LMFDB - Embedded newform 6001.2.a.d.1.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, 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("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51330 q^{2} -2.00286 q^{3} +4.31669 q^{4} +3.06325 q^{5} +5.03379 q^{6} +0.908464 q^{7} -5.82253 q^{8} +1.01144 q^{9} +O(q^{10})$	\(q-2.51330 q^{2} -2.00286 q^{3} +4.31669 q^{4} +3.06325 q^{5} +5.03379 q^{6} +0.908464 q^{7} -5.82253 q^{8} +1.01144 q^{9} -7.69887 q^{10} -1.73017 q^{11} -8.64571 q^{12} +5.68195 q^{13} -2.28324 q^{14} -6.13526 q^{15} +6.00041 q^{16} +1.00000 q^{17} -2.54206 q^{18} +3.91254 q^{19} +13.2231 q^{20} -1.81952 q^{21} +4.34844 q^{22} +8.71137 q^{23} +11.6617 q^{24} +4.38349 q^{25} -14.2805 q^{26} +3.98280 q^{27} +3.92155 q^{28} -0.738799 q^{29} +15.4197 q^{30} +4.32907 q^{31} -3.43577 q^{32} +3.46529 q^{33} -2.51330 q^{34} +2.78285 q^{35} +4.36608 q^{36} +0.482022 q^{37} -9.83340 q^{38} -11.3802 q^{39} -17.8359 q^{40} +4.97594 q^{41} +4.57302 q^{42} -8.18461 q^{43} -7.46860 q^{44} +3.09830 q^{45} -21.8943 q^{46} +11.3717 q^{47} -12.0180 q^{48} -6.17469 q^{49} -11.0170 q^{50} -2.00286 q^{51} +24.5272 q^{52} -5.13585 q^{53} -10.0100 q^{54} -5.29994 q^{55} -5.28956 q^{56} -7.83627 q^{57} +1.85682 q^{58} +11.0653 q^{59} -26.4840 q^{60} +9.21116 q^{61} -10.8803 q^{62} +0.918860 q^{63} -3.36569 q^{64} +17.4052 q^{65} -8.70931 q^{66} -9.20111 q^{67} +4.31669 q^{68} -17.4476 q^{69} -6.99414 q^{70} -2.42617 q^{71} -5.88916 q^{72} +2.12034 q^{73} -1.21147 q^{74} -8.77952 q^{75} +16.8892 q^{76} -1.57180 q^{77} +28.6018 q^{78} +3.54995 q^{79} +18.3807 q^{80} -11.0113 q^{81} -12.5060 q^{82} +12.2162 q^{83} -7.85432 q^{84} +3.06325 q^{85} +20.5704 q^{86} +1.47971 q^{87} +10.0740 q^{88} +9.79890 q^{89} -7.78697 q^{90} +5.16185 q^{91} +37.6042 q^{92} -8.67051 q^{93} -28.5804 q^{94} +11.9851 q^{95} +6.88136 q^{96} -12.5540 q^{97} +15.5189 q^{98} -1.74997 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * 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 $

$2$	−2.51330	−1.77717	−0.888586	−	0.458709i	$-0.848312\pi$
$2$	−2.51330	−1.77717	−0.888586	+	0.458709i	$0.848312\pi$
$3$	−2.00286	−1.15635	−0.578176	−	0.815912i	$-0.696235\pi$
$3$	−2.00286	−1.15635	−0.578176	+	0.815912i	$0.696235\pi$
$4$	4.31669	2.15834
$5$	3.06325	1.36993	0.684963	−	0.728578i	$-0.259818\pi$
$5$	3.06325	1.36993	0.684963	+	0.728578i	$0.259818\pi$
$6$	5.03379	2.05504
$7$	0.908464	0.343367	0.171684	−	0.985152i	$-0.445079\pi$
$7$	0.908464	0.343367	0.171684	+	0.985152i	$0.445079\pi$
$8$	−5.82253	−2.05858
$9$	1.01144	0.337148
$10$	−7.69887	−2.43460
$11$	−1.73017	−0.521666	−0.260833	−	0.965384i	$-0.583997\pi$
$11$	−1.73017	−0.521666	−0.260833	+	0.965384i	$0.583997\pi$
$12$	−8.64571	−2.49580
$13$	5.68195	1.57589	0.787945	−	0.615745i	$-0.211145\pi$
$13$	5.68195	1.57589	0.787945	+	0.615745i	$0.211145\pi$
$14$	−2.28324	−0.610223
$15$	−6.13526	−1.58412
$16$	6.00041	1.50010
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	−2.54206	−0.599170
$19$	3.91254	0.897599	0.448800	−	0.893632i	$-0.351852\pi$
$19$	3.91254	0.897599	0.448800	+	0.893632i	$0.351852\pi$
$20$	13.2231	2.95677
$21$	−1.81952	−0.397053
$22$	4.34844	0.927090
$23$	8.71137	1.81645	0.908223	−	0.418487i	$-0.137439\pi$
$23$	8.71137	1.81645	0.908223	+	0.418487i	$0.137439\pi$
$24$	11.6617	2.38044
$25$	4.38349	0.876699
$26$	−14.2805	−2.80063
$27$	3.98280	0.766490
$28$	3.92155	0.741104
$29$	−0.738799	−0.137191	−0.0685957	−	0.997645i	$-0.521852\pi$
$29$	−0.738799	−0.137191	−0.0685957	+	0.997645i	$0.521852\pi$
$30$	15.4197	2.81525
$31$	4.32907	0.777524	0.388762	−	0.921338i	$-0.372903\pi$
$31$	4.32907	0.777524	0.388762	+	0.921338i	$0.372903\pi$
$32$	−3.43577	−0.607364
$33$	3.46529	0.603229
$34$	−2.51330	−0.431028
$35$	2.78285	0.470388
$36$	4.36608	0.727681
$37$	0.482022	0.0792440	0.0396220	−	0.999215i	$-0.487385\pi$
$37$	0.482022	0.0792440	0.0396220	+	0.999215i	$0.487385\pi$
$38$	−9.83340	−1.59519
$39$	−11.3802	−1.82228
$40$	−17.8359	−2.82010
$41$	4.97594	0.777111	0.388555	−	0.921425i	$-0.372974\pi$
$41$	4.97594	0.777111	0.388555	+	0.921425i	$0.372974\pi$
$42$	4.57302	0.705632
$43$	−8.18461	−1.24814	−0.624070	−	0.781368i	$-0.714522\pi$
$43$	−8.18461	−1.24814	−0.624070	+	0.781368i	$0.714522\pi$
$44$	−7.46860	−1.12593
$45$	3.09830	0.461868
$46$	−21.8943	−3.22814
$47$	11.3717	1.65873	0.829364	−	0.558708i	$-0.188703\pi$
$47$	11.3717	1.65873	0.829364	+	0.558708i	$0.188703\pi$
$48$	−12.0180	−1.73464
$49$	−6.17469	−0.882099
$50$	−11.0170	−1.55805
$51$	−2.00286	−0.280456
$52$	24.5272	3.40131
$53$	−5.13585	−0.705463	−0.352732	−	0.935724i	$-0.614747\pi$
$53$	−5.13585	−0.705463	−0.352732	+	0.935724i	$0.614747\pi$
$54$	−10.0100	−1.36218
$55$	−5.29994	−0.714644
$56$	−5.28956	−0.706847
$57$	−7.83627	−1.03794
$58$	1.85682	0.243813
$59$	11.0653	1.44058	0.720290	−	0.693673i	$-0.244009\pi$
$59$	11.0653	1.44058	0.720290	+	0.693673i	$0.244009\pi$
$60$	−26.4840	−3.41907
$61$	9.21116	1.17937	0.589684	−	0.807634i	$-0.299252\pi$
$61$	9.21116	1.17937	0.589684	+	0.807634i	$0.299252\pi$
$62$	−10.8803	−1.38179
$63$	0.918860	0.115765
$64$	−3.36569	−0.420711
$65$	17.4052	2.15885
$66$	−8.70931	−1.07204
$67$	−9.20111	−1.12409	−0.562047	−	0.827105i	$-0.689986\pi$
$67$	−9.20111	−1.12409	−0.562047	+	0.827105i	$0.689986\pi$
$68$	4.31669	0.523475
$69$	−17.4476	−2.10045
$70$	−6.99414	−0.835960
$71$	−2.42617	−0.287933	−0.143967	−	0.989583i	$-0.545986\pi$
$71$	−2.42617	−0.287933	−0.143967	+	0.989583i	$0.545986\pi$
$72$	−5.88916	−0.694044
$73$	2.12034	0.248167	0.124083	−	0.992272i	$-0.460401\pi$
$73$	2.12034	0.248167	0.124083	+	0.992272i	$0.460401\pi$
$74$	−1.21147	−0.140830
$75$	−8.77952	−1.01377
$76$	16.8892	1.93733
$77$	−1.57180	−0.179123
$78$	28.6018	3.23851
$79$	3.54995	0.399400	0.199700	−	0.979857i	$-0.436003\pi$
