LMFDB - Embedded newform 6019.2.a.b.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6019,2,Mod(1,6019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6019, 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("6019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6019 = 13 \cdot 463 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6019.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:	$48.0619569766$
Analytic rank:	$1$
Dimension:	$101$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.31630 q^{2} +0.457851 q^{3} +3.36526 q^{4} +2.03378 q^{5} -1.06052 q^{6} +1.32033 q^{7} -3.16236 q^{8} -2.79037 q^{9} +O(q^{10})$	\(q-2.31630 q^{2} +0.457851 q^{3} +3.36526 q^{4} +2.03378 q^{5} -1.06052 q^{6} +1.32033 q^{7} -3.16236 q^{8} -2.79037 q^{9} -4.71086 q^{10} +4.58483 q^{11} +1.54079 q^{12} +1.00000 q^{13} -3.05828 q^{14} +0.931170 q^{15} +0.594458 q^{16} -0.622297 q^{17} +6.46335 q^{18} -5.34392 q^{19} +6.84421 q^{20} +0.604513 q^{21} -10.6199 q^{22} +2.37578 q^{23} -1.44789 q^{24} -0.863723 q^{25} -2.31630 q^{26} -2.65113 q^{27} +4.44324 q^{28} +3.13684 q^{29} -2.15687 q^{30} -3.94848 q^{31} +4.94777 q^{32} +2.09917 q^{33} +1.44143 q^{34} +2.68526 q^{35} -9.39033 q^{36} -4.72745 q^{37} +12.3781 q^{38} +0.457851 q^{39} -6.43155 q^{40} -5.96539 q^{41} -1.40023 q^{42} -4.69490 q^{43} +15.4291 q^{44} -5.67501 q^{45} -5.50302 q^{46} -6.32996 q^{47} +0.272173 q^{48} -5.25674 q^{49} +2.00064 q^{50} -0.284919 q^{51} +3.36526 q^{52} -0.195772 q^{53} +6.14082 q^{54} +9.32455 q^{55} -4.17534 q^{56} -2.44672 q^{57} -7.26588 q^{58} +6.46735 q^{59} +3.13363 q^{60} +8.02806 q^{61} +9.14588 q^{62} -3.68420 q^{63} -12.6495 q^{64} +2.03378 q^{65} -4.86231 q^{66} -4.55168 q^{67} -2.09419 q^{68} +1.08775 q^{69} -6.21987 q^{70} -4.11754 q^{71} +8.82416 q^{72} -16.2573 q^{73} +10.9502 q^{74} -0.395456 q^{75} -17.9837 q^{76} +6.05347 q^{77} -1.06052 q^{78} -4.10327 q^{79} +1.20900 q^{80} +7.15730 q^{81} +13.8177 q^{82} -9.54491 q^{83} +2.03434 q^{84} -1.26562 q^{85} +10.8748 q^{86} +1.43621 q^{87} -14.4989 q^{88} -0.827775 q^{89} +13.1451 q^{90} +1.32033 q^{91} +7.99512 q^{92} -1.80782 q^{93} +14.6621 q^{94} -10.8684 q^{95} +2.26534 q^{96} +11.9008 q^{97} +12.1762 q^{98} -12.7934 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) $ 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * 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 $

$2$	−2.31630	−1.63787	−0.818937	−	0.573884i	$-0.805436\pi$
$2$	−2.31630	−1.63787	−0.818937	+	0.573884i	$0.805436\pi$
$3$	0.457851	0.264340	0.132170	−	0.991227i	$-0.457805\pi$
$3$	0.457851	0.264340	0.132170	+	0.991227i	$0.457805\pi$
$4$	3.36526	1.68263
$5$	2.03378	0.909536	0.454768	−	0.890610i	$-0.349722\pi$
$5$	2.03378	0.909536	0.454768	+	0.890610i	$0.349722\pi$
$6$	−1.06052	−0.432956
$7$	1.32033	0.499036	0.249518	−	0.968370i	$-0.419728\pi$
$7$	1.32033	0.499036	0.249518	+	0.968370i	$0.419728\pi$
$8$	−3.16236	−1.11806
$9$	−2.79037	−0.930124
$10$	−4.71086	−1.48970
$11$	4.58483	1.38238	0.691189	−	0.722674i	$-0.257087\pi$
$11$	4.58483	1.38238	0.691189	+	0.722674i	$0.257087\pi$
$12$	1.54079	0.444787
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−3.05828	−0.817359
$15$	0.931170	0.240427
$16$	0.594458	0.148615
$17$	−0.622297	−0.150929	−0.0754646	−	0.997148i	$-0.524044\pi$
$17$	−0.622297	−0.150929	−0.0754646	+	0.997148i	$0.524044\pi$
$18$	6.46335	1.52343
$19$	−5.34392	−1.22598	−0.612990	−	0.790091i	$-0.710033\pi$
$19$	−5.34392	−1.22598	−0.612990	+	0.790091i	$0.710033\pi$
$20$	6.84421	1.53041
$21$	0.604513	0.131915
$22$	−10.6199	−2.26416
$23$	2.37578	0.495384	0.247692	−	0.968839i	$-0.420328\pi$
$23$	2.37578	0.495384	0.247692	+	0.968839i	$0.420328\pi$
$24$	−1.44789	−0.295549
$25$	−0.863723	−0.172745
$26$	−2.31630	−0.454264
$27$	−2.65113	−0.510210
$28$	4.44324	0.839694
$29$	3.13684	0.582497	0.291248	−	0.956647i	$-0.405929\pi$
$29$	3.13684	0.582497	0.291248	+	0.956647i	$0.405929\pi$
$30$	−2.15687	−0.393789
$31$	−3.94848	−0.709168	−0.354584	−	0.935024i	$-0.615378\pi$
$31$	−3.94848	−0.709168	−0.354584	+	0.935024i	$0.615378\pi$
$32$	4.94777	0.874650
$33$	2.09917	0.365418
$34$	1.44143	0.247203
$35$	2.68526	0.453891
$36$	−9.39033	−1.56506
$37$	−4.72745	−0.777188	−0.388594	−	0.921409i	$-0.627039\pi$
$37$	−4.72745	−0.777188	−0.388594	+	0.921409i	$0.627039\pi$
$38$	12.3781	2.00800
$39$	0.457851	0.0733148
$40$	−6.43155	−1.01692
$41$	−5.96539	−0.931637	−0.465819	−	0.884880i	$-0.654240\pi$
$41$	−5.96539	−0.931637	−0.465819	+	0.884880i	$0.654240\pi$
$42$	−1.40023	−0.216061
$43$	−4.69490	−0.715966	−0.357983	−	0.933728i	$-0.616535\pi$
$43$	−4.69490	−0.715966	−0.357983	+	0.933728i	$0.616535\pi$
$44$	15.4291	2.32603
$45$	−5.67501	−0.845981
$46$	−5.50302	−0.811377
$47$	−6.32996	−0.923319	−0.461660	−	0.887057i	$-0.652746\pi$
$47$	−6.32996	−0.923319	−0.461660	+	0.887057i	$0.652746\pi$
$48$	0.272173	0.0392848
$49$	−5.25674	−0.750963
$50$	2.00064	0.282934
$51$	−0.284919	−0.0398967
$52$	3.36526	0.466678
$53$	−0.195772	−0.0268914	−0.0134457	−	0.999910i	$-0.504280\pi$
$53$	−0.195772	−0.0268914	−0.0134457	+	0.999910i	$0.504280\pi$
$54$	6.14082	0.835659
$55$	9.32455	1.25732
$56$	−4.17534	−0.557954
$57$	−2.44672	−0.324076
$58$	−7.26588	−0.954056
$59$	6.46735	0.841977	0.420989	−	0.907066i	$-0.361683\pi$
$59$	6.46735	0.841977	0.420989	+	0.907066i	$0.361683\pi$
$60$	3.13363	0.404550
$61$	8.02806	1.02789	0.513944	−	0.857824i	$-0.328184\pi$
$61$	8.02806	1.02789	0.513944	+	0.857824i	$0.328184\pi$
$62$	9.14588	1.16153
$63$	−3.68420	−0.464166
$64$	−12.6495	−1.58118
$65$	2.03378	0.252260
$66$	−4.86231	−0.598509
$67$	−4.55168	−0.556076	−0.278038	−	0.960570i	$-0.589684\pi$
$67$	−4.55168	−0.556076	−0.278038	+	0.960570i	$0.589684\pi$
$68$	−2.09419	−0.253958
$69$	1.08775	0.130950
$70$	−6.21987	−0.743417
$71$	−4.11754	−0.488662	−0.244331	−	0.969692i	$-0.578568\pi$
$71$	−4.11754	−0.488662	−0.244331	+	0.969692i	$0.578568\pi$
