LMFDB - Embedded newform 4015.2.a.b.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4015,2,Mod(1,4015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4015, 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("4015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4015 = 5 \cdot 11 \cdot 73 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4015.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:	$32.0599364115$
Analytic rank:	$1$
Dimension:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	4015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.79465 q^{2} +0.618778 q^{3} +1.22075 q^{4} +1.00000 q^{5} +1.11049 q^{6} +1.73339 q^{7} -1.39847 q^{8} -2.61711 q^{9} +O(q^{10})$	\(q+1.79465 q^{2} +0.618778 q^{3} +1.22075 q^{4} +1.00000 q^{5} +1.11049 q^{6} +1.73339 q^{7} -1.39847 q^{8} -2.61711 q^{9} +1.79465 q^{10} +1.00000 q^{11} +0.755376 q^{12} -5.27176 q^{13} +3.11082 q^{14} +0.618778 q^{15} -4.95127 q^{16} -3.26989 q^{17} -4.69679 q^{18} -8.26284 q^{19} +1.22075 q^{20} +1.07258 q^{21} +1.79465 q^{22} +3.69682 q^{23} -0.865343 q^{24} +1.00000 q^{25} -9.46094 q^{26} -3.47575 q^{27} +2.11604 q^{28} +2.29388 q^{29} +1.11049 q^{30} -0.564341 q^{31} -6.08883 q^{32} +0.618778 q^{33} -5.86829 q^{34} +1.73339 q^{35} -3.19485 q^{36} -8.00782 q^{37} -14.8289 q^{38} -3.26205 q^{39} -1.39847 q^{40} -5.69799 q^{41} +1.92490 q^{42} -9.16211 q^{43} +1.22075 q^{44} -2.61711 q^{45} +6.63448 q^{46} +2.35742 q^{47} -3.06373 q^{48} -3.99537 q^{49} +1.79465 q^{50} -2.02334 q^{51} -6.43552 q^{52} +13.0424 q^{53} -6.23773 q^{54} +1.00000 q^{55} -2.42409 q^{56} -5.11286 q^{57} +4.11671 q^{58} +4.13316 q^{59} +0.755376 q^{60} +3.95298 q^{61} -1.01279 q^{62} -4.53647 q^{63} -1.02476 q^{64} -5.27176 q^{65} +1.11049 q^{66} +13.1659 q^{67} -3.99173 q^{68} +2.28751 q^{69} +3.11082 q^{70} +8.67726 q^{71} +3.65996 q^{72} -1.00000 q^{73} -14.3712 q^{74} +0.618778 q^{75} -10.0869 q^{76} +1.73339 q^{77} -5.85422 q^{78} -1.71333 q^{79} -4.95127 q^{80} +5.70063 q^{81} -10.2259 q^{82} -12.6513 q^{83} +1.30936 q^{84} -3.26989 q^{85} -16.4427 q^{86} +1.41940 q^{87} -1.39847 q^{88} +3.32327 q^{89} -4.69679 q^{90} -9.13800 q^{91} +4.51291 q^{92} -0.349202 q^{93} +4.23074 q^{94} -8.26284 q^{95} -3.76763 q^{96} +3.74918 q^{97} -7.17027 q^{98} -2.61711 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * 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 $

$2$	1.79465	1.26901	0.634503	−	0.772920i	$-0.281205\pi$
$2$	1.79465	1.26901	0.634503	+	0.772920i	$0.281205\pi$
$3$	0.618778	0.357252	0.178626	−	0.983917i	$-0.442835\pi$
$3$	0.618778	0.357252	0.178626	+	0.983917i	$0.442835\pi$
$4$	1.22075	0.610377
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	1.11049	0.453354
$7$	1.73339	0.655159	0.327579	−	0.944824i	$-0.393767\pi$
$7$	1.73339	0.655159	0.327579	+	0.944824i	$0.393767\pi$
$8$	−1.39847	−0.494434
$9$	−2.61711	−0.872371
$10$	1.79465	0.567517
$11$	1.00000	0.301511
$11$	1.00000	0.301511
$12$	0.755376	0.218058
$13$	−5.27176	−1.46212	−0.731062	−	0.682312i	$-0.760975\pi$
$13$	−5.27176	−1.46212	−0.731062	+	0.682312i	$0.760975\pi$
$14$	3.11082	0.831401
$15$	0.618778	0.159768
$16$	−4.95127	−1.23782
$17$	−3.26989	−0.793065	−0.396532	−	0.918021i	$-0.629787\pi$
$17$	−3.26989	−0.793065	−0.396532	+	0.918021i	$0.629787\pi$
$18$	−4.69679	−1.10704
$19$	−8.26284	−1.89562	−0.947812	−	0.318829i	$-0.896710\pi$
$19$	−8.26284	−1.89562	−0.947812	+	0.318829i	$0.896710\pi$
$20$	1.22075	0.272969
$21$	1.07258	0.234056
$22$	1.79465	0.382620
$23$	3.69682	0.770840	0.385420	−	0.922741i	$-0.374057\pi$
$23$	3.69682	0.770840	0.385420	+	0.922741i	$0.374057\pi$
$24$	−0.865343	−0.176637
$25$	1.00000	0.200000
$26$	−9.46094	−1.85544
$27$	−3.47575	−0.668908
$28$	2.11604	0.399894
$29$	2.29388	0.425963	0.212982	−	0.977056i	$-0.431683\pi$
$29$	2.29388	0.425963	0.212982	+	0.977056i	$0.431683\pi$
$30$	1.11049	0.202746
$31$	−0.564341	−0.101359	−0.0506793	−	0.998715i	$-0.516139\pi$
$31$	−0.564341	−0.101359	−0.0506793	+	0.998715i	$0.516139\pi$
$32$	−6.08883	−1.07636
$33$	0.618778	0.107715
$34$	−5.86829	−1.00640
$35$	1.73339	0.292996
$36$	−3.19485	−0.532475
$37$	−8.00782	−1.31648	−0.658239	−	0.752809i	$-0.728698\pi$
$37$	−8.00782	−1.31648	−0.658239	+	0.752809i	$0.728698\pi$
$38$	−14.8289	−2.40556
$39$	−3.26205	−0.522346
$40$	−1.39847	−0.221118
$41$	−5.69799	−0.889876	−0.444938	−	0.895561i	$-0.646774\pi$
$41$	−5.69799	−0.889876	−0.444938	+	0.895561i	$0.646774\pi$
$42$	1.92490	0.297019
$43$	−9.16211	−1.39721	−0.698604	−	0.715508i	$-0.746195\pi$
$43$	−9.16211	−1.39721	−0.698604	+	0.715508i	$0.746195\pi$
$44$	1.22075	0.184036
$45$	−2.61711	−0.390136
$46$	6.63448	0.978201
$47$	2.35742	0.343865	0.171933	−	0.985109i	$-0.444999\pi$
$47$	2.35742	0.343865	0.171933	+	0.985109i	$0.444999\pi$
$48$	−3.06373	−0.442212
$49$	−3.99537	−0.570767
$50$	1.79465	0.253801
$51$	−2.02334	−0.283324
$52$	−6.43552	−0.892446
$53$	13.0424	1.79151	0.895755	−	0.444548i	$-0.146636\pi$
$53$	13.0424	1.79151	0.895755	+	0.444548i	$0.146636\pi$
$54$	−6.23773	−0.848848
$55$	1.00000	0.134840
$56$	−2.42409	−0.323933
$57$	−5.11286	−0.677215
$58$	4.11671	0.540550
$59$	4.13316	0.538092	0.269046	−	0.963127i	$-0.413292\pi$
$59$	4.13316	0.538092	0.269046	+	0.963127i	$0.413292\pi$
$60$	0.755376	0.0975186
$61$	3.95298	0.506127	0.253064	−	0.967450i	$-0.418562\pi$
$61$	3.95298	0.506127	0.253064	+	0.967450i	$0.418562\pi$
$62$	−1.01279	−0.128625
$63$	−4.53647	−0.571542
$64$	−1.02476	−0.128095
$65$	−5.27176	−0.653881
$66$	1.11049	0.136692
$67$	13.1659	1.60847	0.804235	−	0.594311i	$-0.202575\pi$
$67$	13.1659	1.60847	0.804235	+	0.594311i	$0.202575\pi$
$68$	−3.99173	−0.484068
$69$	2.28751	0.275384
$70$	3.11082	0.371814
$71$	8.67726	1.02980	0.514901	−	0.857250i	$-0.327829\pi$
$71$	8.67726	1.02980	0.514901	+	0.857250i	$0.327829\pi$
$72$	3.65996	0.431330
$73$	−1.00000	−0.117041
$73$	−1.00000	−0.117041
$74$	−14.3712	−1.67062
