LMFDB - Embedded newform 8043.2.a.q.1.15

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:	$44$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q-1.26807 q^{2} +1.00000 q^{3} -0.392010 q^{4} -2.94433 q^{5} -1.26807 q^{6} -1.00000 q^{7} +3.03323 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.26807 q^{2} +1.00000 q^{3} -0.392010 q^{4} -2.94433 q^{5} -1.26807 q^{6} -1.00000 q^{7} +3.03323 q^{8} +1.00000 q^{9} +3.73361 q^{10} -5.27783 q^{11} -0.392010 q^{12} -6.60942 q^{13} +1.26807 q^{14} -2.94433 q^{15} -3.06231 q^{16} +6.62282 q^{17} -1.26807 q^{18} -5.21710 q^{19} +1.15421 q^{20} -1.00000 q^{21} +6.69264 q^{22} -2.02935 q^{23} +3.03323 q^{24} +3.66911 q^{25} +8.38118 q^{26} +1.00000 q^{27} +0.392010 q^{28} +3.94448 q^{29} +3.73361 q^{30} +9.87141 q^{31} -2.18324 q^{32} -5.27783 q^{33} -8.39816 q^{34} +2.94433 q^{35} -0.392010 q^{36} +4.16954 q^{37} +6.61562 q^{38} -6.60942 q^{39} -8.93083 q^{40} +11.2226 q^{41} +1.26807 q^{42} +3.77690 q^{43} +2.06896 q^{44} -2.94433 q^{45} +2.57335 q^{46} +3.09405 q^{47} -3.06231 q^{48} +1.00000 q^{49} -4.65267 q^{50} +6.62282 q^{51} +2.59096 q^{52} -8.64720 q^{53} -1.26807 q^{54} +15.5397 q^{55} -3.03323 q^{56} -5.21710 q^{57} -5.00186 q^{58} -5.24435 q^{59} +1.15421 q^{60} +12.3560 q^{61} -12.5176 q^{62} -1.00000 q^{63} +8.89311 q^{64} +19.4604 q^{65} +6.69264 q^{66} -5.71460 q^{67} -2.59621 q^{68} -2.02935 q^{69} -3.73361 q^{70} +2.74190 q^{71} +3.03323 q^{72} -7.01276 q^{73} -5.28725 q^{74} +3.66911 q^{75} +2.04515 q^{76} +5.27783 q^{77} +8.38118 q^{78} -0.607388 q^{79} +9.01646 q^{80} +1.00000 q^{81} -14.2310 q^{82} +12.0677 q^{83} +0.392010 q^{84} -19.4998 q^{85} -4.78935 q^{86} +3.94448 q^{87} -16.0089 q^{88} +0.507910 q^{89} +3.73361 q^{90} +6.60942 q^{91} +0.795527 q^{92} +9.87141 q^{93} -3.92346 q^{94} +15.3609 q^{95} -2.18324 q^{96} +18.4810 q^{97} -1.26807 q^{98} -5.27783 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) $ 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−1.26807	−0.896658	−0.448329	−	0.893869i	$-0.647981\pi$
$2$	−1.26807	−0.896658	−0.448329	+	0.893869i	$0.647981\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.392010	−0.196005
$5$	−2.94433	−1.31675	−0.658373	−	0.752692i	$-0.728755\pi$
$5$	−2.94433	−1.31675	−0.658373	+	0.752692i	$0.728755\pi$
$6$	−1.26807	−0.517686
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.03323	1.07241
$9$	1.00000	0.333333
$10$	3.73361	1.18067
$11$	−5.27783	−1.59133	−0.795663	−	0.605740i	$-0.792877\pi$
$11$	−5.27783	−1.59133	−0.795663	+	0.605740i	$0.792877\pi$
$12$	−0.392010	−0.113164
$13$	−6.60942	−1.83312	−0.916562	−	0.399892i	$-0.869048\pi$
$13$	−6.60942	−1.83312	−0.916562	+	0.399892i	$0.869048\pi$
$14$	1.26807	0.338905
$15$	−2.94433	−0.760224
$16$	−3.06231	−0.765577
$17$	6.62282	1.60627	0.803134	−	0.595798i	$-0.203164\pi$
$17$	6.62282	1.60627	0.803134	+	0.595798i	$0.203164\pi$
$18$	−1.26807	−0.298886
$19$	−5.21710	−1.19688	−0.598442	−	0.801166i	$-0.704213\pi$
$19$	−5.21710	−1.19688	−0.598442	+	0.801166i	$0.704213\pi$
$20$	1.15421	0.258089
$21$	−1.00000	−0.218218
$22$	6.69264	1.42687
$23$	−2.02935	−0.423149	−0.211575	−	0.977362i	$-0.567859\pi$
$23$	−2.02935	−0.423149	−0.211575	+	0.977362i	$0.567859\pi$
$24$	3.03323	0.619155
$25$	3.66911	0.733822
$26$	8.38118	1.64369
$27$	1.00000	0.192450
$28$	0.392010	0.0740829
$29$	3.94448	0.732471	0.366236	−	0.930522i	$-0.380646\pi$
$29$	3.94448	0.732471	0.366236	+	0.930522i	$0.380646\pi$
$30$	3.73361	0.681661
$31$	9.87141	1.77296	0.886479	−	0.462769i	$-0.153144\pi$
$31$	9.87141	1.77296	0.886479	+	0.462769i	$0.153144\pi$
$32$	−2.18324	−0.385947
$33$	−5.27783	−0.918752
$34$	−8.39816	−1.44027
$35$	2.94433	0.497683
$36$	−0.392010	−0.0653350
$37$	4.16954	0.685469	0.342734	−	0.939432i	$-0.388647\pi$
$37$	4.16954	0.685469	0.342734	+	0.939432i	$0.388647\pi$
$38$	6.61562	1.07320
$39$	−6.60942	−1.05835
$40$	−8.93083	−1.41209
$41$	11.2226	1.75268	0.876338	−	0.481697i	$-0.159980\pi$
$41$	11.2226	1.75268	0.876338	+	0.481697i	$0.159980\pi$
$42$	1.26807	0.195667
$43$	3.77690	0.575971	0.287986	−	0.957635i	$-0.407014\pi$
$43$	3.77690	0.575971	0.287986	+	0.957635i	$0.407014\pi$
$44$	2.06896	0.311908
$45$	−2.94433	−0.438916
$46$	2.57335	0.379420
$47$	3.09405	0.451314	0.225657	−	0.974207i	$-0.427547\pi$
$47$	3.09405	0.451314	0.225657	+	0.974207i	$0.427547\pi$
$48$	−3.06231	−0.442006
$49$	1.00000	0.142857
$50$	−4.65267	−0.657987
$51$	6.62282	0.927380
$52$	2.59096	0.359302
$53$	−8.64720	−1.18778	−0.593892	−	0.804545i	$-0.702409\pi$
$53$	−8.64720	−1.18778	−0.593892	+	0.804545i	$0.702409\pi$
$54$	−1.26807	−0.172562
$55$	15.5397	2.09537
$56$	−3.03323	−0.405332
$57$	−5.21710	−0.691022
$58$	−5.00186	−0.656776
$59$	−5.24435	−0.682756	−0.341378	−	0.939926i	$-0.610894\pi$
$59$	−5.24435	−0.682756	−0.341378	+	0.939926i	$0.610894\pi$
$60$	1.15421	0.149008
$61$	12.3560	1.58202	0.791010	−	0.611803i	$-0.209555\pi$
$61$	12.3560	1.58202	0.791010	+	0.611803i	$0.209555\pi$
$62$	−12.5176	−1.58974
$63$	−1.00000	−0.125988
$64$	8.89311	1.11164
$65$	19.4604	2.41376
$66$	6.69264	0.823806
$67$	−5.71460	−0.698150	−0.349075	−	0.937095i	$-0.613504\pi$
$67$	−5.71460	−0.698150	−0.349075	+	0.937095i	$0.613504\pi$
$68$	−2.59621	−0.314837
$69$	−2.02935	−0.244305
$70$	−3.73361	−0.446252
$71$	2.74190	0.325403	0.162702	−	0.986675i	$-0.447979\pi$
$71$	2.74190	0.325403	0.162702	+	0.986675i	$0.447979\pi$
$72$	3.03323	0.357469
$73$	−7.01276	−0.820782	−0.410391	−	0.911910i	$-0.634608\pi$
$73$	−7.01276	−0.820782	−0.410391	+	0.911910i	$0.634608\pi$
$74$	−5.28725	−0.614631
$75$	3.66911	0.423672
$76$	2.04515	0.234595
$77$	5.27783	0.601465
$78$	8.38118	0.948982
$79$	−0.607388	−0.0683365	−0.0341682	−	0.999416i	$-0.510878\pi$
$79$	−0.607388	−0.0683365	−0.0341682	+	0.999416i	$0.510878\pi$
$80$	9.01646	1.00807
$81$	1.00000	0.111111
$82$	−14.2310	−1.57155
