LMFDB - Embedded newform 8007.2.a.e.1.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8007,2,Mod(1,8007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8007, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8007 = 3 \cdot 17 \cdot 157 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8007.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:	$63.9362168984$
Analytic rank:	$1$
Dimension:	$46$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.8
Character	$\chi$	$=$	8007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.12891 q^{2} +1.00000 q^{3} +2.53226 q^{4} -4.00748 q^{5} -2.12891 q^{6} +2.85209 q^{7} -1.13314 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-2.12891 q^{2} +1.00000 q^{3} +2.53226 q^{4} -4.00748 q^{5} -2.12891 q^{6} +2.85209 q^{7} -1.13314 q^{8} +1.00000 q^{9} +8.53157 q^{10} +0.813194 q^{11} +2.53226 q^{12} -0.802739 q^{13} -6.07185 q^{14} -4.00748 q^{15} -2.65217 q^{16} -1.00000 q^{17} -2.12891 q^{18} +1.48404 q^{19} -10.1480 q^{20} +2.85209 q^{21} -1.73122 q^{22} +0.00429005 q^{23} -1.13314 q^{24} +11.0599 q^{25} +1.70896 q^{26} +1.00000 q^{27} +7.22225 q^{28} -4.50932 q^{29} +8.53157 q^{30} +1.77596 q^{31} +7.91251 q^{32} +0.813194 q^{33} +2.12891 q^{34} -11.4297 q^{35} +2.53226 q^{36} +5.09542 q^{37} -3.15940 q^{38} -0.802739 q^{39} +4.54105 q^{40} -10.8653 q^{41} -6.07185 q^{42} -2.58810 q^{43} +2.05922 q^{44} -4.00748 q^{45} -0.00913315 q^{46} -3.09960 q^{47} -2.65217 q^{48} +1.13443 q^{49} -23.5456 q^{50} -1.00000 q^{51} -2.03275 q^{52} +0.598271 q^{53} -2.12891 q^{54} -3.25886 q^{55} -3.23183 q^{56} +1.48404 q^{57} +9.59994 q^{58} +4.12232 q^{59} -10.1480 q^{60} +5.03103 q^{61} -3.78085 q^{62} +2.85209 q^{63} -11.5407 q^{64} +3.21696 q^{65} -1.73122 q^{66} -1.96620 q^{67} -2.53226 q^{68} +0.00429005 q^{69} +24.3328 q^{70} +8.01047 q^{71} -1.13314 q^{72} +3.22375 q^{73} -10.8477 q^{74} +11.0599 q^{75} +3.75799 q^{76} +2.31930 q^{77} +1.70896 q^{78} +1.07267 q^{79} +10.6285 q^{80} +1.00000 q^{81} +23.1313 q^{82} -10.1842 q^{83} +7.22225 q^{84} +4.00748 q^{85} +5.50984 q^{86} -4.50932 q^{87} -0.921465 q^{88} +5.84226 q^{89} +8.53157 q^{90} -2.28948 q^{91} +0.0108636 q^{92} +1.77596 q^{93} +6.59878 q^{94} -5.94727 q^{95} +7.91251 q^{96} -17.9365 q^{97} -2.41509 q^{98} +0.813194 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) $ 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * 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 $

$2$	−2.12891	−1.50537	−0.752684	−	0.658382i	$-0.771241\pi$
$2$	−2.12891	−1.50537	−0.752684	+	0.658382i	$0.771241\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	2.53226	1.26613
$5$	−4.00748	−1.79220	−0.896100	−	0.443852i	$-0.853612\pi$
$5$	−4.00748	−1.79220	−0.896100	+	0.443852i	$0.853612\pi$
$6$	−2.12891	−0.869124
$7$	2.85209	1.07799	0.538995	−	0.842309i	$-0.318804\pi$
$7$	2.85209	1.07799	0.538995	+	0.842309i	$0.318804\pi$
$8$	−1.13314	−0.400627
$9$	1.00000	0.333333
$10$	8.53157	2.69792
$11$	0.813194	0.245187	0.122594	−	0.992457i	$-0.460879\pi$
$11$	0.813194	0.245187	0.122594	+	0.992457i	$0.460879\pi$
$12$	2.53226	0.731002
$13$	−0.802739	−0.222640	−0.111320	−	0.993785i	$-0.535508\pi$
$13$	−0.802739	−0.222640	−0.111320	+	0.993785i	$0.535508\pi$
$14$	−6.07185	−1.62277
$15$	−4.00748	−1.03473
$16$	−2.65217	−0.663042
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−2.12891	−0.501789
$19$	1.48404	0.340463	0.170231	−	0.985404i	$-0.445548\pi$
$19$	1.48404	0.340463	0.170231	+	0.985404i	$0.445548\pi$
$20$	−10.1480	−2.26916
$21$	2.85209	0.622377
$22$	−1.73122	−0.369097
$23$	0.00429005	0.000894538 0	0.000447269	−	1.00000i	$-0.499858\pi$
$23$	0.00429005	0.000894538 0	0.000447269		1.00000i	$0.499858\pi$
$24$	−1.13314	−0.231302
$25$	11.0599	2.21198
$26$	1.70896	0.335155
$27$	1.00000	0.192450
$28$	7.22225	1.36488
$29$	−4.50932	−0.837360	−0.418680	−	0.908134i	$-0.637507\pi$
$29$	−4.50932	−0.837360	−0.418680	+	0.908134i	$0.637507\pi$
$30$	8.53157	1.55765
$31$	1.77596	0.318971	0.159486	−	0.987200i	$-0.449016\pi$
$31$	1.77596	0.318971	0.159486	+	0.987200i	$0.449016\pi$
$32$	7.91251	1.39875
$33$	0.813194	0.141559
$34$	2.12891	0.365105
$35$	−11.4297	−1.93197
$36$	2.53226	0.422044
$37$	5.09542	0.837681	0.418841	−	0.908060i	$-0.362437\pi$
$37$	5.09542	0.837681	0.418841	+	0.908060i	$0.362437\pi$
$38$	−3.15940	−0.512522
$39$	−0.802739	−0.128541
$40$	4.54105	0.718003
$41$	−10.8653	−1.69688	−0.848438	−	0.529295i	$-0.822456\pi$
$41$	−10.8653	−1.69688	−0.848438	+	0.529295i	$0.822456\pi$
$42$	−6.07185	−0.936907
$43$	−2.58810	−0.394682	−0.197341	−	0.980335i	$-0.563231\pi$
$43$	−2.58810	−0.394682	−0.197341	+	0.980335i	$0.563231\pi$
$44$	2.05922	0.310439
$45$	−4.00748	−0.597400
$46$	−0.00913315	−0.00134661
$47$	−3.09960	−0.452124	−0.226062	−	0.974113i	$-0.572585\pi$
$47$	−3.09960	−0.452124	−0.226062	+	0.974113i	$0.572585\pi$
$48$	−2.65217	−0.382807
$49$	1.13443	0.162061
$50$	−23.5456	−3.32985
$51$	−1.00000	−0.140028
$52$	−2.03275	−0.281891
$53$	0.598271	0.0821788	0.0410894	−	0.999155i	$-0.486917\pi$
$53$	0.598271	0.0821788	0.0410894	+	0.999155i	$0.486917\pi$
$54$	−2.12891	−0.289708
$55$	−3.25886	−0.439425
$56$	−3.23183	−0.431871
$57$	1.48404	0.196566
$58$	9.59994	1.26053
$59$	4.12232	0.536680	0.268340	−	0.963324i	$-0.413525\pi$
$59$	4.12232	0.536680	0.268340	+	0.963324i	$0.413525\pi$
$60$	−10.1480	−1.31010
$61$	5.03103	0.644158	0.322079	−	0.946713i	$-0.395618\pi$
$61$	5.03103	0.644158	0.322079	+	0.946713i	$0.395618\pi$
$62$	−3.78085	−0.480169
$63$	2.85209	0.359330
$64$	−11.5407	−1.44259
$65$	3.21696	0.399015
$66$	−1.73122	−0.213098
$67$	−1.96620	−0.240209	−0.120105	−	0.992761i	$-0.538323\pi$
$67$	−1.96620	−0.240209	−0.120105	+	0.992761i	$0.538323\pi$
$68$	−2.53226	−0.307082
$69$	0.00429005	0.000516462 0
$70$	24.3328	2.90833
$71$	8.01047	0.950668	0.475334	−	0.879806i	$-0.342327\pi$
$71$	8.01047	0.950668	0.475334	+	0.879806i	$0.342327\pi$
$72$	−1.13314	−0.133542
$73$	3.22375	0.377312	0.188656	−	0.982043i	$-0.439587\pi$
