LMFDB - Embedded newform 2011.2.a.b.1.73

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2011,2,Mod(1,2011)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2011, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("2011.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2011 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2011.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:	$16.0579158465$
Analytic rank:	$0$
Dimension:	$90$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.73
Character	$\chi$	$=$	2011.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.09238 q^{2} +1.08626 q^{3} +2.37805 q^{4} +3.15840 q^{5} +2.27286 q^{6} +3.82197 q^{7} +0.791031 q^{8} -1.82005 q^{9} +O(q^{10})$	\(q+2.09238 q^{2} +1.08626 q^{3} +2.37805 q^{4} +3.15840 q^{5} +2.27286 q^{6} +3.82197 q^{7} +0.791031 q^{8} -1.82005 q^{9} +6.60857 q^{10} -0.265923 q^{11} +2.58317 q^{12} +0.0835493 q^{13} +7.99701 q^{14} +3.43082 q^{15} -3.10097 q^{16} -6.78611 q^{17} -3.80824 q^{18} +6.52967 q^{19} +7.51084 q^{20} +4.15163 q^{21} -0.556411 q^{22} +3.60479 q^{23} +0.859262 q^{24} +4.97547 q^{25} +0.174817 q^{26} -5.23580 q^{27} +9.08885 q^{28} -4.81705 q^{29} +7.17859 q^{30} +1.90937 q^{31} -8.07047 q^{32} -0.288860 q^{33} -14.1991 q^{34} +12.0713 q^{35} -4.32818 q^{36} +0.390191 q^{37} +13.6625 q^{38} +0.0907558 q^{39} +2.49839 q^{40} -7.23490 q^{41} +8.68680 q^{42} -6.69586 q^{43} -0.632378 q^{44} -5.74844 q^{45} +7.54260 q^{46} +9.29032 q^{47} -3.36844 q^{48} +7.60745 q^{49} +10.4106 q^{50} -7.37145 q^{51} +0.198685 q^{52} -3.60477 q^{53} -10.9553 q^{54} -0.839889 q^{55} +3.02330 q^{56} +7.09289 q^{57} -10.0791 q^{58} +4.25124 q^{59} +8.15868 q^{60} -8.30595 q^{61} +3.99513 q^{62} -6.95617 q^{63} -10.6845 q^{64} +0.263882 q^{65} -0.604404 q^{66} +1.09939 q^{67} -16.1377 q^{68} +3.91573 q^{69} +25.2577 q^{70} +11.7118 q^{71} -1.43972 q^{72} +0.574352 q^{73} +0.816428 q^{74} +5.40463 q^{75} +15.5279 q^{76} -1.01635 q^{77} +0.189896 q^{78} -6.69767 q^{79} -9.79409 q^{80} -0.227271 q^{81} -15.1382 q^{82} -3.52373 q^{83} +9.87281 q^{84} -21.4332 q^{85} -14.0103 q^{86} -5.23254 q^{87} -0.210353 q^{88} -15.7256 q^{89} -12.0279 q^{90} +0.319323 q^{91} +8.57239 q^{92} +2.07407 q^{93} +19.4389 q^{94} +20.6233 q^{95} -8.76659 q^{96} -3.46004 q^{97} +15.9177 q^{98} +0.483992 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) $ 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * 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 $

$2$	2.09238	1.47954	0.739768	−	0.672862i	$-0.234935\pi$
$2$	2.09238	1.47954	0.739768	+	0.672862i	$0.234935\pi$
$3$	1.08626	0.627150	0.313575	−	0.949563i	$-0.398473\pi$
$3$	1.08626	0.627150	0.313575	+	0.949563i	$0.398473\pi$
$4$	2.37805	1.18903
$5$	3.15840	1.41248	0.706239	−	0.707974i	$-0.250390\pi$
$5$	3.15840	1.41248	0.706239	+	0.707974i	$0.250390\pi$
$6$	2.27286	0.927891
$7$	3.82197	1.44457	0.722284	−	0.691596i	$-0.243092\pi$
$7$	3.82197	1.44457	0.722284	+	0.691596i	$0.243092\pi$
$8$	0.791031	0.279672
$9$	−1.82005	−0.606683
$10$	6.60857	2.08981
$11$	−0.265923	−0.0801787	−0.0400893	−	0.999196i	$-0.512764\pi$
$11$	−0.265923	−0.0801787	−0.0400893	+	0.999196i	$0.512764\pi$
$12$	2.58317	0.745698
$13$	0.0835493	0.0231724	0.0115862	−	0.999933i	$-0.496312\pi$
$13$	0.0835493	0.0231724	0.0115862	+	0.999933i	$0.496312\pi$
$14$	7.99701	2.13729
$15$	3.43082	0.885835
$16$	−3.10097	−0.775242
$17$	−6.78611	−1.64587	−0.822937	−	0.568133i	$-0.807666\pi$
$17$	−6.78611	−1.64587	−0.822937	+	0.568133i	$0.807666\pi$
$18$	−3.80824	−0.897610
$19$	6.52967	1.49801	0.749004	−	0.662565i	$-0.230532\pi$
$19$	6.52967	1.49801	0.749004	+	0.662565i	$0.230532\pi$
$20$	7.51084	1.67947
$21$	4.15163	0.905961
$22$	−0.556411	−0.118627
$23$	3.60479	0.751652	0.375826	−	0.926690i	$-0.377359\pi$
$23$	3.60479	0.751652	0.375826	+	0.926690i	$0.377359\pi$
$24$	0.859262	0.175396
$25$	4.97547	0.995094
$26$	0.174817	0.0342844
$27$	−5.23580	−1.00763
$28$	9.08885	1.71763
$29$	−4.81705	−0.894503	−0.447252	−	0.894408i	$-0.647597\pi$
$29$	−4.81705	−0.894503	−0.447252	+	0.894408i	$0.647597\pi$
$30$	7.17859	1.31062
$31$	1.90937	0.342934	0.171467	−	0.985190i	$-0.445149\pi$
$31$	1.90937	0.342934	0.171467	+	0.985190i	$0.445149\pi$
$32$	−8.07047	−1.42667
$33$	−0.288860	−0.0502840
$34$	−14.1991	−2.43513
$35$	12.0713	2.04042
$36$	−4.32818	−0.721363
$37$	0.390191	0.0641470	0.0320735	−	0.999486i	$-0.489789\pi$
$37$	0.390191	0.0641470	0.0320735	+	0.999486i	$0.489789\pi$
$38$	13.6625	2.21636
$39$	0.0907558	0.0145326
$40$	2.49839	0.395030
$41$	−7.23490	−1.12990	−0.564950	−	0.825125i	$-0.691105\pi$
$41$	−7.23490	−1.12990	−0.564950	+	0.825125i	$0.691105\pi$
$42$	8.68680	1.34040
$43$	−6.69586	−1.02111	−0.510555	−	0.859845i	$-0.670560\pi$
$43$	−6.69586	−1.02111	−0.510555	+	0.859845i	$0.670560\pi$
$44$	−0.632378	−0.0953346
$45$	−5.74844	−0.856927
$46$	7.54260	1.11210
$47$	9.29032	1.35513	0.677566	−	0.735462i	$-0.263035\pi$
$47$	9.29032	1.35513	0.677566	+	0.735462i	$0.263035\pi$
$48$	−3.36844	−0.486193
$49$	7.60745	1.08678
$50$	10.4106	1.47228
$51$	−7.37145	−1.03221
$52$	0.198685	0.0275526
$53$	−3.60477	−0.495154	−0.247577	−	0.968868i	$-0.579634\pi$
$53$	−3.60477	−0.495154	−0.247577	+	0.968868i	$0.579634\pi$
$54$	−10.9553	−1.49083
$55$	−0.839889	−0.113251
$56$	3.02330	0.404005
$57$	7.09289	0.939476
$58$	−10.0791	−1.32345
$59$	4.25124	0.553464	0.276732	−	0.960947i	$-0.410749\pi$
$59$	4.25124	0.553464	0.276732	+	0.960947i	$0.410749\pi$
$60$	8.15868	1.05328
$61$	−8.30595	−1.06347	−0.531734	−	0.846912i	$-0.678459\pi$
$61$	−8.30595	−1.06347	−0.531734	+	0.846912i	$0.678459\pi$
$62$	3.99513	0.507383
$63$	−6.95617	−0.876396
$64$	−10.6845	−1.33557
$65$	0.263882	0.0327305
$66$	−0.604404	−0.0743970
$67$	1.09939	0.134312	0.0671562	−	0.997742i	$-0.478607\pi$
$67$	1.09939	0.134312	0.0671562	+	0.997742i	$0.478607\pi$
$68$	−16.1377	−1.95699
$69$	3.91573	0.471398
$70$	25.2577	3.01888
$71$	11.7118	1.38994	0.694970	−	0.719038i	$-0.255417\pi$
