LMFDB - Embedded newform 6015.2.a.d.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6015,2,Mod(1,6015)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6015, 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("6015.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6015 = 3 \cdot 5 \cdot 401 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6015.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$48.0300168158$
Analytic rank:	$1$
Dimension:	$29$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	6015.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.0247562 q^{2} -1.00000 q^{3} -1.99939 q^{4} +1.00000 q^{5} +0.0247562 q^{6} -4.38402 q^{7} +0.0990096 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.0247562 q^{2} -1.00000 q^{3} -1.99939 q^{4} +1.00000 q^{5} +0.0247562 q^{6} -4.38402 q^{7} +0.0990096 q^{8} +1.00000 q^{9} -0.0247562 q^{10} -2.88256 q^{11} +1.99939 q^{12} -3.62152 q^{13} +0.108532 q^{14} -1.00000 q^{15} +3.99632 q^{16} -4.67786 q^{17} -0.0247562 q^{18} +2.40247 q^{19} -1.99939 q^{20} +4.38402 q^{21} +0.0713612 q^{22} +8.04701 q^{23} -0.0990096 q^{24} +1.00000 q^{25} +0.0896550 q^{26} -1.00000 q^{27} +8.76536 q^{28} +5.33027 q^{29} +0.0247562 q^{30} +4.42864 q^{31} -0.296953 q^{32} +2.88256 q^{33} +0.115806 q^{34} -4.38402 q^{35} -1.99939 q^{36} +5.46544 q^{37} -0.0594761 q^{38} +3.62152 q^{39} +0.0990096 q^{40} -4.06597 q^{41} -0.108532 q^{42} -0.379223 q^{43} +5.76335 q^{44} +1.00000 q^{45} -0.199213 q^{46} +9.24879 q^{47} -3.99632 q^{48} +12.2196 q^{49} -0.0247562 q^{50} +4.67786 q^{51} +7.24081 q^{52} +12.4641 q^{53} +0.0247562 q^{54} -2.88256 q^{55} -0.434060 q^{56} -2.40247 q^{57} -0.131957 q^{58} -4.05740 q^{59} +1.99939 q^{60} -8.53674 q^{61} -0.109636 q^{62} -4.38402 q^{63} -7.98529 q^{64} -3.62152 q^{65} -0.0713612 q^{66} -3.04194 q^{67} +9.35284 q^{68} -8.04701 q^{69} +0.108532 q^{70} -15.3991 q^{71} +0.0990096 q^{72} -2.67908 q^{73} -0.135304 q^{74} -1.00000 q^{75} -4.80347 q^{76} +12.6372 q^{77} -0.0896550 q^{78} -3.47101 q^{79} +3.99632 q^{80} +1.00000 q^{81} +0.100658 q^{82} +12.7553 q^{83} -8.76536 q^{84} -4.67786 q^{85} +0.00938811 q^{86} -5.33027 q^{87} -0.285401 q^{88} -9.48144 q^{89} -0.0247562 q^{90} +15.8768 q^{91} -16.0891 q^{92} -4.42864 q^{93} -0.228965 q^{94} +2.40247 q^{95} +0.296953 q^{96} +7.64797 q^{97} -0.302512 q^{98} -2.88256 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) $ 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * 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 $

$2$	−0.0247562	−0.0175053	−0.00875264	−	0.999962i	$-0.502786\pi$
$2$	−0.0247562	−0.0175053	−0.00875264	+	0.999962i	$0.502786\pi$
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	−1.99939	−0.999694
