LMFDB - Embedded newform 6023.2.a.b.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.62992 q^{2} +1.18387 q^{3} +4.91650 q^{4} +1.04484 q^{5} -3.11349 q^{6} +0.263404 q^{7} -7.67017 q^{8} -1.59845 q^{9} +O(q^{10})$	\(q-2.62992 q^{2} +1.18387 q^{3} +4.91650 q^{4} +1.04484 q^{5} -3.11349 q^{6} +0.263404 q^{7} -7.67017 q^{8} -1.59845 q^{9} -2.74784 q^{10} +0.251144 q^{11} +5.82050 q^{12} +1.19133 q^{13} -0.692732 q^{14} +1.23695 q^{15} +10.3390 q^{16} +4.91921 q^{17} +4.20380 q^{18} -1.00000 q^{19} +5.13694 q^{20} +0.311836 q^{21} -0.660490 q^{22} +5.60894 q^{23} -9.08049 q^{24} -3.90831 q^{25} -3.13310 q^{26} -5.44397 q^{27} +1.29502 q^{28} -5.30224 q^{29} -3.25310 q^{30} -0.922586 q^{31} -11.8503 q^{32} +0.297322 q^{33} -12.9371 q^{34} +0.275214 q^{35} -7.85877 q^{36} +3.52815 q^{37} +2.62992 q^{38} +1.41038 q^{39} -8.01408 q^{40} -0.747366 q^{41} -0.820106 q^{42} -8.78366 q^{43} +1.23475 q^{44} -1.67012 q^{45} -14.7511 q^{46} -10.2885 q^{47} +12.2400 q^{48} -6.93062 q^{49} +10.2786 q^{50} +5.82371 q^{51} +5.85715 q^{52} -1.54648 q^{53} +14.3172 q^{54} +0.262405 q^{55} -2.02035 q^{56} -1.18387 q^{57} +13.9445 q^{58} -11.8987 q^{59} +6.08148 q^{60} -7.30658 q^{61} +2.42633 q^{62} -0.421037 q^{63} +10.4875 q^{64} +1.24474 q^{65} -0.781935 q^{66} +12.3676 q^{67} +24.1853 q^{68} +6.64027 q^{69} -0.723793 q^{70} -4.68121 q^{71} +12.2604 q^{72} -13.7773 q^{73} -9.27876 q^{74} -4.62694 q^{75} -4.91650 q^{76} +0.0661523 q^{77} -3.70918 q^{78} +9.84399 q^{79} +10.8025 q^{80} -1.64962 q^{81} +1.96552 q^{82} -2.19820 q^{83} +1.53314 q^{84} +5.13977 q^{85} +23.1004 q^{86} -6.27717 q^{87} -1.92632 q^{88} +6.15320 q^{89} +4.39229 q^{90} +0.313800 q^{91} +27.5764 q^{92} -1.09222 q^{93} +27.0580 q^{94} -1.04484 q^{95} -14.0293 q^{96} +9.44861 q^{97} +18.2270 q^{98} -0.401441 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.62992	−1.85964	−0.929818	−	0.368019i	$-0.880036\pi$
$2$	−2.62992	−1.85964	−0.929818	+	0.368019i	$0.880036\pi$
$3$	1.18387	0.683509	0.341754	−	0.939789i	$-0.388979\pi$
$3$	1.18387	0.683509	0.341754	+	0.939789i	$0.388979\pi$
$4$	4.91650	2.45825
$5$	1.04484	0.467266	0.233633	−	0.972325i	$-0.424939\pi$
$5$	1.04484	0.467266	0.233633	+	0.972325i	$0.424939\pi$
$6$	−3.11349	−1.27108
$7$	0.263404	0.0995573	0.0497787	−	0.998760i	$-0.484148\pi$
$7$	0.263404	0.0995573	0.0497787	+	0.998760i	$0.484148\pi$
$8$	−7.67017	−2.71181
$9$	−1.59845	−0.532816
$10$	−2.74784	−0.868945
$11$	0.251144	0.0757228	0.0378614	−	0.999283i	$-0.487945\pi$
$11$	0.251144	0.0757228	0.0378614	+	0.999283i	$0.487945\pi$
$12$	5.82050	1.68023
$13$	1.19133	0.330414	0.165207	−	0.986259i	$-0.447171\pi$
$13$	1.19133	0.330414	0.165207	+	0.986259i	$0.447171\pi$
$14$	−0.692732	−0.185140
$15$	1.23695	0.319380
$16$	10.3390	2.58474
$17$	4.91921	1.19308	0.596541	−	0.802582i	$-0.296541\pi$
$17$	4.91921	1.19308	0.596541	+	0.802582i	$0.296541\pi$
$18$	4.20380	0.990844
$19$	−1.00000	−0.229416
$19$	−1.00000	−0.229416
$20$	5.13694	1.14866
$21$	0.311836	0.0680483
$22$	−0.660490	−0.140817
$23$	5.60894	1.16955	0.584773	−	0.811197i	$-0.301184\pi$
$23$	5.60894	1.16955	0.584773	+	0.811197i	$0.301184\pi$
$24$	−9.08049	−1.85355
$25$	−3.90831	−0.781663
$26$	−3.13310	−0.614451
$27$	−5.44397	−1.04769
$28$	1.29502	0.244737
$29$	−5.30224	−0.984602	−0.492301	−	0.870425i	$-0.663844\pi$
$29$	−5.30224	−0.984602	−0.492301	+	0.870425i	$0.663844\pi$
$30$	−3.25310	−0.593931
$31$	−0.922586	−0.165701	−0.0828506	−	0.996562i	$-0.526402\pi$
$31$	−0.922586	−0.165701	−0.0828506	+	0.996562i	$0.526402\pi$
$32$	−11.8503	−2.09486
$33$	0.297322	0.0517572
$34$	−12.9371	−2.21870
$35$	0.275214	0.0465197
$36$	−7.85877	−1.30979
$37$	3.52815	0.580024	0.290012	−	0.957023i	$-0.406341\pi$
$37$	3.52815	0.580024	0.290012	+	0.957023i	$0.406341\pi$
$38$	2.62992	0.426630
$39$	1.41038	0.225841
$40$	−8.01408	−1.26714
$41$	−0.747366	−0.116719	−0.0583595	−	0.998296i	$-0.518587\pi$
$41$	−0.747366	−0.116719	−0.0583595	+	0.998296i	$0.518587\pi$
$42$	−0.820106	−0.126545
$43$	−8.78366	−1.33950	−0.669748	−	0.742588i	$-0.733598\pi$
$43$	−8.78366	−1.33950	−0.669748	+	0.742588i	$0.733598\pi$
$44$	1.23475	0.186146
$45$	−1.67012	−0.248967
$46$	−14.7511	−2.17493
$47$	−10.2885	−1.50073	−0.750366	−	0.661023i	$-0.770123\pi$
$47$	−10.2885	−1.50073	−0.750366	+	0.661023i	$0.770123\pi$
$48$	12.2400	1.76669
$49$	−6.93062	−0.990088
$50$	10.2786	1.45361
$51$	5.82371	0.815482
$52$	5.85715	0.812241
$53$	−1.54648	−0.212425	−0.106212	−	0.994343i	$-0.533872\pi$
$53$	−1.54648	−0.212425	−0.106212	+	0.994343i	$0.533872\pi$
$54$	14.3172	1.94833
$55$	0.262405	0.0353827
$56$	−2.02035	−0.269981
$57$	−1.18387	−0.156808
$58$	13.9445	1.83100
$59$	−11.8987	−1.54908	−0.774542	−	0.632523i	$-0.782019\pi$
$59$	−11.8987	−1.54908	−0.774542	+	0.632523i	$0.782019\pi$
$60$	6.08148	0.785116
$61$	−7.30658	−0.935512	−0.467756	−	0.883858i	$-0.654937\pi$
$61$	−7.30658	−0.935512	−0.467756	+	0.883858i	$0.654937\pi$
$62$	2.42633	0.308144
$63$	−0.421037	−0.0530457
$64$	10.4875	1.31094
$65$	1.24474	0.154391
$66$	−0.781935	−0.0962496
$67$	12.3676	1.51094	0.755472	−	0.655181i	$-0.227408\pi$
$67$	12.3676	1.51094	0.755472	+	0.655181i	$0.227408\pi$
$68$	24.1853	2.93289
$69$	6.64027	0.799395
$70$	−0.723793	−0.0865098
$71$	−4.68121	−0.555557	−0.277779	−	0.960645i	$-0.589598\pi$
$71$	−4.68121	−0.555557	−0.277779	+	0.960645i	$0.589598\pi$
$72$	12.2604	1.44490
$73$	−13.7773	−1.61251	−0.806254	−	0.591570i	$-0.798508\pi$
$73$	−13.7773	−1.61251	−0.806254	+	0.591570i	$0.798508\pi$
$74$	−9.27876	−1.07863
$75$	−4.62694	−0.534273
$76$	−4.91650	−0.563961
