LMFDB - Embedded newform 6017.2.a.e.1.19

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:	$119$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
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)

$f(q)$	$=$	$q-1.97087 q^{2} +1.79688 q^{3} +1.88432 q^{4} -3.99793 q^{5} -3.54141 q^{6} -0.876225 q^{7} +0.227993 q^{8} +0.228774 q^{9} +O(q^{10})$	\(q-1.97087 q^{2} +1.79688 q^{3} +1.88432 q^{4} -3.99793 q^{5} -3.54141 q^{6} -0.876225 q^{7} +0.227993 q^{8} +0.228774 q^{9} +7.87939 q^{10} +1.00000 q^{11} +3.38589 q^{12} -3.27137 q^{13} +1.72692 q^{14} -7.18380 q^{15} -4.21798 q^{16} +5.54888 q^{17} -0.450884 q^{18} -6.22979 q^{19} -7.53337 q^{20} -1.57447 q^{21} -1.97087 q^{22} -0.985910 q^{23} +0.409675 q^{24} +10.9834 q^{25} +6.44744 q^{26} -4.97956 q^{27} -1.65109 q^{28} +2.32036 q^{29} +14.1583 q^{30} +0.681386 q^{31} +7.85710 q^{32} +1.79688 q^{33} -10.9361 q^{34} +3.50309 q^{35} +0.431084 q^{36} +8.03203 q^{37} +12.2781 q^{38} -5.87826 q^{39} -0.911499 q^{40} -7.26698 q^{41} +3.10307 q^{42} -9.19170 q^{43} +1.88432 q^{44} -0.914624 q^{45} +1.94310 q^{46} -4.70338 q^{47} -7.57920 q^{48} -6.23223 q^{49} -21.6469 q^{50} +9.97067 q^{51} -6.16430 q^{52} -12.5615 q^{53} +9.81405 q^{54} -3.99793 q^{55} -0.199773 q^{56} -11.1942 q^{57} -4.57312 q^{58} -6.02829 q^{59} -13.5366 q^{60} +4.02593 q^{61} -1.34292 q^{62} -0.200458 q^{63} -7.04933 q^{64} +13.0787 q^{65} -3.54141 q^{66} +13.2030 q^{67} +10.4559 q^{68} -1.77156 q^{69} -6.90412 q^{70} +5.86127 q^{71} +0.0521589 q^{72} +6.55693 q^{73} -15.8301 q^{74} +19.7359 q^{75} -11.7389 q^{76} -0.876225 q^{77} +11.5853 q^{78} -13.1218 q^{79} +16.8632 q^{80} -9.63399 q^{81} +14.3223 q^{82} -8.99151 q^{83} -2.96680 q^{84} -22.1840 q^{85} +18.1156 q^{86} +4.16940 q^{87} +0.227993 q^{88} +4.40520 q^{89} +1.80260 q^{90} +2.86646 q^{91} -1.85777 q^{92} +1.22437 q^{93} +9.26973 q^{94} +24.9063 q^{95} +14.1183 q^{96} -5.69865 q^{97} +12.2829 q^{98} +0.228774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) $ 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * 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 $

$2$	−1.97087	−1.39361	−0.696807	−	0.717259i	$-0.745397\pi$
$2$	−1.97087	−1.39361	−0.696807	+	0.717259i	$0.745397\pi$
$3$	1.79688	1.03743	0.518714	−	0.854948i	$-0.326411\pi$
$3$	1.79688	1.03743	0.518714	+	0.854948i	$0.326411\pi$
$4$	1.88432	0.942159
$5$	−3.99793	−1.78793	−0.893964	−	0.448139i	$-0.852087\pi$
$5$	−3.99793	−1.78793	−0.893964	+	0.448139i	$0.852087\pi$
$6$	−3.54141	−1.44577
$7$	−0.876225	−0.331182	−0.165591	−	0.986195i	$-0.552953\pi$
$7$	−0.876225	−0.331182	−0.165591	+	0.986195i	$0.552953\pi$
$8$	0.227993	0.0806076
$9$	0.228774	0.0762581
$10$	7.87939	2.49168
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	3.38589	0.977423
$13$	−3.27137	−0.907315	−0.453657	−	0.891176i	$-0.649881\pi$
$13$	−3.27137	−0.907315	−0.453657	+	0.891176i	$0.649881\pi$
$14$	1.72692	0.461540
$15$	−7.18380	−1.85485
$16$	−4.21798	−1.05450
$17$	5.54888	1.34580	0.672901	−	0.739733i	$-0.265048\pi$
$17$	5.54888	1.34580	0.672901	+	0.739733i	$0.265048\pi$
$18$	−0.450884	−0.106274
$19$	−6.22979	−1.42921	−0.714606	−	0.699527i	$-0.753394\pi$
$19$	−6.22979	−1.42921	−0.714606	+	0.699527i	$0.753394\pi$
$20$	−7.53337	−1.68451
$21$	−1.57447	−0.343578
$22$	−1.97087	−0.420190
$23$	−0.985910	−0.205576	−0.102788	−	0.994703i	$-0.532776\pi$
$23$	−0.985910	−0.205576	−0.102788	+	0.994703i	$0.532776\pi$
$24$	0.409675	0.0836246
$25$	10.9834	2.19669
$26$	6.44744	1.26445
$27$	−4.97956	−0.958316
$28$	−1.65109	−0.312026
$29$	2.32036	0.430880	0.215440	−	0.976517i	$-0.430881\pi$
$29$	2.32036	0.430880	0.215440	+	0.976517i	$0.430881\pi$
$30$	14.1583	2.58494
$31$	0.681386	0.122380	0.0611902	−	0.998126i	$-0.480510\pi$
$31$	0.681386	0.122380	0.0611902	+	0.998126i	$0.480510\pi$
$32$	7.85710	1.38895
$33$	1.79688	0.312796
$34$	−10.9361	−1.87553
$35$	3.50309	0.592130
$36$	0.431084	0.0718473
$37$	8.03203	1.32046	0.660228	−	0.751065i	$-0.270459\pi$
$37$	8.03203	1.32046	0.660228	+	0.751065i	$0.270459\pi$
$38$	12.2781	1.99177
$39$	−5.87826	−0.941274
$40$	−0.911499	−0.144121
$41$	−7.26698	−1.13491	−0.567456	−	0.823404i	$-0.692072\pi$
$41$	−7.26698	−1.13491	−0.567456	+	0.823404i	$0.692072\pi$
$42$	3.10307	0.478815
$43$	−9.19170	−1.40172	−0.700860	−	0.713298i	$-0.747200\pi$
$43$	−9.19170	−1.40172	−0.700860	+	0.713298i	$0.747200\pi$
$44$	1.88432	0.284072
$45$	−0.914624	−0.136344
$46$	1.94310	0.286494
$47$	−4.70338	−0.686058	−0.343029	−	0.939325i	$-0.611453\pi$
$47$	−4.70338	−0.686058	−0.343029	+	0.939325i	$0.611453\pi$
$48$	−7.57920	−1.09396
$49$	−6.23223	−0.890318
$50$	−21.6469	−3.06133
$51$	9.97067	1.39617
$52$	−6.16430	−0.854835
$53$	−12.5615	−1.72546	−0.862730	−	0.505664i	$-0.831247\pi$
$53$	−12.5615	−1.72546	−0.862730	+	0.505664i	$0.831247\pi$
$54$	9.81405	1.33552
$55$	−3.99793	−0.539081
$56$	−0.199773	−0.0266958
$57$	−11.1942	−1.48271
$58$	−4.57312	−0.600480
$59$	−6.02829	−0.784817	−0.392408	−	0.919791i	$-0.628358\pi$
$59$	−6.02829	−0.784817	−0.392408	+	0.919791i	$0.628358\pi$
$60$	−13.5366	−1.74756
$61$	4.02593	0.515467	0.257734	−	0.966216i	$-0.417024\pi$
$61$	4.02593	0.515467	0.257734	+	0.966216i	$0.417024\pi$
$62$	−1.34292	−0.170551
$63$	−0.200458	−0.0252553
$64$	−7.04933	−0.881167
$65$	13.0787	1.62221
$66$	−3.54141	−0.435917
$67$	13.2030	1.61300	0.806500	−	0.591234i	$-0.201359\pi$
$67$	13.2030	1.61300	0.806500	+	0.591234i	$0.201359\pi$
$68$	10.4559	1.26796
$69$	−1.77156	−0.213271
$70$	−6.90412	−0.825200
$71$	5.86127	0.695605	0.347802	−	0.937568i	$-0.386928\pi$
$71$	5.86127	0.695605	0.347802	+	0.937568i	$0.386928\pi$
$72$	0.0521589	0.00614698
$73$	6.55693	0.767430	0.383715	−	0.923451i	$-0.374644\pi$
$73$	6.55693	0.767430	0.383715	+	0.923451i	$0.374644\pi$
$74$	−15.8301	−1.84021
$75$	19.7359	2.27891
$76$	−11.7389	−1.34655
$77$	−0.876225	−0.0998551
