LMFDB - Embedded newform 8042.2.a.c.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8042,2,Mod(1,8042)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8042, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("8042.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8042 = 2 \cdot 4021 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8042.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:	$64.2156933055$
Analytic rank:	$0$
Dimension:	$86$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	8042.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -2.78277 q^{3} +1.00000 q^{4} -4.36753 q^{5} +2.78277 q^{6} -3.26500 q^{7} -1.00000 q^{8} +4.74379 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -2.78277 q^{3} +1.00000 q^{4} -4.36753 q^{5} +2.78277 q^{6} -3.26500 q^{7} -1.00000 q^{8} +4.74379 q^{9} +4.36753 q^{10} -3.11755 q^{11} -2.78277 q^{12} +2.74460 q^{13} +3.26500 q^{14} +12.1538 q^{15} +1.00000 q^{16} -0.733217 q^{17} -4.74379 q^{18} +3.29698 q^{19} -4.36753 q^{20} +9.08573 q^{21} +3.11755 q^{22} -3.92947 q^{23} +2.78277 q^{24} +14.0753 q^{25} -2.74460 q^{26} -4.85257 q^{27} -3.26500 q^{28} -0.134478 q^{29} -12.1538 q^{30} -0.0430877 q^{31} -1.00000 q^{32} +8.67541 q^{33} +0.733217 q^{34} +14.2600 q^{35} +4.74379 q^{36} +5.10334 q^{37} -3.29698 q^{38} -7.63758 q^{39} +4.36753 q^{40} -7.00654 q^{41} -9.08573 q^{42} +6.34974 q^{43} -3.11755 q^{44} -20.7187 q^{45} +3.92947 q^{46} +3.45793 q^{47} -2.78277 q^{48} +3.66020 q^{49} -14.0753 q^{50} +2.04037 q^{51} +2.74460 q^{52} -9.77167 q^{53} +4.85257 q^{54} +13.6160 q^{55} +3.26500 q^{56} -9.17474 q^{57} +0.134478 q^{58} -0.605095 q^{59} +12.1538 q^{60} -9.60040 q^{61} +0.0430877 q^{62} -15.4885 q^{63} +1.00000 q^{64} -11.9871 q^{65} -8.67541 q^{66} +2.80505 q^{67} -0.733217 q^{68} +10.9348 q^{69} -14.2600 q^{70} -1.07101 q^{71} -4.74379 q^{72} +10.9618 q^{73} -5.10334 q^{74} -39.1683 q^{75} +3.29698 q^{76} +10.1788 q^{77} +7.63758 q^{78} -4.01696 q^{79} -4.36753 q^{80} -0.727798 q^{81} +7.00654 q^{82} +3.72621 q^{83} +9.08573 q^{84} +3.20234 q^{85} -6.34974 q^{86} +0.374222 q^{87} +3.11755 q^{88} -3.02088 q^{89} +20.7187 q^{90} -8.96111 q^{91} -3.92947 q^{92} +0.119903 q^{93} -3.45793 q^{94} -14.3997 q^{95} +2.78277 q^{96} -15.4949 q^{97} -3.66020 q^{98} -14.7890 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9}+O(q^{10}) $ 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9} + 4 q^{10} + 13 q^{11} + 12 q^{12} + 45 q^{13} - 35 q^{14} + 17 q^{15} + 86 q^{16} + 5 q^{17} - 72 q^{18} + 47 q^{19} - 4 q^{20} + 15 q^{21} - 13 q^{22} + 6 q^{23} - 12 q^{24} + 112 q^{25} - 45 q^{26} + 51 q^{27} + 35 q^{28} - 14 q^{29} - 17 q^{30} + 24 q^{31} - 86 q^{32} + 43 q^{33} - 5 q^{34} + 42 q^{35} + 72 q^{36} + 61 q^{37} - 47 q^{38} + 20 q^{39} + 4 q^{40} - 16 q^{41} - 15 q^{42} + 72 q^{43} + 13 q^{44} + 6 q^{45} - 6 q^{46} + 11 q^{47} + 12 q^{48} + 89 q^{49} - 112 q^{50} + 56 q^{51} + 45 q^{52} - 7 q^{53} - 51 q^{54} + 48 q^{55} - 35 q^{56} + 65 q^{57} + 14 q^{58} + 24 q^{59} + 17 q^{60} + 31 q^{61} - 24 q^{62} + 98 q^{63} + 86 q^{64} - 9 q^{65} - 43 q^{66} + 157 q^{67} + 5 q^{68} + q^{69} - 42 q^{70} - 11 q^{71} - 72 q^{72} + 74 q^{73} - 61 q^{74} + 76 q^{75} + 47 q^{76} - 13 q^{77} - 20 q^{78} + 57 q^{79} - 4 q^{80} + 34 q^{81} + 16 q^{82} + 65 q^{83} + 15 q^{84} + 102 q^{85} - 72 q^{86} + 49 q^{87} - 13 q^{88} - 34 q^{89} - 6 q^{90} + 91 q^{91} + 6 q^{92} + 57 q^{93} - 11 q^{94} - 13 q^{95} - 12 q^{96} + 64 q^{97} - 89 q^{98} + 56 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9 + 4 * q^10 + 13 * q^11 + 12 * q^12 + 45 * q^13 - 35 * q^14 + 17 * q^15 + 86 * q^16 + 5 * q^17 - 72 * q^18 + 47 * q^19 - 4 * q^20 + 15 * q^21 - 13 * q^22 + 6 * q^23 - 12 * q^24 + 112 * q^25 - 45 * q^26 + 51 * q^27 + 35 * q^28 - 14 * q^29 - 17 * q^30 + 24 * q^31 - 86 * q^32 + 43 * q^33 - 5 * q^34 + 42 * q^35 + 72 * q^36 + 61 * q^37 - 47 * q^38 + 20 * q^39 + 4 * q^40 - 16 * q^41 - 15 * q^42 + 72 * q^43 + 13 * q^44 + 6 * q^45 - 6 * q^46 + 11 * q^47 + 12 * q^48 + 89 * q^49 - 112 * q^50 + 56 * q^51 + 45 * q^52 - 7 * q^53 - 51 * q^54 + 48 * q^55 - 35 * q^56 + 65 * q^57 + 14 * q^58 + 24 * q^59 + 17 * q^60 + 31 * q^61 - 24 * q^62 + 98 * q^63 + 86 * q^64 - 9 * q^65 - 43 * q^66 + 157 * q^67 + 5 * q^68 + q^69 - 42 * q^70 - 11 * q^71 - 72 * q^72 + 74 * q^73 - 61 * q^74 + 76 * q^75 + 47 * q^76 - 13 * q^77 - 20 * q^78 + 57 * q^79 - 4 * q^80 + 34 * q^81 + 16 * q^82 + 65 * q^83 + 15 * q^84 + 102 * q^85 - 72 * q^86 + 49 * q^87 - 13 * q^88 - 34 * q^89 - 6 * q^90 + 91 * q^91 + 6 * q^92 + 57 * q^93 - 11 * q^94 - 13 * q^95 - 12 * q^96 + 64 * q^97 - 89 * q^98 + 56 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−2.78277	−1.60663	−0.803316	−	0.595553i	$-0.796933\pi$
$3$	−2.78277	−1.60663	−0.803316	+	0.595553i	$0.796933\pi$
$4$	1.00000	0.500000
$5$	−4.36753	−1.95322	−0.976609	−	0.215024i	$-0.931017\pi$
$5$	−4.36753	−1.95322	−0.976609	+	0.215024i	$0.931017\pi$
$6$	2.78277	1.13606
$7$	−3.26500	−1.23405	−0.617026	−	0.786942i	$-0.711663\pi$
$7$	−3.26500	−1.23405	−0.617026	+	0.786942i	$0.711663\pi$
$8$	−1.00000	−0.353553
$9$	4.74379	1.58126
$10$	4.36753	1.38113
$11$	−3.11755	−0.939976	−0.469988	−	0.882673i	$-0.655742\pi$
$11$	−3.11755	−0.939976	−0.469988	+	0.882673i	$0.655742\pi$
$12$	−2.78277	−0.803316
$13$	2.74460	0.761215	0.380607	−	0.924737i	$-0.375715\pi$
$13$	2.74460	0.761215	0.380607	+	0.924737i	$0.375715\pi$
$14$	3.26500	0.872607
$15$	12.1538	3.13810
$16$	1.00000	0.250000
$17$	−0.733217	−0.177831	−0.0889156	−	0.996039i	$-0.528340\pi$
$17$	−0.733217	−0.177831	−0.0889156	+	0.996039i	$0.528340\pi$
$18$	−4.74379	−1.11812
$19$	3.29698	0.756380	0.378190	−	0.925728i	$-0.376547\pi$
$19$	3.29698	0.756380	0.378190	+	0.925728i	$0.376547\pi$
$20$	−4.36753	−0.976609
$21$	9.08573	1.98267
$22$	3.11755	0.664664
$23$	−3.92947	−0.819352	−0.409676	−	0.912231i	$-0.634358\pi$
$23$	−3.92947	−0.819352	−0.409676	+	0.912231i	$0.634358\pi$
$24$	2.78277	0.568030
$25$	14.0753	2.81506
$26$	−2.74460	−0.538260
$27$	−4.85257	−0.933878
$28$	−3.26500	−0.617026
$29$	−0.134478	−0.0249720	−0.0124860	−	0.999922i	$-0.503975\pi$
$29$	−0.134478	−0.0249720	−0.0124860	+	0.999922i	$0.503975\pi$
$30$	−12.1538	−2.21897