$77$	0.0661523	0.00753876
$78$	−3.70918	−0.419982
$79$	9.84399	1.10754	0.553768	−	0.832671i	$-0.313190\pi$
$79$	9.84399	1.10754	0.553768	+	0.832671i	$0.313190\pi$
$80$	10.8025	1.20776
$81$	−1.64962	−0.183291
$82$	1.96552	0.217055
$83$	−2.19820	−0.241284	−0.120642	−	0.992696i	$-0.538495\pi$
$83$	−2.19820	−0.241284	−0.120642	+	0.992696i	$0.538495\pi$
$84$	1.53314	0.167280
$85$	5.13977	0.557487
$86$	23.1004	2.49098
$87$	−6.27717	−0.672984
$88$	−1.92632	−0.205346
$89$	6.15320	0.652238	0.326119	−	0.945329i	$-0.394259\pi$
$89$	6.15320	0.652238	0.326119	+	0.945329i	$0.394259\pi$
$90$	4.39229	0.462988
$91$	0.313800	0.0328952
$92$	27.5764	2.87503
$93$	−1.09222	−0.113258
$94$	27.0580	2.79082
$95$	−1.04484	−0.107198
$96$	−14.0293	−1.43186
$97$	9.44861	0.959361	0.479680	−	0.877443i	$-0.340753\pi$
$97$	9.44861	0.959361	0.479680	+	0.877443i	$0.340753\pi$
$98$	18.2270	1.84120
$99$	−0.401441	−0.0403463
$100$	−19.2152	−1.92152
$101$	0.0480356	0.00477972	0.00238986	−	0.999997i	$-0.499239\pi$
$101$	0.0480356	0.00477972	0.00238986	+	0.999997i	$0.499239\pi$
$102$	−15.3159	−1.51650
$103$	−8.09539	−0.797663	−0.398831	−	0.917024i	$-0.630584\pi$
$103$	−8.09539	−0.797663	−0.398831	+	0.917024i	$0.630584\pi$
$104$	−9.13767	−0.896022
$105$	0.325819	0.0317966
$106$	4.06711	0.395033
$107$	4.80385	0.464406	0.232203	−	0.972667i	$-0.425407\pi$
$107$	4.80385	0.464406	0.232203	+	0.972667i	$0.425407\pi$
$108$	−26.7653	−2.57549
$109$	−1.08309	−0.103741	−0.0518704	−	0.998654i	$-0.516518\pi$
$109$	−1.08309	−0.103741	−0.0518704	+	0.998654i	$0.516518\pi$
$110$	−0.690105	−0.0657989
$111$	4.17687	0.396451
$112$	2.72332	0.257330
$113$	14.9802	1.40922	0.704611	−	0.709594i	$-0.251121\pi$
$113$	14.9802	1.40922	0.704611	+	0.709594i	$0.251121\pi$
$114$	3.11349	0.291605
$115$	5.86044	0.546489
$116$	−26.0685	−2.42040
$117$	−1.90427	−0.176050
$118$	31.2928	2.88073
$119$	1.29574	0.118780
$120$	−9.48764	−0.866100
$121$	−10.9369	−0.994266
$122$	19.2158	1.73971
$123$	−0.884786	−0.0797784
$124$	−4.53589	−0.407335
$125$	−9.30775	−0.832510
$126$	1.10730	0.0986458
$127$	1.58374	0.140534	0.0702671	−	0.997528i	$-0.477615\pi$
$127$	1.58374	0.140534	0.0702671	+	0.997528i	$0.477615\pi$
$128$	−3.88079	−0.343016
$129$	−10.3987	−0.915557
$130$	−3.27358	−0.287112
$131$	2.77274	0.242255	0.121128	−	0.992637i	$-0.461349\pi$
$131$	2.77274	0.242255	0.121128	+	0.992637i	$0.461349\pi$
$132$	1.46179	0.127232
$133$	−0.263404	−0.0228400
$134$	−32.5259	−2.80981
$135$	−5.68807	−0.489551
$136$	−37.7311	−3.23542
$137$	−8.24803	−0.704676	−0.352338	−	0.935873i	$-0.614613\pi$
$137$	−8.24803	−0.704676	−0.352338	+	0.935873i	$0.614613\pi$
$138$	−17.4634	−1.48658
$139$	1.23571	0.104812	0.0524059	−	0.998626i	$-0.483311\pi$
$139$	1.23571	0.104812	0.0524059	+	0.998626i	$0.483311\pi$
$140$	1.35309	0.114357
$141$	−12.1803	−1.02576
$142$	12.3112	1.03313
$143$	0.299195	0.0250199
$144$	−16.5263	−1.37719
$145$	−5.53999	−0.460071
$146$	36.2332	2.99868
$147$	−8.20496	−0.676734
$148$	17.3461	1.42584
$149$	9.80519	0.803272	0.401636	−	0.915799i	$-0.368442\pi$
$149$	9.80519	0.803272	0.401636	+	0.915799i	$0.368442\pi$
$150$	12.1685	0.993554
$151$	−13.7343	−1.11768	−0.558840	−	0.829275i	$-0.688754\pi$
$151$	−13.7343	−1.11768	−0.558840	+	0.829275i	$0.688754\pi$
$152$	7.67017	0.622133
$153$	−7.86309	−0.635693
$154$	−0.173976	−0.0140194
$155$	−0.963953	−0.0774265
$156$	6.93412	0.555174
$157$	−13.4602	−1.07424	−0.537118	−	0.843507i	$-0.680487\pi$
$157$	−13.4602	−1.07424	−0.537118	+	0.843507i	$0.680487\pi$
$158$	−25.8889	−2.05961
$159$	−1.83083	−0.145194
$160$	−12.3817	−0.978857
$161$	1.47742	0.116437
$162$	4.33838	0.340855
$163$	−16.0892	−1.26020	−0.630101	−	0.776513i	$-0.716986\pi$
$163$	−16.0892	−1.26020	−0.630101	+	0.776513i	$0.716986\pi$
$164$	−3.67442	−0.286924
$165$	0.310654	0.0241844
$166$	5.78110	0.448700
$167$	−1.97454	−0.152794	−0.0763972	−	0.997077i	$-0.524342\pi$
$167$	−1.97454	−0.152794	−0.0763972	+	0.997077i	$0.524342\pi$
$168$	−2.39184	−0.184534
$169$	−11.5807	−0.890826
$170$	−13.5172	−1.03672
$171$	1.59845	0.122236
$172$	−43.1849	−3.29281
$173$	−7.69374	−0.584944	−0.292472	−	0.956274i	$-0.594478\pi$
$173$	−7.69374	−0.584944	−0.292472	+	0.956274i	$0.594478\pi$
$174$	16.5085	1.25151
$175$	−1.02946	−0.0778202
$176$	2.59657	0.195724
$177$	−14.0866	−1.05881
$178$	−16.1824	−1.21293
$179$	−3.35718	−0.250927	−0.125464	−	0.992098i	$-0.540042\pi$
$179$	−3.35718	−0.250927	−0.125464	+	0.992098i	$0.540042\pi$
$180$	−8.21114	−0.612022
$181$	−4.91319	−0.365195	−0.182597	−	0.983188i	$-0.558450\pi$
$181$	−4.91319	−0.365195	−0.182597	+	0.983188i	$0.558450\pi$
$182$	−0.825270	−0.0611731
$183$	−8.65006	−0.639431
$184$	−43.0215	−3.17159
$185$	3.68634	0.271025
$186$	2.87246	0.210619
$187$	1.23543	0.0903436
$188$	−50.5834	−3.68917
$189$	−1.43396	−0.104305
$190$	2.74784	0.199350
$191$	19.1241	1.38377	0.691886	−	0.722007i	$-0.256780\pi$
$191$	19.1241	1.38377	0.691886	+	0.722007i	$0.256780\pi$
$192$	12.4159	0.896041
$193$	13.4331	0.966939	0.483469	−	0.875361i	$-0.339376\pi$
$193$	13.4331	0.966939	0.483469	+	0.875361i	$0.339376\pi$
$194$	−24.8491	−1.78406
$195$	1.47362	0.105528
$196$	−34.0744	−2.43388
$197$	14.0759	1.00287	0.501433	−	0.865196i	$-0.332806\pi$
$197$	14.0759	1.00287	0.501433	+	0.865196i	$0.332806\pi$
$198$	1.05576	0.0750295
$199$	−5.02687	−0.356345	−0.178173	−	0.983999i	$-0.557019\pi$
$199$	−5.02687	−0.356345	−0.178173	+	0.983999i	$0.557019\pi$
$200$	29.9774	2.11972
$201$	14.6417	1.03274
$202$	−0.126330	−0.00888854
$203$	−1.39663	−0.0980243
$204$	28.6322	2.00466
$205$	−0.780877	−0.0545388
