LMFDB - Embedded newform 6017.2.a.f.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$0$
Dimension:	$121$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.73908 q^{2} +1.22981 q^{3} +5.50258 q^{4} -1.73351 q^{5} -3.36855 q^{6} -3.95971 q^{7} -9.59385 q^{8} -1.48757 q^{9} +O(q^{10})$	\(q-2.73908 q^{2} +1.22981 q^{3} +5.50258 q^{4} -1.73351 q^{5} -3.36855 q^{6} -3.95971 q^{7} -9.59385 q^{8} -1.48757 q^{9} +4.74824 q^{10} -1.00000 q^{11} +6.76711 q^{12} +4.72992 q^{13} +10.8460 q^{14} -2.13189 q^{15} +15.2732 q^{16} -1.93056 q^{17} +4.07459 q^{18} -2.39204 q^{19} -9.53879 q^{20} -4.86968 q^{21} +2.73908 q^{22} -7.13275 q^{23} -11.7986 q^{24} -1.99493 q^{25} -12.9557 q^{26} -5.51885 q^{27} -21.7886 q^{28} -8.01568 q^{29} +5.83942 q^{30} +2.04723 q^{31} -22.6469 q^{32} -1.22981 q^{33} +5.28796 q^{34} +6.86421 q^{35} -8.18549 q^{36} -2.64009 q^{37} +6.55199 q^{38} +5.81690 q^{39} +16.6311 q^{40} -9.10855 q^{41} +13.3385 q^{42} -1.45685 q^{43} -5.50258 q^{44} +2.57873 q^{45} +19.5372 q^{46} +6.96189 q^{47} +18.7831 q^{48} +8.67931 q^{49} +5.46429 q^{50} -2.37422 q^{51} +26.0268 q^{52} +0.782647 q^{53} +15.1166 q^{54} +1.73351 q^{55} +37.9889 q^{56} -2.94175 q^{57} +21.9556 q^{58} -4.13959 q^{59} -11.7309 q^{60} -9.39501 q^{61} -5.60752 q^{62} +5.89036 q^{63} +31.4853 q^{64} -8.19938 q^{65} +3.36855 q^{66} +4.47317 q^{67} -10.6230 q^{68} -8.77191 q^{69} -18.8016 q^{70} +0.839471 q^{71} +14.2716 q^{72} +6.96113 q^{73} +7.23142 q^{74} -2.45339 q^{75} -13.1624 q^{76} +3.95971 q^{77} -15.9330 q^{78} -13.0859 q^{79} -26.4763 q^{80} -2.32440 q^{81} +24.9491 q^{82} -0.279730 q^{83} -26.7958 q^{84} +3.34665 q^{85} +3.99043 q^{86} -9.85774 q^{87} +9.59385 q^{88} +6.42994 q^{89} -7.06335 q^{90} -18.7291 q^{91} -39.2485 q^{92} +2.51769 q^{93} -19.0692 q^{94} +4.14663 q^{95} -27.8513 q^{96} -3.44054 q^{97} -23.7734 q^{98} +1.48757 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) $ 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * 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 $

$2$	−2.73908	−1.93682	−0.968412	−	0.249355i	$-0.919782\pi$
$2$	−2.73908	−1.93682	−0.968412	+	0.249355i	$0.919782\pi$
$3$	1.22981	0.710030	0.355015	−	0.934861i	$-0.384476\pi$
$3$	1.22981	0.710030	0.355015	+	0.934861i	$0.384476\pi$
$4$	5.50258	2.75129
$5$	−1.73351	−0.775250	−0.387625	−	0.921817i	$-0.626705\pi$
$5$	−1.73351	−0.775250	−0.387625	+	0.921817i	$0.626705\pi$
$6$	−3.36855	−1.37520
$7$	−3.95971	−1.49663	−0.748315	−	0.663344i	$-0.769137\pi$
$7$	−3.95971	−1.49663	−0.748315	+	0.663344i	$0.769137\pi$
$8$	−9.59385	−3.39194
$9$	−1.48757	−0.495858
$10$	4.74824	1.50152
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	6.76711	1.95350
$13$	4.72992	1.31184	0.655922	−	0.754828i	$-0.272280\pi$
$13$	4.72992	1.31184	0.655922	+	0.754828i	$0.272280\pi$
$14$	10.8460	2.89871
$15$	−2.13189	−0.550451
$16$	15.2732	3.81830
$17$	−1.93056	−0.468229	−0.234115	−	0.972209i	$-0.575219\pi$
$17$	−1.93056	−0.468229	−0.234115	+	0.972209i	$0.575219\pi$
$18$	4.07459	0.960390
$19$	−2.39204	−0.548771	−0.274385	−	0.961620i	$-0.588474\pi$
$19$	−2.39204	−0.548771	−0.274385	+	0.961620i	$0.588474\pi$
$20$	−9.53879	−2.13294
$21$	−4.86968	−1.06265
$22$	2.73908	0.583975
$23$	−7.13275	−1.48728	−0.743640	−	0.668580i	$-0.766902\pi$
$23$	−7.13275	−1.48728	−0.743640	+	0.668580i	$0.766902\pi$
$24$	−11.7986	−2.40838
$25$	−1.99493	−0.398987
$26$	−12.9557	−2.54081
$27$	−5.51885	−1.06210
$28$	−21.7886	−4.11766
$29$	−8.01568	−1.48847	−0.744237	−	0.667916i	$-0.767187\pi$
$29$	−8.01568	−1.48847	−0.744237	+	0.667916i	$0.767187\pi$
$30$	5.83942	1.06613
$31$	2.04723	0.367692	0.183846	−	0.982955i	$-0.441145\pi$
$31$	2.04723	0.367692	0.183846	+	0.982955i	$0.441145\pi$
$32$	−22.6469	−4.00344
$33$	−1.22981	−0.214082
$34$	5.28796	0.906878
$35$	6.86421	1.16026
$36$	−8.18549	−1.36425
$37$	−2.64009	−0.434028	−0.217014	−	0.976168i	$-0.569632\pi$
$37$	−2.64009	−0.434028	−0.217014	+	0.976168i	$0.569632\pi$
$38$	6.55199	1.06287
$39$	5.81690	0.931449
$40$	16.6311	2.62960
$41$	−9.10855	−1.42252	−0.711258	−	0.702931i	$-0.751874\pi$
$41$	−9.10855	−1.42252	−0.711258	+	0.702931i	$0.751874\pi$
$42$	13.3385	2.05817
$43$	−1.45685	−0.222167	−0.111084	−	0.993811i	$-0.535432\pi$
$43$	−1.45685	−0.222167	−0.111084	+	0.993811i	$0.535432\pi$
$44$	−5.50258	−0.829545
$45$	2.57873	0.384414
$46$	19.5372	2.88060
$47$	6.96189	1.01550	0.507748	−	0.861506i	$-0.330478\pi$
$47$	6.96189	1.01550	0.507748	+	0.861506i	$0.330478\pi$
$48$	18.7831	2.71111
$49$	8.67931	1.23990
$50$	5.46429	0.772768
$51$	−2.37422	−0.332457
$52$	26.0268	3.60926
$53$	0.782647	0.107505	0.0537524	−	0.998554i	$-0.482882\pi$
$53$	0.782647	0.107505	0.0537524	+	0.998554i	$0.482882\pi$
$54$	15.1166	2.05711
$55$	1.73351	0.233747
$56$	37.9889	5.07648
$57$	−2.94175	−0.389644
$58$	21.9556	2.88291
$59$	−4.13959	−0.538929	−0.269465	−	0.963010i	$-0.586847\pi$
$59$	−4.13959	−0.538929	−0.269465	+	0.963010i	$0.586847\pi$
$60$	−11.7309	−1.51445
$61$	−9.39501	−1.20291	−0.601454	−	0.798908i	$-0.705412\pi$
$61$	−9.39501	−1.20291	−0.601454	+	0.798908i	$0.705412\pi$
$62$	−5.60752	−0.712156
$63$	5.89036	0.742116
$64$	31.4853	3.93566
$65$	−8.19938	−1.01701
$66$	3.36855	0.414639
$67$	4.47317	0.546484	0.273242	−	0.961945i	$-0.411904\pi$
$67$	4.47317	0.546484	0.273242	+	0.961945i	$0.411904\pi$
$68$	−10.6230	−1.28823
$69$	−8.77191	−1.05601
$70$	−18.8016	−2.24723
$71$	0.839471	0.0996268	0.0498134	−	0.998759i	$-0.484137\pi$
$71$	0.839471	0.0996268	0.0498134	+	0.998759i	$0.484137\pi$
$72$	14.2716	1.68192
$73$	6.96113	0.814738	0.407369	−	0.913264i	$-0.366446\pi$
$73$	6.96113	0.814738	0.407369	+	0.913264i	$0.366446\pi$
$74$	7.23142	0.840636
$75$	−2.45339	−0.283293
$76$	−13.1624	−1.50983
$77$	3.95971	0.451251
$78$	−15.9330	−1.80405
$79$	−13.0859	−1.47228	−0.736142	−	0.676827i	$-0.763354\pi$