$31$	−0.0430877	−0.00773878	−0.00386939	−	0.999993i	$-0.501232\pi$
$31$	−0.0430877	−0.00773878	−0.00386939	+	0.999993i	$0.501232\pi$
$32$	−1.00000	−0.176777
$33$	8.67541	1.51020
$34$	0.733217	0.125746
$35$	14.2600	2.41037
$36$	4.74379	0.790632
$37$	5.10334	0.838983	0.419492	−	0.907759i	$-0.362208\pi$
$37$	5.10334	0.838983	0.419492	+	0.907759i	$0.362208\pi$
$38$	−3.29698	−0.534841
$39$	−7.63758	−1.22299
$40$	4.36753	0.690567
$41$	−7.00654	−1.09424	−0.547119	−	0.837055i	$-0.684275\pi$
$41$	−7.00654	−1.09424	−0.547119	+	0.837055i	$0.684275\pi$
$42$	−9.08573	−1.40196
$43$	6.34974	0.968326	0.484163	−	0.874978i	$-0.339124\pi$
$43$	6.34974	0.968326	0.484163	+	0.874978i	$0.339124\pi$
$44$	−3.11755	−0.469988
$45$	−20.7187	−3.08855
$46$	3.92947	0.579369
$47$	3.45793	0.504392	0.252196	−	0.967676i	$-0.418847\pi$
$47$	3.45793	0.504392	0.252196	+	0.967676i	$0.418847\pi$
$48$	−2.78277	−0.401658
$49$	3.66020	0.522886
$50$	−14.0753	−1.99055
$51$	2.04037	0.285709
$52$	2.74460	0.380607
$53$	−9.77167	−1.34224	−0.671121	−	0.741348i	$-0.734187\pi$
$53$	−9.77167	−1.34224	−0.671121	+	0.741348i	$0.734187\pi$
$54$	4.85257	0.660352
$55$	13.6160	1.83598
$56$	3.26500	0.436304
$57$	−9.17474	−1.21522
$58$	0.134478	0.0176579
$59$	−0.605095	−0.0787767	−0.0393883	−	0.999224i	$-0.512541\pi$
$59$	−0.605095	−0.0787767	−0.0393883	+	0.999224i	$0.512541\pi$
$60$	12.1538	1.56905
$61$	−9.60040	−1.22921	−0.614603	−	0.788837i	$-0.710684\pi$
$61$	−9.60040	−1.22921	−0.614603	+	0.788837i	$0.710684\pi$
$62$	0.0430877	0.00547214
$63$	−15.4885	−1.95136
$64$	1.00000	0.125000
$65$	−11.9871	−1.48682
$66$	−8.67541	−1.06787
$67$	2.80505	0.342692	0.171346	−	0.985211i	$-0.445188\pi$
$67$	2.80505	0.342692	0.171346	+	0.985211i	$0.445188\pi$
$68$	−0.733217	−0.0889156
$69$	10.9348	1.31640
$70$	−14.2600	−1.70439
$71$	−1.07101	−0.127106	−0.0635529	−	0.997978i	$-0.520243\pi$
$71$	−1.07101	−0.127106	−0.0635529	+	0.997978i	$0.520243\pi$
$72$	−4.74379	−0.559062
$73$	10.9618	1.28299	0.641493	−	0.767129i	$-0.278315\pi$
$73$	10.9618	1.28299	0.641493	+	0.767129i	$0.278315\pi$
$74$	−5.10334	−0.593251
$75$	−39.1683	−4.52276
$76$	3.29698	0.378190
$77$	10.1788	1.15998
$78$	7.63758	0.864786
$79$	−4.01696	−0.451943	−0.225971	−	0.974134i	$-0.572556\pi$
$79$	−4.01696	−0.451943	−0.225971	+	0.974134i	$0.572556\pi$
$80$	−4.36753	−0.488304
$81$	−0.727798	−0.0808665
$82$	7.00654	0.773743
$83$	3.72621	0.409004	0.204502	−	0.978866i	$-0.434442\pi$
$83$	3.72621	0.409004	0.204502	+	0.978866i	$0.434442\pi$
$84$	9.08573	0.991334
$85$	3.20234	0.347343
$86$	−6.34974	−0.684710
$87$	0.374222	0.0401208
$88$	3.11755	0.332332
$89$	−3.02088	−0.320212	−0.160106	−	0.987100i	$-0.551184\pi$
$89$	−3.02088	−0.320212	−0.160106	+	0.987100i	$0.551184\pi$
$90$	20.7187	2.18394
$91$	−8.96111	−0.939379
$92$	−3.92947	−0.409676
$93$	0.119903	0.0124334
$94$	−3.45793	−0.356659
$95$	−14.3997	−1.47737
$96$	2.78277	0.284015
$97$	−15.4949	−1.57327	−0.786633	−	0.617421i	$-0.788177\pi$
$97$	−15.4949	−1.57327	−0.786633	+	0.617421i	$0.788177\pi$
$98$	−3.66020	−0.369736
$99$	−14.7890	−1.48635
$100$	14.0753	1.40753
$101$	−15.2192	−1.51436	−0.757181	−	0.653205i	$-0.773424\pi$
$101$	−15.2192	−1.51436	−0.757181	+	0.653205i	$0.773424\pi$
$102$	−2.04037	−0.202027
$103$	4.49261	0.442670	0.221335	−	0.975198i	$-0.428959\pi$
$103$	4.49261	0.442670	0.221335	+	0.975198i	$0.428959\pi$
$104$	−2.74460	−0.269130
$105$	−39.6822	−3.87258
$106$	9.77167	0.949108
$107$	15.0718	1.45704	0.728522	−	0.685022i	$-0.240207\pi$
$107$	15.0718	1.45704	0.728522	+	0.685022i	$0.240207\pi$
$108$	−4.85257	−0.466939
$109$	−10.3524	−0.991580	−0.495790	−	0.868442i	$-0.665121\pi$
$109$	−10.3524	−0.991580	−0.495790	+	0.868442i	$0.665121\pi$
$110$	−13.6160	−1.29823
$111$	−14.2014	−1.34794
$112$	−3.26500	−0.308513
$113$	−8.10425	−0.762384	−0.381192	−	0.924496i	$-0.624486\pi$
$113$	−8.10425	−0.762384	−0.381192	+	0.924496i	$0.624486\pi$
$114$	9.17474	0.859293
$115$	17.1621	1.60037
$116$	−0.134478	−0.0124860
$117$	13.0198	1.20368
$118$	0.605095	0.0557035
$119$	2.39395	0.219453
$120$	−12.1538	−1.10949
$121$	−1.28089	−0.116444
$122$	9.60040	0.869180
$123$	19.4976	1.75804
$124$	−0.0430877	−0.00386939
$125$	−39.6366	−3.54521
$126$	15.4885	1.37982
$127$	5.29846	0.470162	0.235081	−	0.971976i	$-0.424464\pi$
$127$	5.29846	0.470162	0.235081	+	0.971976i	$0.424464\pi$
$128$	−1.00000	−0.0883883
$129$	−17.6699	−1.55574
$130$	11.9871	1.05134
$131$	−1.68600	−0.147307	−0.0736533	−	0.997284i	$-0.523466\pi$
$131$	−1.68600	−0.147307	−0.0736533	+	0.997284i	$0.523466\pi$
$132$	8.67541	0.755098
$133$	−10.7646	−0.933413
$134$	−2.80505	−0.242320
$135$	21.1938	1.82407
$136$	0.733217	0.0628728
$137$	−4.54990	−0.388724	−0.194362	−	0.980930i	$-0.562264\pi$
$137$	−4.54990	−0.388724	−0.194362	+	0.980930i	$0.562264\pi$
$138$	−10.9348	−0.930833
$139$	−3.78163	−0.320753	−0.160377	−	0.987056i	$-0.551271\pi$
$139$	−3.78163	−0.320753	−0.160377	+	0.987056i	$0.551271\pi$
$140$	14.2600	1.20519
$141$	−9.62263	−0.810371
$142$	1.07101	0.0898774
$143$	−8.55642	−0.715524
$144$	4.74379	0.395316
$145$	0.587338	0.0487757
$146$	−10.9618	−0.907208
$147$	−10.1855	−0.840085
$148$	5.10334	0.419492
$149$	−3.03435	−0.248583	−0.124292	−	0.992246i	$-0.539666\pi$
$149$	−3.03435	−0.248583	−0.124292	+	0.992246i	$0.539666\pi$
$150$	39.1683	3.19808
$151$	−11.0635	−0.900338	−0.450169	−	0.892943i	$-0.648636\pi$
$151$	−11.0635	−0.900338	−0.450169	+	0.892943i	$0.648636\pi$
$152$	−3.29698	−0.267421
$153$	−3.47823	−0.281198
$154$	−10.1788	−0.820230
$155$	0.188187	0.0151155
$156$	−7.63758	−0.611496
$157$	−11.2183	−0.895320	−0.447660	−	0.894204i	$-0.647743\pi$
$157$	−11.2183	−0.895320	−0.447660	+	0.894204i	$0.647743\pi$
$158$	4.01696	0.319572
$159$	27.1923	2.15649
$160$	4.36753	0.345283
$161$	12.8297	1.01112
$162$	0.727798	0.0571812
$163$	17.9514	1.40606	0.703029	−	0.711161i	$-0.251830\pi$
$163$	17.9514	1.40606	0.703029	+	0.711161i	$0.251830\pi$
$164$	−7.00654	−0.547119
$165$	−37.8901	−2.94974
$166$	−3.72621	−0.289210
$167$	17.7999	1.37739	0.688697	−	0.725049i	$-0.258183\pi$
$167$	17.7999	1.37739	0.688697	+	0.725049i	$0.258183\pi$
$168$	−9.08573	−0.700979
$169$	−5.46717	−0.420552
$170$	−3.20234	−0.245609
$171$	15.6402	1.19604
$172$	6.34974	0.484163
