LMFDB - Embedded newform 6026.2.a.h.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6026,2,Mod(1,6026)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6026, 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("6026.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6026 = 2 \cdot 23 \cdot 131 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6026.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:	$48.1178522580$
Analytic rank:	$1$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Character	$\chi$	$=$	6026.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.03806 q^{3} +1.00000 q^{4} +2.76911 q^{5} +3.03806 q^{6} -0.589865 q^{7} -1.00000 q^{8} +6.22984 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.03806 q^{3} +1.00000 q^{4} +2.76911 q^{5} +3.03806 q^{6} -0.589865 q^{7} -1.00000 q^{8} +6.22984 q^{9} -2.76911 q^{10} -4.13029 q^{11} -3.03806 q^{12} +2.56341 q^{13} +0.589865 q^{14} -8.41273 q^{15} +1.00000 q^{16} +1.30388 q^{17} -6.22984 q^{18} -5.13670 q^{19} +2.76911 q^{20} +1.79205 q^{21} +4.13029 q^{22} -1.00000 q^{23} +3.03806 q^{24} +2.66796 q^{25} -2.56341 q^{26} -9.81246 q^{27} -0.589865 q^{28} +3.77899 q^{29} +8.41273 q^{30} +6.58712 q^{31} -1.00000 q^{32} +12.5481 q^{33} -1.30388 q^{34} -1.63340 q^{35} +6.22984 q^{36} +6.66887 q^{37} +5.13670 q^{38} -7.78782 q^{39} -2.76911 q^{40} -0.317115 q^{41} -1.79205 q^{42} -4.28351 q^{43} -4.13029 q^{44} +17.2511 q^{45} +1.00000 q^{46} +6.67301 q^{47} -3.03806 q^{48} -6.65206 q^{49} -2.66796 q^{50} -3.96126 q^{51} +2.56341 q^{52} -13.8012 q^{53} +9.81246 q^{54} -11.4372 q^{55} +0.589865 q^{56} +15.6056 q^{57} -3.77899 q^{58} -6.57837 q^{59} -8.41273 q^{60} -4.26115 q^{61} -6.58712 q^{62} -3.67476 q^{63} +1.00000 q^{64} +7.09837 q^{65} -12.5481 q^{66} -6.71973 q^{67} +1.30388 q^{68} +3.03806 q^{69} +1.63340 q^{70} +11.4583 q^{71} -6.22984 q^{72} +5.20789 q^{73} -6.66887 q^{74} -8.10545 q^{75} -5.13670 q^{76} +2.43631 q^{77} +7.78782 q^{78} -4.85884 q^{79} +2.76911 q^{80} +11.1214 q^{81} +0.317115 q^{82} +5.44110 q^{83} +1.79205 q^{84} +3.61057 q^{85} +4.28351 q^{86} -11.4808 q^{87} +4.13029 q^{88} -4.24789 q^{89} -17.2511 q^{90} -1.51207 q^{91} -1.00000 q^{92} -20.0121 q^{93} -6.67301 q^{94} -14.2241 q^{95} +3.03806 q^{96} -9.63313 q^{97} +6.65206 q^{98} -25.7310 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * 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
$3$	−3.03806	−1.75403	−0.877014	−	0.480465i	$-0.840468\pi$
$3$	−3.03806	−1.75403	−0.877014	+	0.480465i	$0.840468\pi$
$4$	1.00000	0.500000
$5$	2.76911	1.23838	0.619192	−	0.785240i	$-0.287460\pi$
$5$	2.76911	1.23838	0.619192	+	0.785240i	$0.287460\pi$
$6$	3.03806	1.24028
$7$	−0.589865	−0.222948	−0.111474	−	0.993767i	$-0.535557\pi$
$7$	−0.589865	−0.222948	−0.111474	+	0.993767i	$0.535557\pi$
$8$	−1.00000	−0.353553
$9$	6.22984	2.07661
$10$	−2.76911	−0.875669
$11$	−4.13029	−1.24533	−0.622665	−	0.782489i	$-0.713950\pi$
$11$	−4.13029	−1.24533	−0.622665	+	0.782489i	$0.713950\pi$
$12$	−3.03806	−0.877014
$13$	2.56341	0.710963	0.355482	−	0.934683i	$-0.384317\pi$
$13$	2.56341	0.710963	0.355482	+	0.934683i	$0.384317\pi$
$14$	0.589865	0.157648
$15$	−8.41273	−2.17216
$16$	1.00000	0.250000
$17$	1.30388	0.316236	0.158118	−	0.987420i	$-0.449457\pi$
$17$	1.30388	0.316236	0.158118	+	0.987420i	$0.449457\pi$
$18$	−6.22984	−1.46839
$19$	−5.13670	−1.17844	−0.589220	−	0.807972i	$-0.700565\pi$
$19$	−5.13670	−1.17844	−0.589220	+	0.807972i	$0.700565\pi$
$20$	2.76911	0.619192
$21$	1.79205	0.391057
$22$	4.13029	0.880581
$23$	−1.00000	−0.208514
$23$	−1.00000	−0.208514
$24$	3.03806	0.620142
$25$	2.66796	0.533593
$26$	−2.56341	−0.502727
$27$	−9.81246	−1.88841
$28$	−0.589865	−0.111474
$29$	3.77899	0.701740	0.350870	−	0.936424i	$-0.385886\pi$
$29$	3.77899	0.701740	0.350870	+	0.936424i	$0.385886\pi$
$30$	8.41273	1.53595
$31$	6.58712	1.18308	0.591540	−	0.806275i	$-0.298520\pi$
$31$	6.58712	1.18308	0.591540	+	0.806275i	$0.298520\pi$
$32$	−1.00000	−0.176777
$33$	12.5481	2.18434
$34$	−1.30388	−0.223613
$35$	−1.63340	−0.276095
$36$	6.22984	1.03831
$37$	6.66887	1.09636	0.548178	−	0.836362i	$-0.315322\pi$
$37$	6.66887	1.09636	0.548178	+	0.836362i	$0.315322\pi$
$38$	5.13670	0.833283
$39$	−7.78782	−1.24705
$40$	−2.76911	−0.437835
$41$	−0.317115	−0.0495250	−0.0247625	−	0.999693i	$-0.507883\pi$
$41$	−0.317115	−0.0495250	−0.0247625	+	0.999693i	$0.507883\pi$
$42$	−1.79205	−0.276519
$43$	−4.28351	−0.653229	−0.326614	−	0.945158i	$-0.605908\pi$
$43$	−4.28351	−0.653229	−0.326614	+	0.945158i	$0.605908\pi$
$44$	−4.13029	−0.622665
$45$	17.2511	2.57164
$46$	1.00000	0.147442
$47$	6.67301	0.973359	0.486680	−	0.873581i	$-0.338208\pi$
$47$	6.67301	0.973359	0.486680	+	0.873581i	$0.338208\pi$
$48$	−3.03806	−0.438507
$49$	−6.65206	−0.950294
$50$	−2.66796	−0.377307
$51$	−3.96126	−0.554687
$52$	2.56341	0.355482
$53$	−13.8012	−1.89575	−0.947873	−	0.318648i	$-0.896771\pi$
$53$	−13.8012	−1.89575	−0.947873	+	0.318648i	$0.896771\pi$
$54$	9.81246	1.33531
$55$	−11.4372	−1.54219
$56$	0.589865	0.0788240
$57$	15.6056	2.06702
$58$	−3.77899	−0.496205
$59$	−6.57837	−0.856431	−0.428216	−	0.903677i	$-0.640858\pi$
$59$	−6.57837	−0.856431	−0.428216	+	0.903677i	$0.640858\pi$
$60$	−8.41273	−1.08608
$61$	−4.26115	−0.545584	−0.272792	−	0.962073i	$-0.587947\pi$
$61$	−4.26115	−0.545584	−0.272792	+	0.962073i	$0.587947\pi$
$62$	−6.58712	−0.836565
$63$	−3.67476	−0.462977
$64$	1.00000	0.125000
$65$	7.09837	0.880445
$66$	−12.5481	−1.54456
$67$	−6.71973	−0.820946	−0.410473	−	0.911873i	$-0.634636\pi$
$67$	−6.71973	−0.820946	−0.410473	+	0.911873i	$0.634636\pi$
$68$	1.30388	0.158118
$69$	3.03806	0.365740
$70$	1.63340	0.195229
$71$	11.4583	1.35985	0.679924	−	0.733283i	$-0.262013\pi$
$71$	11.4583	1.35985	0.679924	+	0.733283i	$0.262013\pi$
$72$	−6.22984	−0.734193
$73$	5.20789	0.609537	0.304769	−	0.952426i	$-0.401421\pi$
