LMFDB - Embedded newform 6023.2.a.b.1.13

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			1.13
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)

$f(q)$	$=$	$q-2.20989 q^{2} -1.74865 q^{3} +2.88361 q^{4} +1.63174 q^{5} +3.86432 q^{6} +4.01021 q^{7} -1.95267 q^{8} +0.0577689 q^{9} +O(q^{10})$	\(q-2.20989 q^{2} -1.74865 q^{3} +2.88361 q^{4} +1.63174 q^{5} +3.86432 q^{6} +4.01021 q^{7} -1.95267 q^{8} +0.0577689 q^{9} -3.60597 q^{10} -3.13294 q^{11} -5.04241 q^{12} -2.02366 q^{13} -8.86212 q^{14} -2.85334 q^{15} -1.45202 q^{16} -1.32438 q^{17} -0.127663 q^{18} -1.00000 q^{19} +4.70530 q^{20} -7.01245 q^{21} +6.92344 q^{22} -0.160657 q^{23} +3.41454 q^{24} -2.33742 q^{25} +4.47206 q^{26} +5.14493 q^{27} +11.5639 q^{28} -3.17316 q^{29} +6.30557 q^{30} +2.56696 q^{31} +7.11416 q^{32} +5.47840 q^{33} +2.92672 q^{34} +6.54363 q^{35} +0.166583 q^{36} +2.99162 q^{37} +2.20989 q^{38} +3.53867 q^{39} -3.18626 q^{40} +9.36527 q^{41} +15.4967 q^{42} -3.77478 q^{43} -9.03416 q^{44} +0.0942640 q^{45} +0.355034 q^{46} -2.24021 q^{47} +2.53908 q^{48} +9.08181 q^{49} +5.16543 q^{50} +2.31587 q^{51} -5.83544 q^{52} +8.94639 q^{53} -11.3697 q^{54} -5.11215 q^{55} -7.83063 q^{56} +1.74865 q^{57} +7.01233 q^{58} +9.63212 q^{59} -8.22792 q^{60} -11.0070 q^{61} -5.67269 q^{62} +0.231666 q^{63} -12.8174 q^{64} -3.30209 q^{65} -12.1067 q^{66} +0.661575 q^{67} -3.81898 q^{68} +0.280933 q^{69} -14.4607 q^{70} -8.70148 q^{71} -0.112804 q^{72} +0.404097 q^{73} -6.61115 q^{74} +4.08732 q^{75} -2.88361 q^{76} -12.5637 q^{77} -7.82006 q^{78} -13.1806 q^{79} -2.36933 q^{80} -9.16997 q^{81} -20.6962 q^{82} +4.71291 q^{83} -20.2211 q^{84} -2.16104 q^{85} +8.34185 q^{86} +5.54874 q^{87} +6.11760 q^{88} -5.22329 q^{89} -0.208313 q^{90} -8.11531 q^{91} -0.463272 q^{92} -4.48871 q^{93} +4.95061 q^{94} -1.63174 q^{95} -12.4402 q^{96} +3.17382 q^{97} -20.0698 q^{98} -0.180987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.20989	−1.56263	−0.781314	−	0.624139i	$-0.785450\pi$
$2$	−2.20989	−1.56263	−0.781314	+	0.624139i	$0.785450\pi$
$3$	−1.74865	−1.00958	−0.504791	−	0.863242i	$-0.668430\pi$
$3$	−1.74865	−1.00958	−0.504791	+	0.863242i	$0.668430\pi$
$4$	2.88361	1.44180
$5$	1.63174	0.729737	0.364869	−	0.931059i	$-0.381114\pi$
$5$	1.63174	0.729737	0.364869	+	0.931059i	$0.381114\pi$
$6$	3.86432	1.57760
$7$	4.01021	1.51572	0.757859	−	0.652418i	$-0.226245\pi$
$7$	4.01021	1.51572	0.757859	+	0.652418i	$0.226245\pi$
$8$	−1.95267	−0.690374
$9$	0.0577689	0.0192563
$10$	−3.60597	−1.14031
$11$	−3.13294	−0.944616	−0.472308	−	0.881433i	$-0.656579\pi$
$11$	−3.13294	−0.944616	−0.472308	+	0.881433i	$0.656579\pi$
$12$	−5.04241	−1.45562
$13$	−2.02366	−0.561262	−0.280631	−	0.959816i	$-0.590544\pi$
$13$	−2.02366	−0.561262	−0.280631	+	0.959816i	$0.590544\pi$
$14$	−8.86212	−2.36850
$15$	−2.85334	−0.736730
$16$	−1.45202	−0.363006
$17$	−1.32438	−0.321209	−0.160604	−	0.987019i	$-0.551344\pi$
$17$	−1.32438	−0.321209	−0.160604	+	0.987019i	$0.551344\pi$
$18$	−0.127663	−0.0300904
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	4.70530	1.05214
$21$	−7.01245	−1.53024
$22$	6.92344	1.47608
$23$	−0.160657	−0.0334993	−0.0167497	−	0.999860i	$-0.505332\pi$
$23$	−0.160657	−0.0334993	−0.0167497	+	0.999860i	$0.505332\pi$
$24$	3.41454	0.696989
$25$	−2.33742	−0.467483
$26$	4.47206	0.877044
$27$	5.14493	0.990141
$28$	11.5639	2.18537
$29$	−3.17316	−0.589241	−0.294621	−	0.955614i	$-0.595193\pi$
$29$	−3.17316	−0.589241	−0.294621	+	0.955614i	$0.595193\pi$
$30$	6.30557	1.15123
$31$	2.56696	0.461039	0.230520	−	0.973068i	$-0.425957\pi$
$31$	2.56696	0.461039	0.230520	+	0.973068i	$0.425957\pi$
$32$	7.11416	1.25762
$33$	5.47840	0.953668
$34$	2.92672	0.501929
$35$	6.54363	1.10608
$36$	0.166583	0.0277638
$37$	2.99162	0.491819	0.245910	−	0.969293i	$-0.420913\pi$
$37$	2.99162	0.491819	0.245910	+	0.969293i	$0.420913\pi$
$38$	2.20989	0.358491
$39$	3.53867	0.566640
$40$	−3.18626	−0.503792
$41$	9.36527	1.46261	0.731304	−	0.682051i	$-0.238912\pi$
$41$	9.36527	1.46261	0.731304	+	0.682051i	$0.238912\pi$
$42$	15.4967	2.39120
$43$	−3.77478	−0.575649	−0.287825	−	0.957683i	$-0.592932\pi$
$43$	−3.77478	−0.575649	−0.287825	+	0.957683i	$0.592932\pi$
$44$	−9.03416	−1.36195
$45$	0.0942640	0.0140521
$46$	0.355034	0.0523470
$47$	−2.24021	−0.326768	−0.163384	−	0.986563i	$-0.552241\pi$
$47$	−2.24021	−0.326768	−0.163384	+	0.986563i	$0.552241\pi$
$48$	2.53908	0.366485
$49$	9.08181	1.29740
$50$	5.16543	0.730502
$51$	2.31587	0.324286
$52$	−5.83544	−0.809230
$53$	8.94639	1.22888	0.614441	−	0.788963i	$-0.289382\pi$
$53$	8.94639	1.22888	0.614441	+	0.788963i	$0.289382\pi$
$54$	−11.3697	−1.54722
$55$	−5.11215	−0.689322
$56$	−7.83063	−1.04641
$57$	1.74865	0.231614
$58$	7.01233	0.920764
$59$	9.63212	1.25400	0.626998	−	0.779021i	$-0.284284\pi$
$59$	9.63212	1.25400	0.626998	+	0.779021i	$0.284284\pi$
$60$	−8.22792	−1.06222
$61$	−11.0070	−1.40930	−0.704652	−	0.709553i	$-0.748897\pi$
$61$	−11.0070	−1.40930	−0.704652	+	0.709553i	$0.748897\pi$
$62$	−5.67269	−0.720433
$63$	0.231666	0.0291871
$64$	−12.8174	−1.60218
$65$	−3.30209	−0.409574
$66$	−12.1067	−1.49023
$67$	0.661575	0.0808242	0.0404121	−	0.999183i	$-0.487133\pi$
$67$	0.661575	0.0808242	0.0404121	+	0.999183i	$0.487133\pi$
$68$	−3.81898	−0.463120
$69$	0.280933	0.0338203
$70$	−14.4607	−1.72838
$71$	−8.70148	−1.03268	−0.516338	−	0.856385i	$-0.672705\pi$
$71$	−8.70148	−1.03268	−0.516338	+	0.856385i	$0.672705\pi$
$72$	−0.112804	−0.0132941
$73$	0.404097	0.0472959	0.0236480	−	0.999720i	$-0.492472\pi$
$73$	0.404097	0.0472959	0.0236480	+	0.999720i	$0.492472\pi$
