LMFDB - Embedded newform 4334.2.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4334,2,Mod(1,4334)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4334, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4334.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4334 = 2 \cdot 11 \cdot 197 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4334.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:	$34.6071642360$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	4334.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -3.05385 q^{3} +1.00000 q^{4} +3.30243 q^{5} +3.05385 q^{6} +4.28183 q^{7} -1.00000 q^{8} +6.32597 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -3.05385 q^{3} +1.00000 q^{4} +3.30243 q^{5} +3.05385 q^{6} +4.28183 q^{7} -1.00000 q^{8} +6.32597 q^{9} -3.30243 q^{10} -1.00000 q^{11} -3.05385 q^{12} +0.990101 q^{13} -4.28183 q^{14} -10.0851 q^{15} +1.00000 q^{16} +4.89617 q^{17} -6.32597 q^{18} -6.22760 q^{19} +3.30243 q^{20} -13.0760 q^{21} +1.00000 q^{22} +1.78775 q^{23} +3.05385 q^{24} +5.90602 q^{25} -0.990101 q^{26} -10.1570 q^{27} +4.28183 q^{28} +1.76892 q^{29} +10.0851 q^{30} -3.94535 q^{31} -1.00000 q^{32} +3.05385 q^{33} -4.89617 q^{34} +14.1404 q^{35} +6.32597 q^{36} -2.50621 q^{37} +6.22760 q^{38} -3.02362 q^{39} -3.30243 q^{40} +7.62097 q^{41} +13.0760 q^{42} -1.19902 q^{43} -1.00000 q^{44} +20.8911 q^{45} -1.78775 q^{46} +11.2885 q^{47} -3.05385 q^{48} +11.3340 q^{49} -5.90602 q^{50} -14.9522 q^{51} +0.990101 q^{52} +8.01980 q^{53} +10.1570 q^{54} -3.30243 q^{55} -4.28183 q^{56} +19.0181 q^{57} -1.76892 q^{58} -0.889962 q^{59} -10.0851 q^{60} -0.0760824 q^{61} +3.94535 q^{62} +27.0867 q^{63} +1.00000 q^{64} +3.26974 q^{65} -3.05385 q^{66} -2.48328 q^{67} +4.89617 q^{68} -5.45951 q^{69} -14.1404 q^{70} +2.16601 q^{71} -6.32597 q^{72} +13.3142 q^{73} +2.50621 q^{74} -18.0361 q^{75} -6.22760 q^{76} -4.28183 q^{77} +3.02362 q^{78} +4.62710 q^{79} +3.30243 q^{80} +12.0400 q^{81} -7.62097 q^{82} -14.4616 q^{83} -13.0760 q^{84} +16.1693 q^{85} +1.19902 q^{86} -5.40199 q^{87} +1.00000 q^{88} -11.7630 q^{89} -20.8911 q^{90} +4.23944 q^{91} +1.78775 q^{92} +12.0485 q^{93} -11.2885 q^{94} -20.5662 q^{95} +3.05385 q^{96} -5.56458 q^{97} -11.3340 q^{98} -6.32597 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) $ 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−3.05385	−1.76314	−0.881569	−	0.472055i	$-0.843512\pi$
$3$	−3.05385	−1.76314	−0.881569	+	0.472055i	$0.843512\pi$
$4$	1.00000	0.500000
$5$	3.30243	1.47689	0.738445	−	0.674314i	$-0.235560\pi$
$5$	3.30243	1.47689	0.738445	+	0.674314i	$0.235560\pi$
$6$	3.05385	1.24673
$7$	4.28183	1.61838	0.809189	−	0.587548i	$-0.199907\pi$
$7$	4.28183	1.61838	0.809189	+	0.587548i	$0.199907\pi$
$8$	−1.00000	−0.353553
$9$	6.32597	2.10866
$10$	−3.30243	−1.04432
$11$	−1.00000	−0.301511
$11$	−1.00000	−0.301511
$12$	−3.05385	−0.881569
$13$	0.990101	0.274605	0.137302	−	0.990529i	$-0.456157\pi$
$13$	0.990101	0.274605	0.137302	+	0.990529i	$0.456157\pi$
$14$	−4.28183	−1.14437
$15$	−10.0851	−2.60396
$16$	1.00000	0.250000
$17$	4.89617	1.18750	0.593748	−	0.804651i	$-0.297647\pi$
$17$	4.89617	1.18750	0.593748	+	0.804651i	$0.297647\pi$
$18$	−6.32597	−1.49105
$19$	−6.22760	−1.42871	−0.714355	−	0.699784i	$-0.753280\pi$
$19$	−6.22760	−1.42871	−0.714355	+	0.699784i	$0.753280\pi$
$20$	3.30243	0.738445
$21$	−13.0760	−2.85342
$22$	1.00000	0.213201
$23$	1.78775	0.372771	0.186386	−	0.982477i	$-0.440323\pi$
$23$	1.78775	0.372771	0.186386	+	0.982477i	$0.440323\pi$
$24$	3.05385	0.623364
$25$	5.90602	1.18120
$26$	−0.990101	−0.194175
$27$	−10.1570	−1.95471
$28$	4.28183	0.809189
$29$	1.76892	0.328479	0.164240	−	0.986420i	$-0.447483\pi$
$29$	1.76892	0.328479	0.164240	+	0.986420i	$0.447483\pi$
$30$	10.0851	1.84128
$31$	−3.94535	−0.708605	−0.354303	−	0.935131i	$-0.615282\pi$
$31$	−3.94535	−0.708605	−0.354303	+	0.935131i	$0.615282\pi$
$32$	−1.00000	−0.176777
$33$	3.05385	0.531606
$34$	−4.89617	−0.839687
$35$	14.1404	2.39017
$36$	6.32597	1.05433
$37$	−2.50621	−0.412018	−0.206009	−	0.978550i	$-0.566048\pi$
$37$	−2.50621	−0.412018	−0.206009	+	0.978550i	$0.566048\pi$
$38$	6.22760	1.01025
$39$	−3.02362	−0.484166
$40$	−3.30243	−0.522159
$41$	7.62097	1.19020	0.595098	−	0.803653i	$-0.297113\pi$
$41$	7.62097	1.19020	0.595098	+	0.803653i	$0.297113\pi$
$42$	13.0760	2.01768
$43$	−1.19902	−0.182848	−0.0914241	−	0.995812i	$-0.529142\pi$
$43$	−1.19902	−0.182848	−0.0914241	+	0.995812i	$0.529142\pi$
$44$	−1.00000	−0.150756
$45$	20.8911	3.11425
$46$	−1.78775	−0.263589
$47$	11.2885	1.64659	0.823296	−	0.567613i	$-0.192133\pi$
$47$	11.2885	1.64659	0.823296	+	0.567613i	$0.192133\pi$
$48$	−3.05385	−0.440785
$49$	11.3340	1.61915
$50$	−5.90602	−0.835237
$51$	−14.9522	−2.09372
$52$	0.990101	0.137302
$53$	8.01980	1.10160	0.550802	−	0.834636i	$-0.314322\pi$
$53$	8.01980	1.10160	0.550802	+	0.834636i	$0.314322\pi$
$54$	10.1570	1.38219
$55$	−3.30243	−0.445299
$56$	−4.28183	−0.572183
$57$	19.0181	2.51901
$58$	−1.76892	−0.232270
$59$	−0.889962	−0.115863	−0.0579316	−	0.998321i	$-0.518451\pi$
$59$	−0.889962	−0.115863	−0.0579316	+	0.998321i	$0.518451\pi$
$60$	−10.0851	−1.30198
$61$	−0.0760824	−0.00974135	−0.00487068	−	0.999988i	$-0.501550\pi$
$61$	−0.0760824	−0.00974135	−0.00487068	+	0.999988i	$0.501550\pi$
$62$	3.94535	0.501059
$63$	27.0867	3.41260
$64$	1.00000	0.125000
$65$	3.26974	0.405561
$66$	−3.05385	−0.375902
$67$	−2.48328	−0.303381	−0.151690	−	0.988428i	$-0.548472\pi$
$67$	−2.48328	−0.303381	−0.151690	+	0.988428i	$0.548472\pi$
$68$	4.89617	0.593748
$69$	−5.45951	−0.657248
$70$	−14.1404	−1.69010
$71$	2.16601	0.257058	0.128529	−	0.991706i	$-0.458975\pi$
$71$	2.16601	0.257058	0.128529	+	0.991706i	$0.458975\pi$
$72$	−6.32597	−0.745523
$73$	13.3142	1.55831	0.779157	−	0.626828i	$-0.215647\pi$
$73$	13.3142	1.55831	0.779157	+	0.626828i	$0.215647\pi$
$74$	2.50621	0.291341