$73$	3.22375	0.377312	0.188656	+	0.982043i	$0.439587\pi$
$74$	−10.8477	−1.26102
$75$	11.0599	1.27709
$76$	3.75799	0.431071
$77$	2.31930	0.264309
$78$	1.70896	0.193502
$79$	1.07267	0.120685	0.0603426	−	0.998178i	$-0.480781\pi$
$79$	1.07267	0.120685	0.0603426	+	0.998178i	$0.480781\pi$
$80$	10.6285	1.18830
$81$	1.00000	0.111111
$82$	23.1313	2.55442
$83$	−10.1842	−1.11786	−0.558931	−	0.829214i	$-0.688788\pi$
$83$	−10.1842	−1.11786	−0.558931	+	0.829214i	$0.688788\pi$
$84$	7.22225	0.788012
$85$	4.00748	0.434672
$86$	5.50984	0.594142
$87$	−4.50932	−0.483450
$88$	−0.921465	−0.0982286
$89$	5.84226	0.619279	0.309639	−	0.950854i	$-0.399792\pi$
$89$	5.84226	0.619279	0.309639	+	0.950854i	$0.399792\pi$
$90$	8.53157	0.899307
$91$	−2.28948	−0.240003
$92$	0.0108636	0.00113260
$93$	1.77596	0.184158
$94$	6.59878	0.680612
$95$	−5.94727	−0.610177
$96$	7.91251	0.807568
$97$	−17.9365	−1.82117	−0.910587	−	0.413319i	$-0.864370\pi$
$97$	−17.9365	−1.82117	−0.910587	+	0.413319i	$0.864370\pi$
$98$	−2.41509	−0.243961
$99$	0.813194	0.0817291
$100$	28.0066	2.80066
$101$	−12.9844	−1.29200	−0.645998	−	0.763339i	$-0.723559\pi$
$101$	−12.9844	−1.29200	−0.645998	+	0.763339i	$0.723559\pi$
$102$	2.12891	0.210794
$103$	−9.54145	−0.940147	−0.470073	−	0.882627i	$-0.655773\pi$
$103$	−9.54145	−0.940147	−0.470073	+	0.882627i	$0.655773\pi$
$104$	0.909618	0.0891954
$105$	−11.4297	−1.11542
$106$	−1.27367	−0.123709
$107$	−0.584447	−0.0565006	−0.0282503	−	0.999601i	$-0.508994\pi$
$107$	−0.584447	−0.0565006	−0.0282503	+	0.999601i	$0.508994\pi$
$108$	2.53226	0.243667
$109$	−9.66169	−0.925422	−0.462711	−	0.886509i	$-0.653123\pi$
$109$	−9.66169	−0.925422	−0.462711	+	0.886509i	$0.653123\pi$
$110$	6.93782	0.661496
$111$	5.09542	0.483636
$112$	−7.56422	−0.714752
$113$	2.48201	0.233488	0.116744	−	0.993162i	$-0.462754\pi$
$113$	2.48201	0.233488	0.116744	+	0.993162i	$0.462754\pi$
$114$	−3.15940	−0.295904
$115$	−0.0171923	−0.00160319
$116$	−11.4188	−1.06021
$117$	−0.802739	−0.0742132
$118$	−8.77605	−0.807901
$119$	−2.85209	−0.261451
$120$	4.54105	0.414539
$121$	−10.3387	−0.939883
$122$	−10.7106	−0.969695
$123$	−10.8653	−0.979692
$124$	4.49719	0.403860
$125$	−24.2850	−2.17211
$126$	−6.07185	−0.540923
$127$	22.1015	1.96119	0.980596	−	0.196040i	$-0.0628082\pi$
$127$	22.1015	1.96119	0.980596	+	0.196040i	$0.0628082\pi$
$128$	8.74412	0.772879
$129$	−2.58810	−0.227870
$130$	−6.84862	−0.600664
$131$	0.556990	0.0486644	0.0243322	−	0.999704i	$-0.492254\pi$
$131$	0.556990	0.0486644	0.0243322	+	0.999704i	$0.492254\pi$
$132$	2.05922	0.179232
$133$	4.23263	0.367015
$134$	4.18586	0.361603
$135$	−4.00748	−0.344909
$136$	1.13314	0.0971663
$137$	6.21709	0.531162	0.265581	−	0.964089i	$-0.414436\pi$
$137$	6.21709	0.531162	0.265581	+	0.964089i	$0.414436\pi$
$138$	−0.00913315	−0.000777465 0
$139$	19.1812	1.62693	0.813466	−	0.581613i	$-0.197578\pi$
$139$	19.1812	1.62693	0.813466	+	0.581613i	$0.197578\pi$
$140$	−28.9430	−2.44613
$141$	−3.09960	−0.261034
$142$	−17.0536	−1.43110
$143$	−0.652782	−0.0545884
$144$	−2.65217	−0.221014
$145$	18.0710	1.50072
$146$	−6.86309	−0.567993
$147$	1.13443	0.0935659
$148$	12.9029	1.06062
$149$	5.65926	0.463624	0.231812	−	0.972761i	$-0.425535\pi$
$149$	5.65926	0.463624	0.231812	+	0.972761i	$0.425535\pi$
$150$	−23.5456	−1.92249
$151$	−17.1460	−1.39532	−0.697661	−	0.716428i	$-0.745776\pi$
$151$	−17.1460	−1.39532	−0.697661	+	0.716428i	$0.745776\pi$
$152$	−1.68163	−0.136398
$153$	−1.00000	−0.0808452
$154$	−4.93759	−0.397883
$155$	−7.11711	−0.571660
$156$	−2.03275	−0.162750
$157$	1.00000	0.0798087
$157$	1.00000	0.0798087
$158$	−2.28363	−0.181676
$159$	0.598271	0.0474460
$160$	−31.7093	−2.50684
$161$	0.0122356	0.000964303 0
$162$	−2.12891	−0.167263
$163$	6.17232	0.483453	0.241727	−	0.970344i	$-0.422286\pi$
$163$	6.17232	0.483453	0.241727	+	0.970344i	$0.422286\pi$
$164$	−27.5138	−2.14847
$165$	−3.25886	−0.253702
$166$	21.6813	1.68279
$167$	16.8847	1.30658	0.653288	−	0.757109i	$-0.273389\pi$
$167$	16.8847	1.30658	0.653288	+	0.757109i	$0.273389\pi$
$168$	−3.23183	−0.249341
$169$	−12.3556	−0.950432
$170$	−8.53157	−0.654342
$171$	1.48404	0.113488
$172$	−6.55376	−0.499720
$173$	18.2355	1.38642	0.693209	−	0.720737i	$-0.256196\pi$
$173$	18.2355	1.38642	0.693209	+	0.720737i	$0.256196\pi$
$174$	9.59994	0.727770
$175$	31.5439	2.38449
$176$	−2.15673	−0.162569
$177$	4.12232	0.309852
$178$	−12.4377	−0.932242
$179$	−14.0904	−1.05317	−0.526583	−	0.850124i	$-0.676527\pi$
$179$	−14.0904	−1.05317	−0.526583	+	0.850124i	$0.676527\pi$
$180$	−10.1480	−0.756387
$181$	−11.4708	−0.852618	−0.426309	−	0.904578i	$-0.640186\pi$
$181$	−11.4708	−0.852618	−0.426309	+	0.904578i	$0.640186\pi$
$182$	4.87411	0.361293
$183$	5.03103	0.371905
$184$	−0.00486125	−0.000358376 0
$185$	−20.4198	−1.50129
$186$	−3.78085	−0.277226
$187$	−0.813194	−0.0594666
$188$	−7.84901	−0.572448
$189$	2.85209	0.207459
$190$	12.6612	0.918541
$191$	−0.0781279	−0.00565314	−0.00282657	−	0.999996i	$-0.500900\pi$
$191$	−0.0781279	−0.00565314	−0.00282657	+	0.999996i	$0.500900\pi$
$192$	−11.5407	−0.832879
$193$	7.50763	0.540411	0.270206	−	0.962803i	$-0.412908\pi$
$193$	7.50763	0.540411	0.270206	+	0.962803i	$0.412908\pi$
$194$	38.1852	2.74154
$195$	3.21696	0.230371
$196$	2.87267	0.205191
$197$	−5.57024	−0.396863	−0.198432	−	0.980115i	$-0.563585\pi$
$197$	−5.57024	−0.396863	−0.198432	+	0.980115i	$0.563585\pi$
$198$	−1.73122	−0.123032
$199$	3.99647	0.283302	0.141651	−	0.989917i	$-0.454759\pi$
$199$	3.99647	0.283302	0.141651	+	0.989917i	$0.454759\pi$
$200$	−12.5325	−0.886179
$201$	−1.96620	−0.138685
$202$	27.6426	1.94493
$203$	−12.8610	−0.902665
$204$	−2.53226	−0.177294
$205$	43.5425	3.04114
$206$	20.3129	1.41527
$207$	0.00429005	0.000298179 0
$208$	2.12900	0.147619
$209$	1.20681	0.0834771
$210$	24.3328	1.67912
$211$	13.2966	0.915377	0.457689	−	0.889113i	$-0.348677\pi$
$211$	13.2966	0.915377	0.457689	+	0.889113i	$0.348677\pi$
$212$	1.51498	0.104049
$213$	8.01047	0.548868