$83$	12.0677	1.32460	0.662299	−	0.749240i	$-0.269581\pi$
$83$	12.0677	1.32460	0.662299	+	0.749240i	$0.269581\pi$
$84$	0.392010	0.0427718
$85$	−19.4998	−2.11505
$86$	−4.78935	−0.516449
$87$	3.94448	0.422892
$88$	−16.0089	−1.70655
$89$	0.507910	0.0538384	0.0269192	−	0.999638i	$-0.491430\pi$
$89$	0.507910	0.0538384	0.0269192	+	0.999638i	$0.491430\pi$
$90$	3.73361	0.393557
$91$	6.60942	0.692856
$92$	0.795527	0.0829394
$93$	9.87141	1.02362
$94$	−3.92346	−0.404674
$95$	15.3609	1.57599
$96$	−2.18324	−0.222826
$97$	18.4810	1.87646	0.938228	−	0.346017i	$-0.112466\pi$
$97$	18.4810	1.87646	0.938228	+	0.346017i	$0.112466\pi$
$98$	−1.26807	−0.128094
$99$	−5.27783	−0.530442
$100$	−1.43833	−0.143833
$101$	3.07197	0.305672	0.152836	−	0.988252i	$-0.451159\pi$
$101$	3.07197	0.305672	0.152836	+	0.988252i	$0.451159\pi$
$102$	−8.39816	−0.831542
$103$	−4.32253	−0.425911	−0.212956	−	0.977062i	$-0.568309\pi$
$103$	−4.32253	−0.425911	−0.212956	+	0.977062i	$0.568309\pi$
$104$	−20.0479	−1.96586
$105$	2.94433	0.287338
$106$	10.9652	1.06504
$107$	−12.0967	−1.16943	−0.584717	−	0.811237i	$-0.698794\pi$
$107$	−12.0967	−1.16943	−0.584717	+	0.811237i	$0.698794\pi$
$108$	−0.392010	−0.0377212
$109$	−4.00392	−0.383506	−0.191753	−	0.981443i	$-0.561417\pi$
$109$	−4.00392	−0.383506	−0.191753	+	0.981443i	$0.561417\pi$
$110$	−19.7054	−1.87883
$111$	4.16954	0.395755
$112$	3.06231	0.289361
$113$	−11.4157	−1.07389	−0.536947	−	0.843616i	$-0.680423\pi$
$113$	−11.4157	−1.07389	−0.536947	+	0.843616i	$0.680423\pi$
$114$	6.61562	0.619610
$115$	5.97509	0.557180
$116$	−1.54627	−0.143568
$117$	−6.60942	−0.611042
$118$	6.65018	0.612199
$119$	−6.62282	−0.607113
$120$	−8.93083	−0.815270
$121$	16.8555	1.53232
$122$	−15.6682	−1.41853
$123$	11.2226	1.01191
$124$	−3.86969	−0.347509
$125$	3.91859	0.350490
$126$	1.26807	0.112968
$127$	9.28734	0.824118	0.412059	−	0.911157i	$-0.364810\pi$
$127$	9.28734	0.824118	0.412059	+	0.911157i	$0.364810\pi$
$128$	−6.91056	−0.610813
$129$	3.77690	0.332537
$130$	−24.6770	−2.16432
$131$	−3.62724	−0.316913	−0.158457	−	0.987366i	$-0.550652\pi$
$131$	−3.62724	−0.316913	−0.158457	+	0.987366i	$0.550652\pi$
$132$	2.06896	0.180080
$133$	5.21710	0.452380
$134$	7.24649	0.626001
$135$	−2.94433	−0.253408
$136$	20.0885	1.72257
$137$	−20.7107	−1.76943	−0.884716	−	0.466131i	$-0.845647\pi$
$137$	−20.7107	−1.76943	−0.884716	+	0.466131i	$0.845647\pi$
$138$	2.57335	0.219058
$139$	−13.6450	−1.15736	−0.578678	−	0.815556i	$-0.696431\pi$
$139$	−13.6450	−1.15736	−0.578678	+	0.815556i	$0.696431\pi$
$140$	−1.15421	−0.0975484
$141$	3.09405	0.260566
$142$	−3.47691	−0.291775
$143$	34.8834	2.91710
$144$	−3.06231	−0.255192
$145$	−11.6139	−0.964479
$146$	8.89264	0.735960
$147$	1.00000	0.0824786
$148$	−1.63450	−0.134355
$149$	−13.0709	−1.07081	−0.535407	−	0.844594i	$-0.679842\pi$
$149$	−13.0709	−1.07081	−0.535407	+	0.844594i	$0.679842\pi$
$150$	−4.65267	−0.379889
$151$	−0.232821	−0.0189467	−0.00947336	−	0.999955i	$-0.503016\pi$
$151$	−0.232821	−0.0189467	−0.00947336	+	0.999955i	$0.503016\pi$
$152$	−15.8246	−1.28355
$153$	6.62282	0.535423
$154$	−6.69264	−0.539308
$155$	−29.0647	−2.33454
$156$	2.59096	0.207443
$157$	−24.6621	−1.96825	−0.984125	−	0.177479i	$-0.943206\pi$
$157$	−24.6621	−1.96825	−0.984125	+	0.177479i	$0.943206\pi$
$158$	0.770208	0.0612744
$159$	−8.64720	−0.685767
$160$	6.42820	0.508194
$161$	2.02935	0.159935
$162$	−1.26807	−0.0996286
$163$	0.180972	0.0141748	0.00708741	−	0.999975i	$-0.497744\pi$
$163$	0.180972	0.0141748	0.00708741	+	0.999975i	$0.497744\pi$
$164$	−4.39937	−0.343533
$165$	15.5397	1.20976
$166$	−15.3026	−1.18771
$167$	−7.92059	−0.612914	−0.306457	−	0.951885i	$-0.599143\pi$
$167$	−7.92059	−0.612914	−0.306457	+	0.951885i	$0.599143\pi$
$168$	−3.03323	−0.234018
$169$	30.6845	2.36035
$170$	24.7270	1.89648
$171$	−5.21710	−0.398962
$172$	−1.48058	−0.112893
$173$	−21.9399	−1.66806	−0.834031	−	0.551718i	$-0.813972\pi$
$173$	−21.9399	−1.66806	−0.834031	+	0.551718i	$0.813972\pi$
$174$	−5.00186	−0.379190
$175$	−3.66911	−0.277358
$176$	16.1623	1.21828
$177$	−5.24435	−0.394190
$178$	−0.644063	−0.0482746
$179$	18.1544	1.35692	0.678460	−	0.734637i	$-0.262648\pi$
$179$	18.1544	1.35692	0.678460	+	0.734637i	$0.262648\pi$
$180$	1.15421	0.0860296
$181$	−5.59343	−0.415756	−0.207878	−	0.978155i	$-0.566656\pi$
$181$	−5.59343	−0.415756	−0.207878	+	0.978155i	$0.566656\pi$
$182$	−8.38118	−0.621255
$183$	12.3560	0.913380
$184$	−6.15548	−0.453788
$185$	−12.2765	−0.902588
$186$	−12.5176	−0.917835
$187$	−34.9541	−2.55610
$188$	−1.21290	−0.0884597
$189$	−1.00000	−0.0727393
$190$	−19.4786	−1.41313
$191$	−9.10581	−0.658874	−0.329437	−	0.944178i	$-0.606859\pi$
$191$	−9.10581	−0.658874	−0.329437	+	0.944178i	$0.606859\pi$
$192$	8.89311	0.641805
$193$	26.5970	1.91449	0.957246	−	0.289275i	$-0.0934142\pi$
$193$	26.5970	1.91449	0.957246	+	0.289275i	$0.0934142\pi$
$194$	−23.4351	−1.68254
$195$	19.4604	1.39359
$196$	−0.392010	−0.0280007
$197$	−2.55554	−0.182075	−0.0910374	−	0.995847i	$-0.529018\pi$
$197$	−2.55554	−0.182075	−0.0910374	+	0.995847i	$0.529018\pi$
$198$	6.69264	0.475625
$199$	6.28642	0.445633	0.222816	−	0.974860i	$-0.428475\pi$
$199$	6.28642	0.445633	0.222816	+	0.974860i	$0.428475\pi$
$200$	11.1292	0.786955
$201$	−5.71460	−0.403077
$202$	−3.89546	−0.274084
$203$	−3.94448	−0.276848
$204$	−2.59621	−0.181771
$205$	−33.0431	−2.30783
$206$	5.48124	0.381896
$207$	−2.02935	−0.141050
$208$	20.2401	1.40340
$209$	27.5350	1.90463
$210$	−3.73361	−0.257644
$211$	19.3529	1.33231	0.666153	−	0.745815i	$-0.267940\pi$
$211$	19.3529	1.33231	0.666153	+	0.745815i	$0.267940\pi$
$212$	3.38979	0.232812
$213$	2.74190	0.187872
$214$	15.3394	1.04858
$215$	−11.1204	−0.758408
$216$	3.03323	0.206385
$217$	−9.87141	−0.670115
$218$	5.07723	0.343874
$219$	−7.01276	−0.473879
$220$	−6.09172	−0.410704
$221$	−43.7730	−2.94449
$222$	−5.28725	−0.354857
