LMFDB - Embedded newform 8043.2.a.o.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8043,2,Mod(1,8043)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8043, 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("8043.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8043 = 3 \cdot 7 \cdot 383 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8043.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:	$64.2236783457$
Analytic rank:	$1$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8043.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.426737 q^{2} -1.00000 q^{3} -1.81790 q^{4} -3.28382 q^{5} +0.426737 q^{6} +1.00000 q^{7} +1.62924 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.426737 q^{2} -1.00000 q^{3} -1.81790 q^{4} -3.28382 q^{5} +0.426737 q^{6} +1.00000 q^{7} +1.62924 q^{8} +1.00000 q^{9} +1.40133 q^{10} -2.62788 q^{11} +1.81790 q^{12} +0.620243 q^{13} -0.426737 q^{14} +3.28382 q^{15} +2.94054 q^{16} -2.07930 q^{17} -0.426737 q^{18} -7.62070 q^{19} +5.96964 q^{20} -1.00000 q^{21} +1.12141 q^{22} +6.98579 q^{23} -1.62924 q^{24} +5.78347 q^{25} -0.264681 q^{26} -1.00000 q^{27} -1.81790 q^{28} -2.98214 q^{29} -1.40133 q^{30} +0.454979 q^{31} -4.51331 q^{32} +2.62788 q^{33} +0.887314 q^{34} -3.28382 q^{35} -1.81790 q^{36} -11.5815 q^{37} +3.25203 q^{38} -0.620243 q^{39} -5.35012 q^{40} +1.52292 q^{41} +0.426737 q^{42} +6.91315 q^{43} +4.77721 q^{44} -3.28382 q^{45} -2.98109 q^{46} +9.49134 q^{47} -2.94054 q^{48} +1.00000 q^{49} -2.46802 q^{50} +2.07930 q^{51} -1.12754 q^{52} -5.26196 q^{53} +0.426737 q^{54} +8.62948 q^{55} +1.62924 q^{56} +7.62070 q^{57} +1.27259 q^{58} -11.6791 q^{59} -5.96964 q^{60} +11.9493 q^{61} -0.194156 q^{62} +1.00000 q^{63} -3.95508 q^{64} -2.03677 q^{65} -1.12141 q^{66} -14.0526 q^{67} +3.77995 q^{68} -6.98579 q^{69} +1.40133 q^{70} +13.3701 q^{71} +1.62924 q^{72} +7.88472 q^{73} +4.94226 q^{74} -5.78347 q^{75} +13.8536 q^{76} -2.62788 q^{77} +0.264681 q^{78} -5.65341 q^{79} -9.65619 q^{80} +1.00000 q^{81} -0.649886 q^{82} +13.6501 q^{83} +1.81790 q^{84} +6.82804 q^{85} -2.95010 q^{86} +2.98214 q^{87} -4.28144 q^{88} +13.9255 q^{89} +1.40133 q^{90} +0.620243 q^{91} -12.6994 q^{92} -0.454979 q^{93} -4.05030 q^{94} +25.0250 q^{95} +4.51331 q^{96} +13.9587 q^{97} -0.426737 q^{98} -2.62788 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * 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 $

$2$	−0.426737	−0.301748	−0.150874	−	0.988553i	$-0.548209\pi$
$2$	−0.426737	−0.301748	−0.150874	+	0.988553i	$0.548209\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.81790	−0.908948
$5$	−3.28382	−1.46857	−0.734284	−	0.678842i	$-0.762482\pi$
$5$	−3.28382	−1.46857	−0.734284	+	0.678842i	$0.762482\pi$
$6$	0.426737	0.174215
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	1.62924	0.576022
$9$	1.00000	0.333333
$10$	1.40133	0.443138
$11$	−2.62788	−0.792335	−0.396168	−	0.918178i	$-0.629660\pi$
$11$	−2.62788	−0.792335	−0.396168	+	0.918178i	$0.629660\pi$
$12$	1.81790	0.524781
$13$	0.620243	0.172025	0.0860123	−	0.996294i	$-0.472588\pi$
$13$	0.620243	0.172025	0.0860123	+	0.996294i	$0.472588\pi$
$14$	−0.426737	−0.114050
$15$	3.28382	0.847878
$16$	2.94054	0.735134
$17$	−2.07930	−0.504304	−0.252152	−	0.967688i	$-0.581138\pi$
$17$	−2.07930	−0.504304	−0.252152	+	0.967688i	$0.581138\pi$
$18$	−0.426737	−0.100583
$19$	−7.62070	−1.74831	−0.874154	−	0.485649i	$-0.838583\pi$
$19$	−7.62070	−1.74831	−0.874154	+	0.485649i	$0.838583\pi$
$20$	5.96964	1.33485
$21$	−1.00000	−0.218218
$22$	1.12141	0.239086
$23$	6.98579	1.45664	0.728319	−	0.685238i	$-0.240302\pi$
$23$	6.98579	1.45664	0.728319	+	0.685238i	$0.240302\pi$
$24$	−1.62924	−0.332567
$25$	5.78347	1.15669
$26$	−0.264681	−0.0519082
$27$	−1.00000	−0.192450
$28$	−1.81790	−0.343550
$29$	−2.98214	−0.553770	−0.276885	−	0.960903i	$-0.589302\pi$
$29$	−2.98214	−0.553770	−0.276885	+	0.960903i	$0.589302\pi$
$30$	−1.40133	−0.255846
$31$	0.454979	0.0817167	0.0408584	−	0.999165i	$-0.486991\pi$
$31$	0.454979	0.0817167	0.0408584	+	0.999165i	$0.486991\pi$
$32$	−4.51331	−0.797848
$33$	2.62788	0.457455
$34$	0.887314	0.152173
$35$	−3.28382	−0.555067
$36$	−1.81790	−0.302983
$37$	−11.5815	−1.90399	−0.951994	−	0.306115i	$-0.900971\pi$
$37$	−11.5815	−1.90399	−0.951994	+	0.306115i	$0.900971\pi$
$38$	3.25203	0.527549
$39$	−0.620243	−0.0993184
$40$	−5.35012	−0.845928
$41$	1.52292	0.237840	0.118920	−	0.992904i	$-0.462057\pi$
$41$	1.52292	0.237840	0.118920	+	0.992904i	$0.462057\pi$
$42$	0.426737	0.0658469
$43$	6.91315	1.05425	0.527123	−	0.849789i	$-0.323271\pi$
$43$	6.91315	1.05425	0.527123	+	0.849789i	$0.323271\pi$
$44$	4.77721	0.720191
$45$	−3.28382	−0.489523
$46$	−2.98109	−0.439538
$47$	9.49134	1.38445	0.692227	−	0.721680i	$-0.256630\pi$
$47$	9.49134	1.38445	0.692227	+	0.721680i	$0.256630\pi$
$48$	−2.94054	−0.424430
$49$	1.00000	0.142857
$50$	−2.46802	−0.349030
$51$	2.07930	0.291160
$52$	−1.12754	−0.156361
$53$	−5.26196	−0.722785	−0.361393	−	0.932414i	$-0.617699\pi$
$53$	−5.26196	−0.722785	−0.361393	+	0.932414i	$0.617699\pi$
$54$	0.426737	0.0580715
$55$	8.62948	1.16360
$56$	1.62924	0.217716
$57$	7.62070	1.00939
$58$	1.27259	0.167099
$59$	−11.6791	−1.52049	−0.760247	−	0.649635i	$-0.774922\pi$
$59$	−11.6791	−1.52049	−0.760247	+	0.649635i	$0.774922\pi$
$60$	−5.96964	−0.770677
$61$	11.9493	1.52995	0.764976	−	0.644059i	$-0.222751\pi$
$61$	11.9493	1.52995	0.764976	+	0.644059i	$0.222751\pi$
$62$	−0.194156	−0.0246579
$63$	1.00000	0.125988
$64$	−3.95508	−0.494385
$65$	−2.03677	−0.252630
$66$	−1.12141	−0.138036
$67$	−14.0526	−1.71680	−0.858400	−	0.512981i	$-0.828541\pi$
$67$	−14.0526	−1.71680	−0.858400	+	0.512981i	$0.828541\pi$
$68$	3.77995	0.458386
$69$	−6.98579	−0.840990
$70$	1.40133	0.167491
$71$	13.3701	1.58674	0.793369	−	0.608740i	$-0.208325\pi$
$71$	13.3701	1.58674	0.793369	+	0.608740i	$0.208325\pi$
$72$	1.62924	0.192007
$73$	7.88472	0.922836	0.461418	−	0.887183i	$-0.347341\pi$
