LMFDB - Embedded newform 889.2.a.b.1.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [889,2,Mod(1,889)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(889, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("889.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 889 = 7 \cdot 127 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	889.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:	$7.09870073969$
Analytic rank:	$0$
Dimension:	$15$
Coefficient field:	$\mathbb{Q}[x]/(x^{15} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{15} - 22 x^{13} + 186 x^{11} - 763 x^{9} - 7 x^{8} + 1588 x^{7} + 64 x^{6} - 1625 x^{5} - 185 x^{4} + \cdots - 13 $ x^15 - 22x^13 + 186x^11 - 763x^9 - 7x^8 + 1588x^7 + 64x^6 - 1625x^5 - 185x^4 + 726x^3 + 145x^2 - 83*x - 13
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$-2.51564$ of defining polynomial
Character	$\chi$	$=$	889.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.51564 q^{2} +2.69647 q^{3} +4.32847 q^{4} -1.19101 q^{5} +6.78336 q^{6} -1.00000 q^{7} +5.85760 q^{8} +4.27094 q^{9} +O(q^{10})$	\(q+2.51564 q^{2} +2.69647 q^{3} +4.32847 q^{4} -1.19101 q^{5} +6.78336 q^{6} -1.00000 q^{7} +5.85760 q^{8} +4.27094 q^{9} -2.99615 q^{10} -4.18912 q^{11} +11.6716 q^{12} +1.43411 q^{13} -2.51564 q^{14} -3.21151 q^{15} +6.07870 q^{16} +1.76349 q^{17} +10.7442 q^{18} -4.92899 q^{19} -5.15524 q^{20} -2.69647 q^{21} -10.5383 q^{22} -0.661413 q^{23} +15.7948 q^{24} -3.58150 q^{25} +3.60772 q^{26} +3.42705 q^{27} -4.32847 q^{28} -0.521062 q^{29} -8.07903 q^{30} +3.67252 q^{31} +3.57666 q^{32} -11.2958 q^{33} +4.43630 q^{34} +1.19101 q^{35} +18.4866 q^{36} +1.30196 q^{37} -12.3996 q^{38} +3.86704 q^{39} -6.97644 q^{40} +8.43934 q^{41} -6.78336 q^{42} +4.56744 q^{43} -18.1325 q^{44} -5.08672 q^{45} -1.66388 q^{46} +0.797594 q^{47} +16.3910 q^{48} +1.00000 q^{49} -9.00978 q^{50} +4.75518 q^{51} +6.20752 q^{52} -9.82487 q^{53} +8.62124 q^{54} +4.98928 q^{55} -5.85760 q^{56} -13.2909 q^{57} -1.31081 q^{58} +12.7579 q^{59} -13.9009 q^{60} +0.0608610 q^{61} +9.23874 q^{62} -4.27094 q^{63} -3.15981 q^{64} -1.70804 q^{65} -28.4163 q^{66} -7.96005 q^{67} +7.63319 q^{68} -1.78348 q^{69} +2.99615 q^{70} +6.48720 q^{71} +25.0175 q^{72} -9.61580 q^{73} +3.27527 q^{74} -9.65740 q^{75} -21.3350 q^{76} +4.18912 q^{77} +9.72810 q^{78} +15.3521 q^{79} -7.23978 q^{80} -3.57189 q^{81} +21.2304 q^{82} +5.82288 q^{83} -11.6716 q^{84} -2.10033 q^{85} +11.4900 q^{86} -1.40503 q^{87} -24.5382 q^{88} +12.1345 q^{89} -12.7964 q^{90} -1.43411 q^{91} -2.86290 q^{92} +9.90282 q^{93} +2.00646 q^{94} +5.87047 q^{95} +9.64434 q^{96} +0.0612387 q^{97} +2.51564 q^{98} -17.8915 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 15 q + 4 q^{3} + 14 q^{4} + 7 q^{5} + 8 q^{6} - 15 q^{7} + 9 q^{9}+O(q^{10}) $ 15 * q + 4 * q^3 + 14 * q^4 + 7 * q^5 + 8 * q^6 - 15 * q^7 + 9 * q^9	\( 15 q + 4 q^{3} + 14 q^{4} + 7 q^{5} + 8 q^{6} - 15 q^{7} + 9 q^{9} + 10 q^{10} + 14 q^{11} + 10 q^{12} + 6 q^{13} + 6 q^{15} + 20 q^{16} + 10 q^{17} + q^{18} + 13 q^{19} + 8 q^{20} - 4 q^{21} - 11 q^{22} + 15 q^{23} + 34 q^{24} + 22 q^{26} + 22 q^{27} - 14 q^{28} + 16 q^{29} + 7 q^{30} + 22 q^{31} + 14 q^{33} - 15 q^{34} - 7 q^{35} + 20 q^{36} - 14 q^{37} - 6 q^{38} + 29 q^{39} + 22 q^{40} + 19 q^{41} - 8 q^{42} - q^{43} + 25 q^{44} - 8 q^{45} - 28 q^{46} + 49 q^{47} - 14 q^{48} + 15 q^{49} + 24 q^{50} - 8 q^{51} - 17 q^{52} - 28 q^{53} + 13 q^{54} + 39 q^{55} - 12 q^{57} - 10 q^{58} + 43 q^{59} - 60 q^{60} + 27 q^{61} + 14 q^{62} - 9 q^{63} + 18 q^{64} - 8 q^{65} - 36 q^{66} + 3 q^{67} + 13 q^{68} - 17 q^{69} - 10 q^{70} + 55 q^{71} - 21 q^{72} - 3 q^{73} - 12 q^{74} + 8 q^{75} - 20 q^{76} - 14 q^{77} - 6 q^{78} + 18 q^{79} + 29 q^{80} - 17 q^{81} + 14 q^{82} + 17 q^{83} - 10 q^{84} + 7 q^{85} + 4 q^{86} + 35 q^{87} - 114 q^{88} + 36 q^{89} - 39 q^{90} - 6 q^{91} + 45 q^{92} + 15 q^{93} - 15 q^{94} + 59 q^{95} + 85 q^{96} - 2 q^{97} + 35 q^{99}+O(q^{100}) \) 15 * q + 4 * q^3 + 14 * q^4 + 7 * q^5 + 8 * q^6 - 15 * q^7 + 9 * q^9 + 10 * q^10 + 14 * q^11 + 10 * q^12 + 6 * q^13 + 6 * q^15 + 20 * q^16 + 10 * q^17 + q^18 + 13 * q^19 + 8 * q^20 - 4 * q^21 - 11 * q^22 + 15 * q^23 + 34 * q^24 + 22 * q^26 + 22 * q^27 - 14 * q^28 + 16 * q^29 + 7 * q^30 + 22 * q^31 + 14 * q^33 - 15 * q^34 - 7 * q^35 + 20 * q^36 - 14 * q^37 - 6 * q^38 + 29 * q^39 + 22 * q^40 + 19 * q^41 - 8 * q^42 - q^43 + 25 * q^44 - 8 * q^45 - 28 * q^46 + 49 * q^47 - 14 * q^48 + 15 * q^49 + 24 * q^50 - 8 * q^51 - 17 * q^52 - 28 * q^53 + 13 * q^54 + 39 * q^55 - 12 * q^57 - 10 * q^58 + 43 * q^59 - 60 * q^60 + 27 * q^61 + 14 * q^62 - 9 * q^63 + 18 * q^64 - 8 * q^65 - 36 * q^66 + 3 * q^67 + 13 * q^68 - 17 * q^69 - 10 * q^70 + 55 * q^71 - 21 * q^72 - 3 * q^73 - 12 * q^74 + 8 * q^75 - 20 * q^76 - 14 * q^77 - 6 * q^78 + 18 * q^79 + 29 * q^80 - 17 * q^81 + 14 * q^82 + 17 * q^83 - 10 * q^84 + 7 * q^85 + 4 * q^86 + 35 * q^87 - 114 * q^88 + 36 * q^89 - 39 * q^90 - 6 * q^91 + 45 * q^92 + 15 * q^93 - 15 * q^94 + 59 * q^95 + 85 * q^96 - 2 * q^97 + 35 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	2.51564	1.77883	0.889415	−	0.457101i	$-0.151112\pi$
$2$	2.51564	1.77883	0.889415	+	0.457101i	$0.151112\pi$
$3$	2.69647	1.55681	0.778403	−	0.627765i	$-0.216030\pi$
$3$	2.69647	1.55681	0.778403	+	0.627765i	$0.216030\pi$
$4$	4.32847	2.16423
$5$	−1.19101	−0.532635	−0.266317	−	0.963885i	$-0.585807\pi$
$5$	−1.19101	−0.532635	−0.266317	+	0.963885i	$0.585807\pi$
$6$	6.78336	2.76929
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	5.85760	2.07097
$9$	4.27094	1.42365
$10$	−2.99615	−0.947466
$11$	−4.18912	−1.26307	−0.631534	−	0.775348i	$-0.717574\pi$
$11$	−4.18912	−1.26307	−0.631534	+	0.775348i	$0.717574\pi$
$12$	11.6716	3.36929
$13$	1.43411	0.397752	0.198876	−	0.980025i	$-0.436271\pi$
$13$	1.43411	0.397752	0.198876	+	0.980025i	$0.436271\pi$
$14$	−2.51564	−0.672334
$15$	−3.21151	−0.829209
$16$	6.07870	1.51968
$17$	1.76349	0.427708	0.213854	−	0.976866i	$-0.431398\pi$
$17$	1.76349	0.427708	0.213854	+	0.976866i	$0.431398\pi$
$18$	10.7442	2.53242
$19$	−4.92899	−1.13079	−0.565394	−	0.824821i	$-0.691276\pi$
$19$	−4.92899	−1.13079	−0.565394	+	0.824821i	$0.691276\pi$
$20$	−5.15524	−1.15275
$21$	−2.69647	−0.588418
