LMFDB - Embedded newform 8021.2.a.a.1.1

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			1.1
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)

$f(q)$	$=$	$q-2.76381 q^{2} -0.591714 q^{3} +5.63866 q^{4} +2.62273 q^{5} +1.63539 q^{6} +1.07036 q^{7} -10.0566 q^{8} -2.64987 q^{9} +O(q^{10})$	\(q-2.76381 q^{2} -0.591714 q^{3} +5.63866 q^{4} +2.62273 q^{5} +1.63539 q^{6} +1.07036 q^{7} -10.0566 q^{8} -2.64987 q^{9} -7.24873 q^{10} -0.657947 q^{11} -3.33648 q^{12} +1.00000 q^{13} -2.95826 q^{14} -1.55191 q^{15} +16.5172 q^{16} -2.81377 q^{17} +7.32376 q^{18} +2.17808 q^{19} +14.7887 q^{20} -0.633345 q^{21} +1.81844 q^{22} -1.05300 q^{23} +5.95062 q^{24} +1.87870 q^{25} -2.76381 q^{26} +3.34311 q^{27} +6.03537 q^{28} +3.46541 q^{29} +4.28918 q^{30} -8.96535 q^{31} -25.5372 q^{32} +0.389317 q^{33} +7.77673 q^{34} +2.80725 q^{35} -14.9417 q^{36} -9.21184 q^{37} -6.01980 q^{38} -0.591714 q^{39} -26.3757 q^{40} +2.58055 q^{41} +1.75045 q^{42} +3.94121 q^{43} -3.70994 q^{44} -6.94990 q^{45} +2.91030 q^{46} +11.5057 q^{47} -9.77345 q^{48} -5.85434 q^{49} -5.19238 q^{50} +1.66495 q^{51} +5.63866 q^{52} +2.79476 q^{53} -9.23973 q^{54} -1.72562 q^{55} -10.7641 q^{56} -1.28880 q^{57} -9.57773 q^{58} +2.89352 q^{59} -8.75067 q^{60} -4.99394 q^{61} +24.7785 q^{62} -2.83631 q^{63} +37.5458 q^{64} +2.62273 q^{65} -1.07600 q^{66} +0.939044 q^{67} -15.8659 q^{68} +0.623077 q^{69} -7.75872 q^{70} +3.82129 q^{71} +26.6487 q^{72} -3.07261 q^{73} +25.4598 q^{74} -1.11166 q^{75} +12.2814 q^{76} -0.704238 q^{77} +1.63539 q^{78} -11.1678 q^{79} +43.3201 q^{80} +5.97146 q^{81} -7.13215 q^{82} +4.05903 q^{83} -3.57122 q^{84} -7.37975 q^{85} -10.8928 q^{86} -2.05053 q^{87} +6.61670 q^{88} +4.43124 q^{89} +19.2082 q^{90} +1.07036 q^{91} -5.93752 q^{92} +5.30493 q^{93} -31.7996 q^{94} +5.71251 q^{95} +15.1107 q^{96} +7.68728 q^{97} +16.1803 q^{98} +1.74348 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76381	−1.95431	−0.977155	−	0.212526i	$-0.931831\pi$
$2$	−2.76381	−1.95431	−0.977155	+	0.212526i	$0.931831\pi$
$3$	−0.591714	−0.341626	−0.170813	−	0.985303i	$-0.554639\pi$
$3$	−0.591714	−0.341626	−0.170813	+	0.985303i	$0.554639\pi$
$4$	5.63866	2.81933
$5$	2.62273	1.17292	0.586460	−	0.809978i	$-0.300521\pi$
$5$	2.62273	1.17292	0.586460	+	0.809978i	$0.300521\pi$
$6$	1.63539	0.667644
$7$	1.07036	0.404556	0.202278	−	0.979328i	$-0.435165\pi$
$7$	1.07036	0.404556	0.202278	+	0.979328i	$0.435165\pi$
$8$	−10.0566	−3.55554
$9$	−2.64987	−0.883291
$10$	−7.24873	−2.29225
$11$	−0.657947	−0.198379	−0.0991893	−	0.995069i	$-0.531625\pi$
$11$	−0.657947	−0.198379	−0.0991893	+	0.995069i	$0.531625\pi$
$12$	−3.33648	−0.963158
$13$	1.00000	0.277350
$13$	1.00000	0.277350
$14$	−2.95826	−0.790629
$15$	−1.55191	−0.400700
$16$	16.5172	4.12929
$17$	−2.81377	−0.682439	−0.341220	−	0.939984i	$-0.610840\pi$
$17$	−2.81377	−0.682439	−0.341220	+	0.939984i	$0.610840\pi$
$18$	7.32376	1.72623
$19$	2.17808	0.499686	0.249843	−	0.968286i	$-0.419621\pi$
$19$	2.17808	0.499686	0.249843	+	0.968286i	$0.419621\pi$
$20$	14.7887	3.30685
$21$	−0.633345	−0.138207
$22$	1.81844	0.387693
$23$	−1.05300	−0.219566	−0.109783	−	0.993956i	$-0.535016\pi$
$23$	−1.05300	−0.219566	−0.109783	+	0.993956i	$0.535016\pi$
$24$	5.95062	1.21467
$25$	1.87870	0.375741
$26$	−2.76381	−0.542028
$27$	3.34311	0.643382
$28$	6.03537	1.14058
$29$	3.46541	0.643510	0.321755	−	0.946823i	$-0.395727\pi$
$29$	3.46541	0.643510	0.321755	+	0.946823i	$0.395727\pi$
$30$	4.28918	0.783093
$31$	−8.96535	−1.61022	−0.805112	−	0.593123i	$-0.797895\pi$
$31$	−8.96535	−1.61022	−0.805112	+	0.593123i	$0.797895\pi$
$32$	−25.5372	−4.51439
$33$	0.389317	0.0677714
$34$	7.77673	1.33370
$35$	2.80725	0.474512
$36$	−14.9417	−2.49029
$37$	−9.21184	−1.51442	−0.757209	−	0.653173i	$-0.773438\pi$
$37$	−9.21184	−1.51442	−0.757209	+	0.653173i	$0.773438\pi$
$38$	−6.01980	−0.976541
$39$	−0.591714	−0.0947501
$40$	−26.3757	−4.17036
$41$	2.58055	0.403014	0.201507	−	0.979487i	$-0.435416\pi$
$41$	2.58055	0.403014	0.201507	+	0.979487i	$0.435416\pi$
$42$	1.75045	0.270100
$43$	3.94121	0.601029	0.300515	−	0.953777i	$-0.402842\pi$
$43$	3.94121	0.601029	0.300515	+	0.953777i	$0.402842\pi$
$44$	−3.70994	−0.559295
$45$	−6.94990	−1.03603
$46$	2.91030	0.429101
$47$	11.5057	1.67828	0.839138	−	0.543918i	$-0.183060\pi$
$47$	11.5057	1.67828	0.839138	+	0.543918i	$0.183060\pi$
$48$	−9.77345	−1.41068
$49$	−5.85434	−0.836334
$50$	−5.19238	−0.734314
$51$	1.66495	0.233139
$52$	5.63866	0.781942
$53$	2.79476	0.383890	0.191945	−	0.981406i	$-0.438520\pi$
$53$	2.79476	0.383890	0.191945	+	0.981406i	$0.438520\pi$
$54$	−9.23973	−1.25737
$55$	−1.72562	−0.232682
$56$	−10.7641	−1.43842
$57$	−1.28880	−0.170706
$58$	−9.57773	−1.25762
$59$	2.89352	0.376704	0.188352	−	0.982102i	$-0.439685\pi$
$59$	2.89352	0.376704	0.188352	+	0.982102i	$0.439685\pi$
$60$	−8.75067	−1.12971
$61$	−4.99394	−0.639408	−0.319704	−	0.947517i	$-0.603584\pi$
$61$	−4.99394	−0.639408	−0.319704	+	0.947517i	$0.603584\pi$
$62$	24.7785	3.14688
$63$	−2.83631	−0.357341
$64$	37.5458	4.69322
$65$	2.62273	0.325309
$66$	−1.07600	−0.132446
$67$	0.939044	0.114722	0.0573612	−	0.998353i	$-0.481731\pi$
$67$	0.939044	0.114722	0.0573612	+	0.998353i	$0.481731\pi$
$68$	−15.8659	−1.92402
$69$	0.623077	0.0750096
$70$	−7.75872	−0.927344
$71$	3.82129	0.453503	0.226752	−	0.973953i	$-0.427189\pi$
$71$	3.82129	0.453503	0.226752	+	0.973953i	$0.427189\pi$
$72$	26.6487	3.14058
$73$	−3.07261	−0.359622	−0.179811	−	0.983701i	$-0.557549\pi$
$73$	−3.07261	−0.359622	−0.179811	+	0.983701i	$0.557549\pi$