$79$	3.54995	0.399400	0.199700	+	0.979857i	$0.436003\pi$
$80$	18.3807	2.05503
$81$	−11.0113	−1.22348
$82$	−12.5060	−1.38106
$83$	12.2162	1.34090	0.670448	−	0.741956i	$-0.266102\pi$
$83$	12.2162	1.34090	0.670448	+	0.741956i	$0.266102\pi$
$84$	−7.85432	−0.856976
$85$	3.06325	0.332256
$86$	20.5704	2.21816
$87$	1.47971	0.158641
$88$	10.0740	1.07389
$89$	9.79890	1.03868	0.519341	−	0.854567i	$-0.326178\pi$
$89$	9.79890	1.03868	0.519341	+	0.854567i	$0.326178\pi$
$90$	−7.78697	−0.820819
$91$	5.16185	0.541109
$92$	37.6042	3.92051
$93$	−8.67051	−0.899090
$94$	−28.5804	−2.94785
$95$	11.9851	1.22964
$96$	6.88136	0.702326
$97$	−12.5540	−1.27467	−0.637334	−	0.770588i	$-0.719963\pi$
$97$	−12.5540	−1.27467	−0.637334	+	0.770588i	$0.719963\pi$
$98$	15.5189	1.56764
$99$	−1.74997	−0.175879
$100$	18.9222	1.89222
$101$	4.23877	0.421773	0.210887	−	0.977511i	$-0.432365\pi$
$101$	4.23877	0.421773	0.210887	+	0.977511i	$0.432365\pi$
$102$	5.03379	0.498419
$103$	7.29113	0.718416	0.359208	−	0.933258i	$-0.383047\pi$
$103$	7.29113	0.718416	0.359208	+	0.933258i	$0.383047\pi$
$104$	−33.0834	−3.24409
$105$	−5.57366	−0.543933
$106$	12.9079	1.25373
$107$	1.50906	0.145887	0.0729433	−	0.997336i	$-0.476761\pi$
$107$	1.50906	0.145887	0.0729433	+	0.997336i	$0.476761\pi$
$108$	17.1925	1.65435
$109$	6.75012	0.646544	0.323272	−	0.946306i	$-0.395217\pi$
$109$	6.75012	0.646544	0.323272	+	0.946306i	$0.395217\pi$
$110$	13.3203	1.27005
$111$	−0.965423	−0.0916338
$112$	5.45115	0.515085
$113$	5.50076	0.517468	0.258734	−	0.965949i	$-0.416695\pi$
$113$	5.50076	0.517468	0.258734	+	0.965949i	$0.416695\pi$
$114$	19.6949	1.84460
$115$	26.6851	2.48840
$116$	−3.18916	−0.296106
$117$	5.74698	0.531308
$118$	−27.8105	−2.56016
$119$	0.908464	0.0832787
$120$	35.7227	3.26102
$121$	−8.00651	−0.727865
$122$	−23.1504	−2.09594
$123$	−9.96610	−0.898613
$124$	18.6872	1.67816
$125$	−1.88851	−0.168914
$126$	−2.30937	−0.205735
$127$	7.70268	0.683502	0.341751	−	0.939791i	$-0.388980\pi$
$127$	7.70268	0.683502	0.341751	+	0.939791i	$0.388980\pi$
$128$	15.3305	1.35504
$129$	16.3926	1.44329
$130$	−43.7446	−3.83666
$131$	8.38890	0.732942	0.366471	−	0.930429i	$-0.380566\pi$
$131$	8.38890	0.732942	0.366471	+	0.930429i	$0.380566\pi$
$132$	14.9585	1.30197
$133$	3.55440	0.308206
$134$	23.1252	1.99771
$135$	12.2003	1.05003
$136$	−5.82253	−0.499278
$137$	2.09374	0.178880	0.0894400	−	0.995992i	$-0.471492\pi$
$137$	2.09374	0.178880	0.0894400	+	0.995992i	$0.471492\pi$
$138$	43.8512	3.73286
$139$	−11.1224	−0.943390	−0.471695	−	0.881762i	$-0.656358\pi$
$139$	−11.1224	−0.943390	−0.471695	+	0.881762i	$0.656358\pi$
$140$	12.0127	1.01526
$141$	−22.7758	−1.91807
$142$	6.09770	0.511707
$143$	−9.83075	−0.822088
$144$	6.06907	0.505756
$145$	−2.26312	−0.187942
$146$	−5.32905	−0.441035
$147$	12.3670	1.02002
$148$	2.08074	0.171036
$149$	−6.03826	−0.494673	−0.247337	−	0.968930i	$-0.579555\pi$
$149$	−6.03826	−0.494673	−0.247337	+	0.968930i	$0.579555\pi$
$150$	22.0656	1.80165
$151$	13.8373	1.12606	0.563031	−	0.826436i	$-0.309635\pi$
$151$	13.8373	1.12606	0.563031	+	0.826436i	$0.309635\pi$
$152$	−22.7809	−1.84778
$153$	1.01144	0.0817704
$154$	3.95040	0.318332
$155$	13.2610	1.06515
$156$	−49.1245	−3.93311
$157$	−15.7461	−1.25668	−0.628340	−	0.777939i	$-0.716265\pi$
$157$	−15.7461	−1.25668	−0.628340	+	0.777939i	$0.716265\pi$
$158$	−8.92208	−0.709803
$159$	10.2864	0.815763
$160$	−10.5246	−0.832044
$161$	7.91396	0.623708
$162$	27.6748	2.17433
$163$	−9.91809	−0.776845	−0.388423	−	0.921481i	$-0.626980\pi$
$163$	−9.91809	−0.776845	−0.388423	+	0.921481i	$0.626980\pi$
$164$	21.4796	1.67727
$165$	10.6150	0.826379
$166$	−30.7029	−2.38301
$167$	−15.4584	−1.19621	−0.598105	−	0.801418i	$-0.704079\pi$
$167$	−15.4584	−1.19621	−0.598105	+	0.801418i	$0.704079\pi$
$168$	10.5942	0.817363
$169$	19.2846	1.48343
$170$	−7.69887	−0.590476
$171$	3.95732	0.302624
$172$	−35.3304	−2.69392
$173$	−14.8791	−1.13123	−0.565617	−	0.824668i	$-0.691362\pi$
$173$	−14.8791	−1.13123	−0.565617	+	0.824668i	$0.691362\pi$
$174$	−3.71896	−0.281933
$175$	3.98225	0.301029
$176$	−10.3817	−0.782551
$177$	−22.1622	−1.66582
$178$	−24.6276	−1.84592
$179$	−1.14717	−0.0857433	−0.0428716	−	0.999081i	$-0.513651\pi$
$179$	−1.14717	−0.0857433	−0.0428716	+	0.999081i	$0.513651\pi$
$180$	13.3744	0.996869
$181$	3.40617	0.253179	0.126589	−	0.991955i	$-0.459597\pi$
$181$	3.40617	0.253179	0.126589	+	0.991955i	$0.459597\pi$
$182$	−12.9733	−0.961644
$183$	−18.4486	−1.36376
$184$	−50.7222	−3.73929
$185$	1.47655	0.108558
$186$	21.7916	1.59784
$187$	−1.73017	−0.126523
$188$	49.0879	3.58010
$189$	3.61823	0.263187
$190$	−30.1222	−2.18529
$191$	19.9504	1.44356	0.721780	−	0.692122i	$-0.243324\pi$
$191$	19.9504	1.44356	0.721780	+	0.692122i	$0.243324\pi$
$192$	6.74100	0.486490
$193$	−16.4755	−1.18594	−0.592968	−	0.805226i	$-0.702044\pi$
$193$	−16.4755	−1.18594	−0.592968	+	0.805226i	$0.702044\pi$
$194$	31.5520	2.26530
$195$	−34.8602	−2.49639
$196$	−26.6542	−1.90387
$197$	2.75614	0.196367	0.0981834	−	0.995168i	$-0.468697\pi$
$197$	2.75614	0.196367	0.0981834	+	0.995168i	$0.468697\pi$
$198$	4.39820	0.312566
$199$	10.9004	0.772706	0.386353	−	0.922351i	$-0.373735\pi$
$199$	10.9004	0.772706	0.386353	+	0.922351i	$0.373735\pi$
$200$	−25.5230	−1.80475
$201$	18.4285	1.29985
$202$	−10.6533	−0.749564
$203$	−0.671172	−0.0471070
$204$	−8.64571	−0.605321
$205$	15.2425	1.06458
$206$	−18.3248	−1.27675
$207$	8.81106	0.612411
$208$	34.0940	2.36400
$209$	−6.76936	−0.468247
$210$	14.0083	0.966663
$211$	16.9400	1.16619	0.583097	−	0.812402i	$-0.301841\pi$
$211$	16.9400	1.16619	0.583097	+	0.812402i	$0.301841\pi$
$212$	−22.1699	−1.52263
$213$	4.85928	0.332952
$214$	−3.79273	−0.259266
$215$	−25.0715	−1.70986
$216$	−23.1900	−1.57788
$217$	3.93280	0.266976
$218$	−16.9651	−1.14902