$74$	−6.61115	−0.768530
$75$	4.08732	0.471963
$76$	−2.88361	−0.330772
$77$	−12.5637	−1.43177
$78$	−7.82006	−0.885448
$79$	−13.1806	−1.48293	−0.741465	−	0.670992i	$-0.765869\pi$
$79$	−13.1806	−1.48293	−0.741465	+	0.670992i	$0.765869\pi$
$80$	−2.36933	−0.264899
$81$	−9.16997	−1.01889
$82$	−20.6962	−2.28551
$83$	4.71291	0.517309	0.258655	−	0.965970i	$-0.416721\pi$
$83$	4.71291	0.517309	0.258655	+	0.965970i	$0.416721\pi$
$84$	−20.2211	−2.20631
$85$	−2.16104	−0.234398
$86$	8.34185	0.899525
$87$	5.54874	0.594887
$88$	6.11760	0.652139
$89$	−5.22329	−0.553668	−0.276834	−	0.960918i	$-0.589285\pi$
$89$	−5.22329	−0.553668	−0.276834	+	0.960918i	$0.589285\pi$
$90$	−0.208313	−0.0219581
$91$	−8.11531	−0.850715
$92$	−0.463272	−0.0482995
$93$	−4.48871	−0.465457
$94$	4.95061	0.510616
$95$	−1.63174	−0.167413
$96$	−12.4402	−1.26967
$97$	3.17382	0.322252	0.161126	−	0.986934i	$-0.448487\pi$
$97$	3.17382	0.322252	0.161126	+	0.986934i	$0.448487\pi$
$98$	−20.0698	−2.02735
$99$	−0.180987	−0.0181898
$100$	−6.74019	−0.674019
$101$	13.6980	1.36300	0.681501	−	0.731817i	$-0.261327\pi$
$101$	13.6980	1.36300	0.681501	+	0.731817i	$0.261327\pi$
$102$	−5.11781	−0.506739
$103$	−2.16215	−0.213043	−0.106521	−	0.994310i	$-0.533971\pi$
$103$	−2.16215	−0.213043	−0.106521	+	0.994310i	$0.533971\pi$
$104$	3.95155	0.387481
$105$	−11.4425	−1.11667
$106$	−19.7705	−1.92028
$107$	15.0798	1.45782	0.728909	−	0.684610i	$-0.240028\pi$
$107$	15.0798	1.45782	0.728909	+	0.684610i	$0.240028\pi$
$108$	14.8359	1.42759
$109$	8.16718	0.782274	0.391137	−	0.920332i	$-0.372082\pi$
$109$	8.16718	0.782274	0.391137	+	0.920332i	$0.372082\pi$
$110$	11.2973	1.07715
$111$	−5.23129	−0.496532
$112$	−5.82293	−0.550215
$113$	7.37268	0.693564	0.346782	−	0.937946i	$-0.387274\pi$
$113$	7.37268	0.693564	0.346782	+	0.937946i	$0.387274\pi$
$114$	−3.86432	−0.361926
$115$	−0.262151	−0.0244457
$116$	−9.15015	−0.849570
$117$	−0.116905	−0.0108078
$118$	−21.2859	−1.95953
$119$	−5.31103	−0.486862
$120$	5.57165	0.508619
$121$	−1.18470	−0.107700
$122$	24.3243	2.20222
$123$	−16.3766	−1.47662
$124$	7.40210	0.664728
$125$	−11.9728	−1.07088
$126$	−0.511955	−0.0456086
$127$	−20.8981	−1.85441	−0.927203	−	0.374560i	$-0.877794\pi$
$127$	−20.8981	−1.85441	−0.927203	+	0.374560i	$0.877794\pi$
$128$	14.0968	1.24599
$129$	6.60077	0.581165
$130$	7.29726	0.640012
$131$	1.96426	0.171619	0.0858093	−	0.996312i	$-0.472652\pi$
$131$	1.96426	0.171619	0.0858093	+	0.996312i	$0.472652\pi$
$132$	15.7976	1.37500
$133$	−4.01021	−0.347730
$134$	−1.46201	−0.126298
$135$	8.39519	0.722543
$136$	2.58607	0.221754
$137$	−8.23158	−0.703272	−0.351636	−	0.936137i	$-0.614374\pi$
$137$	−8.23158	−0.703272	−0.351636	+	0.936137i	$0.614374\pi$
$138$	−0.620830	−0.0528486
$139$	−9.26251	−0.785636	−0.392818	−	0.919616i	$-0.628500\pi$
$139$	−9.26251	−0.785636	−0.392818	+	0.919616i	$0.628500\pi$
$140$	18.8693	1.59474
$141$	3.91733	0.329899
$142$	19.2293	1.61369
$143$	6.34000	0.530178
$144$	−0.0838819	−0.00699016
$145$	−5.17778	−0.429991
$146$	−0.893009	−0.0739059
$147$	−15.8809	−1.30983
$148$	8.62666	0.709107
$149$	−3.04992	−0.249859	−0.124930	−	0.992166i	$-0.539871\pi$
$149$	−3.04992	−0.249859	−0.124930	+	0.992166i	$0.539871\pi$
$150$	−9.03252	−0.737502
$151$	9.66999	0.786933	0.393466	−	0.919339i	$-0.371276\pi$
$151$	9.66999	0.786933	0.393466	+	0.919339i	$0.371276\pi$
$152$	1.95267	0.158383
$153$	−0.0765078	−0.00618529
$154$	27.7645	2.23733
$155$	4.18862	0.336438
$156$	10.2041	0.816984
$157$	0.628130	0.0501302	0.0250651	−	0.999686i	$-0.492021\pi$
$157$	0.628130	0.0501302	0.0250651	+	0.999686i	$0.492021\pi$
$158$	29.1276	2.31727
$159$	−15.6441	−1.24066
$160$	11.6085	0.917730
$161$	−0.644269	−0.0507755
$162$	20.2646	1.59214
$163$	−13.4268	−1.05167	−0.525834	−	0.850587i	$-0.676247\pi$
$163$	−13.4268	−1.05167	−0.525834	+	0.850587i	$0.676247\pi$
$164$	27.0057	2.10879
$165$	8.93935	0.695927
$166$	−10.4150	−0.808362
$167$	−13.5839	−1.05115	−0.525577	−	0.850746i	$-0.676151\pi$
$167$	−13.5839	−1.05115	−0.525577	+	0.850746i	$0.676151\pi$
$168$	13.6930	1.05644
$169$	−8.90480	−0.684985
$170$	4.77566	0.366276
$171$	−0.0577689	−0.00441770
$172$	−10.8850	−0.829973
$173$	1.06143	0.0806988	0.0403494	−	0.999186i	$-0.487153\pi$
$173$	1.06143	0.0806988	0.0403494	+	0.999186i	$0.487153\pi$
$174$	−12.2621	−0.929587
$175$	−9.37354	−0.708573
$176$	4.54910	0.342902
$177$	−16.8432	−1.26601
$178$	11.5429	0.865177
$179$	−22.9892	−1.71829	−0.859147	−	0.511730i	$-0.829005\pi$
$179$	−22.9892	−1.71829	−0.859147	+	0.511730i	$0.829005\pi$
$180$	0.271820	0.0202603
$181$	−19.1628	−1.42436	−0.712179	−	0.701998i	$-0.752291\pi$
$181$	−19.1628	−1.42436	−0.712179	+	0.701998i	$0.752291\pi$
$182$	17.9339	1.32935
$183$	19.2474	1.42281
$184$	0.313711	0.0231271
$185$	4.88156	0.358899
$186$	9.91954	0.727336
$187$	4.14919	0.303419
$188$	−6.45988	−0.471135
$189$	20.6322	1.50078
$190$	3.60597	0.261604
$191$	22.2910	1.61292	0.806462	−	0.591286i	$-0.201380\pi$
$191$	22.2910	1.61292	0.806462	+	0.591286i	$0.201380\pi$
$192$	22.4132	1.61753
$193$	12.7461	0.917481	0.458741	−	0.888570i	$-0.348301\pi$
$193$	12.7461	0.917481	0.458741	+	0.888570i	$0.348301\pi$
$194$	−7.01378	−0.503560
$195$	5.77420	0.413499
$196$	26.1884	1.87060
$197$	11.6970	0.833375	0.416687	−	0.909050i	$-0.363191\pi$
$197$	11.6970	0.833375	0.416687	+	0.909050i	$0.363191\pi$
$198$	0.399960	0.0284239
$199$	8.35501	0.592271	0.296135	−	0.955146i	$-0.404302\pi$
$199$	8.35501	0.592271	0.296135	+	0.955146i	$0.404302\pi$
$200$	4.56421	0.322738
$201$	−1.15686	−0.0815987
$202$	−30.2711	−2.12987