$71$	11.7118	1.38994	0.694970	+	0.719038i	$0.255417\pi$
$72$	−1.43972	−0.169672
$73$	0.574352	0.0672228	0.0336114	−	0.999435i	$-0.489299\pi$
$73$	0.574352	0.0672228	0.0336114	+	0.999435i	$0.489299\pi$
$74$	0.816428	0.0949078
$75$	5.40463	0.624073
$76$	15.5279	1.78117
$77$	−1.01635	−0.115824
$78$	0.189896	0.0215015
$79$	−6.69767	−0.753547	−0.376773	−	0.926305i	$-0.622966\pi$
$79$	−6.69767	−0.753547	−0.376773	+	0.926305i	$0.622966\pi$
$80$	−9.79409	−1.09501
$81$	−0.227271	−0.0252523
$82$	−15.1382	−1.67173
$83$	−3.52373	−0.386779	−0.193390	−	0.981122i	$-0.561948\pi$
$83$	−3.52373	−0.386779	−0.193390	+	0.981122i	$0.561948\pi$
$84$	9.87281	1.07721
$85$	−21.4332	−2.32476
$86$	−14.0103	−1.51077
$87$	−5.23254	−0.560988
$88$	−0.210353	−0.0224237
$89$	−15.7256	−1.66691	−0.833455	−	0.552587i	$-0.813641\pi$
$89$	−15.7256	−1.66691	−0.833455	+	0.552587i	$0.813641\pi$
$90$	−12.0279	−1.26785
$91$	0.319323	0.0334741
$92$	8.57239	0.893734
$93$	2.07407	0.215071
$94$	19.4389	2.00497
$95$	20.6233	2.11590
$96$	−8.76659	−0.894736
$97$	−3.46004	−0.351314	−0.175657	−	0.984451i	$-0.556205\pi$
$97$	−3.46004	−0.351314	−0.175657	+	0.984451i	$0.556205\pi$
$98$	15.9177	1.60793
$99$	0.483992	0.0486430
$100$	11.8319	1.18319
$101$	19.5342	1.94373	0.971864	−	0.235542i	$-0.0756864\pi$
$101$	19.5342	1.94373	0.971864	+	0.235542i	$0.0756864\pi$
$102$	−15.4239	−1.52719
$103$	−10.7920	−1.06337	−0.531686	−	0.846942i	$-0.678441\pi$
$103$	−10.7920	−1.06337	−0.531686	+	0.846942i	$0.678441\pi$
$104$	0.0660901	0.00648067
$105$	13.1125	1.27965
$106$	−7.54256	−0.732598
$107$	7.75052	0.749271	0.374635	−	0.927172i	$-0.377768\pi$
$107$	7.75052	0.749271	0.374635	+	0.927172i	$0.377768\pi$
$108$	−12.4510	−1.19810
$109$	−12.8272	−1.22863	−0.614313	−	0.789062i	$-0.710567\pi$
$109$	−12.8272	−1.22863	−0.614313	+	0.789062i	$0.710567\pi$
$110$	−1.75737	−0.167558
$111$	0.423847	0.0402298
$112$	−11.8518	−1.11989
$113$	14.9378	1.40523	0.702617	−	0.711569i	$-0.252015\pi$
$113$	14.9378	1.40523	0.702617	+	0.711569i	$0.252015\pi$
$114$	14.8410	1.38999
$115$	11.3854	1.06169
$116$	−11.4552	−1.06359
$117$	−0.152064	−0.0140583
$118$	8.89520	0.818870
$119$	−25.9363	−2.37758
$120$	2.71389	0.247743
$121$	−10.9293	−0.993571
$122$	−17.3792	−1.57344
$123$	−7.85894	−0.708617
$124$	4.54059	0.407757
$125$	−0.0774816	−0.00693016
$126$	−14.5550	−1.29666
$127$	14.8822	1.32058	0.660289	−	0.751011i	$-0.270434\pi$
$127$	14.8822	1.32058	0.660289	+	0.751011i	$0.270434\pi$
$128$	−6.21519	−0.549351
$129$	−7.27342	−0.640388
$130$	0.552141	0.0484260
$131$	17.8430	1.55895	0.779476	−	0.626432i	$-0.215486\pi$
$131$	17.8430	1.55895	0.779476	+	0.626432i	$0.215486\pi$
$132$	−0.686924	−0.0597891
$133$	24.9562	2.16398
$134$	2.30035	0.198720
$135$	−16.5367	−1.42326
$136$	−5.36803	−0.460305
$137$	−9.88695	−0.844699	−0.422350	−	0.906433i	$-0.638795\pi$
$137$	−9.88695	−0.844699	−0.422350	+	0.906433i	$0.638795\pi$
$138$	8.19319	0.697451
$139$	10.7417	0.911096	0.455548	−	0.890211i	$-0.349443\pi$
$139$	10.7417	0.911096	0.455548	+	0.890211i	$0.349443\pi$
$140$	28.7062	2.42612
$141$	10.0917	0.849871
$142$	24.5056	2.05647
$143$	−0.0222176	−0.00185793
$144$	5.64392	0.470326
$145$	−15.2141	−1.26347
$146$	1.20176	0.0994586
$147$	8.26364	0.681573
$148$	0.927895	0.0762725
$149$	22.8674	1.87337	0.936684	−	0.350176i	$-0.113878\pi$
$149$	22.8674	1.87337	0.936684	+	0.350176i	$0.113878\pi$
$150$	11.3085	0.923338
$151$	−9.37064	−0.762572	−0.381286	−	0.924457i	$-0.624519\pi$
$151$	−9.37064	−0.762572	−0.381286	+	0.924457i	$0.624519\pi$
$152$	5.16517	0.418951
$153$	12.3511	0.998524
$154$	−2.12659	−0.171365
$155$	6.03056	0.484386
$156$	0.215822	0.0172796
$157$	−12.0218	−0.959440	−0.479720	−	0.877422i	$-0.659262\pi$
$157$	−12.0218	−0.959440	−0.479720	+	0.877422i	$0.659262\pi$
$158$	−14.0141	−1.11490
$159$	−3.91570	−0.310536
$160$	−25.4897	−2.01514
$161$	13.7774	1.08581
$162$	−0.475537	−0.0373617
$163$	−13.7403	−1.07622	−0.538112	−	0.842874i	$-0.680862\pi$
$163$	−13.7403	−1.07622	−0.538112	+	0.842874i	$0.680862\pi$
$164$	−17.2050	−1.34348
$165$	−0.912334	−0.0710251
$166$	−7.37297	−0.572254
$167$	−2.79485	−0.216272	−0.108136	−	0.994136i	$-0.534488\pi$
$167$	−2.79485	−0.216272	−0.108136	+	0.994136i	$0.534488\pi$
$168$	3.28407	0.253372
$169$	−12.9930	−0.999463
$170$	−44.8465	−3.43957
$171$	−11.8843	−0.908817
$172$	−15.9231	−1.21413
$173$	−11.2725	−0.857030	−0.428515	−	0.903535i	$-0.640963\pi$
$173$	−11.2725	−0.857030	−0.428515	+	0.903535i	$0.640963\pi$
$174$	−10.9485	−0.830001
$175$	19.0161	1.43748
$176$	0.824617	0.0621579
$177$	4.61793	0.347105
$178$	−32.9039	−2.46625
$179$	1.41330	0.105635	0.0528174	−	0.998604i	$-0.483180\pi$
$179$	1.41330	0.105635	0.0528174	+	0.998604i	$0.483180\pi$
$180$	−13.6701	−1.01891
$181$	10.8824	0.808882	0.404441	−	0.914564i	$-0.367466\pi$
$181$	10.8824	0.808882	0.404441	+	0.914564i	$0.367466\pi$
$182$	0.668145	0.0495262
$183$	−9.02238	−0.666953
$184$	2.85151	0.210216
$185$	1.23238	0.0906062
$186$	4.33974	0.318205
$187$	1.80458	0.131964
$188$	22.0929	1.61129
$189$	−20.0111	−1.45559
$190$	43.1517	3.13056
$191$	14.9825	1.08409	0.542047	−	0.840348i	$-0.317650\pi$
$191$	14.9825	1.08409	0.542047	+	0.840348i	$0.317650\pi$
$192$	−11.6061	−0.837601
$193$	−2.93284	−0.211111	−0.105555	−	0.994413i	$-0.533662\pi$
$193$	−2.93284	−0.211111	−0.105555	+	0.994413i	$0.533662\pi$
$194$	−7.23972	−0.519782
$195$	0.286643	0.0205269
$196$	18.0909	1.29221
$197$	17.1461	1.22161	0.610806	−	0.791781i	$-0.290846\pi$
$197$	17.1461	1.22161	0.610806	+	0.791781i	$0.290846\pi$
$198$	1.01270	0.0719691
$199$	16.9486	1.20145	0.600726	−	0.799455i	$-0.294878\pi$
$199$	16.9486	1.20145	0.600726	+	0.799455i	$0.294878\pi$
$200$	3.93575	0.278300
$201$	1.19422	0.0842340
$202$	40.8730	2.87582
$203$	−18.4106	−1.29217
$204$	−17.5297	−1.22732
$205$	−22.8507	−1.59596
$206$	−22.5811	−1.57330
$207$	−6.56091	−0.456014
$208$	−0.259084	−0.0179642
$209$	−1.73639	−0.120108
