LMFDB - Embedded newform 8015.2.a.n.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8015,2,Mod(1,8015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8015, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("8015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8015 = 5 \cdot 7 \cdot 229 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8015.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:	$64.0000972201$
Analytic rank:	$0$
Dimension:	$68$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	8015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.17774 q^{2} +0.311923 q^{3} +2.74253 q^{4} -1.00000 q^{5} -0.679286 q^{6} +1.00000 q^{7} -1.61704 q^{8} -2.90270 q^{9} +O(q^{10})$	\(q-2.17774 q^{2} +0.311923 q^{3} +2.74253 q^{4} -1.00000 q^{5} -0.679286 q^{6} +1.00000 q^{7} -1.61704 q^{8} -2.90270 q^{9} +2.17774 q^{10} +2.83060 q^{11} +0.855459 q^{12} +6.81417 q^{13} -2.17774 q^{14} -0.311923 q^{15} -1.96358 q^{16} -5.37853 q^{17} +6.32132 q^{18} -2.03893 q^{19} -2.74253 q^{20} +0.311923 q^{21} -6.16430 q^{22} -5.95637 q^{23} -0.504391 q^{24} +1.00000 q^{25} -14.8395 q^{26} -1.84119 q^{27} +2.74253 q^{28} -8.27512 q^{29} +0.679286 q^{30} -1.61035 q^{31} +7.51024 q^{32} +0.882930 q^{33} +11.7130 q^{34} -1.00000 q^{35} -7.96076 q^{36} -7.22216 q^{37} +4.44024 q^{38} +2.12550 q^{39} +1.61704 q^{40} +10.1945 q^{41} -0.679286 q^{42} -10.6589 q^{43} +7.76301 q^{44} +2.90270 q^{45} +12.9714 q^{46} -7.00788 q^{47} -0.612487 q^{48} +1.00000 q^{49} -2.17774 q^{50} -1.67769 q^{51} +18.6881 q^{52} +1.32162 q^{53} +4.00962 q^{54} -2.83060 q^{55} -1.61704 q^{56} -0.635988 q^{57} +18.0210 q^{58} -3.64418 q^{59} -0.855459 q^{60} +12.9071 q^{61} +3.50692 q^{62} -2.90270 q^{63} -12.4281 q^{64} -6.81417 q^{65} -1.92279 q^{66} +8.06900 q^{67} -14.7508 q^{68} -1.85793 q^{69} +2.17774 q^{70} -7.73188 q^{71} +4.69378 q^{72} +14.9429 q^{73} +15.7280 q^{74} +0.311923 q^{75} -5.59182 q^{76} +2.83060 q^{77} -4.62877 q^{78} +2.59659 q^{79} +1.96358 q^{80} +8.13380 q^{81} -22.2008 q^{82} +0.306656 q^{83} +0.855459 q^{84} +5.37853 q^{85} +23.2124 q^{86} -2.58120 q^{87} -4.57719 q^{88} +16.0326 q^{89} -6.32132 q^{90} +6.81417 q^{91} -16.3355 q^{92} -0.502306 q^{93} +15.2613 q^{94} +2.03893 q^{95} +2.34262 q^{96} +9.87642 q^{97} -2.17774 q^{98} -8.21640 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) $ 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * 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 $

$2$	−2.17774	−1.53989	−0.769946	−	0.638109i	$-0.779717\pi$
$2$	−2.17774	−1.53989	−0.769946	+	0.638109i	$0.779717\pi$
$3$	0.311923	0.180089	0.0900444	−	0.995938i	$-0.471299\pi$
$3$	0.311923	0.180089	0.0900444	+	0.995938i	$0.471299\pi$
$4$	2.74253	1.37127
$5$	−1.00000	−0.447214
$5$	−1.00000	−0.447214
$6$	−0.679286	−0.277317
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	−1.61704	−0.571709
$9$	−2.90270	−0.967568
$10$	2.17774	0.688660
$11$	2.83060	0.853458	0.426729	−	0.904379i	$-0.359666\pi$
$11$	2.83060	0.853458	0.426729	+	0.904379i	$0.359666\pi$
$12$	0.855459	0.246950
$13$	6.81417	1.88991	0.944955	−	0.327199i	$-0.106105\pi$
$13$	6.81417	1.88991	0.944955	+	0.327199i	$0.106105\pi$
$14$	−2.17774	−0.582024
$15$	−0.311923	−0.0805382
$16$	−1.96358	−0.490896
$17$	−5.37853	−1.30449	−0.652243	−	0.758010i	$-0.726172\pi$
$17$	−5.37853	−1.30449	−0.652243	+	0.758010i	$0.726172\pi$
$18$	6.32132	1.48995
$19$	−2.03893	−0.467762	−0.233881	−	0.972265i	$-0.575143\pi$
$19$	−2.03893	−0.467762	−0.233881	+	0.972265i	$0.575143\pi$
$20$	−2.74253	−0.613249
$21$	0.311923	0.0680672
$22$	−6.16430	−1.31423
$23$	−5.95637	−1.24199	−0.620994	−	0.783815i	$-0.713271\pi$
$23$	−5.95637	−1.24199	−0.620994	+	0.783815i	$0.713271\pi$
$24$	−0.504391	−0.102958
$25$	1.00000	0.200000
$26$	−14.8395	−2.91026
$27$	−1.84119	−0.354337
$28$	2.74253	0.518290
$29$	−8.27512	−1.53665	−0.768325	−	0.640059i	$-0.778910\pi$
$29$	−8.27512	−1.53665	−0.768325	+	0.640059i	$0.778910\pi$
$30$	0.679286	0.124020
$31$	−1.61035	−0.289228	−0.144614	−	0.989488i	$-0.546194\pi$
$31$	−1.61035	−0.289228	−0.144614	+	0.989488i	$0.546194\pi$
$32$	7.51024	1.32764
$33$	0.882930	0.153698
$34$	11.7130	2.00877
$35$	−1.00000	−0.169031
$36$	−7.96076	−1.32679
$37$	−7.22216	−1.18732	−0.593658	−	0.804717i	$-0.702317\pi$
$37$	−7.22216	−1.18732	−0.593658	+	0.804717i	$0.702317\pi$
$38$	4.44024	0.720302
$39$	2.12550	0.340352
$40$	1.61704	0.255676
$41$	10.1945	1.59211	0.796053	−	0.605227i	$-0.206918\pi$
$41$	10.1945	1.59211	0.796053	+	0.605227i	$0.206918\pi$
$42$	−0.679286	−0.104816
$43$	−10.6589	−1.62547	−0.812737	−	0.582631i	$-0.802023\pi$
$43$	−10.6589	−1.62547	−0.812737	+	0.582631i	$0.802023\pi$
$44$	7.76301	1.17032
$45$	2.90270	0.432710
$46$	12.9714	1.91253
$47$	−7.00788	−1.02220	−0.511102	−	0.859520i	$-0.670763\pi$
$47$	−7.00788	−1.02220	−0.511102	+	0.859520i	$0.670763\pi$
$48$	−0.612487	−0.0884049
$49$	1.00000	0.142857
$50$	−2.17774	−0.307978
$51$	−1.67769	−0.234923
$52$	18.6881	2.59157
$53$	1.32162	0.181539	0.0907694	−	0.995872i	$-0.471067\pi$
$53$	1.32162	0.181539	0.0907694	+	0.995872i	$0.471067\pi$
$54$	4.00962	0.545641
$55$	−2.83060	−0.381678
$56$	−1.61704	−0.216086
$57$	−0.635988	−0.0842387
$58$	18.0210	2.36628
$59$	−3.64418	−0.474432	−0.237216	−	0.971457i	$-0.576235\pi$
$59$	−3.64418	−0.474432	−0.237216	+	0.971457i	$0.576235\pi$
$60$	−0.855459	−0.110439
$61$	12.9071	1.65258	0.826291	−	0.563244i	$-0.190447\pi$
$61$	12.9071	1.65258	0.826291	+	0.563244i	$0.190447\pi$
$62$	3.50692	0.445379
$63$	−2.90270	−0.365706
$64$	−12.4281	−1.55352
$65$	−6.81417	−0.845194
$66$	−1.92279	−0.236679
$67$	8.06900	0.985786	0.492893	−	0.870090i	$-0.335939\pi$
$67$	8.06900	0.985786	0.492893	+	0.870090i	$0.335939\pi$
$68$	−14.7508	−1.78880
$69$	−1.85793	−0.223668
$70$	2.17774	0.260289
$71$	−7.73188	−0.917606	−0.458803	−	0.888538i	$-0.651722\pi$
$71$	−7.73188	−0.917606	−0.458803	+	0.888538i	$0.651722\pi$