$73$	7.88472	0.922836	0.461418	+	0.887183i	$0.347341\pi$
$74$	4.94226	0.574526
$75$	−5.78347	−0.667817
$76$	13.8536	1.58912
$77$	−2.62788	−0.299475
$78$	0.264681	0.0299692
$79$	−5.65341	−0.636058	−0.318029	−	0.948081i	$-0.603021\pi$
$79$	−5.65341	−0.636058	−0.318029	+	0.948081i	$0.603021\pi$
$80$	−9.65619	−1.07959
$81$	1.00000	0.111111
$82$	−0.649886	−0.0717679
$83$	13.6501	1.49829	0.749146	−	0.662405i	$-0.230464\pi$
$83$	13.6501	1.49829	0.749146	+	0.662405i	$0.230464\pi$
$84$	1.81790	0.198349
$85$	6.82804	0.740605
$86$	−2.95010	−0.318117
$87$	2.98214	0.319719
$88$	−4.28144	−0.456403
$89$	13.9255	1.47610	0.738050	−	0.674746i	$-0.235747\pi$
$89$	13.9255	1.47610	0.738050	+	0.674746i	$0.235747\pi$
$90$	1.40133	0.147713
$91$	0.620243	0.0650192
$92$	−12.6994	−1.32401
$93$	−0.454979	−0.0471792
$94$	−4.05030	−0.417757
$95$	25.0250	2.56751
$96$	4.51331	0.460638
$97$	13.9587	1.41729	0.708643	−	0.705567i	$-0.249308\pi$
$97$	13.9587	1.41729	0.708643	+	0.705567i	$0.249308\pi$
$98$	−0.426737	−0.0431069
$99$	−2.62788	−0.264112
$100$	−10.5137	−1.05137
$101$	3.16595	0.315024	0.157512	−	0.987517i	$-0.449653\pi$
$101$	3.16595	0.315024	0.157512	+	0.987517i	$0.449653\pi$
$102$	−0.887314	−0.0878571
$103$	−11.6184	−1.14479	−0.572397	−	0.819977i	$-0.693986\pi$
$103$	−11.6184	−1.14479	−0.572397	+	0.819977i	$0.693986\pi$
$104$	1.01052	0.0990900
$105$	3.28382	0.320468
$106$	2.24547	0.218099
$107$	15.6211	1.51015	0.755076	−	0.655637i	$-0.227600\pi$
$107$	15.6211	1.51015	0.755076	+	0.655637i	$0.227600\pi$
$108$	1.81790	0.174927
$109$	17.3743	1.66416	0.832080	−	0.554655i	$-0.187150\pi$
$109$	17.3743	1.66416	0.832080	+	0.554655i	$0.187150\pi$
$110$	−3.68252	−0.351114
$111$	11.5815	1.09927
$112$	2.94054	0.277855
$113$	−17.5901	−1.65474	−0.827368	−	0.561660i	$-0.810163\pi$
$113$	−17.5901	−1.65474	−0.827368	+	0.561660i	$0.810163\pi$
$114$	−3.25203	−0.304581
$115$	−22.9401	−2.13917
$116$	5.42122	0.503348
$117$	0.620243	0.0573415
$118$	4.98391	0.458807
$119$	−2.07930	−0.190609
$120$	5.35012	0.488397
$121$	−4.09425	−0.372205
$122$	−5.09921	−0.461661
$123$	−1.52292	−0.137317
$124$	−0.827105	−0.0742762
$125$	−2.57276	−0.230115
$126$	−0.426737	−0.0380167
$127$	6.69394	0.593991	0.296996	−	0.954879i	$-0.404015\pi$
$127$	6.69394	0.593991	0.296996	+	0.954879i	$0.404015\pi$
$128$	10.7144	0.947028
$129$	−6.91315	−0.608669
$130$	0.869163	0.0762307
$131$	6.48167	0.566306	0.283153	−	0.959075i	$-0.408620\pi$
$131$	6.48167	0.566306	0.283153	+	0.959075i	$0.408620\pi$
$132$	−4.77721	−0.415803
$133$	−7.62070	−0.660798
$134$	5.99677	0.518042
$135$	3.28382	0.282626
$136$	−3.38767	−0.290490
$137$	16.6599	1.42335	0.711675	−	0.702509i	$-0.247937\pi$
$137$	16.6599	1.42335	0.711675	+	0.702509i	$0.247937\pi$
$138$	2.98109	0.253767
$139$	−2.96473	−0.251465	−0.125733	−	0.992064i	$-0.540128\pi$
$139$	−2.96473	−0.251465	−0.125733	+	0.992064i	$0.540128\pi$
$140$	5.96964	0.504527
$141$	−9.49134	−0.799315
$142$	−5.70551	−0.478796
$143$	−1.62992	−0.136301
$144$	2.94054	0.245045
$145$	9.79281	0.813249
$146$	−3.36470	−0.278464
$147$	−1.00000	−0.0824786
$148$	21.0540	1.73063
$149$	−8.99353	−0.736779	−0.368389	−	0.929672i	$-0.620091\pi$
$149$	−8.99353	−0.736779	−0.368389	+	0.929672i	$0.620091\pi$
$150$	2.46802	0.201513
$151$	−2.92212	−0.237799	−0.118899	−	0.992906i	$-0.537937\pi$
$151$	−2.92212	−0.237799	−0.118899	+	0.992906i	$0.537937\pi$
$152$	−12.4159	−1.00706
$153$	−2.07930	−0.168101
$154$	1.12141	0.0903660
$155$	−1.49407	−0.120007
$156$	1.12754	0.0902753
$157$	16.8307	1.34323	0.671616	−	0.740899i	$-0.265600\pi$
$157$	16.8307	1.34323	0.671616	+	0.740899i	$0.265600\pi$
$158$	2.41252	0.191930
$159$	5.26196	0.417300
$160$	14.8209	1.17169
$161$	6.98579	0.550557
$162$	−0.426737	−0.0335276
$163$	−22.5177	−1.76373	−0.881863	−	0.471507i	$-0.843710\pi$
$163$	−22.5177	−1.76373	−0.881863	+	0.471507i	$0.843710\pi$
$164$	−2.76851	−0.216184
$165$	−8.62948	−0.671804
$166$	−5.82499	−0.452107
$167$	8.01819	0.620467	0.310233	−	0.950660i	$-0.399593\pi$
$167$	8.01819	0.620467	0.310233	+	0.950660i	$0.399593\pi$
$168$	−1.62924	−0.125698
$169$	−12.6153	−0.970408
$170$	−2.91378	−0.223476
$171$	−7.62070	−0.582769
$172$	−12.5674	−0.958254
$173$	12.0798	0.918412	0.459206	−	0.888330i	$-0.348134\pi$
$173$	12.0798	0.918412	0.459206	+	0.888330i	$0.348134\pi$
$174$	−1.27259	−0.0964748
$175$	5.78347	0.437189
$176$	−7.72737	−0.582473
$177$	11.6791	0.877857
$178$	−5.94252	−0.445411
$179$	−10.9759	−0.820379	−0.410190	−	0.912000i	$-0.634537\pi$
$179$	−10.9759	−0.820379	−0.410190	+	0.912000i	$0.634537\pi$
$180$	5.96964	0.444951
$181$	−5.82133	−0.432696	−0.216348	−	0.976316i	$-0.569415\pi$
$181$	−5.82133	−0.432696	−0.216348	+	0.976316i	$0.569415\pi$
$182$	−0.264681	−0.0196194
$183$	−11.9493	−0.883318
$184$	11.3815	0.839055
$185$	38.0316	2.79614
$186$	0.194156	0.0142362
$187$	5.46415	0.399578
$188$	−17.2543	−1.25840
$189$	−1.00000	−0.0727393
$190$	−10.6791	−0.774742
$191$	10.4215	0.754075	0.377037	−	0.926198i	$-0.376943\pi$
$191$	10.4215	0.754075	0.377037	+	0.926198i	$0.376943\pi$
$192$	3.95508	0.285433
$193$	1.61781	0.116453	0.0582263	−	0.998303i	$-0.481456\pi$
$193$	1.61781	0.116453	0.0582263	+	0.998303i	$0.481456\pi$
$194$	−5.95667	−0.427664
$195$	2.03677	0.145856
$196$	−1.81790	−0.129850
$197$	−6.35580	−0.452832	−0.226416	−	0.974031i	$-0.572701\pi$
$197$	−6.35580	−0.452832	−0.226416	+	0.974031i	$0.572701\pi$
$198$	1.12141	0.0796953
$199$	−10.4643	−0.741795	−0.370897	−	0.928674i	$-0.620950\pi$
$199$	−10.4643	−0.741795	−0.370897	+	0.928674i	$0.620950\pi$
$200$	9.42263	0.666281
$201$	14.0526	0.991195
$202$	−1.35103	−0.0950581
$203$	−2.98214	−0.209305
$204$	−3.77995	−0.264649
$205$	−5.00100	−0.349285
$206$	4.95800	0.345440
$207$	6.98579	0.485546
$208$	1.82385	0.126461
$209$	20.0263	1.38525
$210$	−1.40133	−0.0967007
$211$	−16.7420	−1.15257	−0.576285	−	0.817249i	$-0.695498\pi$
$211$	−16.7420	−1.15257	−0.576285	+	0.817249i	$0.695498\pi$