$79$	−13.0859	−1.47228	−0.736142	+	0.676827i	$0.763354\pi$
$80$	−26.4763	−2.96014
$81$	−2.32440	−0.258267
$82$	24.9491	2.75516
$83$	−0.279730	−0.0307044	−0.0153522	−	0.999882i	$-0.504887\pi$
$83$	−0.279730	−0.0307044	−0.0153522	+	0.999882i	$0.504887\pi$
$84$	−26.7958	−2.92366
$85$	3.34665	0.362995
$86$	3.99043	0.430299
$87$	−9.85774	−1.05686
$88$	9.59385	1.02271
$89$	6.42994	0.681572	0.340786	−	0.940141i	$-0.389307\pi$
$89$	6.42994	0.681572	0.340786	+	0.940141i	$0.389307\pi$
$90$	−7.06335	−0.744542
$91$	−18.7291	−1.96335
$92$	−39.2485	−4.09194
$93$	2.51769	0.261073
$94$	−19.0692	−1.96684
$95$	4.14663	0.425435
$96$	−27.8513	−2.84256
$97$	−3.44054	−0.349334	−0.174667	−	0.984628i	$-0.555885\pi$
$97$	−3.44054	−0.349334	−0.174667	+	0.984628i	$0.555885\pi$
$98$	−23.7734	−2.40147
$99$	1.48757	0.149507
$100$	−10.9773	−1.09773
$101$	7.58996	0.755229	0.377615	−	0.925963i	$-0.376744\pi$
$101$	7.58996	0.755229	0.377615	+	0.925963i	$0.376744\pi$
$102$	6.50317	0.643910
$103$	7.74756	0.763390	0.381695	−	0.924288i	$-0.375340\pi$
$103$	7.74756	0.763390	0.381695	+	0.924288i	$0.375340\pi$
$104$	−45.3782	−4.44970
$105$	8.44165	0.823821
$106$	−2.14373	−0.208218
$107$	−17.0194	−1.64532	−0.822661	−	0.568532i	$-0.807512\pi$
$107$	−17.0194	−1.64532	−0.822661	+	0.568532i	$0.807512\pi$
$108$	−30.3679	−2.92215
$109$	−6.43035	−0.615915	−0.307958	−	0.951400i	$-0.599646\pi$
$109$	−6.43035	−0.615915	−0.307958	+	0.951400i	$0.599646\pi$
$110$	−4.74824	−0.452726
$111$	−3.24680	−0.308173
$112$	−60.4775	−5.71459
$113$	−5.29614	−0.498219	−0.249110	−	0.968475i	$-0.580138\pi$
$113$	−5.29614	−0.498219	−0.249110	+	0.968475i	$0.580138\pi$
$114$	8.05769	0.754671
$115$	12.3647	1.15301
$116$	−44.1069	−4.09522
$117$	−7.03611	−0.650489
$118$	11.3387	1.04381
$119$	7.64445	0.700766
$120$	20.4530	1.86710
$121$	1.00000	0.0909091
$122$	25.7337	2.32982
$123$	−11.2018	−1.01003
$124$	11.2650	1.01163
$125$	12.1258	1.08457
$126$	−16.1342	−1.43735
$127$	10.3702	0.920208	0.460104	−	0.887865i	$-0.347812\pi$
$127$	10.3702	0.920208	0.460104	+	0.887865i	$0.347812\pi$
$128$	−40.9471	−3.61924
$129$	−1.79164	−0.157745
$130$	22.4588	1.96977
$131$	−11.7083	−1.02296	−0.511481	−	0.859295i	$-0.670903\pi$
$131$	−11.7083	−1.02296	−0.511481	+	0.859295i	$0.670903\pi$
$132$	−6.76711	−0.589001
$133$	9.47178	0.821307
$134$	−12.2524	−1.05844
$135$	9.56700	0.823396
$136$	18.5215	1.58821
$137$	10.0482	0.858476	0.429238	−	0.903191i	$-0.358782\pi$
$137$	10.0482	0.858476	0.429238	+	0.903191i	$0.358782\pi$
$138$	24.0270	2.04531
$139$	5.91168	0.501422	0.250711	−	0.968062i	$-0.419336\pi$
$139$	5.91168	0.501422	0.250711	+	0.968062i	$0.419336\pi$
$140$	37.7708	3.19222
$141$	8.56179	0.721032
$142$	−2.29938	−0.192960
$143$	−4.72992	−0.395536
$144$	−22.7200	−1.89333
$145$	13.8953	1.15394
$146$	−19.0671	−1.57800
$147$	10.6739	0.880367
$148$	−14.5273	−1.19414
$149$	17.9451	1.47012	0.735060	−	0.678002i	$-0.237154\pi$
$149$	17.9451	1.47012	0.735060	+	0.678002i	$0.237154\pi$
$150$	6.72003	0.548688
$151$	−14.0846	−1.14619	−0.573094	−	0.819489i	$-0.694257\pi$
$151$	−14.0846	−1.14619	−0.573094	+	0.819489i	$0.694257\pi$
$152$	22.9489	1.86140
$153$	2.87185	0.232175
$154$	−10.8460	−0.873994
$155$	−3.54889	−0.285054
$156$	32.0079	2.56269
$157$	−22.6019	−1.80383	−0.901914	−	0.431916i	$-0.857838\pi$
$157$	−22.6019	−1.80383	−0.901914	+	0.431916i	$0.857838\pi$
$158$	35.8435	2.85156
$159$	0.962505	0.0763316
$160$	39.2587	3.10367
$161$	28.2436	2.22591
$162$	6.36674	0.500218
$163$	11.3171	0.886427	0.443213	−	0.896416i	$-0.353838\pi$
$163$	11.3171	0.886427	0.443213	+	0.896416i	$0.353838\pi$
$164$	−50.1205	−3.91375
$165$	2.13189	0.165967
$166$	0.766204	0.0594689
$167$	−9.10587	−0.704633	−0.352317	−	0.935881i	$-0.614606\pi$
$167$	−9.10587	−0.704633	−0.352317	+	0.935881i	$0.614606\pi$
$168$	46.7190	3.60445
$169$	9.37218	0.720937
$170$	−9.16675	−0.703057
$171$	3.55833	0.272112
$172$	−8.01642	−0.611246
$173$	−21.3921	−1.62641	−0.813205	−	0.581978i	$-0.802279\pi$
$173$	−21.3921	−1.62641	−0.813205	+	0.581978i	$0.802279\pi$
$174$	27.0012	2.04695
$175$	7.89936	0.597136
$176$	−15.2732	−1.15126
$177$	−5.09090	−0.382656
$178$	−17.6121	−1.32009
$179$	−20.6266	−1.54170	−0.770852	−	0.637015i	$-0.780169\pi$
$179$	−20.6266	−1.54170	−0.770852	+	0.637015i	$0.780169\pi$
$180$	14.1896	1.05763
$181$	0.126567	0.00940768	0.00470384	−	0.999989i	$-0.498503\pi$
$181$	0.126567	0.00940768	0.00470384	+	0.999989i	$0.498503\pi$
$182$	51.3007	3.80266
$183$	−11.5540	−0.854100
$184$	68.4305	5.04477
$185$	4.57663	0.336480
$186$	−6.89617	−0.505652
$187$	1.93056	0.141176
$188$	38.3083	2.79392
$189$	21.8531	1.58958
$190$	−11.3580	−0.823993
$191$	−0.0198668	−0.00143751	−0.000718755	−	1.00000i	$-0.500229\pi$
$191$	−0.0198668	−0.00143751	−0.000718755		1.00000i	$0.500229\pi$
$192$	38.7208	2.79444
$193$	2.37822	0.171188	0.0855939	−	0.996330i	$-0.472721\pi$
$193$	2.37822	0.171188	0.0855939	+	0.996330i	$0.472721\pi$
$194$	9.42394	0.676599
$195$	−10.0837	−0.722106
$196$	47.7586	3.41133
$197$	−17.9498	−1.27887	−0.639435	−	0.768845i	$-0.720832\pi$
$197$	−17.9498	−1.27887	−0.639435	+	0.768845i	$0.720832\pi$
$198$	−4.07459	−0.289568
$199$	16.0847	1.14021	0.570107	−	0.821570i	$-0.306902\pi$
$199$	16.0847	1.14021	0.570107	+	0.821570i	$0.306902\pi$
$200$	19.1391	1.35334
$201$	5.50113	0.388020
$202$	−20.7895	−1.46275
$203$	31.7398	2.22769
$204$	−13.0643	−0.914684
$205$	15.7898	1.10281
$206$	−21.2212	−1.47855
$207$	10.6105	0.737480
$208$	72.2411	5.00902
$209$	2.39204	0.165461
$210$	−23.1224	−1.59560
$211$	−20.1847	−1.38957	−0.694785	−	0.719217i	$-0.744501\pi$
$211$	−20.1847	−1.38957	−0.694785	+	0.719217i	$0.744501\pi$
$212$	4.30658	0.295777
$213$	1.03239	0.0707380
$214$	46.6174	3.18670
$215$	2.52546	0.172235
$216$	52.9471	3.60259
$217$	−8.10642	−0.550300