$72$	4.69378	0.553167
$73$	14.9429	1.74893	0.874466	−	0.485086i	$-0.161212\pi$
$73$	14.9429	1.74893	0.874466	+	0.485086i	$0.161212\pi$
$74$	15.7280	1.82834
$75$	0.311923	0.0360178
$76$	−5.59182	−0.641426
$77$	2.83060	0.322577
$78$	−4.62877	−0.524105
$79$	2.59659	0.292140	0.146070	−	0.989274i	$-0.453338\pi$
$79$	2.59659	0.292140	0.146070	+	0.989274i	$0.453338\pi$
$80$	1.96358	0.219535
$81$	8.13380	0.903756
$82$	−22.2008	−2.45167
$83$	0.306656	0.0336598	0.0168299	−	0.999858i	$-0.494643\pi$
$83$	0.306656	0.0336598	0.0168299	+	0.999858i	$0.494643\pi$
$84$	0.855459	0.0933382
$85$	5.37853	0.583384
$86$	23.2124	2.50305
$87$	−2.58120	−0.276734
$88$	−4.57719	−0.487930
$89$	16.0326	1.69945	0.849727	−	0.527224i	$-0.176767\pi$
$89$	16.0326	1.69945	0.849727	+	0.527224i	$0.176767\pi$
$90$	−6.32132	−0.666326
$91$	6.81417	0.714319
$92$	−16.3355	−1.70310
$93$	−0.502306	−0.0520867
$94$	15.2613	1.57408
$95$	2.03893	0.209189
$96$	2.34262	0.239092
$97$	9.87642	1.00280	0.501399	−	0.865216i	$-0.332819\pi$
$97$	9.87642	1.00280	0.501399	+	0.865216i	$0.332819\pi$
$98$	−2.17774	−0.219984
$99$	−8.21640	−0.825779
$100$	2.74253	0.274253
$101$	−3.17073	−0.315499	−0.157750	−	0.987479i	$-0.550424\pi$
$101$	−3.17073	−0.315499	−0.157750	+	0.987479i	$0.550424\pi$
$102$	3.65356	0.361756
$103$	13.5787	1.33795	0.668977	−	0.743283i	$-0.266733\pi$
$103$	13.5787	1.33795	0.668977	+	0.743283i	$0.266733\pi$
$104$	−11.0188	−1.08048
$105$	−0.311923	−0.0304406
$106$	−2.87814	−0.279550
$107$	13.7596	1.33019	0.665097	−	0.746757i	$-0.268390\pi$
$107$	13.7596	1.33019	0.665097	+	0.746757i	$0.268390\pi$
$108$	−5.04952	−0.485890
$109$	−1.60106	−0.153354	−0.0766768	−	0.997056i	$-0.524431\pi$
$109$	−1.60106	−0.153354	−0.0766768	+	0.997056i	$0.524431\pi$
$110$	6.16430	0.587743
$111$	−2.25276	−0.213822
$112$	−1.96358	−0.185541
$113$	3.44862	0.324419	0.162210	−	0.986756i	$-0.448138\pi$
$113$	3.44862	0.324419	0.162210	+	0.986756i	$0.448138\pi$
$114$	1.38501	0.129718
$115$	5.95637	0.555434
$116$	−22.6948	−2.10716
$117$	−19.7795	−1.82862
$118$	7.93606	0.730574
$119$	−5.37853	−0.493049
$120$	0.504391	0.0460444
$121$	−2.98770	−0.271609
$122$	−28.1082	−2.54480
$123$	3.17988	0.286721
$124$	−4.41644	−0.396608
$125$	−1.00000	−0.0894427
$126$	6.32132	0.563148
$127$	−17.5964	−1.56143	−0.780715	−	0.624887i	$-0.785145\pi$
$127$	−17.5964	−1.56143	−0.780715	+	0.624887i	$0.785145\pi$
$128$	12.0447	1.06461
$129$	−3.32477	−0.292730
$130$	14.8395	1.30151
$131$	−6.51216	−0.568970	−0.284485	−	0.958680i	$-0.591823\pi$
$131$	−6.51216	−0.568970	−0.284485	+	0.958680i	$0.591823\pi$
$132$	2.42146	0.210761
$133$	−2.03893	−0.176797
$134$	−17.5722	−1.51800
$135$	1.84119	0.158464
$136$	8.69729	0.745786
$137$	−9.09925	−0.777401	−0.388701	−	0.921364i	$-0.627076\pi$
$137$	−9.09925	−0.777401	−0.388701	+	0.921364i	$0.627076\pi$
$138$	4.04608	0.344425
$139$	10.7891	0.915122	0.457561	−	0.889178i	$-0.348723\pi$
$139$	10.7891	0.915122	0.457561	+	0.889178i	$0.348723\pi$
$140$	−2.74253	−0.231786
$141$	−2.18592	−0.184088
$142$	16.8380	1.41301
$143$	19.2882	1.61296
$144$	5.69970	0.474975
$145$	8.27512	0.687211
$146$	−32.5417	−2.69317
$147$	0.311923	0.0257270
$148$	−19.8070	−1.62813
$149$	−17.4712	−1.43130	−0.715648	−	0.698461i	$-0.753869\pi$
$149$	−17.4712	−1.43130	−0.715648	+	0.698461i	$0.753869\pi$
$150$	−0.679286	−0.0554635
$151$	−7.79057	−0.633988	−0.316994	−	0.948428i	$-0.602673\pi$
$151$	−7.79057	−0.633988	−0.316994	+	0.948428i	$0.602673\pi$
$152$	3.29702	0.267424
$153$	15.6123	1.26218
$154$	−6.16430	−0.496733
$155$	1.61035	0.129347
$156$	5.82924	0.466713
$157$	10.1086	0.806757	0.403378	−	0.915033i	$-0.367836\pi$
$157$	10.1086	0.806757	0.403378	+	0.915033i	$0.367836\pi$
$158$	−5.65469	−0.449863
$159$	0.412245	0.0326931
$160$	−7.51024	−0.593737
$161$	−5.95637	−0.469427
$162$	−17.7133	−1.39169
$163$	−18.2499	−1.42945	−0.714723	−	0.699408i	$-0.753447\pi$
$163$	−18.2499	−1.42945	−0.714723	+	0.699408i	$0.753447\pi$
$164$	27.9586	2.18320
$165$	−0.882930	−0.0687360
$166$	−0.667815	−0.0518325
$167$	−22.2829	−1.72430	−0.862151	−	0.506651i	$-0.830883\pi$
$167$	−22.2829	−1.72430	−0.862151	+	0.506651i	$0.830883\pi$
$168$	−0.504391	−0.0389146
$169$	33.4329	2.57176
$170$	−11.7130	−0.898348
$171$	5.91840	0.452591
$172$	−29.2325	−2.22896
$173$	20.7313	1.57617	0.788087	−	0.615564i	$-0.211072\pi$
$173$	20.7313	1.57617	0.788087	+	0.615564i	$0.211072\pi$
$174$	5.62117	0.426140
$175$	1.00000	0.0755929
$176$	−5.55812	−0.418959
$177$	−1.13670	−0.0854399
$178$	−34.9148	−2.61697
$179$	−17.3837	−1.29932	−0.649659	−	0.760225i	$-0.725089\pi$
$179$	−17.3837	−1.29932	−0.649659	+	0.760225i	$0.725089\pi$
$180$	7.96076	0.593360
$181$	−20.4277	−1.51838	−0.759188	−	0.650871i	$-0.774404\pi$
$181$	−20.4277	−1.51838	−0.759188	+	0.650871i	$0.774404\pi$
$182$	−14.8395	−1.09997
$183$	4.02602	0.297612
$184$	9.63167	0.710056
$185$	7.22216	0.530984
$186$	1.09389	0.0802078
$187$	−15.2245	−1.11332
$188$	−19.2193	−1.40171
$189$	−1.84119	−0.133927
$190$	−4.44024	−0.322129
$191$	20.7038	1.49807	0.749036	−	0.662529i	$-0.230517\pi$
$191$	20.7038	1.49807	0.749036	+	0.662529i	$0.230517\pi$
$192$	−3.87663	−0.279771
$193$	17.0920	1.23031	0.615153	−	0.788408i	$-0.289094\pi$
$193$	17.0920	1.23031	0.615153	+	0.788408i	$0.289094\pi$
$194$	−21.5082	−1.54420
$195$	−2.12550	−0.152210
$196$	2.74253	0.195895
$197$	17.2332	1.22782	0.613909	−	0.789377i	$-0.289596\pi$
$197$	17.2332	1.22782	0.613909	+	0.789377i	$0.289596\pi$
$198$	17.8931	1.27161
$199$	−3.63831	−0.257913	−0.128956	−	0.991650i	$-0.541163\pi$
$199$	−3.63831	−0.257913	−0.128956	+	0.991650i	$0.541163\pi$
$200$	−1.61704	−0.114342
$201$	2.51691	0.177529
$202$	6.90501	0.485835
$203$	−8.27512	−0.580799
$204$	−4.60111	−0.322142
$205$	−10.1945	−0.712011
$206$	−29.5709	−2.06030
$207$	17.2896	1.20171
$208$	−13.3802	−0.927750
$209$	−5.77139	−0.399215
$210$	0.679286	0.0468752
$211$	−2.70062	−0.185918	−0.0929590	−	0.995670i	$-0.529633\pi$
