LMFDB - Embedded newform 6034.2.a.p.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$0$
Dimension:	$27$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.03412 q^{3} +1.00000 q^{4} +1.18387 q^{5} +3.03412 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.20591 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.03412 q^{3} +1.00000 q^{4} +1.18387 q^{5} +3.03412 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.20591 q^{9} -1.18387 q^{10} -3.03030 q^{11} -3.03412 q^{12} -3.36031 q^{13} -1.00000 q^{14} -3.59200 q^{15} +1.00000 q^{16} -3.03667 q^{17} -6.20591 q^{18} +7.99980 q^{19} +1.18387 q^{20} -3.03412 q^{21} +3.03030 q^{22} +0.116752 q^{23} +3.03412 q^{24} -3.59846 q^{25} +3.36031 q^{26} -9.72712 q^{27} +1.00000 q^{28} -2.07972 q^{29} +3.59200 q^{30} -9.45071 q^{31} -1.00000 q^{32} +9.19432 q^{33} +3.03667 q^{34} +1.18387 q^{35} +6.20591 q^{36} +7.78608 q^{37} -7.99980 q^{38} +10.1956 q^{39} -1.18387 q^{40} -10.3791 q^{41} +3.03412 q^{42} -7.64734 q^{43} -3.03030 q^{44} +7.34697 q^{45} -0.116752 q^{46} +5.07456 q^{47} -3.03412 q^{48} +1.00000 q^{49} +3.59846 q^{50} +9.21363 q^{51} -3.36031 q^{52} +5.15049 q^{53} +9.72712 q^{54} -3.58748 q^{55} -1.00000 q^{56} -24.2724 q^{57} +2.07972 q^{58} +8.63546 q^{59} -3.59200 q^{60} -3.51766 q^{61} +9.45071 q^{62} +6.20591 q^{63} +1.00000 q^{64} -3.97815 q^{65} -9.19432 q^{66} -8.37103 q^{67} -3.03667 q^{68} -0.354241 q^{69} -1.18387 q^{70} +13.5915 q^{71} -6.20591 q^{72} -8.24803 q^{73} -7.78608 q^{74} +10.9182 q^{75} +7.99980 q^{76} -3.03030 q^{77} -10.1956 q^{78} +13.8655 q^{79} +1.18387 q^{80} +10.8956 q^{81} +10.3791 q^{82} +7.88035 q^{83} -3.03412 q^{84} -3.59501 q^{85} +7.64734 q^{86} +6.31012 q^{87} +3.03030 q^{88} +15.0909 q^{89} -7.34697 q^{90} -3.36031 q^{91} +0.116752 q^{92} +28.6746 q^{93} -5.07456 q^{94} +9.47070 q^{95} +3.03412 q^{96} -0.500285 q^{97} -1.00000 q^{98} -18.8058 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) $ 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * 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
$3$	−3.03412	−1.75175	−0.875876	−	0.482536i	$-0.839716\pi$
$3$	−3.03412	−1.75175	−0.875876	+	0.482536i	$0.839716\pi$
$4$	1.00000	0.500000
$5$	1.18387	0.529441	0.264721	−	0.964325i	$-0.414720\pi$
$5$	1.18387	0.529441	0.264721	+	0.964325i	$0.414720\pi$
$6$	3.03412	1.23868
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	6.20591	2.06864
$10$	−1.18387	−0.374372
$11$	−3.03030	−0.913671	−0.456835	−	0.889551i	$-0.651017\pi$
$11$	−3.03030	−0.913671	−0.456835	+	0.889551i	$0.651017\pi$
$12$	−3.03412	−0.875876
$13$	−3.36031	−0.931981	−0.465990	−	0.884790i	$-0.654302\pi$
$13$	−3.36031	−0.931981	−0.465990	+	0.884790i	$0.654302\pi$
$14$	−1.00000	−0.267261
$15$	−3.59200	−0.927450
$16$	1.00000	0.250000
$17$	−3.03667	−0.736501	−0.368250	−	0.929727i	$-0.620043\pi$
$17$	−3.03667	−0.736501	−0.368250	+	0.929727i	$0.620043\pi$
$18$	−6.20591	−1.46275
$19$	7.99980	1.83528	0.917640	−	0.397412i	$-0.130092\pi$
$19$	7.99980	1.83528	0.917640	+	0.397412i	$0.130092\pi$
$20$	1.18387	0.264721
$21$	−3.03412	−0.662100
$22$	3.03030	0.646063
$23$	0.116752	0.0243445	0.0121723	−	0.999926i	$-0.496125\pi$
$23$	0.116752	0.0243445	0.0121723	+	0.999926i	$0.496125\pi$
$24$	3.03412	0.619338
$25$	−3.59846	−0.719692
$26$	3.36031	0.659010
$27$	−9.72712	−1.87199
$28$	1.00000	0.188982
$29$	−2.07972	−0.386194	−0.193097	−	0.981180i	$-0.561853\pi$
$29$	−2.07972	−0.386194	−0.193097	+	0.981180i	$0.561853\pi$
$30$	3.59200	0.655806
$31$	−9.45071	−1.69740	−0.848699	−	0.528877i	$-0.822613\pi$
$31$	−9.45071	−1.69740	−0.848699	+	0.528877i	$0.822613\pi$
$32$	−1.00000	−0.176777
$33$	9.19432	1.60053
$34$	3.03667	0.520785
$35$	1.18387	0.200110
$36$	6.20591	1.03432
$37$	7.78608	1.28002	0.640012	−	0.768365i	$-0.278929\pi$
$37$	7.78608	1.28002	0.640012	+	0.768365i	$0.278929\pi$
$38$	−7.99980	−1.29774
$39$	10.1956	1.63260
$40$	−1.18387	−0.187186
$41$	−10.3791	−1.62095	−0.810475	−	0.585774i	$-0.800791\pi$
$41$	−10.3791	−1.62095	−0.810475	+	0.585774i	$0.800791\pi$
$42$	3.03412	0.468175
$43$	−7.64734	−1.16621	−0.583104	−	0.812397i	$-0.698162\pi$
$43$	−7.64734	−1.16621	−0.583104	+	0.812397i	$0.698162\pi$
$44$	−3.03030	−0.456835
$45$	7.34697	1.09522
$46$	−0.116752	−0.0172142
$47$	5.07456	0.740200	0.370100	−	0.928992i	$-0.379323\pi$
$47$	5.07456	0.740200	0.370100	+	0.928992i	$0.379323\pi$
$48$	−3.03412	−0.437938
$49$	1.00000	0.142857
$50$	3.59846	0.508899
$51$	9.21363	1.29017
$52$	−3.36031	−0.465990
$53$	5.15049	0.707475	0.353737	−	0.935345i	$-0.384911\pi$
$53$	5.15049	0.707475	0.353737	+	0.935345i	$0.384911\pi$
$54$	9.72712	1.32369
$55$	−3.58748	−0.483735
$56$	−1.00000	−0.133631
$57$	−24.2724	−3.21496
$58$	2.07972	0.273080
$59$	8.63546	1.12424	0.562121	−	0.827055i	$-0.309986\pi$
$59$	8.63546	1.12424	0.562121	+	0.827055i	$0.309986\pi$
$60$	−3.59200	−0.463725
$61$	−3.51766	−0.450391	−0.225195	−	0.974314i	$-0.572302\pi$
$61$	−3.51766	−0.450391	−0.225195	+	0.974314i	$0.572302\pi$
$62$	9.45071	1.20024
$63$	6.20591	0.781871
$64$	1.00000	0.125000
$65$	−3.97815	−0.493429
$66$	−9.19432	−1.13174
$67$	−8.37103	−1.02268	−0.511342	−	0.859377i	$-0.670851\pi$
$67$	−8.37103	−1.02268	−0.511342	+	0.859377i	$0.670851\pi$
$68$	−3.03667	−0.368250
$69$	−0.354241	−0.0426456
$70$	−1.18387	−0.141499
$71$	13.5915	1.61302	0.806509	−	0.591222i	$-0.201354\pi$
$71$	13.5915	1.61302	0.806509	+	0.591222i	$0.201354\pi$
$72$	−6.20591	−0.731373
$73$	−8.24803	−0.965359	−0.482679	−	0.875797i	$-0.660336\pi$
$73$	−8.24803	−0.965359	−0.482679	+	0.875797i	$0.660336\pi$
$74$	−7.78608	−0.905114
$75$	10.9182	1.26072
$76$	7.99980	0.917640
$77$	−3.03030	−0.345335
$78$	−10.1956	−1.15442
$79$	13.8655	1.55999	0.779996	−	0.625785i	$-0.215221\pi$
$79$	13.8655	1.55999	0.779996	+	0.625785i	$0.215221\pi$