$22$	−10.5383	−2.24678
$23$	−0.661413	−0.137914	−0.0689570	−	0.997620i	$-0.521967\pi$
$23$	−0.661413	−0.137914	−0.0689570	+	0.997620i	$0.521967\pi$
$24$	15.7948	3.22411
$25$	−3.58150	−0.716300
$26$	3.60772	0.707532
$27$	3.42705	0.659536
$28$	−4.32847	−0.818004
$29$	−0.521062	−0.0967588	−0.0483794	−	0.998829i	$-0.515406\pi$
$29$	−0.521062	−0.0967588	−0.0483794	+	0.998829i	$0.515406\pi$
$30$	−8.07903	−1.47502
$31$	3.67252	0.659603	0.329802	−	0.944050i	$-0.393018\pi$
$31$	3.67252	0.659603	0.329802	+	0.944050i	$0.393018\pi$
$32$	3.57666	0.632270
$33$	−11.2958	−1.96635
$34$	4.43630	0.760820
$35$	1.19101	0.201317
$36$	18.4866	3.08111
$37$	1.30196	0.214041	0.107021	−	0.994257i	$-0.465869\pi$
$37$	1.30196	0.214041	0.107021	+	0.994257i	$0.465869\pi$
$38$	−12.3996	−2.01148
$39$	3.86704	0.619222
$40$	−6.97644	−1.10307
$41$	8.43934	1.31800	0.659002	−	0.752142i	$-0.270979\pi$
$41$	8.43934	1.31800	0.659002	+	0.752142i	$0.270979\pi$
$42$	−6.78336	−1.04669
$43$	4.56744	0.696527	0.348264	−	0.937397i	$-0.386771\pi$
$43$	4.56744	0.696527	0.348264	+	0.937397i	$0.386771\pi$
$44$	−18.1325	−2.73358
$45$	−5.08672	−0.758284
$46$	−1.66388	−0.245326
$47$	0.797594	0.116341	0.0581705	−	0.998307i	$-0.481473\pi$
$47$	0.797594	0.116341	0.0581705	+	0.998307i	$0.481473\pi$
$48$	16.3910	2.36584
$49$	1.00000	0.142857
$50$	−9.00978	−1.27418
$51$	4.75518	0.665859
$52$	6.20752	0.860828
$53$	−9.82487	−1.34955	−0.674775	−	0.738023i	$-0.735759\pi$
$53$	−9.82487	−1.34955	−0.674775	+	0.738023i	$0.735759\pi$
$54$	8.62124	1.17320
$55$	4.98928	0.672754
$56$	−5.85760	−0.782755
$57$	−13.2909	−1.76042
$58$	−1.31081	−0.172117
$59$	12.7579	1.66093	0.830466	−	0.557070i	$-0.188074\pi$
$59$	12.7579	1.66093	0.830466	+	0.557070i	$0.188074\pi$
$60$	−13.9009	−1.79460
$61$	0.0608610	0.00779246	0.00389623	−	0.999992i	$-0.498760\pi$
$61$	0.0608610	0.00779246	0.00389623	+	0.999992i	$0.498760\pi$
$62$	9.23874	1.17332
$63$	−4.27094	−0.538088
$64$	−3.15981	−0.394976
$65$	−1.70804	−0.211856
$66$	−28.4163	−3.49781
$67$	−7.96005	−0.972474	−0.486237	−	0.873827i	$-0.661631\pi$
$67$	−7.96005	−0.972474	−0.486237	+	0.873827i	$0.661631\pi$
$68$	7.63319	0.925661
$69$	−1.78348	−0.214705
$70$	2.99615	0.358109
$71$	6.48720	0.769889	0.384945	−	0.922940i	$-0.374221\pi$
$71$	6.48720	0.769889	0.384945	+	0.922940i	$0.374221\pi$
$72$	25.0175	2.94834
$73$	−9.61580	−1.12544	−0.562722	−	0.826646i	$-0.690246\pi$
$73$	−9.61580	−1.12544	−0.562722	+	0.826646i	$0.690246\pi$
$74$	3.27527	0.380743
$75$	−9.65740	−1.11514
$76$	−21.3350	−2.44729
$77$	4.18912	0.477395
$78$	9.72810	1.10149
$79$	15.3521	1.72725	0.863625	−	0.504135i	$-0.168189\pi$
$79$	15.3521	1.72725	0.863625	+	0.504135i	$0.168189\pi$
$80$	−7.23978	−0.809432
$81$	−3.57189	−0.396877
$82$	21.2304	2.34450
$83$	5.82288	0.639144	0.319572	−	0.947562i	$-0.396461\pi$
$83$	5.82288	0.639144	0.319572	+	0.947562i	$0.396461\pi$
$84$	−11.6716	−1.27347
$85$	−2.10033	−0.227812
$86$	11.4900	1.23900
$87$	−1.40503	−0.150635
$88$	−24.5382	−2.61578
$89$	12.1345	1.28625	0.643125	−	0.765761i	$-0.277638\pi$
$89$	12.1345	1.28625	0.643125	+	0.765761i	$0.277638\pi$
$90$	−12.7964	−1.34886
$91$	−1.43411	−0.150336
$92$	−2.86290	−0.298478
$93$	9.90282	1.02687
$94$	2.00646	0.206951
$95$	5.87047	0.602297
$96$	9.64434	0.984322
$97$	0.0612387	0.00621785	0.00310893	−	0.999995i	$-0.499010\pi$
$97$	0.0612387	0.00621785	0.00310893	+	0.999995i	$0.499010\pi$
$98$	2.51564	0.254118
$99$	−17.8915	−1.79816
$100$	−15.5024	−1.55024
$101$	−9.53969	−0.949235	−0.474617	−	0.880192i	$-0.657414\pi$
$101$	−9.53969	−0.949235	−0.474617	+	0.880192i	$0.657414\pi$
$102$	11.9624	1.18445
$103$	−2.73565	−0.269552	−0.134776	−	0.990876i	$-0.543031\pi$
$103$	−2.73565	−0.269552	−0.134776	+	0.990876i	$0.543031\pi$
$104$	8.40046	0.823733
$105$	3.21151	0.313412
$106$	−24.7159	−2.40062
$107$	−6.98917	−0.675669	−0.337834	−	0.941206i	$-0.609694\pi$
$107$	−6.98917	−0.675669	−0.337834	+	0.941206i	$0.609694\pi$
$108$	14.8339	1.42739
$109$	−1.71721	−0.164479	−0.0822395	−	0.996613i	$-0.526207\pi$
$109$	−1.71721	−0.164479	−0.0822395	+	0.996613i	$0.526207\pi$
$110$	12.5512	1.19671
$111$	3.51070	0.333221
$112$	−6.07870	−0.574383
$113$	−19.9992	−1.88136	−0.940682	−	0.339290i	$-0.889813\pi$
$113$	−19.9992	−1.88136	−0.940682	+	0.339290i	$0.889813\pi$
$114$	−33.4351	−3.13148
$115$	0.787747	0.0734578
$116$	−2.25540	−0.209409
$117$	6.12501	0.566258
$118$	32.0942	2.95451
$119$	−1.76349	−0.161659
$120$	−18.8118	−1.71727
$121$	6.54875	0.595341
$122$	0.153105	0.0138615
$123$	22.7564	2.05188
$124$	15.8964	1.42754
$125$	10.2206	0.914161
$126$	−10.7442	−0.957167
$127$	1.00000	0.0887357
$127$	1.00000	0.0887357
$128$	−15.1023	−1.33486
$129$	12.3159	1.08436
$130$	−4.29682	−0.376856
$131$	10.3792	0.906832	0.453416	−	0.891299i	$-0.350205\pi$
$131$	10.3792	0.906832	0.453416	+	0.891299i	$0.350205\pi$
$132$	−48.8937	−4.25565
$133$	4.92899	0.427398
$134$	−20.0246	−1.72987
$135$	−4.08164	−0.351292
$136$	10.3298	0.885773
$137$	13.4955	1.15300	0.576500	−	0.817097i	$-0.304418\pi$
$137$	13.4955	1.15300	0.576500	+	0.817097i	$0.304418\pi$
$138$	−4.48660	−0.381924
$139$	−13.9654	−1.18453	−0.592263	−	0.805745i	$-0.701765\pi$
$139$	−13.9654	−1.18453	−0.592263	+	0.805745i	$0.701765\pi$
$140$	5.15524	0.435697
$141$	2.15069	0.181121
$142$	16.3195	1.36950
$143$	−6.00768	−0.502387
$144$	25.9618	2.16348
$145$	0.620589	0.0515371
$146$	−24.1899	−2.00197
$147$	2.69647	0.222401
$148$	5.63550	0.463235
$149$	−14.4117	−1.18065	−0.590325	−	0.807166i	$-0.701000\pi$
$149$	−14.4117	−1.18065	−0.590325	+	0.807166i	$0.701000\pi$
$150$	−24.2946	−1.98365
$151$	−9.13744	−0.743595	−0.371797	−	0.928314i	$-0.621258\pi$
$151$	−9.13744	−0.743595	−0.371797	+	0.928314i	$0.621258\pi$
$152$	−28.8721	−2.34183
$153$	7.53174	0.608905
$154$	10.5383	0.849204
$155$	−4.37399	−0.351328
$156$	16.7384	1.34014
$157$	9.89040	0.789340	0.394670	−	0.918823i	$-0.370859\pi$
$157$	9.89040	0.789340	0.394670	+	0.918823i	$0.370859\pi$
$158$	38.6205	3.07248
$159$	−26.4925	−2.10099
$160$	−4.25983	−0.336769
$161$	0.661413	0.0521266
$162$	−8.98561	−0.705976
$163$	12.7487	0.998553	0.499276	−	0.866443i	$-0.333599\pi$
$163$	12.7487	0.998553	0.499276	+	0.866443i	$0.333599\pi$
$164$	36.5294	2.85247
$165$	13.4534	1.04735