$173$	3.92053	0.298072	0.149036	−	0.988832i	$-0.452383\pi$
$173$	3.92053	0.298072	0.149036	+	0.988832i	$0.452383\pi$
$174$	−0.374222	−0.0283697
$175$	−45.9558	−3.47393
$176$	−3.11755	−0.234994
$177$	1.68384	0.126565
$178$	3.02088	0.226424
$179$	2.73828	0.204668	0.102334	−	0.994750i	$-0.467369\pi$
$179$	2.73828	0.204668	0.102334	+	0.994750i	$0.467369\pi$
$180$	−20.7187	−1.54428
$181$	7.17351	0.533203	0.266601	−	0.963807i	$-0.414099\pi$
$181$	7.17351	0.533203	0.266601	+	0.963807i	$0.414099\pi$
$182$	8.96111	0.664242
$183$	26.7157	1.97488
$184$	3.92947	0.289685
$185$	−22.2890	−1.63872
$186$	−0.119903	−0.00879172
$187$	2.28584	0.167157
$188$	3.45793	0.252196
$189$	15.8436	1.15246
$190$	14.3997	1.04466
$191$	−17.7616	−1.28519	−0.642593	−	0.766208i	$-0.722141\pi$
$191$	−17.7616	−1.28519	−0.642593	+	0.766208i	$0.722141\pi$
$192$	−2.78277	−0.200829
$193$	−12.3999	−0.892568	−0.446284	−	0.894891i	$-0.647253\pi$
$193$	−12.3999	−0.892568	−0.446284	+	0.894891i	$0.647253\pi$
$194$	15.4949	1.11247
$195$	33.3573	2.38877
$196$	3.66020	0.261443
$197$	−7.82326	−0.557384	−0.278692	−	0.960380i	$-0.589901\pi$
$197$	−7.82326	−0.557384	−0.278692	+	0.960380i	$0.589901\pi$
$198$	14.7890	1.05101
$199$	−7.84733	−0.556283	−0.278141	−	0.960540i	$-0.589718\pi$
$199$	−7.84733	−0.556283	−0.278141	+	0.960540i	$0.589718\pi$
$200$	−14.0753	−0.995274
$201$	−7.80581	−0.550579
$202$	15.2192	1.07082
$203$	0.439071	0.0308168
$204$	2.04037	0.142855
$205$	30.6013	2.13729
$206$	−4.49261	−0.313015
$207$	−18.6406	−1.29561
$208$	2.74460	0.190304
$209$	−10.2785	−0.710979
$210$	39.6822	2.73833
$211$	−17.0065	−1.17078	−0.585388	−	0.810753i	$-0.699058\pi$
$211$	−17.0065	−1.17078	−0.585388	+	0.810753i	$0.699058\pi$
$212$	−9.77167	−0.671121
$213$	2.98038	0.204212
$214$	−15.0718	−1.03029
$215$	−27.7327	−1.89135
$216$	4.85257	0.330176
$217$	0.140681	0.00955006
$218$	10.3524	0.701153
$219$	−30.5042	−2.06128
$220$	13.6160	0.917989
$221$	−2.01239	−0.135368
$222$	14.2014	0.953135
$223$	−8.08309	−0.541283	−0.270642	−	0.962680i	$-0.587236\pi$
$223$	−8.08309	−0.541283	−0.270642	+	0.962680i	$0.587236\pi$
$224$	3.26500	0.218152
$225$	66.7703	4.45135
$226$	8.10425	0.539087
$227$	−11.9799	−0.795133	−0.397566	−	0.917573i	$-0.630145\pi$
$227$	−11.9799	−0.795133	−0.397566	+	0.917573i	$0.630145\pi$
$228$	−9.17474	−0.607612
$229$	3.60531	0.238246	0.119123	−	0.992880i	$-0.461992\pi$
$229$	3.60531	0.238246	0.119123	+	0.992880i	$0.461992\pi$
$230$	−17.1621	−1.13163
$231$	−28.3252	−1.86366
$232$	0.134478	0.00882893
$233$	−15.7848	−1.03409	−0.517047	−	0.855957i	$-0.672969\pi$
$233$	−15.7848	−1.03409	−0.517047	+	0.855957i	$0.672969\pi$
$234$	−13.0198	−0.851132
$235$	−15.1026	−0.985186
$236$	−0.605095	−0.0393883
$237$	11.1783	0.726106
$238$	−2.39395	−0.155177
$239$	23.8660	1.54376	0.771881	−	0.635767i	$-0.219316\pi$
$239$	23.8660	1.54376	0.771881	+	0.635767i	$0.219316\pi$
$240$	12.1538	0.784525
$241$	−10.1267	−0.652321	−0.326160	−	0.945314i	$-0.605755\pi$
$241$	−10.1267	−0.652321	−0.326160	+	0.945314i	$0.605755\pi$
$242$	1.28089	0.0823385
$243$	16.5830	1.06380
$244$	−9.60040	−0.614603
$245$	−15.9860	−1.02131
$246$	−19.4976	−1.24312
$247$	9.04890	0.575768
$248$	0.0430877	0.00273607
$249$	−10.3692	−0.657119
$250$	39.6366	2.50684
$251$	14.6540	0.924955	0.462478	−	0.886631i	$-0.346961\pi$
$251$	14.6540	0.924955	0.462478	+	0.886631i	$0.346961\pi$
$252$	−15.4885	−0.975682
$253$	12.2503	0.770172
$254$	−5.29846	−0.332455
$255$	−8.91138	−0.558052
$256$	1.00000	0.0625000
$257$	17.8500	1.11345	0.556727	−	0.830696i	$-0.312057\pi$
$257$	17.8500	1.11345	0.556727	+	0.830696i	$0.312057\pi$
$258$	17.6699	1.10008
$259$	−16.6624	−1.03535
$260$	−11.9871	−0.743409
$261$	−0.637938	−0.0394873
$262$	1.68600	0.104161
$263$	12.8351	0.791448	0.395724	−	0.918369i	$-0.370494\pi$
$263$	12.8351	0.791448	0.395724	+	0.918369i	$0.370494\pi$
$264$	−8.67541	−0.533935
$265$	42.6780	2.62169
$266$	10.7646	0.660022
$267$	8.40640	0.514463
$268$	2.80505	0.171346
$269$	3.38381	0.206315	0.103157	−	0.994665i	$-0.467105\pi$
$269$	3.38381	0.206315	0.103157	+	0.994665i	$0.467105\pi$
$270$	−21.1938	−1.28981
$271$	−28.7294	−1.74519	−0.872594	−	0.488447i	$-0.837564\pi$
$271$	−28.7294	−1.74519	−0.872594	+	0.488447i	$0.837564\pi$
$272$	−0.733217	−0.0444578
$273$	24.9367	1.50924
$274$	4.54990	0.274870
$275$	−43.8804	−2.64609
$276$	10.9348	0.658198
$277$	31.1705	1.87285	0.936426	−	0.350865i	$-0.114112\pi$
$277$	31.1705	1.87285	0.936426	+	0.350865i	$0.114112\pi$
$278$	3.78163	0.226807
$279$	−0.204399	−0.0122371
$280$	−14.2600	−0.852196
$281$	10.2220	0.609796	0.304898	−	0.952385i	$-0.401378\pi$
$281$	10.2220	0.609796	0.304898	+	0.952385i	$0.401378\pi$
$282$	9.62263	0.573019
$283$	−15.6991	−0.933214	−0.466607	−	0.884465i	$-0.654524\pi$
$283$	−15.6991	−0.933214	−0.466607	+	0.884465i	$0.654524\pi$
$284$	−1.07101	−0.0635529
$285$	40.0709	2.37360
$286$	8.55642	0.505952
$287$	22.8763	1.35035
$288$	−4.74379	−0.279531
$289$	−16.4624	−0.968376
$290$	−0.587338	−0.0344897
$291$	43.1186	2.52766
$292$	10.9618	0.641493
$293$	−12.3158	−0.719495	−0.359748	−	0.933050i	$-0.617137\pi$
$293$	−12.3158	−0.719495	−0.359748	+	0.933050i	$0.617137\pi$
$294$	10.1855	0.594030
$295$	2.64277	0.153868
$296$	−5.10334	−0.296625
$297$	15.1281	0.877824
$298$	3.03435	0.175775
$299$	−10.7848	−0.623703
$300$	−39.1683	−2.26138
$301$	−20.7319	−1.19497
$302$	11.0635	0.636635
$303$	42.3514	2.43302
$304$	3.29698	0.189095
$305$	41.9300	2.40091
$306$	3.47823	0.198837
$307$	−1.13457	−0.0647535	−0.0323767	−	0.999476i	$-0.510308\pi$
$307$	−1.13457	−0.0647535	−0.0323767	+	0.999476i	$0.510308\pi$
$308$	10.1788	0.579990
$309$	−12.5019	−0.711208
$310$	−0.188187	−0.0106883
$311$	−17.2736	−0.979494	−0.489747	−	0.871865i	$-0.662911\pi$
$311$	−17.2736	−0.979494	−0.489747	+	0.871865i	$0.662911\pi$
$312$	7.63758	0.432393
$313$	−11.3761	−0.643015	−0.321507	−	0.946907i	$-0.604189\pi$
$313$	−11.3761	−0.643015	−0.321507	+	0.946907i	$0.604189\pi$
$314$	11.2183	0.633087
$315$	67.6463	3.81144
$316$	−4.01696	−0.225971
$317$	1.16065	0.0651884	0.0325942	−	0.999469i	$-0.489623\pi$
$317$	1.16065	0.0651884	0.0325942	+	0.999469i	$0.489623\pi$
$318$	−27.1923	−1.52487
$319$	0.419243	0.0234731