$75$	0.618778	0.0714503
$76$	−10.0869	−1.15705
$77$	1.73339	0.197538
$78$	−5.85422	−0.662860
$79$	−1.71333	−0.192765	−0.0963824	−	0.995344i	$-0.530727\pi$
$79$	−1.71333	−0.192765	−0.0963824	+	0.995344i	$0.530727\pi$
$80$	−4.95127	−0.553569
$81$	5.70063	0.633403
$82$	−10.2259	−1.12926
$83$	−12.6513	−1.38866	−0.694329	−	0.719657i	$-0.744299\pi$
$83$	−12.6513	−1.38866	−0.694329	+	0.719657i	$0.744299\pi$
$84$	1.30936	0.142863
$85$	−3.26989	−0.354669
$86$	−16.4427	−1.77307
$87$	1.41940	0.152176
$88$	−1.39847	−0.149077
$89$	3.32327	0.352266	0.176133	−	0.984366i	$-0.443641\pi$
$89$	3.32327	0.352266	0.176133	+	0.984366i	$0.443641\pi$
$90$	−4.69679	−0.495085
$91$	−9.13800	−0.957923
$92$	4.51291	0.470503
$93$	−0.349202	−0.0362105
$94$	4.23074	0.436367
$95$	−8.26284	−0.847749
$96$	−3.76763	−0.384532
$97$	3.74918	0.380671	0.190336	−	0.981719i	$-0.439042\pi$
$97$	3.74918	0.380671	0.190336	+	0.981719i	$0.439042\pi$
$98$	−7.17027	−0.724307
$99$	−2.61711	−0.263030
$100$	1.22075	0.122075
$101$	6.39334	0.636161	0.318080	−	0.948064i	$-0.396962\pi$
$101$	6.39334	0.636161	0.318080	+	0.948064i	$0.396962\pi$
$102$	−3.63117	−0.359539
$103$	−18.0075	−1.77433	−0.887166	−	0.461451i	$-0.847329\pi$
$103$	−18.0075	−1.77433	−0.887166	+	0.461451i	$0.847329\pi$
$104$	7.37240	0.722923
$105$	1.07258	0.104673
$106$	23.4065	2.27344
$107$	10.1881	0.984917	0.492459	−	0.870336i	$-0.336098\pi$
$107$	10.1881	0.984917	0.492459	+	0.870336i	$0.336098\pi$
$108$	−4.24303	−0.408286
$109$	−17.9384	−1.71819	−0.859094	−	0.511818i	$-0.828972\pi$
$109$	−17.9384	−1.71819	−0.859094	+	0.511818i	$0.828972\pi$
$110$	1.79465	0.171113
$111$	−4.95506	−0.470314
$112$	−8.58246	−0.810967
$113$	−2.13118	−0.200485	−0.100242	−	0.994963i	$-0.531962\pi$
$113$	−2.13118	−0.200485	−0.100242	+	0.994963i	$0.531962\pi$
$114$	−9.17577	−0.859390
$115$	3.69682	0.344730
$116$	2.80027	0.259998
$117$	13.7968	1.27551
$118$	7.41756	0.682842
$119$	−5.66798	−0.519583
$120$	−0.865343	−0.0789946
$121$	1.00000	0.0909091
$122$	7.09420	0.642279
$123$	−3.52579	−0.317910
$124$	−0.688921	−0.0618670
$125$	1.00000	0.0894427
$126$	−8.14136	−0.725290
$127$	−10.6666	−0.946508	−0.473254	−	0.880926i	$-0.656921\pi$
$127$	−10.6666	−0.946508	−0.473254	+	0.880926i	$0.656921\pi$
$128$	10.3386	0.913810
$129$	−5.66931	−0.499155
$130$	−9.46094	−0.829779
$131$	−4.87907	−0.426286	−0.213143	−	0.977021i	$-0.568370\pi$
$131$	−4.87907	−0.426286	−0.213143	+	0.977021i	$0.568370\pi$
$132$	0.755376	0.0657470
$133$	−14.3227	−1.24193
$134$	23.6281	2.04116
$135$	−3.47575	−0.299145
$136$	4.57284	0.392118
$137$	22.3484	1.90935	0.954674	−	0.297653i	$-0.0962037\pi$
$137$	22.3484	1.90935	0.954674	+	0.297653i	$0.0962037\pi$
$138$	4.10527	0.349464
$139$	−9.16143	−0.777063	−0.388531	−	0.921436i	$-0.627017\pi$
$139$	−9.16143	−0.777063	−0.388531	+	0.921436i	$0.627017\pi$
$140$	2.11604	0.178838
$141$	1.45872	0.122846
$142$	15.5726	1.30682
$143$	−5.27176	−0.440847
$144$	12.9580	1.07984
$145$	2.29388	0.190497
$146$	−1.79465	−0.148526
$147$	−2.47225	−0.203907
$148$	−9.77558	−0.803548
$149$	13.7893	1.12966	0.564831	−	0.825206i	$-0.308941\pi$
$149$	13.7893	1.12966	0.564831	+	0.825206i	$0.308941\pi$
$150$	1.11049	0.0906709
$151$	11.0240	0.897119	0.448559	−	0.893753i	$-0.351937\pi$
$151$	11.0240	0.897119	0.448559	+	0.893753i	$0.351937\pi$
$152$	11.5553	0.937261
$153$	8.55767	0.691847
$154$	3.11082	0.250677
$155$	−0.564341	−0.0453290
$156$	−3.98216	−0.318828
$157$	1.43506	0.114531	0.0572653	−	0.998359i	$-0.481762\pi$
$157$	1.43506	0.114531	0.0572653	+	0.998359i	$0.481762\pi$
$158$	−3.07482	−0.244620
$159$	8.07034	0.640020
$160$	−6.08883	−0.481364
$161$	6.40802	0.505022
$162$	10.2306	0.803793
$163$	13.0576	1.02275	0.511374	−	0.859358i	$-0.329137\pi$
$163$	13.0576	1.02275	0.511374	+	0.859358i	$0.329137\pi$
$164$	−6.95584	−0.543160
$165$	0.618778	0.0481718
$166$	−22.7046	−1.76222
$167$	−8.66962	−0.670876	−0.335438	−	0.942062i	$-0.608884\pi$
$167$	−8.66962	−0.670876	−0.335438	+	0.942062i	$0.608884\pi$
$168$	−1.49997	−0.115725
$169$	14.7914	1.13780
$170$	−5.86829	−0.450078
$171$	21.6248	1.65369
$172$	−11.1847	−0.852824
$173$	−4.02008	−0.305641	−0.152821	−	0.988254i	$-0.548836\pi$
$173$	−4.02008	−0.305641	−0.152821	+	0.988254i	$0.548836\pi$
$174$	2.54733	0.193112
$175$	1.73339	0.131032
$176$	−4.95127	−0.373216
$177$	2.55751	0.192234
$178$	5.96409	0.447028
$179$	−4.17352	−0.311944	−0.155972	−	0.987762i	$-0.549851\pi$
$179$	−4.17352	−0.311944	−0.155972	+	0.987762i	$0.549851\pi$
$180$	−3.19485	−0.238130
$181$	−14.7751	−1.09822	−0.549112	−	0.835749i	$-0.685034\pi$
$181$	−14.7751	−1.09822	−0.549112	+	0.835749i	$0.685034\pi$
$182$	−16.3995	−1.21561
$183$	2.44602	0.180815
$184$	−5.16989	−0.381129
$185$	−8.00782	−0.588747
$186$	−0.626693	−0.0459514
$187$	−3.26989	−0.239118
$188$	2.87783	0.209888
$189$	−6.02481	−0.438241
$190$	−14.8289	−1.07580
$191$	7.95690	0.575741	0.287871	−	0.957669i	$-0.407053\pi$
$191$	7.95690	0.575741	0.287871	+	0.957669i	$0.407053\pi$
$192$	−0.634099	−0.0457622
$193$	5.23372	0.376732	0.188366	−	0.982099i	$-0.439681\pi$
$193$	5.23372	0.376732	0.188366	+	0.982099i	$0.439681\pi$
$194$	6.72844	0.483074
$195$	−3.26205	−0.233600
$196$	−4.87736	−0.348383
$197$	−13.8226	−0.984818	−0.492409	−	0.870364i	$-0.663884\pi$
$197$	−13.8226	−0.984818	−0.492409	+	0.870364i	$0.663884\pi$
$198$	−4.69679	−0.333787
$199$	−21.2272	−1.50476	−0.752379	−	0.658731i	$-0.771094\pi$
$199$	−21.2272	−1.50476	−0.752379	+	0.658731i	$0.771094\pi$
$200$	−1.39847	−0.0988868
$201$	8.14677	0.574629
$202$	11.4738	0.807292
$203$	3.97619	0.279074
$204$	−2.46999	−0.172934
$205$	−5.69799	−0.397965
$206$	−32.3171	−2.25164
$207$	−9.67500	−0.672459
$208$	26.1019	1.80984
$209$	−8.26284	−0.571552
$210$	1.92490	0.132831
$211$	−2.51544	−0.173170	−0.0865849	−	0.996244i	$-0.527595\pi$
$211$	−2.51544	−0.173170	−0.0865849	+	0.996244i	$0.527595\pi$
$212$	15.9216	1.09350
$213$	5.36930	0.367898