$72$	8.82416	1.03994
$73$	−16.2573	−1.90277	−0.951387	−	0.307998i	$-0.900341\pi$
$73$	−16.2573	−1.90277	−0.951387	+	0.307998i	$0.900341\pi$
$74$	10.9502	1.27294
$75$	−0.395456	−0.0456634
$76$	−17.9837	−2.06287
$77$	6.05347	0.689857
$78$	−1.06052	−0.120080
$79$	−4.10327	−0.461654	−0.230827	−	0.972995i	$-0.574143\pi$
$79$	−4.10327	−0.461654	−0.230827	+	0.972995i	$0.574143\pi$
$80$	1.20900	0.135170
$81$	7.15730	0.795255
$82$	13.8177	1.52590
$83$	−9.54491	−1.04769	−0.523845	−	0.851814i	$-0.675503\pi$
$83$	−9.54491	−1.04769	−0.523845	+	0.851814i	$0.675503\pi$
$84$	2.03434	0.221965
$85$	−1.26562	−0.137275
$86$	10.8748	1.17266
$87$	1.43621	0.153977
$88$	−14.4989	−1.54559
$89$	−0.827775	−0.0877439	−0.0438720	−	0.999037i	$-0.513969\pi$
$89$	−0.827775	−0.0877439	−0.0438720	+	0.999037i	$0.513969\pi$
$90$	13.1451	1.38561
$91$	1.32033	0.138408
$92$	7.99512	0.833548
$93$	−1.80782	−0.187462
$94$	14.6621	1.51228
$95$	−10.8684	−1.11507
$96$	2.26534	0.231205
$97$	11.9008	1.20834	0.604170	−	0.796855i	$-0.293505\pi$
$97$	11.9008	1.20834	0.604170	+	0.796855i	$0.293505\pi$
$98$	12.1762	1.22998
$99$	−12.7934	−1.28578
$100$	−2.90665	−0.290665
$101$	−16.1159	−1.60359	−0.801796	−	0.597598i	$-0.796122\pi$
$101$	−16.1159	−1.60359	−0.801796	+	0.597598i	$0.796122\pi$
$102$	0.659959	0.0653457
$103$	2.98226	0.293851	0.146925	−	0.989148i	$-0.453062\pi$
$103$	2.98226	0.293851	0.146925	+	0.989148i	$0.453062\pi$
$104$	−3.16236	−0.310095
$105$	1.22945	0.119982
$106$	0.453468	0.0440447
$107$	2.17289	0.210061	0.105030	−	0.994469i	$-0.466506\pi$
$107$	2.17289	0.210061	0.105030	+	0.994469i	$0.466506\pi$
$108$	−8.92174	−0.858495
$109$	0.231838	0.0222061	0.0111030	−	0.999938i	$-0.496466\pi$
$109$	0.231838	0.0222061	0.0111030	+	0.999938i	$0.496466\pi$
$110$	−21.5985	−2.05934
$111$	−2.16447	−0.205442
$112$	0.784879	0.0741641
$113$	−15.1931	−1.42925	−0.714624	−	0.699509i	$-0.753402\pi$
$113$	−15.1931	−1.42925	−0.714624	+	0.699509i	$0.753402\pi$
$114$	5.66735	0.530796
$115$	4.83182	0.450570
$116$	10.5563	0.980127
$117$	−2.79037	−0.257970
$118$	−14.9803	−1.37905
$119$	−0.821635	−0.0753191
$120$	−2.94469	−0.268812
$121$	10.0207	0.910970
$122$	−18.5954	−1.68355
$123$	−2.73126	−0.246269
$124$	−13.2877	−1.19327
$125$	−11.9255	−1.06665
$126$	8.53373	0.760245
$127$	5.41331	0.480354	0.240177	−	0.970729i	$-0.422795\pi$
$127$	5.41331	0.480354	0.240177	+	0.970729i	$0.422795\pi$
$128$	19.4044	1.71513
$129$	−2.14957	−0.189259
$130$	−4.71086	−0.413170
$131$	−11.0952	−0.969390	−0.484695	−	0.874683i	$-0.661069\pi$
$131$	−11.0952	−0.969390	−0.484695	+	0.874683i	$0.661069\pi$
$132$	7.06425	0.614864
$133$	−7.05572	−0.611809
$134$	10.5431	0.910782
$135$	−5.39182	−0.464054
$136$	1.96792	0.168748
$137$	−20.7346	−1.77147	−0.885737	−	0.464188i	$-0.846346\pi$
$137$	−20.7346	−1.77147	−0.885737	+	0.464188i	$0.846346\pi$
$138$	−2.51957	−0.214480
$139$	5.27725	0.447610	0.223805	−	0.974634i	$-0.428152\pi$
$139$	5.27725	0.447610	0.223805	+	0.974634i	$0.428152\pi$
$140$	9.03659	0.763732
$141$	−2.89818	−0.244071
$142$	9.53747	0.800366
$143$	4.58483	0.383403
$144$	−1.65876	−0.138230
$145$	6.37966	0.529802
$146$	37.6569	3.11650
$147$	−2.40680	−0.198510
$148$	−15.9091	−1.30772
$149$	11.4169	0.935307	0.467653	−	0.883912i	$-0.345100\pi$
$149$	11.4169	0.935307	0.467653	+	0.883912i	$0.345100\pi$
$150$	0.915997	0.0747908
$151$	−13.3255	−1.08441	−0.542207	−	0.840245i	$-0.682411\pi$
$151$	−13.3255	−1.08441	−0.542207	+	0.840245i	$0.682411\pi$
$152$	16.8994	1.37072
$153$	1.73644	0.140383
$154$	−14.0217	−1.12990
$155$	−8.03036	−0.645014
$156$	1.54079	0.123362
$157$	23.3344	1.86228	0.931142	−	0.364656i	$-0.118813\pi$
$157$	23.3344	1.86228	0.931142	+	0.364656i	$0.118813\pi$
$158$	9.50442	0.756131
$159$	−0.0896345	−0.00710847
$160$	10.0627	0.795526
$161$	3.13680	0.247215
$162$	−16.5785	−1.30253
$163$	5.98991	0.469166	0.234583	−	0.972096i	$-0.424628\pi$
$163$	5.98991	0.469166	0.234583	+	0.972096i	$0.424628\pi$
$164$	−20.0751	−1.56760
$165$	4.26926	0.332361
$166$	22.1089	1.71598
$167$	−7.57194	−0.585935	−0.292967	−	0.956122i	$-0.594643\pi$
$167$	−7.57194	−0.585935	−0.292967	+	0.956122i	$0.594643\pi$
$168$	−1.91169	−0.147490
$169$	1.00000	0.0769231
$170$	2.93155	0.224840
$171$	14.9115	1.14031
$172$	−15.7996	−1.20471
$173$	−25.6632	−1.95114	−0.975569	−	0.219693i	$-0.929494\pi$
$173$	−25.6632	−1.95114	−0.975569	+	0.219693i	$0.929494\pi$
$174$	−3.32669	−0.252196
$175$	−1.14040	−0.0862058
$176$	2.72549	0.205442
$177$	2.96108	0.222569
$178$	1.91738	0.143714
$179$	−21.5097	−1.60771	−0.803854	−	0.594827i	$-0.797221\pi$
$179$	−21.5097	−1.60771	−0.803854	+	0.594827i	$0.797221\pi$
$180$	−19.0979	−1.42347
$181$	16.1839	1.20294	0.601471	−	0.798894i	$-0.294581\pi$
$181$	16.1839	1.20294	0.601471	+	0.798894i	$0.294581\pi$
$182$	−3.05828	−0.226694
$183$	3.67566	0.271712
$184$	−7.51306	−0.553870
$185$	−9.61461	−0.706880
$186$	4.18745	0.307039
$187$	−2.85312	−0.208641
$188$	−21.3020	−1.55360
$189$	−3.50035	−0.254613
$190$	25.1745	1.82635
$191$	7.42356	0.537150	0.268575	−	0.963259i	$-0.413447\pi$
$191$	7.42356	0.537150	0.268575	+	0.963259i	$0.413447\pi$
$192$	−5.79157	−0.417970
$193$	−11.4752	−0.826004	−0.413002	−	0.910730i	$-0.635520\pi$
$193$	−11.4752	−0.826004	−0.413002	+	0.910730i	$0.635520\pi$
$194$	−27.5658	−1.97911
$195$	0.931170	0.0666825
$196$	−17.6903	−1.26359
$197$	21.6475	1.54232	0.771159	−	0.636642i	$-0.219677\pi$
$197$	21.6475	1.54232	0.771159	+	0.636642i	$0.219677\pi$
$198$	29.6334	2.10595
$199$	−27.2202	−1.92959	−0.964794	−	0.263007i	$-0.915286\pi$
$199$	−27.2202	−1.92959	−0.964794	+	0.263007i	$0.915286\pi$
$200$	2.73140	0.193139
$201$	−2.08399	−0.146993
$202$	37.3293	2.62648
$203$	4.14165	0.290687
$204$	−0.958827	−0.0671313
$205$	−12.1323	−0.847358
$206$	−6.90782	−0.481291
$207$	−6.62931	−0.460769
$208$	0.594458	0.0412183
$209$	−24.5010	−1.69477
$210$	−2.84778	−0.196515
$211$	−3.57147	−0.245870	−0.122935	−	0.992415i	$-0.539231\pi$
