LMFDB - Embedded newform 8035.2.a.d.1.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8035,2,Mod(1,8035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8035, 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("8035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8035 = 5 \cdot 1607 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8035.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:	$64.1597980241$
Analytic rank:	$1$
Dimension:	$140$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.18
Character	$\chi$	$=$	8035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.40990 q^{2} +2.64302 q^{3} +3.80764 q^{4} -1.00000 q^{5} -6.36944 q^{6} -3.14385 q^{7} -4.35625 q^{8} +3.98558 q^{9} +O(q^{10})$	\(q-2.40990 q^{2} +2.64302 q^{3} +3.80764 q^{4} -1.00000 q^{5} -6.36944 q^{6} -3.14385 q^{7} -4.35625 q^{8} +3.98558 q^{9} +2.40990 q^{10} -1.83644 q^{11} +10.0637 q^{12} +5.52650 q^{13} +7.57638 q^{14} -2.64302 q^{15} +2.88285 q^{16} +1.88414 q^{17} -9.60486 q^{18} -7.48019 q^{19} -3.80764 q^{20} -8.30927 q^{21} +4.42564 q^{22} -1.45966 q^{23} -11.5137 q^{24} +1.00000 q^{25} -13.3183 q^{26} +2.60490 q^{27} -11.9707 q^{28} -6.21996 q^{29} +6.36944 q^{30} +10.1370 q^{31} +1.76509 q^{32} -4.85375 q^{33} -4.54059 q^{34} +3.14385 q^{35} +15.1756 q^{36} +10.5176 q^{37} +18.0265 q^{38} +14.6067 q^{39} +4.35625 q^{40} -10.1847 q^{41} +20.0246 q^{42} -10.1348 q^{43} -6.99250 q^{44} -3.98558 q^{45} +3.51763 q^{46} +10.5390 q^{47} +7.61945 q^{48} +2.88379 q^{49} -2.40990 q^{50} +4.97982 q^{51} +21.0429 q^{52} -1.11974 q^{53} -6.27756 q^{54} +1.83644 q^{55} +13.6954 q^{56} -19.7703 q^{57} +14.9895 q^{58} +10.1908 q^{59} -10.0637 q^{60} +8.03509 q^{61} -24.4292 q^{62} -12.5301 q^{63} -10.0194 q^{64} -5.52650 q^{65} +11.6971 q^{66} +14.5063 q^{67} +7.17412 q^{68} -3.85790 q^{69} -7.57638 q^{70} +0.653619 q^{71} -17.3621 q^{72} +0.399522 q^{73} -25.3463 q^{74} +2.64302 q^{75} -28.4819 q^{76} +5.77349 q^{77} -35.2007 q^{78} -7.55814 q^{79} -2.88285 q^{80} -5.07191 q^{81} +24.5442 q^{82} -13.8924 q^{83} -31.6387 q^{84} -1.88414 q^{85} +24.4238 q^{86} -16.4395 q^{87} +7.99998 q^{88} +0.0535385 q^{89} +9.60486 q^{90} -17.3745 q^{91} -5.55785 q^{92} +26.7923 q^{93} -25.3980 q^{94} +7.48019 q^{95} +4.66517 q^{96} -16.0113 q^{97} -6.94967 q^{98} -7.31927 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) $ 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * 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 $

$2$	−2.40990	−1.70406	−0.852030	−	0.523493i	$-0.824629\pi$
$2$	−2.40990	−1.70406	−0.852030	+	0.523493i	$0.824629\pi$
$3$	2.64302	1.52595	0.762975	−	0.646428i	$-0.223738\pi$
$3$	2.64302	1.52595	0.762975	+	0.646428i	$0.223738\pi$
$4$	3.80764	1.90382
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−6.36944	−2.60031
$7$	−3.14385	−1.18826	−0.594132	−	0.804368i	$-0.702504\pi$
$7$	−3.14385	−1.18826	−0.594132	+	0.804368i	$0.702504\pi$
$8$	−4.35625	−1.54017
$9$	3.98558	1.32853
$10$	2.40990	0.762079
$11$	−1.83644	−0.553707	−0.276854	−	0.960912i	$-0.589292\pi$
$11$	−1.83644	−0.553707	−0.276854	+	0.960912i	$0.589292\pi$
$12$	10.0637	2.90514
$13$	5.52650	1.53278	0.766388	−	0.642378i	$-0.222052\pi$
$13$	5.52650	1.53278	0.766388	+	0.642378i	$0.222052\pi$
$14$	7.57638	2.02487
$15$	−2.64302	−0.682426
$16$	2.88285	0.720713
$17$	1.88414	0.456971	0.228485	−	0.973547i	$-0.426623\pi$
$17$	1.88414	0.456971	0.228485	+	0.973547i	$0.426623\pi$
$18$	−9.60486	−2.26389
$19$	−7.48019	−1.71607	−0.858036	−	0.513589i	$-0.828316\pi$
$19$	−7.48019	−1.71607	−0.858036	+	0.513589i	$0.828316\pi$
$20$	−3.80764	−0.851415
$21$	−8.30927	−1.81323
$22$	4.42564	0.943550
$23$	−1.45966	−0.304359	−0.152180	−	0.988353i	$-0.548629\pi$
$23$	−1.45966	−0.304359	−0.152180	+	0.988353i	$0.548629\pi$
$24$	−11.5137	−2.35022
$25$	1.00000	0.200000
$26$	−13.3183	−2.61194
$27$	2.60490	0.501313
$28$	−11.9707	−2.26224
$29$	−6.21996	−1.15502	−0.577509	−	0.816384i	$-0.695975\pi$
$29$	−6.21996	−1.15502	−0.577509	+	0.816384i	$0.695975\pi$
$30$	6.36944	1.16289
$31$	10.1370	1.82066	0.910330	−	0.413883i	$-0.135828\pi$
$31$	10.1370	1.82066	0.910330	+	0.413883i	$0.135828\pi$
$32$	1.76509	0.312026
$33$	−4.85375	−0.844930
$34$	−4.54059	−0.778706
$35$	3.14385	0.531408
$36$	15.1756	2.52927
$37$	10.5176	1.72908	0.864538	−	0.502567i	$-0.167611\pi$
$37$	10.5176	1.72908	0.864538	+	0.502567i	$0.167611\pi$
$38$	18.0265	2.92429
$39$	14.6067	2.33894
$40$	4.35625	0.688783
$41$	−10.1847	−1.59058	−0.795292	−	0.606227i	$-0.792682\pi$
$41$	−10.1847	−1.59058	−0.795292	+	0.606227i	$0.792682\pi$
$42$	20.0246	3.08986
$43$	−10.1348	−1.54554	−0.772769	−	0.634688i	$-0.781129\pi$
$43$	−10.1348	−1.54554	−0.772769	+	0.634688i	$0.781129\pi$
$44$	−6.99250	−1.05416
$45$	−3.98558	−0.594135
$46$	3.51763	0.518646
$47$	10.5390	1.53727	0.768635	−	0.639687i	$-0.220936\pi$
$47$	10.5390	1.53727	0.768635	+	0.639687i	$0.220936\pi$
$48$	7.61945	1.09977
$49$	2.88379	0.411971
$50$	−2.40990	−0.340812
$51$	4.97982	0.697315
$52$	21.0429	2.91813
$53$	−1.11974	−0.153808	−0.0769038	−	0.997039i	$-0.524503\pi$
$53$	−1.11974	−0.153808	−0.0769038	+	0.997039i	$0.524503\pi$
$54$	−6.27756	−0.854268
$55$	1.83644	0.247625
$56$	13.6954	1.83012
$57$	−19.7703	−2.61864
$58$	14.9895	1.96822
$59$	10.1908	1.32673	0.663367	−	0.748295i	$-0.269127\pi$
$59$	10.1908	1.32673	0.663367	+	0.748295i	$0.269127\pi$
$60$	−10.0637	−1.29922
$61$	8.03509	1.02879	0.514394	−	0.857554i	$-0.328017\pi$
$61$	8.03509	1.02879	0.514394	+	0.857554i	$0.328017\pi$
$62$	−24.4292	−3.10251
$63$	−12.5301	−1.57864
$64$	−10.0194	−1.25243
$65$	−5.52650	−0.685478
$66$	11.6971	1.43981
$67$	14.5063	1.77223	0.886113	−	0.463469i	$-0.153396\pi$
$67$	14.5063	1.77223	0.886113	+	0.463469i	$0.153396\pi$
$68$	7.17412	0.869990
$69$	−3.85790	−0.464437
$70$	−7.57638	−0.905551
$71$	0.653619	0.0775703	0.0387852	−	0.999248i	$-0.487651\pi$
$71$	0.653619	0.0775703	0.0387852	+	0.999248i	$0.487651\pi$