$78$	11.5853	1.31177
$79$	−13.1218	−1.47632	−0.738158	−	0.674628i	$-0.764304\pi$
$79$	−13.1218	−1.47632	−0.738158	+	0.674628i	$0.764304\pi$
$80$	16.8632	1.88536
$81$	−9.63399	−1.07044
$82$	14.3223	1.58163
$83$	−8.99151	−0.986946	−0.493473	−	0.869761i	$-0.664273\pi$
$83$	−8.99151	−0.986946	−0.493473	+	0.869761i	$0.664273\pi$
$84$	−2.96680	−0.323705
$85$	−22.1840	−2.40620
$86$	18.1156	1.95346
$87$	4.16940	0.447007
$88$	0.227993	0.0243041
$89$	4.40520	0.466951	0.233475	−	0.972363i	$-0.424990\pi$
$89$	4.40520	0.466951	0.233475	+	0.972363i	$0.424990\pi$
$90$	1.80260	0.190011
$91$	2.86646	0.300486
$92$	−1.85777	−0.193686
$93$	1.22437	0.126961
$94$	9.26973	0.956100
$95$	24.9063	2.55533
$96$	14.1183	1.44094
$97$	−5.69865	−0.578610	−0.289305	−	0.957237i	$-0.593424\pi$
$97$	−5.69865	−0.578610	−0.289305	+	0.957237i	$0.593424\pi$
$98$	12.2829	1.24076
$99$	0.228774	0.0229927
$100$	20.6963	2.06963
$101$	2.92651	0.291198	0.145599	−	0.989344i	$-0.453489\pi$
$101$	2.92651	0.291198	0.145599	+	0.989344i	$0.453489\pi$
$102$	−19.6509	−1.94573
$103$	4.59479	0.452738	0.226369	−	0.974042i	$-0.427315\pi$
$103$	4.59479	0.452738	0.226369	+	0.974042i	$0.427315\pi$
$104$	−0.745849	−0.0731365
$105$	6.29462	0.614292
$106$	24.7571	2.40463
$107$	−12.1211	−1.17179	−0.585897	−	0.810386i	$-0.699258\pi$
$107$	−12.1211	−1.17179	−0.585897	+	0.810386i	$0.699258\pi$
$108$	−9.38307	−0.902887
$109$	15.2039	1.45627	0.728134	−	0.685435i	$-0.240388\pi$
$109$	15.2039	1.45627	0.728134	+	0.685435i	$0.240388\pi$
$110$	7.87939	0.751270
$111$	14.4326	1.36988
$112$	3.69590	0.349230
$113$	−10.2661	−0.965757	−0.482879	−	0.875687i	$-0.660409\pi$
$113$	−10.2661	−0.965757	−0.482879	+	0.875687i	$0.660409\pi$
$114$	22.0622	2.06632
$115$	3.94160	0.367556
$116$	4.37229	0.405957
$117$	−0.748406	−0.0691901
$118$	11.8810	1.09373
$119$	−4.86207	−0.445705
$120$	−1.63785	−0.149515
$121$	1.00000	0.0909091
$122$	−7.93457	−0.718362
$123$	−13.0579	−1.17739
$124$	1.28395	0.115302
$125$	−23.9214	−2.13959
$126$	0.395076	0.0351962
$127$	−8.47426	−0.751969	−0.375985	−	0.926626i	$-0.622695\pi$
$127$	−8.47426	−0.751969	−0.375985	+	0.926626i	$0.622695\pi$
$128$	−1.82089	−0.160946
$129$	−16.5164	−1.45419
$130$	−25.7764	−2.26074
$131$	−17.1646	−1.49967	−0.749837	−	0.661623i	$-0.769868\pi$
$131$	−17.1646	−1.49967	−0.749837	+	0.661623i	$0.769868\pi$
$132$	3.38589	0.294704
$133$	5.45870	0.473329
$134$	−26.0213	−2.24790
$135$	19.9079	1.71340
$136$	1.26510	0.108482
$137$	−9.93833	−0.849089	−0.424545	−	0.905407i	$-0.639566\pi$
$137$	−9.93833	−0.849089	−0.424545	+	0.905407i	$0.639566\pi$
$138$	3.49151	0.297217
$139$	20.8966	1.77243	0.886214	−	0.463277i	$-0.153326\pi$
$139$	20.8966	1.77243	0.886214	+	0.463277i	$0.153326\pi$
$140$	6.60093	0.557880
$141$	−8.45140	−0.711736
$142$	−11.5518	−0.969404
$143$	−3.27137	−0.273566
$144$	−0.964966	−0.0804138
$145$	−9.27663	−0.770382
$146$	−12.9228	−1.06950
$147$	−11.1986	−0.923642
$148$	15.1349	1.24408
$149$	7.66275	0.627757	0.313879	−	0.949463i	$-0.398372\pi$
$149$	7.66275	0.627757	0.313879	+	0.949463i	$0.398372\pi$
$150$	−38.8969	−3.17592
$151$	16.2361	1.32128	0.660638	−	0.750705i	$-0.270286\pi$
$151$	16.2361	1.32128	0.660638	+	0.750705i	$0.270286\pi$
$152$	−1.42035	−0.115205
$153$	1.26944	0.102628
$154$	1.72692	0.139159
$155$	−2.72413	−0.218808
$156$	−11.0765	−0.886830
$157$	−5.64697	−0.450677	−0.225338	−	0.974281i	$-0.572349\pi$
$157$	−5.64697	−0.450677	−0.225338	+	0.974281i	$0.572349\pi$
$158$	25.8613	2.05742
$159$	−22.5716	−1.79004
$160$	−31.4121	−2.48335
$161$	0.863879	0.0680832
$162$	18.9873	1.49178
$163$	2.34513	0.183685	0.0918423	−	0.995774i	$-0.470724\pi$
$163$	2.34513	0.183685	0.0918423	+	0.995774i	$0.470724\pi$
$164$	−13.6933	−1.06927
$165$	−7.18380	−0.559258
$166$	17.7211	1.37542
$167$	23.8046	1.84206	0.921028	−	0.389498i	$-0.127351\pi$
$167$	23.8046	1.84206	0.921028	+	0.389498i	$0.127351\pi$
$168$	−0.358968	−0.0276950
$169$	−2.29814	−0.176780
$170$	43.7218	3.35331
$171$	−1.42522	−0.108989
$172$	−17.3201	−1.32064
$173$	16.5690	1.25972	0.629859	−	0.776709i	$-0.283113\pi$
$173$	16.5690	1.25972	0.629859	+	0.776709i	$0.283113\pi$
$174$	−8.21734	−0.622955
$175$	−9.62396	−0.727503
$176$	−4.21798	−0.317942
$177$	−10.8321	−0.814191
$178$	−8.68207	−0.650749
$179$	22.8347	1.70675	0.853374	−	0.521299i	$-0.174552\pi$
$179$	22.8347	1.70675	0.853374	+	0.521299i	$0.174552\pi$
$180$	−1.72344	−0.128458
$181$	7.44210	0.553167	0.276583	−	0.960990i	$-0.410798\pi$
$181$	7.44210	0.553167	0.276583	+	0.960990i	$0.410798\pi$
$182$	−5.64941	−0.418762
$183$	7.23411	0.534761
$184$	−0.224780	−0.0165710
$185$	−32.1115	−2.36088
$186$	−2.41307	−0.176935
$187$	5.54888	0.405774
$188$	−8.86266	−0.646376
$189$	4.36321	0.317377
$190$	−49.0869	−3.56114
$191$	−17.1754	−1.24277	−0.621383	−	0.783507i	$-0.713429\pi$
$191$	−17.1754	−1.24277	−0.621383	+	0.783507i	$0.713429\pi$
$192$	−12.6668	−0.914147
$193$	−10.5752	−0.761219	−0.380610	−	0.924736i	$-0.624286\pi$
$193$	−10.5752	−0.761219	−0.380610	+	0.924736i	$0.624286\pi$
$194$	11.2313	0.806359
$195$	23.5009	1.68293
$196$	−11.7435	−0.838822
$197$	−14.9388	−1.06434	−0.532171	−	0.846637i	$-0.678624\pi$
$197$	−14.9388	−1.06434	−0.532171	+	0.846637i	$0.678624\pi$
$198$	−0.450884	−0.0320429
$199$	20.7008	1.46744	0.733719	−	0.679453i	$-0.237783\pi$
$199$	20.7008	1.46744	0.733719	+	0.679453i	$0.237783\pi$
$200$	2.50414	0.177070
$201$	23.7242	1.67337
$202$	−5.76776	−0.405818
$203$	−2.03316	−0.142700
$204$	18.7879	1.31542
$205$	29.0529	2.02914
$206$	−9.05572	−0.630942
$207$	−0.225551	−0.0156769
$208$	13.7986	0.956759
$209$	−6.22979	−0.430924
$210$	−12.4059	−0.856086
$211$	−16.0721	−1.10645	−0.553226	−	0.833031i	$-0.686603\pi$
$211$	−16.0721	−1.10645	−0.553226	+	0.833031i	$0.686603\pi$
$212$	−23.6700	−1.62566
$213$	10.5320	0.721640
$214$	23.8891	1.63303
$215$	36.7478	2.50618
$216$	−1.13530	−0.0772476
