LMFDB - Embedded newform 6017.2.a.c.1.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6017,2,Mod(1,6017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6017, 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("6017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6017 = 11 \cdot 547 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6017.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:	$48.0459868962$
Analytic rank:	$1$
Dimension:	$106$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
Character	$\chi$	$=$	6017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.61585 q^{2} +1.81779 q^{3} +4.84270 q^{4} +3.74717 q^{5} -4.75507 q^{6} +0.406260 q^{7} -7.43608 q^{8} +0.304348 q^{9} +O(q^{10})$	\(q-2.61585 q^{2} +1.81779 q^{3} +4.84270 q^{4} +3.74717 q^{5} -4.75507 q^{6} +0.406260 q^{7} -7.43608 q^{8} +0.304348 q^{9} -9.80206 q^{10} +1.00000 q^{11} +8.80299 q^{12} -3.01331 q^{13} -1.06272 q^{14} +6.81156 q^{15} +9.76632 q^{16} -6.49061 q^{17} -0.796131 q^{18} -1.64413 q^{19} +18.1464 q^{20} +0.738494 q^{21} -2.61585 q^{22} -1.93831 q^{23} -13.5172 q^{24} +9.04131 q^{25} +7.88239 q^{26} -4.90012 q^{27} +1.96740 q^{28} -7.98224 q^{29} -17.8181 q^{30} -2.09748 q^{31} -10.6751 q^{32} +1.81779 q^{33} +16.9785 q^{34} +1.52233 q^{35} +1.47387 q^{36} -4.51913 q^{37} +4.30082 q^{38} -5.47756 q^{39} -27.8643 q^{40} +8.72483 q^{41} -1.93179 q^{42} -11.3450 q^{43} +4.84270 q^{44} +1.14045 q^{45} +5.07033 q^{46} -1.52918 q^{47} +17.7531 q^{48} -6.83495 q^{49} -23.6508 q^{50} -11.7985 q^{51} -14.5926 q^{52} -5.40672 q^{53} +12.8180 q^{54} +3.74717 q^{55} -3.02098 q^{56} -2.98868 q^{57} +20.8804 q^{58} +5.97599 q^{59} +32.9863 q^{60} +13.7626 q^{61} +5.48671 q^{62} +0.123645 q^{63} +8.39191 q^{64} -11.2914 q^{65} -4.75507 q^{66} +7.92550 q^{67} -31.4320 q^{68} -3.52343 q^{69} -3.98219 q^{70} +12.1603 q^{71} -2.26316 q^{72} -6.94597 q^{73} +11.8214 q^{74} +16.4352 q^{75} -7.96204 q^{76} +0.406260 q^{77} +14.3285 q^{78} +7.28573 q^{79} +36.5961 q^{80} -9.82042 q^{81} -22.8229 q^{82} +8.02259 q^{83} +3.57630 q^{84} -24.3214 q^{85} +29.6768 q^{86} -14.5100 q^{87} -7.43608 q^{88} +0.679834 q^{89} -2.98324 q^{90} -1.22419 q^{91} -9.38663 q^{92} -3.81278 q^{93} +4.00012 q^{94} -6.16086 q^{95} -19.4051 q^{96} -14.7354 q^{97} +17.8792 q^{98} +0.304348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) $ 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * 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 $

$2$	−2.61585	−1.84969	−0.924844	−	0.380346i	$-0.875805\pi$
$2$	−2.61585	−1.84969	−0.924844	+	0.380346i	$0.875805\pi$
$3$	1.81779	1.04950	0.524750	−	0.851257i	$-0.324159\pi$
$3$	1.81779	1.04950	0.524750	+	0.851257i	$0.324159\pi$
$4$	4.84270	2.42135
$5$	3.74717	1.67579	0.837894	−	0.545834i	$-0.183787\pi$
$5$	3.74717	1.67579	0.837894	+	0.545834i	$0.183787\pi$
$6$	−4.75507	−1.94125
$7$	0.406260	0.153552	0.0767760	−	0.997048i	$-0.475537\pi$
$7$	0.406260	0.153552	0.0767760	+	0.997048i	$0.475537\pi$
$8$	−7.43608	−2.62905
$9$	0.304348	0.101449
$10$	−9.80206	−3.09968
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	8.80299	2.54120
$13$	−3.01331	−0.835742	−0.417871	−	0.908506i	$-0.637224\pi$
$13$	−3.01331	−0.835742	−0.417871	+	0.908506i	$0.637224\pi$
$14$	−1.06272	−0.284023
$15$	6.81156	1.75874
$16$	9.76632	2.44158
$17$	−6.49061	−1.57420	−0.787102	−	0.616823i	$-0.788419\pi$
$17$	−6.49061	−1.57420	−0.787102	+	0.616823i	$0.788419\pi$
$18$	−0.796131	−0.187650
$19$	−1.64413	−0.377190	−0.188595	−	0.982055i	$-0.560393\pi$
$19$	−1.64413	−0.377190	−0.188595	+	0.982055i	$0.560393\pi$
$20$	18.1464	4.05766
$21$	0.738494	0.161153
$22$	−2.61585	−0.557702
$23$	−1.93831	−0.404165	−0.202082	−	0.979369i	$-0.564771\pi$
$23$	−1.93831	−0.404165	−0.202082	+	0.979369i	$0.564771\pi$
$24$	−13.5172	−2.75919
$25$	9.04131	1.80826
$26$	7.88239	1.54586
$27$	−4.90012	−0.943028
$28$	1.96740	0.371803
$29$	−7.98224	−1.48227	−0.741133	−	0.671359i	$-0.765711\pi$
$29$	−7.98224	−1.48227	−0.741133	+	0.671359i	$0.765711\pi$
$30$	−17.8181	−3.25312
$31$	−2.09748	−0.376719	−0.188360	−	0.982100i	$-0.560317\pi$
$31$	−2.09748	−0.376719	−0.188360	+	0.982100i	$0.560317\pi$
$32$	−10.6751	−1.88711
$33$	1.81779	0.316436
$34$	16.9785	2.91179
$35$	1.52233	0.257320
$36$	1.47387	0.245644
$37$	−4.51913	−0.742940	−0.371470	−	0.928445i	$-0.621146\pi$
$37$	−4.51913	−0.742940	−0.371470	+	0.928445i	$0.621146\pi$
$38$	4.30082	0.697684
$39$	−5.47756	−0.877111
$40$	−27.8643	−4.40573
$41$	8.72483	1.36259	0.681295	−	0.732009i	$-0.261417\pi$
$41$	8.72483	1.36259	0.681295	+	0.732009i	$0.261417\pi$
$42$	−1.93179	−0.298082
$43$	−11.3450	−1.73009	−0.865046	−	0.501693i	$-0.832711\pi$
$43$	−11.3450	−1.73009	−0.865046	+	0.501693i	$0.832711\pi$
$44$	4.84270	0.730064
$45$	1.14045	0.170008
$46$	5.07033	0.747579
$47$	−1.52918	−0.223054	−0.111527	−	0.993761i	$-0.535574\pi$
$47$	−1.52918	−0.223054	−0.111527	+	0.993761i	$0.535574\pi$
$48$	17.7531	2.56244
$49$	−6.83495	−0.976422
$50$	−23.6508	−3.34472
$51$	−11.7985	−1.65213
$52$	−14.5926	−2.02362
$53$	−5.40672	−0.742671	−0.371335	−	0.928499i	$-0.621100\pi$
$53$	−5.40672	−0.742671	−0.371335	+	0.928499i	$0.621100\pi$
$54$	12.8180	1.74431
$55$	3.74717	0.505269
$56$	−3.02098	−0.403696
$57$	−2.98868	−0.395861
$58$	20.8804	2.74173
$59$	5.97599	0.778008	0.389004	−	0.921236i	$-0.372819\pi$
$59$	5.97599	0.778008	0.389004	+	0.921236i	$0.372819\pi$
$60$	32.9863	4.25852
$61$	13.7626	1.76212	0.881062	−	0.473001i	$-0.156829\pi$
$61$	13.7626	1.76212	0.881062	+	0.473001i	$0.156829\pi$
$62$	5.48671	0.696813
$63$	0.123645	0.0155778
$64$	8.39191	1.04899
$65$	−11.2914	−1.40053
$66$	−4.75507	−0.585308
$67$	7.92550	0.968254	0.484127	−	0.874998i	$-0.339137\pi$
$67$	7.92550	0.968254	0.484127	+	0.874998i	$0.339137\pi$
$68$	−31.4320	−3.81170
$69$	−3.52343	−0.424171
$70$	−3.98219	−0.475962
$71$	12.1603	1.44316	0.721581	−	0.692330i	$-0.243416\pi$
