LMFDB - Embedded newform 6038.2.a.e.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6038,2,Mod(1,6038)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6038, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6038.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6038 = 2 \cdot 3019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6038.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:	$48.2136727404$
Analytic rank:	$0$
Dimension:	$70$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6038.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.05123 q^{3} +1.00000 q^{4} +3.94879 q^{5} -2.05123 q^{6} +5.22685 q^{7} +1.00000 q^{8} +1.20754 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.05123 q^{3} +1.00000 q^{4} +3.94879 q^{5} -2.05123 q^{6} +5.22685 q^{7} +1.00000 q^{8} +1.20754 q^{9} +3.94879 q^{10} +2.29906 q^{11} -2.05123 q^{12} +5.61854 q^{13} +5.22685 q^{14} -8.09986 q^{15} +1.00000 q^{16} -4.71908 q^{17} +1.20754 q^{18} -7.26383 q^{19} +3.94879 q^{20} -10.7215 q^{21} +2.29906 q^{22} +8.28480 q^{23} -2.05123 q^{24} +10.5929 q^{25} +5.61854 q^{26} +3.67675 q^{27} +5.22685 q^{28} -9.45263 q^{29} -8.09986 q^{30} +3.16870 q^{31} +1.00000 q^{32} -4.71590 q^{33} -4.71908 q^{34} +20.6397 q^{35} +1.20754 q^{36} +5.53054 q^{37} -7.26383 q^{38} -11.5249 q^{39} +3.94879 q^{40} +2.97053 q^{41} -10.7215 q^{42} -9.11333 q^{43} +2.29906 q^{44} +4.76831 q^{45} +8.28480 q^{46} +4.97633 q^{47} -2.05123 q^{48} +20.3199 q^{49} +10.5929 q^{50} +9.67991 q^{51} +5.61854 q^{52} -4.78479 q^{53} +3.67675 q^{54} +9.07850 q^{55} +5.22685 q^{56} +14.8998 q^{57} -9.45263 q^{58} -14.0617 q^{59} -8.09986 q^{60} -5.40892 q^{61} +3.16870 q^{62} +6.31162 q^{63} +1.00000 q^{64} +22.1864 q^{65} -4.71590 q^{66} -6.05065 q^{67} -4.71908 q^{68} -16.9940 q^{69} +20.6397 q^{70} +13.9226 q^{71} +1.20754 q^{72} +0.686314 q^{73} +5.53054 q^{74} -21.7285 q^{75} -7.26383 q^{76} +12.0168 q^{77} -11.5249 q^{78} +8.43169 q^{79} +3.94879 q^{80} -11.1645 q^{81} +2.97053 q^{82} -5.09002 q^{83} -10.7215 q^{84} -18.6346 q^{85} -9.11333 q^{86} +19.3895 q^{87} +2.29906 q^{88} +12.4281 q^{89} +4.76831 q^{90} +29.3673 q^{91} +8.28480 q^{92} -6.49973 q^{93} +4.97633 q^{94} -28.6833 q^{95} -2.05123 q^{96} +5.45240 q^{97} +20.3199 q^{98} +2.77620 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) $ 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.05123	−1.18428	−0.592139	−	0.805836i	$-0.701716\pi$
$3$	−2.05123	−1.18428	−0.592139	+	0.805836i	$0.701716\pi$
$4$	1.00000	0.500000
$5$	3.94879	1.76595	0.882975	−	0.469419i	$-0.155537\pi$
$5$	3.94879	1.76595	0.882975	+	0.469419i	$0.155537\pi$
$6$	−2.05123	−0.837411
$7$	5.22685	1.97556	0.987782	−	0.155845i	$-0.0498099\pi$
$7$	5.22685	1.97556	0.987782	+	0.155845i	$0.0498099\pi$
$8$	1.00000	0.353553
$9$	1.20754	0.402513
$10$	3.94879	1.24872
$11$	2.29906	0.693193	0.346596	−	0.938014i	$-0.387337\pi$
$11$	2.29906	0.693193	0.346596	+	0.938014i	$0.387337\pi$
$12$	−2.05123	−0.592139
$13$	5.61854	1.55830	0.779152	−	0.626835i	$-0.215650\pi$
$13$	5.61854	1.55830	0.779152	+	0.626835i	$0.215650\pi$
$14$	5.22685	1.39693
$15$	−8.09986	−2.09138
$16$	1.00000	0.250000
$17$	−4.71908	−1.14454	−0.572272	−	0.820064i	$-0.693938\pi$
$17$	−4.71908	−1.14454	−0.572272	+	0.820064i	$0.693938\pi$
$18$	1.20754	0.284619
$19$	−7.26383	−1.66644	−0.833219	−	0.552944i	$-0.813504\pi$
$19$	−7.26383	−1.66644	−0.833219	+	0.552944i	$0.813504\pi$
$20$	3.94879	0.882975
$21$	−10.7215	−2.33961
$22$	2.29906	0.490161
$23$	8.28480	1.72750	0.863750	−	0.503921i	$-0.168110\pi$
$23$	8.28480	1.72750	0.863750	+	0.503921i	$0.168110\pi$
$24$	−2.05123	−0.418705
$25$	10.5929	2.11858
$26$	5.61854	1.10189
$27$	3.67675	0.707591
$28$	5.22685	0.987782
$29$	−9.45263	−1.75531	−0.877655	−	0.479293i	$-0.840893\pi$
$29$	−9.45263	−1.75531	−0.877655	+	0.479293i	$0.840893\pi$
$30$	−8.09986	−1.47883
$31$	3.16870	0.569115	0.284558	−	0.958659i	$-0.408153\pi$
$31$	3.16870	0.569115	0.284558	+	0.958659i	$0.408153\pi$
$32$	1.00000	0.176777
$33$	−4.71590	−0.820932
$34$	−4.71908	−0.809315
$35$	20.6397	3.48875
$36$	1.20754	0.201256
$37$	5.53054	0.909216	0.454608	−	0.890692i	$-0.349779\pi$
$37$	5.53054	0.909216	0.454608	+	0.890692i	$0.349779\pi$
$38$	−7.26383	−1.17835
$39$	−11.5249	−1.84546
$40$	3.94879	0.624358
$41$	2.97053	0.463919	0.231959	−	0.972725i	$-0.425486\pi$
$41$	2.97053	0.463919	0.231959	+	0.972725i	$0.425486\pi$
$42$	−10.7215	−1.65436
$43$	−9.11333	−1.38977	−0.694885	−	0.719121i	$-0.744545\pi$
$43$	−9.11333	−1.38977	−0.694885	+	0.719121i	$0.744545\pi$
$44$	2.29906	0.346596
$45$	4.76831	0.710818
$46$	8.28480	1.22153
$47$	4.97633	0.725873	0.362936	−	0.931814i	$-0.381774\pi$
$47$	4.97633	0.725873	0.362936	+	0.931814i	$0.381774\pi$
$48$	−2.05123	−0.296069
$49$	20.3199	2.90285
$50$	10.5929	1.49806
$51$	9.67991	1.35546
$52$	5.61854	0.779152
$53$	−4.78479	−0.657241	−0.328620	−	0.944462i	$-0.606584\pi$
$53$	−4.78479	−0.657241	−0.328620	+	0.944462i	$0.606584\pi$
$54$	3.67675	0.500342
$55$	9.07850	1.22414
$56$	5.22685	0.698467
$57$	14.8998	1.97352
$58$	−9.45263	−1.24119
$59$	−14.0617	−1.83068	−0.915340	−	0.402682i	$-0.868078\pi$
$59$	−14.0617	−1.83068	−0.915340	+	0.402682i	$0.868078\pi$
$60$	−8.09986	−1.04569
$61$	−5.40892	−0.692541	−0.346271	−	0.938135i	$-0.612552\pi$
$61$	−5.40892	−0.692541	−0.346271	+	0.938135i	$0.612552\pi$
$62$	3.16870	0.402425
$63$	6.31162	0.795189
$64$	1.00000	0.125000
$65$	22.1864	2.75189
$66$	−4.71590	−0.580487
$67$	−6.05065	−0.739205	−0.369602	−	0.929190i	$-0.620506\pi$
$67$	−6.05065	−0.739205	−0.369602	+	0.929190i	$0.620506\pi$
$68$	−4.71908	−0.572272
$69$	−16.9940	−2.04584
$70$	20.6397	2.46692
$71$	13.9226	1.65231	0.826153	−	0.563446i	$-0.190525\pi$
$71$	13.9226	1.65231	0.826153	+	0.563446i	$0.190525\pi$
$72$	1.20754	0.142310
$73$	0.686314	0.0803269	0.0401635	−	0.999193i	$-0.487212\pi$
$73$	0.686314	0.0803269	0.0401635	+	0.999193i	$0.487212\pi$
