LMFDB - Embedded newform 6023.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6023,2,Mod(1,6023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6023, 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("6023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6023 = 19 \cdot 317 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6023.a (trivial)

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$48.0938971374$
Analytic rank:	$1$
Dimension:	$99$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	6023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.57189 q^{2} +2.00338 q^{3} +4.61464 q^{4} +2.67910 q^{5} -5.15249 q^{6} -0.0453210 q^{7} -6.72459 q^{8} +1.01355 q^{9} +O(q^{10})$	\(q-2.57189 q^{2} +2.00338 q^{3} +4.61464 q^{4} +2.67910 q^{5} -5.15249 q^{6} -0.0453210 q^{7} -6.72459 q^{8} +1.01355 q^{9} -6.89035 q^{10} -1.71421 q^{11} +9.24490 q^{12} -0.159583 q^{13} +0.116561 q^{14} +5.36726 q^{15} +8.06564 q^{16} -4.56077 q^{17} -2.60674 q^{18} -1.00000 q^{19} +12.3631 q^{20} -0.0907954 q^{21} +4.40877 q^{22} -0.753976 q^{23} -13.4719 q^{24} +2.17755 q^{25} +0.410432 q^{26} -3.97963 q^{27} -0.209140 q^{28} +5.11629 q^{29} -13.8040 q^{30} -5.02771 q^{31} -7.29481 q^{32} -3.43422 q^{33} +11.7298 q^{34} -0.121419 q^{35} +4.67716 q^{36} -3.38558 q^{37} +2.57189 q^{38} -0.319707 q^{39} -18.0158 q^{40} -5.43845 q^{41} +0.233516 q^{42} +1.37314 q^{43} -7.91047 q^{44} +2.71539 q^{45} +1.93915 q^{46} -3.67114 q^{47} +16.1586 q^{48} -6.99795 q^{49} -5.60044 q^{50} -9.13698 q^{51} -0.736420 q^{52} +3.57753 q^{53} +10.2352 q^{54} -4.59254 q^{55} +0.304765 q^{56} -2.00338 q^{57} -13.1586 q^{58} +5.99338 q^{59} +24.7680 q^{60} +1.57027 q^{61} +12.9308 q^{62} -0.0459350 q^{63} +2.63019 q^{64} -0.427539 q^{65} +8.83246 q^{66} -6.48722 q^{67} -21.0463 q^{68} -1.51050 q^{69} +0.312278 q^{70} +5.31172 q^{71} -6.81569 q^{72} +12.3506 q^{73} +8.70735 q^{74} +4.36248 q^{75} -4.61464 q^{76} +0.0776898 q^{77} +0.822252 q^{78} +3.40787 q^{79} +21.6086 q^{80} -11.0134 q^{81} +13.9871 q^{82} +4.78052 q^{83} -0.418988 q^{84} -12.2187 q^{85} -3.53157 q^{86} +10.2499 q^{87} +11.5274 q^{88} -9.47975 q^{89} -6.98370 q^{90} +0.00723248 q^{91} -3.47933 q^{92} -10.0724 q^{93} +9.44178 q^{94} -2.67910 q^{95} -14.6143 q^{96} -13.4552 q^{97} +17.9980 q^{98} -1.73743 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) $ 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * 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 $

$2$	−2.57189	−1.81860	−0.909302	−	0.416137i	$-0.863384\pi$
$2$	−2.57189	−1.81860	−0.909302	+	0.416137i	$0.863384\pi$
$3$	2.00338	1.15665	0.578327	−	0.815805i	$-0.303706\pi$
$3$	2.00338	1.15665	0.578327	+	0.815805i	$0.303706\pi$
$4$	4.61464	2.30732
$5$	2.67910	1.19813	0.599064	−	0.800701i	$-0.295539\pi$
$5$	2.67910	1.19813	0.599064	+	0.800701i	$0.295539\pi$
$6$	−5.15249	−2.10350
$7$	−0.0453210	−0.0171297	−0.00856487	−	0.999963i	$-0.502726\pi$
$7$	−0.0453210	−0.0171297	−0.00856487	+	0.999963i	$0.502726\pi$
$8$	−6.72459	−2.37750
$9$	1.01355	0.337849
$10$	−6.89035	−2.17892
$11$	−1.71421	−0.516854	−0.258427	−	0.966031i	$-0.583204\pi$
$11$	−1.71421	−0.516854	−0.258427	+	0.966031i	$0.583204\pi$
$12$	9.24490	2.66877
$13$	−0.159583	−0.0442605	−0.0221302	−	0.999755i	$-0.507045\pi$
$13$	−0.159583	−0.0442605	−0.0221302	+	0.999755i	$0.507045\pi$
$14$	0.116561	0.0311522
$15$	5.36726	1.38582
$16$	8.06564	2.01641
$17$	−4.56077	−1.10615	−0.553075	−	0.833131i	$-0.686546\pi$
$17$	−4.56077	−1.10615	−0.553075	+	0.833131i	$0.686546\pi$
$18$	−2.60674	−0.614414
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	12.3631	2.76447
$21$	−0.0907954	−0.0198132
$22$	4.40877	0.939953
$23$	−0.753976	−0.157215	−0.0786074	−	0.996906i	$-0.525047\pi$
$23$	−0.753976	−0.157215	−0.0786074	+	0.996906i	$0.525047\pi$
$24$	−13.4719	−2.74995
$25$	2.17755	0.435511
$26$	0.410432	0.0804922
$27$	−3.97963	−0.765880
$28$	−0.209140	−0.0395238
$29$	5.11629	0.950071	0.475035	−	0.879967i	$-0.342435\pi$
$29$	5.11629	0.950071	0.475035	+	0.879967i	$0.342435\pi$
$30$	−13.8040	−2.52026
$31$	−5.02771	−0.903004	−0.451502	−	0.892270i	$-0.649112\pi$
$31$	−5.02771	−0.903004	−0.451502	+	0.892270i	$0.649112\pi$
$32$	−7.29481	−1.28955
$33$	−3.43422	−0.597822
$34$	11.7298	2.01165
$35$	−0.121419	−0.0205236
$36$	4.67716	0.779526
$37$	−3.38558	−0.556586	−0.278293	−	0.960496i	$-0.589769\pi$
$37$	−3.38558	−0.556586	−0.278293	+	0.960496i	$0.589769\pi$
$38$	2.57189	0.417216
$39$	−0.319707	−0.0511940
$40$	−18.0158	−2.84855
$41$	−5.43845	−0.849344	−0.424672	−	0.905347i	$-0.639610\pi$
$41$	−5.43845	−0.849344	−0.424672	+	0.905347i	$0.639610\pi$
$42$	0.233516	0.0360323
$43$	1.37314	0.209402	0.104701	−	0.994504i	$-0.466611\pi$
$43$	1.37314	0.209402	0.104701	+	0.994504i	$0.466611\pi$
$44$	−7.91047	−1.19255
$45$	2.71539	0.404787
$46$	1.93915	0.285911
$47$	−3.67114	−0.535491	−0.267745	−	0.963490i	$-0.586279\pi$
$47$	−3.67114	−0.535491	−0.267745	+	0.963490i	$0.586279\pi$
$48$	16.1586	2.33229
$49$	−6.99795	−0.999707
$50$	−5.60044	−0.792022
$51$	−9.13698	−1.27943
$52$	−0.736420	−0.102123
$53$	3.57753	0.491411	0.245706	−	0.969344i	$-0.420980\pi$
$53$	3.57753	0.491411	0.245706	+	0.969344i	$0.420980\pi$
$54$	10.2352	1.39283
$55$	−4.59254	−0.619258
$56$	0.304765	0.0407259
$57$	−2.00338	−0.265355
$58$	−13.1586	−1.72780
$59$	5.99338	0.780271	0.390136	−	0.920757i	$-0.372428\pi$
$59$	5.99338	0.780271	0.390136	+	0.920757i	$0.372428\pi$
$60$	24.7680	3.19753
$61$	1.57027	0.201052	0.100526	−	0.994934i	$-0.467947\pi$
$61$	1.57027	0.201052	0.100526	+	0.994934i	$0.467947\pi$
$62$	12.9308	1.64221
$63$	−0.0459350	−0.00578727
$64$	2.63019	0.328774
$65$	−0.427539	−0.0530297
$66$	8.83246	1.08720
$67$	−6.48722	−0.792540	−0.396270	−	0.918134i	$-0.629696\pi$
$67$	−6.48722	−0.792540	−0.396270	+	0.918134i	$0.629696\pi$
$68$	−21.0463	−2.55224
$69$	−1.51050	−0.181843
$70$	0.312278	0.0373243
$71$	5.31172	0.630385	0.315192	−	0.949028i	$-0.397931\pi$