$71$	12.1603	1.44316	0.721581	+	0.692330i	$0.243416\pi$
$72$	−2.26316	−0.266716
$73$	−6.94597	−0.812964	−0.406482	−	0.913659i	$-0.633245\pi$
$73$	−6.94597	−0.812964	−0.406482	+	0.913659i	$0.633245\pi$
$74$	11.8214	1.37421
$75$	16.4352	1.89777
$76$	−7.96204	−0.913309
$77$	0.406260	0.0462976
$78$	14.3285	1.62238
$79$	7.28573	0.819709	0.409854	−	0.912151i	$-0.365580\pi$
$79$	7.28573	0.819709	0.409854	+	0.912151i	$0.365580\pi$
$80$	36.5961	4.09157
$81$	−9.82042	−1.09116
$82$	−22.8229	−2.52037
$83$	8.02259	0.880594	0.440297	−	0.897852i	$-0.354873\pi$
$83$	8.02259	0.880594	0.440297	+	0.897852i	$0.354873\pi$
$84$	3.57630	0.390207
$85$	−24.3214	−2.63803
$86$	29.6768	3.20013
$87$	−14.5100	−1.55564
$88$	−7.43608	−0.792689
$89$	0.679834	0.0720622	0.0360311	−	0.999351i	$-0.488528\pi$
$89$	0.679834	0.0720622	0.0360311	+	0.999351i	$0.488528\pi$
$90$	−2.98324	−0.314461
$91$	−1.22419	−0.128330
$92$	−9.38663	−0.978623
$93$	−3.81278	−0.395366
$94$	4.00012	0.412581
$95$	−6.16086	−0.632090
$96$	−19.4051	−1.98052
$97$	−14.7354	−1.49616	−0.748079	−	0.663610i	$-0.769024\pi$
$97$	−14.7354	−1.49616	−0.748079	+	0.663610i	$0.769024\pi$
$98$	17.8792	1.80608
$99$	0.304348	0.0305881
$100$	43.7843	4.37843
$101$	−10.0124	−0.996272	−0.498136	−	0.867099i	$-0.665982\pi$
$101$	−10.0124	−0.996272	−0.498136	+	0.867099i	$0.665982\pi$
$102$	30.8633	3.05592
$103$	6.17742	0.608679	0.304340	−	0.952564i	$-0.401564\pi$
$103$	6.17742	0.608679	0.304340	+	0.952564i	$0.401564\pi$
$104$	22.4072	2.19721
$105$	2.76727	0.270058
$106$	14.1432	1.37371
$107$	−14.5630	−1.40786	−0.703931	−	0.710268i	$-0.748574\pi$
$107$	−14.5630	−1.40786	−0.703931	+	0.710268i	$0.748574\pi$
$108$	−23.7298	−2.28340
$109$	1.69123	0.161991	0.0809954	−	0.996714i	$-0.474190\pi$
$109$	1.69123	0.161991	0.0809954	+	0.996714i	$0.474190\pi$
$110$	−9.80206	−0.934590
$111$	−8.21481	−0.779715
$112$	3.96767	0.374909
$113$	−10.6778	−1.00448	−0.502242	−	0.864727i	$-0.667491\pi$
$113$	−10.6778	−1.00448	−0.502242	+	0.864727i	$0.667491\pi$
$114$	7.81797	0.732220
$115$	−7.26317	−0.677294
$116$	−38.6556	−3.58908
$117$	−0.917096	−0.0847856
$118$	−15.6323	−1.43907
$119$	−2.63688	−0.241722
$120$	−50.6513	−4.62381
$121$	1.00000	0.0909091
$122$	−36.0010	−3.25938
$123$	15.8599	1.43004
$124$	−10.1575	−0.912168
$125$	15.1435	1.35448
$126$	−0.323436	−0.0288140
$127$	8.81146	0.781891	0.390945	−	0.920414i	$-0.372148\pi$
$127$	8.81146	0.781891	0.390945	+	0.920414i	$0.372148\pi$
$128$	−0.601782	−0.0531905
$129$	−20.6227	−1.81573
$130$	29.5367	2.59054
$131$	−7.45255	−0.651132	−0.325566	−	0.945519i	$-0.605555\pi$
$131$	−7.45255	−0.651132	−0.325566	+	0.945519i	$0.605555\pi$
$132$	8.80299	0.766202
$133$	−0.667946	−0.0579183
$134$	−20.7320	−1.79097
$135$	−18.3616	−1.58031
$136$	48.2647	4.13866
$137$	21.5751	1.84329	0.921644	−	0.388037i	$-0.126847\pi$
$137$	21.5751	1.84329	0.921644	+	0.388037i	$0.126847\pi$
$138$	9.21677	0.784584
$139$	13.6880	1.16100	0.580501	−	0.814260i	$-0.302857\pi$
$139$	13.6880	1.16100	0.580501	+	0.814260i	$0.302857\pi$
$140$	7.37217	0.623062
$141$	−2.77973	−0.234095
$142$	−31.8096	−2.66940
$143$	−3.01331	−0.251986
$144$	2.97236	0.247697
$145$	−29.9108	−2.48396
$146$	18.1696	1.50373
$147$	−12.4245	−1.02475
$148$	−21.8848	−1.79892
$149$	3.22940	0.264563	0.132281	−	0.991212i	$-0.457770\pi$
$149$	3.22940	0.264563	0.132281	+	0.991212i	$0.457770\pi$
$150$	−42.9920	−3.51028
$151$	3.62504	0.295002	0.147501	−	0.989062i	$-0.452877\pi$
$151$	3.62504	0.295002	0.147501	+	0.989062i	$0.452877\pi$
$152$	12.2259	0.991653
$153$	−1.97540	−0.159702
$154$	−1.06272	−0.0856362
$155$	−7.85963	−0.631301
$156$	−26.5262	−2.12379
$157$	−20.4077	−1.62871	−0.814355	−	0.580367i	$-0.802909\pi$
$157$	−20.4077	−1.62871	−0.814355	+	0.580367i	$0.802909\pi$
$158$	−19.0584	−1.51621
$159$	−9.82827	−0.779433
$160$	−40.0015	−3.16240
$161$	−0.787456	−0.0620603
$162$	25.6888	2.01830
$163$	−18.9494	−1.48423	−0.742114	−	0.670273i	$-0.766177\pi$
$163$	−18.9494	−1.48423	−0.742114	+	0.670273i	$0.766177\pi$
$164$	42.2517	3.29931
$165$	6.81156	0.530279
$166$	−20.9859	−1.62883
$167$	−12.6749	−0.980816	−0.490408	−	0.871493i	$-0.663152\pi$
$167$	−12.6749	−0.980816	−0.490408	+	0.871493i	$0.663152\pi$
$168$	−5.49151	−0.423679
$169$	−3.91995	−0.301535
$170$	63.6213	4.87953
$171$	−0.500389	−0.0382657
$172$	−54.9403	−4.18916
$173$	11.1155	0.845096	0.422548	−	0.906340i	$-0.361136\pi$
$173$	11.1155	0.845096	0.422548	+	0.906340i	$0.361136\pi$
$174$	37.9561	2.87744
$175$	3.67312	0.277662
$176$	9.76632	0.736164
$177$	10.8631	0.816519
$178$	−1.77835	−0.133293
$179$	−15.8713	−1.18628	−0.593139	−	0.805100i	$-0.702112\pi$
$179$	−15.8713	−1.18628	−0.593139	+	0.805100i	$0.702112\pi$
$180$	5.52283	0.411648
$181$	−23.4620	−1.74392	−0.871959	−	0.489579i	$-0.837150\pi$
$181$	−23.4620	−1.74392	−0.871959	+	0.489579i	$0.837150\pi$
$182$	3.20230	0.237370
$183$	25.0175	1.84935
$184$	14.4134	1.06257
$185$	−16.9340	−1.24501
$186$	9.97367	0.731305
$187$	−6.49061	−0.474640
$188$	−7.40537	−0.540092
$189$	−1.99072	−0.144804
$190$	16.1159	1.16917
$191$	−14.7215	−1.06521	−0.532606	−	0.846363i	$-0.678787\pi$
$191$	−14.7215	−1.06521	−0.532606	+	0.846363i	$0.678787\pi$
$192$	15.2547	1.10091
$193$	−14.9958	−1.07942	−0.539712	−	0.841850i	$-0.681467\pi$
$193$	−14.9958	−1.07942	−0.539712	+	0.841850i	$0.681467\pi$
$194$	38.5458	2.76743
$195$	−20.5254	−1.46985
$196$	−33.0996	−2.36426
$197$	−13.9415	−0.993293	−0.496647	−	0.867953i	$-0.665436\pi$
$197$	−13.9415	−0.993293	−0.496647	+	0.867953i	$0.665436\pi$
$198$	−0.796131	−0.0565785
$199$	−20.9879	−1.48779	−0.743895	−	0.668296i	$-0.767024\pi$
$199$	−20.9879	−1.48779	−0.743895	+	0.668296i	$0.767024\pi$
$200$	−67.2319	−4.75402
$201$	14.4069	1.01618
$202$	26.1910	1.84279
$203$	−3.24287	−0.227605
$204$	−57.1367	−4.00037
$205$	32.6935	2.28341
$206$	−16.1592	−1.12587
$207$	−0.589920	−0.0410023
$208$	−29.4290	−2.04053