$75$	−18.0361	−2.08263
$76$	−6.22760	−0.714355
$77$	−4.28183	−0.487959
$78$	3.02362	0.342357
$79$	4.62710	0.520589	0.260294	−	0.965529i	$-0.416180\pi$
$79$	4.62710	0.520589	0.260294	+	0.965529i	$0.416180\pi$
$80$	3.30243	0.369223
$81$	12.0400	1.33778
$82$	−7.62097	−0.841596
$83$	−14.4616	−1.58737	−0.793683	−	0.608331i	$-0.791839\pi$
$83$	−14.4616	−1.58737	−0.793683	+	0.608331i	$0.791839\pi$
$84$	−13.0760	−1.42671
$85$	16.1693	1.75380
$86$	1.19902	0.129293
$87$	−5.40199	−0.579155
$88$	1.00000	0.106600
$89$	−11.7630	−1.24688	−0.623440	−	0.781871i	$-0.714265\pi$
$89$	−11.7630	−1.24688	−0.623440	+	0.781871i	$0.714265\pi$
$90$	−20.8911	−2.20211
$91$	4.23944	0.444414
$92$	1.78775	0.186386
$93$	12.0485	1.24937
$94$	−11.2885	−1.16432
$95$	−20.5662	−2.11005
$96$	3.05385	0.311682
$97$	−5.56458	−0.564998	−0.282499	−	0.959268i	$-0.591163\pi$
$97$	−5.56458	−0.564998	−0.282499	+	0.959268i	$0.591163\pi$
$98$	−11.3340	−1.14491
$99$	−6.32597	−0.635784
$100$	5.90602	0.590602
$101$	0.977467	0.0972616	0.0486308	−	0.998817i	$-0.484514\pi$
$101$	0.977467	0.0972616	0.0486308	+	0.998817i	$0.484514\pi$
$102$	14.9522	1.48048
$103$	15.0271	1.48066	0.740331	−	0.672243i	$-0.234669\pi$
$103$	15.0271	1.48066	0.740331	+	0.672243i	$0.234669\pi$
$104$	−0.990101	−0.0970874
$105$	−43.1826	−4.21419
$106$	−8.01980	−0.778951
$107$	0.453184	0.0438110	0.0219055	−	0.999760i	$-0.493027\pi$
$107$	0.453184	0.0438110	0.0219055	+	0.999760i	$0.493027\pi$
$108$	−10.1570	−0.977357
$109$	4.02528	0.385552	0.192776	−	0.981243i	$-0.438251\pi$
$109$	4.02528	0.385552	0.192776	+	0.981243i	$0.438251\pi$
$110$	3.30243	0.314874
$111$	7.65357	0.726445
$112$	4.28183	0.404595
$113$	−2.40508	−0.226251	−0.113125	−	0.993581i	$-0.536086\pi$
$113$	−2.40508	−0.226251	−0.113125	+	0.993581i	$0.536086\pi$
$114$	−19.0181	−1.78121
$115$	5.90391	0.550542
$116$	1.76892	0.164240
$117$	6.26335	0.579047
$118$	0.889962	0.0819276
$119$	20.9646	1.92182
$120$	10.0851	0.920639
$121$	1.00000	0.0909091
$122$	0.0760824	0.00688818
$123$	−23.2733	−2.09848
$124$	−3.94535	−0.354303
$125$	2.99207	0.267619
$126$	−27.0867	−2.41308
$127$	−19.5208	−1.73219	−0.866093	−	0.499882i	$-0.833377\pi$
$127$	−19.5208	−1.73219	−0.866093	+	0.499882i	$0.833377\pi$
$128$	−1.00000	−0.0883883
$129$	3.66161	0.322387
$130$	−3.26974	−0.286775
$131$	5.61736	0.490791	0.245396	−	0.969423i	$-0.421082\pi$
$131$	5.61736	0.490791	0.245396	+	0.969423i	$0.421082\pi$
$132$	3.05385	0.265803
$133$	−26.6655	−2.31219
$134$	2.48328	0.214522
$135$	−33.5427	−2.88690
$136$	−4.89617	−0.419843
$137$	3.78645	0.323498	0.161749	−	0.986832i	$-0.448286\pi$
$137$	3.78645	0.323498	0.161749	+	0.986832i	$0.448286\pi$
$138$	5.45951	0.464744
$139$	20.1505	1.70914	0.854571	−	0.519335i	$-0.173820\pi$
$139$	20.1505	1.70914	0.854571	+	0.519335i	$0.173820\pi$
$140$	14.1404	1.19508
$141$	−34.4732	−2.90317
$142$	−2.16601	−0.181767
$143$	−0.990101	−0.0827964
$144$	6.32597	0.527164
$145$	5.84171	0.485128
$146$	−13.3142	−1.10190
$147$	−34.6124	−2.85478
$148$	−2.50621	−0.206009
$149$	−19.6099	−1.60650	−0.803252	−	0.595639i	$-0.796899\pi$
$149$	−19.6099	−1.60650	−0.803252	+	0.595639i	$0.796899\pi$
$150$	18.0361	1.47264
$151$	21.3587	1.73814	0.869072	−	0.494685i	$-0.164717\pi$
$151$	21.3587	1.73814	0.869072	+	0.494685i	$0.164717\pi$
$152$	6.22760	0.505125
$153$	30.9731	2.50402
$154$	4.28183	0.345039
$155$	−13.0292	−1.04653
$156$	−3.02362	−0.242083
$157$	−16.1373	−1.28789	−0.643947	−	0.765070i	$-0.722704\pi$
$157$	−16.1373	−1.28789	−0.643947	+	0.765070i	$0.722704\pi$
$158$	−4.62710	−0.368112
$159$	−24.4912	−1.94228
$160$	−3.30243	−0.261080
$161$	7.65483	0.603285
$162$	−12.0400	−0.945950
$163$	5.11054	0.400288	0.200144	−	0.979766i	$-0.435859\pi$
$163$	5.11054	0.400288	0.200144	+	0.979766i	$0.435859\pi$
$164$	7.62097	0.595098
$165$	10.0851	0.785124
$166$	14.4616	1.12244
$167$	−14.0722	−1.08894	−0.544471	−	0.838779i	$-0.683270\pi$
$167$	−14.0722	−1.08894	−0.544471	+	0.838779i	$0.683270\pi$
$168$	13.0760	1.00884
$169$	−12.0197	−0.924592
$170$	−16.1693	−1.24013
$171$	−39.3956	−3.01266
$172$	−1.19902	−0.0914241
$173$	−12.1004	−0.919973	−0.459986	−	0.887926i	$-0.652146\pi$
$173$	−12.1004	−0.919973	−0.459986	+	0.887926i	$0.652146\pi$
$174$	5.40199	0.409524
$175$	25.2886	1.91164
$176$	−1.00000	−0.0753778
$177$	2.71780	0.204283
$178$	11.7630	0.881677
$179$	19.1565	1.43182	0.715911	−	0.698191i	$-0.246012\pi$
$179$	19.1565	1.43182	0.715911	+	0.698191i	$0.246012\pi$
$180$	20.8911	1.55713
$181$	22.6468	1.68332	0.841660	−	0.540008i	$-0.181579\pi$
$181$	22.6468	1.68332	0.841660	+	0.540008i	$0.181579\pi$
$182$	−4.23944	−0.314248
$183$	0.232344	0.0171753
$184$	−1.78775	−0.131795
$185$	−8.27657	−0.608505
$186$	−12.0485	−0.883437
$187$	−4.89617	−0.358044
$188$	11.2885	0.823296
$189$	−43.4905	−3.16347
$190$	20.5662	1.49203
$191$	−0.729648	−0.0527955	−0.0263977	−	0.999652i	$-0.508404\pi$
$191$	−0.729648	−0.0527955	−0.0263977	+	0.999652i	$0.508404\pi$
$192$	−3.05385	−0.220392
$193$	3.39498	0.244376	0.122188	−	0.992507i	$-0.461009\pi$
$193$	3.39498	0.244376	0.122188	+	0.992507i	$0.461009\pi$
$194$	5.56458	0.399514
$195$	−9.98527	−0.715060
$196$	11.3340	0.809574
$197$	1.00000	0.0712470
$197$	1.00000	0.0712470
$198$	6.32597	0.449567
$199$	2.98097	0.211315	0.105658	−	0.994403i	$-0.466305\pi$
$199$	2.98097	0.211315	0.105658	+	0.994403i	$0.466305\pi$
$200$	−5.90602	−0.417619
$201$	7.58354	0.534902
$202$	−0.977467	−0.0687743
$203$	7.57419	0.531604
$204$	−14.9522	−1.04686
$205$	25.1677	1.75779
$206$	−15.0271	−1.04699
$207$	11.3092	0.786047
$208$	0.990101	0.0686512
$209$	6.22760	0.430772
$210$	43.1826	2.97989
$211$	15.2412	1.04925	0.524624	−	0.851334i	$-0.324206\pi$
$211$	15.2412	1.04925	0.524624	+	0.851334i	$0.324206\pi$
$212$	8.01980	0.550802
$213$	−6.61465	−0.453228
$214$	−0.453184	−0.0309790
$215$	−3.95966	−0.270047
$216$	10.1570	0.691096
$217$	−16.8933	−1.14679
