LMFDB - Embedded newform 6013.2.a.c.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6013,2,Mod(1,6013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6013, 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("6013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6013 = 7 \cdot 859 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6013.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:	$48.0140467354$
Analytic rank:	$1$
Dimension:	$104$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.79954 q^{2} -0.206703 q^{3} +5.83741 q^{4} +2.43879 q^{5} +0.578672 q^{6} -1.00000 q^{7} -10.7430 q^{8} -2.95727 q^{9} +O(q^{10})$	\(q-2.79954 q^{2} -0.206703 q^{3} +5.83741 q^{4} +2.43879 q^{5} +0.578672 q^{6} -1.00000 q^{7} -10.7430 q^{8} -2.95727 q^{9} -6.82749 q^{10} +1.72511 q^{11} -1.20661 q^{12} -2.89520 q^{13} +2.79954 q^{14} -0.504105 q^{15} +18.4006 q^{16} +4.63912 q^{17} +8.27900 q^{18} +2.54763 q^{19} +14.2362 q^{20} +0.206703 q^{21} -4.82952 q^{22} -7.25845 q^{23} +2.22060 q^{24} +0.947708 q^{25} +8.10522 q^{26} +1.23138 q^{27} -5.83741 q^{28} +0.785031 q^{29} +1.41126 q^{30} +4.25007 q^{31} -30.0271 q^{32} -0.356586 q^{33} -12.9874 q^{34} -2.43879 q^{35} -17.2628 q^{36} -10.6936 q^{37} -7.13219 q^{38} +0.598445 q^{39} -26.1999 q^{40} -5.96178 q^{41} -0.578672 q^{42} +4.81198 q^{43} +10.0702 q^{44} -7.21218 q^{45} +20.3203 q^{46} +4.27524 q^{47} -3.80345 q^{48} +1.00000 q^{49} -2.65315 q^{50} -0.958918 q^{51} -16.9005 q^{52} +3.93458 q^{53} -3.44731 q^{54} +4.20720 q^{55} +10.7430 q^{56} -0.526602 q^{57} -2.19773 q^{58} +4.67984 q^{59} -2.94267 q^{60} +7.59684 q^{61} -11.8982 q^{62} +2.95727 q^{63} +47.2609 q^{64} -7.06079 q^{65} +0.998276 q^{66} +10.8010 q^{67} +27.0805 q^{68} +1.50034 q^{69} +6.82749 q^{70} -9.86579 q^{71} +31.7699 q^{72} -1.77317 q^{73} +29.9372 q^{74} -0.195894 q^{75} +14.8716 q^{76} -1.72511 q^{77} -1.67537 q^{78} -4.86859 q^{79} +44.8752 q^{80} +8.61729 q^{81} +16.6902 q^{82} -4.17385 q^{83} +1.20661 q^{84} +11.3138 q^{85} -13.4713 q^{86} -0.162268 q^{87} -18.5329 q^{88} +1.41142 q^{89} +20.1908 q^{90} +2.89520 q^{91} -42.3705 q^{92} -0.878501 q^{93} -11.9687 q^{94} +6.21314 q^{95} +6.20668 q^{96} -12.2210 q^{97} -2.79954 q^{98} -5.10164 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) $ 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * 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 $

$2$	−2.79954	−1.97957	−0.989786	−	0.142560i	$-0.954467\pi$
$2$	−2.79954	−1.97957	−0.989786	+	0.142560i	$0.954467\pi$
$3$	−0.206703	−0.119340	−0.0596699	−	0.998218i	$-0.519005\pi$
$3$	−0.206703	−0.119340	−0.0596699	+	0.998218i	$0.519005\pi$
$4$	5.83741	2.91871
$5$	2.43879	1.09066	0.545331	−	0.838221i	$-0.316404\pi$
$5$	2.43879	1.09066	0.545331	+	0.838221i	$0.316404\pi$
$6$	0.578672	0.236242
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−10.7430	−3.79822
$9$	−2.95727	−0.985758
$10$	−6.82749	−2.15904
$11$	1.72511	0.520142	0.260071	−	0.965590i	$-0.416254\pi$
$11$	1.72511	0.520142	0.260071	+	0.965590i	$0.416254\pi$
$12$	−1.20661	−0.348318
$13$	−2.89520	−0.802983	−0.401492	−	0.915863i	$-0.631508\pi$
$13$	−2.89520	−0.802983	−0.401492	+	0.915863i	$0.631508\pi$
$14$	2.79954	0.748208
$15$	−0.504105	−0.130159
$16$	18.4006	4.60014
$17$	4.63912	1.12515	0.562576	−	0.826746i	$-0.309810\pi$
$17$	4.63912	1.12515	0.562576	+	0.826746i	$0.309810\pi$
$18$	8.27900	1.95138
$19$	2.54763	0.584467	0.292233	−	0.956347i	$-0.405602\pi$
$19$	2.54763	0.584467	0.292233	+	0.956347i	$0.405602\pi$
$20$	14.2362	3.18332
$21$	0.206703	0.0451062
$22$	−4.82952	−1.02966
$23$	−7.25845	−1.51349	−0.756745	−	0.653710i	$-0.773212\pi$
$23$	−7.25845	−1.51349	−0.756745	+	0.653710i	$0.773212\pi$
$24$	2.22060	0.453279
$25$	0.947708	0.189542
$26$	8.10522	1.58956
$27$	1.23138	0.236980
$28$	−5.83741	−1.10317
$29$	0.785031	0.145777	0.0728883	−	0.997340i	$-0.476778\pi$
$29$	0.785031	0.145777	0.0728883	+	0.997340i	$0.476778\pi$
$30$	1.41126	0.257660
$31$	4.25007	0.763335	0.381668	−	0.924300i	$-0.375350\pi$
$31$	4.25007	0.763335	0.381668	+	0.924300i	$0.375350\pi$
$32$	−30.0271	−5.30809
$33$	−0.356586	−0.0620736
$34$	−12.9874	−2.22732
$35$	−2.43879	−0.412231
$36$	−17.2628	−2.87714
$37$	−10.6936	−1.75802	−0.879009	−	0.476806i	$-0.841795\pi$
$37$	−10.6936	−1.75802	−0.879009	+	0.476806i	$0.841795\pi$
$38$	−7.13219	−1.15699
$39$	0.598445	0.0958279
$40$	−26.1999	−4.14257
$41$	−5.96178	−0.931074	−0.465537	−	0.885029i	$-0.654139\pi$
$41$	−5.96178	−0.931074	−0.465537	+	0.885029i	$0.654139\pi$
$42$	−0.578672	−0.0892910
$43$	4.81198	0.733819	0.366910	−	0.930257i	$-0.380416\pi$
$43$	4.81198	0.733819	0.366910	+	0.930257i	$0.380416\pi$
$44$	10.0702	1.51814
$45$	−7.21218	−1.07513
$46$	20.3203	2.99606
$47$	4.27524	0.623608	0.311804	−	0.950146i	$-0.399067\pi$
$47$	4.27524	0.623608	0.311804	+	0.950146i	$0.399067\pi$
$48$	−3.80345	−0.548980
$49$	1.00000	0.142857
$50$	−2.65315	−0.375211
$51$	−0.958918	−0.134275
$52$	−16.9005	−2.34367
$53$	3.93458	0.540457	0.270228	−	0.962796i	$-0.412901\pi$
$53$	3.93458	0.540457	0.270228	+	0.962796i	$0.412901\pi$
$54$	−3.44731	−0.469119
$55$	4.20720	0.567298
$56$	10.7430	1.43559
$57$	−0.526602	−0.0697502
$58$	−2.19773	−0.288575
$59$	4.67984	0.609264	0.304632	−	0.952470i	$-0.401467\pi$
$59$	4.67984	0.609264	0.304632	+	0.952470i	$0.401467\pi$
$60$	−2.94267	−0.379897
$61$	7.59684	0.972675	0.486338	−	0.873771i	$-0.338333\pi$
$61$	7.59684	0.972675	0.486338	+	0.873771i	$0.338333\pi$
$62$	−11.8982	−1.51108
$63$	2.95727	0.372582
$64$	47.2609	5.90761
$65$	−7.06079	−0.875783
$66$	0.998276	0.122879
$67$	10.8010	1.31955	0.659777	−	0.751462i	$-0.270651\pi$
$67$	10.8010	1.31955	0.659777	+	0.751462i	$0.270651\pi$
$68$	27.0805	3.28399
$69$	1.50034	0.180620
$70$	6.82749	0.816041
$71$	−9.86579	−1.17085	−0.585427	−	0.810725i	$-0.699073\pi$
$71$	−9.86579	−1.17085	−0.585427	+	0.810725i	$0.699073\pi$
$72$	31.7699	3.74412