$206$	21.2903	1.48336
$207$	−8.96560	−0.623153
$208$	12.3171	0.854035
$209$	−0.251144	−0.0173720
$210$	−0.856878	−0.0591302
$211$	−3.09624	−0.213154	−0.106577	−	0.994304i	$-0.533989\pi$
$211$	−3.09624	−0.213154	−0.106577	+	0.994304i	$0.533989\pi$
$212$	−7.60324	−0.522193
$213$	−5.54195	−0.379728
$214$	−12.6338	−0.863626
$215$	−9.17751	−0.625901
$216$	41.7562	2.84115
$217$	−0.243013	−0.0164968
$218$	2.84844	0.192920
$219$	−16.3105	−1.10216
$220$	1.29011	0.0869794
$221$	5.86038	0.394212
$222$	−10.9849	−0.737255
$223$	−18.1100	−1.21274	−0.606369	−	0.795184i	$-0.707374\pi$
$223$	−18.1100	−1.21274	−0.606369	+	0.795184i	$0.707374\pi$
$224$	−3.12142	−0.208559
$225$	6.24723	0.416482
$226$	−39.3969	−2.62064
$227$	10.5126	0.697745	0.348873	−	0.937170i	$-0.386565\pi$
$227$	10.5126	0.697745	0.348873	+	0.937170i	$0.386565\pi$
$228$	−5.82050	−0.385472
$229$	−19.4814	−1.28737	−0.643684	−	0.765291i	$-0.722595\pi$
$229$	−19.4814	−1.28737	−0.643684	+	0.765291i	$0.722595\pi$
$230$	−15.4125	−1.01627
$231$	0.0783159	0.00515281
$232$	40.6691	2.67006
$233$	−23.6833	−1.55154	−0.775772	−	0.631014i	$-0.782639\pi$
$233$	−23.6833	−1.55154	−0.775772	+	0.631014i	$0.782639\pi$
$234$	5.00809	0.327389
$235$	−10.7498	−0.701241
$236$	−58.5001	−3.80803
$237$	11.6540	0.757010
$238$	−3.40769	−0.220888
$239$	25.9761	1.68025	0.840127	−	0.542390i	$-0.182480\pi$
$239$	25.9761	1.68025	0.840127	+	0.542390i	$0.182480\pi$
$240$	12.7888	0.825514
$241$	24.9048	1.60426	0.802129	−	0.597150i	$-0.203700\pi$
$241$	24.9048	1.60426	0.802129	+	0.597150i	$0.203700\pi$
$242$	28.7633	1.84897
$243$	14.3790	0.922412
$244$	−35.9228	−2.29972
$245$	−7.24138	−0.462634
$246$	2.32692	0.148359
$247$	−1.19133	−0.0758023
$248$	7.07638	0.449351
$249$	−2.60239	−0.164919
$250$	24.4787	1.54817
$251$	19.1757	1.21036	0.605180	−	0.796089i	$-0.293101\pi$
$251$	19.1757	1.21036	0.605180	+	0.796089i	$0.293101\pi$
$252$	−2.07003	−0.130400
$253$	1.40865	0.0885613
$254$	−4.16512	−0.261343
$255$	6.08483	0.381047
$256$	−10.7689	−0.673057
$257$	13.9965	0.873081	0.436540	−	0.899685i	$-0.356204\pi$
$257$	13.9965	0.873081	0.436540	+	0.899685i	$0.356204\pi$
$258$	27.3479	1.70260
$259$	0.929327	0.0577456
$260$	6.11978	0.379532
$261$	8.47536	0.524612
$262$	−7.29209	−0.450507
$263$	10.6748	0.658238	0.329119	−	0.944288i	$-0.393248\pi$
$263$	10.6748	0.658238	0.329119	+	0.944288i	$0.393248\pi$
$264$	−2.28051	−0.140356
$265$	−1.61582	−0.0992588
$266$	0.692732	0.0424741
$267$	7.28460	0.445810
$268$	60.8053	3.71428
$269$	17.4146	1.06179	0.530894	−	0.847439i	$-0.321856\pi$
$269$	17.4146	1.06179	0.530894	+	0.847439i	$0.321856\pi$
$270$	14.9592	0.910387
$271$	11.1057	0.674621	0.337311	−	0.941393i	$-0.390483\pi$
$271$	11.1057	0.674621	0.337311	+	0.941393i	$0.390483\pi$
$272$	50.8594	3.08381
$273$	0.371499	0.0224841
$274$	21.6917	1.31044
$275$	−0.981550	−0.0591897
$276$	32.6469	1.96511
$277$	−24.2518	−1.45715	−0.728574	−	0.684968i	$-0.759816\pi$
$277$	−24.2518	−1.45715	−0.728574	+	0.684968i	$0.759816\pi$
$278$	−3.24983	−0.194912
$279$	1.47470	0.0882883
$280$	−2.11094	−0.126153
$281$	−10.7604	−0.641911	−0.320956	−	0.947094i	$-0.604004\pi$
$281$	−10.7604	−0.641911	−0.320956	+	0.947094i	$0.604004\pi$
$282$	32.0332	1.90755
$283$	−16.1672	−0.961039	−0.480519	−	0.876984i	$-0.659552\pi$
$283$	−16.1672	−0.961039	−0.480519	+	0.876984i	$0.659552\pi$
$284$	−23.0151	−1.36570
$285$	−1.23695	−0.0732709
$286$	−0.786859	−0.0465279
$287$	−0.196859	−0.0116202
$288$	18.9421	1.11618
$289$	7.19859	0.423446
$290$	14.5697	0.855565
$291$	11.1859	0.655731
$292$	−67.7359	−3.96394
$293$	−10.8454	−0.633598	−0.316799	−	0.948493i	$-0.602608\pi$
$293$	−10.8454	−0.633598	−0.316799	+	0.948493i	$0.602608\pi$
$294$	21.5784	1.25848
$295$	−12.4323	−0.723834
$296$	−27.0615	−1.57292
$297$	−1.36722	−0.0793343
$298$	−25.7869	−1.49380
$299$	6.68208	0.386435
$300$	−22.7483	−1.31338
$301$	−2.31365	−0.133357
$302$	36.1201	2.07848
$303$	0.0568680	0.00326698
$304$	−10.3390	−0.592980
$305$	−7.63420	−0.437133
$306$	20.6793	1.18216
$307$	−20.0165	−1.14240	−0.571202	−	0.820809i	$-0.693523\pi$
$307$	−20.0165	−1.14240	−0.571202	+	0.820809i	$0.693523\pi$
$308$	0.325238	0.0185321
$309$	−9.58391	−0.545209
$310$	2.53512	0.143985
$311$	−29.7462	−1.68675	−0.843377	−	0.537322i	$-0.819436\pi$
$311$	−29.7462	−1.68675	−0.843377	+	0.537322i	$0.819436\pi$
$312$	−10.8178	−0.612439
$313$	5.87567	0.332113	0.166056	−	0.986116i	$-0.446897\pi$
$313$	5.87567	0.332113	0.166056	+	0.986116i	$0.446897\pi$
$314$	35.3992	1.99769
$315$	−0.439916	−0.0247865
$316$	48.3979	2.72260
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	4.81494	0.270008
$319$	−1.33163	−0.0745568
$320$	10.9578	0.612559
$321$	5.68714	0.317425
$322$	−3.88549	−0.216530
$323$	−4.91921	−0.273712
$324$	−8.11036	−0.450575
$325$	−4.65607	−0.258273
$326$	42.3133	2.34352
$327$	−1.28224	−0.0709078
$328$	5.73242	0.316520
$329$	−2.71003	−0.149409
$330$	−0.816996	−0.0449741
$331$	−26.5504	−1.45934	−0.729670	−	0.683799i	$-0.760326\pi$
$331$	−26.5504	−1.45934	−0.729670	+	0.683799i	$0.760326\pi$
$332$	−10.8074	−0.593135
$333$	−5.63956	−0.309046
$334$	5.19289	0.284142
$335$	12.9221	0.706012
$336$	3.22406	0.175887
$337$	−27.6144	−1.50425	−0.752125	−	0.659021i	$-0.770971\pi$
$337$	−27.6144	−1.50425	−0.752125	+	0.659021i	$0.770971\pi$
$338$	30.4565	1.65661
$339$	17.7347	0.963215
$340$	25.2697	1.37044
$341$	−0.231702	−0.0125474
$342$	−4.20380	−0.227315
$343$	−3.66938	−0.198128
$344$	67.3721	3.63246
$345$	6.93801	0.373530
$346$	20.2339	1.08778
$347$	34.0857	1.82981	0.914907	−	0.403664i	$-0.132264\pi$
