LMFDB - Embedded newform 6001.2.a.c.1.5

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			1.5
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)

$f(q)$	$=$	$q-2.61678 q^{2} -3.27387 q^{3} +4.84754 q^{4} +0.197154 q^{5} +8.56700 q^{6} -1.64878 q^{7} -7.45139 q^{8} +7.71823 q^{9} +O(q^{10})$	\(q-2.61678 q^{2} -3.27387 q^{3} +4.84754 q^{4} +0.197154 q^{5} +8.56700 q^{6} -1.64878 q^{7} -7.45139 q^{8} +7.71823 q^{9} -0.515910 q^{10} -2.85498 q^{11} -15.8702 q^{12} -2.61509 q^{13} +4.31450 q^{14} -0.645458 q^{15} +9.80356 q^{16} -1.00000 q^{17} -20.1969 q^{18} +4.41161 q^{19} +0.955714 q^{20} +5.39790 q^{21} +7.47087 q^{22} +2.62711 q^{23} +24.3949 q^{24} -4.96113 q^{25} +6.84312 q^{26} -15.4469 q^{27} -7.99254 q^{28} -1.64893 q^{29} +1.68902 q^{30} -3.02505 q^{31} -10.7510 q^{32} +9.34685 q^{33} +2.61678 q^{34} -0.325065 q^{35} +37.4144 q^{36} -6.80036 q^{37} -11.5442 q^{38} +8.56147 q^{39} -1.46907 q^{40} +1.26081 q^{41} -14.1251 q^{42} -2.12609 q^{43} -13.8396 q^{44} +1.52168 q^{45} -6.87457 q^{46} +0.401752 q^{47} -32.0956 q^{48} -4.28152 q^{49} +12.9822 q^{50} +3.27387 q^{51} -12.6768 q^{52} +2.75397 q^{53} +40.4211 q^{54} -0.562873 q^{55} +12.2857 q^{56} -14.4431 q^{57} +4.31488 q^{58} -0.173209 q^{59} -3.12888 q^{60} -3.25710 q^{61} +7.91588 q^{62} -12.7257 q^{63} +8.52587 q^{64} -0.515577 q^{65} -24.4587 q^{66} -6.47915 q^{67} -4.84754 q^{68} -8.60081 q^{69} +0.850623 q^{70} +0.851062 q^{71} -57.5115 q^{72} -7.44076 q^{73} +17.7950 q^{74} +16.2421 q^{75} +21.3855 q^{76} +4.70725 q^{77} -22.4035 q^{78} +15.1061 q^{79} +1.93282 q^{80} +27.4164 q^{81} -3.29926 q^{82} +1.07321 q^{83} +26.1665 q^{84} -0.197154 q^{85} +5.56352 q^{86} +5.39837 q^{87} +21.2736 q^{88} +6.77381 q^{89} -3.98191 q^{90} +4.31172 q^{91} +12.7350 q^{92} +9.90361 q^{93} -1.05130 q^{94} +0.869769 q^{95} +35.1974 q^{96} -0.917262 q^{97} +11.2038 q^{98} -22.0354 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) $ 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * 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 $

$2$	−2.61678	−1.85034	−0.925172	−	0.379549i	$-0.876079\pi$
$2$	−2.61678	−1.85034	−0.925172	+	0.379549i	$0.876079\pi$
$3$	−3.27387	−1.89017	−0.945085	−	0.326824i	$-0.894022\pi$
$3$	−3.27387	−1.89017	−0.945085	+	0.326824i	$0.894022\pi$
$4$	4.84754	2.42377
$5$	0.197154	0.0881702	0.0440851	−	0.999028i	$-0.485963\pi$
$5$	0.197154	0.0881702	0.0440851	+	0.999028i	$0.485963\pi$
$6$	8.56700	3.49746
$7$	−1.64878	−0.623181	−0.311591	−	0.950216i	$-0.600862\pi$
$7$	−1.64878	−0.623181	−0.311591	+	0.950216i	$0.600862\pi$
$8$	−7.45139	−2.63446
$9$	7.71823	2.57274
$10$	−0.515910	−0.163145
$11$	−2.85498	−0.860810	−0.430405	−	0.902636i	$-0.641629\pi$
$11$	−2.85498	−0.860810	−0.430405	+	0.902636i	$0.641629\pi$
$12$	−15.8702	−4.58134
$13$	−2.61509	−0.725296	−0.362648	−	0.931926i	$-0.618127\pi$
$13$	−2.61509	−0.725296	−0.362648	+	0.931926i	$0.618127\pi$
$14$	4.31450	1.15310
$15$	−0.645458	−0.166657
$16$	9.80356	2.45089
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−20.1969	−4.76046
$19$	4.41161	1.01209	0.506047	−	0.862506i	$-0.331106\pi$
$19$	4.41161	1.01209	0.506047	+	0.862506i	$0.331106\pi$
$20$	0.955714	0.213704
$21$	5.39790	1.17792
$22$	7.47087	1.59279
$23$	2.62711	0.547790	0.273895	−	0.961760i	$-0.411688\pi$
$23$	2.62711	0.547790	0.273895	+	0.961760i	$0.411688\pi$
$24$	24.3949	4.97958
$25$	−4.96113	−0.992226
$26$	6.84312	1.34205
$27$	−15.4469	−2.97276
$28$	−7.99254	−1.51045
$29$	−1.64893	−0.306198	−0.153099	−	0.988211i	$-0.548925\pi$
$29$	−1.64893	−0.306198	−0.153099	+	0.988211i	$0.548925\pi$
$30$	1.68902	0.308372
$31$	−3.02505	−0.543314	−0.271657	−	0.962394i	$-0.587572\pi$
$31$	−3.02505	−0.543314	−0.271657	+	0.962394i	$0.587572\pi$
$32$	−10.7510	−1.90053
$33$	9.34685	1.62708
$34$	2.61678	0.448774
$35$	−0.325065	−0.0549460
$36$	37.4144	6.23574
$37$	−6.80036	−1.11797	−0.558986	−	0.829177i	$-0.688809\pi$
$37$	−6.80036	−1.11797	−0.558986	+	0.829177i	$0.688809\pi$
$38$	−11.5442	−1.87272
$39$	8.56147	1.37093
$40$	−1.46907	−0.232281
$41$	1.26081	0.196905	0.0984526	−	0.995142i	$-0.468611\pi$
$41$	1.26081	0.196905	0.0984526	+	0.995142i	$0.468611\pi$
$42$	−14.1251	−2.17955
$43$	−2.12609	−0.324226	−0.162113	−	0.986772i	$-0.551831\pi$
$43$	−2.12609	−0.324226	−0.162113	+	0.986772i	$0.551831\pi$
$44$	−13.8396	−2.08641
$45$	1.52168	0.226839
$46$	−6.87457	−1.01360
$47$	0.401752	0.0586015	0.0293008	−	0.999571i	$-0.490672\pi$
$47$	0.401752	0.0586015	0.0293008	+	0.999571i	$0.490672\pi$
$48$	−32.0956	−4.63260
$49$	−4.28152	−0.611645
$50$	12.9822	1.83596
$51$	3.27387	0.458434
$52$	−12.6768	−1.75795
$53$	2.75397	0.378286	0.189143	−	0.981950i	$-0.439429\pi$
$53$	2.75397	0.378286	0.189143	+	0.981950i	$0.439429\pi$
$54$	40.4211	5.50062
$55$	−0.562873	−0.0758978
$56$	12.2857	1.64175
$57$	−14.4431	−1.91303
$58$	4.31488	0.566571
$59$	−0.173209	−0.0225498	−0.0112749	−	0.999936i	$-0.503589\pi$
$59$	−0.173209	−0.0225498	−0.0112749	+	0.999936i	$0.503589\pi$
$60$	−3.12888	−0.403937
$61$	−3.25710	−0.417029	−0.208515	−	0.978019i	$-0.566863\pi$
$61$	−3.25710	−0.417029	−0.208515	+	0.978019i	$0.566863\pi$
$62$	7.91588	1.00532
$63$	−12.7257	−1.60329
$64$	8.52587	1.06573
$65$	−0.515577	−0.0639494
$66$	−24.4587	−3.01065
$67$	−6.47915	−0.791555	−0.395777	−	0.918347i	$-0.629525\pi$
$67$	−6.47915	−0.791555	−0.395777	+	0.918347i	$0.629525\pi$
$68$	−4.84754	−0.587851
$69$	−8.60081	−1.03542
$70$	0.850623	0.101669
$71$	0.851062	0.101002	0.0505012	−	0.998724i	$-0.483918\pi$
$71$	0.851062	0.101002	0.0505012	+	0.998724i	$0.483918\pi$
$72$	−57.5115	−6.77780
$73$	−7.44076	−0.870875	−0.435438	−	0.900219i	$-0.643406\pi$
$73$	−7.44076	−0.870875	−0.435438	+	0.900219i	$0.643406\pi$
$74$	17.7950	2.06863
$75$	16.2421	1.87548
$76$	21.3855	2.45308
$77$	4.70725	0.536441
$78$	−22.4035	−2.53670
$79$	15.1061	1.69956	0.849782	−	0.527134i	$-0.176734\pi$