$73$	−1.77317	−0.207534	−0.103767	−	0.994602i	$-0.533090\pi$
$73$	−1.77317	−0.207534	−0.103767	+	0.994602i	$0.533090\pi$
$74$	29.9372	3.48012
$75$	−0.195894	−0.0226199
$76$	14.8716	1.70589
$77$	−1.72511	−0.196595
$78$	−1.67537	−0.189698
$79$	−4.86859	−0.547759	−0.273879	−	0.961764i	$-0.588307\pi$
$79$	−4.86859	−0.547759	−0.273879	+	0.961764i	$0.588307\pi$
$80$	44.8752	5.01719
$81$	8.61729	0.957477
$82$	16.6902	1.84313
$83$	−4.17385	−0.458139	−0.229070	−	0.973410i	$-0.573568\pi$
$83$	−4.17385	−0.458139	−0.229070	+	0.973410i	$0.573568\pi$
$84$	1.20661	0.131652
$85$	11.3138	1.22716
$86$	−13.4713	−1.45265
$87$	−0.162268	−0.0173970
$88$	−18.5329	−1.97561
$89$	1.41142	0.149610	0.0748050	−	0.997198i	$-0.476167\pi$
$89$	1.41142	0.149610	0.0748050	+	0.997198i	$0.476167\pi$
$90$	20.1908	2.12829
$91$	2.89520	0.303499
$92$	−42.3705	−4.41744
$93$	−0.878501	−0.0910963
$94$	−11.9687	−1.23448
$95$	6.21314	0.637455
$96$	6.20668	0.633467
$97$	−12.2210	−1.24086	−0.620429	−	0.784263i	$-0.713041\pi$
$97$	−12.2210	−1.24086	−0.620429	+	0.784263i	$0.713041\pi$
$98$	−2.79954	−0.282796
$99$	−5.10164	−0.512734
$100$	5.53216	0.553216
$101$	0.556470	0.0553708	0.0276854	−	0.999617i	$-0.491186\pi$
$101$	0.556470	0.0553708	0.0276854	+	0.999617i	$0.491186\pi$
$102$	2.68453	0.265808
$103$	−15.6401	−1.54106	−0.770531	−	0.637403i	$-0.780009\pi$
$103$	−15.6401	−1.54106	−0.770531	+	0.637403i	$0.780009\pi$
$104$	31.1031	3.04991
$105$	0.504105	0.0491956
$106$	−11.0150	−1.06987
$107$	−2.51149	−0.242795	−0.121398	−	0.992604i	$-0.538738\pi$
$107$	−2.51149	−0.242795	−0.121398	+	0.992604i	$0.538738\pi$
$108$	7.18810	0.691675
$109$	6.85111	0.656217	0.328108	−	0.944640i	$-0.393589\pi$
$109$	6.85111	0.656217	0.328108	+	0.944640i	$0.393589\pi$
$110$	−11.7782	−1.12301
$111$	2.21040	0.209802
$112$	−18.4006	−1.73869
$113$	−1.70437	−0.160334	−0.0801668	−	0.996781i	$-0.525545\pi$
$113$	−1.70437	−0.160334	−0.0801668	+	0.996781i	$0.525545\pi$
$114$	1.47424	0.138075
$115$	−17.7018	−1.65071
$116$	4.58255	0.425479
$117$	8.56189	0.791547
$118$	−13.1014	−1.20608
$119$	−4.63912	−0.425267
$120$	5.41559	0.494373
$121$	−8.02398	−0.729453
$122$	−21.2676	−1.92548
$123$	1.23232	0.111114
$124$	24.8094	2.22795
$125$	−9.88270	−0.883935
$126$	−8.27900	−0.737552
$127$	8.11831	0.720384	0.360192	−	0.932878i	$-0.382711\pi$
$127$	8.11831	0.720384	0.360192	+	0.932878i	$0.382711\pi$
$128$	−72.2545	−6.38645
$129$	−0.994648	−0.0875739
$130$	19.7669	1.73368
$131$	4.60540	0.402375	0.201188	−	0.979553i	$-0.435520\pi$
$131$	4.60540	0.402375	0.201188	+	0.979553i	$0.435520\pi$
$132$	−2.08154	−0.181175
$133$	−2.54763	−0.220908
$134$	−30.2378	−2.61215
$135$	3.00309	0.258465
$136$	−49.8380	−4.27357
$137$	−3.29123	−0.281189	−0.140594	−	0.990067i	$-0.544901\pi$
$137$	−3.29123	−0.281189	−0.140594	+	0.990067i	$0.544901\pi$
$138$	−4.20026	−0.357550
$139$	−15.0303	−1.27485	−0.637426	−	0.770512i	$-0.720001\pi$
$139$	−15.0303	−1.27485	−0.637426	+	0.770512i	$0.720001\pi$
$140$	−14.2362	−1.20318
$141$	−0.883703	−0.0744212
$142$	27.6196	2.31779
$143$	−4.99455	−0.417665
$144$	−54.4155	−4.53463
$145$	1.91453	0.158993
$146$	4.96406	0.410829
$147$	−0.206703	−0.0170485
$148$	−62.4230	−5.13114
$149$	6.54315	0.536035	0.268018	−	0.963414i	$-0.413631\pi$
$149$	6.54315	0.536035	0.268018	+	0.963414i	$0.413631\pi$
$150$	0.548412	0.0447777
$151$	9.31105	0.757723	0.378861	−	0.925453i	$-0.376316\pi$
$151$	9.31105	0.757723	0.378861	+	0.925453i	$0.376316\pi$
$152$	−27.3692	−2.21993
$153$	−13.7191	−1.10913
$154$	4.82952	0.389174
$155$	10.3650	0.832540
$156$	3.49337	0.279694
$157$	13.7623	1.09835	0.549174	−	0.835708i	$-0.314943\pi$
$157$	13.7623	1.09835	0.549174	+	0.835708i	$0.314943\pi$
$158$	13.6298	1.08433
$159$	−0.813289	−0.0644980
$160$	−73.2299	−5.78933
$161$	7.25845	0.572046
$162$	−24.1244	−1.89539
$163$	4.47082	0.350181	0.175091	−	0.984552i	$-0.443978\pi$
$163$	4.47082	0.350181	0.175091	+	0.984552i	$0.443978\pi$
$164$	−34.8014	−2.71753
$165$	−0.869639	−0.0677013
$166$	11.6848	0.906920
$167$	−0.539262	−0.0417293	−0.0208647	−	0.999782i	$-0.506642\pi$
$167$	−0.539262	−0.0417293	−0.0208647	+	0.999782i	$0.506642\pi$
$168$	−2.22060	−0.171323
$169$	−4.61783	−0.355218
$170$	−31.6735	−2.42925
$171$	−7.53404	−0.576143
$172$	28.0895	2.14180
$173$	−24.7542	−1.88202	−0.941012	−	0.338374i	$-0.890123\pi$
$173$	−24.7542	−1.88202	−0.941012	+	0.338374i	$0.890123\pi$
$174$	0.454276	0.0344385
$175$	−0.947708	−0.0716400
$176$	31.7431	2.39273
$177$	−0.967336	−0.0727094
$178$	−3.95132	−0.296164
$179$	−7.36085	−0.550176	−0.275088	−	0.961419i	$-0.588707\pi$
$179$	−7.36085	−0.550176	−0.275088	+	0.961419i	$0.588707\pi$
$180$	−42.1005	−3.13798
$181$	10.8873	0.809245	0.404623	−	0.914484i	$-0.367403\pi$
$181$	10.8873	0.809245	0.404623	+	0.914484i	$0.367403\pi$
$182$	−8.10522	−0.600799
$183$	−1.57029	−0.116079
$184$	77.9774	5.74857
$185$	−26.0795	−1.91740
$186$	2.45940	0.180332
$187$	8.00301	0.585238
$188$	24.9563	1.82013
$189$	−1.23138	−0.0895700
$190$	−17.3939	−1.26189
$191$	−2.17271	−0.157212	−0.0786059	−	0.996906i	$-0.525047\pi$
$191$	−2.17271	−0.157212	−0.0786059	+	0.996906i	$0.525047\pi$
$192$	−9.76896	−0.705014
$193$	16.0033	1.15194	0.575971	−	0.817470i	$-0.304624\pi$
$193$	16.0033	1.15194	0.575971	+	0.817470i	$0.304624\pi$
$194$	34.2132	2.45637
$195$	1.45948	0.104516
$196$	5.83741	0.416958
$197$	−12.5716	−0.895691	−0.447846	−	0.894111i	$-0.647809\pi$
$197$	−12.5716	−0.895691	−0.447846	+	0.894111i	$0.647809\pi$
$198$	14.2822	1.01499
$199$	−13.0280	−0.923532	−0.461766	−	0.887002i	$-0.652784\pi$
$199$	−13.0280	−0.923532	−0.461766	+	0.887002i	$0.652784\pi$
$200$	−10.1812	−0.719921
$201$	−2.23260	−0.157475
$202$	−1.55786	−0.109611
$203$	−0.785031	−0.0550984
$204$	−5.59760	−0.391910
$205$	−14.5395	−1.01549
$206$	43.7849	3.05064
$207$	21.4652	1.49194
$208$	−53.2733	−3.69384
$209$	4.39496	0.304005
$210$	−1.41126	−0.0973862
$211$	22.5497	1.55239	0.776194	−	0.630495i	$-0.217148\pi$
