LMFDB - Embedded newform 6002.2.a.b.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6002,2,Mod(1,6002)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6002, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("6002.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6002 = 2 \cdot 3001 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6002.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:	$47.9262112932$
Analytic rank:	$1$
Dimension:	$56$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	6002.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.13871 q^{3} +1.00000 q^{4} -2.43791 q^{5} +3.13871 q^{6} -2.06269 q^{7} -1.00000 q^{8} +6.85148 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.13871 q^{3} +1.00000 q^{4} -2.43791 q^{5} +3.13871 q^{6} -2.06269 q^{7} -1.00000 q^{8} +6.85148 q^{9} +2.43791 q^{10} -1.86663 q^{11} -3.13871 q^{12} -3.54483 q^{13} +2.06269 q^{14} +7.65190 q^{15} +1.00000 q^{16} -3.46765 q^{17} -6.85148 q^{18} +3.67013 q^{19} -2.43791 q^{20} +6.47416 q^{21} +1.86663 q^{22} -5.94081 q^{23} +3.13871 q^{24} +0.943426 q^{25} +3.54483 q^{26} -12.0886 q^{27} -2.06269 q^{28} +5.83563 q^{29} -7.65190 q^{30} -6.15929 q^{31} -1.00000 q^{32} +5.85881 q^{33} +3.46765 q^{34} +5.02865 q^{35} +6.85148 q^{36} +6.49741 q^{37} -3.67013 q^{38} +11.1262 q^{39} +2.43791 q^{40} +3.74314 q^{41} -6.47416 q^{42} -9.52744 q^{43} -1.86663 q^{44} -16.7033 q^{45} +5.94081 q^{46} +3.42979 q^{47} -3.13871 q^{48} -2.74533 q^{49} -0.943426 q^{50} +10.8839 q^{51} -3.54483 q^{52} -6.16637 q^{53} +12.0886 q^{54} +4.55069 q^{55} +2.06269 q^{56} -11.5195 q^{57} -5.83563 q^{58} +5.86777 q^{59} +7.65190 q^{60} +5.57326 q^{61} +6.15929 q^{62} -14.1324 q^{63} +1.00000 q^{64} +8.64200 q^{65} -5.85881 q^{66} -1.94054 q^{67} -3.46765 q^{68} +18.6464 q^{69} -5.02865 q^{70} +13.6104 q^{71} -6.85148 q^{72} -4.89824 q^{73} -6.49741 q^{74} -2.96114 q^{75} +3.67013 q^{76} +3.85028 q^{77} -11.1262 q^{78} -13.9830 q^{79} -2.43791 q^{80} +17.3883 q^{81} -3.74314 q^{82} -7.58398 q^{83} +6.47416 q^{84} +8.45384 q^{85} +9.52744 q^{86} -18.3163 q^{87} +1.86663 q^{88} +10.8986 q^{89} +16.7033 q^{90} +7.31188 q^{91} -5.94081 q^{92} +19.3322 q^{93} -3.42979 q^{94} -8.94747 q^{95} +3.13871 q^{96} +14.7067 q^{97} +2.74533 q^{98} -12.7892 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) $ 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.13871	−1.81213	−0.906066	−	0.423136i	$-0.860929\pi$
$3$	−3.13871	−1.81213	−0.906066	+	0.423136i	$0.860929\pi$
$4$	1.00000	0.500000
$5$	−2.43791	−1.09027	−0.545134	−	0.838349i	$-0.683521\pi$
$5$	−2.43791	−1.09027	−0.545134	+	0.838349i	$0.683521\pi$
$6$	3.13871	1.28137
$7$	−2.06269	−0.779622	−0.389811	−	0.920895i	$-0.627460\pi$
$7$	−2.06269	−0.779622	−0.389811	+	0.920895i	$0.627460\pi$
$8$	−1.00000	−0.353553
$9$	6.85148	2.28383
$10$	2.43791	0.770936
$11$	−1.86663	−0.562811	−0.281405	−	0.959589i	$-0.590801\pi$
$11$	−1.86663	−0.562811	−0.281405	+	0.959589i	$0.590801\pi$
$12$	−3.13871	−0.906066
$13$	−3.54483	−0.983160	−0.491580	−	0.870832i	$-0.663580\pi$
$13$	−3.54483	−0.983160	−0.491580	+	0.870832i	$0.663580\pi$
$14$	2.06269	0.551276
$15$	7.65190	1.97571
$16$	1.00000	0.250000
$17$	−3.46765	−0.841030	−0.420515	−	0.907286i	$-0.638151\pi$
$17$	−3.46765	−0.841030	−0.420515	+	0.907286i	$0.638151\pi$
$18$	−6.85148	−1.61491
$19$	3.67013	0.841987	0.420993	−	0.907064i	$-0.361682\pi$
$19$	3.67013	0.841987	0.420993	+	0.907064i	$0.361682\pi$
$20$	−2.43791	−0.545134
$21$	6.47416	1.41278
$22$	1.86663	0.397967
$23$	−5.94081	−1.23874	−0.619372	−	0.785098i	$-0.712613\pi$
$23$	−5.94081	−1.23874	−0.619372	+	0.785098i	$0.712613\pi$
$24$	3.13871	0.640686
$25$	0.943426	0.188685
$26$	3.54483	0.695199
$27$	−12.0886	−2.32646
$28$	−2.06269	−0.389811
$29$	5.83563	1.08365	0.541825	−	0.840491i	$-0.317734\pi$
$29$	5.83563	1.08365	0.541825	+	0.840491i	$0.317734\pi$
$30$	−7.65190	−1.39704
$31$	−6.15929	−1.10624	−0.553121	−	0.833101i	$-0.686563\pi$
$31$	−6.15929	−1.10624	−0.553121	+	0.833101i	$0.686563\pi$
$32$	−1.00000	−0.176777
$33$	5.85881	1.01989
$34$	3.46765	0.594698
$35$	5.02865	0.849997
$36$	6.85148	1.14191
$37$	6.49741	1.06817	0.534084	−	0.845432i	$-0.320657\pi$
$37$	6.49741	1.06817	0.534084	+	0.845432i	$0.320657\pi$
$38$	−3.67013	−0.595374
$39$	11.1262	1.78162
$40$	2.43791	0.385468
$41$	3.74314	0.584580	0.292290	−	0.956330i	$-0.405583\pi$
$41$	3.74314	0.584580	0.292290	+	0.956330i	$0.405583\pi$
$42$	−6.47416	−0.998985
$43$	−9.52744	−1.45292	−0.726461	−	0.687208i	$-0.758836\pi$
$43$	−9.52744	−1.45292	−0.726461	+	0.687208i	$0.758836\pi$
$44$	−1.86663	−0.281405
$45$	−16.7033	−2.48998
$46$	5.94081	0.875924
$47$	3.42979	0.500286	0.250143	−	0.968209i	$-0.419522\pi$
$47$	3.42979	0.500286	0.250143	+	0.968209i	$0.419522\pi$
$48$	−3.13871	−0.453033
$49$	−2.74533	−0.392190
$50$	−0.943426	−0.133421
$51$	10.8839	1.52406
$52$	−3.54483	−0.491580
$53$	−6.16637	−0.847016	−0.423508	−	0.905892i	$-0.639201\pi$
$53$	−6.16637	−0.847016	−0.423508	+	0.905892i	$0.639201\pi$
$54$	12.0886	1.64506
$55$	4.55069	0.613615
$56$	2.06269	0.275638
$57$	−11.5195	−1.52579
$58$	−5.83563	−0.766256
$59$	5.86777	0.763919	0.381959	−	0.924179i	$-0.375249\pi$
$59$	5.86777	0.763919	0.381959	+	0.924179i	$0.375249\pi$
$60$	7.65190	0.987856
$61$	5.57326	0.713583	0.356791	−	0.934184i	$-0.383871\pi$
$61$	5.57326	0.713583	0.356791	+	0.934184i	$0.383871\pi$
$62$	6.15929	0.782231
$63$	−14.1324	−1.78052
$64$	1.00000	0.125000
$65$	8.64200	1.07191
$66$	−5.85881	−0.721170
$67$	−1.94054	−0.237074	−0.118537	−	0.992950i	$-0.537820\pi$
$67$	−1.94054	−0.237074	−0.118537	+	0.992950i	$0.537820\pi$
$68$	−3.46765	−0.420515
$69$	18.6464	2.24477
$70$	−5.02865	−0.601039
$71$	13.6104	1.61526	0.807630	−	0.589689i	$-0.200750\pi$
$71$	13.6104	1.61526	0.807630	+	0.589689i	$0.200750\pi$
$72$	−6.85148	−0.807454
$73$	−4.89824	−0.573296	−0.286648	−	0.958036i	$-0.592541\pi$