$218$	17.6133	1.19292
$219$	8.56084	0.578488
$220$	9.53879	0.643105
$221$	−9.13140	−0.614244
$222$	8.89326	0.596876
$223$	1.12254	0.0751706	0.0375853	−	0.999293i	$-0.488033\pi$
$223$	1.12254	0.0751706	0.0375853	+	0.999293i	$0.488033\pi$
$224$	89.6751	5.99167
$225$	2.96761	0.197841
$226$	14.5066	0.964963
$227$	9.25146	0.614041	0.307021	−	0.951703i	$-0.400668\pi$
$227$	9.25146	0.614041	0.307021	+	0.951703i	$0.400668\pi$
$228$	−16.1872	−1.07202
$229$	−8.49724	−0.561513	−0.280757	−	0.959779i	$-0.590585\pi$
$229$	−8.49724	−0.561513	−0.280757	+	0.959779i	$0.590585\pi$
$230$	−33.8680	−2.23319
$231$	4.86968	0.320402
$232$	76.9012	5.04881
$233$	12.7681	0.836469	0.418235	−	0.908339i	$-0.362649\pi$
$233$	12.7681	0.836469	0.418235	+	0.908339i	$0.362649\pi$
$234$	19.2725	1.25988
$235$	−12.0685	−0.787264
$236$	−22.7784	−1.48275
$237$	−16.0932	−1.04537
$238$	−20.9388	−1.35726
$239$	−4.43309	−0.286753	−0.143376	−	0.989668i	$-0.545796\pi$
$239$	−4.43309	−0.286753	−0.143376	+	0.989668i	$0.545796\pi$
$240$	−32.5607	−2.10179
$241$	−14.4375	−0.930004	−0.465002	−	0.885310i	$-0.653946\pi$
$241$	−14.4375	−0.930004	−0.465002	+	0.885310i	$0.653946\pi$
$242$	−2.73908	−0.176075
$243$	13.6980	0.878726
$244$	−51.6968	−3.30955
$245$	−15.0457	−0.961234
$246$	30.6826	1.95625
$247$	−11.3142	−0.719902
$248$	−19.6408	−1.24719
$249$	−0.344014	−0.0218010
$250$	−33.2136	−2.10061
$251$	−3.72490	−0.235113	−0.117557	−	0.993066i	$-0.537506\pi$
$251$	−3.72490	−0.235113	−0.117557	+	0.993066i	$0.537506\pi$
$252$	32.4122	2.04177
$253$	7.13275	0.448432
$254$	−28.4049	−1.78228
$255$	4.11573	0.257737
$256$	49.1869	3.07418
$257$	14.7880	0.922448	0.461224	−	0.887284i	$-0.347410\pi$
$257$	14.7880	0.922448	0.461224	+	0.887284i	$0.347410\pi$
$258$	4.90746	0.305525
$259$	10.4540	0.649579
$260$	−45.1177	−2.79808
$261$	11.9239	0.738071
$262$	32.0701	1.98130
$263$	13.5386	0.834824	0.417412	−	0.908717i	$-0.362937\pi$
$263$	13.5386	0.834824	0.417412	+	0.908717i	$0.362937\pi$
$264$	11.7986	0.726153
$265$	−1.35673	−0.0833431
$266$	−25.9440	−1.59073
$267$	7.90759	0.483936
$268$	24.6139	1.50354
$269$	−30.6150	−1.86663	−0.933315	−	0.359060i	$-0.883098\pi$
$269$	−30.6150	−1.86663	−0.933315	+	0.359060i	$0.883098\pi$
$270$	−26.2048	−1.59477
$271$	−10.5041	−0.638081	−0.319040	−	0.947741i	$-0.603361\pi$
$271$	−10.5041	−0.638081	−0.319040	+	0.947741i	$0.603361\pi$
$272$	−29.4858	−1.78784
$273$	−23.0332	−1.39403
$274$	−27.5229	−1.66272
$275$	1.99493	0.120299
$276$	−48.2681	−2.90540
$277$	13.6996	0.823130	0.411565	−	0.911380i	$-0.364982\pi$
$277$	13.6996	0.823130	0.411565	+	0.911380i	$0.364982\pi$
$278$	−16.1926	−0.971167
$279$	−3.04540	−0.182323
$280$	−65.8542	−3.93554
$281$	14.3459	0.855806	0.427903	−	0.903825i	$-0.359253\pi$
$281$	14.3459	0.855806	0.427903	+	0.903825i	$0.359253\pi$
$282$	−23.4514	−1.39651
$283$	20.5828	1.22352	0.611761	−	0.791042i	$-0.290461\pi$
$283$	20.5828	1.22352	0.611761	+	0.791042i	$0.290461\pi$
$284$	4.61925	0.274102
$285$	5.09955	0.302071
$286$	12.9557	0.766084
$287$	36.0672	2.12898
$288$	33.6889	1.98514
$289$	−13.2729	−0.780761
$290$	−38.0603	−2.23498
$291$	−4.23121	−0.248038
$292$	38.3041	2.24158
$293$	4.81884	0.281519	0.140760	−	0.990044i	$-0.455045\pi$
$293$	4.81884	0.281519	0.140760	+	0.990044i	$0.455045\pi$
$294$	−29.2366	−1.70512
$295$	7.17603	0.417805
$296$	25.3286	1.47220
$297$	5.51885	0.320236
$298$	−49.1531	−2.84736
$299$	−33.7374	−1.95108
$300$	−13.4999	−0.779420
$301$	5.76870	0.332502
$302$	38.5789	2.21997
$303$	9.33419	0.536235
$304$	−36.5341	−2.09537
$305$	16.2864	0.932554
$306$	−7.86623	−0.449683
$307$	1.84524	0.105313	0.0526567	−	0.998613i	$-0.483231\pi$
$307$	1.84524	0.105313	0.0526567	+	0.998613i	$0.483231\pi$
$308$	21.7886	1.24152
$309$	9.52801	0.542030
$310$	9.72071	0.552099
$311$	13.1829	0.747533	0.373766	−	0.927523i	$-0.378066\pi$
$311$	13.1829	0.747533	0.373766	+	0.927523i	$0.378066\pi$
$312$	−55.8065	−3.15942
$313$	25.7814	1.45725	0.728625	−	0.684913i	$-0.240160\pi$
$313$	25.7814	1.45725	0.728625	+	0.684913i	$0.240160\pi$
$314$	61.9085	3.49370
$315$	−10.2110	−0.575325
$316$	−72.0064	−4.05068
$317$	−7.78098	−0.437023	−0.218512	−	0.975834i	$-0.570120\pi$
$317$	−7.78098	−0.437023	−0.218512	+	0.975834i	$0.570120\pi$
$318$	−2.63638	−0.147841
$319$	8.01568	0.448792
$320$	−54.5801	−3.05112
$321$	−20.9305	−1.16823
$322$	−77.3616	−4.31119
$323$	4.61797	0.256951
$324$	−12.7902	−0.710568
$325$	−9.43589	−0.523409
$326$	−30.9986	−1.71685
$327$	−7.90809	−0.437318
$328$	87.3861	4.82509
$329$	−27.5671	−1.51982
$330$	−5.83942	−0.321449
$331$	9.43119	0.518385	0.259193	−	0.965826i	$-0.416544\pi$
$331$	9.43119	0.518385	0.259193	+	0.965826i	$0.416544\pi$
$332$	−1.53924	−0.0844766
$333$	3.92733	0.215216
$334$	24.9417	1.36475
$335$	−7.75429	−0.423662
$336$	−74.3757	−4.05753
$337$	−26.7505	−1.45719	−0.728595	−	0.684944i	$-0.759826\pi$
$337$	−26.7505	−1.45719	−0.728595	+	0.684944i	$0.759826\pi$
$338$	−25.6712	−1.39633
$339$	−6.51324	−0.353750
$340$	18.4152	0.998704
$341$	−2.04723	−0.110863
$342$	−9.74657	−0.527034
$343$	−6.64958	−0.359044
$344$	13.9768	0.753578
$345$	15.2062	0.818675
$346$	58.5947	3.15007
$347$	7.77330	0.417292	0.208646	−	0.977991i	$-0.433094\pi$
$347$	7.77330	0.417292	0.208646	+	0.977991i	$0.433094\pi$
$348$	−54.2430	−2.90773
$349$	21.1507	1.13217	0.566085	−	0.824347i	$-0.308457\pi$
$349$	21.1507	1.13217	0.566085	+	0.824347i	$0.308457\pi$
$350$	−21.6370	−1.15655
$351$	−26.1038	−1.39332
$352$	22.6469	1.20708
$353$	26.4425	1.40739	0.703696	−	0.710501i	$-0.251532\pi$
$353$	26.4425	1.40739	0.703696	+	0.710501i	$0.251532\pi$
$354$	13.9444	0.741137
$355$	−1.45523	−0.0772357
$356$	35.3812	1.87520
$357$	9.40121	0.497565
$358$	56.4979	2.98601
$359$	−27.4097	−1.44663	−0.723315	−	0.690518i	$-0.757382\pi$