$210$	27.4363	1.89329
$211$	20.7476	1.42833	0.714163	−	0.699979i	$-0.246808\pi$
$211$	20.7476	1.42833	0.714163	+	0.699979i	$0.246808\pi$
$212$	−8.57234	−0.588751
$213$	12.7221	0.871701
$214$	16.2170	1.10857
$215$	−21.1482	−1.44229
$216$	−4.14169	−0.281806
$217$	7.29757	0.495391
$218$	−26.8394	−1.81780
$219$	0.623893	0.0421588
$220$	−1.99730	−0.134658
$221$	−0.566975	−0.0381388
$222$	0.886849	0.0595214
$223$	1.96867	0.131832	0.0659160	−	0.997825i	$-0.479003\pi$
$223$	1.96867	0.131832	0.0659160	+	0.997825i	$0.479003\pi$
$224$	−30.8451	−2.06092
$225$	−9.05560	−0.603707
$226$	31.2556	2.07909
$227$	16.5384	1.09769	0.548847	−	0.835923i	$-0.315067\pi$
$227$	16.5384	1.09769	0.548847	+	0.835923i	$0.315067\pi$
$228$	16.8673	1.11706
$229$	−9.98089	−0.659556	−0.329778	−	0.944059i	$-0.606974\pi$
$229$	−9.98089	−0.659556	−0.329778	+	0.944059i	$0.606974\pi$
$230$	23.8225	1.57081
$231$	−1.10401	−0.0726387
$232$	−3.81044	−0.250167
$233$	15.0173	0.983818	0.491909	−	0.870647i	$-0.336299\pi$
$233$	15.0173	0.983818	0.491909	+	0.870647i	$0.336299\pi$
$234$	−0.318175	−0.0207998
$235$	29.3425	1.91409
$236$	10.1097	0.658083
$237$	−7.27538	−0.472587
$238$	−54.2686	−3.51771
$239$	21.5973	1.39701	0.698506	−	0.715604i	$-0.253849\pi$
$239$	21.5973	1.39701	0.698506	+	0.715604i	$0.253849\pi$
$240$	−10.6389	−0.686737
$241$	−8.85684	−0.570520	−0.285260	−	0.958450i	$-0.592080\pi$
$241$	−8.85684	−0.570520	−0.285260	+	0.958450i	$0.592080\pi$
$242$	−22.8682	−1.47002
$243$	15.4605	0.991794
$244$	−19.7520	−1.26449
$245$	24.0274	1.53505
$246$	−16.4439	−1.04842
$247$	0.545549	0.0347125
$248$	1.51037	0.0959089
$249$	−3.82767	−0.242568
$250$	−0.162121	−0.0102534
$251$	−12.9601	−0.818035	−0.409018	−	0.912526i	$-0.634129\pi$
$251$	−12.9601	−0.818035	−0.409018	+	0.912526i	$0.634129\pi$
$252$	−16.5422	−1.04206
$253$	−0.958596	−0.0602664
$254$	31.1391	1.95384
$255$	−23.2820	−1.45797
$256$	8.36454	0.522784
$257$	−4.77344	−0.297759	−0.148879	−	0.988855i	$-0.547567\pi$
$257$	−4.77344	−0.297759	−0.148879	+	0.988855i	$0.547567\pi$
$258$	−15.2187	−0.947478
$259$	1.49130	0.0926648
$260$	0.627525	0.0389174
$261$	8.76727	0.542680
$262$	37.3344	2.30653
$263$	−14.3425	−0.884398	−0.442199	−	0.896917i	$-0.645801\pi$
$263$	−14.3425	−0.884398	−0.442199	+	0.896917i	$0.645801\pi$
$264$	−0.228497	−0.0140630
$265$	−11.3853	−0.699394
$266$	52.2179	3.20168
$267$	−17.0820	−1.04540
$268$	2.61442	0.159701
$269$	18.7789	1.14497	0.572486	−	0.819914i	$-0.305979\pi$
$269$	18.7789	1.14497	0.572486	+	0.819914i	$0.305979\pi$
$270$	−34.6012	−2.10576
$271$	−31.4226	−1.90879	−0.954394	−	0.298550i	$-0.903497\pi$
$271$	−31.4226	−1.90879	−0.954394	+	0.298550i	$0.903497\pi$
$272$	21.0435	1.27595
$273$	0.346866	0.0209933
$274$	−20.6873	−1.24976
$275$	−1.32309	−0.0797853
$276$	9.31181	0.560505
$277$	−28.7634	−1.72822	−0.864111	−	0.503301i	$-0.832119\pi$
$277$	−28.7634	−1.72822	−0.864111	+	0.503301i	$0.832119\pi$
$278$	22.4756	1.34800
$279$	−3.47515	−0.208052
$280$	9.54878	0.570648
$281$	14.0449	0.837846	0.418923	−	0.908022i	$-0.362408\pi$
$281$	14.0449	0.837846	0.418923	+	0.908022i	$0.362408\pi$
$282$	21.1156	1.25741
$283$	−6.79683	−0.404030	−0.202015	−	0.979382i	$-0.564749\pi$
$283$	−6.79683	−0.404030	−0.202015	+	0.979382i	$0.564749\pi$
$284$	27.8514	1.65268
$285$	22.4022	1.32699
$286$	−0.0464877	−0.00274888
$287$	−27.6516	−1.63222
$288$	14.6887	0.865537
$289$	29.0513	1.70890
$290$	−31.8338	−1.86934
$291$	−3.75849	−0.220326
$292$	1.36584	0.0799297
$293$	−19.6847	−1.14999	−0.574997	−	0.818156i	$-0.694997\pi$
$293$	−19.6847	−1.14999	−0.574997	+	0.818156i	$0.694997\pi$
$294$	17.2907	1.00841
$295$	13.4271	0.781755
$296$	0.308653	0.0179401
$297$	1.39232	0.0807905
$298$	47.8472	2.77172
$299$	0.301178	0.0174176
$300$	12.8525	0.742039
$301$	−25.5914	−1.47506
$302$	−19.6069	−1.12825
$303$	21.2192	1.21901
$304$	−20.2483	−1.16132
$305$	−26.2335	−1.50212
$306$	25.8431	1.47735
$307$	6.20114	0.353918	0.176959	−	0.984218i	$-0.443374\pi$
$307$	6.20114	0.353918	0.176959	+	0.984218i	$0.443374\pi$
$308$	−2.41693	−0.137717
$309$	−11.7229	−0.666894
$310$	12.6182	0.716667
$311$	−23.7347	−1.34587	−0.672936	−	0.739701i	$-0.734967\pi$
$311$	−23.7347	−1.34587	−0.672936	+	0.739701i	$0.734967\pi$
$312$	0.0717907	0.00406435
$313$	−29.8534	−1.68741	−0.843706	−	0.536805i	$-0.819631\pi$
$313$	−29.8534	−1.68741	−0.843706	+	0.536805i	$0.819631\pi$
$314$	−25.1541	−1.41953
$315$	−21.9704	−1.23789
$316$	−15.9274	−0.895987
$317$	−3.45344	−0.193965	−0.0969823	−	0.995286i	$-0.530919\pi$
$317$	−3.45344	−0.193965	−0.0969823	+	0.995286i	$0.530919\pi$
$318$	−8.19314	−0.459449
$319$	1.28096	0.0717201
$320$	−33.7460	−1.88646
$321$	8.41904	0.469905
$322$	28.8276	1.60650
$323$	−44.3111	−2.46553
$324$	−0.540463	−0.0300257
$325$	0.415697	0.0230587
$326$	−28.7499	−1.59231
$327$	−13.9336	−0.770532
$328$	−5.72303	−0.316001
$329$	35.5073	1.95758
$330$	−1.90895	−0.105084
$331$	−30.0050	−1.64923	−0.824613	−	0.565698i	$-0.808607\pi$
$331$	−30.0050	−1.64923	−0.824613	+	0.565698i	$0.808607\pi$
$332$	−8.37961	−0.459891
$333$	−0.710167	−0.0389169
$334$	−5.84789	−0.319982
$335$	3.47232	0.189713
$336$	−12.8741	−0.702339
$337$	20.4537	1.11418	0.557091	−	0.830451i	$-0.311917\pi$
$337$	20.4537	1.11418	0.557091	+	0.830451i	$0.311917\pi$
$338$	−27.1863	−1.47874
$339$	16.2263	0.881292
$340$	−50.9694	−2.76420
$341$	−0.507745	−0.0274960
$342$	−24.8665	−1.34463
$343$	2.32167	0.125358
$344$	−5.29664	−0.285576
$345$	12.3674	0.665839
$346$	−23.5863	−1.26801
$347$	−2.46211	−0.132173	−0.0660866	−	0.997814i	$-0.521051\pi$
$347$	−2.46211	−0.132173	−0.0660866	+	0.997814i	$0.521051\pi$
$348$	−12.4433	−0.667029
$349$	−3.42892	−0.183546	−0.0917729	−	0.995780i	$-0.529253\pi$
$349$	−3.42892	−0.183546	−0.0917729	+	0.995780i	$0.529253\pi$
$350$	39.7889	2.12681
$351$	−0.437448	−0.0233492
$352$	2.14612	0.114389
$353$	12.8407	0.683440	0.341720	−	0.939802i	$-0.388991\pi$
$353$	12.8407	0.683440	0.341720	+	0.939802i	$0.388991\pi$