$211$	22.5497	1.55239	0.776194	+	0.630495i	$0.217148\pi$
$212$	22.9678	1.57743
$213$	2.03928	0.139729
$214$	7.03101	0.480630
$215$	11.7354	0.800348
$216$	−13.2287	−0.900102
$217$	−4.25007	−0.288514
$218$	−19.1799	−1.29903
$219$	0.366519	0.0247671
$220$	24.5591	1.65578
$221$	−13.4312	−0.903478
$222$	−6.18809	−0.415317
$223$	−10.7108	−0.717247	−0.358624	−	0.933482i	$-0.616754\pi$
$223$	−10.7108	−0.717247	−0.358624	+	0.933482i	$0.616754\pi$
$224$	30.0271	2.00627
$225$	−2.80263	−0.186842
$226$	4.77145	0.317392
$227$	−24.1353	−1.60192	−0.800958	−	0.598721i	$-0.795676\pi$
$227$	−24.1353	−1.60192	−0.800958	+	0.598721i	$0.795676\pi$
$228$	−3.07399	−0.203580
$229$	−13.9322	−0.920665	−0.460333	−	0.887746i	$-0.652270\pi$
$229$	−13.9322	−0.920665	−0.460333	+	0.887746i	$0.652270\pi$
$230$	49.5570	3.26769
$231$	0.356586	0.0234616
$232$	−8.43358	−0.553692
$233$	8.97743	0.588131	0.294065	−	0.955785i	$-0.404992\pi$
$233$	8.97743	0.588131	0.294065	+	0.955785i	$0.404992\pi$
$234$	−23.9693	−1.56693
$235$	10.4264	0.680145
$236$	27.3182	1.77826
$237$	1.00635	0.0653695
$238$	12.9874	0.841847
$239$	−16.9325	−1.09527	−0.547635	−	0.836717i	$-0.684472\pi$
$239$	−16.9325	−1.09527	−0.547635	+	0.836717i	$0.684472\pi$
$240$	−9.27581	−0.598751
$241$	−12.8101	−0.825170	−0.412585	−	0.910919i	$-0.635374\pi$
$241$	−12.8101	−0.825170	−0.412585	+	0.910919i	$0.635374\pi$
$242$	22.4634	1.44400
$243$	−5.47537	−0.351245
$244$	44.3459	2.83895
$245$	2.43879	0.155809
$246$	−3.44991	−0.219959
$247$	−7.37590	−0.469317
$248$	−45.6584	−2.89931
$249$	0.862746	0.0546743
$250$	27.6670	1.74981
$251$	−6.99354	−0.441428	−0.220714	−	0.975339i	$-0.570839\pi$
$251$	−6.99354	−0.441428	−0.220714	+	0.975339i	$0.570839\pi$
$252$	17.2628	1.08746
$253$	−12.5217	−0.787230
$254$	−22.7275	−1.42605
$255$	−2.33860	−0.146449
$256$	107.757	6.73483
$257$	−18.3724	−1.14604	−0.573020	−	0.819541i	$-0.694228\pi$
$257$	−18.3724	−1.14604	−0.573020	+	0.819541i	$0.694228\pi$
$258$	2.78456	0.173359
$259$	10.6936	0.664468
$260$	−41.2167	−2.55615
$261$	−2.32155	−0.143701
$262$	−12.8930	−0.796531
$263$	−25.3953	−1.56594	−0.782971	−	0.622058i	$-0.786297\pi$
$263$	−25.3953	−1.56594	−0.782971	+	0.622058i	$0.786297\pi$
$264$	3.83080	0.235769
$265$	9.59564	0.589455
$266$	7.13219	0.437303
$267$	−0.291744	−0.0178544
$268$	63.0500	3.85139
$269$	−13.9186	−0.848635	−0.424317	−	0.905514i	$-0.639486\pi$
$269$	−13.9186	−0.848635	−0.424317	+	0.905514i	$0.639486\pi$
$270$	−8.40727	−0.511650
$271$	9.64971	0.586178	0.293089	−	0.956085i	$-0.405317\pi$
$271$	9.64971	0.586178	0.293089	+	0.956085i	$0.405317\pi$
$272$	85.3624	5.17586
$273$	−0.598445	−0.0362195
$274$	9.21392	0.556633
$275$	1.63491	0.0985885
$276$	8.75811	0.527176
$277$	1.23006	0.0739072	0.0369536	−	0.999317i	$-0.488235\pi$
$277$	1.23006	0.0739072	0.0369536	+	0.999317i	$0.488235\pi$
$278$	42.0779	2.52366
$279$	−12.5686	−0.752464
$280$	26.1999	1.56574
$281$	10.6321	0.634255	0.317128	−	0.948383i	$-0.397282\pi$
$281$	10.6321	0.634255	0.317128	+	0.948383i	$0.397282\pi$
$282$	2.47396	0.147322
$283$	17.5907	1.04566	0.522829	−	0.852438i	$-0.324877\pi$
$283$	17.5907	1.04566	0.522829	+	0.852438i	$0.324877\pi$
$284$	−57.5907	−3.41738
$285$	−1.28427	−0.0760738
$286$	13.9824	0.826798
$287$	5.96178	0.351913
$288$	88.7984	5.23250
$289$	4.52142	0.265966
$290$	−5.35980	−0.314738
$291$	2.52612	0.148084
$292$	−10.3507	−0.605731
$293$	−5.20705	−0.304199	−0.152100	−	0.988365i	$-0.548603\pi$
$293$	−5.20705	−0.304199	−0.152100	+	0.988365i	$0.548603\pi$
$294$	0.578672	0.0337488
$295$	11.4132	0.664500
$296$	114.881	6.67733
$297$	2.12428	0.123263
$298$	−18.3178	−1.06112
$299$	21.0146	1.21531
$300$	−1.14351	−0.0660208
$301$	−4.81198	−0.277358
$302$	−26.0666	−1.49997
$303$	−0.115024	−0.00660794
$304$	46.8778	2.68863
$305$	18.5271	1.06086
$306$	38.4073	2.19560
$307$	−19.8434	−1.13252	−0.566260	−	0.824227i	$-0.691610\pi$
$307$	−19.8434	−1.13252	−0.566260	+	0.824227i	$0.691610\pi$
$308$	−10.0702	−0.573803
$309$	3.23284	0.183910
$310$	−29.0173	−1.64807
$311$	2.34728	0.133102	0.0665510	−	0.997783i	$-0.478800\pi$
$311$	2.34728	0.133102	0.0665510	+	0.997783i	$0.478800\pi$
$312$	−6.42909	−0.363975
$313$	−18.9432	−1.07073	−0.535366	−	0.844620i	$-0.679826\pi$
$313$	−18.9432	−1.07073	−0.535366	+	0.844620i	$0.679826\pi$
$314$	−38.5279	−2.17426
$315$	7.21218	0.406360
$316$	−28.4200	−1.59875
$317$	26.1777	1.47028	0.735142	−	0.677913i	$-0.237116\pi$
$317$	26.1777	1.47028	0.735142	+	0.677913i	$0.237116\pi$
$318$	2.27683	0.127679
$319$	1.35427	0.0758245
$320$	115.260	6.44320
$321$	0.519132	0.0289751
$322$	−20.3203	−1.13241
$323$	11.8188	0.657614
$324$	50.3027	2.79459
$325$	−2.74380	−0.152199
$326$	−12.5162	−0.693209
$327$	−1.41614	−0.0783128
$328$	64.0473	3.53642
$329$	−4.27524	−0.235702
$330$	2.43459	0.134020
$331$	−19.9677	−1.09752	−0.548762	−	0.835979i	$-0.684900\pi$
$331$	−19.9677	−1.09752	−0.548762	+	0.835979i	$0.684900\pi$
$332$	−24.3645	−1.33717
$333$	31.6239	1.73298
$334$	1.50968	0.0826062
$335$	26.3414	1.43919
$336$	3.80345	0.207495
$337$	−6.94160	−0.378133	−0.189066	−	0.981964i	$-0.560546\pi$
$337$	−6.94160	−0.378133	−0.189066	+	0.981964i	$0.560546\pi$
$338$	12.9278	0.703179
$339$	0.352298	0.0191342
$340$	66.0436	3.58172
$341$	7.33186	0.397042
$342$	21.0918	1.14052
$343$	−1.00000	−0.0539949
$344$	−51.6950	−2.78721
$345$	3.65902	0.196995
$346$	69.3002	3.72560
$347$	−16.9822	−0.911650	−0.455825	−	0.890069i	$-0.650656\pi$
$347$	−16.9822	−0.911650	−0.455825	+	0.890069i	$0.650656\pi$
$348$	−0.947226	−0.0507766
$349$	10.1055	0.540934	0.270467	−	0.962729i	$-0.412822\pi$
$349$	10.1055	0.540934	0.270467	+	0.962729i	$0.412822\pi$
$350$	2.65315	0.141817
$351$	−3.56510	−0.190291
$352$	−51.8002	−2.76096
$353$	−6.68917	−0.356029	−0.178014	−	0.984028i	$-0.556967\pi$
$353$	−6.68917	−0.356029	−0.178014	+	0.984028i	$0.556967\pi$
$354$	2.70809	0.143934
$355$	−24.0606	−1.27700
