LMFDB - Embedded newform 6001.2.a.d.1.6

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			1.6
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)

$f(q)$	$=$	$q-2.58868 q^{2} -1.67883 q^{3} +4.70126 q^{4} -1.30271 q^{5} +4.34594 q^{6} -1.36507 q^{7} -6.99268 q^{8} -0.181538 q^{9} +O(q^{10})$	\(q-2.58868 q^{2} -1.67883 q^{3} +4.70126 q^{4} -1.30271 q^{5} +4.34594 q^{6} -1.36507 q^{7} -6.99268 q^{8} -0.181538 q^{9} +3.37229 q^{10} -1.30658 q^{11} -7.89260 q^{12} +1.74691 q^{13} +3.53372 q^{14} +2.18702 q^{15} +8.69929 q^{16} +1.00000 q^{17} +0.469945 q^{18} -5.27141 q^{19} -6.12436 q^{20} +2.29171 q^{21} +3.38231 q^{22} -4.63670 q^{23} +11.7395 q^{24} -3.30295 q^{25} -4.52220 q^{26} +5.34125 q^{27} -6.41753 q^{28} +5.58363 q^{29} -5.66150 q^{30} -4.40665 q^{31} -8.53430 q^{32} +2.19352 q^{33} -2.58868 q^{34} +1.77828 q^{35} -0.853458 q^{36} -9.50015 q^{37} +13.6460 q^{38} -2.93277 q^{39} +9.10942 q^{40} +6.72808 q^{41} -5.93250 q^{42} +5.46209 q^{43} -6.14255 q^{44} +0.236491 q^{45} +12.0029 q^{46} -2.49124 q^{47} -14.6046 q^{48} -5.13659 q^{49} +8.55028 q^{50} -1.67883 q^{51} +8.21269 q^{52} -6.94432 q^{53} -13.8268 q^{54} +1.70209 q^{55} +9.54548 q^{56} +8.84979 q^{57} -14.4542 q^{58} +3.05708 q^{59} +10.2817 q^{60} -12.2369 q^{61} +11.4074 q^{62} +0.247812 q^{63} +4.69398 q^{64} -2.27572 q^{65} -5.67831 q^{66} -1.38571 q^{67} +4.70126 q^{68} +7.78421 q^{69} -4.60340 q^{70} -4.35067 q^{71} +1.26944 q^{72} -5.17377 q^{73} +24.5928 q^{74} +5.54509 q^{75} -24.7823 q^{76} +1.78356 q^{77} +7.59199 q^{78} +7.73161 q^{79} -11.3326 q^{80} -8.42243 q^{81} -17.4168 q^{82} -3.84365 q^{83} +10.7739 q^{84} -1.30271 q^{85} -14.1396 q^{86} -9.37395 q^{87} +9.13647 q^{88} -2.54870 q^{89} -0.612200 q^{90} -2.38465 q^{91} -21.7983 q^{92} +7.39801 q^{93} +6.44902 q^{94} +6.86711 q^{95} +14.3276 q^{96} -8.95400 q^{97} +13.2970 q^{98} +0.237194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.58868	−1.83047	−0.915236	−	0.402918i	$-0.867996\pi$
$2$	−2.58868	−1.83047	−0.915236	+	0.402918i	$0.867996\pi$
$3$	−1.67883	−0.969271	−0.484636	−	0.874716i	$-0.661048\pi$
$3$	−1.67883	−0.969271	−0.484636	+	0.874716i	$0.661048\pi$
$4$	4.70126	2.35063
$5$	−1.30271	−0.582589	−0.291294	−	0.956633i	$-0.594086\pi$
$5$	−1.30271	−0.582589	−0.291294	+	0.956633i	$0.594086\pi$
$6$	4.34594	1.77422
$7$	−1.36507	−0.515947	−0.257973	−	0.966152i	$-0.583055\pi$
$7$	−1.36507	−0.515947	−0.257973	+	0.966152i	$0.583055\pi$
$8$	−6.99268	−2.47229
$9$	−0.181538	−0.0605128
$10$	3.37229	1.06641
$11$	−1.30658	−0.393948	−0.196974	−	0.980409i	$-0.563111\pi$
$11$	−1.30658	−0.393948	−0.196974	+	0.980409i	$0.563111\pi$
$12$	−7.89260	−2.27840
$13$	1.74691	0.484507	0.242253	−	0.970213i	$-0.422113\pi$
$13$	1.74691	0.484507	0.242253	+	0.970213i	$0.422113\pi$
$14$	3.53372	0.944426
$15$	2.18702	0.564687
$16$	8.69929	2.17482
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	0.469945	0.110767
$19$	−5.27141	−1.20934	−0.604672	−	0.796474i	$-0.706696\pi$
$19$	−5.27141	−1.20934	−0.604672	+	0.796474i	$0.706696\pi$
$20$	−6.12436	−1.36945
$21$	2.29171	0.500092
$22$	3.38231	0.721110
$23$	−4.63670	−0.966818	−0.483409	−	0.875395i	$-0.660602\pi$
$23$	−4.63670	−0.966818	−0.483409	+	0.875395i	$0.660602\pi$
$24$	11.7395	2.39632
$25$	−3.30295	−0.660590
$26$	−4.52220	−0.886876
$27$	5.34125	1.02792
$28$	−6.41753	−1.21280
$29$	5.58363	1.03685	0.518427	−	0.855122i	$-0.326518\pi$
$29$	5.58363	1.03685	0.518427	+	0.855122i	$0.326518\pi$
$30$	−5.66150	−1.03364
$31$	−4.40665	−0.791458	−0.395729	−	0.918367i	$-0.629508\pi$
$31$	−4.40665	−0.791458	−0.395729	+	0.918367i	$0.629508\pi$
$32$	−8.53430	−1.50867
$33$	2.19352	0.381842
$34$	−2.58868	−0.443955
$35$	1.77828	0.300585
$36$	−0.853458	−0.142243
$37$	−9.50015	−1.56181	−0.780907	−	0.624647i	$-0.785243\pi$
$37$	−9.50015	−1.56181	−0.780907	+	0.624647i	$0.785243\pi$
$38$	13.6460	2.21367
$39$	−2.93277	−0.469618
$40$	9.10942	1.44033
$41$	6.72808	1.05075	0.525374	−	0.850871i	$-0.323925\pi$
$41$	6.72808	1.05075	0.525374	+	0.850871i	$0.323925\pi$
$42$	−5.93250	−0.915405
$43$	5.46209	0.832961	0.416481	−	0.909145i	$-0.363263\pi$
$43$	5.46209	0.832961	0.416481	+	0.909145i	$0.363263\pi$
$44$	−6.14255	−0.926024
$45$	0.236491	0.0352541
$46$	12.0029	1.76973
$47$	−2.49124	−0.363385	−0.181692	−	0.983355i	$-0.558158\pi$
$47$	−2.49124	−0.363385	−0.181692	+	0.983355i	$0.558158\pi$
$48$	−14.6046	−2.10799
$49$	−5.13659	−0.733799
$50$	8.55028	1.20919
$51$	−1.67883	−0.235083
$52$	8.21269	1.13889
$53$	−6.94432	−0.953876	−0.476938	−	0.878937i	$-0.658253\pi$
$53$	−6.94432	−0.953876	−0.476938	+	0.878937i	$0.658253\pi$
$54$	−13.8268	−1.88159
$55$	1.70209	0.229509
$56$	9.54548	1.27557
$57$	8.84979	1.17218
$58$	−14.4542	−1.89793
$59$	3.05708	0.397998	0.198999	−	0.980000i	$-0.436231\pi$
$59$	3.05708	0.397998	0.198999	+	0.980000i	$0.436231\pi$
$60$	10.2817	1.32737
$61$	−12.2369	−1.56678	−0.783389	−	0.621532i	$-0.786510\pi$
$61$	−12.2369	−1.56678	−0.783389	+	0.621532i	$0.786510\pi$
$62$	11.4074	1.44874
$63$	0.247812	0.0312214
$64$	4.69398	0.586747
$65$	−2.27572	−0.282268
$66$	−5.67831	−0.698951
$67$	−1.38571	−0.169292	−0.0846460	−	0.996411i	$-0.526976\pi$
$67$	−1.38571	−0.169292	−0.0846460	+	0.996411i	$0.526976\pi$
$68$	4.70126	0.570111
$69$	7.78421	0.937109
$70$	−4.60340	−0.550212
$71$	−4.35067	−0.516330	−0.258165	−	0.966101i	$-0.583118\pi$
$71$	−4.35067	−0.516330	−0.258165	+	0.966101i	$0.583118\pi$
$72$	1.26944	0.149605
$73$	−5.17377	−0.605544	−0.302772	−	0.953063i	$-0.597912\pi$
