LMFDB - Embedded newform 6017.2.a.f.1.12

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			1.12
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)

$f(q)$	$=$	$q-2.37440 q^{2} -0.379878 q^{3} +3.63775 q^{4} -1.52566 q^{5} +0.901981 q^{6} +2.31296 q^{7} -3.88867 q^{8} -2.85569 q^{9} +O(q^{10})$	\(q-2.37440 q^{2} -0.379878 q^{3} +3.63775 q^{4} -1.52566 q^{5} +0.901981 q^{6} +2.31296 q^{7} -3.88867 q^{8} -2.85569 q^{9} +3.62251 q^{10} -1.00000 q^{11} -1.38190 q^{12} +1.64625 q^{13} -5.49189 q^{14} +0.579563 q^{15} +1.95774 q^{16} -7.33107 q^{17} +6.78054 q^{18} +0.596356 q^{19} -5.54996 q^{20} -0.878644 q^{21} +2.37440 q^{22} -4.14341 q^{23} +1.47722 q^{24} -2.67238 q^{25} -3.90884 q^{26} +2.22445 q^{27} +8.41398 q^{28} -1.76317 q^{29} -1.37611 q^{30} -1.69038 q^{31} +3.12890 q^{32} +0.379878 q^{33} +17.4069 q^{34} -3.52878 q^{35} -10.3883 q^{36} +3.15531 q^{37} -1.41598 q^{38} -0.625373 q^{39} +5.93277 q^{40} -11.5466 q^{41} +2.08625 q^{42} -0.926674 q^{43} -3.63775 q^{44} +4.35680 q^{45} +9.83809 q^{46} -7.87778 q^{47} -0.743702 q^{48} -1.65021 q^{49} +6.34528 q^{50} +2.78491 q^{51} +5.98863 q^{52} -2.09800 q^{53} -5.28172 q^{54} +1.52566 q^{55} -8.99435 q^{56} -0.226543 q^{57} +4.18645 q^{58} -6.92361 q^{59} +2.10831 q^{60} +7.40456 q^{61} +4.01364 q^{62} -6.60511 q^{63} -11.3447 q^{64} -2.51160 q^{65} -0.901981 q^{66} -5.55057 q^{67} -26.6686 q^{68} +1.57399 q^{69} +8.37872 q^{70} +14.5635 q^{71} +11.1048 q^{72} +2.39854 q^{73} -7.49195 q^{74} +1.01518 q^{75} +2.16939 q^{76} -2.31296 q^{77} +1.48488 q^{78} +3.21438 q^{79} -2.98683 q^{80} +7.72206 q^{81} +27.4162 q^{82} +6.04068 q^{83} -3.19629 q^{84} +11.1847 q^{85} +2.20029 q^{86} +0.669789 q^{87} +3.88867 q^{88} +11.7278 q^{89} -10.3448 q^{90} +3.80770 q^{91} -15.0727 q^{92} +0.642140 q^{93} +18.7050 q^{94} -0.909833 q^{95} -1.18860 q^{96} +0.507957 q^{97} +3.91825 q^{98} +2.85569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.37440	−1.67895	−0.839475	−	0.543398i	$-0.817138\pi$
$2$	−2.37440	−1.67895	−0.839475	+	0.543398i	$0.817138\pi$
$3$	−0.379878	−0.219323	−0.109661	−	0.993969i	$-0.534977\pi$
$3$	−0.379878	−0.219323	−0.109661	+	0.993969i	$0.534977\pi$
$4$	3.63775	1.81888
$5$	−1.52566	−0.682294	−0.341147	−	0.940010i	$-0.610815\pi$
$5$	−1.52566	−0.682294	−0.341147	+	0.940010i	$0.610815\pi$
$6$	0.901981	0.368232
$7$	2.31296	0.874217	0.437109	−	0.899409i	$-0.356003\pi$
$7$	2.31296	0.874217	0.437109	+	0.899409i	$0.356003\pi$
$8$	−3.88867	−1.37485
$9$	−2.85569	−0.951897
$10$	3.62251	1.14554
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−1.38190	−0.398921
$13$	1.64625	0.456586	0.228293	−	0.973592i	$-0.426686\pi$
$13$	1.64625	0.456586	0.228293	+	0.973592i	$0.426686\pi$
$14$	−5.49189	−1.46777
$15$	0.579563	0.149643
$16$	1.95774	0.489434
$17$	−7.33107	−1.77805	−0.889023	−	0.457863i	$-0.848615\pi$
$17$	−7.33107	−1.77805	−0.889023	+	0.457863i	$0.848615\pi$
$18$	6.78054	1.59819
$19$	0.596356	0.136813	0.0684067	−	0.997658i	$-0.478208\pi$
$19$	0.596356	0.136813	0.0684067	+	0.997658i	$0.478208\pi$
$20$	−5.54996	−1.24101
$21$	−0.878644	−0.191736
$22$	2.37440	0.506223
$23$	−4.14341	−0.863960	−0.431980	−	0.901883i	$-0.642185\pi$
$23$	−4.14341	−0.863960	−0.431980	+	0.901883i	$0.642185\pi$
$24$	1.47722	0.301537
$25$	−2.67238	−0.534475
$26$	−3.90884	−0.766586
$27$	2.22445	0.428096
$28$	8.41398	1.59009
$29$	−1.76317	−0.327412	−0.163706	−	0.986509i	$-0.552345\pi$
$29$	−1.76317	−0.327412	−0.163706	+	0.986509i	$0.552345\pi$
$30$	−1.37611	−0.251243
$31$	−1.69038	−0.303602	−0.151801	−	0.988411i	$-0.548507\pi$
$31$	−1.69038	−0.303602	−0.151801	+	0.988411i	$0.548507\pi$
$32$	3.12890	0.553117
$33$	0.379878	0.0661283
$34$	17.4069	2.98525
$35$	−3.52878	−0.596473
$36$	−10.3883	−1.73138
$37$	3.15531	0.518730	0.259365	−	0.965779i	$-0.416487\pi$
$37$	3.15531	0.518730	0.259365	+	0.965779i	$0.416487\pi$
$38$	−1.41598	−0.229703
$39$	−0.625373	−0.100140
$40$	5.93277	0.938054
$41$	−11.5466	−1.80328	−0.901639	−	0.432490i	$-0.857635\pi$
$41$	−11.5466	−1.80328	−0.901639	+	0.432490i	$0.857635\pi$
$42$	2.08625	0.321915
$43$	−0.926674	−0.141316	−0.0706582	−	0.997501i	$-0.522510\pi$
$43$	−0.926674	−0.141316	−0.0706582	+	0.997501i	$0.522510\pi$
$44$	−3.63775	−0.548412
$45$	4.35680	0.649474
$46$	9.83809	1.45055
$47$	−7.87778	−1.14909	−0.574546	−	0.818472i	$-0.694822\pi$
$47$	−7.87778	−1.14909	−0.574546	+	0.818472i	$0.694822\pi$
$48$	−0.743702	−0.107344
$49$	−1.65021	−0.235744
$50$	6.34528	0.897358
$51$	2.78491	0.389966
$52$	5.98863	0.830474
$53$	−2.09800	−0.288183	−0.144091	−	0.989564i	$-0.546026\pi$
$53$	−2.09800	−0.288183	−0.144091	+	0.989564i	$0.546026\pi$
$54$	−5.28172	−0.718752
$55$	1.52566	0.205719
$56$	−8.99435	−1.20192
$57$	−0.226543	−0.0300063
$58$	4.18645	0.549708
$59$	−6.92361	−0.901377	−0.450689	−	0.892681i	$-0.648821\pi$
$59$	−6.92361	−0.901377	−0.450689	+	0.892681i	$0.648821\pi$
$60$	2.10831	0.272181
$61$	7.40456	0.948057	0.474028	−	0.880510i	$-0.342799\pi$
$61$	7.40456	0.948057	0.474028	+	0.880510i	$0.342799\pi$
$62$	4.01364	0.509732
$63$	−6.60511	−0.832165
$64$	−11.3447	−1.41809
$65$	−2.51160	−0.311526
$66$	−0.901981	−0.111026
$67$	−5.55057	−0.678110	−0.339055	−	0.940767i	$-0.610107\pi$
$67$	−5.55057	−0.678110	−0.339055	+	0.940767i	$0.610107\pi$
$68$	−26.6686	−3.23404
$69$	1.57399	0.189486
$70$	8.37872	1.00145
$71$	14.5635	1.72837	0.864183	−	0.503177i	$-0.167836\pi$
$71$	14.5635	1.72837	0.864183	+	0.503177i	$0.167836\pi$
$72$	11.1048	1.30872
$73$	2.39854	0.280727	0.140364	−	0.990100i	$-0.455173\pi$
$73$	2.39854	0.280727	0.140364	+	0.990100i	$0.455173\pi$