$214$	1.24424	0.0850542
$215$	10.3718	0.707349
$216$	−1.13314	−0.0771007
$217$	5.06519	0.343847
$218$	20.5689	1.39310
$219$	3.22375	0.217841
$220$	−8.25229	−0.556370
$221$	0.802739	0.0539980
$222$	−10.8477	−0.728049
$223$	−4.93797	−0.330671	−0.165335	−	0.986237i	$-0.552871\pi$
$223$	−4.93797	−0.330671	−0.165335	+	0.986237i	$0.552871\pi$
$224$	22.5672	1.50784
$225$	11.0599	0.737327
$226$	−5.28399	−0.351486
$227$	−9.93583	−0.659464	−0.329732	−	0.944075i	$-0.606958\pi$
$227$	−9.93583	−0.659464	−0.329732	+	0.944075i	$0.606958\pi$
$228$	3.75799	0.248879
$229$	−5.59798	−0.369925	−0.184962	−	0.982746i	$-0.559216\pi$
$229$	−5.59798	−0.369925	−0.184962	+	0.982746i	$0.559216\pi$
$230$	0.0366009	0.00241339
$231$	2.31930	0.152599
$232$	5.10971	0.335469
$233$	7.52621	0.493058	0.246529	−	0.969135i	$-0.420710\pi$
$233$	7.52621	0.493058	0.246529	+	0.969135i	$0.420710\pi$
$234$	1.70896	0.111718
$235$	12.4216	0.810296
$236$	10.4388	0.679508
$237$	1.07267	0.0696776
$238$	6.07185	0.393580
$239$	−7.95335	−0.514460	−0.257230	−	0.966350i	$-0.582810\pi$
$239$	−7.95335	−0.514460	−0.257230	+	0.966350i	$0.582810\pi$
$240$	10.6285	0.686067
$241$	3.53315	0.227590	0.113795	−	0.993504i	$-0.463699\pi$
$241$	3.53315	0.227590	0.113795	+	0.993504i	$0.463699\pi$
$242$	22.0102	1.41487
$243$	1.00000	0.0641500
$244$	12.7399	0.815589
$245$	−4.54619	−0.290446
$246$	23.1313	1.47480
$247$	−1.19130	−0.0758005
$248$	−2.01241	−0.127788
$249$	−10.1842	−0.645398
$250$	51.7005	3.26983
$251$	13.5091	0.852685	0.426342	−	0.904562i	$-0.359802\pi$
$251$	13.5091	0.852685	0.426342	+	0.904562i	$0.359802\pi$
$252$	7.22225	0.454959
$253$	0.00348865	0.000219329 0
$254$	−47.0522	−2.95231
$255$	4.00748	0.250958
$256$	4.46596	0.279122
$257$	−2.38848	−0.148990	−0.0744948	−	0.997221i	$-0.523734\pi$
$257$	−2.38848	−0.148990	−0.0744948	+	0.997221i	$0.523734\pi$
$258$	5.50984	0.343028
$259$	14.5326	0.903012
$260$	8.14619	0.505205
$261$	−4.50932	−0.279120
$262$	−1.18578	−0.0732579
$263$	−19.3669	−1.19421	−0.597106	−	0.802163i	$-0.703683\pi$
$263$	−19.3669	−1.19421	−0.597106	+	0.802163i	$0.703683\pi$
$264$	−0.921465	−0.0567123
$265$	−2.39756	−0.147281
$266$	−9.01088	−0.552493
$267$	5.84226	0.357541
$268$	−4.97893	−0.304137
$269$	13.2705	0.809116	0.404558	−	0.914512i	$-0.367425\pi$
$269$	13.2705	0.809116	0.404558	+	0.914512i	$0.367425\pi$
$270$	8.53157	0.519215
$271$	13.5635	0.823925	0.411963	−	0.911201i	$-0.364843\pi$
$271$	13.5635	0.823925	0.411963	+	0.911201i	$0.364843\pi$
$272$	2.65217	0.160811
$273$	−2.28948	−0.138566
$274$	−13.2356	−0.799594
$275$	8.99385	0.542350
$276$	0.0108636	0.000653909 0
$277$	−2.48199	−0.149129	−0.0745643	−	0.997216i	$-0.523757\pi$
$277$	−2.48199	−0.149129	−0.0745643	+	0.997216i	$0.523757\pi$
$278$	−40.8352	−2.44913
$279$	1.77596	0.106324
$280$	12.9515	0.774000
$281$	−14.5413	−0.867463	−0.433731	−	0.901042i	$-0.642803\pi$
$281$	−14.5413	−0.867463	−0.433731	+	0.901042i	$0.642803\pi$
$282$	6.59878	0.392952
$283$	3.02763	0.179974	0.0899868	−	0.995943i	$-0.471318\pi$
$283$	3.02763	0.179974	0.0899868	+	0.995943i	$0.471318\pi$
$284$	20.2846	1.20367
$285$	−5.94727	−0.352286
$286$	1.38972	0.0821756
$287$	−30.9888	−1.82921
$288$	7.91251	0.466249
$289$	1.00000	0.0588235
$290$	−38.4716	−2.25913
$291$	−17.9365	−1.05145
$292$	8.16340	0.477727
$293$	11.9770	0.699706	0.349853	−	0.936805i	$-0.386232\pi$
$293$	11.9770	0.699706	0.349853	+	0.936805i	$0.386232\pi$
$294$	−2.41509	−0.140851
$295$	−16.5201	−0.961838
$296$	−5.77384	−0.335598
$297$	0.813194	0.0471863
$298$	−12.0481	−0.697925
$299$	−0.00344379	−0.000199160 0
$300$	28.0066	1.61696
$301$	−7.38151	−0.425463
$302$	36.5023	2.10047
$303$	−12.9844	−0.745934
$304$	−3.93593	−0.225741
$305$	−20.1618	−1.15446
$306$	2.12891	0.121702
$307$	19.6453	1.12122	0.560609	−	0.828081i	$-0.310567\pi$
$307$	19.6453	1.12122	0.560609	+	0.828081i	$0.310567\pi$
$308$	5.87309	0.334650
$309$	−9.54145	−0.542794
$310$	15.1517	0.860559
$311$	−31.9495	−1.81169	−0.905844	−	0.423612i	$-0.860762\pi$
$311$	−31.9495	−1.81169	−0.905844	+	0.423612i	$0.860762\pi$
$312$	0.909618	0.0514970
$313$	−0.0391080	−0.00221051	−0.00110526	−	0.999999i	$-0.500352\pi$
$313$	−0.0391080	−0.00221051	−0.00110526	+	0.999999i	$0.500352\pi$
$314$	−2.12891	−0.120141
$315$	−11.4297	−0.643991
$316$	2.71629	0.152803
$317$	−26.6746	−1.49819	−0.749097	−	0.662460i	$-0.769512\pi$
$317$	−26.6746	−1.49819	−0.749097	+	0.662460i	$0.769512\pi$
$318$	−1.27367	−0.0714236
$319$	−3.66695	−0.205310
$320$	46.2492	2.58541
$321$	−0.584447	−0.0326206
$322$	−0.0260486	−0.00145163
$323$	−1.48404	−0.0825743
$324$	2.53226	0.140681
$325$	−8.87822	−0.492475
$326$	−13.1403	−0.727775
$327$	−9.66169	−0.534293
$328$	12.3119	0.679814
$329$	−8.84035	−0.487384
$330$	6.93782	0.381915
$331$	25.4564	1.39921	0.699604	−	0.714531i	$-0.253360\pi$
$331$	25.4564	1.39921	0.699604	+	0.714531i	$0.253360\pi$
$332$	−25.7891	−1.41536
$333$	5.09542	0.279227
$334$	−35.9460	−1.96688
$335$	7.87950	0.430503
$336$	−7.56422	−0.412662
$337$	−22.4887	−1.22504	−0.612518	−	0.790457i	$-0.709843\pi$
$337$	−22.4887	−1.22504	−0.612518	+	0.790457i	$0.709843\pi$
$338$	26.3040	1.43075
$339$	2.48201	0.134804
$340$	10.1480	0.550353
$341$	1.44420	0.0782076
$342$	−3.15940	−0.170841
$343$	−16.7292	−0.903289
$344$	2.93269	0.158120
$345$	−0.0171923	−0.000925603 0
$346$	−38.8217	−2.08707
$347$	16.1742	0.868276	0.434138	−	0.900846i	$-0.357053\pi$
$347$	16.1742	0.868276	0.434138	+	0.900846i	$0.357053\pi$
$348$	−11.4188	−0.612111
$349$	1.97956	0.105963	0.0529817	−	0.998595i	$-0.483128\pi$
$349$	1.97956	0.105963	0.0529817	+	0.998595i	$0.483128\pi$
$350$	−67.1541	−3.58954
$351$	−0.802739	−0.0428470
$352$	6.43441	0.342955
$353$	4.39988	0.234182	0.117091	−	0.993121i	$-0.462643\pi$
$353$	4.39988	0.234182	0.117091	+	0.993121i	$0.462643\pi$
$354$	−8.77605	−0.466442
$355$	−32.1018	−1.70379
$356$	14.7942	0.784089
$357$	−2.85209	−0.150949
$358$	29.9972	1.58540
$359$	−6.36032	−0.335685	−0.167842	−	0.985814i	$-0.553680\pi$