$209$	−1.64413	−0.113727
$210$	−7.23877	−0.499522
$211$	−10.0528	−0.692063	−0.346032	−	0.938223i	$-0.612471\pi$
$211$	−10.0528	−0.692063	−0.346032	+	0.938223i	$0.612471\pi$
$212$	−26.1831	−1.79826
$213$	22.1048	1.51460
$214$	38.0948	2.60411
$215$	−42.5116	−2.89927
$216$	36.4377	2.47927
$217$	−0.852124	−0.0578459
$218$	−4.42402	−0.299633
$219$	−12.6263	−0.853206
$220$	18.1464	1.22343
$221$	19.5582	1.31563
$222$	21.4887	1.44223
$223$	15.5038	1.03821	0.519105	−	0.854711i	$-0.326266\pi$
$223$	15.5038	1.03821	0.519105	+	0.854711i	$0.326266\pi$
$224$	−4.33687	−0.289770
$225$	2.75171	0.183447
$226$	27.9316	1.85798
$227$	19.0306	1.26310	0.631552	−	0.775333i	$-0.282418\pi$
$227$	19.0306	1.26310	0.631552	+	0.775333i	$0.282418\pi$
$228$	−14.4733	−0.958517
$229$	−11.7134	−0.774045	−0.387023	−	0.922070i	$-0.626496\pi$
$229$	−11.7134	−0.774045	−0.387023	+	0.922070i	$0.626496\pi$
$230$	18.9994	1.25278
$231$	0.738494	0.0485894
$232$	59.3566	3.89695
$233$	29.3282	1.92135	0.960677	−	0.277669i	$-0.0895617\pi$
$233$	29.3282	1.92135	0.960677	+	0.277669i	$0.0895617\pi$
$234$	2.39899	0.156827
$235$	−5.73012	−0.373792
$236$	28.9399	1.88383
$237$	13.2439	0.860284
$238$	6.89768	0.447110
$239$	−19.7215	−1.27568	−0.637840	−	0.770169i	$-0.720172\pi$
$239$	−19.7215	−1.27568	−0.637840	+	0.770169i	$0.720172\pi$
$240$	66.5239	4.29410
$241$	5.17290	0.333216	0.166608	−	0.986023i	$-0.446719\pi$
$241$	5.17290	0.333216	0.166608	+	0.986023i	$0.446719\pi$
$242$	−2.61585	−0.168154
$243$	−3.15106	−0.202141
$244$	66.6482	4.26672
$245$	−25.6118	−1.63627
$246$	−41.4872	−2.64513
$247$	4.95429	0.315234
$248$	15.5971	0.990414
$249$	14.5834	0.924183
$250$	−39.6132	−2.50536
$251$	−26.9332	−1.70001	−0.850004	−	0.526777i	$-0.823400\pi$
$251$	−26.9332	−1.70001	−0.850004	+	0.526777i	$0.823400\pi$
$252$	0.598773	0.0377192
$253$	−1.93831	−0.121860
$254$	−23.0495	−1.44625
$255$	−44.2112	−2.76861
$256$	−15.2096	−0.950602
$257$	12.4718	0.777969	0.388984	−	0.921244i	$-0.372826\pi$
$257$	12.4718	0.777969	0.388984	+	0.921244i	$0.372826\pi$
$258$	53.9461	3.35854
$259$	−1.83594	−0.114080
$260$	−54.6808	−3.39116
$261$	−2.42938	−0.150375
$262$	19.4948	1.20439
$263$	−22.5282	−1.38915	−0.694575	−	0.719420i	$-0.744408\pi$
$263$	−22.5282	−1.38915	−0.694575	+	0.719420i	$0.744408\pi$
$264$	−13.5172	−0.831927
$265$	−20.2599	−1.24456
$266$	1.74725	0.107131
$267$	1.23579	0.0756293
$268$	38.3808	2.34448
$269$	3.54782	0.216314	0.108157	−	0.994134i	$-0.465505\pi$
$269$	3.54782	0.216314	0.108157	+	0.994134i	$0.465505\pi$
$270$	48.0313	2.92309
$271$	20.4190	1.24037	0.620183	−	0.784457i	$-0.287058\pi$
$271$	20.4190	1.24037	0.620183	+	0.784457i	$0.287058\pi$
$272$	−63.3894	−3.84354
$273$	−2.22531	−0.134682
$274$	−56.4374	−3.40951
$275$	9.04131	0.545212
$276$	−17.0629	−1.02706
$277$	9.98239	0.599784	0.299892	−	0.953973i	$-0.403049\pi$
$277$	9.98239	0.599784	0.299892	+	0.953973i	$0.403049\pi$
$278$	−35.8058	−2.14749
$279$	−0.638365	−0.0382179
$280$	−11.3202	−0.676509
$281$	−4.16711	−0.248589	−0.124294	−	0.992245i	$-0.539667\pi$
$281$	−4.16711	−0.248589	−0.124294	+	0.992245i	$0.539667\pi$
$282$	7.27137	0.433004
$283$	−21.9093	−1.30237	−0.651187	−	0.758917i	$-0.725729\pi$
$283$	−21.9093	−1.30237	−0.651187	+	0.758917i	$0.725729\pi$
$284$	58.8887	3.49440
$285$	−11.1991	−0.663379
$286$	7.88239	0.466095
$287$	3.54455	0.209228
$288$	−3.24895	−0.191446
$289$	25.1280	1.47812
$290$	78.2424	4.59455
$291$	−26.7859	−1.57022
$292$	−33.6372	−1.96847
$293$	1.15469	0.0674579	0.0337289	−	0.999431i	$-0.489262\pi$
$293$	1.15469	0.0674579	0.0337289	+	0.999431i	$0.489262\pi$
$294$	32.5007	1.89548
$295$	22.3931	1.30378
$296$	33.6046	1.95323
$297$	−4.90012	−0.284334
$298$	−8.44764	−0.489359
$299$	5.84072	0.337777
$300$	79.5906	4.59516
$301$	−4.60901	−0.265659
$302$	−9.48258	−0.545661
$303$	−18.2004	−1.04559
$304$	−16.0571	−0.920940
$305$	51.5710	2.95294
$306$	5.16737	0.295399
$307$	−28.8157	−1.64460	−0.822299	−	0.569055i	$-0.807309\pi$
$307$	−28.8157	−1.64460	−0.822299	+	0.569055i	$0.807309\pi$
$308$	1.96740	0.112103
$309$	11.2292	0.638809
$310$	20.5597	1.16771
$311$	7.02554	0.398382	0.199191	−	0.979961i	$-0.436169\pi$
$311$	7.02554	0.398382	0.199191	+	0.979961i	$0.436169\pi$
$312$	40.7316	2.30597
$313$	6.40546	0.362058	0.181029	−	0.983478i	$-0.442057\pi$
$313$	6.40546	0.362058	0.181029	+	0.983478i	$0.442057\pi$
$314$	53.3835	3.01261
$315$	0.463318	0.0261050
$316$	35.2826	1.98480
$317$	−11.0741	−0.621983	−0.310992	−	0.950413i	$-0.600661\pi$
$317$	−11.0741	−0.621983	−0.310992	+	0.950413i	$0.600661\pi$
$318$	25.7093	1.44171
$319$	−7.98224	−0.446920
$320$	31.4459	1.75788
$321$	−26.4725	−1.47755
$322$	2.05987	0.114792
$323$	10.6714	0.593774
$324$	−47.5573	−2.64207
$325$	−27.2443	−1.51124
$326$	49.5688	2.74536
$327$	3.07430	0.170009
$328$	−64.8786	−3.58232
$329$	−0.621246	−0.0342504
$330$	−17.8181	−0.980852
$331$	11.9337	0.655935	0.327968	−	0.944689i	$-0.393636\pi$
$331$	11.9337	0.655935	0.327968	+	0.944689i	$0.393636\pi$
$332$	38.8510	2.13223
$333$	−1.37539	−0.0753708
$334$	33.1558	1.81420
$335$	29.6982	1.62259
$336$	7.21237	0.393467
$337$	−28.8855	−1.57349	−0.786746	−	0.617277i	$-0.788236\pi$
$337$	−28.8855	−1.57349	−0.786746	+	0.617277i	$0.788236\pi$
$338$	10.2540	0.557745
$339$	−19.4100	−1.05421
$340$	−117.781	−6.38759
$341$	−2.09748	−0.113585
$342$	1.30895	0.0707797
$343$	−5.62059	−0.303483
$344$	84.3622	4.54850
$345$	−13.2029	−0.710820
$346$	−29.0766	−1.56317
$347$	32.1910	1.72810	0.864051	−	0.503405i	$-0.167920\pi$
$347$	32.1910	1.72810	0.864051	+	0.503405i	$0.167920\pi$
$348$	−70.2676	−3.76674
$349$	14.0774	0.753547	0.376774	−	0.926305i	$-0.377033\pi$
$349$	14.0774	0.753547	0.376774	+	0.926305i	$0.377033\pi$
$350$	−9.60836	−0.513589
$351$	14.7656	0.788129
$352$	−10.6751	−0.568985
$353$	28.4325	1.51331	0.756656	−	0.653813i	$-0.226832\pi$
$353$	28.4325	1.51331	0.756656	+	0.653813i	$0.226832\pi$