$74$	5.53054	0.642912
$75$	−21.7285	−2.50899
$76$	−7.26383	−0.833219
$77$	12.0168	1.36945
$78$	−11.5249	−1.30494
$79$	8.43169	0.948639	0.474319	−	0.880353i	$-0.342694\pi$
$79$	8.43169	0.948639	0.474319	+	0.880353i	$0.342694\pi$
$80$	3.94879	0.441488
$81$	−11.1645	−1.24050
$82$	2.97053	0.328040
$83$	−5.09002	−0.558703	−0.279351	−	0.960189i	$-0.590119\pi$
$83$	−5.09002	−0.558703	−0.279351	+	0.960189i	$0.590119\pi$
$84$	−10.7215	−1.16981
$85$	−18.6346	−2.02121
$86$	−9.11333	−0.982715
$87$	19.3895	2.07877
$88$	2.29906	0.245081
$89$	12.4281	1.31738	0.658689	−	0.752415i	$-0.271111\pi$
$89$	12.4281	1.31738	0.658689	+	0.752415i	$0.271111\pi$
$90$	4.76831	0.502624
$91$	29.3673	3.07853
$92$	8.28480	0.863750
$93$	−6.49973	−0.673990
$94$	4.97633	0.513270
$95$	−28.6833	−2.94285
$96$	−2.05123	−0.209353
$97$	5.45240	0.553607	0.276804	−	0.960927i	$-0.410725\pi$
$97$	5.45240	0.553607	0.276804	+	0.960927i	$0.410725\pi$
$98$	20.3199	2.05262
$99$	2.77620	0.279019
$100$	10.5929	1.05929
$101$	−15.5089	−1.54319	−0.771597	−	0.636112i	$-0.780542\pi$
$101$	−15.5089	−1.54319	−0.771597	+	0.636112i	$0.780542\pi$
$102$	9.67991	0.958453
$103$	−7.96998	−0.785306	−0.392653	−	0.919687i	$-0.628443\pi$
$103$	−7.96998	−0.785306	−0.392653	+	0.919687i	$0.628443\pi$
$104$	5.61854	0.550943
$105$	−42.3368	−4.13164
$106$	−4.78479	−0.464740
$107$	−11.3789	−1.10004	−0.550022	−	0.835150i	$-0.685381\pi$
$107$	−11.3789	−1.10004	−0.550022	+	0.835150i	$0.685381\pi$
$108$	3.67675	0.353795
$109$	−3.54797	−0.339834	−0.169917	−	0.985458i	$-0.554350\pi$
$109$	−3.54797	−0.339834	−0.169917	+	0.985458i	$0.554350\pi$
$110$	9.07850	0.865601
$111$	−11.3444	−1.07676
$112$	5.22685	0.493891
$113$	−10.9052	−1.02587	−0.512936	−	0.858427i	$-0.671442\pi$
$113$	−10.9052	−1.02587	−0.512936	+	0.858427i	$0.671442\pi$
$114$	14.8998	1.39549
$115$	32.7149	3.05068
$116$	−9.45263	−0.877655
$117$	6.78461	0.627237
$118$	−14.0617	−1.29449
$119$	−24.6659	−2.26112
$120$	−8.09986	−0.739413
$121$	−5.71432	−0.519484
$122$	−5.40892	−0.489701
$123$	−6.09324	−0.549409
$124$	3.16870	0.284558
$125$	22.0852	1.97536
$126$	6.31162	0.562284
$127$	−5.88968	−0.522625	−0.261312	−	0.965254i	$-0.584155\pi$
$127$	−5.88968	−0.522625	−0.261312	+	0.965254i	$0.584155\pi$
$128$	1.00000	0.0883883
$129$	18.6935	1.64587
$130$	22.1864	1.94588
$131$	14.6103	1.27651	0.638255	−	0.769825i	$-0.279657\pi$
$131$	14.6103	1.27651	0.638255	+	0.769825i	$0.279657\pi$
$132$	−4.71590	−0.410466
$133$	−37.9670	−3.29215
$134$	−6.05065	−0.522697
$135$	14.5187	1.24957
$136$	−4.71908	−0.404658
$137$	−10.7227	−0.916103	−0.458051	−	0.888926i	$-0.651452\pi$
$137$	−10.7227	−0.916103	−0.458051	+	0.888926i	$0.651452\pi$
$138$	−16.9940	−1.44663
$139$	−12.6356	−1.07174	−0.535868	−	0.844302i	$-0.680016\pi$
$139$	−12.6356	−1.07174	−0.535868	+	0.844302i	$0.680016\pi$
$140$	20.6397	1.74437
$141$	−10.2076	−0.859635
$142$	13.9226	1.16836
$143$	12.9174	1.08020
$144$	1.20754	0.100628
$145$	−37.3264	−3.09979
$146$	0.686314	0.0567997
$147$	−41.6809	−3.43778
$148$	5.53054	0.454608
$149$	−4.99685	−0.409358	−0.204679	−	0.978829i	$-0.565615\pi$
$149$	−4.99685	−0.409358	−0.204679	+	0.978829i	$0.565615\pi$
$150$	−21.7285	−1.77412
$151$	2.17229	0.176778	0.0883892	−	0.996086i	$-0.471828\pi$
$151$	2.17229	0.176778	0.0883892	+	0.996086i	$0.471828\pi$
$152$	−7.26383	−0.589175
$153$	−5.69847	−0.460694
$154$	12.0168	0.968345
$155$	12.5125	1.00503
$156$	−11.5249	−0.922732
$157$	4.56563	0.364377	0.182189	−	0.983264i	$-0.441682\pi$
$157$	4.56563	0.364377	0.182189	+	0.983264i	$0.441682\pi$
$158$	8.43169	0.670789
$159$	9.81469	0.778356
$160$	3.94879	0.312179
$161$	43.3034	3.41278
$162$	−11.1645	−0.877163
$163$	−3.15559	−0.247165	−0.123582	−	0.992334i	$-0.539438\pi$
$163$	−3.15559	−0.247165	−0.123582	+	0.992334i	$0.539438\pi$
$164$	2.97053	0.231959
$165$	−18.6221	−1.44973
$166$	−5.09002	−0.395062
$167$	−0.997577	−0.0771948	−0.0385974	−	0.999255i	$-0.512289\pi$
$167$	−0.997577	−0.0771948	−0.0385974	+	0.999255i	$0.512289\pi$
$168$	−10.7215	−0.827179
$169$	18.5680	1.42831
$170$	−18.6346	−1.42921
$171$	−8.77135	−0.670762
$172$	−9.11333	−0.694885
$173$	−7.82163	−0.594667	−0.297334	−	0.954774i	$-0.596097\pi$
$173$	−7.82163	−0.594667	−0.297334	+	0.954774i	$0.596097\pi$
$174$	19.3895	1.46992
$175$	55.3675	4.18539
$176$	2.29906	0.173298
$177$	28.8438	2.16803
$178$	12.4281	0.931527
$179$	−0.927587	−0.0693311	−0.0346656	−	0.999399i	$-0.511037\pi$
$179$	−0.927587	−0.0693311	−0.0346656	+	0.999399i	$0.511037\pi$
$180$	4.76831	0.355409
$181$	−8.76120	−0.651215	−0.325608	−	0.945505i	$-0.605569\pi$
$181$	−8.76120	−0.651215	−0.325608	+	0.945505i	$0.605569\pi$
$182$	29.3673	2.17685
$183$	11.0949	0.820161
$184$	8.28480	0.610763
$185$	21.8389	1.60563
$186$	−6.49973	−0.476583
$187$	−10.8494	−0.793390
$188$	4.97633	0.362936
$189$	19.2178	1.39789
$190$	−28.6833	−2.08091
$191$	−15.4042	−1.11461	−0.557305	−	0.830308i	$-0.688164\pi$
$191$	−15.4042	−1.11461	−0.557305	+	0.830308i	$0.688164\pi$
$192$	−2.05123	−0.148035
$193$	−16.5766	−1.19321	−0.596605	−	0.802535i	$-0.703484\pi$
$193$	−16.5766	−1.19321	−0.596605	+	0.802535i	$0.703484\pi$
$194$	5.45240	0.391459
$195$	−45.5094	−3.25900
$196$	20.3199	1.45142
$197$	−14.1542	−1.00845	−0.504224	−	0.863573i	$-0.668221\pi$
$197$	−14.1542	−1.00845	−0.504224	+	0.863573i	$0.668221\pi$
$198$	2.77620	0.197296
$199$	−8.03748	−0.569762	−0.284881	−	0.958563i	$-0.591954\pi$
$199$	−8.03748	−0.569762	−0.284881	+	0.958563i	$0.591954\pi$
$200$	10.5929	0.749032
$201$	12.4113	0.875423
$202$	−15.5089	−1.09120
$203$	−49.4075	−3.46773
$204$	9.67991	0.677729
$205$	11.7300	0.819258
$206$	−7.96998	−0.555295
$207$	10.0042	0.695341
$208$	5.61854	0.389576
$209$	−16.7000	−1.15516
$210$	−42.3368	−2.92151
$211$	21.1668	1.45718	0.728591	−	0.684949i	$-0.240175\pi$
$211$	21.1668	1.45718	0.728591	+	0.684949i	$0.240175\pi$
$212$	−4.78479	−0.328620