$74$	−7.49195	−0.870922
$75$	1.01518	0.117223
$76$	2.16939	0.248847
$77$	−2.31296	−0.263586
$78$	1.48488	0.168130
$79$	3.21438	0.361646	0.180823	−	0.983516i	$-0.442124\pi$
$79$	3.21438	0.361646	0.180823	+	0.983516i	$0.442124\pi$
$80$	−2.98683	−0.333938
$81$	7.72206	0.858006
$82$	27.4162	3.02761
$83$	6.04068	0.663051	0.331525	−	0.943446i	$-0.392437\pi$
$83$	6.04068	0.663051	0.331525	+	0.943446i	$0.392437\pi$
$84$	−3.19629	−0.348744
$85$	11.1847	1.21315
$86$	2.20029	0.237263
$87$	0.669789	0.0718089
$88$	3.88867	0.414534
$89$	11.7278	1.24314	0.621572	−	0.783357i	$-0.286494\pi$
$89$	11.7278	1.24314	0.621572	+	0.783357i	$0.286494\pi$
$90$	−10.3448	−1.09043
$91$	3.80770	0.399156
$92$	−15.0727	−1.57144
$93$	0.642140	0.0665868
$94$	18.7050	1.92927
$95$	−0.909833	−0.0933469
$96$	−1.18860	−0.121311
$97$	0.507957	0.0515753	0.0257876	−	0.999667i	$-0.491791\pi$
$97$	0.507957	0.0515753	0.0257876	+	0.999667i	$0.491791\pi$
$98$	3.91825	0.395803
$99$	2.85569	0.287008
$100$	−9.72144	−0.972144
$101$	1.80900	0.180002	0.0900011	−	0.995942i	$-0.471313\pi$
$101$	1.80900	0.180002	0.0900011	+	0.995942i	$0.471313\pi$
$102$	−6.61249	−0.654734
$103$	−16.4299	−1.61889	−0.809444	−	0.587196i	$-0.800232\pi$
$103$	−16.4299	−1.61889	−0.809444	+	0.587196i	$0.800232\pi$
$104$	−6.40171	−0.627739
$105$	1.34051	0.130820
$106$	4.98149	0.483845
$107$	0.129922	0.0125600	0.00628000	−	0.999980i	$-0.498001\pi$
$107$	0.129922	0.0125600	0.00628000	+	0.999980i	$0.498001\pi$
$108$	8.09200	0.778653
$109$	−7.00572	−0.671027	−0.335513	−	0.942035i	$-0.608910\pi$
$109$	−7.00572	−0.671027	−0.335513	+	0.942035i	$0.608910\pi$
$110$	−3.62251	−0.345393
$111$	−1.19863	−0.113769
$112$	4.52817	0.427872
$113$	−11.3320	−1.06603	−0.533014	−	0.846107i	$-0.678941\pi$
$113$	−11.3320	−1.06603	−0.533014	+	0.846107i	$0.678941\pi$
$114$	0.537902	0.0503791
$115$	6.32141	0.589475
$116$	−6.41396	−0.595521
$117$	−4.70117	−0.434623
$118$	16.4394	1.51337
$119$	−16.9565	−1.55440
$120$	−2.25373	−0.205737
$121$	1.00000	0.0909091
$122$	−17.5814	−1.59174
$123$	4.38631	0.395500
$124$	−6.14919	−0.552214
$125$	11.7054	1.04696
$126$	15.6831	1.39716
$127$	14.8251	1.31551	0.657756	−	0.753231i	$-0.271506\pi$
$127$	14.8251	1.31551	0.657756	+	0.753231i	$0.271506\pi$
$128$	20.6790	1.82779
$129$	0.352023	0.0309939
$130$	5.96354	0.523037
$131$	3.08854	0.269847	0.134923	−	0.990856i	$-0.456921\pi$
$131$	3.08854	0.269847	0.134923	+	0.990856i	$0.456921\pi$
$132$	1.38190	0.120279
$133$	1.37935	0.119605
$134$	13.1792	1.13851
$135$	−3.39374	−0.292087
$136$	28.5081	2.44455
$137$	−20.1994	−1.72575	−0.862876	−	0.505416i	$-0.831339\pi$
$137$	−20.1994	−1.72575	−0.862876	+	0.505416i	$0.831339\pi$
$138$	−3.73728	−0.318138
$139$	11.8822	1.00784	0.503918	−	0.863751i	$-0.331891\pi$
$139$	11.8822	1.00784	0.503918	+	0.863751i	$0.331891\pi$
$140$	−12.8368	−1.08491
$141$	2.99260	0.252022
$142$	−34.5794	−2.90184
$143$	−1.64625	−0.137666
$144$	−5.59070	−0.465891
$145$	2.68998	0.223391
$146$	−5.69507	−0.471327
$147$	0.626878	0.0517041
$148$	11.4782	0.943505
$149$	2.83933	0.232607	0.116304	−	0.993214i	$-0.462895\pi$
$149$	2.83933	0.232607	0.116304	+	0.993214i	$0.462895\pi$
$150$	−2.41043	−0.196811
$151$	−17.8172	−1.44994	−0.724970	−	0.688780i	$-0.758146\pi$
$151$	−17.8172	−1.44994	−0.724970	+	0.688780i	$0.758146\pi$
$152$	−2.31903	−0.188098
$153$	20.9353	1.69252
$154$	5.49189	0.442549
$155$	2.57894	0.207146
$156$	−2.27495	−0.182142
$157$	11.7988	0.941643	0.470821	−	0.882229i	$-0.343958\pi$
$157$	11.7988	0.941643	0.470821	+	0.882229i	$0.343958\pi$
$158$	−7.63222	−0.607187
$159$	0.796986	0.0632051
$160$	−4.77362	−0.377388
$161$	−9.58354	−0.755289
$162$	−18.3352	−1.44055
$163$	3.20119	0.250737	0.125368	−	0.992110i	$-0.459989\pi$
$163$	3.20119	0.250737	0.125368	+	0.992110i	$0.459989\pi$
$164$	−42.0037	−3.27994
$165$	−0.579563	−0.0451189
$166$	−14.3430	−1.11323
$167$	−9.12246	−0.705917	−0.352959	−	0.935639i	$-0.614824\pi$
$167$	−9.12246	−0.705917	−0.352959	+	0.935639i	$0.614824\pi$
$168$	3.41676	0.263609
$169$	−10.2899	−0.791529
$170$	−26.5569	−2.03682
$171$	−1.70301	−0.130232
$172$	−3.37101	−0.257037
$173$	21.7426	1.65306	0.826530	−	0.562893i	$-0.190312\pi$
$173$	21.7426	1.65306	0.826530	+	0.562893i	$0.190312\pi$
$174$	−1.59034	−0.120564
$175$	−6.18110	−0.467247
$176$	−1.95774	−0.147570
$177$	2.63013	0.197693
$178$	−27.8464	−2.08718
$179$	17.8020	1.33058	0.665291	−	0.746584i	$-0.268307\pi$
$179$	17.8020	1.33058	0.665291	+	0.746584i	$0.268307\pi$
$180$	15.8490	1.18131
$181$	−7.42484	−0.551884	−0.275942	−	0.961174i	$-0.588990\pi$
$181$	−7.42484	−0.551884	−0.275942	+	0.961174i	$0.588990\pi$
$182$	−9.04099	−0.670163
$183$	−2.81283	−0.207931
$184$	16.1123	1.18782
$185$	−4.81392	−0.353926
$186$	−1.52469	−0.111796
$187$	7.33107	0.536101
$188$	−28.6574	−2.09006
$189$	5.14507	0.374249
$190$	2.16030	0.156725
$191$	−2.49913	−0.180831	−0.0904153	−	0.995904i	$-0.528819\pi$
$191$	−2.49913	−0.180831	−0.0904153	+	0.995904i	$0.528819\pi$
$192$	4.30961	0.311020
$193$	0.317512	0.0228550	0.0114275	−	0.999935i	$-0.496362\pi$
$193$	0.317512	0.0228550	0.0114275	+	0.999935i	$0.496362\pi$
$194$	−1.20609	−0.0865923
$195$	0.954103	0.0683248
$196$	−6.00305	−0.428789
$197$	26.4283	1.88294	0.941470	−	0.337096i	$-0.109445\pi$
$197$	26.4283	1.88294	0.941470	+	0.337096i	$0.109445\pi$
$198$	−6.78054	−0.481872
$199$	−9.18108	−0.650829	−0.325415	−	0.945571i	$-0.605504\pi$
$199$	−9.18108	−0.650829	−0.325415	+	0.945571i	$0.605504\pi$
$200$	10.3920	0.734825
$201$	2.10854	0.148725
$202$	−4.29528	−0.302215