$73$	−5.17377	−0.605544	−0.302772	+	0.953063i	$0.597912\pi$
$74$	24.5928	2.85886
$75$	5.54509	0.640291
$76$	−24.7823	−2.84272
$77$	1.78356	0.203256
$78$	7.59199	0.859623
$79$	7.73161	0.869874	0.434937	−	0.900461i	$-0.356771\pi$
$79$	7.73161	0.869874	0.434937	+	0.900461i	$0.356771\pi$
$80$	−11.3326	−1.26703
$81$	−8.42243	−0.935825
$82$	−17.4168	−1.92337
$83$	−3.84365	−0.421896	−0.210948	−	0.977497i	$-0.567655\pi$
$83$	−3.84365	−0.421896	−0.210948	+	0.977497i	$0.567655\pi$
$84$	10.7739	1.17553
$85$	−1.30271	−0.141299
$86$	−14.1396	−1.52471
$87$	−9.37395	−1.00499
$88$	9.13647	0.973951
$89$	−2.54870	−0.270161	−0.135081	−	0.990835i	$-0.543129\pi$
$89$	−2.54870	−0.270161	−0.135081	+	0.990835i	$0.543129\pi$
$90$	−0.612200	−0.0645316
$91$	−2.38465	−0.249980
$92$	−21.7983	−2.27263
$93$	7.39801	0.767138
$94$	6.44902	0.665166
$95$	6.86711	0.704551
$96$	14.3276	1.46231
$97$	−8.95400	−0.909141	−0.454570	−	0.890711i	$-0.650207\pi$
$97$	−8.95400	−0.909141	−0.454570	+	0.890711i	$0.650207\pi$
$98$	13.2970	1.34320
$99$	0.237194	0.0238389
$100$	−15.5280	−1.55280
$101$	18.4234	1.83319	0.916596	−	0.399814i	$-0.130925\pi$
$101$	18.4234	1.83319	0.916596	+	0.399814i	$0.130925\pi$
$102$	4.34594	0.430313
$103$	−8.22768	−0.810697	−0.405349	−	0.914162i	$-0.632850\pi$
$103$	−8.22768	−0.810697	−0.405349	+	0.914162i	$0.632850\pi$
$104$	−12.2156	−1.19784
$105$	−2.98543	−0.291348
$106$	17.9766	1.74604
$107$	−5.33680	−0.515928	−0.257964	−	0.966155i	$-0.583052\pi$
$107$	−5.33680	−0.515928	−0.257964	+	0.966155i	$0.583052\pi$
$108$	25.1106	2.41627
$109$	−1.65066	−0.158104	−0.0790521	−	0.996870i	$-0.525189\pi$
$109$	−1.65066	−0.158104	−0.0790521	+	0.996870i	$0.525189\pi$
$110$	−4.40616	−0.420111
$111$	15.9491	1.51382
$112$	−11.8751	−1.12209
$113$	−15.6209	−1.46949	−0.734744	−	0.678344i	$-0.762698\pi$
$113$	−15.6209	−1.46949	−0.734744	+	0.678344i	$0.762698\pi$
$114$	−22.9093	−2.14565
$115$	6.04026	0.563257
$116$	26.2501	2.43726
$117$	−0.317132	−0.0293189
$118$	−7.91379	−0.728523
$119$	−1.36507	−0.125135
$120$	−15.2931	−1.39607
$121$	−9.29286	−0.844805
$122$	31.6775	2.86794
$123$	−11.2953	−1.01846
$124$	−20.7168	−1.86042
$125$	10.8163	0.967441
$126$	−0.641506	−0.0571499
$127$	−16.4858	−1.46288	−0.731439	−	0.681907i	$-0.761151\pi$
$127$	−16.4858	−1.46288	−0.731439	+	0.681907i	$0.761151\pi$
$128$	4.91740	0.434641
$129$	−9.16991	−0.807366
$130$	5.89110	0.516684
$131$	2.83003	0.247261	0.123631	−	0.992328i	$-0.460546\pi$
$131$	2.83003	0.247261	0.123631	+	0.992328i	$0.460546\pi$
$132$	10.3123	0.897569
$133$	7.19583	0.623958
$134$	3.58717	0.309884
$135$	−6.95809	−0.598857
$136$	−6.99268	−0.599617
$137$	10.1998	0.871432	0.435716	−	0.900084i	$-0.356495\pi$
$137$	10.1998	0.871432	0.435716	+	0.900084i	$0.356495\pi$
$138$	−20.1508	−1.71535
$139$	11.3492	0.962630	0.481315	−	0.876548i	$-0.340159\pi$
$139$	11.3492	0.962630	0.481315	+	0.876548i	$0.340159\pi$
$140$	8.36016	0.706563
$141$	4.18236	0.352219
$142$	11.2625	0.945127
$143$	−2.28248	−0.190870
$144$	−1.57925	−0.131605
$145$	−7.27384	−0.604059
$146$	13.3932	1.10843
$147$	8.62345	0.711250
$148$	−44.6626	−3.67124
$149$	−10.6249	−0.870426	−0.435213	−	0.900328i	$-0.643327\pi$
$149$	−10.6249	−0.870426	−0.435213	+	0.900328i	$0.643327\pi$
$150$	−14.3544	−1.17204
$151$	14.3729	1.16965	0.584824	−	0.811160i	$-0.301164\pi$
$151$	14.3729	1.16965	0.584824	+	0.811160i	$0.301164\pi$
$152$	36.8613	2.98985
$153$	−0.181538	−0.0146765
$154$	−4.61707	−0.372054
$155$	5.74058	0.461095
$156$	−13.7877	−1.10390
$157$	−23.5995	−1.88344	−0.941722	−	0.336393i	$-0.890793\pi$
$157$	−23.5995	−1.88344	−0.941722	+	0.336393i	$0.890793\pi$
$158$	−20.0147	−1.59228
$159$	11.6583	0.924564
$160$	11.1177	0.878931
$161$	6.32940	0.498827
$162$	21.8030	1.71300
$163$	14.6698	1.14903	0.574514	−	0.818495i	$-0.305191\pi$
$163$	14.6698	1.14903	0.574514	+	0.818495i	$0.305191\pi$
$164$	31.6304	2.46992
$165$	−2.85751	−0.222457
$166$	9.94998	0.772268
$167$	11.0998	0.858931	0.429466	−	0.903083i	$-0.358702\pi$
$167$	11.0998	0.858931	0.429466	+	0.903083i	$0.358702\pi$
$168$	−16.0252	−1.23637
$169$	−9.94829	−0.765253
$170$	3.37229	0.258643
$171$	0.956964	0.0731808
$172$	25.6787	1.95798
$173$	−13.2304	−1.00589	−0.502946	−	0.864318i	$-0.667751\pi$
$173$	−13.2304	−1.00589	−0.502946	+	0.864318i	$0.667751\pi$
$174$	24.2661	1.83961
$175$	4.50875	0.340830
$176$	−11.3663	−0.856766
$177$	−5.13231	−0.385768
$178$	6.59775	0.494523
$179$	−18.1633	−1.35759	−0.678795	−	0.734328i	$-0.737497\pi$
$179$	−18.1633	−1.35759	−0.678795	+	0.734328i	$0.737497\pi$
$180$	1.11181	0.0828692
$181$	−15.5100	−1.15285	−0.576423	−	0.817151i	$-0.695552\pi$
$181$	−15.5100	−1.15285	−0.576423	+	0.817151i	$0.695552\pi$
$182$	6.17310	0.457581
$183$	20.5437	1.51863
$184$	32.4229	2.39025
$185$	12.3759	0.909896
$186$	−19.1511	−1.40422
$187$	−1.30658	−0.0955463
$188$	−11.7120	−0.854182
$189$	−7.29117	−0.530354
$190$	−17.7767	−1.28966
$191$	11.3635	0.822234	0.411117	−	0.911583i	$-0.365139\pi$
$191$	11.3635	0.822234	0.411117	+	0.911583i	$0.365139\pi$
$192$	−7.88038	−0.568717
$193$	−5.65714	−0.407210	−0.203605	−	0.979053i	$-0.565266\pi$
$193$	−5.65714	−0.407210	−0.203605	+	0.979053i	$0.565266\pi$
$194$	23.1790	1.66416
$195$	3.82054	0.273594
$196$	−24.1484	−1.72489
$197$	2.87384	0.204752	0.102376	−	0.994746i	$-0.467355\pi$
$197$	2.87384	0.204752	0.102376	+	0.994746i	$0.467355\pi$
$198$	−0.614018	−0.0436364
$199$	3.05971	0.216897	0.108449	−	0.994102i	$-0.465412\pi$
$199$	3.05971	0.216897	0.108449	+	0.994102i	$0.465412\pi$
$200$	23.0965	1.63317
$201$	2.32638	0.164090