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.0247562	0.0101067
$7$	−4.38402	−1.65700	−0.828502	−	0.559986i	$-0.810807\pi$
$7$	−4.38402	−1.65700	−0.828502	+	0.559986i	$0.810807\pi$
$8$	0.0990096	0.0350052
$9$	1.00000	0.333333
$10$	−0.0247562	−0.00782860
$11$	−2.88256	−0.869125	−0.434562	−	0.900642i	$-0.643097\pi$
$11$	−2.88256	−0.869125	−0.434562	+	0.900642i	$0.643097\pi$
$12$	1.99939	0.577173
$13$	−3.62152	−1.00443	−0.502214	−	0.864743i	$-0.667481\pi$
$13$	−3.62152	−1.00443	−0.502214	+	0.864743i	$0.667481\pi$
$14$	0.108532	0.0290063
$15$	−1.00000	−0.258199
$16$	3.99632	0.999081
$17$	−4.67786	−1.13455	−0.567273	−	0.823530i	$-0.692002\pi$
$17$	−4.67786	−1.13455	−0.567273	+	0.823530i	$0.692002\pi$
$18$	−0.0247562	−0.00583509
$19$	2.40247	0.551165	0.275583	−	0.961277i	$-0.411129\pi$
$19$	2.40247	0.551165	0.275583	+	0.961277i	$0.411129\pi$
$20$	−1.99939	−0.447077
$21$	4.38402	0.956672
$22$	0.0713612	0.0152143
$23$	8.04701	1.67792	0.838959	−	0.544195i	$-0.183165\pi$
$23$	8.04701	1.67792	0.838959	+	0.544195i	$0.183165\pi$
$24$	−0.0990096	−0.0202103
$25$	1.00000	0.200000
$26$	0.0896550	0.0175828
$27$	−1.00000	−0.192450
$28$	8.76536	1.65650
$29$	5.33027	0.989806	0.494903	−	0.868948i	$-0.335204\pi$
$29$	5.33027	0.989806	0.494903	+	0.868948i	$0.335204\pi$
$30$	0.0247562	0.00451984
$31$	4.42864	0.795408	0.397704	−	0.917514i	$-0.369807\pi$
$31$	4.42864	0.795408	0.397704	+	0.917514i	$0.369807\pi$
$32$	−0.296953	−0.0524944
$33$	2.88256	0.501789
$34$	0.115806	0.0198605
$35$	−4.38402	−0.741035
$36$	−1.99939	−0.333231
$37$	5.46544	0.898513	0.449257	−	0.893403i	$-0.351689\pi$
$37$	5.46544	0.898513	0.449257	+	0.893403i	$0.351689\pi$
$38$	−0.0594761	−0.00964830
$39$	3.62152	0.579907
$40$	0.0990096	0.0156548
$41$	−4.06597	−0.634998	−0.317499	−	0.948259i	$-0.602843\pi$
$41$	−4.06597	−0.634998	−0.317499	+	0.948259i	$0.602843\pi$
$42$	−0.108532	−0.0167468
$43$	−0.379223	−0.0578309	−0.0289155	−	0.999582i	$-0.509205\pi$
$43$	−0.379223	−0.0578309	−0.0289155	+	0.999582i	$0.509205\pi$
$44$	5.76335	0.868858
$45$	1.00000	0.149071
$46$	−0.199213	−0.0293724
$47$	9.24879	1.34907	0.674537	−	0.738241i	$-0.264343\pi$
$47$	9.24879	1.34907	0.674537	+	0.738241i	$0.264343\pi$
$48$	−3.99632	−0.576820
$49$	12.2196	1.74566
$50$	−0.0247562	−0.00350106
$51$	4.67786	0.655031
$52$	7.24081	1.00412
$53$	12.4641	1.71207	0.856036	−	0.516916i	$-0.172920\pi$
$53$	12.4641	1.71207	0.856036	+	0.516916i	$0.172920\pi$
$54$	0.0247562	0.00336889
$55$	−2.88256	−0.388684
$56$	−0.434060	−0.0580037
$57$	−2.40247	−0.318215
$58$	−0.131957	−0.0173268
$59$	−4.05740	−0.528228	−0.264114	−	0.964491i	$-0.585080\pi$
$59$	−4.05740	−0.528228	−0.264114	+	0.964491i	$0.585080\pi$
$60$	1.99939	0.258120
