LMFDB - Embedded newform 8043.2.a.p.1.13

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:	$0$
Dimension:	$41$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
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)

$f(q)$	$=$	$q-1.27831 q^{2} +1.00000 q^{3} -0.365914 q^{4} +2.18195 q^{5} -1.27831 q^{6} -1.00000 q^{7} +3.02438 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-1.27831 q^{2} +1.00000 q^{3} -0.365914 q^{4} +2.18195 q^{5} -1.27831 q^{6} -1.00000 q^{7} +3.02438 q^{8} +1.00000 q^{9} -2.78922 q^{10} +5.98901 q^{11} -0.365914 q^{12} +0.966778 q^{13} +1.27831 q^{14} +2.18195 q^{15} -3.13428 q^{16} -1.23639 q^{17} -1.27831 q^{18} -2.05740 q^{19} -0.798407 q^{20} -1.00000 q^{21} -7.65584 q^{22} +3.38067 q^{23} +3.02438 q^{24} -0.239093 q^{25} -1.23585 q^{26} +1.00000 q^{27} +0.365914 q^{28} -2.99817 q^{29} -2.78922 q^{30} -1.06482 q^{31} -2.04217 q^{32} +5.98901 q^{33} +1.58050 q^{34} -2.18195 q^{35} -0.365914 q^{36} +8.27373 q^{37} +2.63000 q^{38} +0.966778 q^{39} +6.59905 q^{40} -4.35072 q^{41} +1.27831 q^{42} +10.2215 q^{43} -2.19147 q^{44} +2.18195 q^{45} -4.32156 q^{46} -6.72380 q^{47} -3.13428 q^{48} +1.00000 q^{49} +0.305636 q^{50} -1.23639 q^{51} -0.353758 q^{52} -7.99545 q^{53} -1.27831 q^{54} +13.0677 q^{55} -3.02438 q^{56} -2.05740 q^{57} +3.83260 q^{58} +4.70699 q^{59} -0.798407 q^{60} +8.92001 q^{61} +1.36117 q^{62} -1.00000 q^{63} +8.87909 q^{64} +2.10946 q^{65} -7.65584 q^{66} +6.20360 q^{67} +0.452414 q^{68} +3.38067 q^{69} +2.78922 q^{70} +10.9871 q^{71} +3.02438 q^{72} +8.99596 q^{73} -10.5764 q^{74} -0.239093 q^{75} +0.752831 q^{76} -5.98901 q^{77} -1.23585 q^{78} -10.4597 q^{79} -6.83884 q^{80} +1.00000 q^{81} +5.56158 q^{82} +10.8343 q^{83} +0.365914 q^{84} -2.69775 q^{85} -13.0663 q^{86} -2.99817 q^{87} +18.1131 q^{88} -2.90049 q^{89} -2.78922 q^{90} -0.966778 q^{91} -1.23704 q^{92} -1.06482 q^{93} +8.59513 q^{94} -4.48914 q^{95} -2.04217 q^{96} -11.1417 q^{97} -1.27831 q^{98} +5.98901 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9}+O(q^{10}) $ 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9} + 18 q^{10} + 8 q^{11} + 45 q^{12} + 23 q^{13} - 7 q^{14} + 17 q^{15} + 37 q^{16} + 15 q^{17} + 7 q^{18} + 15 q^{19} + 53 q^{20} - 41 q^{21} + 13 q^{22} + 44 q^{23} + 12 q^{24} + 58 q^{25} + 9 q^{26} + 41 q^{27} - 45 q^{28} + 21 q^{29} + 18 q^{30} + 39 q^{31} + 61 q^{32} + 8 q^{33} + 9 q^{34} - 17 q^{35} + 45 q^{36} + 11 q^{37} + 44 q^{38} + 23 q^{39} + 24 q^{40} + 17 q^{41} - 7 q^{42} + 7 q^{43} + 30 q^{44} + 17 q^{45} - 12 q^{46} + 36 q^{47} + 37 q^{48} + 41 q^{49} + 28 q^{50} + 15 q^{51} + 58 q^{52} + 26 q^{53} + 7 q^{54} + 32 q^{55} - 12 q^{56} + 15 q^{57} - 4 q^{58} + 33 q^{59} + 53 q^{60} + 59 q^{61} - q^{62} - 41 q^{63} + 16 q^{64} + 72 q^{65} + 13 q^{66} + 12 q^{67} + 52 q^{68} + 44 q^{69} - 18 q^{70} + 33 q^{71} + 12 q^{72} + 18 q^{73} + 42 q^{74} + 58 q^{75} + 7 q^{76} - 8 q^{77} + 9 q^{78} + 22 q^{79} + 69 q^{80} + 41 q^{81} + 41 q^{82} + 32 q^{83} - 45 q^{84} - 44 q^{85} + 11 q^{86} + 21 q^{87} + 52 q^{88} + 63 q^{89} + 18 q^{90} - 23 q^{91} + 52 q^{92} + 39 q^{93} + 17 q^{94} + 37 q^{95} + 61 q^{96} + 8 q^{97} + 7 q^{98} + 8 q^{99}+O(q^{100}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9 + 18 * q^10 + 8 * q^11 + 45 * q^12 + 23 * q^13 - 7 * q^14 + 17 * q^15 + 37 * q^16 + 15 * q^17 + 7 * q^18 + 15 * q^19 + 53 * q^20 - 41 * q^21 + 13 * q^22 + 44 * q^23 + 12 * q^24 + 58 * q^25 + 9 * q^26 + 41 * q^27 - 45 * q^28 + 21 * q^29 + 18 * q^30 + 39 * q^31 + 61 * q^32 + 8 * q^33 + 9 * q^34 - 17 * q^35 + 45 * q^36 + 11 * q^37 + 44 * q^38 + 23 * q^39 + 24 * q^40 + 17 * q^41 - 7 * q^42 + 7 * q^43 + 30 * q^44 + 17 * q^45 - 12 * q^46 + 36 * q^47 + 37 * q^48 + 41 * q^49 + 28 * q^50 + 15 * q^51 + 58 * q^52 + 26 * q^53 + 7 * q^54 + 32 * q^55 - 12 * q^56 + 15 * q^57 - 4 * q^58 + 33 * q^59 + 53 * q^60 + 59 * q^61 - q^62 - 41 * q^63 + 16 * q^64 + 72 * q^65 + 13 * q^66 + 12 * q^67 + 52 * q^68 + 44 * q^69 - 18 * q^70 + 33 * q^71 + 12 * q^72 + 18 * q^73 + 42 * q^74 + 58 * q^75 + 7 * q^76 - 8 * q^77 + 9 * q^78 + 22 * q^79 + 69 * q^80 + 41 * q^81 + 41 * q^82 + 32 * q^83 - 45 * q^84 - 44 * q^85 + 11 * q^86 + 21 * q^87 + 52 * q^88 + 63 * q^89 + 18 * q^90 - 23 * q^91 + 52 * q^92 + 39 * q^93 + 17 * q^94 + 37 * q^95 + 61 * q^96 + 8 * q^97 + 7 * q^98 + 8 * 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 $

$2$	−1.27831	−0.903904	−0.451952	−	0.892042i	$-0.649272\pi$
$2$	−1.27831	−0.903904	−0.451952	+	0.892042i	$0.649272\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.365914	−0.182957
$5$	2.18195	0.975798	0.487899	−	0.872900i	$-0.337763\pi$
$5$	2.18195	0.975798	0.487899	+	0.872900i	$0.337763\pi$
$6$	−1.27831	−0.521869
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	3.02438	1.06928
$9$	1.00000	0.333333
$10$	−2.78922	−0.882028
$11$	5.98901	1.80576	0.902878	−	0.429897i	$-0.141450\pi$
$11$	5.98901	1.80576	0.902878	+	0.429897i	$0.141450\pi$
$12$	−0.365914	−0.105630
$13$	0.966778	0.268136	0.134068	−	0.990972i	$-0.457196\pi$
$13$	0.966778	0.268136	0.134068	+	0.990972i	$0.457196\pi$
$14$	1.27831	0.341644
$15$	2.18195	0.563377
$16$	−3.13428	−0.783570
$17$	−1.23639	−0.299870	−0.149935	−	0.988696i	$-0.547906\pi$
$17$	−1.23639	−0.299870	−0.149935	+	0.988696i	$0.547906\pi$
$18$	−1.27831	−0.301301
$19$	−2.05740	−0.471999	−0.236000	−	0.971753i	$-0.575836\pi$
$19$	−2.05740	−0.471999	−0.236000	+	0.971753i	$0.575836\pi$
$20$	−0.798407	−0.178529
$21$	−1.00000	−0.218218
$22$	−7.65584	−1.63223
$23$	3.38067	0.704919	0.352460	−	0.935827i	$-0.385345\pi$
$23$	3.38067	0.704919	0.352460	+	0.935827i	$0.385345\pi$
$24$	3.02438	0.617349
$25$	−0.239093	−0.0478186
$26$	−1.23585	−0.242369
$27$	1.00000	0.192450
$28$	0.365914	0.0691513
$29$	−2.99817	−0.556747	−0.278373	−	0.960473i	$-0.589795\pi$
$29$	−2.99817	−0.556747	−0.278373	+	0.960473i	$0.589795\pi$
$30$	−2.78922	−0.509239
$31$	−1.06482	−0.191247	−0.0956237	−	0.995418i	$-0.530485\pi$
$31$	−1.06482	−0.191247	−0.0956237	+	0.995418i	$0.530485\pi$
$32$	−2.04217	−0.361008
$33$	5.98901	1.04255
$34$	1.58050	0.271053
$35$	−2.18195	−0.368817
$36$	−0.365914	−0.0609857