$73$	5.20789	0.609537	0.304769	+	0.952426i	$0.401421\pi$
$74$	−6.66887	−0.775241
$75$	−8.10545	−0.935936
$76$	−5.13670	−0.589220
$77$	2.43631	0.277644
$78$	7.78782	0.881797
$79$	−4.85884	−0.546662	−0.273331	−	0.961920i	$-0.588125\pi$
$79$	−4.85884	−0.546662	−0.273331	+	0.961920i	$0.588125\pi$
$80$	2.76911	0.309596
$81$	11.1214	1.23571
$82$	0.317115	0.0350195
$83$	5.44110	0.597238	0.298619	−	0.954372i	$-0.403474\pi$
$83$	5.44110	0.597238	0.298619	+	0.954372i	$0.403474\pi$
$84$	1.79205	0.195528
$85$	3.61057	0.391622
$86$	4.28351	0.461902
$87$	−11.4808	−1.23087
$88$	4.13029	0.440290
$89$	−4.24789	−0.450275	−0.225138	−	0.974327i	$-0.572283\pi$
$89$	−4.24789	−0.450275	−0.225138	+	0.974327i	$0.572283\pi$
$90$	−17.2511	−1.81843
$91$	−1.51207	−0.158508
$92$	−1.00000	−0.104257
$93$	−20.0121	−2.07516
$94$	−6.67301	−0.688269
$95$	−14.2241	−1.45936
$96$	3.03806	0.310071
$97$	−9.63313	−0.978096	−0.489048	−	0.872257i	$-0.662656\pi$
$97$	−9.63313	−0.978096	−0.489048	+	0.872257i	$0.662656\pi$
$98$	6.65206	0.671959
$99$	−25.7310	−2.58607
$100$	2.66796	0.266796
$101$	10.8490	1.07952	0.539759	−	0.841820i	$-0.318516\pi$
$101$	10.8490	1.07952	0.539759	+	0.841820i	$0.318516\pi$
$102$	3.96126	0.392223
$103$	−3.18569	−0.313895	−0.156948	−	0.987607i	$-0.550165\pi$
$103$	−3.18569	−0.313895	−0.156948	+	0.987607i	$0.550165\pi$
$104$	−2.56341	−0.251363
$105$	4.96238	0.484278
$106$	13.8012	1.34050
$107$	−2.77969	−0.268723	−0.134361	−	0.990932i	$-0.542898\pi$
$107$	−2.77969	−0.268723	−0.134361	+	0.990932i	$0.542898\pi$
$108$	−9.81246	−0.944204
$109$	4.62957	0.443432	0.221716	−	0.975111i	$-0.428834\pi$
$109$	4.62957	0.443432	0.221716	+	0.975111i	$0.428834\pi$
$110$	11.4372	1.09050
$111$	−20.2605	−1.92304
$112$	−0.589865	−0.0557370
$113$	−10.6533	−1.00218	−0.501091	−	0.865395i	$-0.667068\pi$
$113$	−10.6533	−1.00218	−0.501091	+	0.865395i	$0.667068\pi$
$114$	−15.6056	−1.46160
$115$	−2.76911	−0.258221
$116$	3.77899	0.350870
$117$	15.9697	1.47639
$118$	6.57837	0.605588
$119$	−0.769111	−0.0705043
$120$	8.41273	0.767974
$121$	6.05929	0.550845
$122$	4.26115	0.385786
$123$	0.963416	0.0868683
$124$	6.58712	0.591540
$125$	−6.45766	−0.577591
$126$	3.67476	0.327374
$127$	20.6296	1.83058	0.915289	−	0.402797i	$-0.131962\pi$
$127$	20.6296	1.83058	0.915289	+	0.402797i	$0.131962\pi$
$128$	−1.00000	−0.0883883
$129$	13.0136	1.14578
$130$	−7.09837	−0.622568
$131$	−1.00000	−0.0873704
$131$	−1.00000	−0.0873704
$132$	12.5481	1.09217
$133$	3.02996	0.262731
$134$	6.71973	0.580496
$135$	−27.1718	−2.33857
$136$	−1.30388	−0.111806
$137$	19.6959	1.68273	0.841366	−	0.540466i	$-0.181752\pi$
$137$	19.6959	1.68273	0.841366	+	0.540466i	$0.181752\pi$
$138$	−3.03806	−0.258617
$139$	−19.7377	−1.67413	−0.837065	−	0.547104i	$-0.815730\pi$
$139$	−19.7377	−1.67413	−0.837065	+	0.547104i	$0.815730\pi$
$140$	−1.63340	−0.138048
$141$	−20.2730	−1.70730
$142$	−11.4583	−0.961557
$143$	−10.5876	−0.885383
$144$	6.22984	0.519153
$145$	10.4644	0.869024
$146$	−5.20789	−0.431008
$147$	20.2094	1.66684
$148$	6.66887	0.548178
$149$	−3.89948	−0.319458	−0.159729	−	0.987161i	$-0.551062\pi$
$149$	−3.89948	−0.319458	−0.159729	+	0.987161i	$0.551062\pi$
$150$	8.10545	0.661807
$151$	−1.69204	−0.137697	−0.0688483	−	0.997627i	$-0.521932\pi$
$151$	−1.69204	−0.137697	−0.0688483	+	0.997627i	$0.521932\pi$
$152$	5.13670	0.416642
$153$	8.12294	0.656700
$154$	−2.43631	−0.196324
$155$	18.2404	1.46511
$156$	−7.78782	−0.623524
$157$	−5.66849	−0.452394	−0.226197	−	0.974082i	$-0.572629\pi$
$157$	−5.66849	−0.452394	−0.226197	+	0.974082i	$0.572629\pi$
$158$	4.85884	0.386548
$159$	41.9291	3.32519
$160$	−2.76911	−0.218917
$161$	0.589865	0.0464879
$162$	−11.1214	−0.873777
$163$	16.3791	1.28291	0.641455	−	0.767161i	$-0.278331\pi$
$163$	16.3791	1.28291	0.641455	+	0.767161i	$0.278331\pi$
$164$	−0.317115	−0.0247625
$165$	34.7470	2.70505
$166$	−5.44110	−0.422311
$167$	−12.7211	−0.984387	−0.492194	−	0.870486i	$-0.663805\pi$
$167$	−12.7211	−0.984387	−0.492194	+	0.870486i	$0.663805\pi$
$168$	−1.79205	−0.138260
$169$	−6.42891	−0.494531
$170$	−3.61057	−0.276918
$171$	−32.0008	−2.44716
$172$	−4.28351	−0.326614
$173$	4.48202	0.340762	0.170381	−	0.985378i	$-0.445500\pi$
$173$	4.48202	0.340762	0.170381	+	0.985378i	$0.445500\pi$
$174$	11.4808	0.870358
$175$	−1.57374	−0.118963
$176$	−4.13029	−0.311332
$177$	19.9855	1.50220
$178$	4.24789	0.318393
$179$	8.90521	0.665607	0.332803	−	0.942996i	$-0.392005\pi$
$179$	8.90521	0.665607	0.332803	+	0.942996i	$0.392005\pi$
$180$	17.2511	1.28582
$181$	12.3782	0.920067	0.460033	−	0.887902i	$-0.347837\pi$
$181$	12.3782	0.920067	0.460033	+	0.887902i	$0.347837\pi$
$182$	1.51207	0.112082
$183$	12.9456	0.956969
$184$	1.00000	0.0737210
$185$	18.4668	1.35771
$186$	20.0121	1.46736
$187$	−5.38539	−0.393818
$188$	6.67301	0.486680
$189$	5.78802	0.421017
$190$	14.2241	1.03192
$191$	17.1516	1.24105	0.620524	−	0.784187i	$-0.286920\pi$
$191$	17.1516	1.24105	0.620524	+	0.784187i	$0.286920\pi$
$192$	−3.03806	−0.219253
$193$	−9.65340	−0.694867	−0.347433	−	0.937705i	$-0.612947\pi$
$193$	−9.65340	−0.694867	−0.347433	+	0.937705i	$0.612947\pi$
$194$	9.63313	0.691618
$195$	−21.5653	−1.54432
$196$	−6.65206	−0.475147
$197$	9.13171	0.650607	0.325304	−	0.945610i	$-0.394534\pi$
$197$	9.13171	0.650607	0.325304	+	0.945610i	$0.394534\pi$
$198$	25.7310	1.82862
$199$	−2.74921	−0.194886	−0.0974432	−	0.995241i	$-0.531066\pi$
$199$	−2.74921	−0.194886	−0.0974432	+	0.995241i	$0.531066\pi$
$200$	−2.66796	−0.188654
$201$	20.4150	1.43996
$202$	−10.8490	−0.763334
$203$	−2.22909	−0.156452
$204$	−3.96126	−0.277344
$205$	−0.878126	−0.0613310
$206$	3.18569	0.221957
$207$	−6.22984	−0.433004
$208$	2.56341	0.177741
$209$	21.2161	1.46755
$210$	−4.96238	−0.342437
$211$	−15.6704	−1.07880	−0.539399	−	0.842050i	$-0.681349\pi$
$211$	−15.6704	−1.07880	−0.539399	+	0.842050i	$0.681349\pi$
$212$	−13.8012	−0.947873
$213$	−34.8110	−2.38521