$166$	14.6483	1.13693
$167$	20.4473	1.58226	0.791129	−	0.611649i	$-0.209494\pi$
$167$	20.4473	1.58226	0.791129	+	0.611649i	$0.209494\pi$
$168$	−15.7948	−1.21860
$169$	−10.9433	−0.841794
$170$	−5.28367	−0.405239
$171$	−21.0514	−1.60984
$172$	19.7700	1.50745
$173$	21.7709	1.65521	0.827606	−	0.561309i	$-0.189702\pi$
$173$	21.7709	1.65521	0.827606	+	0.561309i	$0.189702\pi$
$174$	−3.53455	−0.267953
$175$	3.58150	0.270736
$176$	−25.4644	−1.91945
$177$	34.4012	2.58575
$178$	30.5260	2.28802
$179$	3.27383	0.244698	0.122349	−	0.992487i	$-0.460957\pi$
$179$	3.27383	0.244698	0.122349	+	0.992487i	$0.460957\pi$
$180$	−22.0177	−1.64110
$181$	−16.5329	−1.22888	−0.614440	−	0.788964i	$-0.710618\pi$
$181$	−16.5329	−1.22888	−0.614440	+	0.788964i	$0.710618\pi$
$182$	−3.60772	−0.267422
$183$	0.164110	0.0121313
$184$	−3.87429	−0.285616
$185$	−1.55065	−0.114006
$186$	24.9120	1.82663
$187$	−7.38746	−0.540225
$188$	3.45236	0.251789
$189$	−3.42705	−0.249281
$190$	14.7680	1.07138
$191$	23.8442	1.72530	0.862651	−	0.505799i	$-0.168802\pi$
$191$	23.8442	1.72530	0.862651	+	0.505799i	$0.168802\pi$
$192$	−8.52032	−0.614901
$193$	2.23275	0.160717	0.0803586	−	0.996766i	$-0.474393\pi$
$193$	2.23275	0.160717	0.0803586	+	0.996766i	$0.474393\pi$
$194$	0.154055	0.0110605
$195$	−4.60568	−0.329819
$196$	4.32847	0.309176
$197$	20.4153	1.45453	0.727266	−	0.686355i	$-0.240791\pi$
$197$	20.4153	1.45453	0.727266	+	0.686355i	$0.240791\pi$
$198$	−45.0086	−3.19862
$199$	9.51842	0.674743	0.337372	−	0.941372i	$-0.390462\pi$
$199$	9.51842	0.674743	0.337372	+	0.941372i	$0.390462\pi$
$200$	−20.9790	−1.48344
$201$	−21.4640	−1.51395
$202$	−23.9985	−1.68853
$203$	0.521062	0.0365714
$204$	20.5827	1.44107
$205$	−10.0513	−0.702014
$206$	−6.88193	−0.479487
$207$	−2.82485	−0.196341
$208$	8.71755	0.604453
$209$	20.6482	1.42826
$210$	8.07903	0.557506
$211$	−12.1258	−0.834773	−0.417386	−	0.908729i	$-0.637054\pi$
$211$	−12.1258	−0.834773	−0.417386	+	0.908729i	$0.637054\pi$
$212$	−42.5267	−2.92074
$213$	17.4925	1.19857
$214$	−17.5823	−1.20190
$215$	−5.43985	−0.370995
$216$	20.0743	1.36588
$217$	−3.67252	−0.249307
$218$	−4.31989	−0.292580
$219$	−25.9287	−1.75210
$220$	21.5959	1.45600
$221$	2.52904	0.170122
$222$	8.83166	0.592743
$223$	6.01349	0.402693	0.201347	−	0.979520i	$-0.435468\pi$
$223$	6.01349	0.402693	0.201347	+	0.979520i	$0.435468\pi$
$224$	−3.57666	−0.238975
$225$	−15.2964	−1.01976
$226$	−50.3108	−3.34662
$227$	−20.1839	−1.33965	−0.669825	−	0.742519i	$-0.733631\pi$
$227$	−20.1839	−1.33965	−0.669825	+	0.742519i	$0.733631\pi$
$228$	−57.5291	−3.80996
$229$	10.8054	0.714043	0.357021	−	0.934096i	$-0.383792\pi$
$229$	10.8054	0.714043	0.357021	+	0.934096i	$0.383792\pi$
$230$	1.98169	0.130669
$231$	11.2958	0.743211
$232$	−3.05217	−0.200385
$233$	−17.7238	−1.16112	−0.580561	−	0.814217i	$-0.697167\pi$
$233$	−17.7238	−1.16112	−0.580561	+	0.814217i	$0.697167\pi$
$234$	15.4084	1.00728
$235$	−0.949941	−0.0619673
$236$	55.2220	3.59465
$237$	41.3965	2.68899
$238$	−4.43630	−0.287563
$239$	16.3003	1.05438	0.527189	−	0.849748i	$-0.323246\pi$
$239$	16.3003	1.05438	0.527189	+	0.849748i	$0.323246\pi$
$240$	−19.5218	−1.26013
$241$	−16.4252	−1.05804	−0.529020	−	0.848609i	$-0.677440\pi$
$241$	−16.4252	−1.05804	−0.529020	+	0.848609i	$0.677440\pi$
$242$	16.4743	1.05901
$243$	−19.9126	−1.27740
$244$	0.263435	0.0168647
$245$	−1.19101	−0.0760907
$246$	57.2470	3.64994
$247$	−7.06874	−0.449773
$248$	21.5121	1.36602
$249$	15.7012	0.995024
$250$	25.7115	1.62614
$251$	−10.0670	−0.635421	−0.317711	−	0.948188i	$-0.602914\pi$
$251$	−10.0670	−0.635421	−0.317711	+	0.948188i	$0.602914\pi$
$252$	−18.4866	−1.16455
$253$	2.77074	0.174195
$254$	2.51564	0.157846
$255$	−5.66346	−0.354660
$256$	−31.6723	−1.97952
$257$	12.9478	0.807664	0.403832	−	0.914833i	$-0.367678\pi$
$257$	12.9478	0.807664	0.403832	+	0.914833i	$0.367678\pi$
$258$	30.9825	1.92889
$259$	−1.30196	−0.0808999
$260$	−7.39320	−0.458507
$261$	−2.22542	−0.137750
$262$	26.1103	1.61310
$263$	−26.8400	−1.65503	−0.827513	−	0.561446i	$-0.810245\pi$
$263$	−26.8400	−1.65503	−0.827513	+	0.561446i	$0.810245\pi$
$264$	−66.1665	−4.07227
$265$	11.7015	0.718817
$266$	12.3996	0.760268
$267$	32.7202	2.00244
$268$	−34.4548	−2.10466
$269$	−17.1313	−1.04451	−0.522256	−	0.852789i	$-0.674910\pi$
$269$	−17.1313	−1.04451	−0.522256	+	0.852789i	$0.674910\pi$
$270$	−10.2680	−0.624888
$271$	25.5813	1.55395	0.776975	−	0.629531i	$-0.216753\pi$
$271$	25.5813	1.55395	0.776975	+	0.629531i	$0.216753\pi$
$272$	10.7197	0.649978
$273$	−3.86704	−0.234044
$274$	33.9499	2.05099
$275$	15.0033	0.904736
$276$	−7.71973	−0.464673
$277$	−14.5241	−0.872669	−0.436334	−	0.899785i	$-0.643724\pi$
$277$	−14.5241	−0.872669	−0.436334	+	0.899785i	$0.643724\pi$
$278$	−35.1319	−2.10707
$279$	15.6851	0.939042
$280$	6.97644	0.416922
$281$	10.3069	0.614857	0.307429	−	0.951571i	$-0.400531\pi$
$281$	10.3069	0.614857	0.307429	+	0.951571i	$0.400531\pi$
$282$	5.41037	0.322183
$283$	−19.8952	−1.18264	−0.591322	−	0.806435i	$-0.701394\pi$
$283$	−19.8952	−1.18264	−0.591322	+	0.806435i	$0.701394\pi$
$284$	28.0796	1.66622
$285$	15.8295	0.937660
$286$	−15.1132	−0.893661
$287$	−8.43934	−0.498158
$288$	15.2757	0.900129
$289$	−13.8901	−0.817066
$290$	1.56118	0.0916757
$291$	0.165128	0.00967999
$292$	−41.6217	−2.43572
$293$	8.29939	0.484855	0.242428	−	0.970169i	$-0.422056\pi$
$293$	8.29939	0.484855	0.242428	+	0.970169i	$0.422056\pi$
$294$	6.78336	0.395613
$295$	−15.1947	−0.884670
$296$	7.62637	0.443274
$297$	−14.3563	−0.833039
$298$	−36.2547	−2.10018
$299$	−0.948541	−0.0548555
$300$	−41.8018	−2.41343
$301$	−4.56744	−0.263263
$302$	−22.9866	−1.32273
$303$	−25.7235	−1.47778
$304$	−29.9619	−1.71843
$305$	−0.0724859	−0.00415053
$306$	18.9472	1.08314
$307$	−16.4163	−0.936927	−0.468464	−	0.883483i	$-0.655192\pi$
$307$	−16.4163	−0.936927	−0.468464	+	0.883483i	$0.655192\pi$
$308$	18.1325	1.03319
$309$	−7.37660	−0.419640
$310$	−11.0034	−0.624952
$311$	−9.12922	−0.517671	−0.258835	−	0.965921i	$-0.583339\pi$
$311$	−9.12922	−0.517671	−0.258835	+	0.965921i	$0.583339\pi$
$312$	22.6516	1.28239
$313$	−3.23344	−0.182765	−0.0913824	−	0.995816i	$-0.529129\pi$
$313$	−3.23344	−0.182765	−0.0913824	+	0.995816i	$0.529129\pi$
$314$	24.8807	1.40410
$315$	5.08672	0.286604