$80$	1.18387	0.132360
$81$	10.8956	1.21062
$82$	10.3791	1.14618
$83$	7.88035	0.864981	0.432490	−	0.901639i	$-0.357635\pi$
$83$	7.88035	0.864981	0.432490	+	0.901639i	$0.357635\pi$
$84$	−3.03412	−0.331050
$85$	−3.59501	−0.389934
$86$	7.64734	0.824634
$87$	6.31012	0.676516
$88$	3.03030	0.323031
$89$	15.0909	1.59964	0.799818	−	0.600243i	$-0.204929\pi$
$89$	15.0909	1.59964	0.799818	+	0.600243i	$0.204929\pi$
$90$	−7.34697	−0.774439
$91$	−3.36031	−0.352256
$92$	0.116752	0.0121723
$93$	28.6746	2.97342
$94$	−5.07456	−0.523401
$95$	9.47070	0.971673
$96$	3.03412	0.309669
$97$	−0.500285	−0.0507963	−0.0253981	−	0.999677i	$-0.508085\pi$
$97$	−0.500285	−0.0507963	−0.0253981	+	0.999677i	$0.508085\pi$
$98$	−1.00000	−0.101015
$99$	−18.8058	−1.89005
$100$	−3.59846	−0.359846
$101$	3.42470	0.340770	0.170385	−	0.985378i	$-0.445499\pi$
$101$	3.42470	0.340770	0.170385	+	0.985378i	$0.445499\pi$
$102$	−9.21363	−0.912286
$103$	−4.21360	−0.415178	−0.207589	−	0.978216i	$-0.566562\pi$
$103$	−4.21360	−0.415178	−0.207589	+	0.978216i	$0.566562\pi$
$104$	3.36031	0.329505
$105$	−3.59200	−0.350543
$106$	−5.15049	−0.500260
$107$	−10.0314	−0.969770	−0.484885	−	0.874578i	$-0.661138\pi$
$107$	−10.0314	−0.969770	−0.484885	+	0.874578i	$0.661138\pi$
$108$	−9.72712	−0.935993
$109$	−13.6309	−1.30561	−0.652803	−	0.757527i	$-0.726407\pi$
$109$	−13.6309	−1.30561	−0.652803	+	0.757527i	$0.726407\pi$
$110$	3.58748	0.342052
$111$	−23.6239	−2.24228
$112$	1.00000	0.0944911
$113$	16.7064	1.57161	0.785805	−	0.618474i	$-0.212249\pi$
$113$	16.7064	1.57161	0.785805	+	0.618474i	$0.212249\pi$
$114$	24.2724	2.27332
$115$	0.138219	0.0128890
$116$	−2.07972	−0.193097
$117$	−20.8537	−1.92793
$118$	−8.63546	−0.794959
$119$	−3.03667	−0.278371
$120$	3.59200	0.327903
$121$	−1.81726	−0.165206
$122$	3.51766	0.318474
$123$	31.4916	2.83950
$124$	−9.45071	−0.848699
$125$	−10.1794	−0.910476
$126$	−6.20591	−0.552866
$127$	3.12557	0.277349	0.138675	−	0.990338i	$-0.455716\pi$
$127$	3.12557	0.277349	0.138675	+	0.990338i	$0.455716\pi$
$128$	−1.00000	−0.0883883
$129$	23.2030	2.04291
$130$	3.97815	0.348907
$131$	−11.3978	−0.995829	−0.497914	−	0.867226i	$-0.665901\pi$
$131$	−11.3978	−0.995829	−0.497914	+	0.867226i	$0.665901\pi$
$132$	9.19432	0.800263
$133$	7.99980	0.693671
$134$	8.37103	0.723147
$135$	−11.5156	−0.991107
$136$	3.03667	0.260392
$137$	−3.03300	−0.259126	−0.129563	−	0.991571i	$-0.541358\pi$
$137$	−3.03300	−0.259126	−0.129563	+	0.991571i	$0.541358\pi$
$138$	0.354241	0.0301550
$139$	15.6742	1.32947	0.664736	−	0.747079i	$-0.268544\pi$
$139$	15.6742	1.32947	0.664736	+	0.747079i	$0.268544\pi$
$140$	1.18387	0.100055
$141$	−15.3968	−1.29665
$142$	−13.5915	−1.14058
$143$	10.1827	0.851524
$144$	6.20591	0.517159
$145$	−2.46211	−0.204467
$146$	8.24803	0.682612
$147$	−3.03412	−0.250250
$148$	7.78608	0.640012
$149$	−10.5115	−0.861132	−0.430566	−	0.902559i	$-0.641686\pi$
$149$	−10.5115	−0.861132	−0.430566	+	0.902559i	$0.641686\pi$
$150$	−10.9182	−0.891465
$151$	4.66745	0.379832	0.189916	−	0.981800i	$-0.439178\pi$
$151$	4.66745	0.379832	0.189916	+	0.981800i	$0.439178\pi$
$152$	−7.99980	−0.648870
$153$	−18.8453	−1.52355
$154$	3.03030	0.244189
$155$	−11.1884	−0.898672
$156$	10.1956	0.816300
$157$	−16.8658	−1.34604	−0.673018	−	0.739626i	$-0.735002\pi$
$157$	−16.8658	−1.34604	−0.673018	+	0.739626i	$0.735002\pi$
$158$	−13.8655	−1.10308
$159$	−15.6272	−1.23932
$160$	−1.18387	−0.0935929
$161$	0.116752	0.00920137
$162$	−10.8956	−0.856037
$163$	−22.3467	−1.75033	−0.875164	−	0.483826i	$-0.839247\pi$
$163$	−22.3467	−1.75033	−0.875164	+	0.483826i	$0.839247\pi$
$164$	−10.3791	−0.810475
$165$	10.8848	0.847384
$166$	−7.88035	−0.611634
$167$	−22.9563	−1.77641	−0.888206	−	0.459446i	$-0.848048\pi$
$167$	−22.9563	−1.77641	−0.888206	+	0.459446i	$0.848048\pi$
$168$	3.03412	0.234088
$169$	−1.70835	−0.131411
$170$	3.59501	0.275725
$171$	49.6460	3.79653
$172$	−7.64734	−0.583104
$173$	−12.8623	−0.977902	−0.488951	−	0.872311i	$-0.662620\pi$
$173$	−12.8623	−0.977902	−0.488951	+	0.872311i	$0.662620\pi$
$174$	−6.31012	−0.478369
$175$	−3.59846	−0.272018
$176$	−3.03030	−0.228418
$177$	−26.2011	−1.96939
$178$	−15.0909	−1.13111
$179$	17.0995	1.27807	0.639037	−	0.769176i	$-0.279333\pi$
$179$	17.0995	1.27807	0.639037	+	0.769176i	$0.279333\pi$
$180$	7.34697	0.547611
$181$	−23.4253	−1.74119	−0.870593	−	0.492003i	$-0.836265\pi$
$181$	−23.4253	−1.74119	−0.870593	+	0.492003i	$0.836265\pi$
$182$	3.36031	0.249082
$183$	10.6730	0.788973
$184$	−0.116752	−0.00860709
$185$	9.21769	0.677698
$186$	−28.6746	−2.10253
$187$	9.20203	0.672919
$188$	5.07456	0.370100
$189$	−9.72712	−0.707544
$190$	−9.47070	−0.687077
$191$	8.99029	0.650515	0.325257	−	0.945626i	$-0.394549\pi$
$191$	8.99029	0.650515	0.325257	+	0.945626i	$0.394549\pi$
$192$	−3.03412	−0.218969
$193$	3.21904	0.231711	0.115856	−	0.993266i	$-0.463039\pi$
$193$	3.21904	0.231711	0.115856	+	0.993266i	$0.463039\pi$
$194$	0.500285	0.0359184
$195$	12.0702	0.864366
$196$	1.00000	0.0714286
$197$	22.5973	1.60999	0.804997	−	0.593279i	$-0.202167\pi$
$197$	22.5973	1.60999	0.804997	+	0.593279i	$0.202167\pi$
$198$	18.8058	1.33647
$199$	−17.1083	−1.21277	−0.606386	−	0.795170i	$-0.707381\pi$
$199$	−17.1083	−1.21277	−0.606386	+	0.795170i	$0.707381\pi$
$200$	3.59846	0.254449
$201$	25.3987	1.79149
$202$	−3.42470	−0.240961
$203$	−2.07972	−0.145968
$204$	9.21363	0.645083
$205$	−12.2875	−0.858198
$206$	4.21360	0.293575
$207$	0.724554	0.0503600
$208$	−3.36031	−0.232995
$209$	−24.2418	−1.67684
$210$	3.59200	0.247872
$211$	16.3832	1.12786	0.563932	−	0.825822i	$-0.309288\pi$
$211$	16.3832	1.12786	0.563932	+	0.825822i	$0.309288\pi$
$212$	5.15049	0.353737
$213$	−41.2384	−2.82561
$214$	10.0314	0.685731
$215$	−9.05343	−0.617439
$216$	9.72712	0.661847
$217$	−9.45071	−0.641556
$218$	13.6309	0.923203
$219$	25.0255	1.69107
