LMFDB - Embedded newform 6023.2.a.c.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:	$0$
Dimension:	$138$
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)

$f(q)$	$=$	$q-2.68395 q^{2} +2.15160 q^{3} +5.20359 q^{4} +1.49960 q^{5} -5.77479 q^{6} +0.747166 q^{7} -8.59827 q^{8} +1.62938 q^{9} +O(q^{10})$	\(q-2.68395 q^{2} +2.15160 q^{3} +5.20359 q^{4} +1.49960 q^{5} -5.77479 q^{6} +0.747166 q^{7} -8.59827 q^{8} +1.62938 q^{9} -4.02486 q^{10} +4.67187 q^{11} +11.1960 q^{12} +4.40163 q^{13} -2.00536 q^{14} +3.22655 q^{15} +12.6701 q^{16} +3.48718 q^{17} -4.37318 q^{18} +1.00000 q^{19} +7.80333 q^{20} +1.60760 q^{21} -12.5391 q^{22} -7.69346 q^{23} -18.5000 q^{24} -2.75118 q^{25} -11.8138 q^{26} -2.94902 q^{27} +3.88794 q^{28} -0.827078 q^{29} -8.65990 q^{30} +7.84439 q^{31} -16.8095 q^{32} +10.0520 q^{33} -9.35941 q^{34} +1.12045 q^{35} +8.47864 q^{36} +1.31278 q^{37} -2.68395 q^{38} +9.47055 q^{39} -12.8940 q^{40} -0.990002 q^{41} -4.31473 q^{42} +3.59148 q^{43} +24.3105 q^{44} +2.44343 q^{45} +20.6489 q^{46} -5.78585 q^{47} +27.2611 q^{48} -6.44174 q^{49} +7.38404 q^{50} +7.50301 q^{51} +22.9043 q^{52} +6.65505 q^{53} +7.91502 q^{54} +7.00595 q^{55} -6.42434 q^{56} +2.15160 q^{57} +2.21984 q^{58} +0.835218 q^{59} +16.7896 q^{60} +7.27081 q^{61} -21.0539 q^{62} +1.21742 q^{63} +19.7756 q^{64} +6.60071 q^{65} -26.9790 q^{66} +8.09758 q^{67} +18.1458 q^{68} -16.5533 q^{69} -3.00724 q^{70} +8.08664 q^{71} -14.0099 q^{72} +14.6739 q^{73} -3.52343 q^{74} -5.91945 q^{75} +5.20359 q^{76} +3.49066 q^{77} -25.4185 q^{78} -11.0487 q^{79} +19.0002 q^{80} -11.2333 q^{81} +2.65712 q^{82} -2.97874 q^{83} +8.36530 q^{84} +5.22939 q^{85} -9.63935 q^{86} -1.77954 q^{87} -40.1700 q^{88} -0.300689 q^{89} -6.55805 q^{90} +3.28875 q^{91} -40.0336 q^{92} +16.8780 q^{93} +15.5289 q^{94} +1.49960 q^{95} -36.1673 q^{96} +0.248079 q^{97} +17.2893 q^{98} +7.61226 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) $ 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.68395	−1.89784	−0.948920	−	0.315518i	$-0.897822\pi$
$2$	−2.68395	−1.89784	−0.948920	+	0.315518i	$0.897822\pi$
$3$	2.15160	1.24223	0.621113	−	0.783721i	$-0.286681\pi$
$3$	2.15160	1.24223	0.621113	+	0.783721i	$0.286681\pi$
$4$	5.20359	2.60179
$5$	1.49960	0.670644	0.335322	−	0.942104i	$-0.391155\pi$
$5$	1.49960	0.670644	0.335322	+	0.942104i	$0.391155\pi$
$6$	−5.77479	−2.35755
$7$	0.747166	0.282402	0.141201	−	0.989981i	$-0.454904\pi$
$7$	0.747166	0.282402	0.141201	+	0.989981i	$0.454904\pi$
$8$	−8.59827	−3.03995
$9$	1.62938	0.543128
$10$	−4.02486	−1.27277
$11$	4.67187	1.40862	0.704310	−	0.709892i	$-0.251256\pi$
$11$	4.67187	1.40862	0.704310	+	0.709892i	$0.251256\pi$
$12$	11.1960	3.23202
$13$	4.40163	1.22079	0.610396	−	0.792096i	$-0.291010\pi$
$13$	4.40163	1.22079	0.610396	+	0.792096i	$0.291010\pi$
$14$	−2.00536	−0.535954
$15$	3.22655	0.833092
$16$	12.6701	3.16754
$17$	3.48718	0.845764	0.422882	−	0.906185i	$-0.361018\pi$
$17$	3.48718	0.845764	0.422882	+	0.906185i	$0.361018\pi$
$18$	−4.37318	−1.03077
$19$	1.00000	0.229416
$19$	1.00000	0.229416
$20$	7.80333	1.74488
$21$	1.60760	0.350808
$22$	−12.5391	−2.67334
$23$	−7.69346	−1.60420	−0.802099	−	0.597192i	$-0.796283\pi$
$23$	−7.69346	−1.60420	−0.802099	+	0.597192i	$0.796283\pi$
$24$	−18.5000	−3.77630
$25$	−2.75118	−0.550237
$26$	−11.8138	−2.31687
$27$	−2.94902	−0.567539
$28$	3.88794	0.734753
$29$	−0.827078	−0.153584	−0.0767922	−	0.997047i	$-0.524468\pi$
$29$	−0.827078	−0.153584	−0.0767922	+	0.997047i	$0.524468\pi$
$30$	−8.65990	−1.58107
$31$	7.84439	1.40889	0.704447	−	0.709757i	$-0.251195\pi$
$31$	7.84439	1.40889	0.704447	+	0.709757i	$0.251195\pi$
$32$	−16.8095	−2.97153
$33$	10.0520	1.74983
$34$	−9.35941	−1.60512
$35$	1.12045	0.189391
$36$	8.47864	1.41311
$37$	1.31278	0.215819	0.107910	−	0.994161i	$-0.465584\pi$
$37$	1.31278	0.215819	0.107910	+	0.994161i	$0.465584\pi$
$38$	−2.68395	−0.435394
$39$	9.47055	1.51650
$40$	−12.8940	−2.03872
$41$	−0.990002	−0.154612	−0.0773062	−	0.997007i	$-0.524632\pi$
$41$	−0.990002	−0.154612	−0.0773062	+	0.997007i	$0.524632\pi$
$42$	−4.31473	−0.665777
$43$	3.59148	0.547696	0.273848	−	0.961773i	$-0.411704\pi$
$43$	3.59148	0.547696	0.273848	+	0.961773i	$0.411704\pi$
$44$	24.3105	3.66494
$45$	2.44343	0.364245
$46$	20.6489	3.04451
$47$	−5.78585	−0.843953	−0.421976	−	0.906607i	$-0.638663\pi$
$47$	−5.78585	−0.843953	−0.421976	+	0.906607i	$0.638663\pi$
$48$	27.2611	3.93480
$49$	−6.44174	−0.920249
$50$	7.38404	1.04426
$51$	7.50301	1.05063
$52$	22.9043	3.17625
$53$	6.65505	0.914141	0.457070	−	0.889430i	$-0.348899\pi$
$53$	6.65505	0.914141	0.457070	+	0.889430i	$0.348899\pi$
$54$	7.91502	1.07710
$55$	7.00595	0.944683
$56$	−6.42434	−0.858488
$57$	2.15160	0.284986
$58$	2.21984	0.291479
$59$	0.835218	0.108736	0.0543680	−	0.998521i	$-0.482686\pi$
$59$	0.835218	0.108736	0.0543680	+	0.998521i	$0.482686\pi$
$60$	16.7896	2.16753
$61$	7.27081	0.930932	0.465466	−	0.885066i	$-0.345887\pi$
$61$	7.27081	0.930932	0.465466	+	0.885066i	$0.345887\pi$
$62$	−21.0539	−2.67385
$63$	1.21742	0.153381
$64$	19.7756	2.47195
$65$	6.60071	0.818717
$66$	−26.9790	−3.32089
$67$	8.09758	0.989277	0.494638	−	0.869099i	$-0.335301\pi$
$67$	8.09758	0.989277	0.494638	+	0.869099i	$0.335301\pi$
$68$	18.1458	2.20050
$69$	−16.5533	−1.99278
$70$	−3.00724	−0.359434
$71$	8.08664	0.959708	0.479854	−	0.877348i	$-0.340690\pi$
$71$	8.08664	0.959708	0.479854	+	0.877348i	$0.340690\pi$
$72$	−14.0099	−1.65108
$73$	14.6739	1.71745	0.858724	−	0.512438i	$-0.171257\pi$
$73$	14.6739	1.71745	0.858724	+	0.512438i	$0.171257\pi$
$74$	−3.52343	−0.409591
$75$	−5.91945	−0.683519
$76$	5.20359	0.596892
$77$	3.49066	0.397798
$78$	−25.4185	−2.87808
$79$	−11.0487	−1.24307	−0.621537	−	0.783385i	$-0.713491\pi$
$79$	−11.0487	−1.24307	−0.621537	+	0.783385i	$0.713491\pi$