$212$	9.56569	0.656974
$213$	−13.3701	−0.916104
$214$	−6.66612	−0.455686
$215$	−22.7015	−1.54823
$216$	−1.62924	−0.110856
$217$	0.454979	0.0308860
$218$	−7.41427	−0.502158
$219$	−7.88472	−0.532800
$220$	−15.6875	−1.05765
$221$	−1.28967	−0.0867527
$222$	−4.94226	−0.331703
$223$	9.81900	0.657529	0.328764	−	0.944412i	$-0.393368\pi$
$223$	9.81900	0.657529	0.328764	+	0.944412i	$0.393368\pi$
$224$	−4.51331	−0.301558
$225$	5.78347	0.385564
$226$	7.50634	0.499314
$227$	18.1308	1.20338	0.601692	−	0.798728i	$-0.294494\pi$
$227$	18.1308	1.20338	0.601692	+	0.798728i	$0.294494\pi$
$228$	−13.8536	−0.917479
$229$	16.5276	1.09218	0.546088	−	0.837728i	$-0.316116\pi$
$229$	16.5276	1.09218	0.546088	+	0.837728i	$0.316116\pi$
$230$	9.78937	0.645492
$231$	2.62788	0.172902
$232$	−4.85861	−0.318984
$233$	−15.6411	−1.02468	−0.512340	−	0.858783i	$-0.671221\pi$
$233$	−15.6411	−1.02468	−0.512340	+	0.858783i	$0.671221\pi$
$234$	−0.264681	−0.0173027
$235$	−31.1678	−2.03317
$236$	21.2314	1.38205
$237$	5.65341	0.367228
$238$	0.887314	0.0575160
$239$	−24.7485	−1.60085	−0.800424	−	0.599434i	$-0.795393\pi$
$239$	−24.7485	−1.60085	−0.800424	+	0.599434i	$0.795393\pi$
$240$	9.65619	0.623304
$241$	−26.4849	−1.70604	−0.853022	−	0.521874i	$-0.825233\pi$
$241$	−26.4849	−1.70604	−0.853022	+	0.521874i	$0.825233\pi$
$242$	1.74717	0.112312
$243$	−1.00000	−0.0641500
$244$	−21.7226	−1.39065
$245$	−3.28382	−0.209795
$246$	0.649886	0.0414352
$247$	−4.72669	−0.300752
$248$	0.741269	0.0470706
$249$	−13.6501	−0.865039
$250$	1.09789	0.0694367
$251$	9.59598	0.605693	0.302847	−	0.953039i	$-0.402063\pi$
$251$	9.59598	0.605693	0.302847	+	0.953039i	$0.402063\pi$
$252$	−1.81790	−0.114517
$253$	−18.3578	−1.15415
$254$	−2.85655	−0.179236
$255$	−6.82804	−0.427589
$256$	3.33793	0.208621
$257$	14.8391	0.925639	0.462819	−	0.886453i	$-0.346838\pi$
$257$	14.8391	0.925639	0.462819	+	0.886453i	$0.346838\pi$
$258$	2.95010	0.183665
$259$	−11.5815	−0.719640
$260$	3.70263	0.229627
$261$	−2.98214	−0.184590
$262$	−2.76597	−0.170882
$263$	16.6847	1.02882	0.514412	−	0.857543i	$-0.328010\pi$
$263$	16.6847	1.02882	0.514412	+	0.857543i	$0.328010\pi$
$264$	4.28144	0.263504
$265$	17.2793	1.06146
$266$	3.25203	0.199395
$267$	−13.9255	−0.852227
$268$	25.5462	1.56048
$269$	−7.78161	−0.474453	−0.237227	−	0.971454i	$-0.576238\pi$
$269$	−7.78161	−0.474453	−0.237227	+	0.971454i	$0.576238\pi$
$270$	−1.40133	−0.0852820
$271$	20.1007	1.22103	0.610514	−	0.792005i	$-0.290963\pi$
$271$	20.1007	1.22103	0.610514	+	0.792005i	$0.290963\pi$
$272$	−6.11425	−0.370731
$273$	−0.620243	−0.0375388
$274$	−7.10939	−0.429494
$275$	−15.1982	−0.916489
$276$	12.6994	0.764416
$277$	−17.9552	−1.07882	−0.539412	−	0.842042i	$-0.681353\pi$
$277$	−17.9552	−1.07882	−0.539412	+	0.842042i	$0.681353\pi$
$278$	1.26516	0.0758793
$279$	0.454979	0.0272389
$280$	−5.35012	−0.319731
$281$	1.71727	0.102444	0.0512219	−	0.998687i	$-0.483688\pi$
$281$	1.71727	0.102444	0.0512219	+	0.998687i	$0.483688\pi$
$282$	4.05030	0.241192
$283$	−6.52811	−0.388056	−0.194028	−	0.980996i	$-0.562155\pi$
$283$	−6.52811	−0.388056	−0.194028	+	0.980996i	$0.562155\pi$
$284$	−24.3054	−1.44226
$285$	−25.0250	−1.48235
$286$	0.695549	0.0411287
$287$	1.52292	0.0898952
$288$	−4.51331	−0.265949
$289$	−12.6765	−0.745677
$290$	−4.17895	−0.245397
$291$	−13.9587	−0.818271
$292$	−14.3336	−0.838810
$293$	3.35466	0.195981	0.0979907	−	0.995187i	$-0.468758\pi$
$293$	3.35466	0.195981	0.0979907	+	0.995187i	$0.468758\pi$
$294$	0.426737	0.0248878
$295$	38.3521	2.23295
$296$	−18.8690	−1.09674
$297$	2.62788	0.152485
$298$	3.83787	0.222322
$299$	4.33289	0.250577
$300$	10.5137	0.607011
$301$	6.91315	0.398467
$302$	1.24698	0.0717555
$303$	−3.16595	−0.181879
$304$	−22.4089	−1.28524
$305$	−39.2393	−2.24684
$306$	0.887314	0.0507243
$307$	6.88211	0.392783	0.196391	−	0.980526i	$-0.437078\pi$
$307$	6.88211	0.392783	0.196391	+	0.980526i	$0.437078\pi$
$308$	4.77721	0.272207
$309$	11.6184	0.660947
$310$	0.637575	0.0362118
$311$	7.00933	0.397463	0.198731	−	0.980054i	$-0.436318\pi$
$311$	7.00933	0.397463	0.198731	+	0.980054i	$0.436318\pi$
$312$	−1.01052	−0.0572096
$313$	−9.50269	−0.537124	−0.268562	−	0.963262i	$-0.586548\pi$
$313$	−9.50269	−0.537124	−0.268562	+	0.963262i	$0.586548\pi$
$314$	−7.18226	−0.405318
$315$	−3.28382	−0.185022
$316$	10.2773	0.578144
$317$	−7.82025	−0.439229	−0.219615	−	0.975587i	$-0.570480\pi$
$317$	−7.82025	−0.439229	−0.219615	+	0.975587i	$0.570480\pi$
$318$	−2.24547	−0.125920
$319$	7.83670	0.438771
$320$	12.9878	0.726038
$321$	−15.6211	−0.871887
$322$	−2.98109	−0.166130
$323$	15.8457	0.881679
$324$	−1.81790	−0.100994
$325$	3.58716	0.198980
$326$	9.60915	0.532201
$327$	−17.3743	−0.960804
$328$	2.48120	0.137001
$329$	9.49134	0.523274
$330$	3.68252	0.202716
$331$	7.32951	0.402866	0.201433	−	0.979502i	$-0.435440\pi$
$331$	7.32951	0.402866	0.201433	+	0.979502i	$0.435440\pi$
$332$	−24.8144	−1.36187
$333$	−11.5815	−0.634663
$334$	−3.42166	−0.187225
$335$	46.1462	2.52124
$336$	−2.94054	−0.160419
$337$	3.95415	0.215396	0.107698	−	0.994184i	$-0.465652\pi$
$337$	3.95415	0.215396	0.107698	+	0.994184i	$0.465652\pi$
$338$	5.38341	0.292819
$339$	17.5901	0.955363
$340$	−12.4127	−0.673171
$341$	−1.19563	−0.0647470
$342$	3.25203	0.175850
$343$	1.00000	0.0539949
$344$	11.2632	0.607269
$345$	22.9401	1.23505
$346$	−5.15491	−0.277130
$347$	6.80849	0.365499	0.182749	−	0.983160i	$-0.441500\pi$
$347$	6.80849	0.365499	0.182749	+	0.983160i	$0.441500\pi$
$348$	−5.42122	−0.290608
$349$	−0.0826098	−0.00442200	−0.00221100	−	0.999998i	$-0.500704\pi$
$349$	−0.0826098	−0.00442200	−0.00221100	+	0.999998i	$0.500704\pi$
$350$	−2.46802	−0.131921
$351$	−0.620243	−0.0331061
$352$	11.8604	0.632163
$353$	−20.3722	−1.08430	−0.542151	−	0.840281i	$-0.682390\pi$
$353$	−20.3722	−1.08430	−0.542151	+	0.840281i	$0.682390\pi$
$354$	−4.98391	−0.264892
$355$	−43.9050	−2.33023
$356$	−25.3151	−1.34170
$357$	2.07930	0.110048