$220$	−3.58748	−0.241868
$221$	10.2041	0.686405
$222$	23.6239	1.58553
$223$	18.7344	1.25455	0.627274	−	0.778798i	$-0.284171\pi$
$223$	18.7344	1.25455	0.627274	+	0.778798i	$0.284171\pi$
$224$	−1.00000	−0.0668153
$225$	−22.3317	−1.48878
$226$	−16.7064	−1.11130
$227$	3.03774	0.201622	0.100811	−	0.994906i	$-0.467856\pi$
$227$	3.03774	0.201622	0.100811	+	0.994906i	$0.467856\pi$
$228$	−24.2724	−1.60748
$229$	19.6090	1.29580	0.647899	−	0.761726i	$-0.275648\pi$
$229$	19.6090	1.29580	0.647899	+	0.761726i	$0.275648\pi$
$230$	−0.138219	−0.00911390
$231$	9.19432	0.604942
$232$	2.07972	0.136540
$233$	17.2439	1.12968	0.564842	−	0.825199i	$-0.308937\pi$
$233$	17.2439	1.12968	0.564842	+	0.825199i	$0.308937\pi$
$234$	20.8537	1.36325
$235$	6.00760	0.391893
$236$	8.63546	0.562121
$237$	−42.0697	−2.73272
$238$	3.03667	0.196838
$239$	11.1424	0.720741	0.360371	−	0.932809i	$-0.382650\pi$
$239$	11.1424	0.720741	0.360371	+	0.932809i	$0.382650\pi$
$240$	−3.59200	−0.231863
$241$	−8.30507	−0.534977	−0.267488	−	0.963561i	$-0.586194\pi$
$241$	−8.30507	−0.534977	−0.267488	+	0.963561i	$0.586194\pi$
$242$	1.81726	0.116818
$243$	−3.87715	−0.248719
$244$	−3.51766	−0.225195
$245$	1.18387	0.0756345
$246$	−31.4916	−2.00783
$247$	−26.8818	−1.71045
$248$	9.45071	0.600121
$249$	−23.9100	−1.51523
$250$	10.1794	0.643804
$251$	27.3655	1.72729	0.863647	−	0.504097i	$-0.168174\pi$
$251$	27.3655	1.72729	0.863647	+	0.504097i	$0.168174\pi$
$252$	6.20591	0.390935
$253$	−0.353795	−0.0222429
$254$	−3.12557	−0.196115
$255$	10.9077	0.683068
$256$	1.00000	0.0625000
$257$	−3.15958	−0.197089	−0.0985445	−	0.995133i	$-0.531419\pi$
$257$	−3.15958	−0.197089	−0.0985445	+	0.995133i	$0.531419\pi$
$258$	−23.2030	−1.44455
$259$	7.78608	0.483804
$260$	−3.97815	−0.246715
$261$	−12.9065	−0.798894
$262$	11.3978	0.704157
$263$	8.67513	0.534932	0.267466	−	0.963567i	$-0.413814\pi$
$263$	8.67513	0.534932	0.267466	+	0.963567i	$0.413814\pi$
$264$	−9.19432	−0.565871
$265$	6.09750	0.374566
$266$	−7.99980	−0.490499
$267$	−45.7878	−2.80217
$268$	−8.37103	−0.511342
$269$	2.93987	0.179247	0.0896235	−	0.995976i	$-0.471434\pi$
$269$	2.93987	0.179247	0.0896235	+	0.995976i	$0.471434\pi$
$270$	11.5156	0.700818
$271$	30.6176	1.85989	0.929943	−	0.367704i	$-0.119856\pi$
$271$	30.6176	1.85989	0.929943	+	0.367704i	$0.119856\pi$
$272$	−3.03667	−0.184125
$273$	10.1956	0.617065
$274$	3.03300	0.183230
$275$	10.9044	0.657561
$276$	−0.354241	−0.0213228
$277$	−24.3794	−1.46481	−0.732407	−	0.680867i	$-0.761603\pi$
$277$	−24.3794	−1.46481	−0.732407	+	0.680867i	$0.761603\pi$
$278$	−15.6742	−0.940078
$279$	−58.6502	−3.51130
$280$	−1.18387	−0.0707496
$281$	−9.27396	−0.553238	−0.276619	−	0.960980i	$-0.589214\pi$
$281$	−9.27396	−0.553238	−0.276619	+	0.960980i	$0.589214\pi$
$282$	15.3968	0.916868
$283$	−27.6919	−1.64611	−0.823056	−	0.567961i	$-0.807733\pi$
$283$	−27.6919	−1.64611	−0.823056	+	0.567961i	$0.807733\pi$
$284$	13.5915	0.806509
$285$	−28.7353	−1.70213
$286$	−10.1827	−0.602118
$287$	−10.3791	−0.612661
$288$	−6.20591	−0.365687
$289$	−7.77864	−0.457567
$290$	2.46211	0.144580
$291$	1.51793	0.0889825
$292$	−8.24803	−0.482679
$293$	−16.1893	−0.945791	−0.472896	−	0.881119i	$-0.656791\pi$
$293$	−16.1893	−0.945791	−0.472896	+	0.881119i	$0.656791\pi$
$294$	3.03412	0.176954
$295$	10.2232	0.595220
$296$	−7.78608	−0.452557
$297$	29.4761	1.71038
$298$	10.5115	0.608913
$299$	−0.392323	−0.0226886
$300$	10.9182	0.630361
$301$	−7.64734	−0.440785
$302$	−4.66745	−0.268582
$303$	−10.3910	−0.596945
$304$	7.99980	0.458820
$305$	−4.16445	−0.238456
$306$	18.8453	1.07731
$307$	4.57379	0.261040	0.130520	−	0.991446i	$-0.458335\pi$
$307$	4.57379	0.261040	0.130520	+	0.991446i	$0.458335\pi$
$308$	−3.03030	−0.172668
$309$	12.7846	0.727289
$310$	11.1884	0.635457
$311$	−1.00696	−0.0570992	−0.0285496	−	0.999592i	$-0.509089\pi$
$311$	−1.00696	−0.0570992	−0.0285496	+	0.999592i	$0.509089\pi$
$312$	−10.1956	−0.577211
$313$	20.0219	1.13171	0.565853	−	0.824506i	$-0.308547\pi$
$313$	20.0219	1.13171	0.565853	+	0.824506i	$0.308547\pi$
$314$	16.8658	0.951791
$315$	7.34697	0.413955
$316$	13.8655	0.779996
$317$	−25.7778	−1.44783	−0.723913	−	0.689891i	$-0.757658\pi$
$317$	−25.7778	−1.44783	−0.723913	+	0.689891i	$0.757658\pi$
$318$	15.6272	0.876332
$319$	6.30217	0.352854
$320$	1.18387	0.0661802
$321$	30.4364	1.69880
$322$	−0.116752	−0.00650635
$323$	−24.2928	−1.35169
$324$	10.8956	0.605310
$325$	12.0919	0.670739
$326$	22.3467	1.23767
$327$	41.3579	2.28710
$328$	10.3791	0.573092
$329$	5.07456	0.279769
$330$	−10.8848	−0.599191
$331$	−7.57879	−0.416568	−0.208284	−	0.978068i	$-0.566788\pi$
$331$	−7.57879	−0.416568	−0.208284	+	0.978068i	$0.566788\pi$
$332$	7.88035	0.432490
$333$	48.3197	2.64790
$334$	22.9563	1.25611
$335$	−9.91019	−0.541451
$336$	−3.03412	−0.165525
$337$	−3.69115	−0.201070	−0.100535	−	0.994934i	$-0.532055\pi$
$337$	−3.69115	−0.201070	−0.100535	+	0.994934i	$0.532055\pi$
$338$	1.70835	0.0929219
$339$	−50.6894	−2.75307
$340$	−3.59501	−0.194967
$341$	28.6385	1.55086
$342$	−49.6460	−2.68455
$343$	1.00000	0.0539949
$344$	7.64734	0.412317
$345$	−0.419374	−0.0225783
$346$	12.8623	0.691481
$347$	14.0151	0.752369	0.376185	−	0.926545i	$-0.377236\pi$
$347$	14.0151	0.752369	0.376185	+	0.926545i	$0.377236\pi$
$348$	6.31012	0.338258
$349$	20.7175	1.10898	0.554490	−	0.832190i	$-0.312913\pi$
$349$	20.7175	1.10898	0.554490	+	0.832190i	$0.312913\pi$
$350$	3.59846	0.192346
$351$	32.6861	1.74465
$352$	3.03030	0.161516
$353$	6.97123	0.371041	0.185521	−	0.982640i	$-0.440603\pi$
$353$	6.97123	0.371041	0.185521	+	0.982640i	$0.440603\pi$
$354$	26.2011	1.39257
$355$	16.0906	0.853998
$356$	15.0909	0.799818
$357$	9.21363	0.487637
$358$	−17.0995	−0.903735
$359$	33.7058	1.77893	0.889463	−	0.457008i	$-0.151079\pi$
$359$	33.7058	1.77893	0.889463	+	0.457008i	$0.151079\pi$