$219$	−4.24674	−0.286968
$220$	−22.8782	−1.54245
$221$	5.68195	0.382210
$222$	2.42640	0.162849
$223$	−11.0972	−0.743123	−0.371562	−	0.928408i	$-0.621178\pi$
$223$	−11.0972	−0.743123	−0.371562	+	0.928408i	$0.621178\pi$
$224$	−3.12127	−0.208549
$225$	4.43366	0.295577
$226$	−13.8251	−0.919630
$227$	−21.8278	−1.44876	−0.724380	−	0.689401i	$-0.757874\pi$
$227$	−21.8278	−1.44876	−0.724380	+	0.689401i	$0.757874\pi$
$228$	−33.8267	−2.24023
$229$	−5.43494	−0.359151	−0.179576	−	0.983744i	$-0.557472\pi$
$229$	−5.43494	−0.359151	−0.179576	+	0.983744i	$0.557472\pi$
$230$	−67.0677	−4.42231
$231$	3.14809	0.207129
$232$	4.30168	0.282419
$233$	−22.7790	−1.49230	−0.746150	−	0.665778i	$-0.768100\pi$
$233$	−22.7790	−1.49230	−0.746150	+	0.665778i	$0.768100\pi$
$234$	−14.4439	−0.944226
$235$	34.8342	2.27234
$236$	47.7654	3.10927
$237$	−7.11004	−0.461847
$238$	−2.28324	−0.148001
$239$	10.2128	0.660614	0.330307	−	0.943874i	$-0.392848\pi$
$239$	10.2128	0.660614	0.330307	+	0.943874i	$0.392848\pi$
$240$	−36.8140	−2.37633
$241$	−17.8799	−1.15175	−0.575873	−	0.817539i	$-0.695338\pi$
$241$	−17.8799	−1.15175	−0.575873	+	0.817539i	$0.695338\pi$
$242$	20.1228	1.29354
$243$	10.1057	0.648282
$244$	39.7617	2.54548
$245$	−18.9146	−1.20841
$246$	25.0478	1.59699
$247$	22.2309	1.41452
$248$	−25.2061	−1.60059
$249$	−24.4672	−1.55055
$250$	4.74640	0.300189
$251$	−4.79817	−0.302858	−0.151429	−	0.988468i	$-0.548387\pi$
$251$	−4.79817	−0.302858	−0.151429	+	0.988468i	$0.548387\pi$
$252$	3.96643	0.249862
$253$	−15.0721	−0.947578
$254$	−19.3592	−1.21470
$255$	−6.13526	−0.384205
$256$	−31.7989	−1.98743
$257$	−7.85533	−0.490002	−0.245001	−	0.969523i	$-0.578788\pi$
$257$	−7.85533	−0.490002	−0.245001	+	0.969523i	$0.578788\pi$
$258$	−41.1996	−2.56497
$259$	0.437900	0.0272098
$260$	75.1330	4.65955
$261$	−0.747253	−0.0462538
$262$	−21.0838	−1.30256
$263$	−1.93056	−0.119044	−0.0595219	−	0.998227i	$-0.518958\pi$
$263$	−1.93056	−0.119044	−0.0595219	+	0.998227i	$0.518958\pi$
$264$	−20.1767	−1.24179
$265$	−15.7324	−0.966433
$266$	−8.93329	−0.547735
$267$	−19.6258	−1.20108
$268$	−39.7183	−2.42618
$269$	8.94434	0.545346	0.272673	−	0.962107i	$-0.412092\pi$
$269$	8.94434	0.545346	0.272673	+	0.962107i	$0.412092\pi$
$270$	−30.6630	−1.86609
$271$	5.68630	0.345418	0.172709	−	0.984973i	$-0.444748\pi$
$271$	5.68630	0.345418	0.172709	+	0.984973i	$0.444748\pi$
$272$	6.00041	0.363828
$273$	−10.3385	−0.625712
$274$	−5.26220	−0.317901
$275$	−7.58419	−0.457344
$276$	−75.3160	−4.53349
$277$	−8.47470	−0.509195	−0.254598	−	0.967047i	$-0.581943\pi$
$277$	−8.47470	−0.509195	−0.254598	+	0.967047i	$0.581943\pi$
$278$	27.9540	1.67657
$279$	4.37861	0.262140
$280$	−16.2032	−0.968329
$281$	−11.7164	−0.698944	−0.349472	−	0.936947i	$-0.613639\pi$
$281$	−11.7164	−0.698944	−0.349472	+	0.936947i	$0.613639\pi$
$282$	57.2426	3.40875
$283$	−17.0569	−1.01393	−0.506965	−	0.861967i	$-0.669233\pi$
$283$	−17.0569	−1.01393	−0.506965	+	0.861967i	$0.669233\pi$
$284$	−10.4730	−0.621459
$285$	−24.0045	−1.42190
$286$	24.7076	1.46099
$287$	4.52046	0.266834
$288$	−3.47509	−0.204771
$289$	1.00000	0.0588235
$290$	5.68791	0.334006
$291$	25.1439	1.47396
$292$	9.15283	0.535629
$293$	−13.8992	−0.812001	−0.406000	−	0.913873i	$-0.633077\pi$
$293$	−13.8992	−0.812001	−0.406000	+	0.913873i	$0.633077\pi$
$294$	−31.0821	−1.81275
$295$	33.8958	1.97349
$296$	−2.80659	−0.163130
$297$	−6.89092	−0.399851
$298$	15.1760	0.879120
$299$	49.4976	2.86252
$300$	−37.8984	−2.18807
$301$	−7.43542	−0.428570
$302$	−34.7773	−2.00121
$303$	−8.48965	−0.487718
$304$	23.4768	1.34649
$305$	28.2161	1.61565
$306$	−2.54206	−0.145320
$307$	−7.67864	−0.438243	−0.219122	−	0.975698i	$-0.570319\pi$
$307$	−7.67864	−0.438243	−0.219122	+	0.975698i	$0.570319\pi$
$308$	−6.78495	−0.386609
$309$	−14.6031	−0.830741
$310$	−33.3289	−1.89296
$311$	6.14397	0.348393	0.174196	−	0.984711i	$-0.444267\pi$
$311$	6.14397	0.348393	0.174196	+	0.984711i	$0.444267\pi$
$312$	66.2613	3.75131
$313$	9.87688	0.558274	0.279137	−	0.960251i	$-0.409952\pi$
$313$	9.87688	0.558274	0.279137	+	0.960251i	$0.409952\pi$
$314$	39.5748	2.23334
$315$	2.81470	0.158590
$316$	15.3240	0.862042
$317$	20.8530	1.17122	0.585610	−	0.810593i	$-0.300855\pi$
$317$	20.8530	1.17122	0.585610	+	0.810593i	$0.300855\pi$
$318$	−25.8528	−1.44975
$319$	1.27825	0.0715681
$320$	−10.3099	−0.576343
$321$	−3.02244	−0.168696
$322$	−19.8902	−1.10844
$323$	3.91254	0.217700
$324$	−47.5324	−2.64069
$325$	24.9068	1.38158
$326$	24.9272	1.38059
$327$	−13.5195	−0.747632
$328$	−28.9725	−1.59974
$329$	10.3307	0.569553
$330$	−26.6788	−1.46862
$331$	−16.7193	−0.918976	−0.459488	−	0.888184i	$-0.651967\pi$
$331$	−16.7193	−0.918976	−0.459488	+	0.888184i	$0.651967\pi$
$332$	52.7333	2.89412
$333$	0.487538	0.0267169
$334$	38.8517	2.12587
$335$	−28.1853	−1.53993
$336$	−10.9179	−0.595620
$337$	7.44056	0.405313	0.202656	−	0.979250i	$-0.435043\pi$
$337$	7.44056	0.405313	0.202656	+	0.979250i	$0.435043\pi$
$338$	−48.4680	−2.63631
$339$	−11.0172	−0.598375
$340$	13.2231	0.717122
$341$	−7.49002	−0.405608
$342$	−9.94593	−0.537814
$343$	−11.9687	−0.646251
$344$	47.6551	2.56939
$345$	−53.4465	−2.87746
$346$	37.3956	2.01040
$347$	−20.9493	−1.12462	−0.562310	−	0.826927i	$-0.690087\pi$
$347$	−20.9493	−1.12462	−0.562310	+	0.826927i	$0.690087\pi$
$348$	6.38744	0.342403
$349$	18.7162	1.00185	0.500927	−	0.865489i	$-0.332992\pi$
$349$	18.7162	1.00185	0.500927	+	0.865489i	$0.332992\pi$
$350$	−10.0086	−0.534981
$351$	22.6301	1.20790
$352$	5.94446	0.316841
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	55.7004	2.96044
$355$	−7.43196	−0.394448
$356$	42.2988	2.24183
$357$	−1.81952	−0.0962995
$358$	2.88318	0.152381
$359$	−4.71922	−0.249071	−0.124535	−	0.992215i	$-0.539744\pi$
$359$	−4.71922	−0.249071	−0.124535	+	0.992215i	$0.539744\pi$