$218$	−4.02528	−0.272626
$219$	−40.6597	−2.74752
$220$	−3.30243	−0.222650
$221$	4.84771	0.326092
$222$	−7.65357	−0.513674
$223$	−7.27115	−0.486912	−0.243456	−	0.969912i	$-0.578281\pi$
$223$	−7.27115	−0.486912	−0.243456	+	0.969912i	$0.578281\pi$
$224$	−4.28183	−0.286092
$225$	37.3613	2.49075
$226$	2.40508	0.159984
$227$	−26.3977	−1.75208	−0.876039	−	0.482239i	$-0.839824\pi$
$227$	−26.3977	−1.75208	−0.876039	+	0.482239i	$0.839824\pi$
$228$	19.0181	1.25951
$229$	9.95214	0.657656	0.328828	−	0.944390i	$-0.393346\pi$
$229$	9.95214	0.657656	0.328828	+	0.944390i	$0.393346\pi$
$230$	−5.90391	−0.389292
$231$	13.0760	0.860340
$232$	−1.76892	−0.116135
$233$	7.65898	0.501757	0.250878	−	0.968019i	$-0.419281\pi$
$233$	7.65898	0.501757	0.250878	+	0.968019i	$0.419281\pi$
$234$	−6.26335	−0.409448
$235$	37.2793	2.43183
$236$	−0.889962	−0.0579316
$237$	−14.1304	−0.917870
$238$	−20.9646	−1.35893
$239$	−1.52515	−0.0986540	−0.0493270	−	0.998783i	$-0.515708\pi$
$239$	−1.52515	−0.0986540	−0.0493270	+	0.998783i	$0.515708\pi$
$240$	−10.0851	−0.650990
$241$	1.51479	0.0975760	0.0487880	−	0.998809i	$-0.484464\pi$
$241$	1.51479	0.0975760	0.0487880	+	0.998809i	$0.484464\pi$
$242$	−1.00000	−0.0642824
$243$	−6.29726	−0.403969
$244$	−0.0760824	−0.00487068
$245$	37.4298	2.39130
$246$	23.2733	1.48385
$247$	−6.16596	−0.392330
$248$	3.94535	0.250530
$249$	44.1635	2.79875
$250$	−2.99207	−0.189235
$251$	−14.1581	−0.893652	−0.446826	−	0.894621i	$-0.647446\pi$
$251$	−14.1581	−0.893652	−0.446826	+	0.894621i	$0.647446\pi$
$252$	27.0867	1.70630
$253$	−1.78775	−0.112395
$254$	19.5208	1.22484
$255$	−49.3784	−3.09220
$256$	1.00000	0.0625000
$257$	−13.9130	−0.867868	−0.433934	−	0.900945i	$-0.642875\pi$
$257$	−13.9130	−0.867868	−0.433934	+	0.900945i	$0.642875\pi$
$258$	−3.66161	−0.227962
$259$	−10.7311	−0.666801
$260$	3.26974	0.202781
$261$	11.1901	0.692650
$262$	−5.61736	−0.347042
$263$	−22.4268	−1.38289	−0.691446	−	0.722428i	$-0.743026\pi$
$263$	−22.4268	−1.38289	−0.691446	+	0.722428i	$0.743026\pi$
$264$	−3.05385	−0.187951
$265$	26.4848	1.62695
$266$	26.6655	1.63497
$267$	35.9225	2.19842
$268$	−2.48328	−0.151690
$269$	−26.8707	−1.63833	−0.819167	−	0.573555i	$-0.805564\pi$
$269$	−26.8707	−1.63833	−0.819167	+	0.573555i	$0.805564\pi$
$270$	33.5427	2.04135
$271$	16.8462	1.02333	0.511667	−	0.859184i	$-0.329028\pi$
$271$	16.8462	1.02333	0.511667	+	0.859184i	$0.329028\pi$
$272$	4.89617	0.296874
$273$	−12.9466	−0.783564
$274$	−3.78645	−0.228748
$275$	−5.90602	−0.356146
$276$	−5.45951	−0.328624
$277$	17.2527	1.03661	0.518306	−	0.855195i	$-0.326563\pi$
$277$	17.2527	1.03661	0.518306	+	0.855195i	$0.326563\pi$
$278$	−20.1505	−1.20855
$279$	−24.9581	−1.49420
$280$	−14.1404	−0.845052
$281$	17.5135	1.04477	0.522385	−	0.852710i	$-0.325043\pi$
$281$	17.5135	1.04477	0.522385	+	0.852710i	$0.325043\pi$
$282$	34.4732	2.05285
$283$	24.3677	1.44851	0.724255	−	0.689532i	$-0.242184\pi$
$283$	24.3677	1.44851	0.724255	+	0.689532i	$0.242184\pi$
$284$	2.16601	0.128529
$285$	62.8060	3.72031
$286$	0.990101	0.0585459
$287$	32.6317	1.92619
$288$	−6.32597	−0.372761
$289$	6.97252	0.410148
$290$	−5.84171	−0.343037
$291$	16.9934	0.996169
$292$	13.3142	0.779157
$293$	−26.1390	−1.52706	−0.763528	−	0.645774i	$-0.776535\pi$
$293$	−26.1390	−1.52706	−0.763528	+	0.645774i	$0.776535\pi$
$294$	34.6124	2.01864
$295$	−2.93903	−0.171117
$296$	2.50621	0.145670
$297$	10.1570	0.589369
$298$	19.6099	1.13597
$299$	1.77005	0.102365
$300$	−18.0361	−1.04131
$301$	−5.13398	−0.295918
$302$	−21.3587	−1.22905
$303$	−2.98503	−0.171486
$304$	−6.22760	−0.357177
$305$	−0.251256	−0.0143869
$306$	−30.9731	−1.77061
$307$	8.35585	0.476894	0.238447	−	0.971156i	$-0.423362\pi$
$307$	8.35585	0.476894	0.238447	+	0.971156i	$0.423362\pi$
$308$	−4.28183	−0.243980
$309$	−45.8904	−2.61061
$310$	13.0292	0.740010
$311$	2.53482	0.143736	0.0718682	−	0.997414i	$-0.477104\pi$
$311$	2.53482	0.143736	0.0718682	+	0.997414i	$0.477104\pi$
$312$	3.02362	0.171179
$313$	26.8973	1.52032	0.760162	−	0.649733i	$-0.225119\pi$
$313$	26.8973	1.52032	0.760162	+	0.649733i	$0.225119\pi$
$314$	16.1373	0.910678
$315$	89.4518	5.04004
$316$	4.62710	0.260294
$317$	4.17338	0.234400	0.117200	−	0.993108i	$-0.462608\pi$
$317$	4.17338	0.234400	0.117200	+	0.993108i	$0.462608\pi$
$318$	24.4912	1.37340
$319$	−1.76892	−0.0990403
$320$	3.30243	0.184611
$321$	−1.38395	−0.0772448
$322$	−7.65483	−0.426587
$323$	−30.4914	−1.69659
$324$	12.0400	0.668888
$325$	5.84756	0.324364
$326$	−5.11054	−0.283046
$327$	−12.2926	−0.679781
$328$	−7.62097	−0.420798
$329$	48.3352	2.66481
$330$	−10.0851	−0.555166
$331$	−8.16653	−0.448873	−0.224436	−	0.974489i	$-0.572054\pi$
$331$	−8.16653	−0.448873	−0.224436	+	0.974489i	$0.572054\pi$
$332$	−14.4616	−0.793683
$333$	−15.8542	−0.868805
$334$	14.0722	0.769999
$335$	−8.20084	−0.448060
$336$	−13.0760	−0.713356
$337$	16.6689	0.908011	0.454006	−	0.890999i	$-0.349995\pi$
$337$	16.6689	0.908011	0.454006	+	0.890999i	$0.349995\pi$
$338$	12.0197	0.653785
$339$	7.34474	0.398912
$340$	16.1693	0.876901
$341$	3.94535	0.213652
$342$	39.3956	2.13027
$343$	18.5576	1.00202
$344$	1.19902	0.0646466
$345$	−18.0296	−0.970682
$346$	12.1004	0.650519
$347$	−11.7634	−0.631491	−0.315745	−	0.948844i	$-0.602255\pi$
$347$	−11.7634	−0.631491	−0.315745	+	0.948844i	$0.602255\pi$
$348$	−5.40199	−0.289577
$349$	22.9309	1.22746	0.613732	−	0.789514i	$-0.289668\pi$
$349$	22.9309	1.22746	0.613732	+	0.789514i	$0.289668\pi$
$350$	−25.2886	−1.35173
$351$	−10.0565	−0.536774
$352$	1.00000	0.0533002
$353$	32.9491	1.75370	0.876852	−	0.480760i	$-0.159639\pi$
$353$	32.9491	1.75370	0.876852	+	0.480760i	$0.159639\pi$
$354$	−2.71780	−0.144450
$355$	7.15308	0.379646
$356$	−11.7630	−0.623440
$357$	−64.0225	−3.38843
$358$	−19.1565	−1.01245
$359$	−5.44489	−0.287370	−0.143685	−	0.989623i	$-0.545895\pi$
$359$	−5.44489	−0.287370	−0.143685	+	0.989623i	$0.545895\pi$
$360$	−20.8911	−1.10106