$360$	−7.34697	−0.387219
$361$	44.9968	2.36825
$362$	23.4253	1.23120
$363$	5.51379	0.289399
$364$	−3.36031	−0.176128
$365$	−9.76457	−0.511101
$366$	−10.6730	−0.557888
$367$	2.77482	0.144845	0.0724223	−	0.997374i	$-0.476927\pi$
$367$	2.77482	0.144845	0.0724223	+	0.997374i	$0.476927\pi$
$368$	0.116752	0.00608613
$369$	−64.4120	−3.35315
$370$	−9.21769	−0.479205
$371$	5.15049	0.267400
$372$	28.6746	1.48671
$373$	22.8504	1.18315	0.591574	−	0.806251i	$-0.298507\pi$
$373$	22.8504	1.18315	0.591574	+	0.806251i	$0.298507\pi$
$374$	−9.20203	−0.475826
$375$	30.8857	1.59493
$376$	−5.07456	−0.261700
$377$	6.98848	0.359925
$378$	9.72712	0.500309
$379$	30.7041	1.57716	0.788582	−	0.614929i	$-0.210815\pi$
$379$	30.7041	1.57716	0.788582	+	0.614929i	$0.210815\pi$
$380$	9.47070	0.485837
$381$	−9.48335	−0.485847
$382$	−8.99029	−0.459983
$383$	−35.7682	−1.82767	−0.913834	−	0.406087i	$-0.866893\pi$
$383$	−35.7682	−1.82767	−0.913834	+	0.406087i	$0.866893\pi$
$384$	3.03412	0.154834
$385$	−3.58748	−0.182835
$386$	−3.21904	−0.163845
$387$	−47.4587	−2.41246
$388$	−0.500285	−0.0253981
$389$	16.8504	0.854350	0.427175	−	0.904169i	$-0.359509\pi$
$389$	16.8504	0.854350	0.427175	+	0.904169i	$0.359509\pi$
$390$	−12.0702	−0.611199
$391$	−0.354538	−0.0179298
$392$	−1.00000	−0.0505076
$393$	34.5823	1.74445
$394$	−22.5973	−1.13844
$395$	16.4149	0.825924
$396$	−18.8058	−0.945026
$397$	0.209575	0.0105183	0.00525914	−	0.999986i	$-0.498326\pi$
$397$	0.209575	0.0105183	0.00525914	+	0.999986i	$0.498326\pi$
$398$	17.1083	0.857560
$399$	−24.2724	−1.21514
$400$	−3.59846	−0.179923
$401$	0.774350	0.0386692	0.0193346	−	0.999813i	$-0.493845\pi$
$401$	0.774350	0.0386692	0.0193346	+	0.999813i	$0.493845\pi$
$402$	−25.3987	−1.26677
$403$	31.7573	1.58194
$404$	3.42470	0.170385
$405$	12.8989	0.640952
$406$	2.07972	0.103215
$407$	−23.5942	−1.16952
$408$	−9.21363	−0.456143
$409$	19.2114	0.949943	0.474971	−	0.880001i	$-0.342458\pi$
$409$	19.2114	0.949943	0.474971	+	0.880001i	$0.342458\pi$
$410$	12.2875	0.606838
$411$	9.20249	0.453925
$412$	−4.21360	−0.207589
$413$	8.63546	0.424923
$414$	−0.724554	−0.0356099
$415$	9.32929	0.457957
$416$	3.36031	0.164753
$417$	−47.5576	−2.32890
$418$	24.2418	1.18571
$419$	25.6416	1.25268	0.626338	−	0.779552i	$-0.284553\pi$
$419$	25.6416	1.25268	0.626338	+	0.779552i	$0.284553\pi$
$420$	−3.59200	−0.175272
$421$	33.0431	1.61042	0.805211	−	0.592989i	$-0.202052\pi$
$421$	33.0431	1.61042	0.805211	+	0.592989i	$0.202052\pi$
$422$	−16.3832	−0.797520
$423$	31.4922	1.53121
$424$	−5.15049	−0.250130
$425$	10.9273	0.530053
$426$	41.2384	1.99801
$427$	−3.51766	−0.170232
$428$	−10.0314	−0.484885
$429$	−30.8957	−1.49166
$430$	9.05343	0.436595
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	−9.72712	−0.467996
$433$	32.4979	1.56175	0.780874	−	0.624689i	$-0.214774\pi$
$433$	32.4979	1.56175	0.780874	+	0.624689i	$0.214774\pi$
$434$	9.45071	0.453648
$435$	7.47034	0.358175
$436$	−13.6309	−0.652803
$437$	0.933995	0.0446790
$438$	−25.0255	−1.19577
$439$	−7.21470	−0.344339	−0.172169	−	0.985067i	$-0.555078\pi$
$439$	−7.21470	−0.344339	−0.172169	+	0.985067i	$0.555078\pi$
$440$	3.58748	0.171026
$441$	6.20591	0.295519
$442$	−10.2041	−0.485361
$443$	5.38931	0.256054	0.128027	−	0.991771i	$-0.459136\pi$
$443$	5.38931	0.256054	0.128027	+	0.991771i	$0.459136\pi$
$444$	−23.6239	−1.12114
$445$	17.8657	0.846913
$446$	−18.7344	−0.887100
$447$	31.8931	1.50849
$448$	1.00000	0.0472456
$449$	19.7980	0.934324	0.467162	−	0.884172i	$-0.345276\pi$
$449$	19.7980	0.934324	0.467162	+	0.884172i	$0.345276\pi$
$450$	22.3317	1.05273
$451$	31.4519	1.48101
$452$	16.7064	0.785805
$453$	−14.1616	−0.665372
$454$	−3.03774	−0.142568
$455$	−3.97815	−0.186499
$456$	24.2724	1.13666
$457$	−38.6842	−1.80957	−0.904785	−	0.425869i	$-0.859968\pi$
$457$	−38.6842	−1.80957	−0.904785	+	0.425869i	$0.859968\pi$
$458$	−19.6090	−0.916268
$459$	29.5381	1.37872
$460$	0.138219	0.00644450
$461$	−24.0943	−1.12218	−0.561091	−	0.827754i	$-0.689618\pi$
$461$	−24.0943	−1.12218	−0.561091	+	0.827754i	$0.689618\pi$
$462$	−9.19432	−0.427758
$463$	31.9478	1.48474	0.742370	−	0.669990i	$-0.233702\pi$
$463$	31.9478	1.48474	0.742370	+	0.669990i	$0.233702\pi$
$464$	−2.07972	−0.0965484
$465$	33.9469	1.57425
$466$	−17.2439	−0.798807
$467$	19.5476	0.904557	0.452279	−	0.891877i	$-0.350611\pi$
$467$	19.5476	0.904557	0.452279	+	0.891877i	$0.350611\pi$
$468$	−20.8537	−0.963965
$469$	−8.37103	−0.386538
$470$	−6.00760	−0.277110
$471$	51.1729	2.35792
$472$	−8.63546	−0.397479
$473$	23.1738	1.06553
$474$	42.0697	1.93232
$475$	−28.7870	−1.32084
$476$	−3.03667	−0.139186
$477$	31.9635	1.46351
$478$	−11.1424	−0.509641
$479$	13.0944	0.598296	0.299148	−	0.954207i	$-0.403298\pi$
$479$	13.0944	0.598296	0.299148	+	0.954207i	$0.403298\pi$
$480$	3.59200	0.163952
$481$	−26.1636	−1.19296
$482$	8.30507	0.378286
$483$	−0.354241	−0.0161185
$484$	−1.81726	−0.0826028
$485$	−0.592271	−0.0268937
$486$	3.87715	0.175871
$487$	26.4373	1.19799	0.598995	−	0.800753i	$-0.295567\pi$
$487$	26.4373	1.19799	0.598995	+	0.800753i	$0.295567\pi$
$488$	3.51766	0.159237
$489$	67.8026	3.06614
$490$	−1.18387	−0.0534817
$491$	−22.3414	−1.00825	−0.504127	−	0.863630i	$-0.668186\pi$
$491$	−22.3414	−1.00825	−0.504127	+	0.863630i	$0.668186\pi$
$492$	31.4916	1.41975
$493$	6.31541	0.284432
$494$	26.8818	1.20947
$495$	−22.2635	−1.00067
$496$	−9.45071	−0.424349
$497$	13.5915	0.609663
$498$	23.9100	1.07143
$499$	36.3753	1.62838	0.814191	−	0.580597i	$-0.197181\pi$
$499$	36.3753	1.62838	0.814191	+	0.580597i	$0.197181\pi$
$500$	−10.1794	−0.455238
$501$	69.6523	3.11183
$502$	−27.3655	−1.22138
$503$	−7.77040	−0.346465	−0.173232	−	0.984881i	$-0.555421\pi$
$503$	−7.77040	−0.346465	−0.173232	+	0.984881i	$0.555421\pi$
$504$	−6.20591	−0.276433
$505$	4.05439	0.180418
$506$	0.353795	0.0157281