$71$	5.31172	0.630385	0.315192	+	0.949028i	$0.397931\pi$
$72$	−6.81569	−0.803236
$73$	12.3506	1.44553	0.722765	−	0.691094i	$-0.242871\pi$
$73$	12.3506	1.44553	0.722765	+	0.691094i	$0.242871\pi$
$74$	8.70735	1.01221
$75$	4.36248	0.503736
$76$	−4.61464	−0.529336
$77$	0.0776898	0.00885357
$78$	0.822252	0.0931017
$79$	3.40787	0.383415	0.191707	−	0.981452i	$-0.438598\pi$
$79$	3.40787	0.383415	0.191707	+	0.981452i	$0.438598\pi$
$80$	21.6086	2.41592
$81$	−11.0134	−1.22371
$82$	13.9871	1.54462
$83$	4.78052	0.524730	0.262365	−	0.964969i	$-0.415498\pi$
$83$	4.78052	0.524730	0.262365	+	0.964969i	$0.415498\pi$
$84$	−0.418988	−0.0457154
$85$	−12.2187	−1.32531
$86$	−3.53157	−0.380819
$87$	10.2499	1.09890
$88$	11.5274	1.22882
$89$	−9.47975	−1.00485	−0.502426	−	0.864620i	$-0.667559\pi$
$89$	−9.47975	−1.00485	−0.502426	+	0.864620i	$0.667559\pi$
$90$	−6.98370	−0.736147
$91$	0.00723248	0.000758170 0
$92$	−3.47933	−0.362745
$93$	−10.0724	−1.04446
$94$	9.44178	0.973846
$95$	−2.67910	−0.274869
$96$	−14.6143	−1.49157
$97$	−13.4552	−1.36617	−0.683084	−	0.730340i	$-0.739362\pi$
$97$	−13.4552	−1.36617	−0.683084	+	0.730340i	$0.739362\pi$
$98$	17.9980	1.81807
$99$	−1.73743	−0.174619
$100$	10.0486	1.00486
$101$	2.82695	0.281292	0.140646	−	0.990060i	$-0.455082\pi$
$101$	2.82695	0.281292	0.140646	+	0.990060i	$0.455082\pi$
$102$	23.4994	2.32678
$103$	−13.4379	−1.32407	−0.662036	−	0.749472i	$-0.730307\pi$
$103$	−13.4379	−1.32407	−0.662036	+	0.749472i	$0.730307\pi$
$104$	1.07313	0.105229
$105$	−0.243250	−0.0237387
$106$	−9.20103	−0.893683
$107$	−11.4303	−1.10501	−0.552504	−	0.833510i	$-0.686328\pi$
$107$	−11.4303	−1.10501	−0.552504	+	0.833510i	$0.686328\pi$
$108$	−18.3646	−1.76713
$109$	13.9902	1.34002	0.670010	−	0.742352i	$-0.266290\pi$
$109$	13.9902	1.34002	0.670010	+	0.742352i	$0.266290\pi$
$110$	11.8115	1.12618
$111$	−6.78261	−0.643777
$112$	−0.365543	−0.0345406
$113$	16.6819	1.56931	0.784653	−	0.619936i	$-0.212841\pi$
$113$	16.6819	1.56931	0.784653	+	0.619936i	$0.212841\pi$
$114$	5.15249	0.482575
$115$	−2.01997	−0.188363
$116$	23.6098	2.19212
$117$	−0.161745	−0.0149534
$118$	−15.4143	−1.41900
$119$	0.206699	0.0189481
$120$	−36.0926	−3.29479
$121$	−8.06148	−0.732862
$122$	−4.03856	−0.365634
$123$	−10.8953	−0.982397
$124$	−23.2011	−2.08352
$125$	−7.56160	−0.676330
$126$	0.118140	0.0105247
$127$	1.53700	0.136387	0.0681933	−	0.997672i	$-0.478277\pi$
$127$	1.53700	0.136387	0.0681933	+	0.997672i	$0.478277\pi$
$128$	7.82503	0.691641
$129$	2.75092	0.242205
$130$	1.09959	0.0964400
$131$	17.9998	1.57265	0.786327	−	0.617811i	$-0.211980\pi$
$131$	17.9998	1.57265	0.786327	+	0.617811i	$0.211980\pi$
$132$	−15.8477	−1.37937
$133$	0.0453210	0.00392983
$134$	16.6844	1.44132
$135$	−10.6618	−0.917622
$136$	30.6693	2.62987
$137$	−8.07232	−0.689665	−0.344832	−	0.938664i	$-0.612064\pi$
$137$	−8.07232	−0.689665	−0.344832	+	0.938664i	$0.612064\pi$
$138$	3.88485	0.330701
$139$	−12.3743	−1.04957	−0.524785	−	0.851235i	$-0.675854\pi$
$139$	−12.3743	−1.04957	−0.524785	+	0.851235i	$0.675854\pi$
$140$	−0.560307	−0.0473546
$141$	−7.35470	−0.619378
$142$	−13.6612	−1.14642
$143$	0.273560	0.0228762
$144$	8.17491	0.681242
$145$	13.7070	1.13831
$146$	−31.7645	−2.62885
$147$	−14.0196	−1.15631
$148$	−15.6232	−1.28422
$149$	−1.44024	−0.117989	−0.0589945	−	0.998258i	$-0.518789\pi$
$149$	−1.44024	−0.117989	−0.0589945	+	0.998258i	$0.518789\pi$
$150$	−11.2198	−0.916096
$151$	−6.66305	−0.542231	−0.271116	−	0.962547i	$-0.587393\pi$
$151$	−6.66305	−0.542231	−0.271116	+	0.962547i	$0.587393\pi$
$152$	6.72459	0.545436
$153$	−4.62256	−0.373712
$154$	−0.199810	−0.0161011
$155$	−13.4697	−1.08191
$156$	−1.47533	−0.118121
$157$	−19.8118	−1.58115	−0.790577	−	0.612362i	$-0.790220\pi$
$157$	−19.8118	−1.58115	−0.790577	+	0.612362i	$0.790220\pi$
$158$	−8.76467	−0.697280
$159$	7.16716	0.568393
$160$	−19.5435	−1.54505
$161$	0.0341709	0.00269305
$162$	28.3252	2.22544
$163$	4.61994	0.361861	0.180931	−	0.983496i	$-0.442089\pi$
$163$	4.61994	0.361861	0.180931	+	0.983496i	$0.442089\pi$
$164$	−25.0965	−1.95971
$165$	−9.20061	−0.716267
$166$	−12.2950	−0.954276
$167$	−5.02867	−0.389130	−0.194565	−	0.980890i	$-0.562330\pi$
$167$	−5.02867	−0.389130	−0.194565	+	0.980890i	$0.562330\pi$
$168$	0.610561	0.0471058
$169$	−12.9745	−0.998041
$170$	31.4253	2.41021
$171$	−1.01355	−0.0775079
$172$	6.33654	0.483157
$173$	−23.5331	−1.78919	−0.894596	−	0.446876i	$-0.852536\pi$
$173$	−23.5331	−1.78919	−0.894596	+	0.446876i	$0.852536\pi$
$174$	−26.3616	−1.99847
$175$	−0.0986890	−0.00746019
$176$	−13.8262	−1.04219
$177$	12.0070	0.902504
$178$	24.3809	1.82743
$179$	1.62641	0.121564	0.0607818	−	0.998151i	$-0.480641\pi$
$179$	1.62641	0.121564	0.0607818	+	0.998151i	$0.480641\pi$
$180$	12.5306	0.933973
$181$	4.49585	0.334174	0.167087	−	0.985942i	$-0.446564\pi$
$181$	4.49585	0.334174	0.167087	+	0.985942i	$0.446564\pi$
$182$	−0.0186012	−0.00137881
$183$	3.14585	0.232548
$184$	5.07017	0.373778
$185$	−9.07029	−0.666861
$186$	25.9053	1.89947
$187$	7.81813	0.571718
$188$	−16.9410	−1.23555
$189$	0.180361	0.0131193
$190$	6.89035	0.499879
$191$	−22.0003	−1.59189	−0.795945	−	0.605369i	$-0.793025\pi$
$191$	−22.0003	−1.59189	−0.795945	+	0.605369i	$0.793025\pi$
$192$	5.26929	0.380278
$193$	−4.43301	−0.319095	−0.159548	−	0.987190i	$-0.551004\pi$
$193$	−4.43301	−0.319095	−0.159548	+	0.987190i	$0.551004\pi$
$194$	34.6053	2.48452
$195$	−0.856525	−0.0613370
$196$	−32.2930	−2.30664
$197$	−17.3597	−1.23683	−0.618413	−	0.785854i	$-0.712224\pi$
$197$	−17.3597	−1.23683	−0.618413	+	0.785854i	$0.712224\pi$
$198$	4.46850	0.317562
$199$	−18.0719	−1.28108	−0.640542	−	0.767923i	$-0.721290\pi$
$199$	−18.0719	−1.28108	−0.640542	+	0.767923i	$0.721290\pi$
$200$	−14.6432	−1.03543
$201$	−12.9964	−0.916694
$202$	−7.27063	−0.511560
$203$	−0.231875	−0.0162745
$204$	−42.1639	−2.95206
$205$	−14.5701	−1.01762
$206$	34.5608	2.40796
$207$	−0.764190	−0.0531149
$208$	−1.28714	−0.0892472