$361$	19.7830	1.04121
$362$	−22.6468	−1.19029
$363$	−3.05385	−0.160285
$364$	4.23944	0.222207
$365$	43.9693	2.30146
$366$	−0.232344	−0.0121448
$367$	4.74207	0.247534	0.123767	−	0.992311i	$-0.460502\pi$
$367$	4.74207	0.247534	0.123767	+	0.992311i	$0.460502\pi$
$368$	1.78775	0.0931929
$369$	48.2100	2.50971
$370$	8.27657	0.430278
$371$	34.3394	1.78281
$372$	12.0485	0.624684
$373$	−8.12515	−0.420705	−0.210352	−	0.977626i	$-0.567461\pi$
$373$	−8.12515	−0.420705	−0.210352	+	0.977626i	$0.567461\pi$
$374$	4.89617	0.253175
$375$	−9.13731	−0.471849
$376$	−11.2885	−0.582158
$377$	1.75141	0.0902020
$378$	43.4905	2.23691
$379$	−32.1967	−1.65384	−0.826918	−	0.562323i	$-0.809908\pi$
$379$	−32.1967	−1.65384	−0.826918	+	0.562323i	$0.809908\pi$
$380$	−20.5662	−1.05502
$381$	59.6133	3.05408
$382$	0.729648	0.0373320
$383$	−16.4711	−0.841632	−0.420816	−	0.907146i	$-0.638256\pi$
$383$	−16.4711	−0.841632	−0.420816	+	0.907146i	$0.638256\pi$
$384$	3.05385	0.155841
$385$	−14.1404	−0.720662
$386$	−3.39498	−0.172800
$387$	−7.58494	−0.385564
$388$	−5.56458	−0.282499
$389$	33.8965	1.71862	0.859309	−	0.511456i	$-0.170894\pi$
$389$	33.8965	1.71862	0.859309	+	0.511456i	$0.170894\pi$
$390$	9.98527	0.505624
$391$	8.75313	0.442665
$392$	−11.3340	−0.572455
$393$	−17.1546	−0.865333
$394$	−1.00000	−0.0503793
$395$	15.2806	0.768853
$396$	−6.32597	−0.317892
$397$	−35.8340	−1.79845	−0.899227	−	0.437481i	$-0.855871\pi$
$397$	−35.8340	−1.79845	−0.899227	+	0.437481i	$0.855871\pi$
$398$	−2.98097	−0.149422
$399$	81.4323	4.07672
$400$	5.90602	0.295301
$401$	1.88871	0.0943175	0.0471587	−	0.998887i	$-0.484983\pi$
$401$	1.88871	0.0943175	0.0471587	+	0.998887i	$0.484983\pi$
$402$	−7.58354	−0.378233
$403$	−3.90629	−0.194586
$404$	0.977467	0.0486308
$405$	39.7612	1.97575
$406$	−7.57419	−0.375901
$407$	2.50621	0.124228
$408$	14.9522	0.740242
$409$	22.5299	1.11403	0.557015	−	0.830502i	$-0.311946\pi$
$409$	22.5299	1.11403	0.557015	+	0.830502i	$0.311946\pi$
$410$	−25.1677	−1.24294
$411$	−11.5632	−0.570372
$412$	15.0271	0.740331
$413$	−3.81066	−0.187510
$414$	−11.3092	−0.555819
$415$	−47.7584	−2.34437
$416$	−0.990101	−0.0485437
$417$	−61.5365	−3.01345
$418$	−6.22760	−0.304602
$419$	13.1875	0.644249	0.322125	−	0.946697i	$-0.395603\pi$
$419$	13.1875	0.644249	0.322125	+	0.946697i	$0.395603\pi$
$420$	−43.1826	−2.10710
$421$	−5.59831	−0.272845	−0.136422	−	0.990651i	$-0.543560\pi$
$421$	−5.59831	−0.272845	−0.136422	+	0.990651i	$0.543560\pi$
$422$	−15.2412	−0.741930
$423$	71.4105	3.47210
$424$	−8.01980	−0.389476
$425$	28.9169	1.40268
$426$	6.61465	0.320481
$427$	−0.325772	−0.0157652
$428$	0.453184	0.0219055
$429$	3.02362	0.145982
$430$	3.95966	0.190952
$431$	−22.3514	−1.07663	−0.538314	−	0.842744i	$-0.680938\pi$
$431$	−22.3514	−1.07663	−0.538314	+	0.842744i	$0.680938\pi$
$432$	−10.1570	−0.488679
$433$	8.34878	0.401217	0.200608	−	0.979672i	$-0.435708\pi$
$433$	8.34878	0.401217	0.200608	+	0.979672i	$0.435708\pi$
$434$	16.8933	0.810904
$435$	−17.8397	−0.855348
$436$	4.02528	0.192776
$437$	−11.1334	−0.532582
$438$	40.6597	1.94279
$439$	−13.0812	−0.624334	−0.312167	−	0.950027i	$-0.601055\pi$
$439$	−13.0812	−0.624334	−0.312167	+	0.950027i	$0.601055\pi$
$440$	3.30243	0.157437
$441$	71.6988	3.41423
$442$	−4.84771	−0.230582
$443$	−4.21913	−0.200457	−0.100229	−	0.994964i	$-0.531957\pi$
$443$	−4.21913	−0.200457	−0.100229	+	0.994964i	$0.531957\pi$
$444$	7.65357	0.363222
$445$	−38.8466	−1.84150
$446$	7.27115	0.344299
$447$	59.8856	2.83249
$448$	4.28183	0.202297
$449$	1.87950	0.0886989	0.0443495	−	0.999016i	$-0.485878\pi$
$449$	1.87950	0.0886989	0.0443495	+	0.999016i	$0.485878\pi$
$450$	−37.3613	−1.76123
$451$	−7.62097	−0.358858
$452$	−2.40508	−0.113125
$453$	−65.2261	−3.06459
$454$	26.3977	1.23891
$455$	14.0004	0.656351
$456$	−19.0181	−0.890606
$457$	−32.8423	−1.53630	−0.768149	−	0.640272i	$-0.778822\pi$
$457$	−32.8423	−1.53630	−0.768149	+	0.640272i	$0.778822\pi$
$458$	−9.95214	−0.465033
$459$	−49.7304	−2.32122
$460$	5.90391	0.275271
$461$	18.0127	0.838935	0.419467	−	0.907770i	$-0.362217\pi$
$461$	18.0127	0.838935	0.419467	+	0.907770i	$0.362217\pi$
$462$	−13.0760	−0.608352
$463$	−15.2403	−0.708279	−0.354139	−	0.935193i	$-0.615226\pi$
$463$	−15.2403	−0.708279	−0.354139	+	0.935193i	$0.615226\pi$
$464$	1.76892	0.0821199
$465$	39.7892	1.84518
$466$	−7.65898	−0.354796
$467$	−9.76486	−0.451864	−0.225932	−	0.974143i	$-0.572543\pi$
$467$	−9.76486	−0.451864	−0.225932	+	0.974143i	$0.572543\pi$
$468$	6.26335	0.289524
$469$	−10.6330	−0.490985
$470$	−37.2793	−1.71957
$471$	49.2807	2.27073
$472$	0.889962	0.0409638
$473$	1.19902	0.0551308
$474$	14.1304	0.649032
$475$	−36.7803	−1.68760
$476$	20.9646	0.960909
$477$	50.7330	2.32290
$478$	1.52515	0.0697589
$479$	−27.9907	−1.27893	−0.639464	−	0.768821i	$-0.720844\pi$
$479$	−27.9907	−1.27893	−0.639464	+	0.768821i	$0.720844\pi$
$480$	10.0851	0.460320
$481$	−2.48140	−0.113142
$482$	−1.51479	−0.0689967
$483$	−23.3767	−1.06368
$484$	1.00000	0.0454545
$485$	−18.3766	−0.834439
$486$	6.29726	0.285649
$487$	6.56576	0.297523	0.148762	−	0.988873i	$-0.452471\pi$
$487$	6.56576	0.297523	0.148762	+	0.988873i	$0.452471\pi$
$488$	0.0760824	0.00344409
$489$	−15.6068	−0.705763
$490$	−37.4298	−1.69091
$491$	24.5470	1.10779	0.553895	−	0.832586i	$-0.313141\pi$
$491$	24.5470	1.10779	0.553895	+	0.832586i	$0.313141\pi$
$492$	−23.2733	−1.04924
$493$	8.66092	0.390068
$494$	6.16596	0.277420
$495$	−20.8911	−0.938983
$496$	−3.94535	−0.177151
$497$	9.27446	0.416017
$498$	−44.1635	−1.97901
$499$	11.8277	0.529481	0.264741	−	0.964320i	$-0.414714\pi$
$499$	11.8277	0.529481	0.264741	+	0.964320i	$0.414714\pi$
$500$	2.99207	0.133809
$501$	42.9745	1.91996
$502$	14.1581	0.631908
$503$	30.9921	1.38187	0.690935	−	0.722917i	$-0.257199\pi$
$503$	30.9921	1.38187	0.690935	+	0.722917i	$0.257199\pi$
$504$	−27.0867	−1.20654
$505$	3.22801	0.143645
$506$	1.78775	0.0794751