$359$	−6.36032	−0.335685	−0.167842	+	0.985814i	$0.553680\pi$
$360$	4.54105	0.239334
$361$	−16.7976	−0.884085
$362$	24.4203	1.28350
$363$	−10.3387	−0.542642
$364$	−5.79758	−0.303876
$365$	−12.9191	−0.676218
$366$	−10.7106	−0.559853
$367$	−19.8848	−1.03798	−0.518989	−	0.854781i	$-0.673692\pi$
$367$	−19.8848	−1.03798	−0.518989	+	0.854781i	$0.673692\pi$
$368$	−0.0113779	−0.000593116 0
$369$	−10.8653	−0.565625
$370$	43.4719	2.26000
$371$	1.70632	0.0885879
$372$	4.49719	0.233168
$373$	−9.40158	−0.486795	−0.243398	−	0.969927i	$-0.578262\pi$
$373$	−9.40158	−0.486795	−0.243398	+	0.969927i	$0.578262\pi$
$374$	1.73122	0.0895192
$375$	−24.2850	−1.25407
$376$	3.51230	0.181133
$377$	3.61981	0.186429
$378$	−6.07185	−0.312302
$379$	−0.205156	−0.0105382	−0.00526909	−	0.999986i	$-0.501677\pi$
$379$	−0.205156	−0.0105382	−0.00526909	+	0.999986i	$0.501677\pi$
$380$	−15.0601	−0.772565
$381$	22.1015	1.13229
$382$	0.166327	0.00851005
$383$	−15.2014	−0.776754	−0.388377	−	0.921501i	$-0.626964\pi$
$383$	−15.2014	−0.776754	−0.388377	+	0.921501i	$0.626964\pi$
$384$	8.74412	0.446222
$385$	−9.29457	−0.473695
$386$	−15.9831	−0.813518
$387$	−2.58810	−0.131561
$388$	−45.4199	−2.30585
$389$	11.2965	0.572757	0.286379	−	0.958117i	$-0.407549\pi$
$389$	11.2965	0.572757	0.286379	+	0.958117i	$0.407549\pi$
$390$	−6.84862	−0.346794
$391$	−0.00429005	−0.000216957 0
$392$	−1.28547	−0.0649259
$393$	0.556990	0.0280964
$394$	11.8586	0.597425
$395$	−4.29872	−0.216292
$396$	2.05922	0.103480
$397$	25.6761	1.28865	0.644324	−	0.764753i	$-0.277139\pi$
$397$	25.6761	1.28865	0.644324	+	0.764753i	$0.277139\pi$
$398$	−8.50813	−0.426474
$399$	4.23263	0.211896
$400$	−29.3327	−1.46664
$401$	−23.4193	−1.16951	−0.584753	−	0.811211i	$-0.698809\pi$
$401$	−23.4193	−1.16951	−0.584753	+	0.811211i	$0.698809\pi$
$402$	4.18586	0.208772
$403$	−1.42563	−0.0710156
$404$	−32.8799	−1.63584
$405$	−4.00748	−0.199133
$406$	27.3799	1.35884
$407$	4.14356	0.205389
$408$	1.13314	0.0560990
$409$	17.5648	0.868525	0.434262	−	0.900786i	$-0.357009\pi$
$409$	17.5648	0.868525	0.434262	+	0.900786i	$0.357009\pi$
$410$	−92.6981	−4.57803
$411$	6.21709	0.306666
$412$	−24.1615	−1.19035
$413$	11.7572	0.578535
$414$	−0.00913315	−0.000448870 0
$415$	40.8130	2.00343
$416$	−6.35168	−0.311417
$417$	19.1812	0.939310
$418$	−2.56920	−0.125664
$419$	25.0494	1.22374	0.611871	−	0.790958i	$-0.290417\pi$
$419$	25.0494	1.22374	0.611871	+	0.790958i	$0.290417\pi$
$420$	−28.9430	−1.41228
$421$	−23.8720	−1.16345	−0.581725	−	0.813385i	$-0.697622\pi$
$421$	−23.8720	−1.16345	−0.581725	+	0.813385i	$0.697622\pi$
$422$	−28.3073	−1.37798
$423$	−3.09960	−0.150708
$424$	−0.677927	−0.0329230
$425$	−11.0599	−0.536484
$426$	−17.0536	−0.826248
$427$	14.3490	0.694395
$428$	−1.47997	−0.0715373
$429$	−0.652782	−0.0315166
$430$	−22.0806	−1.06482
$431$	−38.8204	−1.86991	−0.934957	−	0.354761i	$-0.884562\pi$
$431$	−38.8204	−1.86991	−0.934957	+	0.354761i	$0.884562\pi$
$432$	−2.65217	−0.127602
$433$	25.1126	1.20684	0.603418	−	0.797425i	$-0.293805\pi$
$433$	25.1126	1.20684	0.603418	+	0.797425i	$0.293805\pi$
$434$	−10.7833	−0.517617
$435$	18.0710	0.866439
$436$	−24.4660	−1.17171
$437$	0.00636662	0.000304557 0
$438$	−6.86309	−0.327931
$439$	−9.49343	−0.453097	−0.226548	−	0.974000i	$-0.572744\pi$
$439$	−9.49343	−0.453097	−0.226548	+	0.974000i	$0.572744\pi$
$440$	3.69276	0.176045
$441$	1.13443	0.0540203
$442$	−1.70896	−0.0812869
$443$	−39.2897	−1.86671	−0.933354	−	0.358958i	$-0.883132\pi$
$443$	−39.2897	−1.86671	−0.933354	+	0.358958i	$0.883132\pi$
$444$	12.9029	0.612347
$445$	−23.4128	−1.10987
$446$	10.5125	0.497781
$447$	5.65926	0.267674
$448$	−32.9152	−1.55510
$449$	−18.8579	−0.889959	−0.444979	−	0.895541i	$-0.646789\pi$
$449$	−18.8579	−0.889959	−0.444979	+	0.895541i	$0.646789\pi$
$450$	−23.5456	−1.10995
$451$	−8.83560	−0.416052
$452$	6.28511	0.295627
$453$	−17.1460	−0.805589
$454$	21.1525	0.992736
$455$	9.17507	0.430134
$456$	−1.68163	−0.0787497
$457$	−3.59660	−0.168242	−0.0841208	−	0.996456i	$-0.526808\pi$
$457$	−3.59660	−0.168242	−0.0841208	+	0.996456i	$0.526808\pi$
$458$	11.9176	0.556873
$459$	−1.00000	−0.0466760
$460$	−0.0435355	−0.00202985
$461$	10.4668	0.487488	0.243744	−	0.969840i	$-0.421624\pi$
$461$	10.4668	0.487488	0.243744	+	0.969840i	$0.421624\pi$
$462$	−4.93759	−0.229718
$463$	7.43143	0.345368	0.172684	−	0.984977i	$-0.444756\pi$
$463$	7.43143	0.345368	0.172684	+	0.984977i	$0.444756\pi$
$464$	11.9595	0.555204
$465$	−7.11711	−0.330048
$466$	−16.0226	−0.742234
$467$	9.46868	0.438158	0.219079	−	0.975707i	$-0.429695\pi$
$467$	9.46868	0.438158	0.219079	+	0.975707i	$0.429695\pi$
$468$	−2.03275	−0.0939637
$469$	−5.60777	−0.258943
$470$	−26.4445	−1.21979
$471$	1.00000	0.0460776
$472$	−4.67118	−0.215008
$473$	−2.10463	−0.0967710
$474$	−2.28363	−0.104890
$475$	16.4134	0.753097
$476$	−7.22225	−0.331031
$477$	0.598271	0.0273929
$478$	16.9320	0.774451
$479$	−36.9612	−1.68880	−0.844401	−	0.535712i	$-0.820043\pi$
$479$	−36.9612	−1.68880	−0.844401	+	0.535712i	$0.820043\pi$
$480$	−31.7093	−1.44732
$481$	−4.09029	−0.186501
$482$	−7.52175	−0.342606
$483$	0.0122356	0.000556740 0
$484$	−26.1804	−1.19002
$485$	71.8801	3.26391
$486$	−2.12891	−0.0965694
$487$	1.34006	0.0607240	0.0303620	−	0.999539i	$-0.490334\pi$
$487$	1.34006	0.0607240	0.0303620	+	0.999539i	$0.490334\pi$
$488$	−5.70088	−0.258067
$489$	6.17232	0.279122
$490$	9.67844	0.437227
$491$	12.5707	0.567307	0.283653	−	0.958927i	$-0.408454\pi$
$491$	12.5707	0.567307	0.283653	+	0.958927i	$0.408454\pi$
$492$	−27.5138	−1.24042
$493$	4.50932	0.203090
$494$	2.53617	0.114108
$495$	−3.25886	−0.146475
$496$	−4.71013	−0.211491
$497$	22.8466	1.02481
$498$	21.6813	0.971562
$499$	−33.1031	−1.48190	−0.740948	−	0.671562i	$-0.765624\pi$
$499$	−33.1031	−1.48190	−0.740948	+	0.671562i	$0.765624\pi$
$500$	−61.4959	−2.75018
$501$	16.8847	0.754352
$502$	−28.7596	−1.28360
$503$	−7.14237	−0.318463	−0.159231	−	0.987241i	$-0.550902\pi$