$79$	15.1061	1.69956	0.849782	+	0.527134i	$0.176734\pi$
$80$	1.93282	0.216095
$81$	27.4164	3.04627
$82$	−3.29926	−0.364342
$83$	1.07321	0.117800	0.0588999	−	0.998264i	$-0.481241\pi$
$83$	1.07321	0.117800	0.0588999	+	0.998264i	$0.481241\pi$
$84$	26.1665	2.85500
$85$	−0.197154	−0.0213844
$86$	5.56352	0.599930
$87$	5.39837	0.578766
$88$	21.2736	2.26777
$89$	6.77381	0.718022	0.359011	−	0.933333i	$-0.383114\pi$
$89$	6.77381	0.718022	0.359011	+	0.933333i	$0.383114\pi$
$90$	−3.98191	−0.419731
$91$	4.31172	0.451991
$92$	12.7350	1.32772
$93$	9.90361	1.02696
$94$	−1.05130	−0.108433
$95$	0.869769	0.0892365
$96$	35.1974	3.59232
$97$	−0.917262	−0.0931339	−0.0465669	−	0.998915i	$-0.514828\pi$
$97$	−0.917262	−0.0931339	−0.0465669	+	0.998915i	$0.514828\pi$
$98$	11.2038	1.13175
$99$	−22.0354	−2.21464
$100$	−24.0493	−2.40493
$101$	1.74983	0.174115	0.0870575	−	0.996203i	$-0.472254\pi$
$101$	1.74983	0.174115	0.0870575	+	0.996203i	$0.472254\pi$
$102$	−8.56700	−0.848260
$103$	0.119697	0.0117941	0.00589706	−	0.999983i	$-0.498123\pi$
$103$	0.119697	0.0117941	0.00589706	+	0.999983i	$0.498123\pi$
$104$	19.4861	1.91076
$105$	1.06422	0.103857
$106$	−7.20653	−0.699960
$107$	16.1964	1.56576	0.782882	−	0.622170i	$-0.213749\pi$
$107$	16.1964	1.56576	0.782882	+	0.622170i	$0.213749\pi$
$108$	−74.8794	−7.20527
$109$	−6.16952	−0.590933	−0.295466	−	0.955353i	$-0.595475\pi$
$109$	−6.16952	−0.590933	−0.295466	+	0.955353i	$0.595475\pi$
$110$	1.47291	0.140437
$111$	22.2635	2.11316
$112$	−16.1639	−1.52735
$113$	−13.6979	−1.28859	−0.644294	−	0.764778i	$-0.722848\pi$
$113$	−13.6979	−1.28859	−0.644294	+	0.764778i	$0.722848\pi$
$114$	37.7943	3.53976
$115$	0.517946	0.0482987
$116$	−7.99323	−0.742153
$117$	−20.1839	−1.86600
$118$	0.453249	0.0417249
$119$	1.64878	0.151144
$120$	4.80956	0.439051
$121$	−2.84907	−0.259006
$122$	8.52312	0.771647
$123$	−4.12773	−0.372184
$124$	−14.6640	−1.31687
$125$	−1.96388	−0.175655
$126$	33.3003	2.96663
$127$	13.9560	1.23840	0.619199	−	0.785234i	$-0.287458\pi$
$127$	13.9560	1.23840	0.619199	+	0.785234i	$0.287458\pi$
$128$	−0.808342	−0.0714480
$129$	6.96055	0.612843
$130$	1.34915	0.118328
$131$	6.35368	0.555124	0.277562	−	0.960708i	$-0.410474\pi$
$131$	6.35368	0.555124	0.277562	+	0.960708i	$0.410474\pi$
$132$	45.3092	3.94366
$133$	−7.27379	−0.630718
$134$	16.9545	1.46465
$135$	−3.04542	−0.262108
$136$	7.45139	0.638951
$137$	−14.1878	−1.21215	−0.606073	−	0.795409i	$-0.707256\pi$
$137$	−14.1878	−1.21215	−0.606073	+	0.795409i	$0.707256\pi$
$138$	22.5064	1.91588
$139$	−16.4725	−1.39718	−0.698588	−	0.715524i	$-0.746188\pi$
$139$	−16.4725	−1.39718	−0.698588	+	0.715524i	$0.746188\pi$
$140$	−1.57576	−0.133176
$141$	−1.31528	−0.110767
$142$	−2.22704	−0.186889
$143$	7.46604	0.624342
$144$	75.6662	6.30551
$145$	−0.325093	−0.0269975
$146$	19.4708	1.61142
$147$	14.0171	1.15611
$148$	−32.9650	−2.70971
$149$	−7.15587	−0.586232	−0.293116	−	0.956077i	$-0.594692\pi$
$149$	−7.15587	−0.586232	−0.293116	+	0.956077i	$0.594692\pi$
$150$	−42.5020	−3.47027
$151$	−9.32347	−0.758733	−0.379367	−	0.925246i	$-0.623858\pi$
$151$	−9.32347	−0.758733	−0.379367	+	0.925246i	$0.623858\pi$
$152$	−32.8726	−2.66632
$153$	−7.71823	−0.623982
$154$	−12.3178	−0.992599
$155$	−0.596401	−0.0479041
$156$	41.5021	3.32283
$157$	−2.48473	−0.198303	−0.0991515	−	0.995072i	$-0.531613\pi$
$157$	−2.48473	−0.198303	−0.0991515	+	0.995072i	$0.531613\pi$
$158$	−39.5292	−3.14478
$159$	−9.01613	−0.715026
$160$	−2.11961	−0.167570
$161$	−4.33153	−0.341372
$162$	−71.7428	−5.63664
$163$	8.20105	0.642356	0.321178	−	0.947019i	$-0.395921\pi$
$163$	8.20105	0.642356	0.321178	+	0.947019i	$0.395921\pi$
$164$	6.11182	0.477253
$165$	1.84277	0.143460
$166$	−2.80835	−0.217970
$167$	13.9185	1.07705	0.538523	−	0.842611i	$-0.318982\pi$
$167$	13.9185	1.07705	0.538523	+	0.842611i	$0.318982\pi$
$168$	−40.2219	−3.10318
$169$	−6.16130	−0.473946
$170$	0.515910	0.0395685
$171$	34.0499	2.60386
$172$	−10.3063	−0.785849
$173$	−24.1211	−1.83389	−0.916945	−	0.399014i	$-0.869352\pi$
$173$	−24.1211	−1.83389	−0.916945	+	0.399014i	$0.869352\pi$
$174$	−14.1263	−1.07092
$175$	8.17983	0.618337
$176$	−27.9890	−2.10975
$177$	0.567062	0.0426230
$178$	−17.7256	−1.32859
$179$	5.68154	0.424659	0.212329	−	0.977198i	$-0.431895\pi$
$179$	5.68154	0.424659	0.212329	+	0.977198i	$0.431895\pi$
$180$	7.37642	0.549806
$181$	−10.5660	−0.785367	−0.392684	−	0.919674i	$-0.628453\pi$
$181$	−10.5660	−0.785367	−0.392684	+	0.919674i	$0.628453\pi$
$182$	−11.2828	−0.836338
$183$	10.6633	0.788256
$184$	−19.5756	−1.44313
$185$	−1.34072	−0.0985717
$186$	−25.9156	−1.90022
$187$	2.85498	0.208777
$188$	1.94751	0.142037
$189$	25.4686	1.85257
$190$	−2.27600	−0.165118
$191$	13.6592	0.988346	0.494173	−	0.869364i	$-0.335471\pi$
$191$	13.6592	0.988346	0.494173	+	0.869364i	$0.335471\pi$
$192$	−27.9126	−2.01442
$193$	−8.77597	−0.631708	−0.315854	−	0.948808i	$-0.602291\pi$
$193$	−8.77597	−0.631708	−0.315854	+	0.948808i	$0.602291\pi$
$194$	2.40027	0.172330
$195$	1.68793	0.120875
$196$	−20.7548	−1.48249
$197$	−14.2313	−1.01394	−0.506969	−	0.861964i	$-0.669234\pi$
$197$	−14.2313	−1.01394	−0.506969	+	0.861964i	$0.669234\pi$
$198$	57.6619	4.09785
$199$	−3.66713	−0.259956	−0.129978	−	0.991517i	$-0.541491\pi$
$199$	−3.66713	−0.259956	−0.129978	+	0.991517i	$0.541491\pi$
$200$	36.9673	2.61398
$201$	21.2119	1.49617
$202$	−4.57893	−0.322173
$203$	2.71872	0.190817
$204$	15.8702	1.11114
$205$	0.248574	0.0173612
$206$	−0.313222	−0.0218232
$207$	20.2766	1.40932
$208$	−25.6372	−1.77762
$209$	−12.5951	−0.871220
$210$	−2.78483	−0.192172
$211$	−17.6020	−1.21177	−0.605886	−	0.795551i	$-0.707181\pi$
$211$	−17.6020	−1.21177	−0.605886	+	0.795551i	$0.707181\pi$
$212$	13.3500	0.916879
$213$	−2.78627	−0.190912
$214$	−42.3824	−2.89720
$215$	−0.419169	−0.0285871
$216$	115.101	7.83161
$217$	4.98764	0.338583