$213$	−28.5584	−1.95679
$214$	−11.3789	−0.777849
$215$	−35.9866	−2.45426
$216$	3.67675	0.250171
$217$	16.5623	1.12432
$218$	−3.54797	−0.240299
$219$	−1.40779	−0.0951293
$220$	9.07850	0.612072
$221$	−26.5143	−1.78355
$222$	−11.3444	−0.761387
$223$	5.14524	0.344551	0.172276	−	0.985049i	$-0.444888\pi$
$223$	5.14524	0.344551	0.172276	+	0.985049i	$0.444888\pi$
$224$	5.22685	0.349234
$225$	12.7913	0.852756
$226$	−10.9052	−0.725402
$227$	−1.60696	−0.106658	−0.0533288	−	0.998577i	$-0.516983\pi$
$227$	−1.60696	−0.106658	−0.0533288	+	0.998577i	$0.516983\pi$
$228$	14.8998	0.986762
$229$	−16.3933	−1.08330	−0.541651	−	0.840603i	$-0.682201\pi$
$229$	−16.3933	−1.08330	−0.541651	+	0.840603i	$0.682201\pi$
$230$	32.7149	2.15716
$231$	−24.6493	−1.62180
$232$	−9.45263	−0.620596
$233$	−0.307116	−0.0201199	−0.0100599	−	0.999949i	$-0.503202\pi$
$233$	−0.307116	−0.0201199	−0.0100599	+	0.999949i	$0.503202\pi$
$234$	6.78461	0.443524
$235$	19.6505	1.28186
$236$	−14.0617	−0.915340
$237$	−17.2953	−1.12345
$238$	−24.6659	−1.59885
$239$	16.8801	1.09188	0.545940	−	0.837824i	$-0.316172\pi$
$239$	16.8801	1.09188	0.545940	+	0.837824i	$0.316172\pi$
$240$	−8.09986	−0.522844
$241$	22.0812	1.42237	0.711187	−	0.703003i	$-0.248158\pi$
$241$	22.0812	1.42237	0.711187	+	0.703003i	$0.248158\pi$
$242$	−5.71432	−0.367331
$243$	11.8706	0.761501
$244$	−5.40892	−0.346271
$245$	80.2391	5.12629
$246$	−6.09324	−0.388491
$247$	−40.8121	−2.59681
$248$	3.16870	0.201213
$249$	10.4408	0.661659
$250$	22.0852	1.39679
$251$	14.1845	0.895320	0.447660	−	0.894204i	$-0.352258\pi$
$251$	14.1845	0.895320	0.447660	+	0.894204i	$0.352258\pi$
$252$	6.31162	0.397595
$253$	19.0472	1.19749
$254$	−5.88968	−0.369552
$255$	38.2239	2.39367
$256$	1.00000	0.0625000
$257$	−14.1887	−0.885068	−0.442534	−	0.896752i	$-0.645920\pi$
$257$	−14.1887	−0.885068	−0.442534	+	0.896752i	$0.645920\pi$
$258$	18.6935	1.16381
$259$	28.9073	1.79621
$260$	22.1864	1.37594
$261$	−11.4144	−0.706535
$262$	14.6103	0.902629
$263$	−17.0687	−1.05250	−0.526249	−	0.850330i	$-0.676402\pi$
$263$	−17.0687	−1.05250	−0.526249	+	0.850330i	$0.676402\pi$
$264$	−4.71590	−0.290243
$265$	−18.8941	−1.16066
$266$	−37.9670	−2.32790
$267$	−25.4929	−1.56014
$268$	−6.05065	−0.369602
$269$	−19.0368	−1.16070	−0.580348	−	0.814368i	$-0.697084\pi$
$269$	−19.0368	−1.16070	−0.580348	+	0.814368i	$0.697084\pi$
$270$	14.5187	0.883579
$271$	25.8471	1.57010	0.785050	−	0.619432i	$-0.212637\pi$
$271$	25.8471	1.57010	0.785050	+	0.619432i	$0.212637\pi$
$272$	−4.71908	−0.286136
$273$	−60.2390	−3.64583
$274$	−10.7227	−0.647782
$275$	24.3537	1.46859
$276$	−16.9940	−1.02292
$277$	−9.58327	−0.575803	−0.287901	−	0.957660i	$-0.592958\pi$
$277$	−9.58327	−0.575803	−0.287901	+	0.957660i	$0.592958\pi$
$278$	−12.6356	−0.757832
$279$	3.82633	0.229076
$280$	20.6397	1.23346
$281$	15.3876	0.917944	0.458972	−	0.888451i	$-0.348218\pi$
$281$	15.3876	0.917944	0.458972	+	0.888451i	$0.348218\pi$
$282$	−10.2076	−0.607853
$283$	26.1908	1.55688	0.778441	−	0.627718i	$-0.216011\pi$
$283$	26.1908	1.55688	0.778441	+	0.627718i	$0.216011\pi$
$284$	13.9226	0.826153
$285$	58.8360	3.48515
$286$	12.9174	0.763820
$287$	15.5265	0.916501
$288$	1.20754	0.0711549
$289$	5.26969	0.309982
$290$	−37.3264	−2.19188
$291$	−11.1841	−0.655624
$292$	0.686314	0.0401635
$293$	−1.94224	−0.113467	−0.0567334	−	0.998389i	$-0.518068\pi$
$293$	−1.94224	−0.113467	−0.0567334	+	0.998389i	$0.518068\pi$
$294$	−41.6809	−2.43088
$295$	−55.5267	−3.23289
$296$	5.53054	0.321456
$297$	8.45307	0.490497
$298$	−4.99685	−0.289460
$299$	46.5485	2.69197
$300$	−21.7285	−1.25449
$301$	−47.6340	−2.74558
$302$	2.17229	0.125001
$303$	31.8123	1.82757
$304$	−7.26383	−0.416609
$305$	−21.3587	−1.22299
$306$	−5.69847	−0.325760
$307$	9.38245	0.535484	0.267742	−	0.963491i	$-0.413722\pi$
$307$	9.38245	0.535484	0.267742	+	0.963491i	$0.413722\pi$
$308$	12.0168	0.684723
$309$	16.3483	0.930020
$310$	12.5125	0.710663
$311$	24.3787	1.38239	0.691194	−	0.722669i	$-0.257085\pi$
$311$	24.3787	1.38239	0.691194	+	0.722669i	$0.257085\pi$
$312$	−11.5249	−0.652470
$313$	13.1370	0.742548	0.371274	−	0.928523i	$-0.378921\pi$
$313$	13.1370	0.742548	0.371274	+	0.928523i	$0.378921\pi$
$314$	4.56563	0.257654
$315$	24.9232	1.40427
$316$	8.43169	0.474319
$317$	−6.28830	−0.353186	−0.176593	−	0.984284i	$-0.556508\pi$
$317$	−6.28830	−0.353186	−0.176593	+	0.984284i	$0.556508\pi$
$318$	9.81469	0.550380
$319$	−21.7322	−1.21677
$320$	3.94879	0.220744
$321$	23.3408	1.30276
$322$	43.3034	2.41320
$323$	34.2786	1.90731
$324$	−11.1645	−0.620248
$325$	59.5167	3.30139
$326$	−3.15559	−0.174772
$327$	7.27770	0.402458
$328$	2.97053	0.164020
$329$	26.0105	1.43401
$330$	−18.6221	−1.02511
$331$	13.8106	0.759098	0.379549	−	0.925172i	$-0.376079\pi$
$331$	13.8106	0.759098	0.379549	+	0.925172i	$0.376079\pi$
$332$	−5.09002	−0.279351
$333$	6.67834	0.365971
$334$	−0.997577	−0.0545850
$335$	−23.8927	−1.30540
$336$	−10.7215	−0.584904
$337$	−20.3597	−1.10906	−0.554532	−	0.832162i	$-0.687103\pi$
$337$	−20.3597	−1.10906	−0.554532	+	0.832162i	$0.687103\pi$
$338$	18.5680	1.00997
$339$	22.3690	1.21492
$340$	−18.6346	−1.01060
$341$	7.28503	0.394507
$342$	−8.77135	−0.474301
$343$	69.6214	3.75920
$344$	−9.11333	−0.491358
$345$	−67.1057	−3.61285
$346$	−7.82163	−0.420493
$347$	31.3692	1.68398	0.841992	−	0.539489i	$-0.181383\pi$
$347$	31.3692	1.68398	0.841992	+	0.539489i	$0.181383\pi$
$348$	19.3895	1.03939
$349$	7.85812	0.420636	0.210318	−	0.977633i	$-0.432550\pi$
$349$	7.85812	0.420636	0.210318	+	0.977633i	$0.432550\pi$
$350$	55.3675	2.95952
$351$	20.6580	1.10264
$352$	2.29906	0.122540
$353$	−12.5510	−0.668022	−0.334011	−	0.942569i	$-0.608402\pi$
$353$	−12.5510	−0.668022	−0.334011	+	0.942569i	$0.608402\pi$
$354$	28.8438	1.53303
$355$	54.9772	2.91789
$356$	12.4281	0.658689
$357$	50.5954	2.67779
$358$	−0.927587	−0.0490245
$359$	13.4576	0.710265	0.355133	−	0.934816i	$-0.384436\pi$