$214$	2.77969	0.190016
$215$	−11.8615	−0.808947
$216$	9.81246	0.667653
$217$	−3.88551	−0.263766
$218$	−4.62957	−0.313554
$219$	−15.8219	−1.06914
$220$	−11.4372	−0.771097
$221$	3.34237	0.224832
$222$	20.2605	1.35979
$223$	24.2771	1.62572	0.812859	−	0.582461i	$-0.197910\pi$
$223$	24.2771	1.62572	0.812859	+	0.582461i	$0.197910\pi$
$224$	0.589865	0.0394120
$225$	16.6210	1.10807
$226$	10.6533	0.708649
$227$	−16.8590	−1.11897	−0.559487	−	0.828839i	$-0.689002\pi$
$227$	−16.8590	−1.11897	−0.559487	+	0.828839i	$0.689002\pi$
$228$	15.6056	1.03351
$229$	10.8728	0.718497	0.359249	−	0.933242i	$-0.383033\pi$
$229$	10.8728	0.718497	0.359249	+	0.933242i	$0.383033\pi$
$230$	2.76911	0.182590
$231$	−7.40168	−0.486995
$232$	−3.77899	−0.248103
$233$	4.89569	0.320728	0.160364	−	0.987058i	$-0.448733\pi$
$233$	4.89569	0.320728	0.160364	+	0.987058i	$0.448733\pi$
$234$	−15.9697	−1.04397
$235$	18.4783	1.20539
$236$	−6.57837	−0.428216
$237$	14.7615	0.958860
$238$	0.769111	0.0498541
$239$	−18.8560	−1.21970	−0.609848	−	0.792518i	$-0.708770\pi$
$239$	−18.8560	−1.21970	−0.609848	+	0.792518i	$0.708770\pi$
$240$	−8.41273	−0.543040
$241$	−0.473098	−0.0304749	−0.0152375	−	0.999884i	$-0.504850\pi$
$241$	−0.473098	−0.0304749	−0.0152375	+	0.999884i	$0.504850\pi$
$242$	−6.05929	−0.389506
$243$	−4.35006	−0.279056
$244$	−4.26115	−0.272792
$245$	−18.4203	−1.17683
$246$	−0.963416	−0.0614252
$247$	−13.1675	−0.837828
$248$	−6.58712	−0.418282
$249$	−16.5304	−1.04757
$250$	6.45766	0.408418
$251$	−14.9105	−0.941140	−0.470570	−	0.882363i	$-0.655952\pi$
$251$	−14.9105	−0.941140	−0.470570	+	0.882363i	$0.655952\pi$
$252$	−3.67476	−0.231488
$253$	4.13029	0.259669
$254$	−20.6296	−1.29441
$255$	−10.9692	−0.686915
$256$	1.00000	0.0625000
$257$	7.23043	0.451022	0.225511	−	0.974241i	$-0.427595\pi$
$257$	7.23043	0.451022	0.225511	+	0.974241i	$0.427595\pi$
$258$	−13.0136	−0.810189
$259$	−3.93374	−0.244430
$260$	7.09837	0.440222
$261$	23.5425	1.45724
$262$	1.00000	0.0617802
$263$	18.2639	1.12620	0.563100	−	0.826389i	$-0.309609\pi$
$263$	18.2639	1.12620	0.563100	+	0.826389i	$0.309609\pi$
$264$	−12.5481	−0.772281
$265$	−38.2171	−2.34766
$266$	−3.02996	−0.185779
$267$	12.9054	0.789795
$268$	−6.71973	−0.410473
$269$	−28.2283	−1.72111	−0.860555	−	0.509357i	$-0.829883\pi$
$269$	−28.2283	−1.72111	−0.860555	+	0.509357i	$0.829883\pi$
$270$	27.1718	1.65362
$271$	−9.53661	−0.579308	−0.289654	−	0.957131i	$-0.593540\pi$
$271$	−9.53661	−0.579308	−0.289654	+	0.957131i	$0.593540\pi$
$272$	1.30388	0.0790591
$273$	4.59376	0.278027
$274$	−19.6959	−1.18987
$275$	−11.0195	−0.664499
$276$	3.03806	0.182870
$277$	−29.1023	−1.74859	−0.874294	−	0.485396i	$-0.838675\pi$
$277$	−29.1023	−1.74859	−0.874294	+	0.485396i	$0.838675\pi$
$278$	19.7377	1.18379
$279$	41.0367	2.45680
$280$	1.63340	0.0976143
$281$	0.807882	0.0481942	0.0240971	−	0.999710i	$-0.492329\pi$
$281$	0.807882	0.0481942	0.0240971	+	0.999710i	$0.492329\pi$
$282$	20.2730	1.20724
$283$	16.3162	0.969898	0.484949	−	0.874543i	$-0.338838\pi$
$283$	16.3162	0.969898	0.484949	+	0.874543i	$0.338838\pi$
$284$	11.4583	0.679924
$285$	43.2137	2.55976
$286$	10.5876	0.626060
$287$	0.187055	0.0110415
$288$	−6.22984	−0.367097
$289$	−15.2999	−0.899995
$290$	−10.4644	−0.614492
$291$	29.2661	1.71561
$292$	5.20789	0.304769
$293$	6.07234	0.354750	0.177375	−	0.984143i	$-0.443239\pi$
$293$	6.07234	0.354750	0.177375	+	0.984143i	$0.443239\pi$
$294$	−20.2094	−1.17864
$295$	−18.2162	−1.06059
$296$	−6.66887	−0.387620
$297$	40.5283	2.35169
$298$	3.89948	0.225891
$299$	−2.56341	−0.148246
$300$	−8.10545	−0.467968
$301$	2.52669	0.145636
$302$	1.69204	0.0973661
$303$	−32.9600	−1.89350
$304$	−5.13670	−0.294610
$305$	−11.7996	−0.675642
$306$	−8.12294	−0.464357
$307$	8.54528	0.487705	0.243852	−	0.969812i	$-0.421589\pi$
$307$	8.54528	0.487705	0.243852	+	0.969812i	$0.421589\pi$
$308$	2.43631	0.138822
$309$	9.67833	0.550581
$310$	−18.2404	−1.03599
$311$	1.55722	0.0883020	0.0441510	−	0.999025i	$-0.485942\pi$
$311$	1.55722	0.0883020	0.0441510	+	0.999025i	$0.485942\pi$
$312$	7.78782	0.440898
$313$	1.63197	0.0922446	0.0461223	−	0.998936i	$-0.485314\pi$
$313$	1.63197	0.0922446	0.0461223	+	0.998936i	$0.485314\pi$
$314$	5.66849	0.319891
$315$	−10.1758	−0.573342
$316$	−4.85884	−0.273331
$317$	17.3202	0.972800	0.486400	−	0.873736i	$-0.338310\pi$
$317$	17.3202	0.972800	0.486400	+	0.873736i	$0.338310\pi$
$318$	−41.9291	−2.35127
$319$	−15.6083	−0.873898
$320$	2.76911	0.154798
$321$	8.44488	0.471348
$322$	−0.589865	−0.0328719
$323$	−6.69762	−0.372666
$324$	11.1214	0.617854
$325$	6.83910	0.379365
$326$	−16.3791	−0.907154
$327$	−14.0649	−0.777792
$328$	0.317115	0.0175097
$329$	−3.93618	−0.217008
$330$	−34.7470	−1.91276
$331$	−2.99303	−0.164512	−0.0822559	−	0.996611i	$-0.526212\pi$
$331$	−2.99303	−0.164512	−0.0822559	+	0.996611i	$0.526212\pi$
$332$	5.44110	0.298619
$333$	41.5460	2.27671
$334$	12.7211	0.696067
$335$	−18.6077	−1.01665
$336$	1.79205	0.0977642
$337$	10.7880	0.587660	0.293830	−	0.955858i	$-0.405070\pi$
$337$	10.7880	0.587660	0.293830	+	0.955858i	$0.405070\pi$
$338$	6.42891	0.349687
$339$	32.3655	1.75785
$340$	3.61057	0.195811
$341$	−27.2067	−1.47333
$342$	32.0008	1.73041
$343$	8.05287	0.434814
$344$	4.28351	0.230951
$345$	8.41273	0.452926
$346$	−4.48202	−0.240955
$347$	8.97975	0.482058	0.241029	−	0.970518i	$-0.422515\pi$
$347$	8.97975	0.482058	0.241029	+	0.970518i	$0.422515\pi$
$348$	−11.4808	−0.615436
$349$	−28.1230	−1.50539	−0.752696	−	0.658368i	$-0.771247\pi$
$349$	−28.1230	−1.50539	−0.752696	+	0.658368i	$0.771247\pi$
$350$	1.57374	0.0841199
$351$	−25.1534	−1.34259
$352$	4.13029	0.220145
$353$	−0.475681	−0.0253179	−0.0126590	−	0.999920i	$-0.504030\pi$
$353$	−0.475681	−0.0253179	−0.0126590	+	0.999920i	$0.504030\pi$
$354$	−19.9855	−1.06222
$355$	31.7292	1.68401
$356$	−4.24789	−0.225138
$357$	2.33661	0.123666
$358$	−8.90521	−0.470655