$320$	−4.36753	−0.244152
$321$	−41.9413	−2.34093
$322$	−12.8297	−0.714972
$323$	−2.41740	−0.134508
$324$	−0.727798	−0.0404332
$325$	38.6311	2.14287
$326$	−17.9514	−0.994234
$327$	28.8083	1.59310
$328$	7.00654	0.386872
$329$	−11.2901	−0.622446
$330$	37.8901	2.08578
$331$	18.7672	1.03154	0.515769	−	0.856728i	$-0.327506\pi$
$331$	18.7672	1.03154	0.515769	+	0.856728i	$0.327506\pi$
$332$	3.72621	0.204502
$333$	24.2092	1.32665
$334$	−17.7999	−0.973965
$335$	−12.2511	−0.669351
$336$	9.08573	0.495667
$337$	−18.2617	−0.994781	−0.497390	−	0.867527i	$-0.665708\pi$
$337$	−18.2617	−0.994781	−0.497390	+	0.867527i	$0.665708\pi$
$338$	5.46717	0.297375
$339$	22.5522	1.22487
$340$	3.20234	0.173671
$341$	0.134328	0.00727427
$342$	−15.6402	−0.845726
$343$	10.9044	0.588784
$344$	−6.34974	−0.342355
$345$	−47.7581	−2.57121
$346$	−3.92053	−0.210769
$347$	−0.263336	−0.0141366	−0.00706831	−	0.999975i	$-0.502250\pi$
$347$	−0.263336	−0.0141366	−0.00706831	+	0.999975i	$0.502250\pi$
$348$	0.374222	0.0200604
$349$	1.19989	0.0642287	0.0321144	−	0.999484i	$-0.489776\pi$
$349$	1.19989	0.0642287	0.0321144	+	0.999484i	$0.489776\pi$
$350$	45.9558	2.45644
$351$	−13.3184	−0.710882
$352$	3.11755	0.166166
$353$	5.56876	0.296395	0.148198	−	0.988958i	$-0.452653\pi$
$353$	5.56876	0.296395	0.148198	+	0.988958i	$0.452653\pi$
$354$	−1.68384	−0.0894951
$355$	4.67768	0.248265
$356$	−3.02088	−0.160106
$357$	−6.66180	−0.352580
$358$	−2.73828	−0.144722
$359$	8.04904	0.424812	0.212406	−	0.977182i	$-0.431870\pi$
$359$	8.04904	0.424812	0.212406	+	0.977182i	$0.431870\pi$
$360$	20.7187	1.09197
$361$	−8.12990	−0.427890
$362$	−7.17351	−0.377031
$363$	3.56441	0.187083
$364$	−8.96111	−0.469690
$365$	−47.8761	−2.50595
$366$	−26.7157	−1.39645
$367$	−22.6472	−1.18218	−0.591088	−	0.806607i	$-0.701301\pi$
$367$	−22.6472	−1.18218	−0.591088	+	0.806607i	$0.701301\pi$
$368$	−3.92947	−0.204838
$369$	−33.2376	−1.73028
$370$	22.2890	1.15875
$371$	31.9045	1.65640
$372$	0.119903	0.00621668
$373$	−17.7569	−0.919415	−0.459708	−	0.888070i	$-0.652046\pi$
$373$	−17.7569	−0.919415	−0.459708	+	0.888070i	$0.652046\pi$
$374$	−2.28584	−0.118198
$375$	110.299	5.69584
$376$	−3.45793	−0.178329
$377$	−0.369089	−0.0190091
$378$	−15.8436	−0.814909
$379$	37.0912	1.90525	0.952623	−	0.304154i	$-0.0983737\pi$
$379$	37.0912	1.90525	0.952623	+	0.304154i	$0.0983737\pi$
$380$	−14.3997	−0.738687
$381$	−14.7444	−0.755377
$382$	17.7616	0.908763
$383$	−6.53919	−0.334137	−0.167069	−	0.985945i	$-0.553430\pi$
$383$	−6.53919	−0.334137	−0.167069	+	0.985945i	$0.553430\pi$
$384$	2.78277	0.142008
$385$	−44.4561	−2.26569
$386$	12.3999	0.631141
$387$	30.1219	1.53118
$388$	−15.4949	−0.786633
$389$	2.35711	0.119510	0.0597552	−	0.998213i	$-0.480968\pi$
$389$	2.35711	0.119510	0.0597552	+	0.998213i	$0.480968\pi$
$390$	−33.3573	−1.68911
$391$	2.88116	0.145706
$392$	−3.66020	−0.184868
$393$	4.69175	0.236667
$394$	7.82326	0.394130
$395$	17.5442	0.882743
$396$	−14.7890	−0.743176
$397$	−13.4473	−0.674901	−0.337450	−	0.941343i	$-0.609564\pi$
$397$	−13.4473	−0.674901	−0.337450	+	0.941343i	$0.609564\pi$
$398$	7.84733	0.393351
$399$	29.9555	1.49965
$400$	14.0753	0.703765
$401$	26.5582	1.32626	0.663128	−	0.748506i	$-0.269229\pi$
$401$	26.5582	1.32626	0.663128	+	0.748506i	$0.269229\pi$
$402$	7.80581	0.389318
$403$	−0.118258	−0.00589087
$404$	−15.2192	−0.757181
$405$	3.17868	0.157950
$406$	−0.439071	−0.0217907
$407$	−15.9099	−0.788625
$408$	−2.04037	−0.101013
$409$	20.6602	1.02158	0.510790	−	0.859706i	$-0.329353\pi$
$409$	20.6602	1.02158	0.510790	+	0.859706i	$0.329353\pi$
$410$	−30.6013	−1.51129
$411$	12.6613	0.624537
$412$	4.49261	0.221335
$413$	1.97563	0.0972146
$414$	18.6406	0.916136
$415$	−16.2743	−0.798875
$416$	−2.74460	−0.134565
$417$	10.5234	0.515333
$418$	10.2785	0.502738
$419$	−26.8045	−1.30949	−0.654743	−	0.755851i	$-0.727223\pi$
$419$	−26.8045	−1.30949	−0.654743	+	0.755851i	$0.727223\pi$
$420$	−39.6822	−1.93629
$421$	−6.85131	−0.333912	−0.166956	−	0.985964i	$-0.553394\pi$
$421$	−6.85131	−0.333912	−0.166956	+	0.985964i	$0.553394\pi$
$422$	17.0065	0.827864
$423$	16.4037	0.797577
$424$	9.77167	0.474554
$425$	−10.3202	−0.500605
$426$	−2.98038	−0.144400
$427$	31.3453	1.51690
$428$	15.0718	0.728522
$429$	23.8105	1.14958
$430$	27.7327	1.33739
$431$	−5.53959	−0.266832	−0.133416	−	0.991060i	$-0.542595\pi$
$431$	−5.53959	−0.266832	−0.133416	+	0.991060i	$0.542595\pi$
$432$	−4.85257	−0.233470
$433$	5.11384	0.245755	0.122878	−	0.992422i	$-0.460788\pi$
$433$	5.11384	0.245755	0.122878	+	0.992422i	$0.460788\pi$
$434$	−0.140681	−0.00675291
$435$	−1.63442	−0.0783647
$436$	−10.3524	−0.495790
$437$	−12.9554	−0.619741
$438$	30.5042	1.45755
$439$	8.98166	0.428671	0.214336	−	0.976760i	$-0.431241\pi$
$439$	8.98166	0.428671	0.214336	+	0.976760i	$0.431241\pi$
$440$	−13.6160	−0.649116
$441$	17.3633	0.826822
$442$	2.01239	0.0957194
$443$	5.64420	0.268164	0.134082	−	0.990970i	$-0.457191\pi$
$443$	5.64420	0.268164	0.134082	+	0.990970i	$0.457191\pi$
$444$	−14.2014	−0.673969
$445$	13.1938	0.625445
$446$	8.08309	0.382745
$447$	8.44388	0.399382
$448$	−3.26500	−0.154257
$449$	−23.5286	−1.11038	−0.555191	−	0.831723i	$-0.687355\pi$
$449$	−23.5286	−1.11038	−0.555191	+	0.831723i	$0.687355\pi$
$450$	−66.7703	−3.14758
$451$	21.8432	1.02856
$452$	−8.10425	−0.381192
$453$	30.7873	1.44651
$454$	11.9799	0.562244
$455$	39.1379	1.83481
$456$	9.17474	0.429646
$457$	38.0044	1.77777	0.888885	−	0.458131i	$-0.151481\pi$
$457$	38.0044	1.77777	0.888885	+	0.458131i	$0.151481\pi$
$458$	−3.60531	−0.168465
$459$	3.55799	0.166073
$460$	17.1621	0.800186
$461$	−32.4326	−1.51054	−0.755268	−	0.655416i	$-0.772493\pi$
$461$	−32.4326	−1.51054	−0.755268	+	0.655416i	$0.772493\pi$
$462$	28.3252	1.31781
$463$	−33.2441	−1.54499	−0.772493	−	0.635024i	$-0.780990\pi$
$463$	−33.2441	−1.54499	−0.772493	+	0.635024i	$0.780990\pi$
$464$	−0.134478	−0.00624300
$465$	−0.523680	−0.0242851
$466$	15.7848	0.731215
$467$	17.4265	0.806401	0.403200	−	0.915112i	$-0.367898\pi$
$467$	17.4265	0.806401	0.403200	+	0.915112i	$0.367898\pi$
$468$	13.0198	0.601841
$469$	−9.15848	−0.422900
$470$	15.1026	0.696632
$471$	31.2180	1.43845
$472$	0.605095	0.0278518
$473$	−19.7956	−0.910204
$474$	−11.1783	−0.513434
$475$	46.4060	2.12925
