LMFDB - Embedded newform 8021.2.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8021,2,Mod(1,8021)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8021, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8021.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8021 = 13 \cdot 617 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8021.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0480074613$
Analytic rank:	$1$
Dimension:	$134$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	8021.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.22845 q^{2} -2.09787 q^{3} +2.96601 q^{4} -1.11575 q^{5} +4.67502 q^{6} -1.94623 q^{7} -2.15271 q^{8} +1.40108 q^{9} +O(q^{10})$	\(q-2.22845 q^{2} -2.09787 q^{3} +2.96601 q^{4} -1.11575 q^{5} +4.67502 q^{6} -1.94623 q^{7} -2.15271 q^{8} +1.40108 q^{9} +2.48640 q^{10} +2.64240 q^{11} -6.22232 q^{12} +1.00000 q^{13} +4.33708 q^{14} +2.34071 q^{15} -1.13480 q^{16} +2.48199 q^{17} -3.12224 q^{18} +7.04847 q^{19} -3.30933 q^{20} +4.08294 q^{21} -5.88847 q^{22} -1.41370 q^{23} +4.51612 q^{24} -3.75510 q^{25} -2.22845 q^{26} +3.35434 q^{27} -5.77253 q^{28} -0.0497420 q^{29} -5.21616 q^{30} -1.45582 q^{31} +6.83428 q^{32} -5.54343 q^{33} -5.53100 q^{34} +2.17151 q^{35} +4.15561 q^{36} -5.20017 q^{37} -15.7072 q^{38} -2.09787 q^{39} +2.40189 q^{40} -4.25711 q^{41} -9.09866 q^{42} +6.11301 q^{43} +7.83739 q^{44} -1.56326 q^{45} +3.15037 q^{46} -1.92576 q^{47} +2.38067 q^{48} -3.21219 q^{49} +8.36807 q^{50} -5.20690 q^{51} +2.96601 q^{52} +2.85538 q^{53} -7.47499 q^{54} -2.94826 q^{55} +4.18967 q^{56} -14.7868 q^{57} +0.110848 q^{58} -12.2273 q^{59} +6.94256 q^{60} -2.61160 q^{61} +3.24423 q^{62} -2.72682 q^{63} -12.9603 q^{64} -1.11575 q^{65} +12.3533 q^{66} +11.1248 q^{67} +7.36160 q^{68} +2.96577 q^{69} -4.83911 q^{70} +0.447967 q^{71} -3.01612 q^{72} -6.17299 q^{73} +11.5883 q^{74} +7.87773 q^{75} +20.9058 q^{76} -5.14272 q^{77} +4.67502 q^{78} -2.31526 q^{79} +1.26616 q^{80} -11.2402 q^{81} +9.48677 q^{82} +0.591891 q^{83} +12.1101 q^{84} -2.76928 q^{85} -13.6226 q^{86} +0.104353 q^{87} -5.68833 q^{88} -14.9607 q^{89} +3.48364 q^{90} -1.94623 q^{91} -4.19305 q^{92} +3.05413 q^{93} +4.29146 q^{94} -7.86434 q^{95} -14.3375 q^{96} +10.6926 q^{97} +7.15823 q^{98} +3.70221 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) $ 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.22845	−1.57576	−0.787878	−	0.615832i	$-0.788820\pi$
$2$	−2.22845	−1.57576	−0.787878	+	0.615832i	$0.788820\pi$
$3$	−2.09787	−1.21121	−0.605604	−	0.795766i	$-0.707069\pi$
$3$	−2.09787	−1.21121	−0.605604	+	0.795766i	$0.707069\pi$
$4$	2.96601	1.48301
$5$	−1.11575	−0.498979	−0.249490	−	0.968377i	$-0.580263\pi$
$5$	−1.11575	−0.498979	−0.249490	+	0.968377i	$0.580263\pi$
$6$	4.67502	1.90857
$7$	−1.94623	−0.735605	−0.367803	−	0.929904i	$-0.619890\pi$
$7$	−1.94623	−0.735605	−0.367803	+	0.929904i	$0.619890\pi$
$8$	−2.15271	−0.761098
$9$	1.40108	0.467026
$10$	2.48640	0.786269
$11$	2.64240	0.796714	0.398357	−	0.917230i	$-0.369581\pi$
$11$	2.64240	0.796714	0.398357	+	0.917230i	$0.369581\pi$
$12$	−6.22232	−1.79623
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	4.33708	1.15913
$15$	2.34071	0.604368
$16$	−1.13480	−0.283701
$17$	2.48199	0.601971	0.300985	−	0.953629i	$-0.402684\pi$
$17$	2.48199	0.601971	0.300985	+	0.953629i	$0.402684\pi$
$18$	−3.12224	−0.735919
$19$	7.04847	1.61703	0.808515	−	0.588475i	$-0.200272\pi$
$19$	7.04847	1.61703	0.808515	+	0.588475i	$0.200272\pi$
$20$	−3.30933	−0.739989
$21$	4.08294	0.890972
$22$	−5.88847	−1.25543
$23$	−1.41370	−0.294777	−0.147388	−	0.989079i	$-0.547087\pi$
$23$	−1.41370	−0.294777	−0.147388	+	0.989079i	$0.547087\pi$
$24$	4.51612	0.921849
$25$	−3.75510	−0.751020
$26$	−2.22845	−0.437036
$27$	3.35434	0.645542
$28$	−5.77253	−1.09091
$29$	−0.0497420	−0.00923687	−0.00461843	−	0.999989i	$-0.501470\pi$
$29$	−0.0497420	−0.00923687	−0.00461843	+	0.999989i	$0.501470\pi$
$30$	−5.21616	−0.952336
$31$	−1.45582	−0.261473	−0.130736	−	0.991417i	$-0.541734\pi$
$31$	−1.45582	−0.261473	−0.130736	+	0.991417i	$0.541734\pi$
$32$	6.83428	1.20814
$33$	−5.54343	−0.964987
$34$	−5.53100	−0.948558
$35$	2.17151	0.367052
$36$	4.15561	0.692602
$37$	−5.20017	−0.854903	−0.427451	−	0.904038i	$-0.640588\pi$
$37$	−5.20017	−0.854903	−0.427451	+	0.904038i	$0.640588\pi$
$38$	−15.7072	−2.54804
$39$	−2.09787	−0.335929
$40$	2.40189	0.379772
$41$	−4.25711	−0.664849	−0.332424	−	0.943130i	$-0.607867\pi$
$41$	−4.25711	−0.664849	−0.332424	+	0.943130i	$0.607867\pi$
$42$	−9.09866	−1.40395
$43$	6.11301	0.932225	0.466112	−	0.884726i	$-0.345654\pi$
$43$	6.11301	0.932225	0.466112	+	0.884726i	$0.345654\pi$
$44$	7.83739	1.18153
$45$	−1.56326	−0.233036
$46$	3.15037	0.464496
$47$	−1.92576	−0.280901	−0.140450	−	0.990088i	$-0.544855\pi$
$47$	−1.92576	−0.280901	−0.140450	+	0.990088i	$0.544855\pi$
$48$	2.38067	0.343621
$49$	−3.21219	−0.458885
$50$	8.36807	1.18342
$51$	−5.20690	−0.729112
$52$	2.96601	0.411312
$53$	2.85538	0.392216	0.196108	−	0.980582i	$-0.437170\pi$
$53$	2.85538	0.392216	0.196108	+	0.980582i	$0.437170\pi$
$54$	−7.47499	−1.01722
$55$	−2.94826	−0.397544
$56$	4.18967	0.559868
$57$	−14.7868	−1.95856
$58$	0.110848	0.0145550
$59$	−12.2273	−1.59186	−0.795931	−	0.605388i	$-0.793018\pi$
$59$	−12.2273	−1.59186	−0.795931	+	0.605388i	$0.793018\pi$
$60$	6.94256	0.896281
$61$	−2.61160	−0.334381	−0.167190	−	0.985925i	$-0.553469\pi$
$61$	−2.61160	−0.334381	−0.167190	+	0.985925i	$0.553469\pi$
$62$	3.24423	0.412017
$63$	−2.72682	−0.343547
$64$	−12.9603	−1.62003
$65$	−1.11575	−0.138392
$66$	12.3533	1.52058
$67$	11.1248	1.35911	0.679553	−	0.733626i	$-0.262174\pi$
$67$	11.1248	1.35911	0.679553	+	0.733626i	$0.262174\pi$
$68$	7.36160	0.892725
$69$	2.96577	0.357036
$70$	−4.83911	−0.578384
$71$	0.447967	0.0531639	0.0265820	−	0.999647i	$-0.491538\pi$
$71$	0.447967	0.0531639	0.0265820	+	0.999647i	$0.491538\pi$
$72$	−3.01612	−0.355453