$72$	−17.3621	−2.04615
$73$	0.399522	0.0467605	0.0233802	−	0.999727i	$-0.492557\pi$
$73$	0.399522	0.0467605	0.0233802	+	0.999727i	$0.492557\pi$
$74$	−25.3463	−2.94645
$75$	2.64302	0.305190
$76$	−28.4819	−3.26710
$77$	5.77349	0.657950
$78$	−35.2007	−3.98569
$79$	−7.55814	−0.850357	−0.425179	−	0.905109i	$-0.639789\pi$
$79$	−7.55814	−0.850357	−0.425179	+	0.905109i	$0.639789\pi$
$80$	−2.88285	−0.322313
$81$	−5.07191	−0.563546
$82$	24.5442	2.71045
$83$	−13.8924	−1.52489	−0.762444	−	0.647055i	$-0.776001\pi$
$83$	−13.8924	−1.52489	−0.762444	+	0.647055i	$0.776001\pi$
$84$	−31.6387	−3.45207
$85$	−1.88414	−0.204363
$86$	24.4238	2.63369
$87$	−16.4395	−1.76250
$88$	7.99998	0.852801
$89$	0.0535385	0.00567507	0.00283754	−	0.999996i	$-0.499097\pi$
$89$	0.0535385	0.00567507	0.00283754	+	0.999996i	$0.499097\pi$
$90$	9.60486	1.01244
$91$	−17.3745	−1.82134
$92$	−5.55785	−0.579445
$93$	26.7923	2.77824
$94$	−25.3980	−2.61960
$95$	7.48019	0.767451
$96$	4.66517	0.476137
$97$	−16.0113	−1.62570	−0.812851	−	0.582472i	$-0.802085\pi$
$97$	−16.0113	−1.62570	−0.812851	+	0.582472i	$0.802085\pi$
$98$	−6.94967	−0.702023
$99$	−7.31927	−0.735614
$100$	3.80764	0.380764
$101$	−10.8264	−1.07727	−0.538633	−	0.842541i	$-0.681059\pi$
$101$	−10.8264	−1.07727	−0.538633	+	0.842541i	$0.681059\pi$
$102$	−12.0009	−1.18827
$103$	−9.02007	−0.888774	−0.444387	−	0.895835i	$-0.646578\pi$
$103$	−9.02007	−0.888774	−0.444387	+	0.895835i	$0.646578\pi$
$104$	−24.0748	−2.36073
$105$	8.30927	0.810902
$106$	2.69846	0.262098
$107$	0.678992	0.0656407	0.0328203	−	0.999461i	$-0.489551\pi$
$107$	0.678992	0.0656407	0.0328203	+	0.999461i	$0.489551\pi$
$108$	9.91853	0.954411
$109$	8.45105	0.809463	0.404732	−	0.914435i	$-0.367365\pi$
$109$	8.45105	0.809463	0.404732	+	0.914435i	$0.367365\pi$
$110$	−4.42564	−0.421969
$111$	27.7982	2.63849
$112$	−9.06326	−0.856398
$113$	−8.97701	−0.844486	−0.422243	−	0.906483i	$-0.638757\pi$
$113$	−8.97701	−0.844486	−0.422243	+	0.906483i	$0.638757\pi$
$114$	47.6446	4.46232
$115$	1.45966	0.136114
$116$	−23.6834	−2.19895
$117$	22.0263	2.03633
$118$	−24.5589	−2.26083
$119$	−5.92345	−0.543002
$120$	11.5137	1.05105
$121$	−7.62749	−0.693408
$122$	−19.3638	−1.75312
$123$	−26.9184	−2.42715
$124$	38.5981	3.46621
$125$	−1.00000	−0.0894427
$126$	30.1962	2.69009
$127$	−21.5104	−1.90874	−0.954370	−	0.298628i	$-0.903471\pi$
$127$	−21.5104	−1.90874	−0.954370	+	0.298628i	$0.903471\pi$
$128$	20.6156	1.82218
$129$	−26.7864	−2.35841
$130$	13.3183	1.16810
$131$	14.2868	1.24824	0.624122	−	0.781327i	$-0.285457\pi$
$131$	14.2868	1.24824	0.624122	+	0.781327i	$0.285457\pi$
$132$	−18.4814	−1.60860
$133$	23.5166	2.03915
$134$	−34.9588	−3.01998
$135$	−2.60490	−0.224194
$136$	−8.20777	−0.703810
$137$	4.41039	0.376805	0.188403	−	0.982092i	$-0.439669\pi$
$137$	4.41039	0.376805	0.188403	+	0.982092i	$0.439669\pi$
$138$	9.29718	0.791429
$139$	9.93958	0.843064	0.421532	−	0.906814i	$-0.361493\pi$
$139$	9.93958	0.843064	0.421532	+	0.906814i	$0.361493\pi$
$140$	11.9707	1.01171
$141$	27.8548	2.34580
$142$	−1.57516	−0.132184
$143$	−10.1491	−0.848709
$144$	11.4898	0.957486
$145$	6.21996	0.516540
$146$	−0.962809	−0.0796826
$147$	7.62194	0.628647
$148$	40.0471	3.29185
$149$	−9.58998	−0.785642	−0.392821	−	0.919615i	$-0.628501\pi$
$149$	−9.58998	−0.785642	−0.392821	+	0.919615i	$0.628501\pi$
$150$	−6.36944	−0.520062
$151$	17.1569	1.39621	0.698104	−	0.715996i	$-0.254027\pi$
$151$	17.1569	1.39621	0.698104	+	0.715996i	$0.254027\pi$
$152$	32.5855	2.64304
$153$	7.50938	0.607097
$154$	−13.9136	−1.12119
$155$	−10.1370	−0.814224
$156$	55.6170	4.45292
$157$	14.6268	1.16735	0.583674	−	0.811988i	$-0.301614\pi$
$157$	14.6268	1.16735	0.583674	+	0.811988i	$0.301614\pi$
$158$	18.2144	1.44906
$159$	−2.95949	−0.234703
$160$	−1.76509	−0.139542
$161$	4.58894	0.361659
$162$	12.2228	0.960316
$163$	−8.13707	−0.637344	−0.318672	−	0.947865i	$-0.603237\pi$
$163$	−8.13707	−0.637344	−0.318672	+	0.947865i	$0.603237\pi$
$164$	−38.7797	−3.02819
$165$	4.85375	0.377864
$166$	33.4793	2.59850
$167$	−4.68877	−0.362828	−0.181414	−	0.983407i	$-0.558067\pi$
$167$	−4.68877	−0.362828	−0.181414	+	0.983407i	$0.558067\pi$
$168$	36.1972	2.79268
$169$	17.5422	1.34940
$170$	4.54059	0.348248
$171$	−29.8129	−2.27985
$172$	−38.5896	−2.94243
$173$	−8.70049	−0.661486	−0.330743	−	0.943721i	$-0.607299\pi$
$173$	−8.70049	−0.661486	−0.330743	+	0.943721i	$0.607299\pi$
$174$	39.6176	3.00341
$175$	−3.14385	−0.237653
$176$	−5.29419	−0.399064
$177$	26.9346	2.02453
$178$	−0.129023	−0.00967066
$179$	−10.1356	−0.757567	−0.378784	−	0.925485i	$-0.623658\pi$
$179$	−10.1356	−0.757567	−0.378784	+	0.925485i	$0.623658\pi$
$180$	−15.1756	−1.13113
$181$	−12.9673	−0.963854	−0.481927	−	0.876211i	$-0.660063\pi$
$181$	−12.9673	−0.963854	−0.481927	+	0.876211i	$0.660063\pi$
$182$	41.8709	3.10368
$183$	21.2369	1.56988
$184$	6.35862	0.468764
$185$	−10.5176	−0.773267
$186$	−64.5670	−4.73428
$187$	−3.46011	−0.253028
$188$	40.1287	2.92669
$189$	−8.18941	−0.595692
$190$	−18.0265	−1.30778
$191$	−7.40212	−0.535598	−0.267799	−	0.963475i	$-0.586296\pi$
$191$	−7.40212	−0.535598	−0.267799	+	0.963475i	$0.586296\pi$
$192$	−26.4815	−1.91114
$193$	1.48271	0.106728	0.0533638	−	0.998575i	$-0.483006\pi$
$193$	1.48271	0.106728	0.0533638	+	0.998575i	$0.483006\pi$
$194$	38.5857	2.77029
$195$	−14.6067	−1.04601
$196$	10.9805	0.784318
$197$	−3.94295	−0.280923	−0.140462	−	0.990086i	$-0.544859\pi$
$197$	−3.94295	−0.280923	−0.140462	+	0.990086i	$0.544859\pi$
$198$	17.6387	1.25353
$199$	−8.35966	−0.592601	−0.296300	−	0.955095i	$-0.595753\pi$
$199$	−8.35966	−0.592601	−0.296300	+	0.955095i	$0.595753\pi$
$200$	−4.35625	−0.308033
$201$	38.3405	2.70433
$202$	26.0906	1.83573
$203$	19.5546	1.37247
$204$	18.9614	1.32756
$205$	10.1847	0.711331
$206$	21.7375	1.51452
$207$	−5.81757	−0.404349
$208$	15.9321	1.10469
$209$	13.7369	0.950202
$210$	−20.0246	−1.38183