$354$	9.66246	0.513554
$355$	36.9907	1.96326
$356$	−37.3963	−1.98200
$357$	−28.1735	−1.49110
$358$	2.95715	0.156290
$359$	21.4242	1.13073	0.565364	−	0.824842i	$-0.308736\pi$
$359$	21.4242	1.13073	0.565364	+	0.824842i	$0.308736\pi$
$360$	−4.54720	−0.239658
$361$	23.6366	1.24403
$362$	22.7701	1.19677
$363$	−11.8720	−0.623118
$364$	0.759367	0.0398016
$365$	1.81403	0.0949508
$366$	−18.8782	−0.986781
$367$	−36.2435	−1.89190	−0.945948	−	0.324318i	$-0.894865\pi$
$367$	−36.2435	−1.89190	−0.945948	+	0.324318i	$0.894865\pi$
$368$	−11.1784	−0.582712
$369$	13.1679	0.685492
$370$	2.57860	0.134055
$371$	−13.7773	−0.715284
$372$	4.93224	0.255725
$373$	−17.3998	−0.900925	−0.450463	−	0.892795i	$-0.648741\pi$
$373$	−17.3998	−0.900925	−0.450463	+	0.892795i	$0.648741\pi$
$374$	3.77587	0.195245
$375$	−0.0841648	−0.00434625
$376$	7.34893	0.378992
$377$	−0.402461	−0.0207278
$378$	−41.8708	−2.15360
$379$	24.6786	1.26765	0.633826	−	0.773475i	$-0.281483\pi$
$379$	24.6786	1.26765	0.633826	+	0.773475i	$0.281483\pi$
$380$	49.0433	2.51587
$381$	16.1658	0.828200
$382$	31.3490	1.60395
$383$	−4.04353	−0.206615	−0.103307	−	0.994649i	$-0.532943\pi$
$383$	−4.04353	−0.206615	−0.103307	+	0.994649i	$0.532943\pi$
$384$	−6.75129	−0.344525
$385$	−3.21003	−0.163598
$386$	−6.13662	−0.312346
$387$	12.1868	0.619490
$388$	−8.22816	−0.417722
$389$	−19.9385	−1.01092	−0.505460	−	0.862850i	$-0.668677\pi$
$389$	−19.9385	−1.01092	−0.505460	+	0.862850i	$0.668677\pi$
$390$	0.599766	0.0303703
$391$	−24.4625	−1.23712
$392$	6.01774	0.303942
$393$	19.3821	0.977696
$394$	35.8762	1.80742
$395$	−21.1539	−1.06437
$396$	1.15096	0.0578379
$397$	−25.1219	−1.26083	−0.630416	−	0.776258i	$-0.717116\pi$
$397$	−25.1219	−1.26083	−0.630416	+	0.776258i	$0.717116\pi$
$398$	35.4628	1.77759
$399$	27.1088	1.35714
$400$	−15.4288	−0.771439
$401$	7.42205	0.370640	0.185320	−	0.982678i	$-0.440668\pi$
$401$	7.42205	0.370640	0.185320	+	0.982678i	$0.440668\pi$
$402$	2.49877	0.124627
$403$	0.159527	0.00794659
$404$	46.4534	2.31115
$405$	−0.717812	−0.0356684
$406$	−38.5220	−1.91181
$407$	−0.103761	−0.00514322
$408$	−5.83105	−0.288680
$409$	37.0818	1.83358	0.916788	−	0.399374i	$-0.130772\pi$
$409$	37.0818	1.83358	0.916788	+	0.399374i	$0.130772\pi$
$410$	−47.8123	−2.36128
$411$	−10.7398	−0.529753
$412$	−25.6641	−1.26438
$413$	16.2481	0.799517
$414$	−13.7279	−0.674690
$415$	−11.1293	−0.546317
$416$	−0.674282	−0.0330594
$417$	11.6682	0.571393
$418$	−3.63318	−0.177705
$419$	−30.3561	−1.48299	−0.741496	−	0.670957i	$-0.765883\pi$
$419$	−30.3561	−1.48299	−0.741496	+	0.670957i	$0.765883\pi$
$420$	31.1822	1.52154
$421$	−19.4321	−0.947064	−0.473532	−	0.880777i	$-0.657021\pi$
$421$	−19.4321	−0.947064	−0.473532	+	0.880777i	$0.657021\pi$
$422$	43.4119	2.11326
$423$	−16.9088	−0.822136
$424$	−2.85149	−0.138481
$425$	−33.7641	−1.63780
$426$	26.6194	1.28971
$427$	−31.7451	−1.53625
$428$	18.4311	0.890903
$429$	−0.0241340	−0.00116520
$430$	−44.2500	−2.13393
$431$	−23.6678	−1.14004	−0.570018	−	0.821632i	$-0.693064\pi$
$431$	−23.6678	−1.14004	−0.570018	+	0.821632i	$0.693064\pi$
$432$	16.2361	0.781158
$433$	15.9252	0.765316	0.382658	−	0.923890i	$-0.375009\pi$
$433$	15.9252	0.765316	0.382658	+	0.923890i	$0.375009\pi$
$434$	15.2693	0.732949
$435$	−16.5264	−0.792383
$436$	−30.5038	−1.46087
$437$	23.5381	1.12598
$438$	1.30542	0.0623754
$439$	21.3671	1.01980	0.509898	−	0.860235i	$-0.329683\pi$
$439$	21.3671	1.01980	0.509898	+	0.860235i	$0.329683\pi$
$440$	−0.664378	−0.0316730
$441$	−13.8459	−0.659331
$442$	−1.18633	−0.0564278
$443$	15.9059	0.755713	0.377857	−	0.925864i	$-0.376661\pi$
$443$	15.9059	0.755713	0.377857	+	0.925864i	$0.376661\pi$
$444$	1.00793	0.0478343
$445$	−49.6677	−2.35447
$446$	4.11921	0.195050
$447$	24.8398	1.17488
$448$	−40.8360	−1.92932
$449$	14.0734	0.664165	0.332082	−	0.943250i	$-0.392249\pi$
$449$	14.0734	0.664165	0.332082	+	0.943250i	$0.392249\pi$
$450$	−18.9478	−0.893206
$451$	1.92392	0.0905939
$452$	35.5230	1.67086
$453$	−10.1789	−0.478247
$454$	34.6047	1.62408
$455$	1.00855	0.0472815
$456$	5.61070	0.262745
$457$	9.05044	0.423362	0.211681	−	0.977339i	$-0.432106\pi$
$457$	9.05044	0.423362	0.211681	+	0.977339i	$0.432106\pi$
$458$	−20.8838	−0.975837
$459$	35.5307	1.65843
$460$	27.0750	1.26238
$461$	−2.69097	−0.125331	−0.0626654	−	0.998035i	$-0.519960\pi$
$461$	−2.69097	−0.125331	−0.0626654	+	0.998035i	$0.519960\pi$
$462$	−2.31002	−0.107472
$463$	15.3365	0.712749	0.356375	−	0.934343i	$-0.384013\pi$
$463$	15.3365	0.712749	0.356375	+	0.934343i	$0.384013\pi$
$464$	14.9375	0.693457
$465$	6.55072	0.303783
$466$	31.4220	1.45559
$467$	24.2056	1.12010	0.560051	−	0.828458i	$-0.310781\pi$
$467$	24.2056	1.12010	0.560051	+	0.828458i	$0.310781\pi$
$468$	−0.361616	−0.0167157
$469$	4.20185	0.194024
$470$	61.3957	2.83197
$471$	−13.0587	−0.601713
$472$	3.36286	0.154788
$473$	1.78058	0.0818712
$474$	−15.2229	−0.699209
$475$	32.4882	1.49066
$476$	−61.6779	−2.82700
$477$	6.56087	0.300401
$478$	45.1897	2.06693
$479$	14.9478	0.682980	0.341490	−	0.939885i	$-0.389068\pi$
$479$	14.9478	0.682980	0.341490	+	0.939885i	$0.389068\pi$
$480$	−27.6884	−1.26379
$481$	0.0326002	0.00148644
$482$	−18.5319	−0.844104
$483$	14.9658	0.680967
$484$	−25.9904	−1.18138
$485$	−10.9282	−0.496223
$486$	32.3493	1.46739
$487$	−5.10952	−0.231534	−0.115767	−	0.993276i	$-0.536933\pi$
$487$	−5.10952	−0.231534	−0.115767	+	0.993276i	$0.536933\pi$
$488$	−6.57026	−0.297422
$489$	−14.9255	−0.674953
$490$	50.2744	2.27116
$491$	−17.9854	−0.811669	−0.405834	−	0.913947i	$-0.633019\pi$
$491$	−17.9854	−0.811669	−0.405834	+	0.913947i	$0.633019\pi$
$492$	−18.6890	−0.842565
$493$	32.6890	1.47224
$494$	1.14150	0.0513583
$495$	1.52864	0.0687072
$496$	−5.92091	−0.265857
$497$	44.7623	2.00787
$498$	−8.00893	−0.358889
$499$	4.89013	0.218912	0.109456	−	0.993992i	$-0.465089\pi$
$499$	4.89013	0.218912	0.109456	+	0.993992i	$0.465089\pi$
$500$	−0.184255	−0.00824015
$501$	−3.03592	−0.135635
$502$	−27.1175	−1.21031