$316$	66.4512	3.73817
$317$	−12.6938	−0.712953	−0.356477	−	0.934304i	$-0.616022\pi$
$317$	−12.6938	−0.712953	−0.356477	+	0.934304i	$0.616022\pi$
$318$	−66.6456	−3.73730
$319$	2.18279	0.122213
$320$	3.76335	0.210378
$321$	−18.8461	−1.05189
$322$	1.66388	0.0927243
$323$	−8.69221	−0.483647
$324$	−15.4608	−0.858934
$325$	−5.13628	−0.284910
$326$	32.0711	1.77625
$327$	−4.63040	−0.256062
$328$	49.4343	2.72955
$329$	−0.797594	−0.0439728
$330$	33.8440	1.86305
$331$	2.70814	0.148853	0.0744265	−	0.997227i	$-0.476287\pi$
$331$	2.70814	0.148853	0.0744265	+	0.997227i	$0.476287\pi$
$332$	25.2041	1.38326
$333$	5.56060	0.304719
$334$	51.4381	2.81457
$335$	9.48047	0.517974
$336$	−16.3910	−0.894204
$337$	28.3780	1.54585	0.772924	−	0.634499i	$-0.218793\pi$
$337$	28.3780	1.54585	0.772924	+	0.634499i	$0.218793\pi$
$338$	−27.5295	−1.49741
$339$	−53.9271	−2.92892
$340$	−9.09119	−0.493039
$341$	−15.3846	−0.833124
$342$	−52.9579	−2.86364
$343$	−1.00000	−0.0539949
$344$	26.7542	1.44249
$345$	2.12414	0.114360
$346$	54.7679	2.94434
$347$	−1.19640	−0.0642261	−0.0321131	−	0.999484i	$-0.510224\pi$
$347$	−1.19640	−0.0642261	−0.0321131	+	0.999484i	$0.510224\pi$
$348$	−6.08161	−0.326009
$349$	−6.91527	−0.370166	−0.185083	−	0.982723i	$-0.559255\pi$
$349$	−6.91527	−0.370166	−0.185083	+	0.982723i	$0.559255\pi$
$350$	9.00978	0.481593
$351$	4.91478	0.262332
$352$	−14.9831	−0.798600
$353$	21.1758	1.12707	0.563537	−	0.826091i	$-0.309440\pi$
$353$	21.1758	1.12707	0.563537	+	0.826091i	$0.309440\pi$
$354$	86.5411	4.59961
$355$	−7.72630	−0.410070
$356$	52.5236	2.78375
$357$	−4.75518	−0.251671
$358$	8.23580	0.435276
$359$	−22.4862	−1.18678	−0.593388	−	0.804916i	$-0.702210\pi$
$359$	−22.4862	−1.18678	−0.593388	+	0.804916i	$0.702210\pi$
$360$	−29.7960	−1.57039
$361$	5.29497	0.278682
$362$	−41.5908	−2.18597
$363$	17.6585	0.926831
$364$	−6.20752	−0.325362
$365$	11.4525	0.599450
$366$	0.412842	0.0215796
$367$	17.1938	0.897512	0.448756	−	0.893654i	$-0.351867\pi$
$367$	17.1938	0.897512	0.448756	+	0.893654i	$0.351867\pi$
$368$	−4.02053	−0.209585
$369$	36.0439	1.87637
$370$	−3.90087	−0.202797
$371$	9.82487	0.510082
$372$	42.8640	2.22240
$373$	8.57902	0.444205	0.222102	−	0.975023i	$-0.428708\pi$
$373$	8.57902	0.444205	0.222102	+	0.975023i	$0.428708\pi$
$374$	−18.5842	−0.960967
$375$	27.5596	1.42317
$376$	4.67199	0.240939
$377$	−0.747262	−0.0384860
$378$	−8.62124	−0.443429
$379$	−4.60673	−0.236632	−0.118316	−	0.992976i	$-0.537750\pi$
$379$	−4.60673	−0.236632	−0.118316	+	0.992976i	$0.537750\pi$
$380$	25.4101	1.30351
$381$	2.69647	0.138144
$382$	59.9834	3.06902
$383$	−21.3698	−1.09195	−0.545973	−	0.837803i	$-0.683840\pi$
$383$	−21.3698	−1.09195	−0.545973	+	0.837803i	$0.683840\pi$
$384$	−40.7228	−2.07813
$385$	−4.98928	−0.254277
$386$	5.61682	0.285888
$387$	19.5072	0.991609
$388$	0.265070	0.0134569
$389$	−24.6810	−1.25138	−0.625689	−	0.780073i	$-0.715182\pi$
$389$	−24.6810	−1.25138	−0.625689	+	0.780073i	$0.715182\pi$
$390$	−11.5862	−0.586692
$391$	−1.16639	−0.0589870
$392$	5.85760	0.295853
$393$	27.9871	1.41176
$394$	51.3577	2.58737
$395$	−18.2845	−0.919993
$396$	−77.4428	−3.89165
$397$	21.0436	1.05615	0.528073	−	0.849199i	$-0.322915\pi$
$397$	21.0436	1.05615	0.528073	+	0.849199i	$0.322915\pi$
$398$	23.9450	1.20025
$399$	13.2909	0.665376
$400$	−21.7709	−1.08854
$401$	12.7428	0.636346	0.318173	−	0.948033i	$-0.396931\pi$
$401$	12.7428	0.636346	0.318173	+	0.948033i	$0.396931\pi$
$402$	−53.9958	−2.69307
$403$	5.26681	0.262358
$404$	−41.2923	−2.05437
$405$	4.25415	0.211390
$406$	1.31081	0.0650542
$407$	−5.45407	−0.270348
$408$	27.8540	1.37898
$409$	−10.4497	−0.516703	−0.258351	−	0.966051i	$-0.583179\pi$
$409$	−10.4497	−0.516703	−0.258351	+	0.966051i	$0.583179\pi$
$410$	−25.2855	−1.24876
$411$	36.3902	1.79500
$412$	−11.8412	−0.583374
$413$	−12.7579	−0.627773
$414$	−7.10633	−0.349257
$415$	−6.93509	−0.340430
$416$	5.12933	0.251486
$417$	−37.6571	−1.84408
$418$	51.9434	2.54064
$419$	35.8726	1.75249	0.876246	−	0.481864i	$-0.160040\pi$
$419$	35.8726	1.75249	0.876246	+	0.481864i	$0.160040\pi$
$420$	13.9009	0.678296
$421$	2.32495	0.113311	0.0566555	−	0.998394i	$-0.481956\pi$
$421$	2.32495	0.113311	0.0566555	+	0.998394i	$0.481956\pi$
$422$	−30.5041	−1.48492
$423$	3.40648	0.165629
$424$	−57.5502	−2.79488
$425$	−6.31593	−0.306368
$426$	44.0050	2.13205
$427$	−0.0608610	−0.00294527
$428$	−30.2524	−1.46231
$429$	−16.1995	−0.782120
$430$	−13.6847	−0.659936
$431$	34.8419	1.67828	0.839138	−	0.543919i	$-0.183060\pi$
$431$	34.8419	1.67828	0.839138	+	0.543919i	$0.183060\pi$
$432$	20.8320	1.00228
$433$	−2.46087	−0.118262	−0.0591309	−	0.998250i	$-0.518833\pi$
$433$	−2.46087	−0.118262	−0.0591309	+	0.998250i	$0.518833\pi$
$434$	−9.23874	−0.443474
$435$	1.67340	0.0802333
$436$	−7.43289	−0.355971
$437$	3.26010	0.155952
$438$	−65.2274	−3.11668
$439$	4.86694	0.232286	0.116143	−	0.993232i	$-0.462947\pi$
$439$	4.86694	0.232286	0.116143	+	0.993232i	$0.462947\pi$
$440$	29.2252	1.39326
$441$	4.27094	0.203378
$442$	6.36217	0.302617
$443$	5.94755	0.282577	0.141288	−	0.989968i	$-0.454876\pi$
$443$	5.94755	0.282577	0.141288	+	0.989968i	$0.454876\pi$
$444$	15.1959	0.721167
$445$	−14.4522	−0.685101
$446$	15.1278	0.716323
$447$	−38.8606	−1.83804
$448$	3.15981	0.149287
$449$	−36.7039	−1.73216	−0.866082	−	0.499902i	$-0.833369\pi$
$449$	−36.7039	−1.73216	−0.866082	+	0.499902i	$0.833369\pi$
$450$	−38.4803	−1.81398
$451$	−35.3534	−1.66473
$452$	−86.5658	−4.07171
$453$	−24.6388	−1.15763
$454$	−50.7754	−2.38301
$455$	1.70804	0.0800742
$456$	−77.8526	−3.64578
$457$	−30.5030	−1.42687	−0.713436	−	0.700721i	$-0.752862\pi$
$457$	−30.5030	−1.42687	−0.713436	+	0.700721i	$0.752862\pi$
$458$	27.1826	1.27016
$459$	6.04355	0.282089
$460$	3.40974	0.158980
$461$	26.1775	1.21921	0.609604	−	0.792706i	$-0.291329\pi$
$461$	26.1775	1.21921	0.609604	+	0.792706i	$0.291329\pi$
$462$	28.4163	1.32205
$463$	29.8321	1.38642	0.693208	−	0.720738i	$-0.256197\pi$
$463$	29.8321	1.38642	0.693208	+	0.720738i	$0.256197\pi$
$464$	−3.16738	−0.147042
$465$	−11.7943	−0.546949
$466$	−44.5867	−2.06544
$467$	−26.4147	−1.22233	−0.611163	−	0.791505i	$-0.709298\pi$
$467$	−26.4147	−1.22233	−0.611163	+	0.791505i	$0.709298\pi$
$468$	26.5119	1.22551
$469$	7.96005	0.367561