$211$	12.9200	0.889452	0.444726	−	0.895667i	$-0.353301\pi$
$211$	12.9200	0.889452	0.444726	+	0.895667i	$0.353301\pi$
$212$	−4.26356	−0.292822
$213$	1.72753	0.118368
$214$	−1.63631	−0.111856
$215$	10.1348	0.691185
$216$	−11.3476	−0.772105
$217$	−31.8692	−2.16342
$218$	−20.3662	−1.37937
$219$	1.05595	0.0713542
$220$	6.99250	0.471434
$221$	10.4127	0.700433
$222$	−66.9910	−4.49614
$223$	−21.0747	−1.41127	−0.705635	−	0.708576i	$-0.749338\pi$
$223$	−21.0747	−1.41127	−0.705635	+	0.708576i	$0.749338\pi$
$224$	−5.54917	−0.370769
$225$	3.98558	0.265705
$226$	21.6337	1.43905
$227$	−19.0905	−1.26708	−0.633541	−	0.773709i	$-0.718399\pi$
$227$	−19.0905	−1.26708	−0.633541	+	0.773709i	$0.718399\pi$
$228$	−75.2783	−4.98543
$229$	15.3241	1.01265	0.506323	−	0.862344i	$-0.331004\pi$
$229$	15.3241	1.01265	0.506323	+	0.862344i	$0.331004\pi$
$230$	−3.51763	−0.231946
$231$	15.2595	1.00400
$232$	27.0957	1.77892
$233$	−12.1194	−0.793970	−0.396985	−	0.917825i	$-0.629944\pi$
$233$	−12.1194	−0.793970	−0.396985	+	0.917825i	$0.629944\pi$
$234$	−53.0813	−3.47003
$235$	−10.5390	−0.687488
$236$	38.8030	2.52586
$237$	−19.9763	−1.29760
$238$	14.2749	0.925307
$239$	−2.18418	−0.141283	−0.0706414	−	0.997502i	$-0.522505\pi$
$239$	−2.18418	−0.141283	−0.0706414	+	0.997502i	$0.522505\pi$
$240$	−7.61945	−0.491834
$241$	−24.0969	−1.55221	−0.776107	−	0.630601i	$-0.782809\pi$
$241$	−24.0969	−1.55221	−0.776107	+	0.630601i	$0.782809\pi$
$242$	18.3815	1.18161
$243$	−21.2199	−1.36126
$244$	30.5947	1.95863
$245$	−2.88379	−0.184239
$246$	64.8708	4.13601
$247$	−41.3393	−2.63035
$248$	−44.1593	−2.80412
$249$	−36.7179	−2.32690
$250$	2.40990	0.152416
$251$	18.9968	1.19907	0.599534	−	0.800349i	$-0.295352\pi$
$251$	18.9968	1.19907	0.599534	+	0.800349i	$0.295352\pi$
$252$	−47.7100	−3.00544
$253$	2.68057	0.168526
$254$	51.8380	3.25261
$255$	−4.97982	−0.311849
$256$	−29.6429	−1.85268
$257$	−17.6172	−1.09893	−0.549467	−	0.835516i	$-0.685169\pi$
$257$	−17.6172	−1.09893	−0.549467	+	0.835516i	$0.685169\pi$
$258$	64.5527	4.01888
$259$	−33.0656	−2.05460
$260$	−21.0429	−1.30503
$261$	−24.7901	−1.53447
$262$	−34.4299	−2.12708
$263$	−25.2430	−1.55655	−0.778275	−	0.627924i	$-0.783905\pi$
$263$	−25.2430	−1.55655	−0.778275	+	0.627924i	$0.783905\pi$
$264$	21.1441	1.30133
$265$	1.11974	0.0687849
$266$	−56.6727	−3.47483
$267$	0.141504	0.00865988
$268$	55.2348	3.37400
$269$	−14.7980	−0.902247	−0.451124	−	0.892462i	$-0.648977\pi$
$269$	−14.7980	−0.902247	−0.451124	+	0.892462i	$0.648977\pi$
$270$	6.27756	0.382040
$271$	−0.0133185	−0.000809042 0	−0.000404521	−	1.00000i	$-0.500129\pi$
$271$	−0.0133185	−0.000809042 0	−0.000404521		1.00000i	$0.500129\pi$
$272$	5.43170	0.329345
$273$	−45.9212	−2.77928
$274$	−10.6286	−0.642098
$275$	−1.83644	−0.110741
$276$	−14.6895	−0.884205
$277$	−3.47135	−0.208573	−0.104286	−	0.994547i	$-0.533256\pi$
$277$	−3.47135	−0.208573	−0.104286	+	0.994547i	$0.533256\pi$
$278$	−23.9534	−1.43663
$279$	40.4018	2.41879
$280$	−13.6954	−0.818456
$281$	−1.18319	−0.0705831	−0.0352916	−	0.999377i	$-0.511236\pi$
$281$	−1.18319	−0.0705831	−0.0352916	+	0.999377i	$0.511236\pi$
$282$	−67.1275	−3.99738
$283$	16.9265	1.00618	0.503089	−	0.864235i	$-0.332197\pi$
$283$	16.9265	1.00618	0.503089	+	0.864235i	$0.332197\pi$
$284$	2.48875	0.147680
$285$	19.7703	1.17109
$286$	24.4583	1.44625
$287$	32.0192	1.89003
$288$	7.03489	0.414535
$289$	−13.4500	−0.791178
$290$	−14.9895	−0.880214
$291$	−42.3183	−2.48074
$292$	1.52124	0.0890236
$293$	4.49239	0.262448	0.131224	−	0.991353i	$-0.458109\pi$
$293$	4.49239	0.262448	0.131224	+	0.991353i	$0.458109\pi$
$294$	−18.3681	−1.07125
$295$	−10.1908	−0.593333
$296$	−45.8171	−2.66306
$297$	−4.78374	−0.277581
$298$	23.1110	1.33878
$299$	−8.06679	−0.466514
$300$	10.0637	0.581027
$301$	31.8622	1.83651
$302$	−41.3465	−2.37922
$303$	−28.6144	−1.64385
$304$	−21.5643	−1.23680
$305$	−8.03509	−0.460088
$306$	−18.0969	−1.03453
$307$	−3.77914	−0.215687	−0.107843	−	0.994168i	$-0.534395\pi$
$307$	−3.77914	−0.215687	−0.107843	+	0.994168i	$0.534395\pi$
$308$	21.9834	1.25262
$309$	−23.8403	−1.35622
$310$	24.4292	1.38749
$311$	24.3459	1.38053	0.690265	−	0.723557i	$-0.257494\pi$
$311$	24.3459	1.38053	0.690265	+	0.723557i	$0.257494\pi$
$312$	−63.6303	−3.60235
$313$	4.55063	0.257217	0.128608	−	0.991695i	$-0.458949\pi$
$313$	4.55063	0.257217	0.128608	+	0.991695i	$0.458949\pi$
$314$	−35.2493	−1.98923
$315$	12.5301	0.705988
$316$	−28.7787	−1.61893
$317$	−25.3347	−1.42294	−0.711469	−	0.702717i	$-0.751970\pi$
$317$	−25.3347	−1.42294	−0.711469	+	0.702717i	$0.751970\pi$
$318$	7.13209	0.399948
$319$	11.4226	0.639542
$320$	10.0194	0.560102
$321$	1.79459	0.100164
$322$	−11.0589	−0.616289
$323$	−14.0937	−0.784195
$324$	−19.3120	−1.07289
$325$	5.52650	0.306555
$326$	19.6096	1.08607
$327$	22.3363	1.23520
$328$	44.3671	2.44976
$329$	−33.1330	−1.82668
$330$	−11.6971	−0.643903
$331$	9.05839	0.497894	0.248947	−	0.968517i	$-0.419915\pi$
$331$	9.05839	0.497894	0.248947	+	0.968517i	$0.419915\pi$
$332$	−52.8972	−2.90311
$333$	41.9185	2.29712
$334$	11.2995	0.618281
$335$	−14.5063	−0.792563
$336$	−23.9544	−1.30682
$337$	−24.8514	−1.35374	−0.676871	−	0.736102i	$-0.736664\pi$
$337$	−24.8514	−1.35374	−0.676871	+	0.736102i	$0.736664\pi$
$338$	−42.2751	−2.29946
$339$	−23.7264	−1.28864
$340$	−7.17412	−0.389072
$341$	−18.6160	−1.00811
$342$	71.8461	3.88499
$343$	12.9407	0.698734
$344$	44.1495	2.38038
$345$	3.85790	0.207703
$346$	20.9674	1.12721
$347$	26.2937	1.41152	0.705759	−	0.708452i	$-0.250606\pi$
$347$	26.2937	1.41152	0.705759	+	0.708452i	$0.250606\pi$
$348$	−62.5957	−3.35548
$349$	28.3134	1.51558	0.757791	−	0.652497i	$-0.226279\pi$
$349$	28.3134	1.51558	0.757791	+	0.652497i	$0.226279\pi$
$350$	7.57638	0.404975
$351$	14.3960	0.768401
$352$	−3.24147	−0.172771
$353$	−5.82870	−0.310230	−0.155115	−	0.987896i	$-0.549575\pi$
$353$	−5.82870	−0.310230	−0.155115	+	0.987896i	$0.549575\pi$
$354$	−64.9098	−3.44992
$355$	−0.653619	−0.0346905