$218$	16.1443	1.09343
$219$	24.3601	1.64610
$220$	−2.72855	−0.183959
$221$	2.61509	0.175910
$222$	−58.2587	−3.91007
$223$	−9.25585	−0.619817	−0.309909	−	0.950766i	$-0.600298\pi$
$223$	−9.25585	−0.619817	−0.309909	+	0.950766i	$0.600298\pi$
$224$	17.7261	1.18437
$225$	−38.2912	−2.55274
$226$	35.8443	2.38433
$227$	12.0471	0.799595	0.399798	−	0.916603i	$-0.369080\pi$
$227$	12.0471	0.799595	0.399798	+	0.916603i	$0.369080\pi$
$228$	−70.0133	−4.63674
$229$	4.79315	0.316740	0.158370	−	0.987380i	$-0.449376\pi$
$229$	4.79315	0.316740	0.158370	+	0.987380i	$0.449376\pi$
$230$	−1.35535	−0.0893692
$231$	−15.4109	−1.01396
$232$	12.2868	0.806667
$233$	−11.8605	−0.777009	−0.388505	−	0.921447i	$-0.627008\pi$
$233$	−11.8605	−0.777009	−0.388505	+	0.921447i	$0.627008\pi$
$234$	52.8168	3.45274
$235$	0.0792072	0.00516691
$236$	−0.839635	−0.0546556
$237$	−49.4553	−3.21247
$238$	−4.31450	−0.279668
$239$	−28.9670	−1.87372	−0.936860	−	0.349705i	$-0.886282\pi$
$239$	−28.9670	−1.87372	−0.936860	+	0.349705i	$0.886282\pi$
$240$	−6.32779	−0.408457
$241$	1.68847	0.108764	0.0543819	−	0.998520i	$-0.482681\pi$
$241$	1.68847	0.108764	0.0543819	+	0.998520i	$0.482681\pi$
$242$	7.45538	0.479250
$243$	−43.4172	−2.78521
$244$	−15.7889	−1.01078
$245$	−0.844120	−0.0539288
$246$	10.8014	0.688669
$247$	−11.5368	−0.734067
$248$	22.5408	1.43134
$249$	−3.51355	−0.222662
$250$	5.13905	0.325022
$251$	−28.1239	−1.77516	−0.887581	−	0.460651i	$-0.847616\pi$
$251$	−28.1239	−1.77516	−0.887581	+	0.460651i	$0.847616\pi$
$252$	−61.6883	−3.88600
$253$	−7.50035	−0.471543
$254$	−36.5199	−2.29146
$255$	0.645458	0.0404202
$256$	−14.9365	−0.933531
$257$	10.6287	0.663002	0.331501	−	0.943455i	$-0.392445\pi$
$257$	10.6287	0.663002	0.331501	+	0.943455i	$0.392445\pi$
$258$	−18.2142	−1.13397
$259$	11.2123	0.696699
$260$	−2.49928	−0.154999
$261$	−12.7268	−0.787769
$262$	−16.6262	−1.02717
$263$	5.06987	0.312622	0.156311	−	0.987708i	$-0.450040\pi$
$263$	5.06987	0.312622	0.156311	+	0.987708i	$0.450040\pi$
$264$	−69.6470	−4.28648
$265$	0.542957	0.0333536
$266$	19.0339	1.16704
$267$	−22.1766	−1.35718
$268$	−31.4080	−1.91855
$269$	8.03465	0.489882	0.244941	−	0.969538i	$-0.421231\pi$
$269$	8.03465	0.489882	0.244941	+	0.969538i	$0.421231\pi$
$270$	7.96920	0.484990
$271$	−18.9977	−1.15403	−0.577013	−	0.816735i	$-0.695782\pi$
$271$	−18.9977	−1.15403	−0.577013	+	0.816735i	$0.695782\pi$
$272$	−9.80356	−0.594428
$273$	−14.1160	−0.854340
$274$	37.1264	2.24289
$275$	14.1639	0.854118
$276$	−41.6928	−2.50961
$277$	−25.2848	−1.51922	−0.759608	−	0.650381i	$-0.774609\pi$
$277$	−25.2848	−1.51922	−0.759608	+	0.650381i	$0.774609\pi$
$278$	43.1048	2.58526
$279$	−23.3480	−1.39781
$280$	2.42218	0.144753
$281$	14.6757	0.875478	0.437739	−	0.899102i	$-0.355779\pi$
$281$	14.6757	0.875478	0.437739	+	0.899102i	$0.355779\pi$
$282$	3.44181	0.204957
$283$	−25.6322	−1.52367	−0.761837	−	0.647768i	$-0.775702\pi$
$283$	−25.6322	−1.52367	−0.761837	+	0.647768i	$0.775702\pi$
$284$	4.12555	0.244807
$285$	−2.84751	−0.168672
$286$	−19.5370	−1.15525
$287$	−2.07880	−0.122708
$288$	−82.9787	−4.88957
$289$	1.00000	0.0588235
$290$	0.850697	0.0499547
$291$	3.00300	0.176039
$292$	−36.0694	−2.11080
$293$	−4.37325	−0.255488	−0.127744	−	0.991807i	$-0.540774\pi$
$293$	−4.37325	−0.255488	−0.127744	+	0.991807i	$0.540774\pi$
$294$	−36.6798	−2.13921
$295$	−0.0341488	−0.00198822
$296$	50.6721	2.94525
$297$	44.1006	2.55898
$298$	18.7254	1.08473
$299$	−6.87013	−0.397310
$300$	78.7342	4.54572
$301$	3.50546	0.202052
$302$	24.3975	1.40392
$303$	−5.72873	−0.329107
$304$	43.2495	2.48053
$305$	−0.642152	−0.0367695
$306$	20.1969	1.15458
$307$	11.1634	0.637126	0.318563	−	0.947902i	$-0.396800\pi$
$307$	11.1634	0.637126	0.318563	+	0.947902i	$0.396800\pi$
$308$	22.8186	1.30021
$309$	−0.391874	−0.0222929
$310$	1.56065	0.0886391
$311$	−18.0468	−1.02334	−0.511669	−	0.859183i	$-0.670973\pi$
$311$	−18.0468	−1.02334	−0.511669	+	0.859183i	$0.670973\pi$
$312$	−63.7948	−3.61167
$313$	−11.9126	−0.673338	−0.336669	−	0.941623i	$-0.609300\pi$
$313$	−11.9126	−0.673338	−0.336669	+	0.941623i	$0.609300\pi$
$314$	6.50199	0.366929
$315$	−2.50893	−0.141362
$316$	73.2272	4.11935
$317$	−5.64336	−0.316962	−0.158481	−	0.987362i	$-0.550660\pi$
$317$	−5.64336	−0.316962	−0.158481	+	0.987362i	$0.550660\pi$
$318$	23.5932	1.32304
$319$	4.70766	0.263578
$320$	1.68091	0.0939659
$321$	−53.0249	−2.95956
$322$	11.3347	0.631656
$323$	−4.41161	−0.245469
$324$	132.902	7.38346
$325$	12.9738	0.719657
$326$	−21.4604	−1.18858
$327$	20.1982	1.11696
$328$	−9.39477	−0.518740
$329$	−0.662402	−0.0365194
$330$	−4.82213	−0.265450
$331$	18.1973	1.00021	0.500106	−	0.865964i	$-0.333294\pi$
$331$	18.1973	1.00021	0.500106	+	0.865964i	$0.333294\pi$
$332$	5.20242	0.285520
$333$	−52.4867	−2.87626
$334$	−36.4217	−1.99290
$335$	−1.27739	−0.0697915
$336$	52.9187	2.88695
$337$	15.1297	0.824169	0.412084	−	0.911146i	$-0.364801\pi$
$337$	15.1297	0.824169	0.412084	+	0.911146i	$0.364801\pi$
$338$	16.1228	0.876963
$339$	44.8451	2.43565
$340$	−0.955714	−0.0518309
$341$	8.63646	0.467690
$342$	−89.1010	−4.81803
$343$	18.6008	1.00435
$344$	15.8423	0.854162
$345$	−1.69569	−0.0912928
$346$	63.1195	3.39333
$347$	−34.1548	−1.83353	−0.916763	−	0.399432i	$-0.869208\pi$
$347$	−34.1548	−1.83353	−0.916763	+	0.399432i	$0.869208\pi$
$348$	26.1688	1.40280
$349$	30.7599	1.64654	0.823271	−	0.567649i	$-0.192147\pi$
$349$	30.7599	1.64654	0.823271	+	0.567649i	$0.192147\pi$
$350$	−21.4048	−1.14414
$351$	40.3950	2.15613
$352$	30.6939	1.63599
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−1.48388	−0.0788672
$355$	0.167791	0.00890540
$356$	32.8363	1.74032
$357$	−5.39790	−0.285687
$358$	−14.8674	−0.785764
$359$	14.2332	0.751199	0.375600	−	0.926782i	$-0.377437\pi$
$359$	14.2332	0.751199	0.375600	+	0.926782i	$0.377437\pi$
$360$	−11.3387	−0.597600
$361$	0.462338	0.0243336
$362$	27.6490	1.45320