$359$	−27.4097	−1.44663	−0.723315	+	0.690518i	$0.757382\pi$
$360$	−24.7399	−1.30391
$361$	−13.2782	−0.698850
$362$	−0.346679	−0.0182210
$363$	1.22981	0.0645482
$364$	−103.059	−5.40173
$365$	−12.0672	−0.631626
$366$	31.6475	1.65424
$367$	20.3637	1.06298	0.531488	−	0.847066i	$-0.321633\pi$
$367$	20.3637	1.06298	0.531488	+	0.847066i	$0.321633\pi$
$368$	−108.940	−5.67889
$369$	13.5496	0.705366
$370$	−12.5358	−0.651703
$371$	−3.09906	−0.160895
$372$	13.8538	0.718286
$373$	−2.86738	−0.148467	−0.0742337	−	0.997241i	$-0.523651\pi$
$373$	−2.86738	−0.148467	−0.0742337	+	0.997241i	$0.523651\pi$
$374$	−5.28796	−0.273434
$375$	14.9124	0.770073
$376$	−66.7914	−3.44450
$377$	−37.9135	−1.95265
$378$	−59.8573	−3.07873
$379$	37.6791	1.93545	0.967724	−	0.252014i	$-0.0810929\pi$
$379$	37.6791	1.93545	0.967724	+	0.252014i	$0.0810929\pi$
$380$	22.8171	1.17049
$381$	12.7534	0.653375
$382$	0.0544168	0.00278421
$383$	−0.690341	−0.0352748	−0.0176374	−	0.999844i	$-0.505614\pi$
$383$	−0.690341	−0.0352748	−0.0176374	+	0.999844i	$0.505614\pi$
$384$	−50.3570	−2.56977
$385$	−6.86421	−0.349832
$386$	−6.51413	−0.331561
$387$	2.16717	0.110163
$388$	−18.9319	−0.961120
$389$	2.77315	0.140604	0.0703021	−	0.997526i	$-0.477604\pi$
$389$	2.77315	0.140604	0.0703021	+	0.997526i	$0.477604\pi$
$390$	27.6200	1.39859
$391$	13.7702	0.696388
$392$	−83.2680	−4.20567
$393$	−14.3990	−0.726333
$394$	49.1660	2.47695
$395$	22.6847	1.14139
$396$	8.18549	0.411336
$397$	−3.06928	−0.154043	−0.0770213	−	0.997029i	$-0.524541\pi$
$397$	−3.06928	−0.154043	−0.0770213	+	0.997029i	$0.524541\pi$
$398$	−44.0573	−2.20839
$399$	11.6485	0.583152
$400$	−30.4690	−1.52345
$401$	6.29501	0.314358	0.157179	−	0.987570i	$-0.449760\pi$
$401$	6.29501	0.314358	0.157179	+	0.987570i	$0.449760\pi$
$402$	−15.0681	−0.751527
$403$	9.68322	0.482356
$404$	41.7643	2.07785
$405$	4.02938	0.200222
$406$	−86.9378	−4.31465
$407$	2.64009	0.130864
$408$	22.7779	1.12767
$409$	9.62339	0.475846	0.237923	−	0.971284i	$-0.423533\pi$
$409$	9.62339	0.475846	0.237923	+	0.971284i	$0.423533\pi$
$410$	−43.2495	−2.13594
$411$	12.3574	0.609544
$412$	42.6316	2.10031
$413$	16.3916	0.806577
$414$	−29.0630	−1.42837
$415$	0.484915	0.0238036
$416$	−107.118	−5.25189
$417$	7.27023	0.356025
$418$	−6.55199	−0.320468
$419$	−34.0693	−1.66439	−0.832197	−	0.554480i	$-0.812917\pi$
$419$	−34.0693	−1.66439	−0.832197	+	0.554480i	$0.812917\pi$
$420$	46.4509	2.26657
$421$	25.2422	1.23023	0.615114	−	0.788438i	$-0.289110\pi$
$421$	25.2422	1.23023	0.615114	+	0.788438i	$0.289110\pi$
$422$	55.2875	2.69135
$423$	−10.3563	−0.503542
$424$	−7.50860	−0.364650
$425$	3.85134	0.186817
$426$	−2.82780	−0.137007
$427$	37.2015	1.80031
$428$	−93.6503	−4.52676
$429$	−5.81690	−0.280842
$430$	−6.91746	−0.333589
$431$	36.9030	1.77755	0.888777	−	0.458341i	$-0.151556\pi$
$431$	36.9030	1.77755	0.888777	+	0.458341i	$0.151556\pi$
$432$	−84.2906	−4.05543
$433$	−37.9997	−1.82615	−0.913074	−	0.407795i	$-0.866298\pi$
$433$	−37.9997	−1.82615	−0.913074	+	0.407795i	$0.866298\pi$
$434$	22.2042	1.06583
$435$	17.0885	0.819332
$436$	−35.3835	−1.69456
$437$	17.0618	0.816176
$438$	−23.4489	−1.12043
$439$	−1.37700	−0.0657205	−0.0328603	−	0.999460i	$-0.510462\pi$
$439$	−1.37700	−0.0657205	−0.0328603	+	0.999460i	$0.510462\pi$
$440$	−16.6311	−0.792855
$441$	−12.9111	−0.614815
$442$	25.0117	1.18968
$443$	39.2297	1.86386	0.931929	−	0.362642i	$-0.118125\pi$
$443$	39.2297	1.86386	0.931929	+	0.362642i	$0.118125\pi$
$444$	−17.8658	−0.847872
$445$	−11.1464	−0.528389
$446$	−3.07472	−0.145592
$447$	22.0690	1.04383
$448$	−124.673	−5.89023
$449$	−5.96218	−0.281372	−0.140686	−	0.990054i	$-0.544931\pi$
$449$	−5.96218	−0.281372	−0.140686	+	0.990054i	$0.544931\pi$
$450$	−8.12854	−0.383183
$451$	9.10855	0.428905
$452$	−29.1424	−1.37075
$453$	−17.3214	−0.813828
$454$	−25.3405	−1.18929
$455$	32.4672	1.52209
$456$	28.2227	1.32165
$457$	−3.67345	−0.171837	−0.0859184	−	0.996302i	$-0.527382\pi$
$457$	−3.67345	−0.171837	−0.0859184	+	0.996302i	$0.527382\pi$
$458$	23.2746	1.08755
$459$	10.6545	0.497308
$460$	68.0378	3.17228
$461$	−29.0994	−1.35529	−0.677646	−	0.735388i	$-0.737000\pi$
$461$	−29.0994	−1.35529	−0.677646	+	0.735388i	$0.737000\pi$
$462$	−13.3385	−0.620562
$463$	29.4331	1.36787	0.683936	−	0.729542i	$-0.260267\pi$
$463$	29.4331	1.36787	0.683936	+	0.729542i	$0.260267\pi$
$464$	−122.425	−5.68344
$465$	−4.36445	−0.202397
$466$	−34.9730	−1.62009
$467$	23.9806	1.10969	0.554845	−	0.831954i	$-0.312778\pi$
$467$	23.9806	1.10969	0.554845	+	0.831954i	$0.312778\pi$
$468$	−38.7167	−1.78968
$469$	−17.7124	−0.817885
$470$	33.0567	1.52479
$471$	−27.7960	−1.28077
$472$	39.7146	1.82801
$473$	1.45685	0.0669859
$474$	44.0806	2.02469
$475$	4.77196	0.218952
$476$	42.0642	1.92801
$477$	−1.16424	−0.0533071
$478$	12.1426	0.555390
$479$	26.9887	1.23314	0.616572	−	0.787298i	$-0.288521\pi$
$479$	26.9887	1.23314	0.616572	+	0.787298i	$0.288521\pi$
$480$	48.2806	2.20370
$481$	−12.4874	−0.569377
$482$	39.5456	1.80125
$483$	34.7342	1.58046
$484$	5.50258	0.250117
$485$	5.96423	0.270822
$486$	−37.5199	−1.70194
$487$	−25.4736	−1.15432	−0.577159	−	0.816631i	$-0.695839\pi$
$487$	−25.4736	−1.15432	−0.577159	+	0.816631i	$0.695839\pi$
$488$	90.1343	4.08019
$489$	13.9179	0.629389
$490$	41.2114	1.86174
$491$	7.69386	0.347219	0.173610	−	0.984815i	$-0.444457\pi$
$491$	7.69386	0.347219	0.173610	+	0.984815i	$0.444457\pi$
$492$	−61.6386	−2.77888
$493$	15.4747	0.696947
$494$	30.9904	1.39432
$495$	−2.57873	−0.115905
$496$	31.2677	1.40396
$497$	−3.32406	−0.149105
$498$	0.942283	0.0422247
$499$	2.76216	0.123651	0.0618256	−	0.998087i	$-0.480308\pi$
$499$	2.76216	0.123651	0.0618256	+	0.998087i	$0.480308\pi$
$500$	66.7232	2.98395
$501$	−11.1985	−0.500310
$502$	10.2028	0.455374
$503$	21.0811	0.939958	0.469979	−	0.882677i	$-0.344261\pi$
$503$	21.0811	0.939958	0.469979	+	0.882677i	$0.344261\pi$