$203$	−12.7251	−0.893123
$204$	6.67805	0.467557
$205$	15.2817	1.06732
$206$	4.77811	0.332906
$207$	−0.00928100	−0.000645074 0
$208$	2.93840	0.203742
$209$	3.13294	0.216710
$210$	25.2867	1.74495
$211$	19.4530	1.33920	0.669598	−	0.742724i	$-0.266466\pi$
$211$	19.4530	1.33920	0.669598	+	0.742724i	$0.266466\pi$
$212$	25.7979	1.77181
$213$	15.2158	1.04257
$214$	−33.3247	−2.27803
$215$	−6.15948	−0.420073
$216$	−10.0464	−0.683568
$217$	10.2941	0.698806
$218$	−18.0486	−1.22240
$219$	−0.706623	−0.0477491
$220$	−14.7414	−0.993867
$221$	2.68009	0.180282
$222$	11.5606	0.775895
$223$	16.5342	1.10721	0.553606	−	0.832779i	$-0.313251\pi$
$223$	16.5342	1.10721	0.553606	+	0.832779i	$0.313251\pi$
$224$	28.5293	1.90619
$225$	−0.135030	−0.00900201
$226$	−16.2928	−1.08378
$227$	−14.3082	−0.949669	−0.474835	−	0.880075i	$-0.657492\pi$
$227$	−14.3082	−0.949669	−0.474835	+	0.880075i	$0.657492\pi$
$228$	5.04241	0.333942
$229$	6.81214	0.450159	0.225079	−	0.974340i	$-0.427736\pi$
$229$	6.81214	0.450159	0.225079	+	0.974340i	$0.427736\pi$
$230$	0.579325	0.0381995
$231$	21.9696	1.44549
$232$	6.19615	0.406797
$233$	−17.0827	−1.11913	−0.559563	−	0.828788i	$-0.689031\pi$
$233$	−17.0827	−1.11913	−0.559563	+	0.828788i	$0.689031\pi$
$234$	0.258346	0.0168886
$235$	−3.65544	−0.238455
$236$	27.7753	1.80802
$237$	23.0482	1.49714
$238$	11.7368	0.760783
$239$	−5.96041	−0.385547	−0.192773	−	0.981243i	$-0.561748\pi$
$239$	−5.96041	−0.385547	−0.192773	+	0.981243i	$0.561748\pi$
$240$	4.14312	0.267437
$241$	−26.1699	−1.68575	−0.842875	−	0.538110i	$-0.819139\pi$
$241$	−26.1699	−1.68575	−0.842875	+	0.538110i	$0.819139\pi$
$242$	2.61806	0.168295
$243$	0.600270	0.0385073
$244$	−31.7399	−2.03194
$245$	14.8192	0.946762
$246$	36.1903	2.30741
$247$	2.02366	0.128762
$248$	−5.01243	−0.318290
$249$	−8.24123	−0.522266
$250$	26.4585	1.67338
$251$	−25.6496	−1.61899	−0.809495	−	0.587127i	$-0.800259\pi$
$251$	−25.6496	−1.61899	−0.809495	+	0.587127i	$0.800259\pi$
$252$	0.668033	0.0420821
$253$	0.503329	0.0316440
$254$	46.1824	2.89774
$255$	3.77890	0.236644
$256$	−5.51749	−0.344843
$257$	19.2705	1.20206	0.601030	−	0.799226i	$-0.294757\pi$
$257$	19.2705	1.20206	0.601030	+	0.799226i	$0.294757\pi$
$258$	−14.5870	−0.908145
$259$	11.9970	0.745460
$260$	−9.52194	−0.590525
$261$	−0.183310	−0.0113466
$262$	−4.34081	−0.268176
$263$	22.1794	1.36764	0.683821	−	0.729650i	$-0.260317\pi$
$263$	22.1794	1.36764	0.683821	+	0.729650i	$0.260317\pi$
$264$	−10.6975	−0.658388
$265$	14.5982	0.896761
$266$	8.86212	0.543372
$267$	9.13370	0.558973
$268$	1.90772	0.116533
$269$	−6.52524	−0.397851	−0.198926	−	0.980015i	$-0.563745\pi$
$269$	−6.52524	−0.397851	−0.198926	+	0.980015i	$0.563745\pi$
$270$	−18.5524	−1.12907
$271$	24.7218	1.50174	0.750870	−	0.660450i	$-0.229635\pi$
$271$	24.7218	1.50174	0.750870	+	0.660450i	$0.229635\pi$
$272$	1.92303	0.116601
$273$	14.1908	0.858867
$274$	18.1909	1.09895
$275$	7.32298	0.441592
$276$	0.810100	0.0487623
$277$	−25.1464	−1.51090	−0.755450	−	0.655206i	$-0.772582\pi$
$277$	−25.1464	−1.51090	−0.755450	+	0.655206i	$0.772582\pi$
$278$	20.4691	1.22766
$279$	0.148290	0.00887792
$280$	−12.7776	−0.763606
$281$	10.2901	0.613853	0.306927	−	0.951733i	$-0.400699\pi$
$281$	10.2901	0.613853	0.306927	+	0.951733i	$0.400699\pi$
$282$	−8.65687	−0.515509
$283$	−2.84166	−0.168919	−0.0844597	−	0.996427i	$-0.526916\pi$
$283$	−2.84166	−0.168919	−0.0844597	+	0.996427i	$0.526916\pi$
$284$	−25.0916	−1.48892
$285$	2.85334	0.169017
$286$	−14.0107	−0.828470
$287$	37.5567	2.21690
$288$	0.410977	0.0242171
$289$	−15.2460	−0.896825
$290$	11.4423	0.671916
$291$	−5.54989	−0.325340
$292$	1.16526	0.0681914
$293$	−12.1632	−0.710580	−0.355290	−	0.934756i	$-0.615618\pi$
$293$	−12.1632	−0.710580	−0.355290	+	0.934756i	$0.615618\pi$
$294$	35.0950	2.04678
$295$	15.7171	0.915087
$296$	−5.84166	−0.339539
$297$	−16.1187	−0.935304
$298$	6.73999	0.390437
$299$	0.325116	0.0188019
$300$	11.7862	0.680478
$301$	−15.1377	−0.872522
$302$	−21.3696	−1.22968
$303$	−23.9530	−1.37606
$304$	1.45202	0.0832793
$305$	−17.9606	−1.02842
$306$	0.169074	0.00966530
$307$	−24.4231	−1.39390	−0.696949	−	0.717121i	$-0.745460\pi$
$307$	−24.4231	−1.39390	−0.696949	+	0.717121i	$0.745460\pi$
$308$	−36.2289	−2.06433
$309$	3.78084	0.215084
$310$	−9.25637	−0.525727
$311$	−25.5384	−1.44815	−0.724076	−	0.689721i	$-0.757733\pi$
$311$	−25.5384	−1.44815	−0.724076	+	0.689721i	$0.757733\pi$
$312$	−6.90986	−0.391194
$313$	−1.03364	−0.0584245	−0.0292123	−	0.999573i	$-0.509300\pi$
$313$	−1.03364	−0.0584245	−0.0292123	+	0.999573i	$0.509300\pi$
$314$	−1.38810	−0.0783349
$315$	0.378019	0.0212989
$316$	−38.0076	−2.13809
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	34.5717	1.93868
$319$	9.94132	0.556607
$320$	−20.9148	−1.16917
$321$	−26.3692	−1.47179
$322$	1.42376	0.0793432
$323$	1.32438	0.0736903
$324$	−26.4426	−1.46903
$325$	4.73014	0.262381
$326$	29.6717	1.64337
$327$	−14.2815	−0.789770
$328$	−18.2873	−1.00975
$329$	−8.98371	−0.495288
$330$	−19.7550	−1.08747
$331$	36.0662	1.98238	0.991188	−	0.132464i	$-0.0422888\pi$
$331$	36.0662	1.98238	0.991188	+	0.132464i	$0.0422888\pi$
$332$	13.5902	0.745859
$333$	0.172823	0.00947063
$334$	30.0189	1.64256
$335$	1.07952	0.0589805
$336$	10.1822	0.555487
$337$	−12.3972	−0.675318	−0.337659	−	0.941269i	$-0.609635\pi$
$337$	−12.3972	−0.675318	−0.337659	+	0.941269i	$0.609635\pi$
$338$	19.6786	1.07038
$339$	−12.8922	−0.700210
$340$	−6.23159	−0.337956
$341$	−8.04212	−0.435505
$342$	0.127663	0.00690322
$343$	8.34849	0.450776
$344$	7.37092	0.397413
$345$	0.458410	0.0246800
$346$	−2.34563	−0.126102