$202$	−47.6921	−3.35561
$203$	−7.62203	−0.534962
$204$	−7.89260	−0.552592
$205$	−8.76472	−0.612154
$206$	21.2988	1.48396
$207$	0.841739	0.0585049
$208$	15.1969	1.05372
$209$	6.88750	0.476418
$210$	7.72832	0.533305
$211$	6.09133	0.419344	0.209672	−	0.977772i	$-0.432760\pi$
$211$	6.09133	0.419344	0.209672	+	0.977772i	$0.432760\pi$
$212$	−32.6470	−2.24221
$213$	7.30402	0.500464
$214$	13.8153	0.944392
$215$	−7.11551	−0.485274
$216$	−37.3497	−2.54132
$217$	6.01538	0.408350
$218$	4.27302	0.289405
$219$	8.68586	0.586936
$220$	8.00195	0.539491
$221$	1.74691	0.117510
$222$	−41.2871	−2.77101
$223$	−14.3398	−0.960263	−0.480131	−	0.877197i	$-0.659411\pi$
$223$	−14.3398	−0.960263	−0.480131	+	0.877197i	$0.659411\pi$
$224$	11.6499	0.778391
$225$	0.599613	0.0399742
$226$	40.4374	2.68986
$227$	−14.7485	−0.978889	−0.489445	−	0.872034i	$-0.662801\pi$
$227$	−14.7485	−0.978889	−0.489445	+	0.872034i	$0.662801\pi$
$228$	41.6051	2.75537
$229$	−7.81445	−0.516393	−0.258197	−	0.966092i	$-0.583128\pi$
$229$	−7.81445	−0.516393	−0.258197	+	0.966092i	$0.583128\pi$
$230$	−15.6363	−1.03103
$231$	−2.99430	−0.197010
$232$	−39.0445	−2.56340
$233$	−22.3473	−1.46402	−0.732011	−	0.681293i	$-0.761418\pi$
$233$	−22.3473	−1.46402	−0.732011	+	0.681293i	$0.761418\pi$
$234$	0.820952	0.0536673
$235$	3.24536	0.211704
$236$	14.3721	0.935544
$237$	−12.9800	−0.843145
$238$	3.53372	0.229057
$239$	22.3935	1.44851	0.724257	−	0.689530i	$-0.242183\pi$
$239$	22.3935	1.44851	0.724257	+	0.689530i	$0.242183\pi$
$240$	19.0255	1.22809
$241$	−6.28138	−0.404619	−0.202310	−	0.979322i	$-0.564845\pi$
$241$	−6.28138	−0.404619	−0.202310	+	0.979322i	$0.564845\pi$
$242$	24.0562	1.54639
$243$	−1.88396	−0.120856
$244$	−57.5289	−3.68291
$245$	6.69148	0.427503
$246$	29.2398	1.86426
$247$	−9.20870	−0.585936
$248$	30.8143	1.95671
$249$	6.45283	0.408931
$250$	−28.0000	−1.77087
$251$	−25.5405	−1.61210	−0.806050	−	0.591847i	$-0.798399\pi$
$251$	−25.5405	−1.61210	−0.806050	+	0.591847i	$0.798399\pi$
$252$	1.16503	0.0733898
$253$	6.05820	0.380876
$254$	42.6764	2.67776
$255$	2.18702	0.136957
$256$	−22.1175	−1.38235
$257$	−25.8300	−1.61123	−0.805615	−	0.592440i	$-0.798165\pi$
$257$	−25.8300	−1.61123	−0.805615	+	0.592440i	$0.798165\pi$
$258$	23.7379	1.47786
$259$	12.9683	0.805813
$260$	−10.6987	−0.663507
$261$	−1.01364	−0.0627429
$262$	−7.32605	−0.452605
$263$	−27.8459	−1.71705	−0.858525	−	0.512772i	$-0.828619\pi$
$263$	−27.8459	−1.71705	−0.858525	+	0.512772i	$0.828619\pi$
$264$	−15.3386	−0.944023
$265$	9.04642	0.555717
$266$	−18.6277	−1.14214
$267$	4.27882	0.261860
$268$	−6.51460	−0.397942
$269$	17.4161	1.06188	0.530939	−	0.847410i	$-0.321839\pi$
$269$	17.4161	1.06188	0.530939	+	0.847410i	$0.321839\pi$
$270$	18.0123	1.09619
$271$	−3.23027	−0.196225	−0.0981126	−	0.995175i	$-0.531281\pi$
$271$	−3.23027	−0.196225	−0.0981126	+	0.995175i	$0.531281\pi$
$272$	8.69929	0.527472
$273$	4.00342	0.242298
$274$	−26.4041	−1.59513
$275$	4.31556	0.260238
$276$	36.5956	2.20279
$277$	18.6340	1.11961	0.559804	−	0.828625i	$-0.310876\pi$
$277$	18.6340	1.11961	0.559804	+	0.828625i	$0.310876\pi$
$278$	−29.3795	−1.76207
$279$	0.799977	0.0478934
$280$	−12.4350	−0.743131
$281$	29.2807	1.74674	0.873369	−	0.487059i	$-0.161930\pi$
$281$	29.2807	1.74674	0.873369	+	0.487059i	$0.161930\pi$
$282$	−10.8268	−0.644726
$283$	10.9124	0.648677	0.324339	−	0.945941i	$-0.394858\pi$
$283$	10.9124	0.648677	0.324339	+	0.945941i	$0.394858\pi$
$284$	−20.4536	−1.21370
$285$	−11.5287	−0.682901
$286$	5.90860	0.349383
$287$	−9.18427	−0.542130
$288$	1.54930	0.0912936
$289$	1.00000	0.0588235
$290$	18.8296	1.10571
$291$	15.0322	0.881204
$292$	−24.3232	−1.42341
$293$	−21.2007	−1.23856	−0.619280	−	0.785170i	$-0.712576\pi$
$293$	−21.2007	−1.23856	−0.619280	+	0.785170i	$0.712576\pi$
$294$	−22.3233	−1.30192
$295$	−3.98248	−0.231869
$296$	66.4315	3.86125
$297$	−6.97876	−0.404949
$298$	27.5045	1.59329
$299$	−8.09991	−0.468430
$300$	26.0689	1.50509
$301$	−7.45612	−0.429764
$302$	−37.2067	−2.14101
$303$	−30.9296	−1.77686
$304$	−45.8575	−2.63011
$305$	15.9411	0.912787
$306$	0.469945	0.0268649
$307$	−17.8072	−1.01631	−0.508155	−	0.861265i	$-0.669672\pi$
$307$	−17.8072	−1.01631	−0.508155	+	0.861265i	$0.669672\pi$
$308$	8.38499	0.477779
$309$	13.8128	0.785786
$310$	−14.8605	−0.844021
$311$	−15.1606	−0.859679	−0.429840	−	0.902905i	$-0.641430\pi$
$311$	−15.1606	−0.859679	−0.429840	+	0.902905i	$0.641430\pi$
$312$	20.5079	1.16103
$313$	−9.18320	−0.519065	−0.259533	−	0.965734i	$-0.583569\pi$
$313$	−9.18320	−0.519065	−0.259533	+	0.965734i	$0.583569\pi$
$314$	61.0914	3.44759
$315$	−0.322827	−0.0181892
$316$	36.3483	2.04475
$317$	−17.4834	−0.981967	−0.490984	−	0.871169i	$-0.663363\pi$
$317$	−17.4834	−0.981967	−0.490984	+	0.871169i	$0.663363\pi$
$318$	−30.1796	−1.69239
$319$	−7.29544	−0.408466
$320$	−6.11488	−0.341832
$321$	8.95957	0.500074
$322$	−16.3848	−0.913088
$323$	−5.27141	−0.293309
$324$	−39.5960	−2.19978
$325$	−5.76997	−0.320060
$326$	−37.9754	−2.10326
$327$	2.77117	0.153246
$328$	−47.0473	−2.59775
$329$	3.40071	0.187487
$330$	7.39718	0.407201
$331$	−15.8236	−0.869744	−0.434872	−	0.900492i	$-0.643206\pi$
$331$	−15.8236	−0.869744	−0.434872	+	0.900492i	$0.643206\pi$
$332$	−18.0700	−0.991719
$333$	1.72464	0.0945098
$334$	−28.7339	−1.57225
$335$	1.80518	0.0986276
$336$	19.9363	1.08761
$337$	−29.7888	−1.62270	−0.811350	−	0.584561i	$-0.801267\pi$
$337$	−29.7888	−1.62270	−0.811350	+	0.584561i	$0.801267\pi$
$338$	25.7529	1.40077
$339$	26.2248	1.42433
$340$	−6.12436	−0.332140
$341$	5.75763	0.311793