$360$	−18.0400	−0.950790
$361$	−3.69200	−0.194316
$362$	−8.56074	−0.449943
$363$	16.0359	0.841667
$364$	22.2821	1.16790
$365$	6.49512	0.339970
$366$	46.3670	2.42364
$367$	13.9327	0.727280	0.363640	−	0.931540i	$-0.381534\pi$
$367$	13.9327	0.727280	0.363640	+	0.931540i	$0.381534\pi$
$368$	52.2717	2.72485
$369$	5.03288	0.262001
$370$	−3.71103	−0.192927
$371$	−4.66574	−0.242233
$372$	−37.4279	−1.94055
$373$	10.5306	0.545256	0.272628	−	0.962120i	$-0.412107\pi$
$373$	10.5306	0.545256	0.272628	+	0.962120i	$0.412107\pi$
$374$	4.34844	0.224852
$375$	3.78242	0.195323
$376$	−66.2119	−3.41462
$377$	−4.19782	−0.216199
$378$	−9.09370	−0.467729
$379$	−16.1716	−0.830680	−0.415340	−	0.909666i	$-0.636337\pi$
$379$	−16.1716	−0.830680	−0.415340	+	0.909666i	$0.636337\pi$
$380$	51.7359	2.65400
$381$	−15.4274	−0.790368
$382$	−50.1414	−2.56546
$383$	−7.21138	−0.368484	−0.184242	−	0.982881i	$-0.558983\pi$
$383$	−7.21138	−0.368484	−0.184242	+	0.982881i	$0.558983\pi$
$384$	−30.7049	−1.56690
$385$	−4.81480	−0.245385
$386$	41.4080	2.10761
$387$	−8.27827	−0.420808
$388$	−54.1917	−2.75117
$389$	11.4046	0.578236	0.289118	−	0.957293i	$-0.406638\pi$
$389$	11.4046	0.578236	0.289118	+	0.957293i	$0.406638\pi$
$390$	87.6143	4.43652
$391$	8.71137	0.440553
$392$	35.9523	1.81587
$393$	−16.8018	−0.847538
$394$	−6.92701	−0.348978
$395$	10.8744	0.547149
$396$	−7.55407	−0.379606
$397$	−11.5095	−0.577645	−0.288822	−	0.957383i	$-0.593264\pi$
$397$	−11.5095	−0.577645	−0.288822	+	0.957383i	$0.593264\pi$
$398$	−27.3959	−1.37323
$399$	−7.11897	−0.356394
$400$	26.3027	1.31514
$401$	19.3805	0.967816	0.483908	−	0.875119i	$-0.339217\pi$
$401$	19.3805	0.967816	0.483908	+	0.875119i	$0.339217\pi$
$402$	−46.3164	−2.31005
$403$	24.5976	1.22529
$404$	18.2974	0.910331
$405$	−33.7304	−1.67608
$406$	1.68686	0.0837173
$407$	−0.833980	−0.0413389
$408$	11.6617	0.577341
$409$	5.90767	0.292116	0.146058	−	0.989276i	$-0.453341\pi$
$409$	5.90767	0.292116	0.146058	+	0.989276i	$0.453341\pi$
$410$	−38.3091	−1.89195
$411$	−4.19346	−0.206848
$412$	31.4735	1.55059
$413$	10.0524	0.494648
$414$	−22.1448	−1.08836
$415$	37.4211	1.83693
$416$	−19.5219	−0.957139
$417$	22.2766	1.09089
$418$	17.0135	0.832155
$419$	−36.6244	−1.78922	−0.894610	−	0.446848i	$-0.852546\pi$
$419$	−36.6244	−1.78922	−0.894610	+	0.446848i	$0.852546\pi$
$420$	−24.0597	−1.17399
$421$	−5.02522	−0.244914	−0.122457	−	0.992474i	$-0.539077\pi$
$421$	−5.02522	−0.244914	−0.122457	+	0.992474i	$0.539077\pi$
$422$	−42.5752	−2.07253
$423$	11.5018	0.559237
$424$	29.9037	1.45225
$425$	4.38349	0.212631
$426$	−12.2128	−0.591713
$427$	8.36800	0.404956
$428$	6.51415	0.314873
$429$	19.6896	0.950623
$430$	63.0122	3.03872
$431$	29.3477	1.41363	0.706815	−	0.707398i	$-0.250131\pi$
$431$	29.3477	1.41363	0.706815	+	0.707398i	$0.250131\pi$
$432$	23.8984	1.14981
$433$	−28.9740	−1.39240	−0.696200	−	0.717848i	$-0.745127\pi$
$433$	−28.9740	−1.39240	−0.696200	+	0.717848i	$0.745127\pi$
$434$	−9.88432	−0.474463
$435$	4.53272	0.217327
$436$	29.1381	1.39546
$437$	34.0836	1.63044
$438$	10.6733	0.509991
$439$	−18.4211	−0.879190	−0.439595	−	0.898196i	$-0.644878\pi$
$439$	−18.4211	−0.879190	−0.439595	+	0.898196i	$0.644878\pi$
$440$	30.8591	1.47115
$441$	−6.24535	−0.297398
$442$	−14.2805	−0.679253
$443$	−12.2345	−0.581280	−0.290640	−	0.956832i	$-0.593868\pi$
$443$	−12.2345	−0.581280	−0.290640	+	0.956832i	$0.593868\pi$
$444$	−4.16743	−0.197777
$445$	30.0165	1.42292
$446$	27.8906	1.32066
$447$	12.0938	0.572016
$448$	−3.05761	−0.144458
$449$	−27.9576	−1.31940	−0.659701	−	0.751528i	$-0.729317\pi$
$449$	−27.9576	−1.31940	−0.659701	+	0.751528i	$0.729317\pi$
$450$	−11.1431	−0.525292
$451$	−8.60921	−0.405392
$452$	23.7450	1.11687
$453$	−27.7141	−1.30212
$454$	54.8597	2.57470
$455$	15.8120	0.741280
$456$	45.6269	2.13668
$457$	−33.1719	−1.55172	−0.775858	−	0.630908i	$-0.782683\pi$
$457$	−33.1719	−1.55172	−0.775858	+	0.630908i	$0.782683\pi$
$458$	13.6597	0.638274
$459$	3.98280	0.185901
$460$	115.191	5.37081
$461$	−40.9592	−1.90766	−0.953829	−	0.300350i	$-0.902896\pi$
$461$	−40.9592	−1.90766	−0.953829	+	0.300350i	$0.902896\pi$
$462$	−7.91209	−0.368104
$463$	−21.1623	−0.983496	−0.491748	−	0.870738i	$-0.663642\pi$
$463$	−21.1623	−0.983496	−0.491748	+	0.870738i	$0.663642\pi$
$464$	−4.43309	−0.205801
$465$	−26.5599	−1.23169
$466$	57.2504	2.65208
$467$	20.4554	0.946562	0.473281	−	0.880912i	$-0.343070\pi$
$467$	20.4554	0.946562	0.473281	+	0.880912i	$0.343070\pi$
$468$	24.8079	1.14675
$469$	−8.35887	−0.385977
$470$	−87.5490	−4.03833
$471$	31.5373	1.45316
$472$	−64.4281	−2.96554
$473$	14.1608	0.651112
$474$	17.8697	0.820781
$475$	17.1506	0.786924
$476$	3.92155	0.179744
$477$	−5.19462	−0.237846
$478$	−25.6680	−1.17403
$479$	−17.4906	−0.799168	−0.399584	−	0.916697i	$-0.630845\pi$
$479$	−17.4906	−0.799168	−0.399584	+	0.916697i	$0.630845\pi$
$480$	21.0793	0.962135
$481$	2.73883	0.124880
$482$	44.9376	2.04685
$483$	−15.8505	−0.721225
$484$	−34.5616	−1.57098
$485$	−38.4561	−1.74620
$486$	−25.3987	−1.15211
$487$	−9.67295	−0.438323	−0.219161	−	0.975689i	$-0.570332\pi$
$487$	−9.67295	−0.438323	−0.219161	+	0.975689i	$0.570332\pi$
$488$	−53.6322	−2.42782
$489$	19.8645	0.898306
$490$	47.5382	2.14755
$491$	39.0394	1.76182	0.880911	−	0.473281i	$-0.156931\pi$
$491$	39.0394	1.76182	0.880911	+	0.473281i	$0.156931\pi$
$492$	−43.0205	−1.93951
$493$	−0.738799	−0.0332738
$494$	−55.8730	−2.51384
$495$	−5.36059	−0.240941
$496$	25.9762	1.16636
$497$	−2.20409	−0.0988669
$498$	61.4935	2.75559
$499$	−18.3751	−0.822583	−0.411291	−	0.911504i	$-0.634922\pi$
$499$	−18.3751	−0.822583	−0.411291	+	0.911504i	$0.634922\pi$
$500$	−8.15211	−0.364573
$501$	30.9611	1.38324
$502$	12.0593	0.538231
$503$	−17.3489	−0.773551	−0.386775	−	0.922174i	$-0.626411\pi$
$503$	−17.3489	−0.773551	−0.386775	+	0.922174i	$0.626411\pi$