$356$	8.23903	0.436668
$357$	0.958918	0.0507513
$358$	20.6070	1.08911
$359$	−21.5615	−1.13797	−0.568987	−	0.822347i	$-0.692664\pi$
$359$	−21.5615	−1.13797	−0.568987	+	0.822347i	$0.692664\pi$
$360$	77.4803	4.08357
$361$	−12.5096	−0.658399
$362$	−30.4794	−1.60196
$363$	1.65858	0.0870528
$364$	16.9005	0.885825
$365$	−4.32440	−0.226349
$366$	4.39608	0.229787
$367$	26.3197	1.37388	0.686940	−	0.726714i	$-0.258954\pi$
$367$	26.3197	1.37388	0.686940	+	0.726714i	$0.258954\pi$
$368$	−133.560	−6.96227
$369$	17.6306	0.917813
$370$	73.0105	3.79563
$371$	−3.93458	−0.204273
$372$	−5.12817	−0.265883
$373$	36.3615	1.88272	0.941362	−	0.337397i	$-0.109546\pi$
$373$	36.3615	1.88272	0.941362	+	0.337397i	$0.109546\pi$
$374$	−22.4047	−1.15852
$375$	2.04278	0.105489
$376$	−45.9288	−2.36860
$377$	−2.27282	−0.117056
$378$	3.44731	0.177310
$379$	−28.3454	−1.45601	−0.728003	−	0.685574i	$-0.759551\pi$
$379$	−28.3454	−1.45601	−0.728003	+	0.685574i	$0.759551\pi$
$380$	36.2687	1.86054
$381$	−1.67808	−0.0859705
$382$	6.08259	0.311212
$383$	−37.5318	−1.91779	−0.958893	−	0.283767i	$-0.908416\pi$
$383$	−37.5318	−1.91779	−0.958893	+	0.283767i	$0.908416\pi$
$384$	14.9352	0.762158
$385$	−4.20720	−0.214419
$386$	−44.8019	−2.28035
$387$	−14.2303	−0.723368
$388$	−71.3392	−3.62170
$389$	−9.23863	−0.468417	−0.234209	−	0.972186i	$-0.575250\pi$
$389$	−9.23863	−0.468417	−0.234209	+	0.972186i	$0.575250\pi$
$390$	−4.08588	−0.206897
$391$	−33.6728	−1.70291
$392$	−10.7430	−0.542603
$393$	−0.951948	−0.0480194
$394$	35.1947	1.77309
$395$	−11.8735	−0.597419
$396$	−29.7804	−1.49652
$397$	25.0997	1.25972	0.629858	−	0.776710i	$-0.283113\pi$
$397$	25.0997	1.25972	0.629858	+	0.776710i	$0.283113\pi$
$398$	36.4724	1.82820
$399$	0.526602	0.0263631
$400$	17.4384	0.871918
$401$	−18.3313	−0.915422	−0.457711	−	0.889101i	$-0.651331\pi$
$401$	−18.3313	−0.915422	−0.457711	+	0.889101i	$0.651331\pi$
$402$	6.25024	0.311734
$403$	−12.3048	−0.612945
$404$	3.24834	0.161611
$405$	21.0158	1.04428
$406$	2.19773	0.109071
$407$	−18.4477	−0.914418
$408$	10.3016	0.510007
$409$	32.3048	1.59737	0.798686	−	0.601748i	$-0.205529\pi$
$409$	32.3048	1.59737	0.798686	+	0.601748i	$0.205529\pi$
$410$	40.7040	2.01023
$411$	0.680305	0.0335570
$412$	−91.2975	−4.49790
$413$	−4.67984	−0.230280
$414$	−60.0927	−2.95339
$415$	−10.1792	−0.499675
$416$	86.9344	4.26231
$417$	3.10680	0.152141
$418$	−12.3038	−0.601801
$419$	6.50212	0.317650	0.158825	−	0.987307i	$-0.449230\pi$
$419$	6.50212	0.317650	0.158825	+	0.987307i	$0.449230\pi$
$420$	2.94267	0.143588
$421$	5.94614	0.289797	0.144899	−	0.989447i	$-0.453714\pi$
$421$	5.94614	0.289797	0.144899	+	0.989447i	$0.453714\pi$
$422$	−63.1288	−3.07306
$423$	−12.6431	−0.614726
$424$	−42.2692	−2.05277
$425$	4.39653	0.213263
$426$	−5.70905	−0.276605
$427$	−7.59684	−0.367637
$428$	−14.6606	−0.708647
$429$	1.03239	0.0498441
$430$	−32.8537	−1.58435
$431$	−19.4982	−0.939194	−0.469597	−	0.882881i	$-0.655601\pi$
$431$	−19.4982	−0.939194	−0.469597	+	0.882881i	$0.655601\pi$
$432$	22.6582	1.09014
$433$	24.1372	1.15996	0.579980	−	0.814631i	$-0.303060\pi$
$433$	24.1372	1.15996	0.579980	+	0.814631i	$0.303060\pi$
$434$	11.8982	0.571133
$435$	−0.395738	−0.0189742
$436$	39.9927	1.91530
$437$	−18.4918	−0.884585
$438$	−1.02609	−0.0490282
$439$	16.4151	0.783448	0.391724	−	0.920083i	$-0.371879\pi$
$439$	16.4151	0.783448	0.391724	+	0.920083i	$0.371879\pi$
$440$	−45.1978	−2.15472
$441$	−2.95727	−0.140823
$442$	37.6011	1.78850
$443$	4.51655	0.214588	0.107294	−	0.994227i	$-0.465781\pi$
$443$	4.51655	0.214588	0.107294	+	0.994227i	$0.465781\pi$
$444$	12.9030	0.612349
$445$	3.44215	0.163174
$446$	29.9853	1.41984
$447$	−1.35249	−0.0639704
$448$	−47.2609	−2.23287
$449$	−16.9551	−0.800159	−0.400079	−	0.916480i	$-0.631017\pi$
$449$	−16.9551	−0.800159	−0.400079	+	0.916480i	$0.631017\pi$
$450$	7.84608	0.369868
$451$	−10.2848	−0.484290
$452$	−9.94911	−0.467967
$453$	−1.92462	−0.0904265
$454$	67.5677	3.17111
$455$	7.06079	0.331015
$456$	5.65728	0.264926
$457$	−28.4132	−1.32911	−0.664557	−	0.747238i	$-0.731380\pi$
$457$	−28.4132	−1.32911	−0.664557	+	0.747238i	$0.731380\pi$
$458$	39.0037	1.82252
$459$	5.71254	0.266638
$460$	−103.333	−4.81792
$461$	24.8337	1.15662	0.578311	−	0.815817i	$-0.303712\pi$
$461$	24.8337	1.15662	0.578311	+	0.815817i	$0.303712\pi$
$462$	−0.998276	−0.0464440
$463$	8.78043	0.408061	0.204031	−	0.978965i	$-0.434596\pi$
$463$	8.78043	0.408061	0.204031	+	0.978965i	$0.434596\pi$
$464$	14.4450	0.670593
$465$	−2.14248	−0.0993552
$466$	−25.1327	−1.16425
$467$	27.2068	1.25898	0.629491	−	0.777007i	$-0.283263\pi$
$467$	27.2068	1.25898	0.629491	+	0.777007i	$0.283263\pi$
$468$	49.9793	2.31029
$469$	−10.8010	−0.498744
$470$	−29.1892	−1.34640
$471$	−2.84469	−0.131077
$472$	−50.2755	−2.31412
$473$	8.30121	0.381690
$474$	−2.81732	−0.129404
$475$	2.41441	0.110781
$476$	−27.0805	−1.24123
$477$	−11.6356	−0.532760
$478$	47.4031	2.16817
$479$	26.6708	1.21862	0.609309	−	0.792933i	$-0.291447\pi$
$479$	26.6708	1.21862	0.609309	+	0.792933i	$0.291447\pi$
$480$	15.1368	0.690898
$481$	30.9601	1.41166
$482$	35.8623	1.63348
$483$	−1.50034	−0.0682678
$484$	−46.8393	−2.12906
$485$	−29.8045	−1.35335
$486$	15.3285	0.695315
$487$	−15.9842	−0.724314	−0.362157	−	0.932117i	$-0.617960\pi$
$487$	−15.9842	−0.724314	−0.362157	+	0.932117i	$0.617960\pi$
$488$	−81.6127	−3.69443
$489$	−0.924130	−0.0417906
$490$	−6.82749	−0.308435
$491$	15.2404	0.687790	0.343895	−	0.939008i	$-0.388254\pi$
$491$	15.2404	0.687790	0.343895	+	0.939008i	$0.388254\pi$
$492$	7.19354	0.324310
$493$	3.64185	0.164021
$494$	20.6491	0.929047
$495$	−12.4418	−0.559219
$496$	78.2037	3.51145
$497$	9.86579	0.442541
$498$	−2.41529	−0.108232
$499$	34.6403	1.55071	0.775357	−	0.631523i	$-0.217570\pi$
$499$	34.6403	1.55071	0.775357	+	0.631523i	$0.217570\pi$
$500$	−57.6894	−2.57995
$501$	0.111467	0.00497997
$502$	19.5787	0.873839
$503$	−28.0986	−1.25285	−0.626427	−	0.779480i	$-0.715483\pi$
