LMFDB - Embedded newform 6034.2.a.p.1.9

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			1.9
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.743500 q^{3} +1.00000 q^{4} -1.77052 q^{5} +0.743500 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.44721 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.743500 q^{3} +1.00000 q^{4} -1.77052 q^{5} +0.743500 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.44721 q^{9} +1.77052 q^{10} +2.78507 q^{11} -0.743500 q^{12} +5.15009 q^{13} -1.00000 q^{14} +1.31638 q^{15} +1.00000 q^{16} +0.832902 q^{17} +2.44721 q^{18} +4.69383 q^{19} -1.77052 q^{20} -0.743500 q^{21} -2.78507 q^{22} +5.67585 q^{23} +0.743500 q^{24} -1.86525 q^{25} -5.15009 q^{26} +4.05000 q^{27} +1.00000 q^{28} +5.31032 q^{29} -1.31638 q^{30} -4.78377 q^{31} -1.00000 q^{32} -2.07070 q^{33} -0.832902 q^{34} -1.77052 q^{35} -2.44721 q^{36} -3.10830 q^{37} -4.69383 q^{38} -3.82909 q^{39} +1.77052 q^{40} -0.224205 q^{41} +0.743500 q^{42} +1.94741 q^{43} +2.78507 q^{44} +4.33284 q^{45} -5.67585 q^{46} +6.39559 q^{47} -0.743500 q^{48} +1.00000 q^{49} +1.86525 q^{50} -0.619262 q^{51} +5.15009 q^{52} +6.26838 q^{53} -4.05000 q^{54} -4.93102 q^{55} -1.00000 q^{56} -3.48986 q^{57} -5.31032 q^{58} +13.5983 q^{59} +1.31638 q^{60} +6.18845 q^{61} +4.78377 q^{62} -2.44721 q^{63} +1.00000 q^{64} -9.11835 q^{65} +2.07070 q^{66} -11.3372 q^{67} +0.832902 q^{68} -4.21999 q^{69} +1.77052 q^{70} -14.4224 q^{71} +2.44721 q^{72} +0.347483 q^{73} +3.10830 q^{74} +1.38681 q^{75} +4.69383 q^{76} +2.78507 q^{77} +3.82909 q^{78} -9.73274 q^{79} -1.77052 q^{80} +4.33045 q^{81} +0.224205 q^{82} -11.8026 q^{83} -0.743500 q^{84} -1.47467 q^{85} -1.94741 q^{86} -3.94822 q^{87} -2.78507 q^{88} -6.60822 q^{89} -4.33284 q^{90} +5.15009 q^{91} +5.67585 q^{92} +3.55673 q^{93} -6.39559 q^{94} -8.31053 q^{95} +0.743500 q^{96} -2.27035 q^{97} -1.00000 q^{98} -6.81564 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.743500	−0.429260	−0.214630	−	0.976695i	$-0.568855\pi$
$3$	−0.743500	−0.429260	−0.214630	+	0.976695i	$0.568855\pi$
$4$	1.00000	0.500000
$5$	−1.77052	−0.791801	−0.395901	−	0.918293i	$-0.629568\pi$
$5$	−1.77052	−0.791801	−0.395901	+	0.918293i	$0.629568\pi$
$6$	0.743500	0.303532
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.00000	−0.353553
$9$	−2.44721	−0.815736
$10$	1.77052	0.559888
$11$	2.78507	0.839729	0.419864	−	0.907587i	$-0.362078\pi$
$11$	2.78507	0.839729	0.419864	+	0.907587i	$0.362078\pi$
$12$	−0.743500	−0.214630
$13$	5.15009	1.42838	0.714190	−	0.699952i	$-0.246795\pi$
$13$	5.15009	1.42838	0.714190	+	0.699952i	$0.246795\pi$
$14$	−1.00000	−0.267261
$15$	1.31638	0.339888
$16$	1.00000	0.250000
$17$	0.832902	0.202008	0.101004	−	0.994886i	$-0.467794\pi$
$17$	0.832902	0.202008	0.101004	+	0.994886i	$0.467794\pi$
$18$	2.44721	0.576813
$19$	4.69383	1.07684	0.538420	−	0.842677i	$-0.319022\pi$
$19$	4.69383	1.07684	0.538420	+	0.842677i	$0.319022\pi$
$20$	−1.77052	−0.395901
$21$	−0.743500	−0.162245
$22$	−2.78507	−0.593778
$23$	5.67585	1.18350	0.591748	−	0.806123i	$-0.298438\pi$
$23$	5.67585	1.18350	0.591748	+	0.806123i	$0.298438\pi$
$24$	0.743500	0.151766
$25$	−1.86525	−0.373051
$26$	−5.15009	−1.01002
$27$	4.05000	0.779422
$28$	1.00000	0.188982
$29$	5.31032	0.986102	0.493051	−	0.870000i	$-0.335882\pi$
$29$	5.31032	0.986102	0.493051	+	0.870000i	$0.335882\pi$
$30$	−1.31638	−0.240337
$31$	−4.78377	−0.859191	−0.429595	−	0.903022i	$-0.641344\pi$
$31$	−4.78377	−0.859191	−0.429595	+	0.903022i	$0.641344\pi$
$32$	−1.00000	−0.176777
$33$	−2.07070	−0.360462
$34$	−0.832902	−0.142841
$35$	−1.77052	−0.299273
$36$	−2.44721	−0.407868
$37$	−3.10830	−0.511002	−0.255501	−	0.966809i	$-0.582240\pi$
$37$	−3.10830	−0.511002	−0.255501	+	0.966809i	$0.582240\pi$
$38$	−4.69383	−0.761440
$39$	−3.82909	−0.613145
$40$	1.77052	0.279944
$41$	−0.224205	−0.0350149	−0.0175075	−	0.999847i	$-0.505573\pi$
$41$	−0.224205	−0.0350149	−0.0175075	+	0.999847i	$0.505573\pi$
$42$	0.743500	0.114724
$43$	1.94741	0.296978	0.148489	−	0.988914i	$-0.452559\pi$
$43$	1.94741	0.296978	0.148489	+	0.988914i	$0.452559\pi$
$44$	2.78507	0.419864
$45$	4.33284	0.645901
$46$	−5.67585	−0.836859
$47$	6.39559	0.932893	0.466446	−	0.884549i	$-0.345534\pi$
$47$	6.39559	0.932893	0.466446	+	0.884549i	$0.345534\pi$
$48$	−0.743500	−0.107315
$49$	1.00000	0.142857
$50$	1.86525	0.263787
$51$	−0.619262	−0.0867140
$52$	5.15009	0.714190
$53$	6.26838	0.861028	0.430514	−	0.902584i	$-0.358332\pi$
$53$	6.26838	0.861028	0.430514	+	0.902584i	$0.358332\pi$
$54$	−4.05000	−0.551135
$55$	−4.93102	−0.664899
$56$	−1.00000	−0.133631
$57$	−3.48986	−0.462244
$58$	−5.31032	−0.697280
$59$	13.5983	1.77035	0.885177	−	0.465254i	$-0.154037\pi$
$59$	13.5983	1.77035	0.885177	+	0.465254i	$0.154037\pi$
$60$	1.31638	0.169944
$61$	6.18845	0.792350	0.396175	−	0.918175i	$-0.370337\pi$
$61$	6.18845	0.792350	0.396175	+	0.918175i	$0.370337\pi$
$62$	4.78377	0.607540
$63$	−2.44721	−0.308319
$64$	1.00000	0.125000
$65$	−9.11835	−1.13099
$66$	2.07070	0.254885
$67$	−11.3372	−1.38506	−0.692531	−	0.721388i	$-0.743504\pi$
$67$	−11.3372	−1.38506	−0.692531	+	0.721388i	$0.743504\pi$
$68$	0.832902	0.101004
$69$	−4.21999	−0.508027
$70$	1.77052	0.211618
$71$	−14.4224	−1.71163	−0.855813	−	0.517285i	$-0.826943\pi$
$71$	−14.4224	−1.71163	−0.855813	+	0.517285i	$0.826943\pi$
$72$	2.44721	0.288406
$73$	0.347483	0.0406699	0.0203349	−	0.999793i	$-0.493527\pi$
$73$	0.347483	0.0406699	0.0203349	+	0.999793i	$0.493527\pi$
$74$	3.10830	0.361333
$75$	1.38681	0.160136
$76$	4.69383	0.538420
$77$	2.78507	0.317388
$78$	3.82909	0.433559