$37$	8.27373	1.36019	0.680097	−	0.733122i	$-0.261938\pi$
$37$	8.27373	1.36019	0.680097	+	0.733122i	$0.261938\pi$
$38$	2.63000	0.426642
$39$	0.966778	0.154808
$40$	6.59905	1.04340
$41$	−4.35072	−0.679468	−0.339734	−	0.940522i	$-0.610337\pi$
$41$	−4.35072	−0.679468	−0.339734	+	0.940522i	$0.610337\pi$
$42$	1.27831	0.197248
$43$	10.2215	1.55877	0.779385	−	0.626545i	$-0.215532\pi$
$43$	10.2215	1.55877	0.779385	+	0.626545i	$0.215532\pi$
$44$	−2.19147	−0.330376
$45$	2.18195	0.325266
$46$	−4.32156	−0.637179
$47$	−6.72380	−0.980767	−0.490384	−	0.871507i	$-0.663143\pi$
$47$	−6.72380	−0.980767	−0.490384	+	0.871507i	$0.663143\pi$
$48$	−3.13428	−0.452394
$49$	1.00000	0.142857
$50$	0.305636	0.0432234
$51$	−1.23639	−0.173130
$52$	−0.353758	−0.0490574
$53$	−7.99545	−1.09826	−0.549130	−	0.835737i	$-0.685041\pi$
$53$	−7.99545	−1.09826	−0.549130	+	0.835737i	$0.685041\pi$
$54$	−1.27831	−0.173956
$55$	13.0677	1.76205
$56$	−3.02438	−0.404150
$57$	−2.05740	−0.272509
$58$	3.83260	0.503246
$59$	4.70699	0.612798	0.306399	−	0.951903i	$-0.400876\pi$
$59$	4.70699	0.612798	0.306399	+	0.951903i	$0.400876\pi$
$60$	−0.798407	−0.103074
$61$	8.92001	1.14209	0.571045	−	0.820919i	$-0.306538\pi$
$61$	8.92001	1.14209	0.571045	+	0.820919i	$0.306538\pi$
$62$	1.36117	0.172869
$63$	−1.00000	−0.125988
$64$	8.87909	1.10989
$65$	2.10946	0.261647
$66$	−7.65584	−0.942369
$67$	6.20360	0.757891	0.378945	−	0.925419i	$-0.376287\pi$
$67$	6.20360	0.757891	0.378945	+	0.925419i	$0.376287\pi$
$68$	0.452414	0.0548633
$69$	3.38067	0.406985
$70$	2.78922	0.333375
$71$	10.9871	1.30393	0.651963	−	0.758251i	$-0.273946\pi$
$71$	10.9871	1.30393	0.651963	+	0.758251i	$0.273946\pi$
$72$	3.02438	0.356427
$73$	8.99596	1.05290	0.526449	−	0.850207i	$-0.323523\pi$
$73$	8.99596	1.05290	0.526449	+	0.850207i	$0.323523\pi$
$74$	−10.5764	−1.22948
$75$	−0.239093	−0.0276081
$76$	0.752831	0.0863556
$77$	−5.98901	−0.682512
$78$	−1.23585	−0.139932
$79$	−10.4597	−1.17681	−0.588403	−	0.808568i	$-0.700243\pi$
$79$	−10.4597	−1.17681	−0.588403	+	0.808568i	$0.700243\pi$
$80$	−6.83884	−0.764605
$81$	1.00000	0.111111
$82$	5.56158	0.614174
$83$	10.8343	1.18922	0.594609	−	0.804015i	$-0.297307\pi$
$83$	10.8343	1.18922	0.594609	+	0.804015i	$0.297307\pi$
$84$	0.365914	0.0399245
$85$	−2.69775	−0.292612
$86$	−13.0663	−1.40898
$87$	−2.99817	−0.321438
$88$	18.1131	1.93086
$89$	−2.90049	−0.307452	−0.153726	−	0.988114i	$-0.549127\pi$
$89$	−2.90049	−0.307452	−0.153726	+	0.988114i	$0.549127\pi$
$90$	−2.78922	−0.294009
$91$	−0.966778	−0.101346
$92$	−1.23704	−0.128970
$93$	−1.06482	−0.110417
$94$	8.59513	0.886520
$95$	−4.48914	−0.460576
$96$	−2.04217	−0.208428
$97$	−11.1417	−1.13127	−0.565634	−	0.824656i	$-0.691369\pi$
$97$	−11.1417	−1.13127	−0.565634	+	0.824656i	$0.691369\pi$
$98$	−1.27831	−0.129129
$99$	5.98901	0.601919
$100$	0.0874875	0.00874875
$101$	−4.89876	−0.487445	−0.243722	−	0.969845i	$-0.578369\pi$
$101$	−4.89876	−0.487445	−0.243722	+	0.969845i	$0.578369\pi$
$102$	1.58050	0.156493
$103$	3.23004	0.318265	0.159133	−	0.987257i	$-0.449130\pi$
$103$	3.23004	0.318265	0.159133	+	0.987257i	$0.449130\pi$
$104$	2.92390	0.286712
$105$	−2.18195	−0.212937
$106$	10.2207	0.992721
$107$	9.85939	0.953143	0.476571	−	0.879136i	$-0.341879\pi$
$107$	9.85939	0.953143	0.476571	+	0.879136i	$0.341879\pi$
$108$	−0.365914	−0.0352101
$109$	12.3068	1.17878	0.589391	−	0.807848i	$-0.299368\pi$
$109$	12.3068	1.17878	0.589391	+	0.807848i	$0.299368\pi$
$110$	−16.7047	−1.59273
$111$	8.27373	0.785308
$112$	3.13428	0.296161
$113$	−0.506628	−0.0476595	−0.0238298	−	0.999716i	$-0.507586\pi$
$113$	−0.506628	−0.0476595	−0.0238298	+	0.999716i	$0.507586\pi$
$114$	2.63000	0.246322
$115$	7.37646	0.687859
$116$	1.09707	0.101861
$117$	0.966778	0.0893787
$118$	−6.01701	−0.553911
$119$	1.23639	0.113340
$120$	6.59905	0.602408
$121$	24.8683	2.26075
$122$	−11.4026	−1.03234
$123$	−4.35072	−0.392291
$124$	0.389633	0.0349901
$125$	−11.4314	−1.02246
$126$	1.27831	0.113881
$127$	4.14036	0.367398	0.183699	−	0.982983i	$-0.441193\pi$
$127$	4.14036	0.367398	0.183699	+	0.982983i	$0.441193\pi$
$128$	−7.26592	−0.642223
$129$	10.2215	0.899957
$130$	−2.69655	−0.236503
$131$	16.4845	1.44026	0.720128	−	0.693841i	$-0.244083\pi$
$131$	16.4845	1.44026	0.720128	+	0.693841i	$0.244083\pi$
$132$	−2.19147	−0.190743
$133$	2.05740	0.178399
$134$	−7.93015	−0.685061
$135$	2.18195	0.187792
$136$	−3.73932	−0.320644
$137$	−3.00238	−0.256510	−0.128255	−	0.991741i	$-0.540938\pi$
$137$	−3.00238	−0.256510	−0.128255	+	0.991741i	$0.540938\pi$
$138$	−4.32156	−0.367876
$139$	−15.0192	−1.27392	−0.636958	−	0.770899i	$-0.719807\pi$
$139$	−15.0192	−1.27392	−0.636958	+	0.770899i	$0.719807\pi$
$140$	0.798407	0.0674777
$141$	−6.72380	−0.566246
$142$	−14.0449	−1.17862
$143$	5.79005	0.484188
$144$	−3.13428	−0.261190
$145$	−6.54186	−0.543272
$146$	−11.4997	−0.951719
$147$	1.00000	0.0824786
$148$	−3.02748	−0.248857
$149$	8.56029	0.701286	0.350643	−	0.936509i	$-0.385963\pi$
$149$	8.56029	0.701286	0.350643	+	0.936509i	$0.385963\pi$
$150$	0.305636	0.0249550
$151$	−6.04050	−0.491569	−0.245784	−	0.969325i	$-0.579046\pi$
$151$	−6.04050	−0.491569	−0.245784	+	0.969325i	$0.579046\pi$
$152$	−6.22235	−0.504699
$153$	−1.23639	−0.0999565
$154$	7.65584	0.616925
$155$	−2.32339	−0.186619
$156$	−0.353758	−0.0283233
$157$	−6.68764	−0.533732	−0.266866	−	0.963734i	$-0.585988\pi$
$157$	−6.68764	−0.533732	−0.266866	+	0.963734i	$0.585988\pi$
$158$	13.3707	1.06372
$159$	−7.99545	−0.634080
$160$	−4.45591	−0.352271
$161$	−3.38067	−0.266434
$162$	−1.27831	−0.100434
$163$	−23.8324	−1.86669	−0.933347	−	0.358976i	$-0.883126\pi$
$163$	−23.8324	−1.86669	−0.933347	+	0.358976i	$0.883126\pi$
$164$	1.59199	0.124314
$165$	13.0677	1.01732
$166$	−13.8496	−1.07494
$167$	−4.27854	−0.331084	−0.165542	−	0.986203i	$-0.552937\pi$
$167$	−4.27854	−0.331084	−0.165542	+	0.986203i	$0.552937\pi$
$168$	−3.02438	−0.233336
$169$	−12.0653	−0.928103
$170$	3.44857	0.264493
$171$	−2.05740	−0.157333
$172$	−3.74021	−0.285188
$173$	9.15834	0.696296	0.348148	−	0.937440i	$-0.386811\pi$
$173$	9.15834	0.696296	0.348148	+	0.937440i	$0.386811\pi$
$174$	3.83260	0.290549
$175$	0.239093	0.0180737
$176$	−18.7712	−1.41494
$177$	4.70699	0.353799