$209$	1.71421	0.118574
$210$	0.625612	0.0431713
$211$	0.698799	0.0481073	0.0240537	−	0.999711i	$-0.492343\pi$
$211$	0.698799	0.0481073	0.0240537	+	0.999711i	$0.492343\pi$
$212$	16.5090	1.13384
$213$	10.6414	0.729137
$214$	29.3975	2.00957
$215$	3.67877	0.250890
$216$	26.7613	1.82088
$217$	0.227861	0.0154682
$218$	−35.9814	−2.43697
$219$	24.7430	1.67198
$220$	−21.1929	−1.42883
$221$	0.727823	0.0489587
$222$	17.4442	1.17078
$223$	−1.83991	−0.123209	−0.0616047	−	0.998101i	$-0.519622\pi$
$223$	−1.83991	−0.123209	−0.0616047	+	0.998101i	$0.519622\pi$
$224$	0.330608	0.0220897
$225$	2.20705	0.147137
$226$	−42.9042	−2.85395
$227$	9.77645	0.648886	0.324443	−	0.945905i	$-0.394823\pi$
$227$	9.77645	0.648886	0.324443	+	0.945905i	$0.394823\pi$
$228$	−9.24490	−0.612259
$229$	−21.7250	−1.43563	−0.717815	−	0.696234i	$-0.754857\pi$
$229$	−21.7250	−1.43563	−0.717815	+	0.696234i	$0.754857\pi$
$230$	5.19516	0.342559
$231$	0.155642	0.0102405
$232$	−34.4049	−2.25879
$233$	1.84279	0.120725	0.0603625	−	0.998177i	$-0.480774\pi$
$233$	1.84279	0.120725	0.0603625	+	0.998177i	$0.480774\pi$
$234$	0.415992	0.0271942
$235$	−9.83533	−0.641587
$236$	27.6573	1.80034
$237$	6.82726	0.443478
$238$	−0.531608	−0.0344590
$239$	−4.88031	−0.315681	−0.157841	−	0.987465i	$-0.550453\pi$
$239$	−4.88031	−0.315681	−0.157841	+	0.987465i	$0.550453\pi$
$240$	43.2904	2.79438
$241$	−7.82021	−0.503744	−0.251872	−	0.967761i	$-0.581046\pi$
$241$	−7.82021	−0.503744	−0.251872	+	0.967761i	$0.581046\pi$
$242$	20.7333	1.33279
$243$	−10.1251	−0.649526
$244$	7.24621	0.463891
$245$	−18.7482	−1.19778
$246$	28.0216	1.78659
$247$	0.159583	0.0101540
$248$	33.8093	2.14689
$249$	9.57722	0.606931
$250$	19.4476	1.22998
$251$	6.09664	0.384816	0.192408	−	0.981315i	$-0.438370\pi$
$251$	6.09664	0.384816	0.192408	+	0.981315i	$0.438370\pi$
$252$	−0.211974	−0.0133531
$253$	1.29247	0.0812571
$254$	−3.95300	−0.248033
$255$	−24.4788	−1.53292
$256$	−25.3855	−1.58660
$257$	−1.28324	−0.0800465	−0.0400233	−	0.999199i	$-0.512743\pi$
$257$	−1.28324	−0.0800465	−0.0400233	+	0.999199i	$0.512743\pi$
$258$	−7.07509	−0.440476
$259$	0.153438	0.00953416
$260$	−1.97294	−0.122357
$261$	5.18560	0.320981
$262$	−46.2937	−2.86003
$263$	−3.63017	−0.223846	−0.111923	−	0.993717i	$-0.535701\pi$
$263$	−3.63017	−0.223846	−0.111923	+	0.993717i	$0.535701\pi$
$264$	23.0937	1.42132
$265$	9.58454	0.588774
$266$	−0.116561	−0.00714681
$267$	−18.9916	−1.16227
$268$	−29.9362	−1.82864
$269$	−3.48192	−0.212296	−0.106148	−	0.994350i	$-0.533852\pi$
$269$	−3.48192	−0.212296	−0.106148	+	0.994350i	$0.533852\pi$
$270$	27.4210	1.66879
$271$	19.0482	1.15710	0.578548	−	0.815649i	$-0.303620\pi$
$271$	19.0482	1.15710	0.578548	+	0.815649i	$0.303620\pi$
$272$	−36.7856	−2.23045
$273$	0.0144894	0.000876940 0
$274$	20.7612	1.25423
$275$	−3.73279	−0.225096
$276$	−6.97043	−0.419571
$277$	8.03324	0.482671	0.241335	−	0.970442i	$-0.422415\pi$
$277$	8.03324	0.482671	0.241335	+	0.970442i	$0.422415\pi$
$278$	31.8253	1.90875
$279$	−5.09583	−0.305079
$280$	0.816495	0.0487949
$281$	16.6402	0.992671	0.496336	−	0.868131i	$-0.334679\pi$
$281$	16.6402	0.992671	0.496336	+	0.868131i	$0.334679\pi$
$282$	18.9155	1.12640
$283$	11.4326	0.679600	0.339800	−	0.940498i	$-0.389641\pi$
$283$	11.4326	0.679600	0.339800	+	0.940498i	$0.389641\pi$
$284$	24.5117	1.45450
$285$	−5.36726	−0.317929
$286$	−0.703566	−0.0416028
$287$	0.246476	0.0145490
$288$	−7.39363	−0.435674
$289$	3.80065	0.223568
$290$	−35.2530	−2.07013
$291$	−26.9559	−1.58018
$292$	56.9937	3.33530
$293$	−6.71705	−0.392414	−0.196207	−	0.980562i	$-0.562862\pi$
$293$	−6.71705	−0.392414	−0.196207	+	0.980562i	$0.562862\pi$
$294$	36.0569	2.10288
$295$	16.0568	0.934865
$296$	22.7666	1.32328
$297$	6.82192	0.395848
$298$	3.70415	0.214575
$299$	0.120322	0.00695840
$300$	20.1313	1.16228
$301$	−0.0622320	−0.00358700
$302$	17.1367	0.986104
$303$	5.66347	0.325358
$304$	−8.06564	−0.462596
$305$	4.20689	0.240886
$306$	11.8887	0.679634
$307$	−21.8895	−1.24930	−0.624651	−	0.780904i	$-0.714759\pi$
$307$	−21.8895	−1.24930	−0.624651	+	0.780904i	$0.714759\pi$
$308$	0.358511	0.0204280
$309$	−26.9212	−1.53149
$310$	34.6427	1.96757
$311$	−15.1705	−0.860240	−0.430120	−	0.902772i	$-0.641529\pi$
$311$	−15.1705	−0.860240	−0.430120	+	0.902772i	$0.641529\pi$
$312$	2.14989	0.121714
$313$	13.4554	0.760543	0.380272	−	0.924875i	$-0.375831\pi$
$313$	13.4554	0.760543	0.380272	+	0.924875i	$0.375831\pi$
$314$	50.9539	2.87550
$315$	−0.123064	−0.00693389
$316$	15.7261	0.884661
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−18.4332	−1.03368
$319$	−8.77040	−0.491048
$320$	7.04654	0.393914
$321$	−22.8993	−1.27811
$322$	−0.0878841	−0.00489759
$323$	4.56077	0.253768
$324$	−50.8227	−2.82349
$325$	−0.347501	−0.0192759
$326$	−11.8820	−0.658082
$327$	28.0278	1.54994
$328$	36.5713	2.01931
$329$	0.166380	0.00917281
$330$	23.6630	1.30261
$331$	8.25169	0.453554	0.226777	−	0.973947i	$-0.427181\pi$
$331$	8.25169	0.453554	0.226777	+	0.973947i	$0.427181\pi$
$332$	22.0604	1.21072
$333$	−3.43144	−0.188042
$334$	12.9332	0.707674
$335$	−17.3799	−0.949564
$336$	−0.732323	−0.0399515
$337$	−3.28692	−0.179050	−0.0895250	−	0.995985i	$-0.528535\pi$
$337$	−3.28692	−0.179050	−0.0895250	+	0.995985i	$0.528535\pi$
$338$	33.3691	1.81504
$339$	33.4203	1.81514
$340$	−56.3852	−3.05791
$341$	8.61856	0.466721
$342$	2.60674	0.140956
$343$	0.634401	0.0342544
$344$	−9.23379	−0.497853
$345$	−4.04678	−0.217871
$346$	60.5248	3.25383
$347$	−5.96566	−0.320254	−0.160127	−	0.987096i	$-0.551190\pi$
$347$	−5.96566	−0.320254	−0.160127	+	0.987096i	$0.551190\pi$
$348$	47.2996	2.53552
$349$	−8.39802	−0.449536	−0.224768	−	0.974412i	$-0.572162\pi$
$349$	−8.39802	−0.449536	−0.224768	+	0.974412i	$0.572162\pi$
$350$	0.253818	0.0135671
$351$	0.635082	0.0338982
$352$	12.5048	0.666510
$353$	21.2463	1.13083	0.565414	−	0.824807i	$-0.308716\pi$
$353$	21.2463	1.13083	0.565414	+	0.824807i	$0.308716\pi$
$354$	−30.8808	−1.64130