$80$	19.0002	2.12429
$81$	−11.2333	−1.24814
$82$	2.65712	0.293429
$83$	−2.97874	−0.326959	−0.163480	−	0.986547i	$-0.552272\pi$
$83$	−2.97874	−0.326959	−0.163480	+	0.986547i	$0.552272\pi$
$84$	8.36530	0.912729
$85$	5.22939	0.567207
$86$	−9.63935	−1.03944
$87$	−1.77954	−0.190787
$88$	−40.1700	−4.28213
$89$	−0.300689	−0.0318729	−0.0159365	−	0.999873i	$-0.505073\pi$
$89$	−0.300689	−0.0318729	−0.0159365	+	0.999873i	$0.505073\pi$
$90$	−6.55805	−0.691279
$91$	3.28875	0.344755
$92$	−40.0336	−4.17379
$93$	16.8780	1.75017
$94$	15.5289	1.60169
$95$	1.49960	0.153856
$96$	−36.1673	−3.69131
$97$	0.248079	0.0251886	0.0125943	−	0.999921i	$-0.495991\pi$
$97$	0.248079	0.0251886	0.0125943	+	0.999921i	$0.495991\pi$
$98$	17.2893	1.74648
$99$	7.61226	0.765061
$100$	−14.3160	−1.43160
$101$	1.50834	0.150085	0.0750425	−	0.997180i	$-0.476091\pi$
$101$	1.50834	0.150085	0.0750425	+	0.997180i	$0.476091\pi$
$102$	−20.1377	−1.99393
$103$	−1.99993	−0.197059	−0.0985293	−	0.995134i	$-0.531414\pi$
$103$	−1.99993	−0.197059	−0.0985293	+	0.995134i	$0.531414\pi$
$104$	−37.8464	−3.71114
$105$	2.41077	0.235267
$106$	−17.8618	−1.73489
$107$	3.43218	0.331801	0.165901	−	0.986142i	$-0.446947\pi$
$107$	3.43218	0.331801	0.165901	+	0.986142i	$0.446947\pi$
$108$	−15.3455	−1.47662
$109$	−14.6531	−1.40351	−0.701754	−	0.712419i	$-0.747599\pi$
$109$	−14.6531	−1.40351	−0.701754	+	0.712419i	$0.747599\pi$
$110$	−18.8036	−1.79286
$111$	2.82457	0.268097
$112$	9.46670	0.894520
$113$	16.8885	1.58873	0.794366	−	0.607439i	$-0.207803\pi$
$113$	16.8885	1.58873	0.794366	+	0.607439i	$0.207803\pi$
$114$	−5.77479	−0.540858
$115$	−11.5372	−1.07584
$116$	−4.30377	−0.399595
$117$	7.17194	0.663046
$118$	−2.24168	−0.206364
$119$	2.60550	0.238846
$120$	−27.7427	−2.53255
$121$	10.8263	0.984212
$122$	−19.5145	−1.76676
$123$	−2.13009	−0.192064
$124$	40.8189	3.66565
$125$	−11.6237	−1.03966
$126$	−3.26749	−0.291092
$127$	5.45672	0.484206	0.242103	−	0.970251i	$-0.422163\pi$
$127$	5.45672	0.484206	0.242103	+	0.970251i	$0.422163\pi$
$128$	−19.4576	−1.71983
$129$	7.72743	0.680362
$130$	−17.7160	−1.55379
$131$	−15.6746	−1.36949	−0.684747	−	0.728781i	$-0.740087\pi$
$131$	−15.6746	−1.36949	−0.684747	+	0.728781i	$0.740087\pi$
$132$	52.3064	4.55269
$133$	0.747166	0.0647875
$134$	−21.7335	−1.87749
$135$	−4.42236	−0.380616
$136$	−29.9837	−2.57108
$137$	18.9351	1.61773	0.808867	−	0.587992i	$-0.200081\pi$
$137$	18.9351	1.61773	0.808867	+	0.587992i	$0.200081\pi$
$138$	44.4281	3.78197
$139$	4.37177	0.370809	0.185405	−	0.982662i	$-0.440640\pi$
$139$	4.37177	0.370809	0.185405	+	0.982662i	$0.440640\pi$
$140$	5.83038	0.492757
$141$	−12.4488	−1.04838
$142$	−21.7041	−1.82137
$143$	20.5638	1.71963
$144$	20.6445	1.72038
$145$	−1.24029	−0.103000
$146$	−39.3840	−3.25944
$147$	−13.8601	−1.14316
$148$	6.83116	0.561518
$149$	−9.54636	−0.782068	−0.391034	−	0.920376i	$-0.627883\pi$
$149$	−9.54636	−0.782068	−0.391034	+	0.920376i	$0.627883\pi$
$150$	15.8875	1.29721
$151$	3.68233	0.299664	0.149832	−	0.988711i	$-0.452127\pi$
$151$	3.68233	0.299664	0.149832	+	0.988711i	$0.452127\pi$
$152$	−8.59827	−0.697412
$153$	5.68195	0.459358
$154$	−9.36876	−0.754956
$155$	11.7635	0.944865
$156$	49.2808	3.94562
$157$	3.24042	0.258614	0.129307	−	0.991605i	$-0.458725\pi$
$157$	3.24042	0.258614	0.129307	+	0.991605i	$0.458725\pi$
$158$	29.6541	2.35915
$159$	14.3190	1.13557
$160$	−25.2076	−1.99284
$161$	−5.74829	−0.453029
$162$	30.1495	2.36877
$163$	13.0371	1.02114	0.510572	−	0.859835i	$-0.329434\pi$
$163$	13.0371	1.02114	0.510572	+	0.859835i	$0.329434\pi$
$164$	−5.15156	−0.402270
$165$	15.0740	1.17351
$166$	7.99479	0.620516
$167$	10.0846	0.780373	0.390187	−	0.920736i	$-0.372410\pi$
$167$	10.0846	0.780373	0.390187	+	0.920736i	$0.372410\pi$
$168$	−13.8226	−1.06644
$169$	6.37435	0.490334
$170$	−14.0354	−1.07647
$171$	1.62938	0.124602
$172$	18.6886	1.42499
$173$	−23.4426	−1.78231	−0.891156	−	0.453698i	$-0.850105\pi$
$173$	−23.4426	−1.78231	−0.891156	+	0.453698i	$0.850105\pi$
$174$	4.77620	0.362083
$175$	−2.05559	−0.155388
$176$	59.1932	4.46186
$177$	1.79705	0.135075
$178$	0.807034	0.0604897
$179$	−10.3432	−0.773085	−0.386542	−	0.922272i	$-0.626331\pi$
$179$	−10.3432	−0.773085	−0.386542	+	0.922272i	$0.626331\pi$
$180$	12.7146	0.947691
$181$	14.6894	1.09186	0.545928	−	0.837832i	$-0.316177\pi$
$181$	14.6894	1.09186	0.545928	+	0.837832i	$0.316177\pi$
$182$	−8.82684	−0.654289
$183$	15.6439	1.15643
$184$	66.1504	4.87667
$185$	1.96865	0.144738
$186$	−45.2997	−3.32153
$187$	16.2916	1.19136
$188$	−30.1072	−2.19579
$189$	−2.20341	−0.160274
$190$	−4.02486	−0.291994
$191$	17.3874	1.25811	0.629054	−	0.777362i	$-0.283442\pi$
$191$	17.3874	1.25811	0.629054	+	0.777362i	$0.283442\pi$
$192$	42.5491	3.07072
$193$	18.1257	1.30472	0.652358	−	0.757911i	$-0.273780\pi$
$193$	18.1257	1.30472	0.652358	+	0.757911i	$0.273780\pi$
$194$	−0.665833	−0.0478040
$195$	14.2021	1.01703
$196$	−33.5202	−2.39430
$197$	−22.7667	−1.62206	−0.811030	−	0.585005i	$-0.801093\pi$
$197$	−22.7667	−1.62206	−0.811030	+	0.585005i	$0.801093\pi$
$198$	−20.4309	−1.45196
$199$	−3.16647	−0.224465	−0.112233	−	0.993682i	$-0.535800\pi$
$199$	−3.16647	−0.224465	−0.112233	+	0.993682i	$0.535800\pi$
$200$	23.6554	1.67269
$201$	17.4228	1.22891
$202$	−4.04830	−0.284837
$203$	−0.617965	−0.0433726
$204$	39.0426	2.73353
$205$	−1.48461	−0.103690
$206$	5.36770	0.373985
$207$	−12.5356	−0.871284
$208$	55.7693	3.86690
$209$	4.67187	0.323160
$210$	−6.47039	−0.446499
$211$	−15.3594	−1.05739	−0.528694	−	0.848813i	$-0.677318\pi$
$211$	−15.3594	−1.05739	−0.528694	+	0.848813i	$0.677318\pi$
$212$	34.6301	2.37841
$213$	17.3992	1.19217
$214$	−9.21180	−0.629706
$215$	5.38580	0.367309
$216$	25.3565	1.72529
$217$	5.86106	0.397875
$218$	39.3281	2.66363
$219$	31.5723	2.13346
$220$	36.4561	2.45787
$221$	15.3493	1.03250