$476$	2.39395	0.109726
$477$	−46.3548	−2.12244
$478$	−23.8660	−1.09160
$479$	−39.9799	−1.82673	−0.913363	−	0.407146i	$-0.866524\pi$
$479$	−39.9799	−1.82673	−0.913363	+	0.407146i	$0.866524\pi$
$480$	−12.1538	−0.554743
$481$	14.0066	0.638647
$482$	10.1267	0.461260
$483$	−35.7021	−1.62450
$484$	−1.28089	−0.0582221
$485$	67.6743	3.07293
$486$	−16.5830	−0.752221
$487$	−25.2224	−1.14294	−0.571468	−	0.820624i	$-0.693626\pi$
$487$	−25.2224	−1.14294	−0.571468	+	0.820624i	$0.693626\pi$
$488$	9.60040	0.434590
$489$	−49.9544	−2.25902
$490$	15.9860	0.722176
$491$	14.3680	0.648421	0.324211	−	0.945985i	$-0.394901\pi$
$491$	14.3680	0.648421	0.324211	+	0.945985i	$0.394901\pi$
$492$	19.4976	0.879019
$493$	0.0986017	0.00444080
$494$	−9.04890	−0.407129
$495$	64.5914	2.90317
$496$	−0.0430877	−0.00193469
$497$	3.49685	0.156855
$498$	10.3692	0.464654
$499$	24.4553	1.09477	0.547384	−	0.836882i	$-0.315624\pi$
$499$	24.4553	1.09477	0.547384	+	0.836882i	$0.315624\pi$
$500$	−39.6366	−1.77260
$501$	−49.5329	−2.21296
$502$	−14.6540	−0.654042
$503$	−4.69182	−0.209198	−0.104599	−	0.994514i	$-0.533356\pi$
$503$	−4.69182	−0.209198	−0.104599	+	0.994514i	$0.533356\pi$
$504$	15.4885	0.689911
$505$	66.4701	2.95788
$506$	−12.2503	−0.544594
$507$	15.2139	0.675672
$508$	5.29846	0.235081
$509$	22.5963	1.00157	0.500783	−	0.865573i	$-0.333046\pi$
$509$	22.5963	1.00157	0.500783	+	0.865573i	$0.333046\pi$
$510$	8.91138	0.394602
$511$	−35.7903	−1.58327
$512$	−1.00000	−0.0441942
$513$	−15.9989	−0.706367
$514$	−17.8500	−0.787331
$515$	−19.6216	−0.864631
$516$	−17.6699	−0.777872
$517$	−10.7803	−0.474116
$518$	16.6624	0.732103
$519$	−10.9099	−0.478892
$520$	11.9871	0.525670
$521$	−4.89976	−0.214663	−0.107331	−	0.994223i	$-0.534231\pi$
$521$	−4.89976	−0.214663	−0.107331	+	0.994223i	$0.534231\pi$
$522$	0.637938	0.0279218
$523$	−22.3032	−0.975249	−0.487624	−	0.873054i	$-0.662136\pi$
$523$	−22.3032	−0.975249	−0.487624	+	0.873054i	$0.662136\pi$
$524$	−1.68600	−0.0736533
$525$	127.884	5.58133
$526$	−12.8351	−0.559638
$527$	0.0315926	0.00137620
$528$	8.67541	0.377549
$529$	−7.55924	−0.328662
$530$	−42.6780	−1.85381
$531$	−2.87045	−0.124567
$532$	−10.7646	−0.466706
$533$	−19.2302	−0.832950
$534$	−8.40640	−0.363781
$535$	−65.8265	−2.84593
$536$	−2.80505	−0.121160
$537$	−7.61999	−0.328827
$538$	−3.38381	−0.145886
$539$	−11.4109	−0.491501
$540$	21.1938	0.912034
$541$	4.81851	0.207164	0.103582	−	0.994621i	$-0.466970\pi$
$541$	4.81851	0.207164	0.103582	+	0.994621i	$0.466970\pi$
$542$	28.7294	1.23403
$543$	−19.9622	−0.856661
$544$	0.733217	0.0314364
$545$	45.2144	1.93677
$546$	−24.9367	−1.06719
$547$	−28.8973	−1.23556	−0.617780	−	0.786351i	$-0.711968\pi$
$547$	−28.8973	−1.23556	−0.617780	+	0.786351i	$0.711968\pi$
$548$	−4.54990	−0.194362
$549$	−45.5423	−1.94370
$550$	43.8804	1.87107
$551$	−0.443373	−0.0188883
$552$	−10.9348	−0.465416
$553$	13.1154	0.557721
$554$	−31.1705	−1.32431
$555$	62.0250	2.63281
$556$	−3.78163	−0.160377
$557$	16.9780	0.719380	0.359690	−	0.933072i	$-0.382882\pi$
$557$	16.9780	0.719380	0.359690	+	0.933072i	$0.382882\pi$
$558$	0.204399	0.00865291
$559$	17.4275	0.737105
$560$	14.2600	0.602593
$561$	−6.36096	−0.268560
$562$	−10.2220	−0.431191
$563$	5.42232	0.228524	0.114262	−	0.993451i	$-0.463550\pi$
$563$	5.42232	0.228524	0.114262	+	0.993451i	$0.463550\pi$
$564$	−9.62263	−0.405186
$565$	35.3955	1.48910
$566$	15.6991	0.659882
$567$	2.37626	0.0997935
$568$	1.07101	0.0449387
$569$	−36.6814	−1.53776	−0.768881	−	0.639391i	$-0.779186\pi$
$569$	−36.6814	−1.53776	−0.768881	+	0.639391i	$0.779186\pi$
$570$	−40.0709	−1.67839
$571$	8.07612	0.337975	0.168988	−	0.985618i	$-0.445950\pi$
$571$	8.07612	0.337975	0.168988	+	0.985618i	$0.445950\pi$
$572$	−8.55642	−0.357762
$573$	49.4264	2.06482
$574$	−22.8763	−0.954840
$575$	−55.3085	−2.30652
$576$	4.74379	0.197658
$577$	−13.2727	−0.552551	−0.276276	−	0.961078i	$-0.589100\pi$
$577$	−13.2727	−0.552551	−0.276276	+	0.961078i	$0.589100\pi$
$578$	16.4624	0.684745
$579$	34.5062	1.43403
$580$	0.587338	0.0243879
$581$	−12.1661	−0.504733
$582$	−43.1186	−1.78732
$583$	30.4637	1.26168
$584$	−10.9618	−0.453604
$585$	−56.8644	−2.35105
$586$	12.3158	0.508760
$587$	29.3679	1.21214	0.606071	−	0.795411i	$-0.292745\pi$
$587$	29.3679	1.21214	0.606071	+	0.795411i	$0.292745\pi$
$588$	−10.1855	−0.420043
$589$	−0.142059	−0.00585346
$590$	−2.64277	−0.108801
$591$	21.7703	0.895511
$592$	5.10334	0.209746
$593$	−24.5766	−1.00924	−0.504619	−	0.863342i	$-0.668367\pi$
$593$	−24.5766	−1.00924	−0.504619	+	0.863342i	$0.668367\pi$
$594$	−15.1281	−0.620715
$595$	−10.4556	−0.428639
$596$	−3.03435	−0.124292
$597$	21.8373	0.893741
$598$	10.7848	0.441025
$599$	11.6195	0.474759	0.237380	−	0.971417i	$-0.423711\pi$
$599$	11.6195	0.474759	0.237380	+	0.971417i	$0.423711\pi$
$600$	39.1683	1.59904
$601$	−37.8896	−1.54555	−0.772775	−	0.634680i	$-0.781132\pi$
$601$	−37.8896	−1.54555	−0.772775	+	0.634680i	$0.781132\pi$
$602$	20.7319	0.844969
$603$	13.3066	0.541886
$604$	−11.0635	−0.450169
$605$	5.59431	0.227441
$606$	−42.3514	−1.72041
$607$	−19.7543	−0.801801	−0.400901	−	0.916122i	$-0.631303\pi$
$607$	−19.7543	−0.801801	−0.400901	+	0.916122i	$0.631303\pi$
$608$	−3.29698	−0.133710
$609$	−1.22183	−0.0495112
$610$	−41.9300	−1.69770
$611$	9.49064	0.383950
$612$	−3.47823	−0.140599
$613$	−1.06042	−0.0428302	−0.0214151	−	0.999771i	$-0.506817\pi$
$613$	−1.06042	−0.0428302	−0.0214151	+	0.999771i	$0.506817\pi$
$614$	1.13457	0.0457876
$615$	−85.1562	−3.43383
$616$	−10.1788	−0.410115
$617$	34.5568	1.39120	0.695602	−	0.718428i	$-0.255138\pi$
$617$	34.5568	1.39120	0.695602	+	0.718428i	$0.255138\pi$
$618$	12.5019	0.502900
$619$	−20.9560	−0.842293	−0.421147	−	0.906993i	$-0.638372\pi$
$619$	−20.9560	−0.842293	−0.421147	+	0.906993i	$0.638372\pi$
$620$	0.188187	0.00755776
$621$	19.0681	0.765175
$622$	17.2736	0.692607
$623$	9.86316	0.395159
$624$	−7.63758	−0.305748
$625$	102.737	4.10950
$626$	11.3761	0.454680
$627$	28.6027	1.14228
$628$	−11.2183	−0.447660
$629$	−3.74185	−0.149197
$630$	−67.6463	−2.69509
$631$	−44.2350	−1.76097	−0.880483	−	0.474078i	$-0.842781\pi$
$631$	−44.2350	−1.76097	−0.880483	+	0.474078i	$0.842781\pi$
$632$	4.01696	0.159786
$633$	47.3252	1.88101
$634$	−1.16065	−0.0460951