$363$	9.32748	0.489566
$364$	20.9012	1.09552
$365$	−1.46698	−0.0767852
$366$	−27.9036	−1.45854
$367$	−21.3981	−1.11697	−0.558485	−	0.829515i	$-0.688617\pi$
$367$	−21.3981	−1.11697	−0.558485	+	0.829515i	$0.688617\pi$
$368$	25.7550	1.34257
$369$	9.73122	0.506587
$370$	3.50837	0.182392
$371$	−4.54069	−0.235741
$372$	48.0082	2.48911
$373$	−15.7777	−0.816938	−0.408469	−	0.912772i	$-0.633937\pi$
$373$	−15.7777	−0.816938	−0.408469	+	0.912772i	$0.633937\pi$
$374$	−7.47087	−0.386309
$375$	6.42949	0.332018
$376$	−2.99361	−0.154384
$377$	4.31209	0.222084
$378$	−66.6456	−3.42788
$379$	−10.9105	−0.560437	−0.280218	−	0.959936i	$-0.590407\pi$
$379$	−10.9105	−0.560437	−0.280218	+	0.959936i	$0.590407\pi$
$380$	4.21624	0.216289
$381$	−45.6902	−2.34078
$382$	−35.7432	−1.82878
$383$	8.31119	0.424682	0.212341	−	0.977196i	$-0.431891\pi$
$383$	8.31119	0.424682	0.212341	+	0.977196i	$0.431891\pi$
$384$	2.64641	0.135049
$385$	0.928055	0.0472981
$386$	22.9648	1.16888
$387$	−16.4097	−0.834151
$388$	−4.44646	−0.225735
$389$	15.6492	0.793444	0.396722	−	0.917939i	$-0.370148\pi$
$389$	15.6492	0.793444	0.396722	+	0.917939i	$0.370148\pi$
$390$	−4.41695	−0.223661
$391$	−2.62711	−0.132859
$392$	31.9032	1.61136
$393$	−20.8011	−1.04928
$394$	37.2402	1.87613
$395$	2.97823	0.149851
$396$	−106.818	−5.36779
$397$	−7.80231	−0.391586	−0.195793	−	0.980645i	$-0.562728\pi$
$397$	−7.80231	−0.391586	−0.195793	+	0.980645i	$0.562728\pi$
$398$	9.59607	0.481008
$399$	23.8135	1.19216
$400$	−48.6367	−2.43184
$401$	−2.63629	−0.131650	−0.0658251	−	0.997831i	$-0.520968\pi$
$401$	−2.63629	−0.131650	−0.0658251	+	0.997831i	$0.520968\pi$
$402$	−55.5069	−2.76843
$403$	7.91077	0.394064
$404$	8.48239	0.422015
$405$	5.40527	0.268590
$406$	−7.11429	−0.353076
$407$	19.4149	0.962361
$408$	−24.3949	−1.20773
$409$	7.70912	0.381191	0.190596	−	0.981669i	$-0.438958\pi$
$409$	7.70912	0.381191	0.190596	+	0.981669i	$0.438958\pi$
$410$	−0.650464	−0.0321241
$411$	46.4490	2.29116
$412$	0.580237	0.0285862
$413$	0.285583	0.0140526
$414$	−53.0595	−2.60773
$415$	0.211588	0.0103864
$416$	28.1148	1.37844
$417$	53.9287	2.64090
$418$	32.9586	1.61206
$419$	0.0925371	0.00452074	0.00226037	−	0.999997i	$-0.499281\pi$
$419$	0.0925371	0.00452074	0.00226037	+	0.999997i	$0.499281\pi$
$420$	5.15885	0.251726
$421$	−16.4736	−0.802874	−0.401437	−	0.915887i	$-0.631489\pi$
$421$	−16.4736	−0.802874	−0.401437	+	0.915887i	$0.631489\pi$
$422$	46.0606	2.24220
$423$	3.10081	0.150767
$424$	−20.5209	−0.996581
$425$	4.96113	0.240650
$426$	7.29105	0.353252
$427$	5.37025	0.259885
$428$	78.5127	3.79505
$429$	−24.4429	−1.18011
$430$	1.09687	0.0528959
$431$	−9.90080	−0.476905	−0.238452	−	0.971154i	$-0.576640\pi$
$431$	−9.90080	−0.476905	−0.238452	+	0.971154i	$0.576640\pi$
$432$	−151.435	−7.28590
$433$	38.5957	1.85479	0.927395	−	0.374084i	$-0.122043\pi$
$433$	38.5957	1.85479	0.927395	+	0.374084i	$0.122043\pi$
$434$	−13.0516	−0.626495
$435$	1.06431	0.0510299
$436$	−29.9070	−1.43229
$437$	11.5898	0.554415
$438$	−63.7450	−3.04585
$439$	−23.3353	−1.11373	−0.556867	−	0.830601i	$-0.687997\pi$
$439$	−23.3353	−1.11373	−0.556867	+	0.830601i	$0.687997\pi$
$440$	4.19418	0.199950
$441$	−33.0457	−1.57361
$442$	−6.84312	−0.325494
$443$	−7.80498	−0.370826	−0.185413	−	0.982661i	$-0.559362\pi$
$443$	−7.80498	−0.370826	−0.185413	+	0.982661i	$0.559362\pi$
$444$	107.923	5.12181
$445$	1.33549	0.0633081
$446$	24.2205	1.14687
$447$	23.4274	1.10808
$448$	−14.0573	−0.664145
$449$	26.4092	1.24633	0.623163	−	0.782092i	$-0.285847\pi$
$449$	26.4092	1.24633	0.623163	+	0.782092i	$0.285847\pi$
$450$	100.200	4.72345
$451$	−3.59959	−0.169498
$452$	−66.4010	−3.12324
$453$	30.5238	1.43414
$454$	−31.5247	−1.47953
$455$	0.850074	0.0398521
$456$	107.621	5.03981
$457$	18.0954	0.846469	0.423235	−	0.906020i	$-0.360895\pi$
$457$	18.0954	0.846469	0.423235	+	0.906020i	$0.360895\pi$
$458$	−12.5426	−0.586078
$459$	15.4469	0.720999
$460$	2.51076	0.117065
$461$	23.8432	1.11049	0.555244	−	0.831688i	$-0.312625\pi$
$461$	23.8432	1.11049	0.555244	+	0.831688i	$0.312625\pi$
$462$	40.3270	1.87618
$463$	−9.79489	−0.455207	−0.227604	−	0.973754i	$-0.573089\pi$
$463$	−9.79489	−0.455207	−0.227604	+	0.973754i	$0.573089\pi$
$464$	−16.1653	−0.750457
$465$	1.95254	0.0905469
$466$	31.0364	1.43773
$467$	14.1105	0.652957	0.326478	−	0.945205i	$-0.394138\pi$
$467$	14.1105	0.652957	0.326478	+	0.945205i	$0.394138\pi$
$468$	−97.8422	−4.52276
$469$	10.6827	0.493282
$470$	−0.207268	−0.00956055
$471$	8.13469	0.374827
$472$	1.29064	0.0594067
$473$	6.06996	0.279097
$474$	129.414	5.94416
$475$	−21.8866	−1.00423
$476$	7.99254	0.366337
$477$	21.2558	0.973234
$478$	75.8003	3.46702
$479$	18.9315	0.865002	0.432501	−	0.901634i	$-0.357631\pi$
$479$	18.9315	0.865002	0.432501	+	0.901634i	$0.357631\pi$
$480$	6.93932	0.316735
$481$	17.7836	0.810860
$482$	−4.41835	−0.201250
$483$	14.1809	0.645252
$484$	−13.8110	−0.627771
$485$	−0.180842	−0.00821163
$486$	113.613	5.15360
$487$	41.3861	1.87538	0.937692	−	0.347466i	$-0.112958\pi$
$487$	41.3861	1.87538	0.937692	+	0.347466i	$0.112958\pi$
$488$	24.2699	1.09865
$489$	−26.8492	−1.21416
$490$	2.20888	0.0997869
$491$	−7.59709	−0.342852	−0.171426	−	0.985197i	$-0.554837\pi$
$491$	−7.59709	−0.342852	−0.171426	+	0.985197i	$0.554837\pi$
$492$	−20.0093	−0.902089
$493$	1.64893	0.0742639
$494$	30.1892	1.35828
$495$	−4.34438	−0.195266
$496$	−29.6562	−1.33160
$497$	−1.40322	−0.0629428
$498$	9.19418	0.412001
$499$	−33.4280	−1.49644	−0.748221	−	0.663450i	$-0.769092\pi$
$499$	−33.4280	−1.49644	−0.748221	+	0.663450i	$0.769092\pi$
$500$	−9.51999	−0.425747
$501$	−45.5674	−2.03580
$502$	73.5940	3.28466
$503$	−20.8918	−0.931519	−0.465760	−	0.884911i	$-0.654219\pi$
$503$	−20.8918	−0.931519	−0.465760	+	0.884911i	$0.654219\pi$
$504$	94.8240	4.22380
$505$	0.344988	0.0153517
$506$	19.6268	0.872516
$507$	20.1713	0.895839
