LMFDB - Embedded newform 6023.2.a.c.1.11

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:	$0$
Dimension:	$138$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-2.51157 q^{2} +0.714819 q^{3} +4.30797 q^{4} -1.12509 q^{5} -1.79532 q^{6} -0.994631 q^{7} -5.79662 q^{8} -2.48903 q^{9} +O(q^{10})$	\(q-2.51157 q^{2} +0.714819 q^{3} +4.30797 q^{4} -1.12509 q^{5} -1.79532 q^{6} -0.994631 q^{7} -5.79662 q^{8} -2.48903 q^{9} +2.82573 q^{10} -0.672741 q^{11} +3.07942 q^{12} -2.00360 q^{13} +2.49808 q^{14} -0.804233 q^{15} +5.94266 q^{16} -4.91160 q^{17} +6.25137 q^{18} +1.00000 q^{19} -4.84684 q^{20} -0.710981 q^{21} +1.68963 q^{22} +1.33893 q^{23} -4.14353 q^{24} -3.73418 q^{25} +5.03217 q^{26} -3.92367 q^{27} -4.28484 q^{28} -9.31660 q^{29} +2.01989 q^{30} +2.89942 q^{31} -3.33215 q^{32} -0.480888 q^{33} +12.3358 q^{34} +1.11905 q^{35} -10.7227 q^{36} -0.177209 q^{37} -2.51157 q^{38} -1.43221 q^{39} +6.52170 q^{40} +6.09142 q^{41} +1.78568 q^{42} +0.988493 q^{43} -2.89815 q^{44} +2.80038 q^{45} -3.36281 q^{46} -4.24300 q^{47} +4.24793 q^{48} -6.01071 q^{49} +9.37864 q^{50} -3.51091 q^{51} -8.63143 q^{52} -5.58304 q^{53} +9.85455 q^{54} +0.756892 q^{55} +5.76550 q^{56} +0.714819 q^{57} +23.3993 q^{58} -10.3806 q^{59} -3.46461 q^{60} +3.42256 q^{61} -7.28210 q^{62} +2.47567 q^{63} -3.51641 q^{64} +2.25422 q^{65} +1.20778 q^{66} +6.68139 q^{67} -21.1590 q^{68} +0.957092 q^{69} -2.81056 q^{70} -11.1582 q^{71} +14.4280 q^{72} +7.44529 q^{73} +0.445073 q^{74} -2.66926 q^{75} +4.30797 q^{76} +0.669129 q^{77} +3.59709 q^{78} -6.69252 q^{79} -6.68600 q^{80} +4.66239 q^{81} -15.2990 q^{82} +13.2363 q^{83} -3.06289 q^{84} +5.52598 q^{85} -2.48267 q^{86} -6.65969 q^{87} +3.89962 q^{88} +3.17911 q^{89} -7.03334 q^{90} +1.99284 q^{91} +5.76807 q^{92} +2.07256 q^{93} +10.6566 q^{94} -1.12509 q^{95} -2.38188 q^{96} -17.4351 q^{97} +15.0963 q^{98} +1.67448 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * 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 $

$2$	−2.51157	−1.77595	−0.887973	−	0.459896i	$-0.847887\pi$
$2$	−2.51157	−1.77595	−0.887973	+	0.459896i	$0.847887\pi$
$3$	0.714819	0.412701	0.206351	−	0.978478i	$-0.433841\pi$
$3$	0.714819	0.412701	0.206351	+	0.978478i	$0.433841\pi$
$4$	4.30797	2.15398
$5$	−1.12509	−0.503154	−0.251577	−	0.967837i	$-0.580949\pi$
$5$	−1.12509	−0.503154	−0.251577	+	0.967837i	$0.580949\pi$
$6$	−1.79532	−0.732935
$7$	−0.994631	−0.375935	−0.187968	−	0.982175i	$-0.560190\pi$
$7$	−0.994631	−0.375935	−0.187968	+	0.982175i	$0.560190\pi$
$8$	−5.79662	−2.04941
$9$	−2.48903	−0.829678
$10$	2.82573	0.893574
$11$	−0.672741	−0.202839	−0.101420	−	0.994844i	$-0.532338\pi$
$11$	−0.672741	−0.202839	−0.101420	+	0.994844i	$0.532338\pi$
$12$	3.07942	0.888952
$13$	−2.00360	−0.555698	−0.277849	−	0.960625i	$-0.589621\pi$
$13$	−2.00360	−0.555698	−0.277849	+	0.960625i	$0.589621\pi$
$14$	2.49808	0.667641
$15$	−0.804233	−0.207652
$16$	5.94266	1.48566
$17$	−4.91160	−1.19124	−0.595619	−	0.803267i	$-0.703093\pi$
$17$	−4.91160	−1.19124	−0.595619	+	0.803267i	$0.703093\pi$
$18$	6.25137	1.47346
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	−4.84684	−1.08379
$21$	−0.710981	−0.155149
$22$	1.68963	0.360231
$23$	1.33893	0.279186	0.139593	−	0.990209i	$-0.455421\pi$
$23$	1.33893	0.279186	0.139593	+	0.990209i	$0.455421\pi$
$24$	−4.14353	−0.845795
$25$	−3.73418	−0.746836
$26$	5.03217	0.986889
$27$	−3.92367	−0.755110
$28$	−4.28484	−0.809759
$29$	−9.31660	−1.73005	−0.865025	−	0.501729i	$-0.832697\pi$
$29$	−9.31660	−1.73005	−0.865025	+	0.501729i	$0.832697\pi$
$30$	2.01989	0.368779
$31$	2.89942	0.520752	0.260376	−	0.965507i	$-0.416154\pi$
$31$	2.89942	0.520752	0.260376	+	0.965507i	$0.416154\pi$
$32$	−3.33215	−0.589046
$33$	−0.480888	−0.0837119
$34$	12.3358	2.11558
$35$	1.11905	0.189153
$36$	−10.7227	−1.78711
$37$	−0.177209	−0.0291330	−0.0145665	−	0.999894i	$-0.504637\pi$
$37$	−0.177209	−0.0291330	−0.0145665	+	0.999894i	$0.504637\pi$
$38$	−2.51157	−0.407430
$39$	−1.43221	−0.229337
$40$	6.52170	1.03117
$41$	6.09142	0.951320	0.475660	−	0.879629i	$-0.342209\pi$
$41$	6.09142	0.951320	0.475660	+	0.879629i	$0.342209\pi$
$42$	1.78568	0.275536
$43$	0.988493	0.150744	0.0753719	−	0.997155i	$-0.475986\pi$
$43$	0.988493	0.150744	0.0753719	+	0.997155i	$0.475986\pi$
$44$	−2.89815	−0.436912
$45$	2.80038	0.417456
$46$	−3.36281	−0.495819
$47$	−4.24300	−0.618905	−0.309453	−	0.950915i	$-0.600146\pi$
$47$	−4.24300	−0.618905	−0.309453	+	0.950915i	$0.600146\pi$
$48$	4.24793	0.613135
$49$	−6.01071	−0.858673
$50$	9.37864	1.32634
$51$	−3.51091	−0.491626
$52$	−8.63143	−1.19696
$53$	−5.58304	−0.766889	−0.383445	−	0.923564i	$-0.625262\pi$
$53$	−5.58304	−0.766889	−0.383445	+	0.923564i	$0.625262\pi$
$54$	9.85455	1.34103
$55$	0.756892	0.102059
$56$	5.76550	0.770447
$57$	0.714819	0.0946801
$58$	23.3993	3.07247
$59$	−10.3806	−1.35144	−0.675720	−	0.737158i	$-0.736167\pi$
$59$	−10.3806	−1.35144	−0.675720	+	0.737158i	$0.736167\pi$
$60$	−3.46461	−0.447280
$61$	3.42256	0.438214	0.219107	−	0.975701i	$-0.429686\pi$
$61$	3.42256	0.438214	0.219107	+	0.975701i	$0.429686\pi$
$62$	−7.28210	−0.924827
$63$	2.47567	0.311905
$64$	−3.51641	−0.439551
$65$	2.25422	0.279602
$66$	1.20778	0.148668
$67$	6.68139	0.816262	0.408131	−	0.912923i	$-0.366181\pi$
$67$	6.68139	0.816262	0.408131	+	0.912923i	$0.366181\pi$
$68$	−21.1590	−2.56591
$69$	0.957092	0.115220
$70$	−2.81056	−0.335926
$71$	−11.1582	−1.32424	−0.662118	−	0.749399i	$-0.730342\pi$
$71$	−11.1582	−1.32424	−0.662118	+	0.749399i	$0.730342\pi$
$72$	14.4280	1.70035