$222$	−7.58102	−0.508804
$223$	16.4144	1.09919	0.549596	−	0.835431i	$-0.314782\pi$
$223$	16.4144	1.09919	0.549596	+	0.835431i	$0.314782\pi$
$224$	−12.5595	−0.839166
$225$	−4.48273	−0.298849
$226$	−45.3278	−3.01516
$227$	−16.9697	−1.12632	−0.563160	−	0.826348i	$-0.690415\pi$
$227$	−16.9697	−1.12632	−0.563160	+	0.826348i	$0.690415\pi$
$228$	11.1960	0.741476
$229$	6.74801	0.445921	0.222961	−	0.974827i	$-0.428428\pi$
$229$	6.74801	0.445921	0.222961	+	0.974827i	$0.428428\pi$
$230$	30.9651	2.04178
$231$	7.51051	0.494155
$232$	7.11143	0.466889
$233$	−0.106749	−0.00699333	−0.00349667	−	0.999994i	$-0.501113\pi$
$233$	−0.106749	−0.00699333	−0.00349667	+	0.999994i	$0.501113\pi$
$234$	−19.2491	−1.25836
$235$	−8.67649	−0.565992
$236$	4.34613	0.282909
$237$	−23.7723	−1.54418
$238$	−6.99303	−0.453291
$239$	−15.2188	−0.984425	−0.492212	−	0.870475i	$-0.663812\pi$
$239$	−15.2188	−0.984425	−0.492212	+	0.870475i	$0.663812\pi$
$240$	40.8809	2.63885
$241$	−8.88454	−0.572304	−0.286152	−	0.958184i	$-0.592376\pi$
$241$	−8.88454	−0.572304	−0.286152	+	0.958184i	$0.592376\pi$
$242$	−29.0573	−1.86788
$243$	−15.3224	−0.982934
$244$	37.8343	2.42209
$245$	−9.66007	−0.617159
$246$	5.71705	0.364506
$247$	4.40163	0.280069
$248$	−67.4481	−4.28296
$249$	−6.40906	−0.406157
$250$	31.1975	1.97310
$251$	−10.5725	−0.667328	−0.333664	−	0.942692i	$-0.608285\pi$
$251$	−10.5725	−0.667328	−0.333664	+	0.942692i	$0.608285\pi$
$252$	6.33495	0.399064
$253$	−35.9428	−2.25971
$254$	−14.6456	−0.918944
$255$	11.2515	0.704599
$256$	12.6722	0.792010
$257$	−3.68774	−0.230035	−0.115018	−	0.993363i	$-0.536692\pi$
$257$	−3.68774	−0.230035	−0.115018	+	0.993363i	$0.536692\pi$
$258$	−20.7400	−1.29122
$259$	0.980864	0.0609479
$260$	34.3474	2.13013
$261$	−1.34763	−0.0834160
$262$	42.0698	2.59908
$263$	−9.77748	−0.602905	−0.301453	−	0.953481i	$-0.597472\pi$
$263$	−9.77748	−0.602905	−0.301453	+	0.953481i	$0.597472\pi$
$264$	−86.4297	−5.31938
$265$	9.97994	0.613063
$266$	−2.00536	−0.122956
$267$	−0.646962	−0.0395934
$268$	42.1365	2.57389
$269$	15.9962	0.975307	0.487653	−	0.873037i	$-0.337853\pi$
$269$	15.9962	0.975307	0.487653	+	0.873037i	$0.337853\pi$
$270$	11.8694	0.722349
$271$	−25.9121	−1.57405	−0.787023	−	0.616923i	$-0.788379\pi$
$271$	−25.9121	−1.57405	−0.787023	+	0.616923i	$0.788379\pi$
$272$	44.1830	2.67899
$273$	7.07607	0.428263
$274$	−50.8208	−3.07020
$275$	−12.8532	−0.775075
$276$	−86.1363	−5.18479
$277$	30.9334	1.85861	0.929304	−	0.369315i	$-0.120408\pi$
$277$	30.9334	1.85861	0.929304	+	0.369315i	$0.120408\pi$
$278$	−11.7336	−0.703736
$279$	12.7815	0.765209
$280$	−9.63397	−0.575740
$281$	3.70932	0.221279	0.110640	−	0.993861i	$-0.464710\pi$
$281$	3.70932	0.221279	0.110640	+	0.993861i	$0.464710\pi$
$282$	33.4120	1.98966
$283$	−26.9869	−1.60421	−0.802103	−	0.597186i	$-0.796286\pi$
$283$	−26.9869	−1.60421	−0.802103	+	0.597186i	$0.796286\pi$
$284$	42.0795	2.49696
$285$	3.22655	0.191124
$286$	−55.1923	−3.26359
$287$	−0.739696	−0.0436629
$288$	−27.3891	−1.61392
$289$	−4.83960	−0.284683
$290$	3.32888	0.195478
$291$	0.533768	0.0312900
$292$	76.3569	4.46845
$293$	−3.66584	−0.214161	−0.107080	−	0.994250i	$-0.534150\pi$
$293$	−3.66584	−0.214161	−0.107080	+	0.994250i	$0.534150\pi$
$294$	37.1997	2.16953
$295$	1.25250	0.0729232
$296$	−11.2876	−0.656080
$297$	−13.7774	−0.799447
$298$	25.6219	1.48424
$299$	−33.8638	−1.95839
$300$	−30.8024	−1.77838
$301$	2.68343	0.154671
$302$	−9.88320	−0.568714
$303$	3.24533	0.186440
$304$	12.6701	0.726683
$305$	10.9033	0.624324
$306$	−15.2501	−0.871788
$307$	12.5076	0.713845	0.356923	−	0.934134i	$-0.383826\pi$
$307$	12.5076	0.713845	0.356923	+	0.934134i	$0.383826\pi$
$308$	18.1640	1.03499
$309$	−4.30304	−0.244791
$310$	−31.5726	−1.79320
$311$	22.9520	1.30149	0.650743	−	0.759298i	$-0.274458\pi$
$311$	22.9520	1.30149	0.650743	+	0.759298i	$0.274458\pi$
$312$	−81.4303	−4.61008
$313$	−23.6288	−1.33558	−0.667788	−	0.744351i	$-0.732759\pi$
$313$	−23.6288	−1.33558	−0.667788	+	0.744351i	$0.732759\pi$
$314$	−8.69713	−0.490807
$315$	1.82565	0.102864
$316$	−57.4928	−3.23422
$317$	−1.00000	−0.0561656
$317$	−1.00000	−0.0561656
$318$	−38.4315	−2.15513
$319$	−3.86400	−0.216342
$320$	29.6555	1.65779
$321$	7.38468	0.412173
$322$	15.4281	0.859776
$323$	3.48718	0.194032
$324$	−58.4532	−3.24740
$325$	−12.1097	−0.671725
$326$	−34.9909	−1.93797
$327$	−31.5275	−1.74348
$328$	8.51231	0.470013
$329$	−4.32299	−0.238334
$330$	−40.4579	−2.22713
$331$	31.9784	1.75769	0.878847	−	0.477104i	$-0.158313\pi$
$331$	31.9784	1.75769	0.878847	+	0.477104i	$0.158313\pi$
$332$	−15.5001	−0.850680
$333$	2.13902	0.117218
$334$	−27.0667	−1.48102
$335$	12.1432	0.663452
$336$	20.3686	1.11120
$337$	−15.7233	−0.856504	−0.428252	−	0.903659i	$-0.640870\pi$
$337$	−15.7233	−0.856504	−0.428252	+	0.903659i	$0.640870\pi$
$338$	−17.1084	−0.930576
$339$	36.3372	1.97357
$340$	27.2116	1.47575
$341$	36.6479	1.98460
$342$	−4.37318	−0.236475
$343$	−10.0432	−0.542283
$344$	−30.8805	−1.66497
$345$	−24.8233	−1.33644
$346$	62.9189	3.38254
$347$	13.2263	0.710027	0.355014	−	0.934861i	$-0.384476\pi$
$347$	13.2263	0.710027	0.355014	+	0.934861i	$0.384476\pi$
$348$	−9.25999	−0.496388
$349$	−3.94748	−0.211304	−0.105652	−	0.994403i	$-0.533693\pi$
$349$	−3.94748	−0.211304	−0.105652	+	0.994403i	$0.533693\pi$
$350$	5.51711	0.294902
$351$	−12.9805	−0.692847
$352$	−78.5317	−4.18576
$353$	−18.8925	−1.00555	−0.502774	−	0.864418i	$-0.667687\pi$
$353$	−18.8925	−1.00555	−0.502774	+	0.864418i	$0.667687\pi$
$354$	−4.82320	−0.256350
$355$	12.1268	0.643622
$356$	−1.56466	−0.0829268
$357$	5.60599	0.296701
$358$	27.7605	1.46719
$359$	−23.8006	−1.25615	−0.628073	−	0.778155i	$-0.716156\pi$
$359$	−23.8006	−1.25615	−0.628073	+	0.778155i	$0.716156\pi$
$360$	−21.0093	−1.10729
$361$	1.00000	0.0526316
$362$	−39.4256	−2.07217
$363$	23.2939	1.22261