$503$	5.12538	0.228530	0.114265	−	0.993450i	$-0.463549\pi$
$503$	5.12538	0.228530	0.114265	+	0.993450i	$0.463549\pi$
$504$	−5.50255	−0.245103
$505$	61.6968	2.74547
$506$	−2.00575	−0.0891663
$507$	−14.1137	−0.626813
$508$	35.3906	1.57020
$509$	−24.2819	−1.07627	−0.538137	−	0.842857i	$-0.680872\pi$
$509$	−24.2819	−1.07627	−0.538137	+	0.842857i	$0.680872\pi$
$510$	−48.7147	−2.15712
$511$	2.19516	0.0971080
$512$	29.9322	1.32283
$513$	−34.1881	−1.50944
$514$	−9.98785	−0.440545
$515$	−34.0856	−1.50199
$516$	−17.2966	−0.761439
$517$	−2.47050	−0.108653
$518$	3.12036	0.137101
$519$	−12.2448	−0.537486
$520$	0.208739	0.00915380
$521$	−27.8015	−1.21801	−0.609003	−	0.793168i	$-0.708430\pi$
$521$	−27.8015	−1.21801	−0.609003	+	0.793168i	$0.708430\pi$
$522$	18.3445	0.802915
$523$	10.1920	0.445665	0.222833	−	0.974857i	$-0.428470\pi$
$523$	10.1920	0.445665	0.222833	+	0.974857i	$0.428470\pi$
$524$	42.4316	1.85364
$525$	20.6563	0.901516
$526$	−30.0100	−1.30850
$527$	−12.9572	−0.564425
$528$	0.895745	0.0389823
$529$	−10.0055	−0.435020
$530$	−23.8224	−1.03478
$531$	−7.73746	−0.335777
$532$	59.3472	2.57303
$533$	−0.604470	−0.0261825
$534$	−35.7421	−1.54671
$535$	24.4792	1.05833
$536$	0.869656	0.0375634
$537$	1.53520	0.0662488
$538$	39.2927	1.69403
$539$	−2.02299	−0.0871365
$540$	−39.3253	−1.69229
$541$	5.78200	0.248588	0.124294	−	0.992245i	$-0.460333\pi$
$541$	5.78200	0.248588	0.124294	+	0.992245i	$0.460333\pi$
$542$	−65.7480	−2.82412
$543$	11.8211	0.507290
$544$	54.7671	2.34812
$545$	−40.5135	−1.73541
$546$	0.725776	0.0310603
$547$	31.5020	1.34693	0.673464	−	0.739220i	$-0.264806\pi$
$547$	31.5020	1.34693	0.673464	+	0.739220i	$0.264806\pi$
$548$	−23.5117	−1.00437
$549$	15.1172	0.645188
$550$	−2.76840	−0.118045
$551$	−31.4537	−1.33997
$552$	3.09746	0.131837
$553$	−25.5983	−1.08855
$554$	−60.1839	−2.55697
$555$	1.33868	0.0568237
$556$	25.5442	1.08332
$557$	20.2636	0.858596	0.429298	−	0.903163i	$-0.358761\pi$
$557$	20.2636	0.858596	0.429298	+	0.903163i	$0.358761\pi$
$558$	−7.27134	−0.307820
$559$	−0.559434	−0.0236616
$560$	−37.4327	−1.58182
$561$	1.96023	0.0827612
$562$	29.3872	1.23962
$563$	−2.40848	−0.101506	−0.0507528	−	0.998711i	$-0.516162\pi$
$563$	−2.40848	−0.101506	−0.0507528	+	0.998711i	$0.516162\pi$
$564$	23.9985	1.01052
$565$	47.1796	1.98486
$566$	−14.2216	−0.597777
$567$	−0.868623	−0.0364787
$568$	9.26444	0.388727
$569$	−26.0681	−1.09283	−0.546416	−	0.837514i	$-0.684008\pi$
$569$	−26.0681	−1.09283	−0.546416	+	0.837514i	$0.684008\pi$
$570$	46.8738	1.96333
$571$	−28.7069	−1.20135	−0.600673	−	0.799495i	$-0.705100\pi$
$571$	−28.7069	−1.20135	−0.600673	+	0.799495i	$0.705100\pi$
$572$	−0.0528347	−0.00220913
$573$	16.2748	0.679889
$574$	−57.8576	−2.41493
$575$	17.9355	0.747964
$576$	19.4464	0.810267
$577$	33.6347	1.40023	0.700116	−	0.714029i	$-0.253132\pi$
$577$	33.6347	1.40023	0.700116	+	0.714029i	$0.253132\pi$
$578$	60.7864	2.52838
$579$	−3.18582	−0.132398
$580$	−36.1801	−1.50230
$581$	−13.4676	−0.558729
$582$	−7.86418	−0.325981
$583$	0.958590	0.0397008
$584$	0.454331	0.0188003
$585$	−0.480278	−0.0198570
$586$	−41.1879	−1.70146
$587$	9.53978	0.393749	0.196875	−	0.980429i	$-0.436921\pi$
$587$	9.53978	0.393749	0.196875	+	0.980429i	$0.436921\pi$
$588$	19.6514	0.810409
$589$	12.4676	0.513718
$590$	28.0946	1.15664
$591$	18.6251	0.766133
$592$	−1.20997	−0.0497295
$593$	25.0028	1.02674	0.513371	−	0.858167i	$-0.328397\pi$
$593$	25.0028	1.02674	0.513371	+	0.858167i	$0.328397\pi$
$594$	2.91326	0.119532
$595$	−81.9172	−3.35828
$596$	54.3798	2.22748
$597$	18.4105	0.753491
$598$	0.630179	0.0257699
$599$	30.5877	1.24978	0.624889	−	0.780714i	$-0.285144\pi$
$599$	30.5877	1.24978	0.624889	+	0.780714i	$0.285144\pi$
$600$	4.27523	0.174536
$601$	43.0747	1.75705	0.878527	−	0.477693i	$-0.158527\pi$
$601$	43.0747	1.75705	0.878527	+	0.477693i	$0.158527\pi$
$602$	−53.5469	−2.18241
$603$	−2.00095	−0.0814851
$604$	−22.2839	−0.906718
$605$	−34.5190	−1.40340
$606$	44.3985	1.80357
$607$	13.1903	0.535376	0.267688	−	0.963506i	$-0.413740\pi$
$607$	13.1903	0.535376	0.267688	+	0.963506i	$0.413740\pi$
$608$	−52.6975	−2.13717
$609$	−19.9986	−0.810385
$610$	−54.8904	−2.22245
$611$	0.776199	0.0314017
$612$	29.3715	1.18727
$613$	19.5106	0.788027	0.394013	−	0.919105i	$-0.371086\pi$
$613$	19.5106	0.788027	0.394013	+	0.919105i	$0.371086\pi$
$614$	12.9751	0.523634
$615$	−24.8217	−1.00091
$616$	−0.803963	−0.0323926
$617$	28.3006	1.13934	0.569671	−	0.821873i	$-0.307071\pi$
$617$	28.3006	1.13934	0.569671	+	0.821873i	$0.307071\pi$
$618$	−24.5288	−0.986693
$619$	38.9812	1.56679	0.783393	−	0.621526i	$-0.213487\pi$
$619$	38.9812	1.56679	0.783393	+	0.621526i	$0.213487\pi$
$620$	14.3410	0.575948
$621$	−18.8740	−0.757388
$622$	−49.6620	−1.99127
$623$	−60.1028	−2.40797
$624$	−0.281431	−0.0112663
$625$	−25.1221	−1.00488
$626$	−62.4646	−2.49659
$627$	−1.88616	−0.0753259
$628$	−28.5884	−1.14080
$629$	−2.64788	−0.105578
$630$	−45.9703	−1.83150
$631$	22.2053	0.883981	0.441990	−	0.897020i	$-0.354273\pi$
$631$	22.2053	0.883981	0.441990	+	0.897020i	$0.354273\pi$
$632$	−5.29807	−0.210746
$633$	22.5372	0.895774
$634$	−7.22591	−0.286978
$635$	47.0038	1.86529
$636$	−9.31175	−0.369235
$637$	0.635597	0.0251833
$638$	2.68026	0.106112
$639$	−21.3161	−0.843254
$640$	−19.6300	−0.775946
$641$	39.0715	1.54323	0.771616	−	0.636088i	$-0.219449\pi$
$641$	39.0715	1.54323	0.771616	+	0.636088i	$0.219449\pi$
$642$	17.6158	0.695241
$643$	26.8982	1.06076	0.530380	−	0.847760i	$-0.322049\pi$
$643$	26.8982	1.06076	0.530380	+	0.847760i	$0.322049\pi$
$644$	32.7634	1.29106
$645$	−22.9723	−0.904535
$646$	−92.7156	−3.64785
$647$	8.00590	0.314744	0.157372	−	0.987539i	$-0.449698\pi$
$647$	8.00590	0.314744	0.157372	+	0.987539i	$0.449698\pi$
$648$	−0.179778	−0.00706237
$649$	−1.13050	−0.0443760
$650$	0.869796	0.0341162
$651$	7.92702	0.310684
$652$	−32.6752	−1.27966
$653$	−1.12974	−0.0442100	−0.0221050	−	0.999756i	$-0.507037\pi$