$73$	7.44529	0.871406	0.435703	−	0.900091i	$-0.356500\pi$
$73$	7.44529	0.871406	0.435703	+	0.900091i	$0.356500\pi$
$74$	0.445073	0.0517387
$75$	−2.66926	−0.308220
$76$	4.30797	0.494158
$77$	0.669129	0.0762544
$78$	3.59709	0.407290
$79$	−6.69252	−0.752967	−0.376483	−	0.926423i	$-0.622867\pi$
$79$	−6.69252	−0.752967	−0.376483	+	0.926423i	$0.622867\pi$
$80$	−6.68600	−0.747518
$81$	4.66239	0.518043
$82$	−15.2990	−1.68949
$83$	13.2363	1.45287	0.726435	−	0.687235i	$-0.241176\pi$
$83$	13.2363	1.45287	0.726435	+	0.687235i	$0.241176\pi$
$84$	−3.06289	−0.334188
$85$	5.52598	0.599377
$86$	−2.48267	−0.267713
$87$	−6.65969	−0.713993
$88$	3.89962	0.415701
$89$	3.17911	0.336985	0.168492	−	0.985703i	$-0.446110\pi$
$89$	3.17911	0.336985	0.168492	+	0.985703i	$0.446110\pi$
$90$	−7.03334	−0.741379
$91$	1.99284	0.208906
$92$	5.76807	0.601362
$93$	2.07256	0.214915
$94$	10.6566	1.09914
$95$	−1.12509	−0.115431
$96$	−2.38188	−0.243100
$97$	−17.4351	−1.77027	−0.885133	−	0.465339i	$-0.845933\pi$
$97$	−17.4351	−1.77027	−0.885133	+	0.465339i	$0.845933\pi$
$98$	15.0963	1.52496
$99$	1.67448	0.168291
$100$	−16.0867	−1.60867
$101$	−9.72478	−0.967651	−0.483826	−	0.875164i	$-0.660753\pi$
$101$	−9.72478	−0.967651	−0.483826	+	0.875164i	$0.660753\pi$
$102$	8.81788	0.873100
$103$	−12.0801	−1.19029	−0.595143	−	0.803620i	$-0.702905\pi$
$103$	−12.0801	−1.19029	−0.595143	+	0.803620i	$0.702905\pi$
$104$	11.6141	1.13885
$105$	0.799916	0.0780638
$106$	14.0222	1.36195
$107$	−8.36423	−0.808601	−0.404300	−	0.914626i	$-0.632485\pi$
$107$	−8.36423	−0.808601	−0.404300	+	0.914626i	$0.632485\pi$
$108$	−16.9030	−1.62650
$109$	11.9889	1.14833	0.574163	−	0.818741i	$-0.305328\pi$
$109$	11.9889	1.14833	0.574163	+	0.818741i	$0.305328\pi$
$110$	−1.90099	−0.181252
$111$	−0.126673	−0.0120232
$112$	−5.91075	−0.558514
$113$	−13.0832	−1.23076	−0.615381	−	0.788229i	$-0.710998\pi$
$113$	−13.0832	−1.23076	−0.615381	+	0.788229i	$0.710998\pi$
$114$	−1.79532	−0.168147
$115$	−1.50641	−0.140474
$116$	−40.1356	−3.72650
$117$	4.98702	0.461050
$118$	26.0716	2.40008
$119$	4.88523	0.447829
$120$	4.66183	0.425565
$121$	−10.5474	−0.958856
$122$	−8.59598	−0.778244
$123$	4.35427	0.392611
$124$	12.4906	1.12169
$125$	9.82671	0.878928
$126$	−6.21781	−0.553927
$127$	17.9903	1.59638	0.798189	−	0.602407i	$-0.205792\pi$
$127$	17.9903	1.59638	0.798189	+	0.602407i	$0.205792\pi$
$128$	15.4960	1.36966
$129$	0.706594	0.0622121
$130$	−5.66162	−0.496557
$131$	7.63060	0.666689	0.333345	−	0.942805i	$-0.391823\pi$
$131$	7.63060	0.666689	0.333345	+	0.942805i	$0.391823\pi$
$132$	−2.07165	−0.180314
$133$	−0.994631	−0.0862454
$134$	−16.7808	−1.44964
$135$	4.41446	0.379937
$136$	28.4707	2.44134
$137$	8.39003	0.716809	0.358404	−	0.933566i	$-0.383321\pi$
$137$	8.39003	0.716809	0.358404	+	0.933566i	$0.383321\pi$
$138$	−2.40380	−0.204625
$139$	−6.73394	−0.571166	−0.285583	−	0.958354i	$-0.592187\pi$
$139$	−6.73394	−0.571166	−0.285583	+	0.958354i	$0.592187\pi$
$140$	4.82081	0.407433
$141$	−3.03298	−0.255423
$142$	28.0246	2.35177
$143$	1.34790	0.112717
$144$	−14.7915	−1.23262
$145$	10.4820	0.870481
$146$	−18.6993	−1.54757
$147$	−4.29657	−0.354375
$148$	−0.763413	−0.0627521
$149$	−22.5968	−1.85120	−0.925600	−	0.378504i	$-0.876439\pi$
$149$	−22.5968	−1.85120	−0.925600	+	0.378504i	$0.876439\pi$
$150$	6.70404	0.547382
$151$	13.8926	1.13057	0.565283	−	0.824897i	$-0.308767\pi$
$151$	13.8926	1.13057	0.565283	+	0.824897i	$0.308767\pi$
$152$	−5.79662	−0.470168
$153$	12.2251	0.988344
$154$	−1.68056	−0.135424
$155$	−3.26210	−0.262018
$156$	−6.16991	−0.493988
$157$	15.8940	1.26848	0.634241	−	0.773135i	$-0.281313\pi$
$157$	15.8940	1.26848	0.634241	+	0.773135i	$0.281313\pi$
$158$	16.8087	1.33723
$159$	−3.99086	−0.316496
$160$	3.74895	0.296381
$161$	−1.33174	−0.104956
$162$	−11.7099	−0.920017
$163$	14.9184	1.16850	0.584249	−	0.811575i	$-0.301389\pi$
$163$	14.9184	1.16850	0.584249	+	0.811575i	$0.301389\pi$
$164$	26.2417	2.04913
$165$	0.541041	0.0421200
$166$	−33.2438	−2.58022
$167$	−11.1688	−0.864270	−0.432135	−	0.901809i	$-0.642240\pi$
$167$	−11.1688	−0.864270	−0.432135	+	0.901809i	$0.642240\pi$
$168$	4.12129	0.317964
$169$	−8.98560	−0.691200
$170$	−13.8789	−1.06446
$171$	−2.48903	−0.190341
$172$	4.25840	0.324700
$173$	11.9044	0.905072	0.452536	−	0.891746i	$-0.350519\pi$
$173$	11.9044	0.905072	0.452536	+	0.891746i	$0.350519\pi$
$174$	16.7262	1.26801
$175$	3.71413	0.280762
$176$	−3.99787	−0.301351
$177$	−7.42026	−0.557741
$178$	−7.98454	−0.598466
$179$	20.9686	1.56727	0.783634	−	0.621223i	$-0.213364\pi$
$179$	20.9686	1.56727	0.783634	+	0.621223i	$0.213364\pi$
$180$	12.0639	0.899193
$181$	−0.693832	−0.0515721	−0.0257861	−	0.999667i	$-0.508209\pi$
$181$	−0.693832	−0.0515721	−0.0257861	+	0.999667i	$0.508209\pi$
$182$	−5.00515	−0.371006
$183$	2.44651	0.180851
$184$	−7.76126	−0.572168
$185$	0.199376	0.0146584
$186$	−5.20538	−0.381677
$187$	3.30424	0.241630
$188$	−18.2787	−1.33311
$189$	3.90260	0.283872
$190$	2.82573	0.205000
$191$	16.9115	1.22367	0.611836	−	0.790985i	$-0.290431\pi$
$191$	16.9115	1.22367	0.611836	+	0.790985i	$0.290431\pi$
$192$	−2.51360	−0.181403
$193$	−6.83623	−0.492083	−0.246041	−	0.969259i	$-0.579130\pi$
$193$	−6.83623	−0.492083	−0.246041	+	0.969259i	$0.579130\pi$
$194$	43.7894	3.14390
$195$	1.61136	0.115392
$196$	−25.8939	−1.84957
$197$	−7.27313	−0.518189	−0.259095	−	0.965852i	$-0.583424\pi$
$197$	−7.27313	−0.518189	−0.259095	+	0.965852i	$0.583424\pi$
$198$	−4.20556	−0.298876
$199$	15.2023	1.07766	0.538830	−	0.842415i	$-0.318867\pi$
$199$	15.2023	1.07766	0.538830	+	0.842415i	$0.318867\pi$