$503$	−28.0986	−1.25285	−0.626427	+	0.779480i	$0.715483\pi$
$504$	−31.7699	−1.41515
$505$	1.35711	0.0603908
$506$	35.0548	1.55838
$507$	0.954517	0.0423916
$508$	47.3899	2.10259
$509$	17.9850	0.797171	0.398585	−	0.917131i	$-0.369501\pi$
$509$	17.9850	0.797171	0.398585	+	0.917131i	$0.369501\pi$
$510$	6.54701	0.289906
$511$	1.77317	0.0784405
$512$	−157.162	−6.94564
$513$	3.13711	0.138507
$514$	51.4343	2.26867
$515$	−38.1429	−1.68078
$516$	−5.80617	−0.255602
$517$	7.37528	0.324364
$518$	−29.9372	−1.31536
$519$	5.11675	0.224600
$520$	75.8539	3.32641
$521$	−31.3448	−1.37324	−0.686621	−	0.727015i	$-0.740907\pi$
$521$	−31.3448	−1.37324	−0.686621	+	0.727015i	$0.740907\pi$
$522$	6.49928	0.284466
$523$	−19.9260	−0.871303	−0.435652	−	0.900115i	$-0.643482\pi$
$523$	−19.9260	−0.871303	−0.435652	+	0.900115i	$0.643482\pi$
$524$	26.8836	1.17442
$525$	0.195894	0.00854951
$526$	71.0951	3.09990
$527$	19.7166	0.858868
$528$	−6.56138	−0.285547
$529$	29.6850	1.29065
$530$	−26.8633	−1.16687
$531$	−13.8396	−0.600587
$532$	−14.8716	−0.644765
$533$	17.2605	0.747637
$534$	0.816748	0.0353441
$535$	−6.12501	−0.264807
$536$	−116.035	−5.01195
$537$	1.52151	0.0656579
$538$	38.9658	1.67993
$539$	1.72511	0.0743060
$540$	17.5303	0.754383
$541$	38.5924	1.65921	0.829607	−	0.558347i	$-0.188564\pi$
$541$	38.5924	1.65921	0.829607	+	0.558347i	$0.188564\pi$
$542$	−27.0147	−1.16038
$543$	−2.25043	−0.0965752
$544$	−139.299	−5.97241
$545$	16.7084	0.715710
$546$	1.67537	0.0716992
$547$	25.8456	1.10508	0.552538	−	0.833488i	$-0.313659\pi$
$547$	25.8456	1.10508	0.552538	+	0.833488i	$0.313659\pi$
$548$	−19.2123	−0.820707
$549$	−22.4659	−0.958822
$550$	−4.57698	−0.195163
$551$	1.99997	0.0852016
$552$	−16.1181	−0.686033
$553$	4.86859	0.207033
$554$	−3.44360	−0.146305
$555$	5.39070	0.228822
$556$	−87.7380	−3.72092
$557$	24.9957	1.05910	0.529551	−	0.848278i	$-0.322360\pi$
$557$	24.9957	1.05910	0.529551	+	0.848278i	$0.322360\pi$
$558$	35.1863	1.48956
$559$	−13.9316	−0.589245
$560$	−44.8752	−1.89632
$561$	−1.65424	−0.0698422
$562$	−29.7648	−1.25555
$563$	−39.7260	−1.67425	−0.837126	−	0.547010i	$-0.815766\pi$
$563$	−39.7260	−1.67425	−0.837126	+	0.547010i	$0.815766\pi$
$564$	−5.15854	−0.217214
$565$	−4.15660	−0.174870
$566$	−49.2458	−2.06996
$567$	−8.61729	−0.361892
$568$	105.988	4.44716
$569$	−33.2768	−1.39504	−0.697519	−	0.716566i	$-0.745713\pi$
$569$	−33.2768	−1.39504	−0.697519	+	0.716566i	$0.745713\pi$
$570$	3.59537	0.150594
$571$	20.2270	0.846472	0.423236	−	0.906020i	$-0.360894\pi$
$571$	20.2270	0.846472	0.423236	+	0.906020i	$0.360894\pi$
$572$	−29.1552	−1.21904
$573$	0.449105	0.0187616
$574$	−16.6902	−0.696637
$575$	−6.87889	−0.286870
$576$	−139.763	−5.82348
$577$	−44.4985	−1.85250	−0.926248	−	0.376915i	$-0.876985\pi$
$577$	−44.4985	−1.85250	−0.926248	+	0.376915i	$0.876985\pi$
$578$	−12.6579	−0.526499
$579$	−3.30793	−0.137473
$580$	11.1759	0.464054
$581$	4.17385	0.173160
$582$	−7.07196	−0.293142
$583$	6.78761	0.281114
$584$	19.0492	0.788260
$585$	20.8807	0.863310
$586$	14.5773	0.602184
$587$	−44.7003	−1.84498	−0.922490	−	0.386022i	$-0.873849\pi$
$587$	−44.7003	−1.84498	−0.922490	+	0.386022i	$0.873849\pi$
$588$	−1.20661	−0.0497597
$589$	10.8276	0.446144
$590$	−31.9516	−1.31543
$591$	2.59859	0.106892
$592$	−196.768	−8.08713
$593$	−20.4487	−0.839728	−0.419864	−	0.907587i	$-0.637922\pi$
$593$	−20.4487	−0.839728	−0.419864	+	0.907587i	$0.637922\pi$
$594$	−5.94700	−0.244008
$595$	−11.3138	−0.463823
$596$	38.1950	1.56453
$597$	2.69293	0.110214
$598$	−58.8313	−2.40579
$599$	−38.2358	−1.56227	−0.781136	−	0.624361i	$-0.785359\pi$
$599$	−38.2358	−1.56227	−0.781136	+	0.624361i	$0.785359\pi$
$600$	2.10448	0.0859152
$601$	−20.9768	−0.855662	−0.427831	−	0.903859i	$-0.640722\pi$
$601$	−20.9768	−0.855662	−0.427831	+	0.903859i	$0.640722\pi$
$602$	13.4713	0.549050
$603$	−31.9416	−1.30076
$604$	54.3525	2.21157
$605$	−19.5688	−0.795586
$606$	0.322013	0.0130809
$607$	−10.7533	−0.436465	−0.218232	−	0.975897i	$-0.570029\pi$
$607$	−10.7533	−0.436465	−0.218232	+	0.975897i	$0.570029\pi$
$608$	−76.4980	−3.10240
$609$	0.162268	0.00657543
$610$	−51.8673	−2.10005
$611$	−12.3777	−0.500747
$612$	−80.0843	−3.23722
$613$	21.2569	0.858557	0.429278	−	0.903172i	$-0.358768\pi$
$613$	21.2569	0.858557	0.429278	+	0.903172i	$0.358768\pi$
$614$	55.5522	2.24191
$615$	3.00536	0.121188
$616$	18.5329	0.746711
$617$	−5.90087	−0.237560	−0.118780	−	0.992921i	$-0.537898\pi$
$617$	−5.90087	−0.237560	−0.118780	+	0.992921i	$0.537898\pi$
$618$	−9.05046	−0.364063
$619$	−11.8322	−0.475578	−0.237789	−	0.971317i	$-0.576423\pi$
$619$	−11.8322	−0.475578	−0.237789	+	0.971317i	$0.576423\pi$
$620$	60.5050	2.42994
$621$	−8.93794	−0.358667
$622$	−6.57130	−0.263485
$623$	−1.41142	−0.0565472
$624$	11.0117	0.440822
$625$	−28.8404	−1.15362
$626$	53.0321	2.11959
$627$	−0.908449	−0.0362800
$628$	80.3359	3.20575
$629$	−49.6089	−1.97804
$630$	−20.1908	−0.804419
$631$	26.6365	1.06038	0.530191	−	0.847878i	$-0.322120\pi$
$631$	26.6365	1.06038	0.530191	+	0.847878i	$0.322120\pi$
$632$	52.3032	2.08051
$633$	−4.66109	−0.185262
$634$	−73.2853	−2.91053
$635$	19.7989	0.785694
$636$	−4.74750	−0.188251
$637$	−2.89520	−0.114712
$638$	−3.79133	−0.150100
$639$	29.1758	1.15418
$640$	−176.214	−6.96546
$641$	−10.0325	−0.396259	−0.198129	−	0.980176i	$-0.563487\pi$
$641$	−10.0325	−0.396259	−0.198129	+	0.980176i	$0.563487\pi$
$642$	−1.45333	−0.0573583
$643$	−30.2304	−1.19217	−0.596086	−	0.802921i	$-0.703278\pi$
$643$	−30.2304	−1.19217	−0.596086	+	0.802921i	$0.703278\pi$
$644$	42.3705	1.66963
$645$	−2.42574	−0.0955134
$646$	−33.0871	−1.30179
$647$	30.9753	1.21776	0.608882	−	0.793261i	$-0.291618\pi$
$647$	30.9753	1.21776	0.608882	+	0.793261i	$0.291618\pi$
$648$	−92.5754	−3.63671
$649$	8.07327	0.316903
$650$	7.68138	0.301289
$651$	0.878501	0.0344312
$652$	26.0980	1.02208
$653$	−7.02183	−0.274785	−0.137393	−	0.990517i	$-0.543872\pi$