$217$	−0.597047	−0.0405302
$218$	−29.9648	−2.02947
$219$	11.7820	0.796154
$220$	−7.53337	−0.507900
$221$	−18.1524	−1.22107
$222$	−28.4447	−1.90908
$223$	7.09814	0.475327	0.237663	−	0.971348i	$-0.423618\pi$
$223$	7.09814	0.475327	0.237663	+	0.971348i	$0.423618\pi$
$224$	−6.88459	−0.459996
$225$	2.51273	0.167515
$226$	20.2332	1.34589
$227$	−21.8551	−1.45057	−0.725285	−	0.688448i	$-0.758292\pi$
$227$	−21.8551	−1.45057	−0.725285	+	0.688448i	$0.758292\pi$
$228$	−21.0934	−1.39694
$229$	−7.31386	−0.483313	−0.241657	−	0.970362i	$-0.577691\pi$
$229$	−7.31386	−0.483313	−0.241657	+	0.970362i	$0.577691\pi$
$230$	−7.76837	−0.512231
$231$	−1.57447	−0.103593
$232$	0.529025	0.0347322
$233$	19.6678	1.28848	0.644241	−	0.764822i	$-0.277173\pi$
$233$	19.6678	1.28848	0.644241	+	0.764822i	$0.277173\pi$
$234$	1.47501	0.0964243
$235$	18.8038	1.22662
$236$	−11.3592	−0.739422
$237$	−23.5783	−1.53157
$238$	9.58249	0.621141
$239$	18.8749	1.22092	0.610458	−	0.792049i	$-0.290986\pi$
$239$	18.8749	1.22092	0.610458	+	0.792049i	$0.290986\pi$
$240$	30.3011	1.95593
$241$	−12.6190	−0.812863	−0.406432	−	0.913681i	$-0.633227\pi$
$241$	−12.6190	−0.812863	−0.406432	+	0.913681i	$0.633227\pi$
$242$	−1.97087	−0.126692
$243$	−2.37243	−0.152192
$244$	7.58613	0.485652
$245$	24.9160	1.59183
$246$	25.7354	1.64083
$247$	20.3800	1.29675
$248$	0.155351	0.00986480
$249$	−16.1566	−1.02389
$250$	47.1458	2.98176
$251$	14.9917	0.946265	0.473132	−	0.880991i	$-0.343123\pi$
$251$	14.9917	0.946265	0.473132	+	0.880991i	$0.343123\pi$
$252$	−0.377727	−0.0237945
$253$	−0.985910	−0.0619836
$254$	16.7017	1.04795
$255$	−39.8620	−2.49626
$256$	17.6874	1.10546
$257$	16.9732	1.05876	0.529379	−	0.848386i	$-0.322425\pi$
$257$	16.9732	1.05876	0.529379	+	0.848386i	$0.322425\pi$
$258$	32.5516	2.02657
$259$	−7.03786	−0.437312
$260$	24.6445	1.52838
$261$	0.530839	0.0328581
$262$	33.8291	2.08997
$263$	1.85085	0.114129	0.0570643	−	0.998371i	$-0.481826\pi$
$263$	1.85085	0.114129	0.0570643	+	0.998371i	$0.481826\pi$
$264$	0.409675	0.0252138
$265$	50.2202	3.08500
$266$	−10.7584	−0.659638
$267$	7.91562	0.484428
$268$	24.8786	1.51970
$269$	−1.03551	−0.0631361	−0.0315680	−	0.999502i	$-0.510050\pi$
$269$	−1.03551	−0.0631361	−0.0315680	+	0.999502i	$0.510050\pi$
$270$	−39.2359	−2.38782
$271$	18.6940	1.13558	0.567790	−	0.823173i	$-0.307799\pi$
$271$	18.6940	1.13558	0.567790	+	0.823173i	$0.307799\pi$
$272$	−23.4051	−1.41914
$273$	5.15068	0.311733
$274$	19.5871	1.18330
$275$	10.9834	0.662326
$276$	−3.33818	−0.200935
$277$	−9.43963	−0.567173	−0.283586	−	0.958947i	$-0.591524\pi$
$277$	−9.43963	−0.567173	−0.283586	+	0.958947i	$0.591524\pi$
$278$	−41.1844	−2.47008
$279$	0.155884	0.00933251
$280$	0.798678	0.0477302
$281$	−15.9581	−0.951979	−0.475990	−	0.879451i	$-0.657910\pi$
$281$	−15.9581	−0.951979	−0.475990	+	0.879451i	$0.657910\pi$
$282$	16.6566	0.991885
$283$	5.86892	0.348871	0.174436	−	0.984669i	$-0.444190\pi$
$283$	5.86892	0.348871	0.174436	+	0.984669i	$0.444190\pi$
$284$	11.0445	0.655370
$285$	44.7535	2.65097
$286$	6.44744	0.381245
$287$	6.36751	0.375862
$288$	1.79750	0.105919
$289$	13.7901	0.811181
$290$	18.2830	1.07362
$291$	−10.2398	−0.600267
$292$	12.3553	0.723042
$293$	30.8402	1.80171	0.900853	−	0.434125i	$-0.142942\pi$
$293$	30.8402	1.80171	0.900853	+	0.434125i	$0.142942\pi$
$294$	22.0709	1.28720
$295$	24.1007	1.40320
$296$	1.83124	0.106439
$297$	−4.97956	−0.288943
$298$	−15.1023	−0.874851
$299$	3.22528	0.186523
$300$	37.1887	2.14709
$301$	8.05400	0.464225
$302$	−31.9992	−1.84135
$303$	5.25858	0.302097
$304$	26.2771	1.50710
$305$	−16.0954	−0.921619
$306$	−2.50190	−0.143024
$307$	33.4344	1.90820	0.954102	−	0.299481i	$-0.0968136\pi$
$307$	33.4344	1.90820	0.954102	+	0.299481i	$0.0968136\pi$
$308$	−1.65109	−0.0940794
$309$	8.25628	0.469683
$310$	5.36890	0.304933
$311$	−4.42105	−0.250695	−0.125347	−	0.992113i	$-0.540005\pi$
$311$	−4.42105	−0.250695	−0.125347	+	0.992113i	$0.540005\pi$
$312$	−1.34020	−0.0758739
$313$	−18.8511	−1.06553	−0.532763	−	0.846264i	$-0.678846\pi$
$313$	−18.8511	−1.06553	−0.532763	+	0.846264i	$0.678846\pi$
$314$	11.1294	0.628070
$315$	0.801416	0.0451547
$316$	−24.7256	−1.39093
$317$	8.09615	0.454725	0.227362	−	0.973810i	$-0.426990\pi$
$317$	8.09615	0.454725	0.227362	+	0.973810i	$0.426990\pi$
$318$	44.4856	2.49463
$319$	2.32036	0.129915
$320$	28.1827	1.57546
$321$	−21.7802	−1.21565
$322$	−1.70259	−0.0948817
$323$	−34.5684	−1.92344
$324$	−18.1535	−1.00853
$325$	−35.9309	−1.99309
$326$	−4.62194	−0.255985
$327$	27.3195	1.51077
$328$	−1.65682	−0.0914825
$329$	4.12122	0.227210
$330$	14.1583	0.779389
$331$	31.7773	1.74664	0.873318	−	0.487151i	$-0.161964\pi$
$331$	31.7773	1.74664	0.873318	+	0.487151i	$0.161964\pi$
$332$	−16.9429	−0.929860
$333$	1.83752	0.100696
$334$	−46.9157	−2.56711
$335$	−52.7846	−2.88393
$336$	6.64109	0.362301
$337$	27.6903	1.50839	0.754194	−	0.656651i	$-0.228028\pi$
$337$	27.6903	1.50839	0.754194	+	0.656651i	$0.228028\pi$
$338$	4.52932	0.246363
$339$	−18.4470	−1.00190
$340$	−41.8018	−2.26702
$341$	0.681386	0.0368991
$342$	2.80891	0.151889
$343$	11.5944	0.626039
$344$	−2.09564	−0.112989
$345$	7.08257	0.381313
$346$	−32.6553	−1.75556
$347$	14.7375	0.791151	0.395576	−	0.918433i	$-0.370545\pi$
$347$	14.7375	0.791151	0.395576	+	0.918433i	$0.370545\pi$
$348$	7.85649	0.421152
$349$	−9.50832	−0.508969	−0.254484	−	0.967077i	$-0.581906\pi$
$349$	−9.50832	−0.508969	−0.254484	+	0.967077i	$0.581906\pi$
$350$	18.9676	1.01386
$351$	16.2900	0.869495
$352$	7.85710	0.418785
$353$	−1.30287	−0.0693446	−0.0346723	−	0.999399i	$-0.511039\pi$
$353$	−1.30287	−0.0693446	−0.0346723	+	0.999399i	$0.511039\pi$
$354$	21.3487	1.13467
$355$	−23.4329	−1.24369
$356$	8.30081	0.439942
$357$	−8.73655	−0.462387
$358$	−45.0042	−2.37855
$359$	−31.3104	−1.65250	−0.826251	−	0.563302i	$-0.809531\pi$
$359$	−31.3104	−1.65250	−0.826251	+	0.563302i	$0.809531\pi$