$364$	17.1133	0.896980
$365$	22.0050	1.15180
$366$	−41.9874	−2.19472
$367$	8.91774	0.465502	0.232751	−	0.972536i	$-0.425227\pi$
$367$	8.91774	0.465502	0.232751	+	0.972536i	$0.425227\pi$
$368$	−97.4772	−5.08135
$369$	−1.61309	−0.0839743
$370$	−5.28376	−0.274689
$371$	4.97243	0.258156
$372$	87.8260	4.55357
$373$	25.1384	1.30162	0.650808	−	0.759242i	$-0.274430\pi$
$373$	25.1384	1.30162	0.650808	+	0.759242i	$0.274430\pi$
$374$	−43.7259	−2.26101
$375$	−25.0096	−1.29149
$376$	49.7483	2.56557
$377$	−3.64049	−0.187495
$378$	5.91384	0.304175
$379$	4.62128	0.237379	0.118690	−	0.992931i	$-0.462131\pi$
$379$	4.62128	0.237379	0.118690	+	0.992931i	$0.462131\pi$
$380$	7.80333	0.400302
$381$	11.7407	0.601493
$382$	−46.6669	−2.38769
$383$	−2.20748	−0.112797	−0.0563986	−	0.998408i	$-0.517962\pi$
$383$	−2.20748	−0.112797	−0.0563986	+	0.998408i	$0.517962\pi$
$384$	−41.8650	−2.13642
$385$	5.23461	0.266781
$386$	−48.6484	−2.47614
$387$	5.85190	0.297469
$388$	1.29090	0.0655357
$389$	−1.02795	−0.0521191	−0.0260595	−	0.999660i	$-0.508296\pi$
$389$	−1.02795	−0.0521191	−0.0260595	+	0.999660i	$0.508296\pi$
$390$	−38.1177	−1.93016
$391$	−26.8284	−1.35677
$392$	55.3878	2.79751
$393$	−33.7254	−1.70122
$394$	61.1047	3.07841
$395$	−16.5687	−0.833660
$396$	39.6111	1.99053
$397$	8.19106	0.411098	0.205549	−	0.978647i	$-0.434102\pi$
$397$	8.19106	0.411098	0.205549	+	0.978647i	$0.434102\pi$
$398$	8.49866	0.425999
$399$	1.60760	0.0804808
$400$	−34.8579	−1.74290
$401$	−13.4960	−0.673958	−0.336979	−	0.941512i	$-0.609405\pi$
$401$	−13.4960	−0.673958	−0.336979	+	0.941512i	$0.609405\pi$
$402$	−46.7618	−2.33227
$403$	34.5281	1.71997
$404$	7.84875	0.390490
$405$	−16.8455	−0.837057
$406$	1.65859	0.0823142
$407$	6.13312	0.304008
$408$	−64.5129	−3.19386
$409$	29.5526	1.46128	0.730641	−	0.682762i	$-0.239221\pi$
$409$	29.5526	1.46128	0.730641	+	0.682762i	$0.239221\pi$
$410$	3.98463	0.196787
$411$	40.7407	2.00959
$412$	−10.4068	−0.512706
$413$	0.624046	0.0307073
$414$	33.6449	1.65356
$415$	−4.46693	−0.219273
$416$	−73.9892	−3.62762
$417$	9.40631	0.460629
$418$	−12.5391	−0.613305
$419$	5.17330	0.252732	0.126366	−	0.991984i	$-0.459669\pi$
$419$	5.17330	0.252732	0.126366	+	0.991984i	$0.459669\pi$
$420$	12.5446	0.612116
$421$	−22.9320	−1.11764	−0.558819	−	0.829290i	$-0.688745\pi$
$421$	−22.9320	−1.11764	−0.558819	+	0.829290i	$0.688745\pi$
$422$	41.2240	2.00675
$423$	−9.42736	−0.458374
$424$	−57.2219	−2.77894
$425$	−9.59387	−0.465371
$426$	−46.6986	−2.26256
$427$	5.43251	0.262897
$428$	17.8596	0.863279
$429$	44.2451	2.13618
$430$	−14.4552	−0.697093
$431$	2.74817	0.132375	0.0661874	−	0.997807i	$-0.478916\pi$
$431$	2.74817	0.132375	0.0661874	+	0.997807i	$0.478916\pi$
$432$	−37.3645	−1.79770
$433$	28.2353	1.35690	0.678450	−	0.734647i	$-0.262652\pi$
$433$	28.2353	1.35690	0.678450	+	0.734647i	$0.262652\pi$
$434$	−15.7308	−0.755102
$435$	−2.66861	−0.127950
$436$	−76.2484	−3.65164
$437$	−7.69346	−0.368028
$438$	−84.7386	−4.04897
$439$	−8.57678	−0.409348	−0.204674	−	0.978830i	$-0.565613\pi$
$439$	−8.57678	−0.409348	−0.204674	+	0.978830i	$0.565613\pi$
$440$	−60.2391	−2.87178
$441$	−10.4961	−0.499813
$442$	−41.1966	−1.95952
$443$	−4.81647	−0.228837	−0.114419	−	0.993433i	$-0.536501\pi$
$443$	−4.81647	−0.228837	−0.114419	+	0.993433i	$0.536501\pi$
$444$	14.6979	0.697532
$445$	−0.450914	−0.0213754
$446$	−44.0555	−2.08609
$447$	−20.5399	−0.971506
$448$	14.7756	0.698083
$449$	−0.477699	−0.0225440	−0.0112720	−	0.999936i	$-0.503588\pi$
$449$	−0.477699	−0.0225440	−0.0112720	+	0.999936i	$0.503588\pi$
$450$	12.0314	0.567167
$451$	−4.62516	−0.217790
$452$	87.8806	4.13355
$453$	7.92291	0.372251
$454$	45.5459	2.13758
$455$	4.93183	0.231208
$456$	−18.5000	−0.866343
$457$	−33.5312	−1.56852	−0.784262	−	0.620429i	$-0.786958\pi$
$457$	−33.5312	−1.56852	−0.784262	+	0.620429i	$0.786958\pi$
$458$	−18.1113	−0.846287
$459$	−10.2837	−0.480004
$460$	−60.0346	−2.79913
$461$	10.0870	0.469799	0.234900	−	0.972020i	$-0.424524\pi$
$461$	10.0870	0.469799	0.234900	+	0.972020i	$0.424524\pi$
$462$	−20.1578	−0.937827
$463$	−36.0794	−1.67675	−0.838377	−	0.545091i	$-0.816495\pi$
$463$	−36.0794	−1.67675	−0.838377	+	0.545091i	$0.816495\pi$
$464$	−10.4792	−0.486484
$465$	25.3103	1.17374
$466$	0.286508	0.0132722
$467$	−22.0667	−1.02113	−0.510563	−	0.859841i	$-0.670563\pi$
$467$	−22.0667	−1.02113	−0.510563	+	0.859841i	$0.670563\pi$
$468$	37.3198	1.72511
$469$	6.05024	0.279374
$470$	23.2873	1.07416
$471$	6.97209	0.321257
$472$	−7.18142	−0.330552
$473$	16.7789	0.771495
$474$	63.8038	2.93060
$475$	−2.75118	−0.126233
$476$	13.5579	0.621428
$477$	10.8436	0.496495
$478$	40.8466	1.86828
$479$	−18.2996	−0.836131	−0.418065	−	0.908417i	$-0.637292\pi$
$479$	−18.2996	−0.836131	−0.418065	+	0.908417i	$0.637292\pi$
$480$	−54.2367	−2.47555
$481$	5.77836	0.263471
$482$	23.8457	1.08614
$483$	−12.3680	−0.562765
$484$	56.3358	2.56072
$485$	0.372021	0.0168926
$486$	41.1246	1.86545
$487$	28.3379	1.28411	0.642057	−	0.766657i	$-0.278081\pi$
$487$	28.3379	1.28411	0.642057	+	0.766657i	$0.278081\pi$
$488$	−62.5164	−2.82998
$489$	28.0506	1.26849
$490$	25.9271	1.17127
$491$	−14.9389	−0.674182	−0.337091	−	0.941472i	$-0.609443\pi$
$491$	−14.9389	−0.674182	−0.337091	+	0.941472i	$0.609443\pi$
$492$	−11.0841	−0.499710
$493$	−2.88417	−0.129896
$494$	−11.8138	−0.531526
$495$	11.4154	0.513083
$496$	99.3895	4.46272
$497$	6.04207	0.271024
$498$	17.2016	0.770821
$499$	7.56564	0.338685	0.169342	−	0.985557i	$-0.445836\pi$
$499$	7.56564	0.338685	0.169342	+	0.985557i	$0.445836\pi$
$500$	−60.4850	−2.70497
$501$	21.6981	0.969401
$502$	28.3759	1.26648
$503$	−30.2374	−1.34822	−0.674109	−	0.738632i	$-0.735472\pi$
$503$	−30.2374	−1.34822	−0.674109	+	0.738632i	$0.735472\pi$
$504$	−10.4677	−0.466269
$505$	2.26191	0.100654
$506$	96.4687	4.28856
$507$	13.7150	0.609107
$508$	28.3945	1.25980