$653$	−7.02183	−0.274785	−0.137393	+	0.990517i	$0.543872\pi$
$654$	3.96454	0.155026
$655$	11.2316	0.438855
$656$	−109.700	−4.28307
$657$	5.24376	0.204578
$658$	11.9687	0.466588
$659$	−9.19426	−0.358157	−0.179079	−	0.983835i	$-0.557312\pi$
$659$	−9.19426	−0.358157	−0.179079	+	0.983835i	$0.557312\pi$
$660$	−5.07644	−0.197600
$661$	16.4198	0.638656	0.319328	−	0.947644i	$-0.396543\pi$
$661$	16.4198	0.638656	0.319328	+	0.947644i	$0.396543\pi$
$662$	55.9003	2.17263
$663$	2.77626	0.107821
$664$	44.8396	1.74011
$665$	−6.21314	−0.240935
$666$	−88.5324	−3.43056
$667$	−5.69811	−0.220632
$668$	−3.14789	−0.121796
$669$	2.21395	0.0855962
$670$	−73.7438	−2.84897
$671$	13.1054	0.505929
$672$	−6.20668	−0.239428
$673$	47.1887	1.81899	0.909496	−	0.415713i	$-0.136468\pi$
$673$	47.1887	1.81899	0.909496	+	0.415713i	$0.136468\pi$
$674$	19.4333	0.748541
$675$	1.16699	0.0449176
$676$	−26.9562	−1.03678
$677$	41.5028	1.59508	0.797541	−	0.603265i	$-0.206134\pi$
$677$	41.5028	1.59508	0.797541	+	0.603265i	$0.206134\pi$
$678$	−0.986271	−0.0378775
$679$	12.2210	0.469000
$680$	−121.544	−4.66102
$681$	4.98883	0.191172
$682$	−20.5258	−0.785974
$683$	−4.44559	−0.170106	−0.0850529	−	0.996376i	$-0.527106\pi$
$683$	−4.44559	−0.170106	−0.0850529	+	0.996376i	$0.527106\pi$
$684$	−43.9793	−1.68159
$685$	−8.02662	−0.306681
$686$	2.79954	0.106887
$687$	2.87982	0.109872
$688$	88.5431	3.37567
$689$	−11.3914	−0.433978
$690$	−10.2436	−0.389966
$691$	−20.6104	−0.784058	−0.392029	−	0.919953i	$-0.628227\pi$
$691$	−20.6104	−0.784058	−0.392029	+	0.919953i	$0.628227\pi$
$692$	−144.500	−5.49307
$693$	5.10164	0.193795
$694$	47.5422	1.80468
$695$	−36.6557	−1.39043
$696$	1.74324	0.0660775
$697$	−27.6574	−1.04760
$698$	−28.2907	−1.07082
$699$	−1.85566	−0.0701875
$700$	−5.53216	−0.209096
$701$	27.1890	1.02691	0.513457	−	0.858116i	$-0.328365\pi$
$701$	27.1890	1.02691	0.513457	+	0.858116i	$0.328365\pi$
$702$	9.98064	0.376695
$703$	−27.2434	−1.02750
$704$	81.5305	3.07280
$705$	−2.15517	−0.0811684
$706$	18.7266	0.704784
$707$	−0.556470	−0.0209282
$708$	−5.64674	−0.212217
$709$	−23.7964	−0.893694	−0.446847	−	0.894610i	$-0.647453\pi$
$709$	−23.7964	−0.893694	−0.446847	+	0.894610i	$0.647453\pi$
$710$	67.3586	2.52792
$711$	14.3977	0.539958
$712$	−15.1628	−0.568251
$713$	−30.8489	−1.15530
$714$	−2.68453	−0.100466
$715$	−12.1807	−0.455531
$716$	−42.9683	−1.60580
$717$	3.49999	0.130709
$718$	60.3623	2.25270
$719$	−18.5619	−0.692241	−0.346120	−	0.938190i	$-0.612501\pi$
$719$	−18.5619	−0.692241	−0.346120	+	0.938190i	$0.612501\pi$
$720$	−132.708	−4.94574
$721$	15.6401	0.582466
$722$	35.0210	1.30335
$723$	2.64788	0.0984757
$724$	63.5536	2.36195
$725$	0.743981	0.0276307
$726$	−4.64325	−0.172327
$727$	33.5340	1.24371	0.621853	−	0.783134i	$-0.286380\pi$
$727$	33.5340	1.24371	0.621853	+	0.783134i	$0.286380\pi$
$728$	−31.1031	−1.15276
$729$	−24.7201	−0.915559
$730$	12.1063	0.448075
$731$	22.3233	0.825658
$732$	−9.16641	−0.338800
$733$	33.8442	1.25006	0.625032	−	0.780599i	$-0.285086\pi$
$733$	33.8442	1.25006	0.625032	+	0.780599i	$0.285086\pi$
$734$	−73.6831	−2.71969
$735$	−0.504105	−0.0185942
$736$	217.950	8.03375
$737$	18.6330	0.686355
$738$	−49.3576	−1.81688
$739$	−42.9259	−1.57906	−0.789528	−	0.613715i	$-0.789675\pi$
$739$	−42.9259	−1.57906	−0.789528	+	0.613715i	$0.789675\pi$
$740$	−152.237	−5.59633
$741$	1.52462	0.0560082
$742$	11.0150	0.404374
$743$	6.60784	0.242418	0.121209	−	0.992627i	$-0.461323\pi$
$743$	6.60784	0.242418	0.121209	+	0.992627i	$0.461323\pi$
$744$	9.43772	0.346004
$745$	15.9574	0.584633
$746$	−101.795	−3.72699
$747$	12.3432	0.451615
$748$	46.7169	1.70814
$749$	2.51149	0.0917679
$750$	−5.71884	−0.208823
$751$	−36.8339	−1.34409	−0.672045	−	0.740511i	$-0.734584\pi$
$751$	−36.8339	−1.34409	−0.672045	+	0.740511i	$0.734584\pi$
$752$	78.6668	2.86868
$753$	1.44558	0.0526800
$754$	6.36285	0.231721
$755$	22.7077	0.826419
$756$	−7.18810	−0.261429
$757$	−50.8110	−1.84676	−0.923378	−	0.383891i	$-0.874584\pi$
$757$	−50.8110	−1.84676	−0.923378	+	0.383891i	$0.874584\pi$
$758$	79.3541	2.88227
$759$	2.58826	0.0939479
$760$	−66.7477	−2.42119
$761$	−7.21399	−0.261507	−0.130753	−	0.991415i	$-0.541740\pi$
$761$	−7.21399	−0.261507	−0.130753	+	0.991415i	$0.541740\pi$
$762$	4.69784	0.170185
$763$	−6.85111	−0.248027
$764$	−12.6830	−0.458855
$765$	−33.4581	−1.20968
$766$	105.072	3.79640
$767$	−13.5491	−0.489229
$768$	−22.2737	−0.803734
$769$	9.89435	0.356799	0.178400	−	0.983958i	$-0.442908\pi$
$769$	9.89435	0.356799	0.178400	+	0.983958i	$0.442908\pi$
$770$	11.7782	0.424457
$771$	3.79763	0.136768
$772$	93.4179	3.36218
$773$	−10.2859	−0.369957	−0.184978	−	0.982743i	$-0.559222\pi$
$773$	−10.2859	−0.369957	−0.184978	+	0.982743i	$0.559222\pi$
$774$	39.8383	1.43196
$775$	4.02783	0.144684
$776$	131.290	4.71305
$777$	−2.21040	−0.0792975
$778$	25.8639	0.927266
$779$	−15.1884	−0.544181
$780$	8.51961	0.305051
$781$	−17.0196	−0.609010
$782$	94.2683	3.37103
$783$	0.966675	0.0345462
$784$	18.4006	0.657163
$785$	33.5633	1.19792
$786$	2.66501	0.0950579
$787$	−46.8695	−1.67072	−0.835359	−	0.549705i	$-0.814740\pi$
$787$	−46.8695	−1.67072	−0.835359	+	0.549705i	$0.814740\pi$
$788$	−73.3858	−2.61426
$789$	5.24928	0.186879
$790$	33.2402	1.18263
$791$	1.70437	0.0606004
$792$	54.8068	1.94747
$793$	−21.9943	−0.781042
$794$	−70.2675	−2.49370
$795$	−1.98344	−0.0703455
$796$	−76.0499	−2.69552
$797$	34.1693	1.21034	0.605169	−	0.796097i	$-0.293105\pi$
$797$	34.1693	1.21034	0.605169	+	0.796097i	$0.293105\pi$
$798$	−1.47424	−0.0521876
$799$	19.8333	0.701653
$800$	−28.4569	−1.00610
$801$	−4.17395	−0.147479
$802$	51.3192	1.81214
$803$	−3.05893	−0.107947
$804$	−13.0326	−0.459624
$805$	17.7018	0.623908
$806$	34.4477	1.21337
$807$	2.87702	0.101276
$808$	−5.97815	−0.210310
$809$	−14.9482	−0.525552	−0.262776	−	0.964857i	$-0.584638\pi$
$809$	−14.9482	−0.525552	−0.262776	+	0.964857i	$0.584638\pi$
$810$	−58.8345	−2.06723