$470$	−2.38971	−0.110229
$471$	26.6692	1.22885
$472$	74.7304	3.43975
$473$	−19.1336	−0.879762
$474$	104.139	4.78326
$475$	17.6532	0.809984
$476$	−7.63319	−0.349867
$477$	−41.9614	−1.92128
$478$	41.0057	1.87556
$479$	29.8315	1.36304	0.681519	−	0.731801i	$-0.261320\pi$
$479$	29.8315	1.36304	0.681519	+	0.731801i	$0.261320\pi$
$480$	−11.4865	−0.524284
$481$	1.86716	0.0851352
$482$	−41.3200	−1.88207
$483$	1.78348	0.0811510
$484$	28.3461	1.28846
$485$	−0.0729358	−0.00331184
$486$	−50.0931	−2.27227
$487$	30.4878	1.38153	0.690767	−	0.723077i	$-0.257273\pi$
$487$	30.4878	1.38153	0.690767	+	0.723077i	$0.257273\pi$
$488$	0.356500	0.0161380
$489$	34.3764	1.55455
$490$	−2.99615	−0.135352
$491$	12.6414	0.570496	0.285248	−	0.958454i	$-0.407924\pi$
$491$	12.6414	0.570496	0.285248	+	0.958454i	$0.407924\pi$
$492$	98.5004	4.44074
$493$	−0.918885	−0.0413845
$494$	−17.7824	−0.800069
$495$	21.3089	0.957764
$496$	22.3241	1.00238
$497$	−6.48720	−0.290991
$498$	39.4987	1.76998
$499$	−32.9525	−1.47516	−0.737578	−	0.675262i	$-0.764031\pi$
$499$	−32.9525	−1.47516	−0.737578	+	0.675262i	$0.764031\pi$
$500$	44.2397	1.97846
$501$	55.1354	2.46327
$502$	−25.3249	−1.13031
$503$	6.65795	0.296863	0.148432	−	0.988923i	$-0.452577\pi$
$503$	6.65795	0.296863	0.148432	+	0.988923i	$0.452577\pi$
$504$	−25.0175	−1.11437
$505$	11.3618	0.505595
$506$	6.97019	0.309863
$507$	−29.5083	−1.31051
$508$	4.32847	0.192045
$509$	−30.1687	−1.33721	−0.668603	−	0.743619i	$-0.733107\pi$
$509$	−30.1687	−1.33721	−0.668603	+	0.743619i	$0.733107\pi$
$510$	−14.2473	−0.630879
$511$	9.61580	0.425378
$512$	−49.4718	−2.18636
$513$	−16.8919	−0.745796
$514$	32.5722	1.43670
$515$	3.25818	0.143573
$516$	53.3092	2.34681
$517$	−3.34122	−0.146947
$518$	−3.27527	−0.143907
$519$	58.7046	2.57685
$520$	−10.0050	−0.438749
$521$	−45.2001	−1.98025	−0.990126	−	0.140184i	$-0.955231\pi$
$521$	−45.2001	−1.98025	−0.990126	+	0.140184i	$0.955231\pi$
$522$	−5.59838	−0.245034
$523$	−31.0371	−1.35716	−0.678578	−	0.734528i	$-0.737404\pi$
$523$	−31.0371	−1.35716	−0.678578	+	0.734528i	$0.737404\pi$
$524$	44.9259	1.96260
$525$	9.65740	0.421484
$526$	−67.5199	−2.94401
$527$	6.47643	0.282118
$528$	−68.6640	−2.98822
$529$	−22.5625	−0.980980
$530$	29.4368	1.27865
$531$	54.4880	2.36458
$532$	21.3350	0.924989
$533$	12.1030	0.524238
$534$	82.3123	3.56200
$535$	8.32415	0.359885
$536$	−46.6268	−2.01397
$537$	8.82779	0.380947
$538$	−43.0962	−1.85801
$539$	−4.18912	−0.180438
$540$	−17.6673	−0.760278
$541$	28.5580	1.22781	0.613903	−	0.789381i	$-0.289599\pi$
$541$	28.5580	1.22781	0.613903	+	0.789381i	$0.289599\pi$
$542$	64.3533	2.76421
$543$	−44.5804	−1.91313
$544$	6.30739	0.270427
$545$	2.04521	0.0876072
$546$	−9.72810	−0.416324
$547$	44.5596	1.90523	0.952615	−	0.304179i	$-0.0983822\pi$
$547$	44.5596	1.90523	0.952615	+	0.304179i	$0.0983822\pi$
$548$	58.4149	2.49536
$549$	0.259934	0.0110937
$550$	37.7431	1.60937
$551$	2.56831	0.109414
$552$	−10.4469	−0.444650
$553$	−15.3521	−0.652839
$554$	−36.5375	−1.55233
$555$	−4.18127	−0.177485
$556$	−60.4486	−2.56359
$557$	−4.97061	−0.210612	−0.105306	−	0.994440i	$-0.533582\pi$
$557$	−4.97061	−0.210612	−0.105306	+	0.994440i	$0.533582\pi$
$558$	39.4581	1.67040
$559$	6.55022	0.277045
$560$	7.23978	0.305937
$561$	−19.9201	−0.841025
$562$	25.9285	1.09373
$563$	35.6218	1.50128	0.750641	−	0.660710i	$-0.229745\pi$
$563$	35.6218	1.50128	0.750641	+	0.660710i	$0.229745\pi$
$564$	9.30918	0.391987
$565$	23.8192	1.00208
$566$	−50.0492	−2.10372
$567$	3.57189	0.150005
$568$	37.9994	1.59442
$569$	−3.49593	−0.146557	−0.0732785	−	0.997312i	$-0.523346\pi$
$569$	−3.49593	−0.146557	−0.0732785	+	0.997312i	$0.523346\pi$
$570$	39.8215	1.66794
$571$	−8.82565	−0.369342	−0.184671	−	0.982800i	$-0.559122\pi$
$571$	−8.82565	−0.369342	−0.184671	+	0.982800i	$0.559122\pi$
$572$	−26.0040	−1.08728
$573$	64.2950	2.68596
$574$	−21.2304	−0.886139
$575$	2.36885	0.0987879
$576$	−13.4953	−0.562306
$577$	−23.9481	−0.996972	−0.498486	−	0.866898i	$-0.666110\pi$
$577$	−23.9481	−0.996972	−0.498486	+	0.866898i	$0.666110\pi$
$578$	−34.9426	−1.45342
$579$	6.02055	0.250206
$580$	2.68620	0.111538
$581$	−5.82288	−0.241574
$582$	0.415404	0.0172191
$583$	41.1576	1.70457
$584$	−56.3255	−2.33077
$585$	−7.29494	−0.301609
$586$	20.8783	0.862475
$587$	−23.7662	−0.980935	−0.490468	−	0.871459i	$-0.663174\pi$
$587$	−23.7662	−0.980935	−0.490468	+	0.871459i	$0.663174\pi$
$588$	11.6716	0.481328
$589$	−18.1018	−0.745872
$590$	−38.2245	−1.57368
$591$	55.0493	2.26443
$592$	7.91423	0.325273
$593$	−6.53535	−0.268375	−0.134187	−	0.990956i	$-0.542842\pi$
$593$	−6.53535	−0.268375	−0.134187	+	0.990956i	$0.542842\pi$
$594$	−36.1154	−1.48183
$595$	2.10033	0.0861049
$596$	−62.3805	−2.55520
$597$	25.6661	1.05044
$598$	−2.38619	−0.0975786
$599$	9.00587	0.367970	0.183985	−	0.982929i	$-0.441100\pi$
$599$	9.00587	0.367970	0.183985	+	0.982929i	$0.441100\pi$
$600$	−56.5692	−2.30943
$601$	16.6060	0.677375	0.338687	−	0.940899i	$-0.390017\pi$
$601$	16.6060	0.677375	0.338687	+	0.940899i	$0.390017\pi$
$602$	−11.4900	−0.468299
$603$	−33.9969	−1.38446
$604$	−39.5511	−1.60931
$605$	−7.79961	−0.317099
$606$	−64.7111	−2.62871
$607$	−26.6853	−1.08312	−0.541561	−	0.840661i	$-0.682167\pi$
$607$	−26.6853	−1.08312	−0.541561	+	0.840661i	$0.682167\pi$
$608$	−17.6293	−0.714963
$609$	1.40503	0.0569346
$610$	−0.182349	−0.00738309
$611$	1.14384	0.0462749
$612$	32.6009	1.31781
$613$	−7.72787	−0.312126	−0.156063	−	0.987747i	$-0.549880\pi$
$613$	−7.72787	−0.312126	−0.156063	+	0.987747i	$0.549880\pi$
$614$	−41.2976	−1.66663
$615$	−27.1030	−1.09290
$616$	24.5382	0.988672
$617$	−5.07794	−0.204430	−0.102215	−	0.994762i	$-0.532593\pi$
$617$	−5.07794	−0.204430	−0.102215	+	0.994762i	$0.532593\pi$
$618$	−18.5569	−0.746468
$619$	−27.0052	−1.08543	−0.542715	−	0.839917i	$-0.682604\pi$
$619$	−27.0052	−1.08543	−0.542715	+	0.839917i	$0.682604\pi$
$620$	−18.9327	−0.760355
$621$	−2.26669	−0.0909593
$622$	−22.9659	−0.920848
$623$	−12.1345	−0.486157
$624$	23.5066	0.941017
$625$	5.73466	0.229386
$626$	−8.13418	−0.325107
$627$	55.6771	2.22353
$628$	42.8103	1.70832
$629$	2.29599	0.0915471
$630$	12.7964	0.509820
$631$	−9.84678	−0.391994	−0.195997	−	0.980604i	$-0.562794\pi$
$631$	−9.84678	−0.391994	−0.195997	+	0.980604i	$0.562794\pi$