$223$	23.9632	1.60470	0.802348	−	0.596857i	$-0.203584\pi$
$223$	23.9632	1.60470	0.802348	+	0.596857i	$0.203584\pi$
$224$	2.18324	0.145874
$225$	3.66911	0.244607
$226$	14.4758	0.962916
$227$	20.9741	1.39210	0.696050	−	0.717994i	$-0.254939\pi$
$227$	20.9741	1.39210	0.696050	+	0.717994i	$0.254939\pi$
$228$	2.04515	0.135444
$229$	1.94905	0.128797	0.0643983	−	0.997924i	$-0.479487\pi$
$229$	1.94905	0.128797	0.0643983	+	0.997924i	$0.479487\pi$
$230$	−7.57681	−0.499600
$231$	5.27783	0.347256
$232$	11.9645	0.785507
$233$	−28.3681	−1.85846	−0.929228	−	0.369507i	$-0.879527\pi$
$233$	−28.3681	−1.85846	−0.929228	+	0.369507i	$0.879527\pi$
$234$	8.38118	0.547895
$235$	−9.10992	−0.594266
$236$	2.05584	0.133824
$237$	−0.607388	−0.0394541
$238$	8.39816	0.544372
$239$	−3.88425	−0.251251	−0.125626	−	0.992078i	$-0.540094\pi$
$239$	−3.88425	−0.251251	−0.125626	+	0.992078i	$0.540094\pi$
$240$	9.01646	0.582010
$241$	23.6243	1.52178	0.760888	−	0.648883i	$-0.224763\pi$
$241$	23.6243	1.52178	0.760888	+	0.648883i	$0.224763\pi$
$242$	−21.3739	−1.37396
$243$	1.00000	0.0641500
$244$	−4.84367	−0.310084
$245$	−2.94433	−0.188107
$246$	−14.2310	−0.907335
$247$	34.4820	2.19404
$248$	29.9422	1.90133
$249$	12.0677	0.764757
$250$	−4.96903	−0.314269
$251$	−13.6779	−0.863340	−0.431670	−	0.902032i	$-0.642075\pi$
$251$	−13.6779	−0.863340	−0.431670	+	0.902032i	$0.642075\pi$
$252$	0.392010	0.0246943
$253$	10.7106	0.673368
$254$	−11.7770	−0.738952
$255$	−19.4998	−1.22112
$256$	−9.02318	−0.563949
$257$	27.2291	1.69851	0.849254	−	0.527985i	$-0.177052\pi$
$257$	27.2291	1.69851	0.849254	+	0.527985i	$0.177052\pi$
$258$	−4.78935	−0.298172
$259$	−4.16954	−0.259083
$260$	−7.62866	−0.473109
$261$	3.94448	0.244157
$262$	4.59957	0.284163
$263$	8.55847	0.527738	0.263869	−	0.964559i	$-0.415001\pi$
$263$	8.55847	0.527738	0.263869	+	0.964559i	$0.415001\pi$
$264$	−16.0089	−0.985277
$265$	25.4602	1.56401
$266$	−6.61562	−0.405630
$267$	0.507910	0.0310836
$268$	2.24018	0.136841
$269$	−21.8739	−1.33368	−0.666838	−	0.745203i	$-0.732353\pi$
$269$	−21.8739	−1.33368	−0.666838	+	0.745203i	$0.732353\pi$
$270$	3.73361	0.227220
$271$	2.36328	0.143559	0.0717795	−	0.997421i	$-0.477132\pi$
$271$	2.36328	0.143559	0.0717795	+	0.997421i	$0.477132\pi$
$272$	−20.2811	−1.22972
$273$	6.60942	0.400021
$274$	26.2625	1.58657
$275$	−19.3649	−1.16775
$276$	0.795527	0.0478851
$277$	−21.0994	−1.26774	−0.633870	−	0.773440i	$-0.718535\pi$
$277$	−21.0994	−1.26774	−0.633870	+	0.773440i	$0.718535\pi$
$278$	17.3028	1.03775
$279$	9.87141	0.590986
$280$	8.93083	0.533719
$281$	−18.0818	−1.07867	−0.539336	−	0.842091i	$-0.681325\pi$
$281$	−18.0818	−1.07867	−0.539336	+	0.842091i	$0.681325\pi$
$282$	−3.92346	−0.233639
$283$	−11.6503	−0.692540	−0.346270	−	0.938135i	$-0.612552\pi$
$283$	−11.6503	−0.692540	−0.346270	+	0.938135i	$0.612552\pi$
$284$	−1.07485	−0.0637807
$285$	15.3609	0.909900
$286$	−44.2345	−2.61564
$287$	−11.2226	−0.662449
$288$	−2.18324	−0.128649
$289$	26.8617	1.58010
$290$	14.7271	0.864807
$291$	18.4810	1.08337
$292$	2.74907	0.160877
$293$	−5.33744	−0.311816	−0.155908	−	0.987772i	$-0.549830\pi$
$293$	−5.33744	−0.311816	−0.155908	+	0.987772i	$0.549830\pi$
$294$	−1.26807	−0.0739551
$295$	15.4411	0.899017
$296$	12.6472	0.735101
$297$	−5.27783	−0.306251
$298$	16.5748	0.960153
$299$	13.4129	0.775685
$300$	−1.43833	−0.0830418
$301$	−3.77690	−0.217697
$302$	0.295233	0.0169887
$303$	3.07197	0.176480
$304$	15.9764	0.916307
$305$	−36.3801	−2.08312
$306$	−8.39816	−0.480091
$307$	−3.32076	−0.189526	−0.0947628	−	0.995500i	$-0.530209\pi$
$307$	−3.32076	−0.189526	−0.0947628	+	0.995500i	$0.530209\pi$
$308$	−2.06896	−0.117890
$309$	−4.32253	−0.245900
$310$	36.8560	2.09328
$311$	0.848670	0.0481237	0.0240618	−	0.999710i	$-0.492340\pi$
$311$	0.848670	0.0481237	0.0240618	+	0.999710i	$0.492340\pi$
$312$	−20.0479	−1.13499
$313$	21.8004	1.23223	0.616115	−	0.787656i	$-0.288706\pi$
$313$	21.8004	1.23223	0.616115	+	0.787656i	$0.288706\pi$
$314$	31.2731	1.76485
$315$	2.94433	0.165894
$316$	0.238102	0.0133943
$317$	16.8951	0.948921	0.474461	−	0.880277i	$-0.342643\pi$
$317$	16.8951	0.948921	0.474461	+	0.880277i	$0.342643\pi$
$318$	10.9652	0.614899
$319$	−20.8183	−1.16560
$320$	−26.1843	−1.46375
$321$	−12.0967	−0.675173
$322$	−2.57335	−0.143407
$323$	−34.5519	−1.92252
$324$	−0.392010	−0.0217783
$325$	−24.2507	−1.34519
$326$	−0.229484	−0.0127100
$327$	−4.00392	−0.221417
$328$	34.0407	1.87958
$329$	−3.09405	−0.170581
$330$	−19.7054	−1.08474
$331$	25.3693	1.39442	0.697210	−	0.716867i	$-0.254424\pi$
$331$	25.3693	1.39442	0.697210	+	0.716867i	$0.254424\pi$
$332$	−4.73064	−0.259628
$333$	4.16954	0.228490
$334$	10.0438	0.549574
$335$	16.8257	0.919286
$336$	3.06231	0.167063
$337$	−14.7360	−0.802720	−0.401360	−	0.915920i	$-0.631462\pi$
$337$	−14.7360	−0.802720	−0.401360	+	0.915920i	$0.631462\pi$
$338$	−38.9100	−2.11642
$339$	−11.4157	−0.620013
$340$	7.64411	0.414560
$341$	−52.0996	−2.82135
$342$	6.61562	0.357732
$343$	−1.00000	−0.0539949
$344$	11.4562	0.617676
$345$	5.97509	0.321688
$346$	27.8213	1.49568
$347$	27.6287	1.48319	0.741593	−	0.670850i	$-0.234070\pi$
$347$	27.6287	1.48319	0.741593	+	0.670850i	$0.234070\pi$
$348$	−1.54627	−0.0828890
$349$	−4.42101	−0.236651	−0.118326	−	0.992975i	$-0.537753\pi$
$349$	−4.42101	−0.236651	−0.118326	+	0.992975i	$0.537753\pi$
$350$	4.65267	0.248696
$351$	−6.60942	−0.352785
$352$	11.5228	0.614167
$353$	−2.78492	−0.148227	−0.0741133	−	0.997250i	$-0.523613\pi$
$353$	−2.78492	−0.148227	−0.0741133	+	0.997250i	$0.523613\pi$
$354$	6.65018	0.353453
$355$	−8.07306	−0.428474
$356$	−0.199106	−0.0105526
$357$	−6.62282	−0.350517
$358$	−23.0209	−1.21669
$359$	−9.46299	−0.499438	−0.249719	−	0.968318i	$-0.580338\pi$
$359$	−9.46299	−0.499438	−0.249719	+	0.968318i	$0.580338\pi$
$360$	−8.93083	−0.470696
$361$	8.21812	0.432533
$362$	7.09283	0.372791
$363$	16.8555	0.884684