$358$	4.68383	0.247548
$359$	−6.69510	−0.353354	−0.176677	−	0.984269i	$-0.556535\pi$
$359$	−6.69510	−0.353354	−0.176677	+	0.984269i	$0.556535\pi$
$360$	−5.35012	−0.281976
$361$	39.0750	2.05658
$362$	2.48418	0.130565
$363$	4.09425	0.214893
$364$	−1.12754	−0.0590990
$365$	−25.8920	−1.35525
$366$	5.09921	0.266540
$367$	11.6423	0.607723	0.303862	−	0.952716i	$-0.401724\pi$
$367$	11.6423	0.607723	0.303862	+	0.952716i	$0.401724\pi$
$368$	20.5420	1.07082
$369$	1.52292	0.0792801
$370$	−16.2295	−0.843730
$371$	−5.26196	−0.273187
$372$	0.827105	0.0428834
$373$	32.1923	1.66686	0.833428	−	0.552628i	$-0.186375\pi$
$373$	32.1923	1.66686	0.833428	+	0.552628i	$0.186375\pi$
$374$	−2.33175	−0.120572
$375$	2.57276	0.132857
$376$	15.4636	0.797476
$377$	−1.84965	−0.0952620
$378$	0.426737	0.0219490
$379$	−27.0679	−1.39038	−0.695191	−	0.718825i	$-0.744680\pi$
$379$	−27.0679	−1.39038	−0.695191	+	0.718825i	$0.744680\pi$
$380$	−45.4928	−2.33373
$381$	−6.69394	−0.342941
$382$	−4.44725	−0.227541
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−10.7144	−0.546767
$385$	8.62948	0.439799
$386$	−0.690379	−0.0351394
$387$	6.91315	0.351415
$388$	−25.3754	−1.28824
$389$	−14.3758	−0.728883	−0.364442	−	0.931226i	$-0.618740\pi$
$389$	−14.3758	−0.728883	−0.364442	+	0.931226i	$0.618740\pi$
$390$	−0.869163	−0.0440118
$391$	−14.5255	−0.734588
$392$	1.62924	0.0822889
$393$	−6.48167	−0.326957
$394$	2.71226	0.136641
$395$	18.5648	0.934095
$396$	4.77721	0.240064
$397$	35.7020	1.79183	0.895917	−	0.444221i	$-0.146520\pi$
$397$	35.7020	1.79183	0.895917	+	0.444221i	$0.146520\pi$
$398$	4.46550	0.223836
$399$	7.62070	0.381512
$400$	17.0065	0.850324
$401$	1.27616	0.0637282	0.0318641	−	0.999492i	$-0.489856\pi$
$401$	1.27616	0.0637282	0.0318641	+	0.999492i	$0.489856\pi$
$402$	−5.99677	−0.299092
$403$	0.282198	0.0140573
$404$	−5.75537	−0.286341
$405$	−3.28382	−0.163174
$406$	1.27259	0.0631576
$407$	30.4348	1.50860
$408$	3.38767	0.167715
$409$	−22.4511	−1.11014	−0.555068	−	0.831805i	$-0.687308\pi$
$409$	−22.4511	−1.11014	−0.555068	+	0.831805i	$0.687308\pi$
$410$	2.13411	0.105396
$411$	−16.6599	−0.821771
$412$	21.1210	1.04056
$413$	−11.6791	−0.574692
$414$	−2.98109	−0.146513
$415$	−44.8244	−2.20034
$416$	−2.79935	−0.137249
$417$	2.96473	0.145184
$418$	−8.54595	−0.417996
$419$	−26.2976	−1.28472	−0.642360	−	0.766403i	$-0.722044\pi$
$419$	−26.2976	−1.28472	−0.642360	+	0.766403i	$0.722044\pi$
$420$	−5.96964	−0.291289
$421$	−26.2791	−1.28077	−0.640383	−	0.768056i	$-0.721224\pi$
$421$	−26.2791	−1.28077	−0.640383	+	0.768056i	$0.721224\pi$
$422$	7.14444	0.347786
$423$	9.49134	0.461485
$424$	−8.57297	−0.416340
$425$	−12.0256	−0.583325
$426$	5.70551	0.276433
$427$	11.9493	0.578267
$428$	−28.3976	−1.37265
$429$	1.62992	0.0786935
$430$	9.68758	0.467177
$431$	−3.41779	−0.164629	−0.0823145	−	0.996606i	$-0.526231\pi$
$431$	−3.41779	−0.164629	−0.0823145	+	0.996606i	$0.526231\pi$
$432$	−2.94054	−0.141477
$433$	−4.37913	−0.210448	−0.105224	−	0.994449i	$-0.533556\pi$
$433$	−4.37913	−0.210448	−0.105224	+	0.994449i	$0.533556\pi$
$434$	−0.194156	−0.00931981
$435$	−9.79281	−0.469529
$436$	−31.5848	−1.51264
$437$	−53.2366	−2.54665
$438$	3.36470	0.160772
$439$	−35.7233	−1.70498	−0.852490	−	0.522744i	$-0.824908\pi$
$439$	−35.7233	−1.70498	−0.852490	+	0.522744i	$0.824908\pi$
$440$	14.0595	0.670258
$441$	1.00000	0.0476190
$442$	0.550350	0.0261775
$443$	−33.0415	−1.56985	−0.784925	−	0.619591i	$-0.787298\pi$
$443$	−33.0415	−1.56985	−0.784925	+	0.619591i	$0.787298\pi$
$444$	−21.0540	−0.999178
$445$	−45.7288	−2.16775
$446$	−4.19013	−0.198408
$447$	8.99353	0.425379
$448$	−3.95508	−0.186860
$449$	30.5096	1.43984	0.719919	−	0.694058i	$-0.244179\pi$
$449$	30.5096	1.43984	0.719919	+	0.694058i	$0.244179\pi$
$450$	−2.46802	−0.116343
$451$	−4.00205	−0.188449
$452$	31.9770	1.50407
$453$	2.92212	0.137293
$454$	−7.73708	−0.363119
$455$	−2.03677	−0.0954851
$456$	12.4159	0.581429
$457$	−21.2143	−0.992361	−0.496180	−	0.868219i	$-0.665265\pi$
$457$	−21.2143	−0.992361	−0.496180	+	0.868219i	$0.665265\pi$
$458$	−7.05295	−0.329563
$459$	2.07930	0.0970534
$460$	41.7026	1.94440
$461$	15.1654	0.706322	0.353161	−	0.935563i	$-0.385107\pi$
$461$	15.1654	0.706322	0.353161	+	0.935563i	$0.385107\pi$
$462$	−1.12141	−0.0521728
$463$	31.7926	1.47753	0.738765	−	0.673964i	$-0.235410\pi$
$463$	31.7926	1.47753	0.738765	+	0.673964i	$0.235410\pi$
$464$	−8.76909	−0.407095
$465$	1.49407	0.0692858
$466$	6.67462	0.309196
$467$	−5.27539	−0.244116	−0.122058	−	0.992523i	$-0.538949\pi$
$467$	−5.27539	−0.244116	−0.122058	+	0.992523i	$0.538949\pi$
$468$	−1.12754	−0.0521205
$469$	−14.0526	−0.648889
$470$	13.3005	0.613505
$471$	−16.8307	−0.775516
$472$	−19.0281	−0.875838
$473$	−18.1669	−0.835316
$474$	−2.41252	−0.110811
$475$	−44.0740	−2.02226
$476$	3.77995	0.173254
$477$	−5.26196	−0.240928
$478$	10.5611	0.483054
$479$	−31.7950	−1.45275	−0.726375	−	0.687298i	$-0.758796\pi$
$479$	−31.7950	−1.45275	−0.726375	+	0.687298i	$0.758796\pi$
$480$	−14.8209	−0.676478
$481$	−7.18336	−0.327533
$482$	11.3021	0.514797
$483$	−6.98579	−0.317864
$484$	7.44293	0.338315
$485$	−45.8377	−2.08138
$486$	0.426737	0.0193572
$487$	0.555760	0.0251839	0.0125919	−	0.999921i	$-0.495992\pi$
$487$	0.555760	0.0251839	0.0125919	+	0.999921i	$0.495992\pi$
$488$	19.4682	0.881286
$489$	22.5177	1.01829
$490$	1.40133	0.0633055
$491$	14.4832	0.653616	0.326808	−	0.945091i	$-0.394027\pi$
$491$	14.4832	0.653616	0.326808	+	0.945091i	$0.394027\pi$
$492$	2.76851	0.124814
$493$	6.20076	0.279268
$494$	2.01705	0.0907514
$495$	8.62948	0.387866
$496$	1.33788	0.0600727
$497$	13.3701	0.599731
$498$	5.82499	0.261024
$499$	18.7250	0.838245	0.419123	−	0.907930i	$-0.362338\pi$
$499$	18.7250	0.838245	0.419123	+	0.907930i	$0.362338\pi$
$500$	4.67701	0.209162
$501$	−8.01819	−0.358227
$502$	−4.09496	−0.182767
$503$	−6.01096	−0.268016	−0.134008	−	0.990980i	$-0.542785\pi$
$503$	−6.01096	−0.268016	−0.134008	+	0.990980i	$0.542785\pi$