$356$	0.203856	0.0108043
$357$	−15.6558	−0.828594
$358$	24.4257	1.29094
$359$	−19.7818	−1.04404	−0.522022	−	0.852932i	$-0.674822\pi$
$359$	−19.7818	−1.04404	−0.522022	+	0.852932i	$0.674822\pi$
$360$	17.3621	0.915065
$361$	36.9532	1.94491
$362$	31.2500	1.64247
$363$	−20.1596	−1.05811
$364$	−66.1558	−3.46751
$365$	−0.399522	−0.0209119
$366$	−51.1790	−2.67517
$367$	−21.7004	−1.13275	−0.566376	−	0.824147i	$-0.691655\pi$
$367$	−21.7004	−1.13275	−0.566376	+	0.824147i	$0.691655\pi$
$368$	−4.20797	−0.219356
$369$	−40.5919	−2.11313
$370$	25.3463	1.31769
$371$	3.52029	0.182764
$372$	102.016	5.28927
$373$	14.4933	0.750436	0.375218	−	0.926937i	$-0.377568\pi$
$373$	14.4933	0.750436	0.375218	+	0.926937i	$0.377568\pi$
$374$	8.33852	0.431175
$375$	−2.64302	−0.136485
$376$	−45.9105	−2.36765
$377$	−34.3746	−1.77038
$378$	19.7357	1.01510
$379$	24.0638	1.23607	0.618036	−	0.786150i	$-0.287928\pi$
$379$	24.0638	1.23607	0.618036	+	0.786150i	$0.287928\pi$
$380$	28.4819	1.46109
$381$	−56.8525	−2.91264
$382$	17.8384	0.912692
$383$	−24.1419	−1.23360	−0.616798	−	0.787122i	$-0.711570\pi$
$383$	−24.1419	−1.23360	−0.616798	+	0.787122i	$0.711570\pi$
$384$	54.4876	2.78056
$385$	−5.77349	−0.294244
$386$	−3.57318	−0.181870
$387$	−40.3929	−2.05329
$388$	−60.9653	−3.09504
$389$	−18.1401	−0.919738	−0.459869	−	0.887987i	$-0.652104\pi$
$389$	−18.1401	−0.919738	−0.459869	+	0.887987i	$0.652104\pi$
$390$	35.2007	1.78246
$391$	−2.75019	−0.139083
$392$	−12.5625	−0.634503
$393$	37.7604	1.90476
$394$	9.50213	0.478710
$395$	7.55814	0.380291
$396$	−27.8691	−1.40048
$397$	−14.7502	−0.740291	−0.370145	−	0.928974i	$-0.620692\pi$
$397$	−14.7502	−0.740291	−0.370145	+	0.928974i	$0.620692\pi$
$398$	20.1460	1.00983
$399$	62.1549	3.11164
$400$	2.88285	0.144143
$401$	−36.3401	−1.81474	−0.907369	−	0.420334i	$-0.861913\pi$
$401$	−36.3401	−1.81474	−0.907369	+	0.420334i	$0.861913\pi$
$402$	−92.3969	−4.60834
$403$	56.0222	2.79066
$404$	−41.2230	−2.05092
$405$	5.07191	0.252025
$406$	−47.1248	−2.33876
$407$	−19.3149	−0.957402
$408$	−21.6933	−1.07398
$409$	0.0919201	0.00454515	0.00227258	−	0.999997i	$-0.499277\pi$
$409$	0.0919201	0.00454515	0.00227258	+	0.999997i	$0.499277\pi$
$410$	−24.5442	−1.21215
$411$	11.6568	0.574986
$412$	−34.3452	−1.69207
$413$	−32.0384	−1.57651
$414$	14.0198	0.689035
$415$	13.8924	0.681950
$416$	9.75476	0.478266
$417$	26.2705	1.28647
$418$	−33.1046	−1.61920
$419$	−3.21200	−0.156917	−0.0784583	−	0.996917i	$-0.525000\pi$
$419$	−3.21200	−0.156917	−0.0784583	+	0.996917i	$0.525000\pi$
$420$	31.6387	1.54381
$421$	−32.0211	−1.56061	−0.780307	−	0.625396i	$-0.784937\pi$
$421$	−32.0211	−1.56061	−0.780307	+	0.625396i	$0.784937\pi$
$422$	−31.1360	−1.51568
$423$	42.0040	2.04230
$424$	4.87785	0.236889
$425$	1.88414	0.0913941
$426$	−4.16318	−0.201707
$427$	−25.2611	−1.22247
$428$	2.58536	0.124968
$429$	−26.8243	−1.29509
$430$	−24.4238	−1.17782
$431$	18.8112	0.906102	0.453051	−	0.891484i	$-0.350335\pi$
$431$	18.8112	0.906102	0.453051	+	0.891484i	$0.350335\pi$
$432$	7.50955	0.361303
$433$	1.38474	0.0665462	0.0332731	−	0.999446i	$-0.489407\pi$
$433$	1.38474	0.0665462	0.0332731	+	0.999446i	$0.489407\pi$
$434$	76.8018	3.68660
$435$	16.4395	0.788214
$436$	32.1786	1.54107
$437$	10.9185	0.522303
$438$	−2.54473	−0.121592
$439$	3.58250	0.170983	0.0854917	−	0.996339i	$-0.472754\pi$
$439$	3.58250	0.170983	0.0854917	+	0.996339i	$0.472754\pi$
$440$	−7.99998	−0.381384
$441$	11.4936	0.547313
$442$	−25.0936	−1.19358
$443$	11.7786	0.559619	0.279810	−	0.960055i	$-0.409729\pi$
$443$	11.7786	0.559619	0.279810	+	0.960055i	$0.409729\pi$
$444$	105.845	5.02320
$445$	−0.0535385	−0.00253797
$446$	50.7881	2.40489
$447$	−25.3466	−1.19885
$448$	31.4995	1.48821
$449$	20.5612	0.970341	0.485170	−	0.874420i	$-0.338758\pi$
$449$	20.5612	0.970341	0.485170	+	0.874420i	$0.338758\pi$
$450$	−9.60486	−0.452777
$451$	18.7036	0.880718
$452$	−34.1812	−1.60775
$453$	45.3461	2.13054
$454$	46.0063	2.15918
$455$	17.3745	0.814529
$456$	86.1244	4.03314
$457$	−16.0525	−0.750904	−0.375452	−	0.926842i	$-0.622512\pi$
$457$	−16.0525	−0.750904	−0.375452	+	0.926842i	$0.622512\pi$
$458$	−36.9297	−1.72561
$459$	4.90799	0.229085
$460$	5.55785	0.259136
$461$	26.3078	1.22528	0.612639	−	0.790363i	$-0.290108\pi$
$461$	26.3078	1.22528	0.612639	+	0.790363i	$0.290108\pi$
$462$	−36.7739	−1.71088
$463$	−8.85107	−0.411344	−0.205672	−	0.978621i	$-0.565938\pi$
$463$	−8.85107	−0.411344	−0.205672	+	0.978621i	$0.565938\pi$
$464$	−17.9312	−0.832437
$465$	−26.7923	−1.24247
$466$	29.2067	1.35297
$467$	19.7136	0.912239	0.456119	−	0.889919i	$-0.349239\pi$
$467$	19.7136	0.912239	0.456119	+	0.889919i	$0.349239\pi$
$468$	83.8682	3.87681
$469$	−45.6056	−2.10587
$470$	25.3980	1.17152
$471$	38.6591	1.78132
$472$	−44.3938	−2.04339
$473$	18.6119	0.855775
$474$	48.1411	2.21119
$475$	−7.48019	−0.343215
$476$	−22.5544	−1.03378
$477$	−4.46280	−0.204337
$478$	5.26367	0.240754
$479$	−34.2511	−1.56497	−0.782486	−	0.622668i	$-0.786049\pi$
$479$	−34.2511	−1.56497	−0.782486	+	0.622668i	$0.786049\pi$
$480$	−4.66517	−0.212935
$481$	58.1253	2.65029
$482$	58.0711	2.64507
$483$	12.1287	0.551874
$484$	−29.0428	−1.32013
$485$	16.0113	0.727036
$486$	51.1379	2.31966
$487$	20.4088	0.924813	0.462406	−	0.886668i	$-0.346986\pi$
$487$	20.4088	0.924813	0.462406	+	0.886668i	$0.346986\pi$
$488$	−35.0028	−1.58450
$489$	−21.5065	−0.972556
$490$	6.94967	0.313954
$491$	12.0178	0.542357	0.271178	−	0.962529i	$-0.412587\pi$
$491$	12.0178	0.542357	0.271178	+	0.962529i	$0.412587\pi$
$492$	−102.496	−4.62086
$493$	−11.7193	−0.527809
$494$	99.6237	4.48228
$495$	7.31927	0.328977
$496$	29.2235	1.31217
$497$	−2.05488	−0.0921740
$498$	88.4866	3.96518
$499$	8.29574	0.371368	0.185684	−	0.982609i	$-0.440550\pi$
$499$	8.29574	0.371368	0.185684	+	0.982609i	$0.440550\pi$
$500$	−3.80764	−0.170283
$501$	−12.3925	−0.553658
$502$	−45.7805	−2.04329
$503$	−36.1805	−1.61321	−0.806605	−	0.591091i	$-0.798697\pi$