$354$	−28.4162	−1.51031
$355$	45.5668	2.41843
$356$	3.29223	0.174488
$357$	−4.79328	−0.253687
$358$	41.5171	2.19425
$359$	27.0917	1.42984	0.714922	−	0.699204i	$-0.246462\pi$
$359$	27.0917	1.42984	0.714922	+	0.699204i	$0.246462\pi$
$360$	−8.48045	−0.446959
$361$	−16.2968	−0.857728
$362$	61.3732	3.22570
$363$	1.81779	0.0954091
$364$	−5.92837	−0.310731
$365$	−26.0278	−1.36235
$366$	−65.4422	−3.42072
$367$	23.6316	1.23356	0.616781	−	0.787135i	$-0.288437\pi$
$367$	23.6316	1.23356	0.616781	+	0.787135i	$0.288437\pi$
$368$	−18.9301	−0.986800
$369$	2.65539	0.138234
$370$	44.2968	2.30288
$371$	−2.19654	−0.114039
$372$	−18.4641	−0.957320
$373$	−16.8513	−0.872528	−0.436264	−	0.899819i	$-0.643699\pi$
$373$	−16.8513	−0.872528	−0.436264	+	0.899819i	$0.643699\pi$
$374$	16.9785	0.877937
$375$	27.5276	1.42152
$376$	11.3711	0.586422
$377$	24.0530	1.23879
$378$	5.20744	0.267842
$379$	24.9236	1.28024	0.640120	−	0.768275i	$-0.278885\pi$
$379$	24.9236	1.28024	0.640120	+	0.768275i	$0.278885\pi$
$380$	−29.8352	−1.53051
$381$	16.0174	0.820594
$382$	38.5094	1.97031
$383$	32.0931	1.63988	0.819940	−	0.572450i	$-0.194007\pi$
$383$	32.0931	1.63988	0.819940	+	0.572450i	$0.194007\pi$
$384$	−1.09391	−0.0558234
$385$	1.52233	0.0775850
$386$	39.2269	1.99660
$387$	−3.45282	−0.175517
$388$	−71.3593	−3.62272
$389$	−1.60480	−0.0813666	−0.0406833	−	0.999172i	$-0.512953\pi$
$389$	−1.60480	−0.0813666	−0.0406833	+	0.999172i	$0.512953\pi$
$390$	53.6914	2.71877
$391$	12.5808	0.636237
$392$	50.8253	2.56706
$393$	−13.5471	−0.683363
$394$	36.4690	1.83728
$395$	27.3009	1.37366
$396$	1.47387	0.0740646
$397$	12.0859	0.606575	0.303288	−	0.952899i	$-0.401916\pi$
$397$	12.0859	0.606575	0.303288	+	0.952899i	$0.401916\pi$
$398$	54.9012	2.75195
$399$	−1.21418	−0.0607852
$400$	88.3003	4.41502
$401$	14.8137	0.739761	0.369880	−	0.929079i	$-0.379399\pi$
$401$	14.8137	0.739761	0.369880	+	0.929079i	$0.379399\pi$
$402$	−37.6863	−1.87962
$403$	6.32037	0.314840
$404$	−48.4871	−2.41232
$405$	−36.7988	−1.82855
$406$	8.48287	0.420998
$407$	−4.51913	−0.224005
$408$	87.7349	4.34353
$409$	−25.8299	−1.27721	−0.638603	−	0.769537i	$-0.720487\pi$
$409$	−25.8299	−1.27721	−0.638603	+	0.769537i	$0.720487\pi$
$410$	−85.5214	−4.22360
$411$	39.2190	1.93453
$412$	29.9154	1.47382
$413$	2.42781	0.119465
$414$	1.54314	0.0758414
$415$	30.0621	1.47569
$416$	32.1674	1.57714
$417$	24.8819	1.21847
$418$	4.30082	0.210360
$419$	15.4141	0.753027	0.376514	−	0.926411i	$-0.377123\pi$
$419$	15.4141	0.753027	0.376514	+	0.926411i	$0.377123\pi$
$420$	13.4010	0.653904
$421$	29.8792	1.45622	0.728112	−	0.685458i	$-0.240398\pi$
$421$	29.8792	1.45622	0.728112	+	0.685458i	$0.240398\pi$
$422$	26.2967	1.28010
$423$	−0.465404	−0.0226287
$424$	40.2049	1.95252
$425$	−58.6836	−2.84657
$426$	−57.8230	−2.80154
$427$	5.59121	0.270578
$428$	−70.5244	−3.40893
$429$	−5.47756	−0.264459
$430$	111.204	5.36274
$431$	−4.02678	−0.193963	−0.0969816	−	0.995286i	$-0.530919\pi$
$431$	−4.02678	−0.193963	−0.0969816	+	0.995286i	$0.530919\pi$
$432$	−47.8561	−2.30248
$433$	−10.3919	−0.499403	−0.249701	−	0.968323i	$-0.580332\pi$
$433$	−10.3919	−0.499403	−0.249701	+	0.968323i	$0.580332\pi$
$434$	2.22903	0.106997
$435$	−54.3715	−2.60692
$436$	8.19013	0.392236
$437$	3.18683	0.152447
$438$	33.0285	1.57816
$439$	−27.2829	−1.30214	−0.651071	−	0.759017i	$-0.725680\pi$
$439$	−27.2829	−1.30214	−0.651071	+	0.759017i	$0.725680\pi$
$440$	−27.8643	−1.32838
$441$	−2.08021	−0.0990574
$442$	−51.1615	−2.43350
$443$	−23.9806	−1.13935	−0.569676	−	0.821870i	$-0.692931\pi$
$443$	−23.9806	−1.13935	−0.569676	+	0.821870i	$0.692931\pi$
$444$	−39.7818	−1.88796
$445$	2.54746	0.120761
$446$	−40.5556	−1.92036
$447$	5.87036	0.277659
$448$	3.40930	0.161074
$449$	−4.78234	−0.225692	−0.112846	−	0.993612i	$-0.535997\pi$
$449$	−4.78234	−0.225692	−0.112846	+	0.993612i	$0.535997\pi$
$450$	−7.19807	−0.339320
$451$	8.72483	0.410836
$452$	−51.7094	−2.43221
$453$	6.58955	0.309604
$454$	−49.7813	−2.33635
$455$	−4.58725	−0.215053
$456$	22.2241	1.04074
$457$	−4.10829	−0.192178	−0.0960889	−	0.995373i	$-0.530633\pi$
$457$	−4.10829	−0.192178	−0.0960889	+	0.995373i	$0.530633\pi$
$458$	30.6406	1.43174
$459$	31.8048	1.48452
$460$	−35.1733	−1.63996
$461$	13.1908	0.614357	0.307179	−	0.951652i	$-0.400615\pi$
$461$	13.1908	0.614357	0.307179	+	0.951652i	$0.400615\pi$
$462$	−1.93179	−0.0898752
$463$	−36.4953	−1.69608	−0.848039	−	0.529933i	$-0.822217\pi$
$463$	−36.4953	−1.69608	−0.848039	+	0.529933i	$0.822217\pi$
$464$	−77.9571	−3.61907
$465$	−14.2871	−0.662550
$466$	−76.7183	−3.55391
$467$	3.68289	0.170424	0.0852118	−	0.996363i	$-0.472843\pi$
$467$	3.68289	0.170424	0.0852118	+	0.996363i	$0.472843\pi$
$468$	−4.44122	−0.205295
$469$	3.21982	0.148677
$470$	14.9892	0.691398
$471$	−37.0968	−1.70933
$472$	−44.4380	−2.04542
$473$	−11.3450	−0.521642
$474$	−34.6441	−1.59126
$475$	−14.8651	−0.682059
$476$	−12.7696	−0.585293
$477$	−1.64553	−0.0753435
$478$	51.5886	2.35961
$479$	−8.83130	−0.403512	−0.201756	−	0.979436i	$-0.564665\pi$
$479$	−8.83130	−0.403512	−0.201756	+	0.979436i	$0.564665\pi$
$480$	−72.7142	−3.31893
$481$	13.6175	0.620906
$482$	−13.5315	−0.616345
$483$	−1.43143	−0.0651322
$484$	4.84270	0.220123
$485$	−55.2163	−2.50724
$486$	8.24272	0.373898
$487$	−36.8666	−1.67059	−0.835293	−	0.549805i	$-0.814702\pi$
$487$	−36.8666	−1.67059	−0.835293	+	0.549805i	$0.814702\pi$
$488$	−102.340	−4.63272
$489$	−34.4459	−1.55770
$490$	66.9966	3.02660
$491$	23.7402	1.07138	0.535690	−	0.844415i	$-0.320052\pi$
$491$	23.7402	1.07138	0.535690	+	0.844415i	$0.320052\pi$
$492$	76.8046	3.46262
$493$	51.8096	2.33339
$494$	−12.9597	−0.583084
$495$	1.14045	0.0512592
$496$	−20.4847	−0.919790
$497$	4.94025	0.221600
$498$	−38.1480	−1.70945
$499$	31.8301	1.42491	0.712455	−	0.701718i	$-0.247583\pi$
$499$	31.8301	1.42491	0.712455	+	0.701718i	$0.247583\pi$
$500$	73.3353	3.27966
$501$	−23.0403	−1.02937
$502$	70.4533	3.14448