$203$	−4.07814	−0.286229
$204$	10.1308	0.709300
$205$	17.6161	1.23036
$206$	39.0111	2.71804
$207$	11.8323	0.822401
$208$	3.22292	0.223469
$209$	−0.596356	−0.0412508
$210$	−3.18290	−0.219641
$211$	10.2506	0.705677	0.352839	−	0.935684i	$-0.385216\pi$
$211$	10.2506	0.705677	0.352839	+	0.935684i	$0.385216\pi$
$212$	−7.63202	−0.524169
$213$	−5.53235	−0.379070
$214$	−0.308485	−0.0210876
$215$	1.41378	0.0964193
$216$	−8.65016	−0.588569
$217$	−3.90979	−0.265414
$218$	16.6344	1.12662
$219$	−0.911152	−0.0615699
$220$	5.54996	0.374178
$221$	−12.0687	−0.811831
$222$	2.84603	0.191013
$223$	−1.50988	−0.101109	−0.0505545	−	0.998721i	$-0.516099\pi$
$223$	−1.50988	−0.101109	−0.0505545	+	0.998721i	$0.516099\pi$
$224$	7.23702	0.483544
$225$	7.63148	0.508766
$226$	26.9067	1.78981
$227$	14.5784	0.967600	0.483800	−	0.875178i	$-0.339256\pi$
$227$	14.5784	0.967600	0.483800	+	0.875178i	$0.339256\pi$
$228$	−0.824106	−0.0545777
$229$	−6.95382	−0.459521	−0.229761	−	0.973247i	$-0.573794\pi$
$229$	−6.95382	−0.459521	−0.229761	+	0.973247i	$0.573794\pi$
$230$	−15.0095	−0.989699
$231$	0.878644	0.0578105
$232$	6.85637	0.450143
$233$	−11.6686	−0.764437	−0.382219	−	0.924072i	$-0.624840\pi$
$233$	−11.6686	−0.764437	−0.382219	+	0.924072i	$0.624840\pi$
$234$	11.1624	0.729711
$235$	12.0188	0.784019
$236$	−25.1864	−1.63949
$237$	−1.22107	−0.0793173
$238$	40.2614	2.60976
$239$	−0.604201	−0.0390825	−0.0195413	−	0.999809i	$-0.506221\pi$
$239$	−0.604201	−0.0390825	−0.0195413	+	0.999809i	$0.506221\pi$
$240$	1.13463	0.0732403
$241$	−1.52378	−0.0981555	−0.0490777	−	0.998795i	$-0.515628\pi$
$241$	−1.52378	−0.0981555	−0.0490777	+	0.998795i	$0.515628\pi$
$242$	−2.37440	−0.152632
$243$	−9.60679	−0.616276
$244$	26.9360	1.72440
$245$	2.51765	0.160847
$246$	−10.4148	−0.664025
$247$	0.981748	0.0624671
$248$	6.57334	0.417408
$249$	−2.29472	−0.145422
$250$	−27.7932	−1.75780
$251$	−13.3257	−0.841112	−0.420556	−	0.907267i	$-0.638165\pi$
$251$	−13.3257	−0.841112	−0.420556	+	0.907267i	$0.638165\pi$
$252$	−24.0277	−1.51361
$253$	4.14341	0.260494
$254$	−35.2006	−2.20868
$255$	−4.24882	−0.266071
$256$	−26.4108	−1.65067
$257$	30.6765	1.91355	0.956775	−	0.290831i	$-0.0939316\pi$
$257$	30.6765	1.91355	0.956775	+	0.290831i	$0.0939316\pi$
$258$	−0.835842	−0.0520373
$259$	7.29811	0.453483
$260$	−9.13659	−0.566627
$261$	5.03506	0.311662
$262$	−7.33341	−0.453059
$263$	−32.1757	−1.98404	−0.992019	−	0.126090i	$-0.959757\pi$
$263$	−32.1757	−1.98404	−0.992019	+	0.126090i	$0.959757\pi$
$264$	−1.47722	−0.0909167
$265$	3.20083	0.196625
$266$	−3.27512	−0.200810
$267$	−4.45514	−0.272650
$268$	−20.1916	−1.23340
$269$	4.26628	0.260120	0.130060	−	0.991506i	$-0.458483\pi$
$269$	4.26628	0.260120	0.130060	+	0.991506i	$0.458483\pi$
$270$	8.05809	0.490400
$271$	−7.00480	−0.425511	−0.212756	−	0.977105i	$-0.568244\pi$
$271$	−7.00480	−0.425511	−0.212756	+	0.977105i	$0.568244\pi$
$272$	−14.3523	−0.870237
$273$	−1.44646	−0.0875440
$274$	47.9614	2.89745
$275$	2.67238	0.161150
$276$	5.72579	0.344652
$277$	−32.0766	−1.92729	−0.963647	−	0.267179i	$-0.913908\pi$
$277$	−32.0766	−1.92729	−0.963647	+	0.267179i	$0.913908\pi$
$278$	−28.2131	−1.69211
$279$	4.82721	0.288998
$280$	13.7223	0.820063
$281$	−12.4777	−0.744358	−0.372179	−	0.928161i	$-0.621389\pi$
$281$	−12.4777	−0.744358	−0.372179	+	0.928161i	$0.621389\pi$
$282$	−7.10561	−0.423133
$283$	−17.9083	−1.06454	−0.532270	−	0.846575i	$-0.678661\pi$
$283$	−17.9083	−1.06454	−0.532270	+	0.846575i	$0.678661\pi$
$284$	52.9783	3.14368
$285$	0.345626	0.0204731
$286$	3.90884	0.231134
$287$	−26.7069	−1.57646
$288$	−8.93517	−0.526510
$289$	36.7446	2.16145
$290$	−6.38708	−0.375062
$291$	−0.192962	−0.0113116
$292$	8.72528	0.510608
$293$	−16.2794	−0.951056	−0.475528	−	0.879701i	$-0.657743\pi$
$293$	−16.2794	−0.951056	−0.475528	+	0.879701i	$0.657743\pi$
$294$	−1.48846	−0.0868086
$295$	10.5630	0.615004
$296$	−12.2700	−0.713177
$297$	−2.22445	−0.129076
$298$	−6.74170	−0.390536
$299$	−6.82106	−0.394472
$300$	3.69296	0.213213
$301$	−2.14336	−0.123541
$302$	42.3050	2.43438
$303$	−0.687200	−0.0394786
$304$	1.16751	0.0669612
$305$	−11.2968	−0.646853
$306$	−49.7086	−2.84165
$307$	−19.3620	−1.10505	−0.552524	−	0.833497i	$-0.686335\pi$
$307$	−19.3620	−1.10505	−0.552524	+	0.833497i	$0.686335\pi$
$308$	−8.41398	−0.479431
$309$	6.24137	0.355059
$310$	−6.12343	−0.347787
$311$	−32.2489	−1.82867	−0.914335	−	0.404959i	$-0.867286\pi$
$311$	−32.2489	−1.82867	−0.914335	+	0.404959i	$0.867286\pi$
$312$	2.43187	0.137678
$313$	27.9487	1.57975	0.789877	−	0.613266i	$-0.210144\pi$
$313$	27.9487	1.57975	0.789877	+	0.613266i	$0.210144\pi$
$314$	−28.0149	−1.58097
$315$	10.0771	0.567781
$316$	11.6931	0.657790
$317$	15.0173	0.843458	0.421729	−	0.906722i	$-0.361423\pi$
$317$	15.0173	0.843458	0.421729	+	0.906722i	$0.361423\pi$
$318$	−1.89236	−0.106118
$319$	1.76317	0.0987183
$320$	17.3081	0.967554
$321$	−0.0493544	−0.00275469
$322$	22.7551	1.26809
$323$	−4.37193	−0.243260
$324$	28.0909	1.56061
$325$	−4.39939	−0.244034
$326$	−7.60089	−0.420975
$327$	2.66132	0.147171
$328$	44.9010	2.47924
$329$	−18.2210	−1.00456
$330$	1.37611	0.0757525
$331$	18.8230	1.03461	0.517303	−	0.855802i	$-0.326936\pi$
$331$	18.8230	1.03461	0.517303	+	0.855802i	$0.326936\pi$
$332$	21.9745	1.20601
$333$	−9.01060	−0.493778
$334$	21.6603	1.18520
$335$	8.46825	0.462670
$336$	−1.72015	−0.0938421
$337$	24.9740	1.36042	0.680211	−	0.733017i	$-0.261888\pi$
$337$	24.9740	1.36042	0.680211	+	0.733017i	$0.261888\pi$
$338$	24.4322	1.32894
$339$	4.30479	0.233804
$340$	40.6871	2.20657
$341$	1.69038	0.0915394
$342$	4.04362	0.218654