$359$	6.69582	0.353392	0.176696	−	0.984265i	$-0.443459\pi$
$359$	6.69582	0.353392	0.176696	+	0.984265i	$0.443459\pi$
$360$	−17.2511	−0.909213
$361$	7.38572	0.388722
$362$	−12.3782	−0.650585
$363$	−18.4085	−0.966197
$364$	−1.51207	−0.0792539
$365$	14.4212	0.754840
$366$	−12.9456	−0.676679
$367$	−35.7248	−1.86482	−0.932410	−	0.361402i	$-0.882298\pi$
$367$	−35.7248	−1.86482	−0.932410	+	0.361402i	$0.882298\pi$
$368$	−1.00000	−0.0521286
$369$	−1.97557	−0.102844
$370$	−18.4668	−0.960045
$371$	8.14087	0.422653
$372$	−20.0121	−1.03758
$373$	−14.9145	−0.772243	−0.386121	−	0.922448i	$-0.626185\pi$
$373$	−14.9145	−0.772243	−0.386121	+	0.922448i	$0.626185\pi$
$374$	5.38539	0.278472
$375$	19.6188	1.01311
$376$	−6.67301	−0.344134
$377$	9.68711	0.498912
$378$	−5.78802	−0.297704
$379$	−30.8996	−1.58720	−0.793602	−	0.608437i	$-0.791797\pi$
$379$	−30.8996	−1.58720	−0.793602	+	0.608437i	$0.791797\pi$
$380$	−14.2241	−0.729680
$381$	−62.6740	−3.21088
$382$	−17.1516	−0.877554
$383$	−24.6470	−1.25940	−0.629701	−	0.776837i	$-0.716823\pi$
$383$	−24.6470	−1.25940	−0.629701	+	0.776837i	$0.716823\pi$
$384$	3.03806	0.155036
$385$	6.74642	0.343829
$386$	9.65340	0.491345
$387$	−26.6855	−1.35650
$388$	−9.63313	−0.489048
$389$	−16.0040	−0.811433	−0.405717	−	0.913999i	$-0.632978\pi$
$389$	−16.0040	−0.811433	−0.405717	+	0.913999i	$0.632978\pi$
$390$	21.5653	1.09200
$391$	−1.30388	−0.0659398
$392$	6.65206	0.335980
$393$	3.03806	0.153250
$394$	−9.13171	−0.460049
$395$	−13.4547	−0.676977
$396$	−25.7310	−1.29303
$397$	−10.6544	−0.534727	−0.267363	−	0.963596i	$-0.586152\pi$
$397$	−10.6544	−0.534727	−0.267363	+	0.963596i	$0.586152\pi$
$398$	2.74921	0.137805
$399$	−9.20522	−0.460837
$400$	2.66796	0.133398
$401$	−29.6320	−1.47975	−0.739876	−	0.672743i	$-0.765116\pi$
$401$	−29.6320	−1.47975	−0.739876	+	0.672743i	$0.765116\pi$
$402$	−20.4150	−1.01821
$403$	16.8855	0.841127
$404$	10.8490	0.539759
$405$	30.7963	1.53028
$406$	2.22909	0.110628
$407$	−27.5444	−1.36532
$408$	3.96126	0.196112
$409$	19.2010	0.949430	0.474715	−	0.880140i	$-0.342551\pi$
$409$	19.2010	0.949430	0.474715	+	0.880140i	$0.342551\pi$
$410$	0.878126	0.0433675
$411$	−59.8373	−2.95156
$412$	−3.18569	−0.156948
$413$	3.88035	0.190940
$414$	6.22984	0.306180
$415$	15.0670	0.739609
$416$	−2.56341	−0.125682
$417$	59.9644	2.93647
$418$	−21.2161	−1.03771
$419$	−2.67260	−0.130565	−0.0652826	−	0.997867i	$-0.520795\pi$
$419$	−2.67260	−0.130565	−0.0652826	+	0.997867i	$0.520795\pi$
$420$	4.96238	0.242139
$421$	−12.3364	−0.601239	−0.300619	−	0.953744i	$-0.597193\pi$
$421$	−12.3364	−0.601239	−0.300619	+	0.953744i	$0.597193\pi$
$422$	15.6704	0.762826
$423$	41.5718	2.02129
$424$	13.8012	0.670248
$425$	3.47869	0.168741
$426$	34.8110	1.68660
$427$	2.51350	0.121637
$428$	−2.77969	−0.134361
$429$	32.1659	1.55299
$430$	11.8615	0.572012
$431$	−13.4337	−0.647081	−0.323540	−	0.946214i	$-0.604873\pi$
$431$	−13.4337	−0.647081	−0.323540	+	0.946214i	$0.604873\pi$
$432$	−9.81246	−0.472102
$433$	−11.5891	−0.556938	−0.278469	−	0.960445i	$-0.589827\pi$
$433$	−11.5891	−0.556938	−0.278469	+	0.960445i	$0.589827\pi$
$434$	3.88551	0.186510
$435$	−31.7916	−1.52429
$436$	4.62957	0.221716
$437$	5.13670	0.245722
$438$	15.8219	0.756000
$439$	31.6119	1.50875	0.754376	−	0.656442i	$-0.227939\pi$
$439$	31.6119	1.50875	0.754376	+	0.656442i	$0.227939\pi$
$440$	11.4372	0.545248
$441$	−41.4412	−1.97339
$442$	−3.34237	−0.158981
$443$	0.241028	0.0114516	0.00572578	−	0.999984i	$-0.498177\pi$
$443$	0.241028	0.0114516	0.00572578	+	0.999984i	$0.498177\pi$
$444$	−20.2605	−0.961519
$445$	−11.7629	−0.557613
$446$	−24.2771	−1.14956
$447$	11.8469	0.560338
$448$	−0.589865	−0.0278685
$449$	−7.92471	−0.373990	−0.186995	−	0.982361i	$-0.559875\pi$
$449$	−7.92471	−0.373990	−0.186995	+	0.982361i	$0.559875\pi$
$450$	−16.6210	−0.783521
$451$	1.30978	0.0616750
$452$	−10.6533	−0.501091
$453$	5.14054	0.241523
$454$	16.8590	0.791234
$455$	−4.18708	−0.196293
$456$	−15.6056	−0.730801
$457$	−13.5867	−0.635561	−0.317780	−	0.948164i	$-0.602937\pi$
$457$	−13.5867	−0.635561	−0.317780	+	0.948164i	$0.602937\pi$
$458$	−10.8728	−0.508054
$459$	−12.7942	−0.597183
$460$	−2.76911	−0.129110
$461$	−19.8797	−0.925888	−0.462944	−	0.886388i	$-0.653207\pi$
$461$	−19.8797	−0.925888	−0.462944	+	0.886388i	$0.653207\pi$
$462$	7.40168	0.344357
$463$	29.5355	1.37263	0.686315	−	0.727304i	$-0.259227\pi$
$463$	29.5355	1.37263	0.686315	+	0.727304i	$0.259227\pi$
$464$	3.77899	0.175435
$465$	−55.4156	−2.56984
$466$	−4.89569	−0.226789
$467$	7.06845	0.327089	0.163544	−	0.986536i	$-0.447707\pi$
$467$	7.06845	0.327089	0.163544	+	0.986536i	$0.447707\pi$
$468$	15.9697	0.738197
$469$	3.96373	0.183028
$470$	−18.4783	−0.852340
$471$	17.2212	0.793512
$472$	6.57837	0.302794
$473$	17.6921	0.813485
$474$	−14.7615	−0.678017
$475$	−13.7045	−0.628807
$476$	−0.769111	−0.0352521
$477$	−85.9795	−3.93673
$478$	18.8560	0.862456
$479$	−29.8821	−1.36535	−0.682674	−	0.730723i	$-0.739183\pi$
$479$	−29.8821	−1.36535	−0.682674	+	0.730723i	$0.739183\pi$
$480$	8.41273	0.383987
$481$	17.0951	0.779469
$482$	0.473098	0.0215490
$483$	−1.79205	−0.0815410
$484$	6.05929	0.275422
$485$	−26.6752	−1.21126
$486$	4.35006	0.197323
$487$	−28.4167	−1.28768	−0.643841	−	0.765159i	$-0.722660\pi$
$487$	−28.4167	−1.28768	−0.643841	+	0.765159i	$0.722660\pi$
$488$	4.26115	0.192893
$489$	−49.7608	−2.25026
$490$	18.4203	0.832143
$491$	13.0876	0.590633	0.295317	−	0.955399i	$-0.404575\pi$
$491$	13.0876	0.590633	0.295317	+	0.955399i	$0.404575\pi$
$492$	0.963416	0.0434341
$493$	4.92733	0.221916
$494$	13.1675	0.592434
$495$	−71.2520	−3.20254
$496$	6.58712	0.295770
$497$	−6.75884	−0.303175
$498$	16.5304	0.740745
$499$	30.4548	1.36334	0.681671	−	0.731659i	$-0.261253\pi$
$499$	30.4548	1.36334	0.681671	+	0.731659i	$0.261253\pi$
$500$	−6.45766	−0.288795
$501$	38.6475	1.72664
$502$	14.9105	0.665486
$503$	−0.0897794	−0.00400306	−0.00200153	−	0.999998i	$-0.500637\pi$