$200$	21.6456	1.53058
$201$	4.77599	0.336872
$202$	24.4244	1.71850
$203$	9.26658	0.650386
$204$	−15.1249	−1.05895
$205$	−6.85338	−0.478661
$206$	30.3399	2.11388
$207$	−3.33264	−0.231634
$208$	−11.9067	−0.825580
$209$	−0.672741	−0.0465345
$210$	−2.00904	−0.138637
$211$	14.8365	1.02139	0.510695	−	0.859762i	$-0.329388\pi$
$211$	14.8365	1.02139	0.510695	+	0.859762i	$0.329388\pi$
$212$	−24.0515	−1.65187
$213$	−7.97611	−0.546514
$214$	21.0073	1.43603
$215$	−1.11214	−0.0758474
$216$	22.7440	1.54753
$217$	−2.88386	−0.195769
$218$	−30.1108	−2.03936
$219$	5.32204	0.359630
$220$	3.26067	0.219834
$221$	9.84087	0.661969
$222$	0.318147	0.0213526
$223$	22.9266	1.53528	0.767639	−	0.640883i	$-0.221431\pi$
$223$	22.9266	1.53528	0.767639	+	0.640883i	$0.221431\pi$
$224$	3.31426	0.221443
$225$	9.29450	0.619633
$226$	32.8593	2.18577
$227$	12.7945	0.849204	0.424602	−	0.905380i	$-0.360414\pi$
$227$	12.7945	0.849204	0.424602	+	0.905380i	$0.360414\pi$
$228$	3.07942	0.203940
$229$	−12.1683	−0.804104	−0.402052	−	0.915617i	$-0.631703\pi$
$229$	−12.1683	−0.804104	−0.402052	+	0.915617i	$0.631703\pi$
$230$	3.78345	0.249474
$231$	0.478306	0.0314703
$232$	54.0048	3.54559
$233$	−17.4361	−1.14228	−0.571139	−	0.820854i	$-0.693498\pi$
$233$	−17.4361	−1.14228	−0.571139	+	0.820854i	$0.693498\pi$
$234$	−12.5252	−0.818800
$235$	4.77374	0.311405
$236$	−44.7193	−2.91098
$237$	−4.78394	−0.310750
$238$	−12.2696	−0.795319
$239$	−15.1543	−0.980248	−0.490124	−	0.871653i	$-0.663048\pi$
$239$	−15.1543	−0.980248	−0.490124	+	0.871653i	$0.663048\pi$
$240$	−4.77928	−0.308501
$241$	−21.3159	−1.37308	−0.686540	−	0.727092i	$-0.740871\pi$
$241$	−21.3159	−1.37308	−0.686540	+	0.727092i	$0.740871\pi$
$242$	26.4906	1.70288
$243$	15.1038	0.968907
$244$	14.7443	0.943905
$245$	6.76257	0.432045
$246$	−10.9360	−0.697256
$247$	−2.00360	−0.127486
$248$	−16.8069	−1.06724
$249$	9.46155	0.599601
$250$	−24.6804	−1.56093
$251$	−2.66129	−0.167979	−0.0839895	−	0.996467i	$-0.526766\pi$
$251$	−2.66129	−0.167979	−0.0839895	+	0.996467i	$0.526766\pi$
$252$	10.6651	0.671839
$253$	−0.900753	−0.0566299
$254$	−45.1837	−2.83508
$255$	3.95008	0.247363
$256$	−31.8864	−1.99290
$257$	10.6515	0.664424	0.332212	−	0.943205i	$-0.392205\pi$
$257$	10.6515	0.664424	0.332212	+	0.943205i	$0.392205\pi$
$258$	−1.77466	−0.110485
$259$	0.176258	0.0109521
$260$	9.71111	0.602257
$261$	23.1893	1.43538
$262$	−19.1648	−1.18400
$263$	7.22199	0.445327	0.222663	−	0.974895i	$-0.428525\pi$
$263$	7.22199	0.445327	0.222663	+	0.974895i	$0.428525\pi$
$264$	2.78753	0.171560
$265$	6.28140	0.385863
$266$	2.49808	0.153167
$267$	2.27249	0.139074
$268$	28.7832	1.75822
$269$	−9.08065	−0.553657	−0.276829	−	0.960919i	$-0.589283\pi$
$269$	−9.08065	−0.553657	−0.276829	+	0.960919i	$0.589283\pi$
$270$	−11.0872	−0.674747
$271$	13.3778	0.812644	0.406322	−	0.913730i	$-0.366811\pi$
$271$	13.3778	0.812644	0.406322	+	0.913730i	$0.366811\pi$
$272$	−29.1880	−1.76978
$273$	1.42452	0.0862159
$274$	−21.0721	−1.27301
$275$	2.51214	0.151488
$276$	4.12312	0.248183
$277$	13.0461	0.783867	0.391934	−	0.919994i	$-0.371806\pi$
$277$	13.0461	0.783867	0.391934	+	0.919994i	$0.371806\pi$
$278$	16.9128	1.01436
$279$	−7.21676	−0.432056
$280$	−6.48668	−0.387653
$281$	−15.6108	−0.931260	−0.465630	−	0.884980i	$-0.654172\pi$
$281$	−15.6108	−0.931260	−0.465630	+	0.884980i	$0.654172\pi$
$282$	7.61753	0.453617
$283$	6.43143	0.382309	0.191154	−	0.981560i	$-0.438777\pi$
$283$	6.43143	0.382309	0.191154	+	0.981560i	$0.438777\pi$
$284$	−48.0692	−2.85238
$285$	−0.804233	−0.0476387
$286$	−3.38535	−0.200180
$287$	−6.05872	−0.357635
$288$	8.29382	0.488718
$289$	7.12385	0.419050
$290$	−26.3262	−1.54593
$291$	−12.4629	−0.730590
$292$	32.0741	1.87699
$293$	−14.3673	−0.839347	−0.419673	−	0.907675i	$-0.637855\pi$
$293$	−14.3673	−0.839347	−0.419673	+	0.907675i	$0.637855\pi$
$294$	10.7911	0.629351
$295$	11.6791	0.679982
$296$	1.02722	0.0597057
$297$	2.63961	0.153166
$298$	56.7533	3.28763
$299$	−2.68267	−0.155143
$300$	−11.4991	−0.663901
$301$	−0.983186	−0.0566699
$302$	−34.8923	−2.00782
$303$	−6.95146	−0.399351
$304$	5.94266	0.340835
$305$	−3.85067	−0.220489
$306$	−30.7043	−1.75525
$307$	7.20768	0.411364	0.205682	−	0.978619i	$-0.434059\pi$
$307$	7.20768	0.411364	0.205682	+	0.978619i	$0.434059\pi$
$308$	2.88259	0.164251
$309$	−8.63507	−0.491232
$310$	8.19299	0.465331
$311$	6.74680	0.382576	0.191288	−	0.981534i	$-0.438734\pi$
$311$	6.74680	0.382576	0.191288	+	0.981534i	$0.438734\pi$
$312$	8.30197	0.470007
$313$	−1.86636	−0.105493	−0.0527465	−	0.998608i	$-0.516798\pi$
$313$	−1.86636	−0.105493	−0.0527465	+	0.998608i	$0.516798\pi$
$314$	−39.9189	−2.25276
$315$	−2.78534	−0.156936
$316$	−28.8311	−1.62188
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	10.0233	0.562080
$319$	6.26766	0.350922
$320$	3.95626	0.221162
$321$	−5.97891	−0.333710
$322$	3.34476	0.186396
$323$	−4.91160	−0.273289
$324$	20.0854	1.11586
$325$	7.48179	0.415015
$326$	−37.4685	−2.07519
$327$	8.56987	0.473915
$328$	−35.3096	−1.94965
$329$	4.22022	0.232668
$330$	−1.35886	−0.0748028
$331$	0.283017	0.0155560	0.00777802	−	0.999970i	$-0.497524\pi$
$331$	0.283017	0.0155560	0.00777802	+	0.999970i	$0.497524\pi$
$332$	57.0215	3.12946
$333$	0.441080	0.0241710
$334$	28.0513	1.53490
$335$	−7.51714	−0.410705
$336$	−4.22512	−0.230499
$337$	0.845916	0.0460800	0.0230400	−	0.999735i	$-0.492665\pi$
$337$	0.845916	0.0460800	0.0230400	+	0.999735i	$0.492665\pi$
$338$	22.5679	1.22753
$339$	−9.35211	−0.507937
$340$	23.8057	1.29105
$341$	−1.95056	−0.105629