$364$	−2.59096	−0.135803
$365$	20.6479	1.08076
$366$	−15.6682	−0.818989
$367$	−31.1089	−1.62387	−0.811936	−	0.583747i	$-0.801586\pi$
$367$	−31.1089	−1.62387	−0.811936	+	0.583747i	$0.801586\pi$
$368$	6.21450	0.323953
$369$	11.2226	0.584225
$370$	15.5674	0.809313
$371$	8.64720	0.448940
$372$	−3.86969	−0.200634
$373$	−16.4035	−0.849339	−0.424670	−	0.905348i	$-0.639610\pi$
$373$	−16.4035	−0.849339	−0.424670	+	0.905348i	$0.639610\pi$
$374$	44.3241	2.29194
$375$	3.91859	0.202355
$376$	9.38495	0.483992
$377$	−26.0707	−1.34271
$378$	1.26807	0.0652222
$379$	27.9607	1.43624	0.718121	−	0.695918i	$-0.245002\pi$
$379$	27.9607	1.43624	0.718121	+	0.695918i	$0.245002\pi$
$380$	−6.02162	−0.308903
$381$	9.28734	0.475805
$382$	11.5468	0.590784
$383$	1.00000	0.0510976
$383$	1.00000	0.0510976
$384$	−6.91056	−0.352653
$385$	−15.5397	−0.791977
$386$	−33.7267	−1.71664
$387$	3.77690	0.191990
$388$	−7.24472	−0.367795
$389$	4.22787	0.214361	0.107181	−	0.994240i	$-0.465818\pi$
$389$	4.22787	0.214361	0.107181	+	0.994240i	$0.465818\pi$
$390$	−24.6770	−1.24957
$391$	−13.4400	−0.679692
$392$	3.03323	0.153201
$393$	−3.62724	−0.182970
$394$	3.24059	0.163259
$395$	1.78835	0.0899818
$396$	2.06896	0.103969
$397$	3.73228	0.187318	0.0936589	−	0.995604i	$-0.470144\pi$
$397$	3.73228	0.187318	0.0936589	+	0.995604i	$0.470144\pi$
$398$	−7.97159	−0.399580
$399$	5.21710	0.261182
$400$	−11.2359	−0.561797
$401$	−33.4882	−1.67232	−0.836159	−	0.548486i	$-0.815204\pi$
$401$	−33.4882	−1.67232	−0.836159	+	0.548486i	$0.815204\pi$
$402$	7.24649	0.361422
$403$	−65.2443	−3.25005
$404$	−1.20424	−0.0599133
$405$	−2.94433	−0.146305
$406$	5.00186	0.248238
$407$	−22.0061	−1.09080
$408$	20.0885	0.994529
$409$	−16.5444	−0.818069	−0.409035	−	0.912519i	$-0.634134\pi$
$409$	−16.5444	−0.818069	−0.409035	+	0.912519i	$0.634134\pi$
$410$	41.9008	2.06933
$411$	−20.7107	−1.02158
$412$	1.69447	0.0834807
$413$	5.24435	0.258058
$414$	2.57335	0.126473
$415$	−35.5312	−1.74416
$416$	14.4300	0.707488
$417$	−13.6450	−0.668200
$418$	−34.9161	−1.70780
$419$	−15.6052	−0.762364	−0.381182	−	0.924500i	$-0.624483\pi$
$419$	−15.6052	−0.762364	−0.381182	+	0.924500i	$0.624483\pi$
$420$	−1.15421	−0.0563196
$421$	9.33968	0.455188	0.227594	−	0.973756i	$-0.426914\pi$
$421$	9.33968	0.455188	0.227594	+	0.973756i	$0.426914\pi$
$422$	−24.5407	−1.19462
$423$	3.09405	0.150438
$424$	−26.2289	−1.27379
$425$	24.2998	1.17871
$426$	−3.47691	−0.168457
$427$	−12.3560	−0.597948
$428$	4.74204	0.229215
$429$	34.8834	1.68419
$430$	14.1015	0.680032
$431$	38.5102	1.85497	0.927485	−	0.373861i	$-0.121966\pi$
$431$	38.5102	1.85497	0.927485	+	0.373861i	$0.121966\pi$
$432$	−3.06231	−0.147335
$433$	−27.6179	−1.32723	−0.663616	−	0.748074i	$-0.730979\pi$
$433$	−27.6179	−1.32723	−0.663616	+	0.748074i	$0.730979\pi$
$434$	12.5176	0.600864
$435$	−11.6139	−0.556842
$436$	1.56958	0.0751691
$437$	10.5873	0.506461
$438$	8.89264	0.424907
$439$	−18.3694	−0.876722	−0.438361	−	0.898799i	$-0.644441\pi$
$439$	−18.3694	−0.876722	−0.438361	+	0.898799i	$0.644441\pi$
$440$	47.1354	2.24709
$441$	1.00000	0.0476190
$442$	55.5070	2.64020
$443$	25.2185	1.19817	0.599083	−	0.800687i	$-0.295532\pi$
$443$	25.2185	1.19817	0.599083	+	0.800687i	$0.295532\pi$
$444$	−1.63450	−0.0775700
$445$	−1.49546	−0.0708915
$446$	−30.3869	−1.43886
$447$	−13.0709	−0.618234
$448$	−8.89311	−0.420160
$449$	0.474947	0.0224141	0.0112071	−	0.999937i	$-0.496433\pi$
$449$	0.474947	0.0224141	0.0112071	+	0.999937i	$0.496433\pi$
$450$	−4.65267	−0.219329
$451$	−59.2310	−2.78908
$452$	4.47505	0.210489
$453$	−0.232821	−0.0109389
$454$	−26.5965	−1.24824
$455$	−19.4604	−0.912316
$456$	−15.8246	−0.741056
$457$	−12.5328	−0.586262	−0.293131	−	0.956072i	$-0.594697\pi$
$457$	−12.5328	−0.586262	−0.293131	+	0.956072i	$0.594697\pi$
$458$	−2.47152	−0.115487
$459$	6.62282	0.309127
$460$	−2.34230	−0.109210
$461$	−12.0866	−0.562929	−0.281465	−	0.959572i	$-0.590820\pi$
$461$	−12.0866	−0.562929	−0.281465	+	0.959572i	$0.590820\pi$
$462$	−6.69264	−0.311370
$463$	24.0566	1.11801	0.559003	−	0.829166i	$-0.311184\pi$
$463$	24.0566	1.11801	0.559003	+	0.829166i	$0.311184\pi$
$464$	−12.0792	−0.560763
$465$	−29.0647	−1.34784
$466$	35.9726	1.66640
$467$	−8.76631	−0.405657	−0.202828	−	0.979214i	$-0.565013\pi$
$467$	−8.76631	−0.405657	−0.202828	+	0.979214i	$0.565013\pi$
$468$	2.59096	0.119767
$469$	5.71460	0.263876
$470$	11.5520	0.532853
$471$	−24.6621	−1.13637
$472$	−15.9073	−0.732193
$473$	−19.9338	−0.916558
$474$	0.770208	0.0353768
$475$	−19.1421	−0.878300
$476$	2.59621	0.118997
$477$	−8.64720	−0.395928
$478$	4.92549	0.225286
$479$	−14.7015	−0.671729	−0.335864	−	0.941910i	$-0.609028\pi$
$479$	−14.7015	−0.671729	−0.335864	+	0.941910i	$0.609028\pi$
$480$	6.42820	0.293406
$481$	−27.5583	−1.25655
$482$	−29.9572	−1.36451
$483$	2.02935	0.0923387
$484$	−6.60752	−0.300342
$485$	−54.4141	−2.47082
$486$	−1.26807	−0.0575206
$487$	37.5735	1.70262	0.851309	−	0.524665i	$-0.175810\pi$
$487$	37.5735	1.70262	0.851309	+	0.524665i	$0.175810\pi$
$488$	37.4785	1.69657
$489$	0.180972	0.00818383
$490$	3.73361	0.168667
$491$	−1.42670	−0.0643859	−0.0321929	−	0.999482i	$-0.510249\pi$
$491$	−1.42670	−0.0643859	−0.0321929	+	0.999482i	$0.510249\pi$
$492$	−4.39937	−0.198339
$493$	26.1236	1.17655
$494$	−43.7255	−1.96730
$495$	15.5397	0.698458
$496$	−30.2293	−1.35734
$497$	−2.74190	−0.122991
$498$	−15.3026	−0.685725
$499$	−32.4257	−1.45157	−0.725786	−	0.687920i	$-0.758524\pi$
$499$	−32.4257	−1.45157	−0.725786	+	0.687920i	$0.758524\pi$
$500$	−1.53613	−0.0686977
$501$	−7.92059	−0.353866
$502$	17.3444	0.774120
$503$	−41.2168	−1.83776	−0.918882	−	0.394532i	$-0.870907\pi$
$503$	−41.2168	−1.83776	−0.918882	+	0.394532i	$0.870907\pi$
$504$	−3.03323	−0.135111
$505$	−9.04491	−0.402493
$506$	−13.5817	−0.603781
$507$	30.6845	1.36275
$508$	−3.64073	−0.161531
$509$	12.1301	0.537659	0.268830	−	0.963188i	$-0.413363\pi$