$178$	3.70774	0.277907
$179$	−6.24454	−0.466739	−0.233369	−	0.972388i	$-0.574975\pi$
$179$	−6.24454	−0.466739	−0.233369	+	0.972388i	$0.574975\pi$
$180$	−0.798407	−0.0595097
$181$	11.0690	0.822751	0.411375	−	0.911466i	$-0.365049\pi$
$181$	11.0690	0.822751	0.411375	+	0.911466i	$0.365049\pi$
$182$	1.23585	0.0916070
$183$	8.92001	0.659386
$184$	10.2244	0.753756
$185$	18.0529	1.32727
$186$	1.36117	0.0998062
$187$	−7.40478	−0.541491
$188$	2.46034	0.179438
$189$	−1.00000	−0.0727393
$190$	5.73853	0.416317
$191$	1.88737	0.136566	0.0682828	−	0.997666i	$-0.478248\pi$
$191$	1.88737	0.136566	0.0682828	+	0.997666i	$0.478248\pi$
$192$	8.87909	0.640793
$193$	−12.0286	−0.865838	−0.432919	−	0.901433i	$-0.642516\pi$
$193$	−12.0286	−0.865838	−0.432919	+	0.901433i	$0.642516\pi$
$194$	14.2426	1.02256
$195$	2.10946	0.151062
$196$	−0.365914	−0.0261367
$197$	−23.8328	−1.69802	−0.849009	−	0.528379i	$-0.822800\pi$
$197$	−23.8328	−1.69802	−0.849009	+	0.528379i	$0.822800\pi$
$198$	−7.65584	−0.544077
$199$	14.4270	1.02270	0.511351	−	0.859372i	$-0.329145\pi$
$199$	14.4270	1.02270	0.511351	+	0.859372i	$0.329145\pi$
$200$	−0.723107	−0.0511314
$201$	6.20360	0.437569
$202$	6.26215	0.440603
$203$	2.99817	0.210430
$204$	0.452414	0.0316753
$205$	−9.49305	−0.663023
$206$	−4.12900	−0.287681
$207$	3.38067	0.234973
$208$	−3.03015	−0.210103
$209$	−12.3218	−0.852316
$210$	2.78922	0.192474
$211$	6.56691	0.452085	0.226042	−	0.974117i	$-0.427421\pi$
$211$	6.56691	0.452085	0.226042	+	0.974117i	$0.427421\pi$
$212$	2.92565	0.200934
$213$	10.9871	0.752822
$214$	−12.6034	−0.861550
$215$	22.3029	1.52105
$216$	3.02438	0.205783
$217$	1.06482	0.0722847
$218$	−15.7320	−1.06551
$219$	8.99596	0.607891
$220$	−4.78167	−0.322380
$221$	−1.19532	−0.0804058
$222$	−10.5764	−0.709843
$223$	16.5296	1.10691	0.553453	−	0.832880i	$-0.313310\pi$
$223$	16.5296	1.10691	0.553453	+	0.832880i	$0.313310\pi$
$224$	2.04217	0.136448
$225$	−0.239093	−0.0159395
$226$	0.647629	0.0430796
$227$	14.2465	0.945571	0.472786	−	0.881177i	$-0.343248\pi$
$227$	14.2465	0.945571	0.472786	+	0.881177i	$0.343248\pi$
$228$	0.752831	0.0498575
$229$	14.4495	0.954851	0.477426	−	0.878672i	$-0.341570\pi$
$229$	14.4495	0.954851	0.477426	+	0.878672i	$0.341570\pi$
$230$	−9.42943	−0.621758
$231$	−5.98901	−0.394048
$232$	−9.06761	−0.595318
$233$	−14.7868	−0.968716	−0.484358	−	0.874870i	$-0.660947\pi$
$233$	−14.7868	−0.968716	−0.484358	+	0.874870i	$0.660947\pi$
$234$	−1.23585	−0.0807898
$235$	−14.6710	−0.957031
$236$	−1.72236	−0.112116
$237$	−10.4597	−0.679429
$238$	−1.58050	−0.102449
$239$	−15.6966	−1.01533	−0.507664	−	0.861555i	$-0.669491\pi$
$239$	−15.6966	−1.01533	−0.507664	+	0.861555i	$0.669491\pi$
$240$	−6.83884	−0.441445
$241$	5.75206	0.370523	0.185261	−	0.982689i	$-0.440687\pi$
$241$	5.75206	0.370523	0.185261	+	0.982689i	$0.440687\pi$
$242$	−31.7895	−2.04351
$243$	1.00000	0.0641500
$244$	−3.26396	−0.208953
$245$	2.18195	0.139400
$246$	5.56158	0.354594
$247$	−1.98905	−0.126560
$248$	−3.22042	−0.204497
$249$	10.8343	0.686595
$250$	14.6130	0.924205
$251$	10.1900	0.643186	0.321593	−	0.946878i	$-0.395782\pi$
$251$	10.1900	0.643186	0.321593	+	0.946878i	$0.395782\pi$
$252$	0.365914	0.0230504
$253$	20.2469	1.27291
$254$	−5.29268	−0.332093
$255$	−2.69775	−0.168940
$256$	−8.47005	−0.529378
$257$	−2.96811	−0.185146	−0.0925728	−	0.995706i	$-0.529509\pi$
$257$	−2.96811	−0.185146	−0.0925728	+	0.995706i	$0.529509\pi$
$258$	−13.0663	−0.813475
$259$	−8.27373	−0.514105
$260$	−0.771882	−0.0478701
$261$	−2.99817	−0.185582
$262$	−21.0723	−1.30185
$263$	5.55388	0.342467	0.171233	−	0.985230i	$-0.445225\pi$
$263$	5.55388	0.342467	0.171233	+	0.985230i	$0.445225\pi$
$264$	18.1131	1.11478
$265$	−17.4457	−1.07168
$266$	−2.63000	−0.161256
$267$	−2.90049	−0.177507
$268$	−2.26999	−0.138662
$269$	16.5508	1.00912	0.504561	−	0.863376i	$-0.331654\pi$
$269$	16.5508	1.00912	0.504561	+	0.863376i	$0.331654\pi$
$270$	−2.78922	−0.169746
$271$	−2.85713	−0.173558	−0.0867791	−	0.996228i	$-0.527657\pi$
$271$	−2.85713	−0.173558	−0.0867791	+	0.996228i	$0.527657\pi$
$272$	3.87520	0.234969
$273$	−0.966778	−0.0585121
$274$	3.83798	0.231861
$275$	−1.43193	−0.0863486
$276$	−1.23704	−0.0744609
$277$	−18.6597	−1.12116	−0.560578	−	0.828102i	$-0.689421\pi$
$277$	−18.6597	−1.12116	−0.560578	+	0.828102i	$0.689421\pi$
$278$	19.1993	1.15150
$279$	−1.06482	−0.0637491
$280$	−6.59905	−0.394369
$281$	20.5049	1.22322	0.611609	−	0.791160i	$-0.290522\pi$
$281$	20.5049	1.22322	0.611609	+	0.791160i	$0.290522\pi$
$282$	8.59513	0.511832
$283$	−24.1011	−1.43266	−0.716331	−	0.697761i	$-0.754180\pi$
$283$	−24.1011	−1.43266	−0.716331	+	0.697761i	$0.754180\pi$
$284$	−4.02033	−0.238562
$285$	−4.48914	−0.265914
$286$	−7.40150	−0.437660
$287$	4.35072	0.256815
$288$	−2.04217	−0.120336
$289$	−15.4713	−0.910078
$290$	8.36255	0.491066
$291$	−11.1417	−0.653138
$292$	−3.29175	−0.192635
$293$	10.5653	0.617230	0.308615	−	0.951187i	$-0.400134\pi$
$293$	10.5653	0.617230	0.308615	+	0.951187i	$0.400134\pi$
$294$	−1.27831	−0.0745528
$295$	10.2704	0.597967
$296$	25.0229	1.45443
$297$	5.98901	0.347518
$298$	−10.9427	−0.633896
$299$	3.26836	0.189014
$300$	0.0874875	0.00505109
$301$	−10.2215	−0.589160
$302$	7.72165	0.444331
$303$	−4.89876	−0.281426
$304$	6.44846	0.369844
$305$	19.4630	1.11445
$306$	1.58050	0.0903511
$307$	−18.8420	−1.07537	−0.537685	−	0.843146i	$-0.680701\pi$
$307$	−18.8420	−1.07537	−0.537685	+	0.843146i	$0.680701\pi$
$308$	2.19147	0.124870
$309$	3.23004	0.183750
$310$	2.97002	0.168686
$311$	27.6800	1.56959	0.784794	−	0.619756i	$-0.212769\pi$
$311$	27.6800	1.56959	0.784794	+	0.619756i	$0.212769\pi$
$312$	2.92390	0.165534
$313$	15.4156	0.871344	0.435672	−	0.900106i	$-0.356511\pi$
$313$	15.4156	0.871344	0.435672	+	0.900106i	$0.356511\pi$
$314$	8.54891	0.482443
$315$	−2.18195	−0.122939
$316$	3.82735	0.215305
$317$	−11.6881	−0.656470	−0.328235	−	0.944596i	$-0.606454\pi$
$317$	−11.6881	−0.656470	−0.328235	+	0.944596i	$0.606454\pi$
$318$	10.2207	0.573148
$319$	−17.9561	−1.00535
$320$	19.3737	1.08302
$321$	9.85939	0.550297
$322$	4.32156	0.240831
$323$	2.54375	0.141538
$324$	−0.365914	−0.0203286
$325$	−0.231150	−0.0128219