$508$	67.6524	3.00159
$509$	−22.1618	−0.982306	−0.491153	−	0.871073i	$-0.663424\pi$
$509$	−22.1618	−0.982306	−0.491153	+	0.871073i	$0.663424\pi$
$510$	−1.68902	−0.0747912
$511$	12.2682	0.542713
$512$	40.7022	1.79880
$513$	−68.1457	−3.00871
$514$	−27.8130	−1.22678
$515$	0.0235989	0.00103989
$516$	33.7416	1.48539
$517$	−1.14700	−0.0504448
$518$	−29.3402	−1.28913
$519$	78.9692	3.46636
$520$	3.84176	0.168472
$521$	4.48311	0.196409	0.0982043	−	0.995166i	$-0.468690\pi$
$521$	4.48311	0.196409	0.0982043	+	0.995166i	$0.468690\pi$
$522$	33.3032	1.45764
$523$	36.9114	1.61402	0.807012	−	0.590536i	$-0.201083\pi$
$523$	36.9114	1.61402	0.807012	+	0.590536i	$0.201083\pi$
$524$	30.7997	1.34549
$525$	−26.7797	−1.16876
$526$	−13.2667	−0.578457
$527$	3.02505	0.131773
$528$	91.6324	3.98779
$529$	−16.0983	−0.699926
$530$	−1.42080	−0.0617155
$531$	−1.33686	−0.0580149
$532$	−35.2600	−1.52871
$533$	−3.29713	−0.142815
$534$	58.0312	2.51126
$535$	3.19319	0.138054
$536$	48.2787	2.08532
$537$	−18.6006	−0.802677
$538$	−21.0249	−0.906449
$539$	12.2237	0.526510
$540$	−14.7628	−0.635290
$541$	−13.2176	−0.568271	−0.284135	−	0.958784i	$-0.591707\pi$
$541$	−13.2176	−0.568271	−0.284135	+	0.958784i	$0.591707\pi$
$542$	49.7127	2.13534
$543$	34.5918	1.48448
$544$	10.7510	0.460945
$545$	−1.21635	−0.0521026
$546$	36.9385	1.58082
$547$	22.4366	0.959318	0.479659	−	0.877455i	$-0.340760\pi$
$547$	22.4366	0.959318	0.479659	+	0.877455i	$0.340760\pi$
$548$	−68.7759	−2.93796
$549$	−25.1391	−1.07291
$550$	−37.0639	−1.58041
$551$	−7.27442	−0.309901
$552$	64.0880	2.72777
$553$	−24.9066	−1.05914
$554$	66.1648	2.81107
$555$	4.38935	0.186317
$556$	−79.8509	−3.38643
$557$	5.44984	0.230917	0.115458	−	0.993312i	$-0.463166\pi$
$557$	5.44984	0.230917	0.115458	+	0.993312i	$0.463166\pi$
$558$	61.0966	2.58643
$559$	5.55993	0.235160
$560$	−3.18679	−0.134667
$561$	−9.34685	−0.394624
$562$	−38.4031	−1.61994
$563$	−42.6437	−1.79722	−0.898608	−	0.438752i	$-0.855421\pi$
$563$	−42.6437	−1.79722	−0.898608	+	0.438752i	$0.855421\pi$
$564$	−6.37589	−0.268473
$565$	−2.70060	−0.113615
$566$	67.0738	2.81932
$567$	−45.2037	−1.89838
$568$	−6.34159	−0.266087
$569$	4.78925	0.200776	0.100388	−	0.994948i	$-0.467992\pi$
$569$	4.78925	0.200776	0.100388	+	0.994948i	$0.467992\pi$
$570$	7.45132	0.312101
$571$	−21.1540	−0.885269	−0.442634	−	0.896702i	$-0.645956\pi$
$571$	−21.1540	−0.885269	−0.442634	+	0.896702i	$0.645956\pi$
$572$	36.1919	1.51326
$573$	−44.7185	−1.86814
$574$	5.43976	0.227051
$575$	−13.0334	−0.543531
$576$	65.8047	2.74186
$577$	18.0764	0.752530	0.376265	−	0.926512i	$-0.377208\pi$
$577$	18.0764	0.752530	0.376265	+	0.926512i	$0.377208\pi$
$578$	−2.61678	−0.108844
$579$	28.7314	1.19404
$580$	−1.57590	−0.0654357
$581$	−1.76949	−0.0734107
$582$	−7.85819	−0.325732
$583$	−7.86253	−0.325633
$584$	55.4440	2.29429
$585$	−3.97934	−0.164526
$586$	11.4438	0.472740
$587$	−2.22186	−0.0917062	−0.0458531	−	0.998948i	$-0.514601\pi$
$587$	−2.22186	−0.0917062	−0.0458531	+	0.998948i	$0.514601\pi$
$588$	67.9486	2.80215
$589$	−13.3453	−0.549885
$590$	0.0893600	0.00367889
$591$	46.5915	1.91652
$592$	−66.6677	−2.74003
$593$	12.4000	0.509205	0.254602	−	0.967046i	$-0.418055\pi$
$593$	12.4000	0.509205	0.254602	+	0.967046i	$0.418055\pi$
$594$	−115.402	−4.73499
$595$	0.325065	0.0133264
$596$	−34.6884	−1.42089
$597$	12.0057	0.491361
$598$	17.9776	0.735159
$599$	43.1349	1.76244	0.881221	−	0.472704i	$-0.156722\pi$
$599$	43.1349	1.76244	0.881221	+	0.472704i	$0.156722\pi$
$600$	−121.026	−4.94087
$601$	−44.3249	−1.80805	−0.904026	−	0.427477i	$-0.859402\pi$
$601$	−44.3249	−1.80805	−0.904026	+	0.427477i	$0.859402\pi$
$602$	−9.17303	−0.373865
$603$	−50.0076	−2.03647
$604$	−45.1959	−1.83899
$605$	−0.561706	−0.0228366
$606$	14.9908	0.608961
$607$	−26.2206	−1.06426	−0.532130	−	0.846663i	$-0.678608\pi$
$607$	−26.2206	−1.06426	−0.532130	+	0.846663i	$0.678608\pi$
$608$	−47.4292	−1.92351
$609$	−8.90074	−0.360676
$610$	1.68037	0.0680363
$611$	−1.05062	−0.0425034
$612$	−37.4144	−1.51239
$613$	0.592407	0.0239271	0.0119635	−	0.999928i	$-0.496192\pi$
$613$	0.592407	0.0239271	0.0119635	+	0.999928i	$0.496192\pi$
$614$	−29.2120	−1.17890
$615$	−0.813800	−0.0328156
$616$	−35.0755	−1.41323
$617$	19.3352	0.778407	0.389204	−	0.921152i	$-0.372750\pi$
$617$	19.3352	0.778407	0.389204	+	0.921152i	$0.372750\pi$
$618$	1.02545	0.0412495
$619$	30.2882	1.21738	0.608692	−	0.793407i	$-0.291695\pi$
$619$	30.2882	1.21738	0.608692	+	0.793407i	$0.291695\pi$
$620$	−2.89108	−0.116109
$621$	−40.5806	−1.62845
$622$	47.2244	1.89353
$623$	−11.1685	−0.447458
$624$	83.9329	3.36001
$625$	24.4185	0.976739
$626$	31.1725	1.24591
$627$	41.2347	1.64675
$628$	−12.0448	−0.480641
$629$	6.80036	0.271148
$630$	6.56531	0.261568
$631$	27.7184	1.10345	0.551727	−	0.834025i	$-0.313969\pi$
$631$	27.7184	1.10345	0.551727	+	0.834025i	$0.313969\pi$
$632$	−112.561	−4.47744
$633$	57.6267	2.29046
$634$	14.7674	0.586489
$635$	2.75149	0.109190
$636$	−43.7061	−1.73306
$637$	11.1966	0.443624
$638$	−12.3189	−0.487710
$639$	6.56869	0.259853
$640$	−0.159368	−0.00629958
$641$	−33.6643	−1.32966	−0.664830	−	0.746995i	$-0.731496\pi$
$641$	−33.6643	−1.32966	−0.664830	+	0.746995i	$0.731496\pi$
$642$	138.755	5.47620
$643$	−5.09699	−0.201006	−0.100503	−	0.994937i	$-0.532045\pi$
$643$	−5.09699	−0.201006	−0.100503	+	0.994937i	$0.532045\pi$
$644$	−20.9973	−0.827408
$645$	1.37230	0.0540344
$646$	11.5442	0.454201
$647$	−0.636215	−0.0250122	−0.0125061	−	0.999922i	$-0.503981\pi$
$647$	−0.636215	−0.0250122	−0.0125061	+	0.999922i	$0.503981\pi$
$648$	−204.290	−8.02528
$649$	0.494508	0.0194111
$650$	−33.9496	−1.33161
$651$	−16.3289	−0.639980
$652$	39.7549	1.55692
$653$	21.2512	0.831624	0.415812	−	0.909451i	$-0.363497\pi$
$653$	21.2512	0.831624	0.415812	+	0.909451i	$0.363497\pi$
$654$	−52.8543	−2.06677
$655$	1.25266	0.0489454
$656$	12.3604	0.482593
$657$	−57.4295	−2.24054