$503$	−7.14237	−0.318463	−0.159231	+	0.987241i	$0.550902\pi$
$504$	−3.23183	−0.143957
$505$	52.0347	2.31552
$506$	−0.00742702	−0.000330171 0
$507$	−12.3556	−0.548732
$508$	55.9669	2.48313
$509$	21.6001	0.957409	0.478704	−	0.877976i	$-0.341107\pi$
$509$	21.6001	0.957409	0.478704	+	0.877976i	$0.341107\pi$
$510$	−8.53157	−0.377784
$511$	9.19444	0.406738
$512$	−26.9959	−1.19306
$513$	1.48404	0.0655221
$514$	5.08487	0.224284
$515$	38.2372	1.68493
$516$	−6.55376	−0.288513
$517$	−2.52058	−0.110855
$518$	−30.9386	−1.35936
$519$	18.2355	0.800448
$520$	−3.64528	−0.159856
$521$	21.3291	0.934445	0.467223	−	0.884140i	$-0.345255\pi$
$521$	21.3291	0.934445	0.467223	+	0.884140i	$0.345255\pi$
$522$	9.59994	0.420178
$523$	−25.7677	−1.12674	−0.563371	−	0.826204i	$-0.690496\pi$
$523$	−25.7677	−1.12674	−0.563371	+	0.826204i	$0.690496\pi$
$524$	1.41045	0.0616156
$525$	31.5439	1.37669
$526$	41.2303	1.79773
$527$	−1.77596	−0.0773619
$528$	−2.15673	−0.0938594
$529$	−23.0000	−0.999999
$530$	5.10419	0.221712
$531$	4.12232	0.178893
$532$	10.7181	0.464690
$533$	8.72200	0.377792
$534$	−12.4377	−0.538230
$535$	2.34216	0.101260
$536$	2.22798	0.0962342
$537$	−14.0904	−0.608046
$538$	−28.2517	−1.21802
$539$	0.922509	0.0397353
$540$	−10.1480	−0.436700
$541$	−14.0882	−0.605698	−0.302849	−	0.953039i	$-0.597938\pi$
$541$	−14.0882	−0.605698	−0.302849	+	0.953039i	$0.597938\pi$
$542$	−28.8755	−1.24031
$543$	−11.4708	−0.492259
$544$	−7.91251	−0.339246
$545$	38.7191	1.65854
$546$	4.87411	0.208593
$547$	−19.9739	−0.854024	−0.427012	−	0.904246i	$-0.640434\pi$
$547$	−19.9739	−0.854024	−0.427012	+	0.904246i	$0.640434\pi$
$548$	15.7433	0.672521
$549$	5.03103	0.214719
$550$	−19.1471	−0.816436
$551$	−6.69202	−0.285090
$552$	−0.00486125	−0.000206908 0
$553$	3.05936	0.130097
$554$	5.28395	0.224493
$555$	−20.4198	−0.866772
$556$	48.5720	2.05991
$557$	7.77900	0.329607	0.164803	−	0.986326i	$-0.447301\pi$
$557$	7.77900	0.329607	0.164803	+	0.986326i	$0.447301\pi$
$558$	−3.78085	−0.160056
$559$	2.07757	0.0878719
$560$	30.3135	1.28098
$561$	−0.813194	−0.0343331
$562$	30.9572	1.30585
$563$	−15.9953	−0.674122	−0.337061	−	0.941483i	$-0.609433\pi$
$563$	−15.9953	−0.674122	−0.337061	+	0.941483i	$0.609433\pi$
$564$	−7.84901	−0.330503
$565$	−9.94662	−0.418457
$566$	−6.44555	−0.270926
$567$	2.85209	0.119777
$568$	−9.07701	−0.380863
$569$	2.36336	0.0990772	0.0495386	−	0.998772i	$-0.484225\pi$
$569$	2.36336	0.0990772	0.0495386	+	0.998772i	$0.484225\pi$
$570$	12.6612	0.530320
$571$	−43.0321	−1.80084	−0.900419	−	0.435024i	$-0.856740\pi$
$571$	−43.0321	−1.80084	−0.900419	+	0.435024i	$0.856740\pi$
$572$	−1.65302	−0.0691161
$573$	−0.0781279	−0.00326384
$574$	65.9725	2.75364
$575$	0.0474476	0.00197870
$576$	−11.5407	−0.480863
$577$	−24.7015	−1.02834	−0.514168	−	0.857689i	$-0.671899\pi$
$577$	−24.7015	−1.02834	−0.514168	+	0.857689i	$0.671899\pi$
$578$	−2.12891	−0.0885510
$579$	7.50763	0.312007
$580$	45.7606	1.90011
$581$	−29.0463	−1.20504
$582$	38.1852	1.58283
$583$	0.486510	0.0201492
$584$	−3.65298	−0.151161
$585$	3.21696	0.133005
$586$	−25.4980	−1.05331
$587$	−16.0915	−0.664169	−0.332085	−	0.943250i	$-0.607752\pi$
$587$	−16.0915	−0.664169	−0.332085	+	0.943250i	$0.607752\pi$
$588$	2.87267	0.118467
$589$	2.63559	0.108598
$590$	35.1699	1.44792
$591$	−5.57024	−0.229129
$592$	−13.5139	−0.555418
$593$	3.49542	0.143540	0.0717699	−	0.997421i	$-0.477135\pi$
$593$	3.49542	0.143540	0.0717699	+	0.997421i	$0.477135\pi$
$594$	−1.73122	−0.0710327
$595$	11.4297	0.468572
$596$	14.3307	0.587010
$597$	3.99647	0.163565
$598$	0.00733153	0.000299809 0
$599$	6.85180	0.279957	0.139978	−	0.990155i	$-0.455297\pi$
$599$	6.85180	0.279957	0.139978	+	0.990155i	$0.455297\pi$
$600$	−12.5325	−0.511636
$601$	−25.5562	−1.04246	−0.521229	−	0.853417i	$-0.674526\pi$
$601$	−25.5562	−1.04246	−0.521229	+	0.853417i	$0.674526\pi$
$602$	15.7146	0.640479
$603$	−1.96620	−0.0800697
$604$	−43.4182	−1.76666
$605$	41.4322	1.68446
$606$	27.6426	1.12291
$607$	−17.2478	−0.700067	−0.350033	−	0.936737i	$-0.613830\pi$
$607$	−17.2478	−0.700067	−0.350033	+	0.936737i	$0.613830\pi$
$608$	11.7425	0.476222
$609$	−12.8610	−0.521154
$610$	42.9226	1.73789
$611$	2.48817	0.100661
$612$	−2.53226	−0.102361
$613$	−10.9666	−0.442936	−0.221468	−	0.975168i	$-0.571085\pi$
$613$	−10.9666	−0.442936	−0.221468	+	0.975168i	$0.571085\pi$
$614$	−41.8231	−1.68784
$615$	43.5425	1.75580
$616$	−2.62810	−0.105889
$617$	−18.4491	−0.742733	−0.371366	−	0.928486i	$-0.621111\pi$
$617$	−18.4491	−0.742733	−0.371366	+	0.928486i	$0.621111\pi$
$618$	20.3129	0.817105
$619$	−27.1458	−1.09108	−0.545541	−	0.838084i	$-0.683676\pi$
$619$	−27.1458	−1.09108	−0.545541	+	0.838084i	$0.683676\pi$
$620$	−18.0224	−0.723797
$621$	0.00429005	0.000172154 0
$622$	68.0176	2.72726
$623$	16.6627	0.667576
$624$	2.12900	0.0852281
$625$	42.0220	1.68088
$626$	0.0832574	0.00332763
$627$	1.20681	0.0481955
$628$	2.53226	0.101048
$629$	−5.09542	−0.203168
$630$	24.3328	0.969443
$631$	31.1086	1.23841	0.619207	−	0.785228i	$-0.287454\pi$
$631$	31.1086	1.23841	0.619207	+	0.785228i	$0.287454\pi$
$632$	−1.21549	−0.0483497
$633$	13.2966	0.528493
$634$	56.7878	2.25533
$635$	−88.5714	−3.51485
$636$	1.51498	0.0600728
$637$	−0.910648	−0.0360812
$638$	7.80662	0.309067
$639$	8.01047	0.316889
$640$	−35.0419	−1.38515
$641$	−12.5988	−0.497622	−0.248811	−	0.968552i	$-0.580040\pi$
$641$	−12.5988	−0.497622	−0.248811	+	0.968552i	$0.580040\pi$
$642$	1.24424	0.0491061
$643$	−29.0697	−1.14640	−0.573199	−	0.819416i	$-0.694298\pi$
$643$	−29.0697	−1.14640	−0.573199	+	0.819416i	$0.694298\pi$
$644$	0.0309838	0.00122093
$645$	10.3718	0.408388
$646$	3.15940	0.124305
$647$	10.6663	0.419335	0.209667	−	0.977773i	$-0.432762\pi$
$647$	10.6663	0.419335	0.209667	+	0.977773i	$0.432762\pi$
$648$	−1.13314	−0.0445141
$649$	3.35224	0.131587
$650$	18.9009	0.741356
$651$	5.06519	0.198520
$652$	15.6299	0.612116
$653$	44.9547	1.75921	0.879607	−	0.475700i	$-0.157805\pi$
$653$	44.9547	1.75921	0.879607	+	0.475700i	$0.157805\pi$