$343$	−20.0076	−1.08031
$344$	3.60353	0.194289
$345$	−2.40137	−0.129285
$346$	−51.6255	−2.77541
$347$	1.78528	0.0958390	0.0479195	−	0.998851i	$-0.484741\pi$
$347$	1.78528	0.0958390	0.0479195	+	0.998851i	$0.484741\pi$
$348$	2.43652	0.130611
$349$	−28.2923	−1.51445	−0.757226	−	0.653153i	$-0.773446\pi$
$349$	−28.2923	−1.51445	−0.757226	+	0.653153i	$0.773446\pi$
$350$	14.6764	0.784486
$351$	3.66199	0.195463
$352$	−3.12890	−0.166771
$353$	0.673531	0.0358484	0.0179242	−	0.999839i	$-0.494294\pi$
$353$	0.673531	0.0358484	0.0179242	+	0.999839i	$0.494294\pi$
$354$	−6.24496	−0.331916
$355$	−22.2188	−1.17925
$356$	42.6629	2.26113
$357$	6.44140	0.340915
$358$	−42.2689	−2.23398
$359$	−21.2194	−1.11992	−0.559958	−	0.828521i	$-0.689183\pi$
$359$	−21.2194	−1.11992	−0.559958	+	0.828521i	$0.689183\pi$
$360$	−16.9422	−0.892931
$361$	−18.6444	−0.981282
$362$	17.6295	0.926586
$363$	−0.379878	−0.0199384
$364$	13.8515	0.726015
$365$	−3.65934	−0.191539
$366$	6.67877	0.349105
$367$	11.7727	0.614528	0.307264	−	0.951624i	$-0.400587\pi$
$367$	11.7727	0.614528	0.307264	+	0.951624i	$0.400587\pi$
$368$	−8.11170	−0.422852
$369$	32.9736	1.71654
$370$	11.4301	0.594225
$371$	−4.85260	−0.251934
$372$	2.33595	0.121113
$373$	34.7053	1.79697	0.898485	−	0.439003i	$-0.144668\pi$
$373$	34.7053	1.79697	0.898485	+	0.439003i	$0.144668\pi$
$374$	−17.4069	−0.900087
$375$	−4.44663	−0.229623
$376$	30.6341	1.57983
$377$	−2.90260	−0.149492
$378$	−12.2164	−0.628345
$379$	11.8470	0.608542	0.304271	−	0.952586i	$-0.401587\pi$
$379$	11.8470	0.608542	0.304271	+	0.952586i	$0.401587\pi$
$380$	−3.30975	−0.169787
$381$	−5.63172	−0.288522
$382$	5.93392	0.303606
$383$	2.81172	0.143672	0.0718360	−	0.997416i	$-0.477114\pi$
$383$	2.81172	0.143672	0.0718360	+	0.997416i	$0.477114\pi$
$384$	−7.85552	−0.400875
$385$	3.52878	0.179843
$386$	−0.753900	−0.0383725
$387$	2.64630	0.134519
$388$	1.84782	0.0938090
$389$	29.2873	1.48493	0.742464	−	0.669886i	$-0.233657\pi$
$389$	29.2873	1.48493	0.742464	+	0.669886i	$0.233657\pi$
$390$	−2.26542	−0.114714
$391$	30.3756	1.53616
$392$	6.41712	0.324113
$393$	−1.17327	−0.0591835
$394$	−62.7513	−3.16136
$395$	−4.90404	−0.246749
$396$	10.3883	0.522032
$397$	12.9833	0.651613	0.325806	−	0.945437i	$-0.394364\pi$
$397$	12.9833	0.651613	0.325806	+	0.945437i	$0.394364\pi$
$398$	21.7995	1.09271
$399$	−0.523984	−0.0262320
$400$	−5.23181	−0.261591
$401$	19.2524	0.961419	0.480709	−	0.876880i	$-0.340379\pi$
$401$	19.2524	0.961419	0.480709	+	0.876880i	$0.340379\pi$
$402$	−5.00651	−0.249702
$403$	−2.78279	−0.138620
$404$	6.58069	0.327402
$405$	−11.7812	−0.585412
$406$	9.68311	0.480564
$407$	−3.15531	−0.156403
$408$	−10.8296	−0.536146
$409$	−34.0648	−1.68440	−0.842199	−	0.539167i	$-0.818739\pi$
$409$	−34.0648	−1.68440	−0.842199	+	0.539167i	$0.818739\pi$
$410$	−41.8277	−2.06572
$411$	7.67331	0.378497
$412$	−59.7680	−2.94456
$413$	−16.0140	−0.787999
$414$	−28.0945	−1.38077
$415$	−9.21600	−0.452396
$416$	5.15094	0.252545
$417$	−4.51380	−0.221042
$418$	1.41598	0.0692581
$419$	−26.3897	−1.28922	−0.644610	−	0.764512i	$-0.722980\pi$
$419$	−26.3897	−1.28922	−0.644610	+	0.764512i	$0.722980\pi$
$420$	4.87644	0.237946
$421$	−4.56363	−0.222418	−0.111209	−	0.993797i	$-0.535472\pi$
$421$	−4.56363	−0.222418	−0.111209	+	0.993797i	$0.535472\pi$
$422$	−24.3389	−1.18480
$423$	22.4965	1.09382
$424$	8.15844	0.396209
$425$	19.5914	0.950321
$426$	13.1360	0.636440
$427$	17.1265	0.828808
$428$	0.472623	0.0228451
$429$	0.625373	0.0301933
$430$	−3.35688	−0.161883
$431$	−4.27167	−0.205759	−0.102880	−	0.994694i	$-0.532806\pi$
$431$	−4.27167	−0.205759	−0.102880	+	0.994694i	$0.532806\pi$
$432$	4.35489	0.209525
$433$	31.0919	1.49418	0.747090	−	0.664723i	$-0.231450\pi$
$433$	31.0919	1.49418	0.747090	+	0.664723i	$0.231450\pi$
$434$	9.28339	0.445617
$435$	−1.02187	−0.0489947
$436$	−25.4851	−1.22051
$437$	−2.47094	−0.118201
$438$	2.16343	0.103373
$439$	32.6791	1.55969	0.779844	−	0.625974i	$-0.215298\pi$
$439$	32.6791	1.55969	0.779844	+	0.625974i	$0.215298\pi$
$440$	−5.93277	−0.282834
$441$	4.71249	0.224404
$442$	28.6560	1.36302
$443$	18.8986	0.897897	0.448949	−	0.893558i	$-0.351799\pi$
$443$	18.8986	0.897897	0.448949	+	0.893558i	$0.351799\pi$
$444$	−4.36033	−0.206932
$445$	−17.8926	−0.848190
$446$	3.58505	0.169757
$447$	−1.07860	−0.0510161
$448$	−26.2399	−1.23972
$449$	−7.56865	−0.357187	−0.178593	−	0.983923i	$-0.557155\pi$
$449$	−7.56865	−0.357187	−0.178593	+	0.983923i	$0.557155\pi$
$450$	−18.1202	−0.854192
$451$	11.5466	0.543709
$452$	−41.2231	−1.93897
$453$	6.76835	0.318005
$454$	−34.6148	−1.62455
$455$	−5.80924	−0.272341
$456$	0.880950	0.0412543
$457$	11.6773	0.546242	0.273121	−	0.961980i	$-0.411944\pi$
$457$	11.6773	0.546242	0.273121	+	0.961980i	$0.411944\pi$
$458$	16.5111	0.771514
$459$	−16.3076	−0.761174
$460$	22.9957	1.07218
$461$	−4.24332	−0.197631	−0.0988157	−	0.995106i	$-0.531505\pi$
$461$	−4.24332	−0.197631	−0.0988157	+	0.995106i	$0.531505\pi$
$462$	−2.08625	−0.0970610
$463$	14.9966	0.696949	0.348474	−	0.937318i	$-0.386700\pi$
$463$	14.9966	0.696949	0.348474	+	0.937318i	$0.386700\pi$
$464$	−3.45182	−0.160247
$465$	−0.979684	−0.0454318
$466$	27.7059	1.28345
$467$	34.3602	1.59000	0.795001	−	0.606608i	$-0.207470\pi$
$467$	34.3602	1.59000	0.795001	+	0.606608i	$0.207470\pi$
$468$	−17.1017	−0.790526
$469$	−12.8383	−0.592815
$470$	−28.5373	−1.31633
$471$	−4.48209	−0.206524
$472$	26.9236	1.23926
$473$	0.926674	0.0426085
$474$	2.89931	0.133170
$475$	−1.59369	−0.0731234
$476$	−61.6835	−2.82726
$477$	5.99125	0.274321
$478$	1.43461	0.0656176