$507$	36.7063	1.63018
$508$	−19.5208	−0.866093
$509$	28.1853	1.24929	0.624646	−	0.780908i	$-0.285243\pi$
$509$	28.1853	1.24929	0.624646	+	0.780908i	$0.285243\pi$
$510$	49.3784	2.18651
$511$	57.0093	2.52194
$512$	−1.00000	−0.0441942
$513$	63.2537	2.79272
$514$	13.9130	0.613676
$515$	49.6258	2.18677
$516$	3.66161	0.161193
$517$	−11.2885	−0.496466
$518$	10.7311	0.471500
$519$	36.9526	1.62204
$520$	−3.26974	−0.143387
$521$	−1.93100	−0.0845988	−0.0422994	−	0.999105i	$-0.513468\pi$
$521$	−1.93100	−0.0845988	−0.0422994	+	0.999105i	$0.513468\pi$
$522$	−11.1901	−0.489778
$523$	−35.2782	−1.54261	−0.771305	−	0.636466i	$-0.780396\pi$
$523$	−35.2782	−1.54261	−0.771305	+	0.636466i	$0.780396\pi$
$524$	5.61736	0.245396
$525$	−77.2273	−3.37048
$526$	22.4268	0.977853
$527$	−19.3171	−0.841466
$528$	3.05385	0.132902
$529$	−19.8040	−0.861041
$530$	−26.4848	−1.15043
$531$	−5.62987	−0.244316
$532$	−26.6655	−1.15610
$533$	7.54554	0.326833
$534$	−35.9225	−1.55452
$535$	1.49661	0.0647040
$536$	2.48328	0.107261
$537$	−58.5009	−2.52450
$538$	26.8707	1.15848
$539$	−11.3340	−0.488191
$540$	−33.5427	−1.44345
$541$	31.0209	1.33369	0.666845	−	0.745196i	$-0.267644\pi$
$541$	31.0209	1.33369	0.666845	+	0.745196i	$0.267644\pi$
$542$	−16.8462	−0.723606
$543$	−69.1597	−2.96793
$544$	−4.89617	−0.209922
$545$	13.2932	0.569418
$546$	12.9466	0.554063
$547$	41.1662	1.76014	0.880069	−	0.474846i	$-0.157496\pi$
$547$	41.1662	1.76014	0.880069	+	0.474846i	$0.157496\pi$
$548$	3.78645	0.161749
$549$	−0.481295	−0.0205412
$550$	5.90602	0.251834
$551$	−11.0161	−0.469302
$552$	5.45951	0.232372
$553$	19.8124	0.842510
$554$	−17.2527	−0.732996
$555$	25.2754	1.07288
$556$	20.1505	0.854571
$557$	−3.48328	−0.147591	−0.0737956	−	0.997273i	$-0.523511\pi$
$557$	−3.48328	−0.147591	−0.0737956	+	0.997273i	$0.523511\pi$
$558$	24.9581	1.05656
$559$	−1.18715	−0.0502110
$560$	14.1404	0.597542
$561$	14.9522	0.631281
$562$	−17.5135	−0.738763
$563$	45.4153	1.91403	0.957013	−	0.290046i	$-0.0936705\pi$
$563$	45.4153	1.91403	0.957013	+	0.290046i	$0.0936705\pi$
$564$	−34.4732	−1.45158
$565$	−7.94260	−0.334148
$566$	−24.3677	−1.02425
$567$	51.5531	2.16503
$568$	−2.16601	−0.0908836
$569$	−26.6686	−1.11801	−0.559003	−	0.829166i	$-0.688816\pi$
$569$	−26.6686	−1.11801	−0.559003	+	0.829166i	$0.688816\pi$
$570$	−62.8060	−2.63065
$571$	−26.8098	−1.12196	−0.560978	−	0.827831i	$-0.689575\pi$
$571$	−26.8098	−1.12196	−0.560978	+	0.827831i	$0.689575\pi$
$572$	−0.990101	−0.0413982
$573$	2.22823	0.0930857
$574$	−32.6317	−1.36202
$575$	10.5585	0.440319
$576$	6.32597	0.263582
$577$	−27.7803	−1.15651	−0.578254	−	0.815857i	$-0.696266\pi$
$577$	−27.7803	−1.15651	−0.578254	+	0.815857i	$0.696266\pi$
$578$	−6.97252	−0.290019
$579$	−10.3678	−0.430869
$580$	5.84171	0.242564
$581$	−61.9221	−2.56896
$582$	−16.9934	−0.704398
$583$	−8.01980	−0.332146
$584$	−13.3142	−0.550948
$585$	20.6843	0.855189
$586$	26.1390	1.07979
$587$	9.31715	0.384560	0.192280	−	0.981340i	$-0.438412\pi$
$587$	9.31715	0.384560	0.192280	+	0.981340i	$0.438412\pi$
$588$	−34.6124	−1.42739
$589$	24.5700	1.01239
$590$	2.93903	0.120998
$591$	−3.05385	−0.125618
$592$	−2.50621	−0.103005
$593$	12.2843	0.504457	0.252228	−	0.967668i	$-0.418837\pi$
$593$	12.2843	0.504457	0.252228	+	0.967668i	$0.418837\pi$
$594$	−10.1570	−0.416747
$595$	69.2339	2.83831
$596$	−19.6099	−0.803252
$597$	−9.10341	−0.372578
$598$	−1.77005	−0.0723828
$599$	−27.4787	−1.12275	−0.561375	−	0.827561i	$-0.689728\pi$
$599$	−27.4787	−1.12275	−0.561375	+	0.827561i	$0.689728\pi$
$600$	18.0361	0.736320
$601$	−6.52494	−0.266158	−0.133079	−	0.991105i	$-0.542486\pi$
$601$	−6.52494	−0.266158	−0.133079	+	0.991105i	$0.542486\pi$
$602$	5.13398	0.209245
$603$	−15.7091	−0.639725
$604$	21.3587	0.869072
$605$	3.30243	0.134263
$606$	2.98503	0.121259
$607$	−35.0903	−1.42427	−0.712135	−	0.702043i	$-0.752272\pi$
$607$	−35.0903	−1.42427	−0.712135	+	0.702043i	$0.752272\pi$
$608$	6.22760	0.252563
$609$	−23.1304	−0.937291
$610$	0.251256	0.0101731
$611$	11.1767	0.452162
$612$	30.9731	1.25201
$613$	4.35408	0.175860	0.0879299	−	0.996127i	$-0.471975\pi$
$613$	4.35408	0.175860	0.0879299	+	0.996127i	$0.471975\pi$
$614$	−8.35585	−0.337215
$615$	−76.8583	−3.09922
$616$	4.28183	0.172520
$617$	−0.870317	−0.0350376	−0.0175188	−	0.999847i	$-0.505577\pi$
$617$	−0.870317	−0.0350376	−0.0175188	+	0.999847i	$0.505577\pi$
$618$	45.8904	1.84598
$619$	−41.3659	−1.66263	−0.831317	−	0.555798i	$-0.812413\pi$
$619$	−41.3659	−1.66263	−0.831317	+	0.555798i	$0.812413\pi$
$620$	−13.0292	−0.523266
$621$	−18.1582	−0.728662
$622$	−2.53482	−0.101637
$623$	−50.3673	−2.01792
$624$	−3.02362	−0.121042
$625$	−19.6490	−0.785961
$626$	−26.8973	−1.07503
$627$	−19.0181	−0.759511
$628$	−16.1373	−0.643947
$629$	−12.2708	−0.489270
$630$	−89.4518	−3.56385
$631$	19.2049	0.764536	0.382268	−	0.924052i	$-0.375143\pi$
$631$	19.2049	0.764536	0.382268	+	0.924052i	$0.375143\pi$
$632$	−4.62710	−0.184056
$633$	−46.5442	−1.84997
$634$	−4.17338	−0.165746
$635$	−64.4658	−2.55825
$636$	−24.4912	−0.971140
$637$	11.2218	0.444626
$638$	1.76892	0.0700320
$639$	13.7021	0.542046
$640$	−3.30243	−0.130540
$641$	12.9023	0.509609	0.254804	−	0.966993i	$-0.417989\pi$
$641$	12.9023	0.509609	0.254804	+	0.966993i	$0.417989\pi$
$642$	1.38395	0.0546203
$643$	28.7280	1.13292	0.566461	−	0.824089i	$-0.308312\pi$
$643$	28.7280	1.13292	0.566461	+	0.824089i	$0.308312\pi$
$644$	7.65483	0.301643
$645$	12.0922	0.476130
$646$	30.4914	1.19967
$647$	−4.33605	−0.170468	−0.0852339	−	0.996361i	$-0.527164\pi$
$647$	−4.33605	−0.170468	−0.0852339	+	0.996361i	$0.527164\pi$
$648$	−12.0400	−0.472975
$649$	0.889962	0.0349340
$650$	−5.84756	−0.229360
$651$	51.5895	2.02195
$652$	5.11054	0.200144
$653$	20.9666	0.820485	0.410243	−	0.911976i	$-0.365444\pi$
$653$	20.9666	0.820485	0.410243	+	0.911976i	$0.365444\pi$
$654$	12.2926	0.480678
$655$	18.5509	0.724845
$656$	7.62097	0.297549