$504$	−5.35009	−0.238312
$505$	12.9844	0.577798
$506$	37.8808	1.68401
$507$	−38.6244	−1.71537
$508$	33.2500	1.47523
$509$	11.2313	0.497820	0.248910	−	0.968527i	$-0.419928\pi$
$509$	11.2313	0.497820	0.248910	+	0.968527i	$0.419928\pi$
$510$	15.4197	0.682798
$511$	1.92625	0.0852123
$512$	49.2591	2.17696
$513$	15.5829	0.688001
$514$	19.7428	0.870818
$515$	22.3345	0.984177
$516$	70.7618	3.11511
$517$	−19.6749	−0.865302
$518$	−1.10057	−0.0483565
$519$	29.8007	1.30810
$520$	−101.343	−4.44417
$521$	22.1181	0.969011	0.484506	−	0.874788i	$-0.338999\pi$
$521$	22.1181	0.969011	0.484506	+	0.874788i	$0.338999\pi$
$522$	1.87807	0.0822010
$523$	2.94438	0.128749	0.0643744	−	0.997926i	$-0.479495\pi$
$523$	2.94438	0.128749	0.0643744	+	0.997926i	$0.479495\pi$
$524$	36.2123	1.58194
$525$	−7.97588	−0.348096
$526$	4.85209	0.211561
$527$	4.32907	0.188577
$528$	20.7931	0.904904
$529$	52.8879	2.29947
$530$	39.5403	1.71752
$531$	11.1919	0.485688
$532$	15.3432	0.665214
$533$	28.2730	1.22464
$534$	49.3256	2.13453
$535$	4.62263	0.199854
$536$	53.5737	2.31403
$537$	2.29761	0.0991493
$538$	−22.4798	−0.969174
$539$	10.6833	0.460161
$540$	52.6649	2.26634
$541$	24.1829	1.03971	0.519853	−	0.854256i	$-0.325987\pi$
$541$	24.1829	1.03971	0.519853	+	0.854256i	$0.325987\pi$
$542$	−14.2914	−0.613867
$543$	−6.82209	−0.292764
$544$	−3.43577	−0.147307
$545$	20.6773	0.885718
$546$	25.9837	1.11200
$547$	35.9410	1.53673	0.768364	−	0.640013i	$-0.221071\pi$
$547$	35.9410	1.53673	0.768364	+	0.640013i	$0.221071\pi$
$548$	9.03801	0.386085
$549$	9.31657	0.397621
$550$	19.0614	0.812779
$551$	−2.89058	−0.123143
$552$	101.589	4.32393
$553$	3.22500	0.137141
$554$	21.2995	0.904928
$555$	−2.95733	−0.125532
$556$	−48.0119	−2.03616
$557$	−16.1337	−0.683608	−0.341804	−	0.939771i	$-0.611038\pi$
$557$	−16.1337	−0.683608	−0.341804	+	0.939771i	$0.611038\pi$
$558$	−11.0048	−0.465869
$559$	−46.5046	−1.96693
$560$	16.6982	0.705629
$561$	3.46529	0.146304
$562$	29.4469	1.24214
$563$	29.3959	1.23889	0.619444	−	0.785040i	$-0.287358\pi$
$563$	29.3959	1.23889	0.619444	+	0.785040i	$0.287358\pi$
$564$	−98.3162	−4.13986
$565$	16.8502	0.708893
$566$	42.8693	1.80193
$567$	−10.0034	−0.420102
$568$	14.1265	0.592733
$569$	−19.1250	−0.801762	−0.400881	−	0.916130i	$-0.631296\pi$
$569$	−19.1250	−0.801762	−0.400881	+	0.916130i	$0.631296\pi$
$570$	60.3304	2.52696
$571$	−14.0756	−0.589046	−0.294523	−	0.955644i	$-0.595161\pi$
$571$	−14.0756	−0.589046	−0.294523	+	0.955644i	$0.595161\pi$
$572$	−42.4362	−1.77435
$573$	−39.9578	−1.66926
$574$	−11.3613	−0.474210
$575$	38.1862	1.59248
$576$	−3.40421	−0.141842
$577$	39.4507	1.64235	0.821176	−	0.570675i	$-0.193318\pi$
$577$	39.4507	1.64235	0.821176	+	0.570675i	$0.193318\pi$
$578$	−2.51330	−0.104540
$579$	32.9982	1.37136
$580$	−9.76920	−0.405644
$581$	11.0979	0.460420
$582$	−63.1943	−2.61949
$583$	8.88589	0.368016
$584$	−12.3457	−0.510870
$585$	17.6044	0.727853
$586$	34.9329	1.44307
$587$	25.9423	1.07075	0.535376	−	0.844614i	$-0.320170\pi$
$587$	25.9423	1.07075	0.535376	+	0.844614i	$0.320170\pi$
$588$	53.3846	2.20154
$589$	16.9377	0.697905
$590$	−85.1903	−3.50723
$591$	−5.52016	−0.227069
$592$	2.89233	0.118874
$593$	32.3071	1.32669	0.663346	−	0.748313i	$-0.269136\pi$
$593$	32.3071	1.32669	0.663346	+	0.748313i	$0.269136\pi$
$594$	17.3190	0.710605
$595$	2.78285	0.114086
$596$	−26.0653	−1.06767
$597$	−21.8319	−0.893520
$598$	−124.402	−5.08719
$599$	21.5285	0.879630	0.439815	−	0.898088i	$-0.355044\pi$
$599$	21.5285	0.879630	0.439815	+	0.898088i	$0.355044\pi$
$600$	51.1190	2.08693
$601$	39.5487	1.61323	0.806613	−	0.591080i	$-0.201298\pi$
$601$	39.5487	1.61323	0.806613	+	0.591080i	$0.201298\pi$
$602$	18.6875	0.761644
$603$	−9.30640	−0.378986
$604$	59.7312	2.43043
$605$	−24.5259	−0.997121
$606$	21.3371	0.866759
$607$	29.2589	1.18758	0.593790	−	0.804620i	$-0.297631\pi$
$607$	29.2589	1.18758	0.593790	+	0.804620i	$0.297631\pi$
$608$	−13.4426	−0.545169
$609$	1.34426	0.0544723
$610$	−70.9155	−2.87128
$611$	64.6133	2.61397
$612$	4.36608	0.176489
$613$	8.52428	0.344292	0.172146	−	0.985071i	$-0.444930\pi$
$613$	8.52428	0.344292	0.172146	+	0.985071i	$0.444930\pi$
$614$	19.2988	0.778834
$615$	−30.5286	−1.23103
$616$	9.15183	0.368738
$617$	11.6184	0.467741	0.233870	−	0.972268i	$-0.424861\pi$
$617$	11.6184	0.467741	0.233870	+	0.972268i	$0.424861\pi$
$618$	36.7020	1.47637
$619$	−30.3998	−1.22187	−0.610936	−	0.791680i	$-0.709207\pi$
$619$	−30.3998	−1.22187	−0.610936	+	0.791680i	$0.709207\pi$
$620$	57.2436	2.29896
$621$	34.6956	1.39229
$622$	−15.4417	−0.619154
$623$	8.90195	0.356649
$624$	−68.2855	−2.73361
$625$	−27.7025	−1.10810
$626$	−24.8236	−0.992150
$627$	13.5581	0.541458
$628$	−67.9712	−2.71234
$629$	0.482022	0.0192195
$630$	−7.07418	−0.281842
$631$	−37.3585	−1.48722	−0.743609	−	0.668614i	$-0.766888\pi$
$631$	−37.3585	−1.48722	−0.743609	+	0.668614i	$0.766888\pi$
$632$	−20.6697	−0.822195
$633$	−33.9283	−1.34853
$634$	−52.4099	−2.08146
$635$	23.5952	0.936348
$636$	44.4031	1.76070
$637$	−35.0843	−1.39009
$638$	−3.21262	−0.127189
$639$	−2.45393	−0.0970761
$640$	46.9612	1.85631
$641$	−2.94542	−0.116337	−0.0581685	−	0.998307i	$-0.518526\pi$
$641$	−2.94542	−0.116337	−0.0581685	+	0.998307i	$0.518526\pi$
$642$	7.59630	0.299802
$643$	−20.1096	−0.793044	−0.396522	−	0.918025i	$-0.629783\pi$
$643$	−20.1096	−0.793044	−0.396522	+	0.918025i	$0.629783\pi$
$644$	34.1621	1.34617
$645$	50.2147	1.97720
$646$	−9.83340	−0.386890
$647$	36.8881	1.45022	0.725111	−	0.688632i	$-0.241789\pi$
$647$	36.8881	1.45022	0.725111	+	0.688632i	$0.241789\pi$
$648$	64.1137	2.51862
$649$	−19.1449	−0.751501
$650$	−62.5983	−2.45531
$651$	−7.87685	−0.308718
$652$	−42.8133	−1.67670
$653$	2.96581	0.116061	0.0580305	−	0.998315i	$-0.481518\pi$
$653$	2.96581	0.116061	0.0580305	+	0.998315i	$0.481518\pi$