$479$	24.6064	1.12429	0.562147	−	0.827037i	$-0.309975\pi$
$479$	24.6064	1.12429	0.562147	+	0.827037i	$0.309975\pi$
$480$	1.81340	0.0827698
$481$	5.19441	0.236845
$482$	3.61806	0.164798
$483$	3.64058	0.165652
$484$	3.63775	0.165352
$485$	−0.774968	−0.0351895
$486$	22.8103	1.03470
$487$	0.127499	0.00577752	0.00288876	−	0.999996i	$-0.499080\pi$
$487$	0.127499	0.00577752	0.00288876	+	0.999996i	$0.499080\pi$
$488$	−28.7939	−1.30344
$489$	−1.21606	−0.0549923
$490$	−5.97789	−0.270054
$491$	−36.3290	−1.63951	−0.819753	−	0.572717i	$-0.805889\pi$
$491$	−36.3290	−1.63951	−0.819753	+	0.572717i	$0.805889\pi$
$492$	15.9563	0.719365
$493$	12.9259	0.582153
$494$	−2.33106	−0.104879
$495$	−4.35680	−0.195824
$496$	−3.30933	−0.148593
$497$	33.6848	1.51097
$498$	5.44858	0.244157
$499$	−16.1578	−0.723324	−0.361662	−	0.932309i	$-0.617791\pi$
$499$	−16.1578	−0.723324	−0.361662	+	0.932309i	$0.617791\pi$
$500$	42.5814	1.90430
$501$	3.46542	0.154824
$502$	31.6405	1.41219
$503$	−23.5017	−1.04789	−0.523943	−	0.851753i	$-0.675540\pi$
$503$	−23.5017	−1.04789	−0.523943	+	0.851753i	$0.675540\pi$
$504$	25.6851	1.14410
$505$	−2.75991	−0.122814
$506$	−9.83809	−0.437356
$507$	3.90890	0.173600
$508$	53.9299	2.39275
$509$	39.0973	1.73296	0.866478	−	0.499216i	$-0.166378\pi$
$509$	39.0973	1.73296	0.866478	+	0.499216i	$0.166378\pi$
$510$	10.0884	0.446721
$511$	5.54772	0.245417
$512$	21.3516	0.943615
$513$	1.32656	0.0585692
$514$	−72.8382	−3.21276
$515$	25.0664	1.10456
$516$	1.28057	0.0563741
$517$	7.87778	0.346465
$518$	−17.3286	−0.761375
$519$	−8.25954	−0.362554
$520$	9.76680	0.428302
$521$	28.1116	1.23159	0.615796	−	0.787906i	$-0.288835\pi$
$521$	28.1116	1.23159	0.615796	+	0.787906i	$0.288835\pi$
$522$	−11.9552	−0.523266
$523$	−32.9979	−1.44290	−0.721448	−	0.692468i	$-0.756523\pi$
$523$	−32.9979	−1.44290	−0.721448	+	0.692468i	$0.756523\pi$
$524$	11.2353	0.490818
$525$	2.34807	0.102478
$526$	76.3978	3.33110
$527$	12.3923	0.539818
$528$	0.743702	0.0323655
$529$	−5.83218	−0.253573
$530$	−7.60003	−0.330124
$531$	19.7717	0.858019
$532$	5.01773	0.217546
$533$	−19.0085	−0.823352
$534$	10.5783	0.457766
$535$	−0.198216	−0.00856961
$536$	21.5843	0.932301
$537$	−6.76259	−0.291827
$538$	−10.1298	−0.436728
$539$	1.65021	0.0710795
$540$	−12.3456	−0.531270
$541$	−5.22353	−0.224577	−0.112289	−	0.993676i	$-0.535818\pi$
$541$	−5.22353	−0.224577	−0.112289	+	0.993676i	$0.535818\pi$
$542$	16.6322	0.714413
$543$	2.82053	0.121041
$544$	−22.9382	−0.983466
$545$	10.6883	0.457837
$546$	3.43448	0.146982
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	−73.4804	−3.13893
$549$	−21.1451	−0.902453
$550$	−6.34528	−0.270563
$551$	−1.05147	−0.0447943
$552$	−6.12073	−0.260516
$553$	7.43475	0.316158
$554$	76.1624	3.23583
$555$	1.82870	0.0776241
$556$	43.2246	1.83313
$557$	−28.2444	−1.19675	−0.598377	−	0.801215i	$-0.704187\pi$
$557$	−28.2444	−1.19675	−0.598377	+	0.801215i	$0.704187\pi$
$558$	−11.4617	−0.485213
$559$	−1.52553	−0.0645231
$560$	−6.90843	−0.291934
$561$	−2.78491	−0.117579
$562$	29.6270	1.24974
$563$	32.5021	1.36980	0.684900	−	0.728637i	$-0.259846\pi$
$563$	32.5021	1.36980	0.684900	+	0.728637i	$0.259846\pi$
$564$	10.8863	0.458397
$565$	17.2888	0.727344
$566$	42.5214	1.78731
$567$	17.8608	0.750084
$568$	−56.6326	−2.37625
$569$	−4.88569	−0.204819	−0.102409	−	0.994742i	$-0.532655\pi$
$569$	−4.88569	−0.204819	−0.102409	+	0.994742i	$0.532655\pi$
$570$	−0.820653	−0.0343734
$571$	10.1483	0.424692	0.212346	−	0.977195i	$-0.431890\pi$
$571$	10.1483	0.424692	0.212346	+	0.977195i	$0.431890\pi$
$572$	−5.98863	−0.250397
$573$	0.949364	0.0396603
$574$	63.4126	2.64679
$575$	11.0727	0.461765
$576$	32.3970	1.34988
$577$	18.4933	0.769888	0.384944	−	0.922940i	$-0.374221\pi$
$577$	18.4933	0.769888	0.384944	+	0.922940i	$0.374221\pi$
$578$	−87.2461	−3.62896
$579$	−0.120616	−0.00501263
$580$	9.78549	0.406321
$581$	13.9719	0.579651
$582$	0.458168	0.0189917
$583$	2.09800	0.0868904
$584$	−9.32712	−0.385959
$585$	7.17237	0.296541
$586$	38.6538	1.59678
$587$	−33.4541	−1.38080	−0.690400	−	0.723428i	$-0.742565\pi$
$587$	−33.4541	−1.38080	−0.690400	+	0.723428i	$0.742565\pi$
$588$	2.28043	0.0940433
$589$	−1.00807	−0.0415368
$590$	−25.0808	−1.03256
$591$	−10.0395	−0.412972
$592$	6.17727	0.253884
$593$	20.0698	0.824168	0.412084	−	0.911146i	$-0.364801\pi$
$593$	20.0698	0.824168	0.412084	+	0.911146i	$0.364801\pi$
$594$	5.28172	0.216712
$595$	25.8697	1.06056
$596$	10.3288	0.423084
$597$	3.48769	0.142742
$598$	16.1959	0.662300
$599$	−2.26682	−0.0926197	−0.0463098	−	0.998927i	$-0.514746\pi$
$599$	−2.26682	−0.0926197	−0.0463098	+	0.998927i	$0.514746\pi$
$600$	−3.94769	−0.161164
$601$	21.4662	0.875626	0.437813	−	0.899066i	$-0.355753\pi$
$601$	21.4662	0.875626	0.437813	+	0.899066i	$0.355753\pi$
$602$	5.08919	0.207420
$603$	15.8507	0.645491
$604$	−64.8144	−2.63726
$605$	−1.52566	−0.0620267
$606$	1.63168	0.0662826
$607$	−10.0336	−0.407252	−0.203626	−	0.979049i	$-0.565273\pi$
$607$	−10.0336	−0.407252	−0.203626	+	0.979049i	$0.565273\pi$
$608$	1.86594	0.0756738
$609$	1.54920	0.0627766
$610$	26.8231	1.08604
$611$	−12.9688	−0.524660
$612$	76.1574	3.07848
$613$	−5.97121	−0.241175	−0.120587	−	0.992703i	$-0.538478\pi$
$613$	−5.97121	−0.241175	−0.120587	+	0.992703i	$0.538478\pi$
$614$	45.9730	1.85532
$615$	−6.69199	−0.269847
$616$	8.99435	0.362393
$617$	−11.7149	−0.471622	−0.235811	−	0.971799i	$-0.575775\pi$
$617$	−11.7149	−0.471622	−0.235811	+	0.971799i	$0.575775\pi$
$618$	−14.8195	−0.596127
$619$	33.8837	1.36190	0.680950	−	0.732330i	$-0.261567\pi$
$619$	33.8837	1.36190	0.680950	+	0.732330i	$0.261567\pi$
