LMFDB - Embedded newform 8014.2.a.d.1.19

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8014,2,Mod(1,8014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8014, 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("8014.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8014 = 2 \cdot 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8014.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:	$63.9921121799$
Analytic rank:	$0$
Dimension:	$88$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.19
Character	$\chi$	$=$	8014.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.85163 q^{3} +1.00000 q^{4} +2.24102 q^{5} -1.85163 q^{6} -0.974679 q^{7} +1.00000 q^{8} +0.428551 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.85163 q^{3} +1.00000 q^{4} +2.24102 q^{5} -1.85163 q^{6} -0.974679 q^{7} +1.00000 q^{8} +0.428551 q^{9} +2.24102 q^{10} +6.34024 q^{11} -1.85163 q^{12} +4.97118 q^{13} -0.974679 q^{14} -4.14954 q^{15} +1.00000 q^{16} +4.60011 q^{17} +0.428551 q^{18} +2.21292 q^{19} +2.24102 q^{20} +1.80475 q^{21} +6.34024 q^{22} +7.20543 q^{23} -1.85163 q^{24} +0.0221579 q^{25} +4.97118 q^{26} +4.76138 q^{27} -0.974679 q^{28} -6.41298 q^{29} -4.14954 q^{30} -8.04539 q^{31} +1.00000 q^{32} -11.7398 q^{33} +4.60011 q^{34} -2.18427 q^{35} +0.428551 q^{36} +10.6475 q^{37} +2.21292 q^{38} -9.20480 q^{39} +2.24102 q^{40} -5.52367 q^{41} +1.80475 q^{42} +9.18021 q^{43} +6.34024 q^{44} +0.960389 q^{45} +7.20543 q^{46} +11.4374 q^{47} -1.85163 q^{48} -6.05000 q^{49} +0.0221579 q^{50} -8.51772 q^{51} +4.97118 q^{52} +12.9115 q^{53} +4.76138 q^{54} +14.2086 q^{55} -0.974679 q^{56} -4.09753 q^{57} -6.41298 q^{58} -5.77755 q^{59} -4.14954 q^{60} -4.49815 q^{61} -8.04539 q^{62} -0.417699 q^{63} +1.00000 q^{64} +11.1405 q^{65} -11.7398 q^{66} -5.26672 q^{67} +4.60011 q^{68} -13.3418 q^{69} -2.18427 q^{70} -6.54236 q^{71} +0.428551 q^{72} -0.771275 q^{73} +10.6475 q^{74} -0.0410284 q^{75} +2.21292 q^{76} -6.17970 q^{77} -9.20480 q^{78} -3.79108 q^{79} +2.24102 q^{80} -10.1020 q^{81} -5.52367 q^{82} -15.2792 q^{83} +1.80475 q^{84} +10.3089 q^{85} +9.18021 q^{86} +11.8745 q^{87} +6.34024 q^{88} +1.91557 q^{89} +0.960389 q^{90} -4.84530 q^{91} +7.20543 q^{92} +14.8971 q^{93} +11.4374 q^{94} +4.95920 q^{95} -1.85163 q^{96} -13.2488 q^{97} -6.05000 q^{98} +2.71711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) $ 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * 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
$3$	−1.85163	−1.06904	−0.534521	−	0.845155i	$-0.679508\pi$
$3$	−1.85163	−1.06904	−0.534521	+	0.845155i	$0.679508\pi$
$4$	1.00000	0.500000
$5$	2.24102	1.00221	0.501107	−	0.865386i	$-0.332926\pi$
$5$	2.24102	1.00221	0.501107	+	0.865386i	$0.332926\pi$
$6$	−1.85163	−0.755927
$7$	−0.974679	−0.368394	−0.184197	−	0.982889i	$-0.558968\pi$
$7$	−0.974679	−0.368394	−0.184197	+	0.982889i	$0.558968\pi$
$8$	1.00000	0.353553
$9$	0.428551	0.142850
$10$	2.24102	0.708672
$11$	6.34024	1.91165	0.955827	−	0.293930i	$-0.0949632\pi$
$11$	6.34024	1.91165	0.955827	+	0.293930i	$0.0949632\pi$
$12$	−1.85163	−0.534521
$13$	4.97118	1.37876	0.689378	−	0.724402i	$-0.257884\pi$
$13$	4.97118	1.37876	0.689378	+	0.724402i	$0.257884\pi$
$14$	−0.974679	−0.260494
$15$	−4.14954	−1.07141
$16$	1.00000	0.250000
$17$	4.60011	1.11569	0.557845	−	0.829945i	$-0.311628\pi$
$17$	4.60011	1.11569	0.557845	+	0.829945i	$0.311628\pi$
$18$	0.428551	0.101010
$19$	2.21292	0.507680	0.253840	−	0.967246i	$-0.418306\pi$
$19$	2.21292	0.507680	0.253840	+	0.967246i	$0.418306\pi$
$20$	2.24102	0.501107
$21$	1.80475	0.393828
$22$	6.34024	1.35174
$23$	7.20543	1.50244	0.751218	−	0.660054i	$-0.229467\pi$
$23$	7.20543	1.50244	0.751218	+	0.660054i	$0.229467\pi$
$24$	−1.85163	−0.377963
$25$	0.0221579	0.00443158
$26$	4.97118	0.974928
$27$	4.76138	0.916329
$28$	−0.974679	−0.184197
$29$	−6.41298	−1.19086	−0.595430	−	0.803407i	$-0.703018\pi$
$29$	−6.41298	−1.19086	−0.595430	+	0.803407i	$0.703018\pi$
$30$	−4.14954	−0.757600
$31$	−8.04539	−1.44499	−0.722497	−	0.691374i	$-0.757006\pi$
$31$	−8.04539	−1.44499	−0.722497	+	0.691374i	$0.757006\pi$
$32$	1.00000	0.176777
$33$	−11.7398	−2.04364
$34$	4.60011	0.788912
$35$	−2.18427	−0.369209
$36$	0.428551	0.0714251
$37$	10.6475	1.75044	0.875220	−	0.483725i	$-0.160716\pi$
$37$	10.6475	1.75044	0.875220	+	0.483725i	$0.160716\pi$
$38$	2.21292	0.358984
$39$	−9.20480	−1.47395
$40$	2.24102	0.354336
$41$	−5.52367	−0.862653	−0.431326	−	0.902196i	$-0.641954\pi$
$41$	−5.52367	−0.862653	−0.431326	+	0.902196i	$0.641954\pi$
$42$	1.80475	0.278479
$43$	9.18021	1.39997	0.699985	−	0.714158i	$-0.253190\pi$
$43$	9.18021	1.39997	0.699985	+	0.714158i	$0.253190\pi$
$44$	6.34024	0.955827
$45$	0.960389	0.143166
$46$	7.20543	1.06238
$47$	11.4374	1.66831	0.834156	−	0.551528i	$-0.185955\pi$
$47$	11.4374	1.66831	0.834156	+	0.551528i	$0.185955\pi$
$48$	−1.85163	−0.267260
$49$	−6.05000	−0.864286
$50$	0.0221579	0.00313360
$51$	−8.51772	−1.19272
$52$	4.97118	0.689378
$53$	12.9115	1.77353	0.886765	−	0.462220i	$-0.152947\pi$
$53$	12.9115	1.77353	0.886765	+	0.462220i	$0.152947\pi$
$54$	4.76138	0.647942
$55$	14.2086	1.91589
$56$	−0.974679	−0.130247
$57$	−4.09753	−0.542731
$58$	−6.41298	−0.842065
$59$	−5.77755	−0.752172	−0.376086	−	0.926585i	$-0.622730\pi$
$59$	−5.77755	−0.752172	−0.376086	+	0.926585i	$0.622730\pi$
$60$	−4.14954	−0.535704
$61$	−4.49815	−0.575929	−0.287965	−	0.957641i	$-0.592979\pi$
$61$	−4.49815	−0.575929	−0.287965	+	0.957641i	$0.592979\pi$
$62$	−8.04539	−1.02176
$63$	−0.417699	−0.0526251
$64$	1.00000	0.125000
$65$	11.1405	1.38181
$66$	−11.7398	−1.44507
$67$	−5.26672	−0.643432	−0.321716	−	0.946836i	$-0.604260\pi$
$67$	−5.26672	−0.643432	−0.321716	+	0.946836i	$0.604260\pi$
$68$	4.60011	0.557845
$69$	−13.3418	−1.60617
$70$	−2.18427	−0.261070
$71$	−6.54236	−0.776435	−0.388218	−	0.921568i	$-0.626909\pi$
$71$	−6.54236	−0.776435	−0.388218	+	0.921568i	$0.626909\pi$
$72$	0.428551	0.0505052