$653$	−1.12974	−0.0442100	−0.0221050	+	0.999756i	$0.507037\pi$
$654$	−29.1545	−1.14003
$655$	56.3553	2.20198
$656$	22.4352	0.875947
$657$	−1.04535	−0.0407830
$658$	74.2948	2.89631
$659$	−29.5891	−1.15263	−0.576314	−	0.817228i	$-0.695510\pi$
$659$	−29.5891	−1.15263	−0.576314	+	0.817228i	$0.695510\pi$
$660$	−2.16958	−0.0844507
$661$	−14.9156	−0.580148	−0.290074	−	0.957004i	$-0.593680\pi$
$661$	−14.9156	−0.580148	−0.290074	+	0.957004i	$0.593680\pi$
$662$	−62.7819	−2.44009
$663$	−0.615879	−0.0239188
$664$	−2.78738	−0.108171
$665$	78.8216	3.05657
$666$	−1.48594	−0.0575790
$667$	−17.3645	−0.672355
$668$	−6.64630	−0.257153
$669$	2.13848	0.0826784
$670$	7.26542	0.280688
$671$	2.20874	0.0852674
$672$	−33.5056	−1.29251
$673$	14.4920	0.558627	0.279314	−	0.960200i	$-0.409893\pi$
$673$	14.4920	0.558627	0.279314	+	0.960200i	$0.409893\pi$
$674$	42.7969	1.64847
$675$	−26.0506	−1.00269
$676$	−30.8981	−1.18839
$677$	10.4882	0.403095	0.201547	−	0.979479i	$-0.435403\pi$
$677$	10.4882	0.403095	0.201547	+	0.979479i	$0.435403\pi$
$678$	33.9516	1.30390
$679$	−13.2242	−0.507497
$680$	−16.9544	−0.650170
$681$	17.9650	0.688419
$682$	−1.06240	−0.0406813
$683$	27.2408	1.04234	0.521171	−	0.853452i	$-0.325495\pi$
$683$	27.2408	1.04234	0.521171	+	0.853452i	$0.325495\pi$
$684$	−28.2616	−1.08061
$685$	−31.2269	−1.19312
$686$	4.85781	0.185472
$687$	−10.8418	−0.413640
$688$	20.7637	0.791607
$689$	−0.301176	−0.0114739
$690$	25.8773	0.985133
$691$	−38.6112	−1.46884	−0.734420	−	0.678695i	$-0.762546\pi$
$691$	−38.6112	−1.46884	−0.734420	+	0.678695i	$0.762546\pi$
$692$	−26.8065	−1.01903
$693$	1.84980	0.0702682
$694$	−5.15168	−0.195555
$695$	33.9264	1.28690
$696$	−4.13911	−0.156892
$697$	49.0968	1.85967
$698$	−7.17460	−0.271563
$699$	16.3127	0.617001
$700$	45.2213	1.70920
$701$	−43.5897	−1.64636	−0.823179	−	0.567782i	$-0.807802\pi$
$701$	−43.5897	−1.64636	−0.823179	+	0.567782i	$0.807802\pi$
$702$	−0.915307	−0.0345460
$703$	2.54782	0.0960928
$704$	2.84126	0.107084
$705$	31.8735	1.20042
$706$	26.8676	1.01117
$707$	74.6592	2.80785
$708$	10.9817	0.412717
$709$	−37.5473	−1.41012	−0.705058	−	0.709149i	$-0.749079\pi$
$709$	−37.5473	−1.41012	−0.705058	+	0.709149i	$0.749079\pi$
$710$	77.3985	2.90471
$711$	12.1901	0.457164
$712$	−12.4394	−0.466188
$713$	6.88290	0.257767
$714$	−58.9496	−2.20613
$715$	−0.0701721	−0.00262429
$716$	3.36090	0.125603
$717$	23.4602	0.876135
$718$	44.8276	1.67295
$719$	−26.8653	−1.00191	−0.500954	−	0.865474i	$-0.667017\pi$
$719$	−26.8653	−1.00191	−0.500954	+	0.865474i	$0.667017\pi$
$720$	17.8257	0.664326
$721$	−41.2469	−1.53611
$722$	49.4567	1.84059
$723$	−9.62079	−0.357801
$724$	25.8789	0.961783
$725$	−23.9671	−0.890115
$726$	−24.8407	−0.921926
$727$	35.0769	1.30093	0.650464	−	0.759537i	$-0.274574\pi$
$727$	35.0769	1.30093	0.650464	+	0.759537i	$0.274574\pi$
$728$	0.252594	0.00936177
$729$	17.4759	0.647256
$730$	3.79564	0.140483
$731$	45.4389	1.68062
$732$	−21.4557	−0.793025
$733$	25.7237	0.950127	0.475063	−	0.879952i	$-0.342425\pi$
$733$	25.7237	0.950127	0.475063	+	0.879952i	$0.342425\pi$
$734$	−75.8352	−2.79913
$735$	26.0998	0.962707
$736$	−29.0924	−1.07236
$737$	−0.292354	−0.0107690
$738$	27.5522	1.01421
$739$	38.9678	1.43345	0.716727	−	0.697354i	$-0.245640\pi$
$739$	38.9678	1.43345	0.716727	+	0.697354i	$0.245640\pi$
$740$	2.93066	0.107733
$741$	0.592606	0.0217699
$742$	−28.8274	−1.05829
$743$	−16.7266	−0.613638	−0.306819	−	0.951768i	$-0.599265\pi$
$743$	−16.7266	−0.613638	−0.306819	+	0.951768i	$0.599265\pi$
$744$	1.64065	0.0601492
$745$	72.2242	2.64609
$746$	−36.4069	−1.33295
$747$	6.41336	0.234652
$748$	4.29139	0.156909
$749$	29.6222	1.08237
$750$	−0.176105	−0.00643043
$751$	17.4299	0.636024	0.318012	−	0.948087i	$-0.396985\pi$
$751$	17.4299	0.636024	0.318012	+	0.948087i	$0.396985\pi$
$752$	−28.8090	−1.05056
$753$	−14.0780	−0.513031
$754$	−0.842101	−0.0306675
$755$	−29.5962	−1.07712
$756$	−47.5874	−1.73074
$757$	−2.26896	−0.0824667	−0.0412333	−	0.999150i	$-0.513129\pi$
$757$	−2.26896	−0.0824667	−0.0412333	+	0.999150i	$0.513129\pi$
$758$	51.6369	1.87554
$759$	−1.04128	−0.0377961
$760$	16.3137	0.591759
$761$	36.5162	1.32371	0.661855	−	0.749631i	$-0.269769\pi$
$761$	36.5162	1.32371	0.661855	+	0.749631i	$0.269769\pi$
$762$	33.8251	1.22535
$763$	−49.0253	−1.77483
$764$	35.6291	1.28902
$765$	39.0095	1.41039
$766$	−8.46060	−0.305694
$767$	0.355188	0.0128251
$768$	9.08603	0.327864
$769$	35.8445	1.29259	0.646293	−	0.763090i	$-0.276318\pi$
$769$	35.8445	1.29259	0.646293	+	0.763090i	$0.276318\pi$
$770$	−6.71660	−0.242050
$771$	−5.18517	−0.186739
$772$	−6.97446	−0.251016
$773$	40.6915	1.46357	0.731786	−	0.681535i	$-0.238687\pi$
$773$	40.6915	1.46357	0.731786	+	0.681535i	$0.238687\pi$
$774$	25.4994	0.916558
$775$	9.50003	0.341251
$776$	−2.73700	−0.0982526
$777$	1.61993	0.0581147
$778$	−41.7188	−1.49569
$779$	−47.2415	−1.69260
$780$	0.681652	0.0244071
$781$	−3.11444	−0.111444
$782$	−51.1849	−1.83037
$783$	25.2211	0.901329
$784$	−23.5905	−0.842517
$785$	−37.9695	−1.35519
$786$	40.5547	1.44654
$787$	−23.6703	−0.843756	−0.421878	−	0.906653i	$-0.638629\pi$
$787$	−23.6703	−0.843756	−0.421878	+	0.906653i	$0.638629\pi$
$788$	40.7744	1.45253
$789$	−15.5796	−0.554650
$790$	−44.2620	−1.57477
$791$	57.0920	2.02996
$792$	0.382853	0.0136041
$793$	−0.693956	−0.0246431
$794$	−52.5645	−1.86545
$795$	−12.3673	−0.438625
$796$	40.3046	1.42856
$797$	13.1404	0.465456	0.232728	−	0.972542i	$-0.425235\pi$
$797$	13.1404	0.465456	0.232728	+	0.972542i	$0.425235\pi$
$798$	56.7219	2.00793
$799$	−63.0451	−2.23038
$800$	−40.1544	−1.41967
$801$	28.6214	1.01129
$802$	15.5298	0.548375
$803$	−0.152733	−0.00538984
$804$	2.83993	0.100156
$805$	43.5145	1.53369
$806$	0.333791	0.0117573
$807$	20.3987	0.718069
$808$	15.4522	0.543606
$809$	−21.4187	−0.753042	−0.376521	−	0.926408i	$-0.622880\pi$
$809$	−21.4187	−0.753042	−0.376521	+	0.926408i	$0.622880\pi$
$810$	−1.50194	−0.0527726
$811$	−11.7351	−0.412076	−0.206038	−	0.978544i	$-0.566057\pi$