$620$	9.38155	0.376772
$621$	−9.21680	−0.369858
$622$	76.5717	3.07025
$623$	27.1260	1.08678
$624$	−1.22432	−0.0490119
$625$	−4.49653	−0.179861
$626$	−66.3612	−2.65233
$627$	0.226543	0.00904724
$628$	42.9209	1.71273
$629$	−23.1318	−0.922325
$630$	−23.9271	−0.953277
$631$	35.4607	1.41167	0.705835	−	0.708376i	$-0.250572\pi$
$631$	35.4607	1.41167	0.705835	+	0.708376i	$0.250572\pi$
$632$	−12.4997	−0.497211
$633$	−3.89396	−0.154771
$634$	−35.6571	−1.41612
$635$	−22.6179	−0.897566
$636$	2.89924	0.114962
$637$	−2.71665	−0.107637
$638$	−4.18645	−0.165743
$639$	−41.5888	−1.64523
$640$	−31.5491	−1.24709
$641$	5.77380	0.228051	0.114026	−	0.993478i	$-0.463625\pi$
$641$	5.77380	0.228051	0.114026	+	0.993478i	$0.463625\pi$
$642$	0.117187	0.00462500
$643$	20.6036	0.812528	0.406264	−	0.913756i	$-0.366831\pi$
$643$	20.6036	0.812528	0.406264	+	0.913756i	$0.366831\pi$
$644$	−34.8626	−1.37378
$645$	−0.537066	−0.0211470
$646$	10.3807	0.408422
$647$	−3.12303	−0.122779	−0.0613895	−	0.998114i	$-0.519553\pi$
$647$	−3.12303	−0.122779	−0.0613895	+	0.998114i	$0.519553\pi$
$648$	−30.0285	−1.17963
$649$	6.92361	0.271775
$650$	10.4459	0.409721
$651$	1.48524	0.0582113
$652$	11.6451	0.456059
$653$	23.5311	0.920845	0.460422	−	0.887700i	$-0.347698\pi$
$653$	23.5311	0.920845	0.460422	+	0.887700i	$0.347698\pi$
$654$	−6.31903	−0.247094
$655$	−4.71204	−0.184115
$656$	−22.6052	−0.882586
$657$	−6.84948	−0.267224
$658$	43.2639	1.68660
$659$	44.6544	1.73949	0.869744	−	0.493503i	$-0.164284\pi$
$659$	44.6544	1.73949	0.869744	+	0.493503i	$0.164284\pi$
$660$	−2.10831	−0.0820658
$661$	−13.6967	−0.532741	−0.266371	−	0.963871i	$-0.585825\pi$
$661$	−13.6967	−0.532741	−0.266371	+	0.963871i	$0.585825\pi$
$662$	−44.6933	−1.73705
$663$	4.58465	0.178053
$664$	−23.4902	−0.911598
$665$	−2.10441	−0.0816055
$666$	21.3947	0.829028
$667$	7.30551	0.282871
$668$	−33.1853	−1.28398
$669$	0.573570	0.0221755
$670$	−20.1070	−0.776800
$671$	−7.40456	−0.285850
$672$	−2.74919	−0.106052
$673$	28.3961	1.09459	0.547294	−	0.836940i	$-0.315658\pi$
$673$	28.3961	1.09459	0.547294	+	0.836940i	$0.315658\pi$
$674$	−59.2982	−2.28408
$675$	−5.94457	−0.228807
$676$	−37.4320	−1.43969
$677$	21.7804	0.837088	0.418544	−	0.908197i	$-0.362541\pi$
$677$	21.7804	0.837088	0.418544	+	0.908197i	$0.362541\pi$
$678$	−10.2213	−0.392546
$679$	1.17489	0.0450880
$680$	−43.4936	−1.66790
$681$	−5.53801	−0.212217
$682$	−4.01364	−0.153690
$683$	47.0415	1.79999	0.899997	−	0.435896i	$-0.143568\pi$
$683$	47.0415	1.79999	0.899997	+	0.435896i	$0.143568\pi$
$684$	−6.19512	−0.236876
$685$	30.8173	1.17747
$686$	47.5059	1.81379
$687$	2.64160	0.100783
$688$	−1.81418	−0.0691651
$689$	−3.45383	−0.131580
$690$	5.70179	0.217064
$691$	−45.6569	−1.73687	−0.868435	−	0.495804i	$-0.834874\pi$
$691$	−45.6569	−1.73687	−0.868435	+	0.495804i	$0.834874\pi$
$692$	79.0942	3.00671
$693$	6.60511	0.250907
$694$	−4.23897	−0.160909
$695$	−18.1282	−0.687641
$696$	−2.60459	−0.0987266
$697$	84.6490	3.20631
$698$	67.1771	2.54269
$699$	4.43266	0.167659
$700$	−22.4853	−0.849865
$701$	1.01791	0.0384460	0.0192230	−	0.999815i	$-0.493881\pi$
$701$	1.01791	0.0384460	0.0192230	+	0.999815i	$0.493881\pi$
$702$	−8.69501	−0.328172
$703$	1.88169	0.0709692
$704$	11.3447	0.427570
$705$	−4.56567	−0.171953
$706$	−1.59923	−0.0601878
$707$	4.18415	0.157361
$708$	9.56776	0.359578
$709$	37.3897	1.40420	0.702099	−	0.712079i	$-0.252246\pi$
$709$	37.3897	1.40420	0.702099	+	0.712079i	$0.252246\pi$
$710$	52.7563	1.97991
$711$	−9.17929	−0.344250
$712$	−45.6056	−1.70914
$713$	7.00394	0.262300
$714$	−15.2944	−0.572380
$715$	2.51160	0.0939286
$716$	64.7592	2.42016
$717$	0.229523	0.00857169
$718$	50.3832	1.88028
$719$	−38.6234	−1.44041	−0.720205	−	0.693761i	$-0.755952\pi$
$719$	−38.6234	−1.44041	−0.720205	+	0.693761i	$0.755952\pi$
$720$	8.52948	0.317875
$721$	−38.0018	−1.41526
$722$	44.2691	1.64752
$723$	0.578852	0.0215277
$724$	−27.0097	−1.00381
$725$	4.71184	0.174993
$726$	0.901981	0.0334757
$727$	20.6368	0.765378	0.382689	−	0.923877i	$-0.374998\pi$
$727$	20.6368	0.765378	0.382689	+	0.923877i	$0.374998\pi$
$728$	−14.8069	−0.548780
$729$	−19.5168	−0.722843
$730$	8.68872	0.321584
$731$	6.79351	0.251267
$732$	−10.2324	−0.378200
$733$	−29.8075	−1.10097	−0.550483	−	0.834846i	$-0.685556\pi$
$733$	−29.8075	−1.10097	−0.550483	+	0.834846i	$0.685556\pi$
$734$	−27.9529	−1.03176
$735$	−0.956400	−0.0352774
$736$	−12.9643	−0.477871
$737$	5.55057	0.204458
$738$	−78.2923	−2.88198
$739$	−4.96854	−0.182771	−0.0913853	−	0.995816i	$-0.529129\pi$
$739$	−4.96854	−0.182771	−0.0913853	+	0.995816i	$0.529129\pi$
$740$	−17.5118	−0.643748
$741$	−0.372945	−0.0137005
$742$	11.5220	0.422986
$743$	8.27933	0.303739	0.151870	−	0.988401i	$-0.451471\pi$
$743$	8.27933	0.303739	0.151870	+	0.988401i	$0.451471\pi$
$744$	−2.49707	−0.0915471
$745$	−4.33184	−0.158706
$746$	−82.4040	−3.01703
$747$	−17.2503	−0.631157
$748$	26.6686	0.975101
$749$	0.300504	0.0109802
$750$	10.5581	0.385526
$751$	46.2989	1.68947	0.844735	−	0.535185i	$-0.179758\pi$
$751$	46.2989	1.68947	0.844735	+	0.535185i	$0.179758\pi$
$752$	−15.4226	−0.562406
$753$	5.06215	0.184475
$754$	6.89193	0.250989
$755$	27.1828	0.989285
$756$	18.7165	0.680712
$757$	−18.3597	−0.667295	−0.333647	−	0.942698i	$-0.608279\pi$
$757$	−18.3597	−0.667295	−0.333647	+	0.942698i	$0.608279\pi$
$758$	−28.1296	−1.02171
$759$	−1.57399	−0.0571322
$760$	3.53804	0.128338
$761$	48.2636	1.74955	0.874777	−	0.484526i	$-0.161008\pi$
$761$	48.2636	1.74955	0.874777	+	0.484526i	$0.161008\pi$
$762$	13.3719	0.484414
$763$	−16.2040	−0.586623