$504$	−56.5113	−2.51721
$505$	−13.1573	−0.585492
$506$	−19.5372	−0.868534
$507$	11.5260	0.511887
$508$	57.0629	2.53176
$509$	13.8856	0.615468	0.307734	−	0.951472i	$-0.400429\pi$
$509$	13.8856	0.615468	0.307734	+	0.951472i	$0.400429\pi$
$510$	−11.2733	−0.499192
$511$	−27.5640	−1.21936
$512$	−52.8328	−2.33490
$513$	13.2013	0.582852
$514$	−40.5055	−1.78662
$515$	−13.4305	−0.591818
$516$	−9.85865	−0.434003
$517$	−6.96189	−0.306184
$518$	−28.6343	−1.25812
$519$	−26.3081	−1.15480
$520$	78.6637	3.44963
$521$	−34.6247	−1.51693	−0.758467	−	0.651712i	$-0.774051\pi$
$521$	−34.6247	−1.51693	−0.758467	+	0.651712i	$0.774051\pi$
$522$	−32.6606	−1.42951
$523$	−29.8221	−1.30403	−0.652016	−	0.758205i	$-0.726076\pi$
$523$	−29.8221	−1.30403	−0.652016	+	0.758205i	$0.726076\pi$
$524$	−64.4260	−2.81446
$525$	9.71470	0.423984
$526$	−37.0833	−1.61691
$527$	−3.95229	−0.172164
$528$	−18.7831	−0.817430
$529$	27.8761	1.21200
$530$	3.71619	0.161421
$531$	6.15795	0.267232
$532$	52.1192	2.25965
$533$	−43.0827	−1.86612
$534$	−21.6595	−0.937300
$535$	29.5033	1.27554
$536$	−42.9149	−1.85364
$537$	−25.3667	−1.09466
$538$	83.8570	3.61533
$539$	−8.67931	−0.373844
$540$	52.6432	2.26540
$541$	28.2080	1.21276	0.606378	−	0.795177i	$-0.292622\pi$
$541$	28.2080	1.21276	0.606378	+	0.795177i	$0.292622\pi$
$542$	28.7717	1.23585
$543$	0.155654	0.00667973
$544$	43.7211	1.87453
$545$	11.1471	0.477489
$546$	63.0899	2.70000
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	55.2911	2.36192
$549$	13.9758	0.596471
$550$	−5.46429	−0.232998
$551$	19.1738	0.816831
$552$	84.1564	3.58193
$553$	51.8166	2.20346
$554$	−37.5244	−1.59426
$555$	5.62837	0.238911
$556$	32.5295	1.37956
$557$	−27.9957	−1.18622	−0.593108	−	0.805123i	$-0.702099\pi$
$557$	−27.9957	−1.18622	−0.593108	+	0.805123i	$0.702099\pi$
$558$	8.34160	0.353128
$559$	−6.89078	−0.291449
$560$	104.838	4.43023
$561$	2.37422	0.100239
$562$	−39.2947	−1.65755
$563$	2.65084	0.111720	0.0558599	−	0.998439i	$-0.482210\pi$
$563$	2.65084	0.111720	0.0558599	+	0.998439i	$0.482210\pi$
$564$	47.1119	1.98377
$565$	9.18093	0.386245
$566$	−56.3781	−2.36975
$567$	9.20397	0.386530
$568$	−8.05376	−0.337928
$569$	37.6515	1.57843	0.789216	−	0.614116i	$-0.210487\pi$
$569$	37.6515	1.57843	0.789216	+	0.614116i	$0.210487\pi$
$570$	−13.9681	−0.585059
$571$	29.0869	1.21725	0.608624	−	0.793459i	$-0.291722\pi$
$571$	29.0869	1.21725	0.608624	+	0.793459i	$0.291722\pi$
$572$	−26.0268	−1.08823
$573$	−0.0244323	−0.00102068
$574$	−98.7911	−4.12346
$575$	14.2294	0.593405
$576$	−46.8367	−1.95153
$577$	−8.66197	−0.360603	−0.180301	−	0.983611i	$-0.557707\pi$
$577$	−8.66197	−0.360603	−0.180301	+	0.983611i	$0.557707\pi$
$578$	36.3557	1.51220
$579$	2.92475	0.121548
$580$	76.4598	3.17482
$581$	1.10765	0.0459531
$582$	11.5896	0.480406
$583$	−0.782647	−0.0324139
$584$	−66.7840	−2.76354
$585$	12.1972	0.504292
$586$	−13.1992	−0.545254
$587$	−4.84942	−0.200157	−0.100079	−	0.994980i	$-0.531909\pi$
$587$	−4.84942	−0.200157	−0.100079	+	0.994980i	$0.531909\pi$
$588$	58.7339	2.42214
$589$	−4.89704	−0.201779
$590$	−19.6558	−0.809215
$591$	−22.0748	−0.908036
$592$	−40.3226	−1.65725
$593$	−1.01068	−0.0415036	−0.0207518	−	0.999785i	$-0.506606\pi$
$593$	−1.01068	−0.0415036	−0.0207518	+	0.999785i	$0.506606\pi$
$594$	−15.1166	−0.620241
$595$	−13.2518	−0.543269
$596$	98.7443	4.04473
$597$	19.7811	0.809586
$598$	92.4094	3.77890
$599$	−30.9901	−1.26622	−0.633110	−	0.774062i	$-0.718222\pi$
$599$	−30.9901	−1.26622	−0.633110	+	0.774062i	$0.718222\pi$
$600$	23.5374	0.960911
$601$	−7.02055	−0.286374	−0.143187	−	0.989696i	$-0.545735\pi$
$601$	−7.02055	−0.286374	−0.143187	+	0.989696i	$0.545735\pi$
$602$	−15.8009	−0.643998
$603$	−6.65416	−0.270979
$604$	−77.5016	−3.15350
$605$	−1.73351	−0.0704773
$606$	−25.5671	−1.03859
$607$	35.5691	1.44370	0.721852	−	0.692048i	$-0.243291\pi$
$607$	35.5691	1.44370	0.721852	+	0.692048i	$0.243291\pi$
$608$	54.1722	2.19697
$609$	39.0338	1.58173
$610$	−44.6097	−1.80619
$611$	32.9292	1.33217
$612$	15.8026	0.638781
$613$	−13.5252	−0.546276	−0.273138	−	0.961975i	$-0.588062\pi$
$613$	−13.5252	−0.546276	−0.273138	+	0.961975i	$0.588062\pi$
$614$	−5.05427	−0.203974
$615$	19.4184	0.783025
$616$	−37.9889	−1.53062
$617$	32.6767	1.31551	0.657756	−	0.753231i	$-0.271506\pi$
$617$	32.6767	1.31551	0.657756	+	0.753231i	$0.271506\pi$
$618$	−26.0980	−1.04982
$619$	8.38613	0.337067	0.168534	−	0.985696i	$-0.446097\pi$
$619$	8.38613	0.337067	0.168534	+	0.985696i	$0.446097\pi$
$620$	−19.5280	−0.784265
$621$	39.3646	1.57965
$622$	−36.1090	−1.44784
$623$	−25.4607	−1.02006
$624$	88.8427	3.55655
$625$	−11.0456	−0.441823
$626$	−70.6174	−2.82244
$627$	2.94175	0.117482
$628$	−124.369	−4.96285
$629$	5.09685	0.203225
$630$	27.9688	1.11430
$631$	−21.0747	−0.838971	−0.419485	−	0.907762i	$-0.637789\pi$
$631$	−21.0747	−0.838971	−0.419485	+	0.907762i	$0.637789\pi$
$632$	125.545	4.99390
$633$	−24.8233	−0.986636
$634$	21.3127	0.846437
$635$	−17.9769	−0.713391
$636$	5.29626	0.210010
$637$	41.0525	1.62656
$638$	−21.9556	−0.869231
$639$	−1.24877	−0.0494008
$640$	70.9823	2.80582
$641$	−19.9611	−0.788417	−0.394208	−	0.919021i	$-0.628981\pi$
$641$	−19.9611	−0.788417	−0.394208	+	0.919021i	$0.628981\pi$
$642$	57.3305	2.26265
$643$	−35.7651	−1.41044	−0.705219	−	0.708989i	$-0.749151\pi$
$643$	−35.7651	−1.41044	−0.705219	+	0.708989i	$0.749151\pi$
$644$	155.413	6.12412
$645$	3.10583	0.122292
$646$	−12.6490	−0.497668
$647$	−38.0146	−1.49451	−0.747254	−	0.664539i	$-0.768628\pi$
$647$	−38.0146	−1.49451	−0.747254	+	0.664539i	$0.768628\pi$
$648$	22.3000	0.876027
$649$	4.13959	0.162493
$650$	25.8457	1.01375
$651$	−9.96934	−0.390729
$652$	62.2734	2.43882
$653$	33.7737	1.32167	0.660833	−	0.750533i	$-0.270203\pi$
$653$	33.7737	1.32167	0.660833	+	0.750533i	$0.270203\pi$
