LMFDB - Embedded newform 8013.2.a.a.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8013,2,Mod(1,8013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8013, 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("8013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8013 = 3 \cdot 2671 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8013.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:	$63.9841271397$
Analytic rank:	$1$
Dimension:	$94$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.92790 q^{2} +1.00000 q^{3} +1.71679 q^{4} +3.85366 q^{5} -1.92790 q^{6} -4.10922 q^{7} +0.545993 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.92790 q^{2} +1.00000 q^{3} +1.71679 q^{4} +3.85366 q^{5} -1.92790 q^{6} -4.10922 q^{7} +0.545993 q^{8} +1.00000 q^{9} -7.42947 q^{10} +2.94313 q^{11} +1.71679 q^{12} +0.843859 q^{13} +7.92216 q^{14} +3.85366 q^{15} -4.48621 q^{16} -5.95776 q^{17} -1.92790 q^{18} -0.897040 q^{19} +6.61594 q^{20} -4.10922 q^{21} -5.67406 q^{22} -3.64571 q^{23} +0.545993 q^{24} +9.85069 q^{25} -1.62687 q^{26} +1.00000 q^{27} -7.05468 q^{28} -0.877888 q^{29} -7.42947 q^{30} -1.90856 q^{31} +7.55697 q^{32} +2.94313 q^{33} +11.4860 q^{34} -15.8355 q^{35} +1.71679 q^{36} -5.51381 q^{37} +1.72940 q^{38} +0.843859 q^{39} +2.10407 q^{40} -2.96850 q^{41} +7.92216 q^{42} +10.1312 q^{43} +5.05275 q^{44} +3.85366 q^{45} +7.02855 q^{46} -1.26552 q^{47} -4.48621 q^{48} +9.88567 q^{49} -18.9911 q^{50} -5.95776 q^{51} +1.44873 q^{52} +1.23690 q^{53} -1.92790 q^{54} +11.3418 q^{55} -2.24361 q^{56} -0.897040 q^{57} +1.69248 q^{58} -4.70951 q^{59} +6.61594 q^{60} +3.87195 q^{61} +3.67951 q^{62} -4.10922 q^{63} -5.59665 q^{64} +3.25195 q^{65} -5.67406 q^{66} -3.82029 q^{67} -10.2282 q^{68} -3.64571 q^{69} +30.5293 q^{70} -11.2215 q^{71} +0.545993 q^{72} -14.6270 q^{73} +10.6301 q^{74} +9.85069 q^{75} -1.54003 q^{76} -12.0940 q^{77} -1.62687 q^{78} -0.964228 q^{79} -17.2883 q^{80} +1.00000 q^{81} +5.72297 q^{82} +4.49595 q^{83} -7.05468 q^{84} -22.9592 q^{85} -19.5320 q^{86} -0.877888 q^{87} +1.60693 q^{88} +7.90736 q^{89} -7.42947 q^{90} -3.46760 q^{91} -6.25893 q^{92} -1.90856 q^{93} +2.43980 q^{94} -3.45689 q^{95} +7.55697 q^{96} -2.72181 q^{97} -19.0586 q^{98} +2.94313 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * 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 $

$2$	−1.92790	−1.36323	−0.681615	−	0.731711i	$-0.738722\pi$
$2$	−1.92790	−1.36323	−0.681615	+	0.731711i	$0.738722\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	1.71679	0.858397
$5$	3.85366	1.72341	0.861705	−	0.507410i	$-0.169397\pi$
$5$	3.85366	1.72341	0.861705	+	0.507410i	$0.169397\pi$
$6$	−1.92790	−0.787061
$7$	−4.10922	−1.55314	−0.776569	−	0.630032i	$-0.783042\pi$
$7$	−4.10922	−1.55314	−0.776569	+	0.630032i	$0.783042\pi$
$8$	0.545993	0.193038
$9$	1.00000	0.333333
$10$	−7.42947	−2.34940
$11$	2.94313	0.887387	0.443694	−	0.896178i	$-0.353668\pi$
$11$	2.94313	0.887387	0.443694	+	0.896178i	$0.353668\pi$
$12$	1.71679	0.495596
$13$	0.843859	0.234044	0.117022	−	0.993129i	$-0.462665\pi$
$13$	0.843859	0.234044	0.117022	+	0.993129i	$0.462665\pi$
$14$	7.92216	2.11729
$15$	3.85366	0.995011
$16$	−4.48621	−1.12155
$17$	−5.95776	−1.44497	−0.722485	−	0.691387i	$-0.757000\pi$
$17$	−5.95776	−1.44497	−0.722485	+	0.691387i	$0.757000\pi$
$18$	−1.92790	−0.454410
$19$	−0.897040	−0.205795	−0.102898	−	0.994692i	$-0.532811\pi$
$19$	−0.897040	−0.205795	−0.102898	+	0.994692i	$0.532811\pi$
$20$	6.61594	1.47937
$21$	−4.10922	−0.896705
$22$	−5.67406	−1.20971
$23$	−3.64571	−0.760182	−0.380091	−	0.924949i	$-0.624107\pi$
$23$	−3.64571	−0.760182	−0.380091	+	0.924949i	$0.624107\pi$
$24$	0.545993	0.111450
$25$	9.85069	1.97014
$26$	−1.62687	−0.319056
$27$	1.00000	0.192450
$28$	−7.05468	−1.33321
$29$	−0.877888	−0.163020	−0.0815098	−	0.996673i	$-0.525974\pi$
$29$	−0.877888	−0.163020	−0.0815098	+	0.996673i	$0.525974\pi$
$30$	−7.42947	−1.35643
$31$	−1.90856	−0.342788	−0.171394	−	0.985203i	$-0.554827\pi$
$31$	−1.90856	−0.342788	−0.171394	+	0.985203i	$0.554827\pi$
$32$	7.55697	1.33590
$33$	2.94313	0.512333
$34$	11.4860	1.96983
$35$	−15.8355	−2.67669
$36$	1.71679	0.286132
$37$	−5.51381	−0.906465	−0.453233	−	0.891392i	$-0.649729\pi$
$37$	−5.51381	−0.906465	−0.453233	+	0.891392i	$0.649729\pi$
$38$	1.72940	0.280546
$39$	0.843859	0.135126
$40$	2.10407	0.332683
$41$	−2.96850	−0.463602	−0.231801	−	0.972763i	$-0.574462\pi$
$41$	−2.96850	−0.463602	−0.231801	+	0.972763i	$0.574462\pi$
$42$	7.92216	1.22242
$43$	10.1312	1.54500	0.772499	−	0.635016i	$-0.219006\pi$
$43$	10.1312	1.54500	0.772499	+	0.635016i	$0.219006\pi$
$44$	5.05275	0.761731
$45$	3.85366	0.574470
$46$	7.02855	1.03630
$47$	−1.26552	−0.184595	−0.0922977	−	0.995731i	$-0.529421\pi$
$47$	−1.26552	−0.184595	−0.0922977	+	0.995731i	$0.529421\pi$
$48$	−4.48621	−0.647528
$49$	9.88567	1.41224
$50$	−18.9911	−2.68575
$51$	−5.95776	−0.834254
$52$	1.44873	0.200903
$53$	1.23690	0.169902	0.0849508	−	0.996385i	$-0.472927\pi$
$53$	1.23690	0.169902	0.0849508	+	0.996385i	$0.472927\pi$
$54$	−1.92790	−0.262354
$55$	11.3418	1.52933
$56$	−2.24361	−0.299814
$57$	−0.897040	−0.118816
$58$	1.69248	0.222233
$59$	−4.70951	−0.613126	−0.306563	−	0.951850i	$-0.599179\pi$
$59$	−4.70951	−0.613126	−0.306563	+	0.951850i	$0.599179\pi$
$60$	6.61594	0.854114
$61$	3.87195	0.495753	0.247876	−	0.968792i	$-0.420267\pi$
$61$	3.87195	0.495753	0.247876	+	0.968792i	$0.420267\pi$
$62$	3.67951	0.467299
$63$	−4.10922	−0.517713
$64$	−5.59665	−0.699581
$65$	3.25195	0.403354
$66$	−5.67406	−0.698428
$67$	−3.82029	−0.466722	−0.233361	−	0.972390i	$-0.574972\pi$
$67$	−3.82029	−0.466722	−0.233361	+	0.972390i	$0.574972\pi$
$68$	−10.2282	−1.24036
$69$	−3.64571	−0.438891
$70$	30.5293	3.64895
$71$	−11.2215	−1.33175	−0.665875	−	0.746063i	$-0.731942\pi$
$71$	−11.2215	−1.33175	−0.665875	+	0.746063i	$0.731942\pi$
$72$	0.545993	0.0643459
$73$	−14.6270	−1.71196	−0.855981	−	0.517007i	$-0.827046\pi$
