LMFDB - Embedded newform 6001.2.a.a.1.11

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:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.49146 q^{2} -2.38691 q^{3} +4.20738 q^{4} -2.02282 q^{5} +5.94689 q^{6} +1.32918 q^{7} -5.49960 q^{8} +2.69734 q^{9} +O(q^{10})$	\(q-2.49146 q^{2} -2.38691 q^{3} +4.20738 q^{4} -2.02282 q^{5} +5.94689 q^{6} +1.32918 q^{7} -5.49960 q^{8} +2.69734 q^{9} +5.03978 q^{10} -1.22239 q^{11} -10.0426 q^{12} +2.35128 q^{13} -3.31159 q^{14} +4.82829 q^{15} +5.28728 q^{16} -1.00000 q^{17} -6.72031 q^{18} +0.719962 q^{19} -8.51077 q^{20} -3.17263 q^{21} +3.04554 q^{22} -4.75028 q^{23} +13.1270 q^{24} -0.908198 q^{25} -5.85813 q^{26} +0.722426 q^{27} +5.59235 q^{28} -1.97806 q^{29} -12.0295 q^{30} +9.70448 q^{31} -2.17385 q^{32} +2.91774 q^{33} +2.49146 q^{34} -2.68869 q^{35} +11.3487 q^{36} +6.66745 q^{37} -1.79376 q^{38} -5.61230 q^{39} +11.1247 q^{40} -9.56444 q^{41} +7.90448 q^{42} +8.32205 q^{43} -5.14307 q^{44} -5.45623 q^{45} +11.8351 q^{46} +5.93407 q^{47} -12.6203 q^{48} -5.23329 q^{49} +2.26274 q^{50} +2.38691 q^{51} +9.89273 q^{52} -12.1984 q^{53} -1.79990 q^{54} +2.47268 q^{55} -7.30994 q^{56} -1.71848 q^{57} +4.92827 q^{58} -4.33932 q^{59} +20.3144 q^{60} -5.60577 q^{61} -24.1783 q^{62} +3.58524 q^{63} -5.15849 q^{64} -4.75622 q^{65} -7.26944 q^{66} -7.31982 q^{67} -4.20738 q^{68} +11.3385 q^{69} +6.69876 q^{70} +9.42354 q^{71} -14.8343 q^{72} -5.81720 q^{73} -16.6117 q^{74} +2.16779 q^{75} +3.02915 q^{76} -1.62478 q^{77} +13.9828 q^{78} -2.41892 q^{79} -10.6952 q^{80} -9.81638 q^{81} +23.8294 q^{82} -1.85069 q^{83} -13.3484 q^{84} +2.02282 q^{85} -20.7341 q^{86} +4.72146 q^{87} +6.72267 q^{88} +12.8678 q^{89} +13.5940 q^{90} +3.12527 q^{91} -19.9862 q^{92} -23.1637 q^{93} -14.7845 q^{94} -1.45635 q^{95} +5.18879 q^{96} +2.76207 q^{97} +13.0385 q^{98} -3.29721 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.49146	−1.76173	−0.880865	−	0.473368i	$-0.843038\pi$
$2$	−2.49146	−1.76173	−0.880865	+	0.473368i	$0.843038\pi$
$3$	−2.38691	−1.37808	−0.689042	−	0.724722i	$-0.741968\pi$
$3$	−2.38691	−1.37808	−0.689042	+	0.724722i	$0.741968\pi$
$4$	4.20738	2.10369
$5$	−2.02282	−0.904633	−0.452316	−	0.891858i	$-0.649402\pi$
$5$	−2.02282	−0.904633	−0.452316	+	0.891858i	$0.649402\pi$
$6$	5.94689	2.42781
$7$	1.32918	0.502382	0.251191	−	0.967938i	$-0.419178\pi$
$7$	1.32918	0.502382	0.251191	+	0.967938i	$0.419178\pi$
$8$	−5.49960	−1.94440
$9$	2.69734	0.899113
$10$	5.03978	1.59372
$11$	−1.22239	−0.368565	−0.184283	−	0.982873i	$-0.558996\pi$
$11$	−1.22239	−0.368565	−0.184283	+	0.982873i	$0.558996\pi$
$12$	−10.0426	−2.89906
$13$	2.35128	0.652128	0.326064	−	0.945348i	$-0.394277\pi$
$13$	2.35128	0.652128	0.326064	+	0.945348i	$0.394277\pi$
$14$	−3.31159	−0.885061
$15$	4.82829	1.24666
$16$	5.28728	1.32182
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−6.72031	−1.58399
$19$	0.719962	0.165171	0.0825853	−	0.996584i	$-0.473682\pi$
$19$	0.719962	0.165171	0.0825853	+	0.996584i	$0.473682\pi$
$20$	−8.51077	−1.90307
$21$	−3.17263	−0.692324
$22$	3.04554	0.649312
$23$	−4.75028	−0.990502	−0.495251	−	0.868750i	$-0.664924\pi$
$23$	−4.75028	−0.990502	−0.495251	+	0.868750i	$0.664924\pi$
$24$	13.1270	2.67955
$25$	−0.908198	−0.181640
$26$	−5.85813	−1.14887
$27$	0.722426	0.139031
$28$	5.59235	1.05686
$29$	−1.97806	−0.367317	−0.183659	−	0.982990i	$-0.558794\pi$
$29$	−1.97806	−0.367317	−0.183659	+	0.982990i	$0.558794\pi$
$30$	−12.0295	−2.19628
$31$	9.70448	1.74298	0.871488	−	0.490416i	$-0.163155\pi$
$31$	9.70448	1.74298	0.871488	+	0.490416i	$0.163155\pi$
$32$	−2.17385	−0.384287
$33$	2.91774	0.507913
$34$	2.49146	0.427282
$35$	−2.68869	−0.454471
$36$	11.3487	1.89145
$37$	6.66745	1.09612	0.548061	−	0.836438i	$-0.315366\pi$
$37$	6.66745	1.09612	0.548061	+	0.836438i	$0.315366\pi$
$38$	−1.79376	−0.290986
$39$	−5.61230	−0.898687
$40$	11.1247	1.75897
$41$	−9.56444	−1.49371	−0.746857	−	0.664984i	$-0.768438\pi$
$41$	−9.56444	−1.49371	−0.746857	+	0.664984i	$0.768438\pi$
$42$	7.90448	1.21969
$43$	8.32205	1.26910	0.634551	−	0.772881i	$-0.281185\pi$
$43$	8.32205	1.26910	0.634551	+	0.772881i	$0.281185\pi$
$44$	−5.14307	−0.775347
$45$	−5.45623	−0.813367
$46$	11.8351	1.74500
$47$	5.93407	0.865573	0.432787	−	0.901496i	$-0.357530\pi$
$47$	5.93407	0.865573	0.432787	+	0.901496i	$0.357530\pi$
$48$	−12.6203	−1.82158
$49$	−5.23329	−0.747612
$50$	2.26274	0.320000
$51$	2.38691	0.334234
$52$	9.89273	1.37188
$53$	−12.1984	−1.67557	−0.837787	−	0.545997i	$-0.816151\pi$
$53$	−12.1984	−1.67557	−0.837787	+	0.545997i	$0.816151\pi$
$54$	−1.79990	−0.244935
$55$	2.47268	0.333416
$56$	−7.30994	−0.976832
$57$	−1.71848	−0.227619
$58$	4.92827	0.647113
$59$	−4.33932	−0.564931	−0.282466	−	0.959277i	$-0.591152\pi$
$59$	−4.33932	−0.564931	−0.282466	+	0.959277i	$0.591152\pi$
$60$	20.3144	2.62258
$61$	−5.60577	−0.717745	−0.358873	−	0.933387i	$-0.616839\pi$
$61$	−5.60577	−0.717745	−0.358873	+	0.933387i	$0.616839\pi$
$62$	−24.1783	−3.07065
$63$	3.58524	0.451698
$64$	−5.15849	−0.644811
$65$	−4.75622	−0.589937
$66$	−7.26944	−0.894806
$67$	−7.31982	−0.894259	−0.447129	−	0.894469i	$-0.647554\pi$
$67$	−7.31982	−0.894259	−0.447129	+	0.894469i	$0.647554\pi$
$68$	−4.20738	−0.510220
$69$	11.3385	1.36499
$70$	6.69876	0.800655
$71$	9.42354	1.11837	0.559184	−	0.829044i	$-0.311115\pi$
$71$	9.42354	1.11837	0.559184	+	0.829044i	$0.311115\pi$
$72$	−14.8343	−1.74824
$73$	−5.81720	−0.680852	−0.340426	−	0.940271i	$-0.610571\pi$
$73$	−5.81720	−0.680852	−0.340426	+	0.940271i	$0.610571\pi$