$326$	30.4652	1.68731
$327$	12.3068	0.680570
$328$	−13.1582	−0.726542
$329$	6.72380	0.370695
$330$	−16.7047	−0.919561
$331$	9.26565	0.509286	0.254643	−	0.967035i	$-0.418042\pi$
$331$	9.26565	0.509286	0.254643	+	0.967035i	$0.418042\pi$
$332$	−3.96442	−0.217576
$333$	8.27373	0.453398
$334$	5.46932	0.299268
$335$	13.5360	0.739548
$336$	3.13428	0.170989
$337$	5.52856	0.301160	0.150580	−	0.988598i	$-0.451886\pi$
$337$	5.52856	0.301160	0.150580	+	0.988598i	$0.451886\pi$
$338$	15.4233	0.838916
$339$	−0.506628	−0.0275162
$340$	0.987145	0.0535355
$341$	−6.37723	−0.345346
$342$	2.63000	0.142214
$343$	−1.00000	−0.0539949
$344$	30.9138	1.66676
$345$	7.37646	0.397135
$346$	−11.7072	−0.629385
$347$	−11.9796	−0.643099	−0.321549	−	0.946893i	$-0.604204\pi$
$347$	−11.9796	−0.643099	−0.321549	+	0.946893i	$0.604204\pi$
$348$	1.09707	0.0588093
$349$	9.42972	0.504761	0.252381	−	0.967628i	$-0.418786\pi$
$349$	9.42972	0.504761	0.252381	+	0.967628i	$0.418786\pi$
$350$	−0.305636	−0.0163369
$351$	0.966778	0.0516028
$352$	−12.2306	−0.651893
$353$	30.9446	1.64702	0.823508	−	0.567304i	$-0.192014\pi$
$353$	30.9446	1.64702	0.823508	+	0.567304i	$0.192014\pi$
$354$	−6.01701	−0.319801
$355$	23.9732	1.27237
$356$	1.06133	0.0562505
$357$	1.23639	0.0654369
$358$	7.98248	0.421887
$359$	7.04662	0.371907	0.185953	−	0.982559i	$-0.440463\pi$
$359$	7.04662	0.371907	0.185953	+	0.982559i	$0.440463\pi$
$360$	6.59905	0.347800
$361$	−14.7671	−0.777217
$362$	−14.1496	−0.743688
$363$	24.8683	1.30525
$364$	0.353758	0.0185420
$365$	19.6287	1.02742
$366$	−11.4026	−0.596022
$367$	6.71772	0.350662	0.175331	−	0.984510i	$-0.443900\pi$
$367$	6.71772	0.350662	0.175331	+	0.984510i	$0.443900\pi$
$368$	−10.5960	−0.552353
$369$	−4.35072	−0.226489
$370$	−23.0772	−1.19973
$371$	7.99545	0.415103
$372$	0.389633	0.0202015
$373$	22.0825	1.14339	0.571694	−	0.820467i	$-0.306287\pi$
$373$	22.0825	1.14339	0.571694	+	0.820467i	$0.306287\pi$
$374$	9.46563	0.489456
$375$	−11.4314	−0.590317
$376$	−20.3353	−1.04871
$377$	−2.89857	−0.149284
$378$	1.27831	0.0657494
$379$	10.5033	0.539517	0.269758	−	0.962928i	$-0.413056\pi$
$379$	10.5033	0.539517	0.269758	+	0.962928i	$0.413056\pi$
$380$	1.64264	0.0842657
$381$	4.14036	0.212117
$382$	−2.41266	−0.123442
$383$	−1.00000	−0.0510976
$383$	−1.00000	−0.0510976
$384$	−7.26592	−0.370788
$385$	−13.0677	−0.665993
$386$	15.3763	0.782635
$387$	10.2215	0.519590
$388$	4.07691	0.206974
$389$	10.5295	0.533868	0.266934	−	0.963715i	$-0.413989\pi$
$389$	10.5295	0.533868	0.266934	+	0.963715i	$0.413989\pi$
$390$	−2.69655	−0.136545
$391$	−4.17984	−0.211384
$392$	3.02438	0.152754
$393$	16.4845	0.831533
$394$	30.4658	1.53485
$395$	−22.8225	−1.14832
$396$	−2.19147	−0.110125
$397$	36.4432	1.82903	0.914515	−	0.404551i	$-0.132572\pi$
$397$	36.4432	1.82903	0.914515	+	0.404551i	$0.132572\pi$
$398$	−18.4422	−0.924424
$399$	2.05740	0.102999
$400$	0.749383	0.0374692
$401$	−31.1598	−1.55605	−0.778024	−	0.628235i	$-0.783778\pi$
$401$	−31.1598	−1.55605	−0.778024	+	0.628235i	$0.783778\pi$
$402$	−7.93015	−0.395520
$403$	−1.02944	−0.0512803
$404$	1.79253	0.0891815
$405$	2.18195	0.108422
$406$	−3.83260	−0.190209
$407$	49.5515	2.45618
$408$	−3.73932	−0.185124
$409$	−1.45604	−0.0719966	−0.0359983	−	0.999352i	$-0.511461\pi$
$409$	−1.45604	−0.0719966	−0.0359983	+	0.999352i	$0.511461\pi$
$410$	12.1351	0.599310
$411$	−3.00238	−0.148096
$412$	−1.18192	−0.0582289
$413$	−4.70699	−0.231616
$414$	−4.32156	−0.212393
$415$	23.6399	1.16044
$416$	−1.97433	−0.0967993
$417$	−15.0192	−0.735495
$418$	15.7511	0.770412
$419$	8.00989	0.391309	0.195654	−	0.980673i	$-0.437317\pi$
$419$	8.00989	0.391309	0.195654	+	0.980673i	$0.437317\pi$
$420$	0.798407	0.0389583
$421$	−3.27596	−0.159660	−0.0798302	−	0.996808i	$-0.525438\pi$
$421$	−3.27596	−0.159660	−0.0798302	+	0.996808i	$0.525438\pi$
$422$	−8.39457	−0.408641
$423$	−6.72380	−0.326922
$424$	−24.1813	−1.17435
$425$	0.295613	0.0143393
$426$	−14.0449	−0.680479
$427$	−8.92001	−0.431669
$428$	−3.60769	−0.174384
$429$	5.79005	0.279546
$430$	−28.5101	−1.37488
$431$	−4.28323	−0.206316	−0.103158	−	0.994665i	$-0.532895\pi$
$431$	−4.28323	−0.206316	−0.103158	+	0.994665i	$0.532895\pi$
$432$	−3.13428	−0.150798
$433$	20.6521	0.992475	0.496237	−	0.868187i	$-0.334715\pi$
$433$	20.6521	0.992475	0.496237	+	0.868187i	$0.334715\pi$
$434$	−1.36117	−0.0653385
$435$	−6.54186	−0.313658
$436$	−4.50325	−0.215667
$437$	−6.95539	−0.332721
$438$	−11.4997	−0.549475
$439$	0.778685	0.0371646	0.0185823	−	0.999827i	$-0.494085\pi$
$439$	0.778685	0.0371646	0.0185823	+	0.999827i	$0.494085\pi$
$440$	39.5218	1.88413
$441$	1.00000	0.0476190
$442$	1.52799	0.0726791
$443$	−16.5756	−0.787530	−0.393765	−	0.919211i	$-0.628828\pi$
$443$	−16.5756	−0.787530	−0.393765	+	0.919211i	$0.628828\pi$
$444$	−3.02748	−0.143678
$445$	−6.32873	−0.300011
$446$	−21.1300	−1.00054
$447$	8.56029	0.404888
$448$	−8.87909	−0.419498
$449$	−26.7221	−1.26110	−0.630548	−	0.776151i	$-0.717170\pi$
$449$	−26.7221	−1.26110	−0.630548	+	0.776151i	$0.717170\pi$
$450$	0.305636	0.0144078
$451$	−26.0565	−1.22695
$452$	0.185382	0.00871965
$453$	−6.04050	−0.283807
$454$	−18.2115	−0.854706
$455$	−2.10946	−0.0988931
$456$	−6.22235	−0.291388
$457$	33.8676	1.58426	0.792131	−	0.610352i	$-0.208972\pi$
$457$	33.8676	1.58426	0.792131	+	0.610352i	$0.208972\pi$
$458$	−18.4710	−0.863094
$459$	−1.23639	−0.0577099
$460$	−2.69915	−0.125849
$461$	−13.9009	−0.647430	−0.323715	−	0.946155i	$-0.604932\pi$
$461$	−13.9009	−0.647430	−0.323715	+	0.946155i	$0.604932\pi$
$462$	7.65584	0.356182
$463$	29.8241	1.38604	0.693021	−	0.720917i	$-0.256279\pi$
$463$	29.8241	1.38604	0.693021	+	0.720917i	$0.256279\pi$
$464$	9.39711	0.436250
$465$	−2.32339	−0.107744
$466$	18.9022	0.875626
$467$	28.5379	1.32058	0.660289	−	0.751012i	$-0.270434\pi$
$467$	28.5379	1.32058	0.660289	+	0.751012i	$0.270434\pi$
$468$	−0.353758	−0.0163525
$469$	−6.20360	−0.286456
$470$	18.7541	0.865064
$471$	−6.68764	−0.308150
$472$	14.2357	0.655253
$473$	61.2170	2.81476
$474$	13.3707	0.614139
$475$	0.491909	0.0225703
$476$	−0.452414	−0.0207364
$477$	−7.99545	−0.366086
$478$	20.0652	0.917760
$479$	−18.4212	−0.841685	−0.420843	−	0.907134i	$-0.638266\pi$