$503$	−1.69168	−0.0754281	−0.0377141	−	0.999289i	$-0.512008\pi$
$503$	−1.69168	−0.0754281	−0.0377141	+	0.999289i	$0.512008\pi$
$504$	−0.919431	−0.0409547
$505$	−37.5182	−1.66954
$506$	5.07033	0.225403
$507$	−7.12564	−0.316461
$508$	42.6712	1.89323
$509$	38.9738	1.72748	0.863742	−	0.503934i	$-0.168115\pi$
$509$	38.9738	1.72748	0.863742	+	0.503934i	$0.168115\pi$
$510$	115.650	5.12107
$511$	−2.82187	−0.124832
$512$	40.9898	1.81151
$513$	8.05645	0.355701
$514$	−32.6244	−1.43900
$515$	23.1479	1.02002
$516$	−99.8697	−4.39652
$517$	−1.52918	−0.0672534
$518$	4.80256	0.211012
$519$	20.2056	0.886928
$520$	83.9638	3.68206
$521$	−31.2559	−1.36935	−0.684674	−	0.728850i	$-0.740055\pi$
$521$	−31.2559	−1.36935	−0.684674	+	0.728850i	$0.740055\pi$
$522$	6.35491	0.278147
$523$	−6.31710	−0.276228	−0.138114	−	0.990416i	$-0.544104\pi$
$523$	−6.31710	−0.276228	−0.138114	+	0.990416i	$0.544104\pi$
$524$	−36.0904	−1.57662
$525$	6.67696	0.291406
$526$	58.9306	2.56950
$527$	13.6139	0.593032
$528$	17.7531	0.772604
$529$	−19.2430	−0.836651
$530$	52.9970	2.30204
$531$	1.81878	0.0789284
$532$	−3.23466	−0.140240
$533$	−26.2906	−1.13877
$534$	−3.23265	−0.139891
$535$	−54.5703	−2.35928
$536$	−58.9347	−2.54559
$537$	−28.8507	−1.24500
$538$	−9.28057	−0.400114
$539$	−6.83495	−0.294402
$540$	−88.9197	−3.82649
$541$	−21.8392	−0.938942	−0.469471	−	0.882948i	$-0.655555\pi$
$541$	−21.8392	−0.938942	−0.469471	+	0.882948i	$0.655555\pi$
$542$	−53.4131	−2.29429
$543$	−42.6489	−1.83024
$544$	69.2880	2.97070
$545$	6.33735	0.271462
$546$	5.82110	0.249120
$547$	1.00000	0.0427569
$547$	1.00000	0.0427569
$548$	104.482	4.46324
$549$	4.18863	0.178766
$550$	−23.6508	−1.00847
$551$	13.1239	0.559096
$552$	26.2005	1.11517
$553$	2.95990	0.125868
$554$	−26.1125	−1.10941
$555$	−30.7823	−1.30664
$556$	66.2869	2.81119
$557$	34.1731	1.44796	0.723980	−	0.689821i	$-0.242311\pi$
$557$	34.1731	1.44796	0.723980	+	0.689821i	$0.242311\pi$
$558$	1.66987	0.0706913
$559$	34.1859	1.44591
$560$	14.8675	0.628268
$561$	−11.7985	−0.498135
$562$	10.9006	0.459812
$563$	−1.24870	−0.0526264	−0.0263132	−	0.999654i	$-0.508377\pi$
$563$	−1.24870	−0.0526264	−0.0263132	+	0.999654i	$0.508377\pi$
$564$	−13.4614	−0.566827
$565$	−40.0116	−1.68330
$566$	57.3116	2.40899
$567$	−3.98964	−0.167549
$568$	−90.4250	−3.79415
$569$	−8.39342	−0.351870	−0.175935	−	0.984402i	$-0.556295\pi$
$569$	−8.39342	−0.351870	−0.175935	+	0.984402i	$0.556295\pi$
$570$	29.2953	1.22704
$571$	−13.9183	−0.582465	−0.291232	−	0.956652i	$-0.594065\pi$
$571$	−13.9183	−0.582465	−0.291232	+	0.956652i	$0.594065\pi$
$572$	−14.5926	−0.610145
$573$	−26.7606	−1.11794
$574$	−9.27204	−0.387007
$575$	−17.5248	−0.730836
$576$	2.55406	0.106419
$577$	11.6473	0.484883	0.242441	−	0.970166i	$-0.422052\pi$
$577$	11.6473	0.484883	0.242441	+	0.970166i	$0.422052\pi$
$578$	−65.7311	−2.73405
$579$	−27.2592	−1.13285
$580$	−144.849	−6.01453
$581$	3.25926	0.135217
$582$	70.0680	2.90441
$583$	−5.40672	−0.223924
$584$	51.6508	2.13733
$585$	−3.43652	−0.142083
$586$	−3.02051	−0.124776
$587$	24.8707	1.02653	0.513263	−	0.858232i	$-0.328437\pi$
$587$	24.8707	1.02653	0.513263	+	0.858232i	$0.328437\pi$
$588$	−60.1680	−2.48129
$589$	3.44854	0.142095
$590$	−58.5770	−2.41158
$591$	−25.3427	−1.04246
$592$	−44.1352	−1.81395
$593$	42.3587	1.73946	0.869732	−	0.493524i	$-0.164292\pi$
$593$	42.3587	1.73946	0.869732	+	0.493524i	$0.164292\pi$
$594$	12.8180	0.525929
$595$	−9.88083	−0.405075
$596$	15.6390	0.640599
$597$	−38.1515	−1.56144
$598$	−15.2785	−0.624783
$599$	−21.5127	−0.878987	−0.439494	−	0.898246i	$-0.644842\pi$
$599$	−21.5127	−0.878987	−0.439494	+	0.898246i	$0.644842\pi$
$600$	−122.213	−4.98934
$601$	22.6113	0.922335	0.461168	−	0.887313i	$-0.347431\pi$
$601$	22.6113	0.922335	0.461168	+	0.887313i	$0.347431\pi$
$602$	12.0565	0.491386
$603$	2.41211	0.0982288
$604$	17.5550	0.714302
$605$	3.74717	0.152344
$606$	47.6097	1.93401
$607$	−10.9909	−0.446107	−0.223054	−	0.974806i	$-0.571603\pi$
$607$	−10.9909	−0.446107	−0.223054	+	0.974806i	$0.571603\pi$
$608$	17.5513	0.711800
$609$	−5.89484	−0.238871
$610$	−134.902	−5.46203
$611$	4.60791	0.186416
$612$	−9.56629	−0.386694
$613$	−8.53005	−0.344526	−0.172263	−	0.985051i	$-0.555108\pi$
$613$	−8.53005	−0.344526	−0.172263	+	0.985051i	$0.555108\pi$
$614$	75.3777	3.04200
$615$	59.4298	2.39644
$616$	−3.02098	−0.121719
$617$	−22.1586	−0.892074	−0.446037	−	0.895015i	$-0.647165\pi$
$617$	−22.1586	−0.892074	−0.446037	+	0.895015i	$0.647165\pi$
$618$	−29.3740	−1.18160
$619$	−25.0431	−1.00657	−0.503283	−	0.864122i	$-0.667875\pi$
$619$	−25.0431	−1.00657	−0.503283	+	0.864122i	$0.667875\pi$
$620$	−38.0618	−1.52860
$621$	9.49793	0.381139
$622$	−18.3778	−0.736883
$623$	0.276189	0.0110653
$624$	−53.4956	−2.14154
$625$	11.5387	0.461550
$626$	−16.7557	−0.669694
$627$	−2.98868	−0.119357
$628$	−98.8282	−3.94367
$629$	29.3319	1.16954
$630$	−1.21197	−0.0482861
$631$	8.28732	0.329913	0.164956	−	0.986301i	$-0.447252\pi$
$631$	8.28732	0.329913	0.164956	+	0.986301i	$0.447252\pi$
$632$	−54.1773	−2.15506
$633$	−18.2738	−0.726320
$634$	28.9682	1.15048
$635$	33.0181	1.31028
$636$	−47.5953	−1.88728
$637$	20.5958	0.816037
$638$	20.8804	0.826662
$639$	3.70097	0.146408
$640$	−2.25498	−0.0891359
$641$	19.8980	0.785925	0.392963	−	0.919554i	$-0.371450\pi$
$641$	19.8980	0.785925	0.392963	+	0.919554i	$0.371450\pi$
$642$	69.2482	2.73301
$643$	18.0543	0.711994	0.355997	−	0.934487i	$-0.384141\pi$
$643$	18.0543	0.711994	0.355997	+	0.934487i	$0.384141\pi$
$644$	−3.81341	−0.150270
$645$	−77.2770	−3.04278
$646$	−27.9149	−1.09830
$647$	−16.6657	−0.655196	−0.327598	−	0.944817i	$-0.606239\pi$
$647$	−16.6657	−0.655196	−0.327598	+	0.944817i	$0.606239\pi$
$648$	73.0254	2.86871
$649$	5.97599	0.234578
$650$	71.2671	2.79533
$651$	−1.54898	−0.0607093
$652$	−91.7660	−3.59384
$653$	6.26686	0.245241	0.122621	−	0.992454i	$-0.460870\pi$