$503$	−0.0897794	−0.00400306	−0.00200153	+	0.999998i	$0.500637\pi$
$504$	3.67476	0.163687
$505$	30.0421	1.33686
$506$	−4.13029	−0.183614
$507$	19.5314	0.867422
$508$	20.6296	0.915289
$509$	−16.0198	−0.710066	−0.355033	−	0.934854i	$-0.615530\pi$
$509$	−16.0198	−0.710066	−0.355033	+	0.934854i	$0.615530\pi$
$510$	10.9692	0.485723
$511$	−3.07195	−0.135895
$512$	−1.00000	−0.0441942
$513$	50.4037	2.22538
$514$	−7.23043	−0.318921
$515$	−8.82152	−0.388723
$516$	13.0136	0.572890
$517$	−27.5615	−1.21215
$518$	3.93374	0.172838
$519$	−13.6167	−0.597705
$520$	−7.09837	−0.311284
$521$	−13.5039	−0.591618	−0.295809	−	0.955247i	$-0.595589\pi$
$521$	−13.5039	−0.591618	−0.295809	+	0.955247i	$0.595589\pi$
$522$	−23.5425	−1.03043
$523$	−29.9911	−1.31142	−0.655711	−	0.755012i	$-0.727631\pi$
$523$	−29.9911	−1.31142	−0.655711	+	0.755012i	$0.727631\pi$
$524$	−1.00000	−0.0436852
$525$	4.78112	0.208665
$526$	−18.2639	−0.796344
$527$	8.58878	0.374133
$528$	12.5481	0.546085
$529$	1.00000	0.0434783
$530$	38.2171	1.66005
$531$	−40.9822	−1.77848
$532$	3.02996	0.131365
$533$	−0.812897	−0.0352105
$534$	−12.9054	−0.558469
$535$	−7.69727	−0.332782
$536$	6.71973	0.290248
$537$	−27.0546	−1.16749
$538$	28.2283	1.21701
$539$	27.4749	1.18343
$540$	−27.1718	−1.16929
$541$	−33.2494	−1.42950	−0.714752	−	0.699378i	$-0.753461\pi$
$541$	−33.2494	−1.42950	−0.714752	+	0.699378i	$0.753461\pi$
$542$	9.53661	0.409632
$543$	−37.6059	−1.61382
$544$	−1.30388	−0.0559032
$545$	12.8198	0.549139
$546$	−4.59376	−0.196595
$547$	−1.39779	−0.0597653	−0.0298826	−	0.999553i	$-0.509513\pi$
$547$	−1.39779	−0.0597653	−0.0298826	+	0.999553i	$0.509513\pi$
$548$	19.6959	0.841366
$549$	−26.5463	−1.13297
$550$	11.0195	0.469871
$551$	−19.4115	−0.826959
$552$	−3.03806	−0.129309
$553$	2.86606	0.121877
$554$	29.1023	1.23644
$555$	−56.1034	−2.38146
$556$	−19.7377	−0.837065
$557$	6.23559	0.264210	0.132105	−	0.991236i	$-0.457826\pi$
$557$	6.23559	0.264210	0.132105	+	0.991236i	$0.457826\pi$
$558$	−41.0367	−1.73722
$559$	−10.9804	−0.464421
$560$	−1.63340	−0.0690238
$561$	16.3611	0.690768
$562$	−0.807882	−0.0340784
$563$	6.19742	0.261190	0.130595	−	0.991436i	$-0.458311\pi$
$563$	6.19742	0.261190	0.130595	+	0.991436i	$0.458311\pi$
$564$	−20.2730	−0.853649
$565$	−29.5003	−1.24108
$566$	−16.3162	−0.685821
$567$	−6.56010	−0.275498
$568$	−11.4583	−0.480779
$569$	−36.3951	−1.52576	−0.762882	−	0.646538i	$-0.776216\pi$
$569$	−36.3951	−1.52576	−0.762882	+	0.646538i	$0.776216\pi$
$570$	−43.2137	−1.81002
$571$	−30.6498	−1.28265	−0.641326	−	0.767268i	$-0.721616\pi$
$571$	−30.6498	−1.28265	−0.641326	+	0.767268i	$0.721616\pi$
$572$	−10.5876	−0.442692
$573$	−52.1078	−2.17683
$574$	−0.187055	−0.00780753
$575$	−2.66796	−0.111262
$576$	6.22984	0.259577
$577$	10.7902	0.449201	0.224600	−	0.974451i	$-0.427892\pi$
$577$	10.7902	0.449201	0.224600	+	0.974451i	$0.427892\pi$
$578$	15.2999	0.636392
$579$	29.3277	1.21882
$580$	10.4644	0.434512
$581$	−3.20951	−0.133153
$582$	−29.2661	−1.21312
$583$	57.0031	2.36083
$584$	−5.20789	−0.215504
$585$	44.2217	1.82834
$586$	−6.07234	−0.250846
$587$	−12.9731	−0.535456	−0.267728	−	0.963495i	$-0.586273\pi$
$587$	−12.9731	−0.535456	−0.267728	+	0.963495i	$0.586273\pi$
$588$	20.2094	0.833421
$589$	−33.8361	−1.39419
$590$	18.2162	0.749950
$591$	−27.7427	−1.14118
$592$	6.66887	0.274089
$593$	32.6182	1.33947	0.669735	−	0.742600i	$-0.266408\pi$
$593$	32.6182	1.33947	0.669735	+	0.742600i	$0.266408\pi$
$594$	−40.5283	−1.66290
$595$	−2.12975	−0.0873113
$596$	−3.89948	−0.159729
$597$	8.35228	0.341836
$598$	2.56341	0.104826
$599$	38.8390	1.58692	0.793459	−	0.608624i	$-0.208278\pi$
$599$	38.8390	1.58692	0.793459	+	0.608624i	$0.208278\pi$
$600$	8.10545	0.330903
$601$	−20.7255	−0.845411	−0.422705	−	0.906267i	$-0.638920\pi$
$601$	−20.7255	−0.845411	−0.422705	+	0.906267i	$0.638920\pi$
$602$	−2.52669	−0.102980
$603$	−41.8628	−1.70479
$604$	−1.69204	−0.0688483
$605$	16.7788	0.682157
$606$	32.9600	1.33891
$607$	9.22426	0.374401	0.187201	−	0.982322i	$-0.440059\pi$
$607$	9.22426	0.374401	0.187201	+	0.982322i	$0.440059\pi$
$608$	5.13670	0.208321
$609$	6.77213	0.274420
$610$	11.7996	0.477751
$611$	17.1057	0.692022
$612$	8.12294	0.328350
$613$	−17.7051	−0.715101	−0.357550	−	0.933894i	$-0.616388\pi$
$613$	−17.7051	−0.715101	−0.357550	+	0.933894i	$0.616388\pi$
$614$	−8.54528	−0.344859
$615$	2.66780	0.107576
$616$	−2.43631	−0.0981619
$617$	−16.3562	−0.658477	−0.329238	−	0.944247i	$-0.606792\pi$
$617$	−16.3562	−0.658477	−0.329238	+	0.944247i	$0.606792\pi$
$618$	−9.67833	−0.389320
$619$	−21.1415	−0.849749	−0.424875	−	0.905252i	$-0.639682\pi$
$619$	−21.1415	−0.849749	−0.424875	+	0.905252i	$0.639682\pi$
$620$	18.2404	0.732554
$621$	9.81246	0.393760
$622$	−1.55722	−0.0624390
$623$	2.50568	0.100388
$624$	−7.78782	−0.311762
$625$	−31.2218	−1.24887
$626$	−1.63197	−0.0652268
$627$	−64.4558	−2.57412
$628$	−5.66849	−0.226197
$629$	8.69538	0.346708
$630$	10.1758	0.405414
$631$	26.8050	1.06709	0.533546	−	0.845771i	$-0.320859\pi$
$631$	26.8050	1.06709	0.533546	+	0.845771i	$0.320859\pi$
$632$	4.85884	0.193274
$633$	47.6078	1.89224
$634$	−17.3202	−0.687873
$635$	57.1255	2.26696
$636$	41.9291	1.66260
$637$	−17.0520	−0.675624
$638$	15.6083	0.617939
$639$	71.3832	2.82388
$640$	−2.76911	−0.109459
$641$	−19.8044	−0.782227	−0.391114	−	0.920342i	$-0.627910\pi$
$641$	−19.8044	−0.782227	−0.391114	+	0.920342i	$0.627910\pi$
$642$	−8.44488	−0.333293
$643$	−4.95085	−0.195242	−0.0976211	−	0.995224i	$-0.531123\pi$
$643$	−4.95085	−0.195242	−0.0976211	+	0.995224i	$0.531123\pi$
$644$	0.589865	0.0232439
$645$	36.0360	1.41892
$646$	6.69762	0.263514
$647$	−48.6906	−1.91423	−0.957113	−	0.289713i	$-0.906440\pi$
$647$	−48.6906	−1.91423	−0.957113	+	0.289713i	$0.906440\pi$
$648$	−11.1214	−0.436888
$649$	27.1706	1.06654
$650$	−6.83910	−0.268251
$651$	11.8044	0.462652
$652$	16.3791	0.641455