$79$	−9.73274	−1.09502	−0.547509	−	0.836800i	$-0.684424\pi$
$79$	−9.73274	−1.09502	−0.547509	+	0.836800i	$0.684424\pi$
$80$	−1.77052	−0.197950
$81$	4.33045	0.481162
$82$	0.224205	0.0247593
$83$	−11.8026	−1.29551	−0.647754	−	0.761849i	$-0.724292\pi$
$83$	−11.8026	−1.29551	−0.647754	+	0.761849i	$0.724292\pi$
$84$	−0.743500	−0.0811225
$85$	−1.47467	−0.159951
$86$	−1.94741	−0.209995
$87$	−3.94822	−0.423294
$88$	−2.78507	−0.296889
$89$	−6.60822	−0.700470	−0.350235	−	0.936662i	$-0.613898\pi$
$89$	−6.60822	−0.700470	−0.350235	+	0.936662i	$0.613898\pi$
$90$	−4.33284	−0.456721
$91$	5.15009	0.539877
$92$	5.67585	0.591748
$93$	3.55673	0.368816
$94$	−6.39559	−0.659655
$95$	−8.31053	−0.852643
$96$	0.743500	0.0758831
$97$	−2.27035	−0.230519	−0.115260	−	0.993335i	$-0.536770\pi$
$97$	−2.27035	−0.230519	−0.115260	+	0.993335i	$0.536770\pi$
$98$	−1.00000	−0.101015
$99$	−6.81564	−0.684997
$100$	−1.86525	−0.186525
$101$	−1.39277	−0.138585	−0.0692927	−	0.997596i	$-0.522074\pi$
$101$	−1.39277	−0.138585	−0.0692927	+	0.997596i	$0.522074\pi$
$102$	0.619262	0.0613161
$103$	−7.71647	−0.760327	−0.380163	−	0.924919i	$-0.624132\pi$
$103$	−7.71647	−0.760327	−0.380163	+	0.924919i	$0.624132\pi$
$104$	−5.15009	−0.505008
$105$	1.31638	0.128466
$106$	−6.26838	−0.608838
$107$	−7.49605	−0.724670	−0.362335	−	0.932048i	$-0.618020\pi$
$107$	−7.49605	−0.724670	−0.362335	+	0.932048i	$0.618020\pi$
$108$	4.05000	0.389711
$109$	9.90056	0.948302	0.474151	−	0.880444i	$-0.342755\pi$
$109$	9.90056	0.948302	0.474151	+	0.880444i	$0.342755\pi$
$110$	4.93102	0.470154
$111$	2.31102	0.219353
$112$	1.00000	0.0944911
$113$	8.54464	0.803812	0.401906	−	0.915681i	$-0.368348\pi$
$113$	8.54464	0.803812	0.401906	+	0.915681i	$0.368348\pi$
$114$	3.48986	0.326856
$115$	−10.0492	−0.937094
$116$	5.31032	0.493051
$117$	−12.6034	−1.16518
$118$	−13.5983	−1.25183
$119$	0.832902	0.0763520
$120$	−1.31638	−0.120169
$121$	−3.24341	−0.294855
$122$	−6.18845	−0.560276
$123$	0.166696	0.0150305
$124$	−4.78377	−0.429595
$125$	12.1551	1.08718
$126$	2.44721	0.218015
$127$	4.61128	0.409185	0.204593	−	0.978847i	$-0.434413\pi$
$127$	4.61128	0.409185	0.204593	+	0.978847i	$0.434413\pi$
$128$	−1.00000	−0.0883883
$129$	−1.44790	−0.127481
$130$	9.11835	0.799732
$131$	3.65169	0.319050	0.159525	−	0.987194i	$-0.449004\pi$
$131$	3.65169	0.319050	0.159525	+	0.987194i	$0.449004\pi$
$132$	−2.07070	−0.180231
$133$	4.69383	0.407007
$134$	11.3372	0.979386
$135$	−7.17061	−0.617148
$136$	−0.832902	−0.0714207
$137$	19.3538	1.65351	0.826753	−	0.562566i	$-0.190186\pi$
$137$	19.3538	1.65351	0.826753	+	0.562566i	$0.190186\pi$
$138$	4.21999	0.359230
$139$	4.60882	0.390915	0.195457	−	0.980712i	$-0.437381\pi$
$139$	4.60882	0.390915	0.195457	+	0.980712i	$0.437381\pi$
$140$	−1.77052	−0.149636
$141$	−4.75512	−0.400453
$142$	14.4224	1.21030
$143$	14.3434	1.19945
$144$	−2.44721	−0.203934
$145$	−9.40204	−0.780797
$146$	−0.347483	−0.0287579
$147$	−0.743500	−0.0613228
$148$	−3.10830	−0.255501
$149$	−9.54348	−0.781833	−0.390916	−	0.920426i	$-0.627842\pi$
$149$	−9.54348	−0.781833	−0.390916	+	0.920426i	$0.627842\pi$
$150$	−1.38681	−0.113233
$151$	15.6485	1.27345	0.636727	−	0.771090i	$-0.280288\pi$
$151$	15.6485	1.27345	0.636727	+	0.771090i	$0.280288\pi$
$152$	−4.69383	−0.380720
$153$	−2.03828	−0.164786
$154$	−2.78507	−0.224427
$155$	8.46977	0.680308
$156$	−3.82909	−0.306573
$157$	−1.65581	−0.132148	−0.0660740	−	0.997815i	$-0.521047\pi$
$157$	−1.65581	−0.132148	−0.0660740	+	0.997815i	$0.521047\pi$
$158$	9.73274	0.774295
$159$	−4.66053	−0.369604
$160$	1.77052	0.139972
$161$	5.67585	0.447320
$162$	−4.33045	−0.340233
$163$	0.0711125	0.00556996	0.00278498	−	0.999996i	$-0.499114\pi$
$163$	0.0711125	0.00556996	0.00278498	+	0.999996i	$0.499114\pi$
$164$	−0.224205	−0.0175075
$165$	3.66621	0.285414
$166$	11.8026	0.916063
$167$	1.52123	0.117716	0.0588581	−	0.998266i	$-0.481254\pi$
$167$	1.52123	0.117716	0.0588581	+	0.998266i	$0.481254\pi$
$168$	0.743500	0.0573622
$169$	13.5235	1.04027
$170$	1.47467	0.113102
$171$	−11.4868	−0.878417
$172$	1.94741	0.148489
$173$	8.15788	0.620232	0.310116	−	0.950699i	$-0.399632\pi$
$173$	8.15788	0.620232	0.310116	+	0.950699i	$0.399632\pi$
$174$	3.94822	0.299314
$175$	−1.86525	−0.141000
$176$	2.78507	0.209932
$177$	−10.1104	−0.759942
$178$	6.60822	0.495307
$179$	20.2640	1.51460	0.757302	−	0.653065i	$-0.226517\pi$
$179$	20.2640	1.51460	0.757302	+	0.653065i	$0.226517\pi$
$180$	4.33284	0.322951
$181$	−10.1111	−0.751552	−0.375776	−	0.926711i	$-0.622624\pi$
$181$	−10.1111	−0.751552	−0.375776	+	0.926711i	$0.622624\pi$
$182$	−5.15009	−0.381750
$183$	−4.60111	−0.340124
$184$	−5.67585	−0.418429
$185$	5.50332	0.404612
$186$	−3.55673	−0.260792
$187$	2.31969	0.169632
$188$	6.39559	0.466446
$189$	4.05000	0.294594
$190$	8.31053	0.602910
$191$	−16.7133	−1.20933	−0.604667	−	0.796478i	$-0.706694\pi$
$191$	−16.7133	−1.20933	−0.604667	+	0.796478i	$0.706694\pi$
$192$	−0.743500	−0.0536575
$193$	2.63256	0.189496	0.0947478	−	0.995501i	$-0.469796\pi$
$193$	2.63256	0.189496	0.0947478	+	0.995501i	$0.469796\pi$
$194$	2.27035	0.163002
$195$	6.77949	0.485489
$196$	1.00000	0.0714286
$197$	17.5159	1.24795	0.623977	−	0.781443i	$-0.285516\pi$
$197$	17.5159	1.24795	0.623977	+	0.781443i	$0.285516\pi$
$198$	6.81564	0.484366
$199$	−22.3258	−1.58263	−0.791317	−	0.611406i	$-0.790604\pi$
$199$	−22.3258	−1.58263	−0.791317	+	0.611406i	$0.790604\pi$
$200$	1.86525	0.131893
$201$	8.42921	0.594551
$202$	1.39277	0.0979946
$203$	5.31032	0.372712
$204$	−0.619262	−0.0433570
$205$	0.396960	0.0277249
$206$	7.71647	0.537632