$347$	−26.5853	−1.42717	−0.713587	−	0.700566i	$-0.752931\pi$
$347$	−26.5853	−1.42717	−0.713587	+	0.700566i	$0.752931\pi$
$348$	16.0004	0.857711
$349$	−17.2399	−0.922830	−0.461415	−	0.887184i	$-0.652658\pi$
$349$	−17.2399	−0.922830	−0.461415	+	0.887184i	$0.652658\pi$
$350$	20.7145	1.10724
$351$	−10.4116	−0.555729
$352$	−22.2882	−1.18797
$353$	−22.9712	−1.22264	−0.611318	−	0.791385i	$-0.709360\pi$
$353$	−22.9712	−1.22264	−0.611318	+	0.791385i	$0.709360\pi$
$354$	37.2216	1.97830
$355$	−14.1986	−0.753582
$356$	−15.0619	−0.798281
$357$	9.28712	0.491527
$358$	50.8036	2.68505
$359$	24.5048	1.29331	0.646656	−	0.762782i	$-0.276167\pi$
$359$	24.5048	1.29331	0.646656	+	0.762782i	$0.276167\pi$
$360$	−0.184067	−0.00970117
$361$	1.00000	0.0526316
$362$	42.3476	2.22574
$363$	2.07162	0.108732
$364$	−23.4014	−1.22656
$365$	0.659382	0.0345136
$366$	−42.5346	−2.22332
$367$	−5.28926	−0.276097	−0.138049	−	0.990425i	$-0.544083\pi$
$367$	−5.28926	−0.276097	−0.138049	+	0.990425i	$0.544083\pi$
$368$	0.233278	0.0121605
$369$	0.541021	0.0281645
$370$	−10.7877	−0.560825
$371$	35.8769	1.86264
$372$	−12.9437	−0.671098
$373$	14.1943	0.734954	0.367477	−	0.930033i	$-0.380222\pi$
$373$	14.1943	0.734954	0.367477	+	0.930033i	$0.380222\pi$
$374$	−9.16925	−0.474130
$375$	20.9362	1.08114
$376$	4.37439	0.225592
$377$	6.42140	0.330719
$378$	−45.5950	−2.34515
$379$	−34.5044	−1.77237	−0.886187	−	0.463327i	$-0.846655\pi$
$379$	−34.5044	−1.77237	−0.886187	+	0.463327i	$0.846655\pi$
$380$	−4.70530	−0.241377
$381$	36.5434	1.87217
$382$	−49.2607	−2.52040
$383$	−5.90902	−0.301937	−0.150968	−	0.988539i	$-0.548239\pi$
$383$	−5.90902	−0.301937	−0.150968	+	0.988539i	$0.548239\pi$
$384$	−24.6504	−1.25793
$385$	−20.5008	−1.04482
$386$	−28.1674	−1.43368
$387$	−0.218065	−0.0110849
$388$	9.15204	0.464625
$389$	9.88350	0.501113	0.250557	−	0.968102i	$-0.419386\pi$
$389$	9.88350	0.501113	0.250557	+	0.968102i	$0.419386\pi$
$390$	−12.7603	−0.646144
$391$	0.212771	0.0107603
$392$	−17.7338	−0.895692
$393$	−3.43481	−0.173263
$394$	−25.8490	−1.30225
$395$	−21.5073	−1.08215
$396$	−0.521894	−0.0262262
$397$	−23.2295	−1.16585	−0.582927	−	0.812525i	$-0.698093\pi$
$397$	−23.2295	−1.16585	−0.582927	+	0.812525i	$0.698093\pi$
$398$	−18.4636	−0.925499
$399$	7.01245	0.351062
$400$	3.39399	0.169699
$401$	−14.2443	−0.711326	−0.355663	−	0.934614i	$-0.615745\pi$
$401$	−14.2443	−0.711326	−0.355663	+	0.934614i	$0.615745\pi$
$402$	2.55653	0.127508
$403$	−5.19465	−0.258764
$404$	39.4997	1.96518
$405$	−14.9630	−0.743519
$406$	28.1209	1.39562
$407$	−9.37256	−0.464581
$408$	−4.52213	−0.223879
$409$	3.51946	0.174026	0.0870131	−	0.996207i	$-0.472268\pi$
$409$	3.51946	0.174026	0.0870131	+	0.996207i	$0.472268\pi$
$410$	−33.7709	−1.66782
$411$	14.3941	0.710011
$412$	−6.23479	−0.307166
$413$	38.6269	1.90070
$414$	0.0205100	0.00100801
$415$	7.69026	0.377500
$416$	−14.3966	−0.705853
$417$	16.1969	0.793164
$418$	−6.92344	−0.338637
$419$	−26.3045	−1.28506	−0.642528	−	0.766262i	$-0.722115\pi$
$419$	−26.3045	−1.28506	−0.642528	+	0.766262i	$0.722115\pi$
$420$	−32.9957	−1.61003
$421$	35.8626	1.74783	0.873917	−	0.486075i	$-0.161572\pi$
$421$	35.8626	1.74783	0.873917	+	0.486075i	$0.161572\pi$
$422$	−42.9889	−2.09266
$423$	−0.129414	−0.00629234
$424$	−17.4694	−0.848388
$425$	3.09562	0.150160
$426$	−33.6253	−1.62915
$427$	−44.1405	−2.13611
$428$	43.4842	2.10189
$429$	−11.0864	−0.535258
$430$	13.6118	0.656417
$431$	19.2547	0.927467	0.463734	−	0.885975i	$-0.346510\pi$
$431$	19.2547	0.927467	0.463734	+	0.885975i	$0.346510\pi$
$432$	−7.47056	−0.359427
$433$	−32.9122	−1.58166	−0.790831	−	0.612035i	$-0.790351\pi$
$433$	−32.9122	−1.58166	−0.790831	+	0.612035i	$0.790351\pi$
$434$	−22.7487	−1.09197
$435$	9.05412	0.434112
$436$	23.5509	1.12789
$437$	0.160657	0.00768528
$438$	1.56156	0.0746141
$439$	8.95260	0.427284	0.213642	−	0.976912i	$-0.431467\pi$
$439$	8.95260	0.427284	0.213642	+	0.976912i	$0.431467\pi$
$440$	9.98235	0.475890
$441$	0.524646	0.0249832
$442$	−5.92270	−0.281714
$443$	33.3248	1.58331	0.791653	−	0.610970i	$-0.209221\pi$
$443$	33.3248	1.58331	0.791653	+	0.610970i	$0.209221\pi$
$444$	−15.0850	−0.715902
$445$	−8.52307	−0.404032
$446$	−36.5387	−1.73016
$447$	5.33324	0.252254
$448$	−51.4007	−2.42845
$449$	17.5102	0.826359	0.413179	−	0.910650i	$-0.364418\pi$
$449$	17.5102	0.826359	0.413179	+	0.910650i	$0.364418\pi$
$450$	0.298401	0.0140668
$451$	−29.3408	−1.38160
$452$	21.2599	0.999983
$453$	−16.9094	−0.794473
$454$	31.6196	1.48398
$455$	−13.2421	−0.620799
$456$	−3.41454	−0.159900
$457$	−15.9210	−0.744752	−0.372376	−	0.928082i	$-0.621457\pi$
$457$	−15.9210	−0.744752	−0.372376	+	0.928082i	$0.621457\pi$
$458$	−15.0541	−0.703430
$459$	−6.81382	−0.318042
$460$	−0.755941	−0.0352459
$461$	1.38812	0.0646513	0.0323256	−	0.999477i	$-0.489709\pi$
$461$	1.38812	0.0646513	0.0323256	+	0.999477i	$0.489709\pi$
$462$	−48.5503	−2.25876
$463$	−28.5381	−1.32628	−0.663140	−	0.748496i	$-0.730777\pi$
$463$	−28.5381	−1.32628	−0.663140	+	0.748496i	$0.730777\pi$
$464$	4.60751	0.213898
$465$	−7.32441	−0.339662
$466$	37.7509	1.74878
$467$	24.8163	1.14836	0.574181	−	0.818729i	$-0.305321\pi$
$467$	24.8163	1.14836	0.574181	+	0.818729i	$0.305321\pi$
$468$	−0.337107	−0.0155828
$469$	2.65306	0.122507
$470$	8.07812	0.372616
$471$	−1.09838	−0.0506106
$472$	−18.8084	−0.865726
$473$	11.8262	0.543768
$474$	−50.9339	−2.33947
$475$	2.33742	0.107248
$476$	−15.3149	−0.701959
$477$	0.516824	0.0236637
$478$	13.1718	0.602466
$479$	−23.4699	−1.07237	−0.536185	−	0.844101i	$-0.680135\pi$