$479$	−18.4212	−0.841685	−0.420843	+	0.907134i	$0.638266\pi$
$480$	−4.45591	−0.203384
$481$	7.99886	0.364717
$482$	−7.35294	−0.334917
$483$	−3.38067	−0.153826
$484$	−9.09967	−0.413621
$485$	−24.3106	−1.10389
$486$	−1.27831	−0.0579855
$487$	−31.9159	−1.44625	−0.723123	−	0.690719i	$-0.757294\pi$
$487$	−31.9159	−1.44625	−0.723123	+	0.690719i	$0.757294\pi$
$488$	26.9775	1.22121
$489$	−23.8324	−1.07774
$490$	−2.78922	−0.126004
$491$	−10.4444	−0.471348	−0.235674	−	0.971832i	$-0.575730\pi$
$491$	−10.4444	−0.471348	−0.235674	+	0.971832i	$0.575730\pi$
$492$	1.59199	0.0717724
$493$	3.70692	0.166951
$494$	2.54263	0.114398
$495$	13.0677	0.587351
$496$	3.33744	0.149856
$497$	−10.9871	−0.492837
$498$	−13.8496	−0.620616
$499$	−30.5035	−1.36553	−0.682763	−	0.730640i	$-0.739222\pi$
$499$	−30.5035	−1.36553	−0.682763	+	0.730640i	$0.739222\pi$
$500$	4.18293	0.187066
$501$	−4.27854	−0.191151
$502$	−13.0260	−0.581378
$503$	−22.5821	−1.00689	−0.503444	−	0.864028i	$-0.667934\pi$
$503$	−22.5821	−1.00689	−0.503444	+	0.864028i	$0.667934\pi$
$504$	−3.02438	−0.134717
$505$	−10.6889	−0.475648
$506$	−25.8819	−1.15059
$507$	−12.0653	−0.535841
$508$	−1.51502	−0.0672181
$509$	4.02696	0.178492	0.0892459	−	0.996010i	$-0.471554\pi$
$509$	4.02696	0.178492	0.0892459	+	0.996010i	$0.471554\pi$
$510$	3.44857	0.152705
$511$	−8.99596	−0.397958
$512$	25.3592	1.12073
$513$	−2.05740	−0.0908363
$514$	3.79418	0.167354
$515$	7.04778	0.310562
$516$	−3.74021	−0.164653
$517$	−40.2690	−1.77103
$518$	10.5764	0.464702
$519$	9.15834	0.402007
$520$	6.37981	0.279773
$521$	−11.4242	−0.500503	−0.250252	−	0.968181i	$-0.580513\pi$
$521$	−11.4242	−0.500503	−0.250252	+	0.968181i	$0.580513\pi$
$522$	3.83260	0.167749
$523$	−11.5693	−0.505891	−0.252945	−	0.967481i	$-0.581399\pi$
$523$	−11.5693	−0.505891	−0.252945	+	0.967481i	$0.581399\pi$
$524$	−6.03191	−0.263505
$525$	0.239093	0.0104349
$526$	−7.09960	−0.309557
$527$	1.31654	0.0573493
$528$	−18.7712	−0.816913
$529$	−11.5710	−0.503089
$530$	22.3010	0.968695
$531$	4.70699	0.204266
$532$	−0.752831	−0.0326394
$533$	−4.20618	−0.182190
$534$	3.70774	0.160450
$535$	21.5127	0.930075
$536$	18.7621	0.810398
$537$	−6.24454	−0.269472
$538$	−21.1572	−0.912150
$539$	5.98901	0.257965
$540$	−0.798407	−0.0343580
$541$	34.1986	1.47031	0.735155	−	0.677899i	$-0.237109\pi$
$541$	34.1986	1.47031	0.735155	+	0.677899i	$0.237109\pi$
$542$	3.65231	0.156880
$543$	11.0690	0.475015
$544$	2.52493	0.108255
$545$	26.8529	1.15025
$546$	1.23585	0.0528893
$547$	13.0021	0.555930	0.277965	−	0.960591i	$-0.410340\pi$
$547$	13.0021	0.555930	0.277965	+	0.960591i	$0.410340\pi$
$548$	1.09861	0.0469304
$549$	8.92001	0.380697
$550$	1.83046	0.0780509
$551$	6.16843	0.262784
$552$	10.2244	0.435181
$553$	10.4597	0.444791
$554$	23.8530	1.01342
$555$	18.0529	0.766302
$556$	5.49575	0.233072
$557$	−13.2448	−0.561199	−0.280600	−	0.959825i	$-0.590533\pi$
$557$	−13.2448	−0.561199	−0.280600	+	0.959825i	$0.590533\pi$
$558$	1.36117	0.0576231
$559$	9.88196	0.417962
$560$	6.83884	0.288994
$561$	−7.40478	−0.312630
$562$	−26.2117	−1.10567
$563$	−6.45018	−0.271843	−0.135921	−	0.990720i	$-0.543399\pi$
$563$	−6.45018	−0.271843	−0.135921	+	0.990720i	$0.543399\pi$
$564$	2.46034	0.103599
$565$	−1.10544	−0.0465060
$566$	30.8088	1.29499
$567$	−1.00000	−0.0419961
$568$	33.2291	1.39426
$569$	−44.9605	−1.88484	−0.942421	−	0.334429i	$-0.891456\pi$
$569$	−44.9605	−1.88484	−0.942421	+	0.334429i	$0.891456\pi$
$570$	5.73853	0.240360
$571$	−16.3115	−0.682613	−0.341307	−	0.939952i	$-0.610869\pi$
$571$	−16.3115	−0.682613	−0.341307	+	0.939952i	$0.610869\pi$
$572$	−2.11866	−0.0885857
$573$	1.88737	0.0788462
$574$	−5.56158	−0.232136
$575$	−0.808295	−0.0337082
$576$	8.87909	0.369962
$577$	15.8524	0.659943	0.329972	−	0.943991i	$-0.392961\pi$
$577$	15.8524	0.659943	0.329972	+	0.943991i	$0.392961\pi$
$578$	19.7772	0.822624
$579$	−12.0286	−0.499892
$580$	2.39376	0.0993955
$581$	−10.8343	−0.449482
$582$	14.2426	0.590374
$583$	−47.8848	−1.98319
$584$	27.2072	1.12584
$585$	2.10946	0.0872155
$586$	−13.5057	−0.557917
$587$	−21.2401	−0.876671	−0.438335	−	0.898811i	$-0.644432\pi$
$587$	−21.2401	−0.876671	−0.438335	+	0.898811i	$0.644432\pi$
$588$	−0.365914	−0.0150901
$589$	2.19076	0.0902686
$590$	−13.1288	−0.540505
$591$	−23.8328	−0.980351
$592$	−25.9322	−1.06581
$593$	32.9508	1.35313	0.676563	−	0.736384i	$-0.263469\pi$
$593$	32.9508	1.35313	0.676563	+	0.736384i	$0.263469\pi$
$594$	−7.65584	−0.314123
$595$	2.69775	0.110597
$596$	−3.13233	−0.128305
$597$	14.4270	0.590457
$598$	−4.17799	−0.170851
$599$	−15.1266	−0.618055	−0.309027	−	0.951053i	$-0.600004\pi$
$599$	−15.1266	−0.618055	−0.309027	+	0.951053i	$0.600004\pi$
$600$	−0.723107	−0.0295207
$601$	26.6826	1.08841	0.544203	−	0.838954i	$-0.316832\pi$
$601$	26.6826	1.08841	0.544203	+	0.838954i	$0.316832\pi$
$602$	13.0663	0.532544
$603$	6.20360	0.252630
$604$	2.21030	0.0899360
$605$	54.2614	2.20604
$606$	6.26215	0.254383
$607$	0.243853	0.00989769	0.00494885	−	0.999988i	$-0.498425\pi$
$607$	0.243853	0.00989769	0.00494885	+	0.999988i	$0.498425\pi$
$608$	4.20156	0.170396
$609$	2.99817	0.121492
$610$	−24.8798	−1.00736
$611$	−6.50042	−0.262979
$612$	0.452414	0.0182878
$613$	3.17867	0.128385	0.0641926	−	0.997938i	$-0.479553\pi$
$613$	3.17867	0.128385	0.0641926	+	0.997938i	$0.479553\pi$
$614$	24.0860	0.972032
$615$	−9.49305	−0.382797
$616$	−18.1131	−0.729796
$617$	−12.3126	−0.495686	−0.247843	−	0.968800i	$-0.579722\pi$
$617$	−12.3126	−0.495686	−0.247843	+	0.968800i	$0.579722\pi$
$618$	−4.12900	−0.166093
$619$	2.43901	0.0980321	0.0490160	−	0.998798i	$-0.484391\pi$
$619$	2.43901	0.0980321	0.0490160	+	0.998798i	$0.484391\pi$
$620$	0.850160	0.0341432
$621$	3.38067	0.135662
$622$	−35.3837	−1.41876
$623$	2.90049	0.116206
$624$	−3.03015	−0.121303
$625$	−23.7474	−0.949895
$626$	−19.7060	−0.787611
$627$	−12.3218	−0.492085
$628$	2.44710	0.0976501
$629$	−10.2296	−0.407881
$630$	2.78922	0.111125
$631$	41.1057	1.63639	0.818197	−	0.574938i	$-0.194974\pi$
$631$	41.1057	1.63639	0.818197	+	0.574938i	$0.194974\pi$
$632$	−31.6340	−1.25833
$633$	6.56691	0.261011
$634$	14.9411	0.593386
$635$	9.03407	0.358506
$636$	2.92565	0.116009
$637$	0.966778	0.0383051