$342$	6.25137	0.338036
$343$	12.9409	0.698740
$344$	−5.72992	−0.308937
$345$	−1.07681	−0.0579736
$346$	−29.8986	−1.60736
$347$	−23.9230	−1.28425	−0.642126	−	0.766599i	$-0.721948\pi$
$347$	−23.9230	−1.28425	−0.642126	+	0.766599i	$0.721948\pi$
$348$	−28.6897	−1.53793
$349$	−30.8323	−1.65042	−0.825209	−	0.564828i	$-0.808943\pi$
$349$	−30.8323	−1.65042	−0.825209	+	0.564828i	$0.808943\pi$
$350$	−9.32829	−0.498618
$351$	7.86145	0.419613
$352$	2.24167	0.119482
$353$	−29.1251	−1.55017	−0.775086	−	0.631856i	$-0.782293\pi$
$353$	−29.1251	−1.55017	−0.775086	+	0.631856i	$0.782293\pi$
$354$	18.6365	0.990517
$355$	12.5540	0.666295
$356$	13.6955	0.725860
$357$	3.49206	0.184819
$358$	−52.6641	−2.78338
$359$	0.497546	0.0262595	0.0131297	−	0.999914i	$-0.495821\pi$
$359$	0.497546	0.0262595	0.0131297	+	0.999914i	$0.495821\pi$
$360$	−16.2327	−0.855540
$361$	1.00000	0.0526316
$362$	1.74261	0.0915893
$363$	−7.53950	−0.395721
$364$	8.58509	0.449981
$365$	−8.37660	−0.438451
$366$	−6.14457	−0.321182
$367$	−11.4999	−0.600292	−0.300146	−	0.953893i	$-0.597035\pi$
$367$	−11.4999	−0.600292	−0.300146	+	0.953893i	$0.597035\pi$
$368$	7.95680	0.414777
$369$	−15.1618	−0.789289
$370$	−0.500746	−0.0260325
$371$	5.55306	0.288301
$372$	8.92854	0.462923
$373$	−19.9433	−1.03263	−0.516313	−	0.856400i	$-0.672696\pi$
$373$	−19.9433	−1.03263	−0.516313	+	0.856400i	$0.672696\pi$
$374$	−8.29882	−0.429122
$375$	7.02432	0.362734
$376$	24.5950	1.26839
$377$	18.6667	0.961385
$378$	−9.80164	−0.504142
$379$	20.6323	1.05981	0.529905	−	0.848057i	$-0.322228\pi$
$379$	20.6323	1.05981	0.529905	+	0.848057i	$0.322228\pi$
$380$	−4.84684	−0.248638
$381$	12.8598	0.658827
$382$	−42.4743	−2.17318
$383$	19.2497	0.983613	0.491807	−	0.870705i	$-0.336337\pi$
$383$	19.2497	0.983613	0.491807	+	0.870705i	$0.336337\pi$
$384$	11.0768	0.565262
$385$	−0.752828	−0.0383677
$386$	17.1697	0.873913
$387$	−2.46039	−0.125069
$388$	−75.1098	−3.81312
$389$	−7.60620	−0.385650	−0.192825	−	0.981233i	$-0.561765\pi$
$389$	−7.60620	−0.385650	−0.192825	+	0.981233i	$0.561765\pi$
$390$	−4.04704	−0.204930
$391$	−6.57629	−0.332577
$392$	34.8418	1.75978
$393$	5.45450	0.275143
$394$	18.2670	0.920276
$395$	7.52966	0.378858
$396$	7.21359	0.362496
$397$	0.972569	0.0488118	0.0244059	−	0.999702i	$-0.492231\pi$
$397$	0.972569	0.0488118	0.0244059	+	0.999702i	$0.492231\pi$
$398$	−38.1815	−1.91386
$399$	−0.710981	−0.0355936
$400$	−22.1910	−1.10955
$401$	9.04743	0.451807	0.225904	−	0.974150i	$-0.427467\pi$
$401$	9.04743	0.451807	0.225904	+	0.974150i	$0.427467\pi$
$402$	−11.9952	−0.598267
$403$	−5.80928	−0.289381
$404$	−41.8940	−2.08431
$405$	−5.24559	−0.260655
$406$	−23.2736	−1.15505
$407$	0.119216	0.00590932
$408$	20.3514	1.00754
$409$	1.67428	0.0827876	0.0413938	−	0.999143i	$-0.486820\pi$
$409$	1.67428	0.0827876	0.0413938	+	0.999143i	$0.486820\pi$
$410$	17.2127	0.850075
$411$	5.99736	0.295828
$412$	−52.0406	−2.56386
$413$	10.3249	0.508054
$414$	8.37015	0.411370
$415$	−14.8920	−0.731018
$416$	6.67628	0.327331
$417$	−4.81355	−0.235721
$418$	1.68963	0.0826427
$419$	1.77988	0.0869526	0.0434763	−	0.999054i	$-0.486157\pi$
$419$	1.77988	0.0869526	0.0434763	+	0.999054i	$0.486157\pi$
$420$	3.44601	0.168148
$421$	−4.59660	−0.224025	−0.112012	−	0.993707i	$-0.535730\pi$
$421$	−4.59660	−0.224025	−0.112012	+	0.993707i	$0.535730\pi$
$422$	−37.2630	−1.81393
$423$	10.5610	0.513492
$424$	32.3627	1.57167
$425$	18.3408	0.889660
$426$	20.0325	0.970579
$427$	−3.40418	−0.164740
$428$	−36.0329	−1.74171
$429$	0.963506	0.0465185
$430$	2.79322	0.134701
$431$	−6.86907	−0.330872	−0.165436	−	0.986221i	$-0.552903\pi$
$431$	−6.86907	−0.330872	−0.165436	+	0.986221i	$0.552903\pi$
$432$	−23.3170	−1.12184
$433$	11.7902	0.566599	0.283299	−	0.959032i	$-0.408571\pi$
$433$	11.7902	0.566599	0.283299	+	0.959032i	$0.408571\pi$
$434$	7.24300	0.347675
$435$	7.49272	0.359249
$436$	51.6477	2.47348
$437$	1.33893	0.0640497
$438$	−13.3667	−0.638683
$439$	5.55078	0.264924	0.132462	−	0.991188i	$-0.457712\pi$
$439$	5.55078	0.264924	0.132462	+	0.991188i	$0.457712\pi$
$440$	−4.38741	−0.209162
$441$	14.9609	0.712422
$442$	−24.7160	−1.17562
$443$	30.9519	1.47057	0.735285	−	0.677758i	$-0.237048\pi$
$443$	30.9519	1.47057	0.735285	+	0.677758i	$0.237048\pi$
$444$	−0.545702	−0.0258979
$445$	−3.57677	−0.169555
$446$	−57.5817	−2.72657
$447$	−16.1526	−0.763992
$448$	3.49753	0.165243
$449$	16.3545	0.771816	0.385908	−	0.922537i	$-0.373888\pi$
$449$	16.3545	0.771816	0.385908	+	0.922537i	$0.373888\pi$
$450$	−23.3438	−1.10044
$451$	−4.09795	−0.192965
$452$	−56.3620	−2.65104
$453$	9.93071	0.466586
$454$	−32.1344	−1.50814
$455$	−2.24212	−0.105112
$456$	−4.14353	−0.194039
$457$	21.3602	0.999186	0.499593	−	0.866260i	$-0.333483\pi$
$457$	21.3602	0.999186	0.499593	+	0.866260i	$0.333483\pi$
$458$	30.5615	1.42805
$459$	19.2715	0.899516
$460$	−6.48957	−0.302578
$461$	−32.4729	−1.51241	−0.756207	−	0.654332i	$-0.772950\pi$
$461$	−32.4729	−1.51241	−0.756207	+	0.654332i	$0.772950\pi$
$462$	−1.20130	−0.0558895
$463$	34.6449	1.61009	0.805043	−	0.593217i	$-0.202142\pi$
$463$	34.6449	1.61009	0.805043	+	0.593217i	$0.202142\pi$
$464$	−55.3654	−2.57027
$465$	−2.33181	−0.108135
$466$	43.7920	2.02862
$467$	22.6060	1.04608	0.523039	−	0.852308i	$-0.324798\pi$
$467$	22.6060	1.04608	0.523039	+	0.852308i	$0.324798\pi$
$468$	21.4839	0.993095
$469$	−6.64552	−0.306862
$470$	−11.9896	−0.553038
$471$	11.3614	0.523504
$472$	60.1724	2.76966
$473$	−0.665000	−0.0305767
$474$	12.0152	0.551876
$475$	−3.73418	−0.171336
$476$	21.0454	0.964616
$477$	13.8964	0.636271