$507$	5.18334	0.230200
$508$	3.12557	0.138675
$509$	21.0212	0.931746	0.465873	−	0.884851i	$-0.345740\pi$
$509$	21.0212	0.931746	0.465873	+	0.884851i	$0.345740\pi$
$510$	−10.9077	−0.483002
$511$	−8.24803	−0.364871
$512$	−1.00000	−0.0441942
$513$	−77.8150	−3.43562
$514$	3.15958	0.139363
$515$	−4.98834	−0.219813
$516$	23.2030	1.02145
$517$	−15.3774	−0.676299
$518$	−7.78608	−0.342101
$519$	39.0258	1.71304
$520$	3.97815	0.174454
$521$	−6.25354	−0.273972	−0.136986	−	0.990573i	$-0.543742\pi$
$521$	−6.25354	−0.273972	−0.136986	+	0.990573i	$0.543742\pi$
$522$	12.9065	0.564904
$523$	−16.9498	−0.741163	−0.370582	−	0.928800i	$-0.620842\pi$
$523$	−16.9498	−0.741163	−0.370582	+	0.928800i	$0.620842\pi$
$524$	−11.3978	−0.497914
$525$	10.9182	0.476508
$526$	−8.67513	−0.378254
$527$	28.6987	1.25013
$528$	9.19432	0.400131
$529$	−22.9864	−0.999407
$530$	−6.09750	−0.264858
$531$	53.5909	2.32565
$532$	7.99980	0.346835
$533$	34.8771	1.51069
$534$	45.7878	1.98143
$535$	−11.8758	−0.513436
$536$	8.37103	0.361573
$537$	−51.8819	−2.23887
$538$	−2.93987	−0.126747
$539$	−3.03030	−0.130524
$540$	−11.5156	−0.495553
$541$	6.50320	0.279594	0.139797	−	0.990180i	$-0.455355\pi$
$541$	6.50320	0.279594	0.139797	+	0.990180i	$0.455355\pi$
$542$	−30.6176	−1.31514
$543$	71.0752	3.05013
$544$	3.03667	0.130196
$545$	−16.1372	−0.691242
$546$	−10.1956	−0.436331
$547$	−6.82317	−0.291738	−0.145869	−	0.989304i	$-0.546598\pi$
$547$	−6.82317	−0.291738	−0.145869	+	0.989304i	$0.546598\pi$
$548$	−3.03300	−0.129563
$549$	−21.8303	−0.931695
$550$	−10.9044	−0.464966
$551$	−16.6373	−0.708774
$552$	0.354241	0.0150775
$553$	13.8655	0.589621
$554$	24.3794	1.03578
$555$	−27.9676	−1.18716
$556$	15.6742	0.664736
$557$	22.5620	0.955984	0.477992	−	0.878364i	$-0.341365\pi$
$557$	22.5620	0.955984	0.477992	+	0.878364i	$0.341365\pi$
$558$	58.6502	2.48286
$559$	25.6974	1.08688
$560$	1.18387	0.0500275
$561$	−27.9201	−1.17879
$562$	9.27396	0.391198
$563$	−26.4758	−1.11582	−0.557912	−	0.829900i	$-0.688397\pi$
$563$	−26.4758	−1.11582	−0.557912	+	0.829900i	$0.688397\pi$
$564$	−15.3968	−0.648324
$565$	19.7782	0.832076
$566$	27.6919	1.16398
$567$	10.8956	0.457571
$568$	−13.5915	−0.570288
$569$	30.9503	1.29750	0.648752	−	0.761000i	$-0.275291\pi$
$569$	30.9503	1.29750	0.648752	+	0.761000i	$0.275291\pi$
$570$	28.7353	1.20359
$571$	−18.2918	−0.765489	−0.382744	−	0.923854i	$-0.625021\pi$
$571$	−18.2918	−0.765489	−0.382744	+	0.923854i	$0.625021\pi$
$572$	10.1827	0.425762
$573$	−27.2777	−1.13954
$574$	10.3791	0.433217
$575$	−0.420128	−0.0175206
$576$	6.20591	0.258580
$577$	−8.16507	−0.339916	−0.169958	−	0.985451i	$-0.554363\pi$
$577$	−8.16507	−0.339916	−0.169958	+	0.985451i	$0.554363\pi$
$578$	7.77864	0.323549
$579$	−9.76696	−0.405901
$580$	−2.46211	−0.102233
$581$	7.88035	0.326932
$582$	−1.51793	−0.0629201
$583$	−15.6076	−0.646399
$584$	8.24803	0.341306
$585$	−24.6881	−1.02073
$586$	16.1893	0.668775
$587$	−10.6937	−0.441374	−0.220687	−	0.975345i	$-0.570830\pi$
$587$	−10.6937	−0.441374	−0.220687	+	0.975345i	$0.570830\pi$
$588$	−3.03412	−0.125125
$589$	−75.6038	−3.11520
$590$	−10.2232	−0.420884
$591$	−68.5631	−2.82031
$592$	7.78608	0.320006
$593$	−35.2684	−1.44830	−0.724150	−	0.689642i	$-0.757768\pi$
$593$	−35.2684	−1.44830	−0.724150	+	0.689642i	$0.757768\pi$
$594$	−29.4761	−1.20942
$595$	−3.59501	−0.147381
$596$	−10.5115	−0.430566
$597$	51.9086	2.12448
$598$	0.392323	0.0160433
$599$	29.9025	1.22178	0.610891	−	0.791715i	$-0.290811\pi$
$599$	29.9025	1.22178	0.610891	+	0.791715i	$0.290811\pi$
$600$	−10.9182	−0.445732
$601$	−43.1360	−1.75955	−0.879777	−	0.475387i	$-0.842308\pi$
$601$	−43.1360	−1.75955	−0.879777	+	0.475387i	$0.842308\pi$
$602$	7.64734	0.311682
$603$	−51.9498	−2.11556
$604$	4.66745	0.189916
$605$	−2.15139	−0.0874666
$606$	10.3910	0.422104
$607$	38.9873	1.58245	0.791223	−	0.611528i	$-0.209445\pi$
$607$	38.9873	1.58245	0.791223	+	0.611528i	$0.209445\pi$
$608$	−7.99980	−0.324435
$609$	6.31012	0.255699
$610$	4.16445	0.168614
$611$	−17.0521	−0.689853
$612$	−18.8453	−0.761776
$613$	−10.7422	−0.433873	−0.216937	−	0.976186i	$-0.569607\pi$
$613$	−10.7422	−0.433873	−0.216937	+	0.976186i	$0.569607\pi$
$614$	−4.57379	−0.184583
$615$	37.2819	1.50335
$616$	3.03030	0.122094
$617$	25.8679	1.04140	0.520700	−	0.853739i	$-0.325671\pi$
$617$	25.8679	1.04140	0.520700	+	0.853739i	$0.325671\pi$
$618$	−12.7846	−0.514271
$619$	−38.3386	−1.54096	−0.770480	−	0.637464i	$-0.779983\pi$
$619$	−38.3386	−1.54096	−0.770480	+	0.637464i	$0.779983\pi$
$620$	−11.1884	−0.449336
$621$	−1.13566	−0.0455726
$622$	1.00696	0.0403752
$623$	15.0909	0.604605
$624$	10.1956	0.408150
$625$	5.94120	0.237648
$626$	−20.0219	−0.800236
$627$	73.5527	2.93741
$628$	−16.8658	−0.673018
$629$	−23.6438	−0.942738
$630$	−7.34697	−0.292710
$631$	−23.3527	−0.929657	−0.464828	−	0.885401i	$-0.653884\pi$
$631$	−23.3527	−0.929657	−0.464828	+	0.885401i	$0.653884\pi$
$632$	−13.8655	−0.551540
$633$	−49.7085	−1.97574
$634$	25.7778	1.02377
$635$	3.70025	0.146840
$636$	−15.6272	−0.619660
$637$	−3.36031	−0.133140
$638$	−6.30217	−0.249505
$639$	84.3478	3.33675
$640$	−1.18387	−0.0467965
$641$	39.3249	1.55324	0.776620	−	0.629969i	$-0.216932\pi$
$641$	39.3249	1.55324	0.776620	+	0.629969i	$0.216932\pi$
$642$	−30.4364	−1.20123
$643$	41.6980	1.64441	0.822203	−	0.569194i	$-0.192745\pi$
$643$	41.6980	1.64441	0.822203	+	0.569194i	$0.192745\pi$
$644$	0.116752	0.00460068
$645$	27.4692	1.08160
$646$	24.2928	0.955786
$647$	31.5153	1.23899	0.619497	−	0.784999i	$-0.287337\pi$
$647$	31.5153	1.23899	0.619497	+	0.784999i	$0.287337\pi$
$648$	−10.8956	−0.428018
$649$	−26.1681	−1.02719
$650$	−12.0919	−0.474284
$651$	28.6746	1.12385
$652$	−22.3467	−0.875164
$653$	−10.5750	−0.413831	−0.206915	−	0.978359i	$-0.566342\pi$
$653$	−10.5750	−0.413831	−0.206915	+	0.978359i	$0.566342\pi$