$654$	21.6609	0.847009
$655$	20.2965	0.793051
$656$	−139.117	−5.43160
$657$	−10.3552	−0.403994
$658$	75.5085	2.94363
$659$	−23.9907	−0.934543	−0.467272	−	0.884114i	$-0.654763\pi$
$659$	−23.9907	−0.934543	−0.467272	+	0.884114i	$0.654763\pi$
$660$	11.7309	0.456624
$661$	−9.09448	−0.353734	−0.176867	−	0.984235i	$-0.556596\pi$
$661$	−9.09448	−0.353734	−0.176867	+	0.984235i	$0.556596\pi$
$662$	−25.8328	−1.00402
$663$	−11.2299	−0.436132
$664$	2.68369	0.104147
$665$	−16.4194	−0.636719
$666$	−10.7573	−0.416836
$667$	57.1738	2.21378
$668$	−50.1057	−1.93865
$669$	1.38050	0.0533733
$670$	21.2396	0.820559
$671$	9.39501	0.362690
$672$	110.283	4.25426
$673$	35.2531	1.35891	0.679454	−	0.733718i	$-0.262217\pi$
$673$	35.2531	1.35891	0.679454	+	0.733718i	$0.262217\pi$
$674$	73.2718	2.82232
$675$	11.0097	0.423765
$676$	51.5712	1.98351
$677$	6.73720	0.258932	0.129466	−	0.991584i	$-0.458674\pi$
$677$	6.73720	0.258932	0.129466	+	0.991584i	$0.458674\pi$
$678$	17.8403	0.685153
$679$	13.6236	0.522824
$680$	−32.1072	−1.23126
$681$	11.3775	0.435988
$682$	5.60752	0.214723
$683$	−38.5469	−1.47496	−0.737479	−	0.675370i	$-0.763984\pi$
$683$	−38.5469	−1.47496	−0.737479	+	0.675370i	$0.763984\pi$
$684$	19.5800	0.748660
$685$	−17.4187	−0.665534
$686$	18.2138	0.695404
$687$	−10.4500	−0.398691
$688$	−22.2507	−0.848302
$689$	3.70186	0.141030
$690$	−41.6511	−1.58563
$691$	18.6359	0.708945	0.354472	−	0.935066i	$-0.384660\pi$
$691$	18.6359	0.708945	0.354472	+	0.935066i	$0.384660\pi$
$692$	−117.712	−4.47472
$693$	−5.89036	−0.223756
$694$	−21.2917	−0.808222
$695$	−10.2480	−0.388728
$696$	94.5737	3.58481
$697$	17.5846	0.666064
$698$	−57.9335	−2.19282
$699$	15.7024	0.593918
$700$	43.4669	1.64289
$701$	−44.4192	−1.67769	−0.838844	−	0.544371i	$-0.816768\pi$
$701$	−44.4192	−1.67769	−0.838844	+	0.544371i	$0.816768\pi$
$702$	71.5004	2.69861
$703$	6.31519	0.238182
$704$	−31.4853	−1.18665
$705$	−14.8420	−0.558981
$706$	−72.4282	−2.72587
$707$	−30.0540	−1.13030
$708$	−28.0131	−1.05280
$709$	3.92951	0.147576	0.0737880	−	0.997274i	$-0.476491\pi$
$709$	3.92951	0.147576	0.0737880	+	0.997274i	$0.476491\pi$
$710$	3.98600	0.149592
$711$	19.4663	0.730044
$712$	−61.6879	−2.31185
$713$	−14.6023	−0.546862
$714$	−25.7507	−0.963695
$715$	8.19938	0.306640
$716$	−113.499	−4.24167
$717$	−5.45185	−0.203603
$718$	75.0775	2.80187
$719$	16.2377	0.605563	0.302782	−	0.953060i	$-0.402085\pi$
$719$	16.2377	0.605563	0.302782	+	0.953060i	$0.402085\pi$
$720$	39.3854	1.46781
$721$	−30.6781	−1.14251
$722$	36.3700	1.35355
$723$	−17.7554	−0.660330
$724$	0.696447	0.0258833
$725$	15.9907	0.593881
$726$	−3.36855	−0.125018
$727$	17.7454	0.658142	0.329071	−	0.944305i	$-0.393264\pi$
$727$	17.7454	0.658142	0.329071	+	0.944305i	$0.393264\pi$
$728$	179.685	6.65955
$729$	23.8191	0.882189
$730$	33.0531	1.22335
$731$	2.81253	0.104025
$732$	−63.5771	−2.34988
$733$	39.3367	1.45293	0.726466	−	0.687202i	$-0.241161\pi$
$733$	39.3367	1.45293	0.726466	+	0.687202i	$0.241161\pi$
$734$	−55.7779	−2.05880
$735$	−18.5033	−0.682505
$736$	161.535	5.95424
$737$	−4.47317	−0.164771
$738$	−37.1136	−1.36617
$739$	14.6809	0.540044	0.270022	−	0.962854i	$-0.412969\pi$
$739$	14.6809	0.540044	0.270022	+	0.962854i	$0.412969\pi$
$740$	25.1832	0.925755
$741$	−13.9142	−0.511152
$742$	8.48857	0.311625
$743$	8.58571	0.314979	0.157490	−	0.987521i	$-0.449660\pi$
$743$	8.58571	0.314979	0.157490	+	0.987521i	$0.449660\pi$
$744$	−24.1544	−0.885542
$745$	−31.1081	−1.13971
$746$	7.85399	0.287555
$747$	0.416119	0.0152250
$748$	10.6230	0.388417
$749$	67.3917	2.46244
$750$	−40.8463	−1.49150
$751$	23.8377	0.869851	0.434925	−	0.900466i	$-0.356775\pi$
$751$	23.8377	0.869851	0.434925	+	0.900466i	$0.356775\pi$
$752$	106.330	3.87747
$753$	−4.58091	−0.166938
$754$	103.848	3.78193
$755$	24.4158	0.888583
$756$	120.248	4.37338
$757$	−24.4379	−0.888210	−0.444105	−	0.895975i	$-0.646478\pi$
$757$	−24.4379	−0.888210	−0.444105	+	0.895975i	$0.646478\pi$
$758$	−103.206	−3.74862
$759$	8.77191	0.318400
$760$	−39.7821	−1.44305
$761$	−48.9521	−1.77451	−0.887257	−	0.461276i	$-0.847392\pi$
$761$	−48.9521	−1.77451	−0.887257	+	0.461276i	$0.847392\pi$
$762$	−34.9325	−1.26547
$763$	25.4623	0.921797
$764$	−0.109319	−0.00395501
$765$	−4.97838	−0.179994
$766$	1.89090	0.0683210
$767$	−19.5800	−0.706991
$768$	60.4904	2.18276
$769$	−47.0547	−1.69684	−0.848418	−	0.529327i	$-0.822445\pi$
$769$	−47.0547	−1.69684	−0.848418	+	0.529327i	$0.822445\pi$
$770$	18.8016	0.677564
$771$	18.1864	0.654965
$772$	13.0863	0.470987
$773$	17.8356	0.641504	0.320752	−	0.947163i	$-0.396064\pi$
$773$	17.8356	0.641504	0.320752	+	0.947163i	$0.396064\pi$
$774$	−5.93605	−0.213367
$775$	−4.08408	−0.146704
$776$	33.0081	1.18492
$777$	12.8564	0.461221
$778$	−7.59588	−0.272326
$779$	21.7880	0.780636
$780$	−55.4861	−1.98672
$781$	−0.839471	−0.0300386
$782$	−37.7177	−1.34878
$783$	44.2373	1.58091
$784$	132.561	4.73432
$785$	39.1807	1.39842
$786$	39.4400	1.40678
$787$	−9.06857	−0.323260	−0.161630	−	0.986851i	$-0.551675\pi$
$787$	−9.06857	−0.323260	−0.161630	+	0.986851i	$0.551675\pi$
$788$	−98.7702	−3.51854
$789$	16.6498	0.592750
$790$	−62.1352	−2.21067
$791$	20.9712	0.745650
$792$	−14.2716	−0.507118
$793$	−44.4377	−1.57803
$794$	8.40700	0.298353
$795$	−1.66851	−0.0591761
$796$	88.5073	3.13706
$797$	−24.3483	−0.862460	−0.431230	−	0.902242i	$-0.641920\pi$
$797$	−24.3483	−0.862460	−0.431230	+	0.902242i	$0.641920\pi$
$798$	−31.9061	−1.12946
$799$	−13.4403	−0.475485
$800$	45.1790	1.59732
$801$	−9.56501	−0.337963
$802$	−17.2426	−0.608856
$803$	−6.96113	−0.245653
$804$	30.2704	1.06756
$805$	−48.9607	−1.72564
$806$	−26.5231	−0.934238
$807$	−37.6506	−1.32536
$808$	−72.8169	−2.56169
$809$	26.2578	0.923174	0.461587	−	0.887095i	$-0.347280\pi$
$809$	26.2578	0.923174	0.461587	+	0.887095i	$0.347280\pi$
$810$	−11.0368	−0.387794