$347$	34.0857	1.82981	0.914907	+	0.403664i	$0.132264\pi$
$348$	−30.8617	−1.65436
$349$	23.5853	1.26249	0.631246	−	0.775583i	$-0.282544\pi$
$349$	23.5853	1.26249	0.631246	+	0.775583i	$0.282544\pi$
$350$	2.70741	0.144717
$351$	−6.48555	−0.346173
$352$	−2.97614	−0.158629
$353$	29.6211	1.57657	0.788285	−	0.615310i	$-0.210969\pi$
$353$	29.6211	1.57657	0.788285	+	0.615310i	$0.210969\pi$
$354$	37.0466	1.96901
$355$	−4.89110	−0.259593
$356$	30.2522	1.60336
$357$	1.53399	0.0811872
$358$	8.82913	0.466634
$359$	−20.0543	−1.05842	−0.529212	−	0.848490i	$-0.677512\pi$
$359$	−20.0543	−1.05842	−0.529212	+	0.848490i	$0.677512\pi$
$360$	12.8101	0.675151
$361$	1.00000	0.0526316
$362$	12.9213	0.679129
$363$	−12.9479	−0.679589
$364$	1.54280	0.0808645
$365$	−14.3950	−0.753470
$366$	22.7490	1.18911
$367$	−29.9243	−1.56204	−0.781019	−	0.624508i	$-0.785300\pi$
$367$	−29.9243	−1.56204	−0.781019	+	0.624508i	$0.785300\pi$
$368$	57.9906	3.02297
$369$	1.19463	0.0621897
$370$	−9.69480	−0.504009
$371$	−0.407347	−0.0211484
$372$	−5.36991	−0.278417
$373$	−5.42931	−0.281119	−0.140560	−	0.990072i	$-0.544890\pi$
$373$	−5.42931	−0.281119	−0.140560	+	0.990072i	$0.544890\pi$
$374$	−3.24909	−0.168006
$375$	−11.0192	−0.569028
$376$	78.9145	4.06971
$377$	−6.31670	−0.325327
$378$	3.77121	0.193970
$379$	21.7451	1.11697	0.558484	−	0.829515i	$-0.311383\pi$
$379$	21.7451	1.11697	0.558484	+	0.829515i	$0.311383\pi$
$380$	−5.13694	−0.263520
$381$	1.87495	0.0960564
$382$	−50.2949	−2.57331
$383$	10.9241	0.558194	0.279097	−	0.960263i	$-0.409965\pi$
$383$	10.9241	0.558194	0.279097	+	0.960263i	$0.409965\pi$
$384$	−4.59435	−0.234455
$385$	0.0691185	0.00352260
$386$	−35.3281	−1.79815
$387$	14.0402	0.713705
$388$	46.4540	2.35835
$389$	−27.8001	−1.40952	−0.704760	−	0.709446i	$-0.748945\pi$
$389$	−27.8001	−1.40952	−0.704760	+	0.709446i	$0.748945\pi$
$390$	−3.87550	−0.196243
$391$	27.5915	1.39536
$392$	53.1590	2.68493
$393$	3.28257	0.165584
$394$	−37.0186	−1.86497
$395$	10.2854	0.517513
$396$	−1.97368	−0.0991813
$397$	22.9605	1.15236	0.576178	−	0.817324i	$-0.304543\pi$
$397$	22.9605	1.15236	0.576178	+	0.817324i	$0.304543\pi$
$398$	13.2203	0.662673
$399$	−0.311836	−0.0156113
$400$	−40.4079	−2.02039
$401$	0.770767	0.0384902	0.0192451	−	0.999815i	$-0.493874\pi$
$401$	0.770767	0.0384902	0.0192451	+	0.999815i	$0.493874\pi$
$402$	−38.5064	−1.92053
$403$	−1.09910	−0.0547501
$404$	0.236167	0.0117497
$405$	−1.72359	−0.0856457
$406$	3.67303	0.182290
$407$	0.886073	0.0439210
$408$	−44.6688	−2.21144
$409$	−13.6104	−0.672992	−0.336496	−	0.941685i	$-0.609242\pi$
$409$	−13.6104	−0.672992	−0.336496	+	0.941685i	$0.609242\pi$
$410$	2.05365	0.101422
$411$	−9.76460	−0.481652
$412$	−39.8010	−1.96085
$413$	−3.13417	−0.154223
$414$	23.5789	1.15884
$415$	−2.29676	−0.112744
$416$	−14.1176	−0.692172
$417$	1.46293	0.0716398
$418$	0.660490	0.0323056
$419$	18.2406	0.891111	0.445556	−	0.895254i	$-0.353006\pi$
$419$	18.2406	0.891111	0.445556	+	0.895254i	$0.353006\pi$
$420$	1.60189	0.0781640
$421$	−1.05245	−0.0512932	−0.0256466	−	0.999671i	$-0.508164\pi$
$421$	−1.05245	−0.0512932	−0.0256466	+	0.999671i	$0.508164\pi$
$422$	8.14287	0.396389
$423$	16.4456	0.799614
$424$	11.8617	0.576056
$425$	−19.2258	−0.932588
$426$	14.5749	0.706156
$427$	−1.92458	−0.0931371
$428$	23.6181	1.14163
$429$	0.354208	0.0171013
$430$	24.1361	1.16395
$431$	−23.5803	−1.13582	−0.567911	−	0.823090i	$-0.692248\pi$
$431$	−23.5803	−1.13582	−0.567911	+	0.823090i	$0.692248\pi$
$432$	−56.2850	−2.70801
$433$	35.6289	1.71222	0.856108	−	0.516796i	$-0.172876\pi$
$433$	35.6289	1.71222	0.856108	+	0.516796i	$0.172876\pi$
$434$	0.639105	0.0306780
$435$	−6.55863	−0.314462
$436$	−5.32499	−0.255021
$437$	−5.60894	−0.268312
$438$	42.8954	2.04962
$439$	0.502882	0.0240012	0.0120006	−	0.999928i	$-0.496180\pi$
$439$	0.502882	0.0240012	0.0120006	+	0.999928i	$0.496180\pi$
$440$	−2.01269	−0.0959512
$441$	11.0782	0.527535
$442$	−15.4123	−0.733090
$443$	−39.7468	−1.88843	−0.944214	−	0.329332i	$-0.893177\pi$
$443$	−39.7468	−1.88843	−0.944214	+	0.329332i	$0.893177\pi$
$444$	20.5356	0.974576
$445$	6.42910	0.304769
$446$	47.6280	2.25525
$447$	11.6081	0.549044
$448$	2.76246	0.130514
$449$	−12.3946	−0.584939	−0.292469	−	0.956275i	$-0.594477\pi$
$449$	−12.3946	−0.584939	−0.292469	+	0.956275i	$0.594477\pi$
$450$	−16.4297	−0.774506
$451$	−0.187697	−0.00883829
$452$	73.6503	3.46422
$453$	−16.2596	−0.763944
$454$	−27.6473	−1.29755
$455$	0.327870	0.0153708
$456$	9.08049	0.425233
$457$	−5.43254	−0.254124	−0.127062	−	0.991895i	$-0.540555\pi$
$457$	−5.43254	−0.254124	−0.127062	+	0.991895i	$0.540555\pi$
$458$	51.2346	2.39404
$459$	−26.7800	−1.24998
$460$	28.8128	1.34341
$461$	18.9032	0.880410	0.440205	−	0.897897i	$-0.354906\pi$
$461$	18.9032	0.880410	0.440205	+	0.897897i	$0.354906\pi$
$462$	−0.205965	−0.00958235
$463$	−12.4173	−0.577080	−0.288540	−	0.957468i	$-0.593170\pi$
$463$	−12.4173	−0.577080	−0.288540	+	0.957468i	$0.593170\pi$
$464$	−54.8196	−2.54494
$465$	−1.14120	−0.0529217
$466$	62.2852	2.88531
$467$	0.632894	0.0292868	0.0146434	−	0.999893i	$-0.495339\pi$
$467$	0.632894	0.0292868	0.0146434	+	0.999893i	$0.495339\pi$
$468$	−9.36235	−0.432775
$469$	3.25768	0.150425
$470$	28.2712	1.30405
$471$	−15.9351	−0.734250
$472$	91.2653	4.20082
$473$	−2.20597	−0.101430
$474$	−30.6492	−1.40776
$475$	3.90831	0.179326
$476$	6.37049	0.291991
$477$	2.47196	0.113183
$478$	−68.3151	−3.12466
$479$	5.91138	0.270098	0.135049	−	0.990839i	$-0.456881\pi$
$479$	5.91138	0.270098	0.135049	+	0.990839i	$0.456881\pi$
$480$	−14.6583	−0.669057
$481$	4.20317	0.191648
$482$	−65.4977	−2.98334