$811$	−11.7351	−0.412076	−0.206038	+	0.978544i	$0.566057\pi$
$812$	−43.7814	−1.53643
$813$	−34.1330	−1.19710
$814$	−0.217107	−0.00760958
$815$	−43.3973	−1.52014
$816$	22.8586	0.800212
$817$	−43.7218	−1.52963
$818$	77.5892	2.71284
$819$	−0.581183	−0.0203082
$820$	−54.3401	−1.89764
$821$	21.6230	0.754647	0.377324	−	0.926081i	$-0.376844\pi$
$821$	21.6230	0.754647	0.377324	+	0.926081i	$0.376844\pi$
$822$	−22.4716	−0.783788
$823$	−26.3308	−0.917834	−0.458917	−	0.888479i	$-0.651762\pi$
$823$	−26.3308	−0.917834	−0.458917	+	0.888479i	$0.651762\pi$
$824$	−8.53685	−0.297395
$825$	−1.43721	−0.0500373
$826$	33.9972	1.18291
$827$	24.4133	0.848934	0.424467	−	0.905443i	$-0.360461\pi$
$827$	24.4133	0.848934	0.424467	+	0.905443i	$0.360461\pi$
$828$	−15.6022	−0.542213
$829$	16.5234	0.573883	0.286941	−	0.957948i	$-0.407361\pi$
$829$	16.5234	0.573883	0.286941	+	0.957948i	$0.407361\pi$
$830$	−23.2868	−0.808296
$831$	−31.2444	−1.08385
$832$	−0.892686	−0.0309483
$833$	−51.6250	−1.78870
$834$	24.4143	0.845397
$835$	−8.82724	−0.305479
$836$	−4.12922	−0.142812
$837$	−9.99710	−0.345550
$838$	−63.5165	−2.19414
$839$	35.0659	1.21061	0.605304	−	0.795994i	$-0.293051\pi$
$839$	35.0659	1.21061	0.605304	+	0.795994i	$0.293051\pi$
$840$	10.3724	0.357882
$841$	−5.79604	−0.199864
$842$	−40.6594	−1.40122
$843$	15.2563	0.525455
$844$	49.3390	1.69832
$845$	−41.0371	−1.41172
$846$	−35.3797	−1.21638
$847$	−41.7714	−1.43528
$848$	11.1783	0.383864
$849$	−7.38310	−0.253387
$850$	−70.6473	−2.42318
$851$	1.40656	0.0482162
$852$	30.2537	1.03648
$853$	−18.7954	−0.643543	−0.321772	−	0.946817i	$-0.604278\pi$
$853$	−18.7954	−0.643543	−0.321772	+	0.946817i	$0.604278\pi$
$854$	−66.4228	−2.27294
$855$	−37.5354	−1.28368
$856$	6.13090	0.209550
$857$	−17.8465	−0.609625	−0.304812	−	0.952412i	$-0.598594\pi$
$857$	−17.8465	−0.609625	−0.304812	+	0.952412i	$0.598594\pi$
$858$	−0.0504975	−0.00172396
$859$	−40.4866	−1.38138	−0.690692	−	0.723149i	$-0.742694\pi$
$859$	−40.4866	−1.38138	−0.690692	+	0.723149i	$0.742694\pi$
$860$	−50.2915	−1.71493
$861$	−30.0366	−1.02365
$862$	−49.5219	−1.68672
$863$	−22.5860	−0.768837	−0.384418	−	0.923159i	$-0.625598\pi$
$863$	−22.5860	−0.768837	−0.384418	+	0.923159i	$0.625598\pi$
$864$	42.2554	1.43756
$865$	−35.6029	−1.21054
$866$	33.3216	1.13231
$867$	31.5571	1.07174
$868$	17.3540	0.589033
$869$	1.78106	0.0604184
$870$	−34.5796	−1.17236
$871$	0.0918536	0.00311234
$872$	−10.1467	−0.343612
$873$	6.29745	0.213136
$874$	49.2507	1.66593
$875$	−0.296132	−0.0100111
$876$	1.48365	0.0501279
$877$	−6.66972	−0.225220	−0.112610	−	0.993639i	$-0.535921\pi$
$877$	−6.66972	−0.225220	−0.112610	+	0.993639i	$0.535921\pi$
$878$	44.7081	1.50883
$879$	−21.3826	−0.721218
$880$	2.60447	0.0877966
$881$	−25.1191	−0.846282	−0.423141	−	0.906064i	$-0.639073\pi$
$881$	−25.1191	−0.846282	−0.423141	+	0.906064i	$0.639073\pi$
$882$	−28.9710	−0.975503
$883$	−12.2077	−0.410822	−0.205411	−	0.978676i	$-0.565853\pi$
$883$	−12.2077	−0.410822	−0.205411	+	0.978676i	$0.565853\pi$
$884$	−1.34830	−0.0453481
$885$	14.5852	0.490278
$886$	33.2812	1.11810
$887$	−43.5777	−1.46320	−0.731598	−	0.681736i	$-0.761225\pi$
$887$	−43.5777	−1.46320	−0.731598	+	0.681736i	$0.761225\pi$
$888$	0.335276	0.0112511
$889$	56.8792	1.90767
$890$	−103.924	−3.48353
$891$	0.0604365	0.00202470
$892$	4.68161	0.156752
$893$	60.6627	2.03000
$894$	51.9743	1.73828
$895$	4.46375	0.149207
$896$	−23.7543	−0.793575
$897$	0.327156	0.0109234
$898$	29.4469	0.982656
$899$	−9.19754	−0.306755
$900$	−21.5347	−0.717823
$901$	24.4624	0.814960
$902$	4.02558	0.134037
$903$	−27.7988	−0.925085
$904$	11.8163	0.393004
$905$	34.3709	1.14253
$906$	−21.2981	−0.707583
$907$	−28.8512	−0.957989	−0.478995	−	0.877818i	$-0.658999\pi$
$907$	−28.8512	−0.957989	−0.478995	+	0.877818i	$0.658999\pi$
$908$	39.3293	1.30519
$909$	−35.5533	−1.17923
$910$	2.11027	0.0699546
$911$	42.7684	1.41698	0.708489	−	0.705721i	$-0.249377\pi$
$911$	42.7684	1.41698	0.708489	+	0.705721i	$0.249377\pi$
$912$	−21.9948	−0.728321
$913$	0.937038	0.0310114
$914$	18.9370	0.626379
$915$	−28.4962	−0.942057
$916$	−23.7351	−0.784230
$917$	68.1955	2.25201
$918$	74.3438	2.45371
$919$	−8.08691	−0.266762	−0.133381	−	0.991065i	$-0.542583\pi$
$919$	−8.08691	−0.266762	−0.133381	+	0.991065i	$0.542583\pi$
$920$	9.00619	0.296925
$921$	6.73602	0.221960
$922$	−5.63053	−0.185432
$923$	0.978517	0.0322083
$924$	−2.62540	−0.0863694
$925$	1.94138	0.0638323
$926$	32.0899	1.05454
$927$	19.6421	0.645130
$928$	38.8758	1.27616
$929$	23.5286	0.771948	0.385974	−	0.922510i	$-0.373865\pi$
$929$	23.5286	0.771948	0.385974	+	0.922510i	$0.373865\pi$
$930$	13.7066	0.449457
$931$	49.6742	1.62800
$932$	35.7120	1.16979
$933$	−25.7820	−0.844063
$934$	50.6474	1.65723
$935$	5.69958	0.186396
$936$	−0.120287	−0.00393171
$937$	−19.4622	−0.635803	−0.317901	−	0.948124i	$-0.602978\pi$
$937$	−19.4622	−0.635803	−0.317901	+	0.948124i	$0.602978\pi$
$938$	8.79187	0.287065
$939$	−32.4284	−1.05826
$940$	69.7781	2.27591
$941$	15.8834	0.517783	0.258891	−	0.965906i	$-0.416643\pi$
$941$	15.8834	0.517783	0.258891	+	0.965906i	$0.416643\pi$
$942$	−27.3237	−0.890256
$943$	−26.0803	−0.849292
$944$	−13.1830	−0.429069
$945$	−63.2029	−2.05599
$946$	3.72565	0.121131
$947$	17.8910	0.581380	0.290690	−	0.956817i	$-0.406115\pi$
$947$	17.8910	0.581380	0.290690	+	0.956817i	$0.406115\pi$
$948$	−17.3012	−0.561918
$949$	0.0479867	0.00155771
$950$	67.9776	2.20548
$951$	−3.75132	−0.121645
$952$	−20.5164	−0.664942
$953$	−7.53156	−0.243971	−0.121986	−	0.992532i	$-0.538926\pi$
$953$	−7.53156	−0.243971	−0.121986	+	0.992532i	$0.538926\pi$
$954$	13.7278	0.444455
$955$	47.3206	1.53126
$956$	51.3595	1.66108
$957$	1.39145	0.0449792
$958$	31.2764	1.01049
$959$	−37.7876	−1.22023
$960$	−36.6568	−1.18309
$961$	−27.3543	−0.882397
$962$	0.0682120	0.00219924
$963$	−14.1063	−0.454570
$964$	−21.0621	−0.678363
$965$	−9.26308	−0.298189
$966$	31.3141	1.00752
$967$	31.9549	1.02760	0.513800	−	0.857910i	$-0.328237\pi$