$504$	1.62924	0.0725720
$505$	−10.3964	−0.462635
$506$	7.83395	0.348262
$507$	12.6153	0.560265
$508$	−12.1689	−0.539907
$509$	6.89192	0.305479	0.152739	−	0.988266i	$-0.451190\pi$
$509$	6.89192	0.305479	0.152739	+	0.988266i	$0.451190\pi$
$510$	2.91378	0.129024
$511$	7.88472	0.348799
$512$	−22.8532	−1.00998
$513$	7.62070	0.336462
$514$	−6.33240	−0.279310
$515$	38.1527	1.68121
$516$	12.5674	0.553248
$517$	−24.9421	−1.09695
$518$	4.94226	0.217150
$519$	−12.0798	−0.530246
$520$	−3.31838	−0.145520
$521$	−34.9933	−1.53308	−0.766541	−	0.642195i	$-0.778024\pi$
$521$	−34.9933	−1.53308	−0.766541	+	0.642195i	$0.778024\pi$
$522$	1.27259	0.0556997
$523$	−40.8787	−1.78750	−0.893750	−	0.448566i	$-0.851935\pi$
$523$	−40.8787	−1.78750	−0.893750	+	0.448566i	$0.851935\pi$
$524$	−11.7830	−0.514743
$525$	−5.78347	−0.252411
$526$	−7.11999	−0.310446
$527$	−0.946039	−0.0412101
$528$	7.72737	0.336291
$529$	25.8012	1.12179
$530$	−7.37372	−0.320294
$531$	−11.6791	−0.506831
$532$	13.8536	0.600631
$533$	0.944581	0.0409144
$534$	5.94252	0.257158
$535$	−51.2970	−2.21776
$536$	−22.8950	−0.988915
$537$	10.9759	0.473646
$538$	3.32070	0.143166
$539$	−2.62788	−0.113191
$540$	−5.96964	−0.256892
$541$	−41.8318	−1.79849	−0.899244	−	0.437448i	$-0.855883\pi$
$541$	−41.8318	−1.79849	−0.899244	+	0.437448i	$0.855883\pi$
$542$	−8.57769	−0.368443
$543$	5.82133	0.249817
$544$	9.38452	0.402358
$545$	−57.0542	−2.44393
$546$	0.264681	0.0113273
$547$	4.79672	0.205093	0.102546	−	0.994728i	$-0.467301\pi$
$547$	4.79672	0.205093	0.102546	+	0.994728i	$0.467301\pi$
$548$	−30.2859	−1.29375
$549$	11.9493	0.509984
$550$	6.48565	0.276549
$551$	22.7260	0.968160
$552$	−11.3815	−0.484429
$553$	−5.65341	−0.240407
$554$	7.66215	0.325533
$555$	−38.0316	−1.61435
$556$	5.38957	0.228569
$557$	−22.6413	−0.959343	−0.479672	−	0.877448i	$-0.659244\pi$
$557$	−22.6413	−0.959343	−0.479672	+	0.877448i	$0.659244\pi$
$558$	−0.194156	−0.00821930
$559$	4.28784	0.181356
$560$	−9.65619	−0.408048
$561$	−5.46415	−0.230696
$562$	−0.732823	−0.0309123
$563$	−36.8755	−1.55412	−0.777058	−	0.629429i	$-0.783289\pi$
$563$	−36.8755	−1.55412	−0.777058	+	0.629429i	$0.783289\pi$
$564$	17.2543	0.726536
$565$	57.7627	2.43009
$566$	2.78578	0.117095
$567$	1.00000	0.0419961
$568$	21.7831	0.913997
$569$	−27.4885	−1.15238	−0.576190	−	0.817316i	$-0.695461\pi$
$569$	−27.4885	−1.15238	−0.576190	+	0.817316i	$0.695461\pi$
$570$	10.6791	0.447298
$571$	−32.7613	−1.37102	−0.685510	−	0.728064i	$-0.740421\pi$
$571$	−32.7613	−1.37102	−0.685510	+	0.728064i	$0.740421\pi$
$572$	2.96303	0.123891
$573$	−10.4215	−0.435365
$574$	−0.649886	−0.0271257
$575$	40.4021	1.68488
$576$	−3.95508	−0.164795
$577$	−25.6633	−1.06838	−0.534189	−	0.845365i	$-0.679383\pi$
$577$	−25.6633	−1.06838	−0.534189	+	0.845365i	$0.679383\pi$
$578$	5.40954	0.225007
$579$	−1.61781	−0.0672339
$580$	−17.8023	−0.739201
$581$	13.6501	0.566301
$582$	5.95667	0.246912
$583$	13.8278	0.572688
$584$	12.8461	0.531574
$585$	−2.03677	−0.0842099
$586$	−1.43156	−0.0591371
$587$	22.0720	0.911008	0.455504	−	0.890234i	$-0.349459\pi$
$587$	22.0720	0.911008	0.455504	+	0.890234i	$0.349459\pi$
$588$	1.81790	0.0749688
$589$	−3.46726	−0.142866
$590$	−16.3663	−0.673789
$591$	6.35580	0.261443
$592$	−34.0559	−1.39969
$593$	28.2075	1.15834	0.579172	−	0.815205i	$-0.303376\pi$
$593$	28.2075	1.15834	0.579172	+	0.815205i	$0.303376\pi$
$594$	−1.12141	−0.0460121
$595$	6.82804	0.279922
$596$	16.3493	0.669693
$597$	10.4643	0.428276
$598$	−1.84900	−0.0756114
$599$	−10.0612	−0.411090	−0.205545	−	0.978648i	$-0.565897\pi$
$599$	−10.0612	−0.411090	−0.205545	+	0.978648i	$0.565897\pi$
$600$	−9.42263	−0.384677
$601$	3.79228	0.154690	0.0773452	−	0.997004i	$-0.475356\pi$
$601$	3.79228	0.154690	0.0773452	+	0.997004i	$0.475356\pi$
$602$	−2.95010	−0.120237
$603$	−14.0526	−0.572267
$604$	5.31211	0.216147
$605$	13.4448	0.546608
$606$	1.35103	0.0548818
$607$	−0.700709	−0.0284409	−0.0142205	−	0.999899i	$-0.504527\pi$
$607$	−0.700709	−0.0284409	−0.0142205	+	0.999899i	$0.504527\pi$
$608$	34.3946	1.39488
$609$	2.98214	0.120842
$610$	16.7449	0.677980
$611$	5.88694	0.238160
$612$	3.77995	0.152795
$613$	−2.33635	−0.0943642	−0.0471821	−	0.998886i	$-0.515024\pi$
$613$	−2.33635	−0.0943642	−0.0471821	+	0.998886i	$0.515024\pi$
$614$	−2.93685	−0.118522
$615$	5.00100	0.201660
$616$	−4.28144	−0.172504
$617$	5.63267	0.226763	0.113381	−	0.993552i	$-0.463832\pi$
$617$	5.63267	0.226763	0.113381	+	0.993552i	$0.463832\pi$
$618$	−4.95800	−0.199440
$619$	12.6129	0.506957	0.253478	−	0.967341i	$-0.418425\pi$
$619$	12.6129	0.506957	0.253478	+	0.967341i	$0.418425\pi$
$620$	2.71606	0.109080
$621$	−6.98579	−0.280330
$622$	−2.99114	−0.119934
$623$	13.9255	0.557913
$624$	−1.82385	−0.0730124
$625$	−20.4689	−0.818754
$626$	4.05515	0.162076
$627$	−20.0263	−0.799772
$628$	−30.5964	−1.22093
$629$	24.0814	0.960190
$630$	1.40133	0.0558302
$631$	−16.6390	−0.662386	−0.331193	−	0.943563i	$-0.607451\pi$
$631$	−16.6390	−0.662386	−0.331193	+	0.943563i	$0.607451\pi$
$632$	−9.21074	−0.366384
$633$	16.7420	0.665436
$634$	3.33719	0.132537
$635$	−21.9817	−0.872317
$636$	−9.56569	−0.379304
$637$	0.620243	0.0245749
$638$	−3.34421	−0.132399
$639$	13.3701	0.528913
$640$	−35.1841	−1.39077
$641$	−9.32823	−0.368443	−0.184221	−	0.982885i	$-0.558976\pi$
$641$	−9.32823	−0.368443	−0.184221	+	0.982885i	$0.558976\pi$
$642$	6.66612	0.263091
$643$	33.5044	1.32128	0.660642	−	0.750701i	$-0.270284\pi$
$643$	33.5044	1.32128	0.660642	+	0.750701i	$0.270284\pi$
$644$	−12.6994	−0.500428
$645$	22.7015	0.893872
$646$	−6.76195	−0.266045
$647$	−28.9348	−1.13754	−0.568772	−	0.822495i	$-0.692581\pi$
$647$	−28.9348	−1.13754	−0.568772	+	0.822495i	$0.692581\pi$
$648$	1.62924	0.0640025
$649$	30.6913	1.20474
$650$	−1.53077	−0.0600418
$651$	−0.454979	−0.0178321
$652$	40.9349	1.60313
$653$	35.8792	1.40406	0.702031	−	0.712147i	$-0.252277\pi$
$653$	35.8792	1.40406	0.702031	+	0.712147i	$0.252277\pi$