$503$	−36.1805	−1.61321	−0.806605	+	0.591091i	$0.798697\pi$
$504$	54.5840	2.43136
$505$	10.8264	0.481768
$506$	−6.45992	−0.287178
$507$	46.3645	2.05912
$508$	−81.9039	−3.63390
$509$	−35.6252	−1.57906	−0.789530	−	0.613712i	$-0.789676\pi$
$509$	−35.6252	−1.57906	−0.789530	+	0.613712i	$0.789676\pi$
$510$	12.0009	0.531409
$511$	−1.25604	−0.0555638
$512$	30.2053	1.33490
$513$	−19.4851	−0.860290
$514$	42.4559	1.87265
$515$	9.02007	0.397472
$516$	−101.993	−4.49000
$517$	−19.3542	−0.851198
$518$	79.6851	3.50116
$519$	−22.9956	−1.00940
$520$	24.0748	1.05575
$521$	−1.98915	−0.0871462	−0.0435731	−	0.999050i	$-0.513874\pi$
$521$	−1.98915	−0.0871462	−0.0435731	+	0.999050i	$0.513874\pi$
$522$	59.7418	2.61483
$523$	13.6358	0.596253	0.298126	−	0.954526i	$-0.403638\pi$
$523$	13.6358	0.596253	0.298126	+	0.954526i	$0.403638\pi$
$524$	54.3991	2.37643
$525$	−8.30927	−0.362646
$526$	60.8332	2.65245
$527$	19.0995	0.831988
$528$	−13.9927	−0.608952
$529$	−20.8694	−0.907365
$530$	−2.69846	−0.117214
$531$	40.6163	1.76260
$532$	89.5428	3.88217
$533$	−56.2858	−2.43801
$534$	−0.341010	−0.0147570
$535$	−0.678992	−0.0293554
$536$	−63.1930	−2.72952
$537$	−26.7885	−1.15601
$538$	35.6617	1.53748
$539$	−5.29591	−0.228111
$540$	−9.91853	−0.426825
$541$	0.324568	0.0139543	0.00697714	−	0.999976i	$-0.497779\pi$
$541$	0.324568	0.0139543	0.00697714	+	0.999976i	$0.497779\pi$
$542$	0.0320964	0.00137866
$543$	−34.2730	−1.47079
$544$	3.32567	0.142587
$545$	−8.45105	−0.362003
$546$	110.666	4.73606
$547$	33.7929	1.44488	0.722439	−	0.691434i	$-0.243021\pi$
$547$	33.7929	1.44488	0.722439	+	0.691434i	$0.243021\pi$
$548$	16.7932	0.717369
$549$	32.0244	1.36677
$550$	4.42564	0.188710
$551$	46.5265	1.98209
$552$	16.8060	0.715310
$553$	23.7617	1.01045
$554$	8.36561	0.355421
$555$	−27.7982	−1.17997
$556$	37.8464	1.60504
$557$	16.5972	0.703248	0.351624	−	0.936141i	$-0.385630\pi$
$557$	16.5972	0.703248	0.351624	+	0.936141i	$0.385630\pi$
$558$	−97.3645	−4.12177
$559$	−56.0098	−2.36896
$560$	9.06326	0.382993
$561$	−9.14514	−0.386108
$562$	2.85137	0.120278
$563$	35.0435	1.47691	0.738453	−	0.674305i	$-0.235556\pi$
$563$	35.0435	1.47691	0.738453	+	0.674305i	$0.235556\pi$
$564$	106.061	4.46598
$565$	8.97701	0.377665
$566$	−40.7913	−1.71459
$567$	15.9453	0.669641
$568$	−2.84733	−0.119471
$569$	−28.1769	−1.18124	−0.590619	−	0.806951i	$-0.701116\pi$
$569$	−28.1769	−1.18124	−0.590619	+	0.806951i	$0.701116\pi$
$570$	−47.6446	−1.99561
$571$	−24.6572	−1.03187	−0.515936	−	0.856627i	$-0.672556\pi$
$571$	−24.6572	−1.03187	−0.515936	+	0.856627i	$0.672556\pi$
$572$	−38.6441	−1.61579
$573$	−19.5640	−0.817297
$574$	−77.1632	−3.22073
$575$	−1.45966	−0.0608718
$576$	−39.9331	−1.66388
$577$	4.81444	0.200428	0.100214	−	0.994966i	$-0.468047\pi$
$577$	4.81444	0.200428	0.100214	+	0.994966i	$0.468047\pi$
$578$	32.4133	1.34821
$579$	3.91883	0.162861
$580$	23.6834	0.983399
$581$	43.6756	1.81197
$582$	101.983	4.22733
$583$	2.05633	0.0851644
$584$	−1.74041	−0.0720189
$585$	−22.0263	−0.910675
$586$	−10.8262	−0.447228
$587$	−16.0396	−0.662027	−0.331014	−	0.943626i	$-0.607391\pi$
$587$	−16.0396	−0.662027	−0.331014	+	0.943626i	$0.607391\pi$
$588$	29.0216	1.19683
$589$	−75.8267	−3.12438
$590$	24.5589	1.01108
$591$	−10.4213	−0.428675
$592$	30.3206	1.24617
$593$	−10.8481	−0.445477	−0.222738	−	0.974878i	$-0.571500\pi$
$593$	−10.8481	−0.445477	−0.222738	+	0.974878i	$0.571500\pi$
$594$	11.5284	0.473014
$595$	5.92345	0.242838
$596$	−36.5152	−1.49572
$597$	−22.0948	−0.904279
$598$	19.4402	0.794969
$599$	−20.2557	−0.827627	−0.413813	−	0.910362i	$-0.635803\pi$
$599$	−20.2557	−0.827627	−0.413813	+	0.910362i	$0.635803\pi$
$600$	−11.5137	−0.470043
$601$	−10.7950	−0.440337	−0.220168	−	0.975462i	$-0.570661\pi$
$601$	−10.7950	−0.440337	−0.220168	+	0.975462i	$0.570661\pi$
$602$	−76.7848	−3.12952
$603$	57.8159	2.35445
$604$	65.3273	2.65813
$605$	7.62749	0.310102
$606$	68.9580	2.80123
$607$	−10.5293	−0.427372	−0.213686	−	0.976902i	$-0.568547\pi$
$607$	−10.5293	−0.427372	−0.213686	+	0.976902i	$0.568547\pi$
$608$	−13.2032	−0.535460
$609$	51.6833	2.09431
$610$	19.3638	0.784017
$611$	58.2438	2.35629
$612$	28.5930	1.15580
$613$	46.7935	1.88997	0.944985	−	0.327113i	$-0.106076\pi$
$613$	46.7935	1.88997	0.944985	+	0.327113i	$0.106076\pi$
$614$	9.10737	0.367543
$615$	26.9184	1.08546
$616$	−25.1507	−1.01335
$617$	−20.1650	−0.811813	−0.405907	−	0.913915i	$-0.633044\pi$
$617$	−20.1650	−0.811813	−0.405907	+	0.913915i	$0.633044\pi$
$618$	57.4527	2.31109
$619$	4.56419	0.183450	0.0917252	−	0.995784i	$-0.470762\pi$
$619$	4.56419	0.183450	0.0917252	+	0.995784i	$0.470762\pi$
$620$	−38.5981	−1.55014
$621$	−3.80226	−0.152579
$622$	−58.6713	−2.35251
$623$	−0.168317	−0.00674348
$624$	42.1089	1.68571
$625$	1.00000	0.0400000
$626$	−10.9666	−0.438313
$627$	36.3070	1.44996
$628$	55.6938	2.22242
$629$	19.8165	0.790137
$630$	−30.1962	−1.20305
$631$	19.1311	0.761599	0.380799	−	0.924658i	$-0.375649\pi$
$631$	19.1311	0.761599	0.380799	+	0.924658i	$0.375649\pi$
$632$	32.9251	1.30969
$633$	34.1480	1.35726
$634$	61.0542	2.42477
$635$	21.5104	0.853614
$636$	−11.2687	−0.446832
$637$	15.9373	0.631458
$638$	−27.5273	−1.08982
$639$	2.60505	0.103054
$640$	−20.6156	−0.814904
$641$	−3.21717	−0.127070	−0.0635352	−	0.997980i	$-0.520238\pi$
$641$	−3.21717	−0.127070	−0.0635352	+	0.997980i	$0.520238\pi$
$642$	−4.32480	−0.170686
$643$	0.898257	0.0354238	0.0177119	−	0.999843i	$-0.494362\pi$
$643$	0.898257	0.0354238	0.0177119	+	0.999843i	$0.494362\pi$
$644$	17.4730	0.688534
$645$	26.7864	1.05471
$646$	33.9645	1.33632
$647$	−19.5331	−0.767924	−0.383962	−	0.923349i	$-0.625441\pi$
$647$	−19.5331	−0.767924	−0.383962	+	0.923349i	$0.625441\pi$
$648$	22.0945	0.867954
$649$	−18.7148	−0.734622
$650$	−13.3183	−0.522388
$651$	−84.2311	−3.30128
$652$	−30.9830	−1.21339
$653$	−18.3777	−0.719175	−0.359587	−	0.933111i	$-0.617083\pi$
$653$	−18.3777	−0.719175	−0.359587	+	0.933111i	$0.617083\pi$