$653$	36.4873	1.42786	0.713929	−	0.700218i	$-0.246914\pi$
$653$	36.4873	1.42786	0.713929	+	0.700218i	$0.246914\pi$
$654$	14.0649	0.549982
$655$	−2.76911	−0.108198
$656$	−0.317115	−0.0123813
$657$	32.4443	1.26577
$658$	3.93618	0.153448
$659$	−13.2663	−0.516782	−0.258391	−	0.966040i	$-0.583192\pi$
$659$	−13.2663	−0.516782	−0.258391	+	0.966040i	$0.583192\pi$
$660$	34.7470	1.35253
$661$	34.1640	1.32882	0.664412	−	0.747367i	$-0.268682\pi$
$661$	34.1640	1.32882	0.664412	+	0.747367i	$0.268682\pi$
$662$	2.99303	0.116327
$663$	−10.1543	−0.394362
$664$	−5.44110	−0.211156
$665$	8.39029	0.325362
$666$	−41.5460	−1.60987
$667$	−3.77899	−0.146323
$668$	−12.7211	−0.492194
$669$	−73.7555	−2.85155
$670$	18.6077	0.718877
$671$	17.5998	0.679432
$672$	−1.79205	−0.0691298
$673$	−35.0194	−1.34990	−0.674950	−	0.737863i	$-0.735835\pi$
$673$	−35.0194	−1.34990	−0.674950	+	0.737863i	$0.735835\pi$
$674$	−10.7880	−0.415538
$675$	−26.1793	−1.00764
$676$	−6.42891	−0.247266
$677$	41.6392	1.60033	0.800163	−	0.599783i	$-0.204746\pi$
$677$	41.6392	1.60033	0.800163	+	0.599783i	$0.204746\pi$
$678$	−32.3655	−1.24299
$679$	5.68224	0.218065
$680$	−3.61057	−0.138459
$681$	51.2189	1.96271
$682$	27.2067	1.04180
$683$	43.2998	1.65682	0.828411	−	0.560121i	$-0.189245\pi$
$683$	43.2998	1.65682	0.828411	+	0.560121i	$0.189245\pi$
$684$	−32.0008	−1.22358
$685$	54.5400	2.08387
$686$	−8.05287	−0.307460
$687$	−33.0324	−1.26026
$688$	−4.28351	−0.163307
$689$	−35.3783	−1.34781
$690$	−8.41273	−0.320267
$691$	−12.5483	−0.477361	−0.238680	−	0.971098i	$-0.576715\pi$
$691$	−12.5483	−0.477361	−0.238680	+	0.971098i	$0.576715\pi$
$692$	4.48202	0.170381
$693$	15.1778	0.576558
$694$	−8.97975	−0.340867
$695$	−54.6558	−2.07321
$696$	11.4808	0.435179
$697$	−0.413479	−0.0156616
$698$	28.1230	1.06447
$699$	−14.8734	−0.562565
$700$	−1.57374	−0.0594817
$701$	−8.19024	−0.309341	−0.154671	−	0.987966i	$-0.549432\pi$
$701$	−8.19024	−0.309341	−0.154671	+	0.987966i	$0.549432\pi$
$702$	25.1534	0.949353
$703$	−34.2560	−1.29199
$704$	−4.13029	−0.155666
$705$	−56.1383	−2.11429
$706$	0.475681	0.0179025
$707$	−6.39945	−0.240676
$708$	19.9855	0.751102
$709$	−4.00330	−0.150347	−0.0751736	−	0.997170i	$-0.523951\pi$
$709$	−4.00330	−0.150347	−0.0751736	+	0.997170i	$0.523951\pi$
$710$	−31.7292	−1.19078
$711$	−30.2698	−1.13521
$712$	4.24789	0.159196
$713$	−6.58712	−0.246689
$714$	−2.33661	−0.0874454
$715$	−29.3183	−1.09644
$716$	8.90521	0.332803
$717$	57.2859	2.13938
$718$	−6.69582	−0.249886
$719$	−27.0042	−1.00709	−0.503543	−	0.863970i	$-0.667970\pi$
$719$	−27.0042	−1.00709	−0.503543	+	0.863970i	$0.667970\pi$
$720$	17.2511	0.642910
$721$	1.87913	0.0699823
$722$	−7.38572	−0.274868
$723$	1.43730	0.0534538
$724$	12.3782	0.460033
$725$	10.0822	0.374444
$726$	18.4085	0.683204
$727$	−47.6680	−1.76791	−0.883955	−	0.467572i	$-0.845129\pi$
$727$	−47.6680	−1.76791	−0.883955	+	0.467572i	$0.845129\pi$
$728$	1.51207	0.0560410
$729$	−20.1483	−0.746235
$730$	−14.4212	−0.533753
$731$	−5.58516	−0.206575
$732$	12.9456	0.478485
$733$	24.9077	0.919988	0.459994	−	0.887922i	$-0.347852\pi$
$733$	24.9077	0.919988	0.459994	+	0.887922i	$0.347852\pi$
$734$	35.7248	1.31863
$735$	55.9620	2.06419
$736$	1.00000	0.0368605
$737$	27.7544	1.02235
$738$	1.97557	0.0727219
$739$	−41.7076	−1.53424	−0.767120	−	0.641503i	$-0.778311\pi$
$739$	−41.7076	−1.53424	−0.767120	+	0.641503i	$0.778311\pi$
$740$	18.4668	0.678854
$741$	40.0037	1.46957
$742$	−8.14087	−0.298861
$743$	15.4330	0.566184	0.283092	−	0.959093i	$-0.408640\pi$
$743$	15.4330	0.566184	0.283092	+	0.959093i	$0.408640\pi$
$744$	20.0121	0.733679
$745$	−10.7981	−0.395611
$746$	14.9145	0.546058
$747$	33.8972	1.24023
$748$	−5.38539	−0.196909
$749$	1.63964	0.0599113
$750$	−19.6188	−0.716377
$751$	14.5140	0.529624	0.264812	−	0.964300i	$-0.414690\pi$
$751$	14.5140	0.529624	0.264812	+	0.964300i	$0.414690\pi$
$752$	6.67301	0.243340
$753$	45.2989	1.65079
$754$	−9.68711	−0.352784
$755$	−4.68545	−0.170521
$756$	5.78802	0.210508
$757$	−42.5985	−1.54827	−0.774135	−	0.633021i	$-0.781815\pi$
$757$	−42.5985	−1.54827	−0.774135	+	0.633021i	$0.781815\pi$
$758$	30.8996	1.12232
$759$	−12.5481	−0.455467
$760$	14.2241	0.515962
$761$	−29.8419	−1.08177	−0.540884	−	0.841097i	$-0.681910\pi$
$761$	−29.8419	−1.08177	−0.540884	+	0.841097i	$0.681910\pi$
$762$	62.6740	2.27044
$763$	−2.73082	−0.0988624
$764$	17.1516	0.620524
$765$	22.4933	0.813247
$766$	24.6470	0.890532
$767$	−16.8631	−0.608891
$768$	−3.03806	−0.109627
$769$	−24.5136	−0.883983	−0.441991	−	0.897019i	$-0.645728\pi$
$769$	−24.5136	−0.883983	−0.441991	+	0.897019i	$0.645728\pi$
$770$	−6.74642	−0.243124
$771$	−21.9665	−0.791105
$772$	−9.65340	−0.347433
$773$	0.495664	0.0178278	0.00891390	−	0.999960i	$-0.497163\pi$
$773$	0.495664	0.0178278	0.00891390	+	0.999960i	$0.497163\pi$
$774$	26.6855	0.959192
$775$	17.5742	0.631283
$776$	9.63313	0.345809
$777$	11.9509	0.428738
$778$	16.0040	0.573770
$779$	1.62893	0.0583623
$780$	−21.5653	−0.772162
$781$	−47.3260	−1.69346
$782$	1.30388	0.0466265
$783$	−37.0812	−1.32517
$784$	−6.65206	−0.237574
$785$	−15.6967	−0.560238
$786$	−3.03806	−0.108364
$787$	−8.46695	−0.301814	−0.150907	−	0.988548i	$-0.548219\pi$
$787$	−8.46695	−0.301814	−0.150907	+	0.988548i	$0.548219\pi$
$788$	9.13171	0.325304
$789$	−55.4869	−1.97539
$790$	13.4547	0.478695
$791$	6.28403	0.223434
$792$	25.7310	0.914312
$793$	−10.9231	−0.387890
$794$	10.6544	0.378109
$795$	116.106	4.11786
$796$	−2.74921	−0.0974432
$797$	−51.4113	−1.82108	−0.910540	−	0.413420i	$-0.864334\pi$
$797$	−51.4113	−1.82108	−0.910540	+	0.413420i	$0.864334\pi$
$798$	9.20522	0.325861
$799$	8.70078	0.307812
$800$	−2.66796	−0.0943268
$801$	−26.4637	−0.935047
$802$	29.6320	1.04634
$803$	−21.5101	−0.759074
$804$	20.4150	0.719981
$805$	1.63340	0.0575698
$806$	−16.8855	−0.594767
$807$	85.7594	3.01887
$808$	−10.8490	−0.381667
$809$	−2.24294	−0.0788574	−0.0394287	−	0.999222i	$-0.512554\pi$