$73$	−14.6270	−1.71196	−0.855981	+	0.517007i	$0.827046\pi$
$74$	10.6301	1.23572
$75$	9.85069	1.13746
$76$	−1.54003	−0.176654
$77$	−12.0940	−1.37824
$78$	−1.62687	−0.184207
$79$	−0.964228	−0.108484	−0.0542421	−	0.998528i	$-0.517274\pi$
$79$	−0.964228	−0.108484	−0.0542421	+	0.998528i	$0.517274\pi$
$80$	−17.2883	−1.93289
$81$	1.00000	0.111111
$82$	5.72297	0.631996
$83$	4.49595	0.493495	0.246748	−	0.969080i	$-0.420638\pi$
$83$	4.49595	0.493495	0.246748	+	0.969080i	$0.420638\pi$
$84$	−7.05468	−0.769729
$85$	−22.9592	−2.49027
$86$	−19.5320	−2.10619
$87$	−0.877888	−0.0941194
$88$	1.60693	0.171299
$89$	7.90736	0.838178	0.419089	−	0.907945i	$-0.362349\pi$
$89$	7.90736	0.838178	0.419089	+	0.907945i	$0.362349\pi$
$90$	−7.42947	−0.783134
$91$	−3.46760	−0.363503
$92$	−6.25893	−0.652538
$93$	−1.90856	−0.197909
$94$	2.43980	0.251646
$95$	−3.45689	−0.354669
$96$	7.55697	0.771280
$97$	−2.72181	−0.276358	−0.138179	−	0.990407i	$-0.544125\pi$
$97$	−2.72181	−0.276358	−0.138179	+	0.990407i	$0.544125\pi$
$98$	−19.0586	−1.92521
$99$	2.94313	0.295796
$100$	16.9116	1.69116
$101$	−3.36296	−0.334627	−0.167314	−	0.985904i	$-0.553509\pi$
$101$	−3.36296	−0.334627	−0.167314	+	0.985904i	$0.553509\pi$
$102$	11.4860	1.13728
$103$	3.45349	0.340282	0.170141	−	0.985420i	$-0.445578\pi$
$103$	3.45349	0.340282	0.170141	+	0.985420i	$0.445578\pi$
$104$	0.460741	0.0451794
$105$	−15.8355	−1.54539
$106$	−2.38462	−0.231615
$107$	−13.5997	−1.31473	−0.657364	−	0.753573i	$-0.728329\pi$
$107$	−13.5997	−1.31473	−0.657364	+	0.753573i	$0.728329\pi$
$108$	1.71679	0.165199
$109$	11.8461	1.13465	0.567324	−	0.823495i	$-0.307979\pi$
$109$	11.8461	1.13465	0.567324	+	0.823495i	$0.307979\pi$
$110$	−21.8659	−2.08483
$111$	−5.51381	−0.523348
$112$	18.4348	1.74192
$113$	10.2988	0.968829	0.484414	−	0.874839i	$-0.339033\pi$
$113$	10.2988	0.968829	0.484414	+	0.874839i	$0.339033\pi$
$114$	1.72940	0.161973
$115$	−14.0493	−1.31011
$116$	−1.50715	−0.139936
$117$	0.843859	0.0780148
$118$	9.07947	0.835833
$119$	24.4817	2.24424
$120$	2.10407	0.192075
$121$	−2.33798	−0.212544
$122$	−7.46474	−0.675825
$123$	−2.96850	−0.267661
$124$	−3.27661	−0.294248
$125$	18.6929	1.67195
$126$	7.92216	0.705762
$127$	4.09617	0.363477	0.181738	−	0.983347i	$-0.441828\pi$
$127$	4.09617	0.363477	0.181738	+	0.983347i	$0.441828\pi$
$128$	−4.32415	−0.382205
$129$	10.1312	0.892005
$130$	−6.26942	−0.549865
$131$	−9.64656	−0.842824	−0.421412	−	0.906869i	$-0.638465\pi$
$131$	−9.64656	−0.842824	−0.421412	+	0.906869i	$0.638465\pi$
$132$	5.05275	0.439785
$133$	3.68613	0.319628
$134$	7.36513	0.636250
$135$	3.85366	0.331670
$136$	−3.25290	−0.278934
$137$	−14.1189	−1.20626	−0.603129	−	0.797644i	$-0.706079\pi$
$137$	−14.1189	−1.20626	−0.603129	+	0.797644i	$0.706079\pi$
$138$	7.02855	0.598310
$139$	−0.974972	−0.0826961	−0.0413480	−	0.999145i	$-0.513165\pi$
$139$	−0.974972	−0.0826961	−0.0413480	+	0.999145i	$0.513165\pi$
$140$	−27.1863	−2.29766
$141$	−1.26552	−0.106576
$142$	21.6340	1.81548
$143$	2.48359	0.207688
$144$	−4.48621	−0.373851
$145$	−3.38308	−0.280950
$146$	28.1994	2.33380
$147$	9.88567	0.815356
$148$	−9.46608	−0.778107
$149$	−2.64705	−0.216855	−0.108427	−	0.994104i	$-0.534581\pi$
$149$	−2.64705	−0.216855	−0.108427	+	0.994104i	$0.534581\pi$
$150$	−18.9911	−1.55062
$151$	−7.19041	−0.585147	−0.292574	−	0.956243i	$-0.594512\pi$
$151$	−7.19041	−0.585147	−0.292574	+	0.956243i	$0.594512\pi$
$152$	−0.489778	−0.0397262
$153$	−5.95776	−0.481657
$154$	23.3159	1.87885
$155$	−7.35495	−0.590764
$156$	1.44873	0.115991
$157$	2.83023	0.225877	0.112938	−	0.993602i	$-0.463974\pi$
$157$	2.83023	0.225877	0.112938	+	0.993602i	$0.463974\pi$
$158$	1.85893	0.147889
$159$	1.23690	0.0980927
$160$	29.1220	2.30229
$161$	14.9810	1.18067
$162$	−1.92790	−0.151470
$163$	2.62576	0.205666	0.102833	−	0.994699i	$-0.467209\pi$
$163$	2.62576	0.205666	0.102833	+	0.994699i	$0.467209\pi$
$164$	−5.09630	−0.397954
$165$	11.3418	0.882960
$166$	−8.66774	−0.672747
$167$	−17.0090	−1.31620	−0.658099	−	0.752931i	$-0.728639\pi$
$167$	−17.0090	−1.31620	−0.658099	+	0.752931i	$0.728639\pi$
$168$	−2.24361	−0.173098
$169$	−12.2879	−0.945223
$170$	44.2630	3.39482
$171$	−0.897040	−0.0685984
$172$	17.3932	1.32622
$173$	−11.1493	−0.847667	−0.423834	−	0.905740i	$-0.639316\pi$
$173$	−11.1493	−0.847667	−0.423834	+	0.905740i	$0.639316\pi$
$174$	1.69248	0.128306
$175$	−40.4786	−3.05990
$176$	−13.2035	−0.995251
$177$	−4.70951	−0.353989
$178$	−15.2446	−1.14263
$179$	2.35863	0.176292	0.0881462	−	0.996108i	$-0.471906\pi$
$179$	2.35863	0.176292	0.0881462	+	0.996108i	$0.471906\pi$
$180$	6.61594	0.493123
$181$	3.43531	0.255344	0.127672	−	0.991816i	$-0.459249\pi$
$181$	3.43531	0.255344	0.127672	+	0.991816i	$0.459249\pi$
$182$	6.68518	0.495539
$183$	3.87195	0.286223
$184$	−1.99053	−0.146744
$185$	−21.2484	−1.56221
$186$	3.67951	0.269795
$187$	−17.5345	−1.28225
$188$	−2.17264	−0.158456
$189$	−4.10922	−0.298902
$190$	6.66453	0.483496
$191$	8.32035	0.602039	0.301020	−	0.953618i	$-0.402673\pi$
$191$	8.32035	0.602039	0.301020	+	0.953618i	$0.402673\pi$
$192$	−5.59665	−0.403904
$193$	−8.78215	−0.632153	−0.316077	−	0.948734i	$-0.602366\pi$
$193$	−8.78215	−0.632153	−0.316077	+	0.948734i	$0.602366\pi$
$194$	5.24738	0.376740
$195$	3.25195	0.232877
$196$	16.9717	1.21226
$197$	−6.45407	−0.459833	−0.229917	−	0.973210i	$-0.573845\pi$
$197$	−6.45407	−0.459833	−0.229917	+	0.973210i	$0.573845\pi$
$198$	−5.67406	−0.403238
$199$	0.597338	0.0423442	0.0211721	−	0.999776i	$-0.493260\pi$
$199$	0.597338	0.0423442	0.0211721	+	0.999776i	$0.493260\pi$
$200$	5.37841	0.380311
$201$	−3.82029	−0.269462
$202$	6.48345	0.456174
$203$	3.60743	0.253192
$204$	−10.2282	−0.716121
$205$	−11.4396	−0.798976
$206$	−6.65798	−0.463883
$207$	−3.64571	−0.253394
$208$	−3.78573	−0.262493
$209$	−2.64011	−0.182620
$210$	30.5293	2.10672
$211$	−20.6733	−1.42321	−0.711603	−	0.702582i	$-0.752030\pi$
$211$	−20.6733	−1.42321	−0.711603	+	0.702582i	$0.752030\pi$