$654$	20.5689	0.804307
$655$	−2.23213	−0.0872164
$656$	28.8166	1.12510
$657$	3.22375	0.125771
$658$	18.8203	0.733693
$659$	−9.10096	−0.354523	−0.177262	−	0.984164i	$-0.556724\pi$
$659$	−9.10096	−0.354523	−0.177262	+	0.984164i	$0.556724\pi$
$660$	−8.25229	−0.321220
$661$	24.7809	0.963864	0.481932	−	0.876209i	$-0.339935\pi$
$661$	24.7809	0.963864	0.481932	+	0.876209i	$0.339935\pi$
$662$	−54.1943	−2.10632
$663$	0.802739	0.0311758
$664$	11.5402	0.447846
$665$	−16.9622	−0.657765
$666$	−10.8477	−0.420340
$667$	−0.0193452	−0.000749050 0
$668$	42.7565	1.65430
$669$	−4.93797	−0.190913
$670$	−16.7747	−0.648065
$671$	4.09121	0.157939
$672$	22.5672	0.870549
$673$	−41.7041	−1.60758	−0.803788	−	0.594916i	$-0.797185\pi$
$673$	−41.7041	−1.60758	−0.803788	+	0.594916i	$0.797185\pi$
$674$	47.8764	1.84413
$675$	11.0599	0.425696
$676$	−31.2877	−1.20337
$677$	5.67429	0.218081	0.109040	−	0.994037i	$-0.465222\pi$
$677$	5.67429	0.218081	0.109040	+	0.994037i	$0.465222\pi$
$678$	−5.28399	−0.202930
$679$	−51.1565	−1.96321
$680$	−4.54105	−0.174141
$681$	−9.93583	−0.380742
$682$	−3.07457	−0.117731
$683$	−3.21416	−0.122987	−0.0614933	−	0.998107i	$-0.519586\pi$
$683$	−3.21416	−0.122987	−0.0614933	+	0.998107i	$0.519586\pi$
$684$	3.75799	0.143690
$685$	−24.9149	−0.951948
$686$	35.6149	1.35978
$687$	−5.59798	−0.213576
$688$	6.86408	0.261691
$689$	−0.480255	−0.0182963
$690$	0.0366009	0.00139337
$691$	29.8338	1.13493	0.567466	−	0.823397i	$-0.307924\pi$
$691$	29.8338	1.13493	0.567466	+	0.823397i	$0.307924\pi$
$692$	46.1770	1.75539
$693$	2.31930	0.0881031
$694$	−34.4334	−1.30707
$695$	−76.8685	−2.91579
$696$	5.10971	0.193683
$697$	10.8653	0.411553
$698$	−4.21430	−0.159514
$699$	7.52621	0.284667
$700$	79.8774	3.01908
$701$	11.8409	0.447225	0.223612	−	0.974678i	$-0.428215\pi$
$701$	11.8409	0.447225	0.223612	+	0.974678i	$0.428215\pi$
$702$	1.70896	0.0645005
$703$	7.56182	0.285199
$704$	−9.38484	−0.353704
$705$	12.4216	0.467825
$706$	−9.36695	−0.352530
$707$	−37.0327	−1.39276
$708$	10.4388	0.392314
$709$	−41.8994	−1.57357	−0.786783	−	0.617230i	$-0.788255\pi$
$709$	−41.8994	−1.57357	−0.786783	+	0.617230i	$0.788255\pi$
$710$	68.3419	2.56483
$711$	1.07267	0.0402284
$712$	−6.62012	−0.248100
$713$	0.00761895	0.000285332 0
$714$	6.07185	0.227233
$715$	2.61601	0.0978333
$716$	−35.6806	−1.33345
$717$	−7.95335	−0.297023
$718$	13.5406	0.505329
$719$	44.8695	1.67335	0.836674	−	0.547701i	$-0.184497\pi$
$719$	44.8695	1.67335	0.836674	+	0.547701i	$0.184497\pi$
$720$	10.6285	0.396101
$721$	−27.2131	−1.01347
$722$	35.7606	1.33087
$723$	3.53315	0.131399
$724$	−29.0471	−1.07953
$725$	−49.8727	−1.85222
$726$	22.0102	0.816876
$727$	−12.5972	−0.467204	−0.233602	−	0.972332i	$-0.575051\pi$
$727$	−12.5972	−0.467204	−0.233602	+	0.972332i	$0.575051\pi$
$728$	2.59431	0.0961517
$729$	1.00000	0.0370370
$730$	27.5037	1.01796
$731$	2.58810	0.0957245
$732$	12.7399	0.470881
$733$	22.1920	0.819680	0.409840	−	0.912157i	$-0.365584\pi$
$733$	22.1920	0.819680	0.409840	+	0.912157i	$0.365584\pi$
$734$	42.3330	1.56254
$735$	−4.54619	−0.167689
$736$	0.0339451	0.00125123
$737$	−1.59890	−0.0588962
$738$	23.1313	0.851474
$739$	13.6000	0.500283	0.250142	−	0.968209i	$-0.419523\pi$
$739$	13.6000	0.500283	0.250142	+	0.968209i	$0.419523\pi$
$740$	−51.7083	−1.90083
$741$	−1.19130	−0.0437634
$742$	−3.63261	−0.133357
$743$	−7.79534	−0.285983	−0.142992	−	0.989724i	$-0.545672\pi$
$743$	−7.79534	−0.285983	−0.142992	+	0.989724i	$0.545672\pi$
$744$	−2.01241	−0.0737786
$745$	−22.6794	−0.830908
$746$	20.0151	0.732806
$747$	−10.1842	−0.372621
$748$	−2.05922	−0.0752926
$749$	−1.66690	−0.0609071
$750$	51.7005	1.88784
$751$	−4.17834	−0.152470	−0.0762348	−	0.997090i	$-0.524290\pi$
$751$	−4.17834	−0.152470	−0.0762348	+	0.997090i	$0.524290\pi$
$752$	8.22066	0.299777
$753$	13.5091	0.492298
$754$	−7.70625	−0.280645
$755$	68.7123	2.50069
$756$	7.22225	0.262671
$757$	−38.4381	−1.39706	−0.698528	−	0.715583i	$-0.746161\pi$
$757$	−38.4381	−1.39706	−0.698528	+	0.715583i	$0.746161\pi$
$758$	0.436760	0.0158638
$759$	0.00348865	0.000126630 0
$760$	6.73911	0.244453
$761$	11.1499	0.404185	0.202092	−	0.979366i	$-0.435226\pi$
$761$	11.1499	0.404185	0.202092	+	0.979366i	$0.435226\pi$
$762$	−47.0522	−1.70452
$763$	−27.5560	−0.997595
$764$	−0.197840	−0.00715762
$765$	4.00748	0.144891
$766$	32.3624	1.16930
$767$	−3.30914	−0.119486
$768$	4.46596	0.161151
$769$	8.17689	0.294866	0.147433	−	0.989072i	$-0.452899\pi$
$769$	8.17689	0.294866	0.147433	+	0.989072i	$0.452899\pi$
$770$	19.7873	0.713085
$771$	−2.38848	−0.0860191
$772$	19.0113	0.684232
$773$	−0.970111	−0.0348925	−0.0174462	−	0.999848i	$-0.505554\pi$
$773$	−0.970111	−0.0348925	−0.0174462	+	0.999848i	$0.505554\pi$
$774$	5.50984	0.198047
$775$	19.6419	0.705558
$776$	20.3246	0.729611
$777$	14.5326	0.521354
$778$	−24.0493	−0.862210
$779$	−16.1246	−0.577723
$780$	8.14619	0.291681
$781$	6.51406	0.233092
$782$	0.00913315	0.000326601 0
$783$	−4.50932	−0.161150
$784$	−3.00869	−0.107453
$785$	−4.00748	−0.143033
$786$	−1.18578	−0.0422955
$787$	−34.0222	−1.21276	−0.606380	−	0.795175i	$-0.707379\pi$
$787$	−34.0222	−1.21276	−0.606380	+	0.795175i	$0.707379\pi$
$788$	−14.1053	−0.502482
$789$	−19.3669	−0.689478
$790$	9.15159	0.325599
$791$	7.07893	0.251698
$792$	−0.921465	−0.0327429
$793$	−4.03861	−0.143415
$794$	−54.6622	−1.93989
$795$	−2.39756	−0.0850326
$796$	10.1201	0.358698
$797$	15.1803	0.537714	0.268857	−	0.963180i	$-0.413354\pi$
$797$	15.1803	0.537714	0.268857	+	0.963180i	$0.413354\pi$
$798$	−9.01088	−0.318982
$799$	3.09960	0.109656
$800$	87.5117	3.09400
$801$	5.84226	0.206426
$802$	49.8577	1.76054
$803$	2.62154	0.0925120
$804$	−4.97893	−0.175593
$805$	−0.0490341	−0.00172822
$806$	3.03504	0.106905
$807$	13.2705	0.467143
$808$	14.7132	0.517608
$809$	−44.3717	−1.56003	−0.780013	−	0.625764i	$-0.784787\pi$
$809$	−44.3717	−1.56003	−0.780013	+	0.625764i	$0.784787\pi$
$810$	8.53157	0.299769
$811$	6.16017	0.216313	0.108156	−	0.994134i	$-0.465505\pi$