$342$	−2.47727	−0.133955
$343$	16.5673	0.894548
$344$	−38.1947	−2.05932
$345$	−10.1406	−0.545949
$346$	34.2494	1.84126
$347$	7.83284	0.420489	0.210245	−	0.977649i	$-0.432574\pi$
$347$	7.83284	0.420489	0.210245	+	0.977649i	$0.432574\pi$
$348$	−44.0693	−2.36236
$349$	−18.9706	−1.01547	−0.507737	−	0.861512i	$-0.669518\pi$
$349$	−18.9706	−1.01547	−0.507737	+	0.861512i	$0.669518\pi$
$350$	−11.6717	−0.623879
$351$	9.33071	0.498036
$352$	11.1507	0.594335
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	13.2859	0.706137
$355$	5.66765	0.300808
$356$	−11.9821	−0.635049
$357$	2.29171	0.121290
$358$	47.0190	2.48503
$359$	−13.0889	−0.690805	−0.345403	−	0.938455i	$-0.612258\pi$
$359$	−13.0889	−0.690805	−0.345403	+	0.938455i	$0.612258\pi$
$360$	−1.65371	−0.0871581
$361$	8.78778	0.462515
$362$	40.1503	2.11025
$363$	15.6011	0.818846
$364$	−11.2109	−0.587609
$365$	6.73991	0.352783
$366$	−53.1810	−2.77981
$367$	−13.5207	−0.705774	−0.352887	−	0.935666i	$-0.614800\pi$
$367$	−13.5207	−0.705774	−0.352887	+	0.935666i	$0.614800\pi$
$368$	−40.3360	−2.10266
$369$	−1.22140	−0.0635838
$370$	−32.0373	−1.66554
$371$	9.47946	0.492149
$372$	34.7799	1.80326
$373$	16.4291	0.850664	0.425332	−	0.905037i	$-0.360157\pi$
$373$	16.4291	0.850664	0.425332	+	0.905037i	$0.360157\pi$
$374$	3.38231	0.174895
$375$	−18.1587	−0.937713
$376$	17.4205	0.898391
$377$	9.75412	0.502363
$378$	18.8745	0.970799
$379$	6.56843	0.337397	0.168699	−	0.985668i	$-0.446044\pi$
$379$	6.56843	0.337397	0.168699	+	0.985668i	$0.446044\pi$
$380$	32.2840	1.65614
$381$	27.6768	1.41793
$382$	−29.4164	−1.50508
$383$	8.67021	0.443027	0.221513	−	0.975157i	$-0.428900\pi$
$383$	8.67021	0.443027	0.221513	+	0.975157i	$0.428900\pi$
$384$	−8.25547	−0.421285
$385$	−2.32346	−0.118415
$386$	14.6445	0.745386
$387$	−0.991579	−0.0504048
$388$	−42.0950	−2.13705
$389$	−23.7549	−1.20442	−0.602211	−	0.798337i	$-0.705713\pi$
$389$	−23.7549	−1.20442	−0.602211	+	0.798337i	$0.705713\pi$
$390$	−9.89014	−0.500807
$391$	−4.63670	−0.234488
$392$	35.9185	1.81416
$393$	−4.75114	−0.239663
$394$	−7.43944	−0.374794
$395$	−10.0720	−0.506779
$396$	1.11511	0.0560363
$397$	−20.3601	−1.02184	−0.510922	−	0.859627i	$-0.670696\pi$
$397$	−20.3601	−1.02184	−0.510922	+	0.859627i	$0.670696\pi$
$398$	−7.92061	−0.397024
$399$	−12.0806	−0.604784
$400$	−28.7333	−1.43667
$401$	6.82070	0.340609	0.170305	−	0.985391i	$-0.445525\pi$
$401$	6.82070	0.340609	0.170305	+	0.985391i	$0.445525\pi$
$402$	−6.02224	−0.300362
$403$	−7.69804	−0.383467
$404$	86.6129	4.30915
$405$	10.9720	0.545201
$406$	19.7310	0.979232
$407$	12.4127	0.615273
$408$	11.7395	0.581192
$409$	17.6895	0.874691	0.437345	−	0.899294i	$-0.355919\pi$
$409$	17.6895	0.874691	0.437345	+	0.899294i	$0.355919\pi$
$410$	22.6890	1.12053
$411$	−17.1238	−0.844654
$412$	−38.6804	−1.90565
$413$	−4.17311	−0.205346
$414$	−2.17899	−0.107092
$415$	5.00715	0.245792
$416$	−14.9087	−0.730958
$417$	−19.0534	−0.933050
$418$	−17.8295	−0.872071
$419$	31.5083	1.53928	0.769639	−	0.638479i	$-0.220436\pi$
$419$	31.5083	1.53928	0.769639	+	0.638479i	$0.220436\pi$
$420$	−14.0353	−0.684851
$421$	4.28401	0.208790	0.104395	−	0.994536i	$-0.466709\pi$
$421$	4.28401	0.208790	0.104395	+	0.994536i	$0.466709\pi$
$422$	−15.7685	−0.767598
$423$	0.452256	0.0219894
$424$	48.5594	2.35825
$425$	−3.30295	−0.160217
$426$	−18.9078	−0.916084
$427$	16.7042	0.808374
$428$	−25.0897	−1.21275
$429$	3.83188	0.185005
$430$	18.4198	0.888280
$431$	29.9009	1.44027	0.720137	−	0.693832i	$-0.244079\pi$
$431$	29.9009	1.44027	0.720137	+	0.693832i	$0.244079\pi$
$432$	46.4651	2.23555
$433$	−32.3137	−1.55290	−0.776449	−	0.630180i	$-0.782981\pi$
$433$	−32.3137	−1.55290	−0.776449	+	0.630180i	$0.782981\pi$
$434$	−15.5719	−0.747474
$435$	12.2115	0.585498
$436$	−7.76016	−0.371644
$437$	24.4419	1.16922
$438$	−22.4849	−1.07437
$439$	36.2233	1.72884	0.864421	−	0.502769i	$-0.167685\pi$
$439$	36.2233	1.72884	0.864421	+	0.502769i	$0.167685\pi$
$440$	−11.9022	−0.567413
$441$	0.932489	0.0444042
$442$	−4.52220	−0.215099
$443$	20.7769	0.987141	0.493570	−	0.869706i	$-0.335692\pi$
$443$	20.7769	0.987141	0.493570	+	0.869706i	$0.335692\pi$
$444$	74.9808	3.55843
$445$	3.32021	0.157393
$446$	37.1211	1.75773
$447$	17.8374	0.843679
$448$	−6.40759	−0.302730
$449$	8.43910	0.398266	0.199133	−	0.979973i	$-0.436187\pi$
$449$	8.43910	0.398266	0.199133	+	0.979973i	$0.436187\pi$
$450$	−1.55220	−0.0731716
$451$	−8.79074	−0.413940
$452$	−73.4377	−3.45422
$453$	−24.1296	−1.13371
$454$	38.1790	1.79183
$455$	3.10651	0.145635
$456$	−61.8838	−2.89797
$457$	30.7844	1.44004	0.720018	−	0.693956i	$-0.244134\pi$
$457$	30.7844	1.44004	0.720018	+	0.693956i	$0.244134\pi$
$458$	20.2291	0.945243
$459$	5.34125	0.249308
$460$	28.3968	1.32401
$461$	15.0671	0.701745	0.350872	−	0.936423i	$-0.385885\pi$
$461$	15.0671	0.701745	0.350872	+	0.936423i	$0.385885\pi$
$462$	7.75127	0.360622
$463$	19.6558	0.913485	0.456742	−	0.889599i	$-0.349016\pi$
$463$	19.6558	0.913485	0.456742	+	0.889599i	$0.349016\pi$
$464$	48.5736	2.25497
$465$	−9.63745	−0.446926
$466$	57.8500	2.67985
$467$	31.0438	1.43654	0.718268	−	0.695766i	$-0.244935\pi$
$467$	31.0438	1.43654	0.718268	+	0.695766i	$0.244935\pi$
$468$	−1.49092	−0.0689177
$469$	1.89159	0.0873456
$470$	−8.40119	−0.387518
$471$	39.6194	1.82557
$472$	−21.3772	−0.983964
$473$	−7.13664	−0.328143
$474$	33.6012	1.54335
$475$	17.4112	0.798882
$476$	−6.41753	−0.294147
$477$	1.26066	0.0577217
$478$	−57.9696	−2.65147
$479$	−29.3847	−1.34262	−0.671311	−	0.741175i	$-0.734269\pi$
$479$	−29.3847	−1.34262	−0.671311	+	0.741175i	$0.734269\pi$