$211$	−2.70062	−0.185918	−0.0929590	+	0.995670i	$0.529633\pi$
$212$	3.62459	0.248938
$213$	−2.41175	−0.165251
$214$	−29.9649	−2.04836
$215$	10.6589	0.726934
$216$	2.97727	0.202578
$217$	−1.61035	−0.109318
$218$	3.48668	0.236148
$219$	4.66103	0.314963
$220$	−7.76301	−0.523382
$221$	−36.6502	−2.46536
$222$	4.90591	0.329263
$223$	9.32211	0.624255	0.312127	−	0.950040i	$-0.398958\pi$
$223$	9.32211	0.624255	0.312127	+	0.950040i	$0.398958\pi$
$224$	7.51024	0.501799
$225$	−2.90270	−0.193514
$226$	−7.51019	−0.499571
$227$	23.1576	1.53703	0.768513	−	0.639834i	$-0.220997\pi$
$227$	23.1576	1.53703	0.768513	+	0.639834i	$0.220997\pi$
$228$	−1.74422	−0.115514
$229$	−1.00000	−0.0660819
$229$	−1.00000	−0.0660819
$230$	−12.9714	−0.855308
$231$	0.882930	0.0580925
$232$	13.3812	0.878517
$233$	3.61483	0.236815	0.118408	−	0.992965i	$-0.462221\pi$
$233$	3.61483	0.236815	0.118408	+	0.992965i	$0.462221\pi$
$234$	43.0746	2.81587
$235$	7.00788	0.457144
$236$	−9.99428	−0.650572
$237$	0.809937	0.0526111
$238$	11.7130	0.759242
$239$	−11.5501	−0.747116	−0.373558	−	0.927607i	$-0.621862\pi$
$239$	−11.5501	−0.747116	−0.373558	+	0.927607i	$0.621862\pi$
$240$	0.612487	0.0395359
$241$	29.9607	1.92994	0.964969	−	0.262362i	$-0.0845016\pi$
$241$	29.9607	1.92994	0.964969	+	0.262362i	$0.0845016\pi$
$242$	6.50642	0.418248
$243$	8.06069	0.517094
$244$	35.3981	2.26613
$245$	−1.00000	−0.0638877
$246$	−6.92495	−0.441519
$247$	−13.8936	−0.884028
$248$	2.60400	0.165354
$249$	0.0956529	0.00606176
$250$	2.17774	0.137732
$251$	13.8308	0.872991	0.436496	−	0.899706i	$-0.356219\pi$
$251$	13.8308	0.872991	0.436496	+	0.899706i	$0.356219\pi$
$252$	−7.96076	−0.501481
$253$	−16.8601	−1.05999
$254$	38.3203	2.40443
$255$	1.67769	0.105061
$256$	−1.37396	−0.0858723
$257$	−2.98560	−0.186236	−0.0931182	−	0.995655i	$-0.529683\pi$
$257$	−2.98560	−0.186236	−0.0931182	+	0.995655i	$0.529683\pi$
$258$	7.24047	0.450772
$259$	−7.22216	−0.448763
$260$	−18.6881	−1.15899
$261$	24.0202	1.48681
$262$	14.1818	0.876152
$263$	24.9079	1.53589	0.767945	−	0.640516i	$-0.221280\pi$
$263$	24.9079	1.53589	0.767945	+	0.640516i	$0.221280\pi$
$264$	−1.42773	−0.0878707
$265$	−1.32162	−0.0811866
$266$	4.44024	0.272249
$267$	5.00094	0.306053
$268$	22.1295	1.35177
$269$	−27.7204	−1.69014	−0.845072	−	0.534653i	$-0.820442\pi$
$269$	−27.7204	−1.69014	−0.845072	+	0.534653i	$0.820442\pi$
$270$	−4.00962	−0.244018
$271$	6.96974	0.423381	0.211691	−	0.977337i	$-0.432103\pi$
$271$	6.96974	0.423381	0.211691	+	0.977337i	$0.432103\pi$
$272$	10.5612	0.640367
$273$	2.12550	0.128641
$274$	19.8158	1.19711
$275$	2.83060	0.170692
$276$	−5.09543	−0.306709
$277$	8.93063	0.536590	0.268295	−	0.963337i	$-0.413540\pi$
$277$	8.93063	0.536590	0.268295	+	0.963337i	$0.413540\pi$
$278$	−23.4959	−1.40919
$279$	4.67437	0.279847
$280$	1.61704	0.0966365
$281$	20.2069	1.20544	0.602722	−	0.797951i	$-0.294083\pi$
$281$	20.2069	1.20544	0.602722	+	0.797951i	$0.294083\pi$
$282$	4.76035	0.283475
$283$	31.2583	1.85811	0.929056	−	0.369939i	$-0.120621\pi$
$283$	31.2583	1.85811	0.929056	+	0.369939i	$0.120621\pi$
$284$	−21.2049	−1.25828
$285$	0.635988	0.0376727
$286$	−42.0046	−2.48378
$287$	10.1945	0.601759
$288$	−21.8000	−1.28458
$289$	11.9286	0.701683
$290$	−18.0210	−1.05823
$291$	3.08068	0.180593
$292$	40.9813	2.39825
$293$	−5.89245	−0.344241	−0.172120	−	0.985076i	$-0.555062\pi$
$293$	−5.89245	−0.344241	−0.172120	+	0.985076i	$0.555062\pi$
$294$	−0.679286	−0.0396168
$295$	3.64418	0.212172
$296$	11.6785	0.678799
$297$	−5.21167	−0.302412
$298$	38.0477	2.20404
$299$	−40.5877	−2.34725
$300$	0.855459	0.0493899
$301$	−10.6589	−0.614371
$302$	16.9658	0.976272
$303$	−0.989023	−0.0568179
$304$	4.00360	0.229622
$305$	−12.9071	−0.739057
$306$	−33.9994	−1.94362
$307$	9.15894	0.522728	0.261364	−	0.965240i	$-0.415828\pi$
$307$	9.15894	0.522728	0.261364	+	0.965240i	$0.415828\pi$
$308$	7.76301	0.442339
$309$	4.23552	0.240951
$310$	−3.50692	−0.199180
$311$	10.4173	0.590709	0.295354	−	0.955388i	$-0.404562\pi$
$311$	10.4173	0.590709	0.295354	+	0.955388i	$0.404562\pi$
$312$	−3.43701	−0.194582
$313$	−6.36493	−0.359767	−0.179884	−	0.983688i	$-0.557572\pi$
$313$	−6.36493	−0.359767	−0.179884	+	0.983688i	$0.557572\pi$
$314$	−22.0139	−1.24232
$315$	2.90270	0.163549
$316$	7.12124	0.400601
$317$	7.48351	0.420316	0.210158	−	0.977667i	$-0.432602\pi$
$317$	7.48351	0.420316	0.210158	+	0.977667i	$0.432602\pi$
$318$	−0.897760	−0.0503439
$319$	−23.4236	−1.31147
$320$	12.4281	0.694755
$321$	4.29195	0.239553
$322$	12.9714	0.722867
$323$	10.9664	0.610188
$324$	22.3072	1.23929
$325$	6.81417	0.377982
$326$	39.7435	2.20119
$327$	−0.499407	−0.0276173
$328$	−16.4848	−0.910221
$329$	−7.00788	−0.386357
$330$	1.92279	0.105846
$331$	−16.9277	−0.930430	−0.465215	−	0.885198i	$-0.654023\pi$
$331$	−16.9277	−0.930430	−0.465215	+	0.885198i	$0.654023\pi$
$332$	0.841012	0.0461566
$333$	20.9638	1.14881
$334$	48.5263	2.65524
$335$	−8.06900	−0.440857
$336$	−0.612487	−0.0334139
$337$	35.3953	1.92811	0.964053	−	0.265711i	$-0.0856068\pi$
$337$	35.3953	1.92811	0.964053	+	0.265711i	$0.0856068\pi$
$338$	−72.8080	−3.96024
$339$	1.07571	0.0584243
$340$	14.7508	0.799974
$341$	−4.55826	−0.246844
$342$	−12.8887	−0.696941
$343$	1.00000	0.0539949
$344$	17.2359	0.929298
$345$	1.85793	0.100028
$346$	−45.1474	−2.42714
$347$	13.5196	0.725770	0.362885	−	0.931834i	$-0.381792\pi$
$347$	13.5196	0.725770	0.362885	+	0.931834i	$0.381792\pi$
$348$	−7.07902	−0.379475
$349$	−14.0362	−0.751338	−0.375669	−	0.926754i	$-0.622587\pi$
$349$	−14.0362	−0.751338	−0.375669	+	0.926754i	$0.622587\pi$
$350$	−2.17774	−0.116405
$351$	−12.5462	−0.669666
$352$	21.2585	1.13308
$353$	−25.8680	−1.37681	−0.688406	−	0.725325i	$-0.741689\pi$
$353$	−25.8680	−1.37681	−0.688406	+	0.725325i	$0.741689\pi$
$354$	2.47544	0.131568
$355$	7.73188	0.410366
$356$	43.9699	2.33040
$357$	−1.67769	−0.0887927
$358$	37.8571	2.00081