$73$	−4.89824	−0.573296	−0.286648	+	0.958036i	$0.592541\pi$
$74$	−6.49741	−0.755308
$75$	−2.96114	−0.341923
$76$	3.67013	0.420993
$77$	3.85028	0.438780
$78$	−11.1262	−1.25979
$79$	−13.9830	−1.57322	−0.786608	−	0.617453i	$-0.788165\pi$
$79$	−13.9830	−1.57322	−0.786608	+	0.617453i	$0.788165\pi$
$80$	−2.43791	−0.272567
$81$	17.3883	1.93203
$82$	−3.74314	−0.413360
$83$	−7.58398	−0.832450	−0.416225	−	0.909262i	$-0.636647\pi$
$83$	−7.58398	−0.832450	−0.416225	+	0.909262i	$0.636647\pi$
$84$	6.47416	0.706389
$85$	8.45384	0.916948
$86$	9.52744	1.02737
$87$	−18.3163	−1.96372
$88$	1.86663	0.198984
$89$	10.8986	1.15525	0.577623	−	0.816304i	$-0.303981\pi$
$89$	10.8986	1.15525	0.577623	+	0.816304i	$0.303981\pi$
$90$	16.7033	1.76068
$91$	7.31188	0.766493
$92$	−5.94081	−0.619372
$93$	19.3322	2.00466
$94$	−3.42979	−0.353756
$95$	−8.94747	−0.917991
$96$	3.13871	0.320343
$97$	14.7067	1.49324	0.746620	−	0.665250i	$-0.231675\pi$
$97$	14.7067	1.49324	0.746620	+	0.665250i	$0.231675\pi$
$98$	2.74533	0.277320
$99$	−12.7892	−1.28536
$100$	0.943426	0.0943426
$101$	12.4627	1.24009	0.620043	−	0.784568i	$-0.287115\pi$
$101$	12.4627	1.24009	0.620043	+	0.784568i	$0.287115\pi$
$102$	−10.8839	−1.07767
$103$	11.9252	1.17503	0.587514	−	0.809214i	$-0.300107\pi$
$103$	11.9252	1.17503	0.587514	+	0.809214i	$0.300107\pi$
$104$	3.54483	0.347600
$105$	−15.7835	−1.54031
$106$	6.16637	0.598931
$107$	−1.56522	−0.151316	−0.0756578	−	0.997134i	$-0.524106\pi$
$107$	−1.56522	−0.151316	−0.0756578	+	0.997134i	$0.524106\pi$
$108$	−12.0886	−1.16323
$109$	−11.6531	−1.11617	−0.558084	−	0.829784i	$-0.688463\pi$
$109$	−11.6531	−1.11617	−0.558084	+	0.829784i	$0.688463\pi$
$110$	−4.55069	−0.433891
$111$	−20.3935	−1.93566
$112$	−2.06269	−0.194905
$113$	19.7143	1.85457	0.927283	−	0.374361i	$-0.122138\pi$
$113$	19.7143	1.85457	0.927283	+	0.374361i	$0.122138\pi$
$114$	11.5195	1.07890
$115$	14.4832	1.35056
$116$	5.83563	0.541825
$117$	−24.2873	−2.24537
$118$	−5.86777	−0.540172
$119$	7.15268	0.655685
$120$	−7.65190	−0.698519
$121$	−7.51568	−0.683244
$122$	−5.57326	−0.504579
$123$	−11.7486	−1.05934
$124$	−6.15929	−0.553121
$125$	9.88958	0.884551
$126$	14.1324	1.25902
$127$	15.0219	1.33297	0.666487	−	0.745516i	$-0.267797\pi$
$127$	15.0219	1.33297	0.666487	+	0.745516i	$0.267797\pi$
$128$	−1.00000	−0.0883883
$129$	29.9038	2.63289
$130$	−8.64200	−0.757954
$131$	15.6229	1.36498	0.682489	−	0.730896i	$-0.260897\pi$
$131$	15.6229	1.36498	0.682489	+	0.730896i	$0.260897\pi$
$132$	5.85881	0.509944
$133$	−7.57033	−0.656431
$134$	1.94054	0.167637
$135$	29.4711	2.53647
$136$	3.46765	0.297349
$137$	−18.4010	−1.57210	−0.786052	−	0.618160i	$-0.787878\pi$
$137$	−18.4010	−1.57210	−0.786052	+	0.618160i	$0.787878\pi$
$138$	−18.6464	−1.58729
$139$	7.07170	0.599814	0.299907	−	0.953968i	$-0.403044\pi$
$139$	7.07170	0.599814	0.299907	+	0.953968i	$0.403044\pi$
$140$	5.02865	0.424999
$141$	−10.7651	−0.906585
$142$	−13.6104	−1.14216
$143$	6.61690	0.553333
$144$	6.85148	0.570956
$145$	−14.2268	−1.18147
$146$	4.89824	0.405381
$147$	8.61678	0.710700
$148$	6.49741	0.534084
$149$	−5.62616	−0.460913	−0.230456	−	0.973083i	$-0.574022\pi$
$149$	−5.62616	−0.460913	−0.230456	+	0.973083i	$0.574022\pi$
$150$	2.96114	0.241776
$151$	−2.46952	−0.200967	−0.100483	−	0.994939i	$-0.532039\pi$
$151$	−2.46952	−0.200967	−0.100483	+	0.994939i	$0.532039\pi$
$152$	−3.67013	−0.297687
$153$	−23.7585	−1.92076
$154$	−3.85028	−0.310264
$155$	15.0158	1.20610
$156$	11.1262	0.890808
$157$	17.8007	1.42065	0.710325	−	0.703873i	$-0.248548\pi$
$157$	17.8007	1.42065	0.710325	+	0.703873i	$0.248548\pi$
$158$	13.9830	1.11243
$159$	19.3544	1.53491
$160$	2.43791	0.192734
$161$	12.2540	0.965752
$162$	−17.3883	−1.36615
$163$	−1.34063	−0.105006	−0.0525030	−	0.998621i	$-0.516720\pi$
$163$	−1.34063	−0.105006	−0.0525030	+	0.998621i	$0.516720\pi$
$164$	3.74314	0.292290
$165$	−14.2833	−1.11195
$166$	7.58398	0.588631
$167$	7.11396	0.550495	0.275248	−	0.961373i	$-0.411240\pi$
$167$	7.11396	0.550495	0.275248	+	0.961373i	$0.411240\pi$
$168$	−6.47416	−0.499493
$169$	−0.434151	−0.0333962
$170$	−8.45384	−0.648380
$171$	25.1458	1.92295
$172$	−9.52744	−0.726461
$173$	12.4066	0.943259	0.471630	−	0.881797i	$-0.343666\pi$
$173$	12.4066	0.943259	0.471630	+	0.881797i	$0.343666\pi$
$174$	18.3163	1.38856
$175$	−1.94599	−0.147103
$176$	−1.86663	−0.140703
$177$	−18.4172	−1.38432
$178$	−10.8986	−0.816882
$179$	21.2519	1.58844	0.794220	−	0.607630i	$-0.207880\pi$
$179$	21.2519	1.58844	0.794220	+	0.607630i	$0.207880\pi$
$180$	−16.7033	−1.24499
$181$	2.55531	0.189935	0.0949675	−	0.995480i	$-0.469725\pi$
$181$	2.55531	0.189935	0.0949675	+	0.995480i	$0.469725\pi$
$182$	−7.31188	−0.541992
$183$	−17.4928	−1.29311
$184$	5.94081	0.437962
$185$	−15.8401	−1.16459
$186$	−19.3322	−1.41751
$187$	6.47284	0.473341
$188$	3.42979	0.250143
$189$	24.9351	1.81376
$190$	8.94747	0.649118
$191$	−5.20105	−0.376335	−0.188167	−	0.982137i	$-0.560255\pi$
$191$	−5.20105	−0.376335	−0.188167	+	0.982137i	$0.560255\pi$
$192$	−3.13871	−0.226517
$193$	−2.16315	−0.155707	−0.0778536	−	0.996965i	$-0.524807\pi$
$193$	−2.16315	−0.155707	−0.0778536	+	0.996965i	$0.524807\pi$
$194$	−14.7067	−1.05588
$195$	−27.1247	−1.94244
$196$	−2.74533	−0.196095
$197$	22.2813	1.58748	0.793738	−	0.608260i	$-0.208132\pi$
$197$	22.2813	1.58748	0.793738	+	0.608260i	$0.208132\pi$
$198$	12.7892	0.908888
$199$	−18.3557	−1.30120	−0.650602	−	0.759419i	$-0.725483\pi$
$199$	−18.3557	−1.30120	−0.650602	+	0.759419i	$0.725483\pi$
$200$	−0.943426	−0.0667103
$201$	6.09077	0.429610
$202$	−12.4627	−0.876874
$203$	−12.0371	−0.844837
$204$	10.8839	0.762029
$205$	−9.12545	−0.637349
$206$	−11.9252	−0.830871
$207$	−40.7033	−2.82907
$208$	−3.54483	−0.245790
$209$	−6.85079	−0.473879
$210$	15.7835	1.08916
$211$	10.7783	0.742009	0.371004	−	0.928631i	$-0.379014\pi$
$211$	10.7783	0.742009	0.371004	+	0.928631i	$0.379014\pi$