$73$	−6.17299	−0.722494	−0.361247	−	0.932470i	$-0.617649\pi$
$73$	−6.17299	−0.722494	−0.361247	+	0.932470i	$0.617649\pi$
$74$	11.5883	1.34712
$75$	7.87773	0.909641
$76$	20.9058	2.39806
$77$	−5.14272	−0.586067
$78$	4.67502	0.529342
$79$	−2.31526	−0.260487	−0.130244	−	0.991482i	$-0.541576\pi$
$79$	−2.31526	−0.260487	−0.130244	+	0.991482i	$0.541576\pi$
$80$	1.26616	0.141561
$81$	−11.2402	−1.24891
$82$	9.48677	1.04764
$83$	0.591891	0.0649684	0.0324842	−	0.999472i	$-0.489658\pi$
$83$	0.591891	0.0649684	0.0324842	+	0.999472i	$0.489658\pi$
$84$	12.1101	1.32132
$85$	−2.76928	−0.300371
$86$	−13.6226	−1.46896
$87$	0.104353	0.0111878
$88$	−5.68833	−0.606378
$89$	−14.9607	−1.58583	−0.792913	−	0.609334i	$-0.791437\pi$
$89$	−14.9607	−1.58583	−0.792913	+	0.609334i	$0.791437\pi$
$90$	3.48364	0.367208
$91$	−1.94623	−0.204020
$92$	−4.19305	−0.437156
$93$	3.05413	0.316698
$94$	4.29146	0.442631
$95$	−7.86434	−0.806865
$96$	−14.3375	−1.46331
$97$	10.6926	1.08567	0.542834	−	0.839840i	$-0.317351\pi$
$97$	10.6926	1.08567	0.542834	+	0.839840i	$0.317351\pi$
$98$	7.15823	0.723090
$99$	3.70221	0.372086
$100$	−11.1377	−1.11377
$101$	5.37155	0.534490	0.267245	−	0.963629i	$-0.413887\pi$
$101$	5.37155	0.534490	0.267245	+	0.963629i	$0.413887\pi$
$102$	11.6033	1.14890
$103$	16.2979	1.60588	0.802941	−	0.596059i	$-0.203268\pi$
$103$	16.2979	1.60588	0.802941	+	0.596059i	$0.203268\pi$
$104$	−2.15271	−0.211091
$105$	−4.55555	−0.444576
$106$	−6.36308	−0.618037
$107$	7.87838	0.761632	0.380816	−	0.924651i	$-0.375643\pi$
$107$	7.87838	0.761632	0.380816	+	0.924651i	$0.375643\pi$
$108$	9.94900	0.957343
$109$	−3.85049	−0.368810	−0.184405	−	0.982850i	$-0.559036\pi$
$109$	−3.85049	−0.368810	−0.184405	+	0.982850i	$0.559036\pi$
$110$	6.57007	0.626432
$111$	10.9093	1.03547
$112$	2.20859	0.208692
$113$	−4.72865	−0.444834	−0.222417	−	0.974952i	$-0.571395\pi$
$113$	−4.72865	−0.444834	−0.222417	+	0.974952i	$0.571395\pi$
$114$	32.9517	3.08621
$115$	1.57734	0.147088
$116$	−0.147535	−0.0136983
$117$	1.40108	0.129530
$118$	27.2480	2.50838
$119$	−4.83052	−0.442813
$120$	−5.03887	−0.459983
$121$	−4.01771	−0.365247
$122$	5.81982	0.526902
$123$	8.93088	0.805270
$124$	−4.31798	−0.387766
$125$	9.76852	0.873723
$126$	6.07659	0.541346
$127$	−10.4416	−0.926539	−0.463270	−	0.886217i	$-0.653324\pi$
$127$	−10.4416	−0.926539	−0.463270	+	0.886217i	$0.653324\pi$
$128$	15.2128	1.34464
$129$	−12.8243	−1.12912
$130$	2.48640	0.218072
$131$	−2.67514	−0.233728	−0.116864	−	0.993148i	$-0.537284\pi$
$131$	−2.67514	−0.233728	−0.116864	+	0.993148i	$0.537284\pi$
$132$	−16.4419	−1.43108
$133$	−13.7179	−1.18950
$134$	−24.7910	−2.14162
$135$	−3.74261	−0.322112
$136$	−5.34300	−0.458159
$137$	3.46240	0.295813	0.147906	−	0.989001i	$-0.452747\pi$
$137$	3.46240	0.295813	0.147906	+	0.989001i	$0.452747\pi$
$138$	−6.60907	−0.562602
$139$	−6.09534	−0.517000	−0.258500	−	0.966011i	$-0.583228\pi$
$139$	−6.09534	−0.517000	−0.258500	+	0.966011i	$0.583228\pi$
$140$	6.44072	0.544340
$141$	4.04000	0.340229
$142$	−0.998274	−0.0837733
$143$	2.64240	0.220969
$144$	−1.58995	−0.132496
$145$	0.0554998	0.00460901
$146$	13.7562	1.13847
$147$	6.73878	0.555805
$148$	−15.4238	−1.26783
$149$	22.7341	1.86245	0.931226	−	0.364443i	$-0.118741\pi$
$149$	22.7341	1.86245	0.931226	+	0.364443i	$0.118741\pi$
$150$	−17.5552	−1.43337
$151$	−9.01595	−0.733708	−0.366854	−	0.930279i	$-0.619565\pi$
$151$	−9.01595	−0.733708	−0.366854	+	0.930279i	$0.619565\pi$
$152$	−15.1733	−1.23072
$153$	3.47746	0.281136
$154$	11.4603	0.923498
$155$	1.62433	0.130470
$156$	−6.22232	−0.498184
$157$	17.9212	1.43027	0.715136	−	0.698986i	$-0.246365\pi$
$157$	17.9212	1.43027	0.715136	+	0.698986i	$0.246365\pi$
$158$	5.15945	0.410464
$159$	−5.99022	−0.475055
$160$	−7.62536	−0.602837
$161$	2.75138	0.216839
$162$	25.0483	1.96798
$163$	−1.84638	−0.144620	−0.0723098	−	0.997382i	$-0.523037\pi$
$163$	−1.84638	−0.144620	−0.0723098	+	0.997382i	$0.523037\pi$
$164$	−12.6266	−0.985974
$165$	6.18509	0.481509
$166$	−1.31900	−0.102374
$167$	−1.83493	−0.141991	−0.0709954	−	0.997477i	$-0.522618\pi$
$167$	−1.83493	−0.141991	−0.0709954	+	0.997477i	$0.522618\pi$
$168$	−8.78940	−0.678117
$169$	1.00000	0.0769231
$170$	6.17122	0.473311
$171$	9.87546	0.755195
$172$	18.1312	1.38249
$173$	15.9279	1.21098	0.605488	−	0.795854i	$-0.292978\pi$
$173$	15.9279	1.21098	0.605488	+	0.795854i	$0.292978\pi$
$174$	−0.232545	−0.0176292
$175$	7.30828	0.552454
$176$	−2.99861	−0.226028
$177$	25.6514	1.92808
$178$	33.3392	2.49887
$179$	−15.2925	−1.14302	−0.571508	−	0.820596i	$-0.693642\pi$
$179$	−15.2925	−1.14302	−0.571508	+	0.820596i	$0.693642\pi$
$180$	−4.63663	−0.345594
$181$	−21.3393	−1.58614	−0.793068	−	0.609133i	$-0.791518\pi$
$181$	−21.3393	−1.58614	−0.793068	+	0.609133i	$0.791518\pi$
$182$	4.33708	0.321486
$183$	5.47880	0.405005
$184$	3.04329	0.224354
$185$	5.80210	0.426579
$186$	−6.80598	−0.499039
$187$	6.55841	0.479598
$188$	−5.71182	−0.416577
$189$	−6.52831	−0.474864
$190$	17.5253	1.27142
$191$	−9.65240	−0.698423	−0.349212	−	0.937044i	$-0.613551\pi$
$191$	−9.65240	−0.698423	−0.349212	+	0.937044i	$0.613551\pi$
$192$	27.1890	1.96220
$193$	−8.68965	−0.625494	−0.312747	−	0.949836i	$-0.601249\pi$
$193$	−8.68965	−0.625494	−0.312747	+	0.949836i	$0.601249\pi$
$194$	−23.8280	−1.71075
$195$	2.34071	0.167622
$196$	−9.52740	−0.680528
$197$	10.0940	0.719171	0.359585	−	0.933112i	$-0.382918\pi$
$197$	10.0940	0.719171	0.359585	+	0.933112i	$0.382918\pi$
$198$	−8.25021	−0.586317
$199$	3.13931	0.222540	0.111270	−	0.993790i	$-0.464508\pi$
$199$	3.13931	0.222540	0.111270	+	0.993790i	$0.464508\pi$
$200$	8.08364	0.571600
$201$	−23.3384	−1.64616
$202$	−11.9703	−0.842225
$203$	0.0968094	0.00679469
$204$	−15.4437	−1.08128
$205$	4.74988	0.331746
$206$	−36.3192	−2.53048
$207$	−1.98070	−0.137668
$208$	−1.13480	−0.0786844
$209$	18.6249	1.28831
$210$	10.1518	0.700544
$211$	10.6081	0.730291	0.365145	−	0.930951i	$-0.381019\pi$