$212$	2.12351	0.145843
$213$	−11.2215	−0.768887
$214$	26.2188	1.79228
$215$	39.0423	2.66266
$216$	0.545993	0.0371501
$217$	7.84270	0.532397
$218$	−22.8380	−1.54679
$219$	−14.6270	−0.988402
$220$	19.4716	1.31277
$221$	−5.02751	−0.338187
$222$	10.6301	0.713444
$223$	−11.0728	−0.741490	−0.370745	−	0.928735i	$-0.620898\pi$
$223$	−11.0728	−0.741490	−0.370745	+	0.928735i	$0.620898\pi$
$224$	−31.0532	−2.07483
$225$	9.85069	0.656713
$226$	−19.8550	−1.32074
$227$	−9.88685	−0.656214	−0.328107	−	0.944641i	$-0.606411\pi$
$227$	−9.88685	−0.656214	−0.328107	+	0.944641i	$0.606411\pi$
$228$	−1.54003	−0.101991
$229$	−9.23714	−0.610407	−0.305204	−	0.952287i	$-0.598725\pi$
$229$	−9.23714	−0.610407	−0.305204	+	0.952287i	$0.598725\pi$
$230$	27.0857	1.78598
$231$	−12.0940	−0.795725
$232$	−0.479321	−0.0314690
$233$	6.94982	0.455298	0.227649	−	0.973743i	$-0.426896\pi$
$233$	6.94982	0.455298	0.227649	+	0.973743i	$0.426896\pi$
$234$	−1.62687	−0.106352
$235$	−4.87689	−0.318133
$236$	−8.08526	−0.526306
$237$	−0.964228	−0.0626334
$238$	−47.1983	−3.05941
$239$	−15.1600	−0.980621	−0.490311	−	0.871548i	$-0.663117\pi$
$239$	−15.1600	−0.980621	−0.490311	+	0.871548i	$0.663117\pi$
$240$	−17.2883	−1.11596
$241$	20.8533	1.34328	0.671640	−	0.740878i	$-0.265590\pi$
$241$	20.8533	1.34328	0.671640	+	0.740878i	$0.265590\pi$
$242$	4.50739	0.289746
$243$	1.00000	0.0641500
$244$	6.64735	0.425553
$245$	38.0960	2.43386
$246$	5.72297	0.364883
$247$	−0.756975	−0.0481652
$248$	−1.04206	−0.0661710
$249$	4.49595	0.284920
$250$	−36.0381	−2.27925
$251$	13.6894	0.864067	0.432033	−	0.901858i	$-0.357796\pi$
$251$	13.6894	0.864067	0.432033	+	0.901858i	$0.357796\pi$
$252$	−7.05468	−0.444403
$253$	−10.7298	−0.674576
$254$	−7.89701	−0.495502
$255$	−22.9592	−1.43776
$256$	19.5298	1.22061
$257$	19.0246	1.18672	0.593362	−	0.804935i	$-0.297800\pi$
$257$	19.0246	1.18672	0.593362	+	0.804935i	$0.297800\pi$
$258$	−19.5320	−1.21601
$259$	22.6575	1.40787
$260$	5.58292	0.346238
$261$	−0.877888	−0.0543399
$262$	18.5976	1.14896
$263$	7.45065	0.459427	0.229713	−	0.973258i	$-0.426221\pi$
$263$	7.45065	0.459427	0.229713	+	0.973258i	$0.426221\pi$
$264$	1.60693	0.0988997
$265$	4.76660	0.292810
$266$	−7.10649	−0.435727
$267$	7.90736	0.483922
$268$	−6.55865	−0.400633
$269$	−12.2985	−0.749855	−0.374927	−	0.927054i	$-0.622332\pi$
$269$	−12.2985	−0.749855	−0.374927	+	0.927054i	$0.622332\pi$
$270$	−7.42947	−0.452143
$271$	−28.7040	−1.74364	−0.871821	−	0.489824i	$-0.837061\pi$
$271$	−28.7040	−1.74364	−0.871821	+	0.489824i	$0.837061\pi$
$272$	26.7278	1.62061
$273$	−3.46760	−0.209869
$274$	27.2198	1.64441
$275$	28.9919	1.74828
$276$	−6.25893	−0.376743
$277$	−4.00037	−0.240359	−0.120179	−	0.992752i	$-0.538347\pi$
$277$	−4.00037	−0.240359	−0.120179	+	0.992752i	$0.538347\pi$
$278$	1.87965	0.112734
$279$	−1.90856	−0.114263
$280$	−8.64609	−0.516703
$281$	3.66244	0.218483	0.109241	−	0.994015i	$-0.465158\pi$
$281$	3.66244	0.218483	0.109241	+	0.994015i	$0.465158\pi$
$282$	2.43980	0.145288
$283$	−23.3733	−1.38940	−0.694700	−	0.719299i	$-0.744463\pi$
$283$	−23.3733	−1.38940	−0.694700	+	0.719299i	$0.744463\pi$
$284$	−19.2651	−1.14317
$285$	−3.45689	−0.204768
$286$	−4.78810	−0.283127
$287$	12.1982	0.720038
$288$	7.55697	0.445299
$289$	18.4949	1.08794
$290$	6.52224	0.382999
$291$	−2.72181	−0.159555
$292$	−25.1116	−1.46954
$293$	10.3952	0.607296	0.303648	−	0.952784i	$-0.401795\pi$
$293$	10.3952	0.607296	0.303648	+	0.952784i	$0.401795\pi$
$294$	−19.0586	−1.11152
$295$	−18.1489	−1.05667
$296$	−3.01050	−0.174982
$297$	2.94313	0.170778
$298$	5.10324	0.295623
$299$	−3.07646	−0.177916
$300$	16.9116	0.976392
$301$	−41.6314	−2.39960
$302$	13.8624	0.797691
$303$	−3.36296	−0.193197
$304$	4.02431	0.230810
$305$	14.9212	0.854385
$306$	11.4860	0.656609
$307$	−32.1293	−1.83371	−0.916857	−	0.399215i	$-0.869283\pi$
$307$	−32.1293	−1.83371	−0.916857	+	0.399215i	$0.869283\pi$
$308$	−20.7628	−1.18307
$309$	3.45349	0.196462
$310$	14.1796	0.805347
$311$	12.1852	0.690957	0.345478	−	0.938427i	$-0.387717\pi$
$311$	12.1852	0.690957	0.345478	+	0.938427i	$0.387717\pi$
$312$	0.460741	0.0260843
$313$	19.3706	1.09489	0.547446	−	0.836841i	$-0.315600\pi$
$313$	19.3706	1.09489	0.547446	+	0.836841i	$0.315600\pi$
$314$	−5.45640	−0.307922
$315$	−15.8355	−0.892231
$316$	−1.65538	−0.0931225
$317$	8.90858	0.500356	0.250178	−	0.968200i	$-0.419511\pi$
$317$	8.90858	0.500356	0.250178	+	0.968200i	$0.419511\pi$
$318$	−2.38462	−0.133723
$319$	−2.58374	−0.144662
$320$	−21.5676	−1.20567
$321$	−13.5997	−0.759059
$322$	−28.8819	−1.60952
$323$	5.34435	0.297368
$324$	1.71679	0.0953774
$325$	8.31260	0.461100
$326$	−5.06221	−0.280370
$327$	11.8461	0.655089
$328$	−1.62078	−0.0894927
$329$	5.20030	0.286702
$330$	−21.8659	−1.20368
$331$	−14.0258	−0.770926	−0.385463	−	0.922723i	$-0.625958\pi$
$331$	−14.0258	−0.770926	−0.385463	+	0.922723i	$0.625958\pi$
$332$	7.71863	0.423615
$333$	−5.51381	−0.302155
$334$	32.7917	1.79428
$335$	−14.7221	−0.804354
$336$	18.4348	1.00570
$337$	−12.3866	−0.674742	−0.337371	−	0.941372i	$-0.609538\pi$
$337$	−12.3866	−0.674742	−0.337371	+	0.941372i	$0.609538\pi$
$338$	23.6898	1.28856
$339$	10.2988	0.559354
$340$	−39.4162	−2.13764
$341$	−5.61715	−0.304186
$342$	1.72940	0.0935154
$343$	−11.8578	−0.640263
$344$	5.53159	0.298243
$345$	−14.0493	−0.756390
$346$	21.4948	1.15557
$347$	−17.4178	−0.935036	−0.467518	−	0.883984i	$-0.654852\pi$
$347$	−17.4178	−0.935036	−0.467518	+	0.883984i	$0.654852\pi$
$348$	−1.50715	−0.0807918
$349$	17.3151	0.926857	0.463428	−	0.886134i	$-0.346619\pi$
$349$	17.3151	0.926857	0.463428	+	0.886134i	$0.346619\pi$
$350$	78.0387	4.17135
$351$	0.843859	0.0450419
$352$	22.2411	1.18546
$353$	−32.7614	−1.74371	−0.871857	−	0.489760i	$-0.837084\pi$
$353$	−32.7614	−1.74371	−0.871857	+	0.489760i	$0.837084\pi$
$354$	9.07947	0.482568
$355$	−43.2440	−2.29515
$356$	13.5753	0.719490
$357$	24.4817	1.29571
$358$	−4.54720	−0.240327