$480$	−18.6647	−0.851923
$481$	−16.5959	−0.756710
$482$	16.2605	0.740644
$483$	−10.6260	−0.483498
$484$	−43.6881	−1.98582
$485$	11.6644	0.529655
$486$	4.87696	0.221223
$487$	12.6078	0.571315	0.285658	−	0.958332i	$-0.407788\pi$
$487$	12.6078	0.571315	0.285658	+	0.958332i	$0.407788\pi$
$488$	85.5689	3.87352
$489$	−24.6281	−1.11372
$490$	−17.3221	−0.782532
$491$	−22.8131	−1.02954	−0.514770	−	0.857328i	$-0.672123\pi$
$491$	−22.8131	−1.02954	−0.514770	+	0.857328i	$0.672123\pi$
$492$	−53.1020	−2.39402
$493$	5.58363	0.251474
$494$	23.8384	1.07254
$495$	−0.308994	−0.0138883
$496$	−38.3348	−1.72128
$497$	5.93896	0.266399
$498$	−16.7043	−0.748537
$499$	30.6519	1.37217	0.686083	−	0.727523i	$-0.259329\pi$
$499$	30.6519	1.37217	0.686083	+	0.727523i	$0.259329\pi$
$500$	50.8503	2.27409
$501$	−18.6347	−0.832538
$502$	66.1161	2.95090
$503$	14.1464	0.630757	0.315379	−	0.948966i	$-0.397868\pi$
$503$	14.1464	0.630757	0.315379	+	0.948966i	$0.397868\pi$
$504$	−1.73287	−0.0771882
$505$	−24.0002	−1.06800
$506$	−15.6827	−0.697182
$507$	16.7015	0.741738
$508$	−77.5039	−3.43868
$509$	9.08657	0.402755	0.201378	−	0.979514i	$-0.435458\pi$
$509$	9.08657	0.402755	0.201378	+	0.979514i	$0.435458\pi$
$510$	−5.66150	−0.250695
$511$	7.06254	0.312428
$512$	47.4204	2.09570
$513$	−28.1559	−1.24312
$514$	66.8655	2.94931
$515$	10.7183	0.472303
$516$	−43.1101	−1.89782
$517$	3.25500	0.143155
$518$	−33.5709	−1.47502
$519$	22.2116	0.974982
$520$	15.9134	0.697847
$521$	−30.0411	−1.31613	−0.658063	−	0.752963i	$-0.728624\pi$
$521$	−30.0411	−1.31613	−0.658063	+	0.752963i	$0.728624\pi$
$522$	2.62400	0.114849
$523$	−22.8864	−1.00075	−0.500376	−	0.865808i	$-0.666805\pi$
$523$	−22.8864	−1.00075	−0.500376	+	0.865808i	$0.666805\pi$
$524$	13.3047	0.581219
$525$	−7.56941	−0.330356
$526$	72.0840	3.14301
$527$	−4.40665	−0.191957
$528$	19.0820	0.830439
$529$	−1.50104	−0.0652627
$530$	−23.4183	−1.01722
$531$	−0.554977	−0.0240839
$532$	33.8294	1.46669
$533$	11.7534	0.509095
$534$	−11.0765	−0.479327
$535$	6.95229	0.300574
$536$	9.68986	0.418538
$537$	30.4931	1.31587
$538$	−45.0847	−1.94374
$539$	6.71135	0.289078
$540$	−32.7118	−1.40769
$541$	12.9052	0.554838	0.277419	−	0.960749i	$-0.410521\pi$
$541$	12.9052	0.554838	0.277419	+	0.960749i	$0.410521\pi$
$542$	8.36214	0.359185
$543$	26.0385	1.11742
$544$	−8.53430	−0.365905
$545$	2.15032	0.0921098
$546$	−10.3636	−0.443520
$547$	−17.6526	−0.754771	−0.377385	−	0.926056i	$-0.623177\pi$
$547$	−17.6526	−0.754771	−0.377385	+	0.926056i	$0.623177\pi$
$548$	47.9521	2.04841
$549$	2.22147	0.0948101
$550$	−11.1716	−0.476358
$551$	−29.4336	−1.25391
$552$	−54.4325	−2.31680
$553$	−10.5542	−0.448809
$554$	−48.2374	−2.04941
$555$	−20.7770	−0.881936
$556$	53.3557	2.26279
$557$	33.3942	1.41496	0.707479	−	0.706735i	$-0.249832\pi$
$557$	33.3942	1.41496	0.707479	+	0.706735i	$0.249832\pi$
$558$	−2.07088	−0.0876675
$559$	9.54180	0.403575
$560$	15.4698	0.653718
$561$	2.19352	0.0926103
$562$	−75.7982	−3.19735
$563$	37.5066	1.58071	0.790357	−	0.612646i	$-0.209895\pi$
$563$	37.5066	1.58071	0.790357	+	0.612646i	$0.209895\pi$
$564$	19.6624	0.827935
$565$	20.3494	0.856107
$566$	−28.2488	−1.18739
$567$	11.4972	0.482836
$568$	30.4228	1.27651
$569$	−41.2358	−1.72869	−0.864346	−	0.502897i	$-0.832268\pi$
$569$	−41.2358	−1.72869	−0.864346	+	0.502897i	$0.832268\pi$
$570$	29.8441	1.25003
$571$	−14.1522	−0.592253	−0.296126	−	0.955149i	$-0.595695\pi$
$571$	−14.1522	−0.592253	−0.296126	+	0.955149i	$0.595695\pi$
$572$	−10.7305	−0.448665
$573$	−19.0774	−0.796968
$574$	23.7751	0.992355
$575$	15.3148	0.638671
$576$	−0.852137	−0.0355057
$577$	22.3219	0.929275	0.464637	−	0.885501i	$-0.346185\pi$
$577$	22.3219	0.929275	0.464637	+	0.885501i	$0.346185\pi$
$578$	−2.58868	−0.107675
$579$	9.49735	0.394697
$580$	−34.1962	−1.41992
$581$	5.24684	0.217676
$582$	−38.9136	−1.61302
$583$	9.07328	0.375777
$584$	36.1785	1.49708
$585$	0.413130	0.0170808
$586$	54.8819	2.26715
$587$	−17.4548	−0.720435	−0.360218	−	0.932868i	$-0.617298\pi$
$587$	−17.4548	−0.720435	−0.360218	+	0.932868i	$0.617298\pi$
$588$	40.5411	1.67188
$589$	23.2293	0.957146
$590$	10.3094	0.424429
$591$	−4.82468	−0.198461
$592$	−82.6445	−3.39667
$593$	26.9059	1.10489	0.552446	−	0.833549i	$-0.313695\pi$
$593$	26.9059	1.10489	0.552446	+	0.833549i	$0.313695\pi$
$594$	18.0658	0.741247
$595$	1.77828	0.0729025
$596$	−49.9504	−2.04605
$597$	−5.13673	−0.210232
$598$	20.9681	0.857448
$599$	8.84032	0.361206	0.180603	−	0.983556i	$-0.442195\pi$
$599$	8.84032	0.361206	0.180603	+	0.983556i	$0.442195\pi$
$600$	−38.7750	−1.58298
$601$	41.9857	1.71263	0.856317	−	0.516451i	$-0.172747\pi$
$601$	41.9857	1.71263	0.856317	+	0.516451i	$0.172747\pi$
$602$	19.3015	0.786670
$603$	0.251560	0.0102443
$604$	67.5705	2.74940
$605$	12.1059	0.492174
$606$	80.0669	3.25249
$607$	17.7453	0.720259	0.360129	−	0.932902i	$-0.382733\pi$
$607$	17.7453	0.720259	0.360129	+	0.932902i	$0.382733\pi$
$608$	44.9878	1.82450
$609$	12.7961	0.518523
$610$	−41.2665	−1.67083
$611$	−4.35198	−0.176062
$612$	−0.853458	−0.0344990
$613$	19.5684	0.790358	0.395179	−	0.918604i	$-0.370683\pi$
$613$	19.5684	0.790358	0.395179	+	0.918604i	$0.370683\pi$
$614$	46.0971	1.86033
$615$	14.7144	0.593344
$616$	−12.4719	−0.502507
$617$	1.39946	0.0563402	0.0281701	−	0.999603i	$-0.491032\pi$
$617$	1.39946	0.0563402	0.0281701	+	0.999603i	$0.491032\pi$
$618$	−35.7570	−1.43836
$619$	9.75319	0.392014	0.196007	−	0.980603i	$-0.437203\pi$
$619$	9.75319	0.392014	0.196007	+	0.980603i	$0.437203\pi$
$620$	26.9879	1.08386