$509$	12.1301	0.537659	0.268830	+	0.963188i	$0.413363\pi$
$510$	24.7270	1.09493
$511$	7.01276	0.310226
$512$	25.2631	1.11648
$513$	−5.21710	−0.230341
$514$	−34.5283	−1.52298
$515$	12.7270	0.560817
$516$	−1.48058	−0.0651789
$517$	−16.3299	−0.718187
$518$	5.28725	0.232309
$519$	−21.9399	−0.963056
$520$	59.0277	2.58853
$521$	−27.2802	−1.19517	−0.597584	−	0.801806i	$-0.703873\pi$
$521$	−27.2802	−1.19517	−0.597584	+	0.801806i	$0.703873\pi$
$522$	−5.00186	−0.218925
$523$	5.36947	0.234791	0.117395	−	0.993085i	$-0.462546\pi$
$523$	5.36947	0.234791	0.117395	+	0.993085i	$0.462546\pi$
$524$	1.42191	0.0621166
$525$	−3.66911	−0.160133
$526$	−10.8527	−0.473200
$527$	65.3765	2.84785
$528$	16.1623	0.703376
$529$	−18.8817	−0.820945
$530$	−32.2853	−1.40238
$531$	−5.24435	−0.227585
$532$	−2.04515	−0.0886687
$533$	−74.1749	−3.21287
$534$	−0.644063	−0.0278713
$535$	35.6168	1.53985
$536$	−17.3337	−0.748701
$537$	18.1544	0.783418
$538$	27.7376	1.19585
$539$	−5.27783	−0.227332
$540$	1.15421	0.0496692
$541$	23.6556	1.01703	0.508516	−	0.861053i	$-0.330194\pi$
$541$	23.6556	1.01703	0.508516	+	0.861053i	$0.330194\pi$
$542$	−2.99679	−0.128723
$543$	−5.59343	−0.240037
$544$	−14.4592	−0.619934
$545$	11.7889	0.504980
$546$	−8.38118	−0.358682
$547$	42.6503	1.82359	0.911797	−	0.410641i	$-0.134695\pi$
$547$	42.6503	1.82359	0.911797	+	0.410641i	$0.134695\pi$
$548$	8.11879	0.346817
$549$	12.3560	0.527340
$550$	24.5560	1.04707
$551$	−20.5787	−0.876683
$552$	−6.15548	−0.261995
$553$	0.607388	0.0258288
$554$	26.7554	1.13673
$555$	−12.2765	−0.521110
$556$	5.34899	0.226848
$557$	27.4669	1.16381	0.581904	−	0.813257i	$-0.302308\pi$
$557$	27.4669	1.16381	0.581904	+	0.813257i	$0.302308\pi$
$558$	−12.5176	−0.529912
$559$	−24.9631	−1.05583
$560$	−9.01646	−0.381015
$561$	−34.9541	−1.47576
$562$	22.9289	0.967199
$563$	30.0847	1.26792	0.633960	−	0.773366i	$-0.281428\pi$
$563$	30.0847	1.26792	0.633960	+	0.773366i	$0.281428\pi$
$564$	−1.21290	−0.0510722
$565$	33.6115	1.41405
$566$	14.7734	0.620971
$567$	−1.00000	−0.0419961
$568$	8.31679	0.348965
$569$	−38.9560	−1.63312	−0.816561	−	0.577259i	$-0.804122\pi$
$569$	−38.9560	−1.63312	−0.816561	+	0.577259i	$0.804122\pi$
$570$	−19.4786	−0.815869
$571$	−9.17407	−0.383923	−0.191961	−	0.981402i	$-0.561485\pi$
$571$	−9.17407	−0.383923	−0.191961	+	0.981402i	$0.561485\pi$
$572$	−13.6747	−0.571766
$573$	−9.10581	−0.380401
$574$	14.2310	0.593990
$575$	−7.44591	−0.310516
$576$	8.89311	0.370546
$577$	−26.0464	−1.08433	−0.542163	−	0.840273i	$-0.682394\pi$
$577$	−26.0464	−1.08433	−0.542163	+	0.840273i	$0.682394\pi$
$578$	−34.0624	−1.41681
$579$	26.5970	1.10533
$580$	4.55275	0.189043
$581$	−12.0677	−0.500651
$582$	−23.4351	−0.971415
$583$	45.6384	1.89015
$584$	−21.2713	−0.880212
$585$	19.4604	0.804587
$586$	6.76822	0.279593
$587$	−3.29491	−0.135995	−0.0679977	−	0.997685i	$-0.521661\pi$
$587$	−3.29491	−0.135995	−0.0679977	+	0.997685i	$0.521661\pi$
$588$	−0.392010	−0.0161662
$589$	−51.5001	−2.12203
$590$	−19.5804	−0.806111
$591$	−2.55554	−0.105121
$592$	−12.7684	−0.524779
$593$	−0.339173	−0.0139282	−0.00696408	−	0.999976i	$-0.502217\pi$
$593$	−0.339173	−0.0139282	−0.00696408	+	0.999976i	$0.502217\pi$
$594$	6.69264	0.274602
$595$	19.4998	0.799413
$596$	5.12394	0.209885
$597$	6.28642	0.257286
$598$	−17.0084	−0.695524
$599$	−13.2004	−0.539354	−0.269677	−	0.962951i	$-0.586917\pi$
$599$	−13.2004	−0.539354	−0.269677	+	0.962951i	$0.586917\pi$
$600$	11.1292	0.454349
$601$	−34.0587	−1.38928	−0.694642	−	0.719356i	$-0.744437\pi$
$601$	−34.0587	−1.38928	−0.694642	+	0.719356i	$0.744437\pi$
$602$	4.78935	0.195199
$603$	−5.71460	−0.232717
$604$	0.0912682	0.00371365
$605$	−49.6282	−2.01767
$606$	−3.89546	−0.158242
$607$	−33.3375	−1.35313	−0.676563	−	0.736385i	$-0.736531\pi$
$607$	−33.3375	−1.35313	−0.676563	+	0.736385i	$0.736531\pi$
$608$	11.3902	0.461933
$609$	−3.94448	−0.159838
$610$	46.1324	1.86785
$611$	−20.4499	−0.827314
$612$	−2.59621	−0.104946
$613$	−17.1635	−0.693228	−0.346614	−	0.938008i	$-0.612669\pi$
$613$	−17.1635	−0.693228	−0.346614	+	0.938008i	$0.612669\pi$
$614$	4.21094	0.169940
$615$	−33.0431	−1.33243
$616$	16.0089	0.645015
$617$	−5.81846	−0.234242	−0.117121	−	0.993118i	$-0.537367\pi$
$617$	−5.81846	−0.234242	−0.117121	+	0.993118i	$0.537367\pi$
$618$	5.48124	0.220488
$619$	29.1015	1.16969	0.584843	−	0.811146i	$-0.301156\pi$
$619$	29.1015	1.16969	0.584843	+	0.811146i	$0.301156\pi$
$620$	11.3937	0.457581
$621$	−2.02935	−0.0814351
$622$	−1.07617	−0.0431505
$623$	−0.507910	−0.0203490
$624$	20.2401	0.810252
$625$	−29.8832	−1.19533
$626$	−27.6443	−1.10489
$627$	27.5350	1.09964
$628$	9.66779	0.385787
$629$	27.6141	1.10105
$630$	−3.73361	−0.148751
$631$	34.4964	1.37328	0.686639	−	0.726998i	$-0.259085\pi$
$631$	34.4964	1.37328	0.686639	+	0.726998i	$0.259085\pi$
$632$	−1.84234	−0.0732845
$633$	19.3529	0.769207
$634$	−21.4240	−0.850857
$635$	−27.3450	−1.08515
$636$	3.38979	0.134414
$637$	−6.60942	−0.261875
$638$	26.3990	1.04514
$639$	2.74190	0.108468
$640$	20.3470	0.804286
$641$	−3.26177	−0.128832	−0.0644160	−	0.997923i	$-0.520518\pi$
$641$	−3.26177	−0.128832	−0.0644160	+	0.997923i	$0.520518\pi$
$642$	15.3394	0.605399
$643$	−40.7801	−1.60821	−0.804106	−	0.594486i	$-0.797355\pi$
$643$	−40.7801	−1.60821	−0.804106	+	0.594486i	$0.797355\pi$
$644$	−0.795527	−0.0313481
$645$	−11.1204	−0.437867
$646$	43.8141	1.72384
$647$	−7.61820	−0.299502	−0.149751	−	0.988724i	$-0.547847\pi$
$647$	−7.61820	−0.299502	−0.149751	+	0.988724i	$0.547847\pi$
$648$	3.03323	0.119156
$649$	27.6788	1.08649
$650$	30.7515	1.20617
$651$	−9.87141	−0.386891
$652$	−0.0709428	−0.00277833
$653$	3.86754	0.151349	0.0756743	−	0.997133i	$-0.475889\pi$
$653$	3.86754	0.151349	0.0756743	+	0.997133i	$0.475889\pi$
$654$	5.07723	0.198536
$655$	10.6798	0.417294
$656$	−34.3671	−1.34181
$657$	−7.01276	−0.273594
$658$	3.92346	0.152952