$478$	38.0609	1.74087
$479$	−27.9370	−1.27647	−0.638237	−	0.769840i	$-0.720336\pi$
$479$	−27.9370	−1.27647	−0.638237	+	0.769840i	$0.720336\pi$
$480$	2.67982	0.122317
$481$	0.355056	0.0161892
$482$	53.5364	2.43852
$483$	−0.951954	−0.0433154
$484$	−45.4380	−2.06536
$485$	19.6160	0.890716
$486$	−37.9341	−1.72073
$487$	21.7803	0.986960	0.493480	−	0.869757i	$-0.335725\pi$
$487$	21.7803	0.986960	0.493480	+	0.869757i	$0.335725\pi$
$488$	−19.8393	−0.898081
$489$	10.6639	0.482240
$490$	−16.9846	−0.767288
$491$	−19.6460	−0.886614	−0.443307	−	0.896370i	$-0.646195\pi$
$491$	−19.6460	−0.886614	−0.443307	+	0.896370i	$0.646195\pi$
$492$	18.7580	0.845678
$493$	45.7594	2.06090
$494$	5.03217	0.226408
$495$	−1.88393	−0.0846763
$496$	17.2303	0.773662
$497$	11.0983	0.497827
$498$	−23.7633	−1.06486
$499$	0.574935	0.0257376	0.0128688	−	0.999917i	$-0.495904\pi$
$499$	0.574935	0.0257376	0.0128688	+	0.999917i	$0.495904\pi$
$500$	42.3332	1.89320
$501$	−7.98370	−0.356685
$502$	6.68400	0.298322
$503$	−12.3539	−0.550832	−0.275416	−	0.961325i	$-0.588816\pi$
$503$	−12.3539	−0.550832	−0.275416	+	0.961325i	$0.588816\pi$
$504$	−14.3505	−0.639223
$505$	10.9412	0.486878
$506$	2.26230	0.100572
$507$	−6.42308	−0.285259
$508$	77.5015	3.43857
$509$	−4.78119	−0.211922	−0.105961	−	0.994370i	$-0.533792\pi$
$509$	−4.78119	−0.211922	−0.105961	+	0.994370i	$0.533792\pi$
$510$	−9.92088	−0.439304
$511$	−7.40532	−0.327592
$512$	49.0928	2.16962
$513$	−3.92367	−0.173234
$514$	−26.7520	−1.17998
$515$	13.5911	0.598897
$516$	3.04399	0.134004
$517$	2.85444	0.125538
$518$	−0.442684	−0.0194504
$519$	8.50947	0.373524
$520$	−13.0669	−0.573019
$521$	20.5865	0.901909	0.450955	−	0.892547i	$-0.351084\pi$
$521$	20.5865	0.901909	0.450955	+	0.892547i	$0.351084\pi$
$522$	−58.2416	−2.54916
$523$	−8.46878	−0.370314	−0.185157	−	0.982709i	$-0.559279\pi$
$523$	−8.46878	−0.370314	−0.185157	+	0.982709i	$0.559279\pi$
$524$	32.8724	1.43604
$525$	2.65493	0.115871
$526$	−18.1385	−0.790877
$527$	−14.2408	−0.620340
$528$	−2.85775	−0.124368
$529$	−21.2073	−0.922055
$530$	−15.7762	−0.685272
$531$	25.8377	1.12126
$532$	−4.28484	−0.185771
$533$	−12.2048	−0.528647
$534$	−5.70750	−0.246988
$535$	9.41048	0.406851
$536$	−38.7295	−1.67286
$537$	14.9888	0.646813
$538$	22.8067	0.983265
$539$	4.04365	0.174172
$540$	19.0174	0.818378
$541$	33.4653	1.43879	0.719394	−	0.694603i	$-0.244420\pi$
$541$	33.4653	1.43879	0.719394	+	0.694603i	$0.244420\pi$
$542$	−33.5992	−1.44321
$543$	−0.495965	−0.0212839
$544$	16.3662	0.701694
$545$	−13.4885	−0.577785
$546$	−3.57778	−0.153115
$547$	−12.4326	−0.531577	−0.265789	−	0.964031i	$-0.585632\pi$
$547$	−12.4326	−0.531577	−0.265789	+	0.964031i	$0.585632\pi$
$548$	36.1440	1.54399
$549$	−8.51886	−0.363576
$550$	−6.30940	−0.269034
$551$	−9.31660	−0.396901
$552$	−5.54790	−0.236134
$553$	6.65658	0.283067
$554$	−32.7663	−1.39211
$555$	0.142518	0.00604954
$556$	−29.0096	−1.23028
$557$	−12.5048	−0.529844	−0.264922	−	0.964270i	$-0.585346\pi$
$557$	−12.5048	−0.529844	−0.264922	+	0.964270i	$0.585346\pi$
$558$	18.1254	0.767309
$559$	−1.98054	−0.0837680
$560$	6.65011	0.281018
$561$	2.36193	0.0997209
$562$	39.2075	1.65387
$563$	28.7634	1.21223	0.606116	−	0.795376i	$-0.292727\pi$
$563$	28.7634	1.21223	0.606116	+	0.795376i	$0.292727\pi$
$564$	−13.0660	−0.550177
$565$	14.7197	0.619263
$566$	−16.1530	−0.678960
$567$	−4.63736	−0.194751
$568$	64.6799	2.71391
$569$	17.3310	0.726554	0.363277	−	0.931681i	$-0.381658\pi$
$569$	17.3310	0.726554	0.363277	+	0.931681i	$0.381658\pi$
$570$	2.01989	0.0846037
$571$	−32.4899	−1.35966	−0.679830	−	0.733370i	$-0.737946\pi$
$571$	−32.4899	−1.35966	−0.679830	+	0.733370i	$0.737946\pi$
$572$	5.80672	0.242791
$573$	12.0887	0.505011
$574$	15.2169	0.635140
$575$	−4.99980	−0.208506
$576$	8.75246	0.364686
$577$	12.6604	0.527060	0.263530	−	0.964651i	$-0.415113\pi$
$577$	12.6604	0.527060	0.263530	+	0.964651i	$0.415113\pi$
$578$	−17.8920	−0.744210
$579$	−4.88667	−0.203083
$580$	45.1561	1.87500
$581$	−13.1652	−0.546185
$582$	31.3015	1.29749
$583$	3.75594	0.155555
$584$	−43.1575	−1.78587
$585$	−5.61083	−0.231979
$586$	36.0844	1.49063
$587$	18.6614	0.770238	0.385119	−	0.922867i	$-0.374160\pi$
$587$	18.6614	0.770238	0.385119	+	0.922867i	$0.374160\pi$
$588$	−18.5095	−0.763319
$589$	2.89942	0.119469
$590$	−29.3328	−1.20761
$591$	−5.19897	−0.213857
$592$	−1.05309	−0.0432819
$593$	−19.3215	−0.793438	−0.396719	−	0.917940i	$-0.629851\pi$
$593$	−19.3215	−0.793438	−0.396719	+	0.917940i	$0.629851\pi$
$594$	−6.62956	−0.272014
$595$	−5.49631	−0.225327
$596$	−97.3462	−3.98745
$597$	10.8669	0.444751
$598$	6.73772	0.275526
$599$	−28.2301	−1.15345	−0.576725	−	0.816939i	$-0.695669\pi$
$599$	−28.2301	−1.15345	−0.576725	+	0.816939i	$0.695669\pi$
$600$	15.4727	0.631670
$601$	41.1116	1.67698	0.838488	−	0.544920i	$-0.183440\pi$
$601$	41.1116	1.67698	0.838488	+	0.544920i	$0.183440\pi$
$602$	2.46934	0.100643
$603$	−16.6302	−0.677234
$604$	59.8490	2.43522
$605$	11.8668	0.482452
$606$	17.4591	0.709225
$607$	3.89099	0.157930	0.0789651	−	0.996877i	$-0.474838\pi$
$607$	3.89099	0.157930	0.0789651	+	0.996877i	$0.474838\pi$
$608$	−3.33215	−0.135136
$609$	6.62393	0.268415
$610$	9.67122	0.391576
$611$	8.50126	0.343924
$612$	52.6655	2.12888
$613$	−38.0480	−1.53674	−0.768372	−	0.640003i	$-0.778933\pi$
$613$	−38.0480	−1.53674	−0.768372	+	0.640003i	$0.778933\pi$
$614$	−18.1026	−0.730560
$615$	−4.89893	−0.197544
$616$	−3.87869	−0.156277
$617$	−13.6264	−0.548579	−0.274290	−	0.961647i	$-0.588443\pi$
$617$	−13.6264	−0.548579	−0.274290	+	0.961647i	$0.588443\pi$