$360$	−0.208528	−0.0109904
$361$	19.8103	1.04265
$362$	−14.6674	−0.770901
$363$	1.79688	0.0943117
$364$	5.40132	0.283106
$365$	−26.2141	−1.37211
$366$	−14.2575	−0.745250
$367$	15.8765	0.828748	0.414374	−	0.910107i	$-0.364001\pi$
$367$	15.8765	0.828748	0.414374	+	0.910107i	$0.364001\pi$
$368$	4.15855	0.216779
$369$	−1.66250	−0.0865462
$370$	63.2875	3.29016
$371$	11.0067	0.571442
$372$	2.30710	0.119618
$373$	18.7043	0.968470	0.484235	−	0.874938i	$-0.339098\pi$
$373$	18.7043	0.968470	0.484235	+	0.874938i	$0.339098\pi$
$374$	−10.9361	−0.565493
$375$	−42.9838	−2.21967
$376$	−1.07234	−0.0553015
$377$	−7.59075	−0.390944
$378$	−8.59932	−0.442301
$379$	20.2630	1.04084	0.520421	−	0.853910i	$-0.325775\pi$
$379$	20.2630	1.04084	0.520421	+	0.853910i	$0.325775\pi$
$380$	46.9313	2.40753
$381$	−15.2272	−0.780114
$382$	33.8504	1.73194
$383$	−29.5659	−1.51075	−0.755374	−	0.655294i	$-0.772545\pi$
$383$	−29.5659	−1.51075	−0.755374	+	0.655294i	$0.772545\pi$
$384$	−3.27192	−0.166969
$385$	3.50309	0.178534
$386$	20.8423	1.06085
$387$	−2.10283	−0.106893
$388$	−10.7381	−0.545143
$389$	−15.6615	−0.794069	−0.397035	−	0.917804i	$-0.629961\pi$
$389$	−15.6615	−0.794069	−0.397035	+	0.917804i	$0.629961\pi$
$390$	−46.3171	−2.34536
$391$	−5.47070	−0.276665
$392$	−1.42090	−0.0717664
$393$	−30.8426	−1.55580
$394$	29.4423	1.48328
$395$	52.4600	2.63955
$396$	0.431084	0.0216628
$397$	−15.9990	−0.802964	−0.401482	−	0.915867i	$-0.631505\pi$
$397$	−15.9990	−0.802964	−0.401482	+	0.915867i	$0.631505\pi$
$398$	−40.7985	−2.04504
$399$	9.80862	0.491045
$400$	−46.3279	−2.31640
$401$	19.5983	0.978691	0.489345	−	0.872090i	$-0.337236\pi$
$401$	19.5983	0.978691	0.489345	+	0.872090i	$0.337236\pi$
$402$	−46.7572	−2.33204
$403$	−2.22906	−0.111038
$404$	5.51447	0.274355
$405$	38.5160	1.91387
$406$	4.00708	0.198868
$407$	8.03203	0.398133
$408$	2.27324	0.112542
$409$	−0.873879	−0.0432105	−0.0216053	−	0.999767i	$-0.506878\pi$
$409$	−0.873879	−0.0432105	−0.0216053	+	0.999767i	$0.506878\pi$
$410$	−57.2594	−2.82784
$411$	−17.8580	−0.880869
$412$	8.65804	0.426551
$413$	5.28214	0.259917
$414$	0.444531	0.0218475
$415$	35.9474	1.76459
$416$	−25.7035	−1.26022
$417$	37.5487	1.83877
$418$	12.2781	0.600541
$419$	−4.52699	−0.221158	−0.110579	−	0.993867i	$-0.535270\pi$
$419$	−4.52699	−0.221158	−0.110579	+	0.993867i	$0.535270\pi$
$420$	11.8611	0.578761
$421$	0.680505	0.0331658	0.0165829	−	0.999862i	$-0.494721\pi$
$421$	0.680505	0.0331658	0.0165829	+	0.999862i	$0.494721\pi$
$422$	31.6761	1.54197
$423$	−1.07601	−0.0523175
$424$	−2.86394	−0.139085
$425$	60.9458	2.95630
$426$	−20.7572	−1.00569
$427$	−3.52762	−0.170714
$428$	−22.8401	−1.10402
$429$	−5.87826	−0.283805
$430$	−72.4250	−3.49264
$431$	33.8957	1.63270	0.816350	−	0.577558i	$-0.195994\pi$
$431$	33.8957	1.63270	0.816350	+	0.577558i	$0.195994\pi$
$432$	21.0037	1.01054
$433$	−25.3375	−1.21764	−0.608821	−	0.793308i	$-0.708357\pi$
$433$	−25.3375	−1.21764	−0.608821	+	0.793308i	$0.708357\pi$
$434$	1.17670	0.0564835
$435$	−16.6690	−0.799216
$436$	28.6490	1.37204
$437$	6.14201	0.293812
$438$	−23.2208	−1.10953
$439$	31.3849	1.49792	0.748959	−	0.662616i	$-0.230554\pi$
$439$	31.3849	1.49792	0.748959	+	0.662616i	$0.230554\pi$
$440$	−0.911499	−0.0434540
$441$	−1.42577	−0.0678940
$442$	35.7761	1.70169
$443$	−24.6483	−1.17108	−0.585538	−	0.810645i	$-0.699117\pi$
$443$	−24.6483	−1.17108	−0.585538	+	0.810645i	$0.699117\pi$
$444$	27.1956	1.29065
$445$	−17.6117	−0.834874
$446$	−13.9895	−0.662422
$447$	13.7690	0.651253
$448$	6.17680	0.291827
$449$	3.83570	0.181018	0.0905090	−	0.995896i	$-0.471151\pi$
$449$	3.83570	0.181018	0.0905090	+	0.995896i	$0.471151\pi$
$450$	−4.95226	−0.233452
$451$	−7.26698	−0.342189
$452$	−19.3447	−0.909897
$453$	29.1743	1.37073
$454$	43.0734	2.02154
$455$	−11.4599	−0.537248
$456$	−2.55219	−0.119517
$457$	4.99064	0.233452	0.116726	−	0.993164i	$-0.462760\pi$
$457$	4.99064	0.233452	0.116726	+	0.993164i	$0.462760\pi$
$458$	14.4146	0.673552
$459$	−27.6310	−1.28970
$460$	7.42722	0.346296
$461$	−25.4102	−1.18347	−0.591735	−	0.806133i	$-0.701557\pi$
$461$	−25.4102	−1.18347	−0.591735	+	0.806133i	$0.701557\pi$
$462$	3.10307	0.144368
$463$	−12.6788	−0.589233	−0.294617	−	0.955616i	$-0.595192\pi$
$463$	−12.6788	−0.589233	−0.294617	+	0.955616i	$0.595192\pi$
$464$	−9.78723	−0.454361
$465$	−4.89494	−0.226997
$466$	−38.7627	−1.79565
$467$	−27.4024	−1.26803	−0.634016	−	0.773320i	$-0.718595\pi$
$467$	−27.4024	−1.26803	−0.634016	+	0.773320i	$0.718595\pi$
$468$	−1.41023	−0.0651881
$469$	−11.5688	−0.534197
$470$	−37.0597	−1.70944
$471$	−10.1469	−0.467545
$472$	−1.37441	−0.0632622
$473$	−9.19170	−0.422635
$474$	46.4696	2.13442
$475$	−68.4245	−3.13953
$476$	−9.16169	−0.419925
$477$	−2.87376	−0.131580
$478$	−37.1999	−1.70148
$479$	36.3718	1.66187	0.830935	−	0.556370i	$-0.187806\pi$
$479$	36.3718	1.66187	0.830935	+	0.556370i	$0.187806\pi$
$480$	−56.4438	−2.57629
$481$	−26.2757	−1.19807
$482$	24.8704	1.13282
$483$	1.55229	0.0706315
$484$	1.88432	0.0856508
$485$	22.7828	1.03451
$486$	4.67575	0.212097
$487$	0.212114	0.00961182	0.00480591	−	0.999988i	$-0.498470\pi$
$487$	0.212114	0.00961182	0.00480591	+	0.999988i	$0.498470\pi$
$488$	0.917883	0.0415506
$489$	4.21391	0.190560
$490$	−49.1062	−2.21839
$491$	−23.1555	−1.04499	−0.522496	−	0.852641i	$-0.674999\pi$
$491$	−23.1555	−1.04499	−0.522496	+	0.852641i	$0.674999\pi$
$492$	−24.6052	−1.10929
$493$	12.8754	0.579878
$494$	−40.1662	−1.80716
$495$	−0.914624	−0.0411093
$496$	−2.87407	−0.129050
$497$	−5.13579	−0.230372
$498$	31.8426	1.42690
$499$	1.71735	0.0768793	0.0384397	−	0.999261i	$-0.487761\pi$
$499$	1.71735	0.0768793	0.0384397	+	0.999261i	$0.487761\pi$
$500$	−45.0755	−2.01584
$501$	42.7740	1.91100
$502$	−29.5466	−1.31873
$503$	33.0582	1.47399	0.736997	−	0.675896i	$-0.236243\pi$
$503$	33.0582	1.47399	0.736997	+	0.675896i	$0.236243\pi$
$504$	−0.0457029	−0.00203577