$74$	25.4598	2.95964
$75$	−1.11166	−0.128363
$76$	12.2814	1.40878
$77$	−0.704238	−0.0802553
$78$	1.63539	0.185171
$79$	−11.1678	−1.25647	−0.628236	−	0.778023i	$-0.716223\pi$
$79$	−11.1678	−1.25647	−0.628236	+	0.778023i	$0.716223\pi$
$80$	43.3201	4.84333
$81$	5.97146	0.663495
$82$	−7.13215	−0.787614
$83$	4.05903	0.445537	0.222768	−	0.974871i	$-0.428491\pi$
$83$	4.05903	0.445537	0.222768	+	0.974871i	$0.428491\pi$
$84$	−3.57122	−0.389652
$85$	−7.37975	−0.800446
$86$	−10.8928	−1.17460
$87$	−2.05053	−0.219840
$88$	6.61670	0.705343
$89$	4.43124	0.469711	0.234855	−	0.972030i	$-0.424538\pi$
$89$	4.43124	0.469711	0.234855	+	0.972030i	$0.424538\pi$
$90$	19.2082	2.02472
$91$	1.07036	0.112204
$92$	−5.93752	−0.619030
$93$	5.30493	0.550095
$94$	−31.7996	−3.27987
$95$	5.71251	0.586091
$96$	15.1107	1.54223
$97$	7.68728	0.780525	0.390263	−	0.920704i	$-0.372384\pi$
$97$	7.68728	0.780525	0.390263	+	0.920704i	$0.372384\pi$
$98$	16.1803	1.63446
$99$	1.74348	0.175226
$100$	10.5934	1.05934
$101$	6.13759	0.610713	0.305357	−	0.952238i	$-0.401224\pi$
$101$	6.13759	0.610713	0.305357	+	0.952238i	$0.401224\pi$
$102$	−4.60160	−0.455627
$103$	7.87324	0.775773	0.387886	−	0.921707i	$-0.373205\pi$
$103$	7.87324	0.775773	0.387886	+	0.921707i	$0.373205\pi$
$104$	−10.0566	−0.986129
$105$	−1.66109	−0.162106
$106$	−7.72420	−0.750241
$107$	7.37245	0.712721	0.356361	−	0.934349i	$-0.384017\pi$
$107$	7.37245	0.712721	0.356361	+	0.934349i	$0.384017\pi$
$108$	18.8507	1.81391
$109$	−9.85633	−0.944065	−0.472033	−	0.881581i	$-0.656480\pi$
$109$	−9.85633	−0.944065	−0.472033	+	0.881581i	$0.656480\pi$
$110$	4.76928	0.454733
$111$	5.45078	0.517365
$112$	17.6793	1.67053
$113$	16.6941	1.57045	0.785227	−	0.619209i	$-0.212546\pi$
$113$	16.6941	1.57045	0.785227	+	0.619209i	$0.212546\pi$
$114$	3.56200	0.333612
$115$	−2.76174	−0.257534
$116$	19.5403	1.81427
$117$	−2.64987	−0.244981
$118$	−7.99715	−0.736198
$119$	−3.01173	−0.276085
$120$	15.6069	1.42471
$121$	−10.5671	−0.960646
$122$	13.8023	1.24960
$123$	−1.52695	−0.137680
$124$	−50.5526	−4.53975
$125$	−8.18631	−0.732206
$126$	7.83902	0.698356
$127$	1.87527	0.166404	0.0832018	−	0.996533i	$-0.473485\pi$
$127$	1.87527	0.166404	0.0832018	+	0.996533i	$0.473485\pi$
$128$	−52.6950	−4.65763
$129$	−2.33207	−0.205327
$130$	−7.24873	−0.635756
$131$	−15.1950	−1.32759	−0.663797	−	0.747913i	$-0.731056\pi$
$131$	−15.1950	−1.32759	−0.663797	+	0.747913i	$0.731056\pi$
$132$	2.19523	0.191070
$133$	2.33132	0.202151
$134$	−2.59534	−0.224203
$135$	8.76807	0.754636
$136$	28.2969	2.42644
$137$	4.25230	0.363298	0.181649	−	0.983363i	$-0.441856\pi$
$137$	4.25230	0.363298	0.181649	+	0.983363i	$0.441856\pi$
$138$	−1.72207	−0.146592
$139$	−4.19415	−0.355743	−0.177872	−	0.984054i	$-0.556921\pi$
$139$	−4.19415	−0.355743	−0.177872	+	0.984054i	$0.556921\pi$
$140$	15.8291	1.33781
$141$	−6.80808	−0.573344
$142$	−10.5613	−0.886286
$143$	−0.657947	−0.0550203
$144$	−43.7684	−3.64737
$145$	9.08882	0.754785
$146$	8.49213	0.702813
$147$	3.46410	0.285714
$148$	−51.9425	−4.26964
$149$	−2.17742	−0.178381	−0.0891907	−	0.996015i	$-0.528428\pi$
$149$	−2.17742	−0.178381	−0.0891907	+	0.996015i	$0.528428\pi$
$150$	3.07241	0.250861
$151$	12.2715	0.998641	0.499320	−	0.866417i	$-0.333583\pi$
$151$	12.2715	0.998641	0.499320	+	0.866417i	$0.333583\pi$
$152$	−21.9040	−1.77665
$153$	7.45613	0.602793
$154$	1.94638	0.156844
$155$	−23.5137	−1.88866
$156$	−3.33648	−0.267132
$157$	−21.1098	−1.68475	−0.842373	−	0.538894i	$-0.818842\pi$
$157$	−21.1098	−1.68475	−0.842373	+	0.538894i	$0.818842\pi$
$158$	30.8656	2.45554
$159$	−1.65370	−0.131147
$160$	−66.9772	−5.29501
$161$	−1.12709	−0.0888269
$162$	−16.5040	−1.29668
$163$	−13.2174	−1.03526	−0.517632	−	0.855604i	$-0.673186\pi$
$163$	−13.2174	−1.03526	−0.517632	+	0.855604i	$0.673186\pi$
$164$	14.5508	1.13623
$165$	1.02107	0.0794904
$166$	−11.2184	−0.870718
$167$	−16.7542	−1.29648	−0.648239	−	0.761437i	$-0.724494\pi$
$167$	−16.7542	−1.29648	−0.648239	+	0.761437i	$0.724494\pi$
$168$	6.36928	0.491401
$169$	1.00000	0.0769231
$170$	20.3962	1.56432
$171$	−5.77163	−0.441368
$172$	22.2232	1.69450
$173$	6.70092	0.509462	0.254731	−	0.967012i	$-0.418013\pi$
$173$	6.70092	0.509462	0.254731	+	0.967012i	$0.418013\pi$
$174$	5.66728	0.429636
$175$	2.01088	0.152008
$176$	−10.8674	−0.819164
$177$	−1.71214	−0.128692
$178$	−12.2471	−0.917961
$179$	−10.7996	−0.807198	−0.403599	−	0.914936i	$-0.632241\pi$
$179$	−10.7996	−0.807198	−0.403599	+	0.914936i	$0.632241\pi$
$180$	−39.1881	−2.92091
$181$	8.79495	0.653723	0.326862	−	0.945072i	$-0.394009\pi$
$181$	8.79495	0.653723	0.326862	+	0.945072i	$0.394009\pi$
$182$	−2.95826	−0.219281
$183$	2.95499	0.218439
$184$	10.5896	0.780676
$185$	−24.1602	−1.77629
$186$	−14.6618	−1.07506
$187$	1.85131	0.135381
$188$	64.8767	4.73162
$189$	3.57832	0.260284
$190$	−15.7883	−1.14540
$191$	−10.2555	−0.742062	−0.371031	−	0.928621i	$-0.620996\pi$
$191$	−10.2555	−0.742062	−0.371031	+	0.928621i	$0.620996\pi$
$192$	−22.2164	−1.60333
$193$	−25.0295	−1.80166	−0.900830	−	0.434173i	$-0.857041\pi$
$193$	−25.0295	−1.80166	−0.900830	+	0.434173i	$0.857041\pi$
$194$	−21.2462	−1.52539
$195$	−1.55191	−0.111134
$196$	−33.0106	−2.35790
$197$	−6.47001	−0.460969	−0.230485	−	0.973076i	$-0.574031\pi$
$197$	−6.47001	−0.460969	−0.230485	+	0.973076i	$0.574031\pi$
$198$	−4.81865	−0.342446
$199$	−2.16863	−0.153730	−0.0768651	−	0.997042i	$-0.524491\pi$
$199$	−2.16863	−0.153730	−0.0768651	+	0.997042i	$0.524491\pi$
$200$	−18.8933	−1.33596
$201$	−0.555646	−0.0391922
$202$	−16.9632	−1.19352
$203$	3.70922	0.260336