$359$	13.4576	0.710265	0.355133	+	0.934816i	$0.384436\pi$
$360$	4.76831	0.251312
$361$	33.7633	1.77701
$362$	−8.76120	−0.460479
$363$	11.7214	0.615213
$364$	29.3673	1.53926
$365$	2.71010	0.141853
$366$	11.0949	0.579941
$367$	−12.8843	−0.672555	−0.336277	−	0.941763i	$-0.609168\pi$
$367$	−12.8843	−0.672555	−0.336277	+	0.941763i	$0.609168\pi$
$368$	8.28480	0.431875
$369$	3.58703	0.186733
$370$	21.8389	1.13535
$371$	−25.0094	−1.29842
$372$	−6.49973	−0.336995
$373$	23.5467	1.21920	0.609601	−	0.792709i	$-0.291330\pi$
$373$	23.5467	1.21920	0.609601	+	0.792709i	$0.291330\pi$
$374$	−10.8494	−0.561011
$375$	−45.3018	−2.33937
$376$	4.97633	0.256635
$377$	−53.1100	−2.73531
$378$	19.2178	0.988457
$379$	−22.9928	−1.18106	−0.590530	−	0.807016i	$-0.701081\pi$
$379$	−22.9928	−1.18106	−0.590530	+	0.807016i	$0.701081\pi$
$380$	−28.6833	−1.47142
$381$	12.0811	0.618933
$382$	−15.4042	−0.788148
$383$	5.81782	0.297277	0.148638	−	0.988892i	$-0.452511\pi$
$383$	5.81782	0.297277	0.148638	+	0.988892i	$0.452511\pi$
$384$	−2.05123	−0.104676
$385$	47.4519	2.41837
$386$	−16.5766	−0.843726
$387$	−11.0047	−0.559400
$388$	5.45240	0.276804
$389$	0.159767	0.00810052	0.00405026	−	0.999992i	$-0.498711\pi$
$389$	0.159767	0.00810052	0.00405026	+	0.999992i	$0.498711\pi$
$390$	−45.5094	−2.30446
$391$	−39.0966	−1.97720
$392$	20.3199	1.02631
$393$	−29.9691	−1.51174
$394$	−14.1542	−0.713080
$395$	33.2949	1.67525
$396$	2.77620	0.139509
$397$	30.3752	1.52449	0.762243	−	0.647291i	$-0.224098\pi$
$397$	30.3752	1.52449	0.762243	+	0.647291i	$0.224098\pi$
$398$	−8.03748	−0.402883
$399$	77.8789	3.89882
$400$	10.5929	0.529645
$401$	−7.98208	−0.398606	−0.199303	−	0.979938i	$-0.563868\pi$
$401$	−7.98208	−0.398606	−0.199303	+	0.979938i	$0.563868\pi$
$402$	12.4113	0.619018
$403$	17.8035	0.886854
$404$	−15.5089	−0.771597
$405$	−44.0861	−2.19066
$406$	−49.4075	−2.45205
$407$	12.7150	0.630262
$408$	9.67991	0.479227
$409$	−19.7497	−0.976558	−0.488279	−	0.872688i	$-0.662375\pi$
$409$	−19.7497	−0.976558	−0.488279	+	0.872688i	$0.662375\pi$
$410$	11.7300	0.579303
$411$	21.9947	1.08492
$412$	−7.96998	−0.392653
$413$	−73.4985	−3.61662
$414$	10.0042	0.491680
$415$	−20.0994	−0.986641
$416$	5.61854	0.275472
$417$	25.9185	1.26923
$418$	−16.7000	−0.816823
$419$	20.0563	0.979814	0.489907	−	0.871775i	$-0.337031\pi$
$419$	20.0563	0.979814	0.489907	+	0.871775i	$0.337031\pi$
$420$	−42.3368	−2.06582
$421$	−2.54900	−0.124231	−0.0621153	−	0.998069i	$-0.519785\pi$
$421$	−2.54900	−0.124231	−0.0621153	+	0.998069i	$0.519785\pi$
$422$	21.1668	1.03038
$423$	6.00911	0.292173
$424$	−4.78479	−0.232370
$425$	−49.9887	−2.42481
$426$	−28.5584	−1.38366
$427$	−28.2716	−1.36816
$428$	−11.3789	−0.550022
$429$	−26.4965	−1.27926
$430$	−35.9866	−1.73543
$431$	9.66917	0.465748	0.232874	−	0.972507i	$-0.425187\pi$
$431$	9.66917	0.465748	0.232874	+	0.972507i	$0.425187\pi$
$432$	3.67675	0.176898
$433$	−8.34744	−0.401152	−0.200576	−	0.979678i	$-0.564281\pi$
$433$	−8.34744	−0.401152	−0.200576	+	0.979678i	$0.564281\pi$
$434$	16.5623	0.795016
$435$	76.5650	3.67101
$436$	−3.54797	−0.169917
$437$	−60.1794	−2.87877
$438$	−1.40779	−0.0672666
$439$	2.79738	0.133511	0.0667557	−	0.997769i	$-0.478735\pi$
$439$	2.79738	0.133511	0.0667557	+	0.997769i	$0.478735\pi$
$440$	9.07850	0.432800
$441$	24.5371	1.16843
$442$	−26.5143	−1.26116
$443$	16.6417	0.790673	0.395337	−	0.918536i	$-0.370628\pi$
$443$	16.6417	0.790673	0.395337	+	0.918536i	$0.370628\pi$
$444$	−11.3444	−0.538382
$445$	49.0760	2.32643
$446$	5.14524	0.243634
$447$	10.2497	0.484793
$448$	5.22685	0.246945
$449$	14.5185	0.685170	0.342585	−	0.939487i	$-0.388698\pi$
$449$	14.5185	0.685170	0.342585	+	0.939487i	$0.388698\pi$
$450$	12.7913	0.602990
$451$	6.82943	0.321585
$452$	−10.9052	−0.512936
$453$	−4.45586	−0.209355
$454$	−1.60696	−0.0754183
$455$	115.965	5.43653
$456$	14.8998	0.697746
$457$	−15.1073	−0.706690	−0.353345	−	0.935493i	$-0.614956\pi$
$457$	−15.1073	−0.706690	−0.353345	+	0.935493i	$0.614956\pi$
$458$	−16.3933	−0.766011
$459$	−17.3509	−0.809869
$460$	32.7149	1.52534
$461$	−13.0171	−0.606265	−0.303133	−	0.952948i	$-0.598033\pi$
$461$	−13.0171	−0.606265	−0.303133	+	0.952948i	$0.598033\pi$
$462$	−24.6493	−1.14679
$463$	12.9816	0.603307	0.301653	−	0.953418i	$-0.402461\pi$
$463$	12.9816	0.603307	0.301653	+	0.953418i	$0.402461\pi$
$464$	−9.45263	−0.438828
$465$	−25.6660	−1.19023
$466$	−0.307116	−0.0142269
$467$	1.52561	0.0705969	0.0352985	−	0.999377i	$-0.488762\pi$
$467$	1.52561	0.0705969	0.0352985	+	0.999377i	$0.488762\pi$
$468$	6.78461	0.313618
$469$	−31.6258	−1.46035
$470$	19.6505	0.906409
$471$	−9.36516	−0.431524
$472$	−14.0617	−0.647243
$473$	−20.9521	−0.963378
$474$	−17.2953	−0.794400
$475$	−76.9451	−3.53048
$476$	−24.6659	−1.13056
$477$	−5.77781	−0.264548
$478$	16.8801	0.772076
$479$	−27.4348	−1.25353	−0.626764	−	0.779209i	$-0.715621\pi$
$479$	−27.4348	−1.25353	−0.626764	+	0.779209i	$0.715621\pi$
$480$	−8.09986	−0.369706
$481$	31.0736	1.41683
$482$	22.0812	1.00577
$483$	−88.8251	−4.04168
$484$	−5.71432	−0.259742
$485$	21.5304	0.977643
$486$	11.8706	0.538462
$487$	21.1246	0.957248	0.478624	−	0.878020i	$-0.341136\pi$
$487$	21.1246	0.957248	0.478624	+	0.878020i	$0.341136\pi$
$488$	−5.40892	−0.244850
$489$	6.47283	0.292711
$490$	80.2391	3.62483
$491$	−19.3451	−0.873034	−0.436517	−	0.899696i	$-0.643788\pi$
$491$	−19.3451	−0.873034	−0.436517	+	0.899696i	$0.643788\pi$
$492$	−6.09324	−0.274704
$493$	44.6077	2.00903
$494$	−40.8121	−1.83623
$495$	10.9626	0.492734
$496$	3.16870	0.142279
$497$	72.7712	3.26423
$498$	10.4408	0.467863
$499$	−12.8109	−0.573496	−0.286748	−	0.958006i	$-0.592574\pi$
$499$	−12.8109	−0.573496	−0.286748	+	0.958006i	$0.592574\pi$
$500$	22.0852	0.987680
$501$	2.04626	0.0914201
$502$	14.1845	0.633087
$503$	8.55537	0.381465	0.190733	−	0.981642i	$-0.438914\pi$
$503$	8.55537	0.381465	0.190733	+	0.981642i	$0.438914\pi$
$504$	6.31162	0.281142