$654$	−53.8284	−2.10486
$655$	−14.2868	−0.558232
$656$	−29.3610	−1.14636
$657$	1.59232	0.0621225
$658$	79.8474	3.11278
$659$	33.9412	1.32216	0.661082	−	0.750314i	$-0.270098\pi$
$659$	33.9412	1.32216	0.661082	+	0.750314i	$0.270098\pi$
$660$	18.4814	0.719386
$661$	−10.5824	−0.411609	−0.205805	−	0.978593i	$-0.565981\pi$
$661$	−10.5824	−0.411609	−0.205805	+	0.978593i	$0.565981\pi$
$662$	−21.8299	−0.848442
$663$	27.5210	1.06883
$664$	60.5186	2.34858
$665$	−23.5166	−0.911934
$666$	−101.020	−3.91443
$667$	9.07900	0.351540
$668$	−17.8532	−0.690760
$669$	−55.7010	−2.15353
$670$	34.9588	1.35058
$671$	−14.7559	−0.569647
$672$	−14.6666	−0.565776
$673$	−35.5078	−1.36872	−0.684362	−	0.729142i	$-0.739919\pi$
$673$	−35.5078	−1.36872	−0.684362	+	0.729142i	$0.739919\pi$
$674$	59.8895	2.30686
$675$	2.60490	0.100263
$676$	66.7944	2.56902
$677$	5.83472	0.224247	0.112123	−	0.993694i	$-0.464235\pi$
$677$	5.83472	0.224247	0.112123	+	0.993694i	$0.464235\pi$
$678$	57.1785	2.19593
$679$	50.3371	1.93176
$680$	8.20777	0.314754
$681$	−50.4567	−1.93350
$682$	44.8628	1.71788
$683$	−43.7691	−1.67478	−0.837388	−	0.546609i	$-0.815919\pi$
$683$	−43.7691	−1.67478	−0.837388	+	0.546609i	$0.815919\pi$
$684$	−113.517	−4.34042
$685$	−4.41039	−0.168512
$686$	−31.1859	−1.19068
$687$	40.5020	1.54525
$688$	−29.2170	−1.11389
$689$	−6.18823	−0.235753
$690$	−9.29718	−0.353938
$691$	−2.37886	−0.0904959	−0.0452480	−	0.998976i	$-0.514408\pi$
$691$	−2.37886	−0.0904959	−0.0452480	+	0.998976i	$0.514408\pi$
$692$	−33.1284	−1.25935
$693$	23.0107	0.874103
$694$	−63.3652	−2.40531
$695$	−9.93958	−0.377030
$696$	71.6145	2.71454
$697$	−19.1894	−0.726850
$698$	−68.2326	−2.58264
$699$	−32.0319	−1.21156
$700$	−11.9707	−0.452448
$701$	−23.4208	−0.884590	−0.442295	−	0.896870i	$-0.645836\pi$
$701$	−23.4208	−0.884590	−0.442295	+	0.896870i	$0.645836\pi$
$702$	−34.6929	−1.30940
$703$	−78.6734	−2.96722
$704$	18.4000	0.693477
$705$	−27.8548	−1.04907
$706$	14.0466	0.528651
$707$	34.0365	1.28008
$708$	102.557	3.85434
$709$	−13.0245	−0.489146	−0.244573	−	0.969631i	$-0.578648\pi$
$709$	−13.0245	−0.489146	−0.244573	+	0.969631i	$0.578648\pi$
$710$	1.57516	0.0591147
$711$	−30.1235	−1.12972
$712$	−0.233227	−0.00874055
$713$	−14.7965	−0.554135
$714$	37.7290	1.41197
$715$	10.1491	0.379554
$716$	−38.5926	−1.44227
$717$	−5.77284	−0.215591
$718$	47.6723	1.77911
$719$	−31.7173	−1.18286	−0.591429	−	0.806357i	$-0.701436\pi$
$719$	−31.7173	−1.18286	−0.591429	+	0.806357i	$0.701436\pi$
$720$	−11.4898	−0.428201
$721$	28.3577	1.05610
$722$	−89.0537	−3.31424
$723$	−63.6886	−2.36860
$724$	−49.3750	−1.83501
$725$	−6.21996	−0.231004
$726$	48.5828	1.80308
$727$	5.60479	0.207870	0.103935	−	0.994584i	$-0.466857\pi$
$727$	5.60479	0.207870	0.103935	+	0.994584i	$0.466857\pi$
$728$	75.6875	2.80517
$729$	−40.8689	−1.51366
$730$	0.962809	0.0356352
$731$	−19.0953	−0.706265
$732$	80.8626	2.98877
$733$	15.1489	0.559536	0.279768	−	0.960068i	$-0.409742\pi$
$733$	15.1489	0.559536	0.279768	+	0.960068i	$0.409742\pi$
$734$	52.2959	1.93028
$735$	−7.62194	−0.281139
$736$	−2.57642	−0.0949681
$737$	−26.6399	−0.981294
$738$	97.8227	3.60090
$739$	−33.1174	−1.21824	−0.609122	−	0.793076i	$-0.708478\pi$
$739$	−33.1174	−1.21824	−0.609122	+	0.793076i	$0.708478\pi$
$740$	−40.0471	−1.47216
$741$	−109.261	−4.01379
$742$	−8.48355	−0.311441
$743$	44.9052	1.64741	0.823705	−	0.567018i	$-0.191903\pi$
$743$	44.9052	1.64741	0.823705	+	0.567018i	$0.191903\pi$
$744$	−116.714	−4.27894
$745$	9.58998	0.351350
$746$	−34.9275	−1.27879
$747$	−55.3691	−2.02585
$748$	−13.1748	−0.481720
$749$	−2.13465	−0.0779984
$750$	6.36944	0.232579
$751$	21.4896	0.784166	0.392083	−	0.919930i	$-0.371755\pi$
$751$	21.4896	0.784166	0.392083	+	0.919930i	$0.371755\pi$
$752$	30.3824	1.10793
$753$	50.2091	1.82972
$754$	82.8395	3.01684
$755$	−17.1569	−0.624403
$756$	−31.1824	−1.13409
$757$	36.2314	1.31685	0.658427	−	0.752645i	$-0.271222\pi$
$757$	36.2314	1.31685	0.658427	+	0.752645i	$0.271222\pi$
$758$	−57.9914	−2.10634
$759$	7.08481	0.257162
$760$	−32.5855	−1.18200
$761$	−7.48505	−0.271333	−0.135666	−	0.990755i	$-0.543318\pi$
$761$	−7.48505	−0.271333	−0.135666	+	0.990755i	$0.543318\pi$
$762$	137.009	4.96332
$763$	−26.5688	−0.961856
$764$	−28.1846	−1.01968
$765$	−7.50938	−0.271502
$766$	58.1798	2.10212
$767$	56.3196	2.03358
$768$	−78.3469	−2.82710
$769$	25.0576	0.903601	0.451801	−	0.892119i	$-0.350782\pi$
$769$	25.0576	0.903601	0.451801	+	0.892119i	$0.350782\pi$
$770$	13.9136	0.501410
$771$	−46.5628	−1.67692
$772$	5.64561	0.203190
$773$	6.14748	0.221109	0.110555	−	0.993870i	$-0.464737\pi$
$773$	6.14748	0.221109	0.110555	+	0.993870i	$0.464737\pi$
$774$	97.3430	3.49892
$775$	10.1370	0.364132
$776$	69.7492	2.50385
$777$	−87.3933	−3.13522
$778$	43.7158	1.56729
$779$	76.1835	2.72956
$780$	−55.6170	−1.99141
$781$	−1.20033	−0.0429512
$782$	6.62770	0.237006
$783$	−16.2024	−0.579026
$784$	8.31356	0.296913
$785$	−14.6268	−0.522054
$786$	−90.9990	−3.24583
$787$	−23.7556	−0.846795	−0.423397	−	0.905944i	$-0.639163\pi$
$787$	−23.7556	−0.846795	−0.423397	+	0.905944i	$0.639163\pi$
$788$	−15.0133	−0.534828
$789$	−66.7178	−2.37522
$790$	−18.2144	−0.648039
$791$	28.2224	1.00347
$792$	31.8845	1.13297
$793$	44.4059	1.57690
$794$	35.5466	1.26150
$795$	2.95949	0.104962
$796$	−31.8306	−1.12821
$797$	−3.87108	−0.137121	−0.0685603	−	0.997647i	$-0.521841\pi$
$797$	−3.87108	−0.137121	−0.0685603	+	0.997647i	$0.521841\pi$
$798$	−149.787	−5.30242
$799$	19.8569	0.702488
$800$	1.76509	0.0624053
$801$	0.213382	0.00753947
$802$	87.5762	3.09242
$803$	−0.733697	−0.0258916
$804$	145.987	5.14856
$805$	−4.58894	−0.161739
$806$	−135.008	−4.75546
$807$	−39.1113	−1.37678
$808$	47.1624	1.65917
$809$	−30.5344	−1.07353	−0.536767	−	0.843731i	$-0.680355\pi$
$809$	−30.5344	−1.07353	−0.536767	+	0.843731i	$0.680355\pi$
$810$	−12.2228	−0.429467
$811$	24.1153	0.846804	0.423402	−	0.905942i	$-0.360836\pi$