$618$	21.6876	0.872402
$619$	9.98319	0.401258	0.200629	−	0.979667i	$-0.435701\pi$
$619$	9.98319	0.401258	0.200629	+	0.979667i	$0.435701\pi$
$620$	−14.0530	−0.564383
$621$	−5.25351	−0.210816
$622$	−16.9450	−0.679434
$623$	−3.16204	−0.126684
$624$	−8.51113	−0.340718
$625$	7.61500	0.304600
$626$	4.68749	0.187350
$627$	−0.480888	−0.0192048
$628$	68.4710	2.73229
$629$	0.870382	0.0347044
$630$	6.99558	0.278710
$631$	13.3513	0.531506	0.265753	−	0.964041i	$-0.414379\pi$
$631$	13.3513	0.531506	0.265753	+	0.964041i	$0.414379\pi$
$632$	38.7940	1.54314
$633$	10.6054	0.421529
$634$	2.51157	0.0997471
$635$	−20.2406	−0.803224
$636$	−17.1925	−0.681727
$637$	12.0430	0.477163
$638$	−15.7417	−0.623218
$639$	27.7732	1.09869
$640$	−17.4343	−0.689152
$641$	40.5995	1.60358	0.801791	−	0.597604i	$-0.203881\pi$
$641$	40.5995	1.60358	0.801791	+	0.597604i	$0.203881\pi$
$642$	15.0164	0.592652
$643$	14.5893	0.575347	0.287674	−	0.957729i	$-0.407118\pi$
$643$	14.5893	0.575347	0.287674	+	0.957729i	$0.407118\pi$
$644$	−5.73710	−0.226073
$645$	−0.794980	−0.0313023
$646$	12.3358	0.485346
$647$	42.4658	1.66950	0.834750	−	0.550628i	$-0.185612\pi$
$647$	42.4658	1.66950	0.834750	+	0.550628i	$0.185612\pi$
$648$	−27.0261	−1.06168
$649$	6.98346	0.274125
$650$	−18.7910	−0.737045
$651$	−2.06144	−0.0807941
$652$	64.2679	2.51693
$653$	−11.0406	−0.432050	−0.216025	−	0.976388i	$-0.569309\pi$
$653$	−11.0406	−0.432050	−0.216025	+	0.976388i	$0.569309\pi$
$654$	−21.5238	−0.841648
$655$	−8.58509	−0.335447
$656$	36.1992	1.41334
$657$	−18.5316	−0.722986
$658$	−10.5994	−0.413206
$659$	−8.62031	−0.335800	−0.167900	−	0.985804i	$-0.553698\pi$
$659$	−8.62031	−0.335800	−0.167900	+	0.985804i	$0.553698\pi$
$660$	2.33079	0.0907258
$661$	34.4503	1.33996	0.669980	−	0.742379i	$-0.266302\pi$
$661$	34.4503	1.33996	0.669980	+	0.742379i	$0.266302\pi$
$662$	−0.710817	−0.0276267
$663$	7.03445	0.273195
$664$	−76.7257	−2.97753
$665$	1.11905	0.0433947
$666$	−1.10780	−0.0429265
$667$	−12.4743	−0.483006
$668$	−48.1150	−1.86162
$669$	16.3884	0.633611
$670$	18.8798	0.729391
$671$	−2.30250	−0.0888869
$672$	2.36909	0.0913898
$673$	−7.69835	−0.296750	−0.148375	−	0.988931i	$-0.547404\pi$
$673$	−7.69835	−0.296750	−0.148375	+	0.988931i	$0.547404\pi$
$674$	−2.12458	−0.0818356
$675$	14.6517	0.563943
$676$	−38.7097	−1.48883
$677$	2.89747	0.111359	0.0556793	−	0.998449i	$-0.482268\pi$
$677$	2.89747	0.111359	0.0556793	+	0.998449i	$0.482268\pi$
$678$	23.4885	0.902069
$679$	17.3415	0.665505
$680$	−32.0320	−1.22837
$681$	9.14579	0.350467
$682$	4.89897	0.187591
$683$	14.6994	0.562459	0.281229	−	0.959641i	$-0.409258\pi$
$683$	14.6994	0.562459	0.281229	+	0.959641i	$0.409258\pi$
$684$	−10.7227	−0.409992
$685$	−9.43951	−0.360665
$686$	−32.5018	−1.24093
$687$	−8.69813	−0.331855
$688$	5.87428	0.223955
$689$	11.1862	0.426159
$690$	2.70449	0.102958
$691$	−12.4303	−0.472873	−0.236436	−	0.971647i	$-0.575979\pi$
$691$	−12.4303	−0.472873	−0.236436	+	0.971647i	$0.575979\pi$
$692$	51.2836	1.94951
$693$	−1.66549	−0.0632665
$694$	60.0842	2.28076
$695$	7.57627	0.287384
$696$	38.6037	1.46327
$697$	−29.9186	−1.13325
$698$	77.4375	2.93105
$699$	−12.4637	−0.471419
$700$	16.0004	0.604757
$701$	−28.4254	−1.07361	−0.536806	−	0.843706i	$-0.680369\pi$
$701$	−28.4254	−1.07361	−0.536806	+	0.843706i	$0.680369\pi$
$702$	−19.7445	−0.745210
$703$	−0.177209	−0.00668358
$704$	2.36563	0.0891581
$705$	3.41236	0.128517
$706$	73.1496	2.75302
$707$	9.67256	0.363774
$708$	−31.9662	−1.20136
$709$	−37.8234	−1.42049	−0.710244	−	0.703956i	$-0.751415\pi$
$709$	−37.8234	−1.42049	−0.710244	+	0.703956i	$0.751415\pi$
$710$	−31.5301	−1.18330
$711$	16.6579	0.624720
$712$	−18.4281	−0.690621
$713$	3.88212	0.145387
$714$	−8.77054	−0.328229
$715$	−1.51651	−0.0567141
$716$	90.3321	3.37587
$717$	−10.8326	−0.404549
$718$	−1.24962	−0.0466354
$719$	27.3894	1.02145	0.510727	−	0.859743i	$-0.329376\pi$
$719$	27.3894	1.02145	0.510727	+	0.859743i	$0.329376\pi$
$720$	16.6417	0.620199
$721$	12.0152	0.447470
$722$	−2.51157	−0.0934708
$723$	−15.2370	−0.566672
$724$	−2.98901	−0.111086
$725$	34.7899	1.29206
$726$	18.9360	0.702779
$727$	−44.4107	−1.64710	−0.823550	−	0.567244i	$-0.808010\pi$
$727$	−44.4107	−1.64710	−0.823550	+	0.567244i	$0.808010\pi$
$728$	−11.5517	−0.428136
$729$	−3.19070	−0.118174
$730$	21.0384	0.778666
$731$	−4.85509	−0.179572
$732$	10.5395	0.389551
$733$	25.9772	0.959488	0.479744	−	0.877409i	$-0.340730\pi$
$733$	25.9772	0.959488	0.479744	+	0.877409i	$0.340730\pi$
$734$	28.8829	1.06609
$735$	4.83401	0.178305
$736$	−4.46151	−0.164453
$737$	−4.49485	−0.165570
$738$	38.0798	1.40174
$739$	10.1398	0.373000	0.186500	−	0.982455i	$-0.440286\pi$
$739$	10.1398	0.373000	0.186500	+	0.982455i	$0.440286\pi$
$740$	0.858905	0.0315740
$741$	−1.43221	−0.0526135
$742$	−13.9469	−0.512006
$743$	24.9398	0.914951	0.457476	−	0.889222i	$-0.348754\pi$
$743$	24.9398	0.914951	0.457476	+	0.889222i	$0.348754\pi$
$744$	−12.0139	−0.440450
$745$	25.4233	0.931438
$746$	50.0890	1.83389
$747$	−32.9455	−1.20541
$748$	14.2346	0.520467
$749$	8.31932	0.303982
$750$	−17.6421	−0.644197
$751$	16.2251	0.592064	0.296032	−	0.955178i	$-0.404336\pi$
$751$	16.2251	0.592064	0.296032	+	0.955178i	$0.404336\pi$
$752$	−25.2147	−0.919485
$753$	−1.90234	−0.0693251
$754$	−46.8827	−1.70737
$755$	−15.6304	−0.568849
$756$	16.8123	0.611457
$757$	42.1876	1.53333	0.766667	−	0.642046i	$-0.221914\pi$
$757$	42.1876	1.53333	0.766667	+	0.642046i	$0.221914\pi$
$758$	−51.8194	−1.88217
$759$	−0.643876	−0.0233712
$760$	6.52170	0.236567
$761$	−51.0025	−1.84884	−0.924420	−	0.381376i	$-0.875450\pi$