$811$	6.16017	0.216313	0.108156	+	0.994134i	$0.465505\pi$
$812$	−32.5674	−1.14289
$813$	13.5635	0.475694
$814$	−8.82128	−0.309186
$815$	−24.7354	−0.866445
$816$	2.65217	0.0928444
$817$	−3.84086	−0.134375
$818$	−37.3940	−1.30745
$819$	−2.28948	−0.0800011
$820$	110.261	3.85049
$821$	−7.48370	−0.261183	−0.130591	−	0.991436i	$-0.541688\pi$
$821$	−7.48370	−0.261183	−0.130591	+	0.991436i	$0.541688\pi$
$822$	−13.2356	−0.461646
$823$	−16.6712	−0.581121	−0.290560	−	0.956857i	$-0.593842\pi$
$823$	−16.6712	−0.581121	−0.290560	+	0.956857i	$0.593842\pi$
$824$	10.8118	0.376648
$825$	8.99385	0.313126
$826$	−25.0301	−0.870908
$827$	7.85898	0.273284	0.136642	−	0.990621i	$-0.456369\pi$
$827$	7.85898	0.273284	0.136642	+	0.990621i	$0.456369\pi$
$828$	0.0108636	0.000377535 0
$829$	−21.1657	−0.735114	−0.367557	−	0.930001i	$-0.619806\pi$
$829$	−21.1657	−0.735114	−0.367557	+	0.930001i	$0.619806\pi$
$830$	−86.8873	−3.01590
$831$	−2.48199	−0.0860994
$832$	9.26417	0.321177
$833$	−1.13443	−0.0393055
$834$	−40.8352	−1.41401
$835$	−67.6651	−2.34165
$836$	3.05597	0.105693
$837$	1.77596	0.0613860
$838$	−53.3279	−1.84218
$839$	−11.3070	−0.390361	−0.195180	−	0.980767i	$-0.562529\pi$
$839$	−11.3070	−0.390361	−0.195180	+	0.980767i	$0.562529\pi$
$840$	12.9515	0.446869
$841$	−8.66603	−0.298829
$842$	50.8214	1.75142
$843$	−14.5413	−0.500830
$844$	33.6706	1.15899
$845$	49.5149	1.70336
$846$	6.59878	0.226871
$847$	−29.4870	−1.01318
$848$	−1.58671	−0.0544880
$849$	3.02763	0.103908
$850$	23.5456	0.807606
$851$	0.0218596	0.000749338 0
$852$	20.2846	0.694940
$853$	37.3825	1.27995	0.639976	−	0.768395i	$-0.278944\pi$
$853$	37.3825	1.27995	0.639976	+	0.768395i	$0.278944\pi$
$854$	−30.5477	−1.04532
$855$	−5.94727	−0.203392
$856$	0.662262	0.0226357
$857$	−8.18965	−0.279753	−0.139877	−	0.990169i	$-0.544671\pi$
$857$	−8.18965	−0.279753	−0.139877	+	0.990169i	$0.544671\pi$
$858$	1.38972	0.0474441
$859$	−12.7004	−0.433333	−0.216667	−	0.976246i	$-0.569518\pi$
$859$	−12.7004	−0.433333	−0.216667	+	0.976246i	$0.569518\pi$
$860$	26.2641	0.895598
$861$	−30.9888	−1.05610
$862$	82.6452	2.81491
$863$	−25.0741	−0.853531	−0.426766	−	0.904362i	$-0.640347\pi$
$863$	−25.0741	−0.853531	−0.426766	+	0.904362i	$0.640347\pi$
$864$	7.91251	0.269189
$865$	−73.0783	−2.48474
$866$	−53.4626	−1.81673
$867$	1.00000	0.0339618
$868$	12.8264	0.435356
$869$	0.872292	0.0295905
$870$	−38.4716	−1.30431
$871$	1.57834	0.0534801
$872$	10.9481	0.370749
$873$	−17.9365	−0.607058
$874$	−0.0135540	−0.000458470 0
$875$	−69.2629	−2.34151
$876$	8.16340	0.275816
$877$	−37.2379	−1.25744	−0.628718	−	0.777633i	$-0.716420\pi$
$877$	−37.2379	−1.25744	−0.628718	+	0.777633i	$0.716420\pi$
$878$	20.2107	0.682077
$879$	11.9770	0.403975
$880$	8.64304	0.291357
$881$	−28.0328	−0.944449	−0.472224	−	0.881478i	$-0.656549\pi$
$881$	−28.0328	−0.944449	−0.472224	+	0.881478i	$0.656549\pi$
$882$	−2.41509	−0.0813204
$883$	−14.3024	−0.481316	−0.240658	−	0.970610i	$-0.577363\pi$
$883$	−14.3024	−0.481316	−0.240658	+	0.970610i	$0.577363\pi$
$884$	2.03275	0.0683687
$885$	−16.5201	−0.555317
$886$	83.6442	2.81008
$887$	−27.2040	−0.913422	−0.456711	−	0.889615i	$-0.650973\pi$
$887$	−27.2040	−0.913422	−0.456711	+	0.889615i	$0.650973\pi$
$888$	−5.77384	−0.193757
$889$	63.0355	2.11414
$890$	49.8437	1.67077
$891$	0.813194	0.0272430
$892$	−12.5042	−0.418673
$893$	−4.59994	−0.153931
$894$	−12.0481	−0.402947
$895$	56.4670	1.88748
$896$	24.9390	0.833155
$897$	−0.00344379	−0.000114985 0
$898$	40.1468	1.33972
$899$	−8.00835	−0.267094
$900$	28.0066	0.933554
$901$	−0.598271	−0.0199313
$902$	18.8102	0.626312
$903$	−7.38151	−0.245641
$904$	−2.81248	−0.0935416
$905$	45.9690	1.52806
$906$	36.5023	1.21271
$907$	−38.4472	−1.27662	−0.638309	−	0.769780i	$-0.720366\pi$
$907$	−38.4472	−1.27662	−0.638309	+	0.769780i	$0.720366\pi$
$908$	−25.1601	−0.834969
$909$	−12.9844	−0.430665
$910$	−19.5329	−0.647509
$911$	−28.2072	−0.934548	−0.467274	−	0.884113i	$-0.654764\pi$
$911$	−28.2072	−0.934548	−0.467274	+	0.884113i	$0.654764\pi$
$912$	−3.93593	−0.130332
$913$	−8.28174	−0.274086
$914$	7.65683	0.253266
$915$	−20.1618	−0.666528
$916$	−14.1756	−0.468374
$917$	1.58859	0.0524597
$918$	2.12891	0.0702646
$919$	−46.0460	−1.51892	−0.759459	−	0.650556i	$-0.774536\pi$
$919$	−46.0460	−1.51892	−0.759459	+	0.650556i	$0.774536\pi$
$920$	0.0194814	0.000642281 0
$921$	19.6453	0.647335
$922$	−22.2829	−0.733849
$923$	−6.43031	−0.211656
$924$	5.87309	0.193210
$925$	56.3548	1.85294
$926$	−15.8209	−0.519906
$927$	−9.54145	−0.313382
$928$	−35.6801	−1.17126
$929$	50.7773	1.66595	0.832975	−	0.553310i	$-0.186636\pi$
$929$	50.7773	1.66595	0.832975	+	0.553310i	$0.186636\pi$
$930$	15.1517	0.496844
$931$	1.68354	0.0551757
$932$	19.0584	0.624277
$933$	−31.9495	−1.04598
$934$	−20.1580	−0.659590
$935$	3.25886	0.106576
$936$	0.909618	0.0297318
$937$	−12.4592	−0.407024	−0.203512	−	0.979072i	$-0.565236\pi$
$937$	−12.4592	−0.407024	−0.203512	+	0.979072i	$0.565236\pi$
$938$	11.9385	0.389804
$939$	−0.0391080	−0.00127624
$940$	31.4548	1.02594
$941$	16.4536	0.536373	0.268187	−	0.963367i	$-0.413576\pi$
$941$	16.4536	0.536373	0.268187	+	0.963367i	$0.413576\pi$
$942$	−2.12891	−0.0693637
$943$	−0.0466127	−0.00151792
$944$	−10.9331	−0.355841
$945$	−11.4297	−0.371808
$946$	4.48057	0.145676
$947$	6.70863	0.218001	0.109001	−	0.994042i	$-0.465235\pi$
$947$	6.70863	0.218001	0.109001	+	0.994042i	$0.465235\pi$
$948$	2.71629	0.0882211
$949$	−2.58783	−0.0840046
$950$	−34.9426	−1.13369
$951$	−26.6746	−0.864983
$952$	3.23183	0.104744
$953$	−16.9559	−0.549255	−0.274628	−	0.961551i	$-0.588555\pi$
$953$	−16.9559	−0.549255	−0.274628	+	0.961551i	$0.588555\pi$
$954$	−1.27367	−0.0412364
$955$	0.313096	0.0101316
$956$	−20.1400	−0.651374
$957$	−3.66695	−0.118536
$958$	78.6872	2.54227
$959$	17.7317	0.572587
$960$	46.2492	1.49269
$961$	−27.8460	−0.898257
$962$	8.70786	0.280753
$963$	−0.584447	−0.0188335
$964$	8.94686	0.288159
$965$	−30.0867	−0.968525
$966$	−0.0260486	−0.000838099 0