$658$	1.73336	0.0675734
$659$	−18.1468	−0.706898	−0.353449	−	0.935454i	$-0.614991\pi$
$659$	−18.1468	−0.706898	−0.353449	+	0.935454i	$0.614991\pi$
$660$	8.93292	0.347713
$661$	−34.4373	−1.33945	−0.669727	−	0.742607i	$-0.733589\pi$
$661$	−34.4373	−1.33945	−0.669727	+	0.742607i	$0.733589\pi$
$662$	−47.6182	−1.85074
$663$	−8.56147	−0.332500
$664$	−7.99689	−0.310339
$665$	−1.43406	−0.0556105
$666$	137.346	5.32206
$667$	−4.33191	−0.167732
$668$	67.4705	2.61051
$669$	30.3025	1.17156
$670$	3.34266	0.129138
$671$	9.29898	0.358983
$672$	−58.0328	−2.23866
$673$	25.1117	0.967985	0.483993	−	0.875072i	$-0.339186\pi$
$673$	25.1117	0.967985	0.483993	+	0.875072i	$0.339186\pi$
$674$	−39.5912	−1.52499
$675$	76.6340	2.94964
$676$	−29.8671	−1.14874
$677$	39.9365	1.53489	0.767443	−	0.641118i	$-0.221529\pi$
$677$	39.9365	1.53489	0.767443	+	0.641118i	$0.221529\pi$
$678$	−117.350	−4.50679
$679$	1.51237	0.0580393
$680$	1.46907	0.0563364
$681$	−39.4407	−1.51137
$682$	−22.5997	−0.865388
$683$	−7.62894	−0.291913	−0.145957	−	0.989291i	$-0.546626\pi$
$683$	−7.62894	−0.291913	−0.145957	+	0.989291i	$0.546626\pi$
$684$	165.058	6.31115
$685$	−2.79719	−0.106875
$686$	−48.6741	−1.85839
$687$	−15.6921	−0.598693
$688$	−20.8433	−0.794643
$689$	−7.20187	−0.274370
$690$	4.43725	0.168923
$691$	52.1279	1.98304	0.991519	−	0.129964i	$-0.0414861\pi$
$691$	52.1279	1.98304	0.991519	+	0.129964i	$0.0414861\pi$
$692$	−116.928	−4.44493
$693$	36.3316	1.38012
$694$	89.3756	3.39265
$695$	−3.24762	−0.123189
$696$	−40.2253	−1.52474
$697$	−1.26081	−0.0477565
$698$	−80.4920	−3.04667
$699$	38.8299	1.46868
$700$	39.6520	1.49871
$701$	−52.0994	−1.96777	−0.983884	−	0.178808i	$-0.942776\pi$
$701$	−52.0994	−1.96777	−0.983884	+	0.178808i	$0.942776\pi$
$702$	−105.705	−3.98957
$703$	−30.0005	−1.13149
$704$	−24.3412	−0.917394
$705$	−0.259314	−0.00976633
$706$	−2.61678	−0.0984838
$707$	−2.88510	−0.108505
$708$	2.74886	0.103308
$709$	−48.8254	−1.83368	−0.916839	−	0.399257i	$-0.869268\pi$
$709$	−48.8254	−1.83368	−0.916839	+	0.399257i	$0.869268\pi$
$710$	−0.439071	−0.0164780
$711$	116.592	4.37254
$712$	−50.4742	−1.89160
$713$	−7.94712	−0.297622
$714$	14.1251	0.528620
$715$	1.47196	0.0550483
$716$	27.5415	1.02927
$717$	94.8342	3.54165
$718$	−37.2452	−1.38998
$719$	7.69455	0.286958	0.143479	−	0.989653i	$-0.454171\pi$
$719$	7.69455	0.286958	0.143479	+	0.989653i	$0.454171\pi$
$720$	14.9179	0.555958
$721$	−0.197355	−0.00734988
$722$	−1.20984	−0.0450254
$723$	−5.52782	−0.205582
$724$	−51.2193	−1.90355
$725$	8.18053	0.303817
$726$	−24.4080	−0.905865
$727$	3.86123	0.143205	0.0716026	−	0.997433i	$-0.477189\pi$
$727$	3.86123	0.143205	0.0716026	+	0.997433i	$0.477189\pi$
$728$	−32.1283	−1.19075
$729$	59.8930	2.21826
$730$	3.83876	0.142079
$731$	2.12609	0.0786364
$732$	51.6909	1.91055
$733$	27.0980	1.00089	0.500444	−	0.865769i	$-0.333170\pi$
$733$	27.0980	1.00089	0.500444	+	0.865769i	$0.333170\pi$
$734$	55.9940	2.06678
$735$	2.76354	0.101935
$736$	−28.2440	−1.04109
$737$	18.4979	0.681378
$738$	−25.4645	−0.937360
$739$	43.5122	1.60062	0.800311	−	0.599586i	$-0.204668\pi$
$739$	43.5122	1.60062	0.800311	+	0.599586i	$0.204668\pi$
$740$	−6.49920	−0.238915
$741$	37.7699	1.38751
$742$	11.8820	0.436202
$743$	21.7326	0.797291	0.398645	−	0.917105i	$-0.369480\pi$
$743$	21.7326	0.797291	0.398645	+	0.917105i	$0.369480\pi$
$744$	−73.7956	−2.70548
$745$	−1.41081	−0.0516882
$746$	41.2868	1.51162
$747$	8.28327	0.303069
$748$	13.8396	0.506028
$749$	−26.7043	−0.975755
$750$	−16.8246	−0.614347
$751$	25.7712	0.940403	0.470202	−	0.882559i	$-0.344181\pi$
$751$	25.7712	0.940403	0.470202	+	0.882559i	$0.344181\pi$
$752$	3.93860	0.143626
$753$	92.0739	3.35536
$754$	−11.2838	−0.410932
$755$	−1.83816	−0.0668976
$756$	123.460	4.49019
$757$	−24.0448	−0.873925	−0.436962	−	0.899480i	$-0.643946\pi$
$757$	−24.0448	−0.873925	−0.436962	+	0.899480i	$0.643946\pi$
$758$	28.5505	1.03700
$759$	24.5552	0.891297
$760$	−6.48099	−0.235090
$761$	21.5588	0.781504	0.390752	−	0.920496i	$-0.372215\pi$
$761$	21.5588	0.781504	0.390752	+	0.920496i	$0.372215\pi$
$762$	119.561	4.33125
$763$	10.1722	0.368258
$764$	66.2136	2.39552
$765$	−1.52168	−0.0550166
$766$	−21.7486	−0.785808
$767$	0.452956	0.0163553
$768$	48.9001	1.76453
$769$	39.8366	1.43654	0.718272	−	0.695762i	$-0.244933\pi$
$769$	39.8366	1.43654	0.718272	+	0.695762i	$0.244933\pi$
$770$	−2.42852	−0.0875176
$771$	−34.7971	−1.25319
$772$	−42.5418	−1.53111
$773$	0.394657	0.0141948	0.00709742	−	0.999975i	$-0.497741\pi$
$773$	0.394657	0.0141948	0.00709742	+	0.999975i	$0.497741\pi$
$774$	42.9405	1.54347
$775$	15.0076	0.539091
$776$	6.83487	0.245358
$777$	−36.7077	−1.31688
$778$	−40.9504	−1.46814
$779$	5.56220	0.199287
$780$	8.18232	0.292974
$781$	−2.42977	−0.0869439
$782$	6.87457	0.245834
$783$	25.4708	0.910251
$784$	−41.9741	−1.49908
$785$	−0.489876	−0.0174844
$786$	54.4320	1.94153
$787$	−13.1001	−0.466968	−0.233484	−	0.972361i	$-0.575013\pi$
$787$	−13.1001	−0.466968	−0.233484	+	0.972361i	$0.575013\pi$
$788$	−68.9868	−2.45755
$789$	−16.5981	−0.590908
$790$	−7.79336	−0.277275
$791$	22.5848	0.803023
$792$	164.194	5.83440
$793$	8.51762	0.302470
$794$	20.4169	0.724569
$795$	−1.77757	−0.0630439
$796$	−17.7766	−0.630073
$797$	47.1857	1.67140	0.835701	−	0.549185i	$-0.185062\pi$
$797$	47.1857	1.67140	0.835701	+	0.549185i	$0.185062\pi$
$798$	−62.3146	−2.20591
$799$	−0.401752	−0.0142130
$800$	53.3371	1.88575
$801$	52.2818	1.84729
$802$	6.89860	0.243598
$803$	21.2432	0.749658
$804$	102.826	3.62638
$805$	−0.853981	−0.0300989
$806$	−20.7008	−0.729153
$807$	−26.3044	−0.925960
$808$	−13.0387	−0.458700
$809$	31.6082	1.11129	0.555643	−	0.831421i	$-0.312472\pi$
$809$	31.6082	1.11129	0.555643	+	0.831421i	$0.312472\pi$
$810$	−14.1444	−0.496984
$811$	−17.2171	−0.604573	−0.302287	−	0.953217i	$-0.597750\pi$
$811$	−17.2171	−0.604573	−0.302287	+	0.953217i	$0.597750\pi$