$207$	−13.8900	−0.965421
$208$	5.15009	0.357095
$209$	13.0726	0.904253
$210$	−1.31638	−0.0908390
$211$	15.2668	1.05101	0.525506	−	0.850790i	$-0.323876\pi$
$211$	15.2668	1.05101	0.525506	+	0.850790i	$0.323876\pi$
$212$	6.26838	0.430514
$213$	10.7231	0.734732
$214$	7.49605	0.512419
$215$	−3.44794	−0.235148
$216$	−4.05000	−0.275567
$217$	−4.78377	−0.324744
$218$	−9.90056	−0.670551
$219$	−0.258354	−0.0174579
$220$	−4.93102	−0.332449
$221$	4.28952	0.288545
$222$	−2.31102	−0.155106
$223$	−9.89211	−0.662425	−0.331212	−	0.943556i	$-0.607458\pi$
$223$	−9.89211	−0.662425	−0.331212	+	0.943556i	$0.607458\pi$
$224$	−1.00000	−0.0668153
$225$	4.56466	0.304311
$226$	−8.54464	−0.568381
$227$	4.50463	0.298983	0.149491	−	0.988763i	$-0.452236\pi$
$227$	4.50463	0.298983	0.149491	+	0.988763i	$0.452236\pi$
$228$	−3.48986	−0.231122
$229$	−12.5414	−0.828756	−0.414378	−	0.910105i	$-0.636001\pi$
$229$	−12.5414	−0.828756	−0.414378	+	0.910105i	$0.636001\pi$
$230$	10.0492	0.662626
$231$	−2.07070	−0.136242
$232$	−5.31032	−0.348640
$233$	3.84121	0.251646	0.125823	−	0.992053i	$-0.459843\pi$
$233$	3.84121	0.251646	0.125823	+	0.992053i	$0.459843\pi$
$234$	12.6034	0.823907
$235$	−11.3235	−0.738666
$236$	13.5983	0.885177
$237$	7.23629	0.470047
$238$	−0.832902	−0.0539890
$239$	16.2640	1.05203	0.526016	−	0.850475i	$-0.323685\pi$
$239$	16.2640	1.05203	0.526016	+	0.850475i	$0.323685\pi$
$240$	1.31638	0.0849721
$241$	−23.7399	−1.52922	−0.764609	−	0.644494i	$-0.777068\pi$
$241$	−23.7399	−1.52922	−0.764609	+	0.644494i	$0.777068\pi$
$242$	3.24341	0.208494
$243$	−15.3697	−0.985966
$244$	6.18845	0.396175
$245$	−1.77052	−0.113114
$246$	−0.166696	−0.0106282
$247$	24.1737	1.53813
$248$	4.78377	0.303770
$249$	8.77526	0.556109
$250$	−12.1551	−0.768755
$251$	0.961461	0.0606869	0.0303434	−	0.999540i	$-0.490340\pi$
$251$	0.961461	0.0606869	0.0303434	+	0.999540i	$0.490340\pi$
$252$	−2.44721	−0.154160
$253$	15.8076	0.993816
$254$	−4.61128	−0.289338
$255$	1.09642	0.0686603
$256$	1.00000	0.0625000
$257$	−10.5838	−0.660202	−0.330101	−	0.943946i	$-0.607083\pi$
$257$	−10.5838	−0.660202	−0.330101	+	0.943946i	$0.607083\pi$
$258$	1.44790	0.0901424
$259$	−3.10830	−0.193141
$260$	−9.11835	−0.565496
$261$	−12.9955	−0.804399
$262$	−3.65169	−0.225602
$263$	9.69040	0.597536	0.298768	−	0.954326i	$-0.403424\pi$
$263$	9.69040	0.597536	0.298768	+	0.954326i	$0.403424\pi$
$264$	2.07070	0.127442
$265$	−11.0983	−0.681763
$266$	−4.69383	−0.287797
$267$	4.91321	0.300683
$268$	−11.3372	−0.692531
$269$	12.1456	0.740528	0.370264	−	0.928927i	$-0.379267\pi$
$269$	12.1456	0.740528	0.370264	+	0.928927i	$0.379267\pi$
$270$	7.17061	0.436389
$271$	−12.0684	−0.733104	−0.366552	−	0.930398i	$-0.619462\pi$
$271$	−12.0684	−0.733104	−0.366552	+	0.930398i	$0.619462\pi$
$272$	0.832902	0.0505021
$273$	−3.82909	−0.231747
$274$	−19.3538	−1.16920
$275$	−5.19485	−0.313261
$276$	−4.21999	−0.254014
$277$	−12.9408	−0.777540	−0.388770	−	0.921335i	$-0.627100\pi$
$277$	−12.9408	−0.777540	−0.388770	+	0.921335i	$0.627100\pi$
$278$	−4.60882	−0.276419
$279$	11.7069	0.700873
$280$	1.77052	0.105809
$281$	9.87339	0.588997	0.294498	−	0.955652i	$-0.404847\pi$
$281$	9.87339	0.588997	0.294498	+	0.955652i	$0.404847\pi$
$282$	4.75512	0.283163
$283$	26.7697	1.59129	0.795647	−	0.605760i	$-0.207131\pi$
$283$	26.7697	1.59129	0.795647	+	0.605760i	$0.207131\pi$
$284$	−14.4224	−0.855813
$285$	6.17888	0.366005
$286$	−14.3434	−0.848140
$287$	−0.224205	−0.0132344
$288$	2.44721	0.144203
$289$	−16.3063	−0.959193
$290$	9.40204	0.552107
$291$	1.68801	0.0989526
$292$	0.347483	0.0203349
$293$	20.6496	1.20636	0.603180	−	0.797605i	$-0.293900\pi$
$293$	20.6496	1.20636	0.603180	+	0.797605i	$0.293900\pi$
$294$	0.743500	0.0433618
$295$	−24.0762	−1.40177
$296$	3.10830	0.180667
$297$	11.2795	0.654503
$298$	9.54348	0.552839
$299$	29.2312	1.69048
$300$	1.38681	0.0800678
$301$	1.94741	0.112247
$302$	−15.6485	−0.900468
$303$	1.03552	0.0594891
$304$	4.69383	0.269210
$305$	−10.9568	−0.627384
$306$	2.03828	0.116521
$307$	13.7740	0.786122	0.393061	−	0.919512i	$-0.371416\pi$
$307$	13.7740	0.786122	0.393061	+	0.919512i	$0.371416\pi$
$308$	2.78507	0.158694
$309$	5.73719	0.326378
$310$	−8.46977	−0.481051
$311$	1.40703	0.0797855	0.0398927	−	0.999204i	$-0.487298\pi$
$311$	1.40703	0.0797855	0.0398927	+	0.999204i	$0.487298\pi$
$312$	3.82909	0.216780
$313$	−18.2984	−1.03429	−0.517143	−	0.855899i	$-0.673004\pi$
$313$	−18.2984	−1.03429	−0.517143	+	0.855899i	$0.673004\pi$
$314$	1.65581	0.0934428
$315$	4.33284	0.244128
$316$	−9.73274	−0.547509
$317$	−4.58920	−0.257755	−0.128878	−	0.991660i	$-0.541137\pi$
$317$	−4.58920	−0.257755	−0.128878	+	0.991660i	$0.541137\pi$
$318$	4.66053	0.261350
$319$	14.7896	0.828059
$320$	−1.77052	−0.0989752
$321$	5.57331	0.311072
$322$	−5.67585	−0.316303
$323$	3.90950	0.217531
$324$	4.33045	0.240581
$325$	−9.60623	−0.532858
$326$	−0.0711125	−0.00393856
$327$	−7.36106	−0.407068
$328$	0.224205	0.0123796
$329$	6.39559	0.352600
$330$	−3.66621	−0.201818
$331$	30.7158	1.68829	0.844145	−	0.536114i	$-0.180108\pi$
$331$	30.7158	1.68829	0.844145	+	0.536114i	$0.180108\pi$
$332$	−11.8026	−0.647754
$333$	7.60667	0.416843
$334$	−1.52123	−0.0832379
$335$	20.0728	1.09669
$336$	−0.743500	−0.0405612
$337$	−1.13352	−0.0617470	−0.0308735	−	0.999523i	$-0.509829\pi$
$337$	−1.13352	−0.0617470	−0.0308735	+	0.999523i	$0.509829\pi$
$338$	−13.5235	−0.735580
$339$	−6.35293	−0.345044
$340$	−1.47467	−0.0799753
$341$	−13.3231	−0.721487
$342$	11.4868	0.621134
$343$	1.00000	0.0539949
$344$	−1.94741	−0.104998
$345$	7.47159	0.402257
$346$	−8.15788	−0.438570