$204$	9.38807	0.657297
$205$	6.76807	0.472703
$206$	−21.7602	−1.51610
$207$	2.79032	0.193941
$208$	16.5172	1.14526
$209$	−1.43306	−0.0991269
$210$	4.59095	0.316805
$211$	−17.7708	−1.22339	−0.611695	−	0.791094i	$-0.709512\pi$
$211$	−17.7708	−1.22339	−0.611695	+	0.791094i	$0.709512\pi$
$212$	15.7587	1.08231
$213$	−2.26111	−0.154929
$214$	−20.3761	−1.39288
$215$	10.3367	0.704959
$216$	−33.6203	−2.28757
$217$	−9.59611	−0.651426
$218$	27.2411	1.84500
$219$	1.81811	0.122856
$220$	−9.73017	−0.656008
$221$	−2.81377	−0.189275
$222$	−15.0649	−1.01109
$223$	6.59973	0.441951	0.220975	−	0.975279i	$-0.429076\pi$
$223$	6.59973	0.441951	0.220975	+	0.975279i	$0.429076\pi$
$224$	−27.3339	−1.82632
$225$	−4.97833	−0.331888
$226$	−46.1395	−3.06915
$227$	−4.31146	−0.286161	−0.143081	−	0.989711i	$-0.545701\pi$
$227$	−4.31146	−0.286161	−0.143081	+	0.989711i	$0.545701\pi$
$228$	−7.26711	−0.481276
$229$	−26.0882	−1.72396	−0.861978	−	0.506945i	$-0.830775\pi$
$229$	−26.0882	−1.72396	−0.861978	+	0.506945i	$0.830775\pi$
$230$	7.63293	0.503301
$231$	0.416708	0.0274173
$232$	−34.8501	−2.28802
$233$	0.0653371	0.00428037	0.00214019	−	0.999998i	$-0.499319\pi$
$233$	0.0653371	0.00428037	0.00214019	+	0.999998i	$0.499319\pi$
$234$	7.32376	0.478769
$235$	30.1763	1.96848
$236$	16.3156	1.06205
$237$	6.60813	0.429244
$238$	8.32387	0.539556
$239$	−8.00371	−0.517717	−0.258859	−	0.965915i	$-0.583346\pi$
$239$	−8.00371	−0.517717	−0.258859	+	0.965915i	$0.583346\pi$
$240$	−25.6331	−1.65461
$241$	−3.55639	−0.229087	−0.114544	−	0.993418i	$-0.536541\pi$
$241$	−3.55639	−0.229087	−0.114544	+	0.993418i	$0.536541\pi$
$242$	29.2055	1.87740
$243$	−13.5627	−0.870050
$244$	−28.1591	−1.80270
$245$	−15.3543	−0.980953
$246$	4.22019	0.269070
$247$	2.17808	0.138588
$248$	90.1607	5.72521
$249$	−2.40179	−0.152207
$250$	22.6254	1.43096
$251$	−17.7003	−1.11723	−0.558617	−	0.829426i	$-0.688668\pi$
$251$	−17.7003	−1.11723	−0.558617	+	0.829426i	$0.688668\pi$
$252$	−15.9930	−1.00746
$253$	0.692820	0.0435572
$254$	−5.18291	−0.325205
$255$	4.36670	0.273454
$256$	70.5477	4.40923
$257$	−16.2614	−1.01436	−0.507179	−	0.861841i	$-0.669312\pi$
$257$	−16.2614	−1.01436	−0.507179	+	0.861841i	$0.669312\pi$
$258$	6.44541	0.401274
$259$	−9.85995	−0.612667
$260$	14.7887	0.917155
$261$	−9.18289	−0.568407
$262$	41.9962	2.59453
$263$	2.64511	0.163104	0.0815522	−	0.996669i	$-0.474012\pi$
$263$	2.64511	0.163104	0.0815522	+	0.996669i	$0.474012\pi$
$264$	−3.91520	−0.240964
$265$	7.32991	0.450273
$266$	−6.44333	−0.395066
$267$	−2.62203	−0.160466
$268$	5.29495	0.323441
$269$	22.0815	1.34633	0.673166	−	0.739491i	$-0.264934\pi$
$269$	22.0815	1.34633	0.673166	+	0.739491i	$0.264934\pi$
$270$	−24.2333	−1.47479
$271$	3.29159	0.199950	0.0999750	−	0.994990i	$-0.468124\pi$
$271$	3.29159	0.199950	0.0999750	+	0.994990i	$0.468124\pi$
$272$	−46.4755	−2.81799
$273$	−0.633345	−0.0383318
$274$	−11.7526	−0.709998
$275$	−1.23609	−0.0745389
$276$	3.51332	0.211477
$277$	29.6685	1.78261	0.891303	−	0.453408i	$-0.149792\pi$
$277$	29.6685	1.78261	0.891303	+	0.453408i	$0.149792\pi$
$278$	11.5918	0.695233
$279$	23.7570	1.42230
$280$	−28.2313	−1.68715
$281$	5.42150	0.323419	0.161710	−	0.986838i	$-0.448299\pi$
$281$	5.42150	0.323419	0.161710	+	0.986838i	$0.448299\pi$
$282$	18.8163	1.12049
$283$	20.6290	1.22627	0.613134	−	0.789979i	$-0.289908\pi$
$283$	20.6290	1.22627	0.613134	+	0.789979i	$0.289908\pi$
$284$	21.5469	1.27858
$285$	−3.38017	−0.200224
$286$	1.81844	0.107527
$287$	2.76210	0.163042
$288$	67.6705	3.98752
$289$	−9.08271	−0.534277
$290$	−25.1198	−1.47508
$291$	−4.54868	−0.266648
$292$	−17.3254	−1.01389
$293$	15.5022	0.905648	0.452824	−	0.891600i	$-0.350417\pi$
$293$	15.5022	0.905648	0.452824	+	0.891600i	$0.350417\pi$
$294$	−9.57411	−0.558374
$295$	7.58892	0.441844
$296$	92.6396	5.38457
$297$	−2.19959	−0.127633
$298$	6.01799	0.348613
$299$	−1.05300	−0.0608967
$300$	−6.26825	−0.361898
$301$	4.21850	0.243150
$302$	−33.9161	−1.95165
$303$	−3.63170	−0.208636
$304$	35.9757	2.06335
$305$	−13.0977	−0.749975
$306$	−20.6074	−1.17804
$307$	−0.326751	−0.0186487	−0.00932434	−	0.999957i	$-0.502968\pi$
$307$	−0.326751	−0.0186487	−0.00932434	+	0.999957i	$0.502968\pi$
$308$	−3.97096	−0.226266
$309$	−4.65871	−0.265025
$310$	64.9874	3.69104
$311$	−32.2087	−1.82639	−0.913195	−	0.407522i	$-0.866393\pi$
$311$	−32.2087	−1.82639	−0.913195	+	0.407522i	$0.866393\pi$
$312$	5.95062	0.336888
$313$	−31.5973	−1.78598	−0.892991	−	0.450074i	$-0.851398\pi$
$313$	−31.5973	−1.78598	−0.892991	+	0.450074i	$0.851398\pi$
$314$	58.3436	3.29252
$315$	−7.43886	−0.419132
$316$	−62.9712	−3.54241
$317$	−24.1963	−1.35900	−0.679501	−	0.733675i	$-0.737804\pi$
$317$	−24.1963	−1.35900	−0.679501	+	0.733675i	$0.737804\pi$
$318$	4.57052	0.256302
$319$	−2.28005	−0.127659
$320$	98.4724	5.50477
$321$	−4.36238	−0.243484
$322$	3.11506	0.173595
$323$	−6.12861	−0.341005
$324$	33.6710	1.87061
$325$	1.87870	0.104212
$326$	36.5303	2.02323
$327$	5.83213	0.322518
$328$	−25.9515	−1.43293
$329$	12.3152	0.678957
$330$	−2.82205	−0.155349
$331$	−8.63363	−0.474547	−0.237274	−	0.971443i	$-0.576254\pi$
$331$	−8.63363	−0.474547	−0.237274	+	0.971443i	$0.576254\pi$
$332$	22.8875	1.25612
$333$	24.4102	1.33767
$334$	46.3054	2.53372
$335$	2.46286	0.134560
$336$	−10.4611	−0.570698
$337$	−13.1776	−0.717829	−0.358915	−	0.933370i	$-0.616853\pi$
$337$	−13.1776	−0.717829	−0.358915	+	0.933370i	$0.616853\pi$
$338$	−2.76381	−0.150332
$339$	−9.87817	−0.536508
$340$	−41.6119	−2.25672
$341$	5.89873	0.319434
$342$	15.9517	0.862570
$343$	−13.7587	−0.742901