$214$	18.2840	1.24987
$215$	−9.16211	−0.624851
$216$	4.86073	0.330731
$217$	−0.978221	−0.0664060
$218$	−32.1931	−2.18039
$219$	−0.618778	−0.0418131
$220$	1.22075	0.0823032
$221$	17.2381	1.15956
$222$	−8.89258	−0.596831
$223$	−24.0120	−1.60796	−0.803981	−	0.594656i	$-0.797288\pi$
$223$	−24.0120	−1.60796	−0.803981	+	0.594656i	$0.797288\pi$
$224$	−10.5543	−0.705189
$225$	−2.61711	−0.174474
$226$	−3.82472	−0.254417
$227$	23.2987	1.54639	0.773194	−	0.634170i	$-0.218658\pi$
$227$	23.2987	1.54639	0.773194	+	0.634170i	$0.218658\pi$
$228$	−6.24154	−0.413356
$229$	−16.5483	−1.09354	−0.546772	−	0.837281i	$-0.684144\pi$
$229$	−16.5483	−1.09354	−0.546772	+	0.837281i	$0.684144\pi$
$230$	6.63448	0.437465
$231$	1.07258	0.0705707
$232$	−3.20793	−0.210611
$233$	−7.82788	−0.512821	−0.256411	−	0.966568i	$-0.582540\pi$
$233$	−7.82788	−0.512821	−0.256411	+	0.966568i	$0.582540\pi$
$234$	24.7604	1.61864
$235$	2.35742	0.153781
$236$	5.04557	0.328439
$237$	−1.06017	−0.0688655
$238$	−10.1720	−0.659354
$239$	3.51724	0.227511	0.113756	−	0.993509i	$-0.463712\pi$
$239$	3.51724	0.227511	0.113756	+	0.993509i	$0.463712\pi$
$240$	−3.06373	−0.197763
$241$	5.63667	0.363090	0.181545	−	0.983383i	$-0.441890\pi$
$241$	5.63667	0.363090	0.181545	+	0.983383i	$0.441890\pi$
$242$	1.79465	0.115364
$243$	13.9547	0.895192
$244$	4.82562	0.308928
$245$	−3.99537	−0.255255
$246$	−6.32754	−0.403429
$247$	43.5597	2.77164
$248$	0.789214	0.0501151
$249$	−7.82833	−0.496100
$250$	1.79465	0.113503
$251$	−15.2764	−0.964235	−0.482118	−	0.876106i	$-0.660132\pi$
$251$	−15.2764	−0.964235	−0.482118	+	0.876106i	$0.660132\pi$
$252$	−5.53792	−0.348856
$253$	3.69682	0.232417
$254$	−19.1428	−1.20112
$255$	−2.02334	−0.126706
$256$	20.6036	1.28773
$257$	8.20290	0.511683	0.255841	−	0.966719i	$-0.417647\pi$
$257$	8.20290	0.511683	0.255841	+	0.966719i	$0.417647\pi$
$258$	−10.1744	−0.633431
$259$	−13.8807	−0.862502
$260$	−6.43552	−0.399114
$261$	−6.00336	−0.371598
$262$	−8.75619	−0.540960
$263$	−22.6136	−1.39441	−0.697207	−	0.716870i	$-0.745574\pi$
$263$	−22.6136	−1.39441	−0.697207	+	0.716870i	$0.745574\pi$
$264$	−0.865343	−0.0532582
$265$	13.0424	0.801188
$266$	−25.7042	−1.57602
$267$	2.05637	0.125848
$268$	16.0723	0.981774
$269$	13.5520	0.826278	0.413139	−	0.910668i	$-0.364432\pi$
$269$	13.5520	0.826278	0.413139	+	0.910668i	$0.364432\pi$
$270$	−6.23773	−0.379616
$271$	21.2199	1.28902	0.644508	−	0.764598i	$-0.277062\pi$
$271$	21.2199	1.28902	0.644508	+	0.764598i	$0.277062\pi$
$272$	16.1901	0.981669
$273$	−5.65439	−0.342219
$274$	40.1074	2.42298
$275$	1.00000	0.0603023
$276$	2.79249	0.168088
$277$	−25.8755	−1.55471	−0.777355	−	0.629062i	$-0.783439\pi$
$277$	−25.8755	−1.55471	−0.777355	+	0.629062i	$0.783439\pi$
$278$	−16.4415	−0.986097
$279$	1.47694	0.0884224
$280$	−2.42409	−0.144867
$281$	−28.1797	−1.68106	−0.840531	−	0.541763i	$-0.817757\pi$
$281$	−28.1797	−1.68106	−0.840531	+	0.541763i	$0.817757\pi$
$282$	2.61789	0.155893
$283$	−17.7319	−1.05405	−0.527027	−	0.849849i	$-0.676693\pi$
$283$	−17.7319	−1.05405	−0.527027	+	0.849849i	$0.676693\pi$
$284$	10.5928	0.628567
$285$	−5.11286	−0.302860
$286$	−9.46094	−0.559437
$287$	−9.87682	−0.583010
$288$	15.9352	0.938989
$289$	−6.30782	−0.371048
$290$	4.11671	0.241741
$291$	2.31991	0.135995
$292$	−1.22075	−0.0714392
$293$	15.2249	0.889450	0.444725	−	0.895667i	$-0.353301\pi$
$293$	15.2249	0.889450	0.444725	+	0.895667i	$0.353301\pi$
$294$	−4.43681	−0.258760
$295$	4.13316	0.240642
$296$	11.1987	0.650912
$297$	−3.47575	−0.201683
$298$	24.7469	1.43355
$299$	−19.4887	−1.12706
$300$	0.755376	0.0436116
$301$	−15.8815	−0.915393
$302$	19.7841	1.13845
$303$	3.95606	0.227269
$304$	40.9115	2.34644
$305$	3.95298	0.226347
$306$	15.3580	0.877958
$307$	−31.3929	−1.79169	−0.895845	−	0.444367i	$-0.853429\pi$
$307$	−31.3929	−1.79169	−0.895845	+	0.444367i	$0.853429\pi$
$308$	2.11604	0.120573
$309$	−11.1426	−0.633883
$310$	−1.01279	−0.0575227
$311$	−17.7352	−1.00567	−0.502836	−	0.864382i	$-0.667710\pi$
$311$	−17.7352	−1.00567	−0.502836	+	0.864382i	$0.667710\pi$
$312$	4.56188	0.258265
$313$	−6.39253	−0.361327	−0.180664	−	0.983545i	$-0.557825\pi$
$313$	−6.39253	−0.361327	−0.180664	+	0.983545i	$0.557825\pi$
$314$	2.57543	0.145340
$315$	−4.53647	−0.255601
$316$	−2.09156	−0.117659
$317$	15.9805	0.897556	0.448778	−	0.893643i	$-0.351859\pi$
$317$	15.9805	0.897556	0.448778	+	0.893643i	$0.351859\pi$
$318$	14.4834	0.812189
$319$	2.29388	0.128433
$320$	−1.02476	−0.0572859
$321$	6.30415	0.351863
$322$	11.5001	0.640877
$323$	27.0186	1.50335
$324$	6.95906	0.386615
$325$	−5.27176	−0.292425
$326$	23.4337	1.29787
$327$	−11.0999	−0.613825
$328$	7.96847	0.439985
$329$	4.08632	0.225286
$330$	1.11049	0.0611303
$331$	12.6919	0.697612	0.348806	−	0.937195i	$-0.386587\pi$
$331$	12.6919	0.697612	0.348806	+	0.937195i	$0.386587\pi$
$332$	−15.4441	−0.847605
$333$	20.9574	1.14846
$334$	−15.5589	−0.851345
$335$	13.1659	0.719330
$336$	−5.31064	−0.289719
$337$	−11.1315	−0.606372	−0.303186	−	0.952931i	$-0.598050\pi$
$337$	−11.1315	−0.606372	−0.303186	+	0.952931i	$0.598050\pi$
$338$	26.5454	1.44388
$339$	−1.31873	−0.0716235
$340$	−3.99173	−0.216482
$341$	−0.564341	−0.0305608
$342$	38.8088	2.09854
$343$	−19.0592	−1.02910
$344$	12.8129	0.690828
$345$	2.28751	0.123155
$346$	−7.21463	−0.387861
$347$	−1.02912	−0.0552461	−0.0276231	−	0.999618i	$-0.508794\pi$
$347$	−1.02912	−0.0552461	−0.0276231	+	0.999618i	$0.508794\pi$
$348$	1.73274	0.0928848
$349$	−24.1647	−1.29351	−0.646753	−	0.762700i	$-0.723874\pi$
$349$	−24.1647	−1.29351	−0.646753	+	0.762700i	$0.723874\pi$
$350$	3.11082	0.166280
$351$	18.3233	0.978025
$352$	−6.08883	−0.324536
$353$	3.09244	0.164594	0.0822969	−	0.996608i	$-0.473774\pi$
$353$	3.09244	0.164594	0.0822969	+	0.996608i	$0.473774\pi$
$354$	4.58982	0.243946
$355$	8.67726	0.460541
$356$	4.05690	0.215015
$357$	−3.50722	−0.185622
$358$	−7.48999	−0.395859