$811$	−29.9610	−1.05207	−0.526037	−	0.850462i	$-0.676323\pi$
$811$	−29.9610	−1.05207	−0.526037	+	0.850462i	$0.676323\pi$
$812$	−4.58255	−0.160816
$813$	−1.99462	−0.0699544
$814$	51.6450	1.81016
$815$	10.9034	0.381929
$816$	−17.6446	−0.617686
$817$	12.2591	0.428893
$818$	−90.4386	−3.16211
$819$	−8.56189	−0.299177
$820$	−84.8733	−2.96390
$821$	26.1702	0.913348	0.456674	−	0.889634i	$-0.349041\pi$
$821$	26.1702	0.913348	0.456674	+	0.889634i	$0.349041\pi$
$822$	−1.90454	−0.0664285
$823$	−29.3599	−1.02342	−0.511710	−	0.859158i	$-0.670988\pi$
$823$	−29.3599	−1.02342	−0.511710	+	0.859158i	$0.670988\pi$
$824$	168.021	5.85329
$825$	−0.337939	−0.0117655
$826$	13.1014	0.455856
$827$	14.1411	0.491733	0.245866	−	0.969304i	$-0.420928\pi$
$827$	14.1411	0.491733	0.245866	+	0.969304i	$0.420928\pi$
$828$	125.301	4.35452
$829$	−45.8872	−1.59373	−0.796864	−	0.604159i	$-0.793509\pi$
$829$	−45.8872	−1.59373	−0.796864	+	0.604159i	$0.793509\pi$
$830$	28.4969	0.989143
$831$	−0.254257	−0.00882007
$832$	−136.830	−4.74372
$833$	4.63912	0.160736
$834$	−8.69760	−0.301173
$835$	−1.31515	−0.0455125
$836$	25.6552	0.887303
$837$	5.23347	0.180895
$838$	−18.2029	−0.628810
$839$	17.9731	0.620500	0.310250	−	0.950655i	$-0.399587\pi$
$839$	17.9731	0.620500	0.310250	+	0.950655i	$0.399587\pi$
$840$	−5.41559	−0.186856
$841$	−28.3837	−0.978749
$842$	−16.6464	−0.573675
$843$	−2.19767	−0.0756919
$844$	131.632	4.53096
$845$	−11.2619	−0.387422
$846$	35.3947	1.21690
$847$	8.02398	0.275707
$848$	72.3986	2.48618
$849$	−3.63604	−0.124789
$850$	−12.3083	−0.422170
$851$	77.6190	2.66074
$852$	11.9041	0.407829
$853$	42.1573	1.44344	0.721719	−	0.692186i	$-0.243352\pi$
$853$	42.1573	1.44344	0.721719	+	0.692186i	$0.243352\pi$
$854$	21.2676	0.727763
$855$	−18.3740	−0.628376
$856$	26.9809	0.922188
$857$	−2.59681	−0.0887052	−0.0443526	−	0.999016i	$-0.514123\pi$
$857$	−2.59681	−0.0887052	−0.0443526	+	0.999016i	$0.514123\pi$
$858$	−2.89021	−0.0986700
$859$	−1.00000	−0.0341196
$859$	−1.00000	−0.0341196
$860$	68.5044	2.33598
$861$	−1.23232	−0.0419972
$862$	54.5859	1.85920
$863$	42.8688	1.45927	0.729635	−	0.683836i	$-0.239690\pi$
$863$	42.8688	1.45927	0.729635	+	0.683836i	$0.239690\pi$
$864$	−36.9749	−1.25791
$865$	−60.3702	−2.05265
$866$	−67.5731	−2.29623
$867$	−0.934590	−0.0317404
$868$	−24.8094	−0.842086
$869$	−8.39887	−0.284912
$870$	1.10788	0.0375608
$871$	−31.2711	−1.05958
$872$	−73.6013	−2.49246
$873$	36.1409	1.22318
$874$	51.7686	1.75110
$875$	9.88270	0.334096
$876$	2.13953	0.0722879
$877$	−8.49579	−0.286883	−0.143441	−	0.989659i	$-0.545817\pi$
$877$	−8.49579	−0.286883	−0.143441	+	0.989659i	$0.545817\pi$
$878$	−45.9546	−1.55089
$879$	1.07631	0.0363031
$880$	77.4148	2.60965
$881$	47.2833	1.59302	0.796508	−	0.604628i	$-0.206678\pi$
$881$	47.2833	1.59302	0.796508	+	0.604628i	$0.206678\pi$
$882$	8.27900	0.278768
$883$	−17.5016	−0.588976	−0.294488	−	0.955655i	$-0.595149\pi$
$883$	−17.5016	−0.588976	−0.294488	+	0.955655i	$0.595149\pi$
$884$	−78.4033	−2.63699
$885$	−2.35913	−0.0793013
$886$	−12.6442	−0.424792
$887$	−36.9650	−1.24116	−0.620582	−	0.784141i	$-0.713104\pi$
$887$	−36.9650	−1.24116	−0.620582	+	0.784141i	$0.713104\pi$
$888$	−23.7463	−0.796872
$889$	−8.11831	−0.272279
$890$	−9.63644	−0.323014
$891$	14.8658	0.498024
$892$	−62.5233	−2.09343
$893$	10.8917	0.364478
$894$	3.78633	0.126634
$895$	−17.9516	−0.600055
$896$	72.2545	2.41385
$897$	−4.34378	−0.145035
$898$	47.4663	1.58397
$899$	3.33644	0.111276
$900$	−16.3601	−0.545338
$901$	18.2530	0.608096
$902$	28.7926	0.958687
$903$	0.994648	0.0330998
$904$	18.3100	0.608982
$905$	26.5518	0.882613
$906$	5.38804	0.179006
$907$	−17.2458	−0.572639	−0.286319	−	0.958134i	$-0.592432\pi$
$907$	−17.2458	−0.572639	−0.286319	+	0.958134i	$0.592432\pi$
$908$	−140.888	−4.67552
$909$	−1.64563	−0.0545822
$910$	−19.7669	−0.655268
$911$	49.8515	1.65165	0.825827	−	0.563923i	$-0.190709\pi$
$911$	49.8515	1.65165	0.825827	+	0.563923i	$0.190709\pi$
$912$	−9.68978	−0.320861
$913$	−7.20037	−0.238297
$914$	79.5439	2.63108
$915$	−3.82960	−0.126603
$916$	−81.3280	−2.68715
$917$	−4.60540	−0.152084
$918$	−15.9925	−0.527830
$919$	52.3000	1.72522	0.862609	−	0.505871i	$-0.168829\pi$
$919$	52.3000	1.72522	0.862609	+	0.505871i	$0.168829\pi$
$920$	190.171	6.26974
$921$	4.10167	0.135155
$922$	−69.5229	−2.28962
$923$	28.5634	0.940176
$924$	2.08154	0.0684776
$925$	−10.1344	−0.333218
$926$	−24.5811	−0.807787
$927$	46.2519	1.51911
$928$	−23.5722	−0.773796
$929$	−19.7735	−0.648747	−0.324374	−	0.945929i	$-0.605154\pi$
$929$	−19.7735	−0.648747	−0.324374	+	0.945929i	$0.605154\pi$
$930$	5.99796	0.196681
$931$	2.54763	0.0834952
$932$	52.4050	1.71658
$933$	−0.485189	−0.0158844
$934$	−76.1666	−2.49225
$935$	19.5177	0.638297
$936$	−91.9803	−3.00647
$937$	−9.65710	−0.315484	−0.157742	−	0.987480i	$-0.550421\pi$
$937$	−9.65710	−0.315484	−0.157742	+	0.987480i	$0.550421\pi$
$938$	30.2378	0.987301
$939$	3.91560	0.127781
$940$	60.8633	1.98514
$941$	−17.1496	−0.559061	−0.279530	−	0.960137i	$-0.590179\pi$
$941$	−17.1496	−0.559061	−0.279530	+	0.960137i	$0.590179\pi$
$942$	7.96383	0.259476
$943$	43.2733	1.40917
$944$	86.1117	2.80270
$945$	−3.00309	−0.0976906
$946$	−23.2396	−0.755583
$947$	−35.1411	−1.14193	−0.570967	−	0.820973i	$-0.693431\pi$
$947$	−35.1411	−1.14193	−0.570967	+	0.820973i	$0.693431\pi$
$948$	5.87448	0.190794
$949$	5.13369	0.166647
$950$	−6.75924	−0.219299
$951$	−5.41099	−0.175463
$952$	49.8380	1.61526
$953$	−3.51296	−0.113796	−0.0568980	−	0.998380i	$-0.518121\pi$
$953$	−3.51296	−0.113796	−0.0568980	+	0.998380i	$0.518121\pi$
$954$	32.5744	1.05464
$955$	−5.29879	−0.171465
$956$	−98.8418	−3.19677
$957$	−0.279931	−0.00904889
$958$	−74.6659	−2.41234
$959$	3.29123	0.106279
$960$	−23.8245	−0.768931
$961$	−12.9369	−0.417320
$962$	−86.6740	−2.79448
$963$	7.42717	0.239337
$964$	−74.7777	−2.40843
$965$	39.0287	1.25638
$966$	4.20026	0.135141
$967$	−23.9207	−0.769239	−0.384620	−	0.923075i	$-0.625667\pi$