$359$	30.3763	1.60320	0.801601	−	0.597859i	$-0.203982\pi$
$359$	30.3763	1.60320	0.801601	+	0.597859i	$0.203982\pi$
$360$	2.10407	0.110894
$361$	−18.1953	−0.957648
$362$	−6.62292	−0.348093
$363$	−2.33798	−0.122712
$364$	−5.95315	−0.312030
$365$	−56.3675	−2.95041
$366$	−7.46474	−0.390188
$367$	−27.2982	−1.42496	−0.712478	−	0.701695i	$-0.752427\pi$
$367$	−27.2982	−1.42496	−0.712478	+	0.701695i	$0.752427\pi$
$368$	16.3554	0.852584
$369$	−2.96850	−0.154534
$370$	40.9647	2.12965
$371$	−5.08270	−0.263881
$372$	−3.27661	−0.169884
$373$	−8.34775	−0.432230	−0.216115	−	0.976368i	$-0.569339\pi$
$373$	−8.34775	−0.432230	−0.216115	+	0.976368i	$0.569339\pi$
$374$	33.8047	1.74800
$375$	18.6929	0.965299
$376$	−0.690966	−0.0356339
$377$	−0.740813	−0.0381538
$378$	7.92216	0.407472
$379$	−20.9828	−1.07782	−0.538908	−	0.842364i	$-0.681163\pi$
$379$	−20.9828	−1.07782	−0.538908	+	0.842364i	$0.681163\pi$
$380$	−5.93476	−0.304447
$381$	4.09617	0.209853
$382$	−16.0408	−0.820718
$383$	−6.48946	−0.331596	−0.165798	−	0.986160i	$-0.553020\pi$
$383$	−6.48946	−0.331596	−0.165798	+	0.986160i	$0.553020\pi$
$384$	−4.32415	−0.220666
$385$	−46.6060	−2.37526
$386$	16.9311	0.861770
$387$	10.1312	0.515000
$388$	−4.67279	−0.237225
$389$	15.4939	0.785570	0.392785	−	0.919630i	$-0.371512\pi$
$389$	15.4939	0.785570	0.392785	+	0.919630i	$0.371512\pi$
$390$	−6.26942	−0.317464
$391$	21.7203	1.09844
$392$	5.39751	0.272615
$393$	−9.64656	−0.486604
$394$	12.4428	0.626858
$395$	−3.71581	−0.186963
$396$	5.05275	0.253910
$397$	10.3784	0.520879	0.260440	−	0.965490i	$-0.416133\pi$
$397$	10.3784	0.520879	0.260440	+	0.965490i	$0.416133\pi$
$398$	−1.15161	−0.0577249
$399$	3.68613	0.184537
$400$	−44.1923	−2.20961
$401$	14.0612	0.702181	0.351091	−	0.936341i	$-0.385811\pi$
$401$	14.0612	0.702181	0.351091	+	0.936341i	$0.385811\pi$
$402$	7.36513	0.367339
$403$	−1.61056	−0.0802275
$404$	−5.77352	−0.287243
$405$	3.85366	0.191490
$406$	−6.95476	−0.345159
$407$	−16.2279	−0.804386
$408$	−3.25290	−0.161042
$409$	12.1814	0.602334	0.301167	−	0.953571i	$-0.402624\pi$
$409$	12.1814	0.602334	0.301167	+	0.953571i	$0.402624\pi$
$410$	22.0544	1.08919
$411$	−14.1189	−0.696433
$412$	5.92893	0.292097
$413$	19.3524	0.952270
$414$	7.02855	0.345435
$415$	17.3259	0.850494
$416$	6.37701	0.312659
$417$	−0.974972	−0.0477446
$418$	5.08986	0.248953
$419$	29.6029	1.44620	0.723099	−	0.690745i	$-0.242717\pi$
$419$	29.6029	1.44620	0.723099	+	0.690745i	$0.242717\pi$
$420$	−27.1863	−1.32656
$421$	25.1510	1.22578	0.612892	−	0.790167i	$-0.290006\pi$
$421$	25.1510	1.22578	0.612892	+	0.790167i	$0.290006\pi$
$422$	39.8559	1.94016
$423$	−1.26552	−0.0615318
$424$	0.675340	0.0327974
$425$	−58.6881	−2.84679
$426$	21.6340	1.04817
$427$	−15.9107	−0.769973
$428$	−23.3478	−1.12856
$429$	2.48359	0.119909
$430$	−75.2697	−3.62982
$431$	2.06351	0.0993956	0.0496978	−	0.998764i	$-0.484174\pi$
$431$	2.06351	0.0993956	0.0496978	+	0.998764i	$0.484174\pi$
$432$	−4.48621	−0.215843
$433$	28.4543	1.36743	0.683714	−	0.729750i	$-0.260363\pi$
$433$	28.4543	1.36743	0.683714	+	0.729750i	$0.260363\pi$
$434$	−15.1199	−0.725779
$435$	−3.38308	−0.162206
$436$	20.3373	0.973978
$437$	3.27034	0.156442
$438$	28.1994	1.34742
$439$	31.2431	1.49115	0.745576	−	0.666421i	$-0.232174\pi$
$439$	31.2431	1.49115	0.745576	+	0.666421i	$0.232174\pi$
$440$	6.19256	0.295219
$441$	9.88567	0.470746
$442$	9.69253	0.461027
$443$	9.89200	0.469983	0.234992	−	0.971997i	$-0.424494\pi$
$443$	9.89200	0.469983	0.234992	+	0.971997i	$0.424494\pi$
$444$	−9.46608	−0.449240
$445$	30.4723	1.44452
$446$	21.3473	1.01082
$447$	−2.64705	−0.125201
$448$	22.9979	1.08655
$449$	40.7473	1.92298	0.961491	−	0.274836i	$-0.0886235\pi$
$449$	40.7473	1.92298	0.961491	+	0.274836i	$0.0886235\pi$
$450$	−18.9911	−0.895251
$451$	−8.73668	−0.411394
$452$	17.6809	0.831640
$453$	−7.19041	−0.337835
$454$	19.0609	0.894570
$455$	−13.3630	−0.626465
$456$	−0.489778	−0.0229359
$457$	−24.8150	−1.16079	−0.580397	−	0.814333i	$-0.697103\pi$
$457$	−24.8150	−1.16079	−0.580397	+	0.814333i	$0.697103\pi$
$458$	17.8083	0.832126
$459$	−5.95776	−0.278085
$460$	−24.1198	−1.12459
$461$	−3.51397	−0.163662	−0.0818310	−	0.996646i	$-0.526077\pi$
$461$	−3.51397	−0.163662	−0.0818310	+	0.996646i	$0.526077\pi$
$462$	23.3159	1.08476
$463$	33.2790	1.54661	0.773303	−	0.634036i	$-0.218603\pi$
$463$	33.2790	1.54661	0.773303	+	0.634036i	$0.218603\pi$
$464$	3.93839	0.182835
$465$	−7.35495	−0.341078
$466$	−13.3985	−0.620675
$467$	28.1680	1.30346	0.651730	−	0.758451i	$-0.274044\pi$
$467$	28.1680	1.30346	0.651730	+	0.758451i	$0.274044\pi$
$468$	1.44873	0.0669676
$469$	15.6984	0.724884
$470$	9.40215	0.433689
$471$	2.83023	0.130410
$472$	−2.57136	−0.118357
$473$	29.8175	1.37101
$474$	1.85893	0.0853837
$475$	−8.83647	−0.405445
$476$	42.0301	1.92645
$477$	1.23690	0.0566339
$478$	29.2270	1.33681
$479$	−27.3860	−1.25130	−0.625650	−	0.780104i	$-0.715166\pi$
$479$	−27.3860	−1.25130	−0.625650	+	0.780104i	$0.715166\pi$
$480$	29.1220	1.32923
$481$	−4.65288	−0.212153
$482$	−40.2031	−1.83120
$483$	14.9810	0.681659
$484$	−4.01383	−0.182447
$485$	−10.4889	−0.476278
$486$	−1.92790	−0.0874513
$487$	9.95543	0.451124	0.225562	−	0.974229i	$-0.427578\pi$
$487$	9.95543	0.451124	0.225562	+	0.974229i	$0.427578\pi$
$488$	2.11406	0.0956990
$489$	2.62576	0.118741
$490$	−73.4452	−3.31792
$491$	−34.4873	−1.55639	−0.778194	−	0.628024i	$-0.783864\pi$
$491$	−34.4873	−1.55639	−0.778194	+	0.628024i	$0.783864\pi$
$492$	−5.09630	−0.229759
$493$	5.23025	0.235558
$494$	1.45937	0.0656602
$495$	11.3418	0.509777
$496$	8.56220	0.384454
$497$	46.1117	2.06839
$498$	−8.66774	−0.388411
$499$	5.62945	0.252009	0.126004	−	0.992030i	$-0.459785\pi$
$499$	5.62945	0.252009	0.126004	+	0.992030i	$0.459785\pi$
$500$	32.0919	1.43519
$501$	−17.0090	−0.759908
$502$	−26.3918	−1.17792
$503$	−32.0962	−1.43110	−0.715550	−	0.698562i	$-0.753824\pi$
$503$	−32.0962	−1.43110	−0.715550	+	0.698562i	$0.753824\pi$