$211$	−3.57147	−0.245870	−0.122935	+	0.992415i	$0.539231\pi$
$212$	−0.658824	−0.0452482
$213$	−1.88522	−0.129173
$214$	−5.03306	−0.344053
$215$	−9.54841	−0.651196
$216$	8.38382	0.570446
$217$	−5.21328	−0.353901
$218$	−0.537007	−0.0363707
$219$	−7.44343	−0.502980
$220$	31.3796	2.11561
$221$	−0.622297	−0.0418602
$222$	5.01356	0.336488
$223$	13.7066	0.917859	0.458929	−	0.888473i	$-0.348233\pi$
$223$	13.7066	0.917859	0.458929	+	0.888473i	$0.348233\pi$
$224$	6.53267	0.436482
$225$	2.41011	0.160674
$226$	35.1919	2.34093
$227$	−16.2937	−1.08145	−0.540725	−	0.841200i	$-0.681850\pi$
$227$	−16.2937	−1.08145	−0.540725	+	0.841200i	$0.681850\pi$
$228$	−8.23385	−0.545300
$229$	3.57311	0.236118	0.118059	−	0.993007i	$-0.462333\pi$
$229$	3.57311	0.236118	0.118059	+	0.993007i	$0.462333\pi$
$230$	−11.1920	−0.737976
$231$	2.77159	0.182357
$232$	−9.91981	−0.651268
$233$	13.5249	0.886048	0.443024	−	0.896510i	$-0.353906\pi$
$233$	13.5249	0.886048	0.443024	+	0.896510i	$0.353906\pi$
$234$	6.46335	0.422522
$235$	−12.8738	−0.839792
$236$	21.7643	1.41674
$237$	−1.87869	−0.122034
$238$	1.90315	0.123363
$239$	7.63591	0.493926	0.246963	−	0.969025i	$-0.420567\pi$
$239$	7.63591	0.493926	0.246963	+	0.969025i	$0.420567\pi$
$240$	0.553542	0.0357310
$241$	11.5588	0.744568	0.372284	−	0.928119i	$-0.378575\pi$
$241$	11.5588	0.744568	0.372284	+	0.928119i	$0.378575\pi$
$242$	−23.2109	−1.49205
$243$	11.2304	0.720428
$244$	27.0165	1.72956
$245$	−10.6911	−0.683027
$246$	6.32643	0.403358
$247$	−5.34392	−0.340026
$248$	12.4865	0.792894
$249$	−4.37015	−0.276947
$250$	27.6232	1.74704
$251$	20.2929	1.28088	0.640440	−	0.768008i	$-0.278752\pi$
$251$	20.2929	1.28088	0.640440	+	0.768008i	$0.278752\pi$
$252$	−12.3983	−0.781019
$253$	10.8925	0.684808
$254$	−12.5389	−0.786759
$255$	−0.579464	−0.0362874
$256$	−19.6476	−1.22798
$257$	−14.2445	−0.888547	−0.444273	−	0.895891i	$-0.646538\pi$
$257$	−14.2445	−0.888547	−0.444273	+	0.895891i	$0.646538\pi$
$258$	4.97904	0.309982
$259$	−6.24178	−0.387845
$260$	6.84421	0.424460
$261$	−8.75296	−0.541794
$262$	25.6998	1.58774
$263$	2.16674	0.133607	0.0668036	−	0.997766i	$-0.478720\pi$
$263$	2.16674	0.133607	0.0668036	+	0.997766i	$0.478720\pi$
$264$	−6.63832	−0.408561
$265$	−0.398158	−0.0244587
$266$	16.3432	1.00207
$267$	−0.378998	−0.0231943
$268$	−15.3176	−0.935670
$269$	7.08407	0.431923	0.215962	−	0.976402i	$-0.430711\pi$
$269$	7.08407	0.431923	0.215962	+	0.976402i	$0.430711\pi$
$270$	12.4891	0.760062
$271$	12.7327	0.773458	0.386729	−	0.922193i	$-0.373605\pi$
$271$	12.7327	0.773458	0.386729	+	0.922193i	$0.373605\pi$
$272$	−0.369929	−0.0224303
$273$	0.604513	0.0365868
$274$	48.0275	2.90145
$275$	−3.96002	−0.238798
$276$	3.66057	0.220341
$277$	25.1177	1.50918	0.754589	−	0.656197i	$-0.227836\pi$
$277$	25.1177	1.50918	0.754589	+	0.656197i	$0.227836\pi$
$278$	−12.2237	−0.733129
$279$	11.0177	0.659615
$280$	−8.49175	−0.507479
$281$	15.0509	0.897860	0.448930	−	0.893567i	$-0.351805\pi$
$281$	15.0509	0.897860	0.448930	+	0.893567i	$0.351805\pi$
$282$	6.71306	0.399757
$283$	−14.5455	−0.864638	−0.432319	−	0.901721i	$-0.642305\pi$
$283$	−14.5455	−0.864638	−0.432319	+	0.901721i	$0.642305\pi$
$284$	−13.8566	−0.822237
$285$	−4.97610	−0.294759
$286$	−10.6199	−0.627965
$287$	−7.87626	−0.464921
$288$	−13.8061	−0.813533
$289$	−16.6127	−0.977220
$290$	−14.7772	−0.867748
$291$	5.44878	0.319413
$292$	−54.7101	−3.20166
$293$	−10.3965	−0.607370	−0.303685	−	0.952773i	$-0.598217\pi$
$293$	−10.3965	−0.607370	−0.303685	+	0.952773i	$0.598217\pi$
$294$	5.57489	0.325134
$295$	13.1532	0.765808
$296$	14.9499	0.868945
$297$	−12.1550	−0.705303
$298$	−26.4449	−1.53191
$299$	2.37578	0.137395
$300$	−1.33081	−0.0768346
$301$	−6.19880	−0.357293
$302$	30.8659	1.77613
$303$	−7.37868	−0.423894
$304$	−3.17674	−0.182198
$305$	16.3273	0.934901
$306$	−4.02212	−0.229929
$307$	11.4744	0.654880	0.327440	−	0.944872i	$-0.393814\pi$
$307$	11.4744	0.654880	0.327440	+	0.944872i	$0.393814\pi$
$308$	20.3715	1.16077
$309$	1.36543	0.0776767
$310$	18.6007	1.05645
$311$	15.7603	0.893686	0.446843	−	0.894612i	$-0.352548\pi$
$311$	15.7603	0.893686	0.446843	+	0.894612i	$0.352548\pi$
$312$	−1.44789	−0.0819706
$313$	2.00037	0.113068	0.0565338	−	0.998401i	$-0.481995\pi$
$313$	2.00037	0.113068	0.0565338	+	0.998401i	$0.481995\pi$
$314$	−54.0495	−3.05019
$315$	−7.49287	−0.422175
$316$	−13.8086	−0.776793
$317$	35.3289	1.98427	0.992135	−	0.125169i	$-0.0399472\pi$
$317$	35.3289	1.98427	0.992135	+	0.125169i	$0.0399472\pi$
$318$	0.207621	0.0116428
$319$	14.3819	0.805231
$320$	−25.7263	−1.43814
$321$	0.994858	0.0555276
$322$	−7.26579	−0.404907
$323$	3.32550	0.185036
$324$	24.0862	1.33812
$325$	−0.863723	−0.0479107
$326$	−13.8744	−0.768434
$327$	0.106147	0.00586996
$328$	18.8647	1.04163
$329$	−8.35761	−0.460770
$330$	−9.88889	−0.544366
$331$	9.54367	0.524568	0.262284	−	0.964991i	$-0.415524\pi$
$331$	9.54367	0.524568	0.262284	+	0.964991i	$0.415524\pi$
$332$	−32.1211	−1.76288
$333$	13.1913	0.722881
$334$	17.5389	0.959687
$335$	−9.25713	−0.505771
$336$	0.359358	0.0196046
$337$	−26.0288	−1.41788	−0.708940	−	0.705268i	$-0.750826\pi$
$337$	−26.0288	−1.41788	−0.708940	+	0.705268i	$0.750826\pi$
$338$	−2.31630	−0.125990
$339$	−6.95618	−0.377808
$340$	−4.25913	−0.230984
$341$	−18.1031	−0.980339
$342$	−34.5396	−1.86769
$343$	−16.1829	−0.873794
$344$	14.8470	0.800494
$345$	2.21225	0.119104
$346$	59.4438	3.19572
$347$	9.41392	0.505366	0.252683	−	0.967549i	$-0.418687\pi$
$347$	9.41392	0.505366	0.252683	+	0.967549i	$0.418687\pi$
$348$	4.83321	0.259087
$349$	−10.9242	−0.584759	−0.292379	−	0.956302i	$-0.594447\pi$
$349$	−10.9242	−0.584759	−0.292379	+	0.956302i	$0.594447\pi$
$350$	2.64150	0.141194
$351$	−2.65113	−0.141507
$352$	22.6847	1.20910
$353$	28.2772	1.50505	0.752523	−	0.658566i	$-0.228837\pi$
$353$	28.2772	1.50505	0.752523	+	0.658566i	$0.228837\pi$
$354$	−6.85877	−0.364539
$355$	−8.37418	−0.444455