$657$	84.2255	3.28595
$658$	−48.3352	−1.88430
$659$	−5.78899	−0.225507	−0.112754	−	0.993623i	$-0.535967\pi$
$659$	−5.78899	−0.225507	−0.112754	+	0.993623i	$0.535967\pi$
$660$	10.0851	0.392562
$661$	28.3186	1.10147	0.550734	−	0.834681i	$-0.314348\pi$
$661$	28.3186	1.10147	0.550734	+	0.834681i	$0.314348\pi$
$662$	8.16653	0.317401
$663$	−14.8042	−0.574946
$664$	14.4616	0.561219
$665$	−88.0609	−3.41485
$666$	15.8542	0.614338
$667$	3.16238	0.122448
$668$	−14.0722	−0.544471
$669$	22.2050	0.858494
$670$	8.20084	0.316826
$671$	0.0760824	0.00293713
$672$	13.0760	0.504419
$673$	−27.6864	−1.06723	−0.533615	−	0.845727i	$-0.679167\pi$
$673$	−27.6864	−1.06723	−0.533615	+	0.845727i	$0.679167\pi$
$674$	−16.6689	−0.642061
$675$	−59.9874	−2.30892
$676$	−12.0197	−0.462296
$677$	35.4858	1.36383	0.681914	−	0.731432i	$-0.261148\pi$
$677$	35.4858	1.36383	0.681914	+	0.731432i	$0.261148\pi$
$678$	−7.34474	−0.282073
$679$	−23.8266	−0.914380
$680$	−16.1693	−0.620063
$681$	80.6146	3.08916
$682$	−3.94535	−0.151075
$683$	−26.8802	−1.02854	−0.514270	−	0.857628i	$-0.671937\pi$
$683$	−26.8802	−1.02854	−0.514270	+	0.857628i	$0.671937\pi$
$684$	−39.3956	−1.50633
$685$	12.5045	0.477771
$686$	−18.5576	−0.708532
$687$	−30.3923	−1.15954
$688$	−1.19902	−0.0457120
$689$	7.94041	0.302506
$690$	18.0296	0.686376
$691$	51.7126	1.96724	0.983620	−	0.180254i	$-0.0576919\pi$
$691$	51.7126	1.96724	0.983620	+	0.180254i	$0.0576919\pi$
$692$	−12.1004	−0.459986
$693$	−27.0867	−1.02894
$694$	11.7634	0.446531
$695$	66.5455	2.52421
$696$	5.40199	0.204762
$697$	37.3136	1.41335
$698$	−22.9309	−0.867948
$699$	−23.3894	−0.884667
$700$	25.2886	0.955818
$701$	−10.6294	−0.401468	−0.200734	−	0.979646i	$-0.564333\pi$
$701$	−10.6294	−0.401468	−0.200734	+	0.979646i	$0.564333\pi$
$702$	10.0565	0.379556
$703$	15.6077	0.588654
$704$	−1.00000	−0.0376889
$705$	−113.845	−4.28766
$706$	−32.9491	−1.24006
$707$	4.18534	0.157406
$708$	2.71780	0.102141
$709$	22.1485	0.831804	0.415902	−	0.909409i	$-0.363466\pi$
$709$	22.1485	0.831804	0.415902	+	0.909409i	$0.363466\pi$
$710$	−7.15308	−0.268450
$711$	29.2709	1.09774
$712$	11.7630	0.440839
$713$	−7.05329	−0.264148
$714$	64.0225	2.39598
$715$	−3.26974	−0.122281
$716$	19.1565	0.715911
$717$	4.65758	0.173941
$718$	5.44489	0.203202
$719$	−18.7286	−0.698460	−0.349230	−	0.937037i	$-0.613557\pi$
$719$	−18.7286	−0.698460	−0.349230	+	0.937037i	$0.613557\pi$
$720$	20.8911	0.778563
$721$	64.3433	2.39627
$722$	−19.7830	−0.736248
$723$	−4.62592	−0.172040
$724$	22.6468	0.841660
$725$	10.4473	0.388001
$726$	3.05385	0.113339
$727$	−50.1067	−1.85836	−0.929178	−	0.369632i	$-0.879484\pi$
$727$	−50.1067	−1.85836	−0.929178	+	0.369632i	$0.879484\pi$
$728$	−4.23944	−0.157124
$729$	−16.8891	−0.625522
$730$	−43.9693	−1.62738
$731$	−5.87059	−0.217132
$732$	0.232344	0.00858767
$733$	−36.2599	−1.33929	−0.669645	−	0.742681i	$-0.733554\pi$
$733$	−36.2599	−1.33929	−0.669645	+	0.742681i	$0.733554\pi$
$734$	−4.74207	−0.175033
$735$	−114.305	−4.21620
$736$	−1.78775	−0.0658973
$737$	2.48328	0.0914727
$738$	−48.2100	−1.77464
$739$	−23.4801	−0.863728	−0.431864	−	0.901939i	$-0.642144\pi$
$739$	−23.4801	−0.863728	−0.431864	+	0.901939i	$0.642144\pi$
$740$	−8.27657	−0.304253
$741$	18.8299	0.691733
$742$	−34.3394	−1.26064
$743$	51.9459	1.90571	0.952856	−	0.303423i	$-0.0981296\pi$
$743$	51.9459	1.90571	0.952856	+	0.303423i	$0.0981296\pi$
$744$	−12.0485	−0.441719
$745$	−64.7602	−2.37263
$746$	8.12515	0.297483
$747$	−91.4836	−3.34721
$748$	−4.89617	−0.179022
$749$	1.94046	0.0709027
$750$	9.13731	0.333647
$751$	6.07395	0.221642	0.110821	−	0.993840i	$-0.464652\pi$
$751$	6.07395	0.221642	0.110821	+	0.993840i	$0.464652\pi$
$752$	11.2885	0.411648
$753$	43.2367	1.57563
$754$	−1.75141	−0.0637825
$755$	70.5354	2.56705
$756$	−43.4905	−1.58173
$757$	−38.1200	−1.38549	−0.692747	−	0.721180i	$-0.743600\pi$
$757$	−38.1200	−1.38549	−0.692747	+	0.721180i	$0.743600\pi$
$758$	32.1967	1.16944
$759$	5.45951	0.198168
$760$	20.5662	0.746014
$761$	1.80504	0.0654328	0.0327164	−	0.999465i	$-0.489584\pi$
$761$	1.80504	0.0654328	0.0327164	+	0.999465i	$0.489584\pi$
$762$	−59.6133	−2.15956
$763$	17.2355	0.623969
$764$	−0.729648	−0.0263977
$765$	102.286	3.69817
$766$	16.4711	0.595124
$767$	−0.881152	−0.0318166
$768$	−3.05385	−0.110196
$769$	45.0487	1.62450	0.812249	−	0.583311i	$-0.198243\pi$
$769$	45.0487	1.62450	0.812249	+	0.583311i	$0.198243\pi$
$770$	14.1404	0.509585
$771$	42.4881	1.53017
$772$	3.39498	0.122188
$773$	−23.8151	−0.856569	−0.428285	−	0.903644i	$-0.640882\pi$
$773$	−23.8151	−0.856569	−0.428285	+	0.903644i	$0.640882\pi$
$774$	7.58494	0.272635
$775$	−23.3013	−0.837007
$776$	5.56458	0.199757
$777$	32.7713	1.17566
$778$	−33.8965	−1.21525
$779$	−47.4604	−1.70044
$780$	−9.98527	−0.357530
$781$	−2.16601	−0.0775058
$782$	−8.75313	−0.313011
$783$	−17.9669	−0.642084
$784$	11.3340	0.404787
$785$	−53.2921	−1.90208
$786$	17.1546	0.611883
$787$	19.2732	0.687017	0.343508	−	0.939150i	$-0.388385\pi$
$787$	19.2732	0.687017	0.343508	+	0.939150i	$0.388385\pi$
$788$	1.00000	0.0356235
$789$	68.4878	2.43823
$790$	−15.2806	−0.543661
$791$	−10.2981	−0.366159
$792$	6.32597	0.224784
$793$	−0.0753293	−0.00267502
$794$	35.8340	1.27170
$795$	−80.8804	−2.86853
$796$	2.98097	0.105658
$797$	18.7676	0.664783	0.332392	−	0.943141i	$-0.392144\pi$
$797$	18.7676	0.664783	0.332392	+	0.943141i	$0.392144\pi$
$798$	−81.4323	−2.88267
$799$	55.2703	1.95532
$800$	−5.90602	−0.208809
$801$	−74.4126	−2.62924
$802$	−1.88871	−0.0666925
$803$	−13.3142	−0.469850
$804$	7.58354	0.267451
$805$	25.2795	0.890986
$806$	3.90629	0.137593
$807$	82.0589	2.88861
$808$	−0.977467	−0.0343872
$809$	−35.3800	−1.24390	−0.621948	−	0.783059i	$-0.713658\pi$
$809$	−35.3800	−1.24390	−0.621948	+	0.783059i	$0.713658\pi$
$810$	−39.7612	−1.39706
$811$	41.0475	1.44137	0.720686	−	0.693262i	$-0.243827\pi$
$811$	41.0475	1.44137	0.720686	+	0.693262i	$0.243827\pi$