$504$	−2.24361	−0.0999381
$505$	−12.9597	−0.576700
$506$	20.6860	0.919603
$507$	−12.2879	−0.545725
$508$	7.03229	0.312007
$509$	20.1084	0.891288	0.445644	−	0.895210i	$-0.352975\pi$
$509$	20.1084	0.891288	0.445644	+	0.895210i	$0.352975\pi$
$510$	44.2630	1.96000
$511$	60.1056	2.65891
$512$	−29.0032	−1.28177
$513$	−0.897040	−0.0396053
$514$	−36.6776	−1.61778
$515$	13.3086	0.586446
$516$	17.3932	0.765695
$517$	−3.72460	−0.163808
$518$	−43.6813	−1.91925
$519$	−11.1493	−0.489401
$520$	1.77554	0.0778626
$521$	−0.406395	−0.0178045	−0.00890225	−	0.999960i	$-0.502834\pi$
$521$	−0.406395	−0.0178045	−0.00890225	+	0.999960i	$0.502834\pi$
$522$	1.69248	0.0740778
$523$	12.3877	0.541678	0.270839	−	0.962625i	$-0.412699\pi$
$523$	12.3877	0.541678	0.270839	+	0.962625i	$0.412699\pi$
$524$	−16.5611	−0.723477
$525$	−40.4786	−1.76663
$526$	−14.3641	−0.626305
$527$	11.3708	0.495318
$528$	−13.2035	−0.574608
$529$	−9.70882	−0.422123
$530$	−9.18952	−0.399167
$531$	−4.70951	−0.204375
$532$	6.32833	0.274368
$533$	−2.50500	−0.108503
$534$	−15.2446	−0.659698
$535$	−52.4085	−2.26582
$536$	−2.08585	−0.0900951
$537$	2.35863	0.101782
$538$	23.7103	1.02222
$539$	29.0948	1.25320
$540$	6.61594	0.284705
$541$	26.4159	1.13571	0.567853	−	0.823130i	$-0.307774\pi$
$541$	26.4159	1.13571	0.567853	+	0.823130i	$0.307774\pi$
$542$	55.3384	2.37699
$543$	3.43531	0.147423
$544$	−45.0226	−1.93033
$545$	45.6507	1.95546
$546$	6.68518	0.286099
$547$	−16.3972	−0.701094	−0.350547	−	0.936545i	$-0.614004\pi$
$547$	−16.3972	−0.701094	−0.350547	+	0.936545i	$0.614004\pi$
$548$	−24.2392	−1.03545
$549$	3.87195	0.165251
$550$	−55.8934	−2.38330
$551$	0.787500	0.0335486
$552$	−1.99053	−0.0847226
$553$	3.96222	0.168491
$554$	7.71230	0.327664
$555$	−21.2484	−0.901942
$556$	−1.67383	−0.0709860
$557$	−21.6264	−0.916342	−0.458171	−	0.888864i	$-0.651495\pi$
$557$	−21.6264	−0.916342	−0.458171	+	0.888864i	$0.651495\pi$
$558$	3.67951	0.155766
$559$	8.54933	0.361598
$560$	71.0415	3.00205
$561$	−17.5345	−0.740306
$562$	−7.06081	−0.297842
$563$	3.63046	0.153006	0.0765028	−	0.997069i	$-0.475625\pi$
$563$	3.63046	0.153006	0.0765028	+	0.997069i	$0.475625\pi$
$564$	−2.17264	−0.0914846
$565$	39.6880	1.66969
$566$	45.0614	1.89407
$567$	−4.10922	−0.172571
$568$	−6.12688	−0.257078
$569$	−38.4248	−1.61085	−0.805425	−	0.592698i	$-0.798063\pi$
$569$	−38.4248	−1.61085	−0.805425	+	0.592698i	$0.798063\pi$
$570$	6.66453	0.279146
$571$	27.7412	1.16094	0.580468	−	0.814283i	$-0.302870\pi$
$571$	27.7412	1.16094	0.580468	+	0.814283i	$0.302870\pi$
$572$	4.26381	0.178279
$573$	8.32035	0.347587
$574$	−23.5169	−0.981577
$575$	−35.9127	−1.49766
$576$	−5.59665	−0.233194
$577$	−38.8703	−1.61819	−0.809095	−	0.587678i	$-0.800042\pi$
$577$	−38.8703	−1.61819	−0.809095	+	0.587678i	$0.800042\pi$
$578$	−35.6564	−1.48311
$579$	−8.78215	−0.364974
$580$	−5.80805	−0.241166
$581$	−18.4749	−0.766466
$582$	5.24738	0.217511
$583$	3.64037	0.150769
$584$	−7.98625	−0.330473
$585$	3.25195	0.134451
$586$	−20.0410	−0.827885
$587$	−19.9748	−0.824448	−0.412224	−	0.911082i	$-0.635248\pi$
$587$	−19.9748	−0.824448	−0.412224	+	0.911082i	$0.635248\pi$
$588$	16.9717	0.699899
$589$	1.71206	0.0705440
$590$	34.9892	1.44048
$591$	−6.45407	−0.265485
$592$	24.7361	1.01665
$593$	18.9622	0.778686	0.389343	−	0.921093i	$-0.372702\pi$
$593$	18.9622	0.778686	0.389343	+	0.921093i	$0.372702\pi$
$594$	−5.67406	−0.232809
$595$	94.3443	3.86774
$596$	−4.54444	−0.186147
$597$	0.597338	0.0244474
$598$	5.93111	0.242541
$599$	13.1265	0.536336	0.268168	−	0.963372i	$-0.413582\pi$
$599$	13.1265	0.536336	0.268168	+	0.963372i	$0.413582\pi$
$600$	5.37841	0.219573
$601$	22.7648	0.928596	0.464298	−	0.885679i	$-0.346307\pi$
$601$	22.7648	0.928596	0.464298	+	0.885679i	$0.346307\pi$
$602$	80.2612	3.27120
$603$	−3.82029	−0.155574
$604$	−12.3445	−0.502289
$605$	−9.00978	−0.366300
$606$	6.48345	0.263372
$607$	−10.5360	−0.427643	−0.213822	−	0.976873i	$-0.568591\pi$
$607$	−10.5360	−0.427643	−0.213822	+	0.976873i	$0.568591\pi$
$608$	−6.77890	−0.274921
$609$	3.60743	0.146181
$610$	−28.7666	−1.16472
$611$	−1.06792	−0.0432035
$612$	−10.2282	−0.413452
$613$	−30.1740	−1.21872	−0.609359	−	0.792895i	$-0.708573\pi$
$613$	−30.1740	−1.21872	−0.609359	+	0.792895i	$0.708573\pi$
$614$	61.9420	2.49977
$615$	−11.4396	−0.461289
$616$	−6.60322	−0.266051
$617$	34.1050	1.37302	0.686508	−	0.727122i	$-0.259143\pi$
$617$	34.1050	1.37302	0.686508	+	0.727122i	$0.259143\pi$
$618$	−6.65798	−0.267823
$619$	0.506194	0.0203457	0.0101728	−	0.999948i	$-0.496762\pi$
$619$	0.506194	0.0203457	0.0101728	+	0.999948i	$0.496762\pi$
$620$	−12.6269	−0.507110
$621$	−3.64571	−0.146297
$622$	−23.4918	−0.941933
$623$	−32.4931	−1.30181
$624$	−3.78573	−0.151550
$625$	22.7827	0.911308
$626$	−37.3446	−1.49259
$627$	−2.64011	−0.105436
$628$	4.85892	0.193892
$629$	32.8500	1.30981
$630$	30.5293	1.21632
$631$	19.8285	0.789360	0.394680	−	0.918819i	$-0.370856\pi$
$631$	19.8285	0.789360	0.394680	+	0.918819i	$0.370856\pi$
$632$	−0.526462	−0.0209415
$633$	−20.6733	−0.821688
$634$	−17.1748	−0.682100
$635$	15.7853	0.626419
$636$	2.12351	0.0842025
$637$	8.34211	0.330526
$638$	4.98119	0.197207
$639$	−11.2215	−0.443917
$640$	−16.6638	−0.658695
$641$	−34.9233	−1.37939	−0.689695	−	0.724100i	$-0.742255\pi$
$641$	−34.9233	−1.37939	−0.689695	+	0.724100i	$0.742255\pi$
$642$	26.2188	1.03477
$643$	−33.1614	−1.30776	−0.653879	−	0.756599i	$-0.726860\pi$
$643$	−33.1614	−1.30776	−0.653879	+	0.756599i	$0.726860\pi$
$644$	25.7193	1.01348
$645$	39.0423	1.53729
$646$	−10.3034	−0.405381
$647$	25.5536	1.00461	0.502307	−	0.864689i	$-0.332485\pi$
$647$	25.5536	1.00461	0.502307	+	0.864689i	$0.332485\pi$
$648$	0.545993	0.0214486
$649$	−13.8607	−0.544081
$650$	−16.0258	−0.628585
$651$	7.84270	0.307379
$652$	4.50790	0.176543
$653$	−31.3745	−1.22778	−0.613889	−	0.789392i	$-0.710396\pi$
$653$	−31.3745	−1.22778	−0.613889	+	0.789392i	$0.710396\pi$
$654$	−22.8380	−0.893037