$356$	−2.78568	−0.147641
$357$	−0.376186	−0.0199099
$358$	49.8229	2.63322
$359$	5.51122	0.290871	0.145436	−	0.989368i	$-0.453542\pi$
$359$	5.51122	0.290871	0.145436	+	0.989368i	$0.453542\pi$
$360$	17.9464	0.945860
$361$	9.55751	0.503027
$362$	−37.4869	−1.97027
$363$	4.58797	0.240806
$364$	4.44324	0.232889
$365$	−33.0638	−1.73064
$366$	−8.51393	−0.445030
$367$	13.4609	0.702652	0.351326	−	0.936253i	$-0.385731\pi$
$367$	13.4609	0.702652	0.351326	+	0.936253i	$0.385731\pi$
$368$	1.41230	0.0736213
$369$	16.6457	0.866538
$370$	22.2704	1.15778
$371$	−0.258483	−0.0134198
$372$	−6.08377	−0.315429
$373$	34.5011	1.78640	0.893200	−	0.449659i	$-0.148455\pi$
$373$	34.5011	1.78640	0.893200	+	0.449659i	$0.148455\pi$
$374$	6.60870	0.341728
$375$	−5.46012	−0.281960
$376$	20.0176	1.03233
$377$	3.13684	0.161556
$378$	8.10788	0.417024
$379$	12.6010	0.647269	0.323634	−	0.946182i	$-0.395095\pi$
$379$	12.6010	0.647269	0.323634	+	0.946182i	$0.395095\pi$
$380$	−36.5749	−1.87626
$381$	2.47849	0.126977
$382$	−17.1952	−0.879784
$383$	29.0206	1.48289	0.741443	−	0.671016i	$-0.234142\pi$
$383$	29.0206	1.48289	0.741443	+	0.671016i	$0.234142\pi$
$384$	8.88434	0.453377
$385$	12.3115	0.627450
$386$	26.5801	1.35289
$387$	13.1005	0.665937
$388$	40.0492	2.03319
$389$	−33.0889	−1.67767	−0.838837	−	0.544383i	$-0.816764\pi$
$389$	−33.0889	−1.67767	−0.838837	+	0.544383i	$0.816764\pi$
$390$	−2.15687	−0.109217
$391$	−1.47844	−0.0747679
$392$	16.6237	0.839623
$393$	−5.07994	−0.256249
$394$	−50.1421	−2.52612
$395$	−8.34516	−0.419891
$396$	−43.0531	−2.16350
$397$	10.2386	0.513859	0.256929	−	0.966430i	$-0.417289\pi$
$397$	10.2386	0.513859	0.256929	+	0.966430i	$0.417289\pi$
$398$	63.0502	3.16042
$399$	−3.23047	−0.161726
$400$	−0.513447	−0.0256724
$401$	−19.6795	−0.982747	−0.491374	−	0.870949i	$-0.663505\pi$
$401$	−19.6795	−0.982747	−0.491374	+	0.870949i	$0.663505\pi$
$402$	4.82715	0.240756
$403$	−3.94848	−0.196688
$404$	−54.2342	−2.69825
$405$	14.5564	0.723313
$406$	−9.59333	−0.476109
$407$	−21.6746	−1.07437
$408$	0.901016	0.0446070
$409$	0.627696	0.0310376	0.0155188	−	0.999880i	$-0.495060\pi$
$409$	0.627696	0.0310376	0.0155188	+	0.999880i	$0.495060\pi$
$410$	28.1021	1.38786
$411$	−9.49334	−0.468272
$412$	10.0361	0.494443
$413$	8.53901	0.420177
$414$	15.3555	0.754681
$415$	−19.4123	−0.952912
$416$	4.94777	0.242584
$417$	2.41619	0.118321
$418$	56.7517	2.77582
$419$	14.5105	0.708885	0.354443	−	0.935078i	$-0.384671\pi$
$419$	14.5105	0.708885	0.354443	+	0.935078i	$0.384671\pi$
$420$	4.13741	0.201885
$421$	−13.1598	−0.641369	−0.320684	−	0.947186i	$-0.603913\pi$
$421$	−13.1598	−0.641369	−0.320684	+	0.947186i	$0.603913\pi$
$422$	8.27262	0.402705
$423$	17.6629	0.858801
$424$	0.619101	0.0300662
$425$	0.537492	0.0260722
$426$	4.36674	0.211569
$427$	10.5997	0.512953
$428$	7.31233	0.353455
$429$	2.09917	0.101349
$430$	22.1170	1.06658
$431$	23.5503	1.13438	0.567189	−	0.823588i	$-0.308031\pi$
$431$	23.5503	1.13438	0.567189	+	0.823588i	$0.308031\pi$
$432$	−1.57598	−0.0758246
$433$	34.2702	1.64692	0.823461	−	0.567372i	$-0.192040\pi$
$433$	34.2702	1.64692	0.823461	+	0.567372i	$0.192040\pi$
$434$	12.0755	0.579645
$435$	2.92093	0.140048
$436$	0.780195	0.0373646
$437$	−12.6960	−0.607331
$438$	17.2412	0.823818
$439$	−38.8231	−1.85293	−0.926463	−	0.376386i	$-0.877167\pi$
$439$	−38.8231	−1.85293	−0.926463	+	0.376386i	$0.877167\pi$
$440$	−29.4876	−1.40577
$441$	14.6683	0.698489
$442$	1.44143	0.0685617
$443$	−37.6097	−1.78689	−0.893446	−	0.449171i	$-0.851719\pi$
$443$	−37.6097	−1.78689	−0.893446	+	0.449171i	$0.851719\pi$
$444$	−7.28400	−0.345683
$445$	−1.68351	−0.0798063
$446$	−31.7485	−1.50334
$447$	5.22723	0.247239
$448$	−16.7014	−0.789067
$449$	19.4400	0.917431	0.458715	−	0.888583i	$-0.348310\pi$
$449$	19.4400	0.917431	0.458715	+	0.888583i	$0.348310\pi$
$450$	−5.58254	−0.263164
$451$	−27.3503	−1.28788
$452$	−51.1288	−2.40490
$453$	−6.10110	−0.286655
$454$	37.7411	1.77128
$455$	2.68526	0.125887
$456$	7.73741	0.362337
$457$	−24.0218	−1.12369	−0.561847	−	0.827241i	$-0.689909\pi$
$457$	−24.0218	−1.12369	−0.561847	+	0.827241i	$0.689909\pi$
$458$	−8.27640	−0.386731
$459$	1.64979	0.0770055
$460$	16.2603	0.758142
$461$	25.0585	1.16709	0.583544	−	0.812081i	$-0.301665\pi$
$461$	25.0585	1.16709	0.583544	+	0.812081i	$0.301665\pi$
$462$	−6.41984	−0.298678
$463$	1.00000	0.0464739
$463$	1.00000	0.0464739
$464$	1.86472	0.0865675
$465$	−3.67671	−0.170503
$466$	−31.3278	−1.45123
$467$	7.29831	0.337725	0.168863	−	0.985640i	$-0.445991\pi$
$467$	7.29831	0.337725	0.168863	+	0.985640i	$0.445991\pi$
$468$	−9.39033	−0.434068
$469$	−6.00970	−0.277502
$470$	29.8195	1.37547
$471$	10.6837	0.492277
$472$	−20.4521	−0.941383
$473$	−21.5253	−0.989735
$474$	4.35161	0.199876
$475$	4.61567	0.211781
$476$	−2.76501	−0.126734
$477$	0.546277	0.0250123
$478$	−17.6871	−0.808989
$479$	−25.7762	−1.17775	−0.588873	−	0.808226i	$-0.700428\pi$
$479$	−25.7762	−1.17775	−0.588873	+	0.808226i	$0.700428\pi$
$480$	4.60722	0.210290
$481$	−4.72745	−0.215553
$482$	−26.7737	−1.21951
$483$	1.43619	0.0653488
$484$	33.7222	1.53283
$485$	24.2036	1.09903
$486$	−26.0129	−1.17997
$487$	−22.5173	−1.02035	−0.510177	−	0.860069i	$-0.670420\pi$
$487$	−22.5173	−1.02035	−0.510177	+	0.860069i	$0.670420\pi$
$488$	−25.3876	−1.14924
$489$	2.74249	0.124019
$490$	24.7638	1.11871
$491$	37.7133	1.70198	0.850988	−	0.525185i	$-0.176004\pi$
$491$	37.7133	1.70198	0.850988	+	0.525185i	$0.176004\pi$
$492$	−9.19140	−0.414380
$493$	−1.95205	−0.0879157
$494$	12.3781	0.556919
$495$	−26.0190	−1.16947
$496$	−2.34721	−0.105393
$497$	−5.43649	−0.243860
$498$	10.1226	0.453604
$499$	35.1091	1.57170	0.785849	−	0.618419i	$-0.212226\pi$
$499$	35.1091	1.57170	0.785849	+	0.618419i	$0.212226\pi$
$500$	−40.1326	−1.79478
$501$	−3.46682	−0.154886
$502$	−47.0046	−2.09792
$503$	−5.66239	−0.252474	−0.126237	−	0.992000i	$-0.540290\pi$
$503$	−5.66239	−0.252474	−0.126237	+	0.992000i	$0.540290\pi$