$479$	−23.4699	−1.07237	−0.536185	+	0.844101i	$0.680135\pi$
$480$	−20.2991	−0.926524
$481$	−6.05402	−0.276040
$482$	57.8325	2.63420
$483$	1.12660	0.0512621
$484$	−3.41621	−0.155282
$485$	5.17885	0.235160
$486$	−1.32653	−0.0601726
$487$	−40.0281	−1.81385	−0.906924	−	0.421294i	$-0.861576\pi$
$487$	−40.0281	−1.81385	−0.906924	+	0.421294i	$0.861576\pi$
$488$	21.4931	0.972947
$489$	23.4787	1.06175
$490$	−32.7487	−1.47944
$491$	−4.72827	−0.213384	−0.106692	−	0.994292i	$-0.534026\pi$
$491$	−4.72827	−0.213384	−0.106692	+	0.994292i	$0.534026\pi$
$492$	−47.2235	−2.12900
$493$	4.20246	0.189269
$494$	−4.47206	−0.201208
$495$	−0.295323	−0.0132738
$496$	−3.72729	−0.167360
$497$	−34.8948	−1.56524
$498$	18.2122	0.816108
$499$	21.8266	0.977091	0.488546	−	0.872538i	$-0.337528\pi$
$499$	21.8266	0.977091	0.488546	+	0.872538i	$0.337528\pi$
$500$	−34.5248	−1.54399
$501$	23.7535	1.06123
$502$	56.6828	2.52988
$503$	0.957436	0.0426899	0.0213450	−	0.999772i	$-0.493205\pi$
$503$	0.957436	0.0426899	0.0213450	+	0.999772i	$0.493205\pi$
$504$	−0.452367	−0.0201500
$505$	22.3516	0.994634
$506$	−1.11230	−0.0494478
$507$	15.5714	0.691548
$508$	−60.2619	−2.67369
$509$	4.68920	0.207845	0.103923	−	0.994585i	$-0.466861\pi$
$509$	4.68920	0.207845	0.103923	+	0.994585i	$0.466861\pi$
$510$	−8.35095	−0.369786
$511$	1.62051	0.0716873
$512$	−16.0006	−0.707133
$513$	−5.14493	−0.227154
$514$	−42.5857	−1.87837
$515$	−3.52807	−0.155465
$516$	19.0340	0.837926
$517$	7.01843	0.308670
$518$	−26.5121	−1.16488
$519$	−1.85606	−0.0814721
$520$	6.44791	0.282759
$521$	13.3235	0.583711	0.291856	−	0.956462i	$-0.405727\pi$
$521$	13.3235	0.583711	0.291856	+	0.956462i	$0.405727\pi$
$522$	0.405095	0.0177305
$523$	6.10968	0.267158	0.133579	−	0.991038i	$-0.457353\pi$
$523$	6.10968	0.267158	0.133579	+	0.991038i	$0.457353\pi$
$524$	5.66417	0.247440
$525$	16.3910	0.715363
$526$	−49.0141	−2.13711
$527$	−3.39962	−0.148090
$528$	−7.95478	−0.346187
$529$	−22.9742	−0.998878
$530$	−32.2604	−1.40130
$531$	0.556437	0.0241473
$532$	−11.5639	−0.501358
$533$	−18.9521	−0.820907
$534$	−20.1845	−0.873467
$535$	24.6063	1.06382
$536$	−1.29184	−0.0557990
$537$	40.2000	1.73476
$538$	14.4201	0.621693
$539$	−28.4527	−1.22555
$540$	24.2084	1.04177
$541$	−13.4724	−0.579224	−0.289612	−	0.957144i	$-0.593526\pi$
$541$	−13.4724	−0.579224	−0.289612	+	0.957144i	$0.593526\pi$
$542$	−54.6323	−2.34666
$543$	33.5089	1.43801
$544$	−9.42182	−0.403957
$545$	13.3267	0.570855
$546$	−31.3601	−1.34209
$547$	−1.54302	−0.0659748	−0.0329874	−	0.999456i	$-0.510502\pi$
$547$	−1.54302	−0.0659748	−0.0329874	+	0.999456i	$0.510502\pi$
$548$	−23.7367	−1.01398
$549$	−0.635864	−0.0271380
$550$	−16.1830	−0.690044
$551$	3.17316	0.135181
$552$	−0.548570	−0.0233487
$553$	−52.8569	−2.24770
$554$	55.5707	2.36097
$555$	−8.53612	−0.362338
$556$	−26.7094	−1.13273
$557$	−31.9495	−1.35374	−0.676871	−	0.736101i	$-0.736665\pi$
$557$	−31.9495	−1.35374	−0.676871	+	0.736101i	$0.736665\pi$
$558$	−0.327705	−0.0138729
$559$	7.63888	0.323090
$560$	−9.50152	−0.401512
$561$	−7.25547	−0.306326
$562$	−22.7399	−0.959224
$563$	19.0429	0.802562	0.401281	−	0.915955i	$-0.368565\pi$
$563$	19.0429	0.802562	0.401281	+	0.915955i	$0.368565\pi$
$564$	11.2960	0.475649
$565$	12.0303	0.506119
$566$	6.27976	0.263958
$567$	−36.7735	−1.54434
$568$	16.9911	0.712932
$569$	14.7018	0.616332	0.308166	−	0.951333i	$-0.400285\pi$
$569$	14.7018	0.616332	0.308166	+	0.951333i	$0.400285\pi$
$570$	−6.30557	−0.264111
$571$	28.4859	1.19210	0.596049	−	0.802948i	$-0.296736\pi$
$571$	28.4859	1.19210	0.596049	+	0.802948i	$0.296736\pi$
$572$	18.2821	0.764412
$573$	−38.9792	−1.62838
$574$	−82.9961	−3.46419
$575$	0.375523	0.0156604
$576$	−0.740450	−0.0308521
$577$	−4.14897	−0.172724	−0.0863620	−	0.996264i	$-0.527524\pi$
$577$	−4.14897	−0.172724	−0.0863620	+	0.996264i	$0.527524\pi$
$578$	33.6920	1.40140
$579$	−22.2884	−0.926273
$580$	−14.9307	−0.619963
$581$	18.8998	0.784095
$582$	12.2646	0.508386
$583$	−28.0285	−1.16082
$584$	−0.789069	−0.0326519
$585$	−0.190758	−0.00788689
$586$	26.8793	1.11037
$587$	−0.823707	−0.0339980	−0.0169990	−	0.999856i	$-0.505411\pi$
$587$	−0.823707	−0.0339980	−0.0169990	+	0.999856i	$0.505411\pi$
$588$	−45.7942	−1.88852
$589$	−2.56696	−0.105770
$590$	−34.7331	−1.42994
$591$	−20.4539	−0.841360
$592$	−4.34391	−0.178533
$593$	−44.4248	−1.82431	−0.912153	−	0.409850i	$-0.865581\pi$
$593$	−44.4248	−1.82431	−0.912153	+	0.409850i	$0.865581\pi$
$594$	35.6206	1.46153
$595$	−8.66624	−0.355281
$596$	−8.79478	−0.360248
$597$	−14.6100	−0.597946
$598$	−0.718469	−0.0293804
$599$	5.42162	0.221521	0.110761	−	0.993847i	$-0.464671\pi$
$599$	5.42162	0.221521	0.110761	+	0.993847i	$0.464671\pi$
$600$	−7.98120	−0.325831
$601$	−7.53777	−0.307472	−0.153736	−	0.988112i	$-0.549131\pi$
$601$	−7.53777	−0.307472	−0.153736	+	0.988112i	$0.549131\pi$
$602$	33.4526	1.36343
$603$	0.0382185	0.00155638
$604$	27.8845	1.13460
$605$	−1.93313	−0.0785927
$606$	52.9334	2.15027
$607$	−42.9160	−1.74191	−0.870954	−	0.491365i	$-0.836498\pi$
$607$	−42.9160	−1.74191	−0.870954	+	0.491365i	$0.836498\pi$
$608$	−7.11416	−0.288517
$609$	22.2516	0.901682
$610$	39.6910	1.60704
$611$	4.53342	0.183402
$612$	−0.220619	−0.00891798
$613$	15.8079	0.638474	0.319237	−	0.947675i	$-0.396573\pi$
$613$	15.8079	0.638474	0.319237	+	0.947675i	$0.396573\pi$
$614$	53.9722	2.17814
$615$	−26.7223	−1.07755
$616$	24.5329	0.988458
$617$	18.3443	0.738515	0.369258	−	0.929327i	$-0.379612\pi$
$617$	18.3443	0.738515	0.369258	+	0.929327i	$0.379612\pi$
$618$	−8.35523	−0.336096
$619$	−0.840999	−0.0338026	−0.0169013	−	0.999857i	$-0.505380\pi$