$359$	4.84555	0.255738	0.127869	−	0.991791i	$-0.459186\pi$
$359$	4.84555	0.255738	0.127869	+	0.991791i	$0.459186\pi$
$360$	3.65996	0.192897
$361$	49.2744	2.59339
$362$	−26.5161	−1.39365
$363$	0.618778	0.0324774
$364$	−11.1552	−0.584694
$365$	−1.00000	−0.0523424
$366$	4.38973	0.229455
$367$	−26.6873	−1.39306	−0.696532	−	0.717526i	$-0.745275\pi$
$367$	−26.6873	−1.39306	−0.696532	+	0.717526i	$0.745275\pi$
$368$	−18.3039	−0.954159
$369$	14.9123	0.776303
$370$	−14.3712	−0.747124
$371$	22.6075	1.17372
$372$	−0.426289	−0.0221021
$373$	12.1505	0.629127	0.314564	−	0.949236i	$-0.398142\pi$
$373$	12.1505	0.629127	0.314564	+	0.949236i	$0.398142\pi$
$374$	−5.86829	−0.303442
$375$	0.618778	0.0319535
$376$	−3.29679	−0.170019
$377$	−12.0928	−0.622811
$378$	−10.8124	−0.556130
$379$	37.5737	1.93003	0.965017	−	0.262188i	$-0.0844440\pi$
$379$	37.5737	1.93003	0.965017	+	0.262188i	$0.0844440\pi$
$380$	−10.0869	−0.517447
$381$	−6.60026	−0.338141
$382$	14.2798	0.730620
$383$	−9.86515	−0.504086	−0.252043	−	0.967716i	$-0.581102\pi$
$383$	−9.86515	−0.504086	−0.252043	+	0.967716i	$0.581102\pi$
$384$	6.39728	0.326460
$385$	1.73339	0.0883416
$386$	9.39268	0.478075
$387$	23.9783	1.21888
$388$	4.57682	0.232353
$389$	−4.35817	−0.220968	−0.110484	−	0.993878i	$-0.535240\pi$
$389$	−4.35817	−0.220968	−0.110484	+	0.993878i	$0.535240\pi$
$390$	−5.85422	−0.296440
$391$	−12.0882	−0.611326
$392$	5.58741	0.282207
$393$	−3.01906	−0.152291
$394$	−24.8066	−1.24974
$395$	−1.71333	−0.0862070
$396$	−3.19485	−0.160547
$397$	27.1568	1.36296	0.681479	−	0.731837i	$-0.261337\pi$
$397$	27.1568	1.36296	0.681479	+	0.731837i	$0.261337\pi$
$398$	−38.0953	−1.90955
$399$	−8.86256	−0.443683
$400$	−4.95127	−0.247563
$401$	−29.2580	−1.46108	−0.730538	−	0.682873i	$-0.760730\pi$
$401$	−29.2580	−1.46108	−0.730538	+	0.682873i	$0.760730\pi$
$402$	14.6206	0.729207
$403$	2.97507	0.148199
$404$	7.80469	0.388298
$405$	5.70063	0.283266
$406$	7.13585	0.354146
$407$	−8.00782	−0.396933
$408$	2.82957	0.140085
$409$	18.0935	0.894667	0.447334	−	0.894367i	$-0.352374\pi$
$409$	18.0935	0.894667	0.447334	+	0.894367i	$0.352374\pi$
$410$	−10.2259	−0.505020
$411$	13.8287	0.682118
$412$	−21.9827	−1.08301
$413$	7.16437	0.352535
$414$	−17.3632	−0.853354
$415$	−12.6513	−0.621027
$416$	32.0989	1.57378
$417$	−5.66889	−0.277607
$418$	−14.8289	−0.725303
$419$	−6.96014	−0.340025	−0.170013	−	0.985442i	$-0.554381\pi$
$419$	−6.96014	−0.340025	−0.170013	+	0.985442i	$0.554381\pi$
$420$	1.30936	0.0638901
$421$	−28.1730	−1.37307	−0.686535	−	0.727097i	$-0.740869\pi$
$421$	−28.1730	−1.37307	−0.686535	+	0.727097i	$0.740869\pi$
$422$	−4.51432	−0.219754
$423$	−6.16964	−0.299978
$424$	−18.2394	−0.885784
$425$	−3.26989	−0.158613
$426$	9.63599	0.466865
$427$	6.85204	0.331594
$428$	12.4371	0.601171
$429$	−3.26205	−0.157493
$430$	−16.4427	−0.792940
$431$	4.46798	0.215215	0.107608	−	0.994193i	$-0.465681\pi$
$431$	4.46798	0.215215	0.107608	+	0.994193i	$0.465681\pi$
$432$	17.2093	0.827985
$433$	31.6166	1.51940	0.759699	−	0.650275i	$-0.225346\pi$
$433$	31.6166	1.51940	0.759699	+	0.650275i	$0.225346\pi$
$434$	−1.75556	−0.0842696
$435$	1.41940	0.0680552
$436$	−21.8984	−1.04874
$437$	−30.5462	−1.46122
$438$	−1.11049	−0.0530611
$439$	−11.4661	−0.547245	−0.273623	−	0.961837i	$-0.588222\pi$
$439$	−11.4661	−0.547245	−0.273623	+	0.961837i	$0.588222\pi$
$440$	−1.39847	−0.0666695
$441$	10.4563	0.497921
$442$	30.9362	1.47149
$443$	4.01767	0.190885	0.0954427	−	0.995435i	$-0.469573\pi$
$443$	4.01767	0.190885	0.0954427	+	0.995435i	$0.469573\pi$
$444$	−6.04891	−0.287069
$445$	3.32327	0.157538
$446$	−43.0930	−2.04051
$447$	8.53251	0.403574
$448$	−1.77631	−0.0839226
$449$	10.2870	0.485473	0.242736	−	0.970092i	$-0.421955\pi$
$449$	10.2870	0.485473	0.242736	+	0.970092i	$0.421955\pi$
$450$	−4.69679	−0.221409
$451$	−5.69799	−0.268308
$452$	−2.60165	−0.122371
$453$	6.82140	0.320497
$454$	41.8129	1.96237
$455$	−9.13800	−0.428396
$456$	7.15018	0.334838
$457$	−20.3767	−0.953182	−0.476591	−	0.879125i	$-0.658128\pi$
$457$	−20.3767	−0.953182	−0.476591	+	0.879125i	$0.658128\pi$
$458$	−29.6984	−1.38771
$459$	11.3653	0.530487
$460$	4.51291	0.210415
$461$	6.92395	0.322481	0.161240	−	0.986915i	$-0.448451\pi$
$461$	6.92395	0.322481	0.161240	+	0.986915i	$0.448451\pi$
$462$	1.92490	0.0895546
$463$	−25.5241	−1.18621	−0.593104	−	0.805126i	$-0.702098\pi$
$463$	−25.5241	−1.18621	−0.593104	+	0.805126i	$0.702098\pi$
$464$	−11.3576	−0.527265
$465$	−0.349202	−0.0161938
$466$	−14.0483	−0.650774
$467$	−36.1057	−1.67077	−0.835386	−	0.549664i	$-0.814756\pi$
$467$	−36.1057	−1.67077	−0.835386	+	0.549664i	$0.814756\pi$
$468$	16.8425	0.778545
$469$	22.8216	1.05380
$470$	4.23074	0.195149
$471$	0.887986	0.0409162
$472$	−5.78010	−0.266051
$473$	−9.16211	−0.421274
$474$	−1.90263	−0.0873908
$475$	−8.26284	−0.379125
$476$	−6.91921	−0.317142
$477$	−34.1334	−1.56286
$478$	6.31220	0.288713
$479$	25.8954	1.18319	0.591596	−	0.806235i	$-0.298498\pi$
$479$	25.8954	1.18319	0.591596	+	0.806235i	$0.298498\pi$
$480$	−3.76763	−0.171968
$481$	42.2153	1.92485
$482$	10.1158	0.460763
$483$	3.96514	0.180420
$484$	1.22075	0.0554888
$485$	3.74918	0.170241
$486$	25.0437	1.13600
$487$	−28.9582	−1.31222	−0.656111	−	0.754664i	$-0.727800\pi$
$487$	−28.9582	−1.31222	−0.656111	+	0.754664i	$0.727800\pi$
$488$	−5.52813	−0.250246
$489$	8.07974	0.365378
$490$	−7.17027	−0.323920
$491$	9.25875	0.417841	0.208921	−	0.977933i	$-0.433005\pi$
$491$	9.25875	0.417841	0.208921	+	0.977933i	$0.433005\pi$
$492$	−4.30412	−0.194045
$493$	−7.50075	−0.337817
$494$	78.1742	3.51722
$495$	−2.61711	−0.117631
$496$	2.79420	0.125463
$497$	15.0410	0.674683
$498$	−14.0491	−0.629555
$499$	−10.7984	−0.483402	−0.241701	−	0.970351i	$-0.577705\pi$
$499$	−10.7984	−0.483402	−0.241701	+	0.970351i	$0.577705\pi$
$500$	1.22075	0.0545938
$501$	−5.36457	−0.239671
$502$	−27.4157	−1.22362
$503$	−30.2941	−1.35075	−0.675374	−	0.737475i	$-0.736018\pi$