$653$	6.26686	0.245241	0.122621	+	0.992454i	$0.460870\pi$
$654$	−8.04193	−0.314464
$655$	−27.9260	−1.09116
$656$	85.2095	3.32687
$657$	−2.11399	−0.0824747
$658$	1.62509	0.0633526
$659$	19.3921	0.755409	0.377704	−	0.925926i	$-0.376714\pi$
$659$	19.3921	0.755409	0.377704	+	0.925926i	$0.376714\pi$
$660$	32.9863	1.28399
$661$	25.2995	0.984035	0.492018	−	0.870585i	$-0.336260\pi$
$661$	25.2995	0.984035	0.492018	+	0.870585i	$0.336260\pi$
$662$	−31.2168	−1.21328
$663$	35.5527	1.38075
$664$	−59.6567	−2.31513
$665$	−2.50291	−0.0970587
$666$	3.59782	0.139413
$667$	15.4720	0.599079
$668$	−61.3809	−2.37490
$669$	28.1825	1.08960
$670$	−77.6863	−3.00128
$671$	13.7626	0.531300
$672$	−7.88351	−0.304113
$673$	−20.5174	−0.790888	−0.395444	−	0.918490i	$-0.629409\pi$
$673$	−20.5174	−0.790888	−0.395444	+	0.918490i	$0.629409\pi$
$674$	75.5602	2.91047
$675$	−44.3035	−1.70524
$676$	−18.9831	−0.730121
$677$	−2.52438	−0.0970197	−0.0485099	−	0.998823i	$-0.515447\pi$
$677$	−2.52438	−0.0970197	−0.0485099	+	0.998823i	$0.515447\pi$
$678$	50.7737	1.94995
$679$	−5.98643	−0.229738
$680$	180.856	6.93552
$681$	34.5936	1.32563
$682$	5.48671	0.210097
$683$	−15.0787	−0.576969	−0.288484	−	0.957485i	$-0.593151\pi$
$683$	−15.0787	−0.576969	−0.288484	+	0.957485i	$0.593151\pi$
$684$	−2.42323	−0.0926546
$685$	80.8458	3.08896
$686$	14.7026	0.561350
$687$	−21.2925	−0.812360
$688$	−110.799	−4.22416
$689$	16.2921	0.620681
$690$	34.5368	1.31480
$691$	9.48717	0.360909	0.180455	−	0.983583i	$-0.442243\pi$
$691$	9.48717	0.360909	0.180455	+	0.983583i	$0.442243\pi$
$692$	53.8290	2.04627
$693$	0.123645	0.00469687
$694$	−84.2069	−3.19645
$695$	51.2913	1.94559
$696$	107.898	4.08985
$697$	−56.6295	−2.14499
$698$	−36.8245	−1.39383
$699$	53.3124	2.01646
$700$	17.7878	0.672317
$701$	14.7547	0.557279	0.278639	−	0.960396i	$-0.410117\pi$
$701$	14.7547	0.557279	0.278639	+	0.960396i	$0.410117\pi$
$702$	−38.6246	−1.45779
$703$	7.43005	0.280230
$704$	8.39191	0.316282
$705$	−10.4161	−0.392294
$706$	−74.3754	−2.79916
$707$	−4.06764	−0.152980
$708$	52.6066	1.97708
$709$	−19.5306	−0.733486	−0.366743	−	0.930322i	$-0.619527\pi$
$709$	−19.5306	−0.733486	−0.366743	+	0.930322i	$0.619527\pi$
$710$	−119.196	−4.47335
$711$	2.21740	0.0831590
$712$	−5.05530	−0.189455
$713$	4.06556	0.152257
$714$	12.5385	0.469242
$715$	−11.2914	−0.422275
$716$	−76.8600	−2.87239
$717$	−35.8495	−1.33882
$718$	−70.8679	−2.64477
$719$	9.80130	0.365527	0.182763	−	0.983157i	$-0.441496\pi$
$719$	9.80130	0.365527	0.182763	+	0.983157i	$0.441496\pi$
$720$	11.1380	0.415087
$721$	2.50964	0.0934639
$722$	42.6301	1.58653
$723$	9.40322	0.349710
$724$	−113.619	−4.22263
$725$	−72.1699	−2.68032
$726$	−4.75507	−0.176477
$727$	−37.1944	−1.37947	−0.689733	−	0.724064i	$-0.742272\pi$
$727$	−37.1944	−1.37947	−0.689733	+	0.724064i	$0.742272\pi$
$728$	9.10317	0.337386
$729$	23.7333	0.879011
$730$	68.0848	2.51993
$731$	73.6358	2.72352
$732$	121.152	4.47792
$733$	−39.2717	−1.45054	−0.725268	−	0.688467i	$-0.758284\pi$
$733$	−39.2717	−1.45054	−0.725268	+	0.688467i	$0.758284\pi$
$734$	−61.8169	−2.28170
$735$	−46.5567	−1.71727
$736$	20.6916	0.762704
$737$	7.92550	0.291940
$738$	−6.94611	−0.255690
$739$	4.69533	0.172720	0.0863602	−	0.996264i	$-0.472476\pi$
$739$	4.69533	0.172720	0.0863602	+	0.996264i	$0.472476\pi$
$740$	−82.0060	−3.01460
$741$	9.00584	0.330838
$742$	5.74582	0.210936
$743$	41.5704	1.52507	0.762535	−	0.646947i	$-0.223954\pi$
$743$	41.5704	1.52507	0.762535	+	0.646947i	$0.223954\pi$
$744$	28.3521	1.03944
$745$	12.1011	0.443351
$746$	44.0806	1.61391
$747$	2.44166	0.0893358
$748$	−31.4320	−1.14927
$749$	−5.91639	−0.216180
$750$	−72.0083	−2.62937
$751$	14.5781	0.531963	0.265981	−	0.963978i	$-0.414304\pi$
$751$	14.5781	0.531963	0.265981	+	0.963978i	$0.414304\pi$
$752$	−14.9345	−0.544605
$753$	−48.9588	−1.78416
$754$	−62.9191	−2.29138
$755$	13.5837	0.494360
$756$	−9.64047	−0.350621
$757$	37.7246	1.37112	0.685562	−	0.728014i	$-0.259557\pi$
$757$	37.7246	1.37112	0.685562	+	0.728014i	$0.259557\pi$
$758$	−65.1965	−2.36804
$759$	−3.52343	−0.127892
$760$	45.8126	1.66180
$761$	−31.0762	−1.12651	−0.563256	−	0.826282i	$-0.690452\pi$
$761$	−31.0762	−1.12651	−0.563256	+	0.826282i	$0.690452\pi$
$762$	−41.8991	−1.51784
$763$	0.687081	0.0248740
$764$	−71.2919	−2.57925
$765$	−7.40218	−0.267627
$766$	−83.9508	−3.03327
$767$	−18.0075	−0.650214
$768$	−27.6479	−0.997657
$769$	4.40830	0.158967	0.0794837	−	0.996836i	$-0.474673\pi$
$769$	4.40830	0.158967	0.0794837	+	0.996836i	$0.474673\pi$
$770$	−3.98219	−0.143508
$771$	22.6710	0.816478
$772$	−72.6203	−2.61366
$773$	24.8597	0.894142	0.447071	−	0.894498i	$-0.352467\pi$
$773$	24.8597	0.894142	0.447071	+	0.894498i	$0.352467\pi$
$774$	9.03208	0.324651
$775$	−18.9640	−0.681207
$776$	109.574	3.93348
$777$	−3.33735	−0.119727
$778$	4.19792	0.150503
$779$	−14.3448	−0.513956
$780$	−99.3981	−3.55902
$781$	12.1603	0.435130
$782$	−32.9095	−1.17684
$783$	39.1139	1.39782
$784$	−66.7523	−2.38401
$785$	−76.4711	−2.72937
$786$	35.4374	1.26401
$787$	23.9191	0.852625	0.426313	−	0.904576i	$-0.359812\pi$
$787$	23.9191	0.852625	0.426313	+	0.904576i	$0.359812\pi$
$788$	−67.5146	−2.40511
$789$	−40.9515	−1.45791
$790$	−71.4152	−2.54084
$791$	−4.33797	−0.154241
$792$	−2.26316	−0.0804178
$793$	−41.4711	−1.47268
$794$	−31.6150	−1.12198
$795$	−36.8282	−1.30616
$796$	−101.638	−3.60246
$797$	47.5946	1.68589	0.842944	−	0.538002i	$-0.180821\pi$
$797$	47.5946	1.68589	0.842944	+	0.538002i	$0.180821\pi$
$798$	3.17613	0.112434
$799$	9.92533	0.351133
$800$	−96.5170	−3.41239
$801$	0.206906	0.00731067
$802$	−38.7505	−1.36833
$803$	−6.94597	−0.245118
$804$	69.7681	2.46053
$805$	−2.95074	−0.104000
$806$	−16.5332	−0.582356
$807$	6.44917	0.227022
$808$	74.4531	2.61925
$809$	−51.6584	−1.81621	−0.908107	−	0.418739i	$-0.862472\pi$
$809$	−51.6584	−1.81621	−0.908107	+	0.418739i	$0.862472\pi$
$810$	96.2603	3.38224
$811$	43.9447	1.54311	0.771554	−	0.636163i	$-0.219480\pi$