$655$	−37.1746	−1.45253
$656$	13.3173	0.519953
$657$	−14.6270	−0.570654
$658$	−10.0257	−0.390841
$659$	12.0522	0.469489	0.234744	−	0.972057i	$-0.424575\pi$
$659$	12.0522	0.469489	0.234744	+	0.972057i	$0.424575\pi$
$660$	19.4716	0.757930
$661$	−4.07336	−0.158435	−0.0792176	−	0.996857i	$-0.525242\pi$
$661$	−4.07336	−0.158435	−0.0792176	+	0.996857i	$0.525242\pi$
$662$	27.0403	1.05095
$663$	−5.02751	−0.195252
$664$	2.45476	0.0952632
$665$	14.2051	0.550850
$666$	10.6301	0.411907
$667$	3.20052	0.123925
$668$	−29.2010	−1.12982
$669$	−11.0728	−0.428099
$670$	28.3827	1.09652
$671$	11.3957	0.439925
$672$	−31.0532	−1.19790
$673$	19.4999	0.751667	0.375833	−	0.926687i	$-0.377356\pi$
$673$	19.4999	0.751667	0.375833	+	0.926687i	$0.377356\pi$
$674$	23.8801	0.919828
$675$	9.85069	0.379153
$676$	−21.0958	−0.811377
$677$	−10.6132	−0.407900	−0.203950	−	0.978981i	$-0.565378\pi$
$677$	−10.6132	−0.407900	−0.203950	+	0.978981i	$0.565378\pi$
$678$	−19.8550	−0.762528
$679$	11.1845	0.429222
$680$	−12.5356	−0.480717
$681$	−9.88685	−0.378865
$682$	10.8293	0.414675
$683$	−24.9423	−0.954389	−0.477195	−	0.878798i	$-0.658346\pi$
$683$	−24.9423	−0.954389	−0.477195	+	0.878798i	$0.658346\pi$
$684$	−1.54003	−0.0588846
$685$	−54.4093	−2.07887
$686$	22.8607	0.872826
$687$	−9.23714	−0.352419
$688$	−45.4508	−1.73280
$689$	1.04377	0.0397645
$690$	27.0857	1.03113
$691$	9.66605	0.367714	0.183857	−	0.982953i	$-0.441142\pi$
$691$	9.66605	0.367714	0.183857	+	0.982953i	$0.441142\pi$
$692$	−19.1411	−0.727635
$693$	−12.0940	−0.459412
$694$	33.5797	1.27467
$695$	−3.75721	−0.142519
$696$	−0.479321	−0.0181686
$697$	17.6856	0.669891
$698$	−33.3818	−1.26352
$699$	6.94982	0.262866
$700$	−69.4935	−2.62661
$701$	18.5053	0.698935	0.349467	−	0.936949i	$-0.386363\pi$
$701$	18.5053	0.698935	0.349467	+	0.936949i	$0.386363\pi$
$702$	−1.62687	−0.0614024
$703$	4.94611	0.186546
$704$	−16.4717	−0.620800
$705$	−4.87689	−0.183674
$706$	63.1607	2.37708
$707$	13.8192	0.519723
$708$	−8.08526	−0.303863
$709$	−3.74958	−0.140819	−0.0704093	−	0.997518i	$-0.522431\pi$
$709$	−3.74958	−0.140819	−0.0704093	+	0.997518i	$0.522431\pi$
$710$	83.3700	3.12882
$711$	−0.964228	−0.0361614
$712$	4.31736	0.161800
$713$	6.95806	0.260581
$714$	−47.1983	−1.76635
$715$	9.57090	0.357931
$716$	4.04928	0.151329
$717$	−15.1600	−0.566162
$718$	−58.5625	−2.18553
$719$	−36.6342	−1.36622	−0.683112	−	0.730313i	$-0.739374\pi$
$719$	−36.6342	−1.36622	−0.683112	+	0.730313i	$0.739374\pi$
$720$	−17.2883	−0.644297
$721$	−14.1911	−0.528505
$722$	35.0787	1.30550
$723$	20.8533	0.775543
$724$	5.89771	0.219187
$725$	−8.64780	−0.321171
$726$	4.50739	0.167285
$727$	−4.87327	−0.180740	−0.0903699	−	0.995908i	$-0.528805\pi$
$727$	−4.87327	−0.180740	−0.0903699	+	0.995908i	$0.528805\pi$
$728$	−1.89329	−0.0701699
$729$	1.00000	0.0370370
$730$	108.671	4.02209
$731$	−60.3595	−2.23248
$732$	6.64735	0.245693
$733$	−35.6322	−1.31610	−0.658052	−	0.752973i	$-0.728619\pi$
$733$	−35.6322	−1.31610	−0.658052	+	0.752973i	$0.728619\pi$
$734$	52.6282	1.94254
$735$	38.0960	1.40519
$736$	−27.5505	−1.01552
$737$	−11.2436	−0.414164
$738$	5.72297	0.210665
$739$	−16.9913	−0.625036	−0.312518	−	0.949912i	$-0.601172\pi$
$739$	−16.9913	−0.625036	−0.312518	+	0.949912i	$0.601172\pi$
$740$	−36.4790	−1.34100
$741$	−0.756975	−0.0278082
$742$	9.79893	0.359730
$743$	4.66587	0.171174	0.0855870	−	0.996331i	$-0.472723\pi$
$743$	4.66587	0.171174	0.0855870	+	0.996331i	$0.472723\pi$
$744$	−1.04206	−0.0382038
$745$	−10.2008	−0.373729
$746$	16.0936	0.589229
$747$	4.49595	0.164498
$748$	−30.1031	−1.10068
$749$	55.8840	2.04196
$750$	−36.0381	−1.31592
$751$	39.4075	1.43800	0.719001	−	0.695009i	$-0.244600\pi$
$751$	39.4075	1.43800	0.719001	+	0.695009i	$0.244600\pi$
$752$	5.67739	0.207033
$753$	13.6894	0.498869
$754$	1.42821	0.0520125
$755$	−27.7094	−1.00845
$756$	−7.05468	−0.256576
$757$	−11.1113	−0.403846	−0.201923	−	0.979401i	$-0.564719\pi$
$757$	−11.1113	−0.403846	−0.201923	+	0.979401i	$0.564719\pi$
$758$	40.4528	1.46931
$759$	−10.7298	−0.389467
$760$	−1.88744	−0.0684645
$761$	29.4000	1.06575	0.532875	−	0.846194i	$-0.321112\pi$
$761$	29.4000	1.06575	0.532875	+	0.846194i	$0.321112\pi$
$762$	−7.89701	−0.286078
$763$	−48.6781	−1.76226
$764$	14.2843	0.516789
$765$	−22.9592	−0.830091
$766$	12.5110	0.452042
$767$	−3.97416	−0.143499
$768$	19.5298	0.704722
$769$	−29.5483	−1.06554	−0.532770	−	0.846260i	$-0.678849\pi$
$769$	−29.5483	−1.06554	−0.532770	+	0.846260i	$0.678849\pi$
$770$	89.8517	3.23803
$771$	19.0246	0.685156
$772$	−15.0771	−0.542638
$773$	30.4711	1.09597	0.547985	−	0.836488i	$-0.315395\pi$
$773$	30.4711	1.09597	0.547985	+	0.836488i	$0.315395\pi$
$774$	−19.5320	−0.702063
$775$	−18.8007	−0.675340
$776$	−1.48609	−0.0533476
$777$	22.6575	0.812832
$778$	−29.8706	−1.07091
$779$	2.66286	0.0954070
$780$	5.58292	0.199901
$781$	−33.0264	−1.18178
$782$	−41.8744	−1.49743
$783$	−0.877888	−0.0313731
$784$	−44.3492	−1.58390
$785$	10.9067	0.389278
$786$	18.5976	0.663354
$787$	−45.7394	−1.63043	−0.815216	−	0.579157i	$-0.803382\pi$
$787$	−45.7394	−1.63043	−0.815216	+	0.579157i	$0.803382\pi$
$788$	−11.0803	−0.394719
$789$	7.45065	0.265250
$790$	7.16370	0.254873
$791$	−42.3200	−1.50473
$792$	1.60693	0.0570998
$793$	3.26738	0.116028
$794$	−20.0086	−0.710078
$795$	4.76660	0.169054
$796$	1.02551	0.0363481
$797$	−13.6908	−0.484952	−0.242476	−	0.970157i	$-0.577960\pi$
$797$	−13.6908	−0.484952	−0.242476	+	0.970157i	$0.577960\pi$
$798$	−7.10649	−0.251567
$799$	7.53968	0.266735
$800$	74.4414	2.63190
$801$	7.90736	0.279393
$802$	−27.1085	−0.957235
$803$	−43.0492	−1.51917
$804$	−6.55865	−0.231306
$805$	57.7317	2.03477
$806$	3.10499	0.109369
$807$	−12.2985	−0.432929
$808$	−1.83616	−0.0645957
$809$	−12.3064	−0.432671	−0.216336	−	0.976319i	$-0.569411\pi$
$809$	−12.3064	−0.432671	−0.216336	+	0.976319i	$0.569411\pi$
$810$	−7.42947	−0.261045
$811$	−27.2035	−0.955243	−0.477621	−	0.878566i	$-0.658501\pi$