$509$	−29.7613	−1.31914	−0.659572	−	0.751641i	$-0.729263\pi$
$509$	−29.7613	−1.31914	−0.659572	+	0.751641i	$0.729263\pi$
$510$	−30.1986	−1.33722
$511$	10.9638	0.485012
$512$	4.90381	0.216720
$513$	−2.94902	−0.130202
$514$	9.89772	0.436570
$515$	−2.99910	−0.132156
$516$	40.2104	1.77016
$517$	−27.0307	−1.18881
$518$	−2.63259	−0.115669
$519$	−50.4392	−2.21404
$520$	−56.7546	−2.48886
$521$	−40.0735	−1.75565	−0.877826	−	0.478980i	$-0.841006\pi$
$521$	−40.0735	−1.75565	−0.877826	+	0.478980i	$0.841006\pi$
$522$	3.61696	0.158310
$523$	−13.7948	−0.603202	−0.301601	−	0.953434i	$-0.597521\pi$
$523$	−13.7948	−0.603202	−0.301601	+	0.953434i	$0.597521\pi$
$524$	−81.5640	−3.56314
$525$	−4.42281	−0.193027
$526$	26.2423	1.14422
$527$	27.3548	1.19159
$528$	127.360	5.54264
$529$	36.1893	1.57345
$530$	−26.7857	−1.16349
$531$	1.36089	0.0590576
$532$	3.88794	0.168564
$533$	−4.35762	−0.188750
$534$	1.73641	0.0751420
$535$	5.14691	0.222520
$536$	−69.6251	−3.00735
$537$	−22.2544	−0.960346
$538$	−42.9331	−1.85098
$539$	−30.0950	−1.29628
$540$	−23.0122	−0.990286
$541$	26.5100	1.13976	0.569878	−	0.821729i	$-0.306991\pi$
$541$	26.5100	1.13976	0.569878	+	0.821729i	$0.306991\pi$
$542$	69.5467	2.98729
$543$	31.6057	1.35633
$544$	−58.6177	−2.51321
$545$	−21.9738	−0.941254
$546$	−18.9918	−0.812775
$547$	25.4711	1.08907	0.544533	−	0.838739i	$-0.316707\pi$
$547$	25.4711	1.08907	0.544533	+	0.838739i	$0.316707\pi$
$548$	98.5303	4.20901
$549$	11.8469	0.505615
$550$	34.4973	1.47097
$551$	−0.827078	−0.0352347
$552$	142.329	6.05794
$553$	−8.25520	−0.351047
$554$	−83.0237	−3.52734
$555$	4.23575	0.179797
$556$	22.7489	0.964769
$557$	16.9658	0.718864	0.359432	−	0.933171i	$-0.382970\pi$
$557$	16.9658	0.718864	0.359432	+	0.933171i	$0.382970\pi$
$558$	−34.3049	−1.45224
$559$	15.8084	0.668623
$560$	14.1963	0.599904
$561$	35.0531	1.47994
$562$	−9.95563	−0.419953
$563$	33.9339	1.43014	0.715071	−	0.699052i	$-0.246394\pi$
$563$	33.9339	1.43014	0.715071	+	0.699052i	$0.246394\pi$
$564$	−64.7786	−2.72767
$565$	25.3260	1.06547
$566$	72.4316	3.04453
$567$	−8.39311	−0.352478
$568$	−69.5311	−2.91746
$569$	35.5898	1.49200	0.746001	−	0.665945i	$-0.231971\pi$
$569$	35.5898	1.49200	0.746001	+	0.665945i	$0.231971\pi$
$570$	−8.65990	−0.362723
$571$	29.9240	1.25228	0.626141	−	0.779710i	$-0.284633\pi$
$571$	29.9240	1.25228	0.626141	+	0.779710i	$0.284633\pi$
$572$	107.006	4.47413
$573$	37.4107	1.56286
$574$	1.98531	0.0828652
$575$	21.1661	0.882689
$576$	32.2220	1.34258
$577$	31.1479	1.29670	0.648351	−	0.761341i	$-0.275459\pi$
$577$	31.1479	1.29670	0.648351	+	0.761341i	$0.275459\pi$
$578$	12.9893	0.540282
$579$	38.9992	1.62075
$580$	−6.45396	−0.267986
$581$	−2.22561	−0.0923340
$582$	−1.43261	−0.0593834
$583$	31.0915	1.28768
$584$	−126.170	−5.22095
$585$	10.7551	0.444668
$586$	9.83893	0.406443
$587$	24.8414	1.02531	0.512656	−	0.858594i	$-0.328662\pi$
$587$	24.8414	1.02531	0.512656	+	0.858594i	$0.328662\pi$
$588$	−72.1220	−2.97426
$589$	7.84439	0.323222
$590$	−3.36164	−0.138396
$591$	−48.9848	−2.01497
$592$	16.6331	0.683616
$593$	−24.0095	−0.985953	−0.492976	−	0.870043i	$-0.664091\pi$
$593$	−24.0095	−0.985953	−0.492976	+	0.870043i	$0.664091\pi$
$594$	36.9779	1.51722
$595$	3.90722	0.160180
$596$	−49.6753	−2.03478
$597$	−6.81299	−0.278837
$598$	90.8887	3.71671
$599$	−22.4711	−0.918144	−0.459072	−	0.888399i	$-0.651818\pi$
$599$	−22.4711	−0.918144	−0.459072	+	0.888399i	$0.651818\pi$
$600$	50.8970	2.07786
$601$	37.0180	1.51000	0.754999	−	0.655726i	$-0.227637\pi$
$601$	37.0180	1.51000	0.754999	+	0.655726i	$0.227637\pi$
$602$	−7.20220	−0.293540
$603$	13.1941	0.537304
$604$	19.1613	0.779664
$605$	16.2352	0.660056
$606$	−8.71032	−0.353832
$607$	2.09876	0.0851859	0.0425930	−	0.999093i	$-0.486438\pi$
$607$	2.09876	0.0851859	0.0425930	+	0.999093i	$0.486438\pi$
$608$	−16.8095	−0.681715
$609$	−1.32961	−0.0538786
$610$	−29.2640	−1.18487
$611$	−25.4672	−1.03029
$612$	29.5665	1.19515
$613$	18.4546	0.745373	0.372686	−	0.927957i	$-0.378437\pi$
$613$	18.4546	0.745373	0.372686	+	0.927957i	$0.378437\pi$
$614$	−33.5697	−1.35476
$615$	−3.19429	−0.128806
$616$	−30.0136	−1.20928
$617$	−31.6727	−1.27510	−0.637548	−	0.770411i	$-0.720051\pi$
$617$	−31.6727	−1.27510	−0.637548	+	0.770411i	$0.720051\pi$
$618$	11.5491	0.464575
$619$	−22.2218	−0.893168	−0.446584	−	0.894742i	$-0.647360\pi$
$619$	−22.2218	−0.893168	−0.446584	+	0.894742i	$0.647360\pi$
$620$	61.2123	2.45834
$621$	22.6882	0.910445
$622$	−61.6019	−2.47001
$623$	−0.224665	−0.00900099
$624$	119.993	4.80357
$625$	−3.67506	−0.147002
$626$	63.4184	2.53471
$627$	10.0520	0.401438
$628$	16.8618	0.672860
$629$	4.57789	0.182532
$630$	−4.89995	−0.195219
$631$	16.0948	0.640723	0.320361	−	0.947295i	$-0.396196\pi$
$631$	16.0948	0.640723	0.320361	+	0.947295i	$0.396196\pi$
$632$	94.9995	3.77888
$633$	−33.0474	−1.31352
$634$	2.68395	0.106593
$635$	8.18292	0.324729
$636$	74.5102	2.95452
$637$	−28.3542	−1.12343
$638$	10.3708	0.410583
$639$	13.1762	0.521244
$640$	−29.1787	−1.15339
$641$	5.12448	0.202405	0.101202	−	0.994866i	$-0.467731\pi$
$641$	5.12448	0.202405	0.101202	+	0.994866i	$0.467731\pi$
$642$	−19.8201	−0.782237
$643$	−32.3333	−1.27510	−0.637551	−	0.770408i	$-0.720053\pi$
$643$	−32.3333	−1.27510	−0.637551	+	0.770408i	$0.720053\pi$
$644$	−29.9117	−1.17869
$645$	11.5881	0.456281
$646$	−9.35941	−0.368241
$647$	−22.8036	−0.896503	−0.448252	−	0.893907i	$-0.647953\pi$
$647$	−22.8036	−0.896503	−0.448252	+	0.893907i	$0.647953\pi$
$648$	96.5866	3.79428
$649$	3.90202	0.153168
$650$	32.5018	1.27483
$651$	12.6107	0.494251
$652$	67.8396	2.65680
$653$	4.50055	0.176120	0.0880601	−	0.996115i	$-0.471933\pi$
$653$	4.50055	0.176120	0.0880601	+	0.996115i	$0.471933\pi$
$654$	84.6183	3.30884
$655$	−23.5057	−0.918443
$656$	−12.5435	−0.489740
$657$	23.9094	0.932794