$503$	−30.2941	−1.35075	−0.675374	+	0.737475i	$0.736018\pi$
$504$	6.34412	0.282590
$505$	6.39334	0.284500
$506$	6.63448	0.294939
$507$	9.15262	0.406482
$508$	−13.0213	−0.577727
$509$	28.3095	1.25480	0.627398	−	0.778698i	$-0.284120\pi$
$509$	28.3095	1.25480	0.627398	+	0.778698i	$0.284120\pi$
$510$	−3.63117	−0.160791
$511$	−1.73339	−0.0766805
$512$	16.2990	0.720322
$513$	28.7195	1.26800
$514$	14.7213	0.649329
$515$	−18.0075	−0.793505
$516$	−6.92083	−0.304673
$517$	2.35742	0.103679
$518$	−24.9109	−1.09452
$519$	−2.48754	−0.109191
$520$	7.37240	0.323301
$521$	4.92522	0.215778	0.107889	−	0.994163i	$-0.465591\pi$
$521$	4.92522	0.215778	0.107889	+	0.994163i	$0.465591\pi$
$522$	−10.7739	−0.471561
$523$	30.6180	1.33883	0.669416	−	0.742888i	$-0.266545\pi$
$523$	30.6180	1.33883	0.669416	+	0.742888i	$0.266545\pi$
$524$	−5.95614	−0.260195
$525$	1.07258	0.0468113
$526$	−40.5834	−1.76952
$527$	1.84533	0.0803839
$528$	−3.06373	−0.133332
$529$	−9.33353	−0.405806
$530$	23.4065	1.01671
$531$	−10.8170	−0.469416
$532$	−17.4845	−0.758049
$533$	30.0384	1.30111
$534$	3.69045	0.159701
$535$	10.1881	0.440468
$536$	−18.4121	−0.795283
$537$	−2.58248	−0.111442
$538$	24.3210	1.04855
$539$	−3.99537	−0.172093
$540$	−4.24303	−0.182591
$541$	37.5142	1.61286	0.806431	−	0.591328i	$-0.201396\pi$
$541$	37.5142	1.61286	0.806431	+	0.591328i	$0.201396\pi$
$542$	38.0821	1.63577
$543$	−9.14250	−0.392342
$544$	19.9098	0.853626
$545$	−17.9384	−0.768397
$546$	−10.1476	−0.434278
$547$	26.4337	1.13022	0.565111	−	0.825015i	$-0.308833\pi$
$547$	26.4337	1.13022	0.565111	+	0.825015i	$0.308833\pi$
$548$	27.2818	1.16542
$549$	−10.3454	−0.441531
$550$	1.79465	0.0765240
$551$	−18.9540	−0.807467
$552$	−3.19901	−0.136159
$553$	−2.96987	−0.126292
$554$	−46.4374	−1.97294
$555$	−4.95506	−0.210331
$556$	−11.1839	−0.474301
$557$	16.0430	0.679765	0.339882	−	0.940468i	$-0.389613\pi$
$557$	16.0430	0.679765	0.339882	+	0.940468i	$0.389613\pi$
$558$	2.65059	0.112209
$559$	48.3004	2.04289
$560$	−8.58246	−0.362675
$561$	−2.02334	−0.0854253
$562$	−50.5727	−2.13328
$563$	14.8077	0.624070	0.312035	−	0.950071i	$-0.398989\pi$
$563$	14.8077	0.624070	0.312035	+	0.950071i	$0.398989\pi$
$564$	1.78074	0.0749826
$565$	−2.13118	−0.0896596
$566$	−31.8225	−1.33760
$567$	9.88139	0.414980
$568$	−12.1349	−0.509169
$569$	−39.1357	−1.64065	−0.820326	−	0.571896i	$-0.806208\pi$
$569$	−39.1357	−1.64065	−0.820326	+	0.571896i	$0.806208\pi$
$570$	−9.17577	−0.384331
$571$	24.7166	1.03436	0.517179	−	0.855878i	$-0.326982\pi$
$571$	24.7166	1.03436	0.517179	+	0.855878i	$0.326982\pi$
$572$	−6.43552	−0.269083
$573$	4.92356	0.205685
$574$	−17.7254	−0.739844
$575$	3.69682	0.154168
$576$	2.68192	0.111747
$577$	44.6164	1.85740	0.928702	−	0.370827i	$-0.120926\pi$
$577$	44.6164	1.85740	0.928702	+	0.370827i	$0.120926\pi$
$578$	−11.3203	−0.470863
$579$	3.23851	0.134588
$580$	2.80027	0.116275
$581$	−21.9296	−0.909792
$582$	4.16341	0.172579
$583$	13.0424	0.540161
$584$	1.39847	0.0578691
$585$	13.7968	0.570427
$586$	27.3234	1.12872
$587$	45.4254	1.87491	0.937453	−	0.348113i	$-0.113177\pi$
$587$	45.4254	1.87491	0.937453	+	0.348113i	$0.113177\pi$
$588$	−3.01800	−0.124460
$589$	4.66306	0.192138
$590$	7.41756	0.305376
$591$	−8.55310	−0.351828
$592$	39.6489	1.62956
$593$	27.4662	1.12790	0.563952	−	0.825808i	$-0.309280\pi$
$593$	27.4662	1.12790	0.563952	+	0.825808i	$0.309280\pi$
$594$	−6.23773	−0.255937
$595$	−5.66798	−0.232365
$596$	16.8333	0.689520
$597$	−13.1349	−0.537577
$598$	−34.9754	−1.43025
$599$	−12.2468	−0.500390	−0.250195	−	0.968196i	$-0.580495\pi$
$599$	−12.2468	−0.500390	−0.250195	+	0.968196i	$0.580495\pi$
$600$	−0.865343	−0.0353275
$601$	−11.0294	−0.449900	−0.224950	−	0.974370i	$-0.572222\pi$
$601$	−11.0294	−0.449900	−0.224950	+	0.974370i	$0.572222\pi$
$602$	−28.5016	−1.16164
$603$	−34.4567	−1.40318
$604$	13.4576	0.547581
$605$	1.00000	0.0406558
$606$	7.09972	0.288406
$607$	12.4506	0.505353	0.252676	−	0.967551i	$-0.418689\pi$
$607$	12.4506	0.505353	0.252676	+	0.967551i	$0.418689\pi$
$608$	50.3110	2.04038
$609$	2.46038	0.0996995
$610$	7.09420	0.287236
$611$	−12.4278	−0.502773
$612$	10.4468	0.422287
$613$	−14.1311	−0.570750	−0.285375	−	0.958416i	$-0.592118\pi$
$613$	−14.1311	−0.570750	−0.285375	+	0.958416i	$0.592118\pi$
$614$	−56.3392	−2.27367
$615$	−3.52579	−0.142174
$616$	−2.42409	−0.0976694
$617$	3.51709	0.141593	0.0707963	−	0.997491i	$-0.477446\pi$
$617$	3.51709	0.141593	0.0707963	+	0.997491i	$0.477446\pi$
$618$	−19.9971	−0.804401
$619$	19.9492	0.801825	0.400913	−	0.916116i	$-0.368693\pi$
$619$	19.9492	0.801825	0.400913	+	0.916116i	$0.368693\pi$
$620$	−0.688921	−0.0276678
$621$	−12.8492	−0.515621
$622$	−31.8284	−1.27620
$623$	5.76051	0.230790
$624$	16.1513	0.646568
$625$	1.00000	0.0400000
$626$	−11.4723	−0.458527
$627$	−5.11286	−0.204188
$628$	1.75186	0.0699068
$629$	26.1847	1.04405
$630$	−8.14136	−0.324360
$631$	−14.9778	−0.596258	−0.298129	−	0.954526i	$-0.596363\pi$
$631$	−14.9778	−0.596258	−0.298129	+	0.954526i	$0.596363\pi$
$632$	2.39604	0.0953095
$633$	−1.55650	−0.0618652
$634$	28.6794	1.13900
$635$	−10.6666	−0.423291
$636$	9.85190	0.390653
$637$	21.0626	0.834532
$638$	4.11671	0.162982
$639$	−22.7094	−0.898369
$640$	10.3386	0.408668
$641$	−30.8715	−1.21935	−0.609676	−	0.792651i	$-0.708700\pi$
$641$	−30.8715	−1.21935	−0.609676	+	0.792651i	$0.708700\pi$
$642$	11.3137	0.446517
$643$	−33.1895	−1.30886	−0.654432	−	0.756121i	$-0.727092\pi$
$643$	−33.1895	−1.30886	−0.654432	+	0.756121i	$0.727092\pi$
$644$	7.82261	0.308254
$645$	−5.66931	−0.223229
$646$	48.4887	1.90776
$647$	1.83066	0.0719706	0.0359853	−	0.999352i	$-0.488543\pi$
$647$	1.83066	0.0719706	0.0359853	+	0.999352i	$0.488543\pi$
$648$	−7.97216	−0.313176
$649$	4.13316	0.162241
$650$	−9.46094	−0.371089
$651$	−0.605302	−0.0237236
$652$	15.9401	0.624262
$653$	−46.8376	−1.83290	−0.916448	−	0.400154i	$-0.868956\pi$
$653$	−46.8376	−1.83290	−0.916448	+	0.400154i	$0.868956\pi$