$811$	−27.2035	−0.955243	−0.477621	+	0.878566i	$0.658501\pi$
$812$	6.19322	0.217339
$813$	−28.7040	−1.00669
$814$	31.2857	1.09656
$815$	10.1188	0.354446
$816$	26.7278	0.935659
$817$	−9.08812	−0.317953
$818$	−23.4846	−0.821120
$819$	−3.46760	−0.121168
$820$	−19.6394	−0.685838
$821$	10.5280	0.367429	0.183714	−	0.982980i	$-0.441188\pi$
$821$	10.5280	0.367429	0.183714	+	0.982980i	$0.441188\pi$
$822$	27.2198	0.949398
$823$	51.8894	1.80875	0.904376	−	0.426737i	$-0.140337\pi$
$823$	51.8894	1.80875	0.904376	+	0.426737i	$0.140337\pi$
$824$	1.88558	0.0656873
$825$	28.9919	1.00937
$826$	−37.3095	−1.29816
$827$	−15.3921	−0.535236	−0.267618	−	0.963525i	$-0.586237\pi$
$827$	−15.3921	−0.535236	−0.267618	+	0.963525i	$0.586237\pi$
$828$	−6.25893	−0.217513
$829$	0.121593	0.00422309	0.00211154	−	0.999998i	$-0.499328\pi$
$829$	0.121593	0.00422309	0.00211154	+	0.999998i	$0.499328\pi$
$830$	−33.4025	−1.15942
$831$	−4.00037	−0.138771
$832$	−4.72278	−0.163733
$833$	−58.8965	−2.04064
$834$	1.87965	0.0650869
$835$	−65.5471	−2.26835
$836$	−4.53252	−0.156760
$837$	−1.90856	−0.0659695
$838$	−57.0715	−1.97150
$839$	9.40348	0.324644	0.162322	−	0.986738i	$-0.448102\pi$
$839$	9.40348	0.324644	0.162322	+	0.986738i	$0.448102\pi$
$840$	−8.64609	−0.298319
$841$	−28.2293	−0.973425
$842$	−48.4886	−1.67103
$843$	3.66244	0.126141
$844$	−35.4917	−1.22168
$845$	−47.3534	−1.62901
$846$	2.43980	0.0838820
$847$	9.60727	0.330110
$848$	−5.54900	−0.190553
$849$	−23.3733	−0.802171
$850$	113.145	3.88083
$851$	20.1017	0.689079
$852$	−19.2651	−0.660010
$853$	−9.21486	−0.315511	−0.157755	−	0.987478i	$-0.550426\pi$
$853$	−9.21486	−0.315511	−0.157755	+	0.987478i	$0.550426\pi$
$854$	30.6742	1.04965
$855$	−3.45689	−0.118223
$856$	−7.42532	−0.253792
$857$	−26.4524	−0.903596	−0.451798	−	0.892120i	$-0.649217\pi$
$857$	−26.4524	−0.903596	−0.451798	+	0.892120i	$0.649217\pi$
$858$	−4.78810	−0.163463
$859$	4.89997	0.167185	0.0835924	−	0.996500i	$-0.473361\pi$
$859$	4.89997	0.167185	0.0835924	+	0.996500i	$0.473361\pi$
$860$	67.0276	2.28562
$861$	12.1982	0.415714
$862$	−3.97823	−0.135499
$863$	−32.8975	−1.11985	−0.559923	−	0.828545i	$-0.689169\pi$
$863$	−32.8975	−1.11985	−0.559923	+	0.828545i	$0.689169\pi$
$864$	7.55697	0.257093
$865$	−42.9657	−1.46088
$866$	−54.8571	−1.86412
$867$	18.4949	0.628121
$868$	13.4643	0.457008
$869$	−2.83785	−0.0962675
$870$	6.52224	0.221125
$871$	−3.22378	−0.109234
$872$	6.46787	0.219030
$873$	−2.72181	−0.0921194
$874$	−6.30489	−0.213266
$875$	−76.8133	−2.59676
$876$	−25.1116	−0.848441
$877$	31.2826	1.05634	0.528169	−	0.849140i	$-0.322879\pi$
$877$	31.2826	1.05634	0.528169	+	0.849140i	$0.322879\pi$
$878$	−60.2335	−2.03278
$879$	10.3952	0.350623
$880$	−50.8818	−1.71522
$881$	−9.08501	−0.306082	−0.153041	−	0.988220i	$-0.548907\pi$
$881$	−9.08501	−0.306082	−0.153041	+	0.988220i	$0.548907\pi$
$882$	−19.0586	−0.641735
$883$	−49.3654	−1.66128	−0.830639	−	0.556812i	$-0.812024\pi$
$883$	−49.3654	−1.66128	−0.830639	+	0.556812i	$0.812024\pi$
$884$	−8.63120	−0.290299
$885$	−18.1489	−0.610067
$886$	−19.0708	−0.640695
$887$	−36.2334	−1.21660	−0.608298	−	0.793708i	$-0.708148\pi$
$887$	−36.2334	−1.21660	−0.608298	+	0.793708i	$0.708148\pi$
$888$	−3.01050	−0.101026
$889$	−16.8321	−0.564530
$890$	−58.7474	−1.96922
$891$	2.94313	0.0985986
$892$	−19.0097	−0.636493
$893$	1.13522	0.0379888
$894$	5.10324	0.170678
$895$	9.08936	0.303824
$896$	17.7689	0.593617
$897$	−3.07646	−0.102720
$898$	−78.5566	−2.62147
$899$	1.67550	0.0558811
$900$	16.9116	0.563720
$901$	−7.36917	−0.245503
$902$	16.8434	0.560825
$903$	−41.6314	−1.38541
$904$	5.62307	0.187021
$905$	13.2385	0.440063
$906$	13.8624	0.460547
$907$	−12.3234	−0.409192	−0.204596	−	0.978846i	$-0.565588\pi$
$907$	−12.3234	−0.409192	−0.204596	+	0.978846i	$0.565588\pi$
$908$	−16.9737	−0.563292
$909$	−3.36296	−0.111542
$910$	25.7624	0.854016
$911$	40.4387	1.33979	0.669896	−	0.742455i	$-0.266339\pi$
$911$	40.4387	1.33979	0.669896	+	0.742455i	$0.266339\pi$
$912$	4.02431	0.133258
$913$	13.2322	0.437921
$914$	47.8407	1.58243
$915$	14.9212	0.493279
$916$	−15.8583	−0.523972
$917$	39.6398	1.30902
$918$	11.4860	0.379093
$919$	20.9480	0.691012	0.345506	−	0.938417i	$-0.387707\pi$
$919$	20.9480	0.691012	0.345506	+	0.938417i	$0.387707\pi$
$920$	−7.67083	−0.252900
$921$	−32.1293	−1.05870
$922$	6.77459	0.223109
$923$	−9.46939	−0.311689
$924$	−20.7628	−0.683047
$925$	−54.3149	−1.78586
$926$	−64.1586	−2.10838
$927$	3.45349	0.113427
$928$	−6.63417	−0.217777
$929$	−16.2068	−0.531728	−0.265864	−	0.964011i	$-0.585657\pi$
$929$	−16.2068	−0.531728	−0.265864	+	0.964011i	$0.585657\pi$
$930$	14.1796	0.464967
$931$	−8.86784	−0.290632
$932$	11.9314	0.390826
$933$	12.1852	0.398924
$934$	−54.3050	−1.77692
$935$	−67.5719	−2.20984
$936$	0.460741	0.0150598
$937$	9.64354	0.315041	0.157520	−	0.987516i	$-0.449650\pi$
$937$	9.64354	0.315041	0.157520	+	0.987516i	$0.449650\pi$
$938$	−30.2649	−0.988184
$939$	19.3706	0.632136
$940$	−8.37261	−0.273085
$941$	−24.8563	−0.810292	−0.405146	−	0.914252i	$-0.632779\pi$
$941$	−24.8563	−0.810292	−0.405146	+	0.914252i	$0.632779\pi$
$942$	−5.45640	−0.177779
$943$	10.8223	0.352422
$944$	21.1279	0.687653
$945$	−15.8355	−0.515130
$946$	−57.4852	−1.86901
$947$	−31.8031	−1.03346	−0.516731	−	0.856148i	$-0.672851\pi$
$947$	−31.8031	−1.03346	−0.516731	+	0.856148i	$0.672851\pi$
$948$	−1.65538	−0.0537643
$949$	−12.3431	−0.400675
$950$	17.0358	0.552715
$951$	8.90858	0.288880
$952$	13.3669	0.433223
$953$	3.98330	0.129032	0.0645158	−	0.997917i	$-0.479450\pi$
$953$	3.98330	0.129032	0.0645158	+	0.997917i	$0.479450\pi$
$954$	−2.38462	−0.0772050
$955$	32.0638	1.03756
$956$	−26.0267	−0.841762
$957$	−2.58374	−0.0835204
$958$	52.7975	1.70581
$959$	58.0175	1.87348
$960$	−21.5676	−0.696091
$961$	−27.3574	−0.882497
$962$	8.97028	0.289213
$963$	−13.5997	−0.438243
$964$	35.8008	1.15307
$965$	−33.8434	−1.08946
$966$	−28.8819	−0.929258
$967$	0.653702	0.0210216	0.0105108	−	0.999945i	$-0.496654\pi$