$347$	−5.11455	−0.274564	−0.137282	−	0.990532i	$-0.543837\pi$
$347$	−5.11455	−0.274564	−0.137282	+	0.990532i	$0.543837\pi$
$348$	−3.94822	−0.211647
$349$	19.9778	1.06939	0.534693	−	0.845046i	$-0.320427\pi$
$349$	19.9778	1.06939	0.534693	+	0.845046i	$0.320427\pi$
$350$	1.86525	0.0997019
$351$	20.8579	1.11331
$352$	−2.78507	−0.148445
$353$	11.9493	0.635995	0.317998	−	0.948092i	$-0.396990\pi$
$353$	11.9493	0.635995	0.317998	+	0.948092i	$0.396990\pi$
$354$	10.1104	0.537360
$355$	25.5352	1.35527
$356$	−6.60822	−0.350235
$357$	−0.619262	−0.0327748
$358$	−20.2640	−1.07099
$359$	−3.72963	−0.196842	−0.0984212	−	0.995145i	$-0.531379\pi$
$359$	−3.72963	−0.196842	−0.0984212	+	0.995145i	$0.531379\pi$
$360$	−4.33284	−0.228360
$361$	3.03207	0.159583
$362$	10.1111	0.531427
$363$	2.41147	0.126569
$364$	5.15009	0.269938
$365$	−0.615227	−0.0322024
$366$	4.60111	0.240504
$367$	6.64092	0.346653	0.173327	−	0.984864i	$-0.444548\pi$
$367$	6.64092	0.346653	0.173327	+	0.984864i	$0.444548\pi$
$368$	5.67585	0.295874
$369$	0.548676	0.0285629
$370$	−5.50332	−0.286104
$371$	6.26838	0.325438
$372$	3.55673	0.184408
$373$	−5.71692	−0.296011	−0.148005	−	0.988987i	$-0.547285\pi$
$373$	−5.71692	−0.296011	−0.148005	+	0.988987i	$0.547285\pi$
$374$	−2.31969	−0.119948
$375$	−9.03730	−0.466684
$376$	−6.39559	−0.329827
$377$	27.3487	1.40853
$378$	−4.05000	−0.208309
$379$	−2.82370	−0.145044	−0.0725219	−	0.997367i	$-0.523105\pi$
$379$	−2.82370	−0.145044	−0.0725219	+	0.997367i	$0.523105\pi$
$380$	−8.31053	−0.426321
$381$	−3.42849	−0.175647
$382$	16.7133	0.855129
$383$	21.9662	1.12242	0.561211	−	0.827673i	$-0.310336\pi$
$383$	21.9662	1.12242	0.561211	+	0.827673i	$0.310336\pi$
$384$	0.743500	0.0379416
$385$	−4.93102	−0.251308
$386$	−2.63256	−0.133994
$387$	−4.76573	−0.242256
$388$	−2.27035	−0.115260
$389$	19.4590	0.986608	0.493304	−	0.869857i	$-0.335789\pi$
$389$	19.4590	0.986608	0.493304	+	0.869857i	$0.335789\pi$
$390$	−6.77949	−0.343293
$391$	4.72743	0.239076
$392$	−1.00000	−0.0505076
$393$	−2.71503	−0.136955
$394$	−17.5159	−0.882436
$395$	17.2320	0.867037
$396$	−6.81564	−0.342499
$397$	−1.90765	−0.0957422	−0.0478711	−	0.998854i	$-0.515244\pi$
$397$	−1.90765	−0.0957422	−0.0478711	+	0.998854i	$0.515244\pi$
$398$	22.3258	1.11909
$399$	−3.48986	−0.174712
$400$	−1.86525	−0.0932626
$401$	−26.3291	−1.31481	−0.657405	−	0.753537i	$-0.728346\pi$
$401$	−26.3291	−1.31481	−0.657405	+	0.753537i	$0.728346\pi$
$402$	−8.42921	−0.420411
$403$	−24.6369	−1.22725
$404$	−1.39277	−0.0692927
$405$	−7.66716	−0.380984
$406$	−5.31032	−0.263547
$407$	−8.65683	−0.429103
$408$	0.619262	0.0306580
$409$	6.11226	0.302232	0.151116	−	0.988516i	$-0.451713\pi$
$409$	6.11226	0.302232	0.151116	+	0.988516i	$0.451713\pi$
$410$	−0.396960	−0.0196044
$411$	−14.3895	−0.709783
$412$	−7.71647	−0.380163
$413$	13.5983	0.669131
$414$	13.8900	0.682656
$415$	20.8968	1.02579
$416$	−5.15009	−0.252504
$417$	−3.42665	−0.167804
$418$	−13.0726	−0.639404
$419$	30.5420	1.49208	0.746038	−	0.665904i	$-0.231954\pi$
$419$	30.5420	1.49208	0.746038	+	0.665904i	$0.231954\pi$
$420$	1.31638	0.0642329
$421$	14.5583	0.709526	0.354763	−	0.934956i	$-0.384562\pi$
$421$	14.5583	0.709526	0.354763	+	0.934956i	$0.384562\pi$
$422$	−15.2668	−0.743178
$423$	−15.6513	−0.760994
$424$	−6.26838	−0.304419
$425$	−1.55357	−0.0753593
$426$	−10.7231	−0.519534
$427$	6.18845	0.299480
$428$	−7.49605	−0.362335
$429$	−10.6643	−0.514876
$430$	3.44794	0.166274
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	4.05000	0.194856
$433$	−5.01905	−0.241200	−0.120600	−	0.992701i	$-0.538482\pi$
$433$	−5.01905	−0.241200	−0.120600	+	0.992701i	$0.538482\pi$
$434$	4.78377	0.229628
$435$	6.99042	0.335165
$436$	9.90056	0.474151
$437$	26.6415	1.27444
$438$	0.258354	0.0123446
$439$	−29.7347	−1.41916	−0.709580	−	0.704625i	$-0.751115\pi$
$439$	−29.7347	−1.41916	−0.709580	+	0.704625i	$0.751115\pi$
$440$	4.93102	0.235077
$441$	−2.44721	−0.116534
$442$	−4.28952	−0.204032
$443$	5.15999	0.245158	0.122579	−	0.992459i	$-0.460883\pi$
$443$	5.15999	0.245158	0.122579	+	0.992459i	$0.460883\pi$
$444$	2.31102	0.109676
$445$	11.7000	0.554633
$446$	9.89211	0.468405
$447$	7.09557	0.335609
$448$	1.00000	0.0472456
$449$	21.2997	1.00519	0.502597	−	0.864521i	$-0.332378\pi$
$449$	21.2997	1.00519	0.502597	+	0.864521i	$0.332378\pi$
$450$	−4.56466	−0.215180
$451$	−0.624425	−0.0294030
$452$	8.54464	0.401906
$453$	−11.6346	−0.546642
$454$	−4.50463	−0.211413
$455$	−9.11835	−0.427475
$456$	3.48986	0.163428
$457$	25.8286	1.20821	0.604105	−	0.796905i	$-0.293531\pi$
$457$	25.8286	1.20821	0.604105	+	0.796905i	$0.293531\pi$
$458$	12.5414	0.586019
$459$	3.37325	0.157450
$460$	−10.0492	−0.468547
$461$	3.62661	0.168908	0.0844541	−	0.996427i	$-0.473085\pi$
$461$	3.62661	0.168908	0.0844541	+	0.996427i	$0.473085\pi$
$462$	2.07070	0.0963375
$463$	8.57930	0.398714	0.199357	−	0.979927i	$-0.436115\pi$
$463$	8.57930	0.398714	0.199357	+	0.979927i	$0.436115\pi$
$464$	5.31032	0.246526
$465$	−6.29727	−0.292029
$466$	−3.84121	−0.177941
$467$	−17.5740	−0.813229	−0.406615	−	0.913600i	$-0.633291\pi$
$467$	−17.5740	−0.813229	−0.406615	+	0.913600i	$0.633291\pi$
$468$	−12.6034	−0.582590
$469$	−11.3372	−0.523504
$470$	11.3235	0.522316
$471$	1.23109	0.0567258
$472$	−13.5983	−0.625915
$473$	5.42368	0.249381
$474$	−7.23629	−0.332374
$475$	−8.75519	−0.401715
$476$	0.832902	0.0381760
$477$	−15.3400	−0.702371
$478$	−16.2640	−0.743899
$479$	−13.8756	−0.633991	−0.316996	−	0.948427i	$-0.602674\pi$
$479$	−13.8756	−0.633991	−0.316996	+	0.948427i	$0.602674\pi$
$480$	−1.31638	−0.0600843
$481$	−16.0081	−0.729905