$635$	−23.1412	−0.918329
$636$	27.1923	1.07824
$637$	10.0458	0.398029
$638$	−0.419243	−0.0165980
$639$	−5.08067	−0.200988
$640$	4.36753	0.172642
$641$	33.6782	1.33021	0.665105	−	0.746749i	$-0.268387\pi$
$641$	33.6782	1.33021	0.665105	+	0.746749i	$0.268387\pi$
$642$	41.9413	1.65529
$643$	−46.0220	−1.81493	−0.907464	−	0.420129i	$-0.861985\pi$
$643$	−46.0220	−1.81493	−0.907464	+	0.420129i	$0.861985\pi$
$644$	12.8297	0.505562
$645$	77.1736	3.03871
$646$	2.41740	0.0951114
$647$	−1.36238	−0.0535607	−0.0267803	−	0.999641i	$-0.508525\pi$
$647$	−1.36238	−0.0535607	−0.0267803	+	0.999641i	$0.508525\pi$
$648$	0.727798	0.0285906
$649$	1.88641	0.0740482
$650$	−38.6311	−1.51523
$651$	−0.391483	−0.0153434
$652$	17.9514	0.703029
$653$	−5.64681	−0.220977	−0.110488	−	0.993877i	$-0.535242\pi$
$653$	−5.64681	−0.220977	−0.110488	+	0.993877i	$0.535242\pi$
$654$	−28.8083	−1.12649
$655$	7.36365	0.287722
$656$	−7.00654	−0.273560
$657$	52.0007	2.02874
$658$	11.2901	0.440136
$659$	10.4139	0.405668	0.202834	−	0.979213i	$-0.434985\pi$
$659$	10.4139	0.405668	0.202834	+	0.979213i	$0.434985\pi$
$660$	−37.8901	−1.47487
$661$	−50.4412	−1.96193	−0.980967	−	0.194176i	$-0.937797\pi$
$661$	−50.4412	−1.96193	−0.980967	+	0.194176i	$0.937797\pi$
$662$	−18.7672	−0.729407
$663$	5.60000	0.217486
$664$	−3.72621	−0.144605
$665$	47.0149	1.82316
$666$	−24.2092	−0.938087
$667$	0.528429	0.0204609
$668$	17.7999	0.688697
$669$	22.4933	0.869643
$670$	12.2511	0.473303
$671$	29.9297	1.15542
$672$	−9.08573	−0.350490
$673$	28.6209	1.10326	0.551628	−	0.834090i	$-0.314007\pi$
$673$	28.6209	1.10326	0.551628	+	0.834090i	$0.314007\pi$
$674$	18.2617	0.703416
$675$	−68.3014	−2.62892
$676$	−5.46717	−0.210276
$677$	28.3191	1.08839	0.544195	−	0.838959i	$-0.316835\pi$
$677$	28.3191	1.08839	0.544195	+	0.838959i	$0.316835\pi$
$678$	−22.5522	−0.866114
$679$	50.5907	1.94149
$680$	−3.20234	−0.122804
$681$	33.3372	1.27749
$682$	−0.134328	−0.00514369
$683$	15.8235	0.605469	0.302734	−	0.953075i	$-0.402100\pi$
$683$	15.8235	0.605469	0.302734	+	0.953075i	$0.402100\pi$
$684$	15.6402	0.598018
$685$	19.8718	0.759263
$686$	−10.9044	−0.416333
$687$	−10.0327	−0.382773
$688$	6.34974	0.242082
$689$	−26.8193	−1.02173
$690$	47.7581	1.81812
$691$	−4.54799	−0.173014	−0.0865069	−	0.996251i	$-0.527570\pi$
$691$	−4.54799	−0.173014	−0.0865069	+	0.996251i	$0.527570\pi$
$692$	3.92053	0.149036
$693$	48.2861	1.83424
$694$	0.263336	0.00999610
$695$	16.5164	0.626501
$696$	−0.374222	−0.0141848
$697$	5.13731	0.194590
$698$	−1.19989	−0.0454166
$699$	43.9253	1.66141
$700$	−45.9558	−1.73697
$701$	28.3323	1.07010	0.535048	−	0.844822i	$-0.320294\pi$
$701$	28.3323	1.07010	0.535048	+	0.844822i	$0.320294\pi$
$702$	13.3184	0.502670
$703$	16.8256	0.634590
$704$	−3.11755	−0.117497
$705$	42.0271	1.58283
$706$	−5.56876	−0.209583
$707$	49.6905	1.86880
$708$	1.68384	0.0632826
$709$	36.9052	1.38601	0.693003	−	0.720935i	$-0.256287\pi$
$709$	36.9052	1.38601	0.693003	+	0.720935i	$0.256287\pi$
$710$	−4.67768	−0.175550
$711$	−19.0556	−0.714642
$712$	3.02088	0.113212
$713$	0.169312	0.00634078
$714$	6.66180	0.249312
$715$	37.3704	1.39757
$716$	2.73828	0.102334
$717$	−66.4135	−2.48026
$718$	−8.04904	−0.300387
$719$	−8.35437	−0.311566	−0.155783	−	0.987791i	$-0.549790\pi$
$719$	−8.35437	−0.311566	−0.155783	+	0.987791i	$0.549790\pi$
$720$	−20.7187	−0.772139
$721$	−14.6684	−0.546278
$722$	8.12990	0.302564
$723$	28.1804	1.04804
$724$	7.17351	0.266601
$725$	−1.89282	−0.0702977
$726$	−3.56441	−0.132288
$727$	11.5600	0.428738	0.214369	−	0.976753i	$-0.431230\pi$
$727$	11.5600	0.428738	0.214369	+	0.976753i	$0.431230\pi$
$728$	8.96111	0.332121
$729$	−43.9633	−1.62827
$730$	47.8761	1.77197
$731$	−4.65574	−0.172199
$732$	26.7157	0.987440
$733$	3.06519	0.113216	0.0566078	−	0.998396i	$-0.481972\pi$
$733$	3.06519	0.113216	0.0566078	+	0.998396i	$0.481972\pi$
$734$	22.6472	0.835925
$735$	44.4854	1.64087
$736$	3.92947	0.144842
$737$	−8.74489	−0.322122
$738$	33.2376	1.22349
$739$	25.0419	0.921180	0.460590	−	0.887613i	$-0.347638\pi$
$739$	25.0419	0.921180	0.460590	+	0.887613i	$0.347638\pi$
$740$	−22.2890	−0.819359
$741$	−25.1810	−0.925046
$742$	−31.9045	−1.17125
$743$	14.6721	0.538269	0.269134	−	0.963103i	$-0.413262\pi$
$743$	14.6721	0.538269	0.269134	+	0.963103i	$0.413262\pi$
$744$	−0.119903	−0.00439586
$745$	13.2526	0.485537
$746$	17.7569	0.650125
$747$	17.6764	0.646744
$748$	2.28584	0.0835785
$749$	−49.2093	−1.79807
$750$	−110.299	−4.02757
$751$	24.2778	0.885911	0.442955	−	0.896544i	$-0.353930\pi$
$751$	24.2778	0.885911	0.442955	+	0.896544i	$0.353930\pi$
$752$	3.45793	0.126098
$753$	−40.7788	−1.48606
$754$	0.369089	0.0134414
$755$	48.3203	1.75856
$756$	15.8436	0.576228
$757$	−12.3709	−0.449627	−0.224813	−	0.974402i	$-0.572177\pi$
$757$	−12.3709	−0.449627	−0.224813	+	0.974402i	$0.572177\pi$
$758$	−37.0912	−1.34721
$759$	−34.0898	−1.23738
$760$	14.3997	0.522331
$761$	−31.8090	−1.15307	−0.576537	−	0.817071i	$-0.695596\pi$
$761$	−31.8090	−1.15307	−0.576537	+	0.817071i	$0.695596\pi$
$762$	14.7444	0.534132
$763$	33.8006	1.22366
$764$	−17.7616	−0.642593
$765$	15.1913	0.549241
$766$	6.53919	0.236271
$767$	−1.66074	−0.0599660
$768$	−2.78277	−0.100414
$769$	32.4092	1.16871	0.584353	−	0.811500i	$-0.301348\pi$
$769$	32.4092	1.16871	0.584353	+	0.811500i	$0.301348\pi$
$770$	44.4561	1.60209
$771$	−49.6725	−1.78891
$772$	−12.3999	−0.446284
$773$	26.2329	0.943533	0.471767	−	0.881723i	$-0.343616\pi$
$773$	26.2329	0.943533	0.471767	+	0.881723i	$0.343616\pi$
$774$	−30.1219	−1.08271
$775$	−0.606472	−0.0217851
$776$	15.4949	0.556233
$777$	46.3675	1.66343
$778$	−2.35711	−0.0845066
$779$	−23.1005	−0.827660
$780$	33.3573	1.19438
$781$	3.33894	0.119477
$782$	−2.88116	−0.103030
$783$	0.652566	0.0233208
$784$	3.66020	0.130722
$785$	48.9964	1.74875
$786$	−4.69175	−0.167349
$787$	29.7366	1.06000	0.529998	−	0.847999i	$-0.322193\pi$
$787$	29.7366	1.06000	0.529998	+	0.847999i	$0.322193\pi$
$788$	−7.82326	−0.278692
$789$	−35.7172	−1.27157
$790$	−17.5442	−0.624194
$791$	26.4604	0.940822
$792$	14.7890	0.525505
$793$	−26.3493	−0.935690
$794$	13.4473	0.477227
$795$	−118.763	−4.21209
$796$	−7.84733	−0.278141
$797$	−33.4836	−1.18605	−0.593025	−	0.805184i	$-0.702066\pi$