$211$	10.6081	0.730291	0.365145	+	0.930951i	$0.381019\pi$
$212$	8.46908	0.581658
$213$	−0.939779	−0.0643926
$214$	−17.5566	−1.20015
$215$	−6.82060	−0.465161
$216$	−7.22092	−0.491321
$217$	2.83336	0.192341
$218$	8.58065	0.581155
$219$	12.9502	0.875091
$220$	−8.74458	−0.589560
$221$	2.48199	0.166957
$222$	−24.3109	−1.63164
$223$	5.12964	0.343506	0.171753	−	0.985140i	$-0.445057\pi$
$223$	5.12964	0.343506	0.171753	+	0.985140i	$0.445057\pi$
$224$	−13.3011	−0.888715
$225$	−5.26119	−0.350746
$226$	10.5376	0.700950
$227$	1.50214	0.0997004	0.0498502	−	0.998757i	$-0.484126\pi$
$227$	1.50214	0.0997004	0.0498502	+	0.998757i	$0.484126\pi$
$228$	−43.8578	−2.90456
$229$	−12.3290	−0.814721	−0.407360	−	0.913267i	$-0.633551\pi$
$229$	−12.3290	−0.814721	−0.407360	+	0.913267i	$0.633551\pi$
$230$	−3.51503	−0.231774
$231$	10.7888	0.709850
$232$	0.107080	0.00703016
$233$	−10.1585	−0.665505	−0.332752	−	0.943014i	$-0.607977\pi$
$233$	−10.1585	−0.665505	−0.332752	+	0.943014i	$0.607977\pi$
$234$	−3.12224	−0.204107
$235$	2.14867	0.140164
$236$	−36.2664	−2.36074
$237$	4.85713	0.315504
$238$	10.7646	0.697765
$239$	−12.1406	−0.785308	−0.392654	−	0.919686i	$-0.628443\pi$
$239$	−12.1406	−0.785308	−0.392654	+	0.919686i	$0.628443\pi$
$240$	−2.65624	−0.171460
$241$	−18.8712	−1.21560	−0.607802	−	0.794089i	$-0.707948\pi$
$241$	−18.8712	−1.21560	−0.607802	+	0.794089i	$0.707948\pi$
$242$	8.95329	0.575539
$243$	13.5176	0.867151
$244$	−7.74602	−0.495888
$245$	3.58401	0.228974
$246$	−19.9021	−1.26891
$247$	7.04847	0.448483
$248$	3.13396	0.199007
$249$	−1.24171	−0.0786903
$250$	−21.7687	−1.37677
$251$	27.2093	1.71744	0.858719	−	0.512446i	$-0.171261\pi$
$251$	27.2093	1.71744	0.858719	+	0.512446i	$0.171261\pi$
$252$	−8.08778	−0.509482
$253$	−3.73556	−0.234853
$254$	23.2686	1.46000
$255$	5.80961	0.363812
$256$	−7.98055	−0.498784
$257$	11.0090	0.686721	0.343360	−	0.939204i	$-0.388435\pi$
$257$	11.0090	0.686721	0.343360	+	0.939204i	$0.388435\pi$
$258$	28.5784	1.77921
$259$	10.1207	0.628871
$260$	−3.30933	−0.205236
$261$	−0.0696925	−0.00431386
$262$	5.96143	0.368298
$263$	30.6146	1.88778	0.943888	−	0.330264i	$-0.107138\pi$
$263$	30.6146	1.88778	0.943888	+	0.330264i	$0.107138\pi$
$264$	11.9334	0.734450
$265$	−3.18589	−0.195708
$266$	30.5698	1.87435
$267$	31.3856	1.92077
$268$	32.9962	2.01556
$269$	20.3110	1.23838	0.619191	−	0.785240i	$-0.287461\pi$
$269$	20.3110	1.23838	0.619191	+	0.785240i	$0.287461\pi$
$270$	8.34023	0.507570
$271$	−22.2968	−1.35444	−0.677218	−	0.735782i	$-0.736815\pi$
$271$	−22.2968	−1.35444	−0.677218	+	0.735782i	$0.736815\pi$
$272$	−2.81657	−0.170780
$273$	4.08294	0.247111
$274$	−7.71581	−0.466129
$275$	−9.92248	−0.598348
$276$	8.79649	0.529487
$277$	−10.6369	−0.639107	−0.319554	−	0.947568i	$-0.603533\pi$
$277$	−10.6369	−0.639107	−0.319554	+	0.947568i	$0.603533\pi$
$278$	13.5832	0.814665
$279$	−2.03972	−0.122115
$280$	−4.67463	−0.279362
$281$	23.8463	1.42255	0.711275	−	0.702913i	$-0.248118\pi$
$281$	23.8463	1.42255	0.711275	+	0.702913i	$0.248118\pi$
$282$	−9.00295	−0.536118
$283$	6.52917	0.388119	0.194059	−	0.980990i	$-0.437835\pi$
$283$	6.52917	0.388119	0.194059	+	0.980990i	$0.437835\pi$
$284$	1.32867	0.0788424
$285$	16.4984	0.977281
$286$	−5.88847	−0.348193
$287$	8.28531	0.489066
$288$	9.57536	0.564234
$289$	−10.8397	−0.637631
$290$	−0.123679	−0.00726267
$291$	−22.4317	−1.31497
$292$	−18.3092	−1.07146
$293$	9.58021	0.559682	0.279841	−	0.960046i	$-0.409718\pi$
$293$	9.58021	0.559682	0.279841	+	0.960046i	$0.409718\pi$
$294$	−15.0171	−0.875813
$295$	13.6427	0.794306
$296$	11.1945	0.650665
$297$	8.86351	0.514313
$298$	−50.6619	−2.93477
$299$	−1.41370	−0.0817564
$300$	23.3654	1.34900
$301$	−11.8973	−0.685749
$302$	20.0916	1.15614
$303$	−11.2688	−0.647378
$304$	−7.99863	−0.458753
$305$	2.91389	0.166849
$306$	−7.74936	−0.443002
$307$	−18.9717	−1.08277	−0.541386	−	0.840774i	$-0.682100\pi$
$307$	−18.9717	−1.08277	−0.541386	+	0.840774i	$0.682100\pi$
$308$	−15.2534	−0.869141
$309$	−34.1910	−1.94506
$310$	−3.61975	−0.205588
$311$	−9.47412	−0.537228	−0.268614	−	0.963248i	$-0.586566\pi$
$311$	−9.47412	−0.537228	−0.268614	+	0.963248i	$0.586566\pi$
$312$	4.51612	0.255675
$313$	1.65050	0.0932920	0.0466460	−	0.998911i	$-0.485147\pi$
$313$	1.65050	0.0932920	0.0466460	+	0.998911i	$0.485147\pi$
$314$	−39.9367	−2.25376
$315$	3.04245	0.171423
$316$	−6.86709	−0.386304
$317$	21.4376	1.20405	0.602026	−	0.798476i	$-0.294360\pi$
$317$	21.4376	1.20405	0.602026	+	0.798476i	$0.294360\pi$
$318$	13.3489	0.748571
$319$	−0.131438	−0.00735914
$320$	14.4604	0.808364
$321$	−16.5279	−0.922495
$322$	−6.13133	−0.341686
$323$	17.4942	0.973405
$324$	−33.3386	−1.85214
$325$	−3.75510	−0.208295
$326$	4.11457	0.227885
$327$	8.07785	0.446706
$328$	9.16432	0.506015
$329$	3.74796	0.206632
$330$	−13.7832	−0.758740
$331$	30.5662	1.68007	0.840035	−	0.542532i	$-0.182534\pi$
$331$	30.5662	1.68007	0.840035	+	0.542532i	$0.182534\pi$
$332$	1.75555	0.0963485
$333$	−7.28585	−0.399262
$334$	4.08905	0.223743
$335$	−12.4125	−0.678166
$336$	−4.63334	−0.252769
$337$	13.0044	0.708397	0.354199	−	0.935170i	$-0.384754\pi$
$337$	13.0044	0.708397	0.354199	+	0.935170i	$0.384754\pi$
$338$	−2.22845	−0.121212
$339$	9.92011	0.538787
$340$	−8.21372	−0.445452
$341$	−3.84686	−0.208319
$342$	−22.0070	−1.19000
$343$	19.8753	1.07316
$344$	−13.1595	−0.709514
$345$	−3.30906	−0.178154
$346$	−35.4946	−1.90820
$347$	−22.5538	−1.21075	−0.605375	−	0.795940i	$-0.706977\pi$
$347$	−22.5538	−1.21075	−0.605375	+	0.795940i	$0.706977\pi$
$348$	0.309511	0.0165915
$349$	24.0581	1.28780	0.643899	−	0.765110i	$-0.277316\pi$
$349$	24.0581	1.28780	0.643899	+	0.765110i	$0.277316\pi$
$350$	−16.2862	−0.870532
$351$	3.35434	0.179041
$352$	18.0589	0.962543
$353$	26.4959	1.41024	0.705118	−	0.709090i	$-0.250894\pi$
$353$	26.4959	1.41024	0.705118	+	0.709090i	$0.250894\pi$
$354$	−57.1629	−3.03818
$355$	−0.499820	−0.0265277
$356$	−44.3735	−2.35179