$659$	23.7613	0.925608	0.462804	−	0.886461i	$-0.346843\pi$
$659$	23.7613	0.925608	0.462804	+	0.886461i	$0.346843\pi$
$660$	−6.09172	−0.237120
$661$	47.1703	1.83471	0.917355	−	0.398069i	$-0.130320\pi$
$661$	47.1703	1.83471	0.917355	+	0.398069i	$0.130320\pi$
$662$	−32.1699	−1.25032
$663$	−43.7730	−1.70000
$664$	36.6039	1.42051
$665$	−15.3609	−0.595670
$666$	−5.28725	−0.204877
$667$	−8.00474	−0.309945
$668$	3.10495	0.120134
$669$	23.9632	0.926471
$670$	−21.3361	−0.824285
$671$	−65.2127	−2.51751
$672$	2.18324	0.0842204
$673$	27.9697	1.07815	0.539076	−	0.842257i	$-0.318774\pi$
$673$	27.9697	1.07815	0.539076	+	0.842257i	$0.318774\pi$
$674$	18.6862	0.719765
$675$	3.66911	0.141224
$676$	−12.0286	−0.462640
$677$	−35.6360	−1.36960	−0.684801	−	0.728730i	$-0.740111\pi$
$677$	−35.6360	−1.36960	−0.684801	+	0.728730i	$0.740111\pi$
$678$	14.4758	0.555940
$679$	−18.4810	−0.709234
$680$	−59.1473	−2.26819
$681$	20.9741	0.803729
$682$	66.0658	2.52979
$683$	3.12974	0.119756	0.0598781	−	0.998206i	$-0.480929\pi$
$683$	3.12974	0.119756	0.0598781	+	0.998206i	$0.480929\pi$
$684$	2.04515	0.0781984
$685$	60.9791	2.32989
$686$	1.26807	0.0484150
$687$	1.94905	0.0743608
$688$	−11.5660	−0.440950
$689$	57.1530	2.17736
$690$	−7.57681	−0.288444
$691$	26.1507	0.994821	0.497411	−	0.867515i	$-0.334284\pi$
$691$	26.1507	0.994821	0.497411	+	0.867515i	$0.334284\pi$
$692$	8.60067	0.326948
$693$	5.27783	0.200488
$694$	−35.0350	−1.32991
$695$	40.1755	1.52394
$696$	11.9645	0.453513
$697$	74.3252	2.81527
$698$	5.60613	0.212195
$699$	−28.3681	−1.07298
$700$	1.43833	0.0543636
$701$	45.0197	1.70037	0.850185	−	0.526483i	$-0.176490\pi$
$701$	45.0197	1.70037	0.850185	+	0.526483i	$0.176490\pi$
$702$	8.38118	0.316327
$703$	−21.7529	−0.820427
$704$	−46.9363	−1.76898
$705$	−9.10992	−0.343099
$706$	3.53147	0.132908
$707$	−3.07197	−0.115533
$708$	2.05584	0.0772631
$709$	−21.5223	−0.808286	−0.404143	−	0.914696i	$-0.632430\pi$
$709$	−21.5223	−0.808286	−0.404143	+	0.914696i	$0.632430\pi$
$710$	10.2372	0.384194
$711$	−0.607388	−0.0227788
$712$	1.54061	0.0577366
$713$	−20.0326	−0.750226
$714$	8.39816	0.314293
$715$	−102.708	−3.84108
$716$	−7.11669	−0.265963
$717$	−3.88425	−0.145060
$718$	11.9997	0.447825
$719$	−11.6094	−0.432958	−0.216479	−	0.976287i	$-0.569457\pi$
$719$	−11.6094	−0.432958	−0.216479	+	0.976287i	$0.569457\pi$
$720$	9.01646	0.336024
$721$	4.32253	0.160979
$722$	−10.4211	−0.387834
$723$	23.6243	0.878598
$724$	2.19268	0.0814903
$725$	14.4727	0.537503
$726$	−21.3739	−0.793259
$727$	18.8445	0.698905	0.349452	−	0.936954i	$-0.386368\pi$
$727$	18.8445	0.698905	0.349452	+	0.936954i	$0.386368\pi$
$728$	20.0479	0.743024
$729$	1.00000	0.0370370
$730$	−26.1829	−0.969073
$731$	25.0137	0.925165
$732$	−4.84367	−0.179027
$733$	34.1731	1.26221	0.631107	−	0.775696i	$-0.282601\pi$
$733$	34.1731	1.26221	0.631107	+	0.775696i	$0.282601\pi$
$734$	39.4481	1.45606
$735$	−2.94433	−0.108603
$736$	4.43057	0.163313
$737$	30.1607	1.11098
$738$	−14.2310	−0.523850
$739$	−22.3334	−0.821546	−0.410773	−	0.911738i	$-0.634741\pi$
$739$	−22.3334	−0.821546	−0.410773	+	0.911738i	$0.634741\pi$
$740$	4.81252	0.176912
$741$	34.4820	1.26673
$742$	−10.9652	−0.402546
$743$	0.778397	0.0285566	0.0142783	−	0.999898i	$-0.495455\pi$
$743$	0.778397	0.0285566	0.0142783	+	0.999898i	$0.495455\pi$
$744$	29.9422	1.09773
$745$	38.4852	1.40999
$746$	20.8007	0.761567
$747$	12.0677	0.441532
$748$	13.7024	0.501008
$749$	12.0967	0.442005
$750$	−4.96903	−0.181443
$751$	−33.6439	−1.22768	−0.613841	−	0.789430i	$-0.710376\pi$
$751$	−33.6439	−1.22768	−0.613841	+	0.789430i	$0.710376\pi$
$752$	−9.47494	−0.345515
$753$	−13.6779	−0.498450
$754$	33.0594	1.20395
$755$	0.685504	0.0249480
$756$	0.392010	0.0142573
$757$	5.92842	0.215472	0.107736	−	0.994180i	$-0.465640\pi$
$757$	5.92842	0.215472	0.107736	+	0.994180i	$0.465640\pi$
$758$	−35.4559	−1.28782
$759$	10.7106	0.388769
$760$	46.5930	1.69011
$761$	10.6408	0.385728	0.192864	−	0.981226i	$-0.438222\pi$
$761$	10.6408	0.385728	0.192864	+	0.981226i	$0.438222\pi$
$762$	−11.7770	−0.426634
$763$	4.00392	0.144952
$764$	3.56957	0.129143
$765$	−19.4998	−0.705016
$766$	−1.26807	−0.0458171
$767$	34.6621	1.25158
$768$	−9.02318	−0.325596
$769$	9.34786	0.337093	0.168546	−	0.985694i	$-0.446093\pi$
$769$	9.34786	0.337093	0.168546	+	0.985694i	$0.446093\pi$
$770$	19.7054	0.710132
$771$	27.2291	0.980634
$772$	−10.4263	−0.375250
$773$	−12.4334	−0.447198	−0.223599	−	0.974681i	$-0.571781\pi$
$773$	−12.4334	−0.447198	−0.223599	+	0.974681i	$0.571781\pi$
$774$	−4.78935	−0.172150
$775$	36.2193	1.30103
$776$	56.0569	2.01233
$777$	−4.16954	−0.149581
$778$	−5.36121	−0.192209
$779$	−58.5494	−2.09775
$780$	−7.62866	−0.273150
$781$	−14.4713	−0.517823
$782$	17.0428	0.609451
$783$	3.94448	0.140964
$784$	−3.06231	−0.109368
$785$	72.6135	2.59169
$786$	4.59957	0.164061
$787$	16.2589	0.579566	0.289783	−	0.957092i	$-0.406417\pi$
$787$	16.2589	0.579566	0.289783	+	0.957092i	$0.406417\pi$
$788$	1.00180	0.0356876
$789$	8.55847	0.304690
$790$	−2.26775	−0.0806829
$791$	11.4157	0.405894
$792$	−16.0089	−0.568850
$793$	−81.6659	−2.90004
$794$	−4.73278	−0.167960
$795$	25.4602	0.902982
$796$	−2.46434	−0.0873462
$797$	−25.3712	−0.898695	−0.449347	−	0.893357i	$-0.648343\pi$
$797$	−25.3712	−0.898695	−0.449347	+	0.893357i	$0.648343\pi$
$798$	−6.61562	−0.234191
$799$	20.4913	0.724931
$800$	−8.01055	−0.283216
$801$	0.507910	0.0179461
$802$	42.4652	1.49950
$803$	37.0122	1.30613
$804$	2.24018	0.0790051
$805$	−5.97509	−0.210594
$806$	82.7341	2.91418
$807$	−21.8739	−0.769998
$808$	9.31798	0.327805
$809$	20.4605	0.719352	0.359676	−	0.933077i	$-0.382887\pi$
$809$	20.4605	0.719352	0.359676	+	0.933077i	$0.382887\pi$
$810$	3.73361	0.131186
$811$	−37.0911	−1.30245	−0.651223	−	0.758886i	$-0.725744\pi$
$811$	−37.0911	−1.30245	−0.651223	+	0.758886i	$0.725744\pi$
$812$	1.54627	0.0542636
$813$	2.36328	0.0828838