$344$	−39.6351	−2.13698
$345$	1.63416	0.0879803
$346$	−18.5201	−0.995647
$347$	31.7643	1.70519	0.852597	−	0.522569i	$-0.175026\pi$
$347$	31.7643	1.70519	0.852597	+	0.522569i	$0.175026\pi$
$348$	−11.5622	−0.619801
$349$	12.6312	0.676132	0.338066	−	0.941122i	$-0.390227\pi$
$349$	12.6312	0.676132	0.338066	+	0.941122i	$0.390227\pi$
$350$	−5.55770	−0.297071
$351$	3.34311	0.178442
$352$	16.8022	0.895558
$353$	20.2447	1.07752	0.538759	−	0.842460i	$-0.318893\pi$
$353$	20.2447	1.07752	0.538759	+	0.842460i	$0.318893\pi$
$354$	4.73203	0.251505
$355$	10.0222	0.531923
$356$	24.9863	1.32427
$357$	1.78209	0.0943180
$358$	29.8480	1.57751
$359$	−0.273437	−0.0144314	−0.00721572	−	0.999974i	$-0.502297\pi$
$359$	−0.273437	−0.0144314	−0.00721572	+	0.999974i	$0.502297\pi$
$360$	69.8922	3.68364
$361$	−14.2560	−0.750314
$362$	−24.3076	−1.27758
$363$	6.25271	0.328182
$364$	6.03537	0.316339
$365$	−8.05863	−0.421808
$366$	−8.16703	−0.426897
$367$	−2.08904	−0.109047	−0.0545236	−	0.998512i	$-0.517364\pi$
$367$	−2.08904	−0.109047	−0.0545236	+	0.998512i	$0.517364\pi$
$368$	−17.3926	−0.906654
$369$	−6.83812	−0.355978
$370$	66.7742	3.47142
$371$	2.99139	0.155305
$372$	29.9127	1.55090
$373$	−5.73885	−0.297147	−0.148573	−	0.988901i	$-0.547468\pi$
$373$	−5.73885	−0.297147	−0.148573	+	0.988901i	$0.547468\pi$
$374$	−5.11668	−0.264577
$375$	4.84396	0.250141
$376$	−115.708	−5.96717
$377$	3.46541	0.178477
$378$	−9.88980	−0.508677
$379$	33.1557	1.70309	0.851546	−	0.524280i	$-0.175665\pi$
$379$	33.1557	1.70309	0.851546	+	0.524280i	$0.175665\pi$
$380$	32.2109	1.65238
$381$	−1.10963	−0.0568479
$382$	28.3443	1.45022
$383$	−28.1923	−1.44056	−0.720279	−	0.693684i	$-0.755986\pi$
$383$	−28.1923	−1.44056	−0.720279	+	0.693684i	$0.755986\pi$
$384$	31.1804	1.59117
$385$	−1.84702	−0.0941331
$386$	69.1767	3.52100
$387$	−10.4437	−0.530884
$388$	43.3460	2.20056
$389$	−10.3836	−0.526470	−0.263235	−	0.964732i	$-0.584789\pi$
$389$	−10.3836	−0.526470	−0.263235	+	0.964732i	$0.584789\pi$
$390$	4.28918	0.217191
$391$	2.96291	0.149841
$392$	58.8746	2.97362
$393$	8.99111	0.453541
$394$	17.8819	0.900877
$395$	−29.2900	−1.47374
$396$	9.83088	0.494020
$397$	27.3500	1.37266	0.686329	−	0.727291i	$-0.259221\pi$
$397$	27.3500	1.37266	0.686329	+	0.727291i	$0.259221\pi$
$398$	5.99369	0.300437
$399$	−1.37947	−0.0690601
$400$	31.0309	1.55154
$401$	25.9508	1.29592	0.647961	−	0.761673i	$-0.275622\pi$
$401$	25.9508	1.29592	0.647961	+	0.761673i	$0.275622\pi$
$402$	1.53570	0.0765938
$403$	−8.96535	−0.446596
$404$	34.6078	1.72180
$405$	15.6615	0.778226
$406$	−10.2516	−0.508777
$407$	6.06091	0.300428
$408$	−16.7437	−0.828935
$409$	13.1037	0.647937	0.323969	−	0.946068i	$-0.394983\pi$
$409$	13.1037	0.647937	0.323969	+	0.946068i	$0.394983\pi$
$410$	−18.7057	−0.923808
$411$	−2.51615	−0.124112
$412$	44.3945	2.18716
$413$	3.09710	0.152398
$414$	−7.71193	−0.379021
$415$	10.6457	0.522579
$416$	−25.5372	−1.25207
$417$	2.48174	0.121531
$418$	3.96071	0.193725
$419$	−25.1347	−1.22791	−0.613955	−	0.789341i	$-0.710422\pi$
$419$	−25.1347	−1.22791	−0.613955	+	0.789341i	$0.710422\pi$
$420$	−9.36633	−0.457030
$421$	−7.55314	−0.368118	−0.184059	−	0.982915i	$-0.558924\pi$
$421$	−7.55314	−0.368118	−0.184059	+	0.982915i	$0.558924\pi$
$422$	49.1151	2.39088
$423$	−30.4886	−1.48241
$424$	−28.1058	−1.36494
$425$	−5.28624	−0.256420
$426$	6.24928	0.302779
$427$	−5.34529	−0.258677
$428$	41.5707	2.00940
$429$	0.389317	0.0187964
$430$	−28.5688	−1.37771
$431$	−3.86150	−0.186002	−0.0930010	−	0.995666i	$-0.529646\pi$
$431$	−3.86150	−0.186002	−0.0930010	+	0.995666i	$0.529646\pi$
$432$	55.2188	2.65671
$433$	25.4727	1.22414	0.612069	−	0.790804i	$-0.290337\pi$
$433$	25.4727	1.22414	0.612069	+	0.790804i	$0.290337\pi$
$434$	26.5219	1.27309
$435$	−5.37798	−0.257855
$436$	−55.5765	−2.66163
$437$	−2.29352	−0.109714
$438$	−5.02491	−0.240100
$439$	4.92477	0.235046	0.117523	−	0.993070i	$-0.462505\pi$
$439$	4.92477	0.235046	0.117523	+	0.993070i	$0.462505\pi$
$440$	17.3538	0.827310
$441$	15.5133	0.738727
$442$	7.77673	0.369901
$443$	−20.3603	−0.967347	−0.483674	−	0.875248i	$-0.660698\pi$
$443$	−20.3603	−0.967347	−0.483674	+	0.875248i	$0.660698\pi$
$444$	30.7351	1.45862
$445$	11.6219	0.550933
$446$	−18.2404	−0.863709
$447$	1.28841	0.0609398
$448$	40.1873	1.89867
$449$	−29.5154	−1.39292	−0.696459	−	0.717597i	$-0.745242\pi$
$449$	−29.5154	−1.39292	−0.696459	+	0.717597i	$0.745242\pi$
$450$	13.7592	0.648613
$451$	−1.69786	−0.0799493
$452$	94.1326	4.42763
$453$	−7.26123	−0.341162
$454$	11.9161	0.559248
$455$	2.80725	0.131606
$456$	12.9609	0.606951
$457$	−10.5736	−0.494612	−0.247306	−	0.968937i	$-0.579545\pi$
$457$	−10.5736	−0.494612	−0.247306	+	0.968937i	$0.579545\pi$
$458$	72.1029	3.36915
$459$	−9.40674	−0.439069
$460$	−15.5725	−0.726072
$461$	−15.1162	−0.704030	−0.352015	−	0.935994i	$-0.614503\pi$
$461$	−15.1162	−0.704030	−0.352015	+	0.935994i	$0.614503\pi$
$462$	−1.15170	−0.0535820
$463$	−18.6858	−0.868404	−0.434202	−	0.900815i	$-0.642970\pi$
$463$	−18.6858	−0.868404	−0.434202	+	0.900815i	$0.642970\pi$
$464$	57.2387	2.65724
$465$	13.9134	0.645217
$466$	−0.180579	−0.00836518
$467$	−27.2485	−1.26091	−0.630455	−	0.776226i	$-0.717132\pi$
$467$	−27.2485	−1.26091	−0.630455	+	0.776226i	$0.717132\pi$
$468$	−14.9417	−0.690682
$469$	1.00511	0.0464117
$470$	−83.4016	−3.84703
$471$	12.4910	0.575554
$472$	−29.0989	−1.33939
$473$	−2.59311	−0.119231
$474$	−18.2636	−0.838876
$475$	4.09196	0.187752
$476$	−16.9821	−0.778375
$477$	−7.40577	−0.339087
$478$	22.1208	1.01178
$479$	−9.39706	−0.429362	−0.214681	−	0.976684i	$-0.568871\pi$