$811$	24.1153	0.846804	0.423402	+	0.905942i	$0.360836\pi$
$812$	74.4570	2.61293
$813$	−0.0352012	−0.00123456
$814$	46.5470	1.63147
$815$	8.13707	0.285029
$816$	14.3561	0.502564
$817$	75.8100	2.65225
$818$	−0.221519	−0.00774522
$819$	−69.2473	−2.41970
$820$	38.7797	1.35425
$821$	−42.7615	−1.49239	−0.746193	−	0.665730i	$-0.768120\pi$
$821$	−42.7615	−1.49239	−0.746193	+	0.665730i	$0.768120\pi$
$822$	−28.0917	−0.979810
$823$	−42.4797	−1.48075	−0.740375	−	0.672194i	$-0.765352\pi$
$823$	−42.4797	−1.48075	−0.740375	+	0.672194i	$0.765352\pi$
$824$	39.2936	1.36886
$825$	−4.85375	−0.168986
$826$	77.2096	2.68647
$827$	−0.756051	−0.0262905	−0.0131452	−	0.999914i	$-0.504184\pi$
$827$	−0.756051	−0.0262905	−0.0131452	+	0.999914i	$0.504184\pi$
$828$	−22.1512	−0.769808
$829$	8.84628	0.307244	0.153622	−	0.988130i	$-0.450906\pi$
$829$	8.84628	0.307244	0.153622	+	0.988130i	$0.450906\pi$
$830$	−33.4793	−1.16208
$831$	−9.17485	−0.318272
$832$	−55.3722	−1.91969
$833$	5.43347	0.188258
$834$	−63.3095	−2.19223
$835$	4.68877	0.162262
$836$	52.3052	1.80901
$837$	26.4059	0.912721
$838$	7.74062	0.267395
$839$	11.3634	0.392310	0.196155	−	0.980573i	$-0.437154\pi$
$839$	11.3634	0.392310	0.196155	+	0.980573i	$0.437154\pi$
$840$	−36.1972	−1.24892
$841$	9.68790	0.334066
$842$	77.1679	2.65938
$843$	−3.12720	−0.107706
$844$	49.1949	1.69336
$845$	−17.5422	−0.603470
$846$	−101.226	−3.48021
$847$	23.9797	0.823952
$848$	−3.22804	−0.110851
$849$	44.7372	1.53538
$850$	−4.54059	−0.155741
$851$	−15.3520	−0.526260
$852$	6.57782	0.225352
$853$	−43.7353	−1.49747	−0.748734	−	0.662871i	$-0.769338\pi$
$853$	−43.7353	−1.49747	−0.748734	+	0.662871i	$0.769338\pi$
$854$	60.8769	2.08316
$855$	29.8129	1.01958
$856$	−2.95786	−0.101097
$857$	14.6053	0.498907	0.249453	−	0.968387i	$-0.419749\pi$
$857$	14.6053	0.498907	0.249453	+	0.968387i	$0.419749\pi$
$858$	64.6439	2.20691
$859$	56.0178	1.91130	0.955651	−	0.294502i	$-0.0951536\pi$
$859$	56.0178	1.91130	0.955651	+	0.294502i	$0.0951536\pi$
$860$	38.5896	1.31589
$861$	84.6275	2.88410
$862$	−45.3331	−1.54405
$863$	−25.1271	−0.855336	−0.427668	−	0.903936i	$-0.640665\pi$
$863$	−25.1271	−0.855336	−0.427668	+	0.903936i	$0.640665\pi$
$864$	4.59788	0.156423
$865$	8.70049	0.295826
$866$	−3.33709	−0.113399
$867$	−35.5487	−1.20730
$868$	−121.347	−4.11877
$869$	13.8801	0.470849
$870$	−39.6176	−1.34316
$871$	80.1690	2.71642
$872$	−36.8148	−1.24671
$873$	−63.8142	−2.15979
$874$	−26.3125	−0.890035
$875$	3.14385	0.106282
$876$	4.02066	0.135846
$877$	−48.1714	−1.62663	−0.813317	−	0.581821i	$-0.802341\pi$
$877$	−48.1714	−1.62663	−0.813317	+	0.581821i	$0.802341\pi$
$878$	−8.63348	−0.291366
$879$	11.8735	0.400483
$880$	5.29419	0.178467
$881$	−46.4731	−1.56572	−0.782859	−	0.622199i	$-0.786240\pi$
$881$	−46.4731	−1.56572	−0.782859	+	0.622199i	$0.786240\pi$
$882$	−27.6984	−0.932655
$883$	23.6010	0.794238	0.397119	−	0.917767i	$-0.370010\pi$
$883$	23.6010	0.794238	0.397119	+	0.917767i	$0.370010\pi$
$884$	39.6478	1.33350
$885$	−26.9346	−0.905397
$886$	−28.3854	−0.953625
$887$	31.9952	1.07429	0.537147	−	0.843489i	$-0.319502\pi$
$887$	31.9952	1.07429	0.537147	+	0.843489i	$0.319502\pi$
$888$	−121.096	−4.06370
$889$	67.6255	2.26809
$890$	0.129023	0.00432485
$891$	9.31426	0.312040
$892$	−80.2451	−2.68680
$893$	−78.8337	−2.63807
$894$	61.0828	2.04291
$895$	10.1356	0.338794
$896$	−64.8124	−2.16523
$897$	−21.3207	−0.711878
$898$	−49.5504	−1.65352
$899$	−63.0518	−2.10289
$900$	15.1756	0.505855
$901$	−2.10974	−0.0702856
$902$	−45.0739	−1.50080
$903$	84.2125	2.80242
$904$	39.1060	1.30065
$905$	12.9673	0.431049
$906$	−109.280	−3.63058
$907$	1.14694	0.0380834	0.0190417	−	0.999819i	$-0.493938\pi$
$907$	1.14694	0.0380834	0.0190417	+	0.999819i	$0.493938\pi$
$908$	−72.6898	−2.41230
$909$	−43.1494	−1.43117
$910$	−41.8709	−1.38801
$911$	−29.6519	−0.982412	−0.491206	−	0.871043i	$-0.663444\pi$
$911$	−29.6519	−0.982412	−0.491206	+	0.871043i	$0.663444\pi$
$912$	−56.9949	−1.88729
$913$	25.5125	0.844341
$914$	38.6850	1.27959
$915$	−21.2369	−0.702071
$916$	58.3488	1.92790
$917$	−44.9156	−1.48324
$918$	−11.8278	−0.390375
$919$	34.6539	1.14313	0.571563	−	0.820558i	$-0.306337\pi$
$919$	34.6539	1.14313	0.571563	+	0.820558i	$0.306337\pi$
$920$	−6.35862	−0.209637
$921$	−9.98836	−0.329128
$922$	−63.3994	−2.08795
$923$	3.61223	0.118898
$924$	58.1026	1.91144
$925$	10.5176	0.345815
$926$	21.3302	0.700955
$927$	−35.9502	−1.18076
$928$	−10.9788	−0.360396
$929$	6.21064	0.203765	0.101882	−	0.994796i	$-0.467514\pi$
$929$	6.21064	0.203765	0.101882	+	0.994796i	$0.467514\pi$
$930$	64.5670	2.11724
$931$	−21.5713	−0.706971
$932$	−46.1464	−1.51158
$933$	64.3468	2.10662
$934$	−47.5080	−1.55451
$935$	3.46011	0.113158
$936$	−95.9519	−3.13629
$937$	58.6469	1.91591	0.957956	−	0.286917i	$-0.0926302\pi$
$937$	58.6469	1.91591	0.957956	+	0.286917i	$0.0926302\pi$
$938$	109.905	3.58853
$939$	12.0274	0.392500
$940$	−40.1287	−1.30885
$941$	−11.8725	−0.387034	−0.193517	−	0.981097i	$-0.561989\pi$
$941$	−11.8725	−0.387034	−0.193517	+	0.981097i	$0.561989\pi$
$942$	−93.1647	−3.03547
$943$	14.8662	0.484109
$944$	29.3787	0.956194
$945$	8.18941	0.266402
$946$	−44.8529	−1.45829
$947$	43.7815	1.42271	0.711353	−	0.702835i	$-0.248083\pi$
$947$	43.7815	1.42271	0.711353	+	0.702835i	$0.248083\pi$
$948$	−76.0628	−2.47040
$949$	2.20796	0.0716733
$950$	18.0265	0.584858
$951$	−66.9602	−2.17133
$952$	25.8040	0.836312
$953$	−27.1854	−0.880620	−0.440310	−	0.897846i	$-0.645131\pi$
$953$	−27.1854	−0.880620	−0.440310	+	0.897846i	$0.645131\pi$
$954$	10.7549	0.348203
$955$	7.40212	0.239527
$956$	−8.31658	−0.268977
$957$	30.1901	0.975909
$958$	82.5418	2.66681
$959$	−13.8656	−0.447744
$960$	26.4815	0.854687
$961$	71.7589	2.31480
$962$	−140.077	−4.51625
$963$	2.70618	0.0872053
$964$	−91.7522	−2.95514
$965$	−1.48271	−0.0477300
$966$	−29.2290	−0.940426
$967$	−25.6510	−0.824882	−0.412441	−	0.910984i	$-0.635324\pi$