$74$	−16.6117	−1.93107
$75$	2.16779	0.250314
$76$	3.02915	0.347468
$77$	−1.62478	−0.185160
$78$	13.9828	1.58324
$79$	−2.41892	−0.272150	−0.136075	−	0.990699i	$-0.543449\pi$
$79$	−2.41892	−0.272150	−0.136075	+	0.990699i	$0.543449\pi$
$80$	−10.6952	−1.19576
$81$	−9.81638	−1.09071
$82$	23.8294	2.63152
$83$	−1.85069	−0.203140	−0.101570	−	0.994828i	$-0.532387\pi$
$83$	−1.85069	−0.203140	−0.101570	+	0.994828i	$0.532387\pi$
$84$	−13.3484	−1.45643
$85$	2.02282	0.219406
$86$	−20.7341	−2.23581
$87$	4.72146	0.506194
$88$	6.72267	0.716639
$89$	12.8678	1.36399	0.681994	−	0.731358i	$-0.261113\pi$
$89$	12.8678	1.36399	0.681994	+	0.731358i	$0.261113\pi$
$90$	13.5940	1.43293
$91$	3.12527	0.327617
$92$	−19.9862	−2.08371
$93$	−23.1637	−2.40197
$94$	−14.7845	−1.52491
$95$	−1.45635	−0.149419
$96$	5.18879	0.529579
$97$	2.76207	0.280446	0.140223	−	0.990120i	$-0.455218\pi$
$97$	2.76207	0.280446	0.140223	+	0.990120i	$0.455218\pi$
$98$	13.0385	1.31709
$99$	−3.29721	−0.331382
$100$	−3.82113	−0.382113
$101$	−2.11544	−0.210494	−0.105247	−	0.994446i	$-0.533563\pi$
$101$	−2.11544	−0.210494	−0.105247	+	0.994446i	$0.533563\pi$
$102$	−5.94689	−0.588830
$103$	3.50706	0.345561	0.172780	−	0.984960i	$-0.444725\pi$
$103$	3.50706	0.345561	0.172780	+	0.984960i	$0.444725\pi$
$104$	−12.9311	−1.26800
$105$	6.41765	0.626299
$106$	30.3918	2.95191
$107$	6.89878	0.666930	0.333465	−	0.942762i	$-0.391782\pi$
$107$	6.89878	0.666930	0.333465	+	0.942762i	$0.391782\pi$
$108$	3.03952	0.292478
$109$	1.64876	0.157922	0.0789612	−	0.996878i	$-0.474840\pi$
$109$	1.64876	0.157922	0.0789612	+	0.996878i	$0.474840\pi$
$110$	−6.16059	−0.587389
$111$	−15.9146	−1.51055
$112$	7.02773	0.664058
$113$	1.64542	0.154788	0.0773940	−	0.997001i	$-0.475340\pi$
$113$	1.64542	0.154788	0.0773940	+	0.997001i	$0.475340\pi$
$114$	4.28154	0.401003
$115$	9.60896	0.896040
$116$	−8.32246	−0.772721
$117$	6.34220	0.586337
$118$	10.8112	0.995256
$119$	−1.32918	−0.121846
$120$	−26.5537	−2.42401
$121$	−9.50576	−0.864160
$122$	13.9666	1.26447
$123$	22.8295	2.05846
$124$	40.8304	3.66668
$125$	11.9512	1.06895
$126$	−8.93249	−0.795770
$127$	−5.27044	−0.467676	−0.233838	−	0.972276i	$-0.575129\pi$
$127$	−5.27044	−0.467676	−0.233838	+	0.972276i	$0.575129\pi$
$128$	17.1999	1.52027
$129$	−19.8640	−1.74893
$130$	11.8499	1.03931
$131$	3.55560	0.310654	0.155327	−	0.987863i	$-0.450357\pi$
$131$	3.55560	0.310654	0.155327	+	0.987863i	$0.450357\pi$
$132$	12.2760	1.06849
$133$	0.956957	0.0829787
$134$	18.2371	1.57544
$135$	−1.46134	−0.125772
$136$	5.49960	0.471587
$137$	9.38550	0.801857	0.400928	−	0.916109i	$-0.368688\pi$
$137$	9.38550	0.801857	0.400928	+	0.916109i	$0.368688\pi$
$138$	−28.2494	−2.40475
$139$	−23.2014	−1.96791	−0.983956	−	0.178409i	$-0.942905\pi$
$139$	−23.2014	−1.96791	−0.983956	+	0.178409i	$0.942905\pi$
$140$	−11.3123	−0.956066
$141$	−14.1641	−1.19283
$142$	−23.4784	−1.97026
$143$	−2.87419	−0.240352
$144$	14.2616	1.18847
$145$	4.00127	0.332287
$146$	14.4933	1.19948
$147$	12.4914	1.03027
$148$	28.0525	2.30590
$149$	6.17921	0.506221	0.253110	−	0.967437i	$-0.418546\pi$
$149$	6.17921	0.506221	0.253110	+	0.967437i	$0.418546\pi$
$150$	−5.40095	−0.440986
$151$	8.48941	0.690858	0.345429	−	0.938445i	$-0.387733\pi$
$151$	8.48941	0.690858	0.345429	+	0.938445i	$0.387733\pi$
$152$	−3.95950	−0.321158
$153$	−2.69734	−0.218067
$154$	4.04807	0.326203
$155$	−19.6304	−1.57675
$156$	−23.6131	−1.89056
$157$	14.0333	1.11998	0.559989	−	0.828500i	$-0.310805\pi$
$157$	14.0333	1.11998	0.559989	+	0.828500i	$0.310805\pi$
$158$	6.02665	0.479454
$159$	29.1164	2.30908
$160$	4.39731	0.347638
$161$	−6.31397	−0.497610
$162$	24.4571	1.92153
$163$	6.91170	0.541366	0.270683	−	0.962669i	$-0.412750\pi$
$163$	6.91170	0.541366	0.270683	+	0.962669i	$0.412750\pi$
$164$	−40.2412	−3.14231
$165$	−5.90206	−0.459475
$166$	4.61093	0.357878
$167$	5.79924	0.448759	0.224379	−	0.974502i	$-0.427964\pi$
$167$	5.79924	0.448759	0.224379	+	0.974502i	$0.427964\pi$
$168$	17.4482	1.34616
$169$	−7.47147	−0.574729
$170$	−5.03978	−0.386533
$171$	1.94198	0.148507
$172$	35.0140	2.66980
$173$	10.0638	0.765140	0.382570	−	0.923927i	$-0.375039\pi$
$173$	10.0638	0.765140	0.382570	+	0.923927i	$0.375039\pi$
$174$	−11.7633	−0.891776
$175$	−1.20716	−0.0912524
$176$	−6.46313	−0.487177
$177$	10.3576	0.778522
$178$	−32.0597	−2.40298
$179$	−23.6919	−1.77081	−0.885407	−	0.464817i	$-0.846120\pi$
$179$	−23.6919	−1.77081	−0.885407	+	0.464817i	$0.846120\pi$
$180$	−22.9564	−1.71107
$181$	2.99167	0.222369	0.111185	−	0.993800i	$-0.464536\pi$
$181$	2.99167	0.222369	0.111185	+	0.993800i	$0.464536\pi$
$182$	−7.78649	−0.577173
$183$	13.3805	0.989113
$184$	26.1246	1.92593
$185$	−13.4871	−0.991588
$186$	57.7115	4.23161
$187$	1.22239	0.0893902
$188$	24.9669	1.82090
$189$	0.960232	0.0698466
$190$	3.62845	0.263235
$191$	−3.88044	−0.280779	−0.140389	−	0.990096i	$-0.544835\pi$
$191$	−3.88044	−0.280779	−0.140389	+	0.990096i	$0.544835\pi$
$192$	12.3128	0.888603
$193$	−4.77926	−0.344019	−0.172009	−	0.985095i	$-0.555026\pi$
$193$	−4.77926	−0.344019	−0.172009	+	0.985095i	$0.555026\pi$
$194$	−6.88160	−0.494070
$195$	11.3527	0.812982
$196$	−22.0184	−1.57274
$197$	26.9696	1.92151	0.960754	−	0.277403i	$-0.0894736\pi$
$197$	26.9696	1.92151	0.960754	+	0.277403i	$0.0894736\pi$
$198$	8.21486	0.583805
$199$	−16.4631	−1.16704	−0.583521	−	0.812098i	$-0.698325\pi$
$199$	−16.4631	−1.16704	−0.583521	+	0.812098i	$0.698325\pi$
$200$	4.99472	0.353180
$201$	17.4718	1.23236
$202$	5.27053	0.370834
$203$	−2.62920	−0.184533