$967$	−23.9207	−0.769239	−0.384620	+	0.923075i	$0.625667\pi$
$968$	86.2015	2.77062
$969$	−2.44297	−0.0784795
$970$	83.4389	2.67906
$971$	−55.3837	−1.77735	−0.888674	−	0.458540i	$-0.848372\pi$
$971$	−55.3837	−1.77735	−0.888674	+	0.458540i	$0.848372\pi$
$972$	−31.9620	−1.02518
$973$	15.0303	0.481849
$974$	44.7484	1.43383
$975$	0.567151	0.0181634
$976$	139.786	4.47444
$977$	−26.3730	−0.843748	−0.421874	−	0.906655i	$-0.638628\pi$
$977$	−26.3730	−0.843748	−0.421874	+	0.906655i	$0.638628\pi$
$978$	2.58714	0.0827275
$979$	2.43486	0.0778184
$980$	14.2362	0.454760
$981$	−20.2606	−0.646871
$982$	−42.6661	−1.36153
$983$	36.6928	1.17032	0.585159	−	0.810918i	$-0.301032\pi$
$983$	36.6928	1.17032	0.585159	+	0.810918i	$0.301032\pi$
$984$	−13.2387	−0.422036
$985$	−30.6596	−0.976895
$986$	−10.1955	−0.324691
$987$	0.883703	0.0281286
$988$	−43.0562	−1.36980
$989$	−34.9275	−1.11063
$990$	34.8314	1.10701
$991$	−28.1252	−0.893427	−0.446714	−	0.894677i	$-0.647406\pi$
$991$	−28.1252	−0.893427	−0.446714	+	0.894677i	$0.647406\pi$
$992$	−127.617	−4.05185
$993$	4.12737	0.130978
$994$	−27.6196	−0.876042
$995$	−31.7726	−1.00726
$996$	5.03620	0.159578
$997$	0.295612	0.00936214	0.00468107	−	0.999989i	$-0.498510\pi$
$997$	0.295612	0.00936214	0.00468107	+	0.999989i	$0.498510\pi$
$998$	−96.9770	−3.06975
$999$	−13.1679	−0.416615

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6013.2.a.c.1.2	✓	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6013.2.a.c.1.2	✓	104	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:	\( N \)	\(=\)	\( 6013 = 7 \cdot 859 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.79954 q^{2} -0.206703 q^{3} +5.83741 q^{4} +2.43879 q^{5} +0.578672 q^{6} -1.00000 q^{7} -10.7430 q^{8} -2.95727 q^{9} +O(q^{10})\)	\(q-2.79954 q^{2} -0.206703 q^{3} +5.83741 q^{4} +2.43879 q^{5} +0.578672 q^{6} -1.00000 q^{7} -10.7430 q^{8} -2.95727 q^{9} -6.82749 q^{10} +1.72511 q^{11} -1.20661 q^{12} -2.89520 q^{13} +2.79954 q^{14} -0.504105 q^{15} +18.4006 q^{16} +4.63912 q^{17} +8.27900 q^{18} +2.54763 q^{19} +14.2362 q^{20} +0.206703 q^{21} -4.82952 q^{22} -7.25845 q^{23} +2.22060 q^{24} +0.947708 q^{25} +8.10522 q^{26} +1.23138 q^{27} -5.83741 q^{28} +0.785031 q^{29} +1.41126 q^{30} +4.25007 q^{31} -30.0271 q^{32} -0.356586 q^{33} -12.9874 q^{34} -2.43879 q^{35} -17.2628 q^{36} -10.6936 q^{37} -7.13219 q^{38} +0.598445 q^{39} -26.1999 q^{40} -5.96178 q^{41} -0.578672 q^{42} +4.81198 q^{43} +10.0702 q^{44} -7.21218 q^{45} +20.3203 q^{46} +4.27524 q^{47} -3.80345 q^{48} +1.00000 q^{49} -2.65315 q^{50} -0.958918 q^{51} -16.9005 q^{52} +3.93458 q^{53} -3.44731 q^{54} +4.20720 q^{55} +10.7430 q^{56} -0.526602 q^{57} -2.19773 q^{58} +4.67984 q^{59} -2.94267 q^{60} +7.59684 q^{61} -11.8982 q^{62} +2.95727 q^{63} +47.2609 q^{64} -7.06079 q^{65} +0.998276 q^{66} +10.8010 q^{67} +27.0805 q^{68} +1.50034 q^{69} +6.82749 q^{70} -9.86579 q^{71} +31.7699 q^{72} -1.77317 q^{73} +29.9372 q^{74} -0.195894 q^{75} +14.8716 q^{76} -1.72511 q^{77} -1.67537 q^{78} -4.86859 q^{79} +44.8752 q^{80} +8.61729 q^{81} +16.6902 q^{82} -4.17385 q^{83} +1.20661 q^{84} +11.3138 q^{85} -13.4713 q^{86} -0.162268 q^{87} -18.5329 q^{88} +1.41142 q^{89} +20.1908 q^{90} +2.89520 q^{91} -42.3705 q^{92} -0.878501 q^{93} -11.9687 q^{94} +6.21314 q^{95} +6.20668 q^{96} -12.2210 q^{97} -2.79954 q^{98} -5.10164 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9}+O(q^{10}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9	\( 104 q - 19 q^{2} - 26 q^{3} + 99 q^{4} + 2 q^{5} + 2 q^{6} - 104 q^{7} - 54 q^{8} + 90 q^{9} + 3 q^{10} - 54 q^{11} - 38 q^{12} + 7 q^{13} + 19 q^{14} - 33 q^{15} + 93 q^{16} - 7 q^{17} - 55 q^{18} - 12 q^{19} - 24 q^{20} + 26 q^{21} - 22 q^{22} - 69 q^{23} + 78 q^{25} - 11 q^{26} - 95 q^{27} - 99 q^{28} - 41 q^{29} - 26 q^{30} - 12 q^{31} - 127 q^{32} - 6 q^{33} - 17 q^{34} - 2 q^{35} + 71 q^{36} - 47 q^{37} - 32 q^{38} - 57 q^{39} + 6 q^{40} + 10 q^{41} - 2 q^{42} - 41 q^{43} - 120 q^{44} + 23 q^{45} - 31 q^{46} - 99 q^{47} - 84 q^{48} + 104 q^{49} - 104 q^{50} - 74 q^{51} + 14 q^{52} - 74 q^{53} + 19 q^{54} - 32 q^{55} + 54 q^{56} - 47 q^{57} - 36 q^{58} - 76 q^{59} - 99 q^{60} + 49 q^{61} - 55 q^{62} - 90 q^{63} + 86 q^{64} - 70 q^{65} + 61 q^{66} - 117 q^{67} - 30 q^{68} + 51 q^{69} - 3 q^{70} - 125 q^{71} - 147 q^{72} - 20 q^{73} - 75 q^{74} - 124 q^{75} + 4 q^{76} + 54 q^{77} - 70 q^{78} - 72 q^{79} - 69 q^{80} + 76 q^{81} - 37 q^{82} - 98 q^{83} + 38 q^{84} - 33 q^{85} - 64 q^{86} - 8 q^{87} - 62 q^{88} - 26 q^{89} + 11 q^{90} - 7 q^{91} - 162 q^{92} - 81 q^{93} + 31 q^{94} - 116 q^{95} + 20 q^{96} - 61 q^{97} - 19 q^{98} - 158 q^{99}+O(q^{100}) \) 104 * q - 19 * q^2 - 26 * q^3 + 99 * q^4 + 2 * q^5 + 2 * q^6 - 104 * q^7 - 54 * q^8 + 90 * q^9 + 3 * q^10 - 54 * q^11 - 38 * q^12 + 7 * q^13 + 19 * q^14 - 33 * q^15 + 93 * q^16 - 7 * q^17 - 55 * q^18 - 12 * q^19 - 24 * q^20 + 26 * q^21 - 22 * q^22 - 69 * q^23 + 78 * q^25 - 11 * q^26 - 95 * q^27 - 99 * q^28 - 41 * q^29 - 26 * q^30 - 12 * q^31 - 127 * q^32 - 6 * q^33 - 17 * q^34 - 2 * q^35 + 71 * q^36 - 47 * q^37 - 32 * q^38 - 57 * q^39 + 6 * q^40 + 10 * q^41 - 2 * q^42 - 41 * q^43 - 120 * q^44 + 23 * q^45 - 31 * q^46 - 99 * q^47 - 84 * q^48 + 104 * q^49 - 104 * q^50 - 74 * q^51 + 14 * q^52 - 74 * q^53 + 19 * q^54 - 32 * q^55 + 54 * q^56 - 47 * q^57 - 36 * q^58 - 76 * q^59 - 99 * q^60 + 49 * q^61 - 55 * q^62 - 90 * q^63 + 86 * q^64 - 70 * q^65 + 61 * q^66 - 117 * q^67 - 30 * q^68 + 51 * q^69 - 3 * q^70 - 125 * q^71 - 147 * q^72 - 20 * q^73 - 75 * q^74 - 124 * q^75 + 4 * q^76 + 54 * q^77 - 70 * q^78 - 72 * q^79 - 69 * q^80 + 76 * q^81 - 37 * q^82 - 98 * q^83 + 38 * q^84 - 33 * q^85 - 64 * q^86 - 8 * q^87 - 62 * q^88 - 26 * q^89 + 11 * q^90 - 7 * q^91 - 162 * q^92 - 81 * q^93 + 31 * q^94 - 116 * q^95 + 20 * q^96 - 61 * q^97 - 19 * q^98 - 158 * q^99

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