$483$	1.74907	0.0795856
$484$	−53.7714	−2.44415
$485$	9.87226	0.448276
$486$	−37.8156	−1.71535
$487$	−28.6003	−1.29600	−0.648001	−	0.761640i	$-0.724395\pi$
$487$	−28.6003	−1.29600	−0.648001	+	0.761640i	$0.724395\pi$
$488$	56.0427	2.53693
$489$	−19.0475	−0.861358
$490$	19.0443	0.860332
$491$	−2.89299	−0.130559	−0.0652794	−	0.997867i	$-0.520794\pi$
$491$	−2.89299	−0.130559	−0.0652794	+	0.997867i	$0.520794\pi$
$492$	−4.35005	−0.196115
$493$	−26.0828	−1.17471
$494$	3.13310	0.140965
$495$	−0.419441	−0.0188525
$496$	−9.53857	−0.428294
$497$	−1.23305	−0.0553098
$498$	6.84408	0.306690
$499$	17.5882	0.787355	0.393677	−	0.919249i	$-0.371203\pi$
$499$	17.5882	0.787355	0.393677	+	0.919249i	$0.371203\pi$
$500$	−45.7615	−2.04652
$501$	−2.33760	−0.104436
$502$	−50.4306	−2.25083
$503$	−5.30064	−0.236344	−0.118172	−	0.992993i	$-0.537703\pi$
$503$	−5.30064	−0.236344	−0.118172	+	0.992993i	$0.537703\pi$
$504$	3.22943	0.143850
$505$	0.0501894	0.00223340
$506$	−3.70465	−0.164692
$507$	−13.7101	−0.608887
$508$	7.78646	0.345468
$509$	−29.0533	−1.28777	−0.643883	−	0.765124i	$-0.722678\pi$
$509$	−29.0533	−1.28777	−0.643883	+	0.765124i	$0.722678\pi$
$510$	−16.0026	−0.708609
$511$	−3.62899	−0.160537
$512$	36.0830	1.59466
$513$	5.44397	0.240357
$514$	−36.8098	−1.62361
$515$	−8.45838	−0.372721
$516$	−51.1253	−2.25067
$517$	−2.58390	−0.113640
$518$	−2.44406	−0.107386
$519$	−9.10840	−0.399814
$520$	−9.54738	−0.418680
$521$	−2.23914	−0.0980985	−0.0490493	−	0.998796i	$-0.515619\pi$
$521$	−2.23914	−0.0980985	−0.0490493	+	0.998796i	$0.515619\pi$
$522$	−22.2895	−0.975587
$523$	−1.56898	−0.0686066	−0.0343033	−	0.999411i	$-0.510921\pi$
$523$	−1.56898	−0.0686066	−0.0343033	+	0.999411i	$0.510921\pi$
$524$	13.6322	0.595524
$525$	−1.21875	−0.0531908
$526$	−28.0740	−1.22408
$527$	−4.53839	−0.197695
$528$	3.07400	0.133779
$529$	8.46025	0.367837
$530$	4.24947	0.184585
$531$	19.0195	0.825376
$532$	−1.29502	−0.0561464
$533$	−0.890357	−0.0385656
$534$	−19.1579	−0.829045
$535$	5.01925	0.217001
$536$	−94.8616	−4.09740
$537$	−3.97447	−0.171511
$538$	−45.7991	−1.97454
$539$	−1.74058	−0.0749723
$540$	−27.9654	−1.20344
$541$	20.2731	0.871610	0.435805	−	0.900041i	$-0.356464\pi$
$541$	20.2731	0.871610	0.435805	+	0.900041i	$0.356464\pi$
$542$	−29.2071	−1.25455
$543$	−5.81659	−0.249614
$544$	−58.2942	−2.49934
$545$	−1.13165	−0.0484746
$546$	−0.977013	−0.0418123
$547$	−21.4156	−0.915663	−0.457832	−	0.889039i	$-0.651374\pi$
$547$	−21.4156	−0.915663	−0.457832	+	0.889039i	$0.651374\pi$
$548$	−40.5514	−1.73227
$549$	11.6792	0.498456
$550$	2.58140	0.110071
$551$	5.30224	0.225883
$552$	−50.9320	−2.16781
$553$	2.59294	0.110263
$554$	63.7803	2.70976
$555$	4.36416	0.185248
$556$	6.07538	0.257654
$557$	16.5201	0.699978	0.349989	−	0.936754i	$-0.386185\pi$
$557$	16.5201	0.699978	0.349989	+	0.936754i	$0.386185\pi$
$558$	−3.87836	−0.164184
$559$	−10.4642	−0.442589
$560$	2.84543	0.120241
$561$	1.46259	0.0617506
$562$	28.2990	1.19372
$563$	37.2558	1.57015	0.785073	−	0.619403i	$-0.212625\pi$
$563$	37.2558	1.57015	0.785073	+	0.619403i	$0.212625\pi$
$564$	−59.8842	−2.52158
$565$	15.6519	0.658481
$566$	42.5184	1.78718
$567$	−0.434516	−0.0182480
$568$	35.9056	1.50657
$569$	22.8853	0.959402	0.479701	−	0.877432i	$-0.340745\pi$
$569$	22.8853	0.959402	0.479701	+	0.877432i	$0.340745\pi$
$570$	3.25310	0.136257
$571$	5.33216	0.223144	0.111572	−	0.993756i	$-0.464411\pi$
$571$	5.33216	0.223144	0.111572	+	0.993756i	$0.464411\pi$
$572$	1.47099	0.0615051
$573$	22.6405	0.945820
$574$	0.517725	0.0216094
$575$	−21.9215	−0.914190
$576$	−16.7638	−0.698491
$577$	−25.6445	−1.06759	−0.533797	−	0.845613i	$-0.679235\pi$
$577$	−25.6445	−1.06759	−0.533797	+	0.845613i	$0.679235\pi$
$578$	−18.9317	−0.787456
$579$	15.9031	0.660911
$580$	−27.2373	−1.13097
$581$	−0.579014	−0.0240216
$582$	−29.4182	−1.21942
$583$	−0.388388	−0.0160854
$584$	105.674	4.37282
$585$	−1.98966	−0.0822622
$586$	28.5227	1.17826
$587$	−1.87937	−0.0775699	−0.0387849	−	0.999248i	$-0.512349\pi$
$587$	−1.87937	−0.0775699	−0.0387849	+	0.999248i	$0.512349\pi$
$588$	−40.3397	−1.66358
$589$	0.922586	0.0380145
$590$	32.6959	1.34607
$591$	16.6641	0.685468
$592$	36.4773	1.49921
$593$	−40.3955	−1.65885	−0.829423	−	0.558621i	$-0.811331\pi$
$593$	−40.3955	−1.65885	−0.829423	+	0.558621i	$0.811331\pi$
$594$	3.59569	0.147533
$595$	1.35384	0.0555019
$596$	48.2072	1.97464
$597$	−5.95117	−0.243565
$598$	−17.5734	−0.718628
$599$	29.2214	1.19395	0.596977	−	0.802258i	$-0.296368\pi$
$599$	29.2214	1.19395	0.596977	+	0.802258i	$0.296368\pi$
$600$	35.4894	1.44885
$601$	−20.7180	−0.845104	−0.422552	−	0.906339i	$-0.638866\pi$
$601$	−20.7180	−0.845104	−0.422552	+	0.906339i	$0.638866\pi$
$602$	6.08472	0.247995
$603$	−19.7690	−0.805055
$604$	−67.5246	−2.74754
$605$	−11.4273	−0.464587
$606$	−0.149558	−0.00607539
$607$	−4.37730	−0.177669	−0.0888346	−	0.996046i	$-0.528314\pi$
$607$	−4.37730	−0.177669	−0.0888346	+	0.996046i	$0.528314\pi$
$608$	11.8503	0.480594
$609$	−1.65343	−0.0670004
$610$	20.0774	0.812909
$611$	−12.2570	−0.495863
$612$	−38.6589	−1.56269
$613$	−34.7607	−1.40397	−0.701985	−	0.712191i	$-0.747703\pi$
$613$	−34.7607	−1.40397	−0.701985	+	0.712191i	$0.747703\pi$
$614$	52.6420	2.12446
$615$	−0.924458	−0.0372777
$616$	−0.507399	−0.0204437
$617$	−44.1300	−1.77661	−0.888304	−	0.459255i	$-0.848116\pi$
$617$	−44.1300	−1.77661	−0.888304	+	0.459255i	$0.848116\pi$
$618$	25.2049	1.01389
$619$	−20.2820	−0.815203	−0.407602	−	0.913160i	$-0.633635\pi$
$619$	−20.2820	−0.815203	−0.407602	+	0.913160i	$0.633635\pi$
$620$	−4.73927	−0.190334
$621$	−30.5349	−1.22532