$654$	−41.3579	−1.61722
$655$	−13.4935	−0.527233
$656$	−10.3791	−0.405237
$657$	−51.1865	−1.99698
$658$	−5.07456	−0.197827
$659$	30.0326	1.16990	0.584951	−	0.811068i	$-0.301114\pi$
$659$	30.0326	1.16990	0.584951	+	0.811068i	$0.301114\pi$
$660$	10.8848	0.423692
$661$	−27.1813	−1.05723	−0.528615	−	0.848862i	$-0.677289\pi$
$661$	−27.1813	−1.05723	−0.528615	+	0.848862i	$0.677289\pi$
$662$	7.57879	0.294558
$663$	−30.9606	−1.20241
$664$	−7.88035	−0.305817
$665$	9.47070	0.367258
$666$	−48.3197	−1.87235
$667$	−0.242812	−0.00940171
$668$	−22.9563	−0.888206
$669$	−56.8425	−2.19766
$670$	9.91019	0.382864
$671$	10.6596	0.411509
$672$	3.03412	0.117044
$673$	36.4900	1.40659	0.703294	−	0.710900i	$-0.251712\pi$
$673$	36.4900	1.40659	0.703294	+	0.710900i	$0.251712\pi$
$674$	3.69115	0.142178
$675$	35.0026	1.34725
$676$	−1.70835	−0.0657057
$677$	−23.9159	−0.919162	−0.459581	−	0.888136i	$-0.652000\pi$
$677$	−23.9159	−0.919162	−0.459581	+	0.888136i	$0.652000\pi$
$678$	50.6894	1.94672
$679$	−0.500285	−0.0191992
$680$	3.59501	0.137862
$681$	−9.21687	−0.353191
$682$	−28.6385	−1.09663
$683$	−23.5826	−0.902365	−0.451182	−	0.892432i	$-0.648998\pi$
$683$	−23.5826	−0.902365	−0.451182	+	0.892432i	$0.648998\pi$
$684$	49.6460	1.89826
$685$	−3.59067	−0.137192
$686$	−1.00000	−0.0381802
$687$	−59.4961	−2.26992
$688$	−7.64734	−0.291552
$689$	−17.3072	−0.659353
$690$	0.419374	0.0159653
$691$	−33.3748	−1.26964	−0.634819	−	0.772661i	$-0.718925\pi$
$691$	−33.3748	−1.26964	−0.634819	+	0.772661i	$0.718925\pi$
$692$	−12.8623	−0.488951
$693$	−18.8058	−0.714373
$694$	−14.0151	−0.532005
$695$	18.5562	0.703877
$696$	−6.31012	−0.239184
$697$	31.5180	1.19383
$698$	−20.7175	−0.784167
$699$	−52.3201	−1.97893
$700$	−3.59846	−0.136009
$701$	−37.3266	−1.40981	−0.704903	−	0.709304i	$-0.749010\pi$
$701$	−37.3266	−1.40981	−0.704903	+	0.709304i	$0.749010\pi$
$702$	−32.6861	−1.23366
$703$	62.2871	2.34920
$704$	−3.03030	−0.114209
$705$	−18.2278	−0.686499
$706$	−6.97123	−0.262366
$707$	3.42470	0.128799
$708$	−26.2011	−0.984697
$709$	−9.06311	−0.340372	−0.170186	−	0.985412i	$-0.554437\pi$
$709$	−9.06311	−0.340372	−0.170186	+	0.985412i	$0.554437\pi$
$710$	−16.0906	−0.603868
$711$	86.0481	3.22706
$712$	−15.0909	−0.565557
$713$	−1.10339	−0.0413223
$714$	−9.21363	−0.344812
$715$	12.0550	0.450832
$716$	17.0995	0.639037
$717$	−33.8074	−1.26256
$718$	−33.7058	−1.25789
$719$	23.8707	0.890228	0.445114	−	0.895474i	$-0.353163\pi$
$719$	23.8707	0.890228	0.445114	+	0.895474i	$0.353163\pi$
$720$	7.34697	0.273805
$721$	−4.21360	−0.156923
$722$	−44.9968	−1.67461
$723$	25.1986	0.937147
$724$	−23.4253	−0.870593
$725$	7.48378	0.277940
$726$	−5.51379	−0.204636
$727$	−20.3882	−0.756156	−0.378078	−	0.925774i	$-0.623415\pi$
$727$	−20.3882	−0.756156	−0.378078	+	0.925774i	$0.623415\pi$
$728$	3.36031	0.124541
$729$	−20.9230	−0.774925
$730$	9.76457	0.361403
$731$	23.2224	0.858913
$732$	10.6730	0.394487
$733$	39.5265	1.45994	0.729972	−	0.683478i	$-0.239533\pi$
$733$	39.5265	1.45994	0.729972	+	0.683478i	$0.239533\pi$
$734$	−2.77482	−0.102421
$735$	−3.59200	−0.132493
$736$	−0.116752	−0.00430355
$737$	25.3668	0.934397
$738$	64.4120	2.37104
$739$	42.8508	1.57629	0.788146	−	0.615488i	$-0.211041\pi$
$739$	42.8508	1.57629	0.788146	+	0.615488i	$0.211041\pi$
$740$	9.21769	0.338849
$741$	81.5626	2.99628
$742$	−5.15049	−0.189081
$743$	31.9663	1.17273	0.586365	−	0.810047i	$-0.300558\pi$
$743$	31.9663	1.17273	0.586365	+	0.810047i	$0.300558\pi$
$744$	−28.6746	−1.05126
$745$	−12.4442	−0.455919
$746$	−22.8504	−0.836612
$747$	48.9047	1.78933
$748$	9.20203	0.336460
$749$	−10.0314	−0.366538
$750$	−30.8857	−1.12778
$751$	5.62941	0.205420	0.102710	−	0.994711i	$-0.467249\pi$
$751$	5.62941	0.205420	0.102710	+	0.994711i	$0.467249\pi$
$752$	5.07456	0.185050
$753$	−83.0303	−3.02579
$754$	−6.98848	−0.254506
$755$	5.52564	0.201099
$756$	−9.72712	−0.353772
$757$	1.57752	0.0573361	0.0286681	−	0.999589i	$-0.490873\pi$
$757$	1.57752	0.0573361	0.0286681	+	0.999589i	$0.490873\pi$
$758$	−30.7041	−1.11522
$759$	1.07346	0.0389640
$760$	−9.47070	−0.343538
$761$	−1.29741	−0.0470310	−0.0235155	−	0.999723i	$-0.507486\pi$
$761$	−1.29741	−0.0470310	−0.0235155	+	0.999723i	$0.507486\pi$
$762$	9.48335	0.343546
$763$	−13.6309	−0.493473
$764$	8.99029	0.325257
$765$	−22.3103	−0.806631
$766$	35.7682	1.29236
$767$	−29.0178	−1.04777
$768$	−3.03412	−0.109485
$769$	11.2123	0.404324	0.202162	−	0.979352i	$-0.435203\pi$
$769$	11.2123	0.404324	0.202162	+	0.979352i	$0.435203\pi$
$770$	3.58748	0.129284
$771$	9.58654	0.345251
$772$	3.21904	0.115856
$773$	1.55374	0.0558842	0.0279421	−	0.999610i	$-0.491105\pi$
$773$	1.55374	0.0558842	0.0279421	+	0.999610i	$0.491105\pi$
$774$	47.4587	1.70587
$775$	34.0080	1.22160
$776$	0.500285	0.0179592
$777$	−23.6239	−0.847504
$778$	−16.8504	−0.604116
$779$	−83.0311	−2.97490
$780$	12.0702	0.432183
$781$	−41.1864	−1.47377
$782$	0.354538	0.0126783
$783$	20.2297	0.722949
$784$	1.00000	0.0357143
$785$	−19.9668	−0.712647
$786$	−34.5823	−1.23351
$787$	−26.6356	−0.949457	−0.474729	−	0.880132i	$-0.657454\pi$
$787$	−26.6356	−0.949457	−0.474729	+	0.880132i	$0.657454\pi$
$788$	22.5973	0.804997
$789$	−26.3214	−0.937068
$790$	−16.4149	−0.584017
$791$	16.7064	0.594013
$792$	18.8058	0.668234
$793$	11.8204	0.419756
$794$	−0.209575	−0.00743754
$795$	−18.5006	−0.656147
$796$	−17.1083	−0.606386
$797$	43.0806	1.52599	0.762997	−	0.646402i	$-0.223727\pi$
$797$	43.0806	1.52599	0.762997	+	0.646402i	$0.223727\pi$
$798$	24.2724	0.859233
$799$	−15.4098	−0.545158
$800$	3.59846	0.127225
$801$	93.6529	3.30906
$802$	−0.774350	−0.0273433
$803$	24.9940	0.882020
$804$	25.3987	0.895745
$805$	0.138219	0.00487159
$806$	−31.7573	−1.11860
$807$	−8.91993	−0.313996
$808$	−3.42470	−0.120480
$809$	24.3461	0.855965	0.427982	−	0.903787i	$-0.359224\pi$