$505$	−61.2413	−2.72520
$506$	19.0472	0.846753
$507$	−38.0873	−1.69151
$508$	−5.88968	−0.261312
$509$	−39.0064	−1.72893	−0.864463	−	0.502696i	$-0.832342\pi$
$509$	−39.0064	−1.72893	−0.864463	+	0.502696i	$0.832342\pi$
$510$	38.2239	1.69258
$511$	3.58726	0.158691
$512$	1.00000	0.0441942
$513$	−26.7073	−1.17916
$514$	−14.1887	−0.625838
$515$	−31.4718	−1.38681
$516$	18.6935	0.822936
$517$	11.4409	0.503170
$518$	28.9073	1.27011
$519$	16.0439	0.704251
$520$	22.1864	0.972939
$521$	−4.08059	−0.178774	−0.0893870	−	0.995997i	$-0.528491\pi$
$521$	−4.08059	−0.178774	−0.0893870	+	0.995997i	$0.528491\pi$
$522$	−11.4144	−0.499595
$523$	−6.77182	−0.296111	−0.148056	−	0.988979i	$-0.547301\pi$
$523$	−6.77182	−0.296111	−0.148056	+	0.988979i	$0.547301\pi$
$524$	14.6103	0.638255
$525$	−113.571	−4.95666
$526$	−17.0687	−0.744229
$527$	−14.9533	−0.651378
$528$	−4.71590	−0.205233
$529$	45.6379	1.98425
$530$	−18.8941	−0.820707
$531$	−16.9801	−0.736872
$532$	−37.9670	−1.64608
$533$	16.6900	0.722926
$534$	−25.4929	−1.10319
$535$	−44.9330	−1.94262
$536$	−6.05065	−0.261348
$537$	1.90269	0.0821073
$538$	−19.0368	−0.820737
$539$	46.7168	2.01223
$540$	14.5187	0.624785
$541$	6.93977	0.298364	0.149182	−	0.988810i	$-0.452336\pi$
$541$	6.93977	0.298364	0.149182	+	0.988810i	$0.452336\pi$
$542$	25.8471	1.11023
$543$	17.9712	0.771219
$544$	−4.71908	−0.202329
$545$	−14.0102	−0.600130
$546$	−60.2390	−2.57799
$547$	15.2616	0.652540	0.326270	−	0.945277i	$-0.394208\pi$
$547$	15.2616	0.652540	0.326270	+	0.945277i	$0.394208\pi$
$548$	−10.7227	−0.458051
$549$	−6.53148	−0.278757
$550$	24.3537	1.03845
$551$	68.6623	2.92511
$552$	−16.9940	−0.723313
$553$	44.0712	1.87410
$554$	−9.58327	−0.407154
$555$	−44.7966	−1.90151
$556$	−12.6356	−0.535868
$557$	−41.0315	−1.73856	−0.869280	−	0.494320i	$-0.835417\pi$
$557$	−41.0315	−1.73856	−0.869280	+	0.494320i	$0.835417\pi$
$558$	3.82633	0.161981
$559$	−51.2036	−2.16568
$560$	20.6397	0.872187
$561$	22.2547	0.939594
$562$	15.3876	0.649085
$563$	21.6729	0.913402	0.456701	−	0.889620i	$-0.349031\pi$
$563$	21.6729	0.913402	0.456701	+	0.889620i	$0.349031\pi$
$564$	−10.2076	−0.429817
$565$	−43.0622	−1.81164
$566$	26.1908	1.10088
$567$	−58.3550	−2.45068
$568$	13.9226	0.584178
$569$	−13.5906	−0.569749	−0.284874	−	0.958565i	$-0.591952\pi$
$569$	−13.5906	−0.569749	−0.284874	+	0.958565i	$0.591952\pi$
$570$	58.8360	2.46437
$571$	0.651576	0.0272676	0.0136338	−	0.999907i	$-0.495660\pi$
$571$	0.651576	0.0272676	0.0136338	+	0.999907i	$0.495660\pi$
$572$	12.9174	0.540102
$573$	31.5975	1.32001
$574$	15.5265	0.648064
$575$	87.7601	3.65985
$576$	1.20754	0.0503141
$577$	14.0750	0.585952	0.292976	−	0.956120i	$-0.405354\pi$
$577$	14.0750	0.585952	0.292976	+	0.956120i	$0.405354\pi$
$578$	5.26969	0.219190
$579$	34.0024	1.41309
$580$	−37.3264	−1.54990
$581$	−26.6048	−1.10375
$582$	−11.1841	−0.463596
$583$	−11.0005	−0.455595
$584$	0.686314	0.0283999
$585$	26.7910	1.10767
$586$	−1.94224	−0.0802331
$587$	−15.0573	−0.621481	−0.310740	−	0.950495i	$-0.600577\pi$
$587$	−15.0573	−0.621481	−0.310740	+	0.950495i	$0.600577\pi$
$588$	−41.6809	−1.71889
$589$	−23.0169	−0.948395
$590$	−55.5267	−2.28600
$591$	29.0336	1.19428
$592$	5.53054	0.227304
$593$	14.1417	0.580728	0.290364	−	0.956916i	$-0.406224\pi$
$593$	14.1417	0.580728	0.290364	+	0.956916i	$0.406224\pi$
$594$	8.45307	0.346834
$595$	−97.4004	−3.99303
$596$	−4.99685	−0.204679
$597$	16.4867	0.674756
$598$	46.5485	1.90351
$599$	−14.2289	−0.581377	−0.290688	−	0.956818i	$-0.593884\pi$
$599$	−14.2289	−0.581377	−0.290688	+	0.956818i	$0.593884\pi$
$600$	−21.7285	−0.887061
$601$	−34.6189	−1.41213	−0.706067	−	0.708145i	$-0.749532\pi$
$601$	−34.6189	−1.41213	−0.706067	+	0.708145i	$0.749532\pi$
$602$	−47.6340	−1.94142
$603$	−7.30639	−0.297539
$604$	2.17229	0.0883892
$605$	−22.5646	−0.917383
$606$	31.8123	1.29229
$607$	−35.7563	−1.45130	−0.725652	−	0.688062i	$-0.758462\pi$
$607$	−35.7563	−1.45130	−0.725652	+	0.688062i	$0.758462\pi$
$608$	−7.26383	−0.294587
$609$	101.346	4.10675
$610$	−21.3587	−0.864787
$611$	27.9597	1.13113
$612$	−5.69847	−0.230347
$613$	−28.3849	−1.14645	−0.573227	−	0.819396i	$-0.694309\pi$
$613$	−28.3849	−1.14645	−0.573227	+	0.819396i	$0.694309\pi$
$614$	9.38245	0.378645
$615$	−24.0609	−0.970228
$616$	12.0168	0.484172
$617$	−42.0438	−1.69262	−0.846310	−	0.532691i	$-0.821181\pi$
$617$	−42.0438	−1.69262	−0.846310	+	0.532691i	$0.821181\pi$
$618$	16.3483	0.657623
$619$	10.2714	0.412843	0.206422	−	0.978463i	$-0.433818\pi$
$619$	10.2714	0.412843	0.206422	+	0.978463i	$0.433818\pi$
$620$	12.5125	0.502515
$621$	30.4611	1.22236
$622$	24.3787	0.977496
$623$	64.9599	2.60256
$624$	−11.5249	−0.461366
$625$	34.2452	1.36981
$626$	13.1370	0.525061
$627$	34.2555	1.36803
$628$	4.56563	0.182189
$629$	−26.0991	−1.04064
$630$	24.9232	0.992965
$631$	−25.7327	−1.02440	−0.512201	−	0.858866i	$-0.671170\pi$
$631$	−25.7327	−1.02440	−0.512201	+	0.858866i	$0.671170\pi$
$632$	8.43169	0.335395
$633$	−43.4180	−1.72571
$634$	−6.28830	−0.249740
$635$	−23.2571	−0.922930
$636$	9.81469	0.389178
$637$	114.168	4.52352
$638$	−21.7322	−0.860385
$639$	16.8120	0.665074
$640$	3.94879	0.156089
$641$	−24.5353	−0.969086	−0.484543	−	0.874768i	$-0.661014\pi$
$641$	−24.5353	−0.969086	−0.484543	+	0.874768i	$0.661014\pi$
$642$	23.3408	0.921188
$643$	42.0173	1.65700	0.828500	−	0.559989i	$-0.189195\pi$
$643$	42.0173	1.65700	0.828500	+	0.559989i	$0.189195\pi$
$644$	43.3034	1.70639
$645$	73.8167	2.90653
$646$	34.2786	1.34867
$647$	29.5615	1.16218	0.581091	−	0.813838i	$-0.302626\pi$
$647$	29.5615	1.16218	0.581091	+	0.813838i	$0.302626\pi$
$648$	−11.1645	−0.438582
$649$	−32.3287	−1.26901
$650$	59.5167	2.33444
$651$	−33.9731	−1.33151
$652$	−3.15559	−0.123582
$653$	1.07250	0.0419702	0.0209851	−	0.999780i	$-0.493320\pi$
$653$	1.07250	0.0419702	0.0209851	+	0.999780i	$0.493320\pi$
$654$	7.27770	0.284581
$655$	57.6930	2.25425
$656$	2.97053	0.115980