$764$	−9.09121	−0.328908
$765$	−31.9400	−1.15479
$766$	−6.67613	−0.241218
$767$	−11.3980	−0.411556
$768$	10.0329	0.362031
$769$	−21.0854	−0.760358	−0.380179	−	0.924913i	$-0.624138\pi$
$769$	−21.0854	−0.760358	−0.380179	+	0.924913i	$0.624138\pi$
$770$	−8.37872	−0.301948
$771$	−11.6533	−0.419685
$772$	1.15503	0.0415705
$773$	35.3472	1.27135	0.635674	−	0.771957i	$-0.280722\pi$
$773$	35.3472	1.27135	0.635674	+	0.771957i	$0.280722\pi$
$774$	−6.28335	−0.225850
$775$	4.51734	0.162268
$776$	−1.97528	−0.0709084
$777$	−2.77239	−0.0994591
$778$	−69.5397	−2.49312
$779$	−6.88589	−0.246712
$780$	3.47079	0.124274
$781$	−14.5635	−0.521122
$782$	−72.1237	−2.57914
$783$	−3.92208	−0.140164
$784$	−3.23068	−0.115381
$785$	−18.0008	−0.642477
$786$	2.78580	0.0993663
$787$	31.7552	1.13195	0.565976	−	0.824422i	$-0.308500\pi$
$787$	31.7552	1.13195	0.565976	+	0.824422i	$0.308500\pi$
$788$	96.1397	3.42484
$789$	12.2228	0.435145
$790$	11.6441	0.414280
$791$	−26.2105	−0.931940
$792$	−11.1048	−0.394594
$793$	12.1897	0.432870
$794$	−30.8275	−1.09403
$795$	−1.21593	−0.0431244
$796$	−33.3985	−1.18378
$797$	−18.6362	−0.660129	−0.330064	−	0.943958i	$-0.607070\pi$
$797$	−18.6362	−0.660129	−0.330064	+	0.943958i	$0.607070\pi$
$798$	1.24415	0.0440423
$799$	57.7526	2.04314
$800$	−8.36160	−0.295627
$801$	−33.4910	−1.18335
$802$	−45.7128	−1.61417
$803$	−2.39854	−0.0846425
$804$	7.67035	0.270512
$805$	14.6212	0.515329
$806$	6.60743	0.232737
$807$	−1.62067	−0.0570502
$808$	−7.03461	−0.247477
$809$	18.7206	0.658182	0.329091	−	0.944298i	$-0.393258\pi$
$809$	18.7206	0.658182	0.329091	+	0.944298i	$0.393258\pi$
$810$	27.9732	0.982879
$811$	33.9505	1.19216	0.596082	−	0.802923i	$-0.296723\pi$
$811$	33.9505	1.19216	0.596082	+	0.802923i	$0.296723\pi$
$812$	−14.8352	−0.520615
$813$	2.66097	0.0933244
$814$	7.49195	0.262593
$815$	−4.88391	−0.171076
$816$	5.45213	0.190863
$817$	−0.552627	−0.0193340
$818$	80.8834	2.82802
$819$	−10.8736	−0.379955
$820$	64.0832	2.23788
$821$	0.942862	0.0329061	0.0164530	−	0.999865i	$-0.494763\pi$
$821$	0.942862	0.0329061	0.0164530	+	0.999865i	$0.494763\pi$
$822$	−18.2195	−0.635477
$823$	19.9823	0.696540	0.348270	−	0.937394i	$-0.386769\pi$
$823$	19.9823	0.696540	0.348270	+	0.937394i	$0.386769\pi$
$824$	63.8906	2.22573
$825$	−1.01518	−0.0353439
$826$	38.0237	1.32301
$827$	49.3839	1.71725	0.858624	−	0.512606i	$-0.171320\pi$
$827$	49.3839	1.71725	0.858624	+	0.512606i	$0.171320\pi$
$828$	43.0430	1.49585
$829$	31.0129	1.07712	0.538561	−	0.842587i	$-0.318968\pi$
$829$	31.0129	1.07712	0.538561	+	0.842587i	$0.318968\pi$
$830$	21.8824	0.759550
$831$	12.1852	0.422700
$832$	−18.6762	−0.647480
$833$	12.0978	0.419164
$834$	10.7175	0.371118
$835$	13.9177	0.481643
$836$	−2.16939	−0.0750301
$837$	−3.76017	−0.129971
$838$	62.6595	2.16454
$839$	44.5836	1.53920	0.769598	−	0.638529i	$-0.220457\pi$
$839$	44.5836	1.53920	0.769598	+	0.638529i	$0.220457\pi$
$840$	−5.21279	−0.179858
$841$	−25.8912	−0.892802
$842$	10.8359	0.373428
$843$	4.74001	0.163255
$844$	37.2890	1.28354
$845$	15.6988	0.540055
$846$	−53.4156	−1.83647
$847$	2.31296	0.0794743
$848$	−4.10734	−0.141047
$849$	6.80298	0.233478
$850$	−46.5177	−1.59554
$851$	−13.0737	−0.448162
$852$	−20.1253	−0.689482
$853$	19.1985	0.657345	0.328672	−	0.944444i	$-0.393399\pi$
$853$	19.1985	0.657345	0.328672	+	0.944444i	$0.393399\pi$
$854$	−40.6650	−1.39153
$855$	2.59820	0.0888567
$856$	−0.505223	−0.0172682
$857$	−27.0414	−0.923716	−0.461858	−	0.886954i	$-0.652817\pi$
$857$	−27.0414	−0.923716	−0.461858	+	0.886954i	$0.652817\pi$
$858$	−1.48488	−0.0506930
$859$	−28.9901	−0.989130	−0.494565	−	0.869141i	$-0.664673\pi$
$859$	−28.9901	−0.989130	−0.494565	+	0.869141i	$0.664673\pi$
$860$	5.14300	0.175375
$861$	10.1454	0.345753
$862$	10.1426	0.345460
$863$	−52.5172	−1.78771	−0.893853	−	0.448361i	$-0.852008\pi$
$863$	−52.5172	−1.78771	−0.893853	+	0.448361i	$0.852008\pi$
$864$	6.96008	0.236787
$865$	−33.1717	−1.12787
$866$	−73.8244	−2.50865
$867$	−13.9585	−0.474054
$868$	−14.2229	−0.482755
$869$	−3.21438	−0.109041
$870$	2.42631	0.0822598
$871$	−9.13760	−0.309616
$872$	27.2430	0.922563
$873$	−1.45057	−0.0490944
$874$	5.86700	0.198454
$875$	27.0741	0.915273
$876$	−3.31454	−0.111988
$877$	−17.3204	−0.584867	−0.292434	−	0.956286i	$-0.594465\pi$
$877$	−17.3204	−0.584867	−0.292434	+	0.956286i	$0.594465\pi$
$878$	−77.5931	−2.61864
$879$	6.18421	0.208588
$880$	2.98683	0.100686
$881$	−17.9414	−0.604462	−0.302231	−	0.953235i	$-0.597731\pi$
$881$	−17.9414	−0.604462	−0.302231	+	0.953235i	$0.597731\pi$
$882$	−11.1893	−0.376764
$883$	−7.93763	−0.267123	−0.133561	−	0.991041i	$-0.542641\pi$
$883$	−7.93763	−0.267123	−0.133561	+	0.991041i	$0.542641\pi$
$884$	−43.9031	−1.47662
$885$	−4.01267	−0.134884
$886$	−44.8726	−1.50753
$887$	45.4386	1.52568	0.762840	−	0.646587i	$-0.223804\pi$
$887$	45.4386	1.52568	0.762840	+	0.646587i	$0.223804\pi$
$888$	4.66109	0.156416
$889$	34.2898	1.15004
$890$	42.4841	1.42407
$891$	−7.72206	−0.258699
$892$	−5.49257	−0.183905
$893$	−4.69796	−0.157211
$894$	2.56102	0.0856535
$895$	−27.1597	−0.907848
$896$	47.8298	1.59788
$897$	2.59117	0.0865168
$898$	17.9710	0.599699
$899$	2.98043	0.0994028
$900$	27.7614	0.925382
$901$	15.3806	0.512402
$902$	−27.4162	−0.912860
$903$	0.814216	0.0270954
$904$	44.0665	1.46563
$905$	11.3277	0.376547
$906$	−16.0707	−0.533915
$907$	31.2975	1.03922	0.519609	−	0.854404i	$-0.326078\pi$
$907$	31.2975	1.03922	0.519609	+	0.854404i	$0.326078\pi$
$908$	53.0325	1.75995
$909$	−5.16595	−0.171344
$910$	13.7934	0.457248
$911$	−51.8452	−1.71771	−0.858855	−	0.512219i	$-0.828824\pi$