$61$	−8.53674	−1.09302	−0.546509	−	0.837454i	$-0.684043\pi$
$61$	−8.53674	−1.09302	−0.546509	+	0.837454i	$0.684043\pi$
$62$	−0.109636	−0.0139238
$63$	−4.38402	−0.552335
$64$	−7.98529	−0.998162
$65$	−3.62152	−0.449194
$66$	−0.0713612	−0.00878396
$67$	−3.04194	−0.371632	−0.185816	−	0.982585i	$-0.559493\pi$
$67$	−3.04194	−0.371632	−0.185816	+	0.982585i	$0.559493\pi$
$68$	9.35284	1.13420
$69$	−8.04701	−0.968746
$70$	0.108532	0.0129720
$71$	−15.3991	−1.82753	−0.913767	−	0.406238i	$-0.866840\pi$
$71$	−15.3991	−1.82753	−0.913767	+	0.406238i	$0.866840\pi$
$72$	0.0990096	0.0116684
$73$	−2.67908	−0.313563	−0.156781	−	0.987633i	$-0.550112\pi$
$73$	−2.67908	−0.313563	−0.156781	+	0.987633i	$0.550112\pi$
$74$	−0.135304	−0.0157287
$75$	−1.00000	−0.115470
$76$	−4.80347	−0.550996
$77$	12.6372	1.44014
$78$	−0.0896550	−0.0101514
$79$	−3.47101	−0.390520	−0.195260	−	0.980752i	$-0.562555\pi$
$79$	−3.47101	−0.390520	−0.195260	+	0.980752i	$0.562555\pi$
$80$	3.99632	0.446803
$81$	1.00000	0.111111
$82$	0.100658	0.0111158
$83$	12.7553	1.40008	0.700038	−	0.714106i	$-0.253167\pi$
$83$	12.7553	1.40008	0.700038	+	0.714106i	$0.253167\pi$
$84$	−8.76536	−0.956379
$85$	−4.67786	−0.507385
$86$	0.00938811	0.00101235
$87$	−5.33027	−0.571465
$88$	−0.285401	−0.0304239
$89$	−9.48144	−1.00503	−0.502515	−	0.864568i	$-0.667592\pi$
$89$	−9.48144	−1.00503	−0.502515	+	0.864568i	$0.667592\pi$
$90$	−0.0247562	−0.00260953
$91$	15.8768	1.66434
$92$	−16.0891	−1.67740
$93$	−4.42864	−0.459229
$94$	−0.228965	−0.0236159
$95$	2.40247	0.246489
$96$	0.296953	0.0303076
$97$	7.64797	0.776533	0.388267	−	0.921547i	$-0.373074\pi$
$97$	7.64797	0.776533	0.388267	+	0.921547i	$0.373074\pi$
$98$	−0.302512	−0.0305583
$99$	−2.88256	−0.289708
$100$	−1.99939	−0.199939
$101$	−6.05728	−0.602721	−0.301361	−	0.953510i	$-0.597441\pi$
$101$	−6.05728	−0.602721	−0.301361	+	0.953510i	$0.597441\pi$
$102$	−0.115806	−0.0114665
$103$	−0.0891816	−0.00878732	−0.00439366	−	0.999990i	$-0.501399\pi$
$103$	−0.0891816	−0.00878732	−0.00439366	+	0.999990i	$0.501399\pi$
$104$	−0.358565	−0.0351602
$105$	4.38402	0.427837
$106$	−0.308563	−0.0299703
$107$	9.74591	0.942173	0.471086	−	0.882087i	$-0.343862\pi$
$107$	9.74591	0.942173	0.471086	+	0.882087i	$0.343862\pi$
$108$	1.99939	0.192391
$109$	−17.0393	−1.63206	−0.816032	−	0.578006i	$-0.803831\pi$
$109$	−17.0393	−1.63206	−0.816032	+	0.578006i	$0.803831\pi$
$110$	0.0713612	0.00680403
$111$	−5.46544	−0.518757
$112$	−17.5200	−1.65548
$113$	0.107123	0.0100773	0.00503863	−	0.999987i	$-0.498396\pi$
$113$	0.107123	0.0100773	0.00503863	+	0.999987i	$0.498396\pi$
$114$	0.0594761	0.00557045
$115$	8.04701	0.750388
$116$	−10.6573	−0.989503
$117$	−3.62152	−0.334809
$118$	0.100446	0.00924678
$119$	20.5078	1.87995
$120$	−0.0990096	−0.00903830