$967$	31.9549	1.02760	0.513800	+	0.857910i	$0.328237\pi$
$968$	−8.64541	−0.277874
$969$	−48.1331	−1.54626
$970$	−22.8659	−0.734180
$971$	−38.4715	−1.23461	−0.617305	−	0.786724i	$-0.711775\pi$
$971$	−38.4715	−1.23461	−0.617305	+	0.786724i	$0.711775\pi$
$972$	36.7660	1.17927
$973$	41.0543	1.31614
$974$	−10.6911	−0.342564
$975$	0.451553	0.0144613
$976$	25.7565	0.824445
$977$	−29.7149	−0.950665	−0.475332	−	0.879806i	$-0.657672\pi$
$977$	−29.7149	−0.950665	−0.475332	+	0.879806i	$0.657672\pi$
$978$	−31.2298	−0.998617
$979$	4.18179	0.133651
$980$	57.1383	1.82522
$981$	23.3462	0.745387
$982$	−37.6322	−1.20089
$983$	−21.0940	−0.672795	−0.336398	−	0.941720i	$-0.609209\pi$
$983$	−21.0940	−0.672795	−0.336398	+	0.941720i	$0.609209\pi$
$984$	−6.21667	−0.198180
$985$	54.1543	1.72550
$986$	68.3979	2.17823
$987$	38.5700	1.22770
$988$	1.29735	0.0412740
$989$	−24.1372	−0.767519
$990$	3.19849	0.101655
$991$	−40.0615	−1.27260	−0.636298	−	0.771443i	$-0.719535\pi$
$991$	−40.0615	−1.27260	−0.636298	+	0.771443i	$0.719535\pi$
$992$	−15.4095	−0.489253
$993$	−32.5931	−1.03431
$994$	93.6598	2.97071
$995$	53.5303	1.69702
$996$	−9.10239	−0.288420
$997$	1.06068	0.0335920	0.0167960	−	0.999859i	$-0.494653\pi$
$997$	1.06068	0.0335920	0.0167960	+	0.999859i	$0.494653\pi$
$998$	10.2320	0.323888
$999$	−2.04296	−0.0646365

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2011.2.a.b.1.73	✓	90

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2011.2.a.b.1.73	✓	90	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:	\( N \)	\(=\)	\( 2011 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2011.a (trivial)

\(f(q)\)	\(=\)	\(q+2.09238 q^{2} +1.08626 q^{3} +2.37805 q^{4} +3.15840 q^{5} +2.27286 q^{6} +3.82197 q^{7} +0.791031 q^{8} -1.82005 q^{9} +O(q^{10})\)	\(q+2.09238 q^{2} +1.08626 q^{3} +2.37805 q^{4} +3.15840 q^{5} +2.27286 q^{6} +3.82197 q^{7} +0.791031 q^{8} -1.82005 q^{9} +6.60857 q^{10} -0.265923 q^{11} +2.58317 q^{12} +0.0835493 q^{13} +7.99701 q^{14} +3.43082 q^{15} -3.10097 q^{16} -6.78611 q^{17} -3.80824 q^{18} +6.52967 q^{19} +7.51084 q^{20} +4.15163 q^{21} -0.556411 q^{22} +3.60479 q^{23} +0.859262 q^{24} +4.97547 q^{25} +0.174817 q^{26} -5.23580 q^{27} +9.08885 q^{28} -4.81705 q^{29} +7.17859 q^{30} +1.90937 q^{31} -8.07047 q^{32} -0.288860 q^{33} -14.1991 q^{34} +12.0713 q^{35} -4.32818 q^{36} +0.390191 q^{37} +13.6625 q^{38} +0.0907558 q^{39} +2.49839 q^{40} -7.23490 q^{41} +8.68680 q^{42} -6.69586 q^{43} -0.632378 q^{44} -5.74844 q^{45} +7.54260 q^{46} +9.29032 q^{47} -3.36844 q^{48} +7.60745 q^{49} +10.4106 q^{50} -7.37145 q^{51} +0.198685 q^{52} -3.60477 q^{53} -10.9553 q^{54} -0.839889 q^{55} +3.02330 q^{56} +7.09289 q^{57} -10.0791 q^{58} +4.25124 q^{59} +8.15868 q^{60} -8.30595 q^{61} +3.99513 q^{62} -6.95617 q^{63} -10.6845 q^{64} +0.263882 q^{65} -0.604404 q^{66} +1.09939 q^{67} -16.1377 q^{68} +3.91573 q^{69} +25.2577 q^{70} +11.7118 q^{71} -1.43972 q^{72} +0.574352 q^{73} +0.816428 q^{74} +5.40463 q^{75} +15.5279 q^{76} -1.01635 q^{77} +0.189896 q^{78} -6.69767 q^{79} -9.79409 q^{80} -0.227271 q^{81} -15.1382 q^{82} -3.52373 q^{83} +9.87281 q^{84} -21.4332 q^{85} -14.0103 q^{86} -5.23254 q^{87} -0.210353 q^{88} -15.7256 q^{89} -12.0279 q^{90} +0.319323 q^{91} +8.57239 q^{92} +2.07407 q^{93} +19.4389 q^{94} +20.6233 q^{95} -8.76659 q^{96} -3.46004 q^{97} +15.9177 q^{98} +0.483992 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9}+O(q^{10}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9	\( 90 q + 11 q^{2} + 9 q^{3} + 95 q^{4} + 47 q^{5} + 20 q^{6} + 4 q^{7} + 33 q^{8} + 109 q^{9} + 19 q^{10} + 24 q^{11} + 14 q^{12} + 36 q^{13} + 43 q^{14} + 4 q^{15} + 93 q^{16} + 55 q^{17} + 18 q^{18} + 15 q^{19} + 76 q^{20} + 65 q^{21} - 3 q^{22} + 30 q^{23} + 46 q^{24} + 107 q^{25} + 38 q^{26} + 21 q^{27} + 2 q^{28} + 149 q^{29} + q^{30} + 33 q^{31} + 67 q^{32} + 13 q^{33} + 15 q^{34} + 34 q^{35} + 103 q^{36} + 23 q^{37} + 38 q^{38} + 32 q^{39} + 43 q^{40} + 144 q^{41} - 20 q^{42} - 5 q^{43} + 37 q^{44} + 103 q^{45} + 8 q^{46} + 28 q^{47} + 12 q^{48} + 114 q^{49} + 67 q^{50} + 11 q^{51} + 59 q^{52} + 59 q^{53} + 38 q^{54} + 3 q^{55} + 106 q^{56} + 2 q^{57} - 5 q^{58} + 86 q^{59} - 28 q^{60} + 113 q^{61} + 12 q^{62} - 29 q^{63} + 71 q^{64} + 51 q^{65} + 15 q^{66} - 14 q^{67} + 96 q^{68} + 116 q^{69} - 24 q^{70} + 47 q^{71} + 13 q^{72} + 22 q^{73} + 57 q^{74} + 7 q^{75} + 2 q^{76} + 100 q^{77} - 34 q^{78} + 18 q^{79} + 100 q^{80} + 154 q^{81} - 4 q^{82} + 24 q^{83} + 35 q^{84} + 30 q^{85} - q^{86} + 49 q^{87} - 74 q^{88} + 97 q^{89} + 22 q^{90} - 25 q^{91} + 23 q^{92} + 32 q^{93} + 21 q^{94} + 56 q^{95} + 29 q^{96} + 26 q^{97} + 15 q^{98} - 11 q^{99}+O(q^{100}) \) 90 * q + 11 * q^2 + 9 * q^3 + 95 * q^4 + 47 * q^5 + 20 * q^6 + 4 * q^7 + 33 * q^8 + 109 * q^9 + 19 * q^10 + 24 * q^11 + 14 * q^12 + 36 * q^13 + 43 * q^14 + 4 * q^15 + 93 * q^16 + 55 * q^17 + 18 * q^18 + 15 * q^19 + 76 * q^20 + 65 * q^21 - 3 * q^22 + 30 * q^23 + 46 * q^24 + 107 * q^25 + 38 * q^26 + 21 * q^27 + 2 * q^28 + 149 * q^29 + q^30 + 33 * q^31 + 67 * q^32 + 13 * q^33 + 15 * q^34 + 34 * q^35 + 103 * q^36 + 23 * q^37 + 38 * q^38 + 32 * q^39 + 43 * q^40 + 144 * q^41 - 20 * q^42 - 5 * q^43 + 37 * q^44 + 103 * q^45 + 8 * q^46 + 28 * q^47 + 12 * q^48 + 114 * q^49 + 67 * q^50 + 11 * q^51 + 59 * q^52 + 59 * q^53 + 38 * q^54 + 3 * q^55 + 106 * q^56 + 2 * q^57 - 5 * q^58 + 86 * q^59 - 28 * q^60 + 113 * q^61 + 12 * q^62 - 29 * q^63 + 71 * q^64 + 51 * q^65 + 15 * q^66 - 14 * q^67 + 96 * q^68 + 116 * q^69 - 24 * q^70 + 47 * q^71 + 13 * q^72 + 22 * q^73 + 57 * q^74 + 7 * q^75 + 2 * q^76 + 100 * q^77 - 34 * q^78 + 18 * q^79 + 100 * q^80 + 154 * q^81 - 4 * q^82 + 24 * q^83 + 35 * q^84 + 30 * q^85 - q^86 + 49 * q^87 - 74 * q^88 + 97 * q^89 + 22 * q^90 - 25 * q^91 + 23 * q^92 + 32 * q^93 + 21 * q^94 + 56 * q^95 + 29 * q^96 + 26 * q^97 + 15 * q^98 - 11 * q^99

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