$658$	11.6027	0.452320
$659$	−28.0838	−1.09399	−0.546995	−	0.837136i	$-0.684228\pi$
$659$	−28.0838	−1.09399	−0.546995	+	0.837136i	$0.684228\pi$
$660$	78.4389	3.05323
$661$	−15.1112	−0.587756	−0.293878	−	0.955843i	$-0.594946\pi$
$661$	−15.1112	−0.587756	−0.293878	+	0.955843i	$0.594946\pi$
$662$	−85.8285	−3.33582
$663$	33.0255	1.28260
$664$	25.6120	0.993938
$665$	1.12045	0.0434494
$666$	−5.74102	−0.222460
$667$	6.36309	0.246380
$668$	52.4763	2.03037
$669$	35.3173	1.36545
$670$	−32.5917	−1.25913
$671$	33.9683	1.31133
$672$	−27.0230	−1.04243
$673$	−44.5834	−1.71856	−0.859282	−	0.511502i	$-0.829089\pi$
$673$	−44.5834	−1.71856	−0.859282	+	0.511502i	$0.829089\pi$
$674$	42.2006	1.62551
$675$	8.11330	0.312281
$676$	33.1695	1.27575
$677$	5.02946	0.193298	0.0966490	−	0.995319i	$-0.469188\pi$
$677$	5.02946	0.193298	0.0966490	+	0.995319i	$0.469188\pi$
$678$	−97.5273	−3.74551
$679$	0.185357	0.00711333
$680$	−44.9637	−1.72428
$681$	−36.5121	−1.39915
$682$	−98.3612	−3.76644
$683$	−37.2318	−1.42464	−0.712318	−	0.701857i	$-0.752355\pi$
$683$	−37.2318	−1.42464	−0.712318	+	0.701857i	$0.752355\pi$
$684$	8.47864	0.324189
$685$	28.3951	1.08492
$686$	26.9555	1.02917
$687$	14.5190	0.553935
$688$	45.5046	1.73485
$689$	29.2931	1.11598
$690$	66.6246	2.53635
$691$	−3.83598	−0.145928	−0.0729639	−	0.997335i	$-0.523246\pi$
$691$	−3.83598	−0.145928	−0.0729639	+	0.997335i	$0.523246\pi$
$692$	−121.986	−4.63721
$693$	5.68762	0.216055
$694$	−35.4988	−1.34752
$695$	6.55593	0.248681
$696$	15.3010	0.579982
$697$	−3.45231	−0.130766
$698$	10.5948	0.401021
$699$	−0.229680	−0.00868730
$700$	−10.6965	−0.404288
$701$	−25.4851	−0.962559	−0.481279	−	0.876567i	$-0.659828\pi$
$701$	−25.4851	−0.962559	−0.481279	+	0.876567i	$0.659828\pi$
$702$	34.8390	1.31491
$703$	1.31278	0.0495124
$704$	92.3888	3.48203
$705$	−18.6683	−0.703090
$706$	50.7066	1.90837
$707$	1.12698	0.0423843
$708$	9.35113	0.351437
$709$	9.46240	0.355368	0.177684	−	0.984088i	$-0.443140\pi$
$709$	9.46240	0.355368	0.177684	+	0.984088i	$0.443140\pi$
$710$	−32.5476	−1.22149
$711$	−18.0025	−0.675148
$712$	2.58540	0.0968920
$713$	−60.3505	−2.26014
$714$	−15.0462	−0.563090
$715$	30.8376	1.15326
$716$	−53.8216	−2.01141
$717$	−32.7449	−1.22288
$718$	63.8795	2.38396
$719$	7.05558	0.263129	0.131564	−	0.991308i	$-0.458000\pi$
$719$	7.05558	0.263129	0.131564	+	0.991308i	$0.458000\pi$
$720$	30.9586	1.15376
$721$	−1.49428	−0.0556498
$722$	−2.68395	−0.0998863
$723$	−19.1160	−0.710931
$724$	76.4376	2.84078
$725$	2.27544	0.0845079
$726$	−62.5198	−2.32033
$727$	−7.02694	−0.260615	−0.130307	−	0.991474i	$-0.541596\pi$
$727$	−7.02694	−0.260615	−0.130307	+	0.991474i	$0.541596\pi$
$728$	−28.2775	−1.04804
$729$	0.732046	0.0271128
$730$	−59.0604	−2.18592
$731$	12.5241	0.463221
$732$	81.4043	3.00879
$733$	−26.0473	−0.962079	−0.481040	−	0.876699i	$-0.659741\pi$
$733$	−26.0473	−0.962079	−0.481040	+	0.876699i	$0.659741\pi$
$734$	−23.9348	−0.883448
$735$	−20.7846	−0.766652
$736$	129.323	4.76692
$737$	37.8308	1.39352
$738$	4.32946	0.159370
$739$	50.8437	1.87032	0.935158	−	0.354232i	$-0.115258\pi$
$739$	50.8437	1.87032	0.935158	+	0.354232i	$0.115258\pi$
$740$	10.2440	0.376578
$741$	9.47055	0.347909
$742$	−13.3457	−0.489938
$743$	−37.4633	−1.37440	−0.687198	−	0.726470i	$-0.741160\pi$
$743$	−37.4633	−1.37440	−0.687198	+	0.726470i	$0.741160\pi$
$744$	−145.121	−5.32041
$745$	−14.3158	−0.524489
$746$	−67.4702	−2.47026
$747$	−4.85351	−0.177581
$748$	84.7749	3.09968
$749$	2.56441	0.0937015
$750$	67.1245	2.45104
$751$	38.5318	1.40605	0.703023	−	0.711167i	$-0.251833\pi$
$751$	38.5318	1.40605	0.703023	+	0.711167i	$0.251833\pi$
$752$	−73.3075	−2.67325
$753$	−22.7477	−0.828972
$754$	9.77089	0.355835
$755$	5.52204	0.200968
$756$	−11.4656	−0.417001
$757$	13.4074	0.487299	0.243650	−	0.969863i	$-0.421655\pi$
$757$	13.4074	0.487299	0.243650	+	0.969863i	$0.421655\pi$
$758$	−12.4033	−0.450508
$759$	−77.3346	−2.80707
$760$	−12.8940	−0.467715
$761$	−18.4125	−0.667452	−0.333726	−	0.942670i	$-0.608306\pi$
$761$	−18.4125	−0.667452	−0.333726	+	0.942670i	$0.608306\pi$
$762$	−31.5114	−1.14154
$763$	−10.9483	−0.396354
$764$	90.4768	3.27334
$765$	8.52067	0.308066
$766$	5.92478	0.214071
$767$	3.67632	0.132744
$768$	27.2654	0.983856
$769$	−47.3691	−1.70817	−0.854087	−	0.520130i	$-0.825883\pi$
$769$	−47.3691	−1.70817	−0.854087	+	0.520130i	$0.825883\pi$
$770$	−14.0494	−0.506307
$771$	−7.93455	−0.285756
$772$	94.3186	3.39460
$773$	3.78411	0.136105	0.0680524	−	0.997682i	$-0.478321\pi$
$773$	3.78411	0.136105	0.0680524	+	0.997682i	$0.478321\pi$
$774$	−15.7062	−0.564548
$775$	−21.5814	−0.775225
$776$	−2.13305	−0.0765721
$777$	2.11043	0.0757111
$778$	2.75896	0.0989136
$779$	−0.990002	−0.0354705
$780$	73.9018	2.64611
$781$	37.7797	1.35186
$782$	72.0062	2.57494
$783$	2.43907	0.0871652
$784$	−81.6178	−2.91492
$785$	4.85935	0.173438
$786$	90.5173	3.22865
$787$	−3.48680	−0.124291	−0.0621454	−	0.998067i	$-0.519794\pi$
$787$	−3.48680	−0.124291	−0.0621454	+	0.998067i	$0.519794\pi$
$788$	−118.468	−4.22026
$789$	−21.0372	−0.748945
$790$	44.4694	1.58215
$791$	12.6185	0.448662
$792$	−65.4522	−2.32574
$793$	32.0034	1.13648
$794$	−21.9844	−0.780197
$795$	21.4728	0.761563
$796$	−16.4770	−0.584013
$797$	19.2831	0.683043	0.341521	−	0.939874i	$-0.389058\pi$
$797$	19.2831	0.683043	0.341521	+	0.939874i	$0.389058\pi$
$798$	−4.31473	−0.152740
$799$	−20.1763	−0.713785
$800$	46.2460	1.63504
$801$	−0.489937	−0.0173111
$802$	36.2226	1.27906
$803$	68.5545	2.41923
$804$	90.6608	3.19736
$805$	−8.62017	−0.303821
$806$	−92.6716	−3.26422
$807$	34.4175	1.21155
$808$	−12.9691	−0.456250
$809$	29.0642	1.02184	0.510921	−	0.859627i	$-0.329304\pi$
$809$	29.0642	1.02184	0.510921	+	0.859627i	$0.329304\pi$
$810$	45.2124	1.58860
$811$	4.62799	0.162511	0.0812554	−	0.996693i	$-0.474107\pi$
$811$	4.62799	0.162511	0.0812554	+	0.996693i	$0.474107\pi$