$482$	23.7399	1.08132
$483$	−4.21999	−0.192016
$484$	−3.24341	−0.147428
$485$	4.01971	0.182525
$486$	15.3697	0.697183
$487$	15.1793	0.687842	0.343921	−	0.938999i	$-0.388245\pi$
$487$	15.1793	0.687842	0.343921	+	0.938999i	$0.388245\pi$
$488$	−6.18845	−0.280138
$489$	−0.0528721	−0.00239096
$490$	1.77052	0.0799840
$491$	−1.54389	−0.0696746	−0.0348373	−	0.999393i	$-0.511091\pi$
$491$	−1.54389	−0.0696746	−0.0348373	+	0.999393i	$0.511091\pi$
$492$	0.166696	0.00751525
$493$	4.42298	0.199201
$494$	−24.1737	−1.08763
$495$	12.0672	0.542382
$496$	−4.78377	−0.214798
$497$	−14.4224	−0.646934
$498$	−8.77526	−0.393229
$499$	−1.02240	−0.0457687	−0.0228844	−	0.999738i	$-0.507285\pi$
$499$	−1.02240	−0.0457687	−0.0228844	+	0.999738i	$0.507285\pi$
$500$	12.1551	0.543592
$501$	−1.13103	−0.0505308
$502$	−0.961461	−0.0429121
$503$	−31.9705	−1.42549	−0.712747	−	0.701422i	$-0.752549\pi$
$503$	−31.9705	−1.42549	−0.712747	+	0.701422i	$0.752549\pi$
$504$	2.44721	0.109007
$505$	2.46592	0.109732
$506$	−15.8076	−0.702734
$507$	−10.0547	−0.446545
$508$	4.61128	0.204593
$509$	−7.41341	−0.328593	−0.164297	−	0.986411i	$-0.552535\pi$
$509$	−7.41341	−0.328593	−0.164297	+	0.986411i	$0.552535\pi$
$510$	−1.09642	−0.0485502
$511$	0.347483	0.0153718
$512$	−1.00000	−0.0441942
$513$	19.0100	0.839313
$514$	10.5838	0.466833
$515$	13.6622	0.602028
$516$	−1.44790	−0.0637403
$517$	17.8121	0.783377
$518$	3.10830	0.136571
$519$	−6.06538	−0.266241
$520$	9.11835	0.399866
$521$	34.0052	1.48980	0.744898	−	0.667178i	$-0.232498\pi$
$521$	34.0052	1.48980	0.744898	+	0.667178i	$0.232498\pi$
$522$	12.9955	0.568796
$523$	−0.334948	−0.0146463	−0.00732313	−	0.999973i	$-0.502331\pi$
$523$	−0.334948	−0.0146463	−0.00732313	+	0.999973i	$0.502331\pi$
$524$	3.65169	0.159525
$525$	1.38681	0.0605255
$526$	−9.69040	−0.422522
$527$	−3.98441	−0.173564
$528$	−2.07070	−0.0901154
$529$	9.21528	0.400664
$530$	11.0983	0.482079
$531$	−33.2780	−1.44414
$532$	4.69383	0.203503
$533$	−1.15468	−0.0500146
$534$	−4.91321	−0.212615
$535$	13.2719	0.573795
$536$	11.3372	0.489693
$537$	−15.0663	−0.650159
$538$	−12.1456	−0.523632
$539$	2.78507	0.119961
$540$	−7.17061	−0.308574
$541$	−14.8287	−0.637536	−0.318768	−	0.947833i	$-0.603269\pi$
$541$	−14.8287	−0.637536	−0.318768	+	0.947833i	$0.603269\pi$
$542$	12.0684	0.518383
$543$	7.51759	0.322611
$544$	−0.832902	−0.0357104
$545$	−17.5292	−0.750867
$546$	3.82909	0.163870
$547$	12.4588	0.532700	0.266350	−	0.963876i	$-0.414182\pi$
$547$	12.4588	0.532700	0.266350	+	0.963876i	$0.414182\pi$
$548$	19.3538	0.826753
$549$	−15.1444	−0.646348
$550$	5.19485	0.221509
$551$	24.9258	1.06187
$552$	4.21999	0.179615
$553$	−9.73274	−0.413878
$554$	12.9408	0.549804
$555$	−4.09172	−0.173684
$556$	4.60882	0.195457
$557$	19.9321	0.844548	0.422274	−	0.906468i	$-0.361232\pi$
$557$	19.9321	0.844548	0.422274	+	0.906468i	$0.361232\pi$
$558$	−11.7069	−0.495592
$559$	10.0294	0.424197
$560$	−1.77052	−0.0748182
$561$	−1.72469	−0.0728163
$562$	−9.87339	−0.416484
$563$	−32.4776	−1.36877	−0.684384	−	0.729122i	$-0.739929\pi$
$563$	−32.4776	−1.36877	−0.684384	+	0.729122i	$0.739929\pi$
$564$	−4.75512	−0.200227
$565$	−15.1285	−0.636459
$566$	−26.7697	−1.12521
$567$	4.33045	0.181862
$568$	14.4224	0.605151
$569$	40.8822	1.71387	0.856936	−	0.515423i	$-0.172365\pi$
$569$	40.8822	1.71387	0.856936	+	0.515423i	$0.172365\pi$
$570$	−6.17888	−0.258805
$571$	31.7401	1.32828	0.664141	−	0.747608i	$-0.268798\pi$
$571$	31.7401	1.32828	0.664141	+	0.747608i	$0.268798\pi$
$572$	14.3434	0.599726
$573$	12.4264	0.519119
$574$	0.224205	0.00935813
$575$	−10.5869	−0.441504
$576$	−2.44721	−0.101967
$577$	13.7508	0.572452	0.286226	−	0.958162i	$-0.407599\pi$
$577$	13.7508	0.572452	0.286226	+	0.958162i	$0.407599\pi$
$578$	16.3063	0.678252
$579$	−1.95731	−0.0813428
$580$	−9.40204	−0.390399
$581$	−11.8026	−0.489656
$582$	−1.68801	−0.0699701
$583$	17.4578	0.723030
$584$	−0.347483	−0.0143790
$585$	22.3145	0.922591
$586$	−20.6496	−0.853026
$587$	−4.07845	−0.168336	−0.0841678	−	0.996452i	$-0.526823\pi$
$587$	−4.07845	−0.168336	−0.0841678	+	0.996452i	$0.526823\pi$
$588$	−0.743500	−0.0306614
$589$	−22.4542	−0.925210
$590$	24.0762	0.991200
$591$	−13.0230	−0.535696
$592$	−3.10830	−0.127751
$593$	−15.9740	−0.655974	−0.327987	−	0.944682i	$-0.606370\pi$
$593$	−15.9740	−0.655974	−0.327987	+	0.944682i	$0.606370\pi$
$594$	−11.2795	−0.462804
$595$	−1.47467	−0.0604556
$596$	−9.54348	−0.390916
$597$	16.5992	0.679361
$598$	−29.2312	−1.19535
$599$	13.9825	0.571308	0.285654	−	0.958333i	$-0.407789\pi$
$599$	13.9825	0.571308	0.285654	+	0.958333i	$0.407789\pi$
$600$	−1.38681	−0.0566165
$601$	3.21994	0.131344	0.0656720	−	0.997841i	$-0.479081\pi$
$601$	3.21994	0.131344	0.0656720	+	0.997841i	$0.479081\pi$
$602$	−1.94741	−0.0793707
$603$	27.7445	1.12984
$604$	15.6485	0.636727
$605$	5.74252	0.233467
$606$	−1.03552	−0.0420651
$607$	30.8965	1.25405	0.627024	−	0.779000i	$-0.284273\pi$
$607$	30.8965	1.25405	0.627024	+	0.779000i	$0.284273\pi$
$608$	−4.69383	−0.190360
$609$	−3.94822	−0.159990
$610$	10.9568	0.443627
$611$	32.9379	1.33252
$612$	−2.03828	−0.0823928
$613$	23.8726	0.964206	0.482103	−	0.876114i	$-0.339873\pi$
$613$	23.8726	0.964206	0.482103	+	0.876114i	$0.339873\pi$
$614$	−13.7740	−0.555872
$615$	−0.295139	−0.0119012
$616$	−2.78507	−0.112214
$617$	−37.6334	−1.51507	−0.757533	−	0.652797i	$-0.773595\pi$
$617$	−37.6334	−1.51507	−0.757533	+	0.652797i	$0.773595\pi$
$618$	−5.73719	−0.230784
$619$	7.81777	0.314223	0.157111	−	0.987581i	$-0.449782\pi$
$619$	7.81777	0.314223	0.157111	+	0.987581i	$0.449782\pi$
$620$	8.46977	0.340154