$911$	−51.8452	−1.71771	−0.858855	+	0.512219i	$0.828824\pi$
$912$	−0.443511	−0.0146861
$913$	−6.04068	−0.199917
$914$	−27.7266	−0.917114
$915$	4.29141	0.141870
$916$	−25.2963	−0.835812
$917$	7.14367	0.235905
$918$	38.7207	1.27797
$919$	−22.2196	−0.732958	−0.366479	−	0.930426i	$-0.619437\pi$
$919$	−22.2196	−0.732958	−0.366479	+	0.930426i	$0.619437\pi$
$920$	−24.5819	−0.810441
$921$	7.35520	0.242362
$922$	10.0753	0.331813
$923$	23.9750	0.789148
$924$	3.19629	0.105150
$925$	−8.43217	−0.277248
$926$	−35.6077	−1.17014
$927$	46.9188	1.54102
$928$	−5.51677	−0.181097
$929$	−13.1563	−0.431643	−0.215822	−	0.976433i	$-0.569243\pi$
$929$	−13.1563	−0.431643	−0.215822	+	0.976433i	$0.569243\pi$
$930$	2.32616	0.0762777
$931$	−0.984111	−0.0322529
$932$	−42.4476	−1.39042
$933$	12.2507	0.401069
$934$	−81.5847	−2.66953
$935$	−11.1847	−0.365778
$936$	18.2813	0.597543
$937$	34.2681	1.11949	0.559744	−	0.828665i	$-0.310899\pi$
$937$	34.2681	1.11949	0.559744	+	0.828665i	$0.310899\pi$
$938$	30.4831	0.995308
$939$	−10.6171	−0.346476
$940$	43.7214	1.42603
$941$	−34.9287	−1.13864	−0.569321	−	0.822115i	$-0.692794\pi$
$941$	−34.9287	−1.13864	−0.569321	+	0.822115i	$0.692794\pi$
$942$	10.6423	0.346743
$943$	47.8423	1.55796
$944$	−13.5546	−0.441165
$945$	−7.84960	−0.255348
$946$	−2.20029	−0.0715376
$947$	18.7070	0.607894	0.303947	−	0.952689i	$-0.401695\pi$
$947$	18.7070	0.607894	0.303947	+	0.952689i	$0.401695\pi$
$948$	−4.44197	−0.144268
$949$	3.94858	0.128176
$950$	3.78404	0.122771
$951$	−5.70476	−0.184989
$952$	65.9382	2.13707
$953$	1.52844	0.0495109	0.0247555	−	0.999694i	$-0.492119\pi$
$953$	1.52844	0.0495109	0.0247555	+	0.999694i	$0.492119\pi$
$954$	−14.2256	−0.460571
$955$	3.81281	0.123380
$956$	−2.19793	−0.0710863
$957$	−0.669789	−0.0216512
$958$	−58.4253	−1.88764
$959$	−46.7204	−1.50868
$960$	−6.57498	−0.212207
$961$	−28.1426	−0.907826
$962$	−12.3336	−0.397651
$963$	−0.371016	−0.0119558
$964$	−5.54315	−0.178533
$965$	−0.484414	−0.0155939
$966$	−8.64417	−0.278122
$967$	39.8422	1.28124	0.640619	−	0.767859i	$-0.278678\pi$
$967$	39.8422	1.28124	0.640619	+	0.767859i	$0.278678\pi$
$968$	−3.88867	−0.124987
$969$	1.66080	0.0533526
$970$	1.84008	0.0590814
$971$	7.42297	0.238214	0.119107	−	0.992881i	$-0.461997\pi$
$971$	7.42297	0.238214	0.119107	+	0.992881i	$0.461997\pi$
$972$	−34.9471	−1.12093
$973$	27.4831	0.881068
$974$	−0.302732	−0.00970017
$975$	1.67123	0.0535222
$976$	14.4962	0.464012
$977$	11.9392	0.381970	0.190985	−	0.981593i	$-0.438832\pi$
$977$	11.9392	0.381970	0.190985	+	0.981593i	$0.438832\pi$
$978$	2.88741	0.0923293
$979$	−11.7278	−0.374822
$980$	9.15858	0.292560
$981$	20.0062	0.638749
$982$	86.2595	2.75265
$983$	−18.7762	−0.598869	−0.299434	−	0.954117i	$-0.596798\pi$
$983$	−18.7762	−0.598869	−0.299434	+	0.954117i	$0.596798\pi$
$984$	−17.0569	−0.543754
$985$	−40.3205	−1.28472
$986$	−30.6912	−0.977406
$987$	6.92177	0.220322
$988$	3.57136	0.113620
$989$	3.83959	0.122092
$990$	10.3448	0.328778
$991$	44.9718	1.42858	0.714289	−	0.699851i	$-0.246750\pi$
$991$	44.9718	1.42858	0.714289	+	0.699851i	$0.246750\pi$
$992$	−5.28904	−0.167927
$993$	−7.15046	−0.226913
$994$	−79.9809	−2.53684
$995$	14.0072	0.444057
$996$	−8.34764	−0.264505
$997$	0.591835	0.0187436	0.00937181	−	0.999956i	$-0.497017\pi$
$997$	0.591835	0.0187436	0.00937181	+	0.999956i	$0.497017\pi$
$998$	38.3651	1.21443
$999$	7.01883	0.222066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.f.1.12	✓	121

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.f.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-2.37440 q^{2} -0.379878 q^{3} +3.63775 q^{4} -1.52566 q^{5} +0.901981 q^{6} +2.31296 q^{7} -3.88867 q^{8} -2.85569 q^{9} +O(q^{10})\)	\(q-2.37440 q^{2} -0.379878 q^{3} +3.63775 q^{4} -1.52566 q^{5} +0.901981 q^{6} +2.31296 q^{7} -3.88867 q^{8} -2.85569 q^{9} +3.62251 q^{10} -1.00000 q^{11} -1.38190 q^{12} +1.64625 q^{13} -5.49189 q^{14} +0.579563 q^{15} +1.95774 q^{16} -7.33107 q^{17} +6.78054 q^{18} +0.596356 q^{19} -5.54996 q^{20} -0.878644 q^{21} +2.37440 q^{22} -4.14341 q^{23} +1.47722 q^{24} -2.67238 q^{25} -3.90884 q^{26} +2.22445 q^{27} +8.41398 q^{28} -1.76317 q^{29} -1.37611 q^{30} -1.69038 q^{31} +3.12890 q^{32} +0.379878 q^{33} +17.4069 q^{34} -3.52878 q^{35} -10.3883 q^{36} +3.15531 q^{37} -1.41598 q^{38} -0.625373 q^{39} +5.93277 q^{40} -11.5466 q^{41} +2.08625 q^{42} -0.926674 q^{43} -3.63775 q^{44} +4.35680 q^{45} +9.83809 q^{46} -7.87778 q^{47} -0.743702 q^{48} -1.65021 q^{49} +6.34528 q^{50} +2.78491 q^{51} +5.98863 q^{52} -2.09800 q^{53} -5.28172 q^{54} +1.52566 q^{55} -8.99435 q^{56} -0.226543 q^{57} +4.18645 q^{58} -6.92361 q^{59} +2.10831 q^{60} +7.40456 q^{61} +4.01364 q^{62} -6.60511 q^{63} -11.3447 q^{64} -2.51160 q^{65} -0.901981 q^{66} -5.55057 q^{67} -26.6686 q^{68} +1.57399 q^{69} +8.37872 q^{70} +14.5635 q^{71} +11.1048 q^{72} +2.39854 q^{73} -7.49195 q^{74} +1.01518 q^{75} +2.16939 q^{76} -2.31296 q^{77} +1.48488 q^{78} +3.21438 q^{79} -2.98683 q^{80} +7.72206 q^{81} +27.4162 q^{82} +6.04068 q^{83} -3.19629 q^{84} +11.1847 q^{85} +2.20029 q^{86} +0.669789 q^{87} +3.88867 q^{88} +11.7278 q^{89} -10.3448 q^{90} +3.80770 q^{91} -15.0727 q^{92} +0.642140 q^{93} +18.7050 q^{94} -0.909833 q^{95} -1.18860 q^{96} +0.507957 q^{97} +3.91825 q^{98} +2.85569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 121 q + 2 q^{2} + 18 q^{3} + 138 q^{4} + 13 q^{5} + 10 q^{6} + 56 q^{7} + 12 q^{8} + 143 q^{9}+O(q^{10}) \) 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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