$357$	10.1338	0.536339
$358$	34.0787	1.80112
$359$	−9.35228	−0.493595	−0.246797	−	0.969067i	$-0.579378\pi$
$359$	−9.35228	−0.493595	−0.246797	+	0.969067i	$0.579378\pi$
$360$	3.36524	0.177364
$361$	30.6809	1.61479
$362$	47.5536	2.49936
$363$	8.42866	0.442390
$364$	−5.77253	−0.302563
$365$	6.88753	0.360510
$366$	−12.2093	−0.638188
$367$	−31.9250	−1.66647	−0.833236	−	0.552917i	$-0.813515\pi$
$367$	−31.9250	−1.66647	−0.833236	+	0.552917i	$0.813515\pi$
$368$	1.60427	0.0836284
$369$	−5.96454	−0.310502
$370$	−12.9297	−0.672184
$371$	−5.55722	−0.288516
$372$	9.05857	0.469665
$373$	−9.46315	−0.489983	−0.244992	−	0.969525i	$-0.578785\pi$
$373$	−9.46315	−0.489983	−0.244992	+	0.969525i	$0.578785\pi$
$374$	−14.6151	−0.755730
$375$	−20.4931	−1.05826
$376$	4.14560	0.213793
$377$	−0.0497420	−0.00256185
$378$	14.5480	0.748270
$379$	14.5747	0.748653	0.374327	−	0.927297i	$-0.377874\pi$
$379$	14.5747	0.748653	0.374327	+	0.927297i	$0.377874\pi$
$380$	−23.3257	−1.19658
$381$	21.9051	1.12223
$382$	21.5099	1.10054
$383$	−34.1010	−1.74248	−0.871240	−	0.490857i	$-0.836684\pi$
$383$	−34.1010	−1.74248	−0.871240	+	0.490857i	$0.836684\pi$
$384$	−31.9146	−1.62864
$385$	5.73800	0.292435
$386$	19.3645	0.985626
$387$	8.56480	0.435373
$388$	31.7144	1.61005
$389$	33.1113	1.67881	0.839405	−	0.543506i	$-0.182903\pi$
$389$	33.1113	1.67881	0.839405	+	0.543506i	$0.182903\pi$
$390$	−5.21616	−0.264131
$391$	−3.50879	−0.177447
$392$	6.91492	0.349256
$393$	5.61211	0.283093
$394$	−22.4941	−1.13324
$395$	2.58326	0.129978
$396$	10.9808	0.551806
$397$	−4.89700	−0.245773	−0.122887	−	0.992421i	$-0.539215\pi$
$397$	−4.89700	−0.245773	−0.122887	+	0.992421i	$0.539215\pi$
$398$	−6.99581	−0.350668
$399$	28.7785	1.44073
$400$	4.26130	0.213065
$401$	−15.7321	−0.785623	−0.392812	−	0.919619i	$-0.628498\pi$
$401$	−15.7321	−0.785623	−0.392812	+	0.919619i	$0.628498\pi$
$402$	52.0085	2.59395
$403$	−1.45582	−0.0725195
$404$	15.9321	0.792651
$405$	12.5413	0.623182
$406$	−0.215735	−0.0107068
$407$	−13.7409	−0.681113
$408$	11.2089	0.554926
$409$	5.86652	0.290081	0.145040	−	0.989426i	$-0.453669\pi$
$409$	5.86652	0.290081	0.145040	+	0.989426i	$0.453669\pi$
$410$	−10.5849	−0.522750
$411$	−7.26369	−0.358291
$412$	48.3398	2.38153
$413$	23.7972	1.17098
$414$	4.41391	0.216932
$415$	−0.660403	−0.0324179
$416$	6.83428	0.335078
$417$	12.7873	0.626195
$418$	−41.5047	−2.03006
$419$	21.9232	1.07102	0.535509	−	0.844530i	$-0.320120\pi$
$419$	21.9232	1.07102	0.535509	+	0.844530i	$0.320120\pi$
$420$	−13.5118	−0.659309
$421$	−0.274013	−0.0133546	−0.00667729	−	0.999978i	$-0.502125\pi$
$421$	−0.274013	−0.0133546	−0.00667729	+	0.999978i	$0.502125\pi$
$422$	−23.6396	−1.15076
$423$	−2.69814	−0.131188
$424$	−6.14680	−0.298515
$425$	−9.32011	−0.452092
$426$	2.09425	0.101467
$427$	5.08276	0.245972
$428$	23.3674	1.12950
$429$	−5.54343	−0.267639
$430$	15.1994	0.732980
$431$	37.6269	1.81242	0.906211	−	0.422826i	$-0.138962\pi$
$431$	37.6269	1.81242	0.906211	+	0.422826i	$0.138962\pi$
$432$	−3.80651	−0.183141
$433$	−5.96651	−0.286732	−0.143366	−	0.989670i	$-0.545793\pi$
$433$	−5.96651	−0.286732	−0.143366	+	0.989670i	$0.545793\pi$
$434$	−6.31401	−0.303082
$435$	−0.116432	−0.00558247
$436$	−11.4206	−0.546947
$437$	−9.96442	−0.476663
$438$	−28.8589	−1.37893
$439$	−35.9224	−1.71448	−0.857242	−	0.514913i	$-0.827824\pi$
$439$	−35.9224	−1.71448	−0.857242	+	0.514913i	$0.827824\pi$
$440$	6.34676	0.302570
$441$	−4.50054	−0.214311
$442$	−5.53100	−0.263083
$443$	−0.260570	−0.0123801	−0.00619003	−	0.999981i	$-0.501970\pi$
$443$	−0.260570	−0.0123801	−0.00619003	+	0.999981i	$0.501970\pi$
$444$	32.3571	1.53560
$445$	16.6924	0.791295
$446$	−11.4312	−0.541281
$447$	−47.6933	−2.25582
$448$	25.2237	1.19171
$449$	40.2617	1.90007	0.950033	−	0.312148i	$-0.101049\pi$
$449$	40.2617	1.90007	0.950033	+	0.312148i	$0.101049\pi$
$450$	11.7243	0.552690
$451$	−11.2490	−0.529694
$452$	−14.0252	−0.659691
$453$	18.9143	0.888673
$454$	−3.34745	−0.157103
$455$	2.17151	0.101802
$456$	31.8317	1.49066
$457$	−20.7489	−0.970592	−0.485296	−	0.874350i	$-0.661288\pi$
$457$	−20.7489	−0.970592	−0.485296	+	0.874350i	$0.661288\pi$
$458$	27.4745	1.28380
$459$	8.32542	0.388598
$460$	4.67840	0.218132
$461$	24.5036	1.14125	0.570624	−	0.821212i	$-0.306701\pi$
$461$	24.5036	1.14125	0.570624	+	0.821212i	$0.306701\pi$
$462$	−24.0423	−1.11855
$463$	−30.0195	−1.39512	−0.697562	−	0.716524i	$-0.745732\pi$
$463$	−30.0195	−1.39512	−0.697562	+	0.716524i	$0.745732\pi$
$464$	0.0564474	0.00262051
$465$	−3.40765	−0.158026
$466$	22.6377	1.04867
$467$	−25.0301	−1.15825	−0.579127	−	0.815237i	$-0.696606\pi$
$467$	−25.0301	−1.15825	−0.579127	+	0.815237i	$0.696606\pi$
$468$	4.15561	0.192093
$469$	−21.6513	−0.999766
$470$	−4.78821	−0.220864
$471$	−37.5965	−1.73236
$472$	26.3219	1.21156
$473$	16.1530	0.742717
$474$	−10.8239	−0.497157
$475$	−26.4677	−1.21442
$476$	−14.3274	−0.656694
$477$	4.00061	0.183175
$478$	27.0547	1.23745
$479$	35.4518	1.61983	0.809917	−	0.586544i	$-0.199512\pi$
$479$	35.4518	1.61983	0.809917	+	0.586544i	$0.199512\pi$
$480$	15.9970	0.730162
$481$	−5.20017	−0.237107
$482$	42.0537	1.91549
$483$	−5.77206	−0.262638
$484$	−11.9166	−0.541663
$485$	−11.9303	−0.541726
$486$	−30.1233	−1.36642
$487$	10.0093	0.453562	0.226781	−	0.973946i	$-0.427180\pi$
$487$	10.0093	0.453562	0.226781	+	0.973946i	$0.427180\pi$
$488$	5.62201	0.254496
$489$	3.87347	0.175165
$490$	−7.98680	−0.360807
$491$	−0.753366	−0.0339989	−0.0169995	−	0.999855i	$-0.505411\pi$
$491$	−0.753366	−0.0339989	−0.0169995	+	0.999855i	$0.505411\pi$
$492$	26.4891	1.19422
$493$	−0.123459	−0.00556032
$494$	−15.7072	−0.706700
$495$	−4.13075	−0.185663
$496$	1.65207	0.0741801
$497$	−0.871846	−0.0391077
$498$	2.76710	0.123997
$499$	4.48053	0.200576	0.100288	−	0.994958i	$-0.468024\pi$
$499$	4.48053	0.200576	0.100288	+	0.994958i	$0.468024\pi$
$500$	28.9735	1.29574
$501$	3.84945	0.171981
$502$	−60.6348	−2.70626