$355$	14.2306	0.755282
$356$	−43.7457	−2.31852
$357$	0.414097	0.0219163
$358$	−4.18296	−0.221076
$359$	22.9704	1.21233	0.606165	−	0.795339i	$-0.292707\pi$
$359$	22.9704	1.21233	0.606165	+	0.795339i	$0.292707\pi$
$360$	−18.2599	−0.962380
$361$	1.00000	0.0526316
$362$	−11.5629	−0.607730
$363$	−16.1502	−0.847668
$364$	0.0333753	0.00174934
$365$	33.0885	1.73193
$366$	−8.09078	−0.422912
$367$	−11.3266	−0.591244	−0.295622	−	0.955305i	$-0.595527\pi$
$367$	−11.3266	−0.591244	−0.295622	+	0.955305i	$0.595527\pi$
$368$	−6.08130	−0.317009
$369$	−5.51213	−0.286950
$370$	23.3278	1.21276
$371$	−0.162137	−0.00841775
$372$	−46.4807	−2.40991
$373$	11.8114	0.611573	0.305786	−	0.952100i	$-0.401081\pi$
$373$	11.8114	0.611573	0.305786	+	0.952100i	$0.401081\pi$
$374$	−20.1074	−1.03973
$375$	−15.1488	−0.782280
$376$	24.6869	1.27313
$377$	−0.816474	−0.0420506
$378$	−0.463869	−0.0238588
$379$	24.5631	1.26172	0.630862	−	0.775895i	$-0.282702\pi$
$379$	24.5631	1.26172	0.630862	+	0.775895i	$0.282702\pi$
$380$	−12.3631	−0.634212
$381$	3.07920	0.157752
$382$	56.5826	2.89502
$383$	25.3113	1.29335	0.646675	−	0.762766i	$-0.276159\pi$
$383$	25.3113	1.29335	0.646675	+	0.762766i	$0.276159\pi$
$384$	15.6765	0.799990
$385$	0.208138	0.0106077
$386$	11.4012	0.580308
$387$	1.39174	0.0707462
$388$	−62.0909	−3.15219
$389$	22.3299	1.13217	0.566084	−	0.824347i	$-0.308458\pi$
$389$	22.3299	1.13217	0.566084	+	0.824347i	$0.308458\pi$
$390$	2.20289	0.111548
$391$	3.43871	0.173903
$392$	47.0583	2.37680
$393$	36.0606	1.81902
$394$	44.6472	2.24930
$395$	9.13000	0.459380
$396$	−8.01764	−0.402902
$397$	−29.7196	−1.49158	−0.745791	−	0.666180i	$-0.767928\pi$
$397$	−29.7196	−1.49158	−0.745791	+	0.666180i	$0.767928\pi$
$398$	46.4791	2.32978
$399$	0.0907954	0.00454545
$400$	17.5634	0.878169
$401$	30.9415	1.54515	0.772573	−	0.634926i	$-0.218969\pi$
$401$	30.9415	1.54515	0.772573	+	0.634926i	$0.218969\pi$
$402$	33.4253	1.66710
$403$	0.802339	0.0399674
$404$	13.0454	0.649032
$405$	−29.5059	−1.46616
$406$	0.596359	0.0295968
$407$	5.80360	0.287674
$408$	61.4424	3.04185
$409$	20.8914	1.03302	0.516508	−	0.856283i	$-0.327232\pi$
$409$	20.8914	1.03302	0.516508	+	0.856283i	$0.327232\pi$
$410$	37.4729	1.85065
$411$	−16.1720	−0.797704
$412$	−62.0109	−3.05506
$413$	−0.271626	−0.0133658
$414$	1.96542	0.0965949
$415$	12.8075	0.628694
$416$	1.16413	0.0570761
$417$	−24.7904	−1.21399
$418$	−4.40877	−0.215640
$419$	−25.6788	−1.25449	−0.627246	−	0.778821i	$-0.715818\pi$
$419$	−25.6788	−1.25449	−0.627246	+	0.778821i	$0.715818\pi$
$420$	−1.12251	−0.0547729
$421$	1.29284	0.0630091	0.0315046	−	0.999504i	$-0.489970\pi$
$421$	1.29284	0.0630091	0.0315046	+	0.999504i	$0.489970\pi$
$422$	−1.79724	−0.0874882
$423$	−3.72087	−0.180915
$424$	−24.0574	−1.16833
$425$	−9.93133	−0.481740
$426$	−27.3686	−1.32601
$427$	−0.0711660	−0.00344397
$428$	−52.7467	−2.54961
$429$	0.548045	0.0264599
$430$	−9.46141	−0.456270
$431$	−5.97831	−0.287965	−0.143983	−	0.989580i	$-0.545991\pi$
$431$	−5.97831	−0.287965	−0.143983	+	0.989580i	$0.545991\pi$
$432$	−32.0982	−1.54433
$433$	−10.9615	−0.526777	−0.263388	−	0.964690i	$-0.584840\pi$
$433$	−10.9615	−0.526777	−0.263388	+	0.964690i	$0.584840\pi$
$434$	−0.586035	−0.0281306
$435$	27.4604	1.31663
$436$	64.5599	3.09186
$437$	0.753976	0.0360675
$438$	−63.6364	−3.04067
$439$	25.7960	1.23117	0.615587	−	0.788069i	$-0.288919\pi$
$439$	25.7960	1.23117	0.615587	+	0.788069i	$0.288919\pi$
$440$	30.8829	1.47228
$441$	−7.09275	−0.337750
$442$	−1.87189	−0.0890365
$443$	14.5444	0.691027	0.345514	−	0.938414i	$-0.387705\pi$
$443$	14.5444	0.691027	0.345514	+	0.938414i	$0.387705\pi$
$444$	−31.2993	−1.48540
$445$	−25.3972	−1.20394
$446$	4.73205	0.224069
$447$	−2.88535	−0.136473
$448$	−0.119203	−0.00563182
$449$	22.2306	1.04913	0.524565	−	0.851371i	$-0.324228\pi$
$449$	22.2306	1.04913	0.524565	+	0.851371i	$0.324228\pi$
$450$	−5.67631	−0.267584
$451$	9.32266	0.438987
$452$	76.9812	3.62089
$453$	−13.3487	−0.627174
$454$	−25.1440	−1.18007
$455$	0.0193765	0.000908384 0
$456$	13.4719	0.630881
$457$	−40.2190	−1.88136	−0.940682	−	0.339290i	$-0.889813\pi$
$457$	−40.2190	−1.88136	−0.940682	+	0.339290i	$0.889813\pi$
$458$	55.8744	2.61084
$459$	18.1502	0.847178
$460$	−9.32145	−0.434615
$461$	14.7408	0.686548	0.343274	−	0.939235i	$-0.388464\pi$
$461$	14.7408	0.686548	0.343274	+	0.939235i	$0.388464\pi$
$462$	−0.400296	−0.0186235
$463$	9.70346	0.450958	0.225479	−	0.974248i	$-0.427605\pi$
$463$	9.70346	0.450958	0.225479	+	0.974248i	$0.427605\pi$
$464$	41.2661	1.91573
$465$	−26.9850	−1.25140
$466$	−4.73946	−0.219551
$467$	−20.5076	−0.948980	−0.474490	−	0.880261i	$-0.657367\pi$
$467$	−20.5076	−0.948980	−0.474490	+	0.880261i	$0.657367\pi$
$468$	−0.746397	−0.0345022
$469$	0.294007	0.0135760
$470$	25.2954	1.16679
$471$	−39.6907	−1.82885
$472$	−40.3030	−1.85509
$473$	−2.35385	−0.108230
$474$	−17.5590	−0.806512
$475$	−2.17755	−0.0999131
$476$	0.953841	0.0437192
$477$	3.62600	0.166023
$478$	12.5517	0.574099
$479$	−17.5402	−0.801432	−0.400716	−	0.916202i	$-0.631239\pi$
$479$	−17.5402	−0.801432	−0.400716	+	0.916202i	$0.631239\pi$
$480$	−39.1531	−1.78709
$481$	0.540282	0.0246347
$482$	20.1128	0.916111
$483$	0.0684575	0.00311492
$484$	−37.2008	−1.69095
$485$	−36.0477	−1.63684
$486$	26.0407	1.18123
$487$	−12.8001	−0.580030	−0.290015	−	0.957022i	$-0.593660\pi$
$487$	−12.8001	−0.580030	−0.290015	+	0.957022i	$0.593660\pi$
$488$	−10.5594	−0.478001
$489$	9.25551	0.418548
$490$	48.2183	2.17828
$491$	28.7433	1.29717	0.648584	−	0.761143i	$-0.275361\pi$
$491$	28.7433	1.29717	0.648584	+	0.761143i	$0.275361\pi$
$492$	−50.2780	−2.26671
$493$	−23.3342	−1.05092
$494$	−0.410432	−0.0184662
$495$	−4.65475	−0.209216
$496$	−40.5517	−1.82083
$497$	−0.240732	−0.0107983
$498$	−24.6316	−1.10377
$499$	−11.1429	−0.498823	−0.249412	−	0.968398i	$-0.580237\pi$
$499$	−11.1429	−0.498823	−0.249412	+	0.968398i	$0.580237\pi$
$500$	−34.8941	−1.56051
$501$	−10.0744	−0.450089