$654$	−19.9204	−0.778948
$655$	−4.87907	−0.190641
$656$	28.2123	1.10150
$657$	2.61711	0.102103
$658$	7.33351	0.285890
$659$	18.0494	0.703106	0.351553	−	0.936168i	$-0.385654\pi$
$659$	18.0494	0.703106	0.351553	+	0.936168i	$0.385654\pi$
$660$	0.755376	0.0294030
$661$	2.11347	0.0822046	0.0411023	−	0.999155i	$-0.486913\pi$
$661$	2.11347	0.0822046	0.0411023	+	0.999155i	$0.486913\pi$
$662$	22.7775	0.885274
$663$	10.6665	0.414254
$664$	17.6924	0.686600
$665$	−14.3227	−0.555410
$666$	37.6111	1.45740
$667$	8.48007	0.328350
$668$	−10.5835	−0.409487
$669$	−14.8581	−0.574447
$670$	23.6281	0.912834
$671$	3.95298	0.152603
$672$	−6.53077	−0.251930
$673$	21.5879	0.832152	0.416076	−	0.909330i	$-0.363405\pi$
$673$	21.5879	0.832152	0.416076	+	0.909330i	$0.363405\pi$
$674$	−19.9771	−0.769490
$675$	−3.47575	−0.133782
$676$	18.0567	0.694489
$677$	43.8729	1.68617	0.843086	−	0.537779i	$-0.180737\pi$
$677$	43.8729	1.68617	0.843086	+	0.537779i	$0.180737\pi$
$678$	−2.36665	−0.0908907
$679$	6.49877	0.249400
$680$	4.57284	0.175361
$681$	14.4167	0.552449
$682$	−1.01279	−0.0387818
$683$	−2.33006	−0.0891572	−0.0445786	−	0.999006i	$-0.514195\pi$
$683$	−2.33006	−0.0891572	−0.0445786	+	0.999006i	$0.514195\pi$
$684$	26.3985	1.00937
$685$	22.3484	0.853887
$686$	−34.2046	−1.30594
$687$	−10.2397	−0.390670
$688$	45.3641	1.72949
$689$	−68.7564	−2.61941
$690$	4.10527	0.156285
$691$	45.2589	1.72173	0.860864	−	0.508835i	$-0.169924\pi$
$691$	45.2589	1.72173	0.860864	+	0.508835i	$0.169924\pi$
$692$	−4.90753	−0.186556
$693$	−4.53647	−0.172326
$694$	−1.84691	−0.0701077
$695$	−9.16143	−0.347513
$696$	−1.98500	−0.0752410
$697$	18.6318	0.705730
$698$	−43.3671	−1.64147
$699$	−4.84372	−0.183206
$700$	2.11604	0.0799788
$701$	28.7957	1.08760	0.543798	−	0.839216i	$-0.316986\pi$
$701$	28.7957	1.08760	0.543798	+	0.839216i	$0.316986\pi$
$702$	32.8838	1.24112
$703$	66.1673	2.49555
$704$	−1.02476	−0.0386221
$705$	1.45872	0.0549386
$706$	5.54983	0.208871
$707$	11.0821	0.416786
$708$	3.12209	0.117335
$709$	−20.0902	−0.754502	−0.377251	−	0.926111i	$-0.623131\pi$
$709$	−20.0902	−0.754502	−0.377251	+	0.926111i	$0.623131\pi$
$710$	15.5726	0.584430
$711$	4.48398	0.168162
$712$	−4.64749	−0.174172
$713$	−2.08627	−0.0781313
$714$	−6.29422	−0.235555
$715$	−5.27176	−0.197153
$716$	−5.09484	−0.190403
$717$	2.17639	0.0812788
$718$	8.69604	0.324533
$719$	12.3354	0.460034	0.230017	−	0.973187i	$-0.426122\pi$
$719$	12.3354	0.460034	0.230017	+	0.973187i	$0.426122\pi$
$720$	12.9580	0.482917
$721$	−31.2140	−1.16247
$722$	88.4302	3.29103
$723$	3.48785	0.129714
$724$	−18.0368	−0.670331
$725$	2.29388	0.0851927
$726$	1.11049	0.0412140
$727$	−32.3501	−1.19980	−0.599900	−	0.800075i	$-0.704793\pi$
$727$	−32.3501	−1.19980	−0.599900	+	0.800075i	$0.704793\pi$
$728$	12.7792	0.473630
$729$	−8.46705	−0.313594
$730$	−1.79465	−0.0664228
$731$	29.9591	1.10808
$732$	2.98598	0.110365
$733$	−10.3375	−0.381826	−0.190913	−	0.981607i	$-0.561145\pi$
$733$	−10.3375	−0.381826	−0.190913	+	0.981607i	$0.561145\pi$
$734$	−47.8942	−1.76781
$735$	−2.47225	−0.0911902
$736$	−22.5093	−0.829704
$737$	13.1659	0.484972
$738$	26.7623	0.985133
$739$	−15.1575	−0.557577	−0.278788	−	0.960353i	$-0.589933\pi$
$739$	−15.1575	−0.557577	−0.278788	+	0.960353i	$0.589933\pi$
$740$	−9.77558	−0.359358
$741$	26.9538	0.990171
$742$	40.5725	1.48946
$743$	−26.8288	−0.984252	−0.492126	−	0.870524i	$-0.663780\pi$
$743$	−26.8288	−0.984252	−0.492126	+	0.870524i	$0.663780\pi$
$744$	0.488348	0.0179037
$745$	13.7893	0.505200
$746$	21.8058	0.798366
$747$	33.1098	1.21143
$748$	−3.99173	−0.145952
$749$	17.6599	0.645277
$750$	1.11049	0.0405493
$751$	−27.6445	−1.00876	−0.504382	−	0.863481i	$-0.668280\pi$
$751$	−27.6445	−1.00876	−0.504382	+	0.863481i	$0.668280\pi$
$752$	−11.6722	−0.425642
$753$	−9.45267	−0.344475
$754$	−21.7023	−0.790351
$755$	11.0240	0.401204
$756$	−7.35481	−0.267492
$757$	46.5099	1.69043	0.845216	−	0.534425i	$-0.179472\pi$
$757$	46.5099	1.69043	0.845216	+	0.534425i	$0.179472\pi$
$758$	67.4316	2.44922
$759$	2.28751	0.0830313
$760$	11.5553	0.419156
$761$	−22.9002	−0.830133	−0.415066	−	0.909791i	$-0.636242\pi$
$761$	−22.9002	−0.830133	−0.415066	+	0.909791i	$0.636242\pi$
$762$	−11.8451	−0.429104
$763$	−31.0942	−1.12569
$764$	9.71342	0.351419
$765$	8.55767	0.309403
$766$	−17.7045	−0.639688
$767$	−21.7890	−0.786756
$768$	12.7491	0.460042
$769$	−37.8546	−1.36507	−0.682535	−	0.730853i	$-0.739123\pi$
$769$	−37.8546	−1.36507	−0.682535	+	0.730853i	$0.739123\pi$
$770$	3.11082	0.112106
$771$	5.07577	0.182799
$772$	6.38909	0.229948
$773$	−35.8241	−1.28850	−0.644252	−	0.764813i	$-0.722831\pi$
$773$	−35.8241	−1.28850	−0.644252	+	0.764813i	$0.722831\pi$
$774$	43.0325	1.54677
$775$	−0.564341	−0.0202717
$776$	−5.24311	−0.188217
$777$	−8.58904	−0.308130
$778$	−7.82138	−0.280410
$779$	47.0815	1.68687
$780$	−3.98216	−0.142584
$781$	8.67726	0.310497
$782$	−21.6940	−0.775776
$783$	−7.97296	−0.284930
$784$	19.7821	0.706505
$785$	1.43506	0.0512196
$786$	−5.41814	−0.193259
$787$	−9.27759	−0.330710	−0.165355	−	0.986234i	$-0.552877\pi$
$787$	−9.27759	−0.330710	−0.165355	+	0.986234i	$0.552877\pi$
$788$	−16.8740	−0.601110
$789$	−13.9928	−0.498157
$790$	−3.07482	−0.109397
$791$	−3.69417	−0.131349
$792$	3.65996	0.130051
$793$	−20.8392	−0.740020
$794$	48.7368	1.72960
$795$	8.07034	0.286226
$796$	−25.9132	−0.918470
$797$	−7.51230	−0.266099	−0.133050	−	0.991109i	$-0.542477\pi$
$797$	−7.51230	−0.266099	−0.133050	+	0.991109i	$0.542477\pi$
$798$	−15.9052	−0.563037
$799$	−7.70851	−0.272707
$800$	−6.08883	−0.215273
$801$	−8.69738	−0.307307
$802$	−52.5078	−1.85411
$803$	−1.00000	−0.0352892
$804$	9.94520	0.350740
$805$	6.40802	0.225853
$806$	5.33920	0.188065
$807$	8.38565	0.295189
$808$	−8.94090	−0.314540
$809$	−7.39878	−0.260127	−0.130064	−	0.991506i	$-0.541518\pi$
$809$	−7.39878	−0.260127	−0.130064	+	0.991506i	$0.541518\pi$
$810$	10.2306	0.359467