$359$	−30.8268	−1.62698	−0.813488	−	0.581582i	$-0.802434\pi$
$359$	−30.8268	−1.62698	−0.813488	+	0.581582i	$0.802434\pi$
$360$	−4.69378	−0.247384
$361$	−14.8428	−0.781199
$362$	44.4861	2.33814
$363$	−0.931932	−0.0489137
$364$	18.6881	0.979521
$365$	−14.9429	−0.782146
$366$	−8.76760	−0.458290
$367$	−13.2745	−0.692925	−0.346463	−	0.938064i	$-0.612617\pi$
$367$	−13.2745	−0.692925	−0.346463	+	0.938064i	$0.612617\pi$
$368$	11.6958	0.609687
$369$	−29.5915	−1.54047
$370$	−15.7280	−0.817657
$371$	1.32162	0.0686152
$372$	−1.37759	−0.0714247
$373$	28.9336	1.49812	0.749062	−	0.662500i	$-0.230505\pi$
$373$	28.9336	1.49812	0.749062	+	0.662500i	$0.230505\pi$
$374$	33.1549	1.71440
$375$	−0.311923	−0.0161076
$376$	11.3320	0.584403
$377$	−56.3881	−2.90413
$378$	4.00962	0.206233
$379$	−6.69724	−0.344014	−0.172007	−	0.985096i	$-0.555025\pi$
$379$	−6.69724	−0.344014	−0.172007	+	0.985096i	$0.555025\pi$
$380$	5.59182	0.286854
$381$	−5.48873	−0.281196
$382$	−45.0873	−2.30687
$383$	−10.8344	−0.553612	−0.276806	−	0.960926i	$-0.589276\pi$
$383$	−10.8344	−0.553612	−0.276806	+	0.960926i	$0.589276\pi$
$384$	3.75703	0.191725
$385$	−2.83060	−0.144261
$386$	−37.2218	−1.89454
$387$	30.9398	1.57276
$388$	27.0864	1.37510
$389$	5.24980	0.266175	0.133088	−	0.991104i	$-0.457511\pi$
$389$	5.24980	0.266175	0.133088	+	0.991104i	$0.457511\pi$
$390$	4.62877	0.234387
$391$	32.0365	1.62016
$392$	−1.61704	−0.0816727
$393$	−2.03129	−0.102465
$394$	−37.5294	−1.89070
$395$	−2.59659	−0.130649
$396$	−22.5337	−1.13236
$397$	7.37158	0.369969	0.184984	−	0.982741i	$-0.440777\pi$
$397$	7.37158	0.369969	0.184984	+	0.982741i	$0.440777\pi$
$398$	7.92328	0.397158
$399$	−0.635988	−0.0318392
$400$	−1.96358	−0.0981792
$401$	0.664767	0.0331969	0.0165985	−	0.999862i	$-0.494716\pi$
$401$	0.664767	0.0331969	0.0165985	+	0.999862i	$0.494716\pi$
$402$	−5.48116	−0.273376
$403$	−10.9732	−0.546614
$404$	−8.69582	−0.432633
$405$	−8.13380	−0.404172
$406$	18.0210	0.894368
$407$	−20.4431	−1.01332
$408$	2.71288	0.134308
$409$	29.5804	1.46266	0.731328	−	0.682026i	$-0.238901\pi$
$409$	29.5804	1.46266	0.731328	+	0.682026i	$0.238901\pi$
$410$	22.2008	1.09642
$411$	−2.83827	−0.140001
$412$	37.2401	1.83469
$413$	−3.64418	−0.179318
$414$	−37.6521	−1.85050
$415$	−0.306656	−0.0150531
$416$	51.1761	2.50911
$417$	3.36538	0.164803
$418$	12.5686	0.614748
$419$	−6.55826	−0.320392	−0.160196	−	0.987085i	$-0.551213\pi$
$419$	−6.55826	−0.320392	−0.160196	+	0.987085i	$0.551213\pi$
$420$	−0.855459	−0.0417421
$421$	−14.7405	−0.718407	−0.359204	−	0.933259i	$-0.616952\pi$
$421$	−14.7405	−0.718407	−0.359204	+	0.933259i	$0.616952\pi$
$422$	5.88123	0.286294
$423$	20.3418	0.989052
$424$	−2.13711	−0.103787
$425$	−5.37853	−0.260897
$426$	5.25216	0.254468
$427$	12.9071	0.624617
$428$	37.7363	1.82405
$429$	6.01643	0.290476
$430$	−23.2124	−1.11940
$431$	−0.0570763	−0.00274927	−0.00137463	−	0.999999i	$-0.500438\pi$
$431$	−0.0570763	−0.00274927	−0.00137463	+	0.999999i	$0.500438\pi$
$432$	3.61533	0.173943
$433$	22.1734	1.06559	0.532793	−	0.846246i	$-0.321143\pi$
$433$	22.1734	1.06559	0.532793	+	0.846246i	$0.321143\pi$
$434$	3.50692	0.168338
$435$	2.58120	0.123759
$436$	−4.39095	−0.210288
$437$	12.1446	0.580955
$438$	−10.1505	−0.485009
$439$	3.38823	0.161712	0.0808558	−	0.996726i	$-0.474235\pi$
$439$	3.38823	0.161712	0.0808558	+	0.996726i	$0.474235\pi$
$440$	4.57719	0.218209
$441$	−2.90270	−0.138224
$442$	79.8145	3.79639
$443$	−20.3076	−0.964841	−0.482421	−	0.875940i	$-0.660242\pi$
$443$	−20.3076	−0.964841	−0.482421	+	0.875940i	$0.660242\pi$
$444$	−6.17826	−0.293207
$445$	−16.0326	−0.760019
$446$	−20.3011	−0.961285
$447$	−5.44967	−0.257761
$448$	−12.4281	−0.587175
$449$	4.04600	0.190943	0.0954714	−	0.995432i	$-0.469564\pi$
$449$	4.04600	0.190943	0.0954714	+	0.995432i	$0.469564\pi$
$450$	6.32132	0.297990
$451$	28.8564	1.35880
$452$	9.45796	0.444865
$453$	−2.43006	−0.114174
$454$	−50.4312	−2.36685
$455$	−6.81417	−0.319453
$456$	1.02842	0.0481600
$457$	−19.9716	−0.934231	−0.467116	−	0.884196i	$-0.654707\pi$
$457$	−19.9716	−0.934231	−0.467116	+	0.884196i	$0.654707\pi$
$458$	2.17774	0.101759
$459$	9.90290	0.462228
$460$	16.3355	0.761648
$461$	−16.3403	−0.761045	−0.380523	−	0.924772i	$-0.624256\pi$
$461$	−16.3403	−0.761045	−0.380523	+	0.924772i	$0.624256\pi$
$462$	−1.92279	−0.0894562
$463$	−12.9815	−0.603302	−0.301651	−	0.953418i	$-0.597538\pi$
$463$	−12.9815	−0.603302	−0.301651	+	0.953418i	$0.597538\pi$
$464$	16.2489	0.754336
$465$	0.502306	0.0232939
$466$	−7.87213	−0.364670
$467$	1.12341	0.0519851	0.0259926	−	0.999662i	$-0.491725\pi$
$467$	1.12341	0.0519851	0.0259926	+	0.999662i	$0.491725\pi$
$468$	−54.2460	−2.50752
$469$	8.06900	0.372592
$470$	−15.2613	−0.703951
$471$	3.15312	0.145288
$472$	5.89278	0.271237
$473$	−30.1712	−1.38727
$474$	−1.76383	−0.0810154
$475$	−2.03893	−0.0935523
$476$	−14.7508	−0.676102
$477$	−3.83628	−0.175651
$478$	25.1531	1.15048
$479$	19.0327	0.869627	0.434814	−	0.900520i	$-0.356814\pi$
$479$	19.0327	0.869627	0.434814	+	0.900520i	$0.356814\pi$
$480$	−2.34262	−0.106925
$481$	−49.2130	−2.24392
$482$	−65.2465	−2.97190
$483$	−1.85793	−0.0845387
$484$	−8.19386	−0.372448
$485$	−9.87642	−0.448465
$486$	−17.5540	−0.796268
$487$	11.7313	0.531596	0.265798	−	0.964029i	$-0.414365\pi$
$487$	11.7313	0.531596	0.265798	+	0.964029i	$0.414365\pi$
$488$	−20.8712	−0.944796
$489$	−5.69258	−0.257427
$490$	2.17774	0.0983801
$491$	26.7954	1.20926	0.604629	−	0.796507i	$-0.293321\pi$
$491$	26.7954	1.20926	0.604629	+	0.796507i	$0.293321\pi$
$492$	8.72093	0.393170
$493$	44.5080	2.00454
$494$	30.2566	1.36131
$495$	8.21640	0.369300
$496$	3.16206	0.141981
$497$	−7.73188	−0.346822
$498$	−0.208307	−0.00933445
$499$	−33.0714	−1.48048	−0.740240	−	0.672342i	$-0.765288\pi$
$499$	−33.0714	−1.48048	−0.740240	+	0.672342i	$0.765288\pi$
$500$	−2.74253	−0.122650
$501$	−6.95055	−0.310528
$502$	−30.1198	−1.34431
$503$	18.8011	0.838298	0.419149	−	0.907917i	$-0.362328\pi$