$505$	−11.7000	−0.520642
$506$	1.94310	0.0863812
$507$	−4.12947	−0.183396
$508$	−15.9682	−0.708475
$509$	10.2528	0.454448	0.227224	−	0.973843i	$-0.427035\pi$
$509$	10.2528	0.454448	0.227224	+	0.973843i	$0.427035\pi$
$510$	78.5628	3.47882
$511$	−5.74535	−0.254159
$512$	−31.2177	−1.37964
$513$	31.0216	1.36964
$514$	−33.4519	−1.47550
$515$	−18.3696	−0.809463
$516$	−31.1221	−1.37007
$517$	−4.70338	−0.206854
$518$	13.8707	0.609443
$519$	29.7725	1.30687
$520$	2.98185	0.130763
$521$	−14.1888	−0.621622	−0.310811	−	0.950472i	$-0.600601\pi$
$521$	−14.1888	−0.621622	−0.310811	+	0.950472i	$0.600601\pi$
$522$	−1.04621	−0.0457915
$523$	23.4737	1.02643	0.513217	−	0.858259i	$-0.328453\pi$
$523$	23.4737	1.02643	0.513217	+	0.858259i	$0.328453\pi$
$524$	−32.3435	−1.41293
$525$	−17.2931	−0.754733
$526$	−3.64779	−0.159051
$527$	3.78093	0.164700
$528$	−7.57920	−0.329842
$529$	−22.0280	−0.957738
$530$	−98.9773	−4.29930
$531$	−1.37912	−0.0598487
$532$	10.2859	0.445952
$533$	23.7730	1.02972
$534$	−15.6006	−0.675105
$535$	48.4594	2.09508
$536$	3.01018	0.130020
$537$	41.0313	1.77063
$538$	2.04085	0.0879873
$539$	−6.23223	−0.268441
$540$	37.5129	1.61430
$541$	30.3312	1.30404	0.652021	−	0.758201i	$-0.273921\pi$
$541$	30.3312	1.30404	0.652021	+	0.758201i	$0.273921\pi$
$542$	−36.8434	−1.58256
$543$	13.3725	0.573871
$544$	43.5981	1.86925
$545$	−60.7840	−2.60370
$546$	−10.1513	−0.434436
$547$	−1.00000	−0.0427569
$547$	−1.00000	−0.0427569
$548$	−18.7270	−0.799977
$549$	0.921030	0.0393086
$550$	−21.6469	−0.923027
$551$	−14.4553	−0.615819
$552$	−0.403903	−0.0171913
$553$	11.4976	0.488929
$554$	18.6043	0.790420
$555$	−57.7004	−2.44925
$556$	39.3759	1.66991
$557$	25.4492	1.07832	0.539158	−	0.842205i	$-0.318743\pi$
$557$	25.4492	1.07832	0.539158	+	0.842205i	$0.318743\pi$
$558$	−0.307226	−0.0130059
$559$	30.0694	1.27180
$560$	−14.7759	−0.624398
$561$	9.97067	0.420962
$562$	31.4513	1.32669
$563$	−3.47739	−0.146555	−0.0732773	−	0.997312i	$-0.523346\pi$
$563$	−3.47739	−0.146555	−0.0732773	+	0.997312i	$0.523346\pi$
$564$	−15.9251	−0.670569
$565$	41.0433	1.72670
$566$	−11.5669	−0.486192
$567$	8.44154	0.354511
$568$	1.33633	0.0560710
$569$	3.69963	0.155096	0.0775482	−	0.996989i	$-0.475291\pi$
$569$	3.69963	0.155096	0.0775482	+	0.996989i	$0.475291\pi$
$570$	−88.2033	−3.69443
$571$	−2.38603	−0.0998522	−0.0499261	−	0.998753i	$-0.515899\pi$
$571$	−2.38603	−0.0998522	−0.0499261	+	0.998753i	$0.515899\pi$
$572$	−6.16430	−0.257743
$573$	−30.8621	−1.28928
$574$	−12.5495	−0.523807
$575$	−10.8287	−0.451587
$576$	−1.61271	−0.0671961
$577$	−6.60922	−0.275145	−0.137573	−	0.990492i	$-0.543930\pi$
$577$	−6.60922	−0.275145	−0.137573	+	0.990492i	$0.543930\pi$
$578$	−27.1784	−1.13047
$579$	−19.0024	−0.789711
$580$	−17.4801	−0.725823
$581$	7.87858	0.326859
$582$	20.1813	0.836540
$583$	−12.5615	−0.520246
$584$	1.49493	0.0618607
$585$	2.99207	0.123707
$586$	−60.7820	−2.51088
$587$	−15.0496	−0.621165	−0.310583	−	0.950546i	$-0.600524\pi$
$587$	−15.0496	−0.621165	−0.310583	+	0.950546i	$0.600524\pi$
$588$	−21.1017	−0.870218
$589$	−4.24489	−0.174908
$590$	−47.4992	−1.95551
$591$	−26.8431	−1.10418
$592$	−33.8789	−1.39242
$593$	37.6701	1.54693	0.773463	−	0.633842i	$-0.218523\pi$
$593$	37.6701	1.54693	0.773463	+	0.633842i	$0.218523\pi$
$594$	9.81405	0.402675
$595$	19.4382	0.796889
$596$	14.4391	0.591447
$597$	37.1968	1.52236
$598$	−6.35659	−0.259940
$599$	−5.35321	−0.218726	−0.109363	−	0.994002i	$-0.534881\pi$
$599$	−5.35321	−0.218726	−0.109363	+	0.994002i	$0.534881\pi$
$600$	4.49964	0.183697
$601$	18.2750	0.745451	0.372726	−	0.927942i	$-0.378423\pi$
$601$	18.2750	0.745451	0.372726	+	0.927942i	$0.378423\pi$
$602$	−15.8734	−0.646950
$603$	3.02050	0.123004
$604$	30.5940	1.24485
$605$	−3.99793	−0.162539
$606$	−10.3640	−0.421007
$607$	42.4224	1.72187	0.860935	−	0.508714i	$-0.169879\pi$
$607$	42.4224	1.72187	0.860935	+	0.508714i	$0.169879\pi$
$608$	−48.9481	−1.98511
$609$	−3.65334	−0.148041
$610$	31.7219	1.28438
$611$	15.3865	0.622471
$612$	2.39203	0.0966922
$613$	6.01082	0.242775	0.121387	−	0.992605i	$-0.461266\pi$
$613$	6.01082	0.242775	0.121387	+	0.992605i	$0.461266\pi$
$614$	−65.8949	−2.65930
$615$	52.2045	2.10509
$616$	−0.199773	−0.00804908
$617$	−20.7928	−0.837088	−0.418544	−	0.908197i	$-0.637459\pi$
$617$	−20.7928	−0.837088	−0.418544	+	0.908197i	$0.637459\pi$
$618$	−16.2720	−0.654557
$619$	−31.7604	−1.27656	−0.638278	−	0.769806i	$-0.720353\pi$
$619$	−31.7604	−1.27656	−0.638278	+	0.769806i	$0.720353\pi$
$620$	−5.13313	−0.206152
$621$	4.90939	0.197007
$622$	8.71330	0.349372
$623$	−3.85995	−0.154646
$624$	24.7944	0.992569
$625$	40.7187	1.62875
$626$	37.1530	1.48493
$627$	−11.1942	−0.447053
$628$	−10.6407	−0.424609
$629$	44.5688	1.77707
$630$	−1.57949	−0.0629282
$631$	17.1488	0.682685	0.341342	−	0.939939i	$-0.389118\pi$
$631$	17.1488	0.682685	0.341342	+	0.939939i	$0.389118\pi$
$632$	−2.99167	−0.119002
$633$	−28.8797	−1.14787
$634$	−15.9564	−0.633711
$635$	33.8795	1.34447
$636$	−42.5320	−1.68651
$637$	20.3879	0.807799
$638$	−4.57312	−0.181052
$639$	1.34091	0.0530455
$640$	7.27979	0.287759
$641$	−11.7652	−0.464696	−0.232348	−	0.972633i	$-0.574641\pi$
$641$	−11.7652	−0.464696	−0.232348	+	0.972633i	$0.574641\pi$
$642$	42.9259	1.69415
$643$	47.3407	1.86694	0.933468	−	0.358662i	$-0.116767\pi$
$643$	47.3407	1.86694	0.933468	+	0.358662i	$0.116767\pi$
$644$	1.62782	0.0641452
$645$	66.0313	2.59998
$646$	68.1297	2.68053
$647$	8.93343	0.351209	0.175605	−	0.984461i	$-0.443812\pi$
$647$	8.93343	0.351209	0.175605	+	0.984461i	$0.443812\pi$
$648$	−2.19648	−0.0862858
$649$	−6.02829	−0.236631
$650$	70.8150	2.77759
$651$	−1.07282	−0.0420472
$652$	4.41897	0.173060
$653$	−25.4931	−0.997622	−0.498811	−	0.866711i	$-0.666230\pi$
$653$	−25.4931	−0.997622	−0.498811	+	0.866711i	$0.666230\pi$
$654$	−53.8432	−2.10544
$655$	68.6227	2.68131
$656$	30.6520	1.19676