$212$	−6.16637	−0.423508
$213$	−42.7191	−2.92707
$214$	1.56522	0.106996
$215$	23.2271	1.58407
$216$	12.0886	0.822528
$217$	12.7047	0.862450
$218$	11.6531	0.789250
$219$	15.3741	1.03889
$220$	4.55069	0.306807
$221$	12.2923	0.826867
$222$	20.3935	1.36872
$223$	11.8355	0.792562	0.396281	−	0.918129i	$-0.370301\pi$
$223$	11.8355	0.792562	0.396281	+	0.918129i	$0.370301\pi$
$224$	2.06269	0.137819
$225$	6.46386	0.430924
$226$	−19.7143	−1.31138
$227$	−1.72034	−0.114183	−0.0570915	−	0.998369i	$-0.518183\pi$
$227$	−1.72034	−0.114183	−0.0570915	+	0.998369i	$0.518183\pi$
$228$	−11.5195	−0.762896
$229$	−21.7303	−1.43598	−0.717990	−	0.696054i	$-0.754938\pi$
$229$	−21.7303	−1.43598	−0.717990	+	0.696054i	$0.754938\pi$
$230$	−14.4832	−0.954992
$231$	−12.0849	−0.795127
$232$	−5.83563	−0.383128
$233$	−23.5181	−1.54072	−0.770360	−	0.637610i	$-0.779923\pi$
$233$	−23.5181	−1.54072	−0.770360	+	0.637610i	$0.779923\pi$
$234$	24.2873	1.58771
$235$	−8.36153	−0.545446
$236$	5.86777	0.381959
$237$	43.8887	2.85088
$238$	−7.15268	−0.463639
$239$	−20.6246	−1.33410	−0.667048	−	0.745015i	$-0.732443\pi$
$239$	−20.6246	−1.33410	−0.667048	+	0.745015i	$0.732443\pi$
$240$	7.65190	0.493928
$241$	−0.234157	−0.0150834	−0.00754169	−	0.999972i	$-0.502401\pi$
$241$	−0.234157	−0.0150834	−0.00754169	+	0.999972i	$0.502401\pi$
$242$	7.51568	0.483126
$243$	−18.3108	−1.17464
$244$	5.57326	0.356791
$245$	6.69287	0.427592
$246$	11.7486	0.749064
$247$	−13.0100	−0.827808
$248$	6.15929	0.391115
$249$	23.8039	1.50851
$250$	−9.88958	−0.625472
$251$	−8.77126	−0.553637	−0.276818	−	0.960922i	$-0.589280\pi$
$251$	−8.77126	−0.553637	−0.276818	+	0.960922i	$0.589280\pi$
$252$	−14.1324	−0.890260
$253$	11.0893	0.697178
$254$	−15.0219	−0.942556
$255$	−26.5341	−1.66163
$256$	1.00000	0.0625000
$257$	29.3812	1.83275	0.916376	−	0.400319i	$-0.131101\pi$
$257$	29.3812	1.83275	0.916376	+	0.400319i	$0.131101\pi$
$258$	−29.9038	−1.86173
$259$	−13.4021	−0.832767
$260$	8.64200	0.535954
$261$	39.9827	2.47487
$262$	−15.6229	−0.965185
$263$	−12.2417	−0.754856	−0.377428	−	0.926039i	$-0.623192\pi$
$263$	−12.2417	−0.754856	−0.377428	+	0.926039i	$0.623192\pi$
$264$	−5.85881	−0.360585
$265$	15.0331	0.923475
$266$	7.57033	0.464167
$267$	−34.2074	−2.09346
$268$	−1.94054	−0.118537
$269$	−23.2015	−1.41462	−0.707310	−	0.706903i	$-0.750091\pi$
$269$	−23.2015	−1.41462	−0.707310	+	0.706903i	$0.750091\pi$
$270$	−29.4711	−1.79355
$271$	−6.83199	−0.415014	−0.207507	−	0.978234i	$-0.566535\pi$
$271$	−6.83199	−0.415014	−0.207507	+	0.978234i	$0.566535\pi$
$272$	−3.46765	−0.210257
$273$	−22.9498	−1.38899
$274$	18.4010	1.11165
$275$	−1.76103	−0.106194
$276$	18.6464	1.12238
$277$	5.66118	0.340147	0.170074	−	0.985431i	$-0.445599\pi$
$277$	5.66118	0.340147	0.170074	+	0.985431i	$0.445599\pi$
$278$	−7.07170	−0.424133
$279$	−42.2002	−2.52646
$280$	−5.02865	−0.300519
$281$	6.67784	0.398367	0.199183	−	0.979962i	$-0.436171\pi$
$281$	6.67784	0.398367	0.199183	+	0.979962i	$0.436171\pi$
$282$	10.7651	0.641053
$283$	15.6276	0.928967	0.464484	−	0.885582i	$-0.346240\pi$
$283$	15.6276	0.928967	0.464484	+	0.885582i	$0.346240\pi$
$284$	13.6104	0.807630
$285$	28.0835	1.66352
$286$	−6.61690	−0.391266
$287$	−7.72092	−0.455751
$288$	−6.85148	−0.403727
$289$	−4.97537	−0.292669
$290$	14.2268	0.835425
$291$	−46.1601	−2.70595
$292$	−4.89824	−0.286648
$293$	30.1753	1.76286	0.881429	−	0.472316i	$-0.156582\pi$
$293$	30.1753	1.76286	0.881429	+	0.472316i	$0.156582\pi$
$294$	−8.61678	−0.502541
$295$	−14.3051	−0.832876
$296$	−6.49741	−0.377654
$297$	22.5651	1.30936
$298$	5.62616	0.325914
$299$	21.0592	1.21788
$300$	−2.96114	−0.170961
$301$	19.6521	1.13273
$302$	2.46952	0.142105
$303$	−39.1168	−2.24720
$304$	3.67013	0.210497
$305$	−13.5871	−0.777997
$306$	23.7585	1.35819
$307$	−26.2502	−1.49818	−0.749088	−	0.662470i	$-0.769508\pi$
$307$	−26.2502	−1.49818	−0.749088	+	0.662470i	$0.769508\pi$
$308$	3.85028	0.219390
$309$	−37.4298	−2.12931
$310$	−15.0158	−0.852841
$311$	16.2106	0.919216	0.459608	−	0.888122i	$-0.347990\pi$
$311$	16.2106	0.919216	0.459608	+	0.888122i	$0.347990\pi$
$312$	−11.1262	−0.629897
$313$	−8.50973	−0.480998	−0.240499	−	0.970649i	$-0.577311\pi$
$313$	−8.50973	−0.480998	−0.240499	+	0.970649i	$0.577311\pi$
$314$	−17.8007	−1.00455
$315$	34.4537	1.94124
$316$	−13.9830	−0.786608
$317$	−13.5091	−0.758749	−0.379375	−	0.925243i	$-0.623861\pi$
$317$	−13.5091	−0.758749	−0.379375	+	0.925243i	$0.623861\pi$
$318$	−19.3544	−1.08534
$319$	−10.8930	−0.609890
$320$	−2.43791	−0.136284
$321$	4.91277	0.274204
$322$	−12.2540	−0.682889
$323$	−12.7268	−0.708136
$324$	17.3883	0.966016
$325$	−3.34429	−0.185508
$326$	1.34063	0.0742504
$327$	36.5758	2.02265
$328$	−3.74314	−0.206680
$329$	−7.07458	−0.390034
$330$	14.2833	0.786268
$331$	−13.0129	−0.715255	−0.357627	−	0.933864i	$-0.616414\pi$
$331$	−13.0129	−0.715255	−0.357627	+	0.933864i	$0.616414\pi$
$332$	−7.58398	−0.416225
$333$	44.5168	2.43951
$334$	−7.11396	−0.389259
$335$	4.73086	0.258474
$336$	6.47416	0.353195
$337$	14.6068	0.795683	0.397841	−	0.917454i	$-0.369759\pi$
$337$	14.6068	0.795683	0.397841	+	0.917454i	$0.369759\pi$
$338$	0.434151	0.0236147
$339$	−61.8774	−3.36072
$340$	8.45384	0.458474
$341$	11.4971	0.622605
$342$	−25.1458	−1.35973
$343$	20.1015	1.08538
$344$	9.52744	0.513685
$345$	−45.4584	−2.44740
$346$	−12.4066	−0.666985
$347$	20.4023	1.09525	0.547627	−	0.836722i	$-0.315531\pi$
$347$	20.4023	1.09525	0.547627	+	0.836722i	$0.315531\pi$
$348$	−18.3163	−0.981859
$349$	−3.49374	−0.187015	−0.0935077	−	0.995619i	$-0.529808\pi$
$349$	−3.49374	−0.187015	−0.0935077	+	0.995619i	$0.529808\pi$
$350$	1.94599	0.104018
$351$	42.8523	2.28728
$352$	1.86663	0.0994918
$353$	−26.3058	−1.40012	−0.700059	−	0.714085i	$-0.746843\pi$
$353$	−26.3058	−1.40012	−0.700059	+	0.714085i	$0.746843\pi$
$354$	18.4172	0.978863
$355$	−33.1811	−1.76107
$356$	10.8986	0.577623
$357$	−22.4502	−1.18819