$503$	−6.18239	−0.275659	−0.137830	−	0.990456i	$-0.544013\pi$
$503$	−6.18239	−0.275659	−0.137830	+	0.990456i	$0.544013\pi$
$504$	5.87005	0.261473
$505$	−5.99332	−0.266699
$506$	8.32453	0.370071
$507$	−2.09787	−0.0931699
$508$	−30.9698	−1.37406
$509$	8.33205	0.369312	0.184656	−	0.982803i	$-0.440883\pi$
$509$	8.33205	0.369312	0.184656	+	0.982803i	$0.440883\pi$
$510$	−12.9464	−0.573278
$511$	12.0141	0.531471
$512$	−12.6414	−0.558675
$513$	23.6429	1.04386
$514$	−24.5330	−1.08210
$515$	−18.1844	−0.801302
$516$	−38.0371	−1.67449
$517$	−5.08862	−0.223797
$518$	−22.5536	−0.990947
$519$	−33.4148	−1.46675
$520$	2.40189	0.105330
$521$	−4.87972	−0.213785	−0.106892	−	0.994271i	$-0.534090\pi$
$521$	−4.87972	−0.213785	−0.106892	+	0.994271i	$0.534090\pi$
$522$	0.155307	0.00679759
$523$	−42.1469	−1.84296	−0.921478	−	0.388431i	$-0.873017\pi$
$523$	−42.1469	−1.84296	−0.921478	+	0.388431i	$0.873017\pi$
$524$	−7.93449	−0.346620
$525$	−15.3319	−0.669137
$526$	−68.2232	−2.97467
$527$	−3.61333	−0.157399
$528$	6.29070	0.273768
$529$	−21.0015	−0.913107
$530$	7.09961	0.308388
$531$	−17.1314	−0.743441
$532$	−40.6875	−1.76403
$533$	−4.25711	−0.184396
$534$	−69.9414	−3.02666
$535$	−8.79032	−0.380039
$536$	−23.9484	−1.03441
$537$	32.0818	1.38443
$538$	−45.2621	−1.95139
$539$	−8.48791	−0.365600
$540$	−11.1006	−0.477694
$541$	6.86370	0.295094	0.147547	−	0.989055i	$-0.452862\pi$
$541$	6.86370	0.295094	0.147547	+	0.989055i	$0.452862\pi$
$542$	49.6875	2.13426
$543$	44.7671	1.92114
$544$	16.9626	0.727265
$545$	4.29619	0.184029
$546$	−9.09866	−0.389387
$547$	−36.2035	−1.54795	−0.773974	−	0.633217i	$-0.781734\pi$
$547$	−36.2035	−1.54795	−0.773974	+	0.633217i	$0.781734\pi$
$548$	10.2695	0.438692
$549$	−3.65905	−0.156164
$550$	22.1118	0.942850
$551$	−0.350605	−0.0149363
$552$	−6.38443	−0.271740
$553$	4.50603	0.191616
$554$	23.7038	1.00708
$555$	−12.1721	−0.516676
$556$	−18.0788	−0.766714
$557$	−37.2572	−1.57864	−0.789319	−	0.613983i	$-0.789566\pi$
$557$	−37.2572	−1.57864	−0.789319	+	0.613983i	$0.789566\pi$
$558$	4.54542	0.192423
$559$	6.11301	0.258553
$560$	−2.46423	−0.104133
$561$	−13.7587	−0.580894
$562$	−53.1404	−2.24159
$563$	−0.183521	−0.00773449	−0.00386724	−	0.999993i	$-0.501231\pi$
$563$	−0.183521	−0.00773449	−0.00386724	+	0.999993i	$0.501231\pi$
$564$	11.9827	0.504562
$565$	5.27600	0.221963
$566$	−14.5499	−0.611580
$567$	21.8760	0.918707
$568$	−0.964343	−0.0404629
$569$	3.25164	0.136316	0.0681580	−	0.997675i	$-0.478288\pi$
$569$	3.25164	0.136316	0.0681580	+	0.997675i	$0.478288\pi$
$570$	−36.7660	−1.53996
$571$	16.1936	0.677681	0.338840	−	0.940844i	$-0.389965\pi$
$571$	16.1936	0.677681	0.338840	+	0.940844i	$0.389965\pi$
$572$	7.83739	0.327698
$573$	20.2495	0.845936
$574$	−18.4634	−0.770649
$575$	5.30858	0.221383
$576$	−18.1584	−0.756598
$577$	−39.0247	−1.62462	−0.812309	−	0.583228i	$-0.801790\pi$
$577$	−39.0247	−1.62462	−0.812309	+	0.583228i	$0.801790\pi$
$578$	24.1559	1.00475
$579$	18.2298	0.757604
$580$	0.164613	0.00683518
$581$	−1.15195	−0.0477911
$582$	49.9881	2.07207
$583$	7.54505	0.312484
$584$	13.2887	0.549889
$585$	−1.56326	−0.0646327
$586$	−21.3491	−0.881922
$587$	32.4009	1.33733	0.668663	−	0.743565i	$-0.266867\pi$
$587$	32.4009	1.33733	0.668663	+	0.743565i	$0.266867\pi$
$588$	19.9873	0.824262
$589$	−10.2613	−0.422810
$590$	−30.4020	−1.25163
$591$	−21.1760	−0.871065
$592$	5.90117	0.242537
$593$	−17.6447	−0.724583	−0.362291	−	0.932065i	$-0.618006\pi$
$593$	−17.6447	−0.724583	−0.362291	+	0.932065i	$0.618006\pi$
$594$	−19.7519	−0.810431
$595$	5.38966	0.220954
$596$	67.4296	2.76203
$597$	−6.58588	−0.269542
$598$	3.15037	0.128828
$599$	−34.0824	−1.39257	−0.696284	−	0.717766i	$-0.745165\pi$
$599$	−34.0824	−1.39257	−0.696284	+	0.717766i	$0.745165\pi$
$600$	−16.9585	−0.692326
$601$	7.30524	0.297987	0.148993	−	0.988838i	$-0.452397\pi$
$601$	7.30524	0.297987	0.148993	+	0.988838i	$0.452397\pi$
$602$	26.5126	1.08057
$603$	15.5867	0.634738
$604$	−26.7414	−1.08809
$605$	4.48277	0.182251
$606$	25.1121	1.02011
$607$	13.5351	0.549374	0.274687	−	0.961534i	$-0.411426\pi$
$607$	13.5351	0.549374	0.274687	+	0.961534i	$0.411426\pi$
$608$	48.1712	1.95360
$609$	−0.203094	−0.00822978
$610$	−6.49348	−0.262913
$611$	−1.92576	−0.0779078
$612$	10.3142	0.416926
$613$	13.1736	0.532076	0.266038	−	0.963963i	$-0.414285\pi$
$613$	13.1736	0.532076	0.266038	+	0.963963i	$0.414285\pi$
$614$	42.2776	1.70619
$615$	−9.96465	−0.401813
$616$	11.0708	0.446055
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	76.1931	3.06493
$619$	−15.7170	−0.631720	−0.315860	−	0.948806i	$-0.602293\pi$
$619$	−15.7170	−0.631720	−0.315860	+	0.948806i	$0.602293\pi$
$620$	4.81779	0.193487
$621$	−4.74203	−0.190291
$622$	21.1127	0.846540
$623$	29.1169	1.16654
$624$	2.38067	0.0953033
$625$	7.87625	0.315050
$626$	−3.67807	−0.147005
$627$	−39.0727	−1.56041
$628$	53.1546	2.12110
$629$	−12.9068	−0.514626
$630$	−6.77997	−0.270120
$631$	34.0783	1.35664	0.678319	−	0.734768i	$-0.262709\pi$
$631$	34.0783	1.35664	0.678319	+	0.734768i	$0.262709\pi$
$632$	4.98408	0.198256
$633$	−22.2544	−0.884534
$634$	−47.7726	−1.89729
$635$	11.6502	0.462324
$636$	−17.7671	−0.704510
$637$	−3.21219	−0.127272
$638$	0.292905	0.0115962
$639$	0.627637	0.0248289
$640$	−16.9737	−0.670946
$641$	−49.5871	−1.95857	−0.979286	−	0.202481i	$-0.935100\pi$
$641$	−49.5871	−1.95857	−0.979286	+	0.202481i	$0.935100\pi$
$642$	36.8316	1.45363
$643$	−31.2135	−1.23094	−0.615470	−	0.788160i	$-0.711034\pi$
$643$	−31.2135	−1.23094	−0.615470	+	0.788160i	$0.711034\pi$
$644$	8.16063	0.321574
$645$	14.3088	0.563407
$646$	−38.9851	−1.53385
$647$	−46.0298	−1.80962	−0.904810	−	0.425815i	$-0.859987\pi$
$647$	−46.0298	−1.80962	−0.904810	+	0.425815i	$0.859987\pi$
$648$	24.1969	0.950545
$649$	−32.3095	−1.26826
$650$	8.36807	0.328223
$651$	−5.94403	−0.232965
$652$	−5.47638	−0.214472
$653$	−13.4085	−0.524715	−0.262358	−	0.964971i	$-0.584500\pi$
$653$	−13.4085	−0.524715	−0.262358	+	0.964971i	$0.584500\pi$