$204$	10.0426	0.703125
$205$	19.3471	1.35126
$206$	−8.73770	−0.608785
$207$	−12.8131	−0.890573
$208$	12.4319	0.861996
$209$	−0.880076	−0.0608761
$210$	−15.9893	−1.10337
$211$	15.5374	1.06964	0.534819	−	0.844967i	$-0.320380\pi$
$211$	15.5374	1.06964	0.534819	+	0.844967i	$0.320380\pi$
$212$	−51.3231	−3.52489
$213$	−22.4931	−1.54120
$214$	−17.1880	−1.17495
$215$	−16.8340	−1.14807
$216$	−3.97305	−0.270332
$217$	12.8990	0.875640
$218$	−4.10782	−0.278216
$219$	13.8851	0.938270
$220$	10.4035	0.701404
$221$	−2.35128	−0.158164
$222$	39.6506	2.66118
$223$	−15.8245	−1.05968	−0.529842	−	0.848096i	$-0.677749\pi$
$223$	−15.8245	−1.05968	−0.529842	+	0.848096i	$0.677749\pi$
$224$	−2.88944	−0.193059
$225$	−2.44972	−0.163314
$226$	−4.09950	−0.272694
$227$	23.7219	1.57448	0.787239	−	0.616648i	$-0.211510\pi$
$227$	23.7219	1.57448	0.787239	+	0.616648i	$0.211510\pi$
$228$	−7.23032	−0.478839
$229$	9.40636	0.621589	0.310795	−	0.950477i	$-0.399405\pi$
$229$	9.40636	0.621589	0.310795	+	0.950477i	$0.399405\pi$
$230$	−23.9404	−1.57858
$231$	3.87820	0.255167
$232$	10.8786	0.714212
$233$	10.2783	0.673354	0.336677	−	0.941620i	$-0.390697\pi$
$233$	10.2783	0.673354	0.336677	+	0.941620i	$0.390697\pi$
$234$	−15.8014	−1.03297
$235$	−12.0036	−0.783026
$236$	−18.2572	−1.18844
$237$	5.77375	0.375045
$238$	3.31159	0.214659
$239$	−2.98984	−0.193397	−0.0966984	−	0.995314i	$-0.530828\pi$
$239$	−2.98984	−0.193397	−0.0966984	+	0.995314i	$0.530828\pi$
$240$	25.5285	1.64786
$241$	16.5345	1.06508	0.532541	−	0.846404i	$-0.321237\pi$
$241$	16.5345	1.06508	0.532541	+	0.846404i	$0.321237\pi$
$242$	23.6832	1.52242
$243$	21.2635	1.36406
$244$	−23.5856	−1.50991
$245$	10.5860	0.676315
$246$	−56.8787	−3.62645
$247$	1.69283	0.107712
$248$	−53.3708	−3.38905
$249$	4.41744	0.279944
$250$	−29.7760	−1.88320
$251$	−4.75486	−0.300124	−0.150062	−	0.988677i	$-0.547947\pi$
$251$	−4.75486	−0.300124	−0.150062	+	0.988677i	$0.547947\pi$
$252$	15.0845	0.950232
$253$	5.80671	0.365064
$254$	13.1311	0.823919
$255$	−4.82829	−0.302359
$256$	−32.5359	−2.03349
$257$	−7.56270	−0.471749	−0.235874	−	0.971784i	$-0.575795\pi$
$257$	−7.56270	−0.471749	−0.235874	+	0.971784i	$0.575795\pi$
$258$	49.4904	3.08114
$259$	8.86223	0.550672
$260$	−20.0112	−1.24104
$261$	−5.33551	−0.330260
$262$	−8.85863	−0.547288
$263$	4.81489	0.296899	0.148450	−	0.988920i	$-0.452572\pi$
$263$	4.81489	0.296899	0.148450	+	0.988920i	$0.452572\pi$
$264$	−16.0464	−0.987588
$265$	24.6751	1.51578
$266$	−2.38422	−0.146186
$267$	−30.7144	−1.87969
$268$	−30.7973	−1.88124
$269$	26.1123	1.59210	0.796048	−	0.605233i	$-0.206920\pi$
$269$	26.1123	1.59210	0.796048	+	0.605233i	$0.206920\pi$
$270$	3.64087	0.221576
$271$	20.6874	1.25667	0.628334	−	0.777944i	$-0.283737\pi$
$271$	20.6874	1.25667	0.628334	+	0.777944i	$0.283737\pi$
$272$	−5.28728	−0.320588
$273$	−7.45974	−0.451484
$274$	−23.3836	−1.41265
$275$	1.11017	0.0669460
$276$	47.7053	2.87152
$277$	−11.6600	−0.700581	−0.350290	−	0.936641i	$-0.613917\pi$
$277$	−11.6600	−0.700581	−0.350290	+	0.936641i	$0.613917\pi$
$278$	57.8053	3.46693
$279$	26.1763	1.56713
$280$	14.7867	0.883675
$281$	2.53039	0.150950	0.0754752	−	0.997148i	$-0.475953\pi$
$281$	2.53039	0.150950	0.0754752	+	0.997148i	$0.475953\pi$
$282$	35.2893	2.10145
$283$	−9.44485	−0.561438	−0.280719	−	0.959790i	$-0.590573\pi$
$283$	−9.44485	−0.561438	−0.280719	+	0.959790i	$0.590573\pi$
$284$	39.6484	2.35270
$285$	3.47619	0.205911
$286$	7.16093	0.423435
$287$	−12.7128	−0.750415
$288$	−5.86362	−0.345517
$289$	1.00000	0.0588235
$290$	−9.96900	−0.585400
$291$	−6.59282	−0.386478
$292$	−24.4752	−1.43230
$293$	−0.773972	−0.0452159	−0.0226080	−	0.999744i	$-0.507197\pi$
$293$	−0.773972	−0.0452159	−0.0226080	+	0.999744i	$0.507197\pi$
$294$	−31.1218	−1.81506
$295$	8.77766	0.511055
$296$	−36.6683	−2.13130
$297$	−0.883088	−0.0512419
$298$	−15.3953	−0.891824
$299$	−11.1692	−0.645934
$300$	9.12070	0.526584
$301$	11.0615	0.637574
$302$	−21.1510	−1.21711
$303$	5.04936	0.290078
$304$	3.80664	0.218326
$305$	11.3395	0.649296
$306$	6.72031	0.384175
$307$	−8.77843	−0.501011	−0.250506	−	0.968115i	$-0.580597\pi$
$307$	−8.77843	−0.501011	−0.250506	+	0.968115i	$0.580597\pi$
$308$	−6.83605	−0.389520
$309$	−8.37103	−0.476212
$310$	48.9084	2.77781
$311$	3.21874	0.182518	0.0912589	−	0.995827i	$-0.470911\pi$
$311$	3.21874	0.182518	0.0912589	+	0.995827i	$0.470911\pi$
$312$	30.8654	1.74741
$313$	22.2149	1.25566	0.627830	−	0.778350i	$-0.283943\pi$
$313$	22.2149	1.25566	0.627830	+	0.778350i	$0.283943\pi$
$314$	−34.9634	−1.97310
$315$	−7.25230	−0.408621
$316$	−10.1773	−0.572519
$317$	11.7594	0.660475	0.330238	−	0.943898i	$-0.392871\pi$
$317$	11.7594	0.660475	0.330238	+	0.943898i	$0.392871\pi$
$318$	−72.5424	−4.06797
$319$	2.41797	0.135380
$320$	10.4347	0.583317
$321$	−16.4668	−0.919085
$322$	15.7310	0.876654
$323$	−0.719962	−0.0400598
$324$	−41.3012	−2.29451
$325$	−2.13543	−0.118452
$326$	−17.2202	−0.953740
$327$	−3.93544	−0.217630
$328$	52.6006	2.90438
$329$	7.88743	0.434848
$330$	14.7048	0.809471
$331$	20.9784	1.15308	0.576538	−	0.817070i	$-0.304403\pi$
$331$	20.9784	1.15308	0.576538	+	0.817070i	$0.304403\pi$
$332$	−7.78657	−0.427344
$333$	17.9844	0.985537
$334$	−14.4486	−0.790592
$335$	14.8067	0.808976
$336$	−16.7746	−0.915128
$337$	15.8399	0.862854	0.431427	−	0.902148i	$-0.358010\pi$
$337$	15.8399	0.862854	0.431427	+	0.902148i	$0.358010\pi$
$338$	18.6149	1.01252
$339$	−3.92747	−0.213311
$340$	8.51077	0.461561
$341$	−11.8627	−0.642400
$342$	−4.83837	−0.261629