$967$	−25.6510	−0.824882	−0.412441	+	0.910984i	$0.635324\pi$
$968$	33.2272	1.06796
$969$	−37.2500	−1.19664
$970$	−38.5857	−1.23891
$971$	−32.6771	−1.04866	−0.524329	−	0.851516i	$-0.675684\pi$
$971$	−32.6771	−1.04866	−0.524329	+	0.851516i	$0.675684\pi$
$972$	−80.7977	−2.59159
$973$	−31.2485	−1.00178
$974$	−49.1834	−1.57594
$975$	14.6067	0.467788
$976$	23.1640	0.741461
$977$	8.78875	0.281177	0.140589	−	0.990068i	$-0.455101\pi$
$977$	8.78875	0.281177	0.140589	+	0.990068i	$0.455101\pi$
$978$	51.8285	1.65729
$979$	−0.0983202	−0.00314233
$980$	−10.9805	−0.350758
$981$	33.6823	1.07539
$982$	−28.9618	−0.924209
$983$	−3.29026	−0.104943	−0.0524715	−	0.998622i	$-0.516710\pi$
$983$	−3.29026	−0.104943	−0.0524715	+	0.998622i	$0.516710\pi$
$984$	117.263	3.73822
$985$	3.94295	0.125633
$986$	28.2423	0.899419
$987$	−87.5714	−2.78743
$988$	−157.405	−5.00772
$989$	14.7933	0.470399
$990$	−17.6387	−0.560596
$991$	53.0335	1.68466	0.842332	−	0.538958i	$-0.181182\pi$
$991$	53.0335	1.68466	0.842332	+	0.538958i	$0.181182\pi$
$992$	17.8927	0.568094
$993$	23.9416	0.759762
$994$	4.95207	0.157070
$995$	8.35966	0.265019
$996$	−139.809	−4.43001
$997$	−16.3104	−0.516557	−0.258278	−	0.966071i	$-0.583155\pi$
$997$	−16.3104	−0.516557	−0.258278	+	0.966071i	$0.583155\pi$
$998$	−19.9919	−0.632834
$999$	27.3972	0.866809

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8035.2.a.d.1.18	✓	140

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8035.2.a.d.1.18	✓	140	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:	\( N \)	\(=\)	\( 8035 = 5 \cdot 1607 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.40990 q^{2} +2.64302 q^{3} +3.80764 q^{4} -1.00000 q^{5} -6.36944 q^{6} -3.14385 q^{7} -4.35625 q^{8} +3.98558 q^{9} +O(q^{10})\)	\(q-2.40990 q^{2} +2.64302 q^{3} +3.80764 q^{4} -1.00000 q^{5} -6.36944 q^{6} -3.14385 q^{7} -4.35625 q^{8} +3.98558 q^{9} +2.40990 q^{10} -1.83644 q^{11} +10.0637 q^{12} +5.52650 q^{13} +7.57638 q^{14} -2.64302 q^{15} +2.88285 q^{16} +1.88414 q^{17} -9.60486 q^{18} -7.48019 q^{19} -3.80764 q^{20} -8.30927 q^{21} +4.42564 q^{22} -1.45966 q^{23} -11.5137 q^{24} +1.00000 q^{25} -13.3183 q^{26} +2.60490 q^{27} -11.9707 q^{28} -6.21996 q^{29} +6.36944 q^{30} +10.1370 q^{31} +1.76509 q^{32} -4.85375 q^{33} -4.54059 q^{34} +3.14385 q^{35} +15.1756 q^{36} +10.5176 q^{37} +18.0265 q^{38} +14.6067 q^{39} +4.35625 q^{40} -10.1847 q^{41} +20.0246 q^{42} -10.1348 q^{43} -6.99250 q^{44} -3.98558 q^{45} +3.51763 q^{46} +10.5390 q^{47} +7.61945 q^{48} +2.88379 q^{49} -2.40990 q^{50} +4.97982 q^{51} +21.0429 q^{52} -1.11974 q^{53} -6.27756 q^{54} +1.83644 q^{55} +13.6954 q^{56} -19.7703 q^{57} +14.9895 q^{58} +10.1908 q^{59} -10.0637 q^{60} +8.03509 q^{61} -24.4292 q^{62} -12.5301 q^{63} -10.0194 q^{64} -5.52650 q^{65} +11.6971 q^{66} +14.5063 q^{67} +7.17412 q^{68} -3.85790 q^{69} -7.57638 q^{70} +0.653619 q^{71} -17.3621 q^{72} +0.399522 q^{73} -25.3463 q^{74} +2.64302 q^{75} -28.4819 q^{76} +5.77349 q^{77} -35.2007 q^{78} -7.55814 q^{79} -2.88285 q^{80} -5.07191 q^{81} +24.5442 q^{82} -13.8924 q^{83} -31.6387 q^{84} -1.88414 q^{85} +24.4238 q^{86} -16.4395 q^{87} +7.99998 q^{88} +0.0535385 q^{89} +9.60486 q^{90} -17.3745 q^{91} -5.55785 q^{92} +26.7923 q^{93} -25.3980 q^{94} +7.48019 q^{95} +4.66517 q^{96} -16.0113 q^{97} -6.94967 q^{98} -7.31927 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9}+O(q^{10}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9	\( 140 q - 20 q^{2} - 12 q^{3} + 144 q^{4} - 140 q^{5} - 15 q^{7} - 63 q^{8} + 134 q^{9} + 20 q^{10} - 26 q^{11} - 31 q^{12} - 32 q^{13} - 37 q^{14} + 12 q^{15} + 152 q^{16} - 69 q^{17} - 64 q^{18} + 37 q^{19} - 144 q^{20} - 43 q^{21} - 25 q^{22} - 63 q^{23} - 5 q^{24} + 140 q^{25} - 16 q^{26} - 48 q^{27} - 52 q^{28} - 136 q^{29} + 25 q^{31} - 151 q^{32} - 48 q^{33} + 29 q^{34} + 15 q^{35} + 120 q^{36} - 82 q^{37} - 69 q^{38} - 26 q^{39} + 63 q^{40} - 11 q^{41} - 35 q^{42} - 54 q^{43} - 83 q^{44} - 134 q^{45} + 25 q^{46} - 39 q^{47} - 83 q^{48} + 215 q^{49} - 20 q^{50} - 75 q^{51} - 56 q^{52} - 196 q^{53} - 29 q^{54} + 26 q^{55} - 132 q^{56} - 110 q^{57} - 29 q^{58} - 31 q^{59} + 31 q^{60} - 18 q^{61} - 107 q^{62} - 67 q^{63} + 165 q^{64} + 32 q^{65} - 16 q^{66} - 50 q^{67} - 201 q^{68} - 46 q^{69} + 37 q^{70} - 84 q^{71} - 200 q^{72} - 70 q^{73} - 101 q^{74} - 12 q^{75} + 118 q^{76} - 166 q^{77} - 106 q^{78} - 35 q^{79} - 152 q^{80} + 116 q^{81} - 72 q^{82} - 66 q^{83} - 60 q^{84} + 69 q^{85} - 66 q^{86} - 75 q^{87} - 101 q^{88} + 8 q^{89} + 64 q^{90} + 2 q^{91} - 197 q^{92} - 134 q^{93} + 65 q^{94} - 37 q^{95} + 6 q^{96} - 73 q^{97} - 151 q^{98} - 51 q^{99}+O(q^{100}) \) 140 * q - 20 * q^2 - 12 * q^3 + 144 * q^4 - 140 * q^5 - 15 * q^7 - 63 * q^8 + 134 * q^9 + 20 * q^10 - 26 * q^11 - 31 * q^12 - 32 * q^13 - 37 * q^14 + 12 * q^15 + 152 * q^16 - 69 * q^17 - 64 * q^18 + 37 * q^19 - 144 * q^20 - 43 * q^21 - 25 * q^22 - 63 * q^23 - 5 * q^24 + 140 * q^25 - 16 * q^26 - 48 * q^27 - 52 * q^28 - 136 * q^29 + 25 * q^31 - 151 * q^32 - 48 * q^33 + 29 * q^34 + 15 * q^35 + 120 * q^36 - 82 * q^37 - 69 * q^38 - 26 * q^39 + 63 * q^40 - 11 * q^41 - 35 * q^42 - 54 * q^43 - 83 * q^44 - 134 * q^45 + 25 * q^46 - 39 * q^47 - 83 * q^48 + 215 * q^49 - 20 * q^50 - 75 * q^51 - 56 * q^52 - 196 * q^53 - 29 * q^54 + 26 * q^55 - 132 * q^56 - 110 * q^57 - 29 * q^58 - 31 * q^59 + 31 * q^60 - 18 * q^61 - 107 * q^62 - 67 * q^63 + 165 * q^64 + 32 * q^65 - 16 * q^66 - 50 * q^67 - 201 * q^68 - 46 * q^69 + 37 * q^70 - 84 * q^71 - 200 * q^72 - 70 * q^73 - 101 * q^74 - 12 * q^75 + 118 * q^76 - 166 * q^77 - 106 * q^78 - 35 * q^79 - 152 * q^80 + 116 * q^81 - 72 * q^82 - 66 * q^83 - 60 * q^84 + 69 * q^85 - 66 * q^86 - 75 * q^87 - 101 * q^88 + 8 * q^89 + 64 * q^90 + 2 * q^91 - 197 * q^92 - 134 * q^93 + 65 * q^94 - 37 * q^95 + 6 * q^96 - 73 * q^97 - 151 * q^98 - 51 * q^99

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