$503$	18.8011	0.838298	0.419149	+	0.907917i	$0.362328\pi$
$504$	4.69378	0.209078
$505$	3.17073	0.141096
$506$	36.7168	1.63226
$507$	10.4285	0.463146
$508$	−48.2587	−2.14114
$509$	28.6278	1.26890	0.634452	−	0.772962i	$-0.281226\pi$
$509$	28.6278	1.26890	0.634452	+	0.772962i	$0.281226\pi$
$510$	−3.65356	−0.161782
$511$	14.9429	0.661034
$512$	−21.0974	−0.932381
$513$	3.75405	0.165745
$514$	6.50184	0.286784
$515$	−13.5787	−0.598351
$516$	−9.11829	−0.401410
$517$	−19.8365	−0.872408
$518$	15.7280	0.691047
$519$	6.46658	0.283851
$520$	11.0188	0.483205
$521$	−15.2157	−0.666612	−0.333306	−	0.942819i	$-0.608164\pi$
$521$	−15.2157	−0.666612	−0.333306	+	0.942819i	$0.608164\pi$
$522$	−52.3097	−2.28953
$523$	0.692056	0.0302615	0.0151308	−	0.999886i	$-0.495184\pi$
$523$	0.692056	0.0302615	0.0151308	+	0.999886i	$0.495184\pi$
$524$	−17.8598	−0.780209
$525$	0.311923	0.0136134
$526$	−54.2429	−2.36510
$527$	8.66133	0.377293
$528$	−1.73371	−0.0754499
$529$	12.4783	0.542535
$530$	2.87814	0.125019
$531$	10.5780	0.459045
$532$	−5.59182	−0.242436
$533$	69.4667	3.00894
$534$	−10.8907	−0.471288
$535$	−13.7596	−0.594881
$536$	−13.0479	−0.563583
$537$	−5.42238	−0.233993
$538$	60.3677	2.60264
$539$	2.83060	0.121923
$540$	5.04952	0.217297
$541$	7.62254	0.327719	0.163859	−	0.986484i	$-0.447606\pi$
$541$	7.62254	0.327719	0.163859	+	0.986484i	$0.447606\pi$
$542$	−15.1782	−0.651961
$543$	−6.37186	−0.273443
$544$	−40.3941	−1.73188
$545$	1.60106	0.0685818
$546$	−4.62877	−0.198093
$547$	34.3495	1.46868	0.734338	−	0.678783i	$-0.237493\pi$
$547$	34.3495	1.46868	0.734338	+	0.678783i	$0.237493\pi$
$548$	−24.9550	−1.06602
$549$	−37.4654	−1.59899
$550$	−6.16430	−0.262847
$551$	16.8724	0.718786
$552$	3.00434	0.127873
$553$	2.59659	0.110418
$554$	−19.4486	−0.826290
$555$	2.25276	0.0956243
$556$	29.5895	1.25488
$557$	40.4610	1.71439	0.857194	−	0.514993i	$-0.172206\pi$
$557$	40.4610	1.71439	0.857194	+	0.514993i	$0.172206\pi$
$558$	−10.1795	−0.430935
$559$	−72.6319	−3.07200
$560$	1.96358	0.0829766
$561$	−4.74887	−0.200497
$562$	−44.0054	−1.85625
$563$	−13.5714	−0.571965	−0.285982	−	0.958235i	$-0.592320\pi$
$563$	−13.5714	−0.571965	−0.285982	+	0.958235i	$0.592320\pi$
$564$	−5.99495	−0.252433
$565$	−3.44862	−0.145085
$566$	−68.0723	−2.86129
$567$	8.13380	0.341588
$568$	12.5027	0.524604
$569$	−18.3542	−0.769450	−0.384725	−	0.923031i	$-0.625704\pi$
$569$	−18.3542	−0.769450	−0.384725	+	0.923031i	$0.625704\pi$
$570$	−1.38501	−0.0580118
$571$	41.1226	1.72093	0.860465	−	0.509510i	$-0.170173\pi$
$571$	41.1226	1.72093	0.860465	+	0.509510i	$0.170173\pi$
$572$	52.8985	2.21180
$573$	6.45798	0.269786
$574$	−22.2008	−0.926644
$575$	−5.95637	−0.248398
$576$	36.0752	1.50313
$577$	−13.7059	−0.570584	−0.285292	−	0.958441i	$-0.592091\pi$
$577$	−13.7059	−0.570584	−0.285292	+	0.958441i	$0.592091\pi$
$578$	−25.9774	−1.08052
$579$	5.33138	0.221565
$580$	22.6948	0.942349
$581$	0.306656	0.0127222
$582$	−6.70892	−0.278094
$583$	3.74099	0.154936
$584$	−24.1632	−0.999880
$585$	19.7795	0.817782
$586$	12.8322	0.530093
$587$	22.4517	0.926679	0.463340	−	0.886181i	$-0.346651\pi$
$587$	22.4517	0.926679	0.463340	+	0.886181i	$0.346651\pi$
$588$	0.855459	0.0352785
$589$	3.28339	0.135290
$590$	−7.93606	−0.326722
$591$	5.37544	0.221116
$592$	14.1813	0.582849
$593$	−14.7457	−0.605534	−0.302767	−	0.953065i	$-0.597910\pi$
$593$	−14.7457	−0.605534	−0.302767	+	0.953065i	$0.597910\pi$
$594$	11.3496	0.465682
$595$	5.37853	0.220498
$596$	−47.9153	−1.96269
$597$	−1.13487	−0.0464472
$598$	88.3893	3.61451
$599$	23.9209	0.977380	0.488690	−	0.872457i	$-0.337475\pi$
$599$	23.9209	0.977380	0.488690	+	0.872457i	$0.337475\pi$
$600$	−0.504391	−0.0205917
$601$	16.8422	0.687007	0.343504	−	0.939151i	$-0.388386\pi$
$601$	16.8422	0.687007	0.343504	+	0.939151i	$0.388386\pi$
$602$	23.2124	0.946065
$603$	−23.4219	−0.953815
$604$	−21.3659	−0.869366
$605$	2.98770	0.121467
$606$	2.15383	0.0874934
$607$	23.5546	0.956052	0.478026	−	0.878346i	$-0.341352\pi$
$607$	23.5546	0.956052	0.478026	+	0.878346i	$0.341352\pi$
$608$	−15.3128	−0.621017
$609$	−2.58120	−0.104596
$610$	28.1082	1.13807
$611$	−47.7529	−1.93187
$612$	42.8172	1.73078
$613$	−38.7641	−1.56567	−0.782833	−	0.622232i	$-0.786226\pi$
$613$	−38.7641	−1.56567	−0.782833	+	0.622232i	$0.786226\pi$
$614$	−19.9457	−0.804945
$615$	−3.17988	−0.128225
$616$	−4.57719	−0.184420
$617$	−19.2574	−0.775275	−0.387638	−	0.921812i	$-0.626709\pi$
$617$	−19.2574	−0.775275	−0.387638	+	0.921812i	$0.626709\pi$
$618$	−9.22385	−0.371038
$619$	22.4179	0.901050	0.450525	−	0.892764i	$-0.351237\pi$
$619$	22.4179	0.901050	0.450525	+	0.892764i	$0.351237\pi$
$620$	4.41644	0.177368
$621$	10.9668	0.440083
$622$	−22.6860	−0.909627
$623$	16.0326	0.642333
$624$	−4.17359	−0.167077
$625$	1.00000	0.0400000
$626$	13.8611	0.554002
$627$	−1.80023	−0.0718942
$628$	27.7232	1.10628
$629$	38.8446	1.54884
$630$	−6.32132	−0.251847
$631$	−44.9591	−1.78979	−0.894896	−	0.446274i	$-0.852751\pi$
$631$	−44.9591	−1.78979	−0.894896	+	0.446274i	$0.852751\pi$
$632$	−4.19879	−0.167019
$633$	−0.842385	−0.0334818
$634$	−16.2971	−0.647241
$635$	17.5964	0.698293
$636$	1.13059	0.0448310
$637$	6.81417	0.269987
$638$	51.0103	2.01952
$639$	22.4434	0.887846
$640$	−12.0447	−0.476110
$641$	−4.99751	−0.197390	−0.0986948	−	0.995118i	$-0.531467\pi$
$641$	−4.99751	−0.197390	−0.0986948	+	0.995118i	$0.531467\pi$
$642$	−9.34673	−0.368886
$643$	31.4884	1.24178	0.620891	−	0.783897i	$-0.286771\pi$
$643$	31.4884	1.24178	0.620891	+	0.783897i	$0.286771\pi$
$644$	−16.3355	−0.643710
$645$	3.32477	0.130913
$646$	−23.8820	−0.939624
$647$	24.6962	0.970906	0.485453	−	0.874263i	$-0.338655\pi$
$647$	24.6962	0.970906	0.485453	+	0.874263i	$0.338655\pi$
$648$	−13.1527	−0.516685
$649$	−10.3152	−0.404908
$650$	−14.8395	−0.582051
$651$	−0.502306	−0.0196869
$652$	−50.0510	−1.96015
$653$	16.8210	0.658255	0.329128	−	0.944285i	$-0.393245\pi$