$967$	0.653702	0.0210216	0.0105108	+	0.999945i	$0.496654\pi$
$968$	−1.27652	−0.0410289
$969$	5.34435	0.171685
$970$	20.2216	0.649277
$971$	15.2401	0.489078	0.244539	−	0.969639i	$-0.421363\pi$
$971$	15.2401	0.489078	0.244539	+	0.969639i	$0.421363\pi$
$972$	1.71679	0.0550662
$973$	4.00637	0.128438
$974$	−19.1931	−0.614986
$975$	8.31260	0.266216
$976$	−17.3704	−0.556013
$977$	8.58365	0.274615	0.137308	−	0.990528i	$-0.456155\pi$
$977$	8.58365	0.274615	0.137308	+	0.990528i	$0.456155\pi$
$978$	−5.06221	−0.161872
$979$	23.2724	0.743789
$980$	65.4030	2.08922
$981$	11.8461	0.378216
$982$	66.4879	2.12172
$983$	19.0716	0.608288	0.304144	−	0.952626i	$-0.401630\pi$
$983$	19.0716	0.608288	0.304144	+	0.952626i	$0.401630\pi$
$984$	−1.62078	−0.0516686
$985$	−24.8718	−0.792481
$986$	−10.0834	−0.321120
$987$	5.20030	0.165528
$988$	−1.29957	−0.0413448
$989$	−36.9355	−1.17448
$990$	−21.8659	−0.694944
$991$	13.2359	0.420452	0.210226	−	0.977653i	$-0.432580\pi$
$991$	13.2359	0.420452	0.210226	+	0.977653i	$0.432580\pi$
$992$	−14.4229	−0.457929
$993$	−14.0258	−0.445094
$994$	−88.8987	−2.81970
$995$	2.30194	0.0729763
$996$	7.71863	0.244574
$997$	24.2682	0.768581	0.384291	−	0.923212i	$-0.374446\pi$
$997$	24.2682	0.768581	0.384291	+	0.923212i	$0.374446\pi$
$998$	−10.8530	−0.343546
$999$	−5.51381	−0.174449

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8013.2.a.a.1.20	✓	94

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8013.2.a.a.1.20	✓	94	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:	\( N \)	\(=\)	\( 8013 = 3 \cdot 2671 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8013.a (trivial)

\(f(q)\)	\(=\)	\(q-1.92790 q^{2} +1.00000 q^{3} +1.71679 q^{4} +3.85366 q^{5} -1.92790 q^{6} -4.10922 q^{7} +0.545993 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.92790 q^{2} +1.00000 q^{3} +1.71679 q^{4} +3.85366 q^{5} -1.92790 q^{6} -4.10922 q^{7} +0.545993 q^{8} +1.00000 q^{9} -7.42947 q^{10} +2.94313 q^{11} +1.71679 q^{12} +0.843859 q^{13} +7.92216 q^{14} +3.85366 q^{15} -4.48621 q^{16} -5.95776 q^{17} -1.92790 q^{18} -0.897040 q^{19} +6.61594 q^{20} -4.10922 q^{21} -5.67406 q^{22} -3.64571 q^{23} +0.545993 q^{24} +9.85069 q^{25} -1.62687 q^{26} +1.00000 q^{27} -7.05468 q^{28} -0.877888 q^{29} -7.42947 q^{30} -1.90856 q^{31} +7.55697 q^{32} +2.94313 q^{33} +11.4860 q^{34} -15.8355 q^{35} +1.71679 q^{36} -5.51381 q^{37} +1.72940 q^{38} +0.843859 q^{39} +2.10407 q^{40} -2.96850 q^{41} +7.92216 q^{42} +10.1312 q^{43} +5.05275 q^{44} +3.85366 q^{45} +7.02855 q^{46} -1.26552 q^{47} -4.48621 q^{48} +9.88567 q^{49} -18.9911 q^{50} -5.95776 q^{51} +1.44873 q^{52} +1.23690 q^{53} -1.92790 q^{54} +11.3418 q^{55} -2.24361 q^{56} -0.897040 q^{57} +1.69248 q^{58} -4.70951 q^{59} +6.61594 q^{60} +3.87195 q^{61} +3.67951 q^{62} -4.10922 q^{63} -5.59665 q^{64} +3.25195 q^{65} -5.67406 q^{66} -3.82029 q^{67} -10.2282 q^{68} -3.64571 q^{69} +30.5293 q^{70} -11.2215 q^{71} +0.545993 q^{72} -14.6270 q^{73} +10.6301 q^{74} +9.85069 q^{75} -1.54003 q^{76} -12.0940 q^{77} -1.62687 q^{78} -0.964228 q^{79} -17.2883 q^{80} +1.00000 q^{81} +5.72297 q^{82} +4.49595 q^{83} -7.05468 q^{84} -22.9592 q^{85} -19.5320 q^{86} -0.877888 q^{87} +1.60693 q^{88} +7.90736 q^{89} -7.42947 q^{90} -3.46760 q^{91} -6.25893 q^{92} -1.90856 q^{93} +2.43980 q^{94} -3.45689 q^{95} +7.55697 q^{96} -2.72181 q^{97} -19.0586 q^{98} +2.94313 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9	\( 94 q - 13 q^{2} + 94 q^{3} + 73 q^{4} - 14 q^{5} - 13 q^{6} - 55 q^{7} - 36 q^{8} + 94 q^{9} - 39 q^{10} - 49 q^{11} + 73 q^{12} - 52 q^{13} - 7 q^{14} - 14 q^{15} + 43 q^{16} - 22 q^{17} - 13 q^{18} - 89 q^{19} - 22 q^{20} - 55 q^{21} - 36 q^{22} - 46 q^{23} - 36 q^{24} + 18 q^{25} + q^{26} + 94 q^{27} - 123 q^{28} - 20 q^{29} - 39 q^{30} - 61 q^{31} - 65 q^{32} - 49 q^{33} - 67 q^{34} - 40 q^{35} + 73 q^{36} - 83 q^{37} - 19 q^{38} - 52 q^{39} - 101 q^{40} - 25 q^{41} - 7 q^{42} - 150 q^{43} - 71 q^{44} - 14 q^{45} - 72 q^{46} - 39 q^{47} + 43 q^{48} - q^{49} - 45 q^{50} - 22 q^{51} - 110 q^{52} - 30 q^{53} - 13 q^{54} - 54 q^{55} - 5 q^{56} - 89 q^{57} - 77 q^{58} - 43 q^{59} - 22 q^{60} - 109 q^{61} - 33 q^{62} - 55 q^{63} + 10 q^{64} - 66 q^{65} - 36 q^{66} - 155 q^{67} - 46 q^{68} - 46 q^{69} - 43 q^{70} - 27 q^{71} - 36 q^{72} - 157 q^{73} - 29 q^{74} + 18 q^{75} - 176 q^{76} - 9 q^{77} + q^{78} - 99 q^{79} - 18 q^{80} + 94 q^{81} - 53 q^{82} - 144 q^{83} - 123 q^{84} - 105 q^{85} + 23 q^{86} - 20 q^{87} - 88 q^{88} - 4 q^{89} - 39 q^{90} - 99 q^{91} - 76 q^{92} - 61 q^{93} - 65 q^{94} - 49 q^{95} - 65 q^{96} - 139 q^{97} - 6 q^{98} - 49 q^{99}+O(q^{100}) \) 94 * q - 13 * q^2 + 94 * q^3 + 73 * q^4 - 14 * q^5 - 13 * q^6 - 55 * q^7 - 36 * q^8 + 94 * q^9 - 39 * q^10 - 49 * q^11 + 73 * q^12 - 52 * q^13 - 7 * q^14 - 14 * q^15 + 43 * q^16 - 22 * q^17 - 13 * q^18 - 89 * q^19 - 22 * q^20 - 55 * q^21 - 36 * q^22 - 46 * q^23 - 36 * q^24 + 18 * q^25 + q^26 + 94 * q^27 - 123 * q^28 - 20 * q^29 - 39 * q^30 - 61 * q^31 - 65 * q^32 - 49 * q^33 - 67 * q^34 - 40 * q^35 + 73 * q^36 - 83 * q^37 - 19 * q^38 - 52 * q^39 - 101 * q^40 - 25 * q^41 - 7 * q^42 - 150 * q^43 - 71 * q^44 - 14 * q^45 - 72 * q^46 - 39 * q^47 + 43 * q^48 - q^49 - 45 * q^50 - 22 * q^51 - 110 * q^52 - 30 * q^53 - 13 * q^54 - 54 * q^55 - 5 * q^56 - 89 * q^57 - 77 * q^58 - 43 * q^59 - 22 * q^60 - 109 * q^61 - 33 * q^62 - 55 * q^63 + 10 * q^64 - 66 * q^65 - 36 * q^66 - 155 * q^67 - 46 * q^68 - 46 * q^69 - 43 * q^70 - 27 * q^71 - 36 * q^72 - 157 * q^73 - 29 * q^74 + 18 * q^75 - 176 * q^76 - 9 * q^77 + q^78 - 99 * q^79 - 18 * q^80 + 94 * q^81 - 53 * q^82 - 144 * q^83 - 123 * q^84 - 105 * q^85 + 23 * q^86 - 20 * q^87 - 88 * q^88 - 4 * q^89 - 39 * q^90 - 99 * q^91 - 76 * q^92 - 61 * q^93 - 65 * q^94 - 49 * q^95 - 65 * q^96 - 139 * q^97 - 6 * q^98 - 49 * q^99

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