$657$	1.50006	0.0585228
$658$	−8.12237	−0.316643
$659$	−32.3257	−1.25923	−0.629615	−	0.776907i	$-0.716787\pi$
$659$	−32.3257	−1.25923	−0.629615	+	0.776907i	$0.716787\pi$
$660$	−13.5366	−0.526910
$661$	48.7606	1.89657	0.948284	−	0.317424i	$-0.102818\pi$
$661$	48.7606	1.89657	0.948284	+	0.317424i	$0.102818\pi$
$662$	−62.6288	−2.43414
$663$	−32.6177	−1.26677
$664$	−2.05000	−0.0795553
$665$	−21.8235	−0.846279
$666$	−3.62151	−0.140331
$667$	−2.28766	−0.0885787
$668$	44.8554	1.73551
$669$	12.7545	0.493118
$670$	104.031	4.01908
$671$	4.02593	0.155419
$672$	−12.3708	−0.477213
$673$	5.53717	0.213442	0.106721	−	0.994289i	$-0.465965\pi$
$673$	5.53717	0.213442	0.106721	+	0.994289i	$0.465965\pi$
$674$	−54.5740	−2.10211
$675$	−54.6927	−2.10512
$676$	−4.33042	−0.166555
$677$	4.99678	0.192042	0.0960210	−	0.995379i	$-0.469388\pi$
$677$	4.99678	0.192042	0.0960210	+	0.995379i	$0.469388\pi$
$678$	36.3566	1.39627
$679$	4.99330	0.191625
$680$	−5.05780	−0.193958
$681$	−39.2709	−1.50486
$682$	−1.34292	−0.0514231
$683$	12.4632	0.476892	0.238446	−	0.971156i	$-0.423362\pi$
$683$	12.4632	0.476892	0.238446	+	0.971156i	$0.423362\pi$
$684$	−2.68556	−0.102685
$685$	39.7328	1.51811
$686$	−22.8511	−0.872457
$687$	−13.1421	−0.501403
$688$	38.7704	1.47811
$689$	41.0935	1.56554
$690$	−13.9588	−0.531403
$691$	−40.1153	−1.52606	−0.763029	−	0.646365i	$-0.776288\pi$
$691$	−40.1153	−1.52606	−0.763029	+	0.646365i	$0.776288\pi$
$692$	31.2213	1.18686
$693$	−0.200458	−0.00761477
$694$	−29.0457	−1.10256
$695$	−83.5432	−3.16897
$696$	0.950594	0.0360322
$697$	−40.3236	−1.52737
$698$	18.7396	0.709306
$699$	35.3407	1.33671
$700$	−18.1346	−0.685424
$701$	−46.0417	−1.73897	−0.869486	−	0.493957i	$-0.835550\pi$
$701$	−46.0417	−1.73897	−0.869486	+	0.493957i	$0.835550\pi$
$702$	−32.1054	−1.21174
$703$	−50.0378	−1.88721
$704$	−7.04933	−0.265682
$705$	33.7881	1.27253
$706$	2.56778	0.0966396
$707$	−2.56428	−0.0964396
$708$	−20.4111	−0.767098
$709$	20.2776	0.761542	0.380771	−	0.924669i	$-0.375659\pi$
$709$	20.2776	0.761542	0.380771	+	0.924669i	$0.375659\pi$
$710$	46.1832	1.73322
$711$	−3.00193	−0.112581
$712$	1.00435	0.0376398
$713$	−0.671785	−0.0251585
$714$	17.2186	0.644389
$715$	13.0787	0.489116
$716$	43.0279	1.60803
$717$	33.9159	1.26661
$718$	61.7087	2.30295
$719$	−50.3888	−1.87918	−0.939592	−	0.342295i	$-0.888796\pi$
$719$	−50.3888	−1.87918	−0.939592	+	0.342295i	$0.888796\pi$
$720$	3.85787	0.143774
$721$	−4.02607	−0.149939
$722$	−39.0435	−1.45305
$723$	−22.6749	−0.843288
$724$	14.0233	0.521171
$725$	25.4855	0.946508
$726$	−3.54141	−0.131434
$727$	22.3599	0.829281	0.414641	−	0.909985i	$-0.363907\pi$
$727$	22.3599	0.829281	0.414641	+	0.909985i	$0.363907\pi$
$728$	0.653531	0.0242215
$729$	24.6390	0.912555
$730$	51.6646	1.91219
$731$	−51.0036	−1.88644
$732$	13.6314	0.503830
$733$	9.59632	0.354448	0.177224	−	0.984171i	$-0.443288\pi$
$733$	9.59632	0.354448	0.177224	+	0.984171i	$0.443288\pi$
$734$	−31.2905	−1.15495
$735$	44.7711	1.65141
$736$	−7.74639	−0.285536
$737$	13.2030	0.486338
$738$	3.27657	0.120612
$739$	22.5776	0.830530	0.415265	−	0.909700i	$-0.363689\pi$
$739$	22.5776	0.830530	0.415265	+	0.909700i	$0.363689\pi$
$740$	−60.5082	−2.22433
$741$	36.6203	1.34528
$742$	−21.6928	−0.796369
$743$	−36.2177	−1.32870	−0.664350	−	0.747421i	$-0.731292\pi$
$743$	−36.2177	−1.32870	−0.664350	+	0.747421i	$0.731292\pi$
$744$	0.279147	0.0102340
$745$	−30.6351	−1.12238
$746$	−36.8636	−1.34967
$747$	−2.05703	−0.0752627
$748$	10.4559	0.382304
$749$	10.6208	0.388077
$750$	84.7153	3.09337
$751$	−21.0676	−0.768768	−0.384384	−	0.923173i	$-0.625586\pi$
$751$	−21.0676	−0.768768	−0.384384	+	0.923173i	$0.625586\pi$
$752$	19.8388	0.723445
$753$	26.9382	0.981682
$754$	14.9604	0.544824
$755$	−64.9108	−2.36235
$756$	8.22168	0.299020
$757$	−27.2834	−0.991631	−0.495816	−	0.868428i	$-0.665131\pi$
$757$	−27.2834	−0.991631	−0.495816	+	0.868428i	$0.665131\pi$
$758$	−39.9357	−1.45053
$759$	−1.77156	−0.0643036
$760$	5.67845	0.205979
$761$	−6.62777	−0.240257	−0.120128	−	0.992758i	$-0.538331\pi$
$761$	−6.62777	−0.240257	−0.120128	+	0.992758i	$0.538331\pi$
$762$	30.0108	1.08718
$763$	−13.3220	−0.482290
$764$	−32.3639	−1.17088
$765$	−5.07514	−0.183492
$766$	58.2705	2.10540
$767$	19.7208	0.712076
$768$	31.7821	1.14684
$769$	12.8302	0.462670	0.231335	−	0.972874i	$-0.425691\pi$
$769$	12.8302	0.462670	0.231335	+	0.972874i	$0.425691\pi$
$770$	−6.90412	−0.248807
$771$	30.4987	1.09839
$772$	−19.9270	−0.717190
$773$	−13.3220	−0.479158	−0.239579	−	0.970877i	$-0.577009\pi$
$773$	−13.3220	−0.479158	−0.239579	+	0.970877i	$0.577009\pi$
$774$	4.14439	0.148967
$775$	7.48396	0.268832
$776$	−1.29925	−0.0466404
$777$	−12.6462	−0.453680
$778$	30.8667	1.10663
$779$	45.2718	1.62203
$780$	44.2831	1.58559
$781$	5.86127	0.209733
$782$	10.7820	0.385564
$783$	−11.5544	−0.412919
$784$	26.2874	0.938837
$785$	22.5762	0.805778
$786$	60.7867	2.16819
$787$	14.8332	0.528746	0.264373	−	0.964420i	$-0.414835\pi$
$787$	14.8332	0.528746	0.264373	+	0.964420i	$0.414835\pi$
$788$	−28.1494	−1.00278
$789$	3.32576	0.118400
$790$	−103.392	−3.67851
$791$	8.99545	0.319841
$792$	0.0521589	0.00185339
$793$	−13.1703	−0.467691
$794$	31.5318	1.11902
$795$	90.2396	3.20047
$796$	39.0068	1.38256
$797$	29.1701	1.03326	0.516630	−	0.856209i	$-0.327186\pi$
$797$	29.1701	1.03326	0.516630	+	0.856209i	$0.327186\pi$
$798$	−19.3315	−0.684328
$799$	−26.0985	−0.923298
$800$	86.2979	3.05109
$801$	1.00780	0.0356088
$802$	−38.6256	−1.36392
$803$	6.55693	0.231389
$804$	44.7039	1.57658
$805$	−3.45373	−0.121728
$806$	4.39319	0.154744
$807$	−1.86068	−0.0654992
$808$	0.667222	0.0234728
$809$	27.9726	0.983463	0.491731	−	0.870747i	$-0.336364\pi$
$809$	27.9726	0.983463	0.491731	+	0.870747i	$0.336364\pi$
$810$	−75.9099	−2.66720
$811$	3.61458	0.126925	0.0634625	−	0.997984i	$-0.479786\pi$
$811$	3.61458	0.126925	0.0634625	+	0.997984i	$0.479786\pi$