$73$	−0.771275	−0.0902709	−0.0451354	−	0.998981i	$-0.514372\pi$
$73$	−0.771275	−0.0902709	−0.0451354	+	0.998981i	$0.514372\pi$
$74$	10.6475	1.23775
$75$	−0.0410284	−0.00473755
$76$	2.21292	0.253840
$77$	−6.17970	−0.704242
$78$	−9.20480	−1.04224
$79$	−3.79108	−0.426530	−0.213265	−	0.976994i	$-0.568410\pi$
$79$	−3.79108	−0.426530	−0.213265	+	0.976994i	$0.568410\pi$
$80$	2.24102	0.250553
$81$	−10.1020	−1.12244
$82$	−5.52367	−0.609988
$83$	−15.2792	−1.67712	−0.838558	−	0.544813i	$-0.816601\pi$
$83$	−15.2792	−1.67712	−0.838558	+	0.544813i	$0.816601\pi$
$84$	1.80475	0.196914
$85$	10.3089	1.11816
$86$	9.18021	0.989928
$87$	11.8745	1.27308
$88$	6.34024	0.675872
$89$	1.91557	0.203050	0.101525	−	0.994833i	$-0.467628\pi$
$89$	1.91557	0.203050	0.101525	+	0.994833i	$0.467628\pi$
$90$	0.960389	0.101234
$91$	−4.84530	−0.507925
$92$	7.20543	0.751218
$93$	14.8971	1.54476
$94$	11.4374	1.17967
$95$	4.95920	0.508803
$96$	−1.85163	−0.188982
$97$	−13.2488	−1.34521	−0.672604	−	0.740003i	$-0.734824\pi$
$97$	−13.2488	−1.34521	−0.672604	+	0.740003i	$0.734824\pi$
$98$	−6.05000	−0.611142
$99$	2.71711	0.273080
$100$	0.0221579	0.00221579
$101$	0.525645	0.0523036	0.0261518	−	0.999658i	$-0.491675\pi$
$101$	0.525645	0.0523036	0.0261518	+	0.999658i	$0.491675\pi$
$102$	−8.51772	−0.843380
$103$	−10.1166	−0.996818	−0.498409	−	0.866942i	$-0.666082\pi$
$103$	−10.1166	−0.996818	−0.498409	+	0.866942i	$0.666082\pi$
$104$	4.97118	0.487464
$105$	4.04447	0.394700
$106$	12.9115	1.25408
$107$	−7.87552	−0.761356	−0.380678	−	0.924708i	$-0.624309\pi$
$107$	−7.87552	−0.761356	−0.380678	+	0.924708i	$0.624309\pi$
$108$	4.76138	0.458164
$109$	−4.60381	−0.440965	−0.220483	−	0.975391i	$-0.570763\pi$
$109$	−4.60381	−0.440965	−0.220483	+	0.975391i	$0.570763\pi$
$110$	14.2086	1.35474
$111$	−19.7153	−1.87129
$112$	−0.974679	−0.0920985
$113$	2.31841	0.218098	0.109049	−	0.994036i	$-0.465220\pi$
$113$	2.31841	0.218098	0.109049	+	0.994036i	$0.465220\pi$
$114$	−4.09753	−0.383769
$115$	16.1475	1.50576
$116$	−6.41298	−0.595430
$117$	2.13040	0.196956
$118$	−5.77755	−0.531866
$119$	−4.48363	−0.411014
$120$	−4.14954	−0.378800
$121$	29.1986	2.65442
$122$	−4.49815	−0.407243
$123$	10.2278	0.922212
$124$	−8.04539	−0.722497
$125$	−11.1554	−0.997772
$126$	−0.417699	−0.0372116
$127$	17.8971	1.58811	0.794053	−	0.607848i	$-0.207967\pi$
$127$	17.8971	1.58811	0.794053	+	0.607848i	$0.207967\pi$
$128$	1.00000	0.0883883
$129$	−16.9984	−1.49663
$130$	11.1405	0.977086
$131$	4.84910	0.423668	0.211834	−	0.977306i	$-0.432056\pi$
$131$	4.84910	0.423668	0.211834	+	0.977306i	$0.432056\pi$
$132$	−11.7398	−1.02182
$133$	−2.15689	−0.187026
$134$	−5.26672	−0.454975
$135$	10.6703	0.918357
$136$	4.60011	0.394456
$137$	−4.61595	−0.394367	−0.197184	−	0.980367i	$-0.563179\pi$
$137$	−4.61595	−0.394367	−0.197184	+	0.980367i	$0.563179\pi$
$138$	−13.3418	−1.13573
$139$	3.34364	0.283604	0.141802	−	0.989895i	$-0.454710\pi$
$139$	3.34364	0.283604	0.141802	+	0.989895i	$0.454710\pi$
$140$	−2.18427	−0.184605
$141$	−21.1778	−1.78350
$142$	−6.54236	−0.549023
$143$	31.5184	2.63570
$144$	0.428551	0.0357126
$145$	−14.3716	−1.19350
$146$	−0.771275	−0.0638311
$147$	11.2024	0.923958
$148$	10.6475	0.875220
$149$	−9.59499	−0.786052	−0.393026	−	0.919527i	$-0.628572\pi$
$149$	−9.59499	−0.786052	−0.393026	+	0.919527i	$0.628572\pi$
$150$	−0.0410284	−0.00334995
$151$	6.26170	0.509570	0.254785	−	0.966998i	$-0.417995\pi$
$151$	6.26170	0.509570	0.254785	+	0.966998i	$0.417995\pi$
$152$	2.21292	0.179492
$153$	1.97138	0.159377
$154$	−6.17970	−0.497974
$155$	−18.0298	−1.44819
$156$	−9.20480	−0.736974
$157$	−8.53570	−0.681223	−0.340612	−	0.940204i	$-0.610634\pi$
$157$	−8.53570	−0.681223	−0.340612	+	0.940204i	$0.610634\pi$
$158$	−3.79108	−0.301602
$159$	−23.9074	−1.89598
$160$	2.24102	0.177168
$161$	−7.02298	−0.553488
$162$	−10.1020	−0.793688
$163$	−18.1191	−1.41920	−0.709598	−	0.704606i	$-0.751124\pi$
$163$	−18.1191	−1.41920	−0.709598	+	0.704606i	$0.751124\pi$
$164$	−5.52367	−0.431326
$165$	−26.3091	−2.04816
$166$	−15.2792	−1.18590
$167$	−1.71622	−0.132805	−0.0664026	−	0.997793i	$-0.521152\pi$
$167$	−1.71622	−0.132805	−0.0664026	+	0.997793i	$0.521152\pi$
$168$	1.80475	0.139239
$169$	11.7126	0.900968
$170$	10.3089	0.790658
$171$	0.948350	0.0725222
$172$	9.18021	0.699985
$173$	5.33727	0.405785	0.202893	−	0.979201i	$-0.434966\pi$
$173$	5.33727	0.405785	0.202893	+	0.979201i	$0.434966\pi$
$174$	11.8745	0.900203
$175$	−0.0215969	−0.00163257
$176$	6.34024	0.477914
$177$	10.6979	0.804104
$178$	1.91557	0.143578
$179$	5.79037	0.432793	0.216396	−	0.976306i	$-0.430570\pi$
$179$	5.79037	0.432793	0.216396	+	0.976306i	$0.430570\pi$
$180$	0.960389	0.0715832
$181$	−16.5159	−1.22762	−0.613810	−	0.789454i	$-0.710364\pi$
$181$	−16.5159	−1.22762	−0.613810	+	0.789454i	$0.710364\pi$
$182$	−4.84530	−0.359157
$183$	8.32893	0.615692
$184$	7.20543	0.531191
$185$	23.8613	1.75431
$186$	14.8971	1.09231
$187$	29.1658	2.13281
$188$	11.4374	0.834156
$189$	−4.64082	−0.337570
$190$	4.95920	0.359778
$191$	−15.0894	−1.09183	−0.545916	−	0.837840i	$-0.683818\pi$
$191$	−15.0894	−1.09183	−0.545916	+	0.837840i	$0.683818\pi$
$192$	−1.85163	−0.133630
$193$	14.9213	1.07406	0.537031	−	0.843563i	$-0.319546\pi$
$193$	14.9213	1.07406	0.537031	+	0.843563i	$0.319546\pi$
$194$	−13.2488	−0.951206
$195$	−20.6281	−1.47721
$196$	−6.05000	−0.432143
$197$	−8.79470	−0.626597	−0.313298	−	0.949655i	$-0.601434\pi$
$197$	−8.79470	−0.626597	−0.313298	+	0.949655i	$0.601434\pi$
$198$	2.71711	0.193097
$199$	12.0463	0.853942	0.426971	−	0.904265i	$-0.359581\pi$
$199$	12.0463	0.853942	0.426971	+	0.904265i	$0.359581\pi$
$200$	0.0221579	0.00156680
$201$	9.75203	0.687855
$202$	0.525645	0.0369842
$203$	6.25059	0.438705
$204$	−8.51772	−0.596360
$205$	−12.3786	−0.864562
$206$	−10.1166	−0.704857
$207$	3.08789	0.214623
$208$	4.97118	0.344689
$209$	14.0305	0.970508
$210$	4.04447	0.279095
$211$	4.05974	0.279484	0.139742	−	0.990188i	$-0.455373\pi$