$653$	16.8210	0.658255	0.329128	+	0.944285i	$0.393245\pi$
$654$	1.08758	0.0425276
$655$	6.51216	0.254451
$656$	−20.0177	−0.781558
$657$	−43.3748	−1.69221
$658$	15.2613	0.594948
$659$	−39.6822	−1.54580	−0.772900	−	0.634528i	$-0.781195\pi$
$659$	−39.6822	−1.54580	−0.772900	+	0.634528i	$0.781195\pi$
$660$	−2.42146	−0.0942553
$661$	−27.9307	−1.08638	−0.543189	−	0.839610i	$-0.682783\pi$
$661$	−27.9307	−1.08638	−0.543189	+	0.839610i	$0.682783\pi$
$662$	36.8640	1.43276
$663$	−11.4321	−0.443984
$664$	−0.495873	−0.0192436
$665$	2.03893	0.0790662
$666$	−45.6536	−1.76904
$667$	49.2896	1.90850
$668$	−61.1116	−2.36448
$669$	2.90778	0.112421
$670$	17.5722	0.678872
$671$	36.5348	1.41041
$672$	2.34262	0.0903684
$673$	1.06939	0.0412221	0.0206111	−	0.999788i	$-0.493439\pi$
$673$	1.06939	0.0412221	0.0206111	+	0.999788i	$0.493439\pi$
$674$	−77.0816	−2.96907
$675$	−1.84119	−0.0708674
$676$	91.6908	3.52657
$677$	0.454051	0.0174506	0.00872530	−	0.999962i	$-0.497223\pi$
$677$	0.454051	0.0174506	0.00872530	+	0.999962i	$0.497223\pi$
$678$	−2.34260	−0.0899671
$679$	9.87642	0.379022
$680$	−8.69729	−0.333526
$681$	7.22340	0.276801
$682$	9.92669	0.380113
$683$	18.3146	0.700787	0.350394	−	0.936603i	$-0.386048\pi$
$683$	18.3146	0.700787	0.350394	+	0.936603i	$0.386048\pi$
$684$	16.2314	0.620623
$685$	9.09925	0.347664
$686$	−2.17774	−0.0831463
$687$	−0.311923	−0.0119006
$688$	20.9297	0.797939
$689$	9.00576	0.343092
$690$	−4.04608	−0.154031
$691$	16.4530	0.625902	0.312951	−	0.949769i	$-0.398682\pi$
$691$	16.4530	0.625902	0.312951	+	0.949769i	$0.398682\pi$
$692$	56.8563	2.16135
$693$	−8.21640	−0.312115
$694$	−29.4421	−1.11761
$695$	−10.7891	−0.409255
$696$	4.17390	0.158211
$697$	−54.8312	−2.07688
$698$	30.5670	1.15698
$699$	1.12755	0.0426478
$700$	2.74253	0.103658
$701$	44.0949	1.66544	0.832720	−	0.553695i	$-0.186783\pi$
$701$	44.0949	1.66544	0.832720	+	0.553695i	$0.186783\pi$
$702$	27.3223	1.03121
$703$	14.7255	0.555381
$704$	−35.1791	−1.32586
$705$	2.18592	0.0823265
$706$	56.3336	2.12014
$707$	−3.17073	−0.119248
$708$	−3.11745	−0.117161
$709$	−20.2267	−0.759629	−0.379815	−	0.925063i	$-0.624012\pi$
$709$	−20.2267	−0.759629	−0.379815	+	0.925063i	$0.624012\pi$
$710$	−16.8380	−0.631919
$711$	−7.53714	−0.282665
$712$	−25.9253	−0.971593
$713$	9.59184	0.359217
$714$	3.65356	0.136731
$715$	−19.2882	−0.721338
$716$	−47.6754	−1.78171
$717$	−3.60275	−0.134547
$718$	67.1326	2.50537
$719$	−9.95193	−0.371144	−0.185572	−	0.982631i	$-0.559414\pi$
$719$	−9.95193	−0.371144	−0.185572	+	0.982631i	$0.559414\pi$
$720$	−5.69970	−0.212415
$721$	13.5787	0.505699
$722$	32.3236	1.20296
$723$	9.34544	0.347561
$724$	−56.0235	−2.08210
$725$	−8.27512	−0.307330
$726$	2.02950	0.0753219
$727$	−5.96503	−0.221231	−0.110615	−	0.993863i	$-0.535282\pi$
$727$	−5.96503	−0.221231	−0.110615	+	0.993863i	$0.535282\pi$
$728$	−11.0188	−0.408383
$729$	−21.8871	−0.810633
$730$	32.5417	1.20442
$731$	57.3295	2.12041
$732$	11.0415	0.408105
$733$	39.2968	1.45146	0.725730	−	0.687980i	$-0.241502\pi$
$733$	39.2968	1.45146	0.725730	+	0.687980i	$0.241502\pi$
$734$	28.9084	1.06703
$735$	−0.311923	−0.0115055
$736$	−44.7337	−1.64891
$737$	22.8401	0.841327
$738$	64.4424	2.37216
$739$	−11.3825	−0.418714	−0.209357	−	0.977839i	$-0.567137\pi$
$739$	−11.3825	−0.418714	−0.209357	+	0.977839i	$0.567137\pi$
$740$	19.8070	0.728120
$741$	−4.33373	−0.159204
$742$	−2.87814	−0.105660
$743$	18.4958	0.678546	0.339273	−	0.940688i	$-0.389819\pi$
$743$	18.4958	0.678546	0.339273	+	0.940688i	$0.389819\pi$
$744$	0.812247	0.0297784
$745$	17.4712	0.640095
$746$	−63.0097	−2.30695
$747$	−0.890130	−0.0325682
$748$	−41.7536	−1.52666
$749$	13.7596	0.502766
$750$	0.679286	0.0248040
$751$	7.64605	0.279008	0.139504	−	0.990221i	$-0.455449\pi$
$751$	7.64605	0.279008	0.139504	+	0.990221i	$0.455449\pi$
$752$	13.7606	0.501796
$753$	4.31414	0.157216
$754$	122.798	4.47205
$755$	7.79057	0.283528
$756$	−5.04952	−0.183649
$757$	6.13470	0.222970	0.111485	−	0.993766i	$-0.464439\pi$
$757$	6.13470	0.222970	0.111485	+	0.993766i	$0.464439\pi$
$758$	14.5848	0.529745
$759$	−5.25905	−0.190892
$760$	−3.29702	−0.119595
$761$	−31.7406	−1.15060	−0.575298	−	0.817944i	$-0.695114\pi$
$761$	−31.7406	−1.15060	−0.575298	+	0.817944i	$0.695114\pi$
$762$	11.9530	0.433012
$763$	−1.60106	−0.0579622
$764$	56.7807	2.05426
$765$	−15.6123	−0.564463
$766$	23.5945	0.852503
$767$	−24.8321	−0.896634
$768$	−0.428569	−0.0154646
$769$	38.4645	1.38707	0.693533	−	0.720425i	$-0.256053\pi$
$769$	38.4645	1.38707	0.693533	+	0.720425i	$0.256053\pi$
$770$	6.16430	0.222146
$771$	−0.931276	−0.0335391
$772$	46.8752	1.68708
$773$	−27.4089	−0.985828	−0.492914	−	0.870078i	$-0.664068\pi$
$773$	−27.4089	−0.985828	−0.492914	+	0.870078i	$0.664068\pi$
$774$	−67.3786	−2.42187
$775$	−1.61035	−0.0578455
$776$	−15.9705	−0.573309
$777$	−2.25276	−0.0808173
$778$	−11.4327	−0.409881
$779$	−20.7857	−0.744726
$780$	−5.82924	−0.208720
$781$	−21.8859	−0.783138
$782$	−69.7670	−2.49486
$783$	15.2361	0.544492
$784$	−1.96358	−0.0701280
$785$	−10.1086	−0.360793
$786$	4.42362	0.157785
$787$	−31.8677	−1.13596	−0.567980	−	0.823042i	$-0.692275\pi$
$787$	−31.8677	−1.13596	−0.567980	+	0.823042i	$0.692275\pi$
$788$	47.2627	1.68366
$789$	7.76936	0.276597
$790$	5.65469	0.201185
$791$	3.44862	0.122619
$792$	13.2862	0.472105
$793$	87.9510	3.12323
$794$	−16.0533	−0.569712
$795$	−0.412245	−0.0146208
$796$	−9.97818	−0.353667
$797$	−25.1879	−0.892202	−0.446101	−	0.894983i	$-0.647188\pi$
$797$	−25.1879	−0.892202	−0.446101	+	0.894983i	$0.647188\pi$
$798$	1.38501	0.0490290
$799$	37.6921	1.33345
$800$	7.51024	0.265527
$801$	−46.5379	−1.64434
$802$	−1.44769	−0.0511196
$803$	42.2973	1.49264
$804$	6.90270	0.243440
$805$	5.95637	0.209934
$806$	23.8967	0.841727
$807$	−8.64664	−0.304376
$808$	5.12719	0.180374
$809$	5.80998	0.204268	0.102134	−	0.994771i	$-0.467433\pi$
$809$	5.80998	0.204268	0.102134	+	0.994771i	$0.467433\pi$
$810$	17.7133	0.622381