$812$	−3.21563	−0.112847
$813$	−55.7524	−1.95532
$814$	−16.4610	−0.576958
$815$	19.5505	0.684824
$816$	95.0642	3.32791
$817$	3.59148	0.125650
$818$	−79.3177	−2.77328
$819$	5.35863	0.187246
$820$	−7.72531	−0.269780
$821$	22.0564	0.769774	0.384887	−	0.922964i	$-0.374240\pi$
$821$	22.0564	0.769774	0.384887	+	0.922964i	$0.374240\pi$
$822$	−109.346	−3.81388
$823$	7.09551	0.247334	0.123667	−	0.992324i	$-0.460535\pi$
$823$	7.09551	0.247334	0.123667	+	0.992324i	$0.460535\pi$
$824$	17.1959	0.599047
$825$	−27.6549	−0.962819
$826$	−1.67491	−0.0582776
$827$	12.6143	0.438642	0.219321	−	0.975653i	$-0.429616\pi$
$827$	12.6143	0.438642	0.219321	+	0.975653i	$0.429616\pi$
$828$	−65.2301	−2.26690
$829$	−17.4544	−0.606215	−0.303108	−	0.952956i	$-0.598024\pi$
$829$	−17.4544	−0.606215	−0.303108	+	0.952956i	$0.598024\pi$
$830$	11.9890	0.416145
$831$	66.5563	2.30881
$832$	87.0447	3.01773
$833$	−22.4635	−0.778314
$834$	−25.2461	−0.874200
$835$	15.1230	0.523353
$836$	24.3105	0.840795
$837$	−23.1332	−0.799602
$838$	−13.8849	−0.479645
$839$	−52.1274	−1.79964	−0.899819	−	0.436263i	$-0.856302\pi$
$839$	−52.1274	−1.79964	−0.899819	+	0.436263i	$0.856302\pi$
$840$	−20.7284	−0.715199
$841$	−28.3159	−0.976412
$842$	61.5484	2.12110
$843$	7.98097	0.274879
$844$	−79.9242	−2.75110
$845$	9.55900	0.328840
$846$	25.3026	0.869920
$847$	8.08907	0.277944
$848$	84.3204	2.89557
$849$	−58.0651	−1.99279
$850$	25.7495	0.883199
$851$	−10.0998	−0.346217
$852$	90.5383	3.10179
$853$	−45.2958	−1.55090	−0.775450	−	0.631409i	$-0.782477\pi$
$853$	−45.2958	−1.55090	−0.775450	+	0.631409i	$0.782477\pi$
$854$	−14.5806	−0.498937
$855$	2.44343	0.0835636
$856$	−29.5108	−1.00866
$857$	33.1280	1.13163	0.565815	−	0.824532i	$-0.308562\pi$
$857$	33.1280	1.13163	0.565815	+	0.824532i	$0.308562\pi$
$858$	−118.752	−4.05412
$859$	−48.1570	−1.64310	−0.821548	−	0.570140i	$-0.806889\pi$
$859$	−48.1570	−1.64310	−0.821548	+	0.570140i	$0.806889\pi$
$860$	28.0255	0.955661
$861$	−1.59153	−0.0542392
$862$	−7.37596	−0.251226
$863$	11.0734	0.376941	0.188471	−	0.982079i	$-0.439647\pi$
$863$	11.0734	0.376941	0.188471	+	0.982079i	$0.439647\pi$
$864$	49.5715	1.68646
$865$	−35.1547	−1.19530
$866$	−75.7820	−2.57518
$867$	−10.4129	−0.353640
$868$	30.4985	1.03519
$869$	−51.6180	−1.75102
$870$	7.16241	0.242828
$871$	35.6425	1.20770
$872$	125.991	4.26659
$873$	0.404216	0.0136807
$874$	20.6489	0.698458
$875$	−8.68485	−0.293601
$876$	164.289	5.55083
$877$	−56.6400	−1.91260	−0.956299	−	0.292390i	$-0.905550\pi$
$877$	−56.6400	−1.91260	−0.956299	+	0.292390i	$0.905550\pi$
$878$	23.0197	0.776876
$879$	−7.88742	−0.266036
$880$	88.7664	2.99232
$881$	10.2370	0.344893	0.172447	−	0.985019i	$-0.444833\pi$
$881$	10.2370	0.344893	0.172447	+	0.985019i	$0.444833\pi$
$882$	28.1709	0.948564
$883$	43.2518	1.45554	0.727769	−	0.685823i	$-0.240557\pi$
$883$	43.2518	1.45554	0.727769	+	0.685823i	$0.240557\pi$
$884$	79.8712	2.68636
$885$	2.69487	0.0905871
$886$	12.9272	0.434297
$887$	39.9722	1.34214	0.671068	−	0.741396i	$-0.265836\pi$
$887$	39.9722	1.34214	0.671068	+	0.741396i	$0.265836\pi$
$888$	−24.2864	−0.815000
$889$	4.07708	0.136741
$890$	1.21023	0.0405671
$891$	−52.4803	−1.75816
$892$	85.4140	2.85987
$893$	−5.78585	−0.193616
$894$	55.1282	1.84376
$895$	−15.5107	−0.518464
$896$	−14.5381	−0.485683
$897$	−72.8613	−2.43277
$898$	1.28212	0.0427849
$899$	−6.48792	−0.216384
$900$	−23.3263	−0.777543
$901$	23.2073	0.773148
$902$	12.4137	0.413331
$903$	5.77368	0.192136
$904$	−145.211	−4.82966
$905$	22.0283	0.732246
$906$	−21.2647	−0.706472
$907$	26.4361	0.877795	0.438898	−	0.898537i	$-0.355369\pi$
$907$	26.4361	0.877795	0.438898	+	0.898537i	$0.355369\pi$
$908$	−88.3035	−2.93045
$909$	2.45766	0.0815153
$910$	−13.2368	−0.438795
$911$	26.1886	0.867668	0.433834	−	0.900993i	$-0.357160\pi$
$911$	26.1886	0.867668	0.433834	+	0.900993i	$0.357160\pi$
$912$	27.2611	0.902705
$913$	−13.9163	−0.460561
$914$	89.9961	2.97681
$915$	23.4596	0.775552
$916$	35.1139	1.16019
$917$	−11.7115	−0.386748
$918$	27.6011	0.910971
$919$	11.3956	0.375907	0.187953	−	0.982178i	$-0.439815\pi$
$919$	11.3956	0.375907	0.187953	+	0.982178i	$0.439815\pi$
$920$	99.1995	3.27051
$921$	26.9113	0.886758
$922$	−27.0731	−0.891604
$923$	35.5944	1.17160
$924$	39.0816	1.28569
$925$	−3.61170	−0.118752
$926$	96.8354	3.18221
$927$	−3.25864	−0.107028
$928$	13.9028	0.456380
$929$	49.6463	1.62884	0.814420	−	0.580275i	$-0.197055\pi$
$929$	49.6463	1.62884	0.814420	+	0.580275i	$0.197055\pi$
$930$	−67.9316	−2.22756
$931$	−6.44174	−0.211120
$932$	−0.555475	−0.0181952
$933$	49.3834	1.61674
$934$	59.2259	1.93793
$935$	24.4310	0.798979
$936$	−61.6663	−2.01563
$937$	−27.4006	−0.895138	−0.447569	−	0.894249i	$-0.647710\pi$
$937$	−27.4006	−0.895138	−0.447569	+	0.894249i	$0.647710\pi$
$938$	−16.2385	−0.530207
$939$	−50.8397	−1.65909
$940$	−45.1489	−1.47259
$941$	42.2896	1.37860	0.689300	−	0.724476i	$-0.257918\pi$
$941$	42.2896	1.37860	0.689300	+	0.724476i	$0.257918\pi$
$942$	−18.7127	−0.609694
$943$	7.61654	0.248029
$944$	10.5823	0.344425
$945$	−3.30424	−0.107487
$946$	−45.0338	−1.46417
$947$	45.7447	1.48650	0.743252	−	0.669011i	$-0.233282\pi$
$947$	45.7447	1.48650	0.743252	+	0.669011i	$0.233282\pi$
$948$	−123.701	−4.01764
$949$	64.5890	2.09665
$950$	7.38404	0.239570
$951$	−2.15160	−0.0697704
$952$	−22.4028	−0.726079
$953$	40.9122	1.32528	0.662639	−	0.748939i	$-0.269437\pi$
$953$	40.9122	1.32528	0.662639	+	0.748939i	$0.269437\pi$
$954$	−29.1037	−0.942268
$955$	26.0742	0.843742
$956$	−79.1925	−2.56127
$957$	−8.31378	−0.268746
$958$	49.1152	1.58684
$959$	14.1477	0.456852
$960$	63.8068	2.05936
$961$	30.5344	0.984980
$962$	−15.5088	−0.500025
$963$	5.59234	0.180211
$964$	−46.2315	−1.48902
$965$	27.1814	0.874999
$966$	33.1952	1.06804
$967$	40.9540	1.31699	0.658496	−	0.752585i	$-0.271193\pi$