$211$	4.05974	0.279484	0.139742	+	0.990188i	$0.455373\pi$
$212$	12.9115	0.886765
$213$	12.1141	0.830042
$214$	−7.87552	−0.538360
$215$	20.5730	1.40307
$216$	4.76138	0.323971
$217$	7.84167	0.532327
$218$	−4.60381	−0.311809
$219$	1.42812	0.0965033
$220$	14.2086	0.957943
$221$	22.8680	1.53826
$222$	−19.7153	−1.32320
$223$	−14.3449	−0.960604	−0.480302	−	0.877103i	$-0.659473\pi$
$223$	−14.3449	−0.960604	−0.480302	+	0.877103i	$0.659473\pi$
$224$	−0.974679	−0.0651235
$225$	0.00949579	0.000633053 0
$226$	2.31841	0.154218
$227$	14.0285	0.931102	0.465551	−	0.885021i	$-0.345856\pi$
$227$	14.0285	0.931102	0.465551	+	0.885021i	$0.345856\pi$
$228$	−4.09753	−0.271365
$229$	−12.9133	−0.853336	−0.426668	−	0.904408i	$-0.640313\pi$
$229$	−12.9133	−0.853336	−0.426668	+	0.904408i	$0.640313\pi$
$230$	16.1475	1.06473
$231$	11.4425	0.752864
$232$	−6.41298	−0.421032
$233$	26.7267	1.75092	0.875461	−	0.483288i	$-0.160558\pi$
$233$	26.7267	1.75092	0.875461	+	0.483288i	$0.160558\pi$
$234$	2.13040	0.139269
$235$	25.6313	1.67200
$236$	−5.77755	−0.376086
$237$	7.01969	0.455978
$238$	−4.48363	−0.290630
$239$	−17.2028	−1.11275	−0.556377	−	0.830930i	$-0.687809\pi$
$239$	−17.2028	−1.11275	−0.556377	+	0.830930i	$0.687809\pi$
$240$	−4.14954	−0.267852
$241$	14.6472	0.943510	0.471755	−	0.881730i	$-0.343621\pi$
$241$	14.6472	0.943510	0.471755	+	0.881730i	$0.343621\pi$
$242$	29.1986	1.87696
$243$	4.42105	0.283611
$244$	−4.49815	−0.287965
$245$	−13.5582	−0.866199
$246$	10.2278	0.652102
$247$	11.0008	0.699967
$248$	−8.04539	−0.510882
$249$	28.2916	1.79291
$250$	−11.1554	−0.705531
$251$	3.15109	0.198895	0.0994475	−	0.995043i	$-0.468292\pi$
$251$	3.15109	0.198895	0.0994475	+	0.995043i	$0.468292\pi$
$252$	−0.417699	−0.0263126
$253$	45.6841	2.87214
$254$	17.8971	1.12296
$255$	−19.0884	−1.19536
$256$	1.00000	0.0625000
$257$	−22.1845	−1.38383	−0.691916	−	0.721978i	$-0.743233\pi$
$257$	−22.1845	−1.38383	−0.691916	+	0.721978i	$0.743233\pi$
$258$	−16.9984	−1.05827
$259$	−10.3779	−0.644852
$260$	11.1405	0.690904
$261$	−2.74828	−0.170115
$262$	4.84910	0.299579
$263$	−16.7387	−1.03215	−0.516077	−	0.856542i	$-0.672608\pi$
$263$	−16.7387	−1.03215	−0.516077	+	0.856542i	$0.672608\pi$
$264$	−11.7398	−0.722535
$265$	28.9349	1.77746
$266$	−2.15689	−0.132247
$267$	−3.54694	−0.217069
$268$	−5.26672	−0.321716
$269$	−6.38196	−0.389115	−0.194557	−	0.980891i	$-0.562327\pi$
$269$	−6.38196	−0.389115	−0.194557	+	0.980891i	$0.562327\pi$
$270$	10.6703	0.649376
$271$	9.24674	0.561699	0.280850	−	0.959752i	$-0.409384\pi$
$271$	9.24674	0.561699	0.280850	+	0.959752i	$0.409384\pi$
$272$	4.60011	0.278923
$273$	8.97172	0.542993
$274$	−4.61595	−0.278860
$275$	0.140487	0.00847166
$276$	−13.3418	−0.803083
$277$	−10.6641	−0.640742	−0.320371	−	0.947292i	$-0.603808\pi$
$277$	−10.6641	−0.640742	−0.320371	+	0.947292i	$0.603808\pi$
$278$	3.34364	0.200538
$279$	−3.44785	−0.206418
$280$	−2.18427	−0.130535
$281$	16.8937	1.00779	0.503896	−	0.863764i	$-0.331899\pi$
$281$	16.8937	1.00779	0.503896	+	0.863764i	$0.331899\pi$
$282$	−21.1778	−1.26112
$283$	25.7702	1.53188	0.765938	−	0.642914i	$-0.222275\pi$
$283$	25.7702	1.53188	0.765938	+	0.642914i	$0.222275\pi$
$284$	−6.54236	−0.388218
$285$	−9.18263	−0.543932
$286$	31.5184	1.86372
$287$	5.38381	0.317796
$288$	0.428551	0.0252526
$289$	4.16101	0.244765
$290$	−14.3716	−0.843929
$291$	24.5319	1.43808
$292$	−0.771275	−0.0451354
$293$	9.90807	0.578835	0.289418	−	0.957203i	$-0.406538\pi$
$293$	9.90807	0.578835	0.289418	+	0.957203i	$0.406538\pi$
$294$	11.2024	0.653337
$295$	−12.9476	−0.753837
$296$	10.6475	0.618874
$297$	30.1883	1.75170
$298$	−9.59499	−0.555823
$299$	35.8194	2.07149
$300$	−0.0410284	−0.00236877
$301$	−8.94776	−0.515740
$302$	6.26170	0.360320
$303$	−0.973302	−0.0559148
$304$	2.21292	0.126920
$305$	−10.0804	−0.577204
$306$	1.97138	0.112696
$307$	20.5325	1.17185	0.585926	−	0.810364i	$-0.300731\pi$
$307$	20.5325	1.17185	0.585926	+	0.810364i	$0.300731\pi$
$308$	−6.17970	−0.352121
$309$	18.7323	1.06564
$310$	−18.0298	−1.02403
$311$	23.4921	1.33211	0.666056	−	0.745902i	$-0.267981\pi$
$311$	23.4921	1.33211	0.666056	+	0.745902i	$0.267981\pi$
$312$	−9.20480	−0.521119
$313$	8.37746	0.473522	0.236761	−	0.971568i	$-0.423914\pi$
$313$	8.37746	0.473522	0.236761	+	0.971568i	$0.423914\pi$
$314$	−8.53570	−0.481698
$315$	−0.936071	−0.0527416
$316$	−3.79108	−0.213265
$317$	−31.1631	−1.75029	−0.875146	−	0.483859i	$-0.839235\pi$
$317$	−31.1631	−1.75029	−0.875146	+	0.483859i	$0.839235\pi$
$318$	−23.9074	−1.34066
$319$	−40.6598	−2.27651
$320$	2.24102	0.125277
$321$	14.5826	0.813921
$322$	−7.02298	−0.391375
$323$	10.1797	0.566413
$324$	−10.1020	−0.561222
$325$	0.110151	0.00611007
$326$	−18.1191	−1.00352
$327$	8.52458	0.471410
$328$	−5.52367	−0.304994
$329$	−11.1478	−0.614596
$330$	−26.3091	−1.44827
$331$	32.5613	1.78973	0.894866	−	0.446335i	$-0.147271\pi$
$331$	32.5613	1.78973	0.894866	+	0.446335i	$0.147271\pi$
$332$	−15.2792	−0.838558
$333$	4.56300	0.250051
$334$	−1.71622	−0.0939075
$335$	−11.8028	−0.644856
$336$	1.80475	0.0984571
$337$	−25.3816	−1.38262	−0.691311	−	0.722557i	$-0.742967\pi$
$337$	−25.3816	−1.38262	−0.691311	+	0.722557i	$0.742967\pi$
$338$	11.7126	0.637081
$339$	−4.29285	−0.233155
$340$	10.3089	0.559080
$341$	−51.0097	−2.76233
$342$	0.948350	0.0512809
$343$	12.7196	0.686792
$344$	9.18021	0.494964
$345$	−29.8992	−1.60972
$346$	5.33727	0.286934
$347$	13.4479	0.721919	0.360959	−	0.932582i	$-0.382449\pi$
$347$	13.4479	0.721919	0.360959	+	0.932582i	$0.382449\pi$
$348$	11.8745	0.636539
$349$	−24.3260	−1.30214	−0.651071	−	0.759017i	$-0.725680\pi$
$349$	−24.3260	−1.30214	−0.651071	+	0.759017i	$0.725680\pi$
$350$	−0.0215969	−0.00115440
$351$	23.6697	1.26339
$352$	6.34024	0.337936
$353$	−31.6628	−1.68524	−0.842620	−	0.538509i	$-0.818988\pi$
$353$	−31.6628	−1.68524	−0.842620	+	0.538509i	$0.818988\pi$
$354$	10.6979	0.568587
$355$	−14.6615	−0.778154
$356$	1.91557	0.101525
$357$	8.30204	0.439391
$358$	5.79037	0.306031