$358$	−21.2519	−1.12320
$359$	−13.9551	−0.736522	−0.368261	−	0.929722i	$-0.620047\pi$
$359$	−13.9551	−0.736522	−0.368261	+	0.929722i	$0.620047\pi$
$360$	16.7033	0.880342
$361$	−5.53011	−0.291058
$362$	−2.55531	−0.134304
$363$	23.5895	1.23813
$364$	7.31188	0.383247
$365$	11.9415	0.625047
$366$	17.4928	0.914364
$367$	−11.1834	−0.583767	−0.291884	−	0.956454i	$-0.594282\pi$
$367$	−11.1834	−0.583767	−0.291884	+	0.956454i	$0.594282\pi$
$368$	−5.94081	−0.309686
$369$	25.6460	1.33508
$370$	15.8401	0.823489
$371$	12.7193	0.660352
$372$	19.3322	1.00233
$373$	28.4594	1.47357	0.736786	−	0.676127i	$-0.236343\pi$
$373$	28.4594	1.47357	0.736786	+	0.676127i	$0.236343\pi$
$374$	−6.47284	−0.334702
$375$	−31.0405	−1.60292
$376$	−3.42979	−0.176878
$377$	−20.6864	−1.06540
$378$	−24.9351	−1.28252
$379$	−26.2509	−1.34842	−0.674210	−	0.738539i	$-0.735516\pi$
$379$	−26.2509	−1.34842	−0.674210	+	0.738539i	$0.735516\pi$
$380$	−8.94747	−0.458996
$381$	−47.1492	−2.41553
$382$	5.20105	0.266109
$383$	5.30275	0.270958	0.135479	−	0.990780i	$-0.456743\pi$
$383$	5.30275	0.270958	0.135479	+	0.990780i	$0.456743\pi$
$384$	3.13871	0.160171
$385$	−9.38664	−0.478388
$386$	2.16315	0.110102
$387$	−65.2770	−3.31822
$388$	14.7067	0.746620
$389$	9.46201	0.479743	0.239871	−	0.970805i	$-0.422895\pi$
$389$	9.46201	0.479743	0.239871	+	0.970805i	$0.422895\pi$
$390$	27.1247	1.37351
$391$	20.6007	1.04182
$392$	2.74533	0.138660
$393$	−49.0357	−2.47352
$394$	−22.2813	−1.12251
$395$	34.0895	1.71523
$396$	−12.7892	−0.642681
$397$	22.0519	1.10676	0.553378	−	0.832931i	$-0.313339\pi$
$397$	22.0519	1.10676	0.553378	+	0.832931i	$0.313339\pi$
$398$	18.3557	0.920091
$399$	23.7611	1.18954
$400$	0.943426	0.0471713
$401$	31.8545	1.59074	0.795370	−	0.606124i	$-0.207277\pi$
$401$	31.8545	1.59074	0.795370	+	0.606124i	$0.207277\pi$
$402$	−6.09077	−0.303780
$403$	21.8337	1.08761
$404$	12.4627	0.620043
$405$	−42.3911	−2.10643
$406$	12.0371	0.597390
$407$	−12.1283	−0.601176
$408$	−10.8839	−0.538836
$409$	8.32721	0.411754	0.205877	−	0.978578i	$-0.433995\pi$
$409$	8.32721	0.411754	0.205877	+	0.978578i	$0.433995\pi$
$410$	9.12545	0.450674
$411$	57.7554	2.84886
$412$	11.9252	0.587514
$413$	−12.1034	−0.595568
$414$	40.7033	2.00046
$415$	18.4891	0.907594
$416$	3.54483	0.173800
$417$	−22.1960	−1.08694
$418$	6.85079	0.335083
$419$	−10.5998	−0.517832	−0.258916	−	0.965900i	$-0.583365\pi$
$419$	−10.5998	−0.517832	−0.258916	+	0.965900i	$0.583365\pi$
$420$	−15.7835	−0.770154
$421$	−7.58412	−0.369627	−0.184814	−	0.982774i	$-0.559168\pi$
$421$	−7.58412	−0.369627	−0.184814	+	0.982774i	$0.559168\pi$
$422$	−10.7783	−0.524679
$423$	23.4991	1.14257
$424$	6.16637	0.299465
$425$	−3.27147	−0.158690
$426$	42.7191	2.06975
$427$	−11.4959	−0.556325
$428$	−1.56522	−0.0756578
$429$	−20.7685	−1.00271
$430$	−23.2271	−1.12011
$431$	−6.06614	−0.292196	−0.146098	−	0.989270i	$-0.546671\pi$
$431$	−6.06614	−0.292196	−0.146098	+	0.989270i	$0.546671\pi$
$432$	−12.0886	−0.581615
$433$	−11.8890	−0.571348	−0.285674	−	0.958327i	$-0.592218\pi$
$433$	−11.8890	−0.571348	−0.285674	+	0.958327i	$0.592218\pi$
$434$	−12.7047	−0.609844
$435$	44.6537	2.14098
$436$	−11.6531	−0.558084
$437$	−21.8036	−1.04301
$438$	−15.3741	−0.734605
$439$	−28.2763	−1.34955	−0.674777	−	0.738021i	$-0.735760\pi$
$439$	−28.2763	−1.34955	−0.674777	+	0.738021i	$0.735760\pi$
$440$	−4.55069	−0.216946
$441$	−18.8095	−0.895693
$442$	−12.2923	−0.584683
$443$	−40.9099	−1.94369	−0.971845	−	0.235621i	$-0.924288\pi$
$443$	−40.9099	−1.94369	−0.971845	+	0.235621i	$0.924288\pi$
$444$	−20.3935	−0.967831
$445$	−26.5698	−1.25953
$446$	−11.8355	−0.560426
$447$	17.6588	0.835235
$448$	−2.06269	−0.0974527
$449$	12.0185	0.567190	0.283595	−	0.958944i	$-0.408473\pi$
$449$	12.0185	0.567190	0.283595	+	0.958944i	$0.408473\pi$
$450$	−6.46386	−0.304709
$451$	−6.98706	−0.329008
$452$	19.7143	0.927283
$453$	7.75111	0.364179
$454$	1.72034	0.0807396
$455$	−17.8257	−0.835683
$456$	11.5195	0.539449
$457$	−12.9441	−0.605501	−0.302751	−	0.953070i	$-0.597905\pi$
$457$	−12.9441	−0.605501	−0.302751	+	0.953070i	$0.597905\pi$
$458$	21.7303	1.01539
$459$	41.9193	1.95662
$460$	14.4832	0.675281
$461$	7.28114	0.339116	0.169558	−	0.985520i	$-0.445766\pi$
$461$	7.28114	0.339116	0.169558	+	0.985520i	$0.445766\pi$
$462$	12.0849	0.562240
$463$	−37.7814	−1.75585	−0.877925	−	0.478799i	$-0.841072\pi$
$463$	−37.7814	−1.75585	−0.877925	+	0.478799i	$0.841072\pi$
$464$	5.83563	0.270912
$465$	−47.1303	−2.18561
$466$	23.5181	1.08945
$467$	−21.6171	−1.00032	−0.500160	−	0.865933i	$-0.666726\pi$
$467$	−21.6171	−1.00032	−0.500160	+	0.865933i	$0.666726\pi$
$468$	−24.2873	−1.12268
$469$	4.00271	0.184828
$470$	8.36153	0.385689
$471$	−55.8712	−2.57441
$472$	−5.86777	−0.270086
$473$	17.7842	0.817720
$474$	−43.8887	−2.01587
$475$	3.46250	0.158870
$476$	7.15268	0.327843
$477$	−42.2487	−1.93444
$478$	20.6246	0.943349
$479$	−41.0040	−1.87352	−0.936761	−	0.349969i	$-0.886192\pi$
$479$	−41.0040	−1.87352	−0.936761	+	0.349969i	$0.886192\pi$
$480$	−7.65190	−0.349260
$481$	−23.0322	−1.05018
$482$	0.234157	0.0106656
$483$	−38.4617	−1.75007
$484$	−7.51568	−0.341622
$485$	−35.8537	−1.62803
$486$	18.3108	0.830594
$487$	−19.5446	−0.885650	−0.442825	−	0.896608i	$-0.646024\pi$
$487$	−19.5446	−0.885650	−0.442825	+	0.896608i	$0.646024\pi$
$488$	−5.57326	−0.252290
$489$	4.20783	0.190285
$490$	−6.69287	−0.302353
$491$	6.00647	0.271068	0.135534	−	0.990773i	$-0.456725\pi$
$491$	6.00647	0.271068	0.135534	+	0.990773i	$0.456725\pi$
$492$	−11.7486	−0.529668
$493$	−20.2360	−0.911382
$494$	13.0100	0.585348
$495$	31.1789	1.40139
$496$	−6.15929	−0.276560
$497$	−28.0740	−1.25929
$498$	−23.8039	−1.06668
$499$	5.15279	0.230671	0.115335	−	0.993327i	$-0.463206\pi$
$499$	5.15279	0.230671	0.115335	+	0.993327i	$0.463206\pi$
$500$	9.88958	0.442275
$501$	−22.3286	−0.997570
$502$	8.77126	0.391480
$503$	−24.5845	−1.09617	−0.548085	−	0.836422i	$-0.684643\pi$