$812$	7.57419	0.265802
$813$	−51.4457	−1.80428
$814$	−2.50621	−0.0878426
$815$	16.8772	0.591181
$816$	−14.9522	−0.523430
$817$	7.46699	0.261237
$818$	−22.5299	−0.787738
$819$	26.8186	0.937117
$820$	25.1677	0.878894
$821$	−22.5074	−0.785514	−0.392757	−	0.919642i	$-0.628479\pi$
$821$	−22.5074	−0.785514	−0.392757	+	0.919642i	$0.628479\pi$
$822$	11.5632	0.403314
$823$	6.28407	0.219049	0.109525	−	0.993984i	$-0.465067\pi$
$823$	6.28407	0.219049	0.109525	+	0.993984i	$0.465067\pi$
$824$	−15.0271	−0.523493
$825$	18.0361	0.627935
$826$	3.81066	0.132590
$827$	36.2391	1.26016	0.630079	−	0.776531i	$-0.283022\pi$
$827$	36.2391	1.26016	0.630079	+	0.776531i	$0.283022\pi$
$828$	11.3092	0.393023
$829$	−40.3703	−1.40212	−0.701059	−	0.713103i	$-0.747289\pi$
$829$	−40.3703	−1.40212	−0.701059	+	0.713103i	$0.747289\pi$
$830$	47.7584	1.65772
$831$	−52.6870	−1.82769
$832$	0.990101	0.0343256
$833$	55.4934	1.92273
$834$	61.5365	2.13083
$835$	−46.4726	−1.60825
$836$	6.22760	0.215386
$837$	40.0729	1.38512
$838$	−13.1875	−0.455553
$839$	42.9947	1.48434	0.742171	−	0.670210i	$-0.233796\pi$
$839$	42.9947	1.48434	0.742171	+	0.670210i	$0.233796\pi$
$840$	43.1826	1.48994
$841$	−25.8709	−0.892101
$842$	5.59831	0.192930
$843$	−53.4836	−1.84207
$844$	15.2412	0.524624
$845$	−39.6942	−1.36552
$846$	−71.4105	−2.45514
$847$	4.28183	0.147125
$848$	8.01980	0.275401
$849$	−74.4152	−2.55392
$850$	−28.9169	−0.991842
$851$	−4.48047	−0.153589
$852$	−6.61465	−0.226614
$853$	34.9322	1.19606	0.598028	−	0.801475i	$-0.295951\pi$
$853$	34.9322	1.19606	0.598028	+	0.801475i	$0.295951\pi$
$854$	0.325772	0.0111477
$855$	−130.101	−4.44937
$856$	−0.453184	−0.0154895
$857$	−37.0911	−1.26701	−0.633504	−	0.773739i	$-0.718384\pi$
$857$	−37.0911	−1.26701	−0.633504	+	0.773739i	$0.718384\pi$
$858$	−3.02362	−0.103225
$859$	−3.75558	−0.128139	−0.0640693	−	0.997945i	$-0.520408\pi$
$859$	−3.75558	−0.128139	−0.0640693	+	0.997945i	$0.520408\pi$
$860$	−3.95966	−0.135023
$861$	−99.6521	−3.39613
$862$	22.3514	0.761291
$863$	31.7820	1.08187	0.540936	−	0.841064i	$-0.318070\pi$
$863$	31.7820	1.08187	0.540936	+	0.841064i	$0.318070\pi$
$864$	10.1570	0.345548
$865$	−39.9605	−1.35870
$866$	−8.34878	−0.283703
$867$	−21.2930	−0.723148
$868$	−16.8933	−0.573396
$869$	−4.62710	−0.156963
$870$	17.8397	0.604822
$871$	−2.45870	−0.0833097
$872$	−4.02528	−0.136313
$873$	−35.2014	−1.19139
$874$	11.1334	0.376593
$875$	12.8115	0.433108
$876$	−40.6597	−1.37376
$877$	−12.5725	−0.424542	−0.212271	−	0.977211i	$-0.568086\pi$
$877$	−12.5725	−0.424542	−0.212271	+	0.977211i	$0.568086\pi$
$878$	13.0812	0.441471
$879$	79.8244	2.69241
$880$	−3.30243	−0.111325
$881$	−20.7527	−0.699175	−0.349587	−	0.936904i	$-0.613678\pi$
$881$	−20.7527	−0.699175	−0.349587	+	0.936904i	$0.613678\pi$
$882$	−71.6988	−2.41422
$883$	42.7724	1.43941	0.719703	−	0.694282i	$-0.244278\pi$
$883$	42.7724	1.43941	0.719703	+	0.694282i	$0.244278\pi$
$884$	4.84771	0.163046
$885$	8.97535	0.301703
$886$	4.21913	0.141745
$887$	−40.0014	−1.34312	−0.671558	−	0.740952i	$-0.734375\pi$
$887$	−40.0014	−1.34312	−0.671558	+	0.740952i	$0.734375\pi$
$888$	−7.65357	−0.256837
$889$	−83.5845	−2.80333
$890$	38.8466	1.30214
$891$	−12.0400	−0.403355
$892$	−7.27115	−0.243456
$893$	−70.3000	−2.35250
$894$	−59.8856	−2.00287
$895$	63.2629	2.11464
$896$	−4.28183	−0.143046
$897$	−5.40547	−0.180483
$898$	−1.87950	−0.0627196
$899$	−6.97899	−0.232762
$900$	37.3613	1.24538
$901$	39.2663	1.30815
$902$	7.62097	0.253751
$903$	15.6784	0.521744
$904$	2.40508	0.0799918
$905$	74.7892	2.48608
$906$	65.2261	2.16699
$907$	−17.0981	−0.567735	−0.283867	−	0.958864i	$-0.591618\pi$
$907$	−17.0981	−0.567735	−0.283867	+	0.958864i	$0.591618\pi$
$908$	−26.3977	−0.876039
$909$	6.18343	0.205091
$910$	−14.0004	−0.464110
$911$	−8.41717	−0.278873	−0.139437	−	0.990231i	$-0.544529\pi$
$911$	−8.41717	−0.278873	−0.139437	+	0.990231i	$0.544529\pi$
$912$	19.0181	0.629753
$913$	14.4616	0.478609
$914$	32.8423	1.08633
$915$	0.767298	0.0253661
$916$	9.95214	0.328828
$917$	24.0526	0.794286
$918$	49.7304	1.64135
$919$	1.29669	0.0427738	0.0213869	−	0.999771i	$-0.493192\pi$
$919$	1.29669	0.0427738	0.0213869	+	0.999771i	$0.493192\pi$
$920$	−5.90391	−0.194646
$921$	−25.5175	−0.840829
$922$	−18.0127	−0.593216
$923$	2.14457	0.0705893
$924$	13.0760	0.430170
$925$	−14.8017	−0.486678
$926$	15.2403	0.500829
$927$	95.0608	3.12221
$928$	−1.76892	−0.0580675
$929$	−6.61606	−0.217066	−0.108533	−	0.994093i	$-0.534615\pi$
$929$	−6.61606	−0.217066	−0.108533	+	0.994093i	$0.534615\pi$
$930$	−39.7892	−1.30474
$931$	−70.5839	−2.31329
$932$	7.65898	0.250878
$933$	−7.74094	−0.253427
$934$	9.76486	0.319516
$935$	−16.1693	−0.528791
$936$	−6.26335	−0.204724
$937$	45.1456	1.47484	0.737422	−	0.675433i	$-0.236043\pi$
$937$	45.1456	1.47484	0.737422	+	0.675433i	$0.236043\pi$
$938$	10.6330	0.347178
$939$	−82.1402	−2.68054
$940$	37.2793	1.21592
$941$	39.9336	1.30180	0.650898	−	0.759165i	$-0.274392\pi$
$941$	39.9336	1.30180	0.650898	+	0.759165i	$0.274392\pi$
$942$	−49.2807	−1.60565
$943$	13.6244	0.443671
$944$	−0.889962	−0.0289658
$945$	−143.624	−4.67209
$946$	−1.19902	−0.0389834
$947$	−27.1956	−0.883739	−0.441869	−	0.897079i	$-0.645684\pi$
$947$	−27.1956	−0.883739	−0.441869	+	0.897079i	$0.645684\pi$
$948$	−14.1304	−0.458935
$949$	13.1825	0.427921
$950$	36.7803	1.19331
$951$	−12.7448	−0.413280
$952$	−20.9646	−0.679466
$953$	36.4136	1.17955	0.589777	−	0.807566i	$-0.299216\pi$
$953$	36.4136	1.17955	0.589777	+	0.807566i	$0.299216\pi$
$954$	−50.7330	−1.64254
$955$	−2.40961	−0.0779731
$956$	−1.52515	−0.0493270
$957$	5.40199	0.174622
$958$	27.9907	0.904338
$959$	16.2129	0.523542
$960$	−10.0851	−0.325495
$961$	−15.4342	−0.497879
$962$	2.48140	0.0800036
$963$	2.86683	0.0923823
$964$	1.51479	0.0487880
$965$	11.2117	0.360917
$966$	23.3767	0.752132
$967$	−14.1768	−0.455896	−0.227948	−	0.973673i	$-0.573202\pi$