$621$	−24.7658	−0.993816
$622$	39.2459	1.57362
$623$	3.47914	0.139389
$624$	−25.5130	−1.02134
$625$	2.42426	0.0969702
$626$	23.7724	0.950135
$627$	−11.5629	−0.461779
$628$	−110.947	−4.42727
$629$	−9.50015	−0.378796
$630$	0.835694	0.0332949
$631$	34.6239	1.37836	0.689178	−	0.724592i	$-0.257972\pi$
$631$	34.6239	1.37836	0.689178	+	0.724592i	$0.257972\pi$
$632$	−54.0647	−2.15058
$633$	−10.2263	−0.406458
$634$	45.2590	1.79746
$635$	21.4762	0.852256
$636$	54.8087	2.17331
$637$	−8.97318	−0.355530
$638$	18.8855	0.747686
$639$	0.789814	0.0312445
$640$	−6.40594	−0.253217
$641$	−18.5037	−0.730851	−0.365426	−	0.930841i	$-0.619077\pi$
$641$	−18.5037	−0.730851	−0.365426	+	0.930841i	$0.619077\pi$
$642$	−23.1934	−0.915372
$643$	25.9494	1.02334	0.511672	−	0.859181i	$-0.329026\pi$
$643$	25.9494	1.02334	0.511672	+	0.859181i	$0.329026\pi$
$644$	29.7561	1.17256
$645$	11.9457	0.470362
$646$	13.6460	0.536894
$647$	−23.3560	−0.918217	−0.459109	−	0.888380i	$-0.651831\pi$
$647$	−23.3560	−0.918217	−0.459109	+	0.888380i	$0.651831\pi$
$648$	58.8953	2.31363
$649$	−3.99430	−0.156790
$650$	14.9366	0.585862
$651$	−10.0988	−0.395802
$652$	68.9665	2.70094
$653$	3.22136	0.126061	0.0630307	−	0.998012i	$-0.479923\pi$
$653$	3.22136	0.126061	0.0630307	+	0.998012i	$0.479923\pi$
$654$	−7.17366	−0.280512
$655$	−3.68671	−0.144052
$656$	58.5295	2.28519
$657$	0.939237	0.0366431
$658$	−8.80334	−0.343190
$659$	−10.2324	−0.398599	−0.199300	−	0.979939i	$-0.563867\pi$
$659$	−10.2324	−0.398599	−0.199300	+	0.979939i	$0.563867\pi$
$660$	−13.4339	−0.522913
$661$	3.30175	0.128423	0.0642117	−	0.997936i	$-0.479547\pi$
$661$	3.30175	0.128423	0.0642117	+	0.997936i	$0.479547\pi$
$662$	40.9622	1.59204
$663$	−2.93277	−0.113899
$664$	26.8774	1.04305
$665$	−9.37406	−0.363511
$666$	−4.46454	−0.172998
$667$	−25.8896	−1.00245
$668$	52.1832	2.01903
$669$	24.0740	0.930755
$670$	−4.67303	−0.180535
$671$	15.9885	0.617228
$672$	−19.5582	−0.754472
$673$	6.63791	0.255873	0.127936	−	0.991782i	$-0.459165\pi$
$673$	6.63791	0.255873	0.127936	+	0.991782i	$0.459165\pi$
$674$	77.1136	2.97031
$675$	−17.6419	−0.679037
$676$	−46.7695	−1.79883
$677$	47.7231	1.83415	0.917075	−	0.398715i	$-0.130544\pi$
$677$	47.7231	1.83415	0.917075	+	0.398715i	$0.130544\pi$
$678$	−67.8875	−2.60720
$679$	12.2228	0.469068
$680$	9.10942	0.349330
$681$	24.7601	0.948810
$682$	−14.9047	−0.570729
$683$	−28.9947	−1.10945	−0.554726	−	0.832033i	$-0.687177\pi$
$683$	−28.9947	−1.10945	−0.554726	+	0.832033i	$0.687177\pi$
$684$	4.49893	0.172021
$685$	−13.2874	−0.507686
$686$	−42.8873	−1.63744
$687$	13.1191	0.500525
$688$	47.5163	1.81154
$689$	−12.1311	−0.462159
$690$	26.2506	0.999345
$691$	2.92418	0.111241	0.0556206	−	0.998452i	$-0.482286\pi$
$691$	2.92418	0.111241	0.0556206	+	0.998452i	$0.482286\pi$
$692$	−62.1997	−2.36448
$693$	−0.323785	−0.0122996
$694$	−20.2767	−0.769693
$695$	−14.7847	−0.560817
$696$	65.5490	2.48463
$697$	6.72808	0.254844
$698$	49.1089	1.85880
$699$	37.5173	1.41903
$700$	21.1968	0.801163
$701$	31.1411	1.17618	0.588092	−	0.808794i	$-0.299879\pi$
$701$	31.1411	1.17618	0.588092	+	0.808794i	$0.299879\pi$
$702$	−24.1542	−0.911642
$703$	50.0792	1.88877
$704$	−6.13304	−0.231148
$705$	−5.44840	−0.205199
$706$	2.58868	0.0974262
$707$	−25.1491	−0.945830
$708$	−24.1283	−0.906796
$709$	−4.84687	−0.182028	−0.0910140	−	0.995850i	$-0.529011\pi$
$709$	−4.84687	−0.182028	−0.0910140	+	0.995850i	$0.529011\pi$
$710$	−14.6717	−0.550620
$711$	−1.40358	−0.0526385
$712$	17.8222	0.667916
$713$	20.4323	0.765196
$714$	−5.93250	−0.222018
$715$	2.97340	0.111199
$716$	−85.3903	−3.19119
$717$	−37.5948	−1.40400
$718$	33.8829	1.26450
$719$	−36.2826	−1.35311	−0.676557	−	0.736390i	$-0.736529\pi$
$719$	−36.2826	−1.35311	−0.676557	+	0.736390i	$0.736529\pi$
$720$	2.05731	0.0766713
$721$	11.2313	0.418277
$722$	−22.7487	−0.846620
$723$	10.5454	0.392186
$724$	−72.9163	−2.70991
$725$	−18.4425	−0.684936
$726$	−40.3862	−1.49887
$727$	−5.96351	−0.221174	−0.110587	−	0.993866i	$-0.535273\pi$
$727$	−5.96351	−0.221174	−0.110587	+	0.993866i	$0.535273\pi$
$728$	16.6751	0.618021
$729$	28.4301	1.05297
$730$	−17.4475	−0.645759
$731$	5.46209	0.202023
$732$	96.5811	3.56974
$733$	−15.8275	−0.584602	−0.292301	−	0.956326i	$-0.594421\pi$
$733$	−15.8275	−0.584602	−0.292301	+	0.956326i	$0.594421\pi$
$734$	35.0007	1.29190
$735$	−11.2338	−0.414366
$736$	39.5710	1.45860
$737$	1.81054	0.0666922
$738$	3.16182	0.116388
$739$	−6.53604	−0.240432	−0.120216	−	0.992748i	$-0.538359\pi$
$739$	−6.53604	−0.240432	−0.120216	+	0.992748i	$0.538359\pi$
$740$	58.1823	2.13883
$741$	15.4598	0.567931
$742$	−24.5393	−0.900865
$743$	47.9485	1.75906	0.879530	−	0.475843i	$-0.157857\pi$
$743$	47.9485	1.75906	0.879530	+	0.475843i	$0.157857\pi$
$744$	−51.7319	−1.89658
$745$	13.8411	0.507100
$746$	−42.5295	−1.55712
$747$	0.697770	0.0255301
$748$	−6.14255	−0.224594
$749$	7.28509	0.266191
$750$	47.0071	1.71646
$751$	27.1382	0.990288	0.495144	−	0.868811i	$-0.335115\pi$
$751$	27.1382	0.990288	0.495144	+	0.868811i	$0.335115\pi$
$752$	−21.6720	−0.790297
$753$	42.8780	1.56256
$754$	−25.2503	−0.919561
$755$	−18.7236	−0.681423
$756$	−34.2776	−1.24667
$757$	29.8605	1.08530	0.542650	−	0.839959i	$-0.317421\pi$
$757$	29.8605	1.08530	0.542650	+	0.839959i	$0.317421\pi$
$758$	−17.0035	−0.617596
$759$	−10.1707	−0.369172
$760$	−48.0195	−1.74185
$761$	−24.4630	−0.886782	−0.443391	−	0.896328i	$-0.646225\pi$
$761$	−24.4630	−0.886782	−0.443391	+	0.896328i	$0.646225\pi$
$762$	−71.6463	−2.59547
$763$	2.25326	0.0815734
$764$	53.4227	1.93277
$765$	0.236491	0.00855037