$343$	−16.2602	−0.877969
$344$	−45.7680	−2.46764
$345$	−22.9357	−1.23482
$346$	−25.0737	−1.34797
$347$	27.0178	1.45039	0.725197	−	0.688542i	$-0.241749\pi$
$347$	27.0178	1.45039	0.725197	+	0.688542i	$0.241749\pi$
$348$	19.8650	1.06487
$349$	14.5073	0.776557	0.388279	−	0.921542i	$-0.373070\pi$
$349$	14.5073	0.776557	0.388279	+	0.921542i	$0.373070\pi$
$350$	3.00758	0.160762
$351$	1.69863	0.0906660
$352$	2.65730	0.141635
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−25.8055	−1.37155
$355$	−19.0621	−1.01171
$356$	54.1398	2.86941
$357$	3.17263	0.167913
$358$	59.0274	3.11969
$359$	20.9011	1.10312	0.551559	−	0.834136i	$-0.314033\pi$
$359$	20.9011	1.10312	0.551559	+	0.834136i	$0.314033\pi$
$360$	30.0071	1.58151
$361$	−18.4817	−0.972719
$362$	−7.45363	−0.391754
$363$	22.6894	1.19088
$364$	13.1492	0.689205
$365$	11.7672	0.615921
$366$	−33.3369	−1.74255
$367$	−9.58517	−0.500342	−0.250171	−	0.968202i	$-0.580487\pi$
$367$	−9.58517	−0.500342	−0.250171	+	0.968202i	$0.580487\pi$
$368$	−25.1161	−1.30926
$369$	−25.7985	−1.34302
$370$	33.6025	1.74691
$371$	−16.2138	−0.841778
$372$	−97.4586	−5.05299
$373$	31.2534	1.61824	0.809120	−	0.587643i	$-0.199944\pi$
$373$	31.2534	1.61824	0.809120	+	0.587643i	$0.199944\pi$
$374$	−3.04554	−0.157481
$375$	−28.5265	−1.47310
$376$	−32.6350	−1.68302
$377$	−4.65098	−0.239538
$378$	−2.39238	−0.123051
$379$	−34.5539	−1.77491	−0.887457	−	0.460890i	$-0.847530\pi$
$379$	−34.5539	−1.77491	−0.887457	+	0.460890i	$0.847530\pi$
$380$	−6.12743	−0.314331
$381$	12.5801	0.644497
$382$	9.66797	0.494656
$383$	−2.38583	−0.121910	−0.0609552	−	0.998141i	$-0.519415\pi$
$383$	−2.38583	−0.121910	−0.0609552	+	0.998141i	$0.519415\pi$
$384$	−41.0546	−2.09506
$385$	3.28663	0.167502
$386$	11.9073	0.606068
$387$	22.4474	1.14107
$388$	11.6211	0.589971
$389$	−31.0338	−1.57347	−0.786737	−	0.617288i	$-0.788231\pi$
$389$	−31.0338	−1.57347	−0.786737	+	0.617288i	$0.788231\pi$
$390$	−28.2847	−1.43225
$391$	4.75028	0.240232
$392$	28.7810	1.45366
$393$	−8.48689	−0.428107
$394$	−67.1938	−3.38518
$395$	4.89304	0.246196
$396$	−13.8726	−0.697124
$397$	2.75667	0.138353	0.0691767	−	0.997604i	$-0.477963\pi$
$397$	2.75667	0.138353	0.0691767	+	0.997604i	$0.477963\pi$
$398$	41.0173	2.05601
$399$	−2.28417	−0.114352
$400$	−4.80189	−0.240095
$401$	−30.5652	−1.52635	−0.763175	−	0.646191i	$-0.776361\pi$
$401$	−30.5652	−1.52635	−0.763175	+	0.646191i	$0.776361\pi$
$402$	−43.5302	−2.17109
$403$	22.8180	1.13664
$404$	−8.90045	−0.442814
$405$	19.8568	0.986691
$406$	6.55054	0.325098
$407$	−8.15024	−0.403992
$408$	−13.1270	−0.649886
$409$	−18.4441	−0.912002	−0.456001	−	0.889979i	$-0.650719\pi$
$409$	−18.4441	−0.912002	−0.456001	+	0.889979i	$0.650719\pi$
$410$	−48.2027	−2.38056
$411$	−22.4023	−1.10503
$412$	14.7555	0.726953
$413$	−5.76773	−0.283811
$414$	31.9234	1.56895
$415$	3.74362	0.183767
$416$	−5.11134	−0.250604
$417$	55.3795	2.71195
$418$	2.19268	0.107247
$419$	−11.7254	−0.572823	−0.286412	−	0.958107i	$-0.592462\pi$
$419$	−11.7254	−0.572823	−0.286412	+	0.958107i	$0.592462\pi$
$420$	27.0015	1.31754
$421$	9.49353	0.462687	0.231343	−	0.972872i	$-0.425688\pi$
$421$	9.49353	0.462687	0.231343	+	0.972872i	$0.425688\pi$
$422$	−38.7108	−1.88441
$423$	16.0062	0.778248
$424$	67.0861	3.25799
$425$	0.908198	0.0440541
$426$	56.0408	2.71518
$427$	−7.45106	−0.360582
$428$	29.0258	1.40301
$429$	6.86043	0.331225
$430$	41.9413	2.02259
$431$	−33.4533	−1.61139	−0.805694	−	0.592332i	$-0.798207\pi$
$431$	−33.4533	−1.61139	−0.805694	+	0.592332i	$0.798207\pi$
$432$	3.81967	0.183774
$433$	33.8869	1.62850	0.814251	−	0.580513i	$-0.197148\pi$
$433$	33.8869	1.62850	0.814251	+	0.580513i	$0.197148\pi$
$434$	−32.1373	−1.54264
$435$	−9.55066	−0.457919
$436$	6.93695	0.332220
$437$	−3.42002	−0.163602
$438$	−34.5943	−1.65298
$439$	34.6974	1.65602	0.828008	−	0.560717i	$-0.189474\pi$
$439$	34.6974	1.65602	0.828008	+	0.560717i	$0.189474\pi$
$440$	−13.5987	−0.648295
$441$	−14.1159	−0.672188
$442$	5.85813	0.278643
$443$	1.70058	0.0807969	0.0403985	−	0.999184i	$-0.487137\pi$
$443$	1.70058	0.0807969	0.0403985	+	0.999184i	$0.487137\pi$
$444$	−66.9588	−3.17772
$445$	−26.0293	−1.23391
$446$	39.4261	1.86688
$447$	−14.7492	−0.697614
$448$	−6.85655	−0.323941
$449$	−18.4182	−0.869207	−0.434603	−	0.900622i	$-0.643111\pi$
$449$	−18.4182	−0.869207	−0.434603	+	0.900622i	$0.643111\pi$
$450$	6.10337	0.287716
$451$	11.6915	0.550531
$452$	6.92290	0.325626
$453$	−20.2635	−0.952060
$454$	−59.1022	−2.77380
$455$	−6.32186	−0.296373
$456$	9.45098	0.442582
$457$	−30.1303	−1.40944	−0.704718	−	0.709488i	$-0.748926\pi$
$457$	−30.1303	−1.40944	−0.704718	+	0.709488i	$0.748926\pi$
$458$	−23.4356	−1.09507
$459$	−0.722426	−0.0337199
$460$	40.4285	1.88499
$461$	−25.3187	−1.17921	−0.589604	−	0.807692i	$-0.700716\pi$
$461$	−25.3187	−1.17921	−0.589604	+	0.807692i	$0.700716\pi$
$462$	−9.66237	−0.449534
$463$	−16.3498	−0.759842	−0.379921	−	0.925019i	$-0.624049\pi$
$463$	−16.3498	−0.759842	−0.379921	+	0.925019i	$0.624049\pi$
$464$	−10.4586	−0.485527
$465$	46.8561	2.17290
$466$	−25.6080	−1.18627
$467$	−30.0959	−1.39267	−0.696337	−	0.717715i	$-0.745188\pi$
$467$	−30.0959	−1.39267	−0.696337	+	0.717715i	$0.745188\pi$
$468$	26.6841	1.23347
$469$	−9.72935	−0.449259
$470$	29.9064	1.37948
$471$	−33.4962	−1.54342
$472$	23.8645	1.09845
$473$	−10.1728	−0.467747
$474$	−14.3851	−0.660728
$475$	−0.653868	−0.0300015
$476$	−5.59235	−0.256325
$477$	−32.9031	−1.50653
$478$	7.44908	0.340713
$479$	−13.4235	−0.613337	−0.306669	−	0.951816i	$-0.599214\pi$