$797$	−33.4836	−1.18605	−0.593025	+	0.805184i	$0.702066\pi$
$798$	−29.9555	−1.06041
$799$	−2.53541	−0.0896965
$800$	−14.0753	−0.497637
$801$	−14.3304	−0.506341
$802$	−26.5582	−0.937804
$803$	−34.1740	−1.20598
$804$	−7.80581	−0.275290
$805$	−56.0342	−1.97494
$806$	0.118258	0.00416548
$807$	−9.41636	−0.331472
$808$	15.2192	0.535408
$809$	−21.9896	−0.773114	−0.386557	−	0.922265i	$-0.626336\pi$
$809$	−21.9896	−0.773114	−0.386557	+	0.922265i	$0.626336\pi$
$810$	−3.17868	−0.111687
$811$	45.8776	1.61098	0.805490	−	0.592610i	$-0.201902\pi$
$811$	45.8776	1.61098	0.805490	+	0.592610i	$0.201902\pi$
$812$	0.439071	0.0154084
$813$	79.9473	2.80387
$814$	15.9099	0.557642
$815$	−78.4030	−2.74634
$816$	2.04037	0.0714273
$817$	20.9350	0.732423
$818$	−20.6602	−0.722366
$819$	−42.5097	−1.48541
$820$	30.6013	1.06864
$821$	−45.1300	−1.57505	−0.787523	−	0.616285i	$-0.788637\pi$
$821$	−45.1300	−1.57505	−0.787523	+	0.616285i	$0.788637\pi$
$822$	−12.6613	−0.441614
$823$	−29.7704	−1.03773	−0.518866	−	0.854856i	$-0.673646\pi$
$823$	−29.7704	−1.03773	−0.518866	+	0.854856i	$0.673646\pi$
$824$	−4.49261	−0.156508
$825$	122.109	4.25129
$826$	−1.97563	−0.0687411
$827$	−26.0286	−0.905103	−0.452551	−	0.891738i	$-0.649486\pi$
$827$	−26.0286	−0.905103	−0.452551	+	0.891738i	$0.649486\pi$
$828$	−18.6406	−0.647806
$829$	39.7301	1.37988	0.689942	−	0.723865i	$-0.257636\pi$
$829$	39.7301	1.37988	0.689942	+	0.723865i	$0.257636\pi$
$830$	16.2743	0.564890
$831$	−86.7402	−3.00898
$832$	2.74460	0.0951519
$833$	−2.68372	−0.0929855
$834$	−10.5234	−0.364395
$835$	−77.7414	−2.69035
$836$	−10.2785	−0.355490
$837$	0.209086	0.00722708
$838$	26.8045	0.925947
$839$	−11.1615	−0.385339	−0.192669	−	0.981264i	$-0.561715\pi$
$839$	−11.1615	−0.385339	−0.192669	+	0.981264i	$0.561715\pi$
$840$	39.6822	1.36916
$841$	−28.9819	−0.999376
$842$	6.85131	0.236112
$843$	−28.4456	−0.979718
$844$	−17.0065	−0.585388
$845$	23.8780	0.821429
$846$	−16.4037	−0.563972
$847$	4.18209	0.143698
$848$	−9.77167	−0.335560
$849$	43.6869	1.49933
$850$	10.3202	0.353981
$851$	−20.0534	−0.687423
$852$	2.98038	0.102106
$853$	−18.9199	−0.647804	−0.323902	−	0.946091i	$-0.604995\pi$
$853$	−18.9199	−0.647804	−0.323902	+	0.946091i	$0.604995\pi$
$854$	−31.3453	−1.07261
$855$	−68.3090	−2.33612
$856$	−15.0718	−0.515143
$857$	−48.6070	−1.66038	−0.830191	−	0.557479i	$-0.811769\pi$
$857$	−48.6070	−1.66038	−0.830191	+	0.557479i	$0.811769\pi$
$858$	−23.8105	−0.812878
$859$	9.09030	0.310157	0.155079	−	0.987902i	$-0.450437\pi$
$859$	9.09030	0.310157	0.155079	+	0.987902i	$0.450437\pi$
$860$	−27.7327	−0.945676
$861$	−63.6595	−2.16951
$862$	5.53959	0.188679
$863$	34.9258	1.18889	0.594444	−	0.804137i	$-0.297372\pi$
$863$	34.9258	1.18889	0.594444	+	0.804137i	$0.297372\pi$
$864$	4.85257	0.165088
$865$	−17.1230	−0.582200
$866$	−5.11384	−0.173775
$867$	45.8110	1.55582
$868$	0.140681	0.00477503
$869$	12.5231	0.424816
$870$	1.63442	0.0554122
$871$	7.69874	0.260862
$872$	10.3524	0.350577
$873$	−73.5045	−2.48775
$874$	12.9554	0.438223
$875$	129.413	4.37497
$876$	−30.5042	−1.03064
$877$	33.2890	1.12409	0.562046	−	0.827106i	$-0.310015\pi$
$877$	33.2890	1.12409	0.562046	+	0.827106i	$0.310015\pi$
$878$	−8.98166	−0.303116
$879$	34.2719	1.15596
$880$	13.6160	0.458995
$881$	40.1397	1.35234	0.676170	−	0.736745i	$-0.263638\pi$
$881$	40.1397	1.35234	0.676170	+	0.736745i	$0.263638\pi$
$882$	−17.3633	−0.584651
$883$	−11.4338	−0.384779	−0.192390	−	0.981319i	$-0.561624\pi$
$883$	−11.4338	−0.384779	−0.192390	+	0.981319i	$0.561624\pi$
$884$	−2.01239	−0.0676839
$885$	−7.35421	−0.247209
$886$	−5.64420	−0.189621
$887$	−45.1721	−1.51673	−0.758365	−	0.651830i	$-0.774001\pi$
$887$	−45.1721	−1.51673	−0.758365	+	0.651830i	$0.774001\pi$
$888$	14.2014	0.476568
$889$	−17.2995	−0.580205
$890$	−13.1938	−0.442256
$891$	2.26895	0.0760126
$892$	−8.08309	−0.270642
$893$	11.4008	0.381512
$894$	−8.44388	−0.282406
$895$	−11.9595	−0.399762
$896$	3.26500	0.109076
$897$	30.0117	1.00206
$898$	23.5286	0.785158
$899$	0.00579436	0.000193253 0
$900$	66.7703	2.22568
$901$	7.16475	0.238692
$902$	−21.8432	−0.727300
$903$	57.6920	1.91987
$904$	8.10425	0.269543
$905$	−31.3305	−1.04146
$906$	−30.7873	−1.02284
$907$	−20.0238	−0.664879	−0.332439	−	0.943125i	$-0.607872\pi$
$907$	−20.0238	−0.664879	−0.332439	+	0.943125i	$0.607872\pi$
$908$	−11.9799	−0.397566
$909$	−72.1965	−2.39461
$910$	−39.1379	−1.29741
$911$	−3.09739	−0.102621	−0.0513106	−	0.998683i	$-0.516340\pi$
$911$	−3.09739	−0.102621	−0.0513106	+	0.998683i	$0.516340\pi$
$912$	−9.17474	−0.303806
$913$	−11.6166	−0.384455
$914$	−38.0044	−1.25707
$915$	−116.681	−3.85737
$916$	3.60531	0.119123
$917$	5.50479	0.181784
$918$	−3.55799	−0.117431
$919$	21.8272	0.720012	0.360006	−	0.932950i	$-0.382775\pi$
$919$	21.8272	0.720012	0.360006	+	0.932950i	$0.382775\pi$
$920$	−17.1621	−0.565817
$921$	3.15725	0.104035
$922$	32.4326	1.06811
$923$	−2.93950	−0.0967549
$924$	−28.3252	−0.931831
$925$	71.8310	2.36179
$926$	33.2441	1.09247
$927$	21.3120	0.699979
$928$	0.134478	0.00441447
$929$	27.9214	0.916072	0.458036	−	0.888934i	$-0.348553\pi$
$929$	27.9214	0.916072	0.458036	+	0.888934i	$0.348553\pi$
$930$	0.523680	0.0171721
$931$	12.0676	0.395501
$932$	−15.7848	−0.517047
$933$	48.0683	1.57369
$934$	−17.4265	−0.570211
$935$	−9.98346	−0.326494
$936$	−13.0198	−0.425566
$937$	11.4017	0.372477	0.186238	−	0.982505i	$-0.440370\pi$
$937$	11.4017	0.372477	0.186238	+	0.982505i	$0.440370\pi$
$938$	9.15848	0.299035
$939$	31.6570	1.03309
$940$	−15.1026	−0.492593
$941$	21.0014	0.684625	0.342312	−	0.939586i	$-0.388790\pi$
$941$	21.0014	0.684625	0.342312	+	0.939586i	$0.388790\pi$
$942$	−31.2180	−1.01714
$943$	27.5320	0.896566
$944$	−0.605095	−0.0196942
$945$	−69.1975	−2.25100
$946$	19.7956	0.643611
$947$	−3.80613	−0.123683	−0.0618413	−	0.998086i	$-0.519697\pi$
$947$	−3.80613	−0.123683	−0.0618413	+	0.998086i	$0.519697\pi$
$948$	11.1783	0.363053
$949$	30.0858	0.976628
$950$	−46.4060	−1.50561
$951$	−3.22981	−0.104734
$952$	−2.39395	−0.0775884
$953$	1.64783	0.0533784	0.0266892	−	0.999644i	$-0.491504\pi$
$953$	1.64783	0.0533784	0.0266892	+	0.999644i	$0.491504\pi$
$954$	46.3548	1.50079
$955$	77.5743	2.51025
$956$	23.8660	0.771881
$957$	−1.16666	−0.0377126
$958$	39.9799	1.29169