$657$	0.828750	0.0323326
$658$	26.0105	1.01400
$659$	−15.1320	−0.589457	−0.294729	−	0.955581i	$-0.595229\pi$
$659$	−15.1320	−0.589457	−0.294729	+	0.955581i	$0.595229\pi$
$660$	−18.6221	−0.724863
$661$	−34.2208	−1.33104	−0.665518	−	0.746382i	$-0.731789\pi$
$661$	−34.2208	−1.33104	−0.665518	+	0.746382i	$0.731789\pi$
$662$	13.8106	0.536764
$663$	54.3870	2.11221
$664$	−5.09002	−0.197531
$665$	−149.923	−5.81378
$666$	6.67834	0.258780
$667$	−78.3132	−3.03230
$668$	−0.997577	−0.0385974
$669$	−10.5541	−0.408044
$670$	−23.8927	−0.923056
$671$	−12.4354	−0.480064
$672$	−10.7215	−0.413589
$673$	−3.74403	−0.144322	−0.0721609	−	0.997393i	$-0.522990\pi$
$673$	−3.74403	−0.144322	−0.0721609	+	0.997393i	$0.522990\pi$
$674$	−20.3597	−0.784227
$675$	38.9475	1.49909
$676$	18.5680	0.714155
$677$	7.22099	0.277525	0.138763	−	0.990326i	$-0.455688\pi$
$677$	7.22099	0.277525	0.138763	+	0.990326i	$0.455688\pi$
$678$	22.3690	0.859077
$679$	28.4989	1.09369
$680$	−18.6346	−0.714605
$681$	3.29624	0.126312
$682$	7.28503	0.278958
$683$	4.46046	0.170675	0.0853373	−	0.996352i	$-0.472803\pi$
$683$	4.46046	0.170675	0.0853373	+	0.996352i	$0.472803\pi$
$684$	−8.77135	−0.335381
$685$	−42.3417	−1.61779
$686$	69.6214	2.65816
$687$	33.6265	1.28293
$688$	−9.11333	−0.347442
$689$	−26.8835	−1.02418
$690$	−67.1057	−2.55467
$691$	−1.80785	−0.0687738	−0.0343869	−	0.999409i	$-0.510948\pi$
$691$	−1.80785	−0.0687738	−0.0343869	+	0.999409i	$0.510948\pi$
$692$	−7.82163	−0.297334
$693$	14.5108	0.551219
$694$	31.3692	1.19076
$695$	−49.8952	−1.89263
$696$	19.3895	0.734958
$697$	−14.0182	−0.530976
$698$	7.85812	0.297434
$699$	0.629966	0.0238275
$700$	55.3675	2.09270
$701$	47.3909	1.78993	0.894964	−	0.446139i	$-0.147201\pi$
$701$	47.3909	1.78993	0.894964	+	0.446139i	$0.147201\pi$
$702$	20.6580	0.779685
$703$	−40.1729	−1.51515
$704$	2.29906	0.0866491
$705$	−40.3076	−1.51807
$706$	−12.5510	−0.472363
$707$	−81.0627	−3.04868
$708$	28.8438	1.08402
$709$	46.9707	1.76402	0.882011	−	0.471230i	$-0.156190\pi$
$709$	46.9707	1.76402	0.882011	+	0.471230i	$0.156190\pi$
$710$	54.9772	2.06326
$711$	10.1816	0.381839
$712$	12.4281	0.465764
$713$	26.2520	0.983146
$714$	50.5954	1.89349
$715$	51.0079	1.90759
$716$	−0.927587	−0.0346656
$717$	−34.6249	−1.29309
$718$	13.4576	0.502233
$719$	−18.7388	−0.698839	−0.349419	−	0.936966i	$-0.613621\pi$
$719$	−18.7388	−0.698839	−0.349419	+	0.936966i	$0.613621\pi$
$720$	4.76831	0.177704
$721$	−41.6579	−1.55142
$722$	33.7633	1.25654
$723$	−45.2935	−1.68448
$724$	−8.76120	−0.325608
$725$	−100.131	−3.71877
$726$	11.7214	0.435021
$727$	2.93582	0.108883	0.0544417	−	0.998517i	$-0.482662\pi$
$727$	2.93582	0.108883	0.0544417	+	0.998517i	$0.482662\pi$
$728$	29.3673	1.08842
$729$	9.14403	0.338668
$730$	2.71010	0.100305
$731$	43.0065	1.59065
$732$	11.0949	0.410080
$733$	2.10067	0.0775899	0.0387949	−	0.999247i	$-0.487648\pi$
$733$	2.10067	0.0775899	0.0387949	+	0.999247i	$0.487648\pi$
$734$	−12.8843	−0.475568
$735$	−164.589	−6.07095
$736$	8.28480	0.305382
$737$	−13.9108	−0.512411
$738$	3.58703	0.132040
$739$	47.7328	1.75588	0.877939	−	0.478772i	$-0.158918\pi$
$739$	47.7328	1.75588	0.877939	+	0.478772i	$0.158918\pi$
$740$	21.8389	0.802815
$741$	83.7150	3.07535
$742$	−25.0094	−0.918122
$743$	9.01034	0.330557	0.165279	−	0.986247i	$-0.447148\pi$
$743$	9.01034	0.330557	0.165279	+	0.986247i	$0.447148\pi$
$744$	−6.49973	−0.238292
$745$	−19.7315	−0.722906
$746$	23.5467	0.862106
$747$	−6.14640	−0.224885
$748$	−10.8494	−0.396695
$749$	−59.4760	−2.17321
$750$	−45.3018	−1.65419
$751$	25.6823	0.937160	0.468580	−	0.883421i	$-0.344766\pi$
$751$	25.6823	0.937160	0.468580	+	0.883421i	$0.344766\pi$
$752$	4.97633	0.181468
$753$	−29.0957	−1.06031
$754$	−53.1100	−1.93415
$755$	8.57790	0.312182
$756$	19.2178	0.698945
$757$	−3.62322	−0.131688	−0.0658441	−	0.997830i	$-0.520974\pi$
$757$	−3.62322	−0.131688	−0.0658441	+	0.997830i	$0.520974\pi$
$758$	−22.9928	−0.835135
$759$	−39.0703	−1.41816
$760$	−28.6833	−1.04045
$761$	−5.05808	−0.183355	−0.0916776	−	0.995789i	$-0.529223\pi$
$761$	−5.05808	−0.183355	−0.0916776	+	0.995789i	$0.529223\pi$
$762$	12.0811	0.437652
$763$	−18.5447	−0.671363
$764$	−15.4042	−0.557305
$765$	−22.5020	−0.813562
$766$	5.81782	0.210206
$767$	−79.0064	−2.85275
$768$	−2.05123	−0.0740173
$769$	38.8187	1.39984	0.699918	−	0.714223i	$-0.253220\pi$
$769$	38.8187	1.39984	0.699918	+	0.714223i	$0.253220\pi$
$770$	47.4519	1.71005
$771$	29.1043	1.04817
$772$	−16.5766	−0.596605
$773$	8.10330	0.291455	0.145728	−	0.989325i	$-0.453448\pi$
$773$	8.10330	0.291455	0.145728	+	0.989325i	$0.453448\pi$
$774$	−11.0047	−0.395555
$775$	33.5657	1.20572
$776$	5.45240	0.195730
$777$	−59.2955	−2.12721
$778$	0.159767	0.00572794
$779$	−21.5774	−0.773092
$780$	−45.5094	−1.62950
$781$	32.0088	1.14537
$782$	−39.0966	−1.39809
$783$	−34.7550	−1.24204
$784$	20.3199	0.725712
$785$	18.0287	0.643472
$786$	−29.9691	−1.06896
$787$	16.4880	0.587732	0.293866	−	0.955847i	$-0.405058\pi$
$787$	16.4880	0.587732	0.293866	+	0.955847i	$0.405058\pi$
$788$	−14.1542	−0.504224
$789$	35.0117	1.24645
$790$	33.2949	1.18458
$791$	−56.9997	−2.02668
$792$	2.77620	0.0986481
$793$	−30.3902	−1.07919
$794$	30.3752	1.07797
$795$	38.7561	1.37454
$796$	−8.03748	−0.284881
$797$	14.3775	0.509279	0.254639	−	0.967036i	$-0.418043\pi$
$797$	14.3775	0.509279	0.254639	+	0.967036i	$0.418043\pi$
$798$	77.8789	2.75688
$799$	−23.4837	−0.830793
$800$	10.5929	0.374516
$801$	15.0074	0.530262
$802$	−7.98208	−0.281857
$803$	1.57788	0.0556820
$804$	12.4113	0.437712
$805$	170.996	6.02681
$806$	17.8035	0.627101
$807$	39.0489	1.37459
$808$	−15.5089	−0.545601
$809$	3.42515	0.120422	0.0602110	−	0.998186i	$-0.480823\pi$
$809$	3.42515	0.120422	0.0602110	+	0.998186i	$0.480823\pi$
$810$	−44.0861	−1.54903
$811$	−19.2498	−0.675952	−0.337976	−	0.941155i	$-0.609742\pi$
$811$	−19.2498	−0.675952	−0.337976	+	0.941155i	$0.609742\pi$
$812$	−49.4075	−1.73386