$811$	−49.5592	−1.74026	−0.870129	−	0.492825i	$-0.835964\pi$
$811$	−49.5592	−1.74026	−0.870129	+	0.492825i	$0.835964\pi$
$812$	174.650	6.12903
$813$	−12.9181	−0.453056
$814$	−7.23142	−0.253461
$815$	−19.6184	−0.687202
$816$	−36.2619	−1.26942
$817$	3.48483	0.121919
$818$	−26.3593	−0.921630
$819$	27.8610	0.973541
$820$	86.8845	3.03414
$821$	43.9245	1.53298	0.766488	−	0.642259i	$-0.222003\pi$
$821$	43.9245	1.53298	0.766488	+	0.642259i	$0.222003\pi$
$822$	−33.8478	−1.18058
$823$	7.87402	0.274471	0.137236	−	0.990538i	$-0.456178\pi$
$823$	7.87402	0.274471	0.137236	+	0.990538i	$0.456178\pi$
$824$	−74.3290	−2.58937
$825$	2.45339	0.0854159
$826$	−44.8979	−1.56220
$827$	30.3212	1.05437	0.527185	−	0.849750i	$-0.323247\pi$
$827$	30.3212	1.05437	0.527185	+	0.849750i	$0.323247\pi$
$828$	58.3850	2.02902
$829$	10.7679	0.373984	0.186992	−	0.982361i	$-0.440126\pi$
$829$	10.7679	0.373984	0.186992	+	0.982361i	$0.440126\pi$
$830$	−1.32822	−0.0461033
$831$	16.8479	0.584447
$832$	148.923	5.16298
$833$	−16.7559	−0.580558
$834$	−19.9138	−0.689557
$835$	15.7851	0.546267
$836$	13.1624	0.455230
$837$	−11.2983	−0.390527
$838$	93.3186	3.22364
$839$	−40.3893	−1.39439	−0.697196	−	0.716880i	$-0.745569\pi$
$839$	−40.3893	−1.39439	−0.697196	+	0.716880i	$0.745569\pi$
$840$	−80.9880	−2.79435
$841$	35.2511	1.21555
$842$	−69.1404	−2.38274
$843$	17.6427	0.607648
$844$	−111.068	−3.82311
$845$	−16.2468	−0.558907
$846$	28.3668	0.975272
$847$	−3.95971	−0.136057
$848$	11.9535	0.410486
$849$	25.3129	0.868738
$850$	−10.5491	−0.361832
$851$	18.8311	0.645521
$852$	5.68079	0.194621
$853$	0.938688	0.0321401	0.0160700	−	0.999871i	$-0.494885\pi$
$853$	0.938688	0.0321401	0.0160700	+	0.999871i	$0.494885\pi$
$854$	−101.898	−3.48688
$855$	−6.16841	−0.210955
$856$	163.281	5.58084
$857$	47.4657	1.62140	0.810698	−	0.585464i	$-0.199088\pi$
$857$	47.4657	1.62140	0.810698	+	0.585464i	$0.199088\pi$
$858$	15.9330	0.543942
$859$	15.9173	0.543090	0.271545	−	0.962426i	$-0.412465\pi$
$859$	15.9173	0.543090	0.271545	+	0.962426i	$0.412465\pi$
$860$	13.8966	0.473869
$861$	44.3557	1.51164
$862$	−101.080	−3.44281
$863$	50.9735	1.73516	0.867579	−	0.497299i	$-0.165675\pi$
$863$	50.9735	1.73516	0.867579	+	0.497299i	$0.165675\pi$
$864$	124.985	4.25207
$865$	37.0834	1.26087
$866$	104.084	3.53693
$867$	−16.3232	−0.554364
$868$	−44.6062	−1.51403
$869$	13.0859	0.443910
$870$	−46.8069	−1.58690
$871$	21.1577	0.716903
$872$	61.6918	2.08915
$873$	5.11806	0.173220
$874$	−46.7337	−1.58079
$875$	−48.0147	−1.62319
$876$	47.1067	1.59159
$877$	−16.6641	−0.562708	−0.281354	−	0.959604i	$-0.590783\pi$
$877$	−16.6641	−0.562708	−0.281354	+	0.959604i	$0.590783\pi$
$878$	3.77171	0.127289
$879$	5.92624	0.199887
$880$	26.4763	0.892516
$881$	−47.4762	−1.59951	−0.799757	−	0.600323i	$-0.795039\pi$
$881$	−47.4762	−1.59951	−0.799757	+	0.600323i	$0.795039\pi$
$882$	35.3646	1.19079
$883$	−23.3789	−0.786764	−0.393382	−	0.919375i	$-0.628695\pi$
$883$	−23.3789	−0.786764	−0.393382	+	0.919375i	$0.628695\pi$
$884$	−50.2462	−1.68996
$885$	8.82514	0.296654
$886$	−107.453	−3.60996
$887$	6.01617	0.202003	0.101002	−	0.994886i	$-0.467795\pi$
$887$	6.01617	0.202003	0.101002	+	0.994886i	$0.467795\pi$
$888$	31.1493	1.04530
$889$	−41.0631	−1.37721
$890$	30.5309	1.02340
$891$	2.32440	0.0778705
$892$	6.17684	0.206816
$893$	−16.6531	−0.557275
$894$	−60.4489	−2.02171
$895$	35.7564	1.19521
$896$	162.139	5.41667
$897$	−41.4905	−1.38533
$898$	16.3309	0.544969
$899$	−16.4099	−0.547301
$900$	16.3295	0.544317
$901$	−1.51095	−0.0503369
$902$	−24.9491	−0.830713
$903$	7.09439	0.236086
$904$	50.8104	1.68993
$905$	−0.219406	−0.00729331
$906$	47.4446	1.57624
$907$	13.5416	0.449641	0.224821	−	0.974400i	$-0.427820\pi$
$907$	13.5416	0.449641	0.224821	+	0.974400i	$0.427820\pi$
$908$	50.9069	1.68941
$909$	−11.2906	−0.374486
$910$	−88.9303	−2.94801
$911$	15.6109	0.517213	0.258607	−	0.965983i	$-0.416737\pi$
$911$	15.6109	0.517213	0.258607	+	0.965983i	$0.416737\pi$
$912$	−44.9299	−1.48778
$913$	0.279730	0.00925771
$914$	10.0619	0.332818
$915$	20.0291	0.662141
$916$	−46.7567	−1.54489
$917$	46.3616	1.53099
$918$	−29.1835	−0.963198
$919$	7.44490	0.245585	0.122792	−	0.992432i	$-0.460815\pi$
$919$	7.44490	0.245585	0.122792	+	0.992432i	$0.460815\pi$
$920$	−118.625	−3.91096
$921$	2.26929	0.0747757
$922$	79.7056	2.62496
$923$	3.97063	0.130695
$924$	26.7958	0.881517
$925$	5.26680	0.173171
$926$	−80.6198	−2.64933
$927$	−11.5251	−0.378533
$928$	181.530	5.95902
$929$	49.4252	1.62159	0.810794	−	0.585332i	$-0.199036\pi$
$929$	49.4252	1.62159	0.810794	+	0.585332i	$0.199036\pi$
$930$	11.9546	0.392007
$931$	−20.7612	−0.680422
$932$	70.2577	2.30137
$933$	16.2124	0.530770
$934$	−65.6848	−2.14927
$935$	−3.34665	−0.109447
$936$	67.5034	2.20642
$937$	−22.8820	−0.747523	−0.373761	−	0.927525i	$-0.621932\pi$
$937$	−22.8820	−0.747523	−0.373761	+	0.927525i	$0.621932\pi$
$938$	48.5159	1.58410
$939$	31.7061	1.03469
$940$	−66.4080	−2.16599
$941$	−40.0881	−1.30683	−0.653417	−	0.756998i	$-0.726665\pi$
$941$	−40.0881	−1.30683	−0.653417	+	0.756998i	$0.726665\pi$
$942$	76.1355	2.48063
$943$	64.9690	2.11568
$944$	−63.2249	−2.05779
$945$	−37.8825	−1.23232
$946$	−3.99043	−0.129740
$947$	−56.2411	−1.82759	−0.913794	−	0.406177i	$-0.866862\pi$
$947$	−56.2411	−1.82759	−0.913794	+	0.406177i	$0.866862\pi$
$948$	−88.5541	−2.87610
$949$	32.9256	1.06881
$950$	−13.0708	−0.424072
$951$	−9.56911	−0.310299
$952$	−73.3398	−2.37696
$953$	−4.69397	−0.152053	−0.0760263	−	0.997106i	$-0.524223\pi$
$953$	−4.69397	−0.152053	−0.0760263	+	0.997106i	$0.524223\pi$
$954$	3.18896	0.103246
$955$	0.0344393	0.00111443
$956$	−24.3934	−0.788940
$957$	9.85774	0.318655
$958$	−73.9243	−2.38838
$959$	−39.7880	−1.28482
$960$	−67.1231	−2.16639
$961$	−26.8089	−0.864802
$962$	34.2041	1.10278
$963$	25.3175	0.815846