$654$	7.41427	0.289921
$655$	−21.2846	−0.831659
$656$	4.47820	0.174844
$657$	7.88472	0.307612
$658$	−4.05030	−0.157897
$659$	17.7897	0.692987	0.346493	−	0.938052i	$-0.387372\pi$
$659$	17.7897	0.692987	0.346493	+	0.938052i	$0.387372\pi$
$660$	15.6875	0.610635
$661$	−11.1418	−0.433367	−0.216684	−	0.976242i	$-0.569524\pi$
$661$	−11.1418	−0.433367	−0.216684	+	0.976242i	$0.569524\pi$
$662$	−3.12777	−0.121564
$663$	1.28967	0.0500867
$664$	22.2392	0.863049
$665$	25.0250	0.970427
$666$	4.94226	0.191509
$667$	−20.8326	−0.806642
$668$	−14.5762	−0.563972
$669$	−9.81900	−0.379624
$670$	−19.6923	−0.760780
$671$	−31.4013	−1.21223
$672$	4.51331	0.174105
$673$	49.9492	1.92540	0.962700	−	0.270572i	$-0.0872129\pi$
$673$	49.9492	1.92540	0.962700	+	0.270572i	$0.0872129\pi$
$674$	−1.68738	−0.0649955
$675$	−5.78347	−0.222606
$676$	22.9333	0.882050
$677$	20.5892	0.791306	0.395653	−	0.918400i	$-0.370518\pi$
$677$	20.5892	0.791306	0.395653	+	0.918400i	$0.370518\pi$
$678$	−7.50634	−0.288279
$679$	13.9587	0.535684
$680$	11.1245	0.426605
$681$	−18.1308	−0.694774
$682$	0.510220	0.0195373
$683$	26.0306	0.996032	0.498016	−	0.867168i	$-0.334062\pi$
$683$	26.0306	0.996032	0.498016	+	0.867168i	$0.334062\pi$
$684$	13.8536	0.529707
$685$	−54.7080	−2.09029
$686$	−0.426737	−0.0162929
$687$	−16.5276	−0.630568
$688$	20.3284	0.775012
$689$	−3.26369	−0.124337
$690$	−9.78937	−0.372675
$691$	−21.3915	−0.813770	−0.406885	−	0.913479i	$-0.633385\pi$
$691$	−21.3915	−0.813770	−0.406885	+	0.913479i	$0.633385\pi$
$692$	−21.9599	−0.834789
$693$	−2.62788	−0.0998248
$694$	−2.90543	−0.110289
$695$	9.73564	0.369294
$696$	4.85861	0.184165
$697$	−3.16661	−0.119944
$698$	0.0352527	0.00133433
$699$	15.6411	0.591600
$700$	−10.5137	−0.397382
$701$	−4.65980	−0.175998	−0.0879991	−	0.996121i	$-0.528047\pi$
$701$	−4.65980	−0.175998	−0.0879991	+	0.996121i	$0.528047\pi$
$702$	0.264681	0.00998973
$703$	88.2592	3.32876
$704$	10.3935	0.391718
$705$	31.1678	1.17385
$706$	8.69356	0.327186
$707$	3.16595	0.119068
$708$	−21.2314	−0.797926
$709$	−28.3389	−1.06429	−0.532145	−	0.846653i	$-0.678614\pi$
$709$	−28.3389	−1.06429	−0.532145	+	0.846653i	$0.678614\pi$
$710$	18.7359	0.703145
$711$	−5.65341	−0.212019
$712$	22.6879	0.850266
$713$	3.17839	0.119032
$714$	−0.887314	−0.0332069
$715$	5.35238	0.200168
$716$	19.9531	0.745682
$717$	24.7485	0.924251
$718$	2.85705	0.106624
$719$	−33.3346	−1.24317	−0.621585	−	0.783346i	$-0.713511\pi$
$719$	−33.3346	−1.24317	−0.621585	+	0.783346i	$0.713511\pi$
$720$	−9.65619	−0.359865
$721$	−11.6184	−0.432692
$722$	−16.6748	−0.620570
$723$	26.4849	0.984986
$724$	10.5826	0.393298
$725$	−17.2471	−0.640542
$726$	−1.74717	−0.0648435
$727$	−0.668594	−0.0247968	−0.0123984	−	0.999923i	$-0.503947\pi$
$727$	−0.668594	−0.0247968	−0.0123984	+	0.999923i	$0.503947\pi$
$728$	1.01052	0.0374525
$729$	1.00000	0.0370370
$730$	11.0491	0.408944
$731$	−14.3745	−0.531661
$732$	21.7226	0.802890
$733$	−8.29214	−0.306277	−0.153139	−	0.988205i	$-0.548938\pi$
$733$	−8.29214	−0.306277	−0.153139	+	0.988205i	$0.548938\pi$
$734$	−4.96820	−0.183380
$735$	3.28382	0.121125
$736$	−31.5290	−1.16217
$737$	36.9286	1.36028
$738$	−0.649886	−0.0239226
$739$	−12.3459	−0.454151	−0.227076	−	0.973877i	$-0.572916\pi$
$739$	−12.3459	−0.454151	−0.227076	+	0.973877i	$0.572916\pi$
$740$	−69.1375	−2.54154
$741$	4.72669	0.173639
$742$	2.24547	0.0824338
$743$	−14.6361	−0.536947	−0.268474	−	0.963287i	$-0.586519\pi$
$743$	−14.6361	−0.536947	−0.268474	+	0.963287i	$0.586519\pi$
$744$	−0.741269	−0.0271762
$745$	29.5331	1.08201
$746$	−13.7377	−0.502971
$747$	13.6501	0.499430
$748$	−9.93325	−0.363196
$749$	15.6211	0.570784
$750$	−1.09789	−0.0400893
$751$	31.8082	1.16070	0.580349	−	0.814368i	$-0.302916\pi$
$751$	31.8082	1.16070	0.580349	+	0.814368i	$0.302916\pi$
$752$	27.9096	1.01776
$753$	−9.59598	−0.349697
$754$	0.789315	0.0287452
$755$	9.59572	0.349224
$756$	1.81790	0.0661162
$757$	−3.59738	−0.130749	−0.0653745	−	0.997861i	$-0.520824\pi$
$757$	−3.59738	−0.130749	−0.0653745	+	0.997861i	$0.520824\pi$
$758$	11.5509	0.419546
$759$	18.3578	0.666346
$760$	40.7716	1.47894
$761$	44.5049	1.61330	0.806651	−	0.591028i	$-0.201278\pi$
$761$	44.5049	1.61330	0.806651	+	0.591028i	$0.201278\pi$
$762$	2.85655	0.103482
$763$	17.3743	0.628994
$764$	−18.9452	−0.685414
$765$	6.82804	0.246868
$766$	−0.426737	−0.0154186
$767$	−7.24390	−0.261562
$768$	−3.33793	−0.120447
$769$	−15.9647	−0.575703	−0.287851	−	0.957675i	$-0.592941\pi$
$769$	−15.9647	−0.575703	−0.287851	+	0.957675i	$0.592941\pi$
$770$	−3.68252	−0.132709
$771$	−14.8391	−0.534418
$772$	−2.94101	−0.105849
$773$	25.3571	0.912030	0.456015	−	0.889972i	$-0.349276\pi$
$773$	25.3571	0.912030	0.456015	+	0.889972i	$0.349276\pi$
$774$	−2.95010	−0.106039
$775$	2.63136	0.0945212
$776$	22.7419	0.816388
$777$	11.5815	0.415484
$778$	6.13469	0.219939
$779$	−11.6057	−0.415818
$780$	−3.70263	−0.132575
$781$	−35.1350	−1.25723
$782$	6.19858	0.221661
$783$	2.98214	0.106573
$784$	2.94054	0.105019
$785$	−55.2688	−1.97263
$786$	2.76597	0.0986588
$787$	−32.7435	−1.16718	−0.583590	−	0.812048i	$-0.698352\pi$
$787$	−32.7435	−1.16718	−0.583590	+	0.812048i	$0.698352\pi$
$788$	11.5542	0.411601
$789$	−16.6847	−0.593992
$790$	−7.92227	−0.281862
$791$	−17.5901	−0.625432
$792$	−4.28144	−0.152134
$793$	7.41148	0.263189
$794$	−15.2354	−0.540683
$795$	−17.2793	−0.612834
$796$	19.0230	0.674253
$797$	−8.12071	−0.287650	−0.143825	−	0.989603i	$-0.545940\pi$
$797$	−8.12071	−0.287650	−0.143825	+	0.989603i	$0.545940\pi$
$798$	−3.25203	−0.115121
$799$	−19.7353	−0.698186
$800$	−26.1026	−0.922865
$801$	13.9255	0.492033
$802$	−0.544583	−0.0192299
$803$	−20.7201	−0.731196
$804$	−25.5462	−0.900944
$805$	−22.9401	−0.808531
$806$	−0.120424	−0.00424176
$807$	7.78161	0.273926
$808$	5.15809	0.181461
$809$	40.3439	1.41842	0.709208	−	0.705000i	$-0.249053\pi$
$809$	40.3439	1.41842	0.709208	+	0.705000i	$0.249053\pi$
$810$	1.40133	0.0492376