$654$	33.9787	1.32867
$655$	25.6973	1.00408
$656$	29.8576	1.16574
$657$	2.14460	0.0836689
$658$	−25.9643	−1.01219
$659$	38.4309	1.49705	0.748527	−	0.663105i	$-0.230762\pi$
$659$	38.4309	1.49705	0.748527	+	0.663105i	$0.230762\pi$
$660$	45.8218	1.78361
$661$	−16.9013	−0.657384	−0.328692	−	0.944437i	$-0.606608\pi$
$661$	−16.9013	−0.657384	−0.328692	+	0.944437i	$0.606608\pi$
$662$	42.0206	1.63318
$663$	−11.3802	−0.441969
$664$	−71.1289	−2.76034
$665$	10.8880	0.422220
$666$	−1.22533	−0.0474806
$667$	−6.43595	−0.249201
$668$	−66.7292	−2.58183
$669$	22.2261	0.859311
$670$	70.8381	2.73672
$671$	−15.9369	−0.615236
$672$	6.25146	0.241155
$673$	−10.2439	−0.394872	−0.197436	−	0.980316i	$-0.563261\pi$
$673$	−10.2439	−0.394872	−0.197436	+	0.980316i	$0.563261\pi$
$674$	−18.7004	−0.720311
$675$	17.4586	0.671981
$676$	83.2456	3.20175
$677$	−38.0064	−1.46070	−0.730352	−	0.683070i	$-0.760644\pi$
$677$	−38.0064	−1.46070	−0.730352	+	0.683070i	$0.760644\pi$
$678$	27.6897	1.06341
$679$	−11.4049	−0.437679
$680$	−17.8359	−0.683974
$681$	43.7179	1.67527
$682$	18.8247	0.720835
$683$	44.3112	1.69552	0.847760	−	0.530380i	$-0.177951\pi$
$683$	44.3112	1.69552	0.847760	+	0.530380i	$0.177951\pi$
$684$	17.0825	0.653166
$685$	6.41364	0.245053
$686$	30.0810	1.14850
$687$	10.8854	0.415305
$688$	−49.1110	−1.87234
$689$	−29.1817	−1.11173
$690$	134.327	5.11374
$691$	−42.4989	−1.61673	−0.808367	−	0.588679i	$-0.799648\pi$
$691$	−42.4989	−1.61673	−0.808367	+	0.588679i	$0.799648\pi$
$692$	−64.2282	−2.44159
$693$	−1.58978	−0.0603909
$694$	52.6520	1.99864
$695$	−34.0707	−1.29237
$696$	−8.61565	−0.326575
$697$	4.97594	0.188477
$698$	−47.0394	−1.78047
$699$	45.6231	1.72562
$700$	17.1901	0.649725
$701$	−41.5675	−1.56998	−0.784992	−	0.619506i	$-0.787333\pi$
$701$	−41.5675	−1.56998	−0.784992	+	0.619506i	$0.787333\pi$
$702$	−56.8762	−2.14665
$703$	1.88593	0.0711293
$704$	5.82321	0.219471
$705$	−69.7681	−2.62762
$706$	2.51330	0.0945894
$707$	3.85077	0.144823
$708$	−95.6674	−3.59540
$709$	12.5223	0.470284	0.235142	−	0.971961i	$-0.424445\pi$
$709$	12.5223	0.470284	0.235142	+	0.971961i	$0.424445\pi$
$710$	18.6788	0.701002
$711$	3.59057	0.134657
$712$	−57.0544	−2.13820
$713$	37.7121	1.41233
$714$	4.57302	0.171141
$715$	−30.1140	−1.12620
$716$	−4.95196	−0.185063
$717$	−20.4549	−0.763902
$718$	11.8608	0.442642
$719$	−34.0815	−1.27103	−0.635513	−	0.772090i	$-0.719211\pi$
$719$	−34.0815	−1.27103	−0.635513	+	0.772090i	$0.719211\pi$
$720$	18.5911	0.692849
$721$	6.62372	0.246680
$722$	9.27911	0.345333
$723$	35.8109	1.33182
$724$	14.7034	0.546447
$725$	−3.23852	−0.120276
$726$	−40.3031	−1.49579
$727$	6.34835	0.235447	0.117724	−	0.993046i	$-0.462440\pi$
$727$	6.34835	0.235447	0.117724	+	0.993046i	$0.462440\pi$
$728$	−30.0550	−1.11391
$729$	12.7936	0.473838
$730$	−16.3242	−0.604186
$731$	−8.18461	−0.302719
$732$	−79.6370	−2.94347
$733$	−3.93129	−0.145205	−0.0726027	−	0.997361i	$-0.523130\pi$
$733$	−3.93129	−0.145205	−0.0726027	+	0.997361i	$0.523130\pi$
$734$	−35.0170	−1.29250
$735$	37.8833	1.39735
$736$	−29.9302	−1.10324
$737$	15.9195	0.586401
$738$	−12.6491	−0.465621
$739$	34.9868	1.28701	0.643506	−	0.765441i	$-0.277479\pi$
$739$	34.9868	1.28701	0.643506	+	0.765441i	$0.277479\pi$
$740$	6.37382	0.234306
$741$	−44.5253	−1.63568
$742$	11.7264	0.430490
$743$	−17.6623	−0.647967	−0.323984	−	0.946063i	$-0.605022\pi$
$743$	−17.6623	−0.647967	−0.323984	+	0.946063i	$0.605022\pi$
$744$	50.4843	1.85085
$745$	−18.4967	−0.677666
$746$	−26.4667	−0.969013
$747$	12.3559	0.452081
$748$	−7.46860	−0.273079
$749$	1.37093	0.0500926
$750$	−9.50637	−0.347123
$751$	9.39780	0.342931	0.171465	−	0.985190i	$-0.445150\pi$
$751$	9.39780	0.342931	0.171465	+	0.985190i	$0.445150\pi$
$752$	68.2346	2.48826
$753$	9.61006	0.350210
$754$	10.5504	0.384223
$755$	42.3871	1.54262
$756$	15.6188	0.568049
$757$	3.93722	0.143101	0.0715504	−	0.997437i	$-0.477205\pi$
$757$	3.93722	0.143101	0.0715504	+	0.997437i	$0.477205\pi$
$758$	40.6441	1.47626
$759$	30.1874	1.09573
$760$	−69.7836	−2.53132
$761$	−37.7637	−1.36893	−0.684467	−	0.729044i	$-0.739965\pi$
$761$	−37.7637	−1.36893	−0.684467	+	0.729044i	$0.739965\pi$
$762$	38.7736	1.40462
$763$	6.13224	0.222002
$764$	86.1196	3.11570
$765$	3.09830	0.112019
$766$	18.1244	0.654860
$767$	62.8726	2.27020
$768$	63.6886	2.29817
$769$	−22.2971	−0.804054	−0.402027	−	0.915628i	$-0.631694\pi$
$769$	−22.2971	−0.804054	−0.402027	+	0.915628i	$0.631694\pi$
$770$	12.1011	0.436092
$771$	15.7331	0.566614
$772$	−71.1197	−2.55965
$773$	11.3434	0.407995	0.203998	−	0.978971i	$-0.434606\pi$
$773$	11.3434	0.407995	0.203998	+	0.978971i	$0.434606\pi$
$774$	20.8058	0.747849
$775$	18.9764	0.681654
$776$	73.0961	2.62400
$777$	−0.877051	−0.0314640
$778$	−28.6632	−1.02763
$779$	19.4686	0.697534
$780$	−150.481	−5.38807
$781$	4.19769	0.150205
$782$	−21.8943	−0.782938
$783$	−2.94249	−0.105156
$784$	−37.0507	−1.32324
$785$	−48.2344	−1.72156
$786$	42.2280	1.50622
$787$	−17.8780	−0.637282	−0.318641	−	0.947876i	$-0.603226\pi$
$787$	−17.8780	−0.637282	−0.318641	+	0.947876i	$0.603226\pi$
$788$	11.8974	0.423827
$789$	3.86665	0.137656
$790$	−27.3306	−0.972378
$791$	4.99724	0.177681
$792$	10.1892	0.362059
$793$	52.3374	1.85855
$794$	28.9268	1.02657
$795$	31.5098	1.11754
$796$	47.0534	1.66777
$797$	−51.5774	−1.82696	−0.913482	−	0.406879i	$-0.866617\pi$
$797$	−51.5774	−1.82696	−0.913482	+	0.406879i	$0.866617\pi$
$798$	17.8921	0.633374
$799$	11.3717	0.402301
$800$	−15.0607	−0.532475
$801$	9.91104	0.350189
$802$	−48.7090	−1.71998
$803$	−3.66854	−0.129460
$804$	79.5501	2.80552
$805$	24.2424	0.854434
$806$	−61.8211	−2.17756
$807$	−17.9142	−0.630611
$808$	−24.6804	−0.868252
$809$	−25.9930	−0.913865	−0.456932	−	0.889501i	$-0.651052\pi$
$809$	−25.9930	−0.913865	−0.456932	+	0.889501i	$0.651052\pi$