$964$	−79.4437	−2.55871
$965$	−4.12267	−0.132713
$966$	−95.1399	−3.06108
$967$	−38.9428	−1.25232	−0.626159	−	0.779696i	$-0.715374\pi$
$967$	−38.9428	−1.25232	−0.626159	+	0.779696i	$0.715374\pi$
$968$	−9.59385	−0.308358
$969$	5.67921	0.182443
$970$	−16.3365	−0.524534
$971$	−38.9759	−1.25080	−0.625399	−	0.780305i	$-0.715064\pi$
$971$	−38.9759	−1.25080	−0.625399	+	0.780305i	$0.715064\pi$
$972$	75.3742	2.41763
$973$	−23.4085	−0.750444
$974$	69.7743	2.23571
$975$	−11.6043	−0.371636
$976$	−143.492	−4.59306
$977$	−24.4860	−0.783376	−0.391688	−	0.920098i	$-0.628109\pi$
$977$	−24.4860	−0.783376	−0.391688	+	0.920098i	$0.628109\pi$
$978$	−38.1223	−1.21902
$979$	−6.42994	−0.205502
$980$	−82.7901	−2.64463
$981$	9.56561	0.305406
$982$	−21.0741	−0.672503
$983$	−13.2378	−0.422219	−0.211109	−	0.977462i	$-0.567708\pi$
$983$	−13.2378	−0.422219	−0.211109	+	0.977462i	$0.567708\pi$
$984$	107.468	3.42596
$985$	31.1162	0.991445
$986$	−42.3866	−1.34986
$987$	−33.9022	−1.07912
$988$	−62.2570	−1.98066
$989$	10.3913	0.330425
$990$	7.06335	0.224488
$991$	−27.7822	−0.882531	−0.441265	−	0.897377i	$-0.645470\pi$
$991$	−27.7822	−0.882531	−0.441265	+	0.897377i	$0.645470\pi$
$992$	−46.3633	−1.47204
$993$	11.5985	0.368069
$994$	9.10488	0.288789
$995$	−27.8830	−0.883952
$996$	−1.89296	−0.0599809
$997$	32.4575	1.02794	0.513969	−	0.857809i	$-0.328175\pi$
$997$	32.4575	1.02794	0.513969	+	0.857809i	$0.328175\pi$
$998$	−7.56578	−0.239491
$999$	14.5703	0.460983

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.3	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.3	✓	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.73908 q^{2} +1.22981 q^{3} +5.50258 q^{4} -1.73351 q^{5} -3.36855 q^{6} -3.95971 q^{7} -9.59385 q^{8} -1.48757 q^{9} +O(q^{10})\)	\(q-2.73908 q^{2} +1.22981 q^{3} +5.50258 q^{4} -1.73351 q^{5} -3.36855 q^{6} -3.95971 q^{7} -9.59385 q^{8} -1.48757 q^{9} +4.74824 q^{10} -1.00000 q^{11} +6.76711 q^{12} +4.72992 q^{13} +10.8460 q^{14} -2.13189 q^{15} +15.2732 q^{16} -1.93056 q^{17} +4.07459 q^{18} -2.39204 q^{19} -9.53879 q^{20} -4.86968 q^{21} +2.73908 q^{22} -7.13275 q^{23} -11.7986 q^{24} -1.99493 q^{25} -12.9557 q^{26} -5.51885 q^{27} -21.7886 q^{28} -8.01568 q^{29} +5.83942 q^{30} +2.04723 q^{31} -22.6469 q^{32} -1.22981 q^{33} +5.28796 q^{34} +6.86421 q^{35} -8.18549 q^{36} -2.64009 q^{37} +6.55199 q^{38} +5.81690 q^{39} +16.6311 q^{40} -9.10855 q^{41} +13.3385 q^{42} -1.45685 q^{43} -5.50258 q^{44} +2.57873 q^{45} +19.5372 q^{46} +6.96189 q^{47} +18.7831 q^{48} +8.67931 q^{49} +5.46429 q^{50} -2.37422 q^{51} +26.0268 q^{52} +0.782647 q^{53} +15.1166 q^{54} +1.73351 q^{55} +37.9889 q^{56} -2.94175 q^{57} +21.9556 q^{58} -4.13959 q^{59} -11.7309 q^{60} -9.39501 q^{61} -5.60752 q^{62} +5.89036 q^{63} +31.4853 q^{64} -8.19938 q^{65} +3.36855 q^{66} +4.47317 q^{67} -10.6230 q^{68} -8.77191 q^{69} -18.8016 q^{70} +0.839471 q^{71} +14.2716 q^{72} +6.96113 q^{73} +7.23142 q^{74} -2.45339 q^{75} -13.1624 q^{76} +3.95971 q^{77} -15.9330 q^{78} -13.0859 q^{79} -26.4763 q^{80} -2.32440 q^{81} +24.9491 q^{82} -0.279730 q^{83} -26.7958 q^{84} +3.34665 q^{85} +3.99043 q^{86} -9.85774 q^{87} +9.59385 q^{88} +6.42994 q^{89} -7.06335 q^{90} -18.7291 q^{91} -39.2485 q^{92} +2.51769 q^{93} -19.0692 q^{94} +4.14663 q^{95} -27.8513 q^{96} -3.44054 q^{97} -23.7734 q^{98} +1.48757 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9} + 20 q^{10} - 121 q^{11} + 40 q^{12} + 31 q^{13} + 7 q^{14} + 53 q^{15} + 164 q^{16} - 23 q^{17} + 14 q^{18} + 62 q^{19} + 53 q^{20} + 19 q^{21} - 2 q^{22} + 34 q^{23} + 34 q^{24} + 172 q^{25} + 34 q^{26} + 87 q^{27} + 91 q^{28} - 30 q^{29} + 2 q^{30} + 102 q^{31} + 31 q^{32} - 18 q^{33} + 30 q^{34} + 20 q^{35} + 164 q^{36} + 58 q^{37} + 35 q^{38} + 42 q^{39} + 52 q^{40} - 12 q^{41} + 56 q^{42} + 96 q^{43} - 138 q^{44} + 72 q^{45} + 48 q^{46} + 136 q^{47} + 99 q^{48} + 199 q^{49} - 7 q^{50} + 22 q^{51} + 81 q^{52} + 24 q^{53} + 37 q^{54} - 13 q^{55} + 28 q^{56} + 25 q^{57} + 76 q^{58} + 58 q^{59} + 81 q^{60} + 14 q^{61} - 2 q^{62} + 152 q^{63} + 236 q^{64} - 29 q^{65} - 10 q^{66} + 112 q^{67} - 61 q^{68} + 41 q^{69} + 105 q^{70} + 56 q^{71} + 71 q^{72} + 113 q^{73} - 23 q^{74} + 111 q^{75} + 144 q^{76} - 56 q^{77} + 59 q^{78} + 80 q^{79} + 100 q^{80} + 177 q^{81} + 123 q^{82} + 6 q^{83} + 79 q^{84} + 26 q^{85} + 14 q^{86} + 180 q^{87} - 12 q^{88} + 26 q^{89} + 75 q^{90} + 72 q^{91} + 58 q^{92} + 139 q^{93} + 37 q^{94} + 39 q^{95} + 66 q^{96} + 136 q^{97} + 7 q^{98} - 143 q^{99}+O(q^{100}) \) 121 * q + 2 * q^2 + 18 * q^3 + 138 * q^4 + 13 * q^5 + 10 * q^6 + 56 * q^7 + 12 * q^8 + 143 * q^9 + 20 * q^10 - 121 * q^11 + 40 * q^12 + 31 * q^13 + 7 * q^14 + 53 * q^15 + 164 * q^16 - 23 * q^17 + 14 * q^18 + 62 * q^19 + 53 * q^20 + 19 * q^21 - 2 * q^22 + 34 * q^23 + 34 * q^24 + 172 * q^25 + 34 * q^26 + 87 * q^27 + 91 * q^28 - 30 * q^29 + 2 * q^30 + 102 * q^31 + 31 * q^32 - 18 * q^33 + 30 * q^34 + 20 * q^35 + 164 * q^36 + 58 * q^37 + 35 * q^38 + 42 * q^39 + 52 * q^40 - 12 * q^41 + 56 * q^42 + 96 * q^43 - 138 * q^44 + 72 * q^45 + 48 * q^46 + 136 * q^47 + 99 * q^48 + 199 * q^49 - 7 * q^50 + 22 * q^51 + 81 * q^52 + 24 * q^53 + 37 * q^54 - 13 * q^55 + 28 * q^56 + 25 * q^57 + 76 * q^58 + 58 * q^59 + 81 * q^60 + 14 * q^61 - 2 * q^62 + 152 * q^63 + 236 * q^64 - 29 * q^65 - 10 * q^66 + 112 * q^67 - 61 * q^68 + 41 * q^69 + 105 * q^70 + 56 * q^71 + 71 * q^72 + 113 * q^73 - 23 * q^74 + 111 * q^75 + 144 * q^76 - 56 * q^77 + 59 * q^78 + 80 * q^79 + 100 * q^80 + 177 * q^81 + 123 * q^82 + 6 * q^83 + 79 * q^84 + 26 * q^85 + 14 * q^86 + 180 * q^87 - 12 * q^88 + 26 * q^89 + 75 * q^90 + 72 * q^91 + 58 * q^92 + 139 * q^93 + 37 * q^94 + 39 * q^95 + 66 * q^96 + 136 * q^97 + 7 * q^98 - 143 * q^99

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