +3.64847 q^{4} -3.56190 q^{5} -4.66352 q^{6} -1.00000 q^{7} -3.91784 q^{8} +0.850318 q^{9} +O(q^{10})\)	\(q-2.37665 q^{2} +1.96222 q^{3} +3.64847 q^{4} -3.56190 q^{5} -4.66352 q^{6} -1.00000 q^{7} -3.91784 q^{8} +0.850318 q^{9} +8.46540 q^{10} +4.74907 q^{11} +7.15911 q^{12} +2.97414 q^{13} +2.37665 q^{14} -6.98925 q^{15} +2.01439 q^{16} +0.999446 q^{17} -2.02091 q^{18} -8.30256 q^{19} -12.9955 q^{20} -1.96222 q^{21} -11.2869 q^{22} +2.31262 q^{23} -7.68767 q^{24} +7.68715 q^{25} -7.06850 q^{26} -4.21815 q^{27} -3.64847 q^{28} -5.81439 q^{29} +16.6110 q^{30} +2.26683 q^{31} +3.04816 q^{32} +9.31873 q^{33} -2.37533 q^{34} +3.56190 q^{35} +3.10236 q^{36} -0.420073 q^{37} +19.7323 q^{38} +5.83593 q^{39} +13.9550 q^{40} +10.4563 q^{41} +4.66352 q^{42} +3.28011 q^{43} +17.3268 q^{44} -3.02875 q^{45} -5.49630 q^{46} -6.74227 q^{47} +3.95269 q^{48} +1.00000 q^{49} -18.2697 q^{50} +1.96114 q^{51} +10.8511 q^{52} -1.54907 q^{53} +10.0251 q^{54} -16.9157 q^{55} +3.91784 q^{56} -16.2915 q^{57} +13.8188 q^{58} +5.12395 q^{59} -25.5001 q^{60} -3.66541 q^{61} -5.38747 q^{62} -0.850318 q^{63} -11.2732 q^{64} -10.5936 q^{65} -22.1474 q^{66} -3.50746 q^{67} +3.64645 q^{68} +4.53788 q^{69} -8.46540 q^{70} -6.39439 q^{71} -3.33141 q^{72} +2.33893 q^{73} +0.998368 q^{74} +15.0839 q^{75} -30.2917 q^{76} -4.74907 q^{77} -13.8700 q^{78} -1.77715 q^{79} -7.17507 q^{80} -10.8279 q^{81} -24.8509 q^{82} +1.90168 q^{83} -7.15911 q^{84} -3.55993 q^{85} -7.79567 q^{86} -11.4091 q^{87} -18.6061 q^{88} +13.5931 q^{89} +7.19828 q^{90} -2.97414 q^{91} +8.43753 q^{92} +4.44803 q^{93} +16.0240 q^{94} +29.5729 q^{95} +5.98118 q^{96} +7.75304 q^{97} -2.37665 q^{98} +4.03822 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9}+O(q^{10}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9	\( 101 q + 3 q^{2} - 17 q^{3} + 85 q^{4} - 12 q^{5} - 17 q^{6} - 101 q^{7} - 3 q^{8} + 88 q^{9} - 23 q^{10} - 13 q^{11} - 31 q^{12} - 35 q^{13} - 3 q^{14} - 20 q^{15} + 45 q^{16} - 19 q^{17} + 3 q^{18} - 59 q^{19} - 31 q^{20} + 17 q^{21} - 13 q^{22} - 29 q^{23} - 59 q^{24} + 103 q^{25} - 18 q^{26} - 47 q^{27} - 85 q^{28} - 26 q^{29} - 8 q^{30} - 125 q^{31} + 12 q^{32} - 18 q^{33} - 66 q^{34} + 12 q^{35} + 40 q^{36} + 22 q^{37} - 31 q^{38} - 94 q^{39} - 79 q^{40} - 39 q^{41} + 17 q^{42} - 5 q^{43} - 53 q^{44} - 50 q^{45} - 37 q^{46} - 47 q^{47} - 81 q^{48} + 101 q^{49} + 2 q^{50} - 23 q^{51} - 56 q^{52} - 5 q^{53} - 77 q^{54} - 155 q^{55} + 3 q^{56} + 61 q^{57} - 31 q^{58} - 33 q^{59} - 48 q^{60} - 96 q^{61} - 38 q^{62} - 88 q^{63} - 33 q^{64} - 8 q^{65} - 91 q^{66} + 8 q^{67} - 41 q^{68} - 91 q^{69} + 23 q^{70} - 116 q^{71} - 5 q^{72} - 62 q^{73} - 23 q^{74} - 94 q^{75} - 112 q^{76} + 13 q^{77} + 17 q^{78} - 127 q^{79} - 87 q^{80} + 37 q^{81} - 118 q^{82} - 58 q^{83} + 31 q^{84} - 6 q^{85} - 26 q^{86} - 82 q^{87} - 40 q^{88} - 57 q^{89} - 123 q^{90} + 35 q^{91} - 28 q^{92} - 10 q^{93} - 107 q^{94} - 70 q^{95} - 76 q^{96} - 69 q^{97} + 3 q^{98} - 67 q^{99}+O(q^{100}) \) 101 * q + 3 * q^2 - 17 * q^3 + 85 * q^4 - 12 * q^5 - 17 * q^6 - 101 * q^7 - 3 * q^8 + 88 * q^9 - 23 * q^10 - 13 * q^11 - 31 * q^12 - 35 * q^13 - 3 * q^14 - 20 * q^15 + 45 * q^16 - 19 * q^17 + 3 * q^18 - 59 * q^19 - 31 * q^20 + 17 * q^21 - 13 * q^22 - 29 * q^23 - 59 * q^24 + 103 * q^25 - 18 * q^26 - 47 * q^27 - 85 * q^28 - 26 * q^29 - 8 * q^30 - 125 * q^31 + 12 * q^32 - 18 * q^33 - 66 * q^34 + 12 * q^35 + 40 * q^36 + 22 * q^37 - 31 * q^38 - 94 * q^39 - 79 * q^40 - 39 * q^41 + 17 * q^42 - 5 * q^43 - 53 * q^44 - 50 * q^45 - 37 * q^46 - 47 * q^47 - 81 * q^48 + 101 * q^49 + 2 * q^50 - 23 * q^51 - 56 * q^52 - 5 * q^53 - 77 * q^54 - 155 * q^55 + 3 * q^56 + 61 * q^57 - 31 * q^58 - 33 * q^59 - 48 * q^60 - 96 * q^61 - 38 * q^62 - 88 * q^63 - 33 * q^64 - 8 * q^65 - 91 * q^66 + 8 * q^67 - 41 * q^68 - 91 * q^69 + 23 * q^70 - 116 * q^71 - 5 * q^72 - 62 * q^73 - 23 * q^74 - 94 * q^75 - 112 * q^76 + 13 * q^77 + 17 * q^78 - 127 * q^79 - 87 * q^80 + 37 * q^81 - 118 * q^82 - 58 * q^83 + 31 * q^84 - 6 * q^85 - 26 * q^86 - 82 * q^87 - 40 * q^88 - 57 * q^89 - 123 * q^90 + 35 * q^91 - 28 * q^92 - 10 * q^93 - 107 * q^94 - 70 * q^95 - 76 * q^96 - 69 * q^97 + 3 * q^98 - 67 * q^99

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