$502$	−15.6799	−0.699828
$503$	6.12978	0.273314	0.136657	−	0.990618i	$-0.456364\pi$
$503$	6.12978	0.273314	0.136657	+	0.990618i	$0.456364\pi$
$504$	0.308894	0.0137592
$505$	7.57368	0.337024
$506$	−3.32411	−0.147775
$507$	−25.9930	−1.15439
$508$	7.09270	0.314688
$509$	30.7647	1.36362	0.681810	−	0.731530i	$-0.261193\pi$
$509$	30.7647	1.36362	0.681810	+	0.731530i	$0.261193\pi$
$510$	62.9570	2.78778
$511$	−0.559742	−0.0247615
$512$	49.6389	2.19375
$513$	3.97963	0.175705
$514$	3.30037	0.145573
$515$	−36.0013	−1.58641
$516$	12.6945	0.558846
$517$	6.29311	0.276771
$518$	−0.394626	−0.0173389
$519$	−47.1459	−2.06948
$520$	2.87502	0.126078
$521$	−17.1315	−0.750545	−0.375273	−	0.926915i	$-0.622451\pi$
$521$	−17.1315	−0.750545	−0.375273	+	0.926915i	$0.622451\pi$
$522$	−13.3368	−0.583737
$523$	4.07052	0.177991	0.0889957	−	0.996032i	$-0.471634\pi$
$523$	4.07052	0.177991	0.0889957	+	0.996032i	$0.471634\pi$
$524$	83.0628	3.62862
$525$	−0.197712	−0.00862886
$526$	9.33641	0.407087
$527$	22.9303	0.998858
$528$	−27.6992	−1.20545
$529$	−22.4315	−0.975284
$530$	−24.6504	−1.07075
$531$	6.07457	0.263614
$532$	0.209140	0.00906738
$533$	0.867886	0.0375923
$534$	48.8443	2.11370
$535$	−30.6228	−1.32394
$536$	43.6238	1.88426
$537$	3.25832	0.140607
$538$	8.95512	0.386083
$539$	11.9960	0.516703
$540$	−49.2004	−2.11725
$541$	−42.7257	−1.83692	−0.918461	−	0.395511i	$-0.870567\pi$
$541$	−42.7257	−1.83692	−0.918461	+	0.395511i	$0.870567\pi$
$542$	−48.9899	−2.10430
$543$	9.00691	0.386524
$544$	33.2700	1.42644
$545$	37.4812	1.60552
$546$	−0.0372653	−0.00159481
$547$	15.3241	0.655213	0.327607	−	0.944814i	$-0.393758\pi$
$547$	15.3241	0.655213	0.327607	+	0.944814i	$0.393758\pi$
$548$	−37.2509	−1.59128
$549$	1.59154	0.0679252
$550$	9.60034	0.409360
$551$	−5.11629	−0.217961
$552$	10.1575	0.432332
$553$	−0.154448	−0.00656779
$554$	−20.6606	−0.877787
$555$	−18.1713	−0.771327
$556$	−57.1027	−2.42170
$557$	−23.4583	−0.993960	−0.496980	−	0.867762i	$-0.665558\pi$
$557$	−23.4583	−0.993960	−0.496980	+	0.867762i	$0.665558\pi$
$558$	13.1059	0.554818
$559$	−0.219130	−0.00926821
$560$	−0.979325	−0.0413840
$561$	15.6627	0.661280
$562$	−42.7969	−1.80528
$563$	27.1072	1.14243	0.571216	−	0.820799i	$-0.306472\pi$
$563$	27.1072	1.14243	0.571216	+	0.820799i	$0.306472\pi$
$564$	−33.9393	−1.42910
$565$	44.6925	1.88023
$566$	−29.4036	−1.23592
$567$	0.499137	0.0209618
$568$	−35.7191	−1.49874
$569$	−33.6232	−1.40956	−0.704779	−	0.709427i	$-0.748954\pi$
$569$	−33.6232	−1.40956	−0.704779	+	0.709427i	$0.748954\pi$
$570$	13.8040	0.578187
$571$	−18.3753	−0.768981	−0.384491	−	0.923129i	$-0.625623\pi$
$571$	−18.3753	−0.768981	−0.384491	+	0.923129i	$0.625623\pi$
$572$	1.26238	0.0527827
$573$	−44.0751	−1.84127
$574$	−0.633911	−0.0264589
$575$	−1.64182	−0.0684688
$576$	2.66583	0.111076
$577$	35.7124	1.48673	0.743363	−	0.668888i	$-0.233229\pi$
$577$	35.7124	1.48673	0.743363	+	0.668888i	$0.233229\pi$
$578$	−9.77488	−0.406581
$579$	−8.88103	−0.369083
$580$	63.2530	2.62644
$581$	−0.216658	−0.00898849
$582$	69.3278	2.87373
$583$	−6.13264	−0.253988
$584$	−83.0527	−3.43675
$585$	−0.433331	−0.0179160
$586$	17.2755	0.713646
$587$	−34.5173	−1.42468	−0.712342	−	0.701833i	$-0.752365\pi$
$587$	−34.5173	−1.42468	−0.712342	+	0.701833i	$0.752365\pi$
$588$	−64.6953	−2.66799
$589$	5.02771	0.207163
$590$	−41.2965	−1.70015
$591$	−34.7781	−1.43058
$592$	−27.3069	−1.12230
$593$	3.83383	0.157436	0.0787182	−	0.996897i	$-0.474917\pi$
$593$	3.83383	0.157436	0.0787182	+	0.996897i	$0.474917\pi$
$594$	−17.5453	−0.719891
$595$	0.553766	0.0227022
$596$	−6.64619	−0.272239
$597$	−36.2050	−1.48177
$598$	−0.309455	−0.0126546
$599$	31.8560	1.30160	0.650801	−	0.759248i	$-0.274433\pi$
$599$	31.8560	1.30160	0.650801	+	0.759248i	$0.274433\pi$
$600$	−29.3359	−1.19763
$601$	3.55332	0.144943	0.0724715	−	0.997370i	$-0.476911\pi$
$601$	3.55332	0.144943	0.0724715	+	0.997370i	$0.476911\pi$
$602$	0.160054	0.00652332
$603$	−6.57510	−0.267759
$604$	−30.7476	−1.25110
$605$	−21.5975	−0.878062
$606$	−14.5659	−0.591698
$607$	−20.6847	−0.839566	−0.419783	−	0.907624i	$-0.637894\pi$
$607$	−20.6847	−0.839566	−0.419783	+	0.907624i	$0.637894\pi$
$608$	7.29481	0.295843
$609$	−0.464535	−0.0188239
$610$	−10.8197	−0.438076
$611$	0.585853	0.0237011
$612$	−21.3315	−0.862273
$613$	6.63922	0.268156	0.134078	−	0.990971i	$-0.457193\pi$
$613$	6.63922	0.268156	0.134078	+	0.990971i	$0.457193\pi$
$614$	56.2976	2.27198
$615$	−29.1896	−1.17704
$616$	−0.522432	−0.0210494
$617$	22.9040	0.922080	0.461040	−	0.887379i	$-0.347477\pi$
$617$	22.9040	0.922080	0.461040	+	0.887379i	$0.347477\pi$
$618$	69.2385	2.78518
$619$	−16.9595	−0.681658	−0.340829	−	0.940125i	$-0.610708\pi$
$619$	−16.9595	−0.681658	−0.340829	+	0.940125i	$0.610708\pi$
$620$	−62.1580	−2.49632
$621$	3.00054	0.120408
$622$	39.0169	1.56444
$623$	0.429632	0.0172128
$624$	−2.57864	−0.103228
$625$	−31.1460	−1.24584
$626$	−34.6058	−1.38313
$627$	3.43422	0.137150
$628$	−91.4244	−3.64823
$629$	15.4409	0.615667
$630$	0.316508	0.0126100
$631$	20.6358	0.821498	0.410749	−	0.911748i	$-0.365267\pi$
$631$	20.6358	0.821498	0.410749	+	0.911748i	$0.365267\pi$
$632$	−22.9165	−0.911569
$633$	1.39996	0.0556435
$634$	2.57189	0.102143
$635$	4.11777	0.163409
$636$	33.0739	1.31147
$637$	1.11676	0.0442475
$638$	22.5565	0.893022
$639$	5.38368	0.212975
$640$	20.9640	0.828675
$641$	34.1749	1.34983	0.674913	−	0.737897i	$-0.264181\pi$
$641$	34.1749	1.34983	0.674913	+	0.737897i	$0.264181\pi$
$642$	58.8945	2.32438
$643$	32.9382	1.29896	0.649478	−	0.760381i	$-0.274988\pi$
$643$	32.9382	1.29896	0.649478	+	0.760381i	$0.274988\pi$
$644$	0.157687	0.00621373
$645$	7.36999	0.290193
$646$	−11.7298	−0.461504
$647$	−10.6900	−0.420266	−0.210133	−	0.977673i	$-0.567390\pi$
$647$	−10.6900	−0.420266	−0.210133	+	0.977673i	$0.567390\pi$
$648$	74.0603	2.90936
$649$	−10.2739	−0.403286
$650$	0.893737	0.0350553
$651$	0.456493	0.0178914
$652$	21.3194	0.834930