$761$	−51.0025	−1.84884	−0.924420	+	0.381376i	$0.875450\pi$
$762$	−32.2982	−1.17004
$763$	−11.9245	−0.431696
$764$	72.8542	2.63577
$765$	−13.7543	−0.497289
$766$	−48.3469	−1.74684
$767$	20.7985	0.750992
$768$	−22.7930	−0.822472
$769$	5.48839	0.197917	0.0989583	−	0.995092i	$-0.468449\pi$
$769$	5.48839	0.197917	0.0989583	+	0.995092i	$0.468449\pi$
$770$	1.89078	0.0681389
$771$	7.61391	0.274208
$772$	−29.4503	−1.05994
$773$	−12.5336	−0.450801	−0.225400	−	0.974266i	$-0.572369\pi$
$773$	−12.5336	−0.450801	−0.225400	+	0.974266i	$0.572369\pi$
$774$	6.17944	0.222115
$775$	−10.8270	−0.388916
$776$	101.065	3.62801
$777$	0.125993	0.00451996
$778$	19.1035	0.684893
$779$	6.09142	0.218248
$780$	6.94169	0.248552
$781$	7.50659	0.268607
$782$	16.5168	0.590639
$783$	36.5552	1.30638
$784$	−35.7196	−1.27570
$785$	−17.8822	−0.638242
$786$	−13.6993	−0.488640
$787$	19.5010	0.695135	0.347568	−	0.937655i	$-0.387008\pi$
$787$	19.5010	0.695135	0.347568	+	0.937655i	$0.387008\pi$
$788$	−31.3324	−1.11617
$789$	5.16242	0.183787
$790$	−18.9112	−0.672832
$791$	13.0129	0.462687
$792$	−9.70629	−0.344898
$793$	−6.85743	−0.243514
$794$	−2.44267	−0.0866872
$795$	4.49006	0.159246
$796$	65.4908	2.32126
$797$	5.60710	0.198614	0.0993068	−	0.995057i	$-0.468337\pi$
$797$	5.60710	0.198614	0.0993068	+	0.995057i	$0.468337\pi$
$798$	1.78568	0.0632123
$799$	20.8399	0.737264
$800$	12.4428	0.439921
$801$	−7.91290	−0.279589
$802$	−22.7232	−0.802385
$803$	−5.00875	−0.176755
$804$	20.5748	0.725617
$805$	1.49832	0.0528090
$806$	14.5904	0.513924
$807$	−6.49103	−0.228495
$808$	56.3708	1.98312
$809$	−16.2507	−0.571343	−0.285671	−	0.958328i	$-0.592217\pi$
$809$	−16.2507	−0.571343	−0.285671	+	0.958328i	$0.592217\pi$
$810$	13.1747	0.462910
$811$	42.5044	1.49253	0.746266	−	0.665648i	$-0.231845\pi$
$811$	42.5044	1.49253	0.746266	+	0.665648i	$0.231845\pi$
$812$	39.9201	1.40092
$813$	9.56271	0.335379
$814$	−0.299419	−0.0104946
$815$	−16.7845	−0.587934
$816$	−20.8641	−0.730391
$817$	0.988493	0.0345830
$818$	−4.20506	−0.147026
$819$	−4.96024	−0.173325
$820$	−29.5241	−1.03103
$821$	55.9519	1.95274	0.976368	−	0.216117i	$-0.0693391\pi$
$821$	55.9519	1.95274	0.976368	+	0.216117i	$0.0693391\pi$
$822$	−15.0628	−0.525374
$823$	−37.9833	−1.32401	−0.662007	−	0.749497i	$-0.730295\pi$
$823$	−37.9833	−1.32401	−0.662007	+	0.749497i	$0.730295\pi$
$824$	70.0236	2.43939
$825$	1.79572	0.0625191
$826$	−25.9316	−0.902276
$827$	−35.7623	−1.24358	−0.621788	−	0.783186i	$-0.713593\pi$
$827$	−35.7623	−1.24358	−0.621788	+	0.783186i	$0.713593\pi$
$828$	−14.3569	−0.498937
$829$	42.6414	1.48100	0.740499	−	0.672057i	$-0.234589\pi$
$829$	42.6414	1.48100	0.740499	+	0.672057i	$0.234589\pi$
$830$	37.4022	1.29825
$831$	9.32564	0.323503
$832$	7.04546	0.244257
$833$	29.5222	1.02288
$834$	12.0896	0.418627
$835$	12.5659	0.434861
$836$	−2.89815	−0.100235
$837$	−11.3764	−0.393225
$838$	−4.47028	−0.154423
$839$	21.3112	0.735746	0.367873	−	0.929876i	$-0.380086\pi$
$839$	21.3112	0.735746	0.367873	+	0.929876i	$0.380086\pi$
$840$	−4.63681	−0.159985
$841$	57.7991	1.99307
$842$	11.5447	0.397856
$843$	−11.1589	−0.384332
$844$	63.9154	2.20006
$845$	10.1096	0.347780
$846$	−26.5246	−0.911934
$847$	10.4908	0.360468
$848$	−33.1781	−1.13934
$849$	4.59731	0.157779
$850$	−46.0642	−1.57999
$851$	−0.237271	−0.00813354
$852$	−34.3608	−1.17718
$853$	40.1656	1.37524	0.687622	−	0.726068i	$-0.258654\pi$
$853$	40.1656	1.37524	0.687622	+	0.726068i	$0.258654\pi$
$854$	8.54983	0.292569
$855$	2.80038	0.0957709
$856$	48.4843	1.65716
$857$	31.2422	1.06721	0.533606	−	0.845733i	$-0.320837\pi$
$857$	31.2422	1.06721	0.533606	+	0.845733i	$0.320837\pi$
$858$	−2.41991	−0.0826144
$859$	1.05201	0.0358940	0.0179470	−	0.999839i	$-0.494287\pi$
$859$	1.05201	0.0358940	0.0179470	+	0.999839i	$0.494287\pi$
$860$	−4.79107	−0.163374
$861$	−4.33089	−0.147596
$862$	17.2521	0.587610
$863$	41.0148	1.39616	0.698081	−	0.716019i	$-0.254038\pi$
$863$	41.0148	1.39616	0.698081	+	0.716019i	$0.254038\pi$
$864$	13.0742	0.444794
$865$	−13.3934	−0.455391
$866$	−29.6118	−1.00625
$867$	5.09226	0.172942
$868$	−12.4236	−0.421683
$869$	4.50233	0.152731
$870$	−18.8185	−0.638006
$871$	−13.3868	−0.453595
$872$	−69.4949	−2.35339
$873$	43.3965	1.46875
$874$	−3.36281	−0.113749
$875$	−9.77395	−0.330420
$876$	22.9272	0.774637
$877$	−26.7794	−0.904276	−0.452138	−	0.891948i	$-0.649338\pi$
$877$	−26.7794	−0.904276	−0.452138	+	0.891948i	$0.649338\pi$
$878$	−13.9411	−0.470491
$879$	−10.2700	−0.346399
$880$	4.49795	0.151626
$881$	39.7509	1.33924	0.669621	−	0.742703i	$-0.266457\pi$
$881$	39.7509	1.33924	0.669621	+	0.742703i	$0.266457\pi$
$882$	−37.5752	−1.26522
$883$	−52.6387	−1.77143	−0.885716	−	0.464227i	$-0.846332\pi$
$883$	−52.6387	−1.77143	−0.885716	+	0.464227i	$0.846332\pi$
$884$	42.3942	1.42587
$885$	8.34843	0.280629
$886$	−77.7379	−2.61165
$887$	−48.0737	−1.61416	−0.807079	−	0.590443i	$-0.798953\pi$
$887$	−48.0737	−1.61416	−0.807079	+	0.590443i	$0.798953\pi$
$888$	0.734273	0.0246406
$889$	−17.8937	−0.600134
$890$	8.98330	0.301121
$891$	−3.13658	−0.105079
$892$	98.7670	3.30696
$893$	−4.24300	−0.141987
$894$	40.5683	1.35681
$895$	−23.5915	−0.788577
$896$	−15.4128	−0.514905
$897$	−1.91763	−0.0640277
$898$	−41.0754	−1.37070
$899$	−27.0128	−0.900926
$900$	40.0404	1.33468
$901$	27.4217	0.913548
$902$	10.2923	0.342695
$903$	−0.702800	−0.0233877
$904$	75.8382	2.52234
$905$	0.780621	0.0259487
$906$	−24.9417	−0.828631
$907$	−18.0043	−0.597822	−0.298911	−	0.954281i	$-0.596623\pi$
$907$	−18.0043	−0.597822	−0.298911	+	0.954281i	$0.596623\pi$