$811$	43.9447	1.54311	0.771554	+	0.636163i	$0.219480\pi$
$812$	−15.7042	−0.551110
$813$	37.1174	1.30176
$814$	11.8214	0.414339
$815$	−71.0066	−2.48725
$816$	−115.228	−4.03380
$817$	18.6527	0.652574
$818$	67.5672	2.36243
$819$	−0.372580	−0.0130190
$820$	158.325	5.52893
$821$	−1.53166	−0.0534553	−0.0267277	−	0.999643i	$-0.508509\pi$
$821$	−1.53166	−0.0534553	−0.0267277	+	0.999643i	$0.508509\pi$
$822$	−102.591	−3.57828
$823$	9.87643	0.344271	0.172135	−	0.985073i	$-0.444933\pi$
$823$	9.87643	0.344271	0.172135	+	0.985073i	$0.444933\pi$
$824$	−45.9358	−1.60025
$825$	16.4352	0.572199
$826$	−6.35079	−0.220972
$827$	25.3600	0.881854	0.440927	−	0.897543i	$-0.354650\pi$
$827$	25.3600	0.881854	0.440927	+	0.897543i	$0.354650\pi$
$828$	−2.85680	−0.0992808
$829$	−2.02393	−0.0702940	−0.0351470	−	0.999382i	$-0.511190\pi$
$829$	−2.02393	−0.0702940	−0.0351470	+	0.999382i	$0.511190\pi$
$830$	−78.6380	−2.72956
$831$	18.1459	0.629473
$832$	−25.2874	−0.876684
$833$	44.3630	1.53709
$834$	−65.0874	−2.25379
$835$	−47.4952	−1.64364
$836$	−7.96204	−0.275373
$837$	10.2779	0.355257
$838$	−40.3210	−1.39287
$839$	19.3795	0.669053	0.334526	−	0.942386i	$-0.391424\pi$
$839$	19.3795	0.669053	0.334526	+	0.942386i	$0.391424\pi$
$840$	−20.5776	−0.709996
$841$	34.7162	1.19711
$842$	−78.1597	−2.69356
$843$	−7.57491	−0.260894
$844$	−48.6827	−1.67573
$845$	−14.6887	−0.505308
$846$	1.21743	0.0418561
$847$	0.406260	0.0139593
$848$	−52.8038	−1.81329
$849$	−39.8265	−1.36684
$850$	153.508	5.26527
$851$	8.75945	0.300270
$852$	107.047	3.66737
$853$	15.7500	0.539270	0.269635	−	0.962963i	$-0.413097\pi$
$853$	15.7500	0.539270	0.269635	+	0.962963i	$0.413097\pi$
$854$	−14.6258	−0.500484
$855$	−1.87505	−0.0641252
$856$	108.292	3.70135
$857$	−15.5489	−0.531139	−0.265570	−	0.964092i	$-0.585560\pi$
$857$	−15.5489	−0.531139	−0.265570	+	0.964092i	$0.585560\pi$
$858$	14.3285	0.489167
$859$	−35.3732	−1.20692	−0.603458	−	0.797394i	$-0.706211\pi$
$859$	−35.3732	−1.20692	−0.603458	+	0.797394i	$0.706211\pi$
$860$	−205.871	−7.02013
$861$	6.44324	0.219585
$862$	10.5335	0.358772
$863$	−38.9298	−1.32519	−0.662593	−	0.748980i	$-0.730544\pi$
$863$	−38.9298	−1.32519	−0.662593	+	0.748980i	$0.730544\pi$
$864$	52.3093	1.77960
$865$	41.6517	1.41620
$866$	27.1837	0.923740
$867$	45.6773	1.55128
$868$	−4.12658	−0.140065
$869$	7.28573	0.247151
$870$	142.228	4.82198
$871$	−23.8820	−0.809211
$872$	−12.5762	−0.425882
$873$	−4.48471	−0.151784
$874$	−8.33629	−0.281979
$875$	6.15220	0.207982
$876$	−61.1453	−2.06591
$877$	−32.0277	−1.08150	−0.540750	−	0.841184i	$-0.681859\pi$
$877$	−32.0277	−1.08150	−0.540750	+	0.841184i	$0.681859\pi$
$878$	71.3681	2.40856
$879$	2.09898	0.0707970
$880$	36.5961	1.23365
$881$	50.3338	1.69579	0.847895	−	0.530165i	$-0.177870\pi$
$881$	50.3338	1.69579	0.847895	+	0.530165i	$0.177870\pi$
$882$	5.44152	0.183225
$883$	31.8313	1.07121	0.535604	−	0.844469i	$-0.320084\pi$
$883$	31.8313	1.07121	0.535604	+	0.844469i	$0.320084\pi$
$884$	94.7145	3.18559
$885$	40.7058	1.36831
$886$	62.7297	2.10745
$887$	−0.781354	−0.0262353	−0.0131177	−	0.999914i	$-0.504176\pi$
$887$	−0.781354	−0.0262353	−0.0131177	+	0.999914i	$0.504176\pi$
$888$	61.0860	2.04991
$889$	3.57975	0.120061
$890$	−6.66377	−0.223370
$891$	−9.82042	−0.328996
$892$	75.0800	2.51387
$893$	2.51418	0.0841339
$894$	−15.3560	−0.513582
$895$	−59.4726	−1.98795
$896$	−0.244480	−0.00816750
$897$	10.6172	0.354497
$898$	12.5099	0.417461
$899$	16.7426	0.558397
$900$	13.3257	0.444189
$901$	35.0929	1.16911
$902$	−22.8229	−0.759920
$903$	−8.37820	−0.278809
$904$	79.4011	2.64084
$905$	−87.9162	−2.92243
$906$	−17.2373	−0.572671
$907$	−46.6003	−1.54734	−0.773669	−	0.633591i	$-0.781580\pi$
$907$	−46.6003	−1.54734	−0.773669	+	0.633591i	$0.781580\pi$
$908$	92.1594	3.05842
$909$	−3.04726	−0.101071
$910$	11.9996	0.397782
$911$	−15.8917	−0.526514	−0.263257	−	0.964726i	$-0.584797\pi$
$911$	−15.8917	−0.526514	−0.263257	+	0.964726i	$0.584797\pi$
$912$	−29.1885	−0.966526
$913$	8.02259	0.265509
$914$	10.7467	0.355469
$915$	93.7450	3.09911
$916$	−56.7246	−1.87423
$917$	−3.02767	−0.0999826
$918$	−83.1966	−2.74590
$919$	−18.5713	−0.612611	−0.306306	−	0.951933i	$-0.599093\pi$
$919$	−18.5713	−0.612611	−0.306306	+	0.951933i	$0.599093\pi$
$920$	54.0095	1.78064
$921$	−52.3808	−1.72601
$922$	−34.5052	−1.13637
$923$	−36.6428	−1.20611
$924$	3.57630	0.117652
$925$	−40.8588	−1.34343
$926$	95.4663	3.13722
$927$	1.88009	0.0617501
$928$	85.2113	2.79720
$929$	−26.5792	−0.872035	−0.436018	−	0.899938i	$-0.643611\pi$
$929$	−26.5792	−0.872035	−0.436018	+	0.899938i	$0.643611\pi$
$930$	37.3731	1.22551
$931$	11.2376	0.368297
$932$	142.028	4.65227
$933$	12.7709	0.418102
$934$	−9.63389	−0.315231
$935$	−24.3214	−0.795396
$936$	6.81960	0.222906
$937$	3.86062	0.126121	0.0630605	−	0.998010i	$-0.479914\pi$
$937$	3.86062	0.126121	0.0630605	+	0.998010i	$0.479914\pi$
$938$	−8.42257	−0.275007
$939$	11.6438	0.379980
$940$	−27.7492	−0.905080
$941$	25.4012	0.828055	0.414028	−	0.910264i	$-0.364122\pi$
$941$	25.4012	0.828055	0.414028	+	0.910264i	$0.364122\pi$
$942$	97.0398	3.16173
$943$	−16.9114	−0.550711
$944$	58.3635	1.89957
$945$	−7.45959	−0.242660
$946$	29.6768	0.964876
$947$	10.1398	0.329499	0.164750	−	0.986335i	$-0.447318\pi$
$947$	10.1398	0.329499	0.164750	+	0.986335i	$0.447318\pi$
$948$	64.1362	2.08305
$949$	20.9304	0.679429
$950$	38.8850	1.26160
$951$	−20.1303	−0.652771
$952$	19.6080	0.635500
$953$	55.5328	1.79888	0.899441	−	0.437041i	$-0.143974\pi$
$953$	55.5328	1.79888	0.899441	+	0.437041i	$0.143974\pi$
$954$	4.30446	0.139362
$955$	−55.1641	−1.78507
$956$	−95.5054	−3.08886
$957$	−14.5100	−0.469042
$958$	23.1014	0.746372
$959$	8.76512	0.283040
$960$	57.1620	1.84490
$961$	−26.6006	−0.858083
$962$	−35.6215	−1.14848
$963$	−4.43224	−0.142827
$964$	25.0508	0.806831
$965$	−56.1920	−1.80888
$966$	3.74441	0.120474
$967$	35.4343	1.13949	0.569745	−	0.821821i	$-0.307042\pi$