$638$	22.9535	0.908739
$639$	10.9871	0.434642
$640$	−15.8539	−0.626680
$641$	−20.9000	−0.825502	−0.412751	−	0.910844i	$-0.635432\pi$
$641$	−20.9000	−0.825502	−0.412751	+	0.910844i	$0.635432\pi$
$642$	−12.6034	−0.497416
$643$	20.6451	0.814164	0.407082	−	0.913392i	$-0.366546\pi$
$643$	20.6451	0.814164	0.407082	+	0.913392i	$0.366546\pi$
$644$	1.23704	0.0487461
$645$	22.3029	0.878176
$646$	−3.25171	−0.127937
$647$	−7.34784	−0.288873	−0.144437	−	0.989514i	$-0.546137\pi$
$647$	−7.34784	−0.288873	−0.144437	+	0.989514i	$0.546137\pi$
$648$	3.02438	0.118809
$649$	28.1903	1.10656
$650$	0.295482	0.0115897
$651$	1.06482	0.0417336
$652$	8.72060	0.341525
$653$	13.6659	0.534787	0.267393	−	0.963587i	$-0.413838\pi$
$653$	13.6659	0.534787	0.267393	+	0.963587i	$0.413838\pi$
$654$	−15.7320	−0.615170
$655$	35.9683	1.40540
$656$	13.6364	0.532410
$657$	8.99596	0.350966
$658$	−8.59513	−0.335073
$659$	23.3944	0.911316	0.455658	−	0.890155i	$-0.349404\pi$
$659$	23.3944	0.911316	0.455658	+	0.890155i	$0.349404\pi$
$660$	−4.78167	−0.186126
$661$	−15.0845	−0.586718	−0.293359	−	0.956002i	$-0.594773\pi$
$661$	−15.0845	−0.586718	−0.293359	+	0.956002i	$0.594773\pi$
$662$	−11.8444	−0.460346
$663$	−1.19532	−0.0464223
$664$	32.7670	1.27161
$665$	4.48914	0.174081
$666$	−10.5764	−0.409828
$667$	−10.1358	−0.392461
$668$	1.56558	0.0605741
$669$	16.5296	0.639072
$670$	−17.3032	−0.668481
$671$	53.4221	2.06234
$672$	2.04217	0.0787784
$673$	−40.8109	−1.57314	−0.786571	−	0.617499i	$-0.788146\pi$
$673$	−40.8109	−1.57314	−0.786571	+	0.617499i	$0.788146\pi$
$674$	−7.06723	−0.272220
$675$	−0.239093	−0.00920268
$676$	4.41488	0.169803
$677$	21.8696	0.840518	0.420259	−	0.907404i	$-0.361939\pi$
$677$	21.8696	0.840518	0.420259	+	0.907404i	$0.361939\pi$
$678$	0.647629	0.0248720
$679$	11.1417	0.427579
$680$	−8.15902	−0.312884
$681$	14.2465	0.545926
$682$	8.15209	0.312160
$683$	25.5868	0.979053	0.489527	−	0.871988i	$-0.337170\pi$
$683$	25.5868	0.979053	0.489527	+	0.871988i	$0.337170\pi$
$684$	0.752831	0.0287852
$685$	−6.55104	−0.250302
$686$	1.27831	0.0488062
$687$	14.4495	0.551284
$688$	−32.0372	−1.22141
$689$	−7.72982	−0.294483
$690$	−9.42943	−0.358972
$691$	1.52314	0.0579430	0.0289715	−	0.999580i	$-0.490777\pi$
$691$	1.52314	0.0579430	0.0289715	+	0.999580i	$0.490777\pi$
$692$	−3.35117	−0.127392
$693$	−5.98901	−0.227504
$694$	15.3137	0.581300
$695$	−32.7712	−1.24308
$696$	−9.06761	−0.343707
$697$	5.37920	0.203752
$698$	−12.0541	−0.456256
$699$	−14.7868	−0.559288
$700$	−0.0874875	−0.00330671
$701$	22.2682	0.841059	0.420529	−	0.907279i	$-0.361844\pi$
$701$	22.2682	0.841059	0.420529	+	0.907279i	$0.361844\pi$
$702$	−1.23585	−0.0466440
$703$	−17.0224	−0.642010
$704$	53.1770	2.00418
$705$	−14.6710	−0.552542
$706$	−39.5569	−1.48875
$707$	4.89876	0.184237
$708$	−1.72236	−0.0647301
$709$	−49.5335	−1.86027	−0.930135	−	0.367217i	$-0.880311\pi$
$709$	−49.5335	−1.86027	−0.930135	+	0.367217i	$0.880311\pi$
$710$	−30.6453	−1.15010
$711$	−10.4597	−0.392269
$712$	−8.77220	−0.328752
$713$	−3.59981	−0.134814
$714$	−1.58050	−0.0591487
$715$	12.6336	0.472470
$716$	2.28497	0.0853932
$717$	−15.6966	−0.586200
$718$	−9.00779	−0.336168
$719$	31.8233	1.18681	0.593404	−	0.804905i	$-0.297784\pi$
$719$	31.8233	1.18681	0.593404	+	0.804905i	$0.297784\pi$
$720$	−6.83884	−0.254868
$721$	−3.23004	−0.120293
$722$	18.8770	0.702529
$723$	5.75206	0.213921
$724$	−4.05030	−0.150528
$725$	0.716841	0.0266228
$726$	−31.7895	−1.17982
$727$	13.0638	0.484508	0.242254	−	0.970213i	$-0.422113\pi$
$727$	13.0638	0.484508	0.242254	+	0.970213i	$0.422113\pi$
$728$	−2.92390	−0.108367
$729$	1.00000	0.0370370
$730$	−25.0917	−0.928685
$731$	−12.6379	−0.467428
$732$	−3.26396	−0.120639
$733$	10.6423	0.393081	0.196540	−	0.980496i	$-0.437029\pi$
$733$	10.6423	0.393081	0.196540	+	0.980496i	$0.437029\pi$
$734$	−8.58735	−0.316965
$735$	2.18195	0.0804825
$736$	−6.90391	−0.254482
$737$	37.1535	1.36857
$738$	5.56158	0.204725
$739$	8.79148	0.323400	0.161700	−	0.986840i	$-0.448302\pi$
$739$	8.79148	0.323400	0.161700	+	0.986840i	$0.448302\pi$
$740$	−6.60581	−0.242834
$741$	−1.98905	−0.0730695
$742$	−10.2207	−0.375213
$743$	−21.9301	−0.804536	−0.402268	−	0.915522i	$-0.631778\pi$
$743$	−21.9301	−0.804536	−0.402268	+	0.915522i	$0.631778\pi$
$744$	−3.22042	−0.118066
$745$	18.6781	0.684314
$746$	−28.2283	−1.03351
$747$	10.8343	0.396406
$748$	2.70951	0.0990697
$749$	−9.85939	−0.360254
$750$	14.6130	0.533590
$751$	24.7889	0.904559	0.452280	−	0.891876i	$-0.350611\pi$
$751$	24.7889	0.904559	0.452280	+	0.891876i	$0.350611\pi$
$752$	21.0743	0.768499
$753$	10.1900	0.371343
$754$	3.70528	0.134938
$755$	−13.1801	−0.479672
$756$	0.365914	0.0133082
$757$	−16.8145	−0.611133	−0.305566	−	0.952171i	$-0.598846\pi$
$757$	−16.8145	−0.611133	−0.305566	+	0.952171i	$0.598846\pi$
$758$	−13.4265	−0.487671
$759$	20.2469	0.734916
$760$	−13.5769	−0.492485
$761$	27.7910	1.00742	0.503711	−	0.863872i	$-0.331968\pi$
$761$	27.7910	1.00742	0.503711	+	0.863872i	$0.331968\pi$
$762$	−5.29268	−0.191734
$763$	−12.3068	−0.445538
$764$	−0.690617	−0.0249856
$765$	−2.69775	−0.0975373
$766$	1.27831	0.0461873
$767$	4.55062	0.164313
$768$	−8.47005	−0.305637
$769$	−28.0741	−1.01238	−0.506190	−	0.862422i	$-0.668946\pi$
$769$	−28.0741	−1.01238	−0.506190	+	0.862422i	$0.668946\pi$
$770$	16.7047	0.601994
$771$	−2.96811	−0.106894
$772$	4.40144	0.158411
$773$	10.3229	0.371288	0.185644	−	0.982617i	$-0.440563\pi$
$773$	10.3229	0.371288	0.185644	+	0.982617i	$0.440563\pi$
$774$	−13.0663	−0.469660
$775$	0.254591	0.00914517
$776$	−33.6967	−1.20964
$777$	−8.27373	−0.296819
$778$	−13.4600	−0.482565
$779$	8.95116	0.320708
$780$	−0.771882	−0.0276378
$781$	65.8017	2.35457
$782$	5.34315	0.191071
$783$	−2.99817	−0.107146
$784$	−3.13428	−0.111939
$785$	−14.5921	−0.520815
$786$	−21.0723	−0.751626
$787$	−20.3065	−0.723850	−0.361925	−	0.932207i	$-0.617880\pi$
$787$	−20.3065	−0.723850	−0.361925	+	0.932207i	$0.617880\pi$
$788$	8.72077	0.310664
$789$	5.55388	0.197723
$790$	29.1743	1.03798
$791$	0.506628	0.0180136
$792$	18.1131	0.643620
$793$	8.62367	0.306235
$794$	−46.5858	−1.65327
$795$	−17.4457	−0.618734
$796$	−5.27904	−0.187110