$619$	−0.840999	−0.0338026	−0.0169013	+	0.999857i	$0.505380\pi$
$620$	12.0783	0.485077
$621$	−0.826569	−0.0331691
$622$	56.4371	2.26292
$623$	−20.9465	−0.839205
$624$	−5.13823	−0.205694
$625$	−7.84940	−0.313976
$626$	2.28422	0.0912957
$627$	−5.47840	−0.218786
$628$	1.81128	0.0722780
$629$	−3.96203	−0.157977
$630$	−0.835379	−0.0332823
$631$	20.1842	0.803522	0.401761	−	0.915745i	$-0.368398\pi$
$631$	20.1842	0.803522	0.401761	+	0.915745i	$0.368398\pi$
$632$	25.7373	1.02378
$633$	−34.0164	−1.35203
$634$	2.20989	0.0877659
$635$	−34.1003	−1.35323
$636$	−45.1114	−1.78878
$637$	−18.3785	−0.728182
$638$	−21.9692	−0.869769
$639$	−0.502675	−0.0198855
$640$	23.0024	0.909248
$641$	−35.2797	−1.39346	−0.696732	−	0.717331i	$-0.745363\pi$
$641$	−35.2797	−1.39346	−0.696732	+	0.717331i	$0.745363\pi$
$642$	58.2731	2.29986
$643$	22.6099	0.891649	0.445825	−	0.895120i	$-0.352910\pi$
$643$	22.6099	0.891649	0.445825	+	0.895120i	$0.352910\pi$
$644$	−1.85782	−0.0732084
$645$	10.7708	0.424098
$646$	−2.92672	−0.115150
$647$	−6.06503	−0.238441	−0.119220	−	0.992868i	$-0.538040\pi$
$647$	−6.06503	−0.238441	−0.119220	+	0.992868i	$0.538040\pi$
$648$	17.9060	0.703412
$649$	−30.1768	−1.18454
$650$	−10.4531	−0.410003
$651$	−18.0007	−0.705502
$652$	−38.7176	−1.51630
$653$	16.2842	0.637251	0.318626	−	0.947881i	$-0.396779\pi$
$653$	16.2842	0.637251	0.318626	+	0.947881i	$0.396779\pi$
$654$	31.5606	1.23412
$655$	3.20517	0.125237
$656$	−13.5986	−0.530936
$657$	0.0233442	0.000910745 0
$658$	19.8530	0.773950
$659$	43.7962	1.70606	0.853029	−	0.521863i	$-0.174763\pi$
$659$	43.7962	1.70606	0.853029	+	0.521863i	$0.174763\pi$
$660$	25.7776	1.00339
$661$	−6.23568	−0.242540	−0.121270	−	0.992620i	$-0.538697\pi$
$661$	−6.23568	−0.242540	−0.121270	+	0.992620i	$0.538697\pi$
$662$	−79.7022	−3.09771
$663$	−4.68653	−0.182010
$664$	−9.20278	−0.357137
$665$	−6.54363	−0.253751
$666$	−0.381919	−0.0147991
$667$	0.509791	0.0197392
$668$	−39.1707	−1.51556
$669$	−28.9125	−1.11782
$670$	−2.38562	−0.0921645
$671$	34.4843	1.33125
$672$	−49.8877	−1.92446
$673$	−19.8516	−0.765224	−0.382612	−	0.923909i	$-0.624975\pi$
$673$	−19.8516	−0.765224	−0.382612	+	0.923909i	$0.624975\pi$
$674$	27.3964	1.05527
$675$	−12.0258	−0.462875
$676$	−25.6779	−0.987613
$677$	−5.76841	−0.221698	−0.110849	−	0.993837i	$-0.535357\pi$
$677$	−5.76841	−0.221698	−0.110849	+	0.993837i	$0.535357\pi$
$678$	28.4904	1.09417
$679$	12.7277	0.488444
$680$	4.21981	0.161822
$681$	25.0200	0.958769
$682$	17.7722	0.680532
$683$	−30.6810	−1.17398	−0.586988	−	0.809595i	$-0.699687\pi$
$683$	−30.6810	−1.17398	−0.586988	+	0.809595i	$0.699687\pi$
$684$	−0.166583	−0.00636946
$685$	−13.4318	−0.513204
$686$	−18.4492	−0.704395
$687$	−11.9120	−0.454472
$688$	5.48108	0.208964
$689$	−18.1045	−0.689725
$690$	−1.01303	−0.0385656
$691$	41.6473	1.58434	0.792168	−	0.610303i	$-0.208952\pi$
$691$	41.6473	1.58434	0.792168	+	0.610303i	$0.208952\pi$
$692$	3.06074	0.116352
$693$	−0.725794	−0.0275706
$694$	58.7506	2.23014
$695$	−15.1140	−0.573308
$696$	−10.8349	−0.410695
$697$	−12.4031	−0.469802
$698$	38.0982	1.44204
$699$	29.8717	1.12985
$700$	−27.0296	−1.02162
$701$	−49.0166	−1.85133	−0.925666	−	0.378341i	$-0.876495\pi$
$701$	−49.0166	−1.85133	−0.925666	+	0.378341i	$0.876495\pi$
$702$	23.0084	0.868397
$703$	−2.99162	−0.112831
$704$	40.1563	1.51345
$705$	6.39208	0.240740
$706$	50.7639	1.91052
$707$	54.9319	2.06593
$708$	−48.5691	−1.82534
$709$	−45.2826	−1.70062	−0.850312	−	0.526280i	$-0.823587\pi$
$709$	−45.2826	−1.70062	−0.850312	+	0.526280i	$0.823587\pi$
$710$	31.3773	1.17757
$711$	−0.761427	−0.0285558
$712$	10.1994	0.382238
$713$	−0.412400	−0.0154445
$714$	−20.5235	−0.768073
$715$	10.3452	0.386890
$716$	−66.2918	−2.47744
$717$	10.4226	0.389241
$718$	−54.1528	−2.02096
$719$	46.7159	1.74221	0.871104	−	0.491099i	$-0.163405\pi$
$719$	46.7159	1.74221	0.871104	+	0.491099i	$0.163405\pi$
$720$	−0.136874	−0.00510098
$721$	−8.67068	−0.322913
$722$	−2.20989	−0.0822435
$723$	45.7619	1.70190
$724$	−55.2579	−2.05364
$725$	7.41700	0.275460
$726$	−4.57806	−0.169908
$727$	−32.3260	−1.19891	−0.599453	−	0.800410i	$-0.704615\pi$
$727$	−32.3260	−1.19891	−0.599453	+	0.800410i	$0.704615\pi$
$728$	15.8465	0.587312
$729$	26.4602	0.980009
$730$	−1.45716	−0.0539319
$731$	4.99924	0.184903
$732$	55.5019	2.05141
$733$	49.4555	1.82668	0.913341	−	0.407196i	$-0.133493\pi$
$733$	49.4555	1.82668	0.913341	+	0.407196i	$0.133493\pi$
$734$	11.6887	0.431437
$735$	−25.9135	−0.955834
$736$	−1.14294	−0.0421293
$737$	−2.07267	−0.0763479
$738$	−1.19560	−0.0440105
$739$	−19.9517	−0.733936	−0.366968	−	0.930234i	$-0.619604\pi$
$739$	−19.9517	−0.733936	−0.366968	+	0.930234i	$0.619604\pi$
$740$	14.0765	0.517462
$741$	−3.53867	−0.129996
$742$	−79.2840	−2.91061
$743$	−26.7031	−0.979641	−0.489821	−	0.871823i	$-0.662938\pi$
$743$	−26.7031	−0.979641	−0.489821	+	0.871823i	$0.662938\pi$
$744$	8.76498	0.321340
$745$	−4.97669	−0.182332
$746$	−31.3679	−1.14846
$747$	0.272260	0.00996147
$748$	11.9646	0.437470
$749$	60.4732	2.20964
$750$	−46.2666	−1.68942
$751$	7.58256	0.276691	0.138346	−	0.990384i	$-0.455822\pi$
$751$	7.58256	0.276691	0.138346	+	0.990384i	$0.455822\pi$
$752$	3.25284	0.118619
$753$	44.8521	1.63450
$754$	−14.1906	−0.516790
$755$	15.7789	0.574254
$756$	59.4953	2.16382
$757$	38.8407	1.41169	0.705845	−	0.708367i	$-0.250568\pi$
$757$	38.8407	1.41169	0.705845	+	0.708367i	$0.250568\pi$
$758$	76.2510	2.76956
$759$	−0.880145	−0.0319472
$760$	3.18626	0.115578
$761$	−3.41598	−0.123829	−0.0619146	−	0.998081i	$-0.519721\pi$
$761$	−3.41598	−0.123829	−0.0619146	+	0.998081i	$0.519721\pi$