$959$	14.8554	0.479706
$960$	12.1538	0.392263
$961$	−30.9981	−0.999940
$962$	−14.0066	−0.451591
$963$	71.4975	2.30397
$964$	−10.1267	−0.326160
$965$	54.1571	1.74338
$966$	35.7021	1.14870
$967$	47.0385	1.51266	0.756328	−	0.654192i	$-0.226991\pi$
$967$	47.0385	1.51266	0.756328	+	0.654192i	$0.226991\pi$
$968$	1.28089	0.0411693
$969$	6.72707	0.216105
$970$	−67.6743	−2.17289
$971$	8.15072	0.261569	0.130785	−	0.991411i	$-0.458250\pi$
$971$	8.15072	0.261569	0.130785	+	0.991411i	$0.458250\pi$
$972$	16.5830	0.531900
$973$	12.3470	0.395827
$974$	25.2224	0.808178
$975$	−107.501	−3.44279
$976$	−9.60040	−0.307301
$977$	−30.0991	−0.962957	−0.481478	−	0.876458i	$-0.659900\pi$
$977$	−30.0991	−0.962957	−0.481478	+	0.876458i	$0.659900\pi$
$978$	49.9544	1.59737
$979$	9.41774	0.300992
$980$	−15.9860	−0.510655
$981$	−49.1097	−1.56795
$982$	−14.3680	−0.458503
$983$	−28.1701	−0.898487	−0.449243	−	0.893409i	$-0.648306\pi$
$983$	−28.1701	−0.898487	−0.449243	+	0.893409i	$0.648306\pi$
$984$	−19.4976	−0.621560
$985$	34.1683	1.08869
$986$	−0.0986017	−0.00314012
$987$	31.4178	1.00004
$988$	9.04890	0.287884
$989$	−24.9511	−0.793400
$990$	−64.5914	−2.05285
$991$	45.2685	1.43800	0.719001	−	0.695009i	$-0.244600\pi$
$991$	45.2685	1.43800	0.719001	+	0.695009i	$0.244600\pi$
$992$	0.0430877	0.00136804
$993$	−52.2247	−1.65730
$994$	−3.49685	−0.110913
$995$	34.2734	1.08654
$996$	−10.3692	−0.328560
$997$	−12.6222	−0.399750	−0.199875	−	0.979821i	$-0.564054\pi$
$997$	−12.6222	−0.399750	−0.199875	+	0.979821i	$0.564054\pi$
$998$	−24.4553	−0.774118
$999$	−24.7643	−0.783508

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8042.2.a.c.1.5	✓	86

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8042.2.a.c.1.5	✓	86	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:	\( N \)	\(=\)	\( 8042 = 2 \cdot 4021 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8042.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -2.78277 q^{3} +1.00000 q^{4} -4.36753 q^{5} +2.78277 q^{6} -3.26500 q^{7} -1.00000 q^{8} +4.74379 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -2.78277 q^{3} +1.00000 q^{4} -4.36753 q^{5} +2.78277 q^{6} -3.26500 q^{7} -1.00000 q^{8} +4.74379 q^{9} +4.36753 q^{10} -3.11755 q^{11} -2.78277 q^{12} +2.74460 q^{13} +3.26500 q^{14} +12.1538 q^{15} +1.00000 q^{16} -0.733217 q^{17} -4.74379 q^{18} +3.29698 q^{19} -4.36753 q^{20} +9.08573 q^{21} +3.11755 q^{22} -3.92947 q^{23} +2.78277 q^{24} +14.0753 q^{25} -2.74460 q^{26} -4.85257 q^{27} -3.26500 q^{28} -0.134478 q^{29} -12.1538 q^{30} -0.0430877 q^{31} -1.00000 q^{32} +8.67541 q^{33} +0.733217 q^{34} +14.2600 q^{35} +4.74379 q^{36} +5.10334 q^{37} -3.29698 q^{38} -7.63758 q^{39} +4.36753 q^{40} -7.00654 q^{41} -9.08573 q^{42} +6.34974 q^{43} -3.11755 q^{44} -20.7187 q^{45} +3.92947 q^{46} +3.45793 q^{47} -2.78277 q^{48} +3.66020 q^{49} -14.0753 q^{50} +2.04037 q^{51} +2.74460 q^{52} -9.77167 q^{53} +4.85257 q^{54} +13.6160 q^{55} +3.26500 q^{56} -9.17474 q^{57} +0.134478 q^{58} -0.605095 q^{59} +12.1538 q^{60} -9.60040 q^{61} +0.0430877 q^{62} -15.4885 q^{63} +1.00000 q^{64} -11.9871 q^{65} -8.67541 q^{66} +2.80505 q^{67} -0.733217 q^{68} +10.9348 q^{69} -14.2600 q^{70} -1.07101 q^{71} -4.74379 q^{72} +10.9618 q^{73} -5.10334 q^{74} -39.1683 q^{75} +3.29698 q^{76} +10.1788 q^{77} +7.63758 q^{78} -4.01696 q^{79} -4.36753 q^{80} -0.727798 q^{81} +7.00654 q^{82} +3.72621 q^{83} +9.08573 q^{84} +3.20234 q^{85} -6.34974 q^{86} +0.374222 q^{87} +3.11755 q^{88} -3.02088 q^{89} +20.7187 q^{90} -8.96111 q^{91} -3.92947 q^{92} +0.119903 q^{93} -3.45793 q^{94} -14.3997 q^{95} +2.78277 q^{96} -15.4949 q^{97} -3.66020 q^{98} -14.7890 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9}+O(q^{10}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9	\( 86 q - 86 q^{2} + 12 q^{3} + 86 q^{4} - 4 q^{5} - 12 q^{6} + 35 q^{7} - 86 q^{8} + 72 q^{9} + 4 q^{10} + 13 q^{11} + 12 q^{12} + 45 q^{13} - 35 q^{14} + 17 q^{15} + 86 q^{16} + 5 q^{17} - 72 q^{18} + 47 q^{19} - 4 q^{20} + 15 q^{21} - 13 q^{22} + 6 q^{23} - 12 q^{24} + 112 q^{25} - 45 q^{26} + 51 q^{27} + 35 q^{28} - 14 q^{29} - 17 q^{30} + 24 q^{31} - 86 q^{32} + 43 q^{33} - 5 q^{34} + 42 q^{35} + 72 q^{36} + 61 q^{37} - 47 q^{38} + 20 q^{39} + 4 q^{40} - 16 q^{41} - 15 q^{42} + 72 q^{43} + 13 q^{44} + 6 q^{45} - 6 q^{46} + 11 q^{47} + 12 q^{48} + 89 q^{49} - 112 q^{50} + 56 q^{51} + 45 q^{52} - 7 q^{53} - 51 q^{54} + 48 q^{55} - 35 q^{56} + 65 q^{57} + 14 q^{58} + 24 q^{59} + 17 q^{60} + 31 q^{61} - 24 q^{62} + 98 q^{63} + 86 q^{64} - 9 q^{65} - 43 q^{66} + 157 q^{67} + 5 q^{68} + q^{69} - 42 q^{70} - 11 q^{71} - 72 q^{72} + 74 q^{73} - 61 q^{74} + 76 q^{75} + 47 q^{76} - 13 q^{77} - 20 q^{78} + 57 q^{79} - 4 q^{80} + 34 q^{81} + 16 q^{82} + 65 q^{83} + 15 q^{84} + 102 q^{85} - 72 q^{86} + 49 q^{87} - 13 q^{88} - 34 q^{89} - 6 q^{90} + 91 q^{91} + 6 q^{92} + 57 q^{93} - 11 q^{94} - 13 q^{95} - 12 q^{96} + 64 q^{97} - 89 q^{98} + 56 q^{99}+O(q^{100}) \) 86 * q - 86 * q^2 + 12 * q^3 + 86 * q^4 - 4 * q^5 - 12 * q^6 + 35 * q^7 - 86 * q^8 + 72 * q^9 + 4 * q^10 + 13 * q^11 + 12 * q^12 + 45 * q^13 - 35 * q^14 + 17 * q^15 + 86 * q^16 + 5 * q^17 - 72 * q^18 + 47 * q^19 - 4 * q^20 + 15 * q^21 - 13 * q^22 + 6 * q^23 - 12 * q^24 + 112 * q^25 - 45 * q^26 + 51 * q^27 + 35 * q^28 - 14 * q^29 - 17 * q^30 + 24 * q^31 - 86 * q^32 + 43 * q^33 - 5 * q^34 + 42 * q^35 + 72 * q^36 + 61 * q^37 - 47 * q^38 + 20 * q^39 + 4 * q^40 - 16 * q^41 - 15 * q^42 + 72 * q^43 + 13 * q^44 + 6 * q^45 - 6 * q^46 + 11 * q^47 + 12 * q^48 + 89 * q^49 - 112 * q^50 + 56 * q^51 + 45 * q^52 - 7 * q^53 - 51 * q^54 + 48 * q^55 - 35 * q^56 + 65 * q^57 + 14 * q^58 + 24 * q^59 + 17 * q^60 + 31 * q^61 - 24 * q^62 + 98 * q^63 + 86 * q^64 - 9 * q^65 - 43 * q^66 + 157 * q^67 + 5 * q^68 + q^69 - 42 * q^70 - 11 * q^71 - 72 * q^72 + 74 * q^73 - 61 * q^74 + 76 * q^75 + 47 * q^76 - 13 * q^77 - 20 * q^78 + 57 * q^79 - 4 * q^80 + 34 * q^81 + 16 * q^82 + 65 * q^83 + 15 * q^84 + 102 * q^85 - 72 * q^86 + 49 * q^87 - 13 * q^88 - 34 * q^89 - 6 * q^90 + 91 * q^91 + 6 * q^92 + 57 * q^93 - 11 * q^94 - 13 * q^95 - 12 * q^96 + 64 * q^97 - 89 * q^98 + 56 * q^99

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