$504$	11.6508	0.518966
$505$	−32.7763	−1.45852
$506$	−25.2304	−1.12163
$507$	0.457851	0.0203339
$508$	18.2172	0.808258
$509$	−6.77023	−0.300085	−0.150043	−	0.988680i	$-0.547941\pi$
$509$	−6.77023	−0.300085	−0.150043	+	0.988680i	$0.547941\pi$
$510$	1.34221	0.0594343
$511$	−21.4649	−0.949553
$512$	6.70102	0.296146
$513$	14.1674	0.625507
$514$	32.9946	1.45533
$515$	6.06528	0.267268
$516$	−7.23385	−0.318452
$517$	−29.0218	−1.27638
$518$	14.4578	0.635241
$519$	−11.7499	−0.515765
$520$	−6.43155	−0.282042
$521$	−12.1893	−0.534022	−0.267011	−	0.963693i	$-0.586036\pi$
$521$	−12.1893	−0.534022	−0.267011	+	0.963693i	$0.586036\pi$
$522$	20.2745	0.887391
$523$	−30.6495	−1.34021	−0.670104	−	0.742267i	$-0.733751\pi$
$523$	−30.6495	−1.34021	−0.670104	+	0.742267i	$0.733751\pi$
$524$	−37.3381	−1.63112
$525$	−0.522131	−0.0227877
$526$	−5.01883	−0.218832
$527$	2.45713	0.107034
$528$	1.24787	0.0543065
$529$	−17.3557	−0.754595
$530$	0.922255	0.0400602
$531$	−18.0463	−0.783143
$532$	−23.7443	−1.02945
$533$	−5.96539	−0.258390
$534$	0.877873	0.0379893
$535$	4.41918	0.191058
$536$	14.3940	0.621727
$537$	−9.84822	−0.424982
$538$	−16.4088	−0.707436
$539$	−24.1013	−1.03811
$540$	−18.1449	−0.780832
$541$	15.3929	0.661792	0.330896	−	0.943667i	$-0.392649\pi$
$541$	15.3929	0.661792	0.330896	+	0.943667i	$0.392649\pi$
$542$	−29.4929	−1.26683
$543$	7.40983	0.317986
$544$	−3.07898	−0.132010
$545$	0.471508	0.0201972
$546$	−1.40023	−0.0599245
$547$	10.7353	0.459008	0.229504	−	0.973308i	$-0.426290\pi$
$547$	10.7353	0.459008	0.229504	+	0.973308i	$0.426290\pi$
$548$	−69.7772	−2.98073
$549$	−22.4013	−0.956063
$550$	9.17261	0.391121
$551$	−16.7630	−0.714129
$552$	−3.43986	−0.146410
$553$	−5.41765	−0.230382
$554$	−58.1803	−2.47184
$555$	−4.40206	−0.186857
$556$	17.7593	0.753163
$557$	25.9220	1.09835	0.549174	−	0.835708i	$-0.314942\pi$
$557$	25.9220	1.09835	0.549174	+	0.835708i	$0.314942\pi$
$558$	−25.5204	−1.08037
$559$	−4.69490	−0.198573
$560$	1.59627	0.0674549
$561$	−1.30631	−0.0551523
$562$	−34.8624	−1.47058
$563$	35.3461	1.48966	0.744830	−	0.667254i	$-0.232530\pi$
$563$	35.3461	1.48966	0.744830	+	0.667254i	$0.232530\pi$
$564$	−9.75312	−0.410681
$565$	−30.8995	−1.29995
$566$	33.6917	1.41617
$567$	9.44996	0.396861
$568$	13.0211	0.546354
$569$	−22.2555	−0.932997	−0.466499	−	0.884522i	$-0.654485\pi$
$569$	−22.2555	−0.932997	−0.466499	+	0.884522i	$0.654485\pi$
$570$	11.5262	0.482778
$571$	−29.1649	−1.22051	−0.610256	−	0.792204i	$-0.708934\pi$
$571$	−29.1649	−1.22051	−0.610256	+	0.792204i	$0.708934\pi$
$572$	15.4291	0.645125
$573$	3.39889	0.141991
$574$	18.2438	0.761482
$575$	−2.05201	−0.0855749
$576$	35.2967	1.47070
$577$	−30.3329	−1.26277	−0.631387	−	0.775468i	$-0.717514\pi$
$577$	−30.3329	−1.26277	−0.631387	+	0.775468i	$0.717514\pi$
$578$	38.4802	1.60056
$579$	−5.25394	−0.218346
$580$	21.4692	0.891460
$581$	−12.6024	−0.522836
$582$	−12.6210	−0.523158
$583$	−0.897582	−0.0371740
$584$	51.4114	2.12742
$585$	−5.67501	−0.234633
$586$	24.0814	0.994795
$587$	−42.9039	−1.77083	−0.885416	−	0.464800i	$-0.846126\pi$
$587$	−42.9039	−1.77083	−0.885416	+	0.464800i	$0.846126\pi$
$588$	−8.09952	−0.334019
$589$	21.1004	0.869426
$590$	−30.4668	−1.25430
$591$	9.91132	0.407697
$592$	−2.81027	−0.115501
$593$	−33.9203	−1.39294	−0.696470	−	0.717586i	$-0.745247\pi$
$593$	−33.9203	−1.39294	−0.696470	+	0.717586i	$0.745247\pi$
$594$	28.1546	1.15520
$595$	−1.67103	−0.0685054
$596$	38.4208	1.57378
$597$	−12.4628	−0.510068
$598$	−5.50302	−0.225035
$599$	−44.2211	−1.80682	−0.903412	−	0.428774i	$-0.858946\pi$
$599$	−44.2211	−1.80682	−0.903412	+	0.428774i	$0.858946\pi$
$600$	1.25057	0.0510545
$601$	15.0726	0.614824	0.307412	−	0.951576i	$-0.400537\pi$
$601$	15.0726	0.614824	0.307412	+	0.951576i	$0.400537\pi$
$602$	14.3583	0.585201
$603$	12.7009	0.517219
$604$	−44.8438	−1.82467
$605$	20.3799	0.828560
$606$	17.0913	0.694285
$607$	41.1820	1.67153	0.835763	−	0.549091i	$-0.185026\pi$
$607$	41.1820	1.67153	0.835763	+	0.549091i	$0.185026\pi$
$608$	−26.4405	−1.07230
$609$	1.89626	0.0768404
$610$	−37.8191	−1.53125
$611$	−6.32996	−0.256083
$612$	5.84357	0.236212
$613$	10.2334	0.413322	0.206661	−	0.978413i	$-0.433740\pi$
$613$	10.2334	0.413322	0.206661	+	0.978413i	$0.433740\pi$
$614$	−26.5783	−1.07261
$615$	−5.55479	−0.223991
$616$	−19.1432	−0.771303
$617$	−4.38018	−0.176340	−0.0881698	−	0.996105i	$-0.528102\pi$
$617$	−4.38018	−0.176340	−0.0881698	+	0.996105i	$0.528102\pi$
$618$	−3.16275	−0.127225
$619$	−31.4365	−1.26354	−0.631769	−	0.775156i	$-0.717671\pi$
$619$	−31.4365	−1.26354	−0.631769	+	0.775156i	$0.717671\pi$
$620$	−27.0243	−1.08532
$621$	−6.29849	−0.252750
$622$	−36.5057	−1.46375
$623$	−1.09293	−0.0437874
$624$	0.272173	0.0108957
$625$	−19.9354	−0.797415
$626$	−4.63346	−0.185190
$627$	−11.2178	−0.447996
$628$	78.5262	3.13354
$629$	2.94188	0.117300
$630$	17.3558	0.691470
$631$	1.78694	0.0711370	0.0355685	−	0.999367i	$-0.488676\pi$
$631$	1.78694	0.0711370	0.0355685	+	0.999367i	$0.488676\pi$
$632$	12.9760	0.516158
$633$	−1.63520	−0.0649935
$634$	−81.8325	−3.24999
$635$	11.0095	0.436899
$636$	−0.301643	−0.0119609
$637$	−5.25674	−0.208280
$638$	−33.3128	−1.31887
$639$	11.4895	0.454516
$640$	39.4644	1.55997
$641$	−14.5919	−0.576345	−0.288173	−	0.957578i	$-0.593048\pi$
$641$	−14.5919	−0.576345	−0.288173	+	0.957578i	$0.593048\pi$
$642$	−2.30439	−0.0909471
$643$	−7.62653	−0.300761	−0.150380	−	0.988628i	$-0.548050\pi$
$643$	−7.62653	−0.300761	−0.150380	+	0.988628i	$0.548050\pi$
$644$	10.5562	0.415971
$645$	−4.37175	−0.172138
$646$	−7.70288	−0.303066
$647$	−43.9469	−1.72773	−0.863866	−	0.503722i	$-0.831963\pi$
$647$	−43.9469	−1.72773	−0.863866	+	0.503722i	$0.831963\pi$
$648$	−22.6339	−0.889145
$649$	29.6517	1.16393
$650$	2.00064	0.0784717
$651$	−2.38691	−0.0935503
$652$	20.1576	0.789433
$653$	4.95881	0.194053	0.0970267	−	0.995282i	$-0.469067\pi$
$653$	4.95881	0.194053	0.0970267	+	0.995282i	$0.469067\pi$