$814$	27.9052	0.978078
$815$	−0.532842	−0.0186646
$816$	−20.2811	−0.709981
$817$	−19.7044	−0.689371
$818$	20.9794	0.733528
$819$	6.60942	0.230952
$820$	12.9532	0.452346
$821$	−42.6074	−1.48701	−0.743504	−	0.668731i	$-0.766838\pi$
$821$	−42.6074	−1.48701	−0.743504	+	0.668731i	$0.766838\pi$
$822$	26.2625	0.916009
$823$	−36.9436	−1.28777	−0.643887	−	0.765121i	$-0.722679\pi$
$823$	−36.9436	−1.28777	−0.643887	+	0.765121i	$0.722679\pi$
$824$	−13.1112	−0.456750
$825$	−19.3649	−0.674200
$826$	−6.65018	−0.231389
$827$	−19.0144	−0.661197	−0.330598	−	0.943772i	$-0.607251\pi$
$827$	−19.0144	−0.661197	−0.330598	+	0.943772i	$0.607251\pi$
$828$	0.795527	0.0276465
$829$	−45.8926	−1.59392	−0.796958	−	0.604035i	$-0.793559\pi$
$829$	−45.8926	−1.59392	−0.796958	+	0.604035i	$0.793559\pi$
$830$	45.0559	1.56391
$831$	−21.0994	−0.731930
$832$	−58.7784	−2.03777
$833$	6.62282	0.229467
$834$	17.3028	0.599147
$835$	23.3209	0.807052
$836$	−10.7940	−0.373318
$837$	9.87141	0.341206
$838$	19.7884	0.683580
$839$	1.66414	0.0574524	0.0287262	−	0.999587i	$-0.490855\pi$
$839$	1.66414	0.0574524	0.0287262	+	0.999587i	$0.490855\pi$
$840$	8.93083	0.308143
$841$	−13.4411	−0.463486
$842$	−11.8433	−0.408148
$843$	−18.0818	−0.622771
$844$	−7.58651	−0.261139
$845$	−90.3454	−3.10798
$846$	−3.92346	−0.134891
$847$	−16.8555	−0.579162
$848$	26.4804	0.909340
$849$	−11.6503	−0.399838
$850$	−30.8138	−1.05690
$851$	−8.46147	−0.290056
$852$	−1.07485	−0.0368238
$853$	−44.7819	−1.53330	−0.766651	−	0.642064i	$-0.778078\pi$
$853$	−44.7819	−1.53330	−0.766651	+	0.642064i	$0.778078\pi$
$854$	15.6682	0.536154
$855$	15.3609	0.525331
$856$	−36.6921	−1.25411
$857$	0.593128	0.0202609	0.0101304	−	0.999949i	$-0.496775\pi$
$857$	0.593128	0.0202609	0.0101304	+	0.999949i	$0.496775\pi$
$858$	−44.2345	−1.51014
$859$	−19.7358	−0.673378	−0.336689	−	0.941616i	$-0.609307\pi$
$859$	−19.7358	−0.673378	−0.336689	+	0.941616i	$0.609307\pi$
$860$	4.35933	0.148652
$861$	−11.2226	−0.382465
$862$	−48.8334	−1.66327
$863$	4.37979	0.149090	0.0745449	−	0.997218i	$-0.476250\pi$
$863$	4.37979	0.149090	0.0745449	+	0.997218i	$0.476250\pi$
$864$	−2.18324	−0.0742754
$865$	64.5985	2.19641
$866$	35.0213	1.19007
$867$	26.8617	0.912271
$868$	3.86969	0.131346
$869$	3.20569	0.108746
$870$	14.7271	0.499297
$871$	37.7702	1.27980
$872$	−12.1448	−0.411275
$873$	18.4810	0.625486
$874$	−13.4254	−0.454122
$875$	−3.91859	−0.132473
$876$	2.74907	0.0928826
$877$	−41.3999	−1.39797	−0.698987	−	0.715134i	$-0.746366\pi$
$877$	−41.3999	−1.39797	−0.698987	+	0.715134i	$0.746366\pi$
$878$	23.2936	0.786120
$879$	−5.33744	−0.180027
$880$	−47.5874	−1.60417
$881$	−17.8078	−0.599961	−0.299981	−	0.953945i	$-0.596980\pi$
$881$	−17.8078	−0.599961	−0.299981	+	0.953945i	$0.596980\pi$
$882$	−1.26807	−0.0426980
$883$	16.1153	0.542322	0.271161	−	0.962534i	$-0.412592\pi$
$883$	16.1153	0.542322	0.271161	+	0.962534i	$0.412592\pi$
$884$	17.1595	0.577135
$885$	15.4411	0.519048
$886$	−31.9787	−1.07435
$887$	9.89452	0.332225	0.166113	−	0.986107i	$-0.446878\pi$
$887$	9.89452	0.332225	0.166113	+	0.986107i	$0.446878\pi$
$888$	12.6472	0.424411
$889$	−9.28734	−0.311487
$890$	1.89634	0.0635654
$891$	−5.27783	−0.176814
$892$	−9.39382	−0.314528
$893$	−16.1420	−0.540170
$894$	16.5748	0.554345
$895$	−53.4525	−1.78672
$896$	6.91056	0.230866
$897$	13.4129	0.447842
$898$	−0.602264	−0.0200978
$899$	38.9376	1.29864
$900$	−1.43833	−0.0479442
$901$	−57.2688	−1.90790
$902$	75.1088	2.50085
$903$	−3.77690	−0.125687
$904$	−34.6263	−1.15165
$905$	16.4689	0.547446
$906$	0.295233	0.00980844
$907$	44.6389	1.48221	0.741105	−	0.671389i	$-0.234302\pi$
$907$	44.6389	1.48221	0.741105	+	0.671389i	$0.234302\pi$
$908$	−8.22205	−0.272858
$909$	3.07197	0.101891
$910$	24.6770	0.818035
$911$	19.6130	0.649807	0.324904	−	0.945747i	$-0.394668\pi$
$911$	19.6130	0.649807	0.324904	+	0.945747i	$0.394668\pi$
$912$	15.9764	0.529030
$913$	−63.6910	−2.10787
$914$	15.8925	0.525676
$915$	−36.3801	−1.20269
$916$	−0.764046	−0.0252448
$917$	3.62724	0.119782
$918$	−8.39816	−0.277181
$919$	14.0306	0.462828	0.231414	−	0.972855i	$-0.425665\pi$
$919$	14.0306	0.462828	0.231414	+	0.972855i	$0.425665\pi$
$920$	18.1238	0.597524
$921$	−3.32076	−0.109423
$922$	15.3266	0.504755
$923$	−18.1224	−0.596505
$924$	−2.06896	−0.0680639
$925$	15.2985	0.503012
$926$	−30.5054	−1.00247
$927$	−4.32253	−0.141970
$928$	−8.61175	−0.282695
$929$	−33.5046	−1.09925	−0.549625	−	0.835412i	$-0.685229\pi$
$929$	−33.5046	−1.09925	−0.549625	+	0.835412i	$0.685229\pi$
$930$	36.8560	1.20856
$931$	−5.21710	−0.170984
$932$	11.1206	0.364267
$933$	0.848670	0.0277842
$934$	11.1163	0.363735
$935$	102.917	3.36573
$936$	−20.0479	−0.655285
$937$	−18.3038	−0.597959	−0.298979	−	0.954260i	$-0.596646\pi$
$937$	−18.3038	−0.597959	−0.298979	+	0.954260i	$0.596646\pi$
$938$	−7.24649	−0.236606
$939$	21.8004	0.711428
$940$	3.57118	0.116479
$941$	−25.2424	−0.822878	−0.411439	−	0.911437i	$-0.634974\pi$
$941$	−25.2424	−0.822878	−0.411439	+	0.911437i	$0.634974\pi$
$942$	31.2731	1.01893
$943$	−22.7746	−0.741643
$944$	16.0598	0.522703
$945$	2.94433	0.0957792
$946$	25.2774	0.821839
$947$	31.0261	1.00821	0.504107	−	0.863641i	$-0.331822\pi$
$947$	31.0261	1.00821	0.504107	+	0.863641i	$0.331822\pi$
$948$	0.238102	0.00773320
$949$	46.3503	1.50460
$950$	24.2734	0.787534
$951$	16.8951	0.547860
$952$	−20.0885	−0.651072
$953$	2.60357	0.0843380	0.0421690	−	0.999110i	$-0.486573\pi$
$953$	2.60357	0.0843380	0.0421690	+	0.999110i	$0.486573\pi$
$954$	10.9652	0.355012
$955$	26.8106	0.867570
$956$	1.52267	0.0492465
$957$	−20.8183	−0.672960
$958$	18.6425	0.602311
$959$	20.7107	0.668782
$960$	−26.1843	−0.845095
$961$	66.4447	2.14338
$962$	34.9457	1.12669
$963$	−12.0967	−0.389811
$964$	−9.26097	−0.298276
$965$	−78.3104	−2.52090
$966$	−2.57335	−0.0827962
$967$	−52.2267	−1.67950	−0.839749	−	0.542974i	$-0.817298\pi$