$967$	40.9540	1.31699	0.658496	+	0.752585i	$0.271193\pi$
$968$	−93.0877	−2.99195
$969$	7.50301	0.241031
$970$	−0.998486	−0.0320595
$971$	37.6723	1.20896	0.604481	−	0.796620i	$-0.293381\pi$
$971$	37.6723	1.20896	0.604481	+	0.796620i	$0.293381\pi$
$972$	−79.7316	−2.55739
$973$	3.26644	0.104717
$974$	−76.0576	−2.43704
$975$	−26.0552	−0.834435
$976$	92.1222	2.94876
$977$	37.1319	1.18795	0.593977	−	0.804482i	$-0.297557\pi$
$977$	37.1319	1.18795	0.593977	+	0.804482i	$0.297557\pi$
$978$	−75.2864	−2.40739
$979$	−1.40478	−0.0448969
$980$	−50.2670	−1.60572
$981$	−23.8754	−0.762284
$982$	40.0952	1.27949
$983$	10.4507	0.333325	0.166662	−	0.986014i	$-0.446701\pi$
$983$	10.4507	0.333325	0.166662	+	0.986014i	$0.446701\pi$
$984$	18.3151	0.583863
$985$	−34.1410	−1.08782
$986$	7.74096	0.246522
$987$	−9.30135	−0.296065
$988$	22.9043	0.728682
$989$	−27.6309	−0.878612
$990$	−30.6383	−0.973750
$991$	22.2932	0.708167	0.354084	−	0.935214i	$-0.384793\pi$
$991$	22.2932	0.708167	0.354084	+	0.935214i	$0.384793\pi$
$992$	−131.860	−4.18657
$993$	68.8048	2.18345
$994$	−16.2166	−0.514359
$995$	−4.74846	−0.150536
$996$	−33.3501	−1.05674
$997$	17.3241	0.548660	0.274330	−	0.961636i	$-0.411544\pi$
$997$	17.3241	0.548660	0.274330	+	0.961636i	$0.411544\pi$
$998$	−20.3058	−0.642769
$999$	−3.87141	−0.122486

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6023.2.a.c.1.4	✓	138

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6023.2.a.c.1.4	✓	138	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q-2.68395 q^{2} +2.15160 q^{3} +5.20359 q^{4} +1.49960 q^{5} -5.77479 q^{6} +0.747166 q^{7} -8.59827 q^{8} +1.62938 q^{9} +O(q^{10})\)	\(q-2.68395 q^{2} +2.15160 q^{3} +5.20359 q^{4} +1.49960 q^{5} -5.77479 q^{6} +0.747166 q^{7} -8.59827 q^{8} +1.62938 q^{9} -4.02486 q^{10} +4.67187 q^{11} +11.1960 q^{12} +4.40163 q^{13} -2.00536 q^{14} +3.22655 q^{15} +12.6701 q^{16} +3.48718 q^{17} -4.37318 q^{18} +1.00000 q^{19} +7.80333 q^{20} +1.60760 q^{21} -12.5391 q^{22} -7.69346 q^{23} -18.5000 q^{24} -2.75118 q^{25} -11.8138 q^{26} -2.94902 q^{27} +3.88794 q^{28} -0.827078 q^{29} -8.65990 q^{30} +7.84439 q^{31} -16.8095 q^{32} +10.0520 q^{33} -9.35941 q^{34} +1.12045 q^{35} +8.47864 q^{36} +1.31278 q^{37} -2.68395 q^{38} +9.47055 q^{39} -12.8940 q^{40} -0.990002 q^{41} -4.31473 q^{42} +3.59148 q^{43} +24.3105 q^{44} +2.44343 q^{45} +20.6489 q^{46} -5.78585 q^{47} +27.2611 q^{48} -6.44174 q^{49} +7.38404 q^{50} +7.50301 q^{51} +22.9043 q^{52} +6.65505 q^{53} +7.91502 q^{54} +7.00595 q^{55} -6.42434 q^{56} +2.15160 q^{57} +2.21984 q^{58} +0.835218 q^{59} +16.7896 q^{60} +7.27081 q^{61} -21.0539 q^{62} +1.21742 q^{63} +19.7756 q^{64} +6.60071 q^{65} -26.9790 q^{66} +8.09758 q^{67} +18.1458 q^{68} -16.5533 q^{69} -3.00724 q^{70} +8.08664 q^{71} -14.0099 q^{72} +14.6739 q^{73} -3.52343 q^{74} -5.91945 q^{75} +5.20359 q^{76} +3.49066 q^{77} -25.4185 q^{78} -11.0487 q^{79} +19.0002 q^{80} -11.2333 q^{81} +2.65712 q^{82} -2.97874 q^{83} +8.36530 q^{84} +5.22939 q^{85} -9.63935 q^{86} -1.77954 q^{87} -40.1700 q^{88} -0.300689 q^{89} -6.55805 q^{90} +3.28875 q^{91} -40.0336 q^{92} +16.8780 q^{93} +15.5289 q^{94} +1.49960 q^{95} -36.1673 q^{96} +0.248079 q^{97} +17.2893 q^{98} +7.61226 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9}+O(q^{10}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9	\( 138 q + 11 q^{2} + 29 q^{3} + 157 q^{4} + 12 q^{5} + 8 q^{6} + 18 q^{7} + 33 q^{8} + 171 q^{9} + 40 q^{10} + 4 q^{11} + 69 q^{12} + 72 q^{13} + 3 q^{14} + 30 q^{15} + 191 q^{16} + 31 q^{17} + 31 q^{18} + 138 q^{19} + 16 q^{20} + 16 q^{21} + 95 q^{22} + 34 q^{23} + 3 q^{24} + 244 q^{25} - 13 q^{26} + 107 q^{27} + 43 q^{28} + 30 q^{29} - 14 q^{30} + 60 q^{31} + 62 q^{32} + 77 q^{33} + 36 q^{34} + 2 q^{35} + 205 q^{36} + 142 q^{37} + 11 q^{38} + 20 q^{39} + 76 q^{40} + 46 q^{41} - 21 q^{42} + 69 q^{43} - 7 q^{44} + 30 q^{45} + 39 q^{46} + 8 q^{47} + 116 q^{48} + 236 q^{49} + 34 q^{51} + 165 q^{52} + 49 q^{53} + 6 q^{55} - 33 q^{56} + 29 q^{57} + 75 q^{58} + 8 q^{59} - 24 q^{60} + 38 q^{61} - 10 q^{62} + 2 q^{63} + 251 q^{64} + 72 q^{65} - 15 q^{66} + 158 q^{67} - 19 q^{68} + 33 q^{69} + 48 q^{70} + 23 q^{71} + 88 q^{72} + 134 q^{73} + 4 q^{74} + 118 q^{75} + 157 q^{76} + 13 q^{77} + 12 q^{78} + 78 q^{79} - 48 q^{80} + 254 q^{81} + 89 q^{82} - 27 q^{83} - 15 q^{84} + 37 q^{85} + 66 q^{86} + 43 q^{87} + 224 q^{88} + 26 q^{89} + 38 q^{90} + 108 q^{91} + 113 q^{92} + 83 q^{93} + 48 q^{94} + 12 q^{95} + 40 q^{96} + 254 q^{97} + 47 q^{98} + 11 q^{99}+O(q^{100}) \) 138 * q + 11 * q^2 + 29 * q^3 + 157 * q^4 + 12 * q^5 + 8 * q^6 + 18 * q^7 + 33 * q^8 + 171 * q^9 + 40 * q^10 + 4 * q^11 + 69 * q^12 + 72 * q^13 + 3 * q^14 + 30 * q^15 + 191 * q^16 + 31 * q^17 + 31 * q^18 + 138 * q^19 + 16 * q^20 + 16 * q^21 + 95 * q^22 + 34 * q^23 + 3 * q^24 + 244 * q^25 - 13 * q^26 + 107 * q^27 + 43 * q^28 + 30 * q^29 - 14 * q^30 + 60 * q^31 + 62 * q^32 + 77 * q^33 + 36 * q^34 + 2 * q^35 + 205 * q^36 + 142 * q^37 + 11 * q^38 + 20 * q^39 + 76 * q^40 + 46 * q^41 - 21 * q^42 + 69 * q^43 - 7 * q^44 + 30 * q^45 + 39 * q^46 + 8 * q^47 + 116 * q^48 + 236 * q^49 + 34 * q^51 + 165 * q^52 + 49 * q^53 + 6 * q^55 - 33 * q^56 + 29 * q^57 + 75 * q^58 + 8 * q^59 - 24 * q^60 + 38 * q^61 - 10 * q^62 + 2 * q^63 + 251 * q^64 + 72 * q^65 - 15 * q^66 + 158 * q^67 - 19 * q^68 + 33 * q^69 + 48 * q^70 + 23 * q^71 + 88 * q^72 + 134 * q^73 + 4 * q^74 + 118 * q^75 + 157 * q^76 + 13 * q^77 + 12 * q^78 + 78 * q^79 - 48 * q^80 + 254 * q^81 + 89 * q^82 - 27 * q^83 - 15 * q^84 + 37 * q^85 + 66 * q^86 + 43 * q^87 + 224 * q^88 + 26 * q^89 + 38 * q^90 + 108 * q^91 + 113 * q^92 + 83 * q^93 + 48 * q^94 + 12 * q^95 + 40 * q^96 + 254 * q^97 + 47 * q^98 + 11 * q^99

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