$811$	−1.50320	−0.0527844	−0.0263922	−	0.999652i	$-0.508402\pi$
$811$	−1.50320	−0.0527844	−0.0263922	+	0.999652i	$0.508402\pi$
$812$	4.85395	0.170340
$813$	13.1304	0.460503
$814$	−14.3712	−0.503711
$815$	13.0576	0.457387
$816$	10.0181	0.350703
$817$	75.7050	2.64858
$818$	32.4715	1.13534
$819$	23.9152	0.835664
$820$	−6.95584	−0.242909
$821$	27.2318	0.950397	0.475198	−	0.879879i	$-0.342376\pi$
$821$	27.2318	0.950397	0.475198	+	0.879879i	$0.342376\pi$
$822$	24.8176	0.865612
$823$	34.1042	1.18880	0.594399	−	0.804170i	$-0.297390\pi$
$823$	34.1042	1.18880	0.594399	+	0.804170i	$0.297390\pi$
$824$	25.1830	0.877290
$825$	0.618778	0.0215431
$826$	12.8575	0.447370
$827$	16.3054	0.566995	0.283498	−	0.958973i	$-0.408505\pi$
$827$	16.3054	0.566995	0.283498	+	0.958973i	$0.408505\pi$
$828$	−11.8108	−0.410453
$829$	2.81330	0.0977100	0.0488550	−	0.998806i	$-0.484443\pi$
$829$	2.81330	0.0977100	0.0488550	+	0.998806i	$0.484443\pi$
$830$	−22.7046	−0.788087
$831$	−16.0112	−0.555423
$832$	5.40229	0.187291
$833$	13.0644	0.452655
$834$	−10.1737	−0.352285
$835$	−8.66962	−0.300025
$836$	−10.0869	−0.348862
$837$	1.96151	0.0677995
$838$	−12.4910	−0.431494
$839$	−14.8146	−0.511458	−0.255729	−	0.966749i	$-0.582315\pi$
$839$	−14.8146	−0.511458	−0.255729	+	0.966749i	$0.582315\pi$
$840$	−1.49997	−0.0517540
$841$	−23.7381	−0.818555
$842$	−50.5606	−1.74243
$843$	−17.4370	−0.600562
$844$	−3.07073	−0.105699
$845$	14.7914	0.508841
$846$	−11.0723	−0.380674
$847$	1.73339	0.0595599
$848$	−64.5764	−2.21756
$849$	−10.9721	−0.376562
$850$	−5.86829	−0.201281
$851$	−29.6035	−1.01479
$852$	6.55459	0.224557
$853$	−11.8829	−0.406862	−0.203431	−	0.979089i	$-0.565209\pi$
$853$	−11.8829	−0.406862	−0.203431	+	0.979089i	$0.565209\pi$
$854$	12.2970	0.420794
$855$	21.6248	0.739552
$856$	−14.2477	−0.486977
$857$	−17.4313	−0.595441	−0.297720	−	0.954653i	$-0.596226\pi$
$857$	−17.4313	−0.595441	−0.297720	+	0.954653i	$0.596226\pi$
$858$	−5.85422	−0.199860
$859$	−5.45827	−0.186234	−0.0931168	−	0.995655i	$-0.529683\pi$
$859$	−5.45827	−0.186234	−0.0931168	+	0.995655i	$0.529683\pi$
$860$	−11.1847	−0.381395
$861$	−6.11156	−0.208281
$862$	8.01844	0.273109
$863$	35.1168	1.19539	0.597694	−	0.801724i	$-0.296084\pi$
$863$	35.1168	1.19539	0.597694	+	0.801724i	$0.296084\pi$
$864$	21.1632	0.719988
$865$	−4.02008	−0.136687
$866$	56.7407	1.92813
$867$	−3.90314	−0.132558
$868$	−1.19417	−0.0405327
$869$	−1.71333	−0.0581208
$870$	2.54733	0.0863625
$871$	−69.4075	−2.35178
$872$	25.0863	0.849531
$873$	−9.81202	−0.332087
$874$	−54.8196	−1.85430
$875$	1.73339	0.0585992
$876$	−0.755376	−0.0255218
$877$	8.64364	0.291875	0.145938	−	0.989294i	$-0.453380\pi$
$877$	8.64364	0.291875	0.145938	+	0.989294i	$0.453380\pi$
$878$	−20.5775	−0.694458
$879$	9.42085	0.317757
$880$	−4.95127	−0.166907
$881$	−43.6618	−1.47100	−0.735502	−	0.677522i	$-0.763054\pi$
$881$	−43.6618	−1.47100	−0.735502	+	0.677522i	$0.763054\pi$
$882$	18.7654	0.631865
$883$	−34.2270	−1.15183	−0.575916	−	0.817509i	$-0.695354\pi$
$883$	−34.2270	−1.15183	−0.575916	+	0.817509i	$0.695354\pi$
$884$	21.0434	0.707768
$885$	2.55751	0.0859697
$886$	7.21030	0.242235
$887$	31.5024	1.05775	0.528874	−	0.848700i	$-0.322614\pi$
$887$	31.5024	1.05775	0.528874	+	0.848700i	$0.322614\pi$
$888$	6.92951	0.232539
$889$	−18.4893	−0.620113
$890$	5.96409	0.199917
$891$	5.70063	0.190978
$892$	−29.3127	−0.981462
$893$	−19.4790	−0.651840
$894$	15.3128	0.512138
$895$	−4.17352	−0.139505
$896$	17.9208	0.598691
$897$	−12.0592	−0.402645
$898$	18.4615	0.616068
$899$	−1.29453	−0.0431751
$900$	−3.19485	−0.106495
$901$	−42.6472	−1.42078
$902$	−10.2259	−0.340484
$903$	−9.82711	−0.327026
$904$	2.98040	0.0991265
$905$	−14.7751	−0.491141
$906$	12.2420	0.406713
$907$	−18.3748	−0.610126	−0.305063	−	0.952332i	$-0.598678\pi$
$907$	−18.3748	−0.610126	−0.305063	+	0.952332i	$0.598678\pi$
$908$	28.4419	0.943879
$909$	−16.7321	−0.554969
$910$	−16.3995	−0.543637
$911$	30.4242	1.00800	0.503999	−	0.863704i	$-0.331861\pi$
$911$	30.4242	1.00800	0.503999	+	0.863704i	$0.331861\pi$
$912$	25.3151	0.838268
$913$	−12.6513	−0.418696
$914$	−36.5690	−1.20959
$915$	2.44602	0.0808628
$916$	−20.2014	−0.667475
$917$	−8.45731	−0.279285
$918$	20.3967	0.673191
$919$	50.7167	1.67299	0.836495	−	0.547974i	$-0.184601\pi$
$919$	50.7167	1.67299	0.836495	+	0.547974i	$0.184601\pi$
$920$	−5.16989	−0.170446
$921$	−19.4253	−0.640084
$922$	12.4260	0.409230
$923$	−45.7444	−1.50570
$924$	1.30936	0.0430747
$925$	−8.00782	−0.263296
$926$	−45.8068	−1.50530
$927$	47.1277	1.54788
$928$	−13.9671	−0.458492
$929$	27.0853	0.888640	0.444320	−	0.895868i	$-0.353445\pi$
$929$	27.0853	0.888640	0.444320	+	0.895868i	$0.353445\pi$
$930$	−0.626693	−0.0205501
$931$	33.0131	1.08196
$932$	−9.55592	−0.313014
$933$	−10.9742	−0.359278
$934$	−64.7969	−2.12022
$935$	−3.26989	−0.106937
$936$	−19.2944	−0.630658
$937$	−16.6777	−0.544835	−0.272418	−	0.962179i	$-0.587823\pi$
$937$	−16.6777	−0.544835	−0.272418	+	0.962179i	$0.587823\pi$
$938$	40.9567	1.33728
$939$	−3.95556	−0.129085
$940$	2.87783	0.0938646
$941$	−32.6951	−1.06583	−0.532914	−	0.846169i	$-0.678903\pi$
$941$	−32.6951	−1.06583	−0.532914	+	0.846169i	$0.678903\pi$
$942$	1.59362	0.0519229
$943$	−21.0644	−0.685952
$944$	−20.4644	−0.666059
$945$	−6.02481	−0.195987
$946$	−16.4427	−0.534600
$947$	−38.3251	−1.24540	−0.622698	−	0.782462i	$-0.713964\pi$
$947$	−38.3251	−1.24540	−0.622698	+	0.782462i	$0.713964\pi$
$948$	−1.29421	−0.0420339
$949$	5.27176	0.171129
$950$	−14.8289	−0.481112
$951$	9.88840	0.320653
$952$	7.92651	0.256900
$953$	5.32535	0.172505	0.0862524	−	0.996273i	$-0.472511\pi$
$953$	5.32535	0.172505	0.0862524	+	0.996273i	$0.472511\pi$
$954$	−61.2574	−1.98328
$955$	7.95690	0.257479
$956$	4.29369	0.138868
$957$	1.41940	0.0458828
$958$	46.4731	1.50148
$959$	38.7383	1.25093
$960$	−0.634099	−0.0204655
$961$	−30.6815	−0.989726
$962$	75.7616	2.44265
$963$	−26.6633	−0.859214
$964$	6.88099	0.221622