$813$	−53.0183	−1.85943
$814$	12.7150	0.445662
$815$	−12.4607	−0.436481
$816$	9.67991	0.338864
$817$	66.1977	2.31596
$818$	−19.7497	−0.690530
$819$	35.4621	1.23915
$820$	11.7300	0.409629
$821$	52.4290	1.82979	0.914893	−	0.403697i	$-0.132275\pi$
$821$	52.4290	1.82979	0.914893	+	0.403697i	$0.132275\pi$
$822$	21.9947	0.767154
$823$	−27.6223	−0.962852	−0.481426	−	0.876487i	$-0.659881\pi$
$823$	−27.6223	−0.962852	−0.481426	+	0.876487i	$0.659881\pi$
$824$	−7.96998	−0.277647
$825$	−49.9551	−1.73921
$826$	−73.4985	−2.55734
$827$	−40.1036	−1.39454	−0.697269	−	0.716810i	$-0.745602\pi$
$827$	−40.1036	−1.39454	−0.697269	+	0.716810i	$0.745602\pi$
$828$	10.0042	0.347670
$829$	25.1873	0.874793	0.437396	−	0.899269i	$-0.355901\pi$
$829$	25.1873	0.874793	0.437396	+	0.899269i	$0.355901\pi$
$830$	−20.0994	−0.697661
$831$	19.6575	0.681910
$832$	5.61854	0.194788
$833$	−95.8914	−3.32244
$834$	25.9185	0.897483
$835$	−3.93922	−0.136322
$836$	−16.7000	−0.577581
$837$	11.6505	0.402701
$838$	20.0563	0.692833
$839$	−16.1085	−0.556129	−0.278064	−	0.960562i	$-0.589693\pi$
$839$	−16.1085	−0.556129	−0.278064	+	0.960562i	$0.589693\pi$
$840$	−42.3368	−1.46076
$841$	60.3523	2.08111
$842$	−2.54900	−0.0878444
$843$	−31.5634	−1.08710
$844$	21.1668	0.728591
$845$	73.3211	2.52232
$846$	6.00911	0.206598
$847$	−29.8679	−1.02627
$848$	−4.78479	−0.164310
$849$	−53.7233	−1.84378
$850$	−49.9887	−1.71460
$851$	45.8194	1.57067
$852$	−28.5584	−0.978394
$853$	22.1221	0.757445	0.378723	−	0.925510i	$-0.376363\pi$
$853$	22.1221	0.757445	0.378723	+	0.925510i	$0.376363\pi$
$854$	−28.2716	−0.967434
$855$	−34.6362	−1.18453
$856$	−11.3789	−0.388924
$857$	21.7136	0.741723	0.370861	−	0.928688i	$-0.379062\pi$
$857$	21.7136	0.741723	0.370861	+	0.928688i	$0.379062\pi$
$858$	−26.4965	−0.904575
$859$	3.70096	0.126275	0.0631376	−	0.998005i	$-0.479889\pi$
$859$	3.70096	0.126275	0.0631376	+	0.998005i	$0.479889\pi$
$860$	−35.9866	−1.22713
$861$	−31.8484	−1.08539
$862$	9.66917	0.329333
$863$	23.9871	0.816530	0.408265	−	0.912863i	$-0.366134\pi$
$863$	23.9871	0.816530	0.408265	+	0.912863i	$0.366134\pi$
$864$	3.67675	0.125086
$865$	−30.8859	−1.05015
$866$	−8.34744	−0.283658
$867$	−10.8093	−0.367104
$868$	16.5623	0.562161
$869$	19.3850	0.657590
$870$	76.5650	2.59580
$871$	−33.9958	−1.15191
$872$	−3.54797	−0.120149
$873$	6.58398	0.222834
$874$	−60.1794	−2.03560
$875$	115.436	3.90245
$876$	−1.40779	−0.0475647
$877$	40.7999	1.37772	0.688858	−	0.724897i	$-0.258112\pi$
$877$	40.7999	1.37772	0.688858	+	0.724897i	$0.258112\pi$
$878$	2.79738	0.0944069
$879$	3.98397	0.134376
$880$	9.07850	0.306036
$881$	31.7199	1.06867	0.534335	−	0.845273i	$-0.320562\pi$
$881$	31.7199	1.06867	0.534335	+	0.845273i	$0.320562\pi$
$882$	24.5371	0.826208
$883$	19.4924	0.655972	0.327986	−	0.944683i	$-0.393630\pi$
$883$	19.4924	0.655972	0.327986	+	0.944683i	$0.393630\pi$
$884$	−26.5143	−0.891774
$885$	113.898	3.82864
$886$	16.6417	0.559090
$887$	39.2341	1.31735	0.658677	−	0.752426i	$-0.271117\pi$
$887$	39.2341	1.31735	0.658677	+	0.752426i	$0.271117\pi$
$888$	−11.3444	−0.380693
$889$	−30.7845	−1.03248
$890$	49.0760	1.64503
$891$	−25.6678	−0.859903
$892$	5.14524	0.172276
$893$	−36.1472	−1.20962
$894$	10.2497	0.342801
$895$	−3.66284	−0.122435
$896$	5.22685	0.174617
$897$	−95.4816	−3.18804
$898$	14.5185	0.484488
$899$	−29.9526	−0.998974
$900$	12.7913	0.426378
$901$	22.5798	0.752241
$902$	6.82943	0.227395
$903$	97.7082	3.25152
$904$	−10.9052	−0.362701
$905$	−34.5961	−1.15001
$906$	−4.45586	−0.148036
$907$	−55.7729	−1.85191	−0.925955	−	0.377633i	$-0.876738\pi$
$907$	−55.7729	−1.85191	−0.925955	+	0.377633i	$0.876738\pi$
$908$	−1.60696	−0.0533288
$909$	−18.7276	−0.621155
$910$	115.965	3.84420
$911$	1.65665	0.0548872	0.0274436	−	0.999623i	$-0.491263\pi$
$911$	1.65665	0.0548872	0.0274436	+	0.999623i	$0.491263\pi$
$912$	14.8998	0.493381
$913$	−11.7023	−0.387289
$914$	−15.1073	−0.499705
$915$	43.8115	1.44836
$916$	−16.3933	−0.541651
$917$	76.3659	2.52183
$918$	−17.3509	−0.572664
$919$	−9.37761	−0.309339	−0.154669	−	0.987966i	$-0.549431\pi$
$919$	−9.37761	−0.309339	−0.154669	+	0.987966i	$0.549431\pi$
$920$	32.7149	1.07858
$921$	−19.2455	−0.634162
$922$	−13.0171	−0.428694
$923$	78.2246	2.57479
$924$	−24.6493	−0.810902
$925$	58.5845	1.92625
$926$	12.9816	0.426602
$927$	−9.62406	−0.316096
$928$	−9.45263	−0.310298
$929$	11.8703	0.389453	0.194726	−	0.980858i	$-0.437618\pi$
$929$	11.8703	0.389453	0.194726	+	0.980858i	$0.437618\pi$
$930$	−25.6660	−0.841622
$931$	−147.601	−4.83742
$932$	−0.307116	−0.0100599
$933$	−50.0062	−1.63713
$934$	1.52561	0.0499196
$935$	−42.8421	−1.40109
$936$	6.78461	0.221762
$937$	2.01532	0.0658375	0.0329188	−	0.999458i	$-0.489520\pi$
$937$	2.01532	0.0658375	0.0329188	+	0.999458i	$0.489520\pi$
$938$	−31.6258	−1.03262
$939$	−26.9470	−0.879382
$940$	19.6505	0.640928
$941$	9.86363	0.321545	0.160773	−	0.986991i	$-0.448601\pi$
$941$	9.86363	0.321545	0.160773	+	0.986991i	$0.448601\pi$
$942$	−9.36516	−0.305133
$943$	24.6102	0.801420
$944$	−14.0617	−0.457670
$945$	75.8870	2.46860
$946$	−20.9521	−0.681211
$947$	15.9250	0.517492	0.258746	−	0.965945i	$-0.416691\pi$
$947$	15.9250	0.517492	0.258746	+	0.965945i	$0.416691\pi$
$948$	−17.2953	−0.561726
$949$	3.85608	0.125174
$950$	−76.9451	−2.49643
$951$	12.8987	0.418271
$952$	−24.6659	−0.799426
$953$	15.6104	0.505672	0.252836	−	0.967509i	$-0.418637\pi$
$953$	15.6104	0.505672	0.252836	+	0.967509i	$0.418637\pi$
$954$	−5.77781	−0.187064
$955$	−60.8279	−1.96834
$956$	16.8801	0.545940
$957$	44.5777	1.44099
$958$	−27.4348	−0.886378
$959$	−56.0460	−1.80982
$960$	−8.09986	−0.261422
$961$	−20.9593	−0.676108
$962$	31.0736	1.00185
$963$	−13.7405	−0.442782
$964$	22.0812	0.711187
$965$	−65.4574	−2.10715
$966$	−88.8251	−2.85790
$967$	11.7775	0.378740	0.189370	−	0.981906i	$-0.439355\pi$
$967$	11.7775	0.378740	0.189370	+	0.981906i	$0.439355\pi$
$968$	−5.71432	−0.183665