$812$	13.1791	0.462496
$813$	62.1959	2.18131
$814$	−50.8045	−1.78070
$815$	1.61687	0.0566366
$816$	32.0956	1.12357
$817$	−9.37950	−0.328147
$818$	−20.1731	−0.705335
$819$	33.2788	1.16286
$820$	1.20497	0.0420795
$821$	6.20828	0.216670	0.108335	−	0.994114i	$-0.465448\pi$
$821$	6.20828	0.216670	0.108335	+	0.994114i	$0.465448\pi$
$822$	−121.547	−4.23944
$823$	−21.9230	−0.764186	−0.382093	−	0.924124i	$-0.624797\pi$
$823$	−21.9230	−0.764186	−0.382093	+	0.924124i	$0.624797\pi$
$824$	−0.891911	−0.0310712
$825$	−46.3709	−1.61443
$826$	−0.747309	−0.0260022
$827$	5.93032	0.206217	0.103109	−	0.994670i	$-0.467121\pi$
$827$	5.93032	0.206217	0.103109	+	0.994670i	$0.467121\pi$
$828$	98.2918	3.41588
$829$	9.56171	0.332092	0.166046	−	0.986118i	$-0.446900\pi$
$829$	9.56171	0.332092	0.166046	+	0.986118i	$0.446900\pi$
$830$	−0.553679	−0.0192185
$831$	82.7792	2.87158
$832$	−22.2959	−0.772972
$833$	4.28152	0.148346
$834$	−141.120	−4.88657
$835$	2.74410	0.0949633
$836$	−61.0552	−2.11164
$837$	46.7276	1.61514
$838$	−0.242149	−0.00836491
$839$	−19.6806	−0.679451	−0.339726	−	0.940525i	$-0.610334\pi$
$839$	−19.6806	−0.679451	−0.339726	+	0.940525i	$0.610334\pi$
$840$	−7.92992	−0.273608
$841$	−26.2810	−0.906243
$842$	43.1078	1.48559
$843$	−48.0463	−1.65480
$844$	−85.3265	−2.93706
$845$	−1.21473	−0.0417879
$846$	−8.11415	−0.278970
$847$	4.69749	0.161408
$848$	26.9987	0.927138
$849$	83.9164	2.88000
$850$	−12.9822	−0.445285
$851$	−17.8653	−0.612414
$852$	−13.5065	−0.462726
$853$	−7.20421	−0.246667	−0.123334	−	0.992365i	$-0.539359\pi$
$853$	−7.20421	−0.246667	−0.123334	+	0.992365i	$0.539359\pi$
$854$	−14.0528	−0.480876
$855$	6.71308	0.229583
$856$	−120.686	−4.12495
$857$	53.6422	1.83238	0.916191	−	0.400742i	$-0.131248\pi$
$857$	53.6422	1.83238	0.916191	+	0.400742i	$0.131248\pi$
$858$	63.9616	2.18361
$859$	17.7948	0.607149	0.303575	−	0.952808i	$-0.401820\pi$
$859$	17.7948	0.607149	0.303575	+	0.952808i	$0.401820\pi$
$860$	−2.03194	−0.0692885
$861$	6.80572	0.231938
$862$	25.9082	0.882437
$863$	−21.2483	−0.723300	−0.361650	−	0.932314i	$-0.617786\pi$
$863$	−21.2483	−0.723300	−0.361650	+	0.932314i	$0.617786\pi$
$864$	166.069	5.64980
$865$	−4.75557	−0.161694
$866$	−100.996	−3.43200
$867$	−3.27387	−0.111186
$868$	24.1778	0.820648
$869$	−43.1275	−1.46300
$870$	−2.78507	−0.0944228
$871$	16.9436	0.574111
$872$	45.9715	1.55679
$873$	−7.07964	−0.239610
$874$	−30.3279	−1.02586
$875$	3.23801	0.109465
$876$	118.087	3.98977
$877$	−7.46490	−0.252072	−0.126036	−	0.992026i	$-0.540225\pi$
$877$	−7.46490	−0.252072	−0.126036	+	0.992026i	$0.540225\pi$
$878$	61.0635	2.06079
$879$	14.3175	0.482916
$880$	−5.51816	−0.186017
$881$	1.32732	0.0447186	0.0223593	−	0.999750i	$-0.492882\pi$
$881$	1.32732	0.0447186	0.0223593	+	0.999750i	$0.492882\pi$
$882$	86.4734	2.91171
$883$	32.4119	1.09075	0.545374	−	0.838193i	$-0.316388\pi$
$883$	32.4119	1.09075	0.545374	+	0.838193i	$0.316388\pi$
$884$	12.6768	0.426366
$885$	0.111799	0.00375808
$886$	20.4239	0.686155
$887$	−32.6215	−1.09532	−0.547662	−	0.836700i	$-0.684482\pi$
$887$	−32.6215	−1.09532	−0.547662	+	0.836700i	$0.684482\pi$
$888$	−165.894	−5.56703
$889$	−23.0105	−0.771746
$890$	−3.49467	−0.117142
$891$	−78.2734	−2.62226
$892$	−44.8681	−1.50229
$893$	1.77237	0.0593102
$894$	−61.3044	−2.05033
$895$	1.12014	0.0374422
$896$	1.33278	0.0445251
$897$	22.4919	0.750983
$898$	−69.1070	−2.30613
$899$	4.98808	0.166362
$900$	−185.618	−6.18726
$901$	−2.75397	−0.0917479
$902$	9.41933	0.313629
$903$	−11.4764	−0.381912
$904$	102.068	3.39473
$905$	−2.08314	−0.0692460
$906$	−79.8742	−2.65364
$907$	28.0790	0.932349	0.466175	−	0.884693i	$-0.345632\pi$
$907$	28.0790	0.932349	0.466175	+	0.884693i	$0.345632\pi$
$908$	58.3989	1.93804
$909$	13.5056	0.447953
$910$	−2.22446	−0.0737401
$911$	15.8289	0.524433	0.262217	−	0.965009i	$-0.415546\pi$
$911$	15.8289	0.524433	0.262217	+	0.965009i	$0.415546\pi$
$912$	−141.593	−4.68863
$913$	−3.06399	−0.101403
$914$	−47.3518	−1.56626
$915$	2.10232	0.0695007
$916$	23.2350	0.767705
$917$	−10.4758	−0.345943
$918$	−40.4211	−1.33410
$919$	−32.2774	−1.06473	−0.532366	−	0.846514i	$-0.678697\pi$
$919$	−32.2774	−1.06473	−0.532366	+	0.846514i	$0.678697\pi$
$920$	−3.85942	−0.127241
$921$	−36.5474	−1.20428
$922$	−62.3924	−2.05478
$923$	−2.22560	−0.0732566
$924$	−74.7051	−2.45762
$925$	33.7375	1.10928
$926$	25.6311	0.842290
$927$	0.923852	0.0303433
$928$	17.7276	0.581937
$929$	3.99440	0.131052	0.0655261	−	0.997851i	$-0.479127\pi$
$929$	3.99440	0.131052	0.0655261	+	0.997851i	$0.479127\pi$
$930$	−5.10937	−0.167543
$931$	−18.8884	−0.619042
$932$	−57.4944	−1.88329
$933$	59.0828	1.93428
$934$	−36.9241	−1.20819
$935$	0.562873	0.0184079
$936$	150.398	4.91591
$937$	−22.7500	−0.743211	−0.371605	−	0.928391i	$-0.621193\pi$
$937$	−22.7500	−0.743211	−0.371605	+	0.928391i	$0.621193\pi$
$938$	−27.9543	−0.912741
$939$	39.0002	1.27272
$940$	0.383960	0.0125234
$941$	−22.3539	−0.728716	−0.364358	−	0.931259i	$-0.618712\pi$
$941$	−22.3539	−0.728716	−0.364358	+	0.931259i	$0.618712\pi$
$942$	−21.2867	−0.693558
$943$	3.31228	0.107863
$944$	−1.69806	−0.0552672
$945$	5.02124	0.163341
$946$	−15.8838	−0.516425
$947$	−35.8199	−1.16399	−0.581994	−	0.813193i	$-0.697727\pi$
$947$	−35.8199	−1.16399	−0.581994	+	0.813193i	$0.697727\pi$
$948$	−239.736	−7.78628
$949$	19.4583	0.631642
$950$	57.2724	1.85816
$951$	18.4756	0.599113
$952$	−12.2857	−0.398182
$953$	−33.3547	−1.08046	−0.540232	−	0.841516i	$-0.681664\pi$
$953$	−33.3547	−1.08046	−0.540232	+	0.841516i	$0.681664\pi$
$954$	−55.6216	−1.80082
$955$	2.69298	0.0871426
$956$	−140.419	−4.54147
$957$	−15.4123	−0.498208
$958$	−49.5395	−1.60055
$959$	23.3926	0.755386
$960$	−5.50309	−0.177612
$961$	−21.8491	−0.704809
$962$	−46.5356	−1.50037
$963$	125.008	4.02831
$964$	8.18491	0.263618
$965$	−1.73022	−0.0556978
$966$	−37.1082	−1.19394