$503$	−24.5845	−1.09617	−0.548085	+	0.836422i	$0.684643\pi$
$504$	14.1324	0.629509
$505$	−30.3830	−1.35203
$506$	−11.0893	−0.492979
$507$	1.36267	0.0605184
$508$	15.0219	0.666487
$509$	−15.3475	−0.680266	−0.340133	−	0.940377i	$-0.610472\pi$
$509$	−15.3475	−0.680266	−0.340133	+	0.940377i	$0.610472\pi$
$510$	26.5341	1.17495
$511$	10.1035	0.446954
$512$	−1.00000	−0.0441942
$513$	−44.3670	−1.95885
$514$	−29.3812	−1.29595
$515$	−29.0727	−1.28110
$516$	29.9038	1.31644
$517$	−6.40216	−0.281567
$518$	13.4021	0.588855
$519$	−38.9408	−1.70931
$520$	−8.64200	−0.378977
$521$	13.9975	0.613243	0.306622	−	0.951831i	$-0.400801\pi$
$521$	13.9975	0.613243	0.306622	+	0.951831i	$0.400801\pi$
$522$	−39.9827	−1.75000
$523$	29.3078	1.28154	0.640770	−	0.767733i	$-0.278615\pi$
$523$	29.3078	1.28154	0.640770	+	0.767733i	$0.278615\pi$
$524$	15.6229	0.682489
$525$	6.10789	0.266570
$526$	12.2417	0.533764
$527$	21.3583	0.930382
$528$	5.85881	0.254972
$529$	12.2932	0.534485
$530$	−15.0331	−0.652995
$531$	40.2029	1.74466
$532$	−7.57033	−0.328216
$533$	−13.2688	−0.574736
$534$	34.2074	1.48030
$535$	3.81587	0.164975
$536$	1.94054	0.0838183
$537$	−66.7034	−2.87846
$538$	23.2015	1.00029
$539$	5.12452	0.220729
$540$	29.4711	1.26823
$541$	−17.7050	−0.761198	−0.380599	−	0.924740i	$-0.624282\pi$
$541$	−17.7050	−0.761198	−0.380599	+	0.924740i	$0.624282\pi$
$542$	6.83199	0.293459
$543$	−8.02038	−0.344187
$544$	3.46765	0.148674
$545$	28.4094	1.21692
$546$	22.9498	0.982162
$547$	0.879426	0.0376015	0.0188008	−	0.999823i	$-0.494015\pi$
$547$	0.879426	0.0376015	0.0188008	+	0.999823i	$0.494015\pi$
$548$	−18.4010	−0.786052
$549$	38.1850	1.62970
$550$	1.76103	0.0750905
$551$	21.4176	0.912419
$552$	−18.6464	−0.793645
$553$	28.8426	1.22651
$554$	−5.66118	−0.240521
$555$	49.7175	2.11039
$556$	7.07170	0.299907
$557$	−4.66345	−0.197597	−0.0987984	−	0.995107i	$-0.531500\pi$
$557$	−4.66345	−0.197597	−0.0987984	+	0.995107i	$0.531500\pi$
$558$	42.2002	1.78648
$559$	33.7732	1.42845
$560$	5.02865	0.212499
$561$	−20.3163	−0.857756
$562$	−6.67784	−0.281688
$563$	−5.46298	−0.230237	−0.115119	−	0.993352i	$-0.536725\pi$
$563$	−5.46298	−0.230237	−0.115119	+	0.993352i	$0.536725\pi$
$564$	−10.7651	−0.453293
$565$	−48.0618	−2.02197
$566$	−15.6276	−0.656879
$567$	−35.8666	−1.50625
$568$	−13.6104	−0.571081
$569$	−22.5105	−0.943689	−0.471844	−	0.881682i	$-0.656412\pi$
$569$	−22.5105	−0.943689	−0.471844	+	0.881682i	$0.656412\pi$
$570$	−28.0835	−1.17629
$571$	20.3587	0.851983	0.425992	−	0.904727i	$-0.359925\pi$
$571$	20.3587	0.851983	0.425992	+	0.904727i	$0.359925\pi$
$572$	6.61690	0.276667
$573$	16.3246	0.681968
$574$	7.72092	0.322265
$575$	−5.60471	−0.233733
$576$	6.85148	0.285478
$577$	18.7096	0.778890	0.389445	−	0.921050i	$-0.372667\pi$
$577$	18.7096	0.778890	0.389445	+	0.921050i	$0.372667\pi$
$578$	4.97537	0.206948
$579$	6.78950	0.282162
$580$	−14.2268	−0.590735
$581$	15.6434	0.648996
$582$	46.1601	1.91340
$583$	11.5103	0.476710
$584$	4.89824	0.202691
$585$	59.2105	2.44805
$586$	−30.1753	−1.24653
$587$	−20.2598	−0.836213	−0.418106	−	0.908398i	$-0.637306\pi$
$587$	−20.2598	−0.836213	−0.418106	+	0.908398i	$0.637306\pi$
$588$	8.61678	0.355350
$589$	−22.6054	−0.931440
$590$	14.3051	0.588933
$591$	−69.9344	−2.87672
$592$	6.49741	0.267042
$593$	25.3966	1.04291	0.521457	−	0.853277i	$-0.325389\pi$
$593$	25.3966	1.04291	0.521457	+	0.853277i	$0.325389\pi$
$594$	−22.5651	−0.925856
$595$	−17.4376	−0.714873
$596$	−5.62616	−0.230456
$597$	57.6133	2.35796
$598$	−21.0592	−0.861173
$599$	−31.6849	−1.29461	−0.647306	−	0.762231i	$-0.724104\pi$
$599$	−31.6849	−1.29461	−0.647306	+	0.762231i	$0.724104\pi$
$600$	2.96114	0.120888
$601$	41.4523	1.69088	0.845438	−	0.534074i	$-0.179340\pi$
$601$	41.4523	1.69088	0.845438	+	0.534074i	$0.179340\pi$
$602$	−19.6521	−0.800961
$603$	−13.2955	−0.541436
$604$	−2.46952	−0.100483
$605$	18.3226	0.744919
$606$	39.1168	1.58901
$607$	2.61831	0.106274	0.0531370	−	0.998587i	$-0.483078\pi$
$607$	2.61831	0.106274	0.0531370	+	0.998587i	$0.483078\pi$
$608$	−3.67013	−0.148844
$609$	37.7808	1.53096
$610$	13.5871	0.550127
$611$	−12.1580	−0.491862
$612$	−23.7585	−0.960382
$613$	37.4056	1.51080	0.755399	−	0.655265i	$-0.227443\pi$
$613$	37.4056	1.51080	0.755399	+	0.655265i	$0.227443\pi$
$614$	26.2502	1.05937
$615$	28.6421	1.15496
$616$	−3.85028	−0.155132
$617$	44.7191	1.80032	0.900162	−	0.435555i	$-0.143448\pi$
$617$	44.7191	1.80032	0.900162	+	0.435555i	$0.143448\pi$
$618$	37.4298	1.50565
$619$	14.3266	0.575836	0.287918	−	0.957655i	$-0.407037\pi$
$619$	14.3266	0.575836	0.287918	+	0.957655i	$0.407037\pi$
$620$	15.0158	0.603050
$621$	71.8163	2.88189
$622$	−16.2106	−0.649984
$623$	−22.4803	−0.900654
$624$	11.1262	0.445404
$625$	−28.8271	−1.15308
$626$	8.50973	0.340117
$627$	21.5026	0.858732
$628$	17.8007	0.710325
$629$	−22.5308	−0.898361
$630$	−34.4537	−1.37267
$631$	−1.41632	−0.0563826	−0.0281913	−	0.999603i	$-0.508975\pi$
$631$	−1.41632	−0.0563826	−0.0281913	+	0.999603i	$0.508975\pi$
$632$	13.9830	0.556216
$633$	−33.8299	−1.34462
$634$	13.5091	0.536517
$635$	−36.6220	−1.45330
$636$	19.3544	0.767453
$637$	9.73173	0.385585
$638$	10.8930	0.431257
$639$	93.2515	3.68897
$640$	2.43791	0.0963670
$641$	−38.7952	−1.53232	−0.766159	−	0.642651i	$-0.777835\pi$
$641$	−38.7952	−1.53232	−0.766159	+	0.642651i	$0.777835\pi$
$642$	−4.91277	−0.193891
$643$	22.9517	0.905126	0.452563	−	0.891733i	$-0.350510\pi$
$643$	22.9517	0.905126	0.452563	+	0.891733i	$0.350510\pi$
$644$	12.2540	0.482876
$645$	−72.9030	−2.87055
$646$	12.7268	0.500728
$647$	45.8353	1.80197	0.900987	−	0.433847i	$-0.142844\pi$
$647$	45.8353	1.80197	0.900987	+	0.433847i	$0.142844\pi$
$648$	−17.3883	−0.683076
$649$	−10.9530	−0.429942
$650$	3.34429	0.131174
$651$	−39.8763	−1.56287
$652$	−1.34063	−0.0525030
$653$	30.2908	1.18537	0.592685	−	0.805435i	$-0.298068\pi$
$653$	30.2908	1.18537	0.592685	+	0.805435i	$0.298068\pi$