$653$	−3.83445	−0.150054	−0.0750269	−	0.997182i	$-0.523904\pi$
$653$	−3.83445	−0.150054	−0.0750269	+	0.997182i	$0.523904\pi$
$654$	−72.0845	−2.81873
$655$	48.2233	1.88424
$656$	−43.8646	−1.71262
$657$	12.5179	0.488371
$658$	−0.427911	−0.0166817
$659$	25.7026	1.00123	0.500615	−	0.865670i	$-0.333107\pi$
$659$	25.7026	1.00123	0.500615	+	0.865670i	$0.333107\pi$
$660$	−42.4575	−1.65266
$661$	−2.03423	−0.0791225	−0.0395612	−	0.999217i	$-0.512596\pi$
$661$	−2.03423	−0.0791225	−0.0395612	+	0.999217i	$0.512596\pi$
$662$	−21.2225	−0.824835
$663$	1.45811	0.0566283
$664$	−32.1470	−1.24755
$665$	0.121419	0.00470844
$666$	8.82531	0.341974
$667$	−3.85756	−0.149365
$668$	−23.2055	−0.897849
$669$	−3.68604	−0.142511
$670$	44.6992	1.72688
$671$	−2.69177	−0.103915
$672$	0.662335	0.0255501
$673$	1.58169	0.0609696	0.0304848	−	0.999535i	$-0.490295\pi$
$673$	1.58169	0.0609696	0.0304848	+	0.999535i	$0.490295\pi$
$674$	8.45361	0.325621
$675$	−8.66586	−0.333549
$676$	−59.8728	−2.30280
$677$	10.9675	0.421516	0.210758	−	0.977538i	$-0.432407\pi$
$677$	10.9675	0.421516	0.210758	+	0.977538i	$0.432407\pi$
$678$	−85.9536	−3.30103
$679$	0.609803	0.0234021
$680$	82.1660	3.15092
$681$	19.5860	0.750536
$682$	−22.1660	−0.848782
$683$	0.621889	0.0237959	0.0118980	−	0.999929i	$-0.496213\pi$
$683$	0.621889	0.0237959	0.0118980	+	0.999929i	$0.496213\pi$
$684$	−4.67716	−0.178836
$685$	−21.6265	−0.826307
$686$	−1.63161	−0.0622953
$687$	−43.5235	−1.66053
$688$	11.0752	0.422240
$689$	−0.570914	−0.0217501
$690$	10.4079	0.396222
$691$	2.02479	0.0770267	0.0385134	−	0.999258i	$-0.487738\pi$
$691$	2.02479	0.0770267	0.0385134	+	0.999258i	$0.487738\pi$
$692$	−108.597	−4.12824
$693$	0.0787423	0.00299117
$694$	15.3431	0.582414
$695$	−33.1518	−1.25752
$696$	−68.9262	−2.61264
$697$	24.8035	0.939501
$698$	21.5988	0.817527
$699$	3.69181	0.139637
$700$	−0.455414	−0.0172130
$701$	27.0295	1.02089	0.510445	−	0.859910i	$-0.329481\pi$
$701$	27.0295	1.02089	0.510445	+	0.859910i	$0.329481\pi$
$702$	−1.63336	−0.0616474
$703$	3.38558	0.127689
$704$	−4.50871	−0.169928
$705$	−19.7040	−0.742094
$706$	−54.6433	−2.05653
$707$	−0.128120	−0.00481846
$708$	55.4082	2.08237
$709$	−2.11778	−0.0795348	−0.0397674	−	0.999209i	$-0.512662\pi$
$709$	−2.11778	−0.0795348	−0.0397674	+	0.999209i	$0.512662\pi$
$710$	−36.5996	−1.37356
$711$	3.45403	0.129536
$712$	63.7474	2.38903
$713$	3.79077	0.141966
$714$	−1.06501	−0.0398572
$715$	0.732892	0.0274086
$716$	7.50530	0.280486
$717$	−9.77714	−0.365134
$718$	−59.0774	−2.20475
$719$	−1.97385	−0.0736123	−0.0368062	−	0.999322i	$-0.511718\pi$
$719$	−1.97385	−0.0736123	−0.0368062	+	0.999322i	$0.511718\pi$
$720$	21.9014	0.816216
$721$	0.609018	0.0226810
$722$	−2.57189	−0.0957160
$723$	−15.6669	−0.582658
$724$	20.7467	0.771046
$725$	11.1410	0.413766
$726$	41.5367	1.54157
$727$	−20.3535	−0.754871	−0.377435	−	0.926036i	$-0.623194\pi$
$727$	−20.3535	−0.754871	−0.377435	+	0.926036i	$0.623194\pi$
$728$	−0.0486354	−0.00180255
$729$	12.7556	0.472430
$730$	−85.1001	−3.14969
$731$	−6.26257	−0.231630
$732$	14.5170	0.536562
$733$	44.0849	1.62831	0.814156	−	0.580646i	$-0.197200\pi$
$733$	44.0849	1.62831	0.814156	+	0.580646i	$0.197200\pi$
$734$	29.1308	1.07524
$735$	−37.5598	−1.38541
$736$	5.50011	0.202737
$737$	11.1205	0.409627
$738$	14.1766	0.521848
$739$	−7.25687	−0.266948	−0.133474	−	0.991052i	$-0.542613\pi$
$739$	−7.25687	−0.266948	−0.133474	+	0.991052i	$0.542613\pi$
$740$	−41.8561	−1.53866
$741$	0.319707	0.0117447
$742$	0.417000	0.0153085
$743$	8.83598	0.324161	0.162080	−	0.986778i	$-0.448180\pi$
$743$	8.83598	0.324161	0.162080	+	0.986778i	$0.448180\pi$
$744$	67.7330	2.48321
$745$	−3.85854	−0.141366
$746$	−30.3778	−1.11221
$747$	4.84528	0.177280
$748$	36.0779	1.31914
$749$	0.518032	0.0189285
$750$	38.9611	1.42266
$751$	8.49376	0.309942	0.154971	−	0.987919i	$-0.450472\pi$
$751$	8.49376	0.309942	0.154971	+	0.987919i	$0.450472\pi$
$752$	−29.6101	−1.07977
$753$	12.2139	0.445099
$754$	2.09989	0.0764733
$755$	−17.8510	−0.649663
$756$	0.832300	0.0302705
$757$	−31.7010	−1.15219	−0.576096	−	0.817382i	$-0.695425\pi$
$757$	−31.7010	−1.15219	−0.576096	+	0.817382i	$0.695425\pi$
$758$	−63.1738	−2.29458
$759$	2.58932	0.0939864
$760$	18.0158	0.653502
$761$	11.6770	0.423292	0.211646	−	0.977346i	$-0.432118\pi$
$761$	11.6770	0.423292	0.211646	+	0.977346i	$0.432118\pi$
$762$	−7.91937	−0.286889
$763$	−0.634051	−0.0229542
$764$	−101.524	−3.67300
$765$	−12.3843	−0.447755
$766$	−65.0981	−2.35209
$767$	−0.956443	−0.0345351
$768$	−50.8570	−1.83514
$769$	−5.90563	−0.212963	−0.106481	−	0.994315i	$-0.533958\pi$
$769$	−5.90563	−0.212963	−0.106481	+	0.994315i	$0.533958\pi$
$770$	−0.535310	−0.0192912
$771$	−2.57083	−0.0925862
$772$	−20.4568	−0.736255
$773$	−19.8436	−0.713725	−0.356863	−	0.934157i	$-0.616154\pi$
$773$	−19.8436	−0.713725	−0.356863	+	0.934157i	$0.616154\pi$
$774$	−3.57941	−0.128659
$775$	−10.9481	−0.393268
$776$	90.4806	3.24806
$777$	0.307395	0.0110277
$778$	−57.4300	−2.05897
$779$	5.43845	0.194853
$780$	−3.95256	−0.141524
$781$	−9.10541	−0.325817
$782$	−8.84401	−0.316261
$783$	−20.3609	−0.727640
$784$	−56.4429	−2.01582
$785$	−53.0778	−1.89443
$786$	−92.7441	−3.30807
$787$	−39.3823	−1.40383	−0.701913	−	0.712263i	$-0.747671\pi$
$787$	−39.3823	−1.40383	−0.701913	+	0.712263i	$0.747671\pi$
$788$	−80.1087	−2.85375
$789$	−7.27262	−0.258912
$790$	−23.4814	−0.835431
$791$	−0.756043	−0.0268818
$792$	11.6835	0.415156
$793$	−0.250588	−0.00889865
$794$	76.4356	2.71260
$795$	19.2015	0.681008
$796$	−83.3954	−2.95587
$797$	18.9185	0.670128	0.335064	−	0.942195i	$-0.391242\pi$
$797$	18.9185	0.670128	0.335064	+	0.942195i	$0.391242\pi$
$798$	−0.233516	−0.00826638
$799$	16.7432	0.592333
$800$	−15.8848	−0.561614
$801$	−9.60818	−0.339488
$802$	−79.5784	−2.81001
$803$	−21.1716	−0.747128
$804$	−59.9737	−2.11511
$805$	0.0915472	0.00322662
$806$	−2.06353	−0.0726848
$807$	−6.97562	−0.245553
$808$	−19.0101	−0.668773
$809$	0.467747	0.0164451	0.00822255	−	0.999966i	$-0.497383\pi$