$359$	4.98062	0.262867	0.131434	−	0.991325i	$-0.458042\pi$
$359$	4.98062	0.262867	0.131434	+	0.991325i	$0.458042\pi$
$360$	0.960389	0.0506170
$361$	−14.1030	−0.742261
$362$	−16.5159	−0.868058
$363$	−54.0652	−2.83769
$364$	−4.84530	−0.253963
$365$	−1.72844	−0.0904707
$366$	8.32893	0.435360
$367$	33.6224	1.75507	0.877537	−	0.479509i	$-0.159185\pi$
$367$	33.6224	1.75507	0.877537	+	0.479509i	$0.159185\pi$
$368$	7.20543	0.375609
$369$	−2.36717	−0.123230
$370$	23.8613	1.24049
$371$	−12.5846	−0.653358
$372$	14.8971	0.772379
$373$	−2.70689	−0.140158	−0.0700788	−	0.997541i	$-0.522325\pi$
$373$	−2.70689	−0.140158	−0.0700788	+	0.997541i	$0.522325\pi$
$374$	29.1658	1.50813
$375$	20.6558	1.06666
$376$	11.4374	0.589837
$377$	−31.8800	−1.64190
$378$	−4.64082	−0.238698
$379$	−34.0143	−1.74720	−0.873599	−	0.486646i	$-0.838220\pi$
$379$	−34.0143	−1.74720	−0.873599	+	0.486646i	$0.838220\pi$
$380$	4.95920	0.254402
$381$	−33.1388	−1.69775
$382$	−15.0894	−0.772042
$383$	−2.27872	−0.116437	−0.0582185	−	0.998304i	$-0.518542\pi$
$383$	−2.27872	−0.116437	−0.0582185	+	0.998304i	$0.518542\pi$
$384$	−1.85163	−0.0944908
$385$	−13.8488	−0.705800
$386$	14.9213	0.759476
$387$	3.93419	0.199986
$388$	−13.2488	−0.672604
$389$	5.98919	0.303664	0.151832	−	0.988406i	$-0.451483\pi$
$389$	5.98919	0.303664	0.151832	+	0.988406i	$0.451483\pi$
$390$	−20.6281	−1.04455
$391$	33.1458	1.67625
$392$	−6.05000	−0.305571
$393$	−8.97877	−0.452919
$394$	−8.79470	−0.443071
$395$	−8.49587	−0.427474
$396$	2.71711	0.136540
$397$	8.82618	0.442973	0.221487	−	0.975163i	$-0.428909\pi$
$397$	8.82618	0.442973	0.221487	+	0.975163i	$0.428909\pi$
$398$	12.0463	0.603828
$399$	3.99377	0.199939
$400$	0.0221579	0.00110790
$401$	−21.3560	−1.06647	−0.533234	−	0.845968i	$-0.679023\pi$
$401$	−21.3560	−1.06647	−0.533234	+	0.845968i	$0.679023\pi$
$402$	9.75203	0.486387
$403$	−39.9950	−1.99229
$404$	0.525645	0.0261518
$405$	−22.6387	−1.12493
$406$	6.25059	0.310212
$407$	67.5078	3.34624
$408$	−8.51772	−0.421690
$409$	−22.0650	−1.09104	−0.545522	−	0.838096i	$-0.683669\pi$
$409$	−22.0650	−1.09104	−0.545522	+	0.838096i	$0.683669\pi$
$410$	−12.3786	−0.611338
$411$	8.54705	0.421595
$412$	−10.1166	−0.498409
$413$	5.63125	0.277096
$414$	3.08789	0.151762
$415$	−34.2411	−1.68083
$416$	4.97118	0.243732
$417$	−6.19120	−0.303184
$418$	14.0305	0.686253
$419$	16.3734	0.799891	0.399945	−	0.916539i	$-0.369029\pi$
$419$	16.3734	0.799891	0.399945	+	0.916539i	$0.369029\pi$
$420$	4.04447	0.197350
$421$	−12.8074	−0.624196	−0.312098	−	0.950050i	$-0.601032\pi$
$421$	−12.8074	−0.624196	−0.312098	+	0.950050i	$0.601032\pi$
$422$	4.05974	0.197625
$423$	4.90149	0.238319
$424$	12.9115	0.627038
$425$	0.101929	0.00494428
$426$	12.1141	0.586928
$427$	4.38425	0.212169
$428$	−7.87552	−0.380678
$429$	−58.3606	−2.81768
$430$	20.5730	0.992119
$431$	34.2680	1.65063	0.825316	−	0.564671i	$-0.190997\pi$
$431$	34.2680	1.65063	0.825316	+	0.564671i	$0.190997\pi$
$432$	4.76138	0.229082
$433$	27.3453	1.31413	0.657066	−	0.753833i	$-0.271797\pi$
$433$	27.3453	1.31413	0.657066	+	0.753833i	$0.271797\pi$
$434$	7.84167	0.376412
$435$	26.6109	1.27590
$436$	−4.60381	−0.220483
$437$	15.9451	0.762756
$438$	1.42812	0.0682382
$439$	41.0373	1.95860	0.979302	−	0.202402i	$-0.0648748\pi$
$439$	41.0373	1.95860	0.979302	+	0.202402i	$0.0648748\pi$
$440$	14.2086	0.677368
$441$	−2.59273	−0.123463
$442$	22.8680	1.08772
$443$	32.2957	1.53441	0.767206	−	0.641400i	$-0.221646\pi$
$443$	32.2957	1.53441	0.767206	+	0.641400i	$0.221646\pi$
$444$	−19.7153	−0.935647
$445$	4.29284	0.203500
$446$	−14.3449	−0.679250
$447$	17.7664	0.840322
$448$	−0.974679	−0.0460492
$449$	−14.0167	−0.661490	−0.330745	−	0.943720i	$-0.607300\pi$
$449$	−14.0167	−0.661490	−0.330745	+	0.943720i	$0.607300\pi$
$450$	0.00949579	0.000447636 0
$451$	−35.0214	−1.64909
$452$	2.31841	0.109049
$453$	−11.5944	−0.544751
$454$	14.0285	0.658389
$455$	−10.8584	−0.509050
$456$	−4.09753	−0.191884
$457$	−4.43350	−0.207390	−0.103695	−	0.994609i	$-0.533067\pi$
$457$	−4.43350	−0.207390	−0.103695	+	0.994609i	$0.533067\pi$
$458$	−12.9133	−0.603400
$459$	21.9029	1.02234
$460$	16.1475	0.752881
$461$	−24.0532	−1.12027	−0.560135	−	0.828401i	$-0.689251\pi$
$461$	−24.0532	−1.12027	−0.560135	+	0.828401i	$0.689251\pi$
$462$	11.4425	0.532355
$463$	26.2010	1.21766	0.608832	−	0.793299i	$-0.291638\pi$
$463$	26.2010	1.21766	0.608832	+	0.793299i	$0.291638\pi$
$464$	−6.41298	−0.297715
$465$	33.3847	1.54818
$466$	26.7267	1.23809
$467$	−1.93063	−0.0893389	−0.0446695	−	0.999002i	$-0.514223\pi$
$467$	−1.93063	−0.0893389	−0.0446695	+	0.999002i	$0.514223\pi$
$468$	2.13040	0.0984778
$469$	5.13335	0.237036
$470$	25.6313	1.18229
$471$	15.8050	0.728256
$472$	−5.77755	−0.265933
$473$	58.2047	2.67626
$474$	7.01969	0.322425
$475$	0.0490338	0.00224983
$476$	−4.48363	−0.205507
$477$	5.53323	0.253349
$478$	−17.2028	−0.786836
$479$	−16.9279	−0.773457	−0.386729	−	0.922194i	$-0.626395\pi$
$479$	−16.9279	−0.773457	−0.386729	+	0.922194i	$0.626395\pi$
$480$	−4.14954	−0.189400
$481$	52.9307	2.41343
$482$	14.6472	0.667162
$483$	13.0040	0.591702
$484$	29.1986	1.32721
$485$	−29.6907	−1.34819
$486$	4.42105	0.200543
$487$	20.0506	0.908578	0.454289	−	0.890854i	$-0.349893\pi$
$487$	20.0506	0.908578	0.454289	+	0.890854i	$0.349893\pi$
$488$	−4.49815	−0.203622
$489$	33.5499	1.51718
$490$	−13.5582	−0.612495
$491$	−21.0603	−0.950437	−0.475219	−	0.879868i	$-0.657631\pi$
$491$	−21.0603	−0.950437	−0.475219	+	0.879868i	$0.657631\pi$
$492$	10.2278	0.461106
$493$	−29.5004	−1.32863
$494$	11.0008	0.494951
$495$	6.08910	0.273685
$496$	−8.04539	−0.361248
$497$	6.37670	0.286034
$498$	28.2916	1.26778
$499$	−4.07021	−0.182208	−0.0911038	−	0.995841i	$-0.529040\pi$
$499$	−4.07021	−0.182208	−0.0911038	+	0.995841i	$0.529040\pi$
$500$	−11.1554	−0.498886
$501$	3.17781	0.141974
$502$	3.15109	0.140640
$503$	−10.5071	−0.468488	−0.234244	−	0.972178i	$-0.575261\pi$
$503$	−10.5071	−0.468488	−0.234244	+	0.972178i	$0.575261\pi$