$810$	84.7747	2.97868
$811$	31.7854	1.11614	0.558069	−	0.829795i	$-0.311542\pi$
$811$	31.7854	1.11614	0.558069	+	0.829795i	$0.311542\pi$
$812$	−2.89724	−0.101673
$813$	−11.3888	−0.399424
$814$	2.09604	0.0734663
$815$	−30.3816	−1.06422
$816$	−12.0180	−0.420713
$817$	−32.0226	−1.12033
$818$	−14.8478	−0.519140
$819$	5.22092	0.182434
$820$	65.7972	2.29774
$821$	3.68040	0.128447	0.0642234	−	0.997936i	$-0.479543\pi$
$821$	3.68040	0.128447	0.0642234	+	0.997936i	$0.479543\pi$
$822$	10.5394	0.367605
$823$	5.47791	0.190948	0.0954740	−	0.995432i	$-0.469563\pi$
$823$	5.47791	0.190948	0.0954740	+	0.995432i	$0.469563\pi$
$824$	−42.4528	−1.47891
$825$	15.1901	0.528850
$826$	−25.2648	−0.879074
$827$	30.2802	1.05295	0.526473	−	0.850192i	$-0.323514\pi$
$827$	30.2802	1.05295	0.526473	+	0.850192i	$0.323514\pi$
$828$	38.0346	1.32179
$829$	−19.1452	−0.664942	−0.332471	−	0.943114i	$-0.607882\pi$
$829$	−19.1452	−0.664942	−0.332471	+	0.943114i	$0.607882\pi$
$830$	−94.0506	−3.26454
$831$	16.9736	0.588808
$832$	−19.1237	−0.662995
$833$	−6.17469	−0.213940
$834$	−55.9878	−1.93870
$835$	−47.3531	−1.63872
$836$	−29.2212	−1.01064
$837$	17.2418	0.595964
$838$	92.0482	3.17975
$839$	37.5885	1.29770	0.648850	−	0.760916i	$-0.275250\pi$
$839$	37.5885	1.29770	0.648850	+	0.760916i	$0.275250\pi$
$840$	32.4528	1.11973
$841$	−28.4542	−0.981179
$842$	12.6299	0.435255
$843$	23.4664	0.808224
$844$	73.1245	2.51705
$845$	59.0736	2.03219
$846$	−28.9075	−0.993860
$847$	−7.27363	−0.249925
$848$	−30.8172	−1.05827
$849$	34.1627	1.17246
$850$	−11.0170	−0.377881
$851$	4.19907	0.143942
$852$	20.9760	0.718625
$853$	18.5616	0.635537	0.317769	−	0.948168i	$-0.397067\pi$
$853$	18.5616	0.635537	0.317769	+	0.948168i	$0.397067\pi$
$854$	−21.0313	−0.719677
$855$	12.1222	0.414572
$856$	−8.78656	−0.300318
$857$	−4.66127	−0.159226	−0.0796129	−	0.996826i	$-0.525368\pi$
$857$	−4.66127	−0.159226	−0.0796129	+	0.996826i	$0.525368\pi$
$858$	−49.4859	−1.68942
$859$	−52.0143	−1.77471	−0.887353	−	0.461090i	$-0.847459\pi$
$859$	−52.0143	−1.77471	−0.887353	+	0.461090i	$0.847459\pi$
$860$	−108.226	−3.69047
$861$	−9.05384	−0.308554
$862$	−73.7597	−2.51227
$863$	43.9838	1.49723	0.748613	−	0.663007i	$-0.230720\pi$
$863$	43.9838	1.49723	0.748613	+	0.663007i	$0.230720\pi$
$864$	−13.6840	−0.465538
$865$	−45.5783	−1.54971
$866$	72.8203	2.47454
$867$	−2.00286	−0.0680207
$868$	16.9767	0.576226
$869$	−6.14201	−0.208353
$870$	−11.3921	−0.386228
$871$	−52.2803	−1.77145
$872$	−39.3028	−1.33096
$873$	−12.6977	−0.429751
$874$	−85.6624	−2.89757
$875$	−1.71564	−0.0579994
$876$	−18.3318	−0.619375
$877$	16.7371	0.565172	0.282586	−	0.959242i	$-0.408808\pi$
$877$	16.7371	0.565172	0.282586	+	0.959242i	$0.408808\pi$
$878$	46.2977	1.56247
$879$	27.8382	0.938958
$880$	−31.8018	−1.07204
$881$	−19.2024	−0.646945	−0.323472	−	0.946238i	$-0.604850\pi$
$881$	−19.2024	−0.646945	−0.323472	+	0.946238i	$0.604850\pi$
$882$	15.6965	0.528527
$883$	32.7761	1.10300	0.551501	−	0.834174i	$-0.314055\pi$
$883$	32.7761	1.10300	0.551501	+	0.834174i	$0.314055\pi$
$884$	24.5272	0.824939
$885$	−67.8885	−2.28205
$886$	30.7491	1.03303
$887$	30.8472	1.03575	0.517874	−	0.855457i	$-0.326723\pi$
$887$	30.8472	1.03575	0.517874	+	0.855457i	$0.326723\pi$
$888$	5.62120	0.188635
$889$	6.99760	0.234692
$890$	−75.4405	−2.52877
$891$	19.0514	0.638247
$892$	−47.9031	−1.60391
$893$	44.4921	1.48887
$894$	−30.3953	−1.01657
$895$	−3.51406	−0.117462
$896$	13.9272	0.465276
$897$	−99.1367	−3.31008
$898$	70.2659	2.34480
$899$	−3.19831	−0.106670
$900$	19.1387	0.637957
$901$	−5.13585	−0.171100
$902$	21.6376	0.720452
$903$	14.8921	0.495578
$904$	−32.0283	−1.06525
$905$	10.4340	0.346837
$906$	69.6540	2.31410
$907$	42.1869	1.40079	0.700396	−	0.713754i	$-0.253007\pi$
$907$	42.1869	1.40079	0.700396	+	0.713754i	$0.253007\pi$
$908$	−94.2236	−3.12692
$909$	4.28727	0.142200
$910$	−39.7404	−1.31738
$911$	56.9440	1.88664	0.943319	−	0.331888i	$-0.107686\pi$
$911$	56.9440	1.88664	0.943319	+	0.331888i	$0.107686\pi$
$912$	−47.0208	−1.55701
$913$	−21.1360	−0.699500
$914$	83.3710	2.75767
$915$	−56.5128	−1.86826
$916$	−23.4609	−0.775172
$917$	7.62102	0.251668
$918$	−10.0100	−0.330378
$919$	19.4542	0.641734	0.320867	−	0.947124i	$-0.396026\pi$
$919$	19.4542	0.641734	0.320867	+	0.947124i	$0.396026\pi$
$920$	−155.375	−5.12255
$921$	15.3792	0.506763
$922$	102.943	3.39024
$923$	−13.7854	−0.453752
$924$	13.5893	0.447055
$925$	2.11294	0.0694731
$926$	53.1873	1.74784
$927$	7.37456	0.242212
$928$	2.53834	0.0833251
$929$	−15.6778	−0.514373	−0.257187	−	0.966362i	$-0.582796\pi$
$929$	−15.6778	−0.514373	−0.257187	+	0.966362i	$0.582796\pi$
$930$	66.7532	2.18892
$931$	−24.1588	−0.791771
$932$	−98.3297	−3.22090
$933$	−12.3055	−0.402864
$934$	−51.4105	−1.68220
$935$	−5.29994	−0.173327
$936$	−33.4620	−1.09374
$937$	−34.7840	−1.13634	−0.568172	−	0.822910i	$-0.692349\pi$
$937$	−34.7840	−1.13634	−0.568172	+	0.822910i	$0.692349\pi$
$938$	21.0084	0.685948
$939$	−19.7820	−0.645561
$940$	150.369	4.90448
$941$	32.0199	1.04382	0.521910	−	0.853001i	$-0.325220\pi$
$941$	32.0199	1.04382	0.521910	+	0.853001i	$0.325220\pi$
$942$	−79.2628	−2.58252
$943$	43.3472	1.41158
$944$	66.3963	2.16102
$945$	11.0835	0.360547
$946$	−35.5903	−1.15714
$947$	−10.2291	−0.332400	−0.166200	−	0.986092i	$-0.553150\pi$
$947$	−10.2291	−0.332400	−0.166200	+	0.986092i	$0.553150\pi$
$948$	−30.6918	−0.996824
$949$	12.0477	0.391084
$950$	−43.1047	−1.39850
$951$	−41.7656	−1.35434
$952$	−5.28956	−0.171436
$953$	−29.4358	−0.953519	−0.476760	−	0.879034i	$-0.658189\pi$
$953$	−29.4358	−0.953519	−0.476760	+	0.879034i	$0.658189\pi$
$954$	13.0557	0.422693
$955$	61.1131	1.97757
$956$	44.0856	1.42583
$957$	−2.56015	−0.0827578
$958$	43.9593	1.42026
$959$	1.90209	0.0614215
$960$	20.6494	0.666455
$961$	−12.2592	−0.395457