$766$	−22.4444	−0.810948
$767$	5.34045	0.192832
$768$	37.1315	1.33987
$769$	0.176870	0.00637810	0.00318905	−	0.999995i	$-0.498985\pi$
$769$	0.176870	0.00637810	0.00318905	+	0.999995i	$0.498985\pi$
$770$	6.01470	0.216755
$771$	43.3641	1.56172
$772$	−26.5956	−0.957198
$773$	49.5675	1.78282	0.891409	−	0.453199i	$-0.149717\pi$
$773$	49.5675	1.78282	0.891409	+	0.453199i	$0.149717\pi$
$774$	2.56688	0.0922646
$775$	14.5550	0.522830
$776$	62.6124	2.24766
$777$	−21.7716	−0.781052
$778$	61.4938	2.20466
$779$	−35.4665	−1.27072
$780$	17.9613	0.643119
$781$	5.68448	0.203407
$782$	12.0029	0.429223
$783$	29.8236	1.06581
$784$	−44.6847	−1.59588
$785$	30.7432	1.09727
$786$	12.2992	0.438697
$787$	−27.0932	−0.965768	−0.482884	−	0.875684i	$-0.660411\pi$
$787$	−27.0932	−0.965768	−0.482884	+	0.875684i	$0.660411\pi$
$788$	13.5106	0.481297
$789$	46.7484	1.66429
$790$	26.0733	0.927645
$791$	21.3235	0.758178
$792$	−1.65862	−0.0589365
$793$	−21.3768	−0.759114
$794$	52.7057	1.87046
$795$	−15.1874	−0.538641
$796$	14.3845	0.509845
$797$	−53.6858	−1.90165	−0.950825	−	0.309729i	$-0.899762\pi$
$797$	−53.6858	−1.90165	−0.950825	+	0.309729i	$0.899762\pi$
$798$	31.2727	1.10704
$799$	−2.49124	−0.0881338
$800$	28.1884	0.996610
$801$	0.462686	0.0163482
$802$	−17.6566	−0.623476
$803$	6.75992	0.238552
$804$	10.9369	0.385714
$805$	−8.24536	−0.290611
$806$	19.9278	0.701925
$807$	−29.2386	−1.02925
$808$	−128.829	−4.53218
$809$	10.3471	0.363784	0.181892	−	0.983318i	$-0.441778\pi$
$809$	10.3471	0.363784	0.181892	+	0.983318i	$0.441778\pi$
$810$	−28.4029	−0.997976
$811$	32.9961	1.15865	0.579324	−	0.815097i	$-0.303316\pi$
$811$	32.9961	1.15865	0.579324	+	0.815097i	$0.303316\pi$
$812$	−35.8331	−1.25750
$813$	5.42307	0.190195
$814$	−32.1324	−1.12624
$815$	−19.1105	−0.669411
$816$	−14.6046	−0.511263
$817$	−28.7929	−1.00734
$818$	−45.7925	−1.60110
$819$	0.432906	0.0151270
$820$	−41.2052	−1.43895
$821$	24.6510	0.860325	0.430163	−	0.902751i	$-0.358456\pi$
$821$	24.6510	0.860325	0.430163	+	0.902751i	$0.358456\pi$
$822$	44.3280	1.54612
$823$	19.9677	0.696030	0.348015	−	0.937489i	$-0.386856\pi$
$823$	19.9677	0.696030	0.348015	+	0.937489i	$0.386856\pi$
$824$	57.5335	2.00427
$825$	−7.24508	−0.252241
$826$	10.8029	0.375879
$827$	14.4643	0.502972	0.251486	−	0.967861i	$-0.419081\pi$
$827$	14.4643	0.502972	0.251486	+	0.967861i	$0.419081\pi$
$828$	3.95723	0.137523
$829$	25.8059	0.896277	0.448138	−	0.893964i	$-0.352087\pi$
$829$	25.8059	0.896277	0.448138	+	0.893964i	$0.352087\pi$
$830$	−12.9619	−0.449915
$831$	−31.2833	−1.08520
$832$	8.19997	0.284283
$833$	−5.13659	−0.177972
$834$	49.3232	1.70792
$835$	−14.4598	−0.500404
$836$	32.3799	1.11988
$837$	−23.5371	−0.813560
$838$	−81.5647	−2.81761
$839$	4.28073	0.147787	0.0738936	−	0.997266i	$-0.476457\pi$
$839$	4.28073	0.147787	0.0738936	+	0.997266i	$0.476457\pi$
$840$	20.8762	0.720296
$841$	2.17693	0.0750665
$842$	−11.0899	−0.382184
$843$	−49.1572	−1.69306
$844$	28.6369	0.985722
$845$	12.9597	0.445828
$846$	−1.17074	−0.0402510
$847$	12.6854	0.435875
$848$	−60.4106	−2.07451
$849$	−18.3201	−0.628745
$850$	8.55028	0.293272
$851$	44.0493	1.50999
$852$	34.3381	1.17640
$853$	−11.5125	−0.394179	−0.197089	−	0.980386i	$-0.563149\pi$
$853$	−11.5125	−0.394179	−0.197089	+	0.980386i	$0.563149\pi$
$854$	−43.2418	−1.47971
$855$	−1.24664	−0.0426343
$856$	37.3185	1.27552
$857$	7.35430	0.251218	0.125609	−	0.992080i	$-0.459911\pi$
$857$	7.35430	0.251218	0.125609	+	0.992080i	$0.459911\pi$
$858$	−9.91951	−0.338647
$859$	−23.4653	−0.800625	−0.400313	−	0.916379i	$-0.631098\pi$
$859$	−23.4653	−0.800625	−0.400313	+	0.916379i	$0.631098\pi$
$860$	−33.4518	−1.14070
$861$	15.4188	0.525472
$862$	−77.4037	−2.63638
$863$	40.6181	1.38266	0.691328	−	0.722541i	$-0.257026\pi$
$863$	40.6181	1.38266	0.691328	+	0.722541i	$0.257026\pi$
$864$	−45.5839	−1.55079
$865$	17.2354	0.586021
$866$	83.6498	2.84254
$867$	−1.67883	−0.0570160
$868$	28.2798	0.959880
$869$	−10.1019	−0.342685
$870$	−31.6117	−1.07174
$871$	−2.42072	−0.0820231
$872$	11.5425	0.390879
$873$	1.62549	0.0550147
$874$	−63.2723	−2.14022
$875$	−14.7650	−0.499148
$876$	40.8345	1.37967
$877$	−22.7991	−0.769872	−0.384936	−	0.922943i	$-0.625776\pi$
$877$	−22.7991	−0.769872	−0.384936	+	0.922943i	$0.625776\pi$
$878$	−93.7703	−3.16460
$879$	35.5924	1.20050
$880$	14.8069	0.499142
$881$	−0.592317	−0.0199557	−0.00997784	−	0.999950i	$-0.503176\pi$
$881$	−0.592317	−0.0199557	−0.00997784	+	0.999950i	$0.503176\pi$
$882$	−2.41391	−0.0812807
$883$	6.74661	0.227041	0.113521	−	0.993536i	$-0.463787\pi$
$883$	6.74661	0.227041	0.113521	+	0.993536i	$0.463787\pi$
$884$	8.21269	0.276223
$885$	6.68589	0.224744
$886$	−53.7847	−1.80693
$887$	−7.41305	−0.248906	−0.124453	−	0.992226i	$-0.539718\pi$
$887$	−7.41305	−0.248906	−0.124453	+	0.992226i	$0.539718\pi$
$888$	−111.527	−3.74260
$889$	22.5042	0.754767
$890$	−8.59495	−0.288103
$891$	11.0045	0.368666
$892$	−67.4150	−2.25722
$893$	13.1324	0.439458
$894$	−46.1752	−1.54433
$895$	23.6615	0.790916
$896$	−6.71258	−0.224252
$897$	13.5983	0.454036
$898$	−21.8461	−0.729014
$899$	−24.6051	−0.820627
$900$	2.81893	0.0939644
$901$	−6.94432	−0.231349
$902$	22.7564	0.757706
$903$	12.5175	0.416558
$904$	109.232	3.63300
$905$	20.2049	0.671635
$906$	62.4637	2.07522
$907$	−49.5641	−1.64575	−0.822875	−	0.568223i	$-0.807631\pi$
$907$	−49.5641	−1.64575	−0.822875	+	0.568223i	$0.807631\pi$
$908$	−69.3363	−2.30100
$909$	−3.34455	−0.110932
$910$	−8.04175	−0.266581
$911$	20.6534	0.684277	0.342139	−	0.939649i	$-0.388849\pi$