$504$	−0.417699	−0.0186058
$505$	1.17798	0.0524194
$506$	45.6841	2.03091
$507$	−21.6874	−0.963172
$508$	17.8971	0.794053
$509$	25.1988	1.11692	0.558459	−	0.829532i	$-0.311393\pi$
$509$	25.1988	1.11692	0.558459	+	0.829532i	$0.311393\pi$
$510$	−19.0884	−0.845247
$511$	0.751745	0.0332552
$512$	1.00000	0.0441942
$513$	10.5366	0.465202
$514$	−22.1845	−0.978517
$515$	−22.6715	−0.999025
$516$	−16.9984	−0.748313
$517$	72.5157	3.18924
$518$	−10.3779	−0.455979
$519$	−9.88268	−0.433801
$520$	11.1405	0.488543
$521$	−38.0919	−1.66884	−0.834419	−	0.551130i	$-0.814197\pi$
$521$	−38.0919	−1.66884	−0.834419	+	0.551130i	$0.814197\pi$
$522$	−2.74828	−0.120289
$523$	10.6563	0.465968	0.232984	−	0.972481i	$-0.425151\pi$
$523$	10.6563	0.465968	0.232984	+	0.972481i	$0.425151\pi$
$524$	4.84910	0.211834
$525$	0.0399895	0.00174528
$526$	−16.7387	−0.729843
$527$	−37.0097	−1.61217
$528$	−11.7398	−0.510909
$529$	28.9182	1.25731
$530$	28.9349	1.25685
$531$	−2.47597	−0.107448
$532$	−2.15689	−0.0935131
$533$	−27.4591	−1.18939
$534$	−3.54694	−0.153491
$535$	−17.6492	−0.763041
$536$	−5.26672	−0.227487
$537$	−10.7217	−0.462673
$538$	−6.38196	−0.275146
$539$	−38.3585	−1.65222
$540$	10.6703	0.459179
$541$	24.2118	1.04095	0.520474	−	0.853877i	$-0.325755\pi$
$541$	24.2118	1.04095	0.520474	+	0.853877i	$0.325755\pi$
$542$	9.24674	0.397181
$543$	30.5815	1.31238
$544$	4.60011	0.197228
$545$	−10.3172	−0.441941
$546$	8.97172	0.383954
$547$	23.9185	1.02268	0.511340	−	0.859378i	$-0.329149\pi$
$547$	23.9185	1.02268	0.511340	+	0.859378i	$0.329149\pi$
$548$	−4.61595	−0.197184
$549$	−1.92769	−0.0822716
$550$	0.140487	0.00599037
$551$	−14.1914	−0.604575
$552$	−13.3418	−0.567866
$553$	3.69508	0.157131
$554$	−10.6641	−0.453073
$555$	−44.1823	−1.87544
$556$	3.34364	0.141802
$557$	−39.2965	−1.66505	−0.832523	−	0.553990i	$-0.813105\pi$
$557$	−39.2965	−1.66505	−0.832523	+	0.553990i	$0.813105\pi$
$558$	−3.44785	−0.145959
$559$	45.6364	1.93022
$560$	−2.18427	−0.0923023
$561$	−54.0044	−2.28007
$562$	16.8937	0.712617
$563$	−37.2511	−1.56995	−0.784974	−	0.619529i	$-0.787324\pi$
$563$	−37.2511	−1.56995	−0.784974	+	0.619529i	$0.787324\pi$
$564$	−21.1778	−0.891748
$565$	5.19560	0.218580
$566$	25.7702	1.08320
$567$	9.84620	0.413502
$568$	−6.54236	−0.274511
$569$	−24.6571	−1.03368	−0.516839	−	0.856083i	$-0.672891\pi$
$569$	−24.6571	−1.03368	−0.516839	+	0.856083i	$0.672891\pi$
$570$	−9.18263	−0.384618
$571$	−2.85728	−0.119573	−0.0597866	−	0.998211i	$-0.519042\pi$
$571$	−2.85728	−0.119573	−0.0597866	+	0.998211i	$0.519042\pi$
$572$	31.5184	1.31785
$573$	27.9401	1.16721
$574$	5.38381	0.224716
$575$	0.159657	0.00665817
$576$	0.428551	0.0178563
$577$	−0.616292	−0.0256566	−0.0128283	−	0.999918i	$-0.504083\pi$
$577$	−0.616292	−0.0256566	−0.0128283	+	0.999918i	$0.504083\pi$
$578$	4.16101	0.173075
$579$	−27.6289	−1.14822
$580$	−14.3716	−0.596748
$581$	14.8924	0.617839
$582$	24.5319	1.01688
$583$	81.8620	3.39038
$584$	−0.771275	−0.0319156
$585$	4.77426	0.197392
$586$	9.90807	0.409298
$587$	21.7122	0.896158	0.448079	−	0.893994i	$-0.352108\pi$
$587$	21.7122	0.896158	0.448079	+	0.893994i	$0.352108\pi$
$588$	11.2024	0.461979
$589$	−17.8038	−0.733594
$590$	−12.9476	−0.533043
$591$	16.2846	0.669858
$592$	10.6475	0.437610
$593$	−18.5325	−0.761040	−0.380520	−	0.924773i	$-0.624255\pi$
$593$	−18.5325	−0.761040	−0.380520	+	0.924773i	$0.624255\pi$
$594$	30.1883	1.23864
$595$	−10.0479	−0.411923
$596$	−9.59499	−0.393026
$597$	−22.3054	−0.912900
$598$	35.8194	1.46477
$599$	−19.1027	−0.780515	−0.390257	−	0.920706i	$-0.627614\pi$
$599$	−19.1027	−0.780515	−0.390257	+	0.920706i	$0.627614\pi$
$600$	−0.0410284	−0.00167498
$601$	−28.9123	−1.17936	−0.589679	−	0.807638i	$-0.700746\pi$
$601$	−28.9123	−1.17936	−0.589679	+	0.807638i	$0.700746\pi$
$602$	−8.94776	−0.364683
$603$	−2.25705	−0.0919143
$604$	6.26170	0.254785
$605$	65.4346	2.66030
$606$	−0.973302	−0.0395377
$607$	31.0269	1.25934	0.629672	−	0.776861i	$-0.283189\pi$
$607$	31.0269	1.25934	0.629672	+	0.776861i	$0.283189\pi$
$608$	2.21292	0.0897460
$609$	−11.5738	−0.468994
$610$	−10.0804	−0.408145
$611$	56.8572	2.30020
$612$	1.97138	0.0796883
$613$	−11.8038	−0.476749	−0.238375	−	0.971173i	$-0.576615\pi$
$613$	−11.8038	−0.476749	−0.238375	+	0.971173i	$0.576615\pi$
$614$	20.5325	0.828625
$615$	22.9207	0.924253
$616$	−6.17970	−0.248987
$617$	29.2413	1.17721	0.588605	−	0.808421i	$-0.299677\pi$
$617$	29.2413	1.17721	0.588605	+	0.808421i	$0.299677\pi$
$618$	18.7323	0.753522
$619$	−12.6225	−0.507341	−0.253670	−	0.967291i	$-0.581638\pi$
$619$	−12.6225	−0.507341	−0.253670	+	0.967291i	$0.581638\pi$
$620$	−18.0298	−0.724096
$621$	34.3078	1.37673
$622$	23.4921	0.941946
$623$	−1.86707	−0.0748026
$624$	−9.20480	−0.368487
$625$	−25.1103	−1.00441
$626$	8.37746	0.334831
$627$	−25.9793	−1.03751
$628$	−8.53570	−0.340612
$629$	48.9797	1.95295
$630$	−0.936071	−0.0372940
$631$	21.6151	0.860483	0.430241	−	0.902714i	$-0.358428\pi$
$631$	21.6151	0.860483	0.430241	+	0.902714i	$0.358428\pi$
$632$	−3.79108	−0.150801
$633$	−7.51715	−0.298780
$634$	−31.1631	−1.23764
$635$	40.1076	1.59162
$636$	−23.9074	−0.947989
$637$	−30.0756	−1.19164
$638$	−40.6598	−1.60974
$639$	−2.80373	−0.110914
$640$	2.24102	0.0885840
$641$	28.9954	1.14525	0.572624	−	0.819818i	$-0.305925\pi$
$641$	28.9954	1.14525	0.572624	+	0.819818i	$0.305925\pi$
$642$	14.5826	0.575529
$643$	−11.2720	−0.444524	−0.222262	−	0.974987i	$-0.571344\pi$
$643$	−11.2720	−0.444524	−0.222262	+	0.974987i	$0.571344\pi$
$644$	−7.02298	−0.276744
$645$	−38.0937	−1.49994
$646$	10.1797	0.400515
$647$	−27.7163	−1.08964	−0.544820	−	0.838553i	$-0.683402\pi$
$647$	−27.7163	−1.08964	−0.544820	+	0.838553i	$0.683402\pi$
$648$	−10.1020	−0.396844
$649$	−36.6310	−1.43789
$650$	0.110151	0.00432047
$651$	−14.5199	−0.569080
$652$	−18.1191	−0.709598
$653$	37.2319	1.45700	0.728499	−	0.685047i	$-0.240218\pi$
$653$	37.2319	1.45700	0.728499	+	0.685047i	$0.240218\pi$
$654$	8.52458	0.333337
$655$	10.8669	0.424606