$479$	−9.39706	−0.429362	−0.214681	+	0.976684i	$0.568871\pi$
$480$	39.6314	1.80892
$481$	−9.21184	−0.420024
$482$	9.82920	0.447708
$483$	0.666914	0.0303456
$484$	−59.5843	−2.70838
$485$	20.1617	0.915493
$486$	37.4848	1.70035
$487$	2.73370	0.123876	0.0619378	−	0.998080i	$-0.480272\pi$
$487$	2.73370	0.123876	0.0619378	+	0.998080i	$0.480272\pi$
$488$	50.2219	2.27344
$489$	7.82090	0.353673
$490$	42.4365	1.91709
$491$	−7.89944	−0.356497	−0.178248	−	0.983986i	$-0.557043\pi$
$491$	−7.89944	−0.356497	−0.178248	+	0.983986i	$0.557043\pi$
$492$	−8.60993	−0.388166
$493$	−9.75085	−0.439156
$494$	−6.01980	−0.270844
$495$	4.57267	0.205526
$496$	−148.082	−6.64909
$497$	4.09014	0.183468
$498$	6.63809	0.297460
$499$	6.51790	0.291781	0.145891	−	0.989301i	$-0.453395\pi$
$499$	6.51790	0.291781	0.145891	+	0.989301i	$0.453395\pi$
$500$	−46.1599	−2.06433
$501$	9.91369	0.442911
$502$	48.9204	2.18342
$503$	−6.74036	−0.300538	−0.150269	−	0.988645i	$-0.548014\pi$
$503$	−6.74036	−0.300538	−0.150269	+	0.988645i	$0.548014\pi$
$504$	28.5236	1.27054
$505$	16.0972	0.716317
$506$	−1.91483	−0.0851244
$507$	−0.591714	−0.0262790
$508$	10.5740	0.469147
$509$	15.3183	0.678972	0.339486	−	0.940611i	$-0.389747\pi$
$509$	15.3183	0.678972	0.339486	+	0.940611i	$0.389747\pi$
$510$	−12.0688	−0.534413
$511$	−3.28879	−0.145487
$512$	−89.5904	−3.95938
$513$	7.28156	0.321489
$514$	44.9435	1.98237
$515$	20.6494	0.909919
$516$	−13.1498	−0.578886
$517$	−7.57013	−0.332934
$518$	27.2511	1.19734
$519$	−3.96503	−0.174046
$520$	−26.3757	−1.15665
$521$	10.8121	0.473688	0.236844	−	0.971548i	$-0.423887\pi$
$521$	10.8121	0.473688	0.236844	+	0.971548i	$0.423887\pi$
$522$	25.3798	1.11084
$523$	−0.641001	−0.0280290	−0.0140145	−	0.999902i	$-0.504461\pi$
$523$	−0.641001	−0.0280290	−0.0140145	+	0.999902i	$0.504461\pi$
$524$	−85.6795	−3.74293
$525$	−1.18987	−0.0519300
$526$	−7.31058	−0.318757
$527$	25.2264	1.09888
$528$	6.43042	0.279848
$529$	−21.8912	−0.951791
$530$	−20.2585	−0.879972
$531$	−7.66747	−0.332740
$532$	13.1455	0.569930
$533$	2.58055	0.111776
$534$	7.24680	0.313600
$535$	19.3359	0.835965
$536$	−9.44357	−0.407900
$537$	6.39026	0.275760
$538$	−61.0291	−2.63115
$539$	3.85185	0.165911
$540$	49.4402	2.12757
$541$	16.1527	0.694460	0.347230	−	0.937780i	$-0.387122\pi$
$541$	16.1527	0.694460	0.347230	+	0.937780i	$0.387122\pi$
$542$	−9.09734	−0.390764
$543$	−5.20410	−0.223329
$544$	71.8559	3.08079
$545$	−25.8505	−1.10731
$546$	1.75045	0.0749122
$547$	−40.7182	−1.74098	−0.870492	−	0.492183i	$-0.836199\pi$
$547$	−40.7182	−1.74098	−0.870492	+	0.492183i	$0.836199\pi$
$548$	23.9773	1.02426
$549$	13.2333	0.564784
$550$	3.41632	0.145672
$551$	7.54793	0.321553
$552$	−6.26602	−0.266700
$553$	−11.9535	−0.508314
$554$	−81.9981	−3.48377
$555$	14.2959	0.606828
$556$	−23.6494	−1.00296
$557$	5.09376	0.215829	0.107915	−	0.994160i	$-0.465583\pi$
$557$	5.09376	0.215829	0.107915	+	0.994160i	$0.465583\pi$
$558$	−65.6600	−2.77961
$559$	3.94121	0.166696
$560$	46.3679	1.95940
$561$	−1.09545	−0.0462498
$562$	−14.9840	−0.632062
$563$	−30.2989	−1.27695	−0.638473	−	0.769645i	$-0.720433\pi$
$563$	−30.2989	−1.27695	−0.638473	+	0.769645i	$0.720433\pi$
$564$	−38.3884	−1.61645
$565$	43.7842	1.84202
$566$	−57.0148	−2.39651
$567$	6.39158	0.268421
$568$	−38.4291	−1.61245
$569$	−25.5207	−1.06988	−0.534941	−	0.844889i	$-0.679666\pi$
$569$	−25.5207	−1.06988	−0.534941	+	0.844889i	$0.679666\pi$
$570$	9.34217	0.391300
$571$	−28.3537	−1.18656	−0.593282	−	0.804995i	$-0.702168\pi$
$571$	−28.3537	−1.18656	−0.593282	+	0.804995i	$0.702168\pi$
$572$	−3.70994	−0.155120
$573$	6.06833	0.253508
$574$	−7.63393	−0.318634
$575$	−1.97828	−0.0824999
$576$	−99.4916	−4.14548
$577$	−8.84854	−0.368369	−0.184185	−	0.982892i	$-0.558964\pi$
$577$	−8.84854	−0.368369	−0.184185	+	0.982892i	$0.558964\pi$
$578$	25.1029	1.04414
$579$	14.8103	0.615494
$580$	51.2488	2.12799
$581$	4.34461	0.180245
$582$	12.5717	0.521113
$583$	−1.83881	−0.0761556
$584$	30.9000	1.27865
$585$	−6.94990	−0.287343
$586$	−42.8452	−1.76992
$587$	−7.60866	−0.314043	−0.157021	−	0.987595i	$-0.550189\pi$
$587$	−7.60866	−0.314043	−0.157021	+	0.987595i	$0.550189\pi$
$588$	19.5329	0.805522
$589$	−19.5272	−0.804606
$590$	−20.9744	−0.863501
$591$	3.82840	0.157479
$592$	−152.154	−6.25348
$593$	−26.2359	−1.07738	−0.538689	−	0.842505i	$-0.681080\pi$
$593$	−26.2359	−1.07738	−0.538689	+	0.842505i	$0.681080\pi$
$594$	6.07926	0.249435
$595$	−7.89896	−0.323826
$596$	−12.2777	−0.502916
$597$	1.28321	0.0525183
$598$	2.91030	0.119011
$599$	−15.5694	−0.636147	−0.318073	−	0.948066i	$-0.603036\pi$
$599$	−15.5694	−0.636147	−0.318073	+	0.948066i	$0.603036\pi$
$600$	11.1795	0.456399
$601$	31.2521	1.27480	0.637401	−	0.770532i	$-0.280010\pi$
$601$	31.2521	1.27480	0.637401	+	0.770532i	$0.280010\pi$
$602$	−11.6591	−0.475191
$603$	−2.48835	−0.101333
$604$	69.1949	2.81550
$605$	−27.7146	−1.12676
$606$	10.0373	0.407739
$607$	30.3730	1.23280	0.616401	−	0.787432i	$-0.288590\pi$
$607$	30.3730	1.23280	0.616401	+	0.787432i	$0.288590\pi$
$608$	−55.6221	−2.25577
$609$	−2.19480	−0.0889377
$610$	36.1997	1.46568
$611$	11.5057	0.465470
$612$	42.0426	1.69947
$613$	36.2111	1.46255	0.731277	−	0.682081i	$-0.238925\pi$
$613$	36.2111	1.46255	0.731277	+	0.682081i	$0.238925\pi$
$614$	0.903079	0.0364453
$615$	−4.00476	−0.161488
$616$	7.08222	0.285351
$617$	1.00000	0.0402585
$617$	1.00000	0.0402585
$618$	12.8758	0.517940
$619$	9.44032	0.379439	0.189719	−	0.981838i	$-0.439242\pi$
$619$	9.44032	0.379439	0.189719	+	0.981838i	$0.439242\pi$
$620$	−132.586	−5.32477