$654$	−36.5758	−1.43023
$655$	−38.0873	−1.48819
$656$	3.74314	0.146145
$657$	−33.5602	−1.30931
$658$	7.07458	0.275796
$659$	18.6156	0.725162	0.362581	−	0.931952i	$-0.381896\pi$
$659$	18.6156	0.725162	0.362581	+	0.931952i	$0.381896\pi$
$660$	−14.2833	−0.555976
$661$	−33.2849	−1.29463	−0.647317	−	0.762221i	$-0.724109\pi$
$661$	−33.2849	−1.29463	−0.647317	+	0.762221i	$0.724109\pi$
$662$	13.0129	0.505761
$663$	−38.5818	−1.49839
$664$	7.58398	0.294315
$665$	18.4558	0.715686
$666$	−44.5168	−1.72499
$667$	−34.6684	−1.34236
$668$	7.11396	0.275248
$669$	−37.1481	−1.43623
$670$	−4.73086	−0.182769
$671$	−10.4032	−0.401612
$672$	−6.47416	−0.249746
$673$	−0.484761	−0.0186862	−0.00934309	−	0.999956i	$-0.502974\pi$
$673$	−0.484761	−0.0186862	−0.00934309	+	0.999956i	$0.502974\pi$
$674$	−14.6068	−0.562633
$675$	−11.4047	−0.438969
$676$	−0.434151	−0.0166981
$677$	−31.9317	−1.22723	−0.613617	−	0.789604i	$-0.710286\pi$
$677$	−31.9317	−1.22723	−0.613617	+	0.789604i	$0.710286\pi$
$678$	61.8774	2.37639
$679$	−30.3353	−1.16416
$680$	−8.45384	−0.324190
$681$	5.39964	0.206915
$682$	−11.4971	−0.440248
$683$	−10.4238	−0.398857	−0.199429	−	0.979912i	$-0.563909\pi$
$683$	−10.4238	−0.398857	−0.199429	+	0.979912i	$0.563909\pi$
$684$	25.1458	0.961475
$685$	44.8601	1.71402
$686$	−20.1015	−0.767481
$687$	68.2051	2.60219
$688$	−9.52744	−0.363230
$689$	21.8588	0.832752
$690$	45.4584	1.73057
$691$	20.9728	0.797844	0.398922	−	0.916985i	$-0.369384\pi$
$691$	20.9728	0.797844	0.398922	+	0.916985i	$0.369384\pi$
$692$	12.4066	0.471630
$693$	26.3801	1.00210
$694$	−20.4023	−0.774462
$695$	−17.2402	−0.653958
$696$	18.3163	0.694279
$697$	−12.9799	−0.491649
$698$	3.49374	0.132240
$699$	73.8163	2.79199
$700$	−1.94599	−0.0735515
$701$	44.4660	1.67946	0.839728	−	0.543007i	$-0.182714\pi$
$701$	44.4660	1.67946	0.839728	+	0.543007i	$0.182714\pi$
$702$	−42.8523	−1.61735
$703$	23.8464	0.899383
$704$	−1.86663	−0.0703514
$705$	26.2444	0.988421
$706$	26.3058	0.990032
$707$	−25.7067	−0.966799
$708$	−18.4172	−0.692161
$709$	9.73842	0.365734	0.182867	−	0.983138i	$-0.441462\pi$
$709$	9.73842	0.365734	0.182867	+	0.983138i	$0.441462\pi$
$710$	33.1811	1.24526
$711$	−95.8045	−3.59295
$712$	−10.8986	−0.408441
$713$	36.5911	1.37035
$714$	22.4502	0.840176
$715$	−16.1314	−0.603282
$716$	21.2519	0.794220
$717$	64.7347	2.41756
$718$	13.9551	0.520800
$719$	17.8682	0.666372	0.333186	−	0.942861i	$-0.391876\pi$
$719$	17.8682	0.666372	0.333186	+	0.942861i	$0.391876\pi$
$720$	−16.7033	−0.622496
$721$	−24.5980	−0.916078
$722$	5.53011	0.205809
$723$	0.734950	0.0273331
$724$	2.55531	0.0949675
$725$	5.50549	0.204469
$726$	−23.5895	−0.875489
$727$	−38.8021	−1.43909	−0.719545	−	0.694445i	$-0.755650\pi$
$727$	−38.8021	−1.43909	−0.719545	+	0.694445i	$0.755650\pi$
$728$	−7.31188	−0.270996
$729$	5.30727	0.196566
$730$	−11.9415	−0.441975
$731$	33.0379	1.22195
$732$	−17.4928	−0.646553
$733$	3.93144	0.145211	0.0726055	−	0.997361i	$-0.476869\pi$
$733$	3.93144	0.145211	0.0726055	+	0.997361i	$0.476869\pi$
$734$	11.1834	0.412786
$735$	−21.0070	−0.774854
$736$	5.94081	0.218981
$737$	3.62227	0.133428
$738$	−25.6460	−0.944043
$739$	−23.8046	−0.875666	−0.437833	−	0.899056i	$-0.644254\pi$
$739$	−23.8046	−0.875666	−0.437833	+	0.899056i	$0.644254\pi$
$740$	−15.8401	−0.582295
$741$	40.8346	1.50010
$742$	−12.7193	−0.466939
$743$	−36.9383	−1.35513	−0.677567	−	0.735461i	$-0.736966\pi$
$743$	−36.9383	−1.35513	−0.677567	+	0.735461i	$0.736966\pi$
$744$	−19.3322	−0.708753
$745$	13.7161	0.502518
$746$	−28.4594	−1.04197
$747$	−51.9614	−1.90117
$748$	6.47284	0.236670
$749$	3.22856	0.117969
$750$	31.0405	1.13344
$751$	18.9106	0.690057	0.345028	−	0.938592i	$-0.387869\pi$
$751$	18.9106	0.690057	0.345028	+	0.938592i	$0.387869\pi$
$752$	3.42979	0.125072
$753$	27.5304	1.00326
$754$	20.6864	0.753353
$755$	6.02049	0.219108
$756$	24.9351	0.906880
$757$	29.2120	1.06173	0.530865	−	0.847457i	$-0.321867\pi$
$757$	29.2120	1.06173	0.530865	+	0.847457i	$0.321867\pi$
$758$	26.2509	0.953477
$759$	−34.8060	−1.26338
$760$	8.94747	0.324559
$761$	13.6932	0.496378	0.248189	−	0.968712i	$-0.420165\pi$
$761$	13.6932	0.496378	0.248189	+	0.968712i	$0.420165\pi$
$762$	47.1492	1.70804
$763$	24.0368	0.870189
$764$	−5.20105	−0.188167
$765$	57.9213	2.09415
$766$	−5.30275	−0.191596
$767$	−20.8003	−0.751054
$768$	−3.13871	−0.113258
$769$	−32.1248	−1.15845	−0.579224	−	0.815168i	$-0.696644\pi$
$769$	−32.1248	−1.15845	−0.579224	+	0.815168i	$0.696644\pi$
$770$	9.38664	0.338271
$771$	−92.2191	−3.32119
$772$	−2.16315	−0.0778536
$773$	−6.71785	−0.241624	−0.120812	−	0.992675i	$-0.538550\pi$
$773$	−6.71785	−0.241624	−0.120812	+	0.992675i	$0.538550\pi$
$774$	65.2770	2.34634
$775$	−5.81083	−0.208731
$776$	−14.7067	−0.527940
$777$	42.0653	1.50908
$778$	−9.46201	−0.339230
$779$	13.7378	0.492208
$780$	−27.1247	−0.971220
$781$	−25.4057	−0.909086
$782$	−20.6007	−0.736678
$783$	−70.5449	−2.52107
$784$	−2.74533	−0.0980474
$785$	−43.3966	−1.54889
$786$	49.0357	1.74904
$787$	33.9232	1.20923	0.604616	−	0.796517i	$-0.293327\pi$
$787$	33.9232	1.20923	0.604616	+	0.796517i	$0.293327\pi$
$788$	22.2813	0.793738
$789$	38.4231	1.36790
$790$	−34.0895	−1.21285
$791$	−40.6644	−1.44586
$792$	12.7892	0.454444
$793$	−19.7563	−0.701566
$794$	−22.0519	−0.782594
$795$	−47.1844	−1.67346
$796$	−18.3557	−0.650602
$797$	31.5607	1.11794	0.558969	−	0.829189i	$-0.311197\pi$
$797$	31.5607	1.11794	0.558969	+	0.829189i	$0.311197\pi$
$798$	−23.7611	−0.841132
$799$	−11.8933	−0.420756
$800$	−0.943426	−0.0333551
$801$	74.6712	2.63838
$802$	−31.8545	−1.12482
$803$	9.14322	0.322657
$804$	6.09077	0.214805
$805$	−29.8742	−1.05293
$806$	−21.8337	−0.769058
$807$	72.8227	2.56348
$808$	−12.4627	−0.438437
$809$	−12.2146	−0.429442	−0.214721	−	0.976675i	$-0.568884\pi$
$809$	−12.2146	−0.429442	−0.214721	+	0.976675i	$0.568884\pi$
$810$	42.3911	1.48947