$479$	−13.4235	−0.613337	−0.306669	+	0.951816i	$0.599214\pi$
$480$	−10.4960	−0.479074
$481$	15.6771	0.714812
$482$	−41.1951	−1.87638
$483$	15.0709	0.685748
$484$	−39.9943	−1.81792
$485$	−5.58718	−0.253701
$486$	−52.9773	−2.40310
$487$	−6.83244	−0.309607	−0.154804	−	0.987945i	$-0.549474\pi$
$487$	−6.83244	−0.309607	−0.154804	+	0.987945i	$0.549474\pi$
$488$	30.8295	1.39559
$489$	−16.4976	−0.746047
$490$	−26.3746	−1.19148
$491$	−9.53620	−0.430363	−0.215181	−	0.976574i	$-0.569034\pi$
$491$	−9.53620	−0.430363	−0.215181	+	0.976574i	$0.569034\pi$
$492$	96.0522	4.33037
$493$	1.97806	0.0890875
$494$	−4.21763	−0.189760
$495$	6.66966	0.299779
$496$	51.3103	2.30390
$497$	12.5256	0.561848
$498$	−11.0059	−0.493185
$499$	5.26305	0.235606	0.117803	−	0.993037i	$-0.462415\pi$
$499$	5.26305	0.235606	0.117803	+	0.993037i	$0.462415\pi$
$500$	50.2833	2.24874
$501$	−13.8423	−0.618427
$502$	11.8465	0.528737
$503$	−37.1708	−1.65736	−0.828682	−	0.559720i	$-0.810909\pi$
$503$	−37.1708	−1.65736	−0.828682	+	0.559720i	$0.810909\pi$
$504$	−19.7174	−0.878282
$505$	4.27915	0.190420
$506$	−14.4672	−0.643145
$507$	17.8337	0.792024
$508$	−22.1747	−0.983845
$509$	42.3860	1.87873	0.939364	−	0.342923i	$-0.111417\pi$
$509$	42.3860	1.87873	0.939364	+	0.342923i	$0.111417\pi$
$510$	12.0295	0.532675
$511$	−7.73209	−0.342048
$512$	46.6621	2.06219
$513$	0.520119	0.0229638
$514$	18.8422	0.831093
$515$	−7.09415	−0.312606
$516$	−83.5753	−3.67920
$517$	−7.25376	−0.319020
$518$	−22.0799	−0.970135
$519$	−24.0215	−1.05443
$520$	26.1573	1.14707
$521$	−41.6291	−1.82380	−0.911901	−	0.410409i	$-0.865386\pi$
$521$	−41.6291	−1.82380	−0.911901	+	0.410409i	$0.865386\pi$
$522$	13.2932	0.581828
$523$	−41.1623	−1.79990	−0.899951	−	0.435992i	$-0.856398\pi$
$523$	−41.1623	−1.79990	−0.899951	+	0.435992i	$0.856398\pi$
$524$	14.9597	0.653520
$525$	2.88137	0.125753
$526$	−11.9961	−0.523056
$527$	−9.70448	−0.422734
$528$	15.4269	0.671370
$529$	−0.434841	−0.0189061
$530$	−61.4771	−2.67039
$531$	−11.7046	−0.507937
$532$	4.02628	0.174561
$533$	−22.4887	−0.974094
$534$	76.5236	3.31150
$535$	−13.9550	−0.603327
$536$	40.2561	1.73880
$537$	56.5504	2.44033
$538$	−65.0578	−2.80484
$539$	6.39713	0.275544
$540$	−6.14840	−0.264585
$541$	32.4361	1.39454	0.697269	−	0.716810i	$-0.254399\pi$
$541$	32.4361	1.39454	0.697269	+	0.716810i	$0.254399\pi$
$542$	−51.5417	−2.21391
$543$	−7.14085	−0.306443
$544$	2.17385	0.0932032
$545$	−3.33514	−0.142862
$546$	18.5857	0.795393
$547$	−37.3987	−1.59905	−0.799527	−	0.600630i	$-0.794917\pi$
$547$	−37.3987	−1.59905	−0.799527	+	0.600630i	$0.794917\pi$
$548$	39.4883	1.68686
$549$	−15.1207	−0.645334
$550$	−2.76596	−0.117941
$551$	−1.42413	−0.0606700
$552$	−62.3571	−2.65410
$553$	−3.21518	−0.136723
$554$	29.0504	1.23423
$555$	32.1924	1.36649
$556$	−97.6169	−4.13988
$557$	−24.9394	−1.05672	−0.528359	−	0.849021i	$-0.677192\pi$
$557$	−24.9394	−1.05672	−0.528359	+	0.849021i	$0.677192\pi$
$558$	−65.2172	−2.76086
$559$	19.5675	0.827617
$560$	−14.2158	−0.600729
$561$	−2.91774	−0.123187
$562$	−6.30437	−0.265934
$563$	−5.44478	−0.229470	−0.114735	−	0.993396i	$-0.536602\pi$
$563$	−5.44478	−0.229470	−0.114735	+	0.993396i	$0.536602\pi$
$564$	−59.5937	−2.50935
$565$	−3.32839	−0.140026
$566$	23.5315	0.989102
$567$	−13.0477	−0.547952
$568$	−51.8257	−2.17456
$569$	−19.8773	−0.833302	−0.416651	−	0.909067i	$-0.636796\pi$
$569$	−19.8773	−0.833302	−0.416651	+	0.909067i	$0.636796\pi$
$570$	−8.66078	−0.362760
$571$	7.79847	0.326356	0.163178	−	0.986597i	$-0.447826\pi$
$571$	7.79847	0.326356	0.163178	+	0.986597i	$0.447826\pi$
$572$	−12.0928	−0.505625
$573$	9.26226	0.386937
$574$	31.6735	1.32203
$575$	4.31419	0.179914
$576$	−13.9142	−0.579758
$577$	15.1064	0.628886	0.314443	−	0.949276i	$-0.398182\pi$
$577$	15.1064	0.628886	0.314443	+	0.949276i	$0.398182\pi$
$578$	−2.49146	−0.103631
$579$	11.4077	0.474086
$580$	16.8348	0.699029
$581$	−2.45990	−0.102054
$582$	16.4257	0.680869
$583$	14.9112	0.617558
$584$	31.9923	1.32385
$585$	−12.8291	−0.530420
$586$	1.92832	0.0796582
$587$	36.5539	1.50874	0.754370	−	0.656449i	$-0.227942\pi$
$587$	36.5539	1.50874	0.754370	+	0.656449i	$0.227942\pi$
$588$	52.5560	2.16737
$589$	6.98686	0.287889
$590$	−21.8692	−0.900341
$591$	−64.3741	−2.64800
$592$	35.2527	1.44888
$593$	−39.5290	−1.62326	−0.811632	−	0.584169i	$-0.801420\pi$
$593$	−39.5290	−1.62326	−0.811632	+	0.584169i	$0.801420\pi$
$594$	2.20018	0.0902744
$595$	2.68869	0.110225
$596$	25.9983	1.06493
$597$	39.2961	1.60828
$598$	27.8277	1.13796
$599$	−31.4179	−1.28370	−0.641850	−	0.766830i	$-0.721833\pi$
$599$	−31.4179	−1.28370	−0.641850	+	0.766830i	$0.721833\pi$
$600$	−11.9220	−0.486712
$601$	−5.80442	−0.236767	−0.118384	−	0.992968i	$-0.537771\pi$
$601$	−5.80442	−0.236767	−0.118384	+	0.992968i	$0.537771\pi$
$602$	−27.5593	−1.12323
$603$	−19.7440	−0.804040
$604$	35.7182	1.45335
$605$	19.2284	0.781747
$606$	−12.5803	−0.511039
$607$	−34.4267	−1.39734	−0.698668	−	0.715446i	$-0.746224\pi$
$607$	−34.4267	−1.39734	−0.698668	+	0.715446i	$0.746224\pi$
$608$	−1.56509	−0.0634729
$609$	6.27566	0.254302
$610$	−28.2518	−1.14388
$611$	13.9527	0.564465
$612$	−11.3487	−0.458745
$613$	21.4954	0.868192	0.434096	−	0.900867i	$-0.357068\pi$
$613$	21.4954	0.868192	0.434096	+	0.900867i	$0.357068\pi$
$614$	21.8711	0.882647
$615$	−46.1799	−1.86215
$616$	8.93562	0.360026
$617$	−9.28116	−0.373645	−0.186823	−	0.982394i	$-0.559819\pi$
$617$	−9.28116	−0.373645	−0.186823	+	0.982394i	$0.559819\pi$
$618$	20.8561	0.838956
$619$	16.6491	0.669185	0.334593	−	0.942363i	$-0.391401\pi$