$654$	−0.245869	−0.00961425
$655$	−22.5652	−0.881695
$656$	−3.54617	−0.138455
$657$	45.3639	1.76982
$658$	19.3588	0.754683
$659$	−29.7010	−1.15699	−0.578494	−	0.815687i	$-0.696359\pi$
$659$	−29.7010	−1.15699	−0.578494	+	0.815687i	$0.696359\pi$
$660$	14.3672	0.559241
$661$	−44.0847	−1.71470	−0.857349	−	0.514736i	$-0.827890\pi$
$661$	−44.0847	−1.71470	−0.857349	+	0.514736i	$0.827890\pi$
$662$	−22.1060	−0.859176
$663$	−0.284919	−0.0110653
$664$	30.1844	1.17138
$665$	−14.3498	−0.556462
$666$	−30.5552	−1.18399
$667$	7.45244	0.288560
$668$	−25.4816	−0.985911
$669$	6.27556	0.242627
$670$	21.4423	0.828389
$671$	36.8073	1.42093
$672$	2.99099	0.115380
$673$	−31.5265	−1.21526	−0.607628	−	0.794222i	$-0.707879\pi$
$673$	−31.5265	−1.21526	−0.607628	+	0.794222i	$0.707879\pi$
$674$	60.2907	2.32231
$675$	2.28984	0.0881360
$676$	3.36526	0.129433
$677$	11.3188	0.435016	0.217508	−	0.976059i	$-0.430207\pi$
$677$	11.3188	0.435016	0.217508	+	0.976059i	$0.430207\pi$
$678$	16.1126	0.618802
$679$	15.7129	0.603006
$680$	4.00233	0.153482
$681$	−7.46008	−0.285871
$682$	41.9323	1.60567
$683$	−22.7034	−0.868723	−0.434362	−	0.900739i	$-0.643026\pi$
$683$	−22.7034	−0.868723	−0.434362	+	0.900739i	$0.643026\pi$
$684$	50.1812	1.91873
$685$	−42.1696	−1.61122
$686$	37.4845	1.43116
$687$	1.63595	0.0624155
$688$	−2.79092	−0.106403
$689$	−0.195772	−0.00745832
$690$	−5.12425	−0.195077
$691$	−13.8214	−0.525791	−0.262895	−	0.964824i	$-0.584677\pi$
$691$	−13.8214	−0.525791	−0.262895	+	0.964824i	$0.584677\pi$
$692$	−86.3634	−3.28304
$693$	−16.8914	−0.641653
$694$	−21.8055	−0.827726
$695$	10.7328	0.407118
$696$	−4.54180	−0.172156
$697$	3.71224	0.140611
$698$	25.3038	0.957761
$699$	6.19240	0.234218
$700$	−3.83773	−0.145053
$701$	−35.0201	−1.32269	−0.661345	−	0.750082i	$-0.730014\pi$
$701$	−35.0201	−1.32269	−0.661345	+	0.750082i	$0.730014\pi$
$702$	6.14082	0.231770
$703$	25.2631	0.952817
$704$	−57.9956	−2.18579
$705$	−5.89427	−0.221991
$706$	−65.4987	−2.46507
$707$	−21.2782	−0.800251
$708$	9.96482	0.374501
$709$	−8.98168	−0.337314	−0.168657	−	0.985675i	$-0.553943\pi$
$709$	−8.98168	−0.337314	−0.168657	+	0.985675i	$0.553943\pi$
$710$	19.3971	0.727962
$711$	11.4497	0.429395
$712$	2.61772	0.0981032
$713$	−9.38072	−0.351311
$714$	0.871361	0.0326099
$715$	9.32455	0.348719
$716$	−72.3856	−2.70518
$717$	3.49611	0.130565
$718$	−12.7657	−0.476410
$719$	−51.6358	−1.92569	−0.962844	−	0.270057i	$-0.912957\pi$
$719$	−51.6358	−1.92569	−0.962844	+	0.270057i	$0.912957\pi$
$720$	−3.37356	−0.125725
$721$	3.93756	0.146642
$722$	−22.1381	−0.823894
$723$	5.29221	0.196819
$724$	54.4632	2.02411
$725$	−2.70936	−0.100623
$726$	−10.6271	−0.394410
$727$	16.2038	0.600966	0.300483	−	0.953787i	$-0.402852\pi$
$727$	16.2038	0.600966	0.300483	+	0.953787i	$0.402852\pi$
$728$	−4.17534	−0.154749
$729$	−16.3301	−0.604817
$730$	76.5859	2.83457
$731$	2.92162	0.108060
$732$	12.3695	0.457191
$733$	32.2150	1.18989	0.594943	−	0.803768i	$-0.297174\pi$
$733$	32.2150	1.18989	0.594943	+	0.803768i	$0.297174\pi$
$734$	−31.1795	−1.15086
$735$	−4.89492	−0.180552
$736$	11.7548	0.433288
$737$	−20.8687	−0.768707
$738$	−38.5564	−1.41928
$739$	25.8399	0.950535	0.475267	−	0.879841i	$-0.342351\pi$
$739$	25.8399	0.950535	0.475267	+	0.879841i	$0.342351\pi$
$740$	−32.3557	−1.18942
$741$	−2.44672	−0.0898825
$742$	0.598725	0.0219799
$743$	12.6122	0.462697	0.231348	−	0.972871i	$-0.425686\pi$
$743$	12.6122	0.462697	0.231348	+	0.972871i	$0.425686\pi$
$744$	5.71696	0.209594
$745$	23.2195	0.850695
$746$	−79.9151	−2.92590
$747$	26.6339	0.974482
$748$	−9.60151	−0.351066
$749$	2.86892	0.104828
$750$	12.6473	0.461814
$751$	−2.08013	−0.0759052	−0.0379526	−	0.999280i	$-0.512084\pi$
$751$	−2.08013	−0.0759052	−0.0379526	+	0.999280i	$0.512084\pi$
$752$	−3.76289	−0.137219
$753$	9.29115	0.338588
$754$	−7.26588	−0.264608
$755$	−27.1012	−0.986314
$756$	−11.7796	−0.428420
$757$	−3.40110	−0.123615	−0.0618076	−	0.998088i	$-0.519687\pi$
$757$	−3.40110	−0.123615	−0.0618076	+	0.998088i	$0.519687\pi$
$758$	−29.1877	−1.06014
$759$	4.98716	0.181023
$760$	34.3697	1.24672
$761$	−39.1277	−1.41838	−0.709190	−	0.705018i	$-0.750939\pi$
$761$	−39.1277	−1.41838	−0.709190	+	0.705018i	$0.750939\pi$
$762$	−5.74094	−0.207972
$763$	0.306102	0.0110816
$764$	24.9822	0.903825
$765$	3.53154	0.127683
$766$	−67.2206	−2.42878
$767$	6.46735	0.233522
$768$	−8.99569	−0.324604
$769$	23.5540	0.849379	0.424689	−	0.905339i	$-0.360383\pi$
$769$	23.5540	0.849379	0.424689	+	0.905339i	$0.360383\pi$
$770$	−28.5171	−1.02768
$771$	−6.52186	−0.234879
$772$	−38.6171	−1.38986
$773$	20.7557	0.746531	0.373265	−	0.927725i	$-0.378238\pi$
$773$	20.7557	0.746531	0.373265	+	0.927725i	$0.378238\pi$
$774$	−30.3448	−1.09072
$775$	3.41039	0.122505
$776$	−37.6345	−1.35100
$777$	−2.85780	−0.102523
$778$	76.6439	2.74782
$779$	31.8786	1.14217
$780$	3.13363	0.112202
$781$	−18.8782	−0.675515
$782$	3.42451	0.122460
$783$	−8.31617	−0.297196
$784$	−3.12491	−0.111604
$785$	47.4571	1.69381
$786$	11.7667	0.419703
$787$	11.2829	0.402193	0.201096	−	0.979571i	$-0.435550\pi$
$787$	11.2829	0.402193	0.201096	+	0.979571i	$0.435550\pi$
$788$	72.8494	2.59515
$789$	0.992046	0.0353178
$790$	19.3299	0.687728
$791$	−20.0599	−0.713247
$792$	40.4573	1.43759
$793$	8.02806	0.285085
$794$	−23.7156	−0.841635
$795$	−0.182297	−0.00646541
$796$	−91.6030	−3.24678
$797$	46.7558	1.65618	0.828088	−	0.560598i	$-0.189429\pi$
$797$	46.7558	1.65618	0.828088	+	0.560598i	$0.189429\pi$
$798$	7.48275	0.264886
$799$	3.93911	0.139356
$800$	−4.27350	−0.151091
$801$	2.30980	0.0816128
$802$	45.5837	1.60962
$803$	−74.5370	−2.63035
$804$	−7.01317	−0.247335
$805$	6.37958	0.224851
$806$	9.14588	0.322150
$807$	3.24345	0.114175
$808$	50.9642	1.79292
$809$	−52.0880	−1.83132	−0.915659	−	0.401956i	$-0.868330\pi$
$809$	−52.0880	−1.83132	−0.915659	+	0.401956i	$0.868330\pi$
$810$	−33.7170	−1.18470
$811$	22.1419	0.777507	0.388754	−	0.921342i	$-0.372906\pi$