$811$	−38.5760	−1.35459	−0.677293	−	0.735714i	$-0.736847\pi$
$811$	−38.5760	−1.35459	−0.677293	+	0.735714i	$0.736847\pi$
$812$	−12.0371	−0.422419
$813$	21.4436	0.752060
$814$	12.1283	0.425096
$815$	3.26833	0.114485
$816$	10.8839	0.381014
$817$	−34.9670	−1.22334
$818$	−8.32721	−0.291154
$819$	50.0972	1.75054
$820$	−9.12545	−0.318674
$821$	−1.24138	−0.0433246	−0.0216623	−	0.999765i	$-0.506896\pi$
$821$	−1.24138	−0.0433246	−0.0216623	+	0.999765i	$0.506896\pi$
$822$	−57.7554	−2.01445
$823$	−51.6752	−1.80129	−0.900643	−	0.434560i	$-0.856904\pi$
$823$	−51.6752	−1.80129	−0.900643	+	0.434560i	$0.856904\pi$
$824$	−11.9252	−0.415435
$825$	5.52735	0.192438
$826$	12.1034	0.421130
$827$	22.1807	0.771298	0.385649	−	0.922645i	$-0.373977\pi$
$827$	22.1807	0.771298	0.385649	+	0.922645i	$0.373977\pi$
$828$	−40.7033	−1.41454
$829$	15.7625	0.547456	0.273728	−	0.961807i	$-0.411743\pi$
$829$	15.7625	0.547456	0.273728	+	0.961807i	$0.411743\pi$
$830$	−18.4891	−0.641766
$831$	−17.7688	−0.616392
$832$	−3.54483	−0.122895
$833$	9.51985	0.329843
$834$	22.1960	0.768585
$835$	−17.3432	−0.600187
$836$	−6.85079	−0.236940
$837$	74.4575	2.57363
$838$	10.5998	0.366163
$839$	−16.7124	−0.576977	−0.288488	−	0.957483i	$-0.593153\pi$
$839$	−16.7124	−0.576977	−0.288488	+	0.957483i	$0.593153\pi$
$840$	15.7835	0.544581
$841$	5.05462	0.174297
$842$	7.58412	0.261366
$843$	−20.9598	−0.721893
$844$	10.7783	0.371004
$845$	1.05842	0.0364109
$846$	−23.4991	−0.807916
$847$	15.5025	0.532672
$848$	−6.16637	−0.211754
$849$	−49.0506	−1.68341
$850$	3.27147	0.112211
$851$	−38.5998	−1.32319
$852$	−42.7191	−1.46353
$853$	−3.28365	−0.112430	−0.0562150	−	0.998419i	$-0.517903\pi$
$853$	−3.28365	−0.112430	−0.0562150	+	0.998419i	$0.517903\pi$
$854$	11.4959	0.393381
$855$	−61.3034	−2.09653
$856$	1.56522	0.0534981
$857$	−9.14864	−0.312512	−0.156256	−	0.987717i	$-0.549942\pi$
$857$	−9.14864	−0.312512	−0.156256	+	0.987717i	$0.549942\pi$
$858$	20.7685	0.709025
$859$	−29.9268	−1.02109	−0.510544	−	0.859852i	$-0.670556\pi$
$859$	−29.9268	−1.02109	−0.510544	+	0.859852i	$0.670556\pi$
$860$	23.2271	0.792037
$861$	24.2337	0.825882
$862$	6.06614	0.206613
$863$	−30.9604	−1.05390	−0.526952	−	0.849895i	$-0.676665\pi$
$863$	−30.9604	−1.05390	−0.526952	+	0.849895i	$0.676665\pi$
$864$	12.0886	0.411264
$865$	−30.2463	−1.02841
$866$	11.8890	0.404004
$867$	15.6162	0.530355
$868$	12.7047	0.431225
$869$	26.1012	0.885423
$870$	−44.6537	−1.51390
$871$	6.87887	0.233082
$872$	11.6531	0.394625
$873$	100.763	3.41030
$874$	21.8036	0.737516
$875$	−20.3991	−0.689615
$876$	15.3741	0.519444
$877$	−31.1285	−1.05114	−0.525568	−	0.850752i	$-0.676147\pi$
$877$	−31.1285	−1.05114	−0.525568	+	0.850752i	$0.676147\pi$
$878$	28.2763	0.954279
$879$	−94.7113	−3.19453
$880$	4.55069	0.153404
$881$	15.1587	0.510709	0.255355	−	0.966847i	$-0.417808\pi$
$881$	15.1587	0.510709	0.255355	+	0.966847i	$0.417808\pi$
$882$	18.8095	0.633350
$883$	−25.2635	−0.850185	−0.425093	−	0.905150i	$-0.639759\pi$
$883$	−25.2635	−0.850185	−0.425093	+	0.905150i	$0.639759\pi$
$884$	12.2923	0.413433
$885$	44.8996	1.50928
$886$	40.9099	1.37440
$887$	21.9273	0.736247	0.368123	−	0.929777i	$-0.380000\pi$
$887$	21.9273	0.736247	0.368123	+	0.929777i	$0.380000\pi$
$888$	20.3935	0.684360
$889$	−30.9854	−1.03922
$890$	26.5698	0.890620
$891$	−32.4575	−1.08737
$892$	11.8355	0.396281
$893$	12.5878	0.421234
$894$	−17.6588	−0.590600
$895$	−51.8103	−1.73183
$896$	2.06269	0.0689095
$897$	−66.0985	−2.20697
$898$	−12.0185	−0.401064
$899$	−35.9434	−1.19878
$900$	6.46386	0.215462
$901$	21.3828	0.712366
$902$	6.98706	0.232644
$903$	−61.6822	−2.05266
$904$	−19.7143	−0.655688
$905$	−6.22963	−0.207080
$906$	−7.75111	−0.257513
$907$	15.6375	0.519234	0.259617	−	0.965712i	$-0.416404\pi$
$907$	15.6375	0.519234	0.259617	+	0.965712i	$0.416404\pi$
$908$	−1.72034	−0.0570915
$909$	85.3880	2.83214
$910$	17.8257	0.590917
$911$	−53.9344	−1.78693	−0.893464	−	0.449135i	$-0.851732\pi$
$911$	−53.9344	−1.78693	−0.893464	+	0.449135i	$0.851732\pi$
$912$	−11.5195	−0.381448
$913$	14.1565	0.468512
$914$	12.9441	0.428154
$915$	42.6460	1.40983
$916$	−21.7303	−0.717990
$917$	−32.2251	−1.06417
$918$	−41.9193	−1.38354
$919$	52.0420	1.71671	0.858353	−	0.513059i	$-0.171488\pi$
$919$	52.0420	1.71671	0.858353	+	0.513059i	$0.171488\pi$
$920$	−14.4832	−0.477496
$921$	82.3916	2.71489
$922$	−7.28114	−0.239791
$923$	−48.2467	−1.58806
$924$	−12.0849	−0.397563
$925$	6.12982	0.201547
$926$	37.7814	1.24157
$927$	81.7055	2.68356
$928$	−5.83563	−0.191564
$929$	19.4802	0.639125	0.319562	−	0.947565i	$-0.396464\pi$
$929$	19.4802	0.639125	0.319562	+	0.947565i	$0.396464\pi$
$930$	47.1303	1.54546
$931$	−10.0757	−0.330218
$932$	−23.5181	−0.770360
$933$	−50.8802	−1.66574
$934$	21.6171	0.707333
$935$	−15.7802	−0.516068
$936$	24.2873	0.793857
$937$	−19.4559	−0.635597	−0.317799	−	0.948158i	$-0.602944\pi$
$937$	−19.4559	−0.635597	−0.317799	+	0.948158i	$0.602944\pi$
$938$	−4.00271	−0.130693
$939$	26.7095	0.871633
$940$	−8.36153	−0.272723
$941$	38.2575	1.24716	0.623580	−	0.781760i	$-0.285678\pi$
$941$	38.2575	1.24716	0.623580	+	0.781760i	$0.285678\pi$
$942$	55.8712	1.82038
$943$	−22.2373	−0.724145
$944$	5.86777	0.190980
$945$	−60.7896	−1.97749
$946$	−17.7842	−0.578215
$947$	16.3443	0.531117	0.265559	−	0.964095i	$-0.414444\pi$
$947$	16.3443	0.531117	0.265559	+	0.964095i	$0.414444\pi$
$948$	43.8887	1.42544
$949$	17.3635	0.563642
$950$	−3.46250	−0.112338
$951$	42.4012	1.37495
$952$	−7.15268	−0.231820
$953$	−38.5935	−1.25017	−0.625084	−	0.780558i	$-0.714935\pi$
$953$	−38.5935	−1.25017	−0.625084	+	0.780558i	$0.714935\pi$
$954$	42.2487	1.36785
$955$	12.6797	0.410306
$956$	−20.6246	−0.667048
$957$	34.1899	1.10520
$958$	41.0040	1.32478
$959$	37.9555	1.22565
$960$	7.65190	0.246964
$961$	6.93686	0.223770
$962$	23.0322	0.742589
$963$	−10.7241	−0.345578
$964$	−0.234157	−0.00754169
$965$	5.27358	0.169763
$966$	38.4617	1.23749