$911$	20.6534	0.684277	0.342139	+	0.939649i	$0.388849\pi$
$912$	76.9869	2.54929
$913$	5.02202	0.166205
$914$	−79.6910	−2.63594
$915$	−26.7624	−0.884738
$916$	−36.7377	−1.21385
$917$	−3.86319	−0.127574
$918$	−13.8268	−0.456352
$919$	−36.3247	−1.19824	−0.599120	−	0.800659i	$-0.704483\pi$
$919$	−36.3247	−1.19824	−0.599120	+	0.800659i	$0.704483\pi$
$920$	−42.2376	−1.39253
$921$	29.8952	0.985081
$922$	−39.0039	−1.28452
$923$	−7.60024	−0.250165
$924$	−14.0769	−0.463098
$925$	31.3785	1.03172
$926$	−50.8827	−1.67211
$927$	1.49364	0.0490576
$928$	−47.6524	−1.56427
$929$	38.7718	1.27206	0.636030	−	0.771664i	$-0.280575\pi$
$929$	38.7718	1.27206	0.636030	+	0.771664i	$0.280575\pi$
$930$	24.9483	0.818085
$931$	27.0771	0.887416
$932$	−105.060	−3.44137
$933$	25.4521	0.833263
$934$	−80.3625	−2.62954
$935$	1.70209	0.0556642
$936$	2.21760	0.0724846
$937$	44.2120	1.44434	0.722171	−	0.691715i	$-0.243144\pi$
$937$	44.2120	1.44434	0.722171	+	0.691715i	$0.243144\pi$
$938$	−4.89673	−0.159884
$939$	15.4170	0.503115
$940$	15.2573	0.497637
$941$	−55.6405	−1.81383	−0.906914	−	0.421315i	$-0.861569\pi$
$941$	−55.6405	−1.81383	−0.906914	+	0.421315i	$0.861569\pi$
$942$	−102.562	−3.34165
$943$	−31.1960	−1.01588
$944$	26.5944	0.865574
$945$	9.49826	0.308978
$946$	18.4745	0.600657
$947$	−6.59575	−0.214333	−0.107167	−	0.994241i	$-0.534178\pi$
$947$	−6.59575	−0.214333	−0.107167	+	0.994241i	$0.534178\pi$
$948$	−61.0225	−1.98192
$949$	−9.03812	−0.293390
$950$	−45.0721	−1.46233
$951$	29.3517	0.951793
$952$	9.54548	0.309371
$953$	−58.5647	−1.89710	−0.948548	−	0.316632i	$-0.897448\pi$
$953$	−58.5647	−1.89710	−0.948548	+	0.316632i	$0.897448\pi$
$954$	−3.26344	−0.105658
$955$	−14.8033	−0.479024
$956$	105.278	3.40492
$957$	12.2478	0.395915
$958$	76.0676	2.45763
$959$	−13.9235	−0.449612
$960$	10.2658	0.331328
$961$	−11.5814	−0.373593
$962$	42.9615	1.38514
$963$	0.968834	0.0312202
$964$	−29.5304	−0.951109
$965$	7.36959	0.237236
$966$	27.5072	0.885030
$967$	−54.2860	−1.74572	−0.872860	−	0.487971i	$-0.837737\pi$
$967$	−54.2860	−1.74572	−0.872860	+	0.487971i	$0.837737\pi$
$968$	64.9820	2.08860
$969$	8.84979	0.284296
$970$	−30.1955	−0.969519
$971$	−5.73432	−0.184023	−0.0920115	−	0.995758i	$-0.529330\pi$
$971$	−5.73432	−0.184023	−0.0920115	+	0.995758i	$0.529330\pi$
$972$	−8.85697	−0.284087
$973$	−15.4925	−0.496666
$974$	−32.6376	−1.04578
$975$	9.68679	0.310225
$976$	−106.453	−3.40746
$977$	52.4158	1.67693	0.838465	−	0.544955i	$-0.183453\pi$
$977$	52.4158	1.67693	0.838465	+	0.544955i	$0.183453\pi$
$978$	63.7542	2.03863
$979$	3.33007	0.106429
$980$	31.4584	1.00490
$981$	0.299658	0.00956733
$982$	59.0557	1.88454
$983$	−37.2581	−1.18835	−0.594174	−	0.804336i	$-0.702521\pi$
$983$	−37.2581	−1.18835	−0.594174	+	0.804336i	$0.702521\pi$
$984$	78.9843	2.51793
$985$	−3.74377	−0.119286
$986$	−14.4542	−0.460316
$987$	−5.70921	−0.181726
$988$	−43.2925	−1.37732
$989$	−25.3261	−0.805322
$990$	0.799887	0.0254221
$991$	−16.2786	−0.517107	−0.258554	−	0.965997i	$-0.583246\pi$
$991$	−16.2786	−0.517107	−0.258554	+	0.965997i	$0.583246\pi$
$992$	37.6077	1.19405
$993$	26.5651	0.843018
$994$	−15.3740	−0.487635
$995$	−3.98591	−0.126362
$996$	30.3364	0.961245
$997$	−43.0923	−1.36475	−0.682373	−	0.731004i	$-0.739052\pi$
$997$	−43.0923	−1.36475	−0.682373	+	0.731004i	$0.739052\pi$
$998$	−79.3478	−2.51171
$999$	−50.7427	−1.60543

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.d.1.6	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.d.1.6	✓	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)

\(f(q)\)	\(=\)	\(q-2.58868 q^{2} -1.67883 q^{3} +4.70126 q^{4} -1.30271 q^{5} +4.34594 q^{6} -1.36507 q^{7} -6.99268 q^{8} -0.181538 q^{9} +O(q^{10})\)	\(q-2.58868 q^{2} -1.67883 q^{3} +4.70126 q^{4} -1.30271 q^{5} +4.34594 q^{6} -1.36507 q^{7} -6.99268 q^{8} -0.181538 q^{9} +3.37229 q^{10} -1.30658 q^{11} -7.89260 q^{12} +1.74691 q^{13} +3.53372 q^{14} +2.18702 q^{15} +8.69929 q^{16} +1.00000 q^{17} +0.469945 q^{18} -5.27141 q^{19} -6.12436 q^{20} +2.29171 q^{21} +3.38231 q^{22} -4.63670 q^{23} +11.7395 q^{24} -3.30295 q^{25} -4.52220 q^{26} +5.34125 q^{27} -6.41753 q^{28} +5.58363 q^{29} -5.66150 q^{30} -4.40665 q^{31} -8.53430 q^{32} +2.19352 q^{33} -2.58868 q^{34} +1.77828 q^{35} -0.853458 q^{36} -9.50015 q^{37} +13.6460 q^{38} -2.93277 q^{39} +9.10942 q^{40} +6.72808 q^{41} -5.93250 q^{42} +5.46209 q^{43} -6.14255 q^{44} +0.236491 q^{45} +12.0029 q^{46} -2.49124 q^{47} -14.6046 q^{48} -5.13659 q^{49} +8.55028 q^{50} -1.67883 q^{51} +8.21269 q^{52} -6.94432 q^{53} -13.8268 q^{54} +1.70209 q^{55} +9.54548 q^{56} +8.84979 q^{57} -14.4542 q^{58} +3.05708 q^{59} +10.2817 q^{60} -12.2369 q^{61} +11.4074 q^{62} +0.247812 q^{63} +4.69398 q^{64} -2.27572 q^{65} -5.67831 q^{66} -1.38571 q^{67} +4.70126 q^{68} +7.78421 q^{69} -4.60340 q^{70} -4.35067 q^{71} +1.26944 q^{72} -5.17377 q^{73} +24.5928 q^{74} +5.54509 q^{75} -24.7823 q^{76} +1.78356 q^{77} +7.59199 q^{78} +7.73161 q^{79} -11.3326 q^{80} -8.42243 q^{81} -17.4168 q^{82} -3.84365 q^{83} +10.7739 q^{84} -1.30271 q^{85} -14.1396 q^{86} -9.37395 q^{87} +9.13647 q^{88} -2.54870 q^{89} -0.612200 q^{90} -2.38465 q^{91} -21.7983 q^{92} +7.39801 q^{93} +6.44902 q^{94} +6.86711 q^{95} +14.3276 q^{96} -8.95400 q^{97} +13.2970 q^{98} +0.237194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 21 q^{3} + 127 q^{4} + 27 q^{5} + 17 q^{6} + 39 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 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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