$811$	37.5399	1.31821	0.659103	−	0.752053i	$-0.270936\pi$
$811$	37.5399	1.31821	0.659103	+	0.752053i	$0.270936\pi$
$812$	−22.6948	−0.796430
$813$	2.17402	0.0762463
$814$	44.5196	1.56041
$815$	18.2499	0.639268
$816$	3.29428	0.115323
$817$	21.7328	0.760334
$818$	−64.4183	−2.25233
$819$	−19.7795	−0.691152
$820$	−27.9586	−0.976357
$821$	23.2076	0.809949	0.404975	−	0.914328i	$-0.367280\pi$
$821$	23.2076	0.809949	0.404975	+	0.914328i	$0.367280\pi$
$822$	6.18099	0.215587
$823$	20.1757	0.703279	0.351640	−	0.936135i	$-0.385624\pi$
$823$	20.1757	0.703279	0.351640	+	0.936135i	$0.385624\pi$
$824$	−21.9573	−0.764920
$825$	0.882930	0.0307397
$826$	7.93606	0.276131
$827$	52.2667	1.81749	0.908746	−	0.417349i	$-0.137041\pi$
$827$	52.2667	1.81749	0.908746	+	0.417349i	$0.137041\pi$
$828$	47.4172	1.64786
$829$	19.9397	0.692535	0.346267	−	0.938136i	$-0.387449\pi$
$829$	19.9397	0.692535	0.346267	+	0.938136i	$0.387449\pi$
$830$	0.667815	0.0231802
$831$	2.78567	0.0966338
$832$	−84.6875	−2.93601
$833$	−5.37853	−0.186355
$834$	−7.32890	−0.253779
$835$	22.2829	0.771132
$836$	−15.8282	−0.547430
$837$	2.96496	0.102484
$838$	14.2822	0.493369
$839$	−8.78192	−0.303186	−0.151593	−	0.988443i	$-0.548440\pi$
$839$	−8.78192	−0.303186	−0.151593	+	0.988443i	$0.548440\pi$
$840$	0.504391	0.0174032
$841$	39.4776	1.36130
$842$	32.1009	1.10627
$843$	6.30301	0.217087
$844$	−7.40652	−0.254943
$845$	−33.4329	−1.15013
$846$	−44.2990	−1.52303
$847$	−2.98770	−0.102659
$848$	−2.59512	−0.0891167
$849$	9.75018	0.334625
$850$	11.7130	0.401753
$851$	43.0178	1.47463
$852$	−6.61431	−0.226603
$853$	11.3215	0.387640	0.193820	−	0.981037i	$-0.437912\pi$
$853$	11.3215	0.387640	0.193820	+	0.981037i	$0.437912\pi$
$854$	−28.1082	−0.961843
$855$	−5.91840	−0.202405
$856$	−22.2499	−0.760484
$857$	0.0428415	0.00146344	0.000731719	−	1.00000i	$-0.499767\pi$
$857$	0.0428415	0.00146344	0.000731719		1.00000i	$0.499767\pi$
$858$	−13.1022	−0.447302
$859$	−22.5205	−0.768388	−0.384194	−	0.923252i	$-0.625521\pi$
$859$	−22.5205	−0.768388	−0.384194	+	0.923252i	$0.625521\pi$
$860$	29.2325	0.996820
$861$	3.17988	0.108370
$862$	0.124297	0.00423358
$863$	6.45812	0.219837	0.109918	−	0.993941i	$-0.464941\pi$
$863$	6.45812	0.219837	0.109918	+	0.993941i	$0.464941\pi$
$864$	−13.8278	−0.470431
$865$	−20.7313	−0.704887
$866$	−48.2878	−1.64089
$867$	3.72081	0.126365
$868$	−4.41644	−0.149904
$869$	7.34992	0.249329
$870$	−5.62117	−0.190576
$871$	54.9836	1.86305
$872$	2.58897	0.0876736
$873$	−28.6683	−0.970276
$874$	−26.4477	−0.894607
$875$	−1.00000	−0.0338062
$876$	12.7830	0.431898
$877$	26.3339	0.889232	0.444616	−	0.895721i	$-0.353340\pi$
$877$	26.3339	0.889232	0.444616	+	0.895721i	$0.353340\pi$
$878$	−7.37868	−0.249018
$879$	−1.83799	−0.0619939
$880$	5.55812	0.187364
$881$	40.0379	1.34891	0.674456	−	0.738315i	$-0.264378\pi$
$881$	40.0379	1.34891	0.674456	+	0.738315i	$0.264378\pi$
$882$	6.32132	0.212850
$883$	−10.2538	−0.345067	−0.172533	−	0.985004i	$-0.555195\pi$
$883$	−10.2538	−0.345067	−0.172533	+	0.985004i	$0.555195\pi$
$884$	−100.514	−3.38067
$885$	1.13670	0.0382099
$886$	44.2245	1.48575
$887$	−41.9751	−1.40939	−0.704694	−	0.709512i	$-0.748916\pi$
$887$	−41.9751	−1.40939	−0.704694	+	0.709512i	$0.748916\pi$
$888$	3.64279	0.122244
$889$	−17.5964	−0.590165
$890$	34.9148	1.17035
$891$	23.0235	0.771318
$892$	25.5662	0.856019
$893$	14.2885	0.478148
$894$	11.8679	0.396923
$895$	17.3837	0.581073
$896$	12.0447	0.402386
$897$	−12.6602	−0.422713
$898$	−8.81113	−0.294031
$899$	13.3258	0.444442
$900$	−7.96076	−0.265359
$901$	−7.10839	−0.236815
$902$	−62.8417	−2.09240
$903$	−3.32477	−0.110641
$904$	−5.57655	−0.185473
$905$	20.4277	0.679039
$906$	5.29203	0.175816
$907$	−24.6427	−0.818246	−0.409123	−	0.912479i	$-0.634165\pi$
$907$	−24.6427	−0.818246	−0.409123	+	0.912479i	$0.634165\pi$
$908$	63.5105	2.10767
$909$	9.20369	0.305267
$910$	14.8395	0.491923
$911$	−12.6940	−0.420571	−0.210286	−	0.977640i	$-0.567439\pi$
$911$	−12.6940	−0.420571	−0.210286	+	0.977640i	$0.567439\pi$
$912$	1.24882	0.0413524
$913$	0.868019	0.0287272
$914$	43.4928	1.43861
$915$	−4.02602	−0.133096
$916$	−2.74253	−0.0906158
$917$	−6.51216	−0.215051
$918$	−21.5659	−0.711781
$919$	26.1954	0.864107	0.432054	−	0.901848i	$-0.357789\pi$
$919$	26.1954	0.864107	0.432054	+	0.901848i	$0.357789\pi$
$920$	−9.63167	−0.317547
$921$	2.85688	0.0941375
$922$	35.5849	1.17193
$923$	−52.6864	−1.73419
$924$	2.42146	0.0796603
$925$	−7.22216	−0.237463
$926$	28.2703	0.929020
$927$	−39.4151	−1.29456
$928$	−62.1481	−2.04011
$929$	6.94186	0.227755	0.113877	−	0.993495i	$-0.463673\pi$
$929$	6.94186	0.227755	0.113877	+	0.993495i	$0.463673\pi$
$930$	−1.09389	−0.0358700
$931$	−2.03893	−0.0668231
$932$	9.91377	0.324736
$933$	3.24938	0.106380
$934$	−2.44649	−0.0800515
$935$	15.2245	0.497894
$936$	31.9842	1.04544
$937$	−34.3847	−1.12330	−0.561650	−	0.827375i	$-0.689833\pi$
$937$	−34.3847	−1.12330	−0.561650	+	0.827375i	$0.689833\pi$
$938$	−17.5722	−0.573751
$939$	−1.98537	−0.0647901
$940$	19.2193	0.626865
$941$	−22.0026	−0.717266	−0.358633	−	0.933479i	$-0.616757\pi$
$941$	−22.0026	−0.717266	−0.358633	+	0.933479i	$0.616757\pi$
$942$	−6.86665	−0.223728
$943$	−60.7219	−1.97738
$944$	7.15565	0.232897
$945$	1.84119	0.0598939
$946$	65.7049	2.13625
$947$	−49.4724	−1.60764	−0.803818	−	0.594875i	$-0.797202\pi$
$947$	−49.4724	−1.60764	−0.803818	+	0.594875i	$0.797202\pi$
$948$	2.22128	0.0721438
$949$	101.823	3.30533
$950$	4.44024	0.144060
$951$	2.33428	0.0756942
$952$	8.69729	0.281881
$953$	−16.7603	−0.542919	−0.271460	−	0.962450i	$-0.587506\pi$
$953$	−16.7603	−0.542919	−0.271460	+	0.962450i	$0.587506\pi$
$954$	8.35440	0.270484
$955$	−20.7038	−0.669958
$956$	−31.6766	−1.02449
$957$	−7.30635	−0.236181
$958$	−41.4482	−1.33913
$959$	−9.09925	−0.293830
$960$	3.87663	0.125118
$961$	−28.4068	−0.916347
$962$	107.173	3.45539
$963$	−39.9402	−1.28705
$964$	82.1682	2.64646
$965$	−17.0920	−0.550210
$966$	4.04608	0.130180