$762$	−80.7568	−2.92551
$763$	32.7521	1.18571
$764$	64.2786	2.32552
$765$	−0.124841	−0.00451364
$766$	13.0583	0.471815
$767$	−19.4921	−0.703820
$768$	9.64814	0.348147
$769$	−17.2737	−0.622905	−0.311452	−	0.950262i	$-0.600815\pi$
$769$	−17.2737	−0.622905	−0.311452	+	0.950262i	$0.600815\pi$
$770$	45.3045	1.63266
$771$	−33.6973	−1.21358
$772$	36.7546	1.32283
$773$	−49.2610	−1.77180	−0.885898	−	0.463881i	$-0.846457\pi$
$773$	−49.2610	−1.77180	−0.885898	+	0.463881i	$0.846457\pi$
$774$	0.481900	0.0173215
$775$	−6.00005	−0.215528
$776$	−6.19743	−0.222475
$777$	−20.9786	−0.752603
$778$	−21.8414	−0.783053
$779$	−9.36527	−0.335545
$780$	16.6505	0.596184
$781$	27.2612	0.975482
$782$	−0.470199	−0.0168143
$783$	−16.3257	−0.583432
$784$	−13.1870	−0.470964
$785$	1.02495	0.0365819
$786$	7.59054	0.270746
$787$	38.9695	1.38911	0.694556	−	0.719438i	$-0.255601\pi$
$787$	38.9695	1.38911	0.694556	+	0.719438i	$0.255601\pi$
$788$	33.7295	1.20156
$789$	−38.7840	−1.38075
$790$	47.5287	1.69100
$791$	29.5660	1.05125
$792$	0.353407	0.0125578
$793$	22.2745	0.790989
$794$	51.3345	1.82179
$795$	−25.5271	−0.905354
$796$	24.0926	0.853938
$797$	−29.9676	−1.06151	−0.530753	−	0.847527i	$-0.678091\pi$
$797$	−29.9676	−1.06151	−0.530753	+	0.847527i	$0.678091\pi$
$798$	−15.4967	−0.548578
$799$	2.96688	0.104961
$800$	−16.6288	−0.587915
$801$	−0.301744	−0.0106616
$802$	31.4783	1.11154
$803$	−1.26601	−0.0446765
$804$	−3.33593	−0.117649
$805$	−1.05128	−0.0370528
$806$	11.4796	0.404352
$807$	11.4104	0.401663
$808$	−26.7477	−0.940982
$809$	−16.0591	−0.564607	−0.282303	−	0.959325i	$-0.591098\pi$
$809$	−16.0591	−0.564607	−0.282303	+	0.959325i	$0.591098\pi$
$810$	33.0666	1.16184
$811$	16.6986	0.586366	0.293183	−	0.956056i	$-0.405285\pi$
$811$	16.6986	0.586366	0.293183	+	0.956056i	$0.405285\pi$
$812$	−36.6940	−1.28771
$813$	−43.2296	−1.51613
$814$	20.7123	0.725966
$815$	−21.9091	−0.767442
$816$	−3.36270	−0.117718
$817$	3.77478	0.132063
$818$	−7.77762	−0.271938
$819$	−0.468813	−0.0163816
$820$	44.0664	1.53887
$821$	45.1930	1.57725	0.788623	−	0.614877i	$-0.210794\pi$
$821$	45.1930	1.57725	0.788623	+	0.614877i	$0.210794\pi$
$822$	−31.8094	−1.10948
$823$	−42.8117	−1.49232	−0.746161	−	0.665765i	$-0.768105\pi$
$823$	−42.8117	−1.49232	−0.746161	+	0.665765i	$0.768105\pi$
$824$	4.22197	0.147079
$825$	−12.8053	−0.445824
$826$	−85.3610	−2.97009
$827$	−15.4640	−0.537735	−0.268868	−	0.963177i	$-0.586649\pi$
$827$	−15.4640	−0.537735	−0.268868	+	0.963177i	$0.586649\pi$
$828$	−0.0267627	−0.000930070 0
$829$	13.1407	0.456397	0.228198	−	0.973615i	$-0.426716\pi$
$829$	13.1407	0.456397	0.228198	+	0.973615i	$0.426716\pi$
$830$	−16.9946	−0.589892
$831$	43.9722	1.52538
$832$	25.9382	0.899244
$833$	−12.0277	−0.416736
$834$	−35.7933	−1.23942
$835$	−22.1654	−0.767067
$836$	9.03416	0.312453
$837$	13.2068	0.456494
$838$	58.1299	2.00806
$839$	−52.3665	−1.80789	−0.903946	−	0.427647i	$-0.859343\pi$
$839$	−52.3665	−1.80789	−0.903946	+	0.427647i	$0.859343\pi$
$840$	22.3435	0.770923
$841$	−18.9310	−0.652795
$842$	−79.2522	−2.73121
$843$	−17.9937	−0.619735
$844$	56.0947	1.93086
$845$	−14.5303	−0.499859
$846$	0.285991	0.00983259
$847$	−4.75090	−0.163243
$848$	−12.9904	−0.446091
$849$	4.96907	0.170538
$850$	−6.84097	−0.234643
$851$	−0.480625	−0.0164756
$852$	43.8764	1.50318
$853$	−15.5622	−0.532841	−0.266421	−	0.963857i	$-0.585841\pi$
$853$	−15.5622	−0.532841	−0.266421	+	0.963857i	$0.585841\pi$
$854$	97.5455	3.33794
$855$	−0.0942640	−0.00322376
$856$	−29.4459	−1.00644
$857$	−3.51387	−0.120032	−0.0600158	−	0.998197i	$-0.519115\pi$
$857$	−3.51387	−0.120032	−0.0600158	+	0.998197i	$0.519115\pi$
$858$	24.4998	0.836408
$859$	21.5578	0.735541	0.367771	−	0.929917i	$-0.380121\pi$
$859$	21.5578	0.735541	0.367771	+	0.929917i	$0.380121\pi$
$860$	−17.7615	−0.605662
$861$	−65.6735	−2.23815
$862$	−42.5508	−1.44929
$863$	25.7255	0.875707	0.437854	−	0.899046i	$-0.355739\pi$
$863$	25.7255	0.875707	0.437854	+	0.899046i	$0.355739\pi$
$864$	36.6018	1.24522
$865$	1.73198	0.0588889
$866$	72.7324	2.47155
$867$	26.6599	0.905419
$868$	29.6840	1.00754
$869$	41.2939	1.40080
$870$	−20.0086	−0.678355
$871$	−1.33880	−0.0453636
$872$	−15.9478	−0.540062
$873$	0.183348	0.00620539
$874$	−0.355034	−0.0120092
$875$	−48.0134	−1.62315
$876$	−2.03762	−0.0688449
$877$	−40.8738	−1.38021	−0.690106	−	0.723709i	$-0.742436\pi$
$877$	−40.8738	−1.38021	−0.690106	+	0.723709i	$0.742436\pi$
$878$	−19.7842	−0.667686
$879$	21.2691	0.717389
$880$	7.42296	0.250228
$881$	22.1032	0.744675	0.372338	−	0.928097i	$-0.378556\pi$
$881$	22.1032	0.744675	0.372338	+	0.928097i	$0.378556\pi$
$882$	−1.15941	−0.0390394
$883$	33.6906	1.13378	0.566889	−	0.823794i	$-0.308147\pi$
$883$	33.6906	1.13378	0.566889	+	0.823794i	$0.308147\pi$
$884$	7.72832	0.259932
$885$	−27.4837	−0.923856
$886$	−73.6440	−2.47412
$887$	28.9842	0.973193	0.486597	−	0.873627i	$-0.338238\pi$
$887$	28.9842	0.973193	0.486597	+	0.873627i	$0.338238\pi$
$888$	10.2150	0.342793
$889$	−83.8058	−2.81076
$890$	18.8350	0.631352
$891$	28.7289	0.962456
$892$	47.6781	1.59638
$893$	2.24021	0.0749657
$894$	−11.7859	−0.394178
$895$	−37.5124	−1.25390
$896$	56.5312	1.88858
$897$	−0.568513	−0.0189821
$898$	−38.6956	−1.29129
$899$	−8.14537	−0.271663
$900$	−0.389374	−0.0129791
$901$	−11.8484	−0.394727
$902$	64.8399	2.15893
$903$	26.4705	0.880883
$904$	−14.3964	−0.478819
$905$	−31.2687	−1.03941
$906$	37.3679	1.24147
$907$	−17.7822	−0.590450	−0.295225	−	0.955428i	$-0.595395\pi$
$907$	−17.7822	−0.590450	−0.295225	+	0.955428i	$0.595395\pi$
$908$	−41.2593	−1.36924