$967$	35.4343	1.13949	0.569745	+	0.821821i	$0.307042\pi$
$968$	−7.43608	−0.239005
$969$	19.3984	0.623166
$970$	144.438	4.63762
$971$	21.8054	0.699770	0.349885	−	0.936793i	$-0.386221\pi$
$971$	21.8054	0.699770	0.349885	+	0.936793i	$0.386221\pi$
$972$	−15.2596	−0.489453
$973$	5.56089	0.178274
$974$	96.4377	3.09006
$975$	−49.5243	−1.58605
$976$	134.410	4.30237
$977$	−26.0413	−0.833136	−0.416568	−	0.909104i	$-0.636767\pi$
$977$	−26.0413	−0.833136	−0.416568	+	0.909104i	$0.636767\pi$
$978$	90.1055	2.88126
$979$	0.679834	0.0217276
$980$	−124.030	−3.96199
$981$	0.514724	0.0164339
$982$	−62.1009	−1.98172
$983$	23.9811	0.764877	0.382439	−	0.923981i	$-0.375084\pi$
$983$	23.9811	0.764877	0.382439	+	0.923981i	$0.375084\pi$
$984$	−117.935	−3.75964
$985$	−52.2414	−1.66455
$986$	−135.526	−4.31604
$987$	−1.12929	−0.0359458
$988$	23.9921	0.763291
$989$	21.9900	0.699242
$990$	−2.98324	−0.0948136
$991$	10.5877	0.336329	0.168165	−	0.985759i	$-0.446216\pi$
$991$	10.5877	0.336329	0.168165	+	0.985759i	$0.446216\pi$
$992$	22.3909	0.710911
$993$	21.6929	0.688404
$994$	−12.9230	−0.409892
$995$	−78.6452	−2.49322
$996$	70.6228	2.23777
$997$	19.7017	0.623959	0.311979	−	0.950089i	$-0.399008\pi$
$997$	19.7017	0.623959	0.311979	+	0.950089i	$0.399008\pi$
$998$	−83.2629	−2.63564
$999$	22.1443	0.700613

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6017.2.a.c.1.6	✓	106

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6017.2.a.c.1.6	✓	106	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:	\( N \)	\(=\)	\( 6017 = 11 \cdot 547 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.61585 q^{2} +1.81779 q^{3} +4.84270 q^{4} +3.74717 q^{5} -4.75507 q^{6} +0.406260 q^{7} -7.43608 q^{8} +0.304348 q^{9} +O(q^{10})\)	\(q-2.61585 q^{2} +1.81779 q^{3} +4.84270 q^{4} +3.74717 q^{5} -4.75507 q^{6} +0.406260 q^{7} -7.43608 q^{8} +0.304348 q^{9} -9.80206 q^{10} +1.00000 q^{11} +8.80299 q^{12} -3.01331 q^{13} -1.06272 q^{14} +6.81156 q^{15} +9.76632 q^{16} -6.49061 q^{17} -0.796131 q^{18} -1.64413 q^{19} +18.1464 q^{20} +0.738494 q^{21} -2.61585 q^{22} -1.93831 q^{23} -13.5172 q^{24} +9.04131 q^{25} +7.88239 q^{26} -4.90012 q^{27} +1.96740 q^{28} -7.98224 q^{29} -17.8181 q^{30} -2.09748 q^{31} -10.6751 q^{32} +1.81779 q^{33} +16.9785 q^{34} +1.52233 q^{35} +1.47387 q^{36} -4.51913 q^{37} +4.30082 q^{38} -5.47756 q^{39} -27.8643 q^{40} +8.72483 q^{41} -1.93179 q^{42} -11.3450 q^{43} +4.84270 q^{44} +1.14045 q^{45} +5.07033 q^{46} -1.52918 q^{47} +17.7531 q^{48} -6.83495 q^{49} -23.6508 q^{50} -11.7985 q^{51} -14.5926 q^{52} -5.40672 q^{53} +12.8180 q^{54} +3.74717 q^{55} -3.02098 q^{56} -2.98868 q^{57} +20.8804 q^{58} +5.97599 q^{59} +32.9863 q^{60} +13.7626 q^{61} +5.48671 q^{62} +0.123645 q^{63} +8.39191 q^{64} -11.2914 q^{65} -4.75507 q^{66} +7.92550 q^{67} -31.4320 q^{68} -3.52343 q^{69} -3.98219 q^{70} +12.1603 q^{71} -2.26316 q^{72} -6.94597 q^{73} +11.8214 q^{74} +16.4352 q^{75} -7.96204 q^{76} +0.406260 q^{77} +14.3285 q^{78} +7.28573 q^{79} +36.5961 q^{80} -9.82042 q^{81} -22.8229 q^{82} +8.02259 q^{83} +3.57630 q^{84} -24.3214 q^{85} +29.6768 q^{86} -14.5100 q^{87} -7.43608 q^{88} +0.679834 q^{89} -2.98324 q^{90} -1.22419 q^{91} -9.38663 q^{92} -3.81278 q^{93} +4.00012 q^{94} -6.16086 q^{95} -19.4051 q^{96} -14.7354 q^{97} +17.8792 q^{98} +0.304348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9}+O(q^{10}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9	\( 106 q - 13 q^{2} - 15 q^{3} + 93 q^{4} - 12 q^{5} - 22 q^{6} - 66 q^{7} - 39 q^{8} + 97 q^{9} - 30 q^{10} + 106 q^{11} - 26 q^{12} - 72 q^{13} + 3 q^{14} - 46 q^{15} + 75 q^{16} - 65 q^{17} - 37 q^{18} - 63 q^{19} - 25 q^{20} - 27 q^{21} - 13 q^{22} - 23 q^{23} - 56 q^{24} + 74 q^{25} + 2 q^{26} - 54 q^{27} - 115 q^{28} - 45 q^{29} - 14 q^{30} - 89 q^{31} - 96 q^{32} - 15 q^{33} - 26 q^{34} - 52 q^{35} + 91 q^{36} - 35 q^{37} + 7 q^{38} - 34 q^{39} - 74 q^{40} - 32 q^{41} - 94 q^{43} + 93 q^{44} - 46 q^{45} - 20 q^{46} - 105 q^{47} - 57 q^{48} + 80 q^{49} - 60 q^{50} - 36 q^{51} - 137 q^{52} - 61 q^{54} - 12 q^{55} + 32 q^{56} - 71 q^{57} - 28 q^{58} - 15 q^{59} - 21 q^{60} - 80 q^{61} - 84 q^{62} - 182 q^{63} + 55 q^{64} - 73 q^{65} - 22 q^{66} - 58 q^{67} - 145 q^{68} - 8 q^{69} - 39 q^{70} - 11 q^{71} - 100 q^{72} - 155 q^{73} - 15 q^{74} - 15 q^{75} - 132 q^{76} - 66 q^{77} - 45 q^{78} - 50 q^{79} - 28 q^{80} + 114 q^{81} - 57 q^{82} - 96 q^{83} - 27 q^{84} - 74 q^{85} + 54 q^{86} - 182 q^{87} - 39 q^{88} + 9 q^{89} - 53 q^{90} + 6 q^{91} - 18 q^{92} - 26 q^{93} - 33 q^{94} - 49 q^{95} - 56 q^{96} - 102 q^{97} - 76 q^{98} + 97 q^{99}+O(q^{100}) \) 106 * q - 13 * q^2 - 15 * q^3 + 93 * q^4 - 12 * q^5 - 22 * q^6 - 66 * q^7 - 39 * q^8 + 97 * q^9 - 30 * q^10 + 106 * q^11 - 26 * q^12 - 72 * q^13 + 3 * q^14 - 46 * q^15 + 75 * q^16 - 65 * q^17 - 37 * q^18 - 63 * q^19 - 25 * q^20 - 27 * q^21 - 13 * q^22 - 23 * q^23 - 56 * q^24 + 74 * q^25 + 2 * q^26 - 54 * q^27 - 115 * q^28 - 45 * q^29 - 14 * q^30 - 89 * q^31 - 96 * q^32 - 15 * q^33 - 26 * q^34 - 52 * q^35 + 91 * q^36 - 35 * q^37 + 7 * q^38 - 34 * q^39 - 74 * q^40 - 32 * q^41 - 94 * q^43 + 93 * q^44 - 46 * q^45 - 20 * q^46 - 105 * q^47 - 57 * q^48 + 80 * q^49 - 60 * q^50 - 36 * q^51 - 137 * q^52 - 61 * q^54 - 12 * q^55 + 32 * q^56 - 71 * q^57 - 28 * q^58 - 15 * q^59 - 21 * q^60 - 80 * q^61 - 84 * q^62 - 182 * q^63 + 55 * q^64 - 73 * q^65 - 22 * q^66 - 58 * q^67 - 145 * q^68 - 8 * q^69 - 39 * q^70 - 11 * q^71 - 100 * q^72 - 155 * q^73 - 15 * q^74 - 15 * q^75 - 132 * q^76 - 66 * q^77 - 45 * q^78 - 50 * q^79 - 28 * q^80 + 114 * q^81 - 57 * q^82 - 96 * q^83 - 27 * q^84 - 74 * q^85 + 54 * q^86 - 182 * q^87 - 39 * q^88 + 9 * q^89 - 53 * q^90 + 6 * q^91 - 18 * q^92 - 26 * q^93 - 33 * q^94 - 49 * q^95 - 56 * q^96 - 102 * q^97 - 76 * q^98 + 97 * q^99

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