$812$	−3.83111	−0.134446
$813$	33.5909	1.17808
$814$	−15.8301	−0.554843
$815$	−9.37565	−0.328415
$816$	−42.0561	−1.47226
$817$	57.2624	2.00336
$818$	1.72230	0.0602188
$819$	0.655772	0.0229145
$820$	54.7449	1.91177
$821$	−8.65885	−0.302196	−0.151098	−	0.988519i	$-0.548281\pi$
$821$	−8.65885	−0.302196	−0.151098	+	0.988519i	$0.548281\pi$
$822$	35.1957	1.22759
$823$	5.79184	0.201891	0.100945	−	0.994892i	$-0.467813\pi$
$823$	5.79184	0.201891	0.100945	+	0.994892i	$0.467813\pi$
$824$	1.04758	0.0364941
$825$	19.7359	0.687116
$826$	−10.4104	−0.362224
$827$	29.5787	1.02855	0.514276	−	0.857625i	$-0.328061\pi$
$827$	29.5787	1.02855	0.514276	+	0.857625i	$0.328061\pi$
$828$	−0.425010	−0.0147701
$829$	31.0967	1.08003	0.540016	−	0.841655i	$-0.318418\pi$
$829$	31.0967	1.08003	0.540016	+	0.841655i	$0.318418\pi$
$830$	−70.8476	−2.45915
$831$	−16.9619	−0.588401
$832$	23.0610	0.799496
$833$	−34.5819	−1.19819
$834$	−74.0035	−2.56253
$835$	−95.1691	−3.29346
$836$	−11.7389	−0.405999
$837$	−3.39300	−0.117279
$838$	8.92209	0.308209
$839$	42.8403	1.47901	0.739506	−	0.673150i	$-0.235059\pi$
$839$	42.8403	1.47901	0.739506	+	0.673150i	$0.235059\pi$
$840$	1.43513	0.0495166
$841$	−23.6159	−0.814343
$842$	−1.34119	−0.0462203
$843$	−28.6747	−0.987610
$844$	−30.2850	−1.04245
$845$	9.18778	0.316069
$846$	2.12068	0.0729104
$847$	−0.876225	−0.0301075
$848$	52.9843	1.81949
$849$	10.5457	0.361929
$850$	−120.116	−4.11995
$851$	−7.91885	−0.271455
$852$	19.8456	0.679900
$853$	44.1907	1.51306	0.756530	−	0.653959i	$-0.226893\pi$
$853$	44.1907	1.51306	0.756530	+	0.653959i	$0.226893\pi$
$854$	6.95247	0.237909
$855$	5.69792	0.194865
$856$	−2.76353	−0.0944555
$857$	−6.81869	−0.232922	−0.116461	−	0.993195i	$-0.537155\pi$
$857$	−6.81869	−0.232922	−0.116461	+	0.993195i	$0.537155\pi$
$858$	11.5853	0.395514
$859$	−5.93979	−0.202663	−0.101332	−	0.994853i	$-0.532310\pi$
$859$	−5.93979	−0.202663	−0.101332	+	0.994853i	$0.532310\pi$
$860$	69.2445	2.36122
$861$	11.4416	0.389930
$862$	−66.8040	−2.27535
$863$	−28.6614	−0.975646	−0.487823	−	0.872943i	$-0.662209\pi$
$863$	−28.6614	−0.975646	−0.487823	+	0.872943i	$0.662209\pi$
$864$	−39.1249	−1.33105
$865$	−66.2417	−2.25229
$866$	49.9368	1.69692
$867$	24.7791	0.841542
$868$	−1.12503	−0.0381859
$869$	−13.1218	−0.445126
$870$	32.8524	1.11380
$871$	−43.1918	−1.46350
$872$	3.46637	0.117386
$873$	−1.30371	−0.0441237
$874$	−12.1051	−0.409461
$875$	20.9605	0.708594
$876$	22.2011	0.750104
$877$	18.9421	0.639630	0.319815	−	0.947480i	$-0.396379\pi$
$877$	18.9421	0.639630	0.319815	+	0.947480i	$0.396379\pi$
$878$	−61.8554	−2.08752
$879$	55.4162	1.86914
$880$	16.8632	0.568458
$881$	50.5813	1.70413	0.852064	−	0.523437i	$-0.175351\pi$
$881$	50.5813	1.70413	0.852064	+	0.523437i	$0.175351\pi$
$882$	2.81001	0.0946180
$883$	−1.90645	−0.0641571	−0.0320786	−	0.999485i	$-0.510213\pi$
$883$	−1.90645	−0.0641571	−0.0320786	+	0.999485i	$0.510213\pi$
$884$	−34.2050	−1.15044
$885$	43.3060	1.45572
$886$	48.5785	1.63203
$887$	28.5293	0.957920	0.478960	−	0.877837i	$-0.341014\pi$
$887$	28.5293	0.957920	0.478960	+	0.877837i	$0.341014\pi$
$888$	3.29052	0.110423
$889$	7.42536	0.249039
$890$	34.7103	1.16349
$891$	−9.63399	−0.322751
$892$	13.3752	0.447834
$893$	29.3011	0.980522
$894$	−27.1369	−0.907595
$895$	−91.2916	−3.05154
$896$	1.59551	0.0533023
$897$	5.79543	0.193504
$898$	−7.55966	−0.252269
$899$	1.58106	0.0527313
$900$	4.73478	0.157826
$901$	−69.7025	−2.32213
$902$	14.3223	0.476879
$903$	14.4721	0.481600
$904$	−2.34061	−0.0778474
$905$	−29.7530	−0.989022
$906$	−57.4987	−1.91027
$907$	−2.88534	−0.0958063	−0.0479031	−	0.998852i	$-0.515254\pi$
$907$	−2.88534	−0.0958063	−0.0479031	+	0.998852i	$0.515254\pi$
$908$	−41.1819	−1.36667
$909$	0.669510	0.0222062
$910$	22.5859	0.748716
$911$	−12.7597	−0.422749	−0.211374	−	0.977405i	$-0.567794\pi$
$911$	−12.7597	−0.422749	−0.211374	+	0.977405i	$0.567794\pi$
$912$	47.2168	1.56351
$913$	−8.99151	−0.297575
$914$	−9.83589	−0.325342
$915$	−28.9215	−0.956114
$916$	−13.7816	−0.455358
$917$	15.0400	0.496665
$918$	54.4570	1.79735
$919$	17.2675	0.569604	0.284802	−	0.958586i	$-0.408072\pi$
$919$	17.2675	0.569604	0.284802	+	0.958586i	$0.408072\pi$
$920$	0.898655	0.0296278
$921$	60.0777	1.97963
$922$	50.0801	1.64930
$923$	−19.1744	−0.631132
$924$	−2.96680	−0.0976007
$925$	88.2193	2.90063
$926$	24.9882	0.821164
$927$	1.05117	0.0345249
$928$	18.2313	0.598471
$929$	55.0107	1.80484	0.902422	−	0.430853i	$-0.141787\pi$
$929$	55.0107	1.80484	0.902422	+	0.430853i	$0.141787\pi$
$930$	9.64727	0.316346
$931$	38.8255	1.27245
$932$	37.0605	1.21396
$933$	−7.94409	−0.260078
$934$	54.0065	1.76715
$935$	−22.1840	−0.725495
$936$	−0.170631	−0.00557725
$937$	50.6303	1.65402	0.827010	−	0.562187i	$-0.190040\pi$
$937$	50.6303	1.65402	0.827010	+	0.562187i	$0.190040\pi$
$938$	22.8005	0.744464
$939$	−33.8731	−1.10541
$940$	35.4323	1.15567
$941$	−15.5339	−0.506392	−0.253196	−	0.967415i	$-0.581482\pi$
$941$	−15.5339	−0.506392	−0.253196	+	0.967415i	$0.581482\pi$
$942$	19.9982	0.651577
$943$	7.16459	0.233311
$944$	25.4272	0.827585
$945$	−17.4438	−0.567447
$946$	18.1156	0.588990
$947$	−33.9376	−1.10282	−0.551411	−	0.834234i	$-0.685910\pi$
$947$	−33.9376	−1.10282	−0.551411	+	0.834234i	$0.685910\pi$
$948$	−44.4290	−1.44299
$949$	−21.4501	−0.696301
$950$	134.856	4.37530
$951$	14.5478	0.471745
$952$	−1.10852	−0.0359272
$953$	13.3188	0.431439	0.215719	−	0.976455i	$-0.430790\pi$
$953$	13.3188	0.431439	0.215719	+	0.976455i	$0.430790\pi$
$954$	5.66380	0.183372
$955$	68.6659	2.22198
$956$	35.5663	1.15030
$957$	4.16940	0.134778
$958$	−71.6840	−2.31600
$959$	8.70822	0.281203
$960$	50.6410	1.63443
$961$	−30.5357	−0.985023
$962$	51.7860	1.66965
$963$	−2.77300	−0.0893588
$964$	−23.7783	−0.765847
$965$	42.2789	1.36101
$966$	−3.05935	−0.0984330
$967$	6.66021	0.214178	0.107089	−	0.994249i	$-0.465847\pi$