$619$	16.6491	0.669185	0.334593	+	0.942363i	$0.391401\pi$
$620$	−82.5926	−3.31700
$621$	−3.43172	−0.137710
$622$	−8.01936	−0.321547
$623$	17.1036	0.685243
$624$	−29.6738	−1.18790
$625$	−19.6342	−0.785368
$626$	−55.3475	−2.21213
$627$	2.10066	0.0838924
$628$	59.0434	2.35609
$629$	−6.66745	−0.265849
$630$	18.0688	0.719879
$631$	5.69574	0.226744	0.113372	−	0.993553i	$-0.463835\pi$
$631$	5.69574	0.226744	0.113372	+	0.993553i	$0.463835\pi$
$632$	13.3031	0.529169
$633$	−37.0863	−1.47405
$634$	−29.2982	−1.16358
$635$	10.6612	0.423075
$636$	122.504	4.85759
$637$	−12.3049	−0.487539
$638$	−6.02428	−0.238503
$639$	25.4185	1.00554
$640$	−34.7923	−1.37528
$641$	31.1057	1.22860	0.614302	−	0.789071i	$-0.289438\pi$
$641$	31.1057	1.22860	0.614302	+	0.789071i	$0.289438\pi$
$642$	41.0263	1.61918
$643$	−1.25101	−0.0493348	−0.0246674	−	0.999696i	$-0.507853\pi$
$643$	−1.25101	−0.0493348	−0.0246674	+	0.999696i	$0.507853\pi$
$644$	−26.5652	−1.04682
$645$	40.1813	1.58214
$646$	1.79376	0.0705744
$647$	−30.9383	−1.21631	−0.608155	−	0.793818i	$-0.708090\pi$
$647$	−30.9383	−1.21631	−0.608155	+	0.793818i	$0.708090\pi$
$648$	53.9862	2.12078
$649$	5.30435	0.208214
$650$	5.32034	0.208681
$651$	−30.7887	−1.20670
$652$	29.0801	1.13887
$653$	21.8962	0.856864	0.428432	−	0.903574i	$-0.359066\pi$
$653$	21.8962	0.856864	0.428432	+	0.903574i	$0.359066\pi$
$654$	9.80499	0.383405
$655$	−7.19234	−0.281028
$656$	−50.5699	−1.97442
$657$	−15.6910	−0.612163
$658$	−19.6512	−0.766085
$659$	−27.7913	−1.08259	−0.541297	−	0.840832i	$-0.682066\pi$
$659$	−27.7913	−1.08259	−0.541297	+	0.840832i	$0.682066\pi$
$660$	−24.8322	−0.966593
$661$	25.8464	1.00531	0.502654	−	0.864488i	$-0.332357\pi$
$661$	25.8464	1.00531	0.502654	+	0.864488i	$0.332357\pi$
$662$	−52.2668	−2.03141
$663$	5.61230	0.217964
$664$	10.1781	0.394986
$665$	−1.93575	−0.0750653
$666$	−44.8074	−1.73625
$667$	9.39635	0.363828
$668$	24.3996	0.944050
$669$	37.7716	1.46033
$670$	−36.8903	−1.42520
$671$	6.85245	0.264536
$672$	6.89683	0.266051
$673$	−40.1547	−1.54785	−0.773924	−	0.633278i	$-0.781709\pi$
$673$	−40.1547	−1.54785	−0.773924	+	0.633278i	$0.781709\pi$
$674$	−39.4645	−1.52011
$675$	−0.656105	−0.0252535
$676$	−31.4353	−1.20905
$677$	−1.51317	−0.0581558	−0.0290779	−	0.999577i	$-0.509257\pi$
$677$	−1.51317	−0.0581558	−0.0290779	+	0.999577i	$0.509257\pi$
$678$	9.78513	0.375796
$679$	3.67128	0.140891
$680$	−11.1247	−0.426613
$681$	−56.6220	−2.16976
$682$	29.5554	1.13174
$683$	4.00467	0.153235	0.0766173	−	0.997061i	$-0.475588\pi$
$683$	4.00467	0.153235	0.0766173	+	0.997061i	$0.475588\pi$
$684$	8.17065	0.312413
$685$	−18.9852	−0.725386
$686$	40.5117	1.54674
$687$	−22.4521	−0.856602
$688$	44.0010	1.67752
$689$	−28.6818	−1.09269
$690$	57.1435	2.17542
$691$	0.737159	0.0280429	0.0140214	−	0.999902i	$-0.495537\pi$
$691$	0.737159	0.0280429	0.0140214	+	0.999902i	$0.495537\pi$
$692$	42.3424	1.60962
$693$	−4.38257	−0.166480
$694$	−67.3139	−2.55520
$695$	46.9322	1.78024
$696$	−25.9661	−0.984244
$697$	9.56444	0.362279
$698$	−36.1443	−1.36808
$699$	−24.5334	−0.927938
$700$	−5.07896	−0.191967
$701$	−22.6756	−0.856444	−0.428222	−	0.903674i	$-0.640860\pi$
$701$	−22.6756	−0.856444	−0.428222	+	0.903674i	$0.640860\pi$
$702$	−4.23206	−0.159729
$703$	4.80031	0.181047
$704$	6.30570	0.237655
$705$	28.6514	1.07907
$706$	2.49146	0.0937674
$707$	−2.81179	−0.105748
$708$	43.5782	1.63777
$709$	20.7204	0.778172	0.389086	−	0.921201i	$-0.372791\pi$
$709$	20.7204	0.778172	0.389086	+	0.921201i	$0.372791\pi$
$710$	47.4925	1.78236
$711$	−6.52465	−0.244693
$712$	−70.7679	−2.65214
$713$	−46.0990	−1.72642
$714$	−7.90448	−0.295818
$715$	5.81397	0.217430
$716$	−99.6807	−3.72524
$717$	7.13649	0.266517
$718$	−52.0743	−1.94339
$719$	−2.25522	−0.0841056	−0.0420528	−	0.999115i	$-0.513390\pi$
$719$	−2.25522	−0.0841056	−0.0420528	+	0.999115i	$0.513390\pi$
$720$	−28.8486	−1.07512
$721$	4.66150	0.173604
$722$	46.0463	1.71367
$723$	−39.4664	−1.46777
$724$	12.5871	0.467796
$725$	1.79647	0.0667193
$726$	−56.5297	−2.09801
$727$	38.8814	1.44203	0.721015	−	0.692919i	$-0.243676\pi$
$727$	38.8814	1.44203	0.721015	+	0.692919i	$0.243676\pi$
$728$	−17.1877	−0.637020
$729$	−21.3050	−0.789074
$730$	−29.3174	−1.08509
$731$	−8.32205	−0.307802
$732$	56.2967	2.08079
$733$	−39.9325	−1.47494	−0.737470	−	0.675380i	$-0.763980\pi$
$733$	−39.9325	−1.47494	−0.737470	+	0.675380i	$0.763980\pi$
$734$	23.8811	0.881467
$735$	−25.2678	−0.932018
$736$	10.3264	0.380637
$737$	8.94770	0.329593
$738$	64.2760	2.36603
$739$	−49.9569	−1.83769	−0.918846	−	0.394615i	$-0.870878\pi$
$739$	−49.9569	−1.83769	−0.918846	+	0.394615i	$0.870878\pi$
$740$	−56.7451	−2.08599
$741$	−4.04064	−0.148437
$742$	40.3960	1.48299
$743$	4.22509	0.155004	0.0775018	−	0.996992i	$-0.475306\pi$
$743$	4.22509	0.155004	0.0775018	+	0.996992i	$0.475306\pi$
$744$	127.391	4.67039
$745$	−12.4994	−0.457944
$746$	−77.8666	−2.85090
$747$	−4.99195	−0.182646
$748$	5.14307	0.188049
$749$	9.16970	0.335054
$750$	71.0726	2.59521
$751$	30.6135	1.11710	0.558552	−	0.829470i	$-0.311357\pi$
$751$	30.6135	1.11710	0.558552	+	0.829470i	$0.311357\pi$
$752$	31.3751	1.14413
$753$	11.3494	0.413596
$754$	11.5877	0.422001
$755$	−17.1726	−0.624973
$756$	4.04006	0.146936
$757$	31.4942	1.14467	0.572337	−	0.820018i	$-0.306037\pi$
$757$	31.4942	1.14467	0.572337	+	0.820018i	$0.306037\pi$
$758$	86.0897	3.12692
$759$	−13.8601	−0.503089
$760$	8.00936	0.290530
$761$	−2.66186	−0.0964924	−0.0482462	−	0.998835i	$-0.515363\pi$