$809$	24.3461	0.855965	0.427982	+	0.903787i	$0.359224\pi$
$810$	−12.8989	−0.453221
$811$	11.3242	0.397648	0.198824	−	0.980035i	$-0.436288\pi$
$811$	11.3242	0.397648	0.198824	+	0.980035i	$0.436288\pi$
$812$	−2.07972	−0.0729838
$813$	−92.8975	−3.25806
$814$	23.5942	0.826976
$815$	−26.4555	−0.926696
$816$	9.21363	0.322542
$817$	−61.1772	−2.14032
$818$	−19.2114	−0.671711
$819$	−20.8537	−0.728689
$820$	−12.2875	−0.429099
$821$	−7.73256	−0.269868	−0.134934	−	0.990855i	$-0.543082\pi$
$821$	−7.73256	−0.269868	−0.134934	+	0.990855i	$0.543082\pi$
$822$	−9.20249	−0.320974
$823$	34.7343	1.21076	0.605381	−	0.795936i	$-0.293021\pi$
$823$	34.7343	1.21076	0.605381	+	0.795936i	$0.293021\pi$
$824$	4.21360	0.146788
$825$	−33.0854	−1.15188
$826$	−8.63546	−0.300466
$827$	−10.6271	−0.369539	−0.184770	−	0.982782i	$-0.559154\pi$
$827$	−10.6271	−0.369539	−0.184770	+	0.982782i	$0.559154\pi$
$828$	0.724554	0.0251800
$829$	−16.6510	−0.578314	−0.289157	−	0.957282i	$-0.593375\pi$
$829$	−16.6510	−0.578314	−0.289157	+	0.957282i	$0.593375\pi$
$830$	−9.32929	−0.323824
$831$	73.9700	2.56599
$832$	−3.36031	−0.116498
$833$	−3.03667	−0.105214
$834$	47.5576	1.64678
$835$	−27.1772	−0.940506
$836$	−24.2418	−0.838421
$837$	91.9282	3.17750
$838$	−25.6416	−0.885775
$839$	1.25887	0.0434609	0.0217304	−	0.999764i	$-0.493082\pi$
$839$	1.25887	0.0434609	0.0217304	+	0.999764i	$0.493082\pi$
$840$	3.59200	0.123936
$841$	−24.6748	−0.850854
$842$	−33.0431	−1.13874
$843$	28.1383	0.969136
$844$	16.3832	0.563932
$845$	−2.02246	−0.0695747
$846$	−31.4922	−1.08273
$847$	−1.81726	−0.0624418
$848$	5.15049	0.176869
$849$	84.0206	2.88358
$850$	−10.9273	−0.374804
$851$	0.909043	0.0311616
$852$	−41.2384	−1.41280
$853$	−3.00260	−0.102807	−0.0514035	−	0.998678i	$-0.516369\pi$
$853$	−3.00260	−0.102807	−0.0514035	+	0.998678i	$0.516369\pi$
$854$	3.51766	0.120372
$855$	58.7743	2.01004
$856$	10.0314	0.342865
$857$	−22.3279	−0.762705	−0.381352	−	0.924430i	$-0.624542\pi$
$857$	−22.3279	−0.762705	−0.381352	+	0.924430i	$0.624542\pi$
$858$	30.8957	1.05476
$859$	−35.0293	−1.19518	−0.597592	−	0.801801i	$-0.703876\pi$
$859$	−35.0293	−1.19518	−0.597592	+	0.801801i	$0.703876\pi$
$860$	−9.05343	−0.308720
$861$	31.4916	1.07323
$862$	1.00000	0.0340601
$863$	34.5011	1.17443	0.587215	−	0.809431i	$-0.300224\pi$
$863$	34.5011	1.17443	0.587215	+	0.809431i	$0.300224\pi$
$864$	9.72712	0.330923
$865$	−15.2272	−0.517742
$866$	−32.4979	−1.10432
$867$	23.6013	0.801544
$868$	−9.45071	−0.320778
$869$	−42.0167	−1.42532
$870$	−7.47034	−0.253268
$871$	28.1292	0.953122
$872$	13.6309	0.461602
$873$	−3.10473	−0.105079
$874$	−0.933995	−0.0315929
$875$	−10.1794	−0.344128
$876$	25.0255	0.845535
$877$	31.8062	1.07402	0.537009	−	0.843576i	$-0.319554\pi$
$877$	31.8062	1.07402	0.537009	+	0.843576i	$0.319554\pi$
$878$	7.21470	0.243484
$879$	49.1204	1.65679
$880$	−3.58748	−0.120934
$881$	29.6529	0.999032	0.499516	−	0.866305i	$-0.333511\pi$
$881$	29.6529	0.999032	0.499516	+	0.866305i	$0.333511\pi$
$882$	−6.20591	−0.208964
$883$	10.6830	0.359511	0.179755	−	0.983711i	$-0.442469\pi$
$883$	10.6830	0.359511	0.179755	+	0.983711i	$0.442469\pi$
$884$	10.2041	0.343202
$885$	−31.0186	−1.04268
$886$	−5.38931	−0.181058
$887$	15.2559	0.512241	0.256121	−	0.966645i	$-0.417556\pi$
$887$	15.2559	0.512241	0.256121	+	0.966645i	$0.417556\pi$
$888$	23.6239	0.792767
$889$	3.12557	0.104828
$890$	−17.8657	−0.598858
$891$	−33.0169	−1.10611
$892$	18.7344	0.627274
$893$	40.5955	1.35848
$894$	−31.8931	−1.06666
$895$	20.2435	0.676665
$896$	−1.00000	−0.0334077
$897$	1.19036	0.0397449
$898$	−19.7980	−0.660667
$899$	19.6548	0.655524
$900$	−22.3317	−0.744390
$901$	−15.6403	−0.521055
$902$	−31.4519	−1.04724
$903$	23.2030	0.772147
$904$	−16.7064	−0.555648
$905$	−27.7324	−0.921856
$906$	14.1616	0.470489
$907$	18.5827	0.617028	0.308514	−	0.951220i	$-0.400168\pi$
$907$	18.5827	0.617028	0.308514	+	0.951220i	$0.400168\pi$
$908$	3.03774	0.100811
$909$	21.2534	0.704929
$910$	3.97815	0.131875
$911$	36.2034	1.19947	0.599736	−	0.800198i	$-0.295272\pi$
$911$	36.2034	1.19947	0.599736	+	0.800198i	$0.295272\pi$
$912$	−24.2724	−0.803739
$913$	−23.8799	−0.790308
$914$	38.6842	1.27956
$915$	12.6354	0.417715
$916$	19.6090	0.647899
$917$	−11.3978	−0.376388
$918$	−29.5381	−0.974901
$919$	−27.7105	−0.914085	−0.457042	−	0.889445i	$-0.651091\pi$
$919$	−27.7105	−0.914085	−0.457042	+	0.889445i	$0.651091\pi$
$920$	−0.138219	−0.00455695
$921$	−13.8775	−0.457278
$922$	24.0943	0.793503
$923$	−45.6717	−1.50330
$924$	9.19432	0.302471
$925$	−28.0179	−0.921223
$926$	−31.9478	−1.04987
$927$	−26.1492	−0.858853
$928$	2.07972	0.0682701
$929$	17.6060	0.577636	0.288818	−	0.957384i	$-0.406738\pi$
$929$	17.6060	0.577636	0.288818	+	0.957384i	$0.406738\pi$
$930$	−33.9469	−1.11316
$931$	7.99980	0.262183
$932$	17.2439	0.564842
$933$	3.05523	0.100024
$934$	−19.5476	−0.639618
$935$	10.8940	0.356271
$936$	20.8537	0.681626
$937$	5.79394	0.189280	0.0946398	−	0.995512i	$-0.469830\pi$
$937$	5.79394	0.189280	0.0946398	+	0.995512i	$0.469830\pi$
$938$	8.37103	0.273324
$939$	−60.7490	−1.98247
$940$	6.00760	0.195946
$941$	22.9288	0.747459	0.373729	−	0.927538i	$-0.378079\pi$
$941$	22.9288	0.747459	0.373729	+	0.927538i	$0.378079\pi$
$942$	−51.1729	−1.66730
$943$	−1.21179	−0.0394613
$944$	8.63546	0.281060
$945$	−11.5156	−0.374603
$946$	−23.1738	−0.753444
$947$	12.7619	0.414707	0.207353	−	0.978266i	$-0.433515\pi$
$947$	12.7619	0.414707	0.207353	+	0.978266i	$0.433515\pi$
$948$	−42.0697	−1.36636
$949$	27.7159	0.899696
$950$	28.7870	0.933972
$951$	78.2131	2.53623
$952$	3.03667	0.0984190
$953$	17.7769	0.575850	0.287925	−	0.957653i	$-0.407035\pi$
$953$	17.7769	0.575850	0.287925	+	0.957653i	$0.407035\pi$
$954$	−31.9635	−1.03486
$955$	10.6433	0.344410
$956$	11.1424	0.360371
$957$	−19.1216	−0.618113