$632$	89.9266	3.57709
$633$	−32.6968	−1.29958
$634$	−31.9330	−1.26822
$635$	−1.19101	−0.0472637
$636$	−114.672	−4.54703
$637$	1.43411	0.0568217
$638$	5.49113	0.217396
$639$	27.7064	1.09605
$640$	17.9869	0.710995
$641$	37.7457	1.49087	0.745433	−	0.666580i	$-0.232243\pi$
$641$	37.7457	1.49087	0.745433	+	0.666580i	$0.232243\pi$
$642$	−47.4100	−1.87112
$643$	47.5016	1.87328	0.936640	−	0.350293i	$-0.113918\pi$
$643$	47.5016	1.87328	0.936640	+	0.350293i	$0.113918\pi$
$644$	2.86290	0.112814
$645$	−14.6684	−0.577567
$646$	−21.8665	−0.860326
$647$	34.5662	1.35894	0.679469	−	0.733704i	$-0.262210\pi$
$647$	34.5662	1.35894	0.679469	+	0.733704i	$0.262210\pi$
$648$	−20.9227	−0.821921
$649$	−53.4442	−2.09787
$650$	−12.9211	−0.506806
$651$	−9.90282	−0.388122
$652$	55.1822	2.16110
$653$	−4.89201	−0.191439	−0.0957196	−	0.995408i	$-0.530515\pi$
$653$	−4.89201	−0.191439	−0.0957196	+	0.995408i	$0.530515\pi$
$654$	−11.6485	−0.455491
$655$	−12.3617	−0.483010
$656$	51.3002	2.00294
$657$	−41.0685	−1.60223
$658$	−2.00646	−0.0782201
$659$	22.2731	0.867635	0.433817	−	0.901001i	$-0.357166\pi$
$659$	22.2731	0.867635	0.433817	+	0.901001i	$0.357166\pi$
$660$	58.2327	2.26671
$661$	24.9111	0.968929	0.484464	−	0.874811i	$-0.339015\pi$
$661$	24.9111	0.968929	0.484464	+	0.874811i	$0.339015\pi$
$662$	6.81273	0.264784
$663$	6.81948	0.264846
$664$	34.1081	1.32365
$665$	−5.87047	−0.227647
$666$	13.9885	0.542043
$667$	0.344637	0.0133444
$668$	88.5054	3.42438
$669$	16.2152	0.626915
$670$	23.8495	0.921387
$671$	−0.254954	−0.00984240
$672$	−9.64434	−0.372039
$673$	−18.1608	−0.700048	−0.350024	−	0.936741i	$-0.613827\pi$
$673$	−18.1608	−0.700048	−0.350024	+	0.936741i	$0.613827\pi$
$674$	71.3890	2.74980
$675$	−12.2740	−0.472426
$676$	−47.3678	−1.82184
$677$	13.4238	0.515920	0.257960	−	0.966156i	$-0.416950\pi$
$677$	13.4238	0.515920	0.257960	+	0.966156i	$0.416950\pi$
$678$	−135.661	−5.21005
$679$	−0.0612387	−0.00235013
$680$	−12.3029	−0.471793
$681$	−54.4251	−2.08557
$682$	−38.7022	−1.48199
$683$	37.8944	1.44999	0.724995	−	0.688754i	$-0.241842\pi$
$683$	37.8944	1.44999	0.724995	+	0.688754i	$0.241842\pi$
$684$	−91.1205	−3.48408
$685$	−16.0733	−0.614128
$686$	−2.51564	−0.0960478
$687$	29.1365	1.11163
$688$	27.7641	1.05850
$689$	−14.0900	−0.536786
$690$	5.34357	0.203426
$691$	−16.2233	−0.617162	−0.308581	−	0.951198i	$-0.599854\pi$
$691$	−16.2233	−0.617162	−0.308581	+	0.951198i	$0.599854\pi$
$692$	94.2348	3.58227
$693$	17.8915	0.679642
$694$	−3.00972	−0.114247
$695$	16.6328	0.630920
$696$	−8.23008	−0.311961
$697$	14.8827	0.563721
$698$	−17.3964	−0.658462
$699$	−47.7915	−1.80764
$700$	15.5024	0.585936
$701$	38.4189	1.45106	0.725530	−	0.688190i	$-0.241594\pi$
$701$	38.4189	1.45106	0.725530	+	0.688190i	$0.241594\pi$
$702$	12.3638	0.466643
$703$	−6.41736	−0.242035
$704$	13.2368	0.498881
$705$	−2.56148	−0.0964711
$706$	53.2708	2.00487
$707$	9.53969	0.358777
$708$	148.904	5.59617
$709$	29.6978	1.11532	0.557662	−	0.830068i	$-0.311698\pi$
$709$	29.6978	1.11532	0.557662	+	0.830068i	$0.311698\pi$
$710$	−19.4366	−0.729444
$711$	65.5680	2.45899
$712$	71.0788	2.66379
$713$	−2.42905	−0.0909686
$714$	−11.9624	−0.447680
$715$	7.15519	0.267589
$716$	14.1707	0.529583
$717$	43.9532	1.64146
$718$	−56.5673	−2.11107
$719$	−45.3102	−1.68979	−0.844893	−	0.534935i	$-0.820336\pi$
$719$	−45.3102	−1.68979	−0.844893	+	0.534935i	$0.820336\pi$
$720$	−30.9207	−1.15235
$721$	2.73565	0.101881
$722$	13.3203	0.495728
$723$	−44.2900	−1.64716
$724$	−71.5620	−2.65958
$725$	1.86618	0.0693083
$726$	44.4225	1.64867
$727$	−39.3597	−1.45977	−0.729885	−	0.683570i	$-0.760426\pi$
$727$	−39.3597	−1.45977	−0.729885	+	0.683570i	$0.760426\pi$
$728$	−8.40046	−0.311342
$729$	−42.9781	−1.59178
$730$	28.8104	1.06632
$731$	8.05461	0.297911
$732$	0.710344	0.0262551
$733$	−27.2312	−1.00581	−0.502903	−	0.864343i	$-0.667735\pi$
$733$	−27.2312	−1.00581	−0.502903	+	0.864343i	$0.667735\pi$
$734$	43.2536	1.59652
$735$	−3.21151	−0.118458
$736$	−2.36565	−0.0871989
$737$	33.3456	1.22830
$738$	90.6737	3.33774
$739$	−22.2361	−0.817967	−0.408984	−	0.912542i	$-0.634117\pi$
$739$	−22.2361	−0.817967	−0.408984	+	0.912542i	$0.634117\pi$
$740$	−6.71192	−0.246735
$741$	−19.0606	−0.700209
$742$	24.7159	0.907349
$743$	28.0249	1.02814	0.514068	−	0.857750i	$-0.328138\pi$
$743$	28.0249	1.02814	0.514068	+	0.857750i	$0.328138\pi$
$744$	58.0068	2.12663
$745$	17.1644	0.628855
$746$	21.5818	0.790165
$747$	24.8692	0.909915
$748$	−31.9764	−1.16917
$749$	6.98917	0.255379
$750$	69.3302	2.53158
$751$	9.19486	0.335525	0.167763	−	0.985827i	$-0.446346\pi$
$751$	9.19486	0.335525	0.167763	+	0.985827i	$0.446346\pi$
$752$	4.84834	0.176801
$753$	−27.1453	−0.989228
$754$	−1.87985	−0.0684599
$755$	10.8828	0.396064
$756$	−14.8339	−0.539503
$757$	8.04507	0.292403	0.146202	−	0.989255i	$-0.453295\pi$
$757$	8.04507	0.292403	0.146202	+	0.989255i	$0.453295\pi$
$758$	−11.5889	−0.420928
$759$	7.47121	0.271188
$760$	34.3868	1.24734
$761$	7.85377	0.284699	0.142350	−	0.989816i	$-0.454534\pi$
$761$	7.85377	0.284699	0.142350	+	0.989816i	$0.454534\pi$
$762$	6.78336	0.245735
$763$	1.71721	0.0621672
$764$	103.209	3.73396
$765$	−8.97036	−0.324324
$766$	−53.7589	−1.94239
$767$	18.2962	0.660638
$768$	−85.4034	−3.08173
$769$	−20.0308	−0.722331	−0.361165	−	0.932502i	$-0.617621\pi$
$769$	−20.0308	−0.722331	−0.361165	+	0.932502i	$0.617621\pi$
$770$	−12.5512	−0.452316
$771$	34.9134	1.25738
$772$	9.66441	0.347830
$773$	−28.9847	−1.04251	−0.521253	−	0.853402i	$-0.674535\pi$
$773$	−28.9847	−1.04251	−0.521253	+	0.853402i	$0.674535\pi$
$774$	49.0733	1.76390
$775$	−13.1531	−0.472474
$776$	0.358712	0.0128770
$777$	−3.51070	−0.125946
$778$	−62.0887	−2.22599
$779$	−41.5974	−1.49038
$780$	−19.9355	−0.713806
$781$	−27.1757	−0.972422
$782$	−2.93423	−0.104928
$783$	−1.78570	−0.0638159
$784$	6.07870	0.217097
$785$	−11.7795	−0.420430
$786$	70.4056	2.51128
$787$	−24.5826	−0.876276	−0.438138	−	0.898908i	$-0.644362\pi$
$787$	−24.5826	−0.876276	−0.438138	+	0.898908i	$0.644362\pi$
$788$	88.3671	3.14795
$789$	−72.3732	−2.57656
$790$	−45.9973	−1.63651
$791$	19.9992	0.711089
$792$	−104.801	−3.72395
$793$	0.0872816	0.00309946
$794$	52.9381	1.87870
$795$	31.5527	1.11906
$796$	41.2002	1.46030