$967$	8.88473	0.285714	0.142857	−	0.989743i	$-0.454371\pi$
$967$	8.88473	0.285714	0.142857	+	0.989743i	$0.454371\pi$
$968$	4.83122	0.155281
$969$	3.42068	0.109888
$970$	21.5082	0.690588
$971$	0.479458	0.0153865	0.00769327	−	0.999970i	$-0.497551\pi$
$971$	0.479458	0.0153865	0.00769327	+	0.999970i	$0.497551\pi$
$972$	22.1067	0.709073
$973$	10.7891	0.345884
$974$	−25.5477	−0.818600
$975$	2.12550	0.0680704
$976$	−25.3441	−0.811246
$977$	−6.22821	−0.199258	−0.0996290	−	0.995025i	$-0.531766\pi$
$977$	−6.22821	−0.199258	−0.0996290	+	0.995025i	$0.531766\pi$
$978$	12.3969	0.396410
$979$	45.3819	1.45041
$980$	−2.74253	−0.0876070
$981$	4.64740	0.148380
$982$	−58.3532	−1.86213
$983$	36.3053	1.15796	0.578979	−	0.815342i	$-0.303451\pi$
$983$	36.3053	1.15796	0.578979	+	0.815342i	$0.303451\pi$
$984$	−5.14199	−0.163921
$985$	−17.2332	−0.549096
$986$	−96.9266	−3.08677
$987$	−2.18592	−0.0695786
$988$	−38.1036	−1.21224
$989$	63.4886	2.01882
$990$	−17.8931	−0.568681
$991$	4.79732	0.152392	0.0761959	−	0.997093i	$-0.475723\pi$
$991$	4.79732	0.152392	0.0761959	+	0.997093i	$0.475723\pi$
$992$	−12.0941	−0.383989
$993$	−5.28014	−0.167560
$994$	16.8380	0.534069
$995$	3.63831	0.115342
$996$	0.262331	0.00831228
$997$	−2.92465	−0.0926245	−0.0463123	−	0.998927i	$-0.514747\pi$
$997$	−2.92465	−0.0926245	−0.0463123	+	0.998927i	$0.514747\pi$
$998$	72.0208	2.27978
$999$	13.2974	0.420710

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8015.2.a.n.1.10	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8015.2.a.n.1.10	✓	68	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:	\( N \)	\(=\)	\( 8015 = 5 \cdot 7 \cdot 229 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8015.a (trivial)

\(f(q)\)	\(=\)	\(q-2.17774 q^{2} +0.311923 q^{3} +2.74253 q^{4} -1.00000 q^{5} -0.679286 q^{6} +1.00000 q^{7} -1.61704 q^{8} -2.90270 q^{9} +O(q^{10})\)	\(q-2.17774 q^{2} +0.311923 q^{3} +2.74253 q^{4} -1.00000 q^{5} -0.679286 q^{6} +1.00000 q^{7} -1.61704 q^{8} -2.90270 q^{9} +2.17774 q^{10} +2.83060 q^{11} +0.855459 q^{12} +6.81417 q^{13} -2.17774 q^{14} -0.311923 q^{15} -1.96358 q^{16} -5.37853 q^{17} +6.32132 q^{18} -2.03893 q^{19} -2.74253 q^{20} +0.311923 q^{21} -6.16430 q^{22} -5.95637 q^{23} -0.504391 q^{24} +1.00000 q^{25} -14.8395 q^{26} -1.84119 q^{27} +2.74253 q^{28} -8.27512 q^{29} +0.679286 q^{30} -1.61035 q^{31} +7.51024 q^{32} +0.882930 q^{33} +11.7130 q^{34} -1.00000 q^{35} -7.96076 q^{36} -7.22216 q^{37} +4.44024 q^{38} +2.12550 q^{39} +1.61704 q^{40} +10.1945 q^{41} -0.679286 q^{42} -10.6589 q^{43} +7.76301 q^{44} +2.90270 q^{45} +12.9714 q^{46} -7.00788 q^{47} -0.612487 q^{48} +1.00000 q^{49} -2.17774 q^{50} -1.67769 q^{51} +18.6881 q^{52} +1.32162 q^{53} +4.00962 q^{54} -2.83060 q^{55} -1.61704 q^{56} -0.635988 q^{57} +18.0210 q^{58} -3.64418 q^{59} -0.855459 q^{60} +12.9071 q^{61} +3.50692 q^{62} -2.90270 q^{63} -12.4281 q^{64} -6.81417 q^{65} -1.92279 q^{66} +8.06900 q^{67} -14.7508 q^{68} -1.85793 q^{69} +2.17774 q^{70} -7.73188 q^{71} +4.69378 q^{72} +14.9429 q^{73} +15.7280 q^{74} +0.311923 q^{75} -5.59182 q^{76} +2.83060 q^{77} -4.62877 q^{78} +2.59659 q^{79} +1.96358 q^{80} +8.13380 q^{81} -22.2008 q^{82} +0.306656 q^{83} +0.855459 q^{84} +5.37853 q^{85} +23.2124 q^{86} -2.58120 q^{87} -4.57719 q^{88} +16.0326 q^{89} -6.32132 q^{90} +6.81417 q^{91} -16.3355 q^{92} -0.502306 q^{93} +15.2613 q^{94} +2.03893 q^{95} +2.34262 q^{96} +9.87642 q^{97} -2.17774 q^{98} -8.21640 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9}+O(q^{10}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9	\( 68 q + 9 q^{2} + 83 q^{4} - 68 q^{5} + 5 q^{6} + 68 q^{7} + 30 q^{8} + 86 q^{9} - 9 q^{10} + 5 q^{11} + 9 q^{12} + 15 q^{13} + 9 q^{14} + 109 q^{16} + 7 q^{17} + 39 q^{18} + 20 q^{19} - 83 q^{20} + 56 q^{22} + 36 q^{23} + q^{24} + 68 q^{25} + q^{26} + 12 q^{27} + 83 q^{28} - 16 q^{29} - 5 q^{30} + 31 q^{31} + 79 q^{32} + 45 q^{33} + 31 q^{34} - 68 q^{35} + 114 q^{36} + 72 q^{37} + 8 q^{38} + 47 q^{39} - 30 q^{40} + 6 q^{41} + 5 q^{42} + 75 q^{43} + 15 q^{44} - 86 q^{45} + 29 q^{46} - 10 q^{47} + 44 q^{48} + 68 q^{49} + 9 q^{50} + 23 q^{51} + 37 q^{52} + 41 q^{53} + 4 q^{54} - 5 q^{55} + 30 q^{56} + 55 q^{57} + 66 q^{58} - 5 q^{59} - 9 q^{60} - 2 q^{61} + 3 q^{62} + 86 q^{63} + 162 q^{64} - 15 q^{65} - 23 q^{66} + 92 q^{67} + 35 q^{68} - 25 q^{69} - 9 q^{70} - 2 q^{71} + 128 q^{72} + 80 q^{73} + 18 q^{74} + 71 q^{76} + 5 q^{77} + 20 q^{78} + 100 q^{79} - 109 q^{80} + 140 q^{81} + 36 q^{82} - 60 q^{83} + 9 q^{84} - 7 q^{85} - 27 q^{86} + 24 q^{87} + 175 q^{88} + 19 q^{89} - 39 q^{90} + 15 q^{91} + 75 q^{92} + 37 q^{93} + 11 q^{94} - 20 q^{95} + 15 q^{96} + 96 q^{97} + 9 q^{98} + 3 q^{99}+O(q^{100}) \) 68 * q + 9 * q^2 + 83 * q^4 - 68 * q^5 + 5 * q^6 + 68 * q^7 + 30 * q^8 + 86 * q^9 - 9 * q^10 + 5 * q^11 + 9 * q^12 + 15 * q^13 + 9 * q^14 + 109 * q^16 + 7 * q^17 + 39 * q^18 + 20 * q^19 - 83 * q^20 + 56 * q^22 + 36 * q^23 + q^24 + 68 * q^25 + q^26 + 12 * q^27 + 83 * q^28 - 16 * q^29 - 5 * q^30 + 31 * q^31 + 79 * q^32 + 45 * q^33 + 31 * q^34 - 68 * q^35 + 114 * q^36 + 72 * q^37 + 8 * q^38 + 47 * q^39 - 30 * q^40 + 6 * q^41 + 5 * q^42 + 75 * q^43 + 15 * q^44 - 86 * q^45 + 29 * q^46 - 10 * q^47 + 44 * q^48 + 68 * q^49 + 9 * q^50 + 23 * q^51 + 37 * q^52 + 41 * q^53 + 4 * q^54 - 5 * q^55 + 30 * q^56 + 55 * q^57 + 66 * q^58 - 5 * q^59 - 9 * q^60 - 2 * q^61 + 3 * q^62 + 86 * q^63 + 162 * q^64 - 15 * q^65 - 23 * q^66 + 92 * q^67 + 35 * q^68 - 25 * q^69 - 9 * q^70 - 2 * q^71 + 128 * q^72 + 80 * q^73 + 18 * q^74 + 71 * q^76 + 5 * q^77 + 20 * q^78 + 100 * q^79 - 109 * q^80 + 140 * q^81 + 36 * q^82 - 60 * q^83 + 9 * q^84 - 7 * q^85 - 27 * q^86 + 24 * q^87 + 175 * q^88 + 19 * q^89 - 39 * q^90 + 15 * q^91 + 75 * q^92 + 37 * q^93 + 11 * q^94 - 20 * q^95 + 15 * q^96 + 96 * q^97 + 9 * q^98 + 3 * q^99

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