$656$	−5.52367	−0.215663
$657$	−0.330530	−0.0128952
$658$	−11.1478	−0.434585
$659$	−17.1172	−0.666793	−0.333397	−	0.942787i	$-0.608195\pi$
$659$	−17.1172	−0.666793	−0.333397	+	0.942787i	$0.608195\pi$
$660$	−26.3091	−1.02408
$661$	4.66520	0.181455	0.0907276	−	0.995876i	$-0.471081\pi$
$661$	4.66520	0.181455	0.0907276	+	0.995876i	$0.471081\pi$
$662$	32.5613	1.26553
$663$	−42.3431	−1.64447
$664$	−15.2792	−0.592950
$665$	−4.83363	−0.187440
$666$	4.56300	0.176813
$667$	−46.2082	−1.78919
$668$	−1.71622	−0.0664026
$669$	26.5615	1.02693
$670$	−11.8028	−0.455982
$671$	−28.5194	−1.10098
$672$	1.80475	0.0696197
$673$	−1.54553	−0.0595758	−0.0297879	−	0.999556i	$-0.509483\pi$
$673$	−1.54553	−0.0595758	−0.0297879	+	0.999556i	$0.509483\pi$
$674$	−25.3816	−0.977662
$675$	0.105502	0.00406079
$676$	11.7126	0.450484
$677$	0.305013	0.0117226	0.00586130	−	0.999983i	$-0.498134\pi$
$677$	0.305013	0.0117226	0.00586130	+	0.999983i	$0.498134\pi$
$678$	−4.29285	−0.164866
$679$	12.9133	0.495566
$680$	10.3089	0.395329
$681$	−25.9756	−0.995387
$682$	−51.0097	−1.95326
$683$	9.73213	0.372390	0.186195	−	0.982513i	$-0.440384\pi$
$683$	9.73213	0.372390	0.186195	+	0.982513i	$0.440384\pi$
$684$	0.948350	0.0362611
$685$	−10.3444	−0.395240
$686$	12.7196	0.485635
$687$	23.9108	0.912252
$688$	9.18021	0.349992
$689$	64.1853	2.44527
$690$	−29.8992	−1.13824
$691$	−44.5972	−1.69656	−0.848278	−	0.529551i	$-0.822360\pi$
$691$	−44.5972	−1.69656	−0.848278	+	0.529551i	$0.822360\pi$
$692$	5.33727	0.202893
$693$	−2.64831	−0.100601
$694$	13.4479	0.510474
$695$	7.49316	0.284232
$696$	11.8745	0.450101
$697$	−25.4095	−0.962453
$698$	−24.3260	−0.920753
$699$	−49.4880	−1.87181
$700$	−0.0215969	−0.000816284 0
$701$	−24.5750	−0.928186	−0.464093	−	0.885787i	$-0.653620\pi$
$701$	−24.5750	−0.928186	−0.464093	+	0.885787i	$0.653620\pi$
$702$	23.6697	0.893354
$703$	23.5621	0.888663
$704$	6.34024	0.238957
$705$	−47.4599	−1.78744
$706$	−31.6628	−1.19164
$707$	−0.512335	−0.0192683
$708$	10.6979	0.402052
$709$	−34.5462	−1.29741	−0.648705	−	0.761040i	$-0.724689\pi$
$709$	−34.5462	−1.29741	−0.648705	+	0.761040i	$0.724689\pi$
$710$	−14.6615	−0.550238
$711$	−1.62467	−0.0609298
$712$	1.91557	0.0717892
$713$	−57.9704	−2.17101
$714$	8.30204	0.310696
$715$	70.6334	2.64154
$716$	5.79037	0.216396
$717$	31.8532	1.18958
$718$	4.98062	0.185875
$719$	−28.1811	−1.05098	−0.525489	−	0.850800i	$-0.676118\pi$
$719$	−28.1811	−1.05098	−0.525489	+	0.850800i	$0.676118\pi$
$720$	0.960389	0.0357916
$721$	9.86044	0.367222
$722$	−14.1030	−0.524858
$723$	−27.1213	−1.00865
$724$	−16.5159	−0.613810
$725$	−0.142098	−0.00527740
$726$	−54.0652	−2.00655
$727$	−44.5818	−1.65345	−0.826724	−	0.562608i	$-0.809798\pi$
$727$	−44.5818	−1.65345	−0.826724	+	0.562608i	$0.809798\pi$
$728$	−4.84530	−0.179579
$729$	22.1198	0.819252
$730$	−1.72844	−0.0639724
$731$	42.2300	1.56193
$732$	8.32893	0.307846
$733$	34.1567	1.26161	0.630804	−	0.775942i	$-0.282725\pi$
$733$	34.1567	1.26161	0.630804	+	0.775942i	$0.282725\pi$
$734$	33.6224	1.24102
$735$	25.1048	0.926003
$736$	7.20543	0.265596
$737$	−33.3922	−1.23002
$738$	−2.36717	−0.0871368
$739$	−8.57448	−0.315417	−0.157709	−	0.987486i	$-0.550411\pi$
$739$	−8.57448	−0.315417	−0.157709	+	0.987486i	$0.550411\pi$
$740$	23.8613	0.877157
$741$	−20.3695	−0.748293
$742$	−12.5846	−0.461994
$743$	42.1343	1.54576	0.772879	−	0.634554i	$-0.218816\pi$
$743$	42.1343	1.54576	0.772879	+	0.634554i	$0.218816\pi$
$744$	14.8971	0.546155
$745$	−21.5025	−0.787792
$746$	−2.70689	−0.0991064
$747$	−6.54793	−0.239576
$748$	29.1658	1.06641
$749$	7.67610	0.280479
$750$	20.6558	0.754242
$751$	5.19970	0.189740	0.0948699	−	0.995490i	$-0.469756\pi$
$751$	5.19970	0.189740	0.0948699	+	0.995490i	$0.469756\pi$
$752$	11.4374	0.417078
$753$	−5.83467	−0.212627
$754$	−31.8800	−1.16100
$755$	14.0326	0.510698
$756$	−4.64082	−0.168785
$757$	−10.2866	−0.373874	−0.186937	−	0.982372i	$-0.559856\pi$
$757$	−10.2866	−0.373874	−0.186937	+	0.982372i	$0.559856\pi$
$758$	−34.0143	−1.23546
$759$	−84.5903	−3.07043
$760$	4.95920	0.179889
$761$	44.0135	1.59549	0.797744	−	0.602996i	$-0.206027\pi$
$761$	44.0135	1.59549	0.797744	+	0.602996i	$0.206027\pi$
$762$	−33.1388	−1.20049
$763$	4.48724	0.162449
$764$	−15.0894	−0.545916
$765$	4.41790	0.159729
$766$	−2.27872	−0.0823334
$767$	−28.7212	−1.03706
$768$	−1.85163	−0.0668151
$769$	21.4671	0.774125	0.387063	−	0.922053i	$-0.373490\pi$
$769$	21.4671	0.774125	0.387063	+	0.922053i	$0.373490\pi$
$770$	−13.8488	−0.499076
$771$	41.0776	1.47937
$772$	14.9213	0.537031
$773$	−37.5903	−1.35203	−0.676014	−	0.736889i	$-0.736294\pi$
$773$	−37.5903	−1.35203	−0.676014	+	0.736889i	$0.736294\pi$
$774$	3.93419	0.141411
$775$	−0.178269	−0.00640361
$776$	−13.2488	−0.475603
$777$	19.2161	0.689373
$778$	5.98919	0.214723
$779$	−12.2235	−0.437951
$780$	−20.6281	−0.738605
$781$	−41.4801	−1.48428
$782$	33.1458	1.18529
$783$	−30.5346	−1.09122
$784$	−6.05000	−0.216071
$785$	−19.1287	−0.682731
$786$	−8.97877	−0.320262
$787$	27.9049	0.994704	0.497352	−	0.867549i	$-0.334306\pi$
$787$	27.9049	0.994704	0.497352	+	0.867549i	$0.334306\pi$
$788$	−8.79470	−0.313298
$789$	30.9940	1.10342
$790$	−8.49587	−0.302269
$791$	−2.25970	−0.0803458
$792$	2.71711	0.0965484
$793$	−22.3611	−0.794066
$794$	8.82618	0.313229
$795$	−53.5768	−1.90017
$796$	12.0463	0.426971
$797$	46.8843	1.66073	0.830363	−	0.557222i	$-0.188133\pi$
$797$	46.8843	1.66073	0.830363	+	0.557222i	$0.188133\pi$
$798$	3.99377	0.141378
$799$	52.6132	1.86132
$800$	0.0221579	0.000783401 0
$801$	0.820921	0.0290058
$802$	−21.3560	−0.754106
$803$	−4.89007	−0.172567
$804$	9.75203	0.343928
$805$	−15.7386	−0.554713
$806$	−39.9950	−1.40876
$807$	11.8171	0.415980
$808$	0.525645	0.0184921
$809$	39.4942	1.38854	0.694271	−	0.719714i	$-0.255727\pi$
$809$	39.4942	1.38854	0.694271	+	0.719714i	$0.255727\pi$
$810$	−22.6387	−0.795444
$811$	20.0272	0.703251	0.351626	−	0.936141i	$-0.385629\pi$
$811$	20.0272	0.703251	0.351626	+	0.936141i	$0.385629\pi$