$967$	−18.1967	−0.585165	−0.292583	−	0.956240i	$-0.594515\pi$
$967$	−18.1967	−0.585165	−0.292583	+	0.956240i	$0.594515\pi$
$968$	7.51568	0.241563
$969$	39.9456	1.28324
$970$	35.8537	1.15119
$971$	45.8234	1.47054	0.735271	−	0.677773i	$-0.237055\pi$
$971$	45.8234	1.47054	0.735271	+	0.677773i	$0.237055\pi$
$972$	−18.3108	−0.587318
$973$	−14.5867	−0.467628
$974$	19.5446	0.626249
$975$	10.4967	0.336165
$976$	5.57326	0.178396
$977$	−14.1526	−0.452780	−0.226390	−	0.974037i	$-0.572692\pi$
$977$	−14.1526	−0.452780	−0.226390	+	0.974037i	$0.572692\pi$
$978$	−4.20783	−0.134552
$979$	−20.3436	−0.650185
$980$	6.69287	0.213796
$981$	−79.8412	−2.54913
$982$	−6.00647	−0.191674
$983$	−2.42348	−0.0772970	−0.0386485	−	0.999253i	$-0.512305\pi$
$983$	−2.42348	−0.0772970	−0.0386485	+	0.999253i	$0.512305\pi$
$984$	11.7486	0.374532
$985$	−54.3198	−1.73077
$986$	20.2360	0.644444
$987$	22.2050	0.706794
$988$	−13.0100	−0.413904
$989$	56.6007	1.79980
$990$	−31.1789	−0.990932
$991$	−36.2002	−1.14994	−0.574969	−	0.818175i	$-0.694986\pi$
$991$	−36.2002	−1.14994	−0.574969	+	0.818175i	$0.694986\pi$
$992$	6.15929	0.195558
$993$	40.8437	1.29614
$994$	28.0740	0.890455
$995$	44.7497	1.41866
$996$	23.8039	0.754255
$997$	−55.8724	−1.76950	−0.884749	−	0.466069i	$-0.845670\pi$
$997$	−55.8724	−1.76950	−0.884749	+	0.466069i	$0.845670\pi$
$998$	−5.15279	−0.163109
$999$	−78.5449	−2.48505

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6002.2.a.b.1.4	✓	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6002.2.a.b.1.4	✓	56	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:	\( N \)	\(=\)	\( 6002 = 2 \cdot 3001 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6002.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.13871 q^{3} +1.00000 q^{4} -2.43791 q^{5} +3.13871 q^{6} -2.06269 q^{7} -1.00000 q^{8} +6.85148 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.13871 q^{3} +1.00000 q^{4} -2.43791 q^{5} +3.13871 q^{6} -2.06269 q^{7} -1.00000 q^{8} +6.85148 q^{9} +2.43791 q^{10} -1.86663 q^{11} -3.13871 q^{12} -3.54483 q^{13} +2.06269 q^{14} +7.65190 q^{15} +1.00000 q^{16} -3.46765 q^{17} -6.85148 q^{18} +3.67013 q^{19} -2.43791 q^{20} +6.47416 q^{21} +1.86663 q^{22} -5.94081 q^{23} +3.13871 q^{24} +0.943426 q^{25} +3.54483 q^{26} -12.0886 q^{27} -2.06269 q^{28} +5.83563 q^{29} -7.65190 q^{30} -6.15929 q^{31} -1.00000 q^{32} +5.85881 q^{33} +3.46765 q^{34} +5.02865 q^{35} +6.85148 q^{36} +6.49741 q^{37} -3.67013 q^{38} +11.1262 q^{39} +2.43791 q^{40} +3.74314 q^{41} -6.47416 q^{42} -9.52744 q^{43} -1.86663 q^{44} -16.7033 q^{45} +5.94081 q^{46} +3.42979 q^{47} -3.13871 q^{48} -2.74533 q^{49} -0.943426 q^{50} +10.8839 q^{51} -3.54483 q^{52} -6.16637 q^{53} +12.0886 q^{54} +4.55069 q^{55} +2.06269 q^{56} -11.5195 q^{57} -5.83563 q^{58} +5.86777 q^{59} +7.65190 q^{60} +5.57326 q^{61} +6.15929 q^{62} -14.1324 q^{63} +1.00000 q^{64} +8.64200 q^{65} -5.85881 q^{66} -1.94054 q^{67} -3.46765 q^{68} +18.6464 q^{69} -5.02865 q^{70} +13.6104 q^{71} -6.85148 q^{72} -4.89824 q^{73} -6.49741 q^{74} -2.96114 q^{75} +3.67013 q^{76} +3.85028 q^{77} -11.1262 q^{78} -13.9830 q^{79} -2.43791 q^{80} +17.3883 q^{81} -3.74314 q^{82} -7.58398 q^{83} +6.47416 q^{84} +8.45384 q^{85} +9.52744 q^{86} -18.3163 q^{87} +1.86663 q^{88} +10.8986 q^{89} +16.7033 q^{90} +7.31188 q^{91} -5.94081 q^{92} +19.3322 q^{93} -3.42979 q^{94} -8.94747 q^{95} +3.13871 q^{96} +14.7067 q^{97} +2.74533 q^{98} -12.7892 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9}+O(q^{10}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9	\( 56 q - 56 q^{2} - 11 q^{3} + 56 q^{4} + 11 q^{6} - 21 q^{7} - 56 q^{8} + 53 q^{9} + 12 q^{11} - 11 q^{12} - 31 q^{13} + 21 q^{14} - 22 q^{15} + 56 q^{16} - 4 q^{17} - 53 q^{18} - 9 q^{19} + 13 q^{21} - 12 q^{22} - 39 q^{23} + 11 q^{24} + 8 q^{25} + 31 q^{26} - 44 q^{27} - 21 q^{28} + 13 q^{29} + 22 q^{30} - 35 q^{31} - 56 q^{32} - 26 q^{33} + 4 q^{34} - 7 q^{35} + 53 q^{36} - 65 q^{37} + 9 q^{38} - 27 q^{39} + 38 q^{41} - 13 q^{42} - 76 q^{43} + 12 q^{44} - 21 q^{45} + 39 q^{46} - 43 q^{47} - 11 q^{48} + 9 q^{49} - 8 q^{50} - 19 q^{51} - 31 q^{52} - 26 q^{53} + 44 q^{54} - 67 q^{55} + 21 q^{56} - 26 q^{57} - 13 q^{58} + 11 q^{59} - 22 q^{60} - 17 q^{61} + 35 q^{62} - 67 q^{63} + 56 q^{64} + 31 q^{65} + 26 q^{66} - 93 q^{67} - 4 q^{68} - 13 q^{69} + 7 q^{70} - 33 q^{71} - 53 q^{72} - 41 q^{73} + 65 q^{74} - 21 q^{75} - 9 q^{76} + 5 q^{77} + 27 q^{78} - 69 q^{79} + 36 q^{81} - 38 q^{82} + 4 q^{83} + 13 q^{84} - 40 q^{85} + 76 q^{86} - 69 q^{87} - 12 q^{88} + 40 q^{89} + 21 q^{90} - 64 q^{91} - 39 q^{92} - 57 q^{93} + 43 q^{94} - 22 q^{95} + 11 q^{96} - 71 q^{97} - 9 q^{98} + 17 q^{99}+O(q^{100}) \) 56 * q - 56 * q^2 - 11 * q^3 + 56 * q^4 + 11 * q^6 - 21 * q^7 - 56 * q^8 + 53 * q^9 + 12 * q^11 - 11 * q^12 - 31 * q^13 + 21 * q^14 - 22 * q^15 + 56 * q^16 - 4 * q^17 - 53 * q^18 - 9 * q^19 + 13 * q^21 - 12 * q^22 - 39 * q^23 + 11 * q^24 + 8 * q^25 + 31 * q^26 - 44 * q^27 - 21 * q^28 + 13 * q^29 + 22 * q^30 - 35 * q^31 - 56 * q^32 - 26 * q^33 + 4 * q^34 - 7 * q^35 + 53 * q^36 - 65 * q^37 + 9 * q^38 - 27 * q^39 + 38 * q^41 - 13 * q^42 - 76 * q^43 + 12 * q^44 - 21 * q^45 + 39 * q^46 - 43 * q^47 - 11 * q^48 + 9 * q^49 - 8 * q^50 - 19 * q^51 - 31 * q^52 - 26 * q^53 + 44 * q^54 - 67 * q^55 + 21 * q^56 - 26 * q^57 - 13 * q^58 + 11 * q^59 - 22 * q^60 - 17 * q^61 + 35 * q^62 - 67 * q^63 + 56 * q^64 + 31 * q^65 + 26 * q^66 - 93 * q^67 - 4 * q^68 - 13 * q^69 + 7 * q^70 - 33 * q^71 - 53 * q^72 - 41 * q^73 + 65 * q^74 - 21 * q^75 - 9 * q^76 + 5 * q^77 + 27 * q^78 - 69 * q^79 + 36 * q^81 - 38 * q^82 + 4 * q^83 + 13 * q^84 - 40 * q^85 + 76 * q^86 - 69 * q^87 - 12 * q^88 + 40 * q^89 + 21 * q^90 - 64 * q^91 - 39 * q^92 - 57 * q^93 + 43 * q^94 - 22 * q^95 + 11 * q^96 - 71 * q^97 - 9 * q^98 + 17 * q^99

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