$969$	−70.3132	−2.25879
$970$	21.5304	0.691298
$971$	−22.3886	−0.718483	−0.359241	−	0.933245i	$-0.616965\pi$
$971$	−22.3886	−0.718483	−0.359241	+	0.933245i	$0.616965\pi$
$972$	11.8706	0.380750
$973$	−66.0443	−2.11728
$974$	21.1246	0.676876
$975$	−122.082	−3.90976
$976$	−5.40892	−0.173135
$977$	1.47883	0.0473119	0.0236560	−	0.999720i	$-0.492469\pi$
$977$	1.47883	0.0473119	0.0236560	+	0.999720i	$0.492469\pi$
$978$	6.47283	0.206978
$979$	28.5730	0.913197
$980$	80.2391	2.56314
$981$	−4.28431	−0.136788
$982$	−19.3451	−0.617328
$983$	−21.8317	−0.696324	−0.348162	−	0.937434i	$-0.613194\pi$
$983$	−21.8317	−0.696324	−0.348162	+	0.937434i	$0.613194\pi$
$984$	−6.09324	−0.194245
$985$	−55.8921	−1.78087
$986$	44.6077	1.42060
$987$	−53.3536	−1.69826
$988$	−40.8121	−1.29841
$989$	−75.5021	−2.40083
$990$	10.9626	0.348415
$991$	13.3532	0.424179	0.212089	−	0.977250i	$-0.431973\pi$
$991$	13.3532	0.424179	0.212089	+	0.977250i	$0.431973\pi$
$992$	3.16870	0.100606
$993$	−28.3287	−0.898983
$994$	72.7712	2.30816
$995$	−31.7383	−1.00617
$996$	10.4408	0.330829
$997$	−50.2274	−1.59072	−0.795360	−	0.606138i	$-0.792718\pi$
$997$	−50.2274	−1.59072	−0.795360	+	0.606138i	$0.792718\pi$
$998$	−12.8109	−0.405523
$999$	20.3344	0.643352

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6038.2.a.e.1.13	✓	70

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6038.2.a.e.1.13	✓	70	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:	\( N \)	\(=\)	\( 6038 = 2 \cdot 3019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6038.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.05123 q^{3} +1.00000 q^{4} +3.94879 q^{5} -2.05123 q^{6} +5.22685 q^{7} +1.00000 q^{8} +1.20754 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.05123 q^{3} +1.00000 q^{4} +3.94879 q^{5} -2.05123 q^{6} +5.22685 q^{7} +1.00000 q^{8} +1.20754 q^{9} +3.94879 q^{10} +2.29906 q^{11} -2.05123 q^{12} +5.61854 q^{13} +5.22685 q^{14} -8.09986 q^{15} +1.00000 q^{16} -4.71908 q^{17} +1.20754 q^{18} -7.26383 q^{19} +3.94879 q^{20} -10.7215 q^{21} +2.29906 q^{22} +8.28480 q^{23} -2.05123 q^{24} +10.5929 q^{25} +5.61854 q^{26} +3.67675 q^{27} +5.22685 q^{28} -9.45263 q^{29} -8.09986 q^{30} +3.16870 q^{31} +1.00000 q^{32} -4.71590 q^{33} -4.71908 q^{34} +20.6397 q^{35} +1.20754 q^{36} +5.53054 q^{37} -7.26383 q^{38} -11.5249 q^{39} +3.94879 q^{40} +2.97053 q^{41} -10.7215 q^{42} -9.11333 q^{43} +2.29906 q^{44} +4.76831 q^{45} +8.28480 q^{46} +4.97633 q^{47} -2.05123 q^{48} +20.3199 q^{49} +10.5929 q^{50} +9.67991 q^{51} +5.61854 q^{52} -4.78479 q^{53} +3.67675 q^{54} +9.07850 q^{55} +5.22685 q^{56} +14.8998 q^{57} -9.45263 q^{58} -14.0617 q^{59} -8.09986 q^{60} -5.40892 q^{61} +3.16870 q^{62} +6.31162 q^{63} +1.00000 q^{64} +22.1864 q^{65} -4.71590 q^{66} -6.05065 q^{67} -4.71908 q^{68} -16.9940 q^{69} +20.6397 q^{70} +13.9226 q^{71} +1.20754 q^{72} +0.686314 q^{73} +5.53054 q^{74} -21.7285 q^{75} -7.26383 q^{76} +12.0168 q^{77} -11.5249 q^{78} +8.43169 q^{79} +3.94879 q^{80} -11.1645 q^{81} +2.97053 q^{82} -5.09002 q^{83} -10.7215 q^{84} -18.6346 q^{85} -9.11333 q^{86} +19.3895 q^{87} +2.29906 q^{88} +12.4281 q^{89} +4.76831 q^{90} +29.3673 q^{91} +8.28480 q^{92} -6.49973 q^{93} +4.97633 q^{94} -28.6833 q^{95} -2.05123 q^{96} +5.45240 q^{97} +20.3199 q^{98} +2.77620 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9}+O(q^{10}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9	\( 70 q + 70 q^{2} + 25 q^{3} + 70 q^{4} + 18 q^{5} + 25 q^{6} + 50 q^{7} + 70 q^{8} + 89 q^{9} + 18 q^{10} + 41 q^{11} + 25 q^{12} + 41 q^{13} + 50 q^{14} + 13 q^{15} + 70 q^{16} + 40 q^{17} + 89 q^{18} + 55 q^{19} + 18 q^{20} + 2 q^{21} + 41 q^{22} + 41 q^{23} + 25 q^{24} + 104 q^{25} + 41 q^{26} + 82 q^{27} + 50 q^{28} + 11 q^{29} + 13 q^{30} + 78 q^{31} + 70 q^{32} + 45 q^{33} + 40 q^{34} + 25 q^{35} + 89 q^{36} + 46 q^{37} + 55 q^{38} + 19 q^{39} + 18 q^{40} + 51 q^{41} + 2 q^{42} + 68 q^{43} + 41 q^{44} + 37 q^{45} + 41 q^{46} + 69 q^{47} + 25 q^{48} + 126 q^{49} + 104 q^{50} + 36 q^{51} + 41 q^{52} + 23 q^{53} + 82 q^{54} + 42 q^{55} + 50 q^{56} + 14 q^{57} + 11 q^{58} + 89 q^{59} + 13 q^{60} + 32 q^{61} + 78 q^{62} + 106 q^{63} + 70 q^{64} + 18 q^{65} + 45 q^{66} + 90 q^{67} + 40 q^{68} - 12 q^{69} + 25 q^{70} + 54 q^{71} + 89 q^{72} + 94 q^{73} + 46 q^{74} + 72 q^{75} + 55 q^{76} - 16 q^{77} + 19 q^{78} + 54 q^{79} + 18 q^{80} + 102 q^{81} + 51 q^{82} + 60 q^{83} + 2 q^{84} - 5 q^{85} + 68 q^{86} + 9 q^{87} + 41 q^{88} + 77 q^{89} + 37 q^{90} + 54 q^{91} + 41 q^{92} - 2 q^{93} + 69 q^{94} + 39 q^{95} + 25 q^{96} + 139 q^{97} + 126 q^{98} + 60 q^{99}+O(q^{100}) \) 70 * q + 70 * q^2 + 25 * q^3 + 70 * q^4 + 18 * q^5 + 25 * q^6 + 50 * q^7 + 70 * q^8 + 89 * q^9 + 18 * q^10 + 41 * q^11 + 25 * q^12 + 41 * q^13 + 50 * q^14 + 13 * q^15 + 70 * q^16 + 40 * q^17 + 89 * q^18 + 55 * q^19 + 18 * q^20 + 2 * q^21 + 41 * q^22 + 41 * q^23 + 25 * q^24 + 104 * q^25 + 41 * q^26 + 82 * q^27 + 50 * q^28 + 11 * q^29 + 13 * q^30 + 78 * q^31 + 70 * q^32 + 45 * q^33 + 40 * q^34 + 25 * q^35 + 89 * q^36 + 46 * q^37 + 55 * q^38 + 19 * q^39 + 18 * q^40 + 51 * q^41 + 2 * q^42 + 68 * q^43 + 41 * q^44 + 37 * q^45 + 41 * q^46 + 69 * q^47 + 25 * q^48 + 126 * q^49 + 104 * q^50 + 36 * q^51 + 41 * q^52 + 23 * q^53 + 82 * q^54 + 42 * q^55 + 50 * q^56 + 14 * q^57 + 11 * q^58 + 89 * q^59 + 13 * q^60 + 32 * q^61 + 78 * q^62 + 106 * q^63 + 70 * q^64 + 18 * q^65 + 45 * q^66 + 90 * q^67 + 40 * q^68 - 12 * q^69 + 25 * q^70 + 54 * q^71 + 89 * q^72 + 94 * q^73 + 46 * q^74 + 72 * q^75 + 55 * q^76 - 16 * q^77 + 19 * q^78 + 54 * q^79 + 18 * q^80 + 102 * q^81 + 51 * q^82 + 60 * q^83 + 2 * q^84 - 5 * q^85 + 68 * q^86 + 9 * q^87 + 41 * q^88 + 77 * q^89 + 37 * q^90 + 54 * q^91 + 41 * q^92 - 2 * q^93 + 69 * q^94 + 39 * q^95 + 25 * q^96 + 139 * q^97 + 126 * q^98 + 60 * q^99

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