$811$	35.4070	1.24331	0.621653	−	0.783292i	$-0.286461\pi$
$811$	35.4070	1.24331	0.621653	+	0.783292i	$0.286461\pi$
$812$	5.42122	0.190248
$813$	−20.1007	−0.704961
$814$	−12.9877	−0.455217
$815$	73.9442	2.59015
$816$	6.11425	0.214042
$817$	−52.6830	−1.84315
$818$	9.58072	0.334982
$819$	0.620243	0.0216731
$820$	9.09129	0.317482
$821$	8.31790	0.290297	0.145148	−	0.989410i	$-0.453634\pi$
$821$	8.31790	0.290297	0.145148	+	0.989410i	$0.453634\pi$
$822$	7.10939	0.247968
$823$	42.7277	1.48940	0.744698	−	0.667402i	$-0.232594\pi$
$823$	42.7277	1.48940	0.744698	+	0.667402i	$0.232594\pi$
$824$	−18.9291	−0.659427
$825$	15.1982	0.529135
$826$	4.98391	0.173413
$827$	−9.83244	−0.341908	−0.170954	−	0.985279i	$-0.554685\pi$
$827$	−9.83244	−0.341908	−0.170954	+	0.985279i	$0.554685\pi$
$828$	−12.6994	−0.441336
$829$	−3.96124	−0.137580	−0.0687898	−	0.997631i	$-0.521914\pi$
$829$	−3.96124	−0.137580	−0.0687898	+	0.997631i	$0.521914\pi$
$830$	19.1282	0.663950
$831$	17.9552	0.622859
$832$	−2.45311	−0.0850463
$833$	−2.07930	−0.0720435
$834$	−1.26516	−0.0438089
$835$	−26.3303	−0.911198
$836$	−36.4057	−1.25912
$837$	−0.454979	−0.0157264
$838$	11.2221	0.387662
$839$	−36.4922	−1.25985	−0.629925	−	0.776656i	$-0.716914\pi$
$839$	−36.4922	−1.25985	−0.629925	+	0.776656i	$0.716914\pi$
$840$	5.35012	0.184597
$841$	−20.1068	−0.693339
$842$	11.2143	0.386469
$843$	−1.71727	−0.0591460
$844$	30.4353	1.04763
$845$	41.4264	1.42511
$846$	−4.05030	−0.139252
$847$	−4.09425	−0.140680
$848$	−15.4730	−0.531344
$849$	6.52811	0.224044
$850$	5.13175	0.176017
$851$	−80.9060	−2.77342
$852$	24.3054	0.832691
$853$	−47.9076	−1.64032	−0.820162	−	0.572132i	$-0.806117\pi$
$853$	−47.9076	−1.64032	−0.820162	+	0.572132i	$0.806117\pi$
$854$	−5.09921	−0.174491
$855$	25.0250	0.855837
$856$	25.4505	0.869881
$857$	−4.41416	−0.150785	−0.0753925	−	0.997154i	$-0.524021\pi$
$857$	−4.41416	−0.150785	−0.0753925	+	0.997154i	$0.524021\pi$
$858$	−0.695549	−0.0237456
$859$	8.86569	0.302493	0.151247	−	0.988496i	$-0.451671\pi$
$859$	8.86569	0.302493	0.151247	+	0.988496i	$0.451671\pi$
$860$	41.2690	1.40726
$861$	−1.52292	−0.0519010
$862$	1.45850	0.0496765
$863$	35.3044	1.20178	0.600888	−	0.799333i	$-0.294814\pi$
$863$	35.3044	1.20178	0.600888	+	0.799333i	$0.294814\pi$
$864$	4.51331	0.153546
$865$	−39.6680	−1.34875
$866$	1.86874	0.0635023
$867$	12.6765	0.430517
$868$	−0.827105	−0.0280738
$869$	14.8565	0.503971
$870$	4.17895	0.141680
$871$	−8.71604	−0.295332
$872$	28.3069	0.958593
$873$	13.9587	0.472429
$874$	22.7180	0.768448
$875$	−2.57276	−0.0869751
$876$	14.3336	0.484287
$877$	32.4427	1.09551	0.547757	−	0.836638i	$-0.315482\pi$
$877$	32.4427	1.09551	0.547757	+	0.836638i	$0.315482\pi$
$878$	15.2444	0.514475
$879$	−3.35466	−0.113150
$880$	25.3753	0.855401
$881$	−5.11150	−0.172211	−0.0861054	−	0.996286i	$-0.527442\pi$
$881$	−5.11150	−0.172211	−0.0861054	+	0.996286i	$0.527442\pi$
$882$	−0.426737	−0.0143690
$883$	15.9059	0.535277	0.267638	−	0.963519i	$-0.413757\pi$
$883$	15.9059	0.535277	0.267638	+	0.963519i	$0.413757\pi$
$884$	2.34449	0.0788537
$885$	−38.3521	−1.28919
$886$	14.1000	0.473700
$887$	12.3203	0.413674	0.206837	−	0.978375i	$-0.433683\pi$
$887$	12.3203	0.413674	0.206837	+	0.978375i	$0.433683\pi$
$888$	18.8690	0.633203
$889$	6.69394	0.224508
$890$	19.5142	0.654116
$891$	−2.62788	−0.0880372
$892$	−17.8499	−0.597659
$893$	−72.3306	−2.42045
$894$	−3.83787	−0.128358
$895$	36.0429	1.20478
$896$	10.7144	0.357943
$897$	−4.33289	−0.144671
$898$	−13.0196	−0.434469
$899$	−1.35681	−0.0452522
$900$	−10.5137	−0.350458
$901$	10.9412	0.364504
$902$	1.70782	0.0568643
$903$	−6.91315	−0.230055
$904$	−28.6584	−0.953165
$905$	19.1162	0.635444
$906$	−1.24698	−0.0414280
$907$	−14.2200	−0.472167	−0.236083	−	0.971733i	$-0.575864\pi$
$907$	−14.2200	−0.472167	−0.236083	+	0.971733i	$0.575864\pi$
$908$	−32.9599	−1.09381
$909$	3.16595	0.105008
$910$	0.869163	0.0288125
$911$	40.8990	1.35504	0.677522	−	0.735503i	$-0.263054\pi$
$911$	40.8990	1.35504	0.677522	+	0.735503i	$0.263054\pi$
$912$	22.4089	0.742034
$913$	−35.8708	−1.18715
$914$	9.05290	0.299443
$915$	39.2393	1.29721
$916$	−30.0455	−0.992731
$917$	6.48167	0.214044
$918$	−0.887314	−0.0292857
$919$	38.6145	1.27377	0.636887	−	0.770957i	$-0.280222\pi$
$919$	38.6145	1.27377	0.636887	+	0.770957i	$0.280222\pi$
$920$	−37.3748	−1.23221
$921$	−6.88211	−0.226773
$922$	−6.47163	−0.213132
$923$	8.29272	0.272958
$924$	−4.77721	−0.157159
$925$	−66.9813	−2.20233
$926$	−13.5671	−0.445842
$927$	−11.6184	−0.381598
$928$	13.4593	0.441824
$929$	−5.47883	−0.179754	−0.0898772	−	0.995953i	$-0.528647\pi$
$929$	−5.47883	−0.179754	−0.0898772	+	0.995953i	$0.528647\pi$
$930$	−0.637575	−0.0209069
$931$	−7.62070	−0.249758
$932$	28.4338	0.931381
$933$	−7.00933	−0.229475
$934$	2.25120	0.0736616
$935$	−17.9433	−0.586808
$936$	1.01052	0.0330300
$937$	−33.8209	−1.10488	−0.552441	−	0.833552i	$-0.686303\pi$
$937$	−33.8209	−1.10488	−0.552441	+	0.833552i	$0.686303\pi$
$938$	5.99677	0.195801
$939$	9.50269	0.310109
$940$	56.6599	1.84804
$941$	21.1606	0.689816	0.344908	−	0.938637i	$-0.387910\pi$
$941$	21.1606	0.689816	0.344908	+	0.938637i	$0.387910\pi$
$942$	7.18226	0.234011
$943$	10.6388	0.346447
$944$	−34.3429	−1.11777
$945$	3.28382	0.106823
$946$	7.75249	0.252055
$947$	18.4744	0.600337	0.300168	−	0.953886i	$-0.402957\pi$
$947$	18.4744	0.600337	0.300168	+	0.953886i	$0.402957\pi$
$948$	−10.2773	−0.333791
$949$	4.89044	0.158750
$950$	18.8080	0.610213
$951$	7.82025	0.253589
$952$	−3.38767	−0.109795
$953$	−8.52192	−0.276052	−0.138026	−	0.990429i	$-0.544076\pi$
$953$	−8.52192	−0.276052	−0.138026	+	0.990429i	$0.544076\pi$
$954$	2.24547	0.0726998
$955$	−34.2224	−1.10741
$956$	44.9902	1.45509
$957$	−7.83670	−0.253325
$958$	13.5681	0.438365
$959$	16.6599	0.537976
$960$	−12.9878	−0.419178
$961$	−30.7930	−0.993322
$962$	3.06540	0.0988325
$963$	15.6211	0.503384
$964$	48.1469	1.55071
$965$	−5.31259	−0.171018
$966$	2.98109	0.0959151