$121$	−2.69084	−0.244622
$122$	0.211337	0.0191336
$123$	4.06597	0.366616
$124$	−8.85457	−0.795164
$125$	1.00000	0.0894427
$126$	0.108532	0.00966877
$127$	4.09930	0.363754	0.181877	−	0.983321i	$-0.441783\pi$
$127$	4.09930	0.363754	0.181877	+	0.983321i	$0.441783\pi$
$128$	0.791592	0.0699675
$129$	0.379223	0.0333887
$130$	0.0896550	0.00786326
$131$	−3.27105	−0.285793	−0.142896	−	0.989738i	$-0.545642\pi$
$131$	−3.27105	−0.285793	−0.142896	+	0.989738i	$0.545642\pi$
$132$	−5.76335	−0.501636
$133$	−10.5325	−0.913283
$134$	0.0753069	0.00650553
$135$	−1.00000	−0.0860663
$136$	−0.463153	−0.0397150
$137$	12.2860	1.04967	0.524834	−	0.851205i	$-0.324127\pi$
$137$	12.2860	1.04967	0.524834	+	0.851205i	$0.324127\pi$
$138$	0.199213	0.0169582
$139$	8.96658	0.760535	0.380268	−	0.924876i	$-0.375832\pi$
$139$	8.96658	0.760535	0.380268	+	0.924876i	$0.375832\pi$
$140$	8.76536	0.740808
$141$	−9.24879	−0.778888
$142$	0.381223	0.0319915
$143$	10.4392	0.872973
$144$	3.99632	0.333027
$145$	5.33027	0.442655
$146$	0.0663239	0.00548900
$147$	−12.2196	−1.00786
$148$	−10.9275	−0.898238
$149$	8.07373	0.661426	0.330713	−	0.943731i	$-0.392711\pi$
$149$	8.07373	0.661426	0.330713	+	0.943731i	$0.392711\pi$
$150$	0.0247562	0.00202134
$151$	−20.3162	−1.65331	−0.826653	−	0.562712i	$-0.809758\pi$
$151$	−20.3162	−1.65331	−0.826653	+	0.562712i	$0.809758\pi$
$152$	0.237868	0.0192936
$153$	−4.67786	−0.378182
$154$	−0.312849	−0.0252101
$155$	4.42864	0.355717
$156$	−7.24081	−0.579729
$157$	−9.43218	−0.752770	−0.376385	−	0.926463i	$-0.622833\pi$
$157$	−9.43218	−0.752770	−0.376385	+	0.926463i	$0.622833\pi$
$158$	0.0859291	0.00683615
$159$	−12.4641	−0.988465
$160$	−0.296953	−0.0234762
$161$	−35.2783	−2.78032
$162$	−0.0247562	−0.00194503
$163$	1.66345	0.130292	0.0651459	−	0.997876i	$-0.479249\pi$
$163$	1.66345	0.130292	0.0651459	+	0.997876i	$0.479249\pi$
$164$	8.12945	0.634803
$165$	2.88256	0.224407
$166$	−0.315773	−0.0245087
$167$	3.01971	0.233672	0.116836	−	0.993151i	$-0.462725\pi$
$167$	3.01971	0.233672	0.116836	+	0.993151i	$0.462725\pi$
$168$	0.434060	0.0334885
$169$	0.115386	0.00887583
$170$	0.115806	0.00888191
$171$	2.40247	0.183722
$172$	0.758213	0.0578132
$173$	−14.8911	−1.13215	−0.566074	−	0.824355i	$-0.691538\pi$
$173$	−14.8911	−1.13215	−0.566074	+	0.824355i	$0.691538\pi$
$174$	0.131957	0.0100037
$175$	−4.38402	−0.331401
$176$	−11.5196	−0.868326
$177$	4.05740	0.304973
$178$	0.234724	0.0175933
$179$	4.88371	0.365026	0.182513	−	0.983203i	$-0.441577\pi$
$179$	4.88371	0.365026	0.182513	+	0.983203i	$0.441577\pi$
$180$	−1.99939	−0.149026
$181$	−12.8046	−0.951758	−0.475879	−	0.879511i	$-0.657870\pi$
$181$	−12.8046	−0.951758	−0.475879	+	0.879511i	$0.657870\pi$
$182$	−0.393049	−0.0291348
$183$	8.53674	0.631054