$797$	4.89243	0.173299	0.0866494	−	0.996239i	$-0.472384\pi$
$797$	4.89243	0.173299	0.0866494	+	0.996239i	$0.472384\pi$
$798$	−2.63000	−0.0931010
$799$	8.31327	0.294102
$800$	0.488268	0.0172629
$801$	−2.90049	−0.102484
$802$	39.8320	1.40652
$803$	53.8770	1.90128
$804$	−2.26999	−0.0800563
$805$	−7.37646	−0.259986
$806$	1.31595	0.0463525
$807$	16.5508	0.582617
$808$	−14.8157	−0.521215
$809$	33.8533	1.19022	0.595110	−	0.803644i	$-0.297109\pi$
$809$	33.8533	1.19022	0.595110	+	0.803644i	$0.297109\pi$
$810$	−2.78922	−0.0980031
$811$	−5.86161	−0.205829	−0.102915	−	0.994690i	$-0.532817\pi$
$811$	−5.86161	−0.205829	−0.102915	+	0.994690i	$0.532817\pi$
$812$	−1.09707	−0.0384998
$813$	−2.85713	−0.100204
$814$	−63.3424	−2.22015
$815$	−52.0010	−1.82152
$816$	3.87520	0.135659
$817$	−21.0298	−0.735739
$818$	1.86128	0.0650780
$819$	−0.966778	−0.0337820
$820$	3.47364	0.121305
$821$	5.12307	0.178796	0.0893982	−	0.995996i	$-0.471506\pi$
$821$	5.12307	0.178796	0.0893982	+	0.995996i	$0.471506\pi$
$822$	3.83798	0.133865
$823$	−30.6358	−1.06790	−0.533948	−	0.845517i	$-0.679292\pi$
$823$	−30.6358	−1.06790	−0.533948	+	0.845517i	$0.679292\pi$
$824$	9.76886	0.340314
$825$	−1.43193	−0.0498534
$826$	6.01701	0.209359
$827$	−7.56970	−0.263224	−0.131612	−	0.991301i	$-0.542015\pi$
$827$	−7.56970	−0.263224	−0.131612	+	0.991301i	$0.542015\pi$
$828$	−1.23704	−0.0429900
$829$	8.03813	0.279176	0.139588	−	0.990210i	$-0.455422\pi$
$829$	8.03813	0.279176	0.139588	+	0.990210i	$0.455422\pi$
$830$	−30.2192	−1.04892
$831$	−18.6597	−0.647299
$832$	8.58411	0.297600
$833$	−1.23639	−0.0428385
$834$	19.1993	0.664817
$835$	−9.33557	−0.323071
$836$	4.50872	0.155937
$837$	−1.06482	−0.0368056
$838$	−10.2392	−0.353706
$839$	−9.33675	−0.322340	−0.161170	−	0.986927i	$-0.551527\pi$
$839$	−9.33675	−0.322340	−0.161170	+	0.986927i	$0.551527\pi$
$840$	−6.59905	−0.227689
$841$	−20.0110	−0.690033
$842$	4.18770	0.144318
$843$	20.5049	0.706226
$844$	−2.40293	−0.0827121
$845$	−26.3260	−0.905641
$846$	8.59513	0.295507
$847$	−24.8683	−0.854485
$848$	25.0600	0.860562
$849$	−24.1011	−0.827148
$850$	−0.377886	−0.0129614
$851$	27.9708	0.958827
$852$	−4.02033	−0.137734
$853$	−35.2938	−1.20844	−0.604219	−	0.796818i	$-0.706515\pi$
$853$	−35.2938	−1.20844	−0.604219	+	0.796818i	$0.706515\pi$
$854$	11.4026	0.390188
$855$	−4.48914	−0.153525
$856$	29.8185	1.01918
$857$	46.3593	1.58360	0.791801	−	0.610779i	$-0.209144\pi$
$857$	46.3593	1.58360	0.791801	+	0.610779i	$0.209144\pi$
$858$	−7.40150	−0.252683
$859$	42.5615	1.45218	0.726090	−	0.687599i	$-0.241335\pi$
$859$	42.5615	1.45218	0.726090	+	0.687599i	$0.241335\pi$
$860$	−8.16095	−0.278286
$861$	4.35072	0.148272
$862$	5.47531	0.186490
$863$	55.1959	1.87889	0.939446	−	0.342697i	$-0.111340\pi$
$863$	55.1959	1.87889	0.939446	+	0.342697i	$0.111340\pi$
$864$	−2.04217	−0.0694760
$865$	19.9831	0.679444
$866$	−26.3998	−0.897102
$867$	−15.4713	−0.525434
$868$	−0.389633	−0.0132250
$869$	−62.6432	−2.12502
$870$	8.36255	0.283517
$871$	5.99751	0.203218
$872$	37.2206	1.26045
$873$	−11.1417	−0.377089
$874$	8.89117	0.300748
$875$	11.4314	0.386453
$876$	−3.29175	−0.111218
$877$	−8.98312	−0.303338	−0.151669	−	0.988431i	$-0.548465\pi$
$877$	−8.98312	−0.303338	−0.151669	+	0.988431i	$0.548465\pi$
$878$	−0.995404	−0.0335933
$879$	10.5653	0.356358
$880$	−40.9579	−1.38069
$881$	−35.2913	−1.18899	−0.594497	−	0.804098i	$-0.702649\pi$
$881$	−35.2913	−1.18899	−0.594497	+	0.804098i	$0.702649\pi$
$882$	−1.27831	−0.0430431
$883$	7.02651	0.236461	0.118230	−	0.992986i	$-0.462278\pi$
$883$	7.02651	0.236461	0.118230	+	0.992986i	$0.462278\pi$
$884$	0.437384	0.0147108
$885$	10.2704	0.345237
$886$	21.1888	0.711851
$887$	22.5249	0.756312	0.378156	−	0.925742i	$-0.376558\pi$
$887$	22.5249	0.756312	0.378156	+	0.925742i	$0.376558\pi$
$888$	25.0229	0.839714
$889$	−4.14036	−0.138863
$890$	8.09011	0.271181
$891$	5.98901	0.200640
$892$	−6.04843	−0.202516
$893$	13.8335	0.462922
$894$	−10.9427	−0.365980
$895$	−13.6253	−0.455443
$896$	7.26592	0.242737
$897$	3.26836	0.109127
$898$	34.1593	1.13991
$899$	3.19252	0.106476
$900$	0.0874875	0.00291625
$901$	9.88552	0.329334
$902$	33.3084	1.10905
$903$	−10.2215	−0.340152
$904$	−1.53223	−0.0509614
$905$	24.1520	0.802839
$906$	7.72165	0.256535
$907$	−21.1718	−0.702997	−0.351498	−	0.936188i	$-0.614328\pi$
$907$	−21.1718	−0.702997	−0.351498	+	0.936188i	$0.614328\pi$
$908$	−5.21299	−0.172999
$909$	−4.89876	−0.162482
$910$	2.69655	0.0893899
$911$	38.4154	1.27276	0.636380	−	0.771376i	$-0.280431\pi$
$911$	38.4154	1.27276	0.636380	+	0.771376i	$0.280431\pi$
$912$	6.44846	0.213530
$913$	64.8867	2.14744
$914$	−43.2935	−1.43202
$915$	19.4630	0.643427
$916$	−5.28729	−0.174697
$917$	−16.4845	−0.544366
$918$	1.58050	0.0521642
$919$	44.8426	1.47922	0.739611	−	0.673035i	$-0.235010\pi$
$919$	44.8426	1.47922	0.739611	+	0.673035i	$0.235010\pi$
$920$	22.3092	0.735513
$921$	−18.8420	−0.620865
$922$	17.7697	0.585214
$923$	10.6221	0.349629
$924$	2.19147	0.0720939
$925$	−1.97819	−0.0650425
$926$	−38.1245	−1.25285
$927$	3.23004	0.106088
$928$	6.12278	0.200990
$929$	35.8474	1.17611	0.588057	−	0.808819i	$-0.299893\pi$
$929$	35.8474	1.17611	0.588057	+	0.808819i	$0.299893\pi$
$930$	2.97002	0.0973906
$931$	−2.05740	−0.0674285
$932$	5.41070	0.177233
$933$	27.6800	0.906202
$934$	−36.4804	−1.19368
$935$	−16.1569	−0.528386
$936$	2.92390	0.0955708
$937$	−25.5694	−0.835317	−0.417659	−	0.908604i	$-0.637149\pi$
$937$	−25.5694	−0.835317	−0.417659	+	0.908604i	$0.637149\pi$
$938$	7.93015	0.258929
$939$	15.4156	0.503071
$940$	5.36833	0.175096
$941$	−32.9939	−1.07557	−0.537785	−	0.843082i	$-0.680739\pi$
$941$	−32.9939	−1.07557	−0.537785	+	0.843082i	$0.680739\pi$
$942$	8.54891	0.278538
$943$	−14.7084	−0.478970
$944$	−14.7530	−0.480170
$945$	−2.18195	−0.0709788
$946$	−78.2545	−2.54427
$947$	17.2382	0.560166	0.280083	−	0.959976i	$-0.409638\pi$
$947$	17.2382	0.560166	0.280083	+	0.959976i	$0.409638\pi$
$948$	3.82735	0.124306
$949$	8.69710	0.282320
$950$	−0.628814	−0.0204014
$951$	−11.6881	−0.379013
$952$	3.73932	0.121192
$953$	38.0555	1.23274	0.616369	−	0.787457i	$-0.288603\pi$
$953$	38.0555	1.23274	0.616369	+	0.787457i	$0.288603\pi$
$954$	10.2207	0.330907