$797$	−36.3224	−1.28661	−0.643303	−	0.765611i	$-0.722437\pi$
$797$	−36.3224	−1.28661	−0.643303	+	0.765611i	$0.722437\pi$
$798$	33.4351	1.18359
$799$	1.40655	0.0497600
$800$	−12.8098	−0.452895
$801$	51.8255	1.83117
$802$	32.0564	1.13195
$803$	40.2818	1.42151
$804$	−92.9063	−3.27655
$805$	−0.787747	−0.0277644
$806$	13.2494	0.466691
$807$	−46.1939	−1.62610
$808$	−55.8797	−1.96584
$809$	36.0132	1.26616	0.633079	−	0.774087i	$-0.281791\pi$
$809$	36.0132	1.26616	0.633079	+	0.774087i	$0.281791\pi$
$810$	10.7019	0.376027
$811$	−26.6085	−0.934350	−0.467175	−	0.884165i	$-0.654728\pi$
$811$	−26.6085	−0.934350	−0.467175	+	0.884165i	$0.654728\pi$
$812$	2.25540	0.0791490
$813$	68.9790	2.41920
$814$	−13.7205	−0.480904
$815$	−15.1838	−0.531864
$816$	28.9054	1.01189
$817$	−22.5129	−0.787625
$818$	−26.2876	−0.919126
$819$	−6.12501	−0.214025
$820$	−43.5068	−1.51932
$821$	−26.1926	−0.914130	−0.457065	−	0.889433i	$-0.651099\pi$
$821$	−26.1926	−0.914130	−0.457065	+	0.889433i	$0.651099\pi$
$822$	91.5449	3.19299
$823$	11.7091	0.408155	0.204077	−	0.978955i	$-0.434581\pi$
$823$	11.7091	0.408155	0.204077	+	0.978955i	$0.434581\pi$
$824$	−16.0244	−0.558235
$825$	40.4561	1.40850
$826$	−32.0942	−1.11670
$827$	18.5235	0.644126	0.322063	−	0.946718i	$-0.395624\pi$
$827$	18.5235	0.644126	0.322063	+	0.946718i	$0.395624\pi$
$828$	−12.2273	−0.424928
$829$	−42.3461	−1.47074	−0.735370	−	0.677666i	$-0.762992\pi$
$829$	−42.3461	−1.47074	−0.735370	+	0.677666i	$0.762992\pi$
$830$	−17.4462	−0.605567
$831$	−39.1638	−1.35858
$832$	−4.53152	−0.157102
$833$	1.76349	0.0611012
$834$	−94.7320	−3.28030
$835$	−24.3529	−0.842766
$836$	89.3749	3.09110
$837$	12.5859	0.435032
$838$	90.2428	3.11738
$839$	−44.7000	−1.54322	−0.771608	−	0.636098i	$-0.780547\pi$
$839$	−44.7000	−1.54322	−0.771608	+	0.636098i	$0.780547\pi$
$840$	18.8118	0.649067
$841$	−28.7285	−0.990638
$842$	5.84875	0.201561
$843$	27.7922	0.957214
$844$	−52.4860	−1.80664
$845$	13.0336	0.448369
$846$	8.56949	0.294625
$847$	−6.54875	−0.225018
$848$	−59.7225	−2.05088
$849$	−53.6467	−1.84115
$850$	−15.8886	−0.544976
$851$	−0.861133	−0.0295193
$852$	75.7159	2.59398
$853$	7.80530	0.267248	0.133624	−	0.991032i	$-0.457338\pi$
$853$	7.80530	0.267248	0.133624	+	0.991032i	$0.457338\pi$
$854$	−0.153105	−0.00523914
$855$	25.0724	0.857458
$856$	−40.9398	−1.39929
$857$	−1.90271	−0.0649954	−0.0324977	−	0.999472i	$-0.510346\pi$
$857$	−1.90271	−0.0649954	−0.0324977	+	0.999472i	$0.510346\pi$
$858$	−40.7522	−1.39126
$859$	−28.4688	−0.971343	−0.485671	−	0.874142i	$-0.661425\pi$
$859$	−28.4688	−0.971343	−0.485671	+	0.874142i	$0.661425\pi$
$860$	−23.5462	−0.802919
$861$	−22.7564	−0.775536
$862$	87.6499	2.98537
$863$	−13.4857	−0.459058	−0.229529	−	0.973302i	$-0.573719\pi$
$863$	−13.4857	−0.459058	−0.229529	+	0.973302i	$0.573719\pi$
$864$	12.2574	0.417005
$865$	−25.9293	−0.881624
$866$	−6.19067	−0.210368
$867$	−37.4543	−1.27201
$868$	−15.8964	−0.539558
$869$	−64.3120	−2.18163
$870$	4.20967	0.142721
$871$	−11.4156	−0.386803
$872$	−10.0587	−0.340632
$873$	0.261547	0.00885202
$874$	8.20125	0.277411
$875$	−10.2206	−0.345520
$876$	−112.232	−3.79195
$877$	−44.3003	−1.49592	−0.747958	−	0.663746i	$-0.768965\pi$
$877$	−44.3003	−1.49592	−0.747958	+	0.663746i	$0.768965\pi$
$878$	12.2435	0.413198
$879$	22.3790	0.754826
$880$	30.3283	1.02237
$881$	−6.63739	−0.223619	−0.111810	−	0.993730i	$-0.535665\pi$
$881$	−6.63739	−0.223619	−0.111810	+	0.993730i	$0.535665\pi$
$882$	10.7442	0.361775
$883$	−2.05879	−0.0692840	−0.0346420	−	0.999400i	$-0.511029\pi$
$883$	−2.05879	−0.0692840	−0.0346420	+	0.999400i	$0.511029\pi$
$884$	10.9469	0.368183
$885$	−40.9720	−1.37726
$886$	14.9619	0.502655
$887$	−30.8935	−1.03730	−0.518650	−	0.854986i	$-0.673565\pi$
$887$	−30.8935	−1.03730	−0.518650	+	0.854986i	$0.673565\pi$
$888$	20.5643	0.690091
$889$	−1.00000	−0.0335389
$890$	−36.3567	−1.21868
$891$	14.9631	0.501282
$892$	26.0292	0.871522
$893$	−3.93134	−0.131557
$894$	−97.7595	−3.26957
$895$	−3.89916	−0.130335
$896$	15.1023	0.504531
$897$	−2.55771	−0.0853995
$898$	−92.3340	−3.08122
$899$	−1.91361	−0.0638224
$900$	−66.2099	−2.20700
$901$	−17.3260	−0.577214
$902$	−88.9367	−2.96127
$903$	−12.3159	−0.409849
$904$	−117.147	−3.89625
$905$	19.6908	0.654544
$906$	−61.9825	−2.05923
$907$	−41.0485	−1.36299	−0.681496	−	0.731822i	$-0.738670\pi$
$907$	−41.0485	−1.36299	−0.681496	+	0.731822i	$0.738670\pi$
$908$	−87.3652	−2.89931
$909$	−40.7435	−1.35138
$910$	4.29682	0.142438
$911$	26.5615	0.880022	0.440011	−	0.897992i	$-0.354975\pi$
$911$	26.5615	0.880022	0.440011	+	0.897992i	$0.354975\pi$
$912$	−80.7912	−2.67527
$913$	−24.3928	−0.807282
$914$	−76.7348	−2.53816
$915$	−0.195456	−0.00646158
$916$	46.7710	1.54536
$917$	−10.3792	−0.342750
$918$	15.2034	0.501788
$919$	17.7417	0.585244	0.292622	−	0.956228i	$-0.405472\pi$
$919$	17.7417	0.585244	0.292622	+	0.956228i	$0.405472\pi$
$920$	4.61431	0.152129
$921$	−44.2660	−1.45861
$922$	65.8533	2.16876
$923$	9.30338	0.306225
$924$	48.8937	1.60848
$925$	−4.66297	−0.153318
$926$	75.0470	2.46620
$927$	−11.6838	−0.383747
$928$	−1.86366	−0.0611776
$929$	7.81515	0.256407	0.128203	−	0.991748i	$-0.459079\pi$
$929$	7.81515	0.256407	0.128203	+	0.991748i	$0.459079\pi$
$930$	−29.6704	−0.972929
$931$	−4.92899	−0.161541
$932$	−76.7167	−2.51294
$933$	−24.6167	−0.805913
$934$	−66.4500	−2.17431
$935$	8.79852	0.287742
$936$	35.8779	1.17271
$937$	8.84523	0.288961	0.144481	−	0.989508i	$-0.453849\pi$
$937$	8.84523	0.288961	0.144481	+	0.989508i	$0.453849\pi$
$938$	20.0246	0.653828
$939$	−8.71886	−0.284529
$940$	−4.11179	−0.134112
$941$	49.2706	1.60618	0.803089	−	0.595860i	$-0.203189\pi$
$941$	49.2706	1.60618	0.803089	+	0.595860i	$0.203189\pi$
$942$	67.0901	2.18591
$943$	−5.58188	−0.181771
$944$	77.5512	2.52408
$945$	4.08164	0.132776
$946$	−48.1332	−1.56495
$947$	13.1496	0.427304	0.213652	−	0.976910i	$-0.431464\pi$
$947$	13.1496	0.427304	0.213652	+	0.976910i	$0.431464\pi$
$948$	179.184	5.81961
$949$	−13.7901	−0.447647
$950$	44.4092	1.44082
$951$	−34.2284	−1.10993
$952$	−10.3298	−0.334791
$953$	−28.3848	−0.919474	−0.459737	−	0.888055i	$-0.652056\pi$
$953$	−28.3848	−0.919474	−0.459737	+	0.888055i	$0.652056\pi$
$954$	−105.560	−3.41763
$955$	−28.3986	−0.918956
$956$	70.5552	2.28192
$957$	5.88583	0.190262