$621$	22.9872	0.922444
$622$	−1.40703	−0.0564169
$623$	−6.60822	−0.264753
$624$	−3.82909	−0.153286
$625$	−12.1946	−0.487783
$626$	18.2984	0.731351
$627$	−9.71950	−0.388159
$628$	−1.65581	−0.0660740
$629$	−2.58891	−0.103227
$630$	−4.33284	−0.172624
$631$	30.8477	1.22803	0.614015	−	0.789295i	$-0.289554\pi$
$631$	30.8477	1.22803	0.614015	+	0.789295i	$0.289554\pi$
$632$	9.73274	0.387147
$633$	−11.3509	−0.451157
$634$	4.58920	0.182261
$635$	−8.16438	−0.323994
$636$	−4.66053	−0.184802
$637$	5.15009	0.204054
$638$	−14.7896	−0.585526
$639$	35.2947	1.39624
$640$	1.77052	0.0699860
$641$	19.7106	0.778522	0.389261	−	0.921128i	$-0.372730\pi$
$641$	19.7106	0.778522	0.389261	+	0.921128i	$0.372730\pi$
$642$	−5.57331	−0.219961
$643$	4.52902	0.178607	0.0893035	−	0.996004i	$-0.471536\pi$
$643$	4.52902	0.178607	0.0893035	+	0.996004i	$0.471536\pi$
$644$	5.67585	0.223660
$645$	2.56354	0.100939
$646$	−3.90950	−0.153817
$647$	26.5960	1.04560	0.522798	−	0.852457i	$-0.324888\pi$
$647$	26.5960	1.04560	0.522798	+	0.852457i	$0.324888\pi$
$648$	−4.33045	−0.170116
$649$	37.8723	1.48662
$650$	9.60623	0.376787
$651$	3.55673	0.139399
$652$	0.0711125	0.00278498
$653$	−47.8235	−1.87148	−0.935739	−	0.352694i	$-0.885266\pi$
$653$	−47.8235	−1.87148	−0.935739	+	0.352694i	$0.885266\pi$
$654$	7.36106	0.287840
$655$	−6.46539	−0.252624
$656$	−0.224205	−0.00875373
$657$	−0.850364	−0.0331759
$658$	−6.39559	−0.249326
$659$	−22.2280	−0.865881	−0.432940	−	0.901423i	$-0.642524\pi$
$659$	−22.2280	−0.865881	−0.432940	+	0.901423i	$0.642524\pi$
$660$	3.66621	0.142707
$661$	32.7979	1.27569	0.637846	−	0.770164i	$-0.279826\pi$
$661$	32.7979	1.27569	0.637846	+	0.770164i	$0.279826\pi$
$662$	−30.7158	−1.19380
$663$	−3.18926	−0.123861
$664$	11.8026	0.458031
$665$	−8.31053	−0.322269
$666$	−7.60667	−0.294752
$667$	30.1406	1.16705
$668$	1.52123	0.0588581
$669$	7.35478	0.284352
$670$	−20.0728	−0.775479
$671$	17.2352	0.665359
$672$	0.743500	0.0286811
$673$	−19.3755	−0.746869	−0.373434	−	0.927657i	$-0.621820\pi$
$673$	−19.3755	−0.746869	−0.373434	+	0.927657i	$0.621820\pi$
$674$	1.13352	0.0436617
$675$	−7.55427	−0.290764
$676$	13.5235	0.520133
$677$	11.5952	0.445638	0.222819	−	0.974860i	$-0.428474\pi$
$677$	11.5952	0.445638	0.222819	+	0.974860i	$0.428474\pi$
$678$	6.35293	0.243983
$679$	−2.27035	−0.0871281
$680$	1.47467	0.0565510
$681$	−3.34919	−0.128341
$682$	13.3231	0.510169
$683$	8.44625	0.323187	0.161593	−	0.986857i	$-0.448337\pi$
$683$	8.44625	0.323187	0.161593	+	0.986857i	$0.448337\pi$
$684$	−11.4868	−0.439208
$685$	−34.2663	−1.30925
$686$	−1.00000	−0.0381802
$687$	9.32449	0.355751
$688$	1.94741	0.0742445
$689$	32.2827	1.22987
$690$	−7.47159	−0.284439
$691$	8.38884	0.319127	0.159563	−	0.987188i	$-0.448991\pi$
$691$	8.38884	0.319127	0.159563	+	0.987188i	$0.448991\pi$
$692$	8.15788	0.310116
$693$	−6.81564	−0.258905
$694$	5.11455	0.194146
$695$	−8.16001	−0.309527
$696$	3.94822	0.149657
$697$	−0.186741	−0.00707331
$698$	−19.9778	−0.756170
$699$	−2.85594	−0.108021
$700$	−1.86525	−0.0704999
$701$	18.3085	0.691502	0.345751	−	0.938326i	$-0.387624\pi$
$701$	18.3085	0.691502	0.345751	+	0.938326i	$0.387624\pi$
$702$	−20.8579	−0.787229
$703$	−14.5899	−0.550267
$704$	2.78507	0.104966
$705$	8.41904	0.317079
$706$	−11.9493	−0.449717
$707$	−1.39277	−0.0523803
$708$	−10.1104	−0.379971
$709$	39.7526	1.49294	0.746471	−	0.665418i	$-0.231747\pi$
$709$	39.7526	1.49294	0.746471	+	0.665418i	$0.231747\pi$
$710$	−25.5352	−0.958319
$711$	23.8180	0.893246
$712$	6.60822	0.247653
$713$	−27.1520	−1.01685
$714$	0.619262	0.0231753
$715$	−25.3952	−0.949727
$716$	20.2640	0.757302
$717$	−12.0923	−0.451595
$718$	3.72963	0.139189
$719$	4.35792	0.162523	0.0812615	−	0.996693i	$-0.474105\pi$
$719$	4.35792	0.162523	0.0812615	+	0.996693i	$0.474105\pi$
$720$	4.33284	0.161475
$721$	−7.71647	−0.287376
$722$	−3.03207	−0.112842
$723$	17.6506	0.656432
$724$	−10.1111	−0.375776
$725$	−9.90510	−0.367866
$726$	−2.41147	−0.0894981
$727$	−11.5616	−0.428797	−0.214399	−	0.976746i	$-0.568779\pi$
$727$	−11.5616	−0.428797	−0.214399	+	0.976746i	$0.568779\pi$
$728$	−5.15009	−0.190875
$729$	−1.56401	−0.0579264
$730$	0.615227	0.0227706
$731$	1.62201	0.0599920
$732$	−4.60111	−0.170062
$733$	−31.9654	−1.18067	−0.590334	−	0.807159i	$-0.701004\pi$
$733$	−31.9654	−1.18067	−0.590334	+	0.807159i	$0.701004\pi$
$734$	−6.64092	−0.245121
$735$	1.31638	0.0485555
$736$	−5.67585	−0.209215
$737$	−31.5749	−1.16308
$738$	−0.548676	−0.0201970
$739$	17.8654	0.657189	0.328594	−	0.944471i	$-0.393425\pi$
$739$	17.8654	0.657189	0.328594	+	0.944471i	$0.393425\pi$
$740$	5.50332	0.202306
$741$	−17.9731	−0.660259
$742$	−6.26838	−0.230119
$743$	22.1762	0.813567	0.406783	−	0.913525i	$-0.366650\pi$
$743$	22.1762	0.813567	0.406783	+	0.913525i	$0.366650\pi$
$744$	−3.55673	−0.130396
$745$	16.8969	0.619056
$746$	5.71692	0.209311
$747$	28.8835	1.05679
$748$	2.31969	0.0848161
$749$	−7.49605	−0.273900
$750$	9.03730	0.329995
$751$	15.8667	0.578983	0.289492	−	0.957181i	$-0.406514\pi$
$751$	15.8667	0.578983	0.289492	+	0.957181i	$0.406514\pi$
$752$	6.39559	0.233223
$753$	−0.714846	−0.0260504
$754$	−27.3487	−0.995980
$755$	−27.7059	−1.00832
$756$	4.05000	0.147297
$757$	−20.4943	−0.744879	−0.372439	−	0.928057i	$-0.621479\pi$
$757$	−20.4943	−0.744879	−0.372439	+	0.928057i	$0.621479\pi$
$758$	2.82370	0.102561
$759$	−11.7530	−0.426605
$760$	8.31053	0.301455
$761$	−13.0993	−0.474848	−0.237424	−	0.971406i	$-0.576303\pi$
$761$	−13.0993	−0.474848	−0.237424	+	0.971406i	$0.576303\pi$
$762$	3.42849	0.124201
$763$	9.90056	0.358424
$764$	−16.7133	−0.604667
$765$	3.60883	0.130477