$908$	55.1185	1.82917
$909$	24.2053	0.802839
$910$	5.63123	0.186673
$911$	27.5254	0.911958	0.455979	−	0.889990i	$-0.349289\pi$
$911$	27.5254	0.911958	0.455979	+	0.889990i	$0.349289\pi$
$912$	4.24793	0.140663
$913$	−8.90459	−0.294699
$914$	−53.6475	−1.77450
$915$	−2.75254	−0.0909960
$916$	−52.4207	−1.73203
$917$	−7.58964	−0.250632
$918$	−48.4017	−1.59749
$919$	−31.6675	−1.04461	−0.522307	−	0.852757i	$-0.674929\pi$
$919$	−31.6675	−1.04461	−0.522307	+	0.852757i	$0.674929\pi$
$920$	8.73209	0.287889
$921$	5.15219	0.169770
$922$	81.5579	2.68597
$923$	22.3566	0.735875
$924$	2.06053	0.0677864
$925$	0.661732	0.0217576
$926$	−87.0130	−2.85942
$927$	30.0677	0.987554
$928$	31.0443	1.01908
$929$	−28.6706	−0.940652	−0.470326	−	0.882493i	$-0.655864\pi$
$929$	−28.6706	−0.940652	−0.470326	+	0.882493i	$0.655864\pi$
$930$	5.85651	0.192042
$931$	−6.01071	−0.196993
$932$	−75.1142	−2.46045
$933$	4.82274	0.157890
$934$	−56.7764	−1.85778
$935$	−3.71755	−0.121577
$936$	−28.9078	−0.944883
$937$	55.8848	1.82568	0.912838	−	0.408323i	$-0.133886\pi$
$937$	55.8848	1.82568	0.912838	+	0.408323i	$0.133886\pi$
$938$	16.6907	0.544970
$939$	−1.33411	−0.0435371
$940$	20.5651	0.670761
$941$	−43.2056	−1.40846	−0.704230	−	0.709971i	$-0.748708\pi$
$941$	−43.2056	−1.40846	−0.704230	+	0.709971i	$0.748708\pi$
$942$	−28.5348	−0.929715
$943$	8.15598	0.265595
$944$	−61.6884	−2.00779
$945$	−4.39076	−0.142832
$946$	1.67019	0.0543026
$947$	46.3530	1.50627	0.753136	−	0.657865i	$-0.228540\pi$
$947$	46.3530	1.50627	0.753136	+	0.657865i	$0.228540\pi$
$948$	−20.6091	−0.669351
$949$	−14.9174	−0.484238
$950$	9.37864	0.304283
$951$	−0.714819	−0.0231796
$952$	−28.3178	−0.917786
$953$	57.5211	1.86329	0.931646	−	0.363368i	$-0.118373\pi$
$953$	57.5211	1.86329	0.931646	+	0.363368i	$0.118373\pi$
$954$	−34.9017	−1.12998
$955$	−19.0269	−0.615696
$956$	−65.2841	−2.11144
$957$	4.48024	0.144826
$958$	70.1656	2.26695
$959$	−8.34499	−0.269474
$960$	2.82801	0.0912737
$961$	−22.5933	−0.728817
$962$	−0.891748	−0.0287511
$963$	20.8189	0.670878
$964$	−91.8284	−2.95759
$965$	7.69135	0.247593
$966$	2.39090	0.0769258
$967$	56.7168	1.82389	0.911945	−	0.410313i	$-0.134580\pi$
$967$	56.7168	1.82389	0.911945	+	0.410313i	$0.134580\pi$
$968$	61.1394	1.96509
$969$	−3.51091	−0.112787
$970$	−49.2669	−1.58186
$971$	55.9350	1.79504	0.897519	−	0.440976i	$-0.145368\pi$
$971$	55.9350	1.79504	0.897519	+	0.440976i	$0.145368\pi$
$972$	65.0665	2.08701
$973$	6.69779	0.214721
$974$	−54.7027	−1.75279
$975$	5.34813	0.171277
$976$	20.3391	0.651038
$977$	22.4859	0.719387	0.359693	−	0.933071i	$-0.382881\pi$
$977$	22.4859	0.719387	0.359693	+	0.933071i	$0.382881\pi$
$978$	−26.7832	−0.856433
$979$	−2.13872	−0.0683536
$980$	29.1329	0.930617
$981$	−29.8407	−0.952740
$982$	49.3424	1.57458
$983$	4.98547	0.159012	0.0795059	−	0.996834i	$-0.474666\pi$
$983$	4.98547	0.159012	0.0795059	+	0.996834i	$0.474666\pi$
$984$	−25.2400	−0.804622
$985$	8.18290	0.260729
$986$	−114.928	−3.66005
$987$	3.01669	0.0960224
$988$	−8.63143	−0.274602
$989$	1.32352	0.0420856
$990$	4.73162	0.150381
$991$	−43.1430	−1.37048	−0.685242	−	0.728316i	$-0.740303\pi$
$991$	−43.1430	−1.37048	−0.685242	+	0.728316i	$0.740303\pi$
$992$	−9.66130	−0.306747
$993$	0.202306	0.00641999
$994$	−27.8741	−0.884114
$995$	−17.1039	−0.542229
$996$	40.7601	1.29153
$997$	−6.53256	−0.206888	−0.103444	−	0.994635i	$-0.532986\pi$
$997$	−6.53256	−0.206888	−0.103444	+	0.994635i	$0.532986\pi$
$998$	−1.44399	−0.0457086
$999$	0.695311	0.0219987

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.11	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.11	✓	138	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)

\(f(q)\)	\(=\)	\(q-2.51157 q^{2} +0.714819 q^{3} +4.30797 q^{4} -1.12509 q^{5} -1.79532 q^{6} -0.994631 q^{7} -5.79662 q^{8} -2.48903 q^{9} +O(q^{10})\)	\(q-2.51157 q^{2} +0.714819 q^{3} +4.30797 q^{4} -1.12509 q^{5} -1.79532 q^{6} -0.994631 q^{7} -5.79662 q^{8} -2.48903 q^{9} +2.82573 q^{10} -0.672741 q^{11} +3.07942 q^{12} -2.00360 q^{13} +2.49808 q^{14} -0.804233 q^{15} +5.94266 q^{16} -4.91160 q^{17} +6.25137 q^{18} +1.00000 q^{19} -4.84684 q^{20} -0.710981 q^{21} +1.68963 q^{22} +1.33893 q^{23} -4.14353 q^{24} -3.73418 q^{25} +5.03217 q^{26} -3.92367 q^{27} -4.28484 q^{28} -9.31660 q^{29} +2.01989 q^{30} +2.89942 q^{31} -3.33215 q^{32} -0.480888 q^{33} +12.3358 q^{34} +1.11905 q^{35} -10.7227 q^{36} -0.177209 q^{37} -2.51157 q^{38} -1.43221 q^{39} +6.52170 q^{40} +6.09142 q^{41} +1.78568 q^{42} +0.988493 q^{43} -2.89815 q^{44} +2.80038 q^{45} -3.36281 q^{46} -4.24300 q^{47} +4.24793 q^{48} -6.01071 q^{49} +9.37864 q^{50} -3.51091 q^{51} -8.63143 q^{52} -5.58304 q^{53} +9.85455 q^{54} +0.756892 q^{55} +5.76550 q^{56} +0.714819 q^{57} +23.3993 q^{58} -10.3806 q^{59} -3.46461 q^{60} +3.42256 q^{61} -7.28210 q^{62} +2.47567 q^{63} -3.51641 q^{64} +2.25422 q^{65} +1.20778 q^{66} +6.68139 q^{67} -21.1590 q^{68} +0.957092 q^{69} -2.81056 q^{70} -11.1582 q^{71} +14.4280 q^{72} +7.44529 q^{73} +0.445073 q^{74} -2.66926 q^{75} +4.30797 q^{76} +0.669129 q^{77} +3.59709 q^{78} -6.69252 q^{79} -6.68600 q^{80} +4.66239 q^{81} -15.2990 q^{82} +13.2363 q^{83} -3.06289 q^{84} +5.52598 q^{85} -2.48267 q^{86} -6.65969 q^{87} +3.89962 q^{88} +3.17911 q^{89} -7.03334 q^{90} +1.99284 q^{91} +5.76807 q^{92} +2.07256 q^{93} +10.6566 q^{94} -1.12509 q^{95} -2.38188 q^{96} -17.4351 q^{97} +15.0963 q^{98} +1.67448 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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