$184$	0.796732	0.0587358
$185$	5.46544	0.401827
$186$	0.109636	0.00803893
$187$	13.4842	0.986062
$188$	−18.4919	−1.34866
$189$	4.38402	0.318891
$190$	−0.0594761	−0.00431485
$191$	26.3753	1.90845	0.954227	−	0.299085i	$-0.0966813\pi$
$191$	26.3753	1.90845	0.954227	+	0.299085i	$0.0966813\pi$
$192$	7.98529	0.576289
$193$	−6.95072	−0.500324	−0.250162	−	0.968204i	$-0.580484\pi$
$193$	−6.95072	−0.500324	−0.250162	+	0.968204i	$0.580484\pi$
$194$	−0.189335	−0.0135934
$195$	3.62152	0.259342
$196$	−24.4318	−1.74513
$197$	23.1464	1.64911	0.824556	−	0.565781i	$-0.191425\pi$
$197$	23.1464	1.64911	0.824556	+	0.565781i	$0.191425\pi$
$198$	0.0713612	0.00507142
$199$	21.4538	1.52082	0.760410	−	0.649443i	$-0.224998\pi$
$199$	21.4538	1.52082	0.760410	+	0.649443i	$0.224998\pi$
$200$	0.0990096	0.00700104
$201$	3.04194	0.214562
$202$	0.149955	0.0105508
$203$	−23.3680	−1.64011
$204$	−9.35284	−0.654830
$205$	−4.06597	−0.283980
$206$	0.00220780	0.000153825 0
$207$	8.04701	0.559306
$208$	−14.4728	−1.00350
$209$	−6.92527	−0.479031
$210$	−0.108532	−0.00748940
$211$	−19.6955	−1.35590	−0.677948	−	0.735109i	$-0.737131\pi$
$211$	−19.6955	−1.35590	−0.677948	+	0.735109i	$0.737131\pi$
$212$	−24.9205	−1.71155
$213$	15.3991	1.05513
$214$	−0.241272	−0.0164930
$215$	−0.379223	−0.0258628
$216$	−0.0990096	−0.00673675
$217$	−19.4153	−1.31799
$218$	0.421827	0.0285697
$219$	2.67908	0.181036
$220$	5.76335	0.388565
$221$	16.9409	1.13957
$222$	0.135304	0.00908098
$223$	−7.95656	−0.532811	−0.266405	−	0.963861i	$-0.585836\pi$
$223$	−7.95656	−0.532811	−0.266405	+	0.963861i	$0.585836\pi$
$224$	1.30185	0.0869834
$225$	1.00000	0.0666667
$226$	−0.00265195	−0.000176405 0
$227$	−6.76427	−0.448960	−0.224480	−	0.974479i	$-0.572068\pi$
$227$	−6.76427	−0.448960	−0.224480	+	0.974479i	$0.572068\pi$
$228$	4.80347	0.318118
$229$	−9.25278	−0.611441	−0.305720	−	0.952121i	$-0.598897\pi$
$229$	−9.25278	−0.611441	−0.305720	+	0.952121i	$0.598897\pi$
$230$	−0.199213	−0.0131357
$231$	−12.6372	−0.831467
$232$	0.527748	0.0346484
$233$	2.60804	0.170858	0.0854291	−	0.996344i	$-0.472774\pi$
$233$	2.60804	0.170858	0.0854291	+	0.996344i	$0.472774\pi$
$234$	0.0896550	0.00586093
$235$	9.24879	0.603324
$236$	8.11231	0.528067
$237$	3.47101	0.225467
$238$	−0.507696	−0.0329090
$239$	−14.7366	−0.953234	−0.476617	−	0.879111i	$-0.658137\pi$
$239$	−14.7366	−0.953234	−0.476617	+	0.879111i	$0.658137\pi$
$240$	−3.99632	−0.257962
$241$	22.2690	1.43447	0.717237	−	0.696829i	$-0.245406\pi$
$241$	22.2690	1.43447	0.717237	+	0.696829i	$0.245406\pi$
$242$	0.0666151	0.00428218
$243$	−1.00000	−0.0641500
$244$	17.0682	1.09268
$245$	12.2196	0.780684
$246$	−0.100658	−0.00641772
$247$	−8.70060	−0.553606
$248$	0.438478	0.0278434
$249$	−12.7553	−0.808334
$250$	−0.0247562	−0.00156572