$761$	−2.66186	−0.0964924	−0.0482462	+	0.998835i	$0.515363\pi$
$762$	−31.3428	−1.13543
$763$	2.19149	0.0793374
$764$	−16.3265	−0.590672
$765$	5.45623	0.197270
$766$	5.94421	0.214773
$767$	−10.2030	−0.368408
$768$	77.6601	2.80232
$769$	−43.1355	−1.55551	−0.777753	−	0.628570i	$-0.783641\pi$
$769$	−43.1355	−1.55551	−0.777753	+	0.628570i	$0.783641\pi$
$770$	−8.18851	−0.295094
$771$	18.0515	0.650109
$772$	−20.1082	−0.723708
$773$	−37.5501	−1.35058	−0.675292	−	0.737551i	$-0.735982\pi$
$773$	−37.5501	−1.35058	−0.675292	+	0.737551i	$0.735982\pi$
$774$	−55.9268	−2.01025
$775$	−8.81359	−0.316593
$776$	−15.1903	−0.545300
$777$	−21.1533	−0.758872
$778$	77.3194	2.77204
$779$	−6.88603	−0.246718
$780$	47.7650	1.71026
$781$	−11.5193	−0.412191
$782$	−11.8351	−0.423224
$783$	−1.42900	−0.0510684
$784$	−27.6698	−0.988209
$785$	−28.3868	−1.01317
$786$	21.1448	0.754209
$787$	23.6094	0.841585	0.420793	−	0.907157i	$-0.361752\pi$
$787$	23.6094	0.841585	0.420793	+	0.907157i	$0.361752\pi$
$788$	113.472	4.04226
$789$	−11.4927	−0.409151
$790$	−12.1908	−0.433730
$791$	2.18705	0.0777627
$792$	18.1333	0.644339
$793$	−13.1807	−0.468062
$794$	−6.86814	−0.243741
$795$	−58.8972	−2.08887
$796$	−69.2667	−2.45509
$797$	34.8441	1.23424	0.617121	−	0.786868i	$-0.288299\pi$
$797$	34.8441	1.23424	0.617121	+	0.786868i	$0.288299\pi$
$798$	5.69092	0.201457
$799$	−5.93407	−0.209932
$800$	1.97429	0.0698016
$801$	34.7089	1.22638
$802$	76.1519	2.68902
$803$	7.11090	0.250938
$804$	73.5103	2.59251
$805$	12.7720	0.450155
$806$	−56.8501	−2.00246
$807$	−62.3278	−2.19404
$808$	11.6341	0.409285
$809$	10.8563	0.381687	0.190843	−	0.981621i	$-0.438878\pi$
$809$	10.8563	0.381687	0.190843	+	0.981621i	$0.438878\pi$
$810$	−49.4724	−1.73828
$811$	21.6879	0.761565	0.380782	−	0.924665i	$-0.375655\pi$
$811$	21.6879	0.761565	0.380782	+	0.924665i	$0.375655\pi$
$812$	−11.0620	−0.388201
$813$	−49.3788	−1.73179
$814$	20.3060	0.711725
$815$	−13.9811	−0.489738
$816$	12.6203	0.441797
$817$	5.99156	0.209618
$818$	45.9528	1.60670
$819$	8.42991	0.294565
$820$	81.4008	2.84264
$821$	25.5375	0.891264	0.445632	−	0.895216i	$-0.352979\pi$
$821$	25.5375	0.891264	0.445632	+	0.895216i	$0.352979\pi$
$822$	55.8145	1.94676
$823$	17.6793	0.616262	0.308131	−	0.951344i	$-0.400296\pi$
$823$	17.6793	0.616262	0.308131	+	0.951344i	$0.400296\pi$
$824$	−19.2874	−0.671909
$825$	−2.64988	−0.0922572
$826$	14.3701	0.499999
$827$	−29.8019	−1.03632	−0.518158	−	0.855285i	$-0.673382\pi$
$827$	−29.8019	−1.03632	−0.518158	+	0.855285i	$0.673382\pi$
$828$	−53.9096	−1.87349
$829$	−31.7727	−1.10351	−0.551756	−	0.834006i	$-0.686042\pi$
$829$	−31.7727	−1.10351	−0.551756	+	0.834006i	$0.686042\pi$
$830$	−9.32709	−0.323748
$831$	27.8313	0.965459
$832$	−12.1291	−0.420499
$833$	5.23329	0.181323
$834$	−137.976	−4.77772
$835$	−11.7308	−0.405962
$836$	−3.70281	−0.128064
$837$	7.01077	0.242328
$838$	29.2134	1.00916
$839$	1.05865	0.0365488	0.0182744	−	0.999833i	$-0.494183\pi$
$839$	1.05865	0.0365488	0.0182744	+	0.999833i	$0.494183\pi$
$840$	−35.2945	−1.21778
$841$	−25.0873	−0.865078
$842$	−23.6528	−0.815128
$843$	−6.03981	−0.208022
$844$	65.3716	2.25018
$845$	15.1134	0.519918
$846$	−39.8788	−1.37106
$847$	−12.6348	−0.434138
$848$	−64.4962	−2.21481
$849$	22.5440	0.773708
$850$	−2.26274	−0.0776113
$851$	−31.6723	−1.08571
$852$	−94.6371	−3.24221
$853$	1.05609	0.0361599	0.0180799	−	0.999837i	$-0.494245\pi$
$853$	1.05609	0.0361599	0.0180799	+	0.999837i	$0.494245\pi$
$854$	18.5640	0.635248
$855$	−3.92828	−0.134344
$856$	−37.9405	−1.29678
$857$	0.245513	0.00838655	0.00419327	−	0.999991i	$-0.498665\pi$
$857$	0.245513	0.00838655	0.00419327	+	0.999991i	$0.498665\pi$
$858$	−17.0925	−0.583528
$859$	−16.0700	−0.548303	−0.274151	−	0.961687i	$-0.588397\pi$
$859$	−16.0700	−0.548303	−0.274151	+	0.961687i	$0.588397\pi$
$860$	−70.8271	−2.41518
$861$	30.3444	1.03413
$862$	83.3476	2.83883
$863$	24.3543	0.829030	0.414515	−	0.910042i	$-0.363951\pi$
$863$	24.3543	0.829030	0.414515	+	0.910042i	$0.363951\pi$
$864$	−1.57045	−0.0534277
$865$	−20.3573	−0.692170
$866$	−84.4280	−2.86898
$867$	−2.38691	−0.0810637
$868$	54.2709	1.84207
$869$	2.95687	0.100305
$870$	23.7951	0.806730
$871$	−17.2110	−0.583171
$872$	−9.06751	−0.307065
$873$	7.45024	0.252153
$874$	8.52085	0.288222
$875$	15.8853	0.537021
$876$	58.4200	1.97383
$877$	16.7420	0.565338	0.282669	−	0.959217i	$-0.408780\pi$
$877$	16.7420	0.565338	0.282669	+	0.959217i	$0.408780\pi$
$878$	−86.4471	−2.91745
$879$	1.84740	0.0623113
$880$	13.0738	0.440716
$881$	−4.18517	−0.141002	−0.0705009	−	0.997512i	$-0.522460\pi$
$881$	−4.18517	−0.141002	−0.0705009	+	0.997512i	$0.522460\pi$
$882$	35.1693	1.18421
$883$	43.4131	1.46097	0.730484	−	0.682930i	$-0.239295\pi$
$883$	43.4131	1.46097	0.730484	+	0.682930i	$0.239295\pi$
$884$	−9.89273	−0.332729
$885$	−20.9515	−0.704277
$886$	−4.23693	−0.142342
$887$	36.2893	1.21848	0.609238	−	0.792987i	$-0.291475\pi$
$887$	36.2893	1.21848	0.609238	+	0.792987i	$0.291475\pi$
$888$	87.5239	2.93711
$889$	−7.00535	−0.234952
$890$	64.8510	2.17381
$891$	11.9995	0.401997
$892$	−66.5795	−2.22925
$893$	4.27231	0.142967
$894$	36.7471	1.22901
$895$	47.9244	1.60194
$896$	22.8617	0.763756
$897$	26.6600	0.890151
$898$	45.8881	1.53131
$899$	−19.1961	−0.640225
$900$	−10.3069	−0.343563
$901$	12.1984	0.406386
$902$	−29.1289	−0.969887
$903$	−26.4028	−0.878629
$904$	−9.04914	−0.300970
$905$	−6.05161	−0.201162
$906$	50.4856	1.67727
$907$	40.9296	1.35905	0.679523	−	0.733655i	$-0.262187\pi$
$907$	40.9296	1.35905	0.679523	+	0.733655i	$0.262187\pi$