$809$	0.467747	0.0164451	0.00822255	+	0.999966i	$0.497383\pi$
$810$	75.8860	2.66636
$811$	−8.85342	−0.310886	−0.155443	−	0.987845i	$-0.549680\pi$
$811$	−8.85342	−0.310886	−0.155443	+	0.987845i	$0.549680\pi$
$812$	−1.07002	−0.0375504
$813$	38.1608	1.33836
$814$	−14.9262	−0.523164
$815$	12.3773	0.433556
$816$	−73.6956	−2.57986
$817$	−1.37314	−0.0480400
$818$	−53.7306	−1.87865
$819$	0.00733046	0.000256147 0
$820$	−67.2360	−2.34798
$821$	−33.8258	−1.18053	−0.590264	−	0.807210i	$-0.700976\pi$
$821$	−33.8258	−1.18053	−0.590264	+	0.807210i	$0.700976\pi$
$822$	41.5926	1.45071
$823$	−23.5885	−0.822243	−0.411122	−	0.911581i	$-0.634863\pi$
$823$	−23.5885	−0.822243	−0.411122	+	0.911581i	$0.634863\pi$
$824$	90.3641	3.14798
$825$	−7.47821	−0.260358
$826$	0.698593	0.0243072
$827$	−15.0842	−0.524528	−0.262264	−	0.964996i	$-0.584469\pi$
$827$	−15.0842	−0.524528	−0.262264	+	0.964996i	$0.584469\pi$
$828$	−3.52646	−0.122553
$829$	35.0074	1.21586	0.607929	−	0.793991i	$-0.292000\pi$
$829$	35.0074	1.21586	0.607929	+	0.793991i	$0.292000\pi$
$830$	−32.9395	−1.14335
$831$	16.0937	0.558283
$832$	−0.419735	−0.0145517
$833$	31.9160	1.10583
$834$	63.7582	2.20777
$835$	−13.4723	−0.466228
$836$	7.91047	0.273589
$837$	20.0084	0.691592
$838$	66.0432	2.28142
$839$	25.9029	0.894266	0.447133	−	0.894467i	$-0.352445\pi$
$839$	25.9029	0.894266	0.447133	+	0.894467i	$0.352445\pi$
$840$	1.63575	0.0564388
$841$	−2.82361	−0.0973659
$842$	−3.32505	−0.114589
$843$	33.3367	1.14818
$844$	3.22471	0.110999
$845$	−34.7600	−1.19578
$846$	9.56970	0.329013
$847$	0.365354	0.0125537
$848$	28.8551	0.990887
$849$	22.9040	0.786063
$850$	25.5423	0.876095
$851$	2.55264	0.0875035
$852$	49.1063	1.68235
$853$	−0.0269675	−0.000923348 0	−0.000461674	−	1.00000i	$-0.500147\pi$
$853$	−0.0269675	−0.000923348 0	−0.000461674		1.00000i	$0.500147\pi$
$854$	0.183032	0.00626321
$855$	−2.71539	−0.0928644
$856$	76.8640	2.62716
$857$	−17.7820	−0.607422	−0.303711	−	0.952764i	$-0.598226\pi$
$857$	−17.7820	−0.607422	−0.303711	+	0.952764i	$0.598226\pi$
$858$	−1.40951	−0.0481200
$859$	7.60240	0.259391	0.129695	−	0.991554i	$-0.458600\pi$
$859$	7.60240	0.259391	0.129695	+	0.991554i	$0.458600\pi$
$860$	16.9762	0.578884
$861$	0.493786	0.0168282
$862$	15.3756	0.523694
$863$	48.1787	1.64002	0.820012	−	0.572347i	$-0.193967\pi$
$863$	48.1787	1.64002	0.820012	+	0.572347i	$0.193967\pi$
$864$	29.0306	0.987641
$865$	−63.0475	−2.14368
$866$	28.1919	0.957998
$867$	7.61417	0.258591
$868$	1.05150	0.0356901
$869$	−5.84180	−0.198170
$870$	−70.6253	−2.39442
$871$	1.03525	0.0350782
$872$	−94.0785	−3.18590
$873$	−13.6375	−0.461558
$874$	−1.93915	−0.0655926
$875$	0.342699	0.0115854
$876$	114.180	3.85779
$877$	17.0383	0.575343	0.287671	−	0.957729i	$-0.407119\pi$
$877$	17.0383	0.575343	0.287671	+	0.957729i	$0.407119\pi$
$878$	−66.3445	−2.23902
$879$	−13.4568	−0.453887
$880$	−37.0417	−1.24868
$881$	−4.15433	−0.139963	−0.0699815	−	0.997548i	$-0.522294\pi$
$881$	−4.15433	−0.139963	−0.0699815	+	0.997548i	$0.522294\pi$
$882$	18.2418	0.614234
$883$	3.83532	0.129069	0.0645343	−	0.997915i	$-0.479444\pi$
$883$	3.83532	0.129069	0.0645343	+	0.997915i	$0.479444\pi$
$884$	3.35864	0.112963
$885$	32.1680	1.08132
$886$	−37.4068	−1.25670
$887$	30.6609	1.02949	0.514746	−	0.857343i	$-0.327886\pi$
$887$	30.6609	1.02949	0.514746	+	0.857343i	$0.327886\pi$
$888$	45.6103	1.53058
$889$	−0.0696583	−0.00233626
$890$	65.3188	2.18949
$891$	18.8792	0.632478
$892$	−8.49051	−0.284283
$893$	3.67114	0.122850
$894$	7.42083	0.248190
$895$	4.35731	0.145649
$896$	−0.354638	−0.0118476
$897$	0.241051	0.00804846
$898$	−57.1749	−1.90795
$899$	−25.7232	−0.857918
$900$	10.1848	0.339492
$901$	−16.3163	−0.543575
$902$	−23.9769	−0.798343
$903$	−0.124675	−0.00414891
$904$	−112.179	−3.73102
$905$	12.0448	0.400383
$906$	34.3313	1.14058
$907$	6.81760	0.226375	0.113187	−	0.993574i	$-0.463894\pi$
$907$	6.81760	0.226375	0.113187	+	0.993574i	$0.463894\pi$
$908$	45.1148	1.49719
$909$	2.86525	0.0950344
$910$	−0.0498343	−0.00165199
$911$	−11.1877	−0.370665	−0.185332	−	0.982676i	$-0.559336\pi$
$911$	−11.1877	−0.370665	−0.185332	+	0.982676i	$0.559336\pi$
$912$	−16.1586	−0.535064
$913$	−8.19482	−0.271209
$914$	103.439	3.42146
$915$	8.42802	0.278622
$916$	−100.253	−3.31246
$917$	−0.815771	−0.0269391
$918$	−46.6803	−1.54068
$919$	−37.4569	−1.23559	−0.617794	−	0.786340i	$-0.711973\pi$
$919$	−37.4569	−1.23559	−0.617794	+	0.786340i	$0.711973\pi$
$920$	13.5835	0.447834
$921$	−43.8531	−1.44501
$922$	−37.9118	−1.24856
$923$	−0.847662	−0.0279011
$924$	0.718234	0.0236282
$925$	−7.37228	−0.242399
$926$	−24.9563	−0.820114
$927$	−13.6199	−0.447337
$928$	−37.3223	−1.22517
$929$	17.4845	0.573649	0.286824	−	0.957983i	$-0.407400\pi$
$929$	17.4845	0.573649	0.286824	+	0.957983i	$0.407400\pi$
$930$	69.4027	2.27580
$931$	6.99795	0.229348
$932$	8.50381	0.278551
$933$	−30.3923	−0.995001
$934$	52.7434	1.72582
$935$	20.9455	0.684992
$936$	1.08767	0.0355516
$937$	51.8037	1.69235	0.846176	−	0.532904i	$-0.178899\pi$
$937$	51.8037	1.69235	0.846176	+	0.532904i	$0.178899\pi$
$938$	−0.756156	−0.0246894
$939$	26.9563	0.879685
$940$	−45.3866	−1.48035
$941$	−16.7658	−0.546549	−0.273275	−	0.961936i	$-0.588107\pi$
$941$	−16.7658	−0.546549	−0.273275	+	0.961936i	$0.588107\pi$
$942$	102.080	3.32595
$943$	4.10046	0.133529
$944$	48.3404	1.57335
$945$	0.483204	0.0157186
$946$	6.05386	0.196828
$947$	−7.57306	−0.246091	−0.123046	−	0.992401i	$-0.539266\pi$
$947$	−7.57306	−0.246091	−0.123046	+	0.992401i	$0.539266\pi$
$948$	31.5054	1.02325
$949$	−1.97095	−0.0639798
$950$	5.60044	0.181702
$951$	−2.00338	−0.0649642
$952$	−1.38996	−0.0450490
$953$	−42.8439	−1.38785	−0.693925	−	0.720048i	$-0.744120\pi$
$953$	−42.8439	−1.38785	−0.693925	+	0.720048i	$0.744120\pi$
$954$	−9.32568	−0.301930
$955$	−58.9410	−1.90729
$956$	−22.5209	−0.728378
$957$	−17.5705	−0.567973
$958$	45.1115	1.45749
$959$	0.365846	0.0118138
$960$	14.1169	0.455622