$766$	−21.9662	−0.793672
$767$	70.0328	2.52874
$768$	−0.743500	−0.0268287
$769$	28.6535	1.03327	0.516636	−	0.856205i	$-0.327184\pi$
$769$	28.6535	1.03327	0.516636	+	0.856205i	$0.327184\pi$
$770$	4.93102	0.177702
$771$	7.86908	0.283398
$772$	2.63256	0.0947478
$773$	−30.4528	−1.09531	−0.547656	−	0.836704i	$-0.684480\pi$
$773$	−30.4528	−1.09531	−0.547656	+	0.836704i	$0.684480\pi$
$774$	4.76573	0.171301
$775$	8.92294	0.320522
$776$	2.27035	0.0815009
$777$	2.31102	0.0829075
$778$	−19.4590	−0.697637
$779$	−1.05238	−0.0377054
$780$	6.77949	0.242745
$781$	−40.1674	−1.43730
$782$	−4.72743	−0.169052
$783$	21.5068	0.768590
$784$	1.00000	0.0357143
$785$	2.93165	0.104635
$786$	2.71503	0.0968419
$787$	−1.10296	−0.0393164	−0.0196582	−	0.999807i	$-0.506258\pi$
$787$	−1.10296	−0.0393164	−0.0196582	+	0.999807i	$0.506258\pi$
$788$	17.5159	0.623977
$789$	−7.20481	−0.256498
$790$	−17.2320	−0.613088
$791$	8.54464	0.303812
$792$	6.81564	0.242183
$793$	31.8711	1.13178
$794$	1.90765	0.0676999
$795$	8.25158	0.292653
$796$	−22.3258	−0.791317
$797$	29.7113	1.05243	0.526214	−	0.850352i	$-0.323611\pi$
$797$	29.7113	1.05243	0.526214	+	0.850352i	$0.323611\pi$
$798$	3.48986	0.123540
$799$	5.32690	0.188452
$800$	1.86525	0.0659466
$801$	16.1717	0.571398
$802$	26.3291	0.929711
$803$	0.967764	0.0341517
$804$	8.42921	0.297275
$805$	−10.0492	−0.354188
$806$	24.6369	0.867797
$807$	−9.03022	−0.317879
$808$	1.39277	0.0489973
$809$	−11.3116	−0.397695	−0.198847	−	0.980030i	$-0.563720\pi$
$809$	−11.3116	−0.397695	−0.198847	+	0.980030i	$0.563720\pi$
$810$	7.66716	0.269397
$811$	7.46748	0.262219	0.131109	−	0.991368i	$-0.458146\pi$
$811$	7.46748	0.262219	0.131109	+	0.991368i	$0.458146\pi$
$812$	5.31032	0.186356
$813$	8.97286	0.314692
$814$	8.65683	0.303422
$815$	−0.125906	−0.00441030
$816$	−0.619262	−0.0216785
$817$	9.14084	0.319798
$818$	−6.11226	−0.213710
$819$	−12.6034	−0.440397
$820$	0.396960	0.0138624
$821$	19.0655	0.665392	0.332696	−	0.943034i	$-0.392042\pi$
$821$	19.0655	0.665392	0.332696	+	0.943034i	$0.392042\pi$
$822$	14.3895	0.501892
$823$	−21.7484	−0.758102	−0.379051	−	0.925376i	$-0.623749\pi$
$823$	−21.7484	−0.758102	−0.379051	+	0.925376i	$0.623749\pi$
$824$	7.71647	0.268816
$825$	3.86237	0.134470
$826$	−13.5983	−0.473147
$827$	−11.0805	−0.385306	−0.192653	−	0.981267i	$-0.561709\pi$
$827$	−11.0805	−0.385306	−0.192653	+	0.981267i	$0.561709\pi$
$828$	−13.8900	−0.482711
$829$	−32.3122	−1.12225	−0.561124	−	0.827732i	$-0.689631\pi$
$829$	−32.3122	−1.12225	−0.561124	+	0.827732i	$0.689631\pi$
$830$	−20.8968	−0.725340
$831$	9.62151	0.333767
$832$	5.15009	0.178547
$833$	0.832902	0.0288583
$834$	3.42665	0.118655
$835$	−2.69337	−0.0932078
$836$	13.0726	0.452127
$837$	−19.3743	−0.669672
$838$	−30.5420	−1.05506
$839$	0.416642	0.0143841	0.00719204	−	0.999974i	$-0.497711\pi$
$839$	0.416642	0.0143841	0.00719204	+	0.999974i	$0.497711\pi$
$840$	−1.31638	−0.0454195
$841$	−0.800455	−0.0276019
$842$	−14.5583	−0.501711
$843$	−7.34086	−0.252833
$844$	15.2668	0.525506
$845$	−23.9436	−0.823685
$846$	15.6513	0.538104
$847$	−3.24341	−0.111445
$848$	6.26838	0.215257
$849$	−19.9033	−0.683078
$850$	1.55357	0.0532871
$851$	−17.6423	−0.604769
$852$	10.7231	0.367366
$853$	−40.5532	−1.38852	−0.694258	−	0.719726i	$-0.744267\pi$
$853$	−40.5532	−1.38852	−0.694258	+	0.719726i	$0.744267\pi$
$854$	−6.18845	−0.211764
$855$	20.3376	0.695532
$856$	7.49605	0.256210
$857$	21.2988	0.727553	0.363776	−	0.931486i	$-0.381487\pi$
$857$	21.2988	0.727553	0.363776	+	0.931486i	$0.381487\pi$
$858$	10.6643	0.364072
$859$	−32.4175	−1.10607	−0.553035	−	0.833158i	$-0.686530\pi$
$859$	−32.4175	−1.10607	−0.553035	+	0.833158i	$0.686530\pi$
$860$	−3.44794	−0.117574
$861$	0.166696	0.00568099
$862$	1.00000	0.0340601
$863$	−41.1824	−1.40187	−0.700933	−	0.713227i	$-0.747233\pi$
$863$	−41.1824	−1.40187	−0.700933	+	0.713227i	$0.747233\pi$
$864$	−4.05000	−0.137784
$865$	−14.4437	−0.491101
$866$	5.01905	0.170554
$867$	12.1237	0.411743
$868$	−4.78377	−0.162372
$869$	−27.1063	−0.919519
$870$	−6.99042	−0.236997
$871$	−58.3877	−1.97839
$872$	−9.90056	−0.335275
$873$	5.55602	0.188043
$874$	−26.6415	−0.901162
$875$	12.1551	0.410917
$876$	−0.258354	−0.00872896
$877$	−5.61119	−0.189477	−0.0947383	−	0.995502i	$-0.530201\pi$
$877$	−5.61119	−0.189477	−0.0947383	+	0.995502i	$0.530201\pi$
$878$	29.7347	1.00350
$879$	−15.3529	−0.517842
$880$	−4.93102	−0.166225
$881$	14.3500	0.483462	0.241731	−	0.970343i	$-0.422285\pi$
$881$	14.3500	0.483462	0.241731	+	0.970343i	$0.422285\pi$
$882$	2.44721	0.0824018
$883$	−32.0451	−1.07840	−0.539202	−	0.842176i	$-0.681274\pi$
$883$	−32.0451	−1.07840	−0.539202	+	0.842176i	$0.681274\pi$
$884$	4.28952	0.144272
$885$	17.9006	0.601723
$886$	−5.15999	−0.173353
$887$	−16.3524	−0.549059	−0.274529	−	0.961579i	$-0.588522\pi$
$887$	−16.3524	−0.549059	−0.274529	+	0.961579i	$0.588522\pi$
$888$	−2.31102	−0.0775528
$889$	4.61128	0.154658
$890$	−11.7000	−0.392185
$891$	12.0606	0.404045
$892$	−9.89211	−0.331212
$893$	30.0198	1.00458
$894$	−7.09557	−0.237312
$895$	−35.8779	−1.19927
$896$	−1.00000	−0.0334077
$897$	−21.7334	−0.725656
$898$	−21.2997	−0.710780
$899$	−25.4034	−0.847250
$900$	4.56466	0.152155
$901$	5.22094	0.173935
$902$	0.624425	0.0207911
$903$	−1.44790	−0.0481832
$904$	−8.54464	−0.284190
$905$	17.9019	0.595080
$906$	11.6346	0.386534
$907$	27.3362	0.907683	0.453842	−	0.891082i	$-0.350053\pi$
$907$	27.3362	0.907683	0.453842	+	0.891082i	$0.350053\pi$
$908$	4.50463	0.149491
$909$	3.40839	0.113049
$910$	9.11835	0.302270
$911$	−9.61630	−0.318602	−0.159301	−	0.987230i	$-0.550924\pi$