$908$	99.8070	3.31221
$909$	−5.70606	−0.189258
$910$	15.7507	0.522130
$911$	−2.46358	−0.0816220	−0.0408110	−	0.999167i	$-0.512994\pi$
$911$	−2.46358	−0.0816220	−0.0408110	+	0.999167i	$0.512994\pi$
$912$	−9.08611	−0.300871
$913$	2.26227	0.0748704
$914$	75.0684	2.48304
$915$	−27.0663	−0.894784
$916$	39.5761	1.30763
$917$	4.72602	0.156067
$918$	1.79990	0.0594054
$919$	19.3679	0.638889	0.319444	−	0.947605i	$-0.396504\pi$
$919$	19.3679	0.638889	0.319444	+	0.947605i	$0.396504\pi$
$920$	−52.8454	−1.74226
$921$	20.9533	0.690435
$922$	63.0805	2.07745
$923$	22.1574	0.729319
$924$	16.3170	0.536791
$925$	−6.05536	−0.199099
$926$	40.7350	1.33864
$927$	9.45973	0.310698
$928$	4.30002	0.141155
$929$	−22.0537	−0.723559	−0.361779	−	0.932264i	$-0.617831\pi$
$929$	−22.0537	−0.723559	−0.361779	+	0.932264i	$0.617831\pi$
$930$	−116.740	−3.82806
$931$	−3.76777	−0.123484
$932$	43.2447	1.41653
$933$	−7.68283	−0.251525
$934$	74.9828	2.45351
$935$	−2.47268	−0.0808653
$936$	−34.8796	−1.14007
$937$	−2.87637	−0.0939669	−0.0469834	−	0.998896i	$-0.514961\pi$
$937$	−2.87637	−0.0939669	−0.0469834	+	0.998896i	$0.514961\pi$
$938$	24.2403	0.791474
$939$	−53.0249	−1.73040
$940$	−50.5035	−1.64724
$941$	−24.5258	−0.799520	−0.399760	−	0.916620i	$-0.630906\pi$
$941$	−24.5258	−0.799520	−0.399760	+	0.916620i	$0.630906\pi$
$942$	83.4545	2.71909
$943$	45.4338	1.47953
$944$	−22.9432	−0.746737
$945$	−1.94238	−0.0631855
$946$	25.3452	0.824043
$947$	−18.6591	−0.606339	−0.303170	−	0.952937i	$-0.598045\pi$
$947$	−18.6591	−0.606339	−0.303170	+	0.952937i	$0.598045\pi$
$948$	24.2923	0.788978
$949$	−13.6779	−0.444003
$950$	1.62909	0.0528545
$951$	−28.0687	−0.910190
$952$	7.30994	0.236917
$953$	49.9431	1.61782	0.808908	−	0.587935i	$-0.200059\pi$
$953$	49.9431	1.61782	0.808908	+	0.587935i	$0.200059\pi$
$954$	81.9768	2.65410
$955$	7.84944	0.254002
$956$	−12.5794	−0.406847
$957$	−5.77148	−0.186565
$958$	33.4442	1.08053
$959$	12.4750	0.402838
$960$	−24.9067	−0.803859
$961$	63.1770	2.03797
$962$	−39.0588	−1.25931
$963$	18.6083	0.599645
$964$	69.5669	2.24060
$965$	9.66758	0.311211
$966$	−37.5485	−1.20810
$967$	−28.1743	−0.906025	−0.453012	−	0.891504i	$-0.649651\pi$
$967$	−28.1743	−0.906025	−0.453012	+	0.891504i	$0.649651\pi$
$968$	52.2778	1.68027
$969$	1.71848	0.0552057
$970$	13.9202	0.446952
$971$	−29.8743	−0.958712	−0.479356	−	0.877621i	$-0.659130\pi$
$971$	−29.8743	−0.958712	−0.479356	+	0.877621i	$0.659130\pi$
$972$	89.4638	2.86955
$973$	−30.8387	−0.988644
$974$	17.0227	0.545444
$975$	5.09708	0.163237
$976$	−29.6393	−0.948730
$977$	48.0773	1.53813	0.769064	−	0.639171i	$-0.220723\pi$
$977$	48.0773	1.53813	0.769064	+	0.639171i	$0.220723\pi$
$978$	41.1031	1.31433
$979$	−15.7295	−0.502718
$980$	44.5393	1.42276
$981$	4.44726	0.141990
$982$	23.7591	0.758182
$983$	9.30828	0.296888	0.148444	−	0.988921i	$-0.452574\pi$
$983$	9.30828	0.296888	0.148444	+	0.988921i	$0.452574\pi$
$984$	−125.553	−4.00248
$985$	−54.5547	−1.73826
$986$	−4.92827	−0.156948
$987$	−18.8266	−0.599257
$988$	7.12239	0.226594
$989$	−39.5321	−1.25705
$990$	−16.6172	−0.528129
$991$	−33.7837	−1.07318	−0.536588	−	0.843845i	$-0.680287\pi$
$991$	−33.7837	−1.07318	−0.536588	+	0.843845i	$0.680287\pi$
$992$	−21.0961	−0.669802
$993$	−50.0735	−1.58903
$994$	−31.2069	−0.989824
$995$	33.3020	1.05574
$996$	18.5858	0.588915
$997$	−41.6950	−1.32050	−0.660248	−	0.751048i	$-0.729549\pi$
$997$	−41.6950	−1.32050	−0.660248	+	0.751048i	$0.729549\pi$
$998$	−13.1127	−0.415074
$999$	4.81674	0.152395

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.11	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.11	✓	113	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)

\(f(q)\)	\(=\)	\(q-2.49146 q^{2} -2.38691 q^{3} +4.20738 q^{4} -2.02282 q^{5} +5.94689 q^{6} +1.32918 q^{7} -5.49960 q^{8} +2.69734 q^{9} +O(q^{10})\)	\(q-2.49146 q^{2} -2.38691 q^{3} +4.20738 q^{4} -2.02282 q^{5} +5.94689 q^{6} +1.32918 q^{7} -5.49960 q^{8} +2.69734 q^{9} +5.03978 q^{10} -1.22239 q^{11} -10.0426 q^{12} +2.35128 q^{13} -3.31159 q^{14} +4.82829 q^{15} +5.28728 q^{16} -1.00000 q^{17} -6.72031 q^{18} +0.719962 q^{19} -8.51077 q^{20} -3.17263 q^{21} +3.04554 q^{22} -4.75028 q^{23} +13.1270 q^{24} -0.908198 q^{25} -5.85813 q^{26} +0.722426 q^{27} +5.59235 q^{28} -1.97806 q^{29} -12.0295 q^{30} +9.70448 q^{31} -2.17385 q^{32} +2.91774 q^{33} +2.49146 q^{34} -2.68869 q^{35} +11.3487 q^{36} +6.66745 q^{37} -1.79376 q^{38} -5.61230 q^{39} +11.1247 q^{40} -9.56444 q^{41} +7.90448 q^{42} +8.32205 q^{43} -5.14307 q^{44} -5.45623 q^{45} +11.8351 q^{46} +5.93407 q^{47} -12.6203 q^{48} -5.23329 q^{49} +2.26274 q^{50} +2.38691 q^{51} +9.89273 q^{52} -12.1984 q^{53} -1.79990 q^{54} +2.47268 q^{55} -7.30994 q^{56} -1.71848 q^{57} +4.92827 q^{58} -4.33932 q^{59} +20.3144 q^{60} -5.60577 q^{61} -24.1783 q^{62} +3.58524 q^{63} -5.15849 q^{64} -4.75622 q^{65} -7.26944 q^{66} -7.31982 q^{67} -4.20738 q^{68} +11.3385 q^{69} +6.69876 q^{70} +9.42354 q^{71} -14.8343 q^{72} -5.81720 q^{73} -16.6117 q^{74} +2.16779 q^{75} +3.02915 q^{76} -1.62478 q^{77} +13.9828 q^{78} -2.41892 q^{79} -10.6952 q^{80} -9.81638 q^{81} +23.8294 q^{82} -1.85069 q^{83} -13.3484 q^{84} +2.02282 q^{85} -20.7341 q^{86} +4.72146 q^{87} +6.72267 q^{88} +12.8678 q^{89} +13.5940 q^{90} +3.12527 q^{91} -19.9862 q^{92} -23.1637 q^{93} -14.7845 q^{94} -1.45635 q^{95} +5.18879 q^{96} +2.76207 q^{97} +13.0385 q^{98} -3.29721 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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