$967$	2.15984	0.0694557	0.0347278	−	0.999397i	$-0.488944\pi$
$967$	2.15984	0.0694557	0.0347278	+	0.999397i	$0.488944\pi$
$968$	−6.67051	−0.214398
$969$	−15.8457	−0.509038
$970$	19.5606	0.628054
$971$	−31.2026	−1.00134	−0.500670	−	0.865638i	$-0.666913\pi$
$971$	−31.2026	−1.00134	−0.500670	+	0.865638i	$0.666913\pi$
$972$	1.81790	0.0583090
$973$	−2.96473	−0.0950449
$974$	−0.237163	−0.00759919
$975$	−3.58716	−0.114881
$976$	35.1374	1.12472
$977$	−25.1859	−0.805768	−0.402884	−	0.915251i	$-0.631992\pi$
$977$	−25.1859	−0.805768	−0.402884	+	0.915251i	$0.631992\pi$
$978$	−9.60915	−0.307267
$979$	−36.5945	−1.16957
$980$	5.96964	0.190693
$981$	17.3743	0.554720
$982$	−6.18050	−0.197228
$983$	−41.0778	−1.31018	−0.655089	−	0.755552i	$-0.727369\pi$
$983$	−41.0778	−1.31018	−0.655089	+	0.755552i	$0.727369\pi$
$984$	−2.48120	−0.0790977
$985$	20.8713	0.665015
$986$	−2.64609	−0.0842688
$987$	−9.49134	−0.302113
$988$	8.59262	0.273368
$989$	48.2938	1.53565
$990$	−3.68252	−0.117038
$991$	−22.6102	−0.718235	−0.359118	−	0.933292i	$-0.616922\pi$
$991$	−22.6102	−0.718235	−0.359118	+	0.933292i	$0.616922\pi$
$992$	−2.05346	−0.0651975
$993$	−7.32951	−0.232595
$994$	−5.70551	−0.180968
$995$	34.3629	1.08938
$996$	24.8144	0.786275
$997$	39.2121	1.24186	0.620930	−	0.783866i	$-0.286755\pi$
$997$	39.2121	1.24186	0.620930	+	0.783866i	$0.286755\pi$
$998$	−7.99064	−0.252939
$999$	11.5815	0.366423

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.o.1.19	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.o.1.19	✓	41	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:	\( N \)	\(=\)	\( 8043 = 3 \cdot 7 \cdot 383 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8043.a (trivial)

\(f(q)\)	\(=\)	\(q-0.426737 q^{2} -1.00000 q^{3} -1.81790 q^{4} -3.28382 q^{5} +0.426737 q^{6} +1.00000 q^{7} +1.62924 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.426737 q^{2} -1.00000 q^{3} -1.81790 q^{4} -3.28382 q^{5} +0.426737 q^{6} +1.00000 q^{7} +1.62924 q^{8} +1.00000 q^{9} +1.40133 q^{10} -2.62788 q^{11} +1.81790 q^{12} +0.620243 q^{13} -0.426737 q^{14} +3.28382 q^{15} +2.94054 q^{16} -2.07930 q^{17} -0.426737 q^{18} -7.62070 q^{19} +5.96964 q^{20} -1.00000 q^{21} +1.12141 q^{22} +6.98579 q^{23} -1.62924 q^{24} +5.78347 q^{25} -0.264681 q^{26} -1.00000 q^{27} -1.81790 q^{28} -2.98214 q^{29} -1.40133 q^{30} +0.454979 q^{31} -4.51331 q^{32} +2.62788 q^{33} +0.887314 q^{34} -3.28382 q^{35} -1.81790 q^{36} -11.5815 q^{37} +3.25203 q^{38} -0.620243 q^{39} -5.35012 q^{40} +1.52292 q^{41} +0.426737 q^{42} +6.91315 q^{43} +4.77721 q^{44} -3.28382 q^{45} -2.98109 q^{46} +9.49134 q^{47} -2.94054 q^{48} +1.00000 q^{49} -2.46802 q^{50} +2.07930 q^{51} -1.12754 q^{52} -5.26196 q^{53} +0.426737 q^{54} +8.62948 q^{55} +1.62924 q^{56} +7.62070 q^{57} +1.27259 q^{58} -11.6791 q^{59} -5.96964 q^{60} +11.9493 q^{61} -0.194156 q^{62} +1.00000 q^{63} -3.95508 q^{64} -2.03677 q^{65} -1.12141 q^{66} -14.0526 q^{67} +3.77995 q^{68} -6.98579 q^{69} +1.40133 q^{70} +13.3701 q^{71} +1.62924 q^{72} +7.88472 q^{73} +4.94226 q^{74} -5.78347 q^{75} +13.8536 q^{76} -2.62788 q^{77} +0.264681 q^{78} -5.65341 q^{79} -9.65619 q^{80} +1.00000 q^{81} -0.649886 q^{82} +13.6501 q^{83} +1.81790 q^{84} +6.82804 q^{85} -2.95010 q^{86} +2.98214 q^{87} -4.28144 q^{88} +13.9255 q^{89} +1.40133 q^{90} +0.620243 q^{91} -12.6994 q^{92} -0.454979 q^{93} -4.05030 q^{94} +25.0250 q^{95} +4.51331 q^{96} +13.9587 q^{97} -0.426737 q^{98} -2.62788 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9	\( 41 q - 4 q^{2} - 41 q^{3} + 34 q^{4} + 5 q^{5} + 4 q^{6} + 41 q^{7} - 15 q^{8} + 41 q^{9} - 18 q^{10} - 17 q^{11} - 34 q^{12} - 38 q^{13} - 4 q^{14} - 5 q^{15} + 16 q^{16} + 4 q^{17} - 4 q^{18} - 15 q^{19} + 23 q^{20} - 41 q^{21} - 31 q^{22} - 8 q^{23} + 15 q^{24} + 16 q^{25} + 15 q^{26} - 41 q^{27} + 34 q^{28} - 27 q^{29} + 18 q^{30} - 23 q^{31} - 24 q^{32} + 17 q^{33} - 9 q^{34} + 5 q^{35} + 34 q^{36} - 81 q^{37} + 38 q^{39} - 52 q^{40} + 29 q^{41} + 4 q^{42} - 47 q^{43} - 20 q^{44} + 5 q^{45} - 40 q^{46} + 26 q^{47} - 16 q^{48} + 41 q^{49} - 23 q^{50} - 4 q^{51} - 64 q^{52} - 66 q^{53} + 4 q^{54} - 14 q^{55} - 15 q^{56} + 15 q^{57} - 50 q^{58} + 41 q^{59} - 23 q^{60} - 47 q^{61} + 5 q^{62} + 41 q^{63} - 37 q^{64} - 24 q^{65} + 31 q^{66} - 73 q^{67} + 10 q^{68} + 8 q^{69} - 18 q^{70} + q^{71} - 15 q^{72} - 14 q^{73} + 18 q^{74} - 16 q^{75} - 37 q^{76} - 17 q^{77} - 15 q^{78} - 80 q^{79} + 63 q^{80} + 41 q^{81} - 31 q^{82} + 20 q^{83} - 34 q^{84} - 82 q^{85} - 39 q^{86} + 27 q^{87} - 132 q^{88} + 17 q^{89} - 18 q^{90} - 38 q^{91} - 26 q^{92} + 23 q^{93} - 9 q^{94} - q^{95} + 24 q^{96} - 73 q^{97} - 4 q^{98} - 17 q^{99}+O(q^{100}) \) 41 * q - 4 * q^2 - 41 * q^3 + 34 * q^4 + 5 * q^5 + 4 * q^6 + 41 * q^7 - 15 * q^8 + 41 * q^9 - 18 * q^10 - 17 * q^11 - 34 * q^12 - 38 * q^13 - 4 * q^14 - 5 * q^15 + 16 * q^16 + 4 * q^17 - 4 * q^18 - 15 * q^19 + 23 * q^20 - 41 * q^21 - 31 * q^22 - 8 * q^23 + 15 * q^24 + 16 * q^25 + 15 * q^26 - 41 * q^27 + 34 * q^28 - 27 * q^29 + 18 * q^30 - 23 * q^31 - 24 * q^32 + 17 * q^33 - 9 * q^34 + 5 * q^35 + 34 * q^36 - 81 * q^37 + 38 * q^39 - 52 * q^40 + 29 * q^41 + 4 * q^42 - 47 * q^43 - 20 * q^44 + 5 * q^45 - 40 * q^46 + 26 * q^47 - 16 * q^48 + 41 * q^49 - 23 * q^50 - 4 * q^51 - 64 * q^52 - 66 * q^53 + 4 * q^54 - 14 * q^55 - 15 * q^56 + 15 * q^57 - 50 * q^58 + 41 * q^59 - 23 * q^60 - 47 * q^61 + 5 * q^62 + 41 * q^63 - 37 * q^64 - 24 * q^65 + 31 * q^66 - 73 * q^67 + 10 * q^68 + 8 * q^69 - 18 * q^70 + q^71 - 15 * q^72 - 14 * q^73 + 18 * q^74 - 16 * q^75 - 37 * q^76 - 17 * q^77 - 15 * q^78 - 80 * q^79 + 63 * q^80 + 41 * q^81 - 31 * q^82 + 20 * q^83 - 34 * q^84 - 82 * q^85 - 39 * q^86 + 27 * q^87 - 132 * q^88 + 17 * q^89 - 18 * q^90 - 38 * q^91 - 26 * q^92 + 23 * q^93 - 9 * q^94 - q^95 + 24 * q^96 - 73 * q^97 - 4 * q^98 - 17 * q^99

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