$809$	−2.24294	−0.0788574	−0.0394287	+	0.999222i	$0.512554\pi$
$810$	−30.7963	−1.08207
$811$	−23.1867	−0.814194	−0.407097	−	0.913385i	$-0.633459\pi$
$811$	−23.1867	−0.814194	−0.407097	+	0.913385i	$0.633459\pi$
$812$	−2.22909	−0.0782258
$813$	28.9728	1.01612
$814$	27.5444	0.965430
$815$	45.3555	1.58873
$816$	−3.96126	−0.138672
$817$	22.0031	0.769791
$818$	−19.2010	−0.671348
$819$	−9.41994	−0.329159
$820$	−0.878126	−0.0306655
$821$	7.94110	0.277146	0.138573	−	0.990352i	$-0.455748\pi$
$821$	7.94110	0.277146	0.138573	+	0.990352i	$0.455748\pi$
$822$	59.8373	2.08707
$823$	−37.1219	−1.29399	−0.646993	−	0.762496i	$-0.723974\pi$
$823$	−37.1219	−1.29399	−0.646993	+	0.762496i	$0.723974\pi$
$824$	3.18569	0.110979
$825$	33.4778	1.16555
$826$	−3.88035	−0.135015
$827$	−17.6195	−0.612689	−0.306345	−	0.951921i	$-0.599106\pi$
$827$	−17.6195	−0.612689	−0.306345	+	0.951921i	$0.599106\pi$
$828$	−6.22984	−0.216502
$829$	14.1377	0.491021	0.245511	−	0.969394i	$-0.421044\pi$
$829$	14.1377	0.491021	0.245511	+	0.969394i	$0.421044\pi$
$830$	−15.0670	−0.522983
$831$	88.4147	3.06707
$832$	2.56341	0.0888704
$833$	−8.67346	−0.300518
$834$	−59.9644	−2.07640
$835$	−35.2261	−1.21905
$836$	21.2161	0.733773
$837$	−64.6358	−2.23414
$838$	2.67260	0.0923236
$839$	−56.8226	−1.96173	−0.980867	−	0.194680i	$-0.937633\pi$
$839$	−56.8226	−1.96173	−0.980867	+	0.194680i	$0.937633\pi$
$840$	−4.96238	−0.171218
$841$	−14.7193	−0.507560
$842$	12.3364	0.425140
$843$	−2.45440	−0.0845339
$844$	−15.6704	−0.539399
$845$	−17.8023	−0.612419
$846$	−41.5718	−1.42927
$847$	−3.57416	−0.122810
$848$	−13.8012	−0.473937
$849$	−49.5697	−1.70123
$850$	−3.47869	−0.119318
$851$	−6.66887	−0.228606
$852$	−34.8110	−1.19260
$853$	24.3191	0.832669	0.416334	−	0.909212i	$-0.363315\pi$
$853$	24.3191	0.832669	0.416334	+	0.909212i	$0.363315\pi$
$854$	−2.51350	−0.0860103
$855$	−88.6138	−3.03053
$856$	2.77969	0.0950079
$857$	41.4078	1.41446	0.707231	−	0.706982i	$-0.249944\pi$
$857$	41.4078	1.41446	0.707231	+	0.706982i	$0.249944\pi$
$858$	−32.1659	−1.09813
$859$	−4.90502	−0.167357	−0.0836786	−	0.996493i	$-0.526667\pi$
$859$	−4.90502	−0.167357	−0.0836786	+	0.996493i	$0.526667\pi$
$860$	−11.8615	−0.404474
$861$	−0.568285	−0.0193671
$862$	13.4337	0.457555
$863$	11.6332	0.395999	0.197999	−	0.980202i	$-0.436556\pi$
$863$	11.6332	0.395999	0.197999	+	0.980202i	$0.436556\pi$
$864$	9.81246	0.333827
$865$	12.4112	0.421994
$866$	11.5891	0.393815
$867$	46.4821	1.57862
$868$	−3.88551	−0.131883
$869$	20.0684	0.680774
$870$	31.7916	1.07784
$871$	−17.2255	−0.583662
$872$	−4.62957	−0.156777
$873$	−60.0128	−2.03113
$874$	−5.13670	−0.173752
$875$	3.80915	0.128773
$876$	−15.8219	−0.534572
$877$	−28.2073	−0.952492	−0.476246	−	0.879312i	$-0.658003\pi$
$877$	−28.2073	−0.952492	−0.476246	+	0.879312i	$0.658003\pi$
$878$	−31.6119	−1.06685
$879$	−18.4482	−0.622241
$880$	−11.4372	−0.385549
$881$	20.1941	0.680358	0.340179	−	0.940361i	$-0.389512\pi$
$881$	20.1941	0.680358	0.340179	+	0.940361i	$0.389512\pi$
$882$	41.4412	1.39540
$883$	5.53717	0.186341	0.0931703	−	0.995650i	$-0.470300\pi$
$883$	5.53717	0.186341	0.0931703	+	0.995650i	$0.470300\pi$
$884$	3.34237	0.112416
$885$	55.3421	1.86030
$886$	−0.241028	−0.00809748
$887$	27.1557	0.911799	0.455900	−	0.890031i	$-0.349318\pi$
$887$	27.1557	0.911799	0.455900	+	0.890031i	$0.349318\pi$
$888$	20.2605	0.679897
$889$	−12.1687	−0.408124
$890$	11.7629	0.394292
$891$	−45.9345	−1.53886
$892$	24.2771	0.812859
$893$	−34.2773	−1.14705
$894$	−11.8469	−0.396219
$895$	24.6595	0.824276
$896$	0.589865	0.0197060
$897$	7.78782	0.260028
$898$	7.92471	0.264451
$899$	24.8926	0.830216
$900$	16.6210	0.554033
$901$	−17.9951	−0.599504
$902$	−1.30978	−0.0436108
$903$	−7.67625	−0.255450
$904$	10.6533	0.354325
$905$	34.2767	1.13939
$906$	−5.14054	−0.170783
$907$	−5.61529	−0.186453	−0.0932264	−	0.995645i	$-0.529718\pi$
$907$	−5.61529	−0.186453	−0.0932264	+	0.995645i	$0.529718\pi$
$908$	−16.8590	−0.559487
$909$	67.5876	2.24174
$910$	4.18708	0.138800
$911$	51.9923	1.72258	0.861291	−	0.508111i	$-0.169656\pi$
$911$	51.9923	1.72258	0.861291	+	0.508111i	$0.169656\pi$
$912$	15.6056	0.516754
$913$	−22.4733	−0.743758
$914$	13.5867	0.449409
$915$	35.8479	1.18509
$916$	10.8728	0.359249
$917$	0.589865	0.0194791
$918$	12.7942	0.422272
$919$	−44.7524	−1.47624	−0.738122	−	0.674667i	$-0.764287\pi$
$919$	−44.7524	−1.47624	−0.738122	+	0.674667i	$0.764287\pi$
$920$	2.76911	0.0912948
$921$	−25.9611	−0.855448
$922$	19.8797	0.654702
$923$	29.3723	0.966801
$924$	−7.40168	−0.243497
$925$	17.7923	0.585008
$926$	−29.5355	−0.970597
$927$	−19.8463	−0.651839
$928$	−3.77899	−0.124051
$929$	−10.8104	−0.354679	−0.177340	−	0.984150i	$-0.556749\pi$
$929$	−10.8104	−0.354679	−0.177340	+	0.984150i	$0.556749\pi$
$930$	55.4156	1.81715
$931$	34.1697	1.11987
$932$	4.89569	0.160364
$933$	−4.73095	−0.154884
$934$	−7.06845	−0.231287
$935$	−14.9127	−0.487698
$936$	−15.9697	−0.521984
$937$	−43.4874	−1.42067	−0.710336	−	0.703863i	$-0.751457\pi$
$937$	−43.4874	−1.42067	−0.710336	+	0.703863i	$0.751457\pi$
$938$	−3.96373	−0.129421
$939$	−4.95804	−0.161800
$940$	18.4783	0.602696
$941$	8.68636	0.283167	0.141584	−	0.989926i	$-0.454781\pi$
$941$	8.68636	0.283167	0.141584	+	0.989926i	$0.454781\pi$
$942$	−17.2212	−0.561098
$943$	0.317115	0.0103267
$944$	−6.57837	−0.214108
$945$	16.0277	0.521380
$946$	−17.6921	−0.575220
$947$	56.3932	1.83253	0.916267	−	0.400569i	$-0.131187\pi$
$947$	56.3932	1.83253	0.916267	+	0.400569i	$0.131187\pi$
$948$	14.7615	0.479430
$949$	13.3500	0.433358
$950$	13.7045	0.444634
$951$	−52.6199	−1.70632
$952$	0.769111	0.0249270
$953$	8.97819	0.290832	0.145416	−	0.989371i	$-0.453548\pi$
$953$	8.97819	0.290832	0.145416	+	0.989371i	$0.453548\pi$
$954$	85.9795	2.78369
$955$	47.4947	1.53689
$956$	−18.8560	−0.609848
$957$	47.4191	1.53284
$958$	29.8821	0.965447
$959$	−11.6179	−0.375162
$960$	−8.41273	−0.271520