$811$	22.1419	0.777507	0.388754	+	0.921342i	$0.372906\pi$
$812$	13.9377	0.489119
$813$	5.82969	0.204456
$814$	50.2048	1.75968
$815$	12.1822	0.426723
$816$	−0.169373	−0.00592922
$817$	25.0892	0.877759
$818$	−1.45393	−0.0508356
$819$	−3.68420	−0.128736
$820$	−40.8284	−1.42579
$821$	−10.0694	−0.351424	−0.175712	−	0.984442i	$-0.556223\pi$
$821$	−10.0694	−0.351424	−0.175712	+	0.984442i	$0.556223\pi$
$822$	21.9895	0.766970
$823$	55.0985	1.92061	0.960307	−	0.278945i	$-0.0899848\pi$
$823$	55.0985	1.92061	0.960307	+	0.278945i	$0.0899848\pi$
$824$	−9.43098	−0.328544
$825$	−1.81310	−0.0631240
$826$	−19.7789	−0.688197
$827$	3.62458	0.126039	0.0630196	−	0.998012i	$-0.479927\pi$
$827$	3.62458	0.126039	0.0630196	+	0.998012i	$0.479927\pi$
$828$	−22.3094	−0.775304
$829$	27.7172	0.962658	0.481329	−	0.876540i	$-0.340154\pi$
$829$	27.7172	0.962658	0.481329	+	0.876540i	$0.340154\pi$
$830$	44.9647	1.56075
$831$	11.5002	0.398937
$832$	−12.6495	−0.438541
$833$	3.27125	0.113342
$834$	−5.59664	−0.193796
$835$	−15.3997	−0.532929
$836$	−82.4522	−2.85167
$837$	10.4679	0.361825
$838$	−33.6108	−1.16106
$839$	7.48678	0.258472	0.129236	−	0.991614i	$-0.458747\pi$
$839$	7.48678	0.258472	0.129236	+	0.991614i	$0.458747\pi$
$840$	−3.88796	−0.134147
$841$	−19.1602	−0.660697
$842$	30.4821	1.05048
$843$	6.89106	0.237341
$844$	−12.0189	−0.413709
$845$	2.03378	0.0699643
$846$	−40.9127	−1.40661
$847$	13.2305	0.454607
$848$	−0.116378	−0.00399645
$849$	−6.65965	−0.228559
$850$	−1.24499	−0.0427029
$851$	−11.2314	−0.385007
$852$	−6.34425	−0.217351
$853$	−0.741843	−0.0254002	−0.0127001	−	0.999919i	$-0.504043\pi$
$853$	−0.741843	−0.0254002	−0.0127001	+	0.999919i	$0.504043\pi$
$854$	−24.5520	−0.840153
$855$	30.3268	1.03716
$856$	−6.87144	−0.234861
$857$	−11.5185	−0.393464	−0.196732	−	0.980457i	$-0.563033\pi$
$857$	−11.5185	−0.393464	−0.196732	+	0.980457i	$0.563033\pi$
$858$	−4.86231	−0.165997
$859$	−34.6591	−1.18255	−0.591277	−	0.806468i	$-0.701376\pi$
$859$	−34.6591	−1.18255	−0.591277	+	0.806468i	$0.701376\pi$
$860$	−32.1329	−1.09572
$861$	−3.60615	−0.122897
$862$	−54.5496	−1.85797
$863$	25.1189	0.855059	0.427529	−	0.904001i	$-0.359384\pi$
$863$	25.1189	0.855059	0.427529	+	0.904001i	$0.359384\pi$
$864$	−13.1172	−0.446255
$865$	−52.1934	−1.77463
$866$	−79.3803	−2.69745
$867$	−7.60616	−0.258319
$868$	−17.5441	−0.595484
$869$	−18.8128	−0.638180
$870$	−6.76577	−0.229381
$871$	−4.55168	−0.154228
$872$	−0.733155	−0.0248278
$873$	−33.2076	−1.12391
$874$	29.4077	0.994732
$875$	−15.7456	−0.532299
$876$	−25.0491	−0.846330
$877$	54.2246	1.83104	0.915518	−	0.402278i	$-0.131781\pi$
$877$	54.2246	1.83104	0.915518	+	0.402278i	$0.131781\pi$
$878$	89.9261	3.03486
$879$	−4.76005	−0.160552
$880$	5.54306	0.186856
$881$	−4.90232	−0.165163	−0.0825817	−	0.996584i	$-0.526317\pi$
$881$	−4.90232	−0.165163	−0.0825817	+	0.996584i	$0.526317\pi$
$882$	−33.9761	−1.14404
$883$	−6.39265	−0.215130	−0.107565	−	0.994198i	$-0.534305\pi$
$883$	−6.39265	−0.215130	−0.107565	+	0.994198i	$0.534305\pi$
$884$	−2.09419	−0.0704352
$885$	6.02220	0.202434
$886$	87.1155	2.92670
$887$	43.6226	1.46470	0.732351	−	0.680927i	$-0.238423\pi$
$887$	43.6226	1.46470	0.732351	+	0.680927i	$0.238423\pi$
$888$	6.84482	0.229697
$889$	7.14734	0.239714
$890$	3.89953	0.130713
$891$	32.8150	1.09934
$892$	46.1261	1.54442
$893$	33.8268	1.13197
$894$	−12.1078	−0.404947
$895$	−43.7460	−1.46227
$896$	25.6202	0.855910
$897$	1.08775	0.0363190
$898$	−45.0290	−1.50264
$899$	−12.3858	−0.413088
$900$	8.11064	0.270355
$901$	0.121828	0.00405869
$902$	63.3516	2.10938
$903$	−2.83813	−0.0944470
$904$	48.0461	1.59799
$905$	32.9146	1.09412
$906$	14.1320	0.469504
$907$	−8.27889	−0.274896	−0.137448	−	0.990509i	$-0.543890\pi$
$907$	−8.27889	−0.274896	−0.137448	+	0.990509i	$0.543890\pi$
$908$	−54.8325	−1.81968
$909$	44.9694	1.49154
$910$	−6.21987	−0.206187
$911$	−7.16435	−0.237366	−0.118683	−	0.992932i	$-0.537867\pi$
$911$	−7.16435	−0.237366	−0.118683	+	0.992932i	$0.537867\pi$
$912$	−1.45447	−0.0481624
$913$	−43.7618	−1.44830
$914$	55.6418	1.84047
$915$	7.47549	0.247132
$916$	12.0244	0.397299
$917$	−14.6492	−0.483761
$918$	−3.82141	−0.126125
$919$	−49.4162	−1.63009	−0.815044	−	0.579399i	$-0.803287\pi$
$919$	−49.4162	−1.63009	−0.815044	+	0.579399i	$0.803287\pi$
$920$	−15.2799	−0.503765
$921$	5.25358	0.173111
$922$	−58.0430	−1.91154
$923$	−4.11754	−0.135530
$924$	9.32712	0.306840
$925$	4.08321	0.134255
$926$	−2.31630	−0.0761184
$927$	−8.32162	−0.273318
$928$	15.5204	0.509481
$929$	20.4540	0.671073	0.335537	−	0.942027i	$-0.391082\pi$
$929$	20.4540	0.671073	0.335537	+	0.942027i	$0.391082\pi$
$930$	8.51637	0.279263
$931$	28.0916	0.920665
$932$	45.5149	1.49089
$933$	7.21589	0.236237
$934$	−16.9051	−0.553151
$935$	−5.80264	−0.189767
$936$	8.82416	0.288427
$937$	36.4239	1.18992	0.594959	−	0.803756i	$-0.297168\pi$
$937$	36.4239	1.18992	0.594959	+	0.803756i	$0.297168\pi$
$938$	13.9203	0.454513
$939$	0.915871	0.0298883
$940$	−43.3236	−1.41306
$941$	37.5657	1.22461	0.612304	−	0.790622i	$-0.290243\pi$
$941$	37.5657	1.22461	0.612304	+	0.790622i	$0.290243\pi$
$942$	−24.7466	−0.806288
$943$	−14.1724	−0.461518
$944$	3.84457	0.125130
$945$	−7.11896	−0.231580
$946$	49.8592	1.62106
$947$	22.1352	0.719298	0.359649	−	0.933088i	$-0.382896\pi$
$947$	22.1352	0.719298	0.359649	+	0.933088i	$0.382896\pi$
$948$	−6.32227	−0.205338
$949$	−16.2573	−0.527735
$950$	−10.6913	−0.346871
$951$	16.1754	0.524523
$952$	2.59830	0.0842115
$953$	−8.49360	−0.275135	−0.137567	−	0.990492i	$-0.543928\pi$
$953$	−8.49360	−0.275135	−0.137567	+	0.990492i	$0.543928\pi$
$954$	−1.26534	−0.0409670
$955$	15.0979	0.488557
$956$	25.6968	0.831095
$957$	6.58476	0.212855
$958$	59.7056	1.92900
$959$	−27.3764	−0.884030
$960$	−11.7788	−0.380159
$961$	−15.4095	−0.497080
$962$	10.9502	0.353049
$963$	−6.06316	−0.195383
$964$	38.8984	1.25283
$965$	−23.3381	−0.751281
$966$	−3.32665	−0.107033