$967$	−14.1768	−0.455896	−0.227948	+	0.973673i	$0.573202\pi$
$968$	−1.00000	−0.0321412
$969$	93.1161	2.99132
$970$	18.3766	0.590038
$971$	−48.4161	−1.55375	−0.776873	−	0.629658i	$-0.783195\pi$
$971$	−48.4161	−1.55375	−0.776873	+	0.629658i	$0.783195\pi$
$972$	−6.29726	−0.201985
$973$	86.2809	2.76604
$974$	−6.56576	−0.210381
$975$	−17.8575	−0.571899
$976$	−0.0760824	−0.00243534
$977$	12.2516	0.391964	0.195982	−	0.980607i	$-0.437211\pi$
$977$	12.2516	0.391964	0.195982	+	0.980607i	$0.437211\pi$
$978$	15.6068	0.499050
$979$	11.7630	0.375948
$980$	37.4298	1.19565
$981$	25.4638	0.812996
$982$	−24.5470	−0.783326
$983$	49.1327	1.56709	0.783546	−	0.621334i	$-0.213409\pi$
$983$	49.1327	1.56709	0.783546	+	0.621334i	$0.213409\pi$
$984$	23.2733	0.741925
$985$	3.30243	0.105224
$986$	−8.66092	−0.275820
$987$	−147.608	−4.69842
$988$	−6.16596	−0.196165
$989$	−2.14354	−0.0681606
$990$	20.8911	0.663961
$991$	43.5365	1.38298	0.691491	−	0.722385i	$-0.256954\pi$
$991$	43.5365	1.38298	0.691491	+	0.722385i	$0.256954\pi$
$992$	3.94535	0.125265
$993$	24.9393	0.791425
$994$	−9.27446	−0.294168
$995$	9.84443	0.312089
$996$	44.1635	1.39937
$997$	47.6894	1.51034	0.755169	−	0.655530i	$-0.227555\pi$
$997$	47.6894	1.51034	0.755169	+	0.655530i	$0.227555\pi$
$998$	−11.8277	−0.374400
$999$	25.4555	0.805378

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4334.2.a.e.1.3	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4334.2.a.e.1.3	✓	24	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:	\( N \)	\(=\)	\( 4334 = 2 \cdot 11 \cdot 197 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4334.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -3.05385 q^{3} +1.00000 q^{4} +3.30243 q^{5} +3.05385 q^{6} +4.28183 q^{7} -1.00000 q^{8} +6.32597 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -3.05385 q^{3} +1.00000 q^{4} +3.30243 q^{5} +3.05385 q^{6} +4.28183 q^{7} -1.00000 q^{8} +6.32597 q^{9} -3.30243 q^{10} -1.00000 q^{11} -3.05385 q^{12} +0.990101 q^{13} -4.28183 q^{14} -10.0851 q^{15} +1.00000 q^{16} +4.89617 q^{17} -6.32597 q^{18} -6.22760 q^{19} +3.30243 q^{20} -13.0760 q^{21} +1.00000 q^{22} +1.78775 q^{23} +3.05385 q^{24} +5.90602 q^{25} -0.990101 q^{26} -10.1570 q^{27} +4.28183 q^{28} +1.76892 q^{29} +10.0851 q^{30} -3.94535 q^{31} -1.00000 q^{32} +3.05385 q^{33} -4.89617 q^{34} +14.1404 q^{35} +6.32597 q^{36} -2.50621 q^{37} +6.22760 q^{38} -3.02362 q^{39} -3.30243 q^{40} +7.62097 q^{41} +13.0760 q^{42} -1.19902 q^{43} -1.00000 q^{44} +20.8911 q^{45} -1.78775 q^{46} +11.2885 q^{47} -3.05385 q^{48} +11.3340 q^{49} -5.90602 q^{50} -14.9522 q^{51} +0.990101 q^{52} +8.01980 q^{53} +10.1570 q^{54} -3.30243 q^{55} -4.28183 q^{56} +19.0181 q^{57} -1.76892 q^{58} -0.889962 q^{59} -10.0851 q^{60} -0.0760824 q^{61} +3.94535 q^{62} +27.0867 q^{63} +1.00000 q^{64} +3.26974 q^{65} -3.05385 q^{66} -2.48328 q^{67} +4.89617 q^{68} -5.45951 q^{69} -14.1404 q^{70} +2.16601 q^{71} -6.32597 q^{72} +13.3142 q^{73} +2.50621 q^{74} -18.0361 q^{75} -6.22760 q^{76} -4.28183 q^{77} +3.02362 q^{78} +4.62710 q^{79} +3.30243 q^{80} +12.0400 q^{81} -7.62097 q^{82} -14.4616 q^{83} -13.0760 q^{84} +16.1693 q^{85} +1.19902 q^{86} -5.40199 q^{87} +1.00000 q^{88} -11.7630 q^{89} -20.8911 q^{90} +4.23944 q^{91} +1.78775 q^{92} +12.0485 q^{93} -11.2885 q^{94} -20.5662 q^{95} +3.05385 q^{96} -5.56458 q^{97} -11.3340 q^{98} -6.32597 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9}+O(q^{10}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9	\( 24 q - 24 q^{2} - 4 q^{3} + 24 q^{4} - 4 q^{5} + 4 q^{6} + 7 q^{7} - 24 q^{8} + 28 q^{9} + 4 q^{10} - 24 q^{11} - 4 q^{12} + 21 q^{13} - 7 q^{14} - 2 q^{15} + 24 q^{16} + 15 q^{17} - 28 q^{18} + 21 q^{19} - 4 q^{20} + 15 q^{21} + 24 q^{22} - 17 q^{23} + 4 q^{24} + 46 q^{25} - 21 q^{26} - 19 q^{27} + 7 q^{28} + 9 q^{29} + 2 q^{30} + 27 q^{31} - 24 q^{32} + 4 q^{33} - 15 q^{34} - 2 q^{35} + 28 q^{36} + 5 q^{37} - 21 q^{38} + 17 q^{39} + 4 q^{40} + 16 q^{41} - 15 q^{42} + 3 q^{43} - 24 q^{44} - 21 q^{45} + 17 q^{46} - 24 q^{47} - 4 q^{48} + 55 q^{49} - 46 q^{50} - 12 q^{51} + 21 q^{52} - 26 q^{53} + 19 q^{54} + 4 q^{55} - 7 q^{56} + 30 q^{57} - 9 q^{58} - 17 q^{59} - 2 q^{60} + 44 q^{61} - 27 q^{62} + 4 q^{63} + 24 q^{64} + 35 q^{65} - 4 q^{66} + 10 q^{67} + 15 q^{68} + 3 q^{69} + 2 q^{70} - 6 q^{71} - 28 q^{72} + 77 q^{73} - 5 q^{74} - 32 q^{75} + 21 q^{76} - 7 q^{77} - 17 q^{78} + 43 q^{79} - 4 q^{80} + 48 q^{81} - 16 q^{82} - 20 q^{83} + 15 q^{84} + 35 q^{85} - 3 q^{86} + 36 q^{87} + 24 q^{88} + 3 q^{89} + 21 q^{90} + 63 q^{91} - 17 q^{92} + 36 q^{93} + 24 q^{94} - 3 q^{95} + 4 q^{96} + 16 q^{97} - 55 q^{98} - 28 q^{99}+O(q^{100}) \) 24 * q - 24 * q^2 - 4 * q^3 + 24 * q^4 - 4 * q^5 + 4 * q^6 + 7 * q^7 - 24 * q^8 + 28 * q^9 + 4 * q^10 - 24 * q^11 - 4 * q^12 + 21 * q^13 - 7 * q^14 - 2 * q^15 + 24 * q^16 + 15 * q^17 - 28 * q^18 + 21 * q^19 - 4 * q^20 + 15 * q^21 + 24 * q^22 - 17 * q^23 + 4 * q^24 + 46 * q^25 - 21 * q^26 - 19 * q^27 + 7 * q^28 + 9 * q^29 + 2 * q^30 + 27 * q^31 - 24 * q^32 + 4 * q^33 - 15 * q^34 - 2 * q^35 + 28 * q^36 + 5 * q^37 - 21 * q^38 + 17 * q^39 + 4 * q^40 + 16 * q^41 - 15 * q^42 + 3 * q^43 - 24 * q^44 - 21 * q^45 + 17 * q^46 - 24 * q^47 - 4 * q^48 + 55 * q^49 - 46 * q^50 - 12 * q^51 + 21 * q^52 - 26 * q^53 + 19 * q^54 + 4 * q^55 - 7 * q^56 + 30 * q^57 - 9 * q^58 - 17 * q^59 - 2 * q^60 + 44 * q^61 - 27 * q^62 + 4 * q^63 + 24 * q^64 + 35 * q^65 - 4 * q^66 + 10 * q^67 + 15 * q^68 + 3 * q^69 + 2 * q^70 - 6 * q^71 - 28 * q^72 + 77 * q^73 - 5 * q^74 - 32 * q^75 + 21 * q^76 - 7 * q^77 - 17 * q^78 + 43 * q^79 - 4 * q^80 + 48 * q^81 - 16 * q^82 - 20 * q^83 + 15 * q^84 + 35 * q^85 - 3 * q^86 + 36 * q^87 + 24 * q^88 + 3 * q^89 + 21 * q^90 + 63 * q^91 - 17 * q^92 + 36 * q^93 + 24 * q^94 - 3 * q^95 + 4 * q^96 + 16 * q^97 - 55 * q^98 - 28 * q^99

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