$967$	−52.2267	−1.67950	−0.839749	+	0.542974i	$0.817298\pi$
$968$	51.1265	1.64327
$969$	−34.5519	−1.10997
$970$	69.0007	2.21548
$971$	−15.6493	−0.502208	−0.251104	−	0.967960i	$-0.580794\pi$
$971$	−15.6493	−0.502208	−0.251104	+	0.967960i	$0.580794\pi$
$972$	−0.392010	−0.0125737
$973$	13.6450	0.437439
$974$	−47.6456	−1.52666
$975$	−24.2507	−0.776644
$976$	−37.8378	−1.21116
$977$	−5.49181	−0.175699	−0.0878493	−	0.996134i	$-0.527999\pi$
$977$	−5.49181	−0.175699	−0.0878493	+	0.996134i	$0.527999\pi$
$978$	−0.229484	−0.00733810
$979$	−2.68066	−0.0856744
$980$	1.15421	0.0368698
$981$	−4.00392	−0.127835
$982$	1.80914	0.0577321
$983$	−50.4618	−1.60948	−0.804740	−	0.593627i	$-0.797695\pi$
$983$	−50.4618	−1.60948	−0.804740	+	0.593627i	$0.797695\pi$
$984$	34.0407	1.08518
$985$	7.52437	0.239746
$986$	−33.1264	−1.05496
$987$	−3.09405	−0.0984847
$988$	−13.5173	−0.430043
$989$	−7.66465	−0.243722
$990$	−19.7054	−0.626277
$991$	−9.98142	−0.317070	−0.158535	−	0.987353i	$-0.550677\pi$
$991$	−9.98142	−0.317070	−0.158535	+	0.987353i	$0.550677\pi$
$992$	−21.5517	−0.684267
$993$	25.3693	0.805069
$994$	3.47691	0.110281
$995$	−18.5093	−0.586785
$996$	−4.73064	−0.149896
$997$	15.4547	0.489455	0.244728	−	0.969592i	$-0.421301\pi$
$997$	15.4547	0.489455	0.244728	+	0.969592i	$0.421301\pi$
$998$	41.1179	1.30156
$999$	4.16954	0.131918

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.q.1.15	✓	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.q.1.15	✓	44	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)

\(f(q)\)	\(=\)	\(q-1.26807 q^{2} +1.00000 q^{3} -0.392010 q^{4} -2.94433 q^{5} -1.26807 q^{6} -1.00000 q^{7} +3.03323 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.26807 q^{2} +1.00000 q^{3} -0.392010 q^{4} -2.94433 q^{5} -1.26807 q^{6} -1.00000 q^{7} +3.03323 q^{8} +1.00000 q^{9} +3.73361 q^{10} -5.27783 q^{11} -0.392010 q^{12} -6.60942 q^{13} +1.26807 q^{14} -2.94433 q^{15} -3.06231 q^{16} +6.62282 q^{17} -1.26807 q^{18} -5.21710 q^{19} +1.15421 q^{20} -1.00000 q^{21} +6.69264 q^{22} -2.02935 q^{23} +3.03323 q^{24} +3.66911 q^{25} +8.38118 q^{26} +1.00000 q^{27} +0.392010 q^{28} +3.94448 q^{29} +3.73361 q^{30} +9.87141 q^{31} -2.18324 q^{32} -5.27783 q^{33} -8.39816 q^{34} +2.94433 q^{35} -0.392010 q^{36} +4.16954 q^{37} +6.61562 q^{38} -6.60942 q^{39} -8.93083 q^{40} +11.2226 q^{41} +1.26807 q^{42} +3.77690 q^{43} +2.06896 q^{44} -2.94433 q^{45} +2.57335 q^{46} +3.09405 q^{47} -3.06231 q^{48} +1.00000 q^{49} -4.65267 q^{50} +6.62282 q^{51} +2.59096 q^{52} -8.64720 q^{53} -1.26807 q^{54} +15.5397 q^{55} -3.03323 q^{56} -5.21710 q^{57} -5.00186 q^{58} -5.24435 q^{59} +1.15421 q^{60} +12.3560 q^{61} -12.5176 q^{62} -1.00000 q^{63} +8.89311 q^{64} +19.4604 q^{65} +6.69264 q^{66} -5.71460 q^{67} -2.59621 q^{68} -2.02935 q^{69} -3.73361 q^{70} +2.74190 q^{71} +3.03323 q^{72} -7.01276 q^{73} -5.28725 q^{74} +3.66911 q^{75} +2.04515 q^{76} +5.27783 q^{77} +8.38118 q^{78} -0.607388 q^{79} +9.01646 q^{80} +1.00000 q^{81} -14.2310 q^{82} +12.0677 q^{83} +0.392010 q^{84} -19.4998 q^{85} -4.78935 q^{86} +3.94448 q^{87} -16.0089 q^{88} +0.507910 q^{89} +3.73361 q^{90} +6.60942 q^{91} +0.795527 q^{92} +9.87141 q^{93} -3.92346 q^{94} +15.3609 q^{95} -2.18324 q^{96} +18.4810 q^{97} -1.26807 q^{98} -5.27783 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9}+O(q^{10}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9	\( 44 q - 4 q^{2} + 44 q^{3} + 44 q^{4} - 16 q^{5} - 4 q^{6} - 44 q^{7} - 15 q^{8} + 44 q^{9} - 16 q^{10} - 2 q^{11} + 44 q^{12} - 34 q^{13} + 4 q^{14} - 16 q^{15} + 24 q^{16} - 4 q^{17} - 4 q^{18} - 22 q^{19} - 39 q^{20} - 44 q^{21} - 23 q^{22} - 56 q^{23} - 15 q^{24} + 32 q^{25} - 17 q^{26} + 44 q^{27} - 44 q^{28} - 33 q^{29} - 16 q^{30} - 32 q^{31} - 34 q^{32} - 2 q^{33} - 25 q^{34} + 16 q^{35} + 44 q^{36} - 47 q^{37} - 40 q^{38} - 34 q^{39} - 50 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} - 22 q^{44} - 16 q^{45} + 8 q^{46} - 27 q^{47} + 24 q^{48} + 44 q^{49} - 21 q^{50} - 4 q^{51} - 82 q^{52} - 114 q^{53} - 4 q^{54} - 29 q^{55} + 15 q^{56} - 22 q^{57} - 26 q^{58} - 40 q^{59} - 39 q^{60} - 47 q^{61} - 37 q^{62} - 44 q^{63} - 5 q^{64} - 20 q^{65} - 23 q^{66} - 14 q^{67} - 72 q^{68} - 56 q^{69} + 16 q^{70} - 65 q^{71} - 15 q^{72} - 21 q^{73} - 26 q^{74} + 32 q^{75} - 15 q^{76} + 2 q^{77} - 17 q^{78} + 6 q^{79} - 77 q^{80} + 44 q^{81} - 51 q^{82} - 30 q^{83} - 44 q^{84} - 26 q^{85} - 65 q^{86} - 33 q^{87} - 84 q^{88} - 32 q^{89} - 16 q^{90} + 34 q^{91} - 140 q^{92} - 32 q^{93} - 35 q^{94} - 50 q^{95} - 34 q^{96} - 83 q^{97} - 4 q^{98} - 2 q^{99}+O(q^{100}) \) 44 * q - 4 * q^2 + 44 * q^3 + 44 * q^4 - 16 * q^5 - 4 * q^6 - 44 * q^7 - 15 * q^8 + 44 * q^9 - 16 * q^10 - 2 * q^11 + 44 * q^12 - 34 * q^13 + 4 * q^14 - 16 * q^15 + 24 * q^16 - 4 * q^17 - 4 * q^18 - 22 * q^19 - 39 * q^20 - 44 * q^21 - 23 * q^22 - 56 * q^23 - 15 * q^24 + 32 * q^25 - 17 * q^26 + 44 * q^27 - 44 * q^28 - 33 * q^29 - 16 * q^30 - 32 * q^31 - 34 * q^32 - 2 * q^33 - 25 * q^34 + 16 * q^35 + 44 * q^36 - 47 * q^37 - 40 * q^38 - 34 * q^39 - 50 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 - 22 * q^44 - 16 * q^45 + 8 * q^46 - 27 * q^47 + 24 * q^48 + 44 * q^49 - 21 * q^50 - 4 * q^51 - 82 * q^52 - 114 * q^53 - 4 * q^54 - 29 * q^55 + 15 * q^56 - 22 * q^57 - 26 * q^58 - 40 * q^59 - 39 * q^60 - 47 * q^61 - 37 * q^62 - 44 * q^63 - 5 * q^64 - 20 * q^65 - 23 * q^66 - 14 * q^67 - 72 * q^68 - 56 * q^69 + 16 * q^70 - 65 * q^71 - 15 * q^72 - 21 * q^73 - 26 * q^74 + 32 * q^75 - 15 * q^76 + 2 * q^77 - 17 * q^78 + 6 * q^79 - 77 * q^80 + 44 * q^81 - 51 * q^82 - 30 * q^83 - 44 * q^84 - 26 * q^85 - 65 * q^86 - 33 * q^87 - 84 * q^88 - 32 * q^89 - 16 * q^90 + 34 * q^91 - 140 * q^92 - 32 * q^93 - 35 * q^94 - 50 * q^95 - 34 * q^96 - 83 * q^97 - 4 * q^98 - 2 * q^99

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