$967$	1.19107	0.0383023	0.0191511	−	0.999817i	$-0.493904\pi$
$967$	1.19107	0.0383023	0.0191511	+	0.999817i	$0.493904\pi$
$968$	−31.6889	−1.01852
$969$	1.52259	0.0489125
$970$	−56.0629	−1.80007
$971$	28.1395	0.903039	0.451520	−	0.892261i	$-0.350882\pi$
$971$	28.1395	0.903039	0.451520	+	0.892261i	$0.350882\pi$
$972$	37.7931	1.21221
$973$	6.96769	0.223374
$974$	52.1568	1.67121
$975$	−0.395456	−0.0126647
$976$	4.77235	0.152759
$977$	−53.4226	−1.70914	−0.854570	−	0.519336i	$-0.826179\pi$
$977$	−53.4226	−1.70914	−0.854570	+	0.519336i	$0.826179\pi$
$978$	−6.35243	−0.203128
$979$	−3.79521	−0.121295
$980$	−35.9782	−1.14928
$981$	−0.646914	−0.0206544
$982$	−87.3554	−2.78762
$983$	−58.0170	−1.85045	−0.925227	−	0.379413i	$-0.876126\pi$
$983$	−58.0170	−1.85045	−0.925227	+	0.379413i	$0.876126\pi$
$984$	8.63722	0.275345
$985$	44.0263	1.40279
$986$	4.52153	0.143995
$987$	−3.82654	−0.121800
$988$	−17.9837	−0.572137
$989$	−11.1540	−0.354678
$990$	60.2678	1.91544
$991$	10.2965	0.327080	0.163540	−	0.986537i	$-0.447709\pi$
$991$	10.2965	0.327080	0.163540	+	0.986537i	$0.447709\pi$
$992$	−19.5362	−0.620274
$993$	4.36958	0.138664
$994$	12.5926	0.399412
$995$	−55.3600	−1.75503
$996$	−14.7067	−0.465999
$997$	52.1539	1.65173	0.825866	−	0.563867i	$-0.190687\pi$
$997$	52.1539	1.65173	0.825866	+	0.563867i	$0.190687\pi$
$998$	−81.3233	−2.57424
$999$	12.5331	0.396529

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6019.2.a.b.1.13	✓	101

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6019.2.a.b.1.13	✓	101	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:	\( N \)	\(=\)	\( 6019 = 13 \cdot 463 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.31630 q^{2} +0.457851 q^{3} +3.36526 q^{4} +2.03378 q^{5} -1.06052 q^{6} +1.32033 q^{7} -3.16236 q^{8} -2.79037 q^{9} +O(q^{10})\)	\(q-2.31630 q^{2} +0.457851 q^{3} +3.36526 q^{4} +2.03378 q^{5} -1.06052 q^{6} +1.32033 q^{7} -3.16236 q^{8} -2.79037 q^{9} -4.71086 q^{10} +4.58483 q^{11} +1.54079 q^{12} +1.00000 q^{13} -3.05828 q^{14} +0.931170 q^{15} +0.594458 q^{16} -0.622297 q^{17} +6.46335 q^{18} -5.34392 q^{19} +6.84421 q^{20} +0.604513 q^{21} -10.6199 q^{22} +2.37578 q^{23} -1.44789 q^{24} -0.863723 q^{25} -2.31630 q^{26} -2.65113 q^{27} +4.44324 q^{28} +3.13684 q^{29} -2.15687 q^{30} -3.94848 q^{31} +4.94777 q^{32} +2.09917 q^{33} +1.44143 q^{34} +2.68526 q^{35} -9.39033 q^{36} -4.72745 q^{37} +12.3781 q^{38} +0.457851 q^{39} -6.43155 q^{40} -5.96539 q^{41} -1.40023 q^{42} -4.69490 q^{43} +15.4291 q^{44} -5.67501 q^{45} -5.50302 q^{46} -6.32996 q^{47} +0.272173 q^{48} -5.25674 q^{49} +2.00064 q^{50} -0.284919 q^{51} +3.36526 q^{52} -0.195772 q^{53} +6.14082 q^{54} +9.32455 q^{55} -4.17534 q^{56} -2.44672 q^{57} -7.26588 q^{58} +6.46735 q^{59} +3.13363 q^{60} +8.02806 q^{61} +9.14588 q^{62} -3.68420 q^{63} -12.6495 q^{64} +2.03378 q^{65} -4.86231 q^{66} -4.55168 q^{67} -2.09419 q^{68} +1.08775 q^{69} -6.21987 q^{70} -4.11754 q^{71} +8.82416 q^{72} -16.2573 q^{73} +10.9502 q^{74} -0.395456 q^{75} -17.9837 q^{76} +6.05347 q^{77} -1.06052 q^{78} -4.10327 q^{79} +1.20900 q^{80} +7.15730 q^{81} +13.8177 q^{82} -9.54491 q^{83} +2.03434 q^{84} -1.26562 q^{85} +10.8748 q^{86} +1.43621 q^{87} -14.4989 q^{88} -0.827775 q^{89} +13.1451 q^{90} +1.32033 q^{91} +7.99512 q^{92} -1.80782 q^{93} +14.6621 q^{94} -10.8684 q^{95} +2.26534 q^{96} +11.9008 q^{97} +12.1762 q^{98} -12.7934 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9}+O(q^{10}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9	\( 101 q - 8 q^{2} - 13 q^{3} + 86 q^{4} - 43 q^{5} - 10 q^{6} - q^{7} - 24 q^{8} + 52 q^{9} - 19 q^{10} - 42 q^{11} - 28 q^{12} + 101 q^{13} - 45 q^{14} - 15 q^{15} + 48 q^{16} - 83 q^{17} - 4 q^{18} - 18 q^{19} - 51 q^{20} - 50 q^{21} - 20 q^{22} - 64 q^{23} - 23 q^{24} + 46 q^{25} - 8 q^{26} - 37 q^{27} - 11 q^{28} - 117 q^{29} - 28 q^{30} - 10 q^{31} - 36 q^{32} - 20 q^{33} - 10 q^{34} - 53 q^{35} - 16 q^{36} - 27 q^{37} - 68 q^{38} - 13 q^{39} - 42 q^{40} - 60 q^{41} - 31 q^{42} - 16 q^{43} - 89 q^{44} - 56 q^{45} + 5 q^{46} - 23 q^{47} - 37 q^{48} + 48 q^{49} - 30 q^{50} - 68 q^{51} + 86 q^{52} - 189 q^{53} - 23 q^{54} + 3 q^{55} - 106 q^{56} - 25 q^{57} - 82 q^{59} + 6 q^{60} - 68 q^{61} - 57 q^{62} + 3 q^{63} - 2 q^{64} - 43 q^{65} - 40 q^{66} - 13 q^{67} - 138 q^{68} - 92 q^{69} + 18 q^{70} - 39 q^{71} - 20 q^{72} + 19 q^{73} - 88 q^{74} - 21 q^{75} - 53 q^{76} - 147 q^{77} - 10 q^{78} - 19 q^{79} - 104 q^{80} - 55 q^{81} + 27 q^{82} - 49 q^{83} - 59 q^{84} - 27 q^{85} - 99 q^{86} - 33 q^{87} - 41 q^{88} - 70 q^{89} - 49 q^{90} - q^{91} - 111 q^{92} - 84 q^{93} + 4 q^{94} - 82 q^{95} - 7 q^{96} + 25 q^{97} - 37 q^{98} - 41 q^{99}+O(q^{100}) \) 101 * q - 8 * q^2 - 13 * q^3 + 86 * q^4 - 43 * q^5 - 10 * q^6 - q^7 - 24 * q^8 + 52 * q^9 - 19 * q^10 - 42 * q^11 - 28 * q^12 + 101 * q^13 - 45 * q^14 - 15 * q^15 + 48 * q^16 - 83 * q^17 - 4 * q^18 - 18 * q^19 - 51 * q^20 - 50 * q^21 - 20 * q^22 - 64 * q^23 - 23 * q^24 + 46 * q^25 - 8 * q^26 - 37 * q^27 - 11 * q^28 - 117 * q^29 - 28 * q^30 - 10 * q^31 - 36 * q^32 - 20 * q^33 - 10 * q^34 - 53 * q^35 - 16 * q^36 - 27 * q^37 - 68 * q^38 - 13 * q^39 - 42 * q^40 - 60 * q^41 - 31 * q^42 - 16 * q^43 - 89 * q^44 - 56 * q^45 + 5 * q^46 - 23 * q^47 - 37 * q^48 + 48 * q^49 - 30 * q^50 - 68 * q^51 + 86 * q^52 - 189 * q^53 - 23 * q^54 + 3 * q^55 - 106 * q^56 - 25 * q^57 - 82 * q^59 + 6 * q^60 - 68 * q^61 - 57 * q^62 + 3 * q^63 - 2 * q^64 - 43 * q^65 - 40 * q^66 - 13 * q^67 - 138 * q^68 - 92 * q^69 + 18 * q^70 - 39 * q^71 - 20 * q^72 + 19 * q^73 - 88 * q^74 - 21 * q^75 - 53 * q^76 - 147 * q^77 - 10 * q^78 - 19 * q^79 - 104 * q^80 - 55 * q^81 + 27 * q^82 - 49 * q^83 - 59 * q^84 - 27 * q^85 - 99 * q^86 - 33 * q^87 - 41 * q^88 - 70 * q^89 - 49 * q^90 - q^91 - 111 * q^92 - 84 * q^93 + 4 * q^94 - 82 * q^95 - 7 * q^96 + 25 * q^97 - 37 * q^98 - 41 * q^99

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