$967$	39.3501	1.26541	0.632707	−	0.774392i	$-0.281944\pi$
$967$	39.3501	1.26541	0.632707	+	0.774392i	$0.281944\pi$
$968$	11.7152	0.376542
$969$	−1.48404	−0.0476743
$970$	−153.026	−4.91338
$971$	19.0567	0.611558	0.305779	−	0.952103i	$-0.401083\pi$
$971$	19.0567	0.611558	0.305779	+	0.952103i	$0.401083\pi$
$972$	2.53226	0.0812224
$973$	54.7067	1.75382
$974$	−2.85287	−0.0914120
$975$	−8.87822	−0.284330
$976$	−13.3431	−0.427103
$977$	−14.3622	−0.459489	−0.229744	−	0.973251i	$-0.573789\pi$
$977$	−14.3622	−0.459489	−0.229744	+	0.973251i	$0.573789\pi$
$978$	−13.1403	−0.420181
$979$	4.75089	0.151839
$980$	−11.5122	−0.367742
$981$	−9.66169	−0.308474
$982$	−26.7619	−0.854005
$983$	54.5242	1.73905	0.869526	−	0.493886i	$-0.164424\pi$
$983$	54.5242	1.73905	0.869526	+	0.493886i	$0.164424\pi$
$984$	12.3119	0.392491
$985$	22.3226	0.711259
$986$	−9.59994	−0.305725
$987$	−8.84035	−0.281392
$988$	−3.01668	−0.0959734
$989$	−0.0111031	−0.000353058 0
$990$	6.93782	0.220499
$991$	19.3655	0.615167	0.307583	−	0.951521i	$-0.400480\pi$
$991$	19.3655	0.615167	0.307583	+	0.951521i	$0.400480\pi$
$992$	14.0523	0.446160
$993$	25.4564	0.807833
$994$	−48.6384	−1.54272
$995$	−16.0158	−0.507734
$996$	−25.7891	−0.817159
$997$	−20.2359	−0.640877	−0.320439	−	0.947269i	$-0.603830\pi$
$997$	−20.2359	−0.640877	−0.320439	+	0.947269i	$0.603830\pi$
$998$	70.4735	2.23080
$999$	5.09542	0.161212

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8007.2.a.e.1.8	✓	46

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8007.2.a.e.1.8	✓	46	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:	\( N \)	\(=\)	\( 8007 = 3 \cdot 17 \cdot 157 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.12891 q^{2} +1.00000 q^{3} +2.53226 q^{4} -4.00748 q^{5} -2.12891 q^{6} +2.85209 q^{7} -1.13314 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-2.12891 q^{2} +1.00000 q^{3} +2.53226 q^{4} -4.00748 q^{5} -2.12891 q^{6} +2.85209 q^{7} -1.13314 q^{8} +1.00000 q^{9} +8.53157 q^{10} +0.813194 q^{11} +2.53226 q^{12} -0.802739 q^{13} -6.07185 q^{14} -4.00748 q^{15} -2.65217 q^{16} -1.00000 q^{17} -2.12891 q^{18} +1.48404 q^{19} -10.1480 q^{20} +2.85209 q^{21} -1.73122 q^{22} +0.00429005 q^{23} -1.13314 q^{24} +11.0599 q^{25} +1.70896 q^{26} +1.00000 q^{27} +7.22225 q^{28} -4.50932 q^{29} +8.53157 q^{30} +1.77596 q^{31} +7.91251 q^{32} +0.813194 q^{33} +2.12891 q^{34} -11.4297 q^{35} +2.53226 q^{36} +5.09542 q^{37} -3.15940 q^{38} -0.802739 q^{39} +4.54105 q^{40} -10.8653 q^{41} -6.07185 q^{42} -2.58810 q^{43} +2.05922 q^{44} -4.00748 q^{45} -0.00913315 q^{46} -3.09960 q^{47} -2.65217 q^{48} +1.13443 q^{49} -23.5456 q^{50} -1.00000 q^{51} -2.03275 q^{52} +0.598271 q^{53} -2.12891 q^{54} -3.25886 q^{55} -3.23183 q^{56} +1.48404 q^{57} +9.59994 q^{58} +4.12232 q^{59} -10.1480 q^{60} +5.03103 q^{61} -3.78085 q^{62} +2.85209 q^{63} -11.5407 q^{64} +3.21696 q^{65} -1.73122 q^{66} -1.96620 q^{67} -2.53226 q^{68} +0.00429005 q^{69} +24.3328 q^{70} +8.01047 q^{71} -1.13314 q^{72} +3.22375 q^{73} -10.8477 q^{74} +11.0599 q^{75} +3.75799 q^{76} +2.31930 q^{77} +1.70896 q^{78} +1.07267 q^{79} +10.6285 q^{80} +1.00000 q^{81} +23.1313 q^{82} -10.1842 q^{83} +7.22225 q^{84} +4.00748 q^{85} +5.50984 q^{86} -4.50932 q^{87} -0.921465 q^{88} +5.84226 q^{89} +8.53157 q^{90} -2.28948 q^{91} +0.0108636 q^{92} +1.77596 q^{93} +6.59878 q^{94} -5.94727 q^{95} +7.91251 q^{96} -17.9365 q^{97} -2.41509 q^{98} +0.813194 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9}+O(q^{10}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9	\( 46 q - 5 q^{2} + 46 q^{3} + 43 q^{4} - 19 q^{5} - 5 q^{6} + q^{7} - 18 q^{8} + 46 q^{9} - 10 q^{10} - 25 q^{11} + 43 q^{12} - 8 q^{13} - 28 q^{14} - 19 q^{15} + 33 q^{16} - 46 q^{17} - 5 q^{18} - 2 q^{19} - 56 q^{20} + q^{21} - 19 q^{22} - 64 q^{23} - 18 q^{24} + 11 q^{25} - 13 q^{26} + 46 q^{27} - 38 q^{28} - 51 q^{29} - 10 q^{30} - 19 q^{31} - 61 q^{32} - 25 q^{33} + 5 q^{34} - 39 q^{35} + 43 q^{36} - 46 q^{37} - 48 q^{38} - 8 q^{39} - 10 q^{40} - 53 q^{41} - 28 q^{42} - 33 q^{43} - 62 q^{44} - 19 q^{45} + 2 q^{46} - 45 q^{47} + 33 q^{48} + 21 q^{49} - 60 q^{50} - 46 q^{51} - 63 q^{52} - 47 q^{53} - 5 q^{54} + 5 q^{55} - 82 q^{56} - 2 q^{57} - 21 q^{58} - 65 q^{59} - 56 q^{60} - 37 q^{61} - 46 q^{62} + q^{63} + 74 q^{64} - 85 q^{65} - 19 q^{66} - 52 q^{67} - 43 q^{68} - 64 q^{69} - 20 q^{70} - 48 q^{71} - 18 q^{72} - 39 q^{73} - 16 q^{74} + 11 q^{75} + 42 q^{76} - 78 q^{77} - 13 q^{78} - 26 q^{79} - 78 q^{80} + 46 q^{81} + 3 q^{82} - 47 q^{83} - 38 q^{84} + 19 q^{85} - 6 q^{86} - 51 q^{87} - 58 q^{88} - 58 q^{89} - 10 q^{90} - 43 q^{91} - 68 q^{92} - 19 q^{93} - 78 q^{95} - 61 q^{96} - 44 q^{97} - 4 q^{98} - 25 q^{99}+O(q^{100}) \) 46 * q - 5 * q^2 + 46 * q^3 + 43 * q^4 - 19 * q^5 - 5 * q^6 + q^7 - 18 * q^8 + 46 * q^9 - 10 * q^10 - 25 * q^11 + 43 * q^12 - 8 * q^13 - 28 * q^14 - 19 * q^15 + 33 * q^16 - 46 * q^17 - 5 * q^18 - 2 * q^19 - 56 * q^20 + q^21 - 19 * q^22 - 64 * q^23 - 18 * q^24 + 11 * q^25 - 13 * q^26 + 46 * q^27 - 38 * q^28 - 51 * q^29 - 10 * q^30 - 19 * q^31 - 61 * q^32 - 25 * q^33 + 5 * q^34 - 39 * q^35 + 43 * q^36 - 46 * q^37 - 48 * q^38 - 8 * q^39 - 10 * q^40 - 53 * q^41 - 28 * q^42 - 33 * q^43 - 62 * q^44 - 19 * q^45 + 2 * q^46 - 45 * q^47 + 33 * q^48 + 21 * q^49 - 60 * q^50 - 46 * q^51 - 63 * q^52 - 47 * q^53 - 5 * q^54 + 5 * q^55 - 82 * q^56 - 2 * q^57 - 21 * q^58 - 65 * q^59 - 56 * q^60 - 37 * q^61 - 46 * q^62 + q^63 + 74 * q^64 - 85 * q^65 - 19 * q^66 - 52 * q^67 - 43 * q^68 - 64 * q^69 - 20 * q^70 - 48 * q^71 - 18 * q^72 - 39 * q^73 - 16 * q^74 + 11 * q^75 + 42 * q^76 - 78 * q^77 - 13 * q^78 - 26 * q^79 - 78 * q^80 + 46 * q^81 + 3 * q^82 - 47 * q^83 - 38 * q^84 + 19 * q^85 - 6 * q^86 - 51 * q^87 - 58 * q^88 - 58 * q^89 - 10 * q^90 - 43 * q^91 - 68 * q^92 - 19 * q^93 - 78 * q^95 - 61 * q^96 - 44 * q^97 - 4 * q^98 - 25 * q^99

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