$958$	75.0456	2.42461
$959$	−13.4955	−0.435793
$960$	10.1478	0.327518
$961$	−17.5126	−0.564924
$962$	4.69711	0.151441
$963$	−29.8503	−0.961913
$964$	−71.0959	−2.28985
$965$	−2.65923	−0.0856035
$966$	4.48660	0.144354
$967$	0.655032	0.0210644	0.0105322	−	0.999945i	$-0.496647\pi$
$967$	0.655032	0.0210644	0.0105322	+	0.999945i	$0.496647\pi$
$968$	38.3600	1.23294
$969$	−23.4383	−0.752946
$970$	−0.183481	−0.00589120
$971$	13.2088	0.423892	0.211946	−	0.977281i	$-0.432020\pi$
$971$	13.2088	0.423892	0.211946	+	0.977281i	$0.432020\pi$
$972$	−86.1912	−2.76458
$973$	13.9654	0.447709
$974$	76.6965	2.45751
$975$	−13.8498	−0.443549
$976$	0.369956	0.0118420
$977$	−41.1030	−1.31500	−0.657501	−	0.753454i	$-0.728386\pi$
$977$	−41.1030	−1.31500	−0.657501	+	0.753454i	$0.728386\pi$
$978$	86.4787	2.76528
$979$	−50.8327	−1.62462
$980$	−5.15524	−0.164678
$981$	−7.33410	−0.234160
$982$	31.8012	1.01482
$983$	31.5908	1.00759	0.503795	−	0.863823i	$-0.331937\pi$
$983$	31.5908	1.00759	0.503795	+	0.863823i	$0.331937\pi$
$984$	133.298	4.24938
$985$	−24.3148	−0.774735
$986$	−2.31159	−0.0736160
$987$	−2.15069	−0.0684571
$988$	−30.5968	−0.973414
$989$	−3.02096	−0.0960609
$990$	53.6056	1.70370
$991$	−18.8619	−0.599168	−0.299584	−	0.954070i	$-0.596848\pi$
$991$	−18.8619	−0.599168	−0.299584	+	0.954070i	$0.596848\pi$
$992$	13.1353	0.417047
$993$	7.30242	0.231735
$994$	−16.3195	−0.517623
$995$	−11.3365	−0.359392
$996$	67.9622	2.15346
$997$	10.7025	0.338952	0.169476	−	0.985534i	$-0.445793\pi$
$997$	10.7025	0.338952	0.169476	+	0.985534i	$0.445793\pi$
$998$	−82.8967	−2.62405
$999$	4.46188	0.141168

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	889.2.a.b.1.14	✓	15
3.2	odd	2		8001.2.a.q.1.2		15
7.6	odd	2		6223.2.a.j.1.14		15

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
889.2.a.b.1.14	✓	15	1.1	even	1	trivial
6223.2.a.j.1.14		15	7.6	odd	2
8001.2.a.q.1.2		15	3.2	odd	2

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:	\( N \)	\(=\)	\( 889 = 7 \cdot 127 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	889.a (trivial)

\(f(q)\)	\(=\)	\(q+2.51564 q^{2} +2.69647 q^{3} +4.32847 q^{4} -1.19101 q^{5} +6.78336 q^{6} -1.00000 q^{7} +5.85760 q^{8} +4.27094 q^{9} +O(q^{10})\)	\(q+2.51564 q^{2} +2.69647 q^{3} +4.32847 q^{4} -1.19101 q^{5} +6.78336 q^{6} -1.00000 q^{7} +5.85760 q^{8} +4.27094 q^{9} -2.99615 q^{10} -4.18912 q^{11} +11.6716 q^{12} +1.43411 q^{13} -2.51564 q^{14} -3.21151 q^{15} +6.07870 q^{16} +1.76349 q^{17} +10.7442 q^{18} -4.92899 q^{19} -5.15524 q^{20} -2.69647 q^{21} -10.5383 q^{22} -0.661413 q^{23} +15.7948 q^{24} -3.58150 q^{25} +3.60772 q^{26} +3.42705 q^{27} -4.32847 q^{28} -0.521062 q^{29} -8.07903 q^{30} +3.67252 q^{31} +3.57666 q^{32} -11.2958 q^{33} +4.43630 q^{34} +1.19101 q^{35} +18.4866 q^{36} +1.30196 q^{37} -12.3996 q^{38} +3.86704 q^{39} -6.97644 q^{40} +8.43934 q^{41} -6.78336 q^{42} +4.56744 q^{43} -18.1325 q^{44} -5.08672 q^{45} -1.66388 q^{46} +0.797594 q^{47} +16.3910 q^{48} +1.00000 q^{49} -9.00978 q^{50} +4.75518 q^{51} +6.20752 q^{52} -9.82487 q^{53} +8.62124 q^{54} +4.98928 q^{55} -5.85760 q^{56} -13.2909 q^{57} -1.31081 q^{58} +12.7579 q^{59} -13.9009 q^{60} +0.0608610 q^{61} +9.23874 q^{62} -4.27094 q^{63} -3.15981 q^{64} -1.70804 q^{65} -28.4163 q^{66} -7.96005 q^{67} +7.63319 q^{68} -1.78348 q^{69} +2.99615 q^{70} +6.48720 q^{71} +25.0175 q^{72} -9.61580 q^{73} +3.27527 q^{74} -9.65740 q^{75} -21.3350 q^{76} +4.18912 q^{77} +9.72810 q^{78} +15.3521 q^{79} -7.23978 q^{80} -3.57189 q^{81} +21.2304 q^{82} +5.82288 q^{83} -11.6716 q^{84} -2.10033 q^{85} +11.4900 q^{86} -1.40503 q^{87} -24.5382 q^{88} +12.1345 q^{89} -12.7964 q^{90} -1.43411 q^{91} -2.86290 q^{92} +9.90282 q^{93} +2.00646 q^{94} +5.87047 q^{95} +9.64434 q^{96} +0.0612387 q^{97} +2.51564 q^{98} -17.8915 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 15 q + 4 q^{3} + 14 q^{4} + 7 q^{5} + 8 q^{6} - 15 q^{7} + 9 q^{9}+O(q^{10}) \) 15 * q + 4 * q^3 + 14 * q^4 + 7 * q^5 + 8 * q^6 - 15 * q^7 + 9 * q^9	\( 15 q + 4 q^{3} + 14 q^{4} + 7 q^{5} + 8 q^{6} - 15 q^{7} + 9 q^{9} + 10 q^{10} + 14 q^{11} + 10 q^{12} + 6 q^{13} + 6 q^{15} + 20 q^{16} + 10 q^{17} + q^{18} + 13 q^{19} + 8 q^{20} - 4 q^{21} - 11 q^{22} + 15 q^{23} + 34 q^{24} + 22 q^{26} + 22 q^{27} - 14 q^{28} + 16 q^{29} + 7 q^{30} + 22 q^{31} + 14 q^{33} - 15 q^{34} - 7 q^{35} + 20 q^{36} - 14 q^{37} - 6 q^{38} + 29 q^{39} + 22 q^{40} + 19 q^{41} - 8 q^{42} - q^{43} + 25 q^{44} - 8 q^{45} - 28 q^{46} + 49 q^{47} - 14 q^{48} + 15 q^{49} + 24 q^{50} - 8 q^{51} - 17 q^{52} - 28 q^{53} + 13 q^{54} + 39 q^{55} - 12 q^{57} - 10 q^{58} + 43 q^{59} - 60 q^{60} + 27 q^{61} + 14 q^{62} - 9 q^{63} + 18 q^{64} - 8 q^{65} - 36 q^{66} + 3 q^{67} + 13 q^{68} - 17 q^{69} - 10 q^{70} + 55 q^{71} - 21 q^{72} - 3 q^{73} - 12 q^{74} + 8 q^{75} - 20 q^{76} - 14 q^{77} - 6 q^{78} + 18 q^{79} + 29 q^{80} - 17 q^{81} + 14 q^{82} + 17 q^{83} - 10 q^{84} + 7 q^{85} + 4 q^{86} + 35 q^{87} - 114 q^{88} + 36 q^{89} - 39 q^{90} - 6 q^{91} + 45 q^{92} + 15 q^{93} - 15 q^{94} + 59 q^{95} + 85 q^{96} - 2 q^{97} + 35 q^{99}+O(q^{100}) \) 15 * q + 4 * q^3 + 14 * q^4 + 7 * q^5 + 8 * q^6 - 15 * q^7 + 9 * q^9 + 10 * q^10 + 14 * q^11 + 10 * q^12 + 6 * q^13 + 6 * q^15 + 20 * q^16 + 10 * q^17 + q^18 + 13 * q^19 + 8 * q^20 - 4 * q^21 - 11 * q^22 + 15 * q^23 + 34 * q^24 + 22 * q^26 + 22 * q^27 - 14 * q^28 + 16 * q^29 + 7 * q^30 + 22 * q^31 + 14 * q^33 - 15 * q^34 - 7 * q^35 + 20 * q^36 - 14 * q^37 - 6 * q^38 + 29 * q^39 + 22 * q^40 + 19 * q^41 - 8 * q^42 - q^43 + 25 * q^44 - 8 * q^45 - 28 * q^46 + 49 * q^47 - 14 * q^48 + 15 * q^49 + 24 * q^50 - 8 * q^51 - 17 * q^52 - 28 * q^53 + 13 * q^54 + 39 * q^55 - 12 * q^57 - 10 * q^58 + 43 * q^59 - 60 * q^60 + 27 * q^61 + 14 * q^62 - 9 * q^63 + 18 * q^64 - 8 * q^65 - 36 * q^66 + 3 * q^67 + 13 * q^68 - 17 * q^69 - 10 * q^70 + 55 * q^71 - 21 * q^72 - 3 * q^73 - 12 * q^74 + 8 * q^75 - 20 * q^76 - 14 * q^77 - 6 * q^78 + 18 * q^79 + 29 * q^80 - 17 * q^81 + 14 * q^82 + 17 * q^83 - 10 * q^84 + 7 * q^85 + 4 * q^86 + 35 * q^87 - 114 * q^88 + 36 * q^89 - 39 * q^90 - 6 * q^91 + 45 * q^92 + 15 * q^93 - 15 * q^94 + 59 * q^95 + 85 * q^96 - 2 * q^97 + 35 * q^99

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