$967$	6.66021	0.214178	0.107089	+	0.994249i	$0.465847\pi$
$968$	0.227993	0.00732796
$969$	−62.1152	−1.99543
$970$	−44.9019	−1.44171
$971$	−36.6818	−1.17718	−0.588588	−	0.808433i	$-0.700316\pi$
$971$	−36.6818	−1.17718	−0.588588	+	0.808433i	$0.700316\pi$
$972$	−4.47042	−0.143389
$973$	−18.3101	−0.586996
$974$	−0.418049	−0.0133952
$975$	−64.5635	−2.06769
$976$	−16.9813	−0.543558
$977$	16.2495	0.519866	0.259933	−	0.965627i	$-0.416299\pi$
$977$	16.2495	0.519866	0.259933	+	0.965627i	$0.416299\pi$
$978$	−8.30506	−0.265566
$979$	4.40520	0.140791
$980$	46.9497	1.49975
$981$	3.47826	0.111052
$982$	45.6364	1.45632
$983$	43.6479	1.39215	0.696076	−	0.717968i	$-0.254928\pi$
$983$	43.6479	1.39215	0.696076	+	0.717968i	$0.254928\pi$
$984$	−2.97710	−0.0949066
$985$	59.7241	1.90297
$986$	−25.3757	−0.808127
$987$	7.40533	0.235714
$988$	38.4023	1.22174
$989$	9.06218	0.288161
$990$	1.80260	0.0572905
$991$	2.46301	0.0782401	0.0391201	−	0.999235i	$-0.487545\pi$
$991$	2.46301	0.0782401	0.0391201	+	0.999235i	$0.487545\pi$
$992$	5.35371	0.169981
$993$	57.0999	1.81201
$994$	10.1220	0.321049
$995$	−82.7602	−2.62367
$996$	−30.4443	−0.964664
$997$	2.55225	0.0808306	0.0404153	−	0.999183i	$-0.487132\pi$
$997$	2.55225	0.0808306	0.0404153	+	0.999183i	$0.487132\pi$
$998$	−3.38468	−0.107140
$999$	−39.9959	−1.26542

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.e.1.19	✓	119

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.e.1.19	✓	119	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)

\(f(q)\)	\(=\)	\(q-1.97087 q^{2} +1.79688 q^{3} +1.88432 q^{4} -3.99793 q^{5} -3.54141 q^{6} -0.876225 q^{7} +0.227993 q^{8} +0.228774 q^{9} +O(q^{10})\)	\(q-1.97087 q^{2} +1.79688 q^{3} +1.88432 q^{4} -3.99793 q^{5} -3.54141 q^{6} -0.876225 q^{7} +0.227993 q^{8} +0.228774 q^{9} +7.87939 q^{10} +1.00000 q^{11} +3.38589 q^{12} -3.27137 q^{13} +1.72692 q^{14} -7.18380 q^{15} -4.21798 q^{16} +5.54888 q^{17} -0.450884 q^{18} -6.22979 q^{19} -7.53337 q^{20} -1.57447 q^{21} -1.97087 q^{22} -0.985910 q^{23} +0.409675 q^{24} +10.9834 q^{25} +6.44744 q^{26} -4.97956 q^{27} -1.65109 q^{28} +2.32036 q^{29} +14.1583 q^{30} +0.681386 q^{31} +7.85710 q^{32} +1.79688 q^{33} -10.9361 q^{34} +3.50309 q^{35} +0.431084 q^{36} +8.03203 q^{37} +12.2781 q^{38} -5.87826 q^{39} -0.911499 q^{40} -7.26698 q^{41} +3.10307 q^{42} -9.19170 q^{43} +1.88432 q^{44} -0.914624 q^{45} +1.94310 q^{46} -4.70338 q^{47} -7.57920 q^{48} -6.23223 q^{49} -21.6469 q^{50} +9.97067 q^{51} -6.16430 q^{52} -12.5615 q^{53} +9.81405 q^{54} -3.99793 q^{55} -0.199773 q^{56} -11.1942 q^{57} -4.57312 q^{58} -6.02829 q^{59} -13.5366 q^{60} +4.02593 q^{61} -1.34292 q^{62} -0.200458 q^{63} -7.04933 q^{64} +13.0787 q^{65} -3.54141 q^{66} +13.2030 q^{67} +10.4559 q^{68} -1.77156 q^{69} -6.90412 q^{70} +5.86127 q^{71} +0.0521589 q^{72} +6.55693 q^{73} -15.8301 q^{74} +19.7359 q^{75} -11.7389 q^{76} -0.876225 q^{77} +11.5853 q^{78} -13.1218 q^{79} +16.8632 q^{80} -9.63399 q^{81} +14.3223 q^{82} -8.99151 q^{83} -2.96680 q^{84} -22.1840 q^{85} +18.1156 q^{86} +4.16940 q^{87} +0.227993 q^{88} +4.40520 q^{89} +1.80260 q^{90} +2.86646 q^{91} -1.85777 q^{92} +1.22437 q^{93} +9.26973 q^{94} +24.9063 q^{95} +14.1183 q^{96} -5.69865 q^{97} +12.2829 q^{98} +0.228774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9}+O(q^{10}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9	\( 119 q + 15 q^{2} + 15 q^{3} + 133 q^{4} + 6 q^{5} + 16 q^{6} + 72 q^{7} + 39 q^{8} + 128 q^{9} + 22 q^{10} + 119 q^{11} + 40 q^{12} + 67 q^{13} + 3 q^{14} + 22 q^{15} + 145 q^{16} + 57 q^{17} + 53 q^{18} + 68 q^{19} + 25 q^{20} + 21 q^{21} + 15 q^{22} + 21 q^{23} + 34 q^{24} + 137 q^{25} + 10 q^{26} + 54 q^{27} + 149 q^{28} + 46 q^{29} + 10 q^{30} + 87 q^{31} + 58 q^{32} + 15 q^{33} + 16 q^{34} + 40 q^{35} + 137 q^{36} + 39 q^{37} + 27 q^{38} + 72 q^{39} + 46 q^{40} + 50 q^{41} - 4 q^{42} + 122 q^{43} + 133 q^{44} + 12 q^{45} + 22 q^{46} + 92 q^{47} + 9 q^{48} + 161 q^{49} + 2 q^{50} - 12 q^{51} + 177 q^{52} + 12 q^{53} + 19 q^{54} + 6 q^{55} - 16 q^{56} + 43 q^{57} + 56 q^{58} + 39 q^{59} + 27 q^{60} + 114 q^{61} + 66 q^{62} + 196 q^{63} + 161 q^{64} + 7 q^{65} + 16 q^{66} + 59 q^{67} + 139 q^{68} - 24 q^{69} + 9 q^{70} + 11 q^{71} + 92 q^{72} + 123 q^{73} + q^{74} + 19 q^{75} + 92 q^{76} + 72 q^{77} - 101 q^{78} + 78 q^{79} - 34 q^{80} + 139 q^{81} + 73 q^{82} + 108 q^{83} - 31 q^{84} + 30 q^{85} - 18 q^{86} + 164 q^{87} + 39 q^{88} + 15 q^{89} - 41 q^{90} + 60 q^{91} - 26 q^{92} - 2 q^{93} + 45 q^{94} + 75 q^{95} + 42 q^{96} + 73 q^{97} + 32 q^{98} + 128 q^{99}+O(q^{100}) \) 119 * q + 15 * q^2 + 15 * q^3 + 133 * q^4 + 6 * q^5 + 16 * q^6 + 72 * q^7 + 39 * q^8 + 128 * q^9 + 22 * q^10 + 119 * q^11 + 40 * q^12 + 67 * q^13 + 3 * q^14 + 22 * q^15 + 145 * q^16 + 57 * q^17 + 53 * q^18 + 68 * q^19 + 25 * q^20 + 21 * q^21 + 15 * q^22 + 21 * q^23 + 34 * q^24 + 137 * q^25 + 10 * q^26 + 54 * q^27 + 149 * q^28 + 46 * q^29 + 10 * q^30 + 87 * q^31 + 58 * q^32 + 15 * q^33 + 16 * q^34 + 40 * q^35 + 137 * q^36 + 39 * q^37 + 27 * q^38 + 72 * q^39 + 46 * q^40 + 50 * q^41 - 4 * q^42 + 122 * q^43 + 133 * q^44 + 12 * q^45 + 22 * q^46 + 92 * q^47 + 9 * q^48 + 161 * q^49 + 2 * q^50 - 12 * q^51 + 177 * q^52 + 12 * q^53 + 19 * q^54 + 6 * q^55 - 16 * q^56 + 43 * q^57 + 56 * q^58 + 39 * q^59 + 27 * q^60 + 114 * q^61 + 66 * q^62 + 196 * q^63 + 161 * q^64 + 7 * q^65 + 16 * q^66 + 59 * q^67 + 139 * q^68 - 24 * q^69 + 9 * q^70 + 11 * q^71 + 92 * q^72 + 123 * q^73 + q^74 + 19 * q^75 + 92 * q^76 + 72 * q^77 - 101 * q^78 + 78 * q^79 - 34 * q^80 + 139 * q^81 + 73 * q^82 + 108 * q^83 - 31 * q^84 + 30 * q^85 - 18 * q^86 + 164 * q^87 + 39 * q^88 + 15 * q^89 - 41 * q^90 + 60 * q^91 - 26 * q^92 - 2 * q^93 + 45 * q^94 + 75 * q^95 + 42 * q^96 + 73 * q^97 + 32 * q^98 + 128 * q^99

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