$812$	6.25059	0.219353
$813$	−17.1216	−0.600480
$814$	67.5078	2.36615
$815$	−40.6052	−1.42234
$816$	−8.51772	−0.298180
$817$	20.3151	0.710736
$818$	−22.0650	−0.771485
$819$	−2.07646	−0.0725572
$820$	−12.3786	−0.432281
$821$	14.0631	0.490806	0.245403	−	0.969421i	$-0.421080\pi$
$821$	14.0631	0.490806	0.245403	+	0.969421i	$0.421080\pi$
$822$	8.54705	0.298113
$823$	3.62910	0.126503	0.0632513	−	0.997998i	$-0.479853\pi$
$823$	3.62910	0.126503	0.0632513	+	0.997998i	$0.479853\pi$
$824$	−10.1166	−0.352429
$825$	−0.260130	−0.00905655
$826$	5.63125	0.195936
$827$	−53.1835	−1.84937	−0.924685	−	0.380732i	$-0.875672\pi$
$827$	−53.1835	−1.84937	−0.924685	+	0.380732i	$0.875672\pi$
$828$	3.08789	0.107312
$829$	−44.4540	−1.54395	−0.771976	−	0.635652i	$-0.780731\pi$
$829$	−44.4540	−1.54395	−0.771976	+	0.635652i	$0.780731\pi$
$830$	−34.2411	−1.18852
$831$	19.7460	0.684980
$832$	4.97118	0.172344
$833$	−27.8307	−0.964276
$834$	−6.19120	−0.214384
$835$	−3.84608	−0.133099
$836$	14.0305	0.485254
$837$	−38.3072	−1.32409
$838$	16.3734	0.565608
$839$	−31.5787	−1.09022	−0.545109	−	0.838365i	$-0.683512\pi$
$839$	−31.5787	−1.09022	−0.545109	+	0.838365i	$0.683512\pi$
$840$	4.04447	0.139548
$841$	12.1263	0.418147
$842$	−12.8074	−0.441373
$843$	−31.2809	−1.07737
$844$	4.05974	0.139742
$845$	26.2481	0.902962
$846$	4.90149	0.168517
$847$	−28.4593	−0.977873
$848$	12.9115	0.443383
$849$	−47.7169	−1.63764
$850$	0.101929	0.00349613
$851$	76.7199	2.62992
$852$	12.1141	0.415021
$853$	−49.3394	−1.68935	−0.844675	−	0.535279i	$-0.820206\pi$
$853$	−49.3394	−1.68935	−0.844675	+	0.535279i	$0.820206\pi$
$854$	4.38425	0.150026
$855$	2.12527	0.0726827
$856$	−7.87552	−0.269180
$857$	45.8838	1.56736	0.783680	−	0.621164i	$-0.213340\pi$
$857$	45.8838	1.56736	0.783680	+	0.621164i	$0.213340\pi$
$858$	−58.3606	−1.99240
$859$	21.0621	0.718628	0.359314	−	0.933217i	$-0.383011\pi$
$859$	21.0621	0.718628	0.359314	+	0.933217i	$0.383011\pi$
$860$	20.5730	0.701534
$861$	−9.96884	−0.339737
$862$	34.2680	1.16717
$863$	−23.0040	−0.783066	−0.391533	−	0.920164i	$-0.628055\pi$
$863$	−23.0040	−0.783066	−0.391533	+	0.920164i	$0.628055\pi$
$864$	4.76138	0.161986
$865$	11.9609	0.406683
$866$	27.3453	0.929231
$867$	−7.70466	−0.261664
$868$	7.84167	0.266163
$869$	−24.0363	−0.815377
$870$	26.6109	0.902195
$871$	−26.1818	−0.887135
$872$	−4.60381	−0.155905
$873$	−5.67776	−0.192163
$874$	15.9451	0.539350
$875$	10.8730	0.367573
$876$	1.42812	0.0482517
$877$	−32.6472	−1.10242	−0.551209	−	0.834367i	$-0.685833\pi$
$877$	−32.6472	−1.10242	−0.551209	+	0.834367i	$0.685833\pi$
$878$	41.0373	1.38494
$879$	−18.3461	−0.618799
$880$	14.2086	0.478971
$881$	21.7895	0.734108	0.367054	−	0.930200i	$-0.380366\pi$
$881$	21.7895	0.734108	0.367054	+	0.930200i	$0.380366\pi$
$882$	−2.59273	−0.0873018
$883$	54.2059	1.82417	0.912087	−	0.409997i	$-0.134470\pi$
$883$	54.2059	1.82417	0.912087	+	0.409997i	$0.134470\pi$
$884$	22.8680	0.769132
$885$	23.9742	0.805883
$886$	32.2957	1.08499
$887$	22.4787	0.754760	0.377380	−	0.926058i	$-0.376825\pi$
$887$	22.4787	0.754760	0.377380	+	0.926058i	$0.376825\pi$
$888$	−19.7153	−0.661602
$889$	−17.4439	−0.585049
$890$	4.29284	0.143896
$891$	−64.0491	−2.14572
$892$	−14.3449	−0.480302
$893$	25.3100	0.846968
$894$	17.7664	0.594198
$895$	12.9763	0.433751
$896$	−0.974679	−0.0325617
$897$	−66.3245	−2.21451
$898$	−14.0167	−0.467744
$899$	51.5949	1.72078
$900$	0.00949579	0.000316526 0
$901$	59.3943	1.97871
$902$	−35.0214	−1.16609
$903$	16.5680	0.551348
$904$	2.31841	0.0771092
$905$	−37.0125	−1.23034
$906$	−11.5944	−0.385197
$907$	16.3409	0.542589	0.271295	−	0.962496i	$-0.412548\pi$
$907$	16.3409	0.542589	0.271295	+	0.962496i	$0.412548\pi$
$908$	14.0285	0.465551
$909$	0.225265	0.00747158
$910$	−10.8584	−0.359952
$911$	−51.2649	−1.69848	−0.849242	−	0.528005i	$-0.822940\pi$
$911$	−51.2649	−1.69848	−0.849242	+	0.528005i	$0.822940\pi$
$912$	−4.09753	−0.135683
$913$	−96.8741	−3.20606
$914$	−4.43350	−0.146647
$915$	18.6653	0.617055
$916$	−12.9133	−0.426668
$917$	−4.72632	−0.156077
$918$	21.9029	0.722903
$919$	32.5616	1.07411	0.537055	−	0.843548i	$-0.319537\pi$
$919$	32.5616	1.07411	0.537055	+	0.843548i	$0.319537\pi$
$920$	16.1475	0.532367
$921$	−38.0187	−1.25276
$922$	−24.0532	−0.792150
$923$	−32.5232	−1.07051
$924$	11.4425	0.376432
$925$	0.235927	0.00775722
$926$	26.2010	0.861019
$927$	−4.33548	−0.142396
$928$	−6.41298	−0.210516
$929$	45.1164	1.48022	0.740111	−	0.672485i	$-0.234773\pi$
$929$	45.1164	1.48022	0.740111	+	0.672485i	$0.234773\pi$
$930$	33.3847	1.09473
$931$	−13.3882	−0.438781
$932$	26.7267	0.875461
$933$	−43.4987	−1.42408
$934$	−1.93063	−0.0631722
$935$	65.3610	2.13753
$936$	2.13040	0.0696343
$937$	−4.53712	−0.148221	−0.0741107	−	0.997250i	$-0.523612\pi$
$937$	−4.53712	−0.148221	−0.0741107	+	0.997250i	$0.523612\pi$
$938$	5.13335	0.167610
$939$	−15.5120	−0.506215
$940$	25.6313	0.836002
$941$	−11.0288	−0.359529	−0.179764	−	0.983710i	$-0.557534\pi$
$941$	−11.0288	−0.359529	−0.179764	+	0.983710i	$0.557534\pi$
$942$	15.8050	0.514955
$943$	−39.8004	−1.29608
$944$	−5.77755	−0.188043
$945$	−10.4002	−0.338317
$946$	58.2047	1.89240
$947$	−12.9017	−0.419248	−0.209624	−	0.977782i	$-0.567224\pi$
$947$	−12.9017	−0.419248	−0.209624	+	0.977782i	$0.567224\pi$
$948$	7.01969	0.227989
$949$	−3.83414	−0.124462
$950$	0.0490338	0.00159087
$951$	57.7026	1.87113
$952$	−4.48363	−0.145315
$953$	−17.4657	−0.565769	−0.282884	−	0.959154i	$-0.591291\pi$
$953$	−17.4657	−0.565769	−0.282884	+	0.959154i	$0.591291\pi$
$954$	5.53323	0.179145
$955$	−33.8156	−1.09425
$956$	−17.2028	−0.556377
$957$	75.2871	2.43369
$958$	−16.9279	−0.546917
$959$	4.49907	0.145282
$960$	−4.14954	−0.133926
$961$	33.7282	1.08801
$962$	52.9307	1.70655
$963$	−3.37506	−0.108760
$964$	14.6472	0.471755
$965$	33.4390	1.07644
$966$	13.0040	0.418396
$967$	40.3041	1.29609	0.648046	−	0.761601i	$-0.275586\pi$
$967$	40.3041	1.29609	0.648046	+	0.761601i	$0.275586\pi$
$968$	29.1986	0.938480