$621$	−3.52031	−0.141265
$622$	89.0189	3.56933
$623$	4.74301	0.190025
$624$	−9.77345	−0.391251
$625$	−30.8640	−1.23456
$626$	87.3289	3.49037
$627$	0.847963	0.0338644
$628$	−119.031	−4.74986
$629$	25.9200	1.03350
$630$	20.5596	0.819115
$631$	−26.6434	−1.06066	−0.530328	−	0.847792i	$-0.677931\pi$
$631$	−26.6434	−1.06066	−0.530328	+	0.847792i	$0.677931\pi$
$632$	112.310	4.46743
$633$	10.5152	0.417942
$634$	66.8741	2.65591
$635$	4.91833	0.195178
$636$	−9.32466	−0.369747
$637$	−5.85434	−0.231957
$638$	6.30164	0.249485
$639$	−10.1259	−0.400576
$640$	−138.205	−5.46302
$641$	36.8946	1.45725	0.728624	−	0.684914i	$-0.240160\pi$
$641$	36.8946	1.45725	0.728624	+	0.684914i	$0.240160\pi$
$642$	12.0568	0.475844
$643$	41.7028	1.64460	0.822298	−	0.569057i	$-0.192692\pi$
$643$	41.7028	1.64460	0.822298	+	0.569057i	$0.192692\pi$
$644$	−6.35526	−0.250432
$645$	−6.11639	−0.240833
$646$	16.9383	0.666430
$647$	−33.0707	−1.30014	−0.650072	−	0.759873i	$-0.725261\pi$
$647$	−33.0707	−1.30014	−0.650072	+	0.759873i	$0.725261\pi$
$648$	−60.0524	−2.35908
$649$	−1.90379	−0.0747301
$650$	−5.19238	−0.203662
$651$	5.67816	0.222544
$652$	−74.5282	−2.91875
$653$	41.3500	1.61815	0.809076	−	0.587704i	$-0.199968\pi$
$653$	41.3500	1.61815	0.809076	+	0.587704i	$0.199968\pi$
$654$	−16.1189	−0.630300
$655$	−39.8524	−1.55716
$656$	42.6233	1.66416
$657$	8.14204	0.317651
$658$	−34.0368	−1.32689
$659$	6.34947	0.247340	0.123670	−	0.992323i	$-0.460534\pi$
$659$	6.34947	0.247340	0.123670	+	0.992323i	$0.460534\pi$
$660$	5.75748	0.224110
$661$	23.8071	0.925991	0.462995	−	0.886361i	$-0.346775\pi$
$661$	23.8071	0.925991	0.462995	+	0.886361i	$0.346775\pi$
$662$	23.8617	0.927413
$663$	1.66495	0.0646612
$664$	−40.8200	−1.58412
$665$	6.11442	0.237107
$666$	−67.4653	−2.61423
$667$	−3.64908	−0.141293
$668$	−94.4712	−3.65520
$669$	−3.90516	−0.150982
$670$	−6.80688	−0.262973
$671$	3.28575	0.126845
$672$	16.1739	0.623921
$673$	−11.9508	−0.460670	−0.230335	−	0.973111i	$-0.573982\pi$
$673$	−11.9508	−0.460670	−0.230335	+	0.973111i	$0.573982\pi$
$674$	36.4204	1.40286
$675$	6.28071	0.241745
$676$	5.63866	0.216872
$677$	−0.0527022	−0.00202551	−0.00101276	−	0.999999i	$-0.500322\pi$
$677$	−0.0527022	−0.00202551	−0.00101276	+	0.999999i	$0.500322\pi$
$678$	27.3014	1.04850
$679$	8.22813	0.315766
$680$	74.2150	2.84602
$681$	2.55115	0.0977603
$682$	−16.3030	−0.624273
$683$	19.9939	0.765043	0.382522	−	0.923947i	$-0.375056\pi$
$683$	19.9939	0.765043	0.382522	+	0.923947i	$0.375056\pi$
$684$	−32.5443	−1.24436
$685$	11.1526	0.426120
$686$	38.0265	1.45186
$687$	15.4368	0.588949
$688$	65.0977	2.48183
$689$	2.79476	0.106472
$690$	−4.51651	−0.171941
$691$	−24.9762	−0.950140	−0.475070	−	0.879948i	$-0.657577\pi$
$691$	−24.9762	−0.950140	−0.475070	+	0.879948i	$0.657577\pi$
$692$	37.7842	1.43634
$693$	1.86614	0.0708888
$694$	−87.7905	−3.33248
$695$	−11.0001	−0.417258
$696$	20.6213	0.781649
$697$	−7.26106	−0.275032
$698$	−34.9103	−1.32137
$699$	−0.0386609	−0.00146229
$700$	11.3387	0.428562
$701$	−0.758884	−0.0286627	−0.0143313	−	0.999897i	$-0.504562\pi$
$701$	−0.758884	−0.0286627	−0.0143313	+	0.999897i	$0.504562\pi$
$702$	−9.23973	−0.348731
$703$	−20.0641	−0.756733
$704$	−24.7031	−0.931035
$705$	−17.8557	−0.672486
$706$	−55.9527	−2.10581
$707$	6.56940	0.247068
$708$	−9.65417	−0.362826
$709$	−0.373531	−0.0140282	−0.00701412	−	0.999975i	$-0.502233\pi$
$709$	−0.373531	−0.0140282	−0.00701412	+	0.999975i	$0.502233\pi$
$710$	−27.6995	−1.03954
$711$	29.5932	1.10983
$712$	−44.5632	−1.67007
$713$	9.44053	0.353551
$714$	−4.92535	−0.184327
$715$	−1.72562	−0.0645344
$716$	−60.8951	−2.27576
$717$	4.73591	0.176866
$718$	0.755728	0.0282035
$719$	−30.6445	−1.14285	−0.571423	−	0.820656i	$-0.693608\pi$
$719$	−30.6445	−1.14285	−0.571423	+	0.820656i	$0.693608\pi$
$720$	−114.793	−4.27807
$721$	8.42716	0.313844
$722$	39.4008	1.46635
$723$	2.10437	0.0782622
$724$	49.5917	1.84306
$725$	6.51047	0.241793
$726$	−17.2813	−0.641370
$727$	−11.8581	−0.439792	−0.219896	−	0.975523i	$-0.570572\pi$
$727$	−11.8581	−0.439792	−0.219896	+	0.975523i	$0.570572\pi$
$728$	−10.7641	−0.398945
$729$	−9.88910	−0.366263
$730$	22.2725	0.824344
$731$	−11.0897	−0.410166
$732$	16.6622	0.615851
$733$	30.5238	1.12742	0.563712	−	0.825972i	$-0.309373\pi$
$733$	30.5238	1.12742	0.563712	+	0.825972i	$0.309373\pi$
$734$	5.77373	0.213112
$735$	9.08538	0.335119
$736$	26.8908	0.991207
$737$	−0.617841	−0.0227585
$738$	18.8993	0.695692
$739$	26.4789	0.974042	0.487021	−	0.873390i	$-0.338084\pi$
$739$	26.4789	0.974042	0.487021	+	0.873390i	$0.338084\pi$
$740$	−136.231	−5.00795
$741$	−1.28880	−0.0473453
$742$	−8.26764	−0.303515
$743$	17.9438	0.658295	0.329148	−	0.944279i	$-0.393239\pi$
$743$	17.9438	0.658295	0.329148	+	0.944279i	$0.393239\pi$
$744$	−53.3494	−1.95588
$745$	−5.71079	−0.209227
$746$	15.8611	0.580717
$747$	−10.7559	−0.393539
$748$	10.4389	0.381685
$749$	7.89114	0.288336
$750$	−13.3878	−0.488853
$751$	−5.63418	−0.205594	−0.102797	−	0.994702i	$-0.532779\pi$
$751$	−5.63418	−0.205594	−0.102797	+	0.994702i	$0.532779\pi$
$752$	190.041	6.93010
$753$	10.4735	0.381677
$754$	−9.57773	−0.348800
$755$	32.1848	1.17133
$756$	20.1769	0.733828
$757$	−11.7033	−0.425365	−0.212683	−	0.977121i	$-0.568220\pi$
$757$	−11.7033	−0.425365	−0.212683	+	0.977121i	$0.568220\pi$
$758$	−91.6360	−3.32837
$759$	−0.409952	−0.0148803
$760$	−57.4483	−2.08387
$761$	−19.5736	−0.709543	−0.354771	−	0.934953i	$-0.615441\pi$
$761$	−19.5736	−0.709543	−0.354771	+	0.934953i	$0.615441\pi$
$762$	3.06680	0.111098
$763$	−10.5498	−0.381928