$909$	0.791319	0.0262464
$910$	29.2635	0.970077
$911$	−24.7058	−0.818540	−0.409270	−	0.912413i	$-0.634217\pi$
$911$	−24.7058	−0.818540	−0.409270	+	0.912413i	$0.634217\pi$
$912$	−2.53908	−0.0840773
$913$	−14.7653	−0.488659
$914$	35.1836	1.16377
$915$	31.4068	1.03828
$916$	19.6435	0.649040
$917$	7.87712	0.260125
$918$	15.0578	0.496981
$919$	25.8814	0.853749	0.426875	−	0.904311i	$-0.359615\pi$
$919$	25.8814	0.853749	0.426875	+	0.904311i	$0.359615\pi$
$920$	0.511895	0.0168767
$921$	42.7073	1.40725
$922$	−3.06759	−0.101026
$923$	17.6088	0.579602
$924$	63.3516	2.08411
$925$	−6.99266	−0.229917
$926$	63.0661	2.07248
$927$	−0.124905	−0.00410242
$928$	−22.5744	−0.741040
$929$	−24.6722	−0.809468	−0.404734	−	0.914434i	$-0.632636\pi$
$929$	−24.6722	−0.809468	−0.404734	+	0.914434i	$0.632636\pi$
$930$	16.1861	0.530764
$931$	−9.08181	−0.297644
$932$	−49.2599	−1.61356
$933$	44.6577	1.46203
$934$	−54.8412	−1.79446
$935$	6.77041	0.221416
$936$	0.228277	0.00746146
$937$	−57.7633	−1.88704	−0.943522	−	0.331311i	$-0.892509\pi$
$937$	−57.7633	−1.88704	−0.943522	+	0.331311i	$0.892509\pi$
$938$	−5.86296	−0.191432
$939$	1.80746	0.0589843
$940$	−10.5409	−0.343805
$941$	42.0207	1.36984	0.684918	−	0.728620i	$-0.259838\pi$
$941$	42.0207	1.36984	0.684918	+	0.728620i	$0.259838\pi$
$942$	2.42729	0.0790855
$943$	−1.50460	−0.0489964
$944$	−13.9861	−0.455208
$945$	33.6665	1.09517
$946$	−26.1345	−0.849706
$947$	−0.527420	−0.0171389	−0.00856943	−	0.999963i	$-0.502728\pi$
$947$	−0.527420	−0.0171389	−0.00856943	+	0.999963i	$0.502728\pi$
$948$	66.4618	2.15858
$949$	−0.817754	−0.0265454
$950$	−5.16543	−0.167589
$951$	1.74865	0.0567038
$952$	10.3707	0.336117
$953$	5.86206	0.189891	0.0949453	−	0.995482i	$-0.469732\pi$
$953$	5.86206	0.189891	0.0949453	+	0.995482i	$0.469732\pi$
$954$	−1.14212	−0.0369776
$955$	36.3732	1.17701
$956$	−17.1875	−0.555882
$957$	−17.3839	−0.561940
$958$	51.8660	1.67571
$959$	−33.0104	−1.06596
$960$	36.5726	1.18037
$961$	−24.4107	−0.787443
$962$	13.3787	0.431347
$963$	0.871144	0.0280722
$964$	−75.4636	−2.43052
$965$	20.7983	0.669520
$966$	−2.48966	−0.0801035
$967$	−27.7812	−0.893384	−0.446692	−	0.894688i	$-0.647398\pi$
$967$	−27.7812	−0.893384	−0.446692	+	0.894688i	$0.647398\pi$
$968$	2.31333	0.0743533
$969$	−2.31587	−0.0743964
$970$	−11.4447	−0.367467
$971$	12.3910	0.397647	0.198824	−	0.980035i	$-0.436288\pi$
$971$	12.3910	0.397647	0.198824	+	0.980035i	$0.436288\pi$
$972$	1.73094	0.0555200
$973$	−37.1446	−1.19080
$974$	88.4577	2.83437
$975$	−8.27134	−0.264895
$976$	15.9825	0.511586
$977$	1.52197	0.0486921	0.0243461	−	0.999704i	$-0.492250\pi$
$977$	1.52197	0.0486921	0.0243461	+	0.999704i	$0.492250\pi$
$978$	−51.8854	−1.65911
$979$	16.3643	0.523004
$980$	42.7327	1.36504
$981$	0.471809	0.0150637
$982$	10.4490	0.333440
$983$	−39.6194	−1.26366	−0.631832	−	0.775105i	$-0.717697\pi$
$983$	−39.6194	−1.26366	−0.631832	+	0.775105i	$0.717697\pi$
$984$	31.9780	1.01942
$985$	19.0864	0.608145
$986$	−9.28697	−0.295757
$987$	15.7093	0.500034
$988$	5.83544	0.185650
$989$	0.606446	0.0192839
$990$	0.652632	0.0207420
$991$	27.6644	0.878790	0.439395	−	0.898294i	$-0.355193\pi$
$991$	27.6644	0.878790	0.439395	+	0.898294i	$0.355193\pi$
$992$	18.2617	0.579811
$993$	−63.0670	−2.00137
$994$	77.1136	2.44589
$995$	13.6332	0.432202
$996$	−23.7645	−0.753006
$997$	8.83091	0.279678	0.139839	−	0.990174i	$-0.455342\pi$
$997$	8.83091	0.279678	0.139839	+	0.990174i	$0.455342\pi$
$998$	−48.2343	−1.52683
$999$	15.3917	0.486971

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.13	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.13	✓	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)

\(f(q)\)	\(=\)	\(q-2.20989 q^{2} -1.74865 q^{3} +2.88361 q^{4} +1.63174 q^{5} +3.86432 q^{6} +4.01021 q^{7} -1.95267 q^{8} +0.0577689 q^{9} +O(q^{10})\)	\(q-2.20989 q^{2} -1.74865 q^{3} +2.88361 q^{4} +1.63174 q^{5} +3.86432 q^{6} +4.01021 q^{7} -1.95267 q^{8} +0.0577689 q^{9} -3.60597 q^{10} -3.13294 q^{11} -5.04241 q^{12} -2.02366 q^{13} -8.86212 q^{14} -2.85334 q^{15} -1.45202 q^{16} -1.32438 q^{17} -0.127663 q^{18} -1.00000 q^{19} +4.70530 q^{20} -7.01245 q^{21} +6.92344 q^{22} -0.160657 q^{23} +3.41454 q^{24} -2.33742 q^{25} +4.47206 q^{26} +5.14493 q^{27} +11.5639 q^{28} -3.17316 q^{29} +6.30557 q^{30} +2.56696 q^{31} +7.11416 q^{32} +5.47840 q^{33} +2.92672 q^{34} +6.54363 q^{35} +0.166583 q^{36} +2.99162 q^{37} +2.20989 q^{38} +3.53867 q^{39} -3.18626 q^{40} +9.36527 q^{41} +15.4967 q^{42} -3.77478 q^{43} -9.03416 q^{44} +0.0942640 q^{45} +0.355034 q^{46} -2.24021 q^{47} +2.53908 q^{48} +9.08181 q^{49} +5.16543 q^{50} +2.31587 q^{51} -5.83544 q^{52} +8.94639 q^{53} -11.3697 q^{54} -5.11215 q^{55} -7.83063 q^{56} +1.74865 q^{57} +7.01233 q^{58} +9.63212 q^{59} -8.22792 q^{60} -11.0070 q^{61} -5.67269 q^{62} +0.231666 q^{63} -12.8174 q^{64} -3.30209 q^{65} -12.1067 q^{66} +0.661575 q^{67} -3.81898 q^{68} +0.280933 q^{69} -14.4607 q^{70} -8.70148 q^{71} -0.112804 q^{72} +0.404097 q^{73} -6.61115 q^{74} +4.08732 q^{75} -2.88361 q^{76} -12.5637 q^{77} -7.82006 q^{78} -13.1806 q^{79} -2.36933 q^{80} -9.16997 q^{81} -20.6962 q^{82} +4.71291 q^{83} -20.2211 q^{84} -2.16104 q^{85} +8.34185 q^{86} +5.54874 q^{87} +6.11760 q^{88} -5.22329 q^{89} -0.208313 q^{90} -8.11531 q^{91} -0.463272 q^{92} -4.48871 q^{93} +4.95061 q^{94} -1.63174 q^{95} -12.4402 q^{96} +3.17382 q^{97} -20.0698 q^{98} -0.180987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 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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