$961$	12.3901	0.399680
$962$	−17.0951	−0.551168
$963$	−17.3170	−0.558034
$964$	−0.473098	−0.0152375
$965$	−26.7313	−0.860511
$966$	1.79205	0.0576582
$967$	39.7055	1.27684	0.638422	−	0.769686i	$-0.279587\pi$
$967$	39.7055	1.27684	0.638422	+	0.769686i	$0.279587\pi$
$968$	−6.05929	−0.194753
$969$	20.3478	0.653666
$970$	26.6752	0.856488
$971$	20.6915	0.664021	0.332011	−	0.943276i	$-0.392273\pi$
$971$	20.6915	0.664021	0.332011	+	0.943276i	$0.392273\pi$
$972$	−4.35006	−0.139528
$973$	11.6426	0.373244
$974$	28.4167	0.910529
$975$	−20.7776	−0.665416
$976$	−4.26115	−0.136396
$977$	10.6967	0.342219	0.171109	−	0.985252i	$-0.445265\pi$
$977$	10.6967	0.342219	0.171109	+	0.985252i	$0.445265\pi$
$978$	49.7608	1.59117
$979$	17.5450	0.560741
$980$	−18.4203	−0.588414
$981$	28.8415	0.920837
$982$	−13.0876	−0.417641
$983$	−0.589921	−0.0188155	−0.00940777	−	0.999956i	$-0.502995\pi$
$983$	−0.589921	−0.0188155	−0.00940777	+	0.999956i	$0.502995\pi$
$984$	−0.963416	−0.0307126
$985$	25.2867	0.805701
$986$	−4.92733	−0.156918
$987$	11.9584	0.380639
$988$	−13.1675	−0.418914
$989$	4.28351	0.136208
$990$	71.2520	2.26454
$991$	43.9059	1.39472	0.697359	−	0.716722i	$-0.254359\pi$
$991$	43.9059	1.39472	0.697359	+	0.716722i	$0.254359\pi$
$992$	−6.58712	−0.209141
$993$	9.09301	0.288558
$994$	6.75884	0.214377
$995$	−7.61286	−0.241344
$996$	−16.5304	−0.523786
$997$	−44.6498	−1.41407	−0.707036	−	0.707178i	$-0.749968\pi$
$997$	−44.6498	−1.41407	−0.707036	+	0.707178i	$0.749968\pi$
$998$	−30.4548	−0.964029
$999$	−65.4380	−2.07037

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6026.2.a.h.1.2	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6026.2.a.h.1.2	✓	24	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:	\( N \)	\(=\)	\( 6026 = 2 \cdot 23 \cdot 131 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6026.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.03806 q^{3} +1.00000 q^{4} +2.76911 q^{5} +3.03806 q^{6} -0.589865 q^{7} -1.00000 q^{8} +6.22984 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.03806 q^{3} +1.00000 q^{4} +2.76911 q^{5} +3.03806 q^{6} -0.589865 q^{7} -1.00000 q^{8} +6.22984 q^{9} -2.76911 q^{10} -4.13029 q^{11} -3.03806 q^{12} +2.56341 q^{13} +0.589865 q^{14} -8.41273 q^{15} +1.00000 q^{16} +1.30388 q^{17} -6.22984 q^{18} -5.13670 q^{19} +2.76911 q^{20} +1.79205 q^{21} +4.13029 q^{22} -1.00000 q^{23} +3.03806 q^{24} +2.66796 q^{25} -2.56341 q^{26} -9.81246 q^{27} -0.589865 q^{28} +3.77899 q^{29} +8.41273 q^{30} +6.58712 q^{31} -1.00000 q^{32} +12.5481 q^{33} -1.30388 q^{34} -1.63340 q^{35} +6.22984 q^{36} +6.66887 q^{37} +5.13670 q^{38} -7.78782 q^{39} -2.76911 q^{40} -0.317115 q^{41} -1.79205 q^{42} -4.28351 q^{43} -4.13029 q^{44} +17.2511 q^{45} +1.00000 q^{46} +6.67301 q^{47} -3.03806 q^{48} -6.65206 q^{49} -2.66796 q^{50} -3.96126 q^{51} +2.56341 q^{52} -13.8012 q^{53} +9.81246 q^{54} -11.4372 q^{55} +0.589865 q^{56} +15.6056 q^{57} -3.77899 q^{58} -6.57837 q^{59} -8.41273 q^{60} -4.26115 q^{61} -6.58712 q^{62} -3.67476 q^{63} +1.00000 q^{64} +7.09837 q^{65} -12.5481 q^{66} -6.71973 q^{67} +1.30388 q^{68} +3.03806 q^{69} +1.63340 q^{70} +11.4583 q^{71} -6.22984 q^{72} +5.20789 q^{73} -6.66887 q^{74} -8.10545 q^{75} -5.13670 q^{76} +2.43631 q^{77} +7.78782 q^{78} -4.85884 q^{79} +2.76911 q^{80} +11.1214 q^{81} +0.317115 q^{82} +5.44110 q^{83} +1.79205 q^{84} +3.61057 q^{85} +4.28351 q^{86} -11.4808 q^{87} +4.13029 q^{88} -4.24789 q^{89} -17.2511 q^{90} -1.51207 q^{91} -1.00000 q^{92} -20.0121 q^{93} -6.67301 q^{94} -14.2241 q^{95} +3.03806 q^{96} -9.63313 q^{97} +6.65206 q^{98} -25.7310 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9	\( 24 q - 24 q^{2} - q^{3} + 24 q^{4} - q^{5} + q^{6} - 7 q^{7} - 24 q^{8} + 27 q^{9} + q^{10} - 4 q^{11} - q^{12} - 5 q^{13} + 7 q^{14} - 6 q^{15} + 24 q^{16} + 5 q^{17} - 27 q^{18} - 20 q^{19} - q^{20} + 4 q^{22} - 24 q^{23} + q^{24} + q^{25} + 5 q^{26} - q^{27} - 7 q^{28} - 6 q^{29} + 6 q^{30} - 23 q^{31} - 24 q^{32} - 6 q^{33} - 5 q^{34} + 5 q^{35} + 27 q^{36} - 6 q^{37} + 20 q^{38} - 39 q^{39} + q^{40} - q^{41} - 44 q^{43} - 4 q^{44} - 13 q^{45} + 24 q^{46} + 32 q^{47} - q^{48} - 13 q^{49} - q^{50} - 44 q^{51} - 5 q^{52} + 21 q^{53} + q^{54} - 13 q^{55} + 7 q^{56} + 10 q^{57} + 6 q^{58} - 24 q^{59} - 6 q^{60} - 40 q^{61} + 23 q^{62} - 54 q^{63} + 24 q^{64} - 29 q^{65} + 6 q^{66} - 17 q^{67} + 5 q^{68} + q^{69} - 5 q^{70} + 4 q^{71} - 27 q^{72} - 16 q^{73} + 6 q^{74} - 36 q^{75} - 20 q^{76} + 24 q^{77} + 39 q^{78} - 53 q^{79} - q^{80} + 24 q^{81} + q^{82} - 9 q^{83} - 37 q^{85} + 44 q^{86} + 7 q^{87} + 4 q^{88} - 46 q^{89} + 13 q^{90} - 44 q^{91} - 24 q^{92} + 23 q^{93} - 32 q^{94} + 28 q^{95} + q^{96} - 20 q^{97} + 13 q^{98} - 78 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - q^3 + 24 * q^4 - q^5 + q^6 - 7 * q^7 - 24 * q^8 + 27 * q^9 + q^10 - 4 * q^11 - q^12 - 5 * q^13 + 7 * q^14 - 6 * q^15 + 24 * q^16 + 5 * q^17 - 27 * q^18 - 20 * q^19 - q^20 + 4 * q^22 - 24 * q^23 + q^24 + q^25 + 5 * q^26 - q^27 - 7 * q^28 - 6 * q^29 + 6 * q^30 - 23 * q^31 - 24 * q^32 - 6 * q^33 - 5 * q^34 + 5 * q^35 + 27 * q^36 - 6 * q^37 + 20 * q^38 - 39 * q^39 + q^40 - q^41 - 44 * q^43 - 4 * q^44 - 13 * q^45 + 24 * q^46 + 32 * q^47 - q^48 - 13 * q^49 - q^50 - 44 * q^51 - 5 * q^52 + 21 * q^53 + q^54 - 13 * q^55 + 7 * q^56 + 10 * q^57 + 6 * q^58 - 24 * q^59 - 6 * q^60 - 40 * q^61 + 23 * q^62 - 54 * q^63 + 24 * q^64 - 29 * q^65 + 6 * q^66 - 17 * q^67 + 5 * q^68 + q^69 - 5 * q^70 + 4 * q^71 - 27 * q^72 - 16 * q^73 + 6 * q^74 - 36 * q^75 - 20 * q^76 + 24 * q^77 + 39 * q^78 - 53 * q^79 - q^80 + 24 * q^81 + q^82 - 9 * q^83 - 37 * q^85 + 44 * q^86 + 7 * q^87 + 4 * q^88 - 46 * q^89 + 13 * q^90 - 44 * q^91 - 24 * q^92 + 23 * q^93 - 32 * q^94 + 28 * q^95 + q^96 - 20 * q^97 + 13 * q^98 - 78 * q^99

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