$764$	−57.8273	−2.09212
$765$	19.5554	0.707027
$766$	77.9182	2.81530
$767$	2.89352	0.104479
$768$	−41.7441	−1.50631
$769$	−45.4659	−1.63954	−0.819771	−	0.572691i	$-0.805899\pi$
$769$	−45.4659	−1.63954	−0.819771	+	0.572691i	$0.805899\pi$
$770$	5.10483	0.183965
$771$	9.62210	0.346532
$772$	−141.133	−5.07947
$773$	−46.3230	−1.66612	−0.833062	−	0.553179i	$-0.813414\pi$
$773$	−46.3230	−1.66612	−0.833062	+	0.553179i	$0.813414\pi$
$774$	28.8645	1.03751
$775$	−16.8432	−0.605027
$776$	−77.3078	−2.77519
$777$	5.83427	0.209303
$778$	28.6983	1.02889
$779$	5.62063	0.201380
$780$	−8.75067	−0.313324
$781$	−2.51421	−0.0899653
$782$	−8.18892	−0.292835
$783$	11.5852	0.414023
$784$	−96.6972	−3.45347
$785$	−55.3653	−1.97607
$786$	−24.8497	−0.886361
$787$	17.6876	0.630495	0.315247	−	0.949010i	$-0.397912\pi$
$787$	17.6876	0.630495	0.315247	+	0.949010i	$0.397912\pi$
$788$	−36.4822	−1.29962
$789$	−1.56515	−0.0557207
$790$	80.9521	2.88015
$791$	17.8687	0.635337
$792$	−17.5334	−0.623023
$793$	−4.99394	−0.177340
$794$	−75.5903	−2.68260
$795$	−4.33721	−0.153825
$796$	−12.2282	−0.433416
$797$	25.9172	0.918036	0.459018	−	0.888427i	$-0.348201\pi$
$797$	25.9172	0.918036	0.459018	+	0.888427i	$0.348201\pi$
$798$	3.81261	0.134965
$799$	−32.3743	−1.14532
$800$	−47.9769	−1.69624
$801$	−11.7422	−0.414892
$802$	−71.7233	−2.53264
$803$	2.02162	0.0713413
$804$	−3.13310	−0.110496
$805$	−2.95604	−0.104187
$806$	24.7785	0.872787
$807$	−13.0659	−0.459943
$808$	−61.7232	−2.17141
$809$	−9.94255	−0.349562	−0.174781	−	0.984607i	$-0.555922\pi$
$809$	−9.94255	−0.349562	−0.174781	+	0.984607i	$0.555922\pi$
$810$	−43.2855	−1.52090
$811$	19.9864	0.701819	0.350909	−	0.936409i	$-0.385872\pi$
$811$	19.9864	0.701819	0.350909	+	0.936409i	$0.385872\pi$
$812$	20.9150	0.733973
$813$	−1.94768	−0.0683082
$814$	−16.7512	−0.587130
$815$	−34.6655	−1.21428
$816$	27.5002	0.962701
$817$	8.58427	0.300326
$818$	−36.2162	−1.26627
$819$	−2.83631	−0.0991086
$820$	38.1629	1.33270
$821$	−20.2305	−0.706049	−0.353025	−	0.935614i	$-0.614847\pi$
$821$	−20.2305	−0.706049	−0.353025	+	0.935614i	$0.614847\pi$
$822$	6.95415	0.242554
$823$	−37.0117	−1.29015	−0.645074	−	0.764120i	$-0.723173\pi$
$823$	−37.0117	−1.29015	−0.645074	+	0.764120i	$0.723173\pi$
$824$	−79.1778	−2.75829
$825$	0.731411	0.0254645
$826$	−8.55980	−0.297833
$827$	11.7570	0.408832	0.204416	−	0.978884i	$-0.434471\pi$
$827$	11.7570	0.408832	0.204416	+	0.978884i	$0.434471\pi$
$828$	15.7337	0.546784
$829$	−37.4925	−1.30217	−0.651083	−	0.759006i	$-0.725685\pi$
$829$	−37.4925	−1.30217	−0.651083	+	0.759006i	$0.725685\pi$
$830$	−29.4228	−1.02128
$831$	−17.5553	−0.608985
$832$	37.5458	1.30167
$833$	16.4728	0.570747
$834$	−6.85906	−0.237510
$835$	−43.9417	−1.52066
$836$	−8.08055	−0.279472
$837$	−29.9722	−1.03599
$838$	69.4675	2.39972
$839$	7.71813	0.266459	0.133230	−	0.991085i	$-0.457465\pi$
$839$	7.71813	0.266459	0.133230	+	0.991085i	$0.457465\pi$
$840$	16.7049	0.576374
$841$	−16.9910	−0.585895
$842$	20.8755	0.719416
$843$	−3.20798	−0.110489
$844$	−100.203	−3.44914
$845$	2.62273	0.0902246
$846$	84.2648	2.89708
$847$	−11.3106	−0.388635
$848$	46.1616	1.58520
$849$	−12.2065	−0.418926
$850$	14.6102	0.501125
$851$	9.70010	0.332515
$852$	−12.7496	−0.436795
$853$	4.28554	0.146734	0.0733670	−	0.997305i	$-0.476626\pi$
$853$	4.28554	0.146734	0.0733670	+	0.997305i	$0.476626\pi$
$854$	14.7734	0.505535
$855$	−15.1374	−0.517689
$856$	−74.1416	−2.53411
$857$	−3.82734	−0.130739	−0.0653697	−	0.997861i	$-0.520823\pi$
$857$	−3.82734	−0.130739	−0.0653697	+	0.997861i	$0.520823\pi$
$858$	−1.07600	−0.0367340
$859$	−46.2933	−1.57951	−0.789754	−	0.613424i	$-0.789792\pi$
$859$	−46.2933	−1.57951	−0.789754	+	0.613424i	$0.789792\pi$
$860$	58.2853	1.98751
$861$	−1.63438	−0.0556994
$862$	10.6725	0.363506
$863$	45.4221	1.54619	0.773093	−	0.634292i	$-0.218708\pi$
$863$	45.4221	1.54619	0.773093	+	0.634292i	$0.218708\pi$
$864$	−85.3738	−2.90448
$865$	17.5747	0.597558
$866$	−70.4017	−2.39235
$867$	5.37437	0.182523
$868$	−54.1092	−1.83659
$869$	7.34780	0.249257
$870$	14.8637	0.503928
$871$	0.939044	0.0318183
$872$	99.1210	3.35666
$873$	−20.3703	−0.689431
$874$	6.33887	0.214415
$875$	−8.76227	−0.296219
$876$	10.2517	0.346373
$877$	33.3700	1.12682	0.563412	−	0.826176i	$-0.309488\pi$
$877$	33.3700	1.12682	0.563412	+	0.826176i	$0.309488\pi$
$878$	−13.6111	−0.459353
$879$	−9.17287	−0.309393
$880$	−28.5023	−0.960813
$881$	−17.3514	−0.584584	−0.292292	−	0.956329i	$-0.594418\pi$
$881$	−17.3514	−0.584584	−0.292292	+	0.956329i	$0.594418\pi$
$882$	−42.8758	−1.44370
$883$	6.25962	0.210653	0.105326	−	0.994438i	$-0.466411\pi$
$883$	6.25962	0.210653	0.105326	+	0.994438i	$0.466411\pi$
$884$	−15.8659	−0.533628
$885$	−4.49047	−0.150946
$886$	56.2721	1.89050
$887$	14.9361	0.501506	0.250753	−	0.968051i	$-0.419322\pi$
$887$	14.9361	0.501506	0.250753	+	0.968051i	$0.419322\pi$
$888$	−54.8162	−1.83951
$889$	2.00721	0.0673197
$890$	−32.1209	−1.07669
$891$	−3.92890	−0.131623
$892$	37.2136	1.24600
$893$	25.0603	0.838610
$894$	−3.56093	−0.119095
$895$	−28.3243	−0.946778
$896$	−56.4024	−1.88427
$897$	0.623077	0.0208039
$898$	81.5750	2.72219
$899$	−31.0686	−1.03619
$900$	−28.0711	−0.935703
$901$	−7.86382	−0.261982
$902$	4.69258	0.156246
$903$	−2.49615	−0.0830665
$904$	−167.886	−5.58381
$905$	23.0668	0.766765
$906$	20.0687	0.666737
$907$	10.0400	0.333373	0.166686	−	0.986010i	$-0.446693\pi$
$907$	10.0400	0.333373	0.166686	+	0.986010i	$0.446693\pi$
$908$	−24.3108	−0.806784
$909$	−16.2638	−0.539438
$910$	−7.75872	−0.257199
$911$	22.5816	0.748160	0.374080	−	0.927396i	$-0.377958\pi$