$965$	5.23372	0.168480
$966$	7.11602	0.228954
$967$	16.7737	0.539405	0.269702	−	0.962944i	$-0.413075\pi$
$967$	16.7737	0.539405	0.269702	+	0.962944i	$0.413075\pi$
$968$	−1.39847	−0.0449485
$969$	16.7185	0.537075
$970$	6.72844	0.216037
$971$	−5.72832	−0.183830	−0.0919152	−	0.995767i	$-0.529299\pi$
$971$	−5.72832	−0.183830	−0.0919152	+	0.995767i	$0.529299\pi$
$972$	17.0352	0.546404
$973$	−15.8803	−0.509099
$974$	−51.9698	−1.66522
$975$	−3.26205	−0.104469
$976$	−19.5723	−0.626493
$977$	−43.0020	−1.37576	−0.687878	−	0.725826i	$-0.741458\pi$
$977$	−43.0020	−1.37576	−0.687878	+	0.725826i	$0.741458\pi$
$978$	14.5003	0.463667
$979$	3.32327	0.106212
$980$	−4.87736	−0.155802
$981$	46.9469	1.49890
$982$	16.6162	0.530243
$983$	−15.7354	−0.501881	−0.250941	−	0.968003i	$-0.580740\pi$
$983$	−15.7354	−0.501881	−0.250941	+	0.968003i	$0.580740\pi$
$984$	4.93071	0.157185
$985$	−13.8226	−0.440424
$986$	−13.4612	−0.428691
$987$	2.52853	0.0804839
$988$	53.1757	1.69174
$989$	−33.8707	−1.07702
$990$	−4.69679	−0.149274
$991$	−10.5878	−0.336331	−0.168166	−	0.985759i	$-0.553784\pi$
$991$	−10.5878	−0.336331	−0.168166	+	0.985759i	$0.553784\pi$
$992$	3.43618	0.109099
$993$	7.85349	0.249223
$994$	26.9934	0.856177
$995$	−21.2272	−0.672948
$996$	−9.55647	−0.302808
$997$	1.99284	0.0631140	0.0315570	−	0.999502i	$-0.489953\pi$
$997$	1.99284	0.0631140	0.0315570	+	0.999502i	$0.489953\pi$
$998$	−19.3793	−0.613440
$999$	27.8332	0.880602

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4015.2.a.b.1.20	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4015.2.a.b.1.20	✓	23	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:	\( N \)	\(=\)	\( 4015 = 5 \cdot 11 \cdot 73 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4015.a (trivial)

\(f(q)\)	\(=\)	\(q+1.79465 q^{2} +0.618778 q^{3} +1.22075 q^{4} +1.00000 q^{5} +1.11049 q^{6} +1.73339 q^{7} -1.39847 q^{8} -2.61711 q^{9} +O(q^{10})\)	\(q+1.79465 q^{2} +0.618778 q^{3} +1.22075 q^{4} +1.00000 q^{5} +1.11049 q^{6} +1.73339 q^{7} -1.39847 q^{8} -2.61711 q^{9} +1.79465 q^{10} +1.00000 q^{11} +0.755376 q^{12} -5.27176 q^{13} +3.11082 q^{14} +0.618778 q^{15} -4.95127 q^{16} -3.26989 q^{17} -4.69679 q^{18} -8.26284 q^{19} +1.22075 q^{20} +1.07258 q^{21} +1.79465 q^{22} +3.69682 q^{23} -0.865343 q^{24} +1.00000 q^{25} -9.46094 q^{26} -3.47575 q^{27} +2.11604 q^{28} +2.29388 q^{29} +1.11049 q^{30} -0.564341 q^{31} -6.08883 q^{32} +0.618778 q^{33} -5.86829 q^{34} +1.73339 q^{35} -3.19485 q^{36} -8.00782 q^{37} -14.8289 q^{38} -3.26205 q^{39} -1.39847 q^{40} -5.69799 q^{41} +1.92490 q^{42} -9.16211 q^{43} +1.22075 q^{44} -2.61711 q^{45} +6.63448 q^{46} +2.35742 q^{47} -3.06373 q^{48} -3.99537 q^{49} +1.79465 q^{50} -2.02334 q^{51} -6.43552 q^{52} +13.0424 q^{53} -6.23773 q^{54} +1.00000 q^{55} -2.42409 q^{56} -5.11286 q^{57} +4.11671 q^{58} +4.13316 q^{59} +0.755376 q^{60} +3.95298 q^{61} -1.01279 q^{62} -4.53647 q^{63} -1.02476 q^{64} -5.27176 q^{65} +1.11049 q^{66} +13.1659 q^{67} -3.99173 q^{68} +2.28751 q^{69} +3.11082 q^{70} +8.67726 q^{71} +3.65996 q^{72} -1.00000 q^{73} -14.3712 q^{74} +0.618778 q^{75} -10.0869 q^{76} +1.73339 q^{77} -5.85422 q^{78} -1.71333 q^{79} -4.95127 q^{80} +5.70063 q^{81} -10.2259 q^{82} -12.6513 q^{83} +1.30936 q^{84} -3.26989 q^{85} -16.4427 q^{86} +1.41940 q^{87} -1.39847 q^{88} +3.32327 q^{89} -4.69679 q^{90} -9.13800 q^{91} +4.51291 q^{92} -0.349202 q^{93} +4.23074 q^{94} -8.26284 q^{95} -3.76763 q^{96} +3.74918 q^{97} -7.17027 q^{98} -2.61711 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9	\( 23 q - 5 q^{2} - 3 q^{3} + 15 q^{4} + 23 q^{5} - 15 q^{6} - 10 q^{7} - 12 q^{8} + 8 q^{9} - 5 q^{10} + 23 q^{11} + 4 q^{12} - 19 q^{13} - 5 q^{14} - 3 q^{15} - q^{16} - 26 q^{17} + 5 q^{18} - 34 q^{19} + 15 q^{20} - 26 q^{21} - 5 q^{22} - 4 q^{23} - 23 q^{24} + 23 q^{25} - 13 q^{26} - 3 q^{27} - 28 q^{28} - 36 q^{29} - 15 q^{30} - 24 q^{31} - 19 q^{32} - 3 q^{33} - 4 q^{34} - 10 q^{35} - 14 q^{36} + 4 q^{37} - 15 q^{38} - 34 q^{39} - 12 q^{40} - 74 q^{41} + 7 q^{42} - 15 q^{43} + 15 q^{44} + 8 q^{45} + 3 q^{46} + q^{47} + 29 q^{48} + q^{49} - 5 q^{50} - 47 q^{51} - 23 q^{52} - 6 q^{53} - 11 q^{54} + 23 q^{55} - 20 q^{56} - 19 q^{57} + 22 q^{58} - 17 q^{59} + 4 q^{60} - 59 q^{61} + 38 q^{62} - 21 q^{63} - 18 q^{64} - 19 q^{65} - 15 q^{66} + 12 q^{67} + 5 q^{68} - 8 q^{69} - 5 q^{70} - 34 q^{71} + 21 q^{72} - 23 q^{73} - 9 q^{74} - 3 q^{75} - 53 q^{76} - 10 q^{77} + 23 q^{78} - 62 q^{79} - q^{80} + 7 q^{81} + 24 q^{82} - 8 q^{83} + 46 q^{84} - 26 q^{85} - 11 q^{86} + q^{87} - 12 q^{88} - 77 q^{89} + 5 q^{90} - 6 q^{91} + 47 q^{92} - 32 q^{94} - 34 q^{95} - 53 q^{96} - 21 q^{97} - 3 q^{98} + 8 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 - 3 * q^3 + 15 * q^4 + 23 * q^5 - 15 * q^6 - 10 * q^7 - 12 * q^8 + 8 * q^9 - 5 * q^10 + 23 * q^11 + 4 * q^12 - 19 * q^13 - 5 * q^14 - 3 * q^15 - q^16 - 26 * q^17 + 5 * q^18 - 34 * q^19 + 15 * q^20 - 26 * q^21 - 5 * q^22 - 4 * q^23 - 23 * q^24 + 23 * q^25 - 13 * q^26 - 3 * q^27 - 28 * q^28 - 36 * q^29 - 15 * q^30 - 24 * q^31 - 19 * q^32 - 3 * q^33 - 4 * q^34 - 10 * q^35 - 14 * q^36 + 4 * q^37 - 15 * q^38 - 34 * q^39 - 12 * q^40 - 74 * q^41 + 7 * q^42 - 15 * q^43 + 15 * q^44 + 8 * q^45 + 3 * q^46 + q^47 + 29 * q^48 + q^49 - 5 * q^50 - 47 * q^51 - 23 * q^52 - 6 * q^53 - 11 * q^54 + 23 * q^55 - 20 * q^56 - 19 * q^57 + 22 * q^58 - 17 * q^59 + 4 * q^60 - 59 * q^61 + 38 * q^62 - 21 * q^63 - 18 * q^64 - 19 * q^65 - 15 * q^66 + 12 * q^67 + 5 * q^68 - 8 * q^69 - 5 * q^70 - 34 * q^71 + 21 * q^72 - 23 * q^73 - 9 * q^74 - 3 * q^75 - 53 * q^76 - 10 * q^77 + 23 * q^78 - 62 * q^79 - q^80 + 7 * q^81 + 24 * q^82 - 8 * q^83 + 46 * q^84 - 26 * q^85 - 11 * q^86 + q^87 - 12 * q^88 - 77 * q^89 + 5 * q^90 - 6 * q^91 + 47 * q^92 - 32 * q^94 - 34 * q^95 - 53 * q^96 - 21 * q^97 - 3 * q^98 + 8 * q^99

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