$654$	−18.0011	−0.703899
$655$	2.98479	0.116625
$656$	4.83098	0.188618
$657$	−8.64885	−0.337424
$658$	−8.35217	−0.325601
$659$	−21.1462	−0.823739	−0.411870	−	0.911243i	$-0.635124\pi$
$659$	−21.1462	−0.823739	−0.411870	+	0.911243i	$0.635124\pi$
$660$	18.3450	0.714080
$661$	7.83165	0.304616	0.152308	−	0.988333i	$-0.451329\pi$
$661$	7.83165	0.304616	0.152308	+	0.988333i	$0.451329\pi$
$662$	−68.1154	−2.64738
$663$	−5.20690	−0.202219
$664$	−1.27417	−0.0494474
$665$	15.3058	0.593534
$666$	16.2362	0.629139
$667$	0.0703203	0.00272281
$668$	−5.44241	−0.210573
$669$	−10.7613	−0.416057
$670$	27.6606	1.06862
$671$	−6.90088	−0.266406
$672$	27.9040	1.07642
$673$	0.461437	0.0177871	0.00889354	−	0.999960i	$-0.497169\pi$
$673$	0.461437	0.0177871	0.00889354	+	0.999960i	$0.497169\pi$
$674$	−28.9798	−1.11626
$675$	−12.5959	−0.484815
$676$	2.96601	0.114077
$677$	37.0573	1.42423	0.712113	−	0.702065i	$-0.247738\pi$
$677$	37.0573	1.42423	0.712113	+	0.702065i	$0.247738\pi$
$678$	−22.1065	−0.848996
$679$	−20.8102	−0.798624
$680$	5.96146	0.228612
$681$	−3.15130	−0.120758
$682$	8.57255	0.328260
$683$	36.0696	1.38016	0.690082	−	0.723731i	$-0.257574\pi$
$683$	36.0696	1.38016	0.690082	+	0.723731i	$0.257574\pi$
$684$	29.2907	1.11996
$685$	−3.86318	−0.147605
$686$	−44.2911	−1.69104
$687$	25.8646	0.986797
$688$	−6.93706	−0.264473
$689$	2.85538	0.108781
$690$	7.37409	0.280727
$691$	6.70549	0.255089	0.127544	−	0.991833i	$-0.459290\pi$
$691$	6.70549	0.255089	0.127544	+	0.991833i	$0.459290\pi$
$692$	47.2424	1.79588
$693$	−7.20535	−0.273709
$694$	50.2601	1.90785
$695$	6.80089	0.257972
$696$	−0.224641	−0.00851499
$697$	−10.5661	−0.400219
$698$	−53.6123	−2.02926
$699$	21.3112	0.806065
$700$	21.6764	0.819292
$701$	−36.7222	−1.38698	−0.693490	−	0.720466i	$-0.743928\pi$
$701$	−36.7222	−1.38698	−0.693490	+	0.720466i	$0.743928\pi$
$702$	−7.47499	−0.282125
$703$	−36.6533	−1.38240
$704$	−34.2462	−1.29070
$705$	−4.50763	−0.169767
$706$	−59.0450	−2.22219
$707$	−10.4543	−0.393173
$708$	76.0823	2.85935
$709$	21.0457	0.790387	0.395193	−	0.918598i	$-0.370678\pi$
$709$	21.0457	0.790387	0.395193	+	0.918598i	$0.370678\pi$
$710$	1.11383	0.0418012
$711$	−3.24386	−0.121654
$712$	32.2060	1.20697
$713$	2.05809	0.0770762
$714$	−22.5828	−0.845138
$715$	−2.94826	−0.110259
$716$	−45.3578	−1.69510
$717$	25.4694	0.951172
$718$	20.8411	0.777784
$719$	−31.4717	−1.17370	−0.586848	−	0.809697i	$-0.699631\pi$
$719$	−31.4717	−1.17370	−0.586848	+	0.809697i	$0.699631\pi$
$720$	1.77399	0.0661126
$721$	−31.7195	−1.18129
$722$	−68.3711	−2.54451
$723$	39.5895	1.47235
$724$	−63.2925	−2.35225
$725$	0.186786	0.00693707
$726$	−18.7829	−0.697098
$727$	−1.52070	−0.0563995	−0.0281998	−	0.999602i	$-0.508977\pi$
$727$	−1.52070	−0.0563995	−0.0281998	+	0.999602i	$0.508977\pi$
$728$	4.18967	0.155279
$729$	5.36251	0.198612
$730$	−15.3485	−0.568075
$731$	15.1724	0.561172
$732$	16.2502	0.600624
$733$	−18.0405	−0.666342	−0.333171	−	0.942866i	$-0.608119\pi$
$733$	−18.0405	−0.666342	−0.333171	+	0.942866i	$0.608119\pi$
$734$	71.1435	2.62595
$735$	−7.51880	−0.277335
$736$	−9.66162	−0.356132
$737$	29.3961	1.08282
$738$	13.2917	0.489275
$739$	−3.86883	−0.142317	−0.0711586	−	0.997465i	$-0.522670\pi$
$739$	−3.86883	−0.142317	−0.0711586	+	0.997465i	$0.522670\pi$
$740$	17.2091	0.632619
$741$	−14.7868	−0.543207
$742$	12.3840	0.454631
$743$	−12.7292	−0.466988	−0.233494	−	0.972358i	$-0.575016\pi$
$743$	−12.7292	−0.466988	−0.233494	+	0.972358i	$0.575016\pi$
$744$	−6.57465	−0.241038
$745$	−25.3656	−0.929325
$746$	21.0882	0.772094
$747$	0.829285	0.0303420
$748$	19.4523	0.711247
$749$	−15.3331	−0.560260
$750$	45.6680	1.66756
$751$	−13.4646	−0.491330	−0.245665	−	0.969355i	$-0.579006\pi$
$751$	−13.4646	−0.491330	−0.245665	+	0.969355i	$0.579006\pi$
$752$	2.18536	0.0796917
$753$	−57.0818	−2.08018
$754$	0.110848	0.00403684
$755$	10.0596	0.366105
$756$	−19.3630	−0.704226
$757$	20.2729	0.736832	0.368416	−	0.929661i	$-0.379900\pi$
$757$	20.2729	0.736832	0.368416	+	0.929661i	$0.379900\pi$
$758$	−32.4791	−1.17969
$759$	7.83674	0.284456
$760$	16.9297	0.614103
$761$	−2.48948	−0.0902435	−0.0451218	−	0.998981i	$-0.514368\pi$
$761$	−2.48948	−0.0902435	−0.0451218	+	0.998981i	$0.514368\pi$
$762$	−48.8145	−1.76836
$763$	7.49394	0.271299
$764$	−28.6291	−1.03577
$765$	−3.87998	−0.140281
$766$	75.9926	2.74572
$767$	−12.2273	−0.441503
$768$	16.7422	0.604132
$769$	−12.1961	−0.439803	−0.219902	−	0.975522i	$-0.570574\pi$
$769$	−12.1961	−0.439803	−0.219902	+	0.975522i	$0.570574\pi$
$770$	−12.7869	−0.460807
$771$	−23.0954	−0.831762
$772$	−25.7736	−0.927612
$773$	−5.36128	−0.192832	−0.0964160	−	0.995341i	$-0.530738\pi$
$773$	−5.36128	−0.192832	−0.0964160	+	0.995341i	$0.530738\pi$
$774$	−19.0863	−0.686042
$775$	5.46675	0.196371
$776$	−23.0181	−0.826300
$777$	−21.2320	−0.761694
$778$	−73.7871	−2.64540
$779$	−30.0061	−1.07508
$780$	6.94256	0.248584
$781$	1.18371	0.0423564
$782$	7.81917	0.279613
$783$	−0.166852	−0.00596279
$784$	3.64521	0.130186
$785$	−19.9957	−0.713676
$786$	−12.5063	−0.446086
$787$	−0.227609	−0.00811340	−0.00405670	−	0.999992i	$-0.501291\pi$
$787$	−0.227609	−0.00811340	−0.00405670	+	0.999992i	$0.501291\pi$
$788$	29.9390	1.06653
$789$	−64.2256	−2.28649
$790$	−5.75667	−0.204813
$791$	9.20303	0.327222
$792$	−7.96979	−0.283194
$793$	−2.61160	−0.0927405
$794$	10.9127	0.387279
$795$	6.68360	0.237043
$796$	9.31123	0.330028
$797$	−0.667487	−0.0236436	−0.0118218	−	0.999930i	$-0.503763\pi$
$797$	−0.667487	−0.0236436	−0.0118218	+	0.999930i	$0.503763\pi$
$798$	−64.1316	−2.27023
$799$	−4.77971	−0.169094
$800$	−25.6634	−0.907338
$801$	−20.9611	−0.740623
$802$	35.0583	1.23795
$803$	−16.3115	−0.575621
$804$	−69.2218	−2.44127
$805$	−3.06986	−0.108198
$806$	3.24423	0.114273
$807$	−42.6099	−1.49994
$808$	−11.5634	−0.406799
$809$	−20.2496	−0.711939	−0.355970	−	0.934498i	$-0.615849\pi$
$809$	−20.2496	−0.711939	−0.355970	+	0.934498i	$0.615849\pi$