$622$	78.2303	3.13675
$623$	1.62078	0.0649351
$624$	14.5818	0.583740
$625$	9.81648	0.392659
$626$	−15.4526	−0.617609
$627$	−0.297322	−0.0118739
$628$	−66.1768	−2.64074
$629$	17.3557	0.692016
$630$	1.15695	0.0460938
$631$	22.0725	0.878692	0.439346	−	0.898318i	$-0.355210\pi$
$631$	22.0725	0.878692	0.439346	+	0.898318i	$0.355210\pi$
$632$	−75.5050	−3.00343
$633$	−3.66555	−0.145692
$634$	2.62992	0.104448
$635$	1.65475	0.0656669
$636$	−9.00126	−0.356923
$637$	−8.25663	−0.327139
$638$	3.50208	0.138649
$639$	7.48267	0.296010
$640$	−4.05479	−0.160280
$641$	−32.5323	−1.28495	−0.642473	−	0.766308i	$-0.722092\pi$
$641$	−32.5323	−1.28495	−0.642473	+	0.766308i	$0.722092\pi$
$642$	−14.9568	−0.590296
$643$	−4.51285	−0.177970	−0.0889848	−	0.996033i	$-0.528362\pi$
$643$	−4.51285	−0.177970	−0.0889848	+	0.996033i	$0.528362\pi$
$644$	7.26372	0.286231
$645$	−10.8650	−0.427809
$646$	12.9371	0.509005
$647$	−3.53958	−0.139155	−0.0695776	−	0.997577i	$-0.522165\pi$
$647$	−3.53958	−0.139155	−0.0695776	+	0.997577i	$0.522165\pi$
$648$	12.6529	0.497051
$649$	−2.98830	−0.117301
$650$	12.2451	0.480293
$651$	−0.287696	−0.0112757
$652$	−79.1024	−3.09789
$653$	−43.2427	−1.69222	−0.846110	−	0.533009i	$-0.821061\pi$
$653$	−43.2427	−1.69222	−0.846110	+	0.533009i	$0.821061\pi$
$654$	3.37218	0.131863
$655$	2.89706	0.113198
$656$	−7.72699	−0.301688
$657$	22.0222	0.859170
$658$	7.12717	0.277846
$659$	18.9540	0.738344	0.369172	−	0.929361i	$-0.379641\pi$
$659$	18.9540	0.738344	0.369172	+	0.929361i	$0.379641\pi$
$660$	1.52733	0.0594512
$661$	25.2018	0.980235	0.490117	−	0.871657i	$-0.336954\pi$
$661$	25.2018	0.980235	0.490117	+	0.871657i	$0.336954\pi$
$662$	69.8255	2.71384
$663$	6.93793	0.269447
$664$	16.8606	0.654316
$665$	−0.275214	−0.0106724
$666$	14.8316	0.574713
$667$	−29.7400	−1.15154
$668$	−9.70782	−0.375607
$669$	−21.4399	−0.828916
$670$	−33.9843	−1.31293
$671$	−1.83501	−0.0708396
$672$	−3.69536	−0.142552
$673$	−0.0694157	−0.00267578	−0.00133789	−	0.999999i	$-0.500426\pi$
$673$	−0.0694157	−0.00267578	−0.00133789	+	0.999999i	$0.500426\pi$
$674$	72.6236	2.79736
$675$	21.2767	0.818942
$676$	−56.9367	−2.18987
$677$	3.90032	0.149901	0.0749507	−	0.997187i	$-0.476120\pi$
$677$	3.90032	0.149901	0.0749507	+	0.997187i	$0.476120\pi$
$678$	−46.6408	−1.79123
$679$	2.48880	0.0955113
$680$	−39.4229	−1.51180
$681$	12.4456	0.476915
$682$	0.609358	0.0233335
$683$	−16.6897	−0.638614	−0.319307	−	0.947651i	$-0.603450\pi$
$683$	−16.6897	−0.638614	−0.319307	+	0.947651i	$0.603450\pi$
$684$	7.85877	0.300487
$685$	−8.61785	−0.329271
$686$	9.65019	0.368446
$687$	−23.0635	−0.879927
$688$	−90.8139	−3.46225
$689$	−1.84236	−0.0701882
$690$	−18.2464	−0.694630
$691$	21.7352	0.826847	0.413424	−	0.910539i	$-0.364333\pi$
$691$	21.7352	0.826847	0.413424	+	0.910539i	$0.364333\pi$
$692$	−37.8262	−1.43794
$693$	−0.105741	−0.00401677
$694$	−89.6427	−3.40279
$695$	1.29112	0.0489750
$696$	48.1470	1.82501
$697$	−3.67645	−0.139255
$698$	−62.0275	−2.34778
$699$	−28.0380	−1.06049
$700$	−5.06136	−0.191301
$701$	−42.8313	−1.61771	−0.808857	−	0.588005i	$-0.799914\pi$
$701$	−42.8313	−1.61771	−0.808857	+	0.588005i	$0.799914\pi$
$702$	17.0565	0.643756
$703$	−3.52815	−0.133067
$704$	2.63389	0.0992683
$705$	−12.7264	−0.479304
$706$	−77.9012	−2.93185
$707$	0.0126528	0.000475856 0
$708$	−69.2566	−2.60282
$709$	−19.0320	−0.714762	−0.357381	−	0.933959i	$-0.616330\pi$
$709$	−19.0320	−0.714762	−0.357381	+	0.933959i	$0.616330\pi$
$710$	12.8632	0.482748
$711$	−15.7351	−0.590112
$712$	−47.1961	−1.76875
$713$	−5.17473	−0.193795
$714$	−4.03427	−0.150979
$715$	0.312610	0.0116909
$716$	−16.5056	−0.616842
$717$	30.7524	1.14847
$718$	52.7412	1.96828
$719$	18.2726	0.681452	0.340726	−	0.940163i	$-0.389327\pi$
$719$	18.2726	0.681452	0.340726	+	0.940163i	$0.389327\pi$
$720$	−17.2673	−0.643514
$721$	−2.13236	−0.0794132
$722$	−2.62992	−0.0978756
$723$	29.4841	1.09652
$724$	−24.1557	−0.897739
$725$	20.7228	0.769626
$726$	34.0520	1.26379
$727$	−10.7757	−0.399649	−0.199824	−	0.979832i	$-0.564037\pi$
$727$	−10.7757	−0.399649	−0.199824	+	0.979832i	$0.564037\pi$
$728$	−2.40690	−0.0892055
$729$	21.9717	0.813768
$730$	37.8578	1.40118
$731$	−43.2086	−1.59813
$732$	−42.5280	−1.57188
$733$	46.7699	1.72748	0.863742	−	0.503934i	$-0.168115\pi$
$733$	46.7699	1.72748	0.863742	+	0.503934i	$0.168115\pi$
$734$	78.6987	2.90482
$735$	−8.57286	−0.316215
$736$	−66.4678	−2.45004
$737$	3.10605	0.114413
$738$	−3.14178	−0.115650
$739$	1.15395	0.0424489	0.0212245	−	0.999775i	$-0.493244\pi$
$739$	1.15395	0.0424489	0.0212245	+	0.999775i	$0.493244\pi$
$740$	18.1239	0.666248
$741$	−1.41038	−0.0518115
$742$	1.07129	0.0393284
$743$	28.7073	1.05317	0.526585	−	0.850123i	$-0.323472\pi$
$743$	28.7073	1.05317	0.526585	+	0.850123i	$0.323472\pi$
$744$	8.37753	0.307135
$745$	10.2448	0.375342
$746$	14.2787	0.522779
$747$	3.51371	0.128560
$748$	6.07399	0.222087
$749$	1.26535	0.0462350
$750$	28.9796	1.05819
$751$	−40.0982	−1.46321	−0.731603	−	0.681731i	$-0.761227\pi$
$751$	−40.0982	−1.46321	−0.731603	+	0.681731i	$0.761227\pi$
$752$	−106.372	−3.87900
$753$	22.7016	0.827291
$754$	16.6124	0.604989
$755$	−14.3501	−0.522254
$756$	−7.05008	−0.256409
$757$	21.7046	0.788866	0.394433	−	0.918925i	$-0.370941\pi$
$757$	21.7046	0.788866	0.394433	+	0.918925i	$0.370941\pi$
$758$	−57.1878	−2.07716
$759$	1.66766	0.0605324
$760$	8.01408	0.290701
$761$	−7.97656	−0.289150	−0.144575	−	0.989494i	$-0.546181\pi$
$761$	−7.97656	−0.289150	−0.144575	+	0.989494i	$0.546181\pi$
$762$	−4.93096	−0.178630
$763$	−0.285289	−0.0103282
$764$	94.0236	3.40165
$765$	−8.21566	−0.297038