$251$	−6.58630	−0.415723	−0.207862	−	0.978158i	$-0.566650\pi$
$251$	−6.58630	−0.415723	−0.207862	+	0.978158i	$0.566650\pi$
$252$	8.76536	0.552166
$253$	−23.1960	−1.45832
$254$	−0.101483	−0.00636762
$255$	4.67786	0.292939
$256$	15.9510	0.996937
$257$	−9.52308	−0.594033	−0.297017	−	0.954872i	$-0.595992\pi$
$257$	−9.52308	−0.594033	−0.297017	+	0.954872i	$0.595992\pi$
$258$	−0.00938811	−0.000584478 0
$259$	−23.9606	−1.48884
$260$	7.24081	0.449056
$261$	5.33027	0.329935
$262$	0.0809787	0.00500288
$263$	31.0750	1.91616	0.958082	−	0.286493i	$-0.0924896\pi$
$263$	31.0750	1.91616	0.958082	+	0.286493i	$0.0924896\pi$
$264$	0.285401	0.0175652
$265$	12.4641	0.765662
$266$	0.260744	0.0159873
$267$	9.48144	0.580255
$268$	6.08202	0.371519
$269$	−13.4675	−0.821128	−0.410564	−	0.911832i	$-0.634668\pi$
$269$	−13.4675	−0.821128	−0.410564	+	0.911832i	$0.634668\pi$
$270$	0.0247562	0.00150661
$271$	18.8145	1.14290	0.571449	−	0.820638i	$-0.306382\pi$
$271$	18.8145	1.14290	0.571449	+	0.820638i	$0.306382\pi$
$272$	−18.6942	−1.13350
$273$	−15.8768	−0.960908
$274$	−0.304156	−0.0183747
$275$	−2.88256	−0.173825
$276$	16.0891	0.968450
$277$	27.1130	1.62906	0.814531	−	0.580120i	$-0.196994\pi$
$277$	27.1130	1.62906	0.814531	+	0.580120i	$0.196994\pi$
$278$	−0.221978	−0.0133134
$279$	4.42864	0.265136
$280$	−0.434060	−0.0259401
$281$	13.4303	0.801184	0.400592	−	0.916256i	$-0.368804\pi$
$281$	13.4303	0.801184	0.400592	+	0.916256i	$0.368804\pi$
$282$	0.228965	0.0136347
$283$	4.00785	0.238242	0.119121	−	0.992880i	$-0.461992\pi$
$283$	4.00785	0.238242	0.119121	+	0.992880i	$0.461992\pi$
$284$	30.7887	1.82697
$285$	−2.40247	−0.142310
$286$	−0.258436	−0.0152816
$287$	17.8253	1.05219
$288$	−0.296953	−0.0174981
$289$	4.88233	0.287196
$290$	−0.131957	−0.00774880
$291$	−7.64797	−0.448332
$292$	5.35652	0.313467
$293$	−32.7213	−1.91160	−0.955800	−	0.294018i	$-0.905008\pi$
$293$	−32.7213	−1.91160	−0.955800	+	0.294018i	$0.905008\pi$
$294$	0.302512	0.0176429
$295$	−4.05740	−0.236231
$296$	0.541131	0.0314526
$297$	2.88256	0.167263
$298$	−0.199875	−0.0115784
$299$	−29.1424	−1.68535
$300$	1.99939	0.115435
$301$	1.66252	0.0958261
$302$	0.502951	0.0289416
$303$	6.05728	0.347981
$304$	9.60106	0.550658
$305$	−8.53674	−0.488812
$306$	0.115806	0.00662018
$307$	9.80801	0.559773	0.279886	−	0.960033i	$-0.409703\pi$
$307$	9.80801	0.559773	0.279886	+	0.960033i	$0.409703\pi$
$308$	−25.2667	−1.43970
$309$	0.0891816	0.00507336
$310$	−0.109636	−0.00622693
$311$	−28.6266	−1.62327	−0.811634	−	0.584167i	$-0.801421\pi$
$311$	−28.6266	−1.62327	−0.811634	+	0.584167i	$0.801421\pi$
$312$	0.358565	0.0202997
$313$	−15.1414	−0.855841	−0.427921	−	0.903816i	$-0.640754\pi$
$313$	−15.1414	−0.855841	−0.427921	+	0.903816i	$0.640754\pi$