$969$	−18.8491	−0.605520
$970$	−29.6907	−0.953311
$971$	−44.2758	−1.42088	−0.710440	−	0.703758i	$-0.751504\pi$
$971$	−44.2758	−1.42088	−0.710440	+	0.703758i	$0.751504\pi$
$972$	4.42105	0.141805
$973$	−3.25898	−0.104478
$974$	20.0506	0.642462
$975$	−0.203959	−0.00653192
$976$	−4.49815	−0.143982
$977$	−17.8058	−0.569659	−0.284830	−	0.958578i	$-0.591937\pi$
$977$	−17.8058	−0.569659	−0.284830	+	0.958578i	$0.591937\pi$
$978$	33.5499	1.07281
$979$	12.1452	0.388162
$980$	−13.5582	−0.433099
$981$	−1.97297	−0.0629920
$982$	−21.0603	−0.672061
$983$	−26.9704	−0.860222	−0.430111	−	0.902776i	$-0.641526\pi$
$983$	−26.9704	−0.860222	−0.430111	+	0.902776i	$0.641526\pi$
$984$	10.2278	0.326051
$985$	−19.7091	−0.627984
$986$	−29.5004	−0.939484
$987$	20.6416	0.657029
$988$	11.0008	0.349983
$989$	66.1474	2.10336
$990$	6.08910	0.193524
$991$	−7.96340	−0.252966	−0.126483	−	0.991969i	$-0.540369\pi$
$991$	−7.96340	−0.252966	−0.126483	+	0.991969i	$0.540369\pi$
$992$	−8.04539	−0.255441
$993$	−60.2917	−1.91330
$994$	6.37670	0.202257
$995$	26.9960	0.855832
$996$	28.2916	0.896453
$997$	−6.28594	−0.199078	−0.0995388	−	0.995034i	$-0.531737\pi$
$997$	−6.28594	−0.199078	−0.0995388	+	0.995034i	$0.531737\pi$
$998$	−4.07021	−0.128840
$999$	50.6969	1.60398

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8014.2.a.d.1.19	✓	88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8014.2.a.d.1.19	✓	88	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:	\( N \)	\(=\)	\( 8014 = 2 \cdot 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8014.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.85163 q^{3} +1.00000 q^{4} +2.24102 q^{5} -1.85163 q^{6} -0.974679 q^{7} +1.00000 q^{8} +0.428551 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.85163 q^{3} +1.00000 q^{4} +2.24102 q^{5} -1.85163 q^{6} -0.974679 q^{7} +1.00000 q^{8} +0.428551 q^{9} +2.24102 q^{10} +6.34024 q^{11} -1.85163 q^{12} +4.97118 q^{13} -0.974679 q^{14} -4.14954 q^{15} +1.00000 q^{16} +4.60011 q^{17} +0.428551 q^{18} +2.21292 q^{19} +2.24102 q^{20} +1.80475 q^{21} +6.34024 q^{22} +7.20543 q^{23} -1.85163 q^{24} +0.0221579 q^{25} +4.97118 q^{26} +4.76138 q^{27} -0.974679 q^{28} -6.41298 q^{29} -4.14954 q^{30} -8.04539 q^{31} +1.00000 q^{32} -11.7398 q^{33} +4.60011 q^{34} -2.18427 q^{35} +0.428551 q^{36} +10.6475 q^{37} +2.21292 q^{38} -9.20480 q^{39} +2.24102 q^{40} -5.52367 q^{41} +1.80475 q^{42} +9.18021 q^{43} +6.34024 q^{44} +0.960389 q^{45} +7.20543 q^{46} +11.4374 q^{47} -1.85163 q^{48} -6.05000 q^{49} +0.0221579 q^{50} -8.51772 q^{51} +4.97118 q^{52} +12.9115 q^{53} +4.76138 q^{54} +14.2086 q^{55} -0.974679 q^{56} -4.09753 q^{57} -6.41298 q^{58} -5.77755 q^{59} -4.14954 q^{60} -4.49815 q^{61} -8.04539 q^{62} -0.417699 q^{63} +1.00000 q^{64} +11.1405 q^{65} -11.7398 q^{66} -5.26672 q^{67} +4.60011 q^{68} -13.3418 q^{69} -2.18427 q^{70} -6.54236 q^{71} +0.428551 q^{72} -0.771275 q^{73} +10.6475 q^{74} -0.0410284 q^{75} +2.21292 q^{76} -6.17970 q^{77} -9.20480 q^{78} -3.79108 q^{79} +2.24102 q^{80} -10.1020 q^{81} -5.52367 q^{82} -15.2792 q^{83} +1.80475 q^{84} +10.3089 q^{85} +9.18021 q^{86} +11.8745 q^{87} +6.34024 q^{88} +1.91557 q^{89} +0.960389 q^{90} -4.84530 q^{91} +7.20543 q^{92} +14.8971 q^{93} +11.4374 q^{94} +4.95920 q^{95} -1.85163 q^{96} -13.2488 q^{97} -6.05000 q^{98} +2.71711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9}+O(q^{10}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9	\( 88 q + 88 q^{2} + 22 q^{3} + 88 q^{4} + 25 q^{5} + 22 q^{6} + 33 q^{7} + 88 q^{8} + 108 q^{9} + 25 q^{10} + 70 q^{11} + 22 q^{12} + 31 q^{13} + 33 q^{14} + 47 q^{15} + 88 q^{16} + 19 q^{17} + 108 q^{18} + 33 q^{19} + 25 q^{20} + 48 q^{21} + 70 q^{22} + 77 q^{23} + 22 q^{24} + 109 q^{25} + 31 q^{26} + 88 q^{27} + 33 q^{28} + 83 q^{29} + 47 q^{30} + 51 q^{31} + 88 q^{32} + 30 q^{33} + 19 q^{34} + 40 q^{35} + 108 q^{36} + 45 q^{37} + 33 q^{38} + 82 q^{39} + 25 q^{40} + 35 q^{41} + 48 q^{42} + 78 q^{43} + 70 q^{44} + 37 q^{45} + 77 q^{46} + 59 q^{47} + 22 q^{48} + 103 q^{49} + 109 q^{50} + 21 q^{51} + 31 q^{52} + 58 q^{53} + 88 q^{54} + 35 q^{55} + 33 q^{56} - 16 q^{57} + 83 q^{58} + 54 q^{59} + 47 q^{60} + 18 q^{61} + 51 q^{62} + 47 q^{63} + 88 q^{64} + 34 q^{65} + 30 q^{66} + 88 q^{67} + 19 q^{68} + 62 q^{69} + 40 q^{70} + 139 q^{71} + 108 q^{72} - 6 q^{73} + 45 q^{74} + 45 q^{75} + 33 q^{76} + 37 q^{77} + 82 q^{78} + 94 q^{79} + 25 q^{80} + 112 q^{81} + 35 q^{82} + 58 q^{83} + 48 q^{84} + 83 q^{85} + 78 q^{86} + 21 q^{87} + 70 q^{88} + 99 q^{89} + 37 q^{90} + 53 q^{91} + 77 q^{92} + 57 q^{93} + 59 q^{94} + 92 q^{95} + 22 q^{96} + 16 q^{97} + 103 q^{98} + 150 q^{99}+O(q^{100}) \) 88 * q + 88 * q^2 + 22 * q^3 + 88 * q^4 + 25 * q^5 + 22 * q^6 + 33 * q^7 + 88 * q^8 + 108 * q^9 + 25 * q^10 + 70 * q^11 + 22 * q^12 + 31 * q^13 + 33 * q^14 + 47 * q^15 + 88 * q^16 + 19 * q^17 + 108 * q^18 + 33 * q^19 + 25 * q^20 + 48 * q^21 + 70 * q^22 + 77 * q^23 + 22 * q^24 + 109 * q^25 + 31 * q^26 + 88 * q^27 + 33 * q^28 + 83 * q^29 + 47 * q^30 + 51 * q^31 + 88 * q^32 + 30 * q^33 + 19 * q^34 + 40 * q^35 + 108 * q^36 + 45 * q^37 + 33 * q^38 + 82 * q^39 + 25 * q^40 + 35 * q^41 + 48 * q^42 + 78 * q^43 + 70 * q^44 + 37 * q^45 + 77 * q^46 + 59 * q^47 + 22 * q^48 + 103 * q^49 + 109 * q^50 + 21 * q^51 + 31 * q^52 + 58 * q^53 + 88 * q^54 + 35 * q^55 + 33 * q^56 - 16 * q^57 + 83 * q^58 + 54 * q^59 + 47 * q^60 + 18 * q^61 + 51 * q^62 + 47 * q^63 + 88 * q^64 + 34 * q^65 + 30 * q^66 + 88 * q^67 + 19 * q^68 + 62 * q^69 + 40 * q^70 + 139 * q^71 + 108 * q^72 - 6 * q^73 + 45 * q^74 + 45 * q^75 + 33 * q^76 + 37 * q^77 + 82 * q^78 + 94 * q^79 + 25 * q^80 + 112 * q^81 + 35 * q^82 + 58 * q^83 + 48 * q^84 + 83 * q^85 + 78 * q^86 + 21 * q^87 + 70 * q^88 + 99 * q^89 + 37 * q^90 + 53 * q^91 + 77 * q^92 + 57 * q^93 + 59 * q^94 + 92 * q^95 + 22 * q^96 + 16 * q^97 + 103 * q^98 + 150 * q^99

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