$766$	−28.7295	−1.03804
$767$	−14.1753	−0.511839
$768$	−12.7490	−0.460041
$769$	29.3837	1.05960	0.529802	−	0.848121i	$-0.322266\pi$
$769$	29.3837	1.05960	0.529802	+	0.848121i	$0.322266\pi$
$770$	−0.181776	−0.00655076
$771$	16.5701	0.596758
$772$	66.0440	2.37698
$773$	−24.3509	−0.875841	−0.437920	−	0.899014i	$-0.644285\pi$
$773$	−24.3509	−0.875841	−0.437920	+	0.899014i	$0.644285\pi$
$774$	−36.9247	−1.32723
$775$	3.60575	0.129522
$776$	−72.4724	−2.60161
$777$	1.10020	0.0394696
$778$	73.1121	2.62120
$779$	0.747366	0.0267772
$780$	7.24503	0.259414
$781$	−1.17566	−0.0420683
$782$	−72.5637	−2.59487
$783$	28.8653	1.03156
$784$	−71.6553	−2.55912
$785$	−14.0637	−0.501954
$786$	−8.63290	−0.307925
$787$	40.7835	1.45377	0.726887	−	0.686758i	$-0.240967\pi$
$787$	40.7835	1.45377	0.726887	+	0.686758i	$0.240967\pi$
$788$	69.2042	2.46530
$789$	12.6376	0.449911
$790$	−27.0497	−0.962387
$791$	3.94585	0.140298
$792$	3.07912	0.109412
$793$	−8.70452	−0.309107
$794$	−60.3845	−2.14296
$795$	−1.91292	−0.0678442
$796$	−24.7146	−0.875985
$797$	−2.21305	−0.0783903	−0.0391952	−	0.999232i	$-0.512479\pi$
$797$	−2.21305	−0.0783903	−0.0391952	+	0.999232i	$0.512479\pi$
$798$	0.820106	0.0290314
$799$	−50.6113	−1.79050
$800$	46.3148	1.63747
$801$	−9.83557	−0.347523
$802$	−2.02706	−0.0715779
$803$	−3.46008	−0.122104
$804$	71.9857	2.53874
$805$	1.54366	0.0544069
$806$	2.89055	0.101815
$807$	20.6167	0.725741
$808$	−0.368441	−0.0129617
$809$	22.3825	0.786927	0.393463	−	0.919340i	$-0.371277\pi$
$809$	22.3825	0.786927	0.393463	+	0.919340i	$0.371277\pi$
$810$	4.53290	0.159270
$811$	15.9590	0.560395	0.280198	−	0.959942i	$-0.409600\pi$
$811$	15.9590	0.560395	0.280198	+	0.959942i	$0.409600\pi$
$812$	−6.86653	−0.240968
$813$	13.1477	0.461110
$814$	−2.33031	−0.0816772
$815$	−16.8106	−0.588849
$816$	60.2111	2.10781
$817$	8.78366	0.307301
$818$	35.7943	1.25152
$819$	−0.501593	−0.0175271
$820$	−3.83918	−0.134070
$821$	27.4173	0.956871	0.478435	−	0.878123i	$-0.341204\pi$
$821$	27.4173	0.956871	0.478435	+	0.878123i	$0.341204\pi$
$822$	25.6802	0.895698
$823$	−13.0830	−0.456045	−0.228022	−	0.973656i	$-0.573226\pi$
$823$	−13.0830	−0.456045	−0.228022	+	0.973656i	$0.573226\pi$
$824$	62.0930	2.16311
$825$	−1.16203	−0.0404567
$826$	8.24263	0.286798
$827$	23.9751	0.833696	0.416848	−	0.908976i	$-0.363135\pi$
$827$	23.9751	0.833696	0.416848	+	0.908976i	$0.363135\pi$
$828$	−44.0794	−1.53186
$829$	0.260194	0.00903692	0.00451846	−	0.999990i	$-0.498562\pi$
$829$	0.260194	0.00903692	0.00451846	+	0.999990i	$0.498562\pi$
$830$	6.04031	0.209662
$831$	−28.7110	−0.995973
$832$	12.4941	0.433154
$833$	−34.0931	−1.18126
$834$	−3.84738	−0.133224
$835$	−2.06307	−0.0713956
$836$	−1.23475	−0.0427047
$837$	5.02253	0.173604
$838$	−47.9714	−1.65714
$839$	−16.6983	−0.576489	−0.288245	−	0.957557i	$-0.593072\pi$
$839$	−16.6983	−0.576489	−0.288245	+	0.957557i	$0.593072\pi$
$840$	−2.49908	−0.0862265
$841$	−0.886223	−0.0305594
$842$	2.76786	0.0953868
$843$	−12.7389	−0.438752
$844$	−15.2226	−0.523985
$845$	−12.1000	−0.416253
$846$	−43.2508	−1.48699
$847$	−2.88083	−0.0989864
$848$	−15.9889	−0.549062
$849$	−19.1399	−0.656878
$850$	50.5624	1.73428
$851$	19.7892	0.678364
$852$	−27.2470	−0.933466
$853$	−27.5458	−0.943149	−0.471575	−	0.881826i	$-0.656314\pi$
$853$	−27.5458	−0.943149	−0.471575	+	0.881826i	$0.656314\pi$
$854$	5.06151	0.173201
$855$	1.67012	0.0571169
$856$	−36.8463	−1.25938
$857$	−25.1205	−0.858099	−0.429050	−	0.903281i	$-0.641151\pi$
$857$	−25.1205	−0.858099	−0.429050	+	0.903281i	$0.641151\pi$
$858$	−0.931540	−0.0318022
$859$	14.6868	0.501106	0.250553	−	0.968103i	$-0.419388\pi$
$859$	14.6868	0.501106	0.250553	+	0.968103i	$0.419388\pi$
$860$	−45.1212	−1.53862
$861$	−0.233056	−0.00794253
$862$	62.0144	2.11222
$863$	−43.8691	−1.49332	−0.746661	−	0.665205i	$-0.768344\pi$
$863$	−43.8691	−1.49332	−0.746661	+	0.665205i	$0.768344\pi$
$864$	64.5128	2.19477
$865$	−8.03871	−0.273324
$866$	−93.7013	−3.18410
$867$	8.52220	0.289429
$868$	−1.19477	−0.0405532
$869$	2.47226	0.0838657
$870$	17.2487	0.584786
$871$	14.7339	0.499238
$872$	8.30745	0.281326
$873$	−15.1031	−0.511163
$874$	14.7511	0.498963
$875$	−2.45170	−0.0828825
$876$	−80.1906	−2.70939
$877$	13.0008	0.439005	0.219503	−	0.975612i	$-0.429557\pi$
$877$	13.0008	0.439005	0.219503	+	0.975612i	$0.429557\pi$
$878$	−1.32254	−0.0446336
$879$	−12.8396	−0.433069
$880$	2.71299	0.0914550
$881$	−39.8300	−1.34191	−0.670954	−	0.741499i	$-0.734115\pi$
$881$	−39.8300	−1.34191	−0.670954	+	0.741499i	$0.734115\pi$
$882$	−29.1349	−0.981023
$883$	2.66769	0.0897750	0.0448875	−	0.998992i	$-0.485707\pi$
$883$	2.66769	0.0897750	0.0448875	+	0.998992i	$0.485707\pi$
$884$	28.8125	0.969070
$885$	−14.7182	−0.494747
$886$	104.531	3.51179
$887$	−25.6166	−0.860123	−0.430061	−	0.902800i	$-0.641508\pi$
$887$	−25.6166	−0.860123	−0.430061	+	0.902800i	$0.641508\pi$
$888$	−32.0373	−1.07510
$889$	0.417163	0.0139912
$890$	−16.9080	−0.566759
$891$	−0.414293	−0.0138793
$892$	−89.0379	−2.98121
$893$	10.2885	0.344292
$894$	−30.5284	−1.02102
$895$	−3.50771	−0.117250
$896$	−1.02221	−0.0341498
$897$	7.91073	0.264131
$898$	32.5969	1.08777
$899$	4.89177	0.163150
$900$	30.7145	1.02382
$901$	−7.60743	−0.253440
$902$	0.493628	0.0164360
$903$	−2.73907	−0.0911504
$904$	−114.901	−3.82155
$905$	−5.13349	−0.170643
$906$	42.7616	1.42066
$907$	−8.73472	−0.290032	−0.145016	−	0.989429i	$-0.546323\pi$
$907$	−8.73472	−0.290032	−0.145016	+	0.989429i	$0.546323\pi$
$908$	51.6851	1.71523
$909$	−0.0767824	−0.00254671
$910$	−0.862273	−0.0285841
$911$	42.1382	1.39610	0.698051	−	0.716048i	$-0.254051\pi$