$911$	22.5816	0.748160	0.374080	+	0.927396i	$0.377958\pi$
$912$	−21.2873	−0.704895
$913$	−2.67063	−0.0883850
$914$	29.2235	0.966626
$915$	7.75012	0.256211
$916$	−147.103	−4.86040
$917$	−16.2641	−0.537087
$918$	25.9985	0.858078
$919$	−16.4113	−0.541359	−0.270680	−	0.962669i	$-0.587248\pi$
$919$	−16.4113	−0.541359	−0.270680	+	0.962669i	$0.587248\pi$
$920$	27.7737	0.915670
$921$	0.193343	0.00637088
$922$	41.7782	1.37589
$923$	3.82129	0.125779
$924$	2.34967	0.0772986
$925$	−17.3063	−0.569028
$926$	51.6441	1.69713
$927$	−20.8631	−0.685234
$928$	−88.4969	−2.90505
$929$	9.66178	0.316993	0.158496	−	0.987360i	$-0.449335\pi$
$929$	9.66178	0.316993	0.158496	+	0.987360i	$0.449335\pi$
$930$	−38.4540	−1.26096
$931$	−12.7512	−0.417904
$932$	0.368414	0.0120678
$933$	19.0584	0.623943
$934$	75.3097	2.46421
$935$	4.85549	0.158791
$936$	26.6487	0.871039
$937$	29.8658	0.975672	0.487836	−	0.872935i	$-0.337786\pi$
$937$	29.8658	0.975672	0.487836	+	0.872935i	$0.337786\pi$
$938$	−2.77794	−0.0907029
$939$	18.6966	0.610139
$940$	170.154	5.54981
$941$	42.7510	1.39364	0.696822	−	0.717244i	$-0.254597\pi$
$941$	42.7510	1.39364	0.696822	+	0.717244i	$0.254597\pi$
$942$	−34.5227	−1.12481
$943$	−2.71732	−0.0884882
$944$	47.7928	1.55552
$945$	9.38496	0.305293
$946$	7.16687	0.233015
$947$	26.4031	0.857986	0.428993	−	0.903308i	$-0.358868\pi$
$947$	26.4031	0.857986	0.428993	+	0.903308i	$0.358868\pi$
$948$	37.2610	1.21018
$949$	−3.07261	−0.0997412
$950$	−11.3094	−0.366926
$951$	14.3173	0.464271
$952$	30.2877	0.981631
$953$	−2.84048	−0.0920122	−0.0460061	−	0.998941i	$-0.514649\pi$
$953$	−2.84048	−0.0920122	−0.0460061	+	0.998941i	$0.514649\pi$
$954$	20.4682	0.662681
$955$	−26.8974	−0.870379
$956$	−45.1302	−1.45962
$957$	1.34914	0.0436115
$958$	25.9717	0.839108
$959$	4.55147	0.146975
$960$	−58.2675	−1.88058
$961$	49.3775	1.59282
$962$	25.4598	0.820857
$963$	−19.5361	−0.629540
$964$	−20.0533	−0.645873
$965$	−65.6454	−2.11320
$966$	−1.84322	−0.0593048
$967$	−4.16013	−0.133781	−0.0668903	−	0.997760i	$-0.521308\pi$
$967$	−4.16013	−0.133781	−0.0668903	+	0.997760i	$0.521308\pi$
$968$	106.269	3.41561
$969$	3.62639	0.116496
$970$	−55.7230	−1.78916
$971$	−8.29182	−0.266097	−0.133049	−	0.991110i	$-0.542477\pi$
$971$	−8.29182	−0.266097	−0.133049	+	0.991110i	$0.542477\pi$
$972$	−76.4756	−2.45296
$973$	−4.48923	−0.143918
$974$	−7.55543	−0.242092
$975$	−1.11166	−0.0356015
$976$	−82.4858	−2.64031
$977$	−9.24599	−0.295805	−0.147903	−	0.989002i	$-0.547252\pi$
$977$	−9.24599	−0.295805	−0.147903	+	0.989002i	$0.547252\pi$
$978$	−21.6155	−0.691188
$979$	−2.91553	−0.0931806
$980$	−86.5779	−2.76563
$981$	26.1180	0.833885
$982$	21.8326	0.696706
$983$	−26.3320	−0.839859	−0.419930	−	0.907557i	$-0.637945\pi$
$983$	−26.3320	−0.839859	−0.419930	+	0.907557i	$0.637945\pi$
$984$	15.3559	0.489527
$985$	−16.9691	−0.540680
$986$	26.9495	0.858248
$987$	−7.28706	−0.231950
$988$	12.2814	0.390725
$989$	−4.15011	−0.131966
$990$	−12.6380	−0.401662
$991$	−59.9221	−1.90349	−0.951745	−	0.306891i	$-0.900711\pi$
$991$	−59.9221	−1.90349	−0.951745	+	0.306891i	$0.900711\pi$
$992$	228.950	7.26918
$993$	5.10864	0.162118
$994$	−11.3044	−0.358553
$995$	−5.68773	−0.180313
$996$	−13.5429	−0.429122
$997$	−10.2703	−0.325264	−0.162632	−	0.986687i	$-0.551998\pi$
$997$	−10.2703	−0.325264	−0.162632	+	0.986687i	$0.551998\pi$
$998$	−18.0143	−0.570231
$999$	−30.7962	−0.974349

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8021.2.a.a.1.1	✓	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)

\(f(q)\)	\(=\)	\(q-2.76381 q^{2} -0.591714 q^{3} +5.63866 q^{4} +2.62273 q^{5} +1.63539 q^{6} +1.07036 q^{7} -10.0566 q^{8} -2.64987 q^{9} +O(q^{10})\)	\(q-2.76381 q^{2} -0.591714 q^{3} +5.63866 q^{4} +2.62273 q^{5} +1.63539 q^{6} +1.07036 q^{7} -10.0566 q^{8} -2.64987 q^{9} -7.24873 q^{10} -0.657947 q^{11} -3.33648 q^{12} +1.00000 q^{13} -2.95826 q^{14} -1.55191 q^{15} +16.5172 q^{16} -2.81377 q^{17} +7.32376 q^{18} +2.17808 q^{19} +14.7887 q^{20} -0.633345 q^{21} +1.81844 q^{22} -1.05300 q^{23} +5.95062 q^{24} +1.87870 q^{25} -2.76381 q^{26} +3.34311 q^{27} +6.03537 q^{28} +3.46541 q^{29} +4.28918 q^{30} -8.96535 q^{31} -25.5372 q^{32} +0.389317 q^{33} +7.77673 q^{34} +2.80725 q^{35} -14.9417 q^{36} -9.21184 q^{37} -6.01980 q^{38} -0.591714 q^{39} -26.3757 q^{40} +2.58055 q^{41} +1.75045 q^{42} +3.94121 q^{43} -3.70994 q^{44} -6.94990 q^{45} +2.91030 q^{46} +11.5057 q^{47} -9.77345 q^{48} -5.85434 q^{49} -5.19238 q^{50} +1.66495 q^{51} +5.63866 q^{52} +2.79476 q^{53} -9.23973 q^{54} -1.72562 q^{55} -10.7641 q^{56} -1.28880 q^{57} -9.57773 q^{58} +2.89352 q^{59} -8.75067 q^{60} -4.99394 q^{61} +24.7785 q^{62} -2.83631 q^{63} +37.5458 q^{64} +2.62273 q^{65} -1.07600 q^{66} +0.939044 q^{67} -15.8659 q^{68} +0.623077 q^{69} -7.75872 q^{70} +3.82129 q^{71} +26.6487 q^{72} -3.07261 q^{73} +25.4598 q^{74} -1.11166 q^{75} +12.2814 q^{76} -0.704238 q^{77} +1.63539 q^{78} -11.1678 q^{79} +43.3201 q^{80} +5.97146 q^{81} -7.13215 q^{82} +4.05903 q^{83} -3.57122 q^{84} -7.37975 q^{85} -10.8928 q^{86} -2.05053 q^{87} +6.61670 q^{88} +4.43124 q^{89} +19.2082 q^{90} +1.07036 q^{91} -5.93752 q^{92} +5.30493 q^{93} -31.7996 q^{94} +5.71251 q^{95} +15.1107 q^{96} +7.68728 q^{97} +16.1803 q^{98} +1.74348 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 134 q - 6 q^{2} - 33 q^{3} + 98 q^{4} - 8 q^{5} - 16 q^{6} - 32 q^{7} - 15 q^{8} + 101 q^{9}+O(q^{10}) \) 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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