$967$	13.2680	0.426671	0.213335	−	0.976979i	$-0.431567\pi$
$967$	13.2680	0.426671	0.213335	+	0.976979i	$0.431567\pi$
$968$	21.2295	0.682342
$969$	14.4431	0.463978
$970$	0.473225	0.0151943
$971$	52.7633	1.69325	0.846627	−	0.532187i	$-0.178630\pi$
$971$	52.7633	1.69325	0.846627	+	0.532187i	$0.178630\pi$
$972$	−210.466	−6.75072
$973$	27.1595	0.870694
$974$	−108.298	−3.47011
$975$	−42.4746	−1.36028
$976$	−31.9312	−1.02209
$977$	38.5764	1.23417	0.617084	−	0.786898i	$-0.288314\pi$
$977$	38.5764	1.23417	0.617084	+	0.786898i	$0.288314\pi$
$978$	70.2584	2.24662
$979$	−19.3391	−0.618081
$980$	−4.09190	−0.130711
$981$	−47.6178	−1.52032
$982$	19.8799	0.634394
$983$	17.4098	0.555285	0.277642	−	0.960684i	$-0.410447\pi$
$983$	17.4098	0.555285	0.277642	+	0.960684i	$0.410447\pi$
$984$	30.7573	0.980506
$985$	−2.80577	−0.0893991
$986$	−4.31488	−0.137414
$987$	2.16862	0.0690278
$988$	−55.9250	−1.77921
$989$	−5.58548	−0.177608
$990$	11.3683	0.361308
$991$	28.4431	0.903524	0.451762	−	0.892139i	$-0.350796\pi$
$991$	28.4431	0.903524	0.451762	+	0.892139i	$0.350796\pi$
$992$	32.5223	1.03258
$993$	−59.5755	−1.89057
$994$	3.67191	0.116466
$995$	−0.722991	−0.0229204
$996$	−17.0321	−0.539681
$997$	−1.42766	−0.0452144	−0.0226072	−	0.999744i	$-0.507197\pi$
$997$	−1.42766	−0.0452144	−0.0226072	+	0.999744i	$0.507197\pi$
$998$	87.4736	2.76893
$999$	105.044	3.32346

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.c.1.5	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.c.1.5	✓	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)

\(f(q)\)	\(=\)	\(q-2.61678 q^{2} -3.27387 q^{3} +4.84754 q^{4} +0.197154 q^{5} +8.56700 q^{6} -1.64878 q^{7} -7.45139 q^{8} +7.71823 q^{9} +O(q^{10})\)	\(q-2.61678 q^{2} -3.27387 q^{3} +4.84754 q^{4} +0.197154 q^{5} +8.56700 q^{6} -1.64878 q^{7} -7.45139 q^{8} +7.71823 q^{9} -0.515910 q^{10} -2.85498 q^{11} -15.8702 q^{12} -2.61509 q^{13} +4.31450 q^{14} -0.645458 q^{15} +9.80356 q^{16} -1.00000 q^{17} -20.1969 q^{18} +4.41161 q^{19} +0.955714 q^{20} +5.39790 q^{21} +7.47087 q^{22} +2.62711 q^{23} +24.3949 q^{24} -4.96113 q^{25} +6.84312 q^{26} -15.4469 q^{27} -7.99254 q^{28} -1.64893 q^{29} +1.68902 q^{30} -3.02505 q^{31} -10.7510 q^{32} +9.34685 q^{33} +2.61678 q^{34} -0.325065 q^{35} +37.4144 q^{36} -6.80036 q^{37} -11.5442 q^{38} +8.56147 q^{39} -1.46907 q^{40} +1.26081 q^{41} -14.1251 q^{42} -2.12609 q^{43} -13.8396 q^{44} +1.52168 q^{45} -6.87457 q^{46} +0.401752 q^{47} -32.0956 q^{48} -4.28152 q^{49} +12.9822 q^{50} +3.27387 q^{51} -12.6768 q^{52} +2.75397 q^{53} +40.4211 q^{54} -0.562873 q^{55} +12.2857 q^{56} -14.4431 q^{57} +4.31488 q^{58} -0.173209 q^{59} -3.12888 q^{60} -3.25710 q^{61} +7.91588 q^{62} -12.7257 q^{63} +8.52587 q^{64} -0.515577 q^{65} -24.4587 q^{66} -6.47915 q^{67} -4.84754 q^{68} -8.60081 q^{69} +0.850623 q^{70} +0.851062 q^{71} -57.5115 q^{72} -7.44076 q^{73} +17.7950 q^{74} +16.2421 q^{75} +21.3855 q^{76} +4.70725 q^{77} -22.4035 q^{78} +15.1061 q^{79} +1.93282 q^{80} +27.4164 q^{81} -3.29926 q^{82} +1.07321 q^{83} +26.1665 q^{84} -0.197154 q^{85} +5.56352 q^{86} +5.39837 q^{87} +21.2736 q^{88} +6.77381 q^{89} -3.98191 q^{90} +4.31172 q^{91} +12.7350 q^{92} +9.90361 q^{93} -1.05130 q^{94} +0.869769 q^{95} +35.1974 q^{96} -0.917262 q^{97} +11.2038 q^{98} -22.0354 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9}+O(q^{10}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9	\( 121 q + 9 q^{2} + 13 q^{3} + 127 q^{4} + 21 q^{5} + 19 q^{6} - 13 q^{7} + 24 q^{8} + 134 q^{9} - q^{10} + 40 q^{11} + 41 q^{12} + 14 q^{13} + 32 q^{14} + 49 q^{15} + 135 q^{16} - 121 q^{17} + 28 q^{18} + 34 q^{19} + 64 q^{20} + 34 q^{21} - 18 q^{22} + 37 q^{23} + 54 q^{24} + 128 q^{25} + 91 q^{26} + 55 q^{27} - 28 q^{28} + 45 q^{29} + 30 q^{30} + 67 q^{31} + 47 q^{32} + 40 q^{33} - 9 q^{34} + 59 q^{35} + 138 q^{36} - 16 q^{37} + 30 q^{38} + 37 q^{39} + 14 q^{40} + 89 q^{41} + 33 q^{42} + 16 q^{43} + 90 q^{44} + 83 q^{45} - 9 q^{46} + 135 q^{47} + 96 q^{48} + 128 q^{49} + 71 q^{50} - 13 q^{51} + 47 q^{52} + 52 q^{53} + 90 q^{54} + 93 q^{55} + 69 q^{56} - 4 q^{57} + 5 q^{58} + 170 q^{59} + 78 q^{60} - 2 q^{61} + 46 q^{62} - 10 q^{63} + 182 q^{64} + 50 q^{65} + 68 q^{66} + 46 q^{67} - 127 q^{68} + 97 q^{69} + 46 q^{70} + 191 q^{71} + 57 q^{72} - 12 q^{73} + 68 q^{74} + 86 q^{75} + 108 q^{76} + 62 q^{77} - 10 q^{78} + 130 q^{80} + 149 q^{81} + 14 q^{82} + 83 q^{83} + 126 q^{84} - 21 q^{85} + 132 q^{86} + 50 q^{87} - 42 q^{88} + 144 q^{89} + 9 q^{90} + 13 q^{91} + 50 q^{92} + 43 q^{93} + 41 q^{94} + 82 q^{95} + 110 q^{96} - 3 q^{97} + 36 q^{98} + 89 q^{99}+O(q^{100}) \) 121 * q + 9 * q^2 + 13 * q^3 + 127 * q^4 + 21 * q^5 + 19 * q^6 - 13 * q^7 + 24 * q^8 + 134 * q^9 - q^10 + 40 * q^11 + 41 * q^12 + 14 * q^13 + 32 * q^14 + 49 * q^15 + 135 * q^16 - 121 * q^17 + 28 * q^18 + 34 * q^19 + 64 * q^20 + 34 * q^21 - 18 * q^22 + 37 * q^23 + 54 * q^24 + 128 * q^25 + 91 * q^26 + 55 * q^27 - 28 * q^28 + 45 * q^29 + 30 * q^30 + 67 * q^31 + 47 * q^32 + 40 * q^33 - 9 * q^34 + 59 * q^35 + 138 * q^36 - 16 * q^37 + 30 * q^38 + 37 * q^39 + 14 * q^40 + 89 * q^41 + 33 * q^42 + 16 * q^43 + 90 * q^44 + 83 * q^45 - 9 * q^46 + 135 * q^47 + 96 * q^48 + 128 * q^49 + 71 * q^50 - 13 * q^51 + 47 * q^52 + 52 * q^53 + 90 * q^54 + 93 * q^55 + 69 * q^56 - 4 * q^57 + 5 * q^58 + 170 * q^59 + 78 * q^60 - 2 * q^61 + 46 * q^62 - 10 * q^63 + 182 * q^64 + 50 * q^65 + 68 * q^66 + 46 * q^67 - 127 * q^68 + 97 * q^69 + 46 * q^70 + 191 * q^71 + 57 * q^72 - 12 * q^73 + 68 * q^74 + 86 * q^75 + 108 * q^76 + 62 * q^77 - 10 * q^78 + 130 * q^80 + 149 * q^81 + 14 * q^82 + 83 * q^83 + 126 * q^84 - 21 * q^85 + 132 * q^86 + 50 * q^87 - 42 * q^88 + 144 * q^89 + 9 * q^90 + 13 * q^91 + 50 * q^92 + 43 * q^93 + 41 * q^94 + 82 * q^95 + 110 * q^96 - 3 * q^97 + 36 * q^98 + 89 * q^99

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