$955$	4.11816	0.133260
$956$	5.74361	0.185762
$957$	−17.9561	−0.580438
$958$	23.5481	0.760803
$959$	3.00238	0.0969518
$960$	19.3737	0.625285
$961$	−29.8662	−0.963424
$962$	−10.2251	−0.329669
$963$	9.85939	0.317714
$964$	−2.10476	−0.0677898
$965$	−26.2458	−0.844883
$966$	4.32156	0.139044
$967$	29.8575	0.960153	0.480076	−	0.877227i	$-0.340609\pi$
$967$	29.8575	0.960153	0.480076	+	0.877227i	$0.340609\pi$
$968$	75.2112	2.41738
$969$	2.54375	0.0817171
$970$	31.0766	0.997810
$971$	−31.3190	−1.00507	−0.502537	−	0.864556i	$-0.667600\pi$
$971$	−31.3190	−1.00507	−0.502537	+	0.864556i	$0.667600\pi$
$972$	−0.365914	−0.0117367
$973$	15.0192	0.481495
$974$	40.7985	1.30727
$975$	−0.231150	−0.00740271
$976$	−27.9578	−0.894907
$977$	4.78653	0.153135	0.0765673	−	0.997064i	$-0.475604\pi$
$977$	4.78653	0.153135	0.0765673	+	0.997064i	$0.475604\pi$
$978$	30.4652	0.974170
$979$	−17.3711	−0.555183
$980$	−0.798407	−0.0255042
$981$	12.3068	0.392927
$982$	13.3512	0.426054
$983$	8.85366	0.282388	0.141194	−	0.989982i	$-0.454906\pi$
$983$	8.85366	0.282388	0.141194	+	0.989982i	$0.454906\pi$
$984$	−13.1582	−0.419469
$985$	−52.0020	−1.65692
$986$	−4.73861	−0.150908
$987$	6.72380	0.214021
$988$	0.727821	0.0231551
$989$	34.5557	1.09881
$990$	−16.7047	−0.530909
$991$	−20.7524	−0.659221	−0.329610	−	0.944117i	$-0.606917\pi$
$991$	−20.7524	−0.659221	−0.329610	+	0.944117i	$0.606917\pi$
$992$	2.17454	0.0690419
$993$	9.26565	0.294036
$994$	14.0449	0.445478
$995$	31.4789	0.997950
$996$	−3.96442	−0.125617
$997$	10.7970	0.341945	0.170973	−	0.985276i	$-0.445309\pi$
$997$	10.7970	0.341945	0.170973	+	0.985276i	$0.445309\pi$
$998$	38.9931	1.23431
$999$	8.27373	0.261769

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8043.2.a.p.1.13	✓	41

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8043.2.a.p.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-1.27831 q^{2} +1.00000 q^{3} -0.365914 q^{4} +2.18195 q^{5} -1.27831 q^{6} -1.00000 q^{7} +3.02438 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-1.27831 q^{2} +1.00000 q^{3} -0.365914 q^{4} +2.18195 q^{5} -1.27831 q^{6} -1.00000 q^{7} +3.02438 q^{8} +1.00000 q^{9} -2.78922 q^{10} +5.98901 q^{11} -0.365914 q^{12} +0.966778 q^{13} +1.27831 q^{14} +2.18195 q^{15} -3.13428 q^{16} -1.23639 q^{17} -1.27831 q^{18} -2.05740 q^{19} -0.798407 q^{20} -1.00000 q^{21} -7.65584 q^{22} +3.38067 q^{23} +3.02438 q^{24} -0.239093 q^{25} -1.23585 q^{26} +1.00000 q^{27} +0.365914 q^{28} -2.99817 q^{29} -2.78922 q^{30} -1.06482 q^{31} -2.04217 q^{32} +5.98901 q^{33} +1.58050 q^{34} -2.18195 q^{35} -0.365914 q^{36} +8.27373 q^{37} +2.63000 q^{38} +0.966778 q^{39} +6.59905 q^{40} -4.35072 q^{41} +1.27831 q^{42} +10.2215 q^{43} -2.19147 q^{44} +2.18195 q^{45} -4.32156 q^{46} -6.72380 q^{47} -3.13428 q^{48} +1.00000 q^{49} +0.305636 q^{50} -1.23639 q^{51} -0.353758 q^{52} -7.99545 q^{53} -1.27831 q^{54} +13.0677 q^{55} -3.02438 q^{56} -2.05740 q^{57} +3.83260 q^{58} +4.70699 q^{59} -0.798407 q^{60} +8.92001 q^{61} +1.36117 q^{62} -1.00000 q^{63} +8.87909 q^{64} +2.10946 q^{65} -7.65584 q^{66} +6.20360 q^{67} +0.452414 q^{68} +3.38067 q^{69} +2.78922 q^{70} +10.9871 q^{71} +3.02438 q^{72} +8.99596 q^{73} -10.5764 q^{74} -0.239093 q^{75} +0.752831 q^{76} -5.98901 q^{77} -1.23585 q^{78} -10.4597 q^{79} -6.83884 q^{80} +1.00000 q^{81} +5.56158 q^{82} +10.8343 q^{83} +0.365914 q^{84} -2.69775 q^{85} -13.0663 q^{86} -2.99817 q^{87} +18.1131 q^{88} -2.90049 q^{89} -2.78922 q^{90} -0.966778 q^{91} -1.23704 q^{92} -1.06482 q^{93} +8.59513 q^{94} -4.48914 q^{95} -2.04217 q^{96} -11.1417 q^{97} -1.27831 q^{98} +5.98901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9}+O(q^{10}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9	\( 41 q + 7 q^{2} + 41 q^{3} + 45 q^{4} + 17 q^{5} + 7 q^{6} - 41 q^{7} + 12 q^{8} + 41 q^{9} + 18 q^{10} + 8 q^{11} + 45 q^{12} + 23 q^{13} - 7 q^{14} + 17 q^{15} + 37 q^{16} + 15 q^{17} + 7 q^{18} + 15 q^{19} + 53 q^{20} - 41 q^{21} + 13 q^{22} + 44 q^{23} + 12 q^{24} + 58 q^{25} + 9 q^{26} + 41 q^{27} - 45 q^{28} + 21 q^{29} + 18 q^{30} + 39 q^{31} + 61 q^{32} + 8 q^{33} + 9 q^{34} - 17 q^{35} + 45 q^{36} + 11 q^{37} + 44 q^{38} + 23 q^{39} + 24 q^{40} + 17 q^{41} - 7 q^{42} + 7 q^{43} + 30 q^{44} + 17 q^{45} - 12 q^{46} + 36 q^{47} + 37 q^{48} + 41 q^{49} + 28 q^{50} + 15 q^{51} + 58 q^{52} + 26 q^{53} + 7 q^{54} + 32 q^{55} - 12 q^{56} + 15 q^{57} - 4 q^{58} + 33 q^{59} + 53 q^{60} + 59 q^{61} - q^{62} - 41 q^{63} + 16 q^{64} + 72 q^{65} + 13 q^{66} + 12 q^{67} + 52 q^{68} + 44 q^{69} - 18 q^{70} + 33 q^{71} + 12 q^{72} + 18 q^{73} + 42 q^{74} + 58 q^{75} + 7 q^{76} - 8 q^{77} + 9 q^{78} + 22 q^{79} + 69 q^{80} + 41 q^{81} + 41 q^{82} + 32 q^{83} - 45 q^{84} - 44 q^{85} + 11 q^{86} + 21 q^{87} + 52 q^{88} + 63 q^{89} + 18 q^{90} - 23 q^{91} + 52 q^{92} + 39 q^{93} + 17 q^{94} + 37 q^{95} + 61 q^{96} + 8 q^{97} + 7 q^{98} + 8 q^{99}+O(q^{100}) \) 41 * q + 7 * q^2 + 41 * q^3 + 45 * q^4 + 17 * q^5 + 7 * q^6 - 41 * q^7 + 12 * q^8 + 41 * q^9 + 18 * q^10 + 8 * q^11 + 45 * q^12 + 23 * q^13 - 7 * q^14 + 17 * q^15 + 37 * q^16 + 15 * q^17 + 7 * q^18 + 15 * q^19 + 53 * q^20 - 41 * q^21 + 13 * q^22 + 44 * q^23 + 12 * q^24 + 58 * q^25 + 9 * q^26 + 41 * q^27 - 45 * q^28 + 21 * q^29 + 18 * q^30 + 39 * q^31 + 61 * q^32 + 8 * q^33 + 9 * q^34 - 17 * q^35 + 45 * q^36 + 11 * q^37 + 44 * q^38 + 23 * q^39 + 24 * q^40 + 17 * q^41 - 7 * q^42 + 7 * q^43 + 30 * q^44 + 17 * q^45 - 12 * q^46 + 36 * q^47 + 37 * q^48 + 41 * q^49 + 28 * q^50 + 15 * q^51 + 58 * q^52 + 26 * q^53 + 7 * q^54 + 32 * q^55 - 12 * q^56 + 15 * q^57 - 4 * q^58 + 33 * q^59 + 53 * q^60 + 59 * q^61 - q^62 - 41 * q^63 + 16 * q^64 + 72 * q^65 + 13 * q^66 + 12 * q^67 + 52 * q^68 + 44 * q^69 - 18 * q^70 + 33 * q^71 + 12 * q^72 + 18 * q^73 + 42 * q^74 + 58 * q^75 + 7 * q^76 - 8 * q^77 + 9 * q^78 + 22 * q^79 + 69 * q^80 + 41 * q^81 + 41 * q^82 + 32 * q^83 - 45 * q^84 - 44 * q^85 + 11 * q^86 + 21 * q^87 + 52 * q^88 + 63 * q^89 + 18 * q^90 - 23 * q^91 + 52 * q^92 + 39 * q^93 + 17 * q^94 + 37 * q^95 + 61 * q^96 + 8 * q^97 + 7 * q^98 + 8 * q^99

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