$962$	−6.88350	−0.221933
$963$	1.52633	0.0491853
$964$	−77.1819	−2.48586
$965$	−50.4687	−1.62464
$966$	39.8372	1.28174
$967$	−8.06690	−0.259414	−0.129707	−	0.991552i	$-0.541404\pi$
$967$	−8.06690	−0.259414	−0.129707	+	0.991552i	$0.541404\pi$
$968$	46.6182	1.49836
$969$	−7.83627	−0.251737
$970$	96.6517	3.10330
$971$	−54.1995	−1.73934	−0.869672	−	0.493630i	$-0.835670\pi$
$971$	−54.1995	−1.73934	−0.869672	+	0.493630i	$0.835670\pi$
$972$	43.6232	1.39921
$973$	−10.1043	−0.323929
$974$	24.3110	0.778976
$975$	−49.8848	−1.59759
$976$	55.2707	1.76917
$977$	17.4468	0.558173	0.279087	−	0.960266i	$-0.409968\pi$
$977$	17.4468	0.558173	0.279087	+	0.960266i	$0.409968\pi$
$978$	−49.9256	−1.59644
$979$	−16.9538	−0.541845
$980$	−81.6485	−2.60817
$981$	6.82736	0.217981
$982$	−98.1178	−3.13106
$983$	−10.3374	−0.329713	−0.164857	−	0.986318i	$-0.552716\pi$
$983$	−10.3374	−0.329713	−0.164857	+	0.986318i	$0.552716\pi$
$984$	58.0279	1.84986
$985$	8.44274	0.269008
$986$	1.85682	0.0591333
$987$	−20.6910	−0.658603
$988$	95.9638	3.05302
$989$	−71.2991	−2.26718
$990$	13.4728	0.428193
$991$	20.0720	0.637608	0.318804	−	0.947821i	$-0.396719\pi$
$991$	20.0720	0.637608	0.318804	+	0.947821i	$0.396719\pi$
$992$	−14.8737	−0.472240
$993$	33.4864	1.06266
$994$	5.53954	0.175703
$995$	33.3905	1.05855
$996$	−105.617	−3.34661
$997$	37.1620	1.17693	0.588467	−	0.808521i	$-0.299732\pi$
$997$	37.1620	1.17693	0.588467	+	0.808521i	$0.299732\pi$
$998$	46.1822	1.46187
$999$	1.91980	0.0607397

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.9	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.9	✓	121	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51330 q^{2} -2.00286 q^{3} +4.31669 q^{4} +3.06325 q^{5} +5.03379 q^{6} +0.908464 q^{7} -5.82253 q^{8} +1.01144 q^{9} +O(q^{10})\)	\(q-2.51330 q^{2} -2.00286 q^{3} +4.31669 q^{4} +3.06325 q^{5} +5.03379 q^{6} +0.908464 q^{7} -5.82253 q^{8} +1.01144 q^{9} -7.69887 q^{10} -1.73017 q^{11} -8.64571 q^{12} +5.68195 q^{13} -2.28324 q^{14} -6.13526 q^{15} +6.00041 q^{16} +1.00000 q^{17} -2.54206 q^{18} +3.91254 q^{19} +13.2231 q^{20} -1.81952 q^{21} +4.34844 q^{22} +8.71137 q^{23} +11.6617 q^{24} +4.38349 q^{25} -14.2805 q^{26} +3.98280 q^{27} +3.92155 q^{28} -0.738799 q^{29} +15.4197 q^{30} +4.32907 q^{31} -3.43577 q^{32} +3.46529 q^{33} -2.51330 q^{34} +2.78285 q^{35} +4.36608 q^{36} +0.482022 q^{37} -9.83340 q^{38} -11.3802 q^{39} -17.8359 q^{40} +4.97594 q^{41} +4.57302 q^{42} -8.18461 q^{43} -7.46860 q^{44} +3.09830 q^{45} -21.8943 q^{46} +11.3717 q^{47} -12.0180 q^{48} -6.17469 q^{49} -11.0170 q^{50} -2.00286 q^{51} +24.5272 q^{52} -5.13585 q^{53} -10.0100 q^{54} -5.29994 q^{55} -5.28956 q^{56} -7.83627 q^{57} +1.85682 q^{58} +11.0653 q^{59} -26.4840 q^{60} +9.21116 q^{61} -10.8803 q^{62} +0.918860 q^{63} -3.36569 q^{64} +17.4052 q^{65} -8.70931 q^{66} -9.20111 q^{67} +4.31669 q^{68} -17.4476 q^{69} -6.99414 q^{70} -2.42617 q^{71} -5.88916 q^{72} +2.12034 q^{73} -1.21147 q^{74} -8.77952 q^{75} +16.8892 q^{76} -1.57180 q^{77} +28.6018 q^{78} +3.54995 q^{79} +18.3807 q^{80} -11.0113 q^{81} -12.5060 q^{82} +12.2162 q^{83} -7.85432 q^{84} +3.06325 q^{85} +20.5704 q^{86} +1.47971 q^{87} +10.0740 q^{88} +9.79890 q^{89} -7.78697 q^{90} +5.16185 q^{91} +37.6042 q^{92} -8.67051 q^{93} -28.5804 q^{94} +11.9851 q^{95} +6.88136 q^{96} -12.5540 q^{97} +15.5189 q^{98} -1.74997 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9} + 19 q^{10} + 48 q^{11} + 43 q^{12} + 6 q^{13} + 40 q^{14} + 49 q^{15} + 135 q^{16} + 121 q^{17} + 30 q^{19} + 50 q^{20} + 18 q^{21} + 24 q^{22} + 75 q^{23} + 24 q^{24} + 128 q^{25} + 59 q^{26} + 75 q^{27} + 52 q^{28} + 49 q^{29} - 34 q^{30} + 101 q^{31} + 47 q^{32} + 20 q^{33} + 9 q^{34} + 47 q^{35} + 138 q^{36} + 32 q^{37} + 30 q^{38} + 101 q^{39} + 36 q^{40} + 83 q^{41} - 11 q^{42} + 8 q^{43} + 98 q^{44} + 49 q^{45} + 45 q^{46} + 135 q^{47} + 54 q^{48} + 116 q^{49} + 3 q^{50} + 21 q^{51} - 5 q^{52} + 28 q^{53} + 10 q^{54} + 37 q^{55} + 75 q^{56} + 31 q^{58} + 150 q^{59} + 50 q^{60} + 36 q^{61} + 34 q^{62} + 118 q^{63} + 110 q^{64} + 18 q^{65} - 28 q^{66} - 6 q^{67} + 127 q^{68} + 25 q^{69} - 22 q^{70} + 223 q^{71} + q^{72} + 38 q^{73} - 10 q^{74} + 88 q^{75} - 4 q^{76} + 38 q^{77} + 42 q^{78} + 74 q^{79} + 106 q^{80} + 133 q^{81} + 28 q^{82} + 55 q^{83} + 10 q^{84} + 27 q^{85} + 64 q^{86} + 14 q^{87} + 56 q^{88} + 118 q^{89} + 51 q^{90} + 73 q^{91} + 82 q^{92} + 31 q^{93} + 33 q^{94} + 106 q^{95} + 38 q^{96} + 37 q^{97} + 88 q^{98} + 81 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 21 * q^3 + 127 * q^4 + 27 * q^5 + 17 * q^6 + 39 * q^7 + 24 * q^8 + 134 * q^9 + 19 * q^10 + 48 * q^11 + 43 * q^12 + 6 * q^13 + 40 * q^14 + 49 * q^15 + 135 * q^16 + 121 * q^17 + 30 * q^19 + 50 * q^20 + 18 * q^21 + 24 * q^22 + 75 * q^23 + 24 * q^24 + 128 * q^25 + 59 * q^26 + 75 * q^27 + 52 * q^28 + 49 * q^29 - 34 * q^30 + 101 * q^31 + 47 * q^32 + 20 * q^33 + 9 * q^34 + 47 * q^35 + 138 * q^36 + 32 * q^37 + 30 * q^38 + 101 * q^39 + 36 * q^40 + 83 * q^41 - 11 * q^42 + 8 * q^43 + 98 * q^44 + 49 * q^45 + 45 * q^46 + 135 * q^47 + 54 * q^48 + 116 * q^49 + 3 * q^50 + 21 * q^51 - 5 * q^52 + 28 * q^53 + 10 * q^54 + 37 * q^55 + 75 * q^56 + 31 * q^58 + 150 * q^59 + 50 * q^60 + 36 * q^61 + 34 * q^62 + 118 * q^63 + 110 * q^64 + 18 * q^65 - 28 * q^66 - 6 * q^67 + 127 * q^68 + 25 * q^69 - 22 * q^70 + 223 * q^71 + q^72 + 38 * q^73 - 10 * q^74 + 88 * q^75 - 4 * q^76 + 38 * q^77 + 42 * q^78 + 74 * q^79 + 106 * q^80 + 133 * q^81 + 28 * q^82 + 55 * q^83 + 10 * q^84 + 27 * q^85 + 64 * q^86 + 14 * q^87 + 56 * q^88 + 118 * q^89 + 51 * q^90 + 73 * q^91 + 82 * q^92 + 31 * q^93 + 33 * q^94 + 106 * q^95 + 38 * q^96 + 37 * q^97 + 88 * q^98 + 81 * q^99

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