$911$	42.1382	1.39610	0.698051	+	0.716048i	$0.254051\pi$
$912$	−12.2400	−0.405307
$913$	−0.552065	−0.0182707
$914$	14.2872	0.472577
$915$	−9.03791	−0.298784
$916$	−95.7803	−3.16467
$917$	0.730350	0.0241183
$918$	70.4294	2.32452
$919$	20.0060	0.659936	0.329968	−	0.943992i	$-0.392962\pi$
$919$	20.0060	0.659936	0.329968	+	0.943992i	$0.392962\pi$
$920$	−44.9505	−1.48198
$921$	−23.6970	−0.780843
$922$	−49.7140	−1.63724
$923$	−5.57684	−0.183564
$924$	0.385040	0.0126669
$925$	−13.7891	−0.453383
$926$	32.6565	1.07316
$927$	12.9401	0.425007
$928$	62.8333	2.06260
$929$	41.5578	1.36347	0.681733	−	0.731601i	$-0.261227\pi$
$929$	41.5578	1.36347	0.681733	+	0.731601i	$0.261227\pi$
$930$	3.00126	0.0984152
$931$	6.93062	0.227142
$932$	−116.439	−3.81408
$933$	−35.2157	−1.15291
$934$	−1.66446	−0.0544629
$935$	1.29082	0.0422145
$936$	14.6061	0.477415
$937$	−17.5115	−0.572075	−0.286038	−	0.958218i	$-0.592338\pi$
$937$	−17.5115	−0.572075	−0.286038	+	0.958218i	$0.592338\pi$
$938$	−8.56744	−0.279737
$939$	6.95604	0.227002
$940$	−52.8515	−1.72382
$941$	−53.3300	−1.73851	−0.869254	−	0.494365i	$-0.835401\pi$
$941$	−53.3300	−1.73851	−0.869254	+	0.494365i	$0.835401\pi$
$942$	41.9081	1.36544
$943$	−4.19194	−0.136508
$944$	−123.020	−4.00397
$945$	−1.49826	−0.0487384
$946$	5.80152	0.188624
$947$	−19.6566	−0.638755	−0.319377	−	0.947628i	$-0.603474\pi$
$947$	−19.6566	−0.638755	−0.319377	+	0.947628i	$0.603474\pi$
$948$	57.2970	1.86092
$949$	−16.4132	−0.532796
$950$	−10.2786	−0.333481
$951$	−1.18387	−0.0383897
$952$	−9.93852	−0.322109
$953$	−9.14726	−0.296309	−0.148154	−	0.988964i	$-0.547333\pi$
$953$	−9.14726	−0.296309	−0.148154	+	0.988964i	$0.547333\pi$
$954$	−6.50106	−0.210480
$955$	19.9816	0.646589
$956$	127.711	4.13048
$957$	−1.57648	−0.0509602
$958$	−15.5465	−0.502284
$959$	−2.17256	−0.0701557
$960$	12.9726	0.418689
$961$	−30.1488	−0.972543
$962$	−11.0540	−0.356396
$963$	−7.67871	−0.247443
$964$	122.444	3.94367
$965$	14.0355	0.451817
$966$	−4.59993	−0.148000
$967$	−5.89343	−0.189520	−0.0947599	−	0.995500i	$-0.530208\pi$
$967$	−5.89343	−0.189520	−0.0947599	+	0.995500i	$0.530208\pi$
$968$	83.8880	2.69626
$969$	−5.82371	−0.187084
$970$	−25.9633	−0.833631
$971$	−30.5805	−0.981376	−0.490688	−	0.871335i	$-0.663255\pi$
$971$	−30.5805	−0.981376	−0.490688	+	0.871335i	$0.663255\pi$
$972$	70.6942	2.26752
$973$	0.325492	0.0104348
$974$	75.2165	2.41009
$975$	−5.51219	−0.176532
$976$	−75.5424	−2.41805
$977$	40.5759	1.29814	0.649069	−	0.760729i	$-0.275159\pi$
$977$	40.5759	1.29814	0.649069	+	0.760729i	$0.275159\pi$
$978$	50.0935	1.60181
$979$	1.54534	0.0493893
$980$	−35.6022	−1.13727
$981$	1.73126	0.0552748
$982$	7.60834	0.242792
$983$	−41.5123	−1.32404	−0.662018	−	0.749488i	$-0.730300\pi$
$983$	−41.5123	−1.32404	−0.662018	+	0.749488i	$0.730300\pi$
$984$	6.78645	0.216344
$985$	14.7070	0.468605
$986$	68.5958	2.18454
$987$	−3.20833	−0.102122
$988$	−5.85715	−0.186341
$989$	−49.2671	−1.56660
$990$	1.10310	0.0350587
$991$	−50.9193	−1.61750	−0.808752	−	0.588150i	$-0.799856\pi$
$991$	−50.9193	−1.61750	−0.808752	+	0.588150i	$0.799856\pi$
$992$	10.9329	0.347121
$993$	−31.4322	−0.997472
$994$	3.24282	0.102856
$995$	−5.25226	−0.166508
$996$	−12.7946	−0.405413
$997$	26.1999	0.829760	0.414880	−	0.909876i	$-0.363824\pi$
$997$	26.1999	0.829760	0.414880	+	0.909876i	$0.363824\pi$
$998$	−46.2555	−1.46419
$999$	−19.2071	−0.607687

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.b.1.4	✓	99

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.b.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.62992 q^{2} +1.18387 q^{3} +4.91650 q^{4} +1.04484 q^{5} -3.11349 q^{6} +0.263404 q^{7} -7.67017 q^{8} -1.59845 q^{9} +O(q^{10})\)	\(q-2.62992 q^{2} +1.18387 q^{3} +4.91650 q^{4} +1.04484 q^{5} -3.11349 q^{6} +0.263404 q^{7} -7.67017 q^{8} -1.59845 q^{9} -2.74784 q^{10} +0.251144 q^{11} +5.82050 q^{12} +1.19133 q^{13} -0.692732 q^{14} +1.23695 q^{15} +10.3390 q^{16} +4.91921 q^{17} +4.20380 q^{18} -1.00000 q^{19} +5.13694 q^{20} +0.311836 q^{21} -0.660490 q^{22} +5.60894 q^{23} -9.08049 q^{24} -3.90831 q^{25} -3.13310 q^{26} -5.44397 q^{27} +1.29502 q^{28} -5.30224 q^{29} -3.25310 q^{30} -0.922586 q^{31} -11.8503 q^{32} +0.297322 q^{33} -12.9371 q^{34} +0.275214 q^{35} -7.85877 q^{36} +3.52815 q^{37} +2.62992 q^{38} +1.41038 q^{39} -8.01408 q^{40} -0.747366 q^{41} -0.820106 q^{42} -8.78366 q^{43} +1.23475 q^{44} -1.67012 q^{45} -14.7511 q^{46} -10.2885 q^{47} +12.2400 q^{48} -6.93062 q^{49} +10.2786 q^{50} +5.82371 q^{51} +5.85715 q^{52} -1.54648 q^{53} +14.3172 q^{54} +0.262405 q^{55} -2.02035 q^{56} -1.18387 q^{57} +13.9445 q^{58} -11.8987 q^{59} +6.08148 q^{60} -7.30658 q^{61} +2.42633 q^{62} -0.421037 q^{63} +10.4875 q^{64} +1.24474 q^{65} -0.781935 q^{66} +12.3676 q^{67} +24.1853 q^{68} +6.64027 q^{69} -0.723793 q^{70} -4.68121 q^{71} +12.2604 q^{72} -13.7773 q^{73} -9.27876 q^{74} -4.62694 q^{75} -4.91650 q^{76} +0.0661523 q^{77} -3.70918 q^{78} +9.84399 q^{79} +10.8025 q^{80} -1.64962 q^{81} +1.96552 q^{82} -2.19820 q^{83} +1.53314 q^{84} +5.13977 q^{85} +23.1004 q^{86} -6.27717 q^{87} -1.92632 q^{88} +6.15320 q^{89} +4.39229 q^{90} +0.313800 q^{91} +27.5764 q^{92} -1.09222 q^{93} +27.0580 q^{94} -1.04484 q^{95} -14.0293 q^{96} +9.44861 q^{97} +18.2270 q^{98} -0.401441 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 99 q - 4 q^{2} - 3 q^{3} + 80 q^{4} - 15 q^{5} - 12 q^{6} - 19 q^{7} - 12 q^{8} + 58 q^{9}+O(q^{10}) \) 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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