$961$	−5.72209	−0.184584
$962$	−1.38955	−0.0448008
$963$	−11.5851	−0.373326
$964$	−36.0875	−1.16230
$965$	−11.8765	−0.382317
$966$	−0.176066	−0.00566482
$967$	4.42419	0.142272	0.0711362	−	0.997467i	$-0.477338\pi$
$967$	4.42419	0.142272	0.0711362	+	0.997467i	$0.477338\pi$
$968$	54.2101	1.74238
$969$	9.13698	0.293522
$970$	92.7110	2.97677
$971$	−3.11268	−0.0998907	−0.0499454	−	0.998752i	$-0.515905\pi$
$971$	−3.11268	−0.0998907	−0.0499454	+	0.998752i	$0.515905\pi$
$972$	−46.7238	−1.49867
$973$	0.560814	0.0179789
$974$	32.9206	1.05484
$975$	−0.696179	−0.0222956
$976$	12.6652	0.405403
$977$	−56.1802	−1.79736	−0.898682	−	0.438600i	$-0.855474\pi$
$977$	−56.1802	−1.79736	−0.898682	+	0.438600i	$0.855474\pi$
$978$	−23.8042	−0.761174
$979$	16.2503	0.519362
$980$	−86.5161	−2.76366
$981$	14.1798	0.452725
$982$	−73.9248	−2.35904
$983$	47.9941	1.53077	0.765386	−	0.643571i	$-0.222548\pi$
$983$	47.9941	1.53077	0.765386	+	0.643571i	$0.222548\pi$
$984$	73.2664	2.33565
$985$	−46.5082	−1.48187
$986$	60.0132	1.91121
$987$	0.333323	0.0106098
$988$	0.736420	0.0234286
$989$	−1.03531	−0.0329210
$990$	11.9715	0.380480
$991$	−21.1237	−0.671016	−0.335508	−	0.942037i	$-0.608908\pi$
$991$	−21.1237	−0.671016	−0.335508	+	0.942037i	$0.608908\pi$
$992$	36.6762	1.16447
$993$	16.5313	0.524605
$994$	0.619138	0.0196379
$995$	−48.4164	−1.53490
$996$	44.1954	1.40039
$997$	7.11560	0.225353	0.112677	−	0.993632i	$-0.464058\pi$
$997$	7.11560	0.225353	0.112677	+	0.993632i	$0.464058\pi$
$998$	28.6583	0.907162
$999$	13.4733	0.426278

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.5	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.5	✓	99	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:	\( N \)	\(=\)	\( 6023 = 19 \cdot 317 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.57189 q^{2} +2.00338 q^{3} +4.61464 q^{4} +2.67910 q^{5} -5.15249 q^{6} -0.0453210 q^{7} -6.72459 q^{8} +1.01355 q^{9} +O(q^{10})\)	\(q-2.57189 q^{2} +2.00338 q^{3} +4.61464 q^{4} +2.67910 q^{5} -5.15249 q^{6} -0.0453210 q^{7} -6.72459 q^{8} +1.01355 q^{9} -6.89035 q^{10} -1.71421 q^{11} +9.24490 q^{12} -0.159583 q^{13} +0.116561 q^{14} +5.36726 q^{15} +8.06564 q^{16} -4.56077 q^{17} -2.60674 q^{18} -1.00000 q^{19} +12.3631 q^{20} -0.0907954 q^{21} +4.40877 q^{22} -0.753976 q^{23} -13.4719 q^{24} +2.17755 q^{25} +0.410432 q^{26} -3.97963 q^{27} -0.209140 q^{28} +5.11629 q^{29} -13.8040 q^{30} -5.02771 q^{31} -7.29481 q^{32} -3.43422 q^{33} +11.7298 q^{34} -0.121419 q^{35} +4.67716 q^{36} -3.38558 q^{37} +2.57189 q^{38} -0.319707 q^{39} -18.0158 q^{40} -5.43845 q^{41} +0.233516 q^{42} +1.37314 q^{43} -7.91047 q^{44} +2.71539 q^{45} +1.93915 q^{46} -3.67114 q^{47} +16.1586 q^{48} -6.99795 q^{49} -5.60044 q^{50} -9.13698 q^{51} -0.736420 q^{52} +3.57753 q^{53} +10.2352 q^{54} -4.59254 q^{55} +0.304765 q^{56} -2.00338 q^{57} -13.1586 q^{58} +5.99338 q^{59} +24.7680 q^{60} +1.57027 q^{61} +12.9308 q^{62} -0.0459350 q^{63} +2.63019 q^{64} -0.427539 q^{65} +8.83246 q^{66} -6.48722 q^{67} -21.0463 q^{68} -1.51050 q^{69} +0.312278 q^{70} +5.31172 q^{71} -6.81569 q^{72} +12.3506 q^{73} +8.70735 q^{74} +4.36248 q^{75} -4.61464 q^{76} +0.0776898 q^{77} +0.822252 q^{78} +3.40787 q^{79} +21.6086 q^{80} -11.0134 q^{81} +13.9871 q^{82} +4.78052 q^{83} -0.418988 q^{84} -12.2187 q^{85} -3.53157 q^{86} +10.2499 q^{87} +11.5274 q^{88} -9.47975 q^{89} -6.98370 q^{90} +0.00723248 q^{91} -3.47933 q^{92} -10.0724 q^{93} +9.44178 q^{94} -2.67910 q^{95} -14.6143 q^{96} -13.4552 q^{97} +17.9980 q^{98} -1.73743 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9} - 6 q^{10} - 9 q^{11} - 27 q^{12} - 28 q^{13} - 13 q^{14} - 10 q^{15} + 38 q^{16} - 36 q^{17} - 14 q^{18} - 99 q^{19} - 34 q^{20} - 20 q^{21} - 53 q^{22} - 38 q^{23} - 25 q^{24} - 8 q^{25} - 3 q^{26} - 3 q^{27} - 63 q^{28} - 34 q^{29} - 30 q^{30} - 16 q^{31} - 43 q^{32} - 41 q^{33} - 14 q^{34} - 25 q^{35} - 16 q^{36} - 80 q^{37} + 4 q^{38} - 48 q^{39} - 10 q^{40} - 32 q^{41} - 37 q^{42} - 76 q^{43} - 21 q^{44} - 53 q^{45} - 23 q^{46} - 31 q^{47} - 74 q^{48} - 32 q^{49} - 29 q^{50} - 30 q^{51} - 71 q^{52} - 35 q^{53} - 80 q^{54} - 45 q^{55} - 33 q^{56} + 3 q^{57} - 91 q^{58} + 12 q^{59} - 56 q^{60} - 61 q^{61} - 46 q^{62} - 43 q^{63} - 30 q^{64} - 46 q^{65} - 75 q^{66} - 26 q^{67} - 55 q^{68} - 45 q^{69} - 76 q^{70} - 41 q^{71} - 77 q^{72} - 143 q^{73} - 64 q^{74} - 8 q^{75} - 80 q^{76} - 58 q^{77} - 34 q^{78} - 22 q^{79} - 36 q^{80} - 81 q^{81} - 109 q^{82} - 7 q^{83} - 6 q^{84} - 80 q^{85} + 32 q^{86} - 57 q^{87} - 120 q^{88} - 28 q^{89} - 12 q^{90} - 30 q^{91} - 107 q^{92} - 121 q^{93} + 8 q^{94} + 15 q^{95} + 4 q^{96} - 128 q^{97} + 54 q^{98} - 34 q^{99}+O(q^{100}) \) 99 * q - 4 * q^2 - 3 * q^3 + 80 * q^4 - 15 * q^5 - 12 * q^6 - 19 * q^7 - 12 * q^8 + 58 * q^9 - 6 * q^10 - 9 * q^11 - 27 * q^12 - 28 * q^13 - 13 * q^14 - 10 * q^15 + 38 * q^16 - 36 * q^17 - 14 * q^18 - 99 * q^19 - 34 * q^20 - 20 * q^21 - 53 * q^22 - 38 * q^23 - 25 * q^24 - 8 * q^25 - 3 * q^26 - 3 * q^27 - 63 * q^28 - 34 * q^29 - 30 * q^30 - 16 * q^31 - 43 * q^32 - 41 * q^33 - 14 * q^34 - 25 * q^35 - 16 * q^36 - 80 * q^37 + 4 * q^38 - 48 * q^39 - 10 * q^40 - 32 * q^41 - 37 * q^42 - 76 * q^43 - 21 * q^44 - 53 * q^45 - 23 * q^46 - 31 * q^47 - 74 * q^48 - 32 * q^49 - 29 * q^50 - 30 * q^51 - 71 * q^52 - 35 * q^53 - 80 * q^54 - 45 * q^55 - 33 * q^56 + 3 * q^57 - 91 * q^58 + 12 * q^59 - 56 * q^60 - 61 * q^61 - 46 * q^62 - 43 * q^63 - 30 * q^64 - 46 * q^65 - 75 * q^66 - 26 * q^67 - 55 * q^68 - 45 * q^69 - 76 * q^70 - 41 * q^71 - 77 * q^72 - 143 * q^73 - 64 * q^74 - 8 * q^75 - 80 * q^76 - 58 * q^77 - 34 * q^78 - 22 * q^79 - 36 * q^80 - 81 * q^81 - 109 * q^82 - 7 * q^83 - 6 * q^84 - 80 * q^85 + 32 * q^86 - 57 * q^87 - 120 * q^88 - 28 * q^89 - 12 * q^90 - 30 * q^91 - 107 * q^92 - 121 * q^93 + 8 * q^94 + 15 * q^95 + 4 * q^96 - 128 * q^97 + 54 * q^98 - 34 * q^99

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