$810$	−27.9477	−0.981982
$811$	−29.6930	−1.04266	−0.521332	−	0.853354i	$-0.674565\pi$
$811$	−29.6930	−1.04266	−0.521332	+	0.853354i	$0.674565\pi$
$812$	0.287138	0.0100766
$813$	46.7760	1.64051
$814$	30.6211	1.07327
$815$	2.06010	0.0721622
$816$	5.90881	0.206850
$817$	43.0873	1.50744
$818$	−13.0733	−0.457096
$819$	−2.72682	−0.0952828
$820$	14.0882	0.491981
$821$	−24.6566	−0.860520	−0.430260	−	0.902705i	$-0.641578\pi$
$821$	−24.6566	−0.860520	−0.430260	+	0.902705i	$0.641578\pi$
$822$	16.1868	0.564579
$823$	52.6876	1.83657	0.918287	−	0.395914i	$-0.129572\pi$
$823$	52.6876	1.83657	0.918287	+	0.395914i	$0.129572\pi$
$824$	−35.0847	−1.22223
$825$	20.8161	0.724724
$826$	−53.0309	−1.84518
$827$	−26.0073	−0.904362	−0.452181	−	0.891926i	$-0.649354\pi$
$827$	−26.0073	−0.904362	−0.452181	+	0.891926i	$0.649354\pi$
$828$	−5.87479	−0.204163
$829$	39.1046	1.35816	0.679080	−	0.734065i	$-0.262379\pi$
$829$	39.1046	1.35816	0.679080	+	0.734065i	$0.262379\pi$
$830$	1.47168	0.0510827
$831$	22.3148	0.774092
$832$	−12.9603	−0.449317
$833$	−7.97263	−0.276235
$834$	−28.4958	−0.986730
$835$	2.04732	0.0708505
$836$	55.2416	1.91057
$837$	−4.88331	−0.168792
$838$	−48.8548	−1.68766
$839$	−8.53239	−0.294571	−0.147285	−	0.989094i	$-0.547054\pi$
$839$	−8.53239	−0.294571	−0.147285	+	0.989094i	$0.547054\pi$
$840$	9.80679	0.338366
$841$	−28.9975	−0.999915
$842$	0.610626	0.0210436
$843$	−50.0266	−1.72301
$844$	31.4637	1.08302
$845$	−1.11575	−0.0383830
$846$	6.01268	0.206720
$847$	7.81939	0.268677
$848$	−3.24029	−0.111272
$849$	−13.6974	−0.470093
$850$	20.7694	0.712386
$851$	7.35148	0.252006
$852$	−2.78739	−0.0954945
$853$	37.3126	1.27756	0.638780	−	0.769390i	$-0.279440\pi$
$853$	37.3126	1.27756	0.638780	+	0.769390i	$0.279440\pi$
$854$	−11.3267	−0.387592
$855$	−11.0186	−0.376827
$856$	−16.9599	−0.579677
$857$	−30.7291	−1.04969	−0.524843	−	0.851199i	$-0.675876\pi$
$857$	−30.7291	−1.04969	−0.524843	+	0.851199i	$0.675876\pi$
$858$	12.3533	0.421734
$859$	−20.4159	−0.696583	−0.348292	−	0.937386i	$-0.613238\pi$
$859$	−20.4159	−0.696583	−0.348292	+	0.937386i	$0.613238\pi$
$860$	−20.2300	−0.689836
$861$	−17.3815	−0.592361
$862$	−83.8497	−2.85593
$863$	−16.6693	−0.567429	−0.283715	−	0.958909i	$-0.591567\pi$
$863$	−16.6693	−0.567429	−0.283715	+	0.958909i	$0.591567\pi$
$864$	22.9245	0.779906
$865$	−17.7716	−0.604252
$866$	13.2961	0.451820
$867$	22.7404	0.772305
$868$	8.40377	0.285243
$869$	−6.11785	−0.207534
$870$	0.259462	0.00879660
$871$	11.1248	0.376948
$872$	8.28899	0.280701
$873$	14.9812	0.507036
$874$	22.2053	0.751104
$875$	−19.0118	−0.642715
$876$	38.4103	1.29776
$877$	−26.1274	−0.882261	−0.441131	−	0.897443i	$-0.645422\pi$
$877$	−26.1274	−0.882261	−0.441131	+	0.897443i	$0.645422\pi$
$878$	80.0515	2.70161
$879$	−20.0981	−0.677892
$880$	3.34570	0.112784
$881$	−0.715902	−0.0241194	−0.0120597	−	0.999927i	$-0.503839\pi$
$881$	−0.715902	−0.0241194	−0.0120597	+	0.999927i	$0.503839\pi$
$882$	10.0292	0.337702
$883$	8.44911	0.284335	0.142168	−	0.989843i	$-0.454593\pi$
$883$	8.44911	0.284335	0.142168	+	0.989843i	$0.454593\pi$
$884$	7.36160	0.247597
$885$	−28.6206	−0.962070
$886$	0.580669	0.0195080
$887$	10.7174	0.359855	0.179928	−	0.983680i	$-0.442414\pi$
$887$	10.7174	0.359855	0.179928	+	0.983680i	$0.442414\pi$
$888$	−23.4846	−0.788091
$889$	20.3217	0.681567
$890$	−37.1982	−1.24689
$891$	−29.7012	−0.995026
$892$	15.2146	0.509421
$893$	−13.5736	−0.454225
$894$	106.282	3.55462
$895$	17.0627	0.570342
$896$	−29.6076	−0.989122
$897$	2.96577	0.0990240
$898$	−89.7214	−2.99404
$899$	0.0724155	0.00241519
$900$	−15.6047	−0.520158
$901$	7.08701	0.236103
$902$	25.0679	0.834669
$903$	24.9591	0.830586
$904$	10.1794	0.338562
$905$	23.8093	0.791449
$906$	−42.1497	−1.40033
$907$	−54.7313	−1.81732	−0.908662	−	0.417532i	$-0.862895\pi$
$907$	−54.7313	−1.81732	−0.908662	+	0.417532i	$0.862895\pi$
$908$	4.45536	0.147856
$909$	7.52597	0.249621
$910$	−4.83911	−0.160415
$911$	−25.7493	−0.853111	−0.426556	−	0.904461i	$-0.640273\pi$
$911$	−25.7493	−0.853111	−0.426556	+	0.904461i	$0.640273\pi$
$912$	16.7801	0.555645
$913$	1.56401	0.0517613
$914$	46.2380	1.52942
$915$	−6.11298	−0.202089
$916$	−36.5678	−1.20824
$917$	5.20643	0.171932
$918$	−18.5528	−0.612335
$919$	−20.9144	−0.689903	−0.344951	−	0.938621i	$-0.612105\pi$
$919$	−20.9144	−0.689903	−0.344951	+	0.938621i	$0.612105\pi$
$920$	−3.39555	−0.111948
$921$	39.8003	1.31146
$922$	−54.6052	−1.79833
$923$	0.447967	0.0147450
$924$	31.9996	1.05271
$925$	19.5272	0.642049
$926$	66.8971	2.19838
$927$	22.8347	0.749989
$928$	−0.339951	−0.0111594
$929$	31.9503	1.04826	0.524128	−	0.851640i	$-0.324391\pi$
$929$	31.9503	1.04826	0.524128	+	0.851640i	$0.324391\pi$
$930$	7.59379	0.249010
$931$	−22.6411	−0.742031
$932$	−30.1302	−0.986947
$933$	19.8755	0.650695
$934$	55.7784	1.82512
$935$	−7.31756	−0.239310
$936$	−3.01612	−0.0985849
$937$	−20.7257	−0.677079	−0.338540	−	0.940952i	$-0.609933\pi$
$937$	−20.7257	−0.677079	−0.338540	+	0.940952i	$0.609933\pi$
$938$	48.2490	1.57539
$939$	−3.46255	−0.112996
$940$	6.37297	0.207863
$941$	−22.7201	−0.740653	−0.370326	−	0.928902i	$-0.620754\pi$
$941$	−22.7201	−0.740653	−0.370326	+	0.928902i	$0.620754\pi$
$942$	83.7822	2.72977
$943$	6.01827	0.195982
$944$	13.8756	0.451612
$945$	7.28397	0.236948
$946$	−35.9963	−1.17034
$947$	54.4270	1.76864	0.884320	−	0.466881i	$-0.154622\pi$
$947$	54.4270	1.76864	0.884320	+	0.466881i	$0.154622\pi$
$948$	14.4063	0.467894
$949$	−6.17299	−0.200384
$950$	58.9821	1.91363
$951$	−44.9733	−1.45836
$952$	10.3987	0.337024
$953$	−18.9848	−0.614977	−0.307489	−	0.951552i	$-0.599489\pi$
$953$	−18.9848	−0.614977	−0.307489	+	0.951552i	$0.599489\pi$
$954$	−8.91517	−0.288639
$955$	10.7697	0.348499
$956$	−36.0091	−1.16462
$957$	0.275741	0.00891345
$958$	−79.0028	−2.55246
$959$	−6.73863	−0.217602
$960$	−30.3362	−0.979097
$961$	−28.8806	−0.931632
$962$	11.5883	0.373623
$963$	11.0382	0.355702