$911$	−9.61630	−0.318602	−0.159301	+	0.987230i	$0.550924\pi$
$912$	−3.48986	−0.115561
$913$	−32.8711	−1.08788
$914$	−25.8286	−0.854333
$915$	8.14637	0.269311
$916$	−12.5414	−0.414378
$917$	3.65169	0.120589
$918$	−3.37325	−0.111334
$919$	53.7562	1.77325	0.886627	−	0.462485i	$-0.153042\pi$
$919$	53.7562	1.77325	0.886627	+	0.462485i	$0.153042\pi$
$920$	10.0492	0.331313
$921$	−10.2409	−0.337450
$922$	−3.62661	−0.119436
$923$	−74.2768	−2.44485
$924$	−2.07070	−0.0681209
$925$	5.79777	0.190630
$926$	−8.57930	−0.281933
$927$	18.8838	0.620226
$928$	−5.31032	−0.174320
$929$	−3.46124	−0.113560	−0.0567798	−	0.998387i	$-0.518083\pi$
$929$	−3.46124	−0.113560	−0.0567798	+	0.998387i	$0.518083\pi$
$930$	6.29727	0.206496
$931$	4.69383	0.153834
$932$	3.84121	0.125823
$933$	−1.04613	−0.0342487
$934$	17.5740	0.575040
$935$	−4.10706	−0.134315
$936$	12.6034	0.411953
$937$	−11.7937	−0.385284	−0.192642	−	0.981269i	$-0.561706\pi$
$937$	−11.7937	−0.385284	−0.192642	+	0.981269i	$0.561706\pi$
$938$	11.3372	0.370173
$939$	13.6048	0.443977
$940$	−11.3235	−0.369333
$941$	−9.84401	−0.320906	−0.160453	−	0.987044i	$-0.551295\pi$
$941$	−9.84401	−0.320906	−0.160453	+	0.987044i	$0.551295\pi$
$942$	−1.23109	−0.0401112
$943$	−1.27255	−0.0414400
$944$	13.5983	0.442589
$945$	−7.17061	−0.233260
$946$	−5.42368	−0.176339
$947$	−40.0283	−1.30075	−0.650373	−	0.759615i	$-0.725387\pi$
$947$	−40.0283	−1.30075	−0.650373	+	0.759615i	$0.725387\pi$
$948$	7.23629	0.235024
$949$	1.78957	0.0580920
$950$	8.75519	0.284056
$951$	3.41207	0.110644
$952$	−0.832902	−0.0269945
$953$	37.0592	1.20047	0.600233	−	0.799825i	$-0.295075\pi$
$953$	37.0592	1.20047	0.600233	+	0.799825i	$0.295075\pi$
$954$	15.3400	0.496652
$955$	29.5913	0.957553
$956$	16.2640	0.526016
$957$	−10.9961	−0.355452
$958$	13.8756	0.448300
$959$	19.3538	0.624966
$960$	1.31638	0.0424861
$961$	−8.11554	−0.261792
$962$	16.0081	0.516121
$963$	18.3444	0.591140
$964$	−23.7399	−0.764609
$965$	−4.66100	−0.150043
$966$	4.21999	0.135776
$967$	15.3179	0.492590	0.246295	−	0.969195i	$-0.420787\pi$
$967$	15.3179	0.492590	0.246295	+	0.969195i	$0.420787\pi$
$968$	3.24341	0.104247
$969$	−2.90671	−0.0933771
$970$	−4.01971	−0.129065
$971$	29.8338	0.957413	0.478707	−	0.877975i	$-0.341106\pi$
$971$	29.8338	0.957413	0.478707	+	0.877975i	$0.341106\pi$
$972$	−15.3697	−0.492983
$973$	4.60882	0.147752
$974$	−15.1793	−0.486377
$975$	7.14222	0.228734
$976$	6.18845	0.198087
$977$	3.42818	0.109677	0.0548386	−	0.998495i	$-0.482536\pi$
$977$	3.42818	0.109677	0.0548386	+	0.998495i	$0.482536\pi$
$978$	0.0528721	0.00169066
$979$	−18.4043	−0.588205
$980$	−1.77052	−0.0565572
$981$	−24.2287	−0.773564
$982$	1.54389	0.0492674
$983$	−58.1650	−1.85517	−0.927587	−	0.373607i	$-0.878121\pi$
$983$	−58.1650	−1.85517	−0.927587	+	0.373607i	$0.878121\pi$
$984$	−0.166696	−0.00531408
$985$	−31.0122	−0.988131
$986$	−4.42298	−0.140856
$987$	−4.75512	−0.151357
$988$	24.1737	0.769067
$989$	11.0532	0.351472
$990$	−12.0672	−0.383522
$991$	9.42932	0.299532	0.149766	−	0.988721i	$-0.452148\pi$
$991$	9.42932	0.299532	0.149766	+	0.988721i	$0.452148\pi$
$992$	4.78377	0.151885
$993$	−22.8372	−0.724715
$994$	14.4224	0.457451
$995$	39.5283	1.25313
$996$	8.77526	0.278055
$997$	21.1600	0.670144	0.335072	−	0.942193i	$-0.391239\pi$
$997$	21.1600	0.670144	0.335072	+	0.942193i	$0.391239\pi$
$998$	1.02240	0.0323634
$999$	−12.5886	−0.398286

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.p.1.9	✓	27

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.p.1.9	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.743500 q^{3} +1.00000 q^{4} -1.77052 q^{5} +0.743500 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.44721 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.743500 q^{3} +1.00000 q^{4} -1.77052 q^{5} +0.743500 q^{6} +1.00000 q^{7} -1.00000 q^{8} -2.44721 q^{9} +1.77052 q^{10} +2.78507 q^{11} -0.743500 q^{12} +5.15009 q^{13} -1.00000 q^{14} +1.31638 q^{15} +1.00000 q^{16} +0.832902 q^{17} +2.44721 q^{18} +4.69383 q^{19} -1.77052 q^{20} -0.743500 q^{21} -2.78507 q^{22} +5.67585 q^{23} +0.743500 q^{24} -1.86525 q^{25} -5.15009 q^{26} +4.05000 q^{27} +1.00000 q^{28} +5.31032 q^{29} -1.31638 q^{30} -4.78377 q^{31} -1.00000 q^{32} -2.07070 q^{33} -0.832902 q^{34} -1.77052 q^{35} -2.44721 q^{36} -3.10830 q^{37} -4.69383 q^{38} -3.82909 q^{39} +1.77052 q^{40} -0.224205 q^{41} +0.743500 q^{42} +1.94741 q^{43} +2.78507 q^{44} +4.33284 q^{45} -5.67585 q^{46} +6.39559 q^{47} -0.743500 q^{48} +1.00000 q^{49} +1.86525 q^{50} -0.619262 q^{51} +5.15009 q^{52} +6.26838 q^{53} -4.05000 q^{54} -4.93102 q^{55} -1.00000 q^{56} -3.48986 q^{57} -5.31032 q^{58} +13.5983 q^{59} +1.31638 q^{60} +6.18845 q^{61} +4.78377 q^{62} -2.44721 q^{63} +1.00000 q^{64} -9.11835 q^{65} +2.07070 q^{66} -11.3372 q^{67} +0.832902 q^{68} -4.21999 q^{69} +1.77052 q^{70} -14.4224 q^{71} +2.44721 q^{72} +0.347483 q^{73} +3.10830 q^{74} +1.38681 q^{75} +4.69383 q^{76} +2.78507 q^{77} +3.82909 q^{78} -9.73274 q^{79} -1.77052 q^{80} +4.33045 q^{81} +0.224205 q^{82} -11.8026 q^{83} -0.743500 q^{84} -1.47467 q^{85} -1.94741 q^{86} -3.94822 q^{87} -2.78507 q^{88} -6.60822 q^{89} -4.33284 q^{90} +5.15009 q^{91} +5.67585 q^{92} +3.55673 q^{93} -6.39559 q^{94} -8.31053 q^{95} +0.743500 q^{96} -2.27035 q^{97} -1.00000 q^{98} -6.81564 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 27 q - 27 q^{2} + 4 q^{3} + 27 q^{4} + 9 q^{5} - 4 q^{6} + 27 q^{7} - 27 q^{8} + 35 q^{9}+O(q^{10}) \) 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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