$958$	−13.0944	−0.423059
$959$	−3.03300	−0.0979406
$960$	−3.59200	−0.115931
$961$	58.3159	1.88116
$962$	26.1636	0.843549
$963$	−62.2538	−2.00610
$964$	−8.30507	−0.267488
$965$	3.81091	0.122678
$966$	0.354241	0.0113975
$967$	−34.4431	−1.10762	−0.553808	−	0.832644i	$-0.686826\pi$
$967$	−34.4431	−1.10762	−0.553808	+	0.832644i	$0.686826\pi$
$968$	1.81726	0.0584090
$969$	73.7072	2.36782
$970$	0.592271	0.0190167
$971$	10.9122	0.350191	0.175095	−	0.984551i	$-0.443977\pi$
$971$	10.9122	0.350191	0.175095	+	0.984551i	$0.443977\pi$
$972$	−3.87715	−0.124359
$973$	15.6742	0.502493
$974$	−26.4373	−0.847107
$975$	−36.6884	−1.17497
$976$	−3.51766	−0.112598
$977$	44.4314	1.42149	0.710744	−	0.703451i	$-0.248359\pi$
$977$	44.4314	1.42149	0.710744	+	0.703451i	$0.248359\pi$
$978$	−67.8026	−2.16809
$979$	−45.7301	−1.46154
$980$	1.18387	0.0378172
$981$	−84.5923	−2.70083
$982$	22.3414	0.712943
$983$	5.01493	0.159951	0.0799756	−	0.996797i	$-0.474516\pi$
$983$	5.01493	0.159951	0.0799756	+	0.996797i	$0.474516\pi$
$984$	−31.4916	−1.00392
$985$	26.7522	0.852397
$986$	−6.31541	−0.201124
$987$	−15.3968	−0.490087
$988$	−26.8818	−0.855223
$989$	−0.892844	−0.0283908
$990$	22.2635	0.707582
$991$	28.6181	0.909085	0.454542	−	0.890725i	$-0.349803\pi$
$991$	28.6181	0.909085	0.454542	+	0.890725i	$0.349803\pi$
$992$	9.45071	0.300060
$993$	22.9950	0.729724
$994$	−13.5915	−0.431097
$995$	−20.2539	−0.642092
$996$	−23.9100	−0.757616
$997$	−40.9366	−1.29647	−0.648237	−	0.761439i	$-0.724493\pi$
$997$	−40.9366	−1.29647	−0.648237	+	0.761439i	$0.724493\pi$
$998$	−36.3753	−1.15144
$999$	−75.7362	−2.39619

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.3	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.3	✓	27	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.03412 q^{3} +1.00000 q^{4} +1.18387 q^{5} +3.03412 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.20591 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.03412 q^{3} +1.00000 q^{4} +1.18387 q^{5} +3.03412 q^{6} +1.00000 q^{7} -1.00000 q^{8} +6.20591 q^{9} -1.18387 q^{10} -3.03030 q^{11} -3.03412 q^{12} -3.36031 q^{13} -1.00000 q^{14} -3.59200 q^{15} +1.00000 q^{16} -3.03667 q^{17} -6.20591 q^{18} +7.99980 q^{19} +1.18387 q^{20} -3.03412 q^{21} +3.03030 q^{22} +0.116752 q^{23} +3.03412 q^{24} -3.59846 q^{25} +3.36031 q^{26} -9.72712 q^{27} +1.00000 q^{28} -2.07972 q^{29} +3.59200 q^{30} -9.45071 q^{31} -1.00000 q^{32} +9.19432 q^{33} +3.03667 q^{34} +1.18387 q^{35} +6.20591 q^{36} +7.78608 q^{37} -7.99980 q^{38} +10.1956 q^{39} -1.18387 q^{40} -10.3791 q^{41} +3.03412 q^{42} -7.64734 q^{43} -3.03030 q^{44} +7.34697 q^{45} -0.116752 q^{46} +5.07456 q^{47} -3.03412 q^{48} +1.00000 q^{49} +3.59846 q^{50} +9.21363 q^{51} -3.36031 q^{52} +5.15049 q^{53} +9.72712 q^{54} -3.58748 q^{55} -1.00000 q^{56} -24.2724 q^{57} +2.07972 q^{58} +8.63546 q^{59} -3.59200 q^{60} -3.51766 q^{61} +9.45071 q^{62} +6.20591 q^{63} +1.00000 q^{64} -3.97815 q^{65} -9.19432 q^{66} -8.37103 q^{67} -3.03667 q^{68} -0.354241 q^{69} -1.18387 q^{70} +13.5915 q^{71} -6.20591 q^{72} -8.24803 q^{73} -7.78608 q^{74} +10.9182 q^{75} +7.99980 q^{76} -3.03030 q^{77} -10.1956 q^{78} +13.8655 q^{79} +1.18387 q^{80} +10.8956 q^{81} +10.3791 q^{82} +7.88035 q^{83} -3.03412 q^{84} -3.59501 q^{85} +7.64734 q^{86} +6.31012 q^{87} +3.03030 q^{88} +15.0909 q^{89} -7.34697 q^{90} -3.36031 q^{91} +0.116752 q^{92} +28.6746 q^{93} -5.07456 q^{94} +9.47070 q^{95} +3.03412 q^{96} -0.500285 q^{97} -1.00000 q^{98} -18.8058 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9} - 9 q^{10} + 24 q^{11} + 4 q^{12} - 13 q^{13} - 27 q^{14} + 16 q^{15} + 27 q^{16} - 5 q^{17} - 35 q^{18} + q^{19} + 9 q^{20} + 4 q^{21} - 24 q^{22} + 32 q^{23} - 4 q^{24} + 30 q^{25} + 13 q^{26} + q^{27} + 27 q^{28} + 26 q^{29} - 16 q^{30} + 21 q^{31} - 27 q^{32} + 7 q^{33} + 5 q^{34} + 9 q^{35} + 35 q^{36} + 4 q^{37} - q^{38} + 13 q^{39} - 9 q^{40} + 31 q^{41} - 4 q^{42} - 13 q^{43} + 24 q^{44} + 19 q^{45} - 32 q^{46} + 41 q^{47} + 4 q^{48} + 27 q^{49} - 30 q^{50} + 21 q^{51} - 13 q^{52} + 29 q^{53} - q^{54} + 9 q^{55} - 27 q^{56} - 26 q^{58} + 36 q^{59} + 16 q^{60} + q^{61} - 21 q^{62} + 35 q^{63} + 27 q^{64} + 46 q^{65} - 7 q^{66} - 2 q^{67} - 5 q^{68} + 43 q^{69} - 9 q^{70} + 70 q^{71} - 35 q^{72} - 21 q^{73} - 4 q^{74} + 37 q^{75} + q^{76} + 24 q^{77} - 13 q^{78} + 19 q^{79} + 9 q^{80} + 67 q^{81} - 31 q^{82} + 25 q^{83} + 4 q^{84} - 6 q^{85} + 13 q^{86} - 9 q^{87} - 24 q^{88} + 85 q^{89} - 19 q^{90} - 13 q^{91} + 32 q^{92} + 23 q^{93} - 41 q^{94} + 77 q^{95} - 4 q^{96} - 2 q^{97} - 27 q^{98} + 38 q^{99}+O(q^{100}) \) 27 * q - 27 * q^2 + 4 * q^3 + 27 * q^4 + 9 * q^5 - 4 * q^6 + 27 * q^7 - 27 * q^8 + 35 * q^9 - 9 * q^10 + 24 * q^11 + 4 * q^12 - 13 * q^13 - 27 * q^14 + 16 * q^15 + 27 * q^16 - 5 * q^17 - 35 * q^18 + q^19 + 9 * q^20 + 4 * q^21 - 24 * q^22 + 32 * q^23 - 4 * q^24 + 30 * q^25 + 13 * q^26 + q^27 + 27 * q^28 + 26 * q^29 - 16 * q^30 + 21 * q^31 - 27 * q^32 + 7 * q^33 + 5 * q^34 + 9 * q^35 + 35 * q^36 + 4 * q^37 - q^38 + 13 * q^39 - 9 * q^40 + 31 * q^41 - 4 * q^42 - 13 * q^43 + 24 * q^44 + 19 * q^45 - 32 * q^46 + 41 * q^47 + 4 * q^48 + 27 * q^49 - 30 * q^50 + 21 * q^51 - 13 * q^52 + 29 * q^53 - q^54 + 9 * q^55 - 27 * q^56 - 26 * q^58 + 36 * q^59 + 16 * q^60 + q^61 - 21 * q^62 + 35 * q^63 + 27 * q^64 + 46 * q^65 - 7 * q^66 - 2 * q^67 - 5 * q^68 + 43 * q^69 - 9 * q^70 + 70 * q^71 - 35 * q^72 - 21 * q^73 - 4 * q^74 + 37 * q^75 + q^76 + 24 * q^77 - 13 * q^78 + 19 * q^79 + 9 * q^80 + 67 * q^81 - 31 * q^82 + 25 * q^83 + 4 * q^84 - 6 * q^85 + 13 * q^86 - 9 * q^87 - 24 * q^88 + 85 * q^89 - 19 * q^90 - 13 * q^91 + 32 * q^92 + 23 * q^93 - 41 * q^94 + 77 * q^95 - 4 * q^96 - 2 * q^97 - 27 * q^98 + 38 * q^99

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