$964$	−55.9723	−1.80275
$965$	9.69549	0.312109
$966$	12.8628	0.413853
$967$	19.1002	0.614221	0.307111	−	0.951674i	$-0.400638\pi$
$967$	19.1002	0.614221	0.307111	+	0.951674i	$0.400638\pi$
$968$	8.64897	0.277989
$969$	−36.7007	−1.17900
$970$	26.5861	0.853628
$971$	8.80471	0.282556	0.141278	−	0.989970i	$-0.454879\pi$
$971$	8.80471	0.282556	0.141278	+	0.989970i	$0.454879\pi$
$972$	40.0932	1.28599
$973$	11.8629	0.380308
$974$	−22.3052	−0.714703
$975$	7.87773	0.252289
$976$	2.96365	0.0948640
$977$	52.1468	1.66832	0.834162	−	0.551519i	$-0.185952\pi$
$977$	52.1468	1.66832	0.834162	+	0.551519i	$0.185952\pi$
$978$	−8.63186	−0.276017
$979$	−39.5321	−1.26345
$980$	10.6302	0.339570
$981$	−5.39484	−0.172244
$982$	1.67884	0.0535740
$983$	−7.98141	−0.254568	−0.127284	−	0.991866i	$-0.540626\pi$
$983$	−7.98141	−0.254568	−0.127284	+	0.991866i	$0.540626\pi$
$984$	−19.2256	−0.612890
$985$	−11.2624	−0.358851
$986$	0.275123	0.00876171
$987$	−7.86276	−0.250274
$988$	20.9058	0.665103
$989$	−8.64196	−0.274798
$990$	9.20519	0.292560
$991$	−47.0376	−1.49420	−0.747099	−	0.664713i	$-0.768554\pi$
$991$	−47.0376	−1.49420	−0.747099	+	0.664713i	$0.768554\pi$
$992$	−9.94948	−0.315896
$993$	−64.1241	−2.03492
$994$	1.94287	0.0616241
$995$	−3.50269	−0.111043
$996$	−3.68293	−0.116698
$997$	1.12498	0.0356285	0.0178142	−	0.999841i	$-0.494329\pi$
$997$	1.12498	0.0356285	0.0178142	+	0.999841i	$0.494329\pi$
$998$	−9.98466	−0.316059
$999$	−17.4431	−0.551876

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8021.2.a.a.1.17	✓	134

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.17	✓	134	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:	\( N \)	\(=\)	\( 8021 = 13 \cdot 617 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8021.a (trivial)

\(f(q)\)	\(=\)	\(q-2.22845 q^{2} -2.09787 q^{3} +2.96601 q^{4} -1.11575 q^{5} +4.67502 q^{6} -1.94623 q^{7} -2.15271 q^{8} +1.40108 q^{9} +O(q^{10})\)	\(q-2.22845 q^{2} -2.09787 q^{3} +2.96601 q^{4} -1.11575 q^{5} +4.67502 q^{6} -1.94623 q^{7} -2.15271 q^{8} +1.40108 q^{9} +2.48640 q^{10} +2.64240 q^{11} -6.22232 q^{12} +1.00000 q^{13} +4.33708 q^{14} +2.34071 q^{15} -1.13480 q^{16} +2.48199 q^{17} -3.12224 q^{18} +7.04847 q^{19} -3.30933 q^{20} +4.08294 q^{21} -5.88847 q^{22} -1.41370 q^{23} +4.51612 q^{24} -3.75510 q^{25} -2.22845 q^{26} +3.35434 q^{27} -5.77253 q^{28} -0.0497420 q^{29} -5.21616 q^{30} -1.45582 q^{31} +6.83428 q^{32} -5.54343 q^{33} -5.53100 q^{34} +2.17151 q^{35} +4.15561 q^{36} -5.20017 q^{37} -15.7072 q^{38} -2.09787 q^{39} +2.40189 q^{40} -4.25711 q^{41} -9.09866 q^{42} +6.11301 q^{43} +7.83739 q^{44} -1.56326 q^{45} +3.15037 q^{46} -1.92576 q^{47} +2.38067 q^{48} -3.21219 q^{49} +8.36807 q^{50} -5.20690 q^{51} +2.96601 q^{52} +2.85538 q^{53} -7.47499 q^{54} -2.94826 q^{55} +4.18967 q^{56} -14.7868 q^{57} +0.110848 q^{58} -12.2273 q^{59} +6.94256 q^{60} -2.61160 q^{61} +3.24423 q^{62} -2.72682 q^{63} -12.9603 q^{64} -1.11575 q^{65} +12.3533 q^{66} +11.1248 q^{67} +7.36160 q^{68} +2.96577 q^{69} -4.83911 q^{70} +0.447967 q^{71} -3.01612 q^{72} -6.17299 q^{73} +11.5883 q^{74} +7.87773 q^{75} +20.9058 q^{76} -5.14272 q^{77} +4.67502 q^{78} -2.31526 q^{79} +1.26616 q^{80} -11.2402 q^{81} +9.48677 q^{82} +0.591891 q^{83} +12.1101 q^{84} -2.76928 q^{85} -13.6226 q^{86} +0.104353 q^{87} -5.68833 q^{88} -14.9607 q^{89} +3.48364 q^{90} -1.94623 q^{91} -4.19305 q^{92} +3.05413 q^{93} +4.29146 q^{94} -7.86434 q^{95} -14.3375 q^{96} +10.6926 q^{97} +7.15823 q^{98} +3.70221 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9} - 33 q^{10} - 47 q^{11} - 53 q^{12} + 134 q^{13} - 28 q^{14} - 30 q^{15} + 30 q^{16} - 17 q^{17} - 14 q^{18} - 87 q^{19} - 12 q^{20} - 24 q^{21} - 52 q^{22} - 44 q^{23} - 36 q^{24} + 58 q^{25} - 6 q^{26} - 117 q^{27} - 71 q^{28} - 42 q^{29} - 21 q^{30} - 82 q^{31} - 31 q^{32} + 12 q^{33} - 30 q^{34} - 54 q^{35} + 32 q^{36} - 55 q^{37} - 12 q^{38} - 33 q^{39} - 86 q^{40} - 16 q^{41} + 6 q^{42} - 148 q^{43} - 54 q^{44} - 24 q^{45} - 57 q^{46} - 21 q^{47} - 82 q^{48} + 12 q^{49} - 17 q^{50} - 123 q^{51} + 98 q^{52} - 17 q^{53} - 10 q^{54} - 148 q^{55} - 47 q^{56} - q^{57} - 58 q^{58} - 64 q^{59} - 16 q^{60} - 112 q^{61} - 15 q^{62} - 58 q^{63} - 65 q^{64} - 8 q^{65} - 20 q^{66} - 110 q^{67} - 8 q^{68} - 57 q^{69} - 40 q^{70} - 78 q^{71} - 28 q^{72} - 43 q^{73} - 52 q^{74} - 150 q^{75} - 96 q^{76} - 24 q^{77} - 16 q^{78} - 228 q^{79} + 20 q^{80} + 54 q^{81} - 89 q^{82} - 12 q^{83} + 6 q^{84} - 77 q^{85} + 29 q^{86} - 77 q^{87} - 95 q^{88} - 32 q^{89} - 46 q^{90} - 32 q^{91} - 62 q^{92} - 9 q^{93} - 87 q^{94} - 61 q^{95} - 54 q^{96} - 38 q^{97} + 6 q^{98} - 193 q^{99}+O(q^{100}) \) 134 * q - 6 * q^2 - 33 * q^3 + 98 * q^4 - 8 * q^5 - 16 * q^6 - 32 * q^7 - 15 * q^8 + 101 * q^9 - 33 * q^10 - 47 * q^11 - 53 * q^12 + 134 * q^13 - 28 * q^14 - 30 * q^15 + 30 * q^16 - 17 * q^17 - 14 * q^18 - 87 * q^19 - 12 * q^20 - 24 * q^21 - 52 * q^22 - 44 * q^23 - 36 * q^24 + 58 * q^25 - 6 * q^26 - 117 * q^27 - 71 * q^28 - 42 * q^29 - 21 * q^30 - 82 * q^31 - 31 * q^32 + 12 * q^33 - 30 * q^34 - 54 * q^35 + 32 * q^36 - 55 * q^37 - 12 * q^38 - 33 * q^39 - 86 * q^40 - 16 * q^41 + 6 * q^42 - 148 * q^43 - 54 * q^44 - 24 * q^45 - 57 * q^46 - 21 * q^47 - 82 * q^48 + 12 * q^49 - 17 * q^50 - 123 * q^51 + 98 * q^52 - 17 * q^53 - 10 * q^54 - 148 * q^55 - 47 * q^56 - q^57 - 58 * q^58 - 64 * q^59 - 16 * q^60 - 112 * q^61 - 15 * q^62 - 58 * q^63 - 65 * q^64 - 8 * q^65 - 20 * q^66 - 110 * q^67 - 8 * q^68 - 57 * q^69 - 40 * q^70 - 78 * q^71 - 28 * q^72 - 43 * q^73 - 52 * q^74 - 150 * q^75 - 96 * q^76 - 24 * q^77 - 16 * q^78 - 228 * q^79 + 20 * q^80 + 54 * q^81 - 89 * q^82 - 12 * q^83 + 6 * q^84 - 77 * q^85 + 29 * q^86 - 77 * q^87 - 95 * q^88 - 32 * q^89 - 46 * q^90 - 32 * q^91 - 62 * q^92 - 9 * q^93 - 87 * q^94 - 61 * q^95 - 54 * q^96 - 38 * q^97 + 6 * q^98 - 193 * q^99

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