$314$	0.233505	0.0131774
$315$	−4.38402	−0.247012
$316$	6.93990	0.390400
$317$	−33.6626	−1.89068	−0.945339	−	0.326090i	$-0.894269\pi$
$317$	−33.6626	−1.89068	−0.945339	+	0.326090i	$0.894269\pi$
$318$	0.308563	0.0173034
$319$	−15.3648	−0.860265
$320$	−7.98529	−0.446392
$321$	−9.74591	−0.543964
$322$	0.873356	0.0486702
$323$	−11.2384	−0.625322
$324$	−1.99939	−0.111077
$325$	−3.62152	−0.200886
$326$	−0.0411808	−0.00228079
$327$	17.0393	0.942273
$328$	−0.402570	−0.0222282
$329$	−40.5469	−2.23542
$330$	−0.0713612	−0.00392831
$331$	−14.5835	−0.801583	−0.400791	−	0.916169i	$-0.631265\pi$
$331$	−14.5835	−0.801583	−0.400791	+	0.916169i	$0.631265\pi$
$332$	−25.5028	−1.39965
$333$	5.46544	0.299504
$334$	−0.0747566	−0.00409050
$335$	−3.04194	−0.166199
$336$	17.5200	0.955792
$337$	−9.45906	−0.515268	−0.257634	−	0.966243i	$-0.582943\pi$
$337$	−9.45906	−0.515268	−0.257634	+	0.966243i	$0.582943\pi$
$338$	−0.00285651	−0.000155374 0
$339$	−0.107123	−0.00581811
$340$	9.35284	0.507229
$341$	−12.7658	−0.691309
$342$	−0.0594761	−0.00321610
$343$	−22.8830	−1.23557
$344$	−0.0375467	−0.00202438
$345$	−8.04701	−0.433237
$346$	0.368646	0.0198185
$347$	26.5458	1.42505	0.712527	−	0.701645i	$-0.247551\pi$
$347$	26.5458	1.42505	0.712527	+	0.701645i	$0.247551\pi$
$348$	10.6573	0.571290
$349$	−24.1527	−1.29286	−0.646432	−	0.762972i	$-0.723739\pi$
$349$	−24.1527	−1.29286	−0.646432	+	0.762972i	$0.723739\pi$
$350$	0.108532	0.00580126
$351$	3.62152	0.193302
$352$	0.855985	0.0456242
$353$	30.0208	1.59785	0.798924	−	0.601432i	$-0.205403\pi$
$353$	30.0208	1.59785	0.798924	+	0.601432i	$0.205403\pi$
$354$	−0.100446	−0.00533863
$355$	−15.3991	−0.817298
$356$	18.9571	1.00472
$357$	−20.5078	−1.08539
$358$	−0.120902	−0.00638987
$359$	−12.3761	−0.653187	−0.326593	−	0.945165i	$-0.605901\pi$
$359$	−12.3761	−0.653187	−0.326593	+	0.945165i	$0.605901\pi$
$360$	0.0990096	0.00521827
$361$	−13.2281	−0.696217
$362$	0.316993	0.0166608
$363$	2.69084	0.141233
$364$	−31.7439	−1.66383
$365$	−2.67908	−0.140230
$366$	−0.211337	−0.0110468
$367$	−27.6362	−1.44260	−0.721299	−	0.692624i	$-0.756454\pi$
$367$	−27.6362	−1.44260	−0.721299	+	0.692624i	$0.756454\pi$
$368$	32.1585	1.67638
$369$	−4.06597	−0.211666
$370$	−0.135304	−0.00703410
$371$	−54.6428	−2.83691
$372$	8.85457	0.459088
$373$	−29.8091	−1.54346	−0.771729	−	0.635951i	$-0.780608\pi$
$373$	−29.8091	−1.54346	−0.771729	+	0.635951i	$0.780608\pi$
$374$	−0.333818	−0.0172613
$375$	−1.00000	−0.0516398
$376$	0.915719	0.0472246
$377$	−19.3037	−0.994189
$378$	−0.108532	−0.00558227
$379$	22.8575	1.17411	0.587055	−	0.809547i	$-0.300287\pi$
$379$	22.8575	1.17411	0.587055	+	0.809547i	$0.300287\pi$
$380$	−4.80347	−0.246413
$381$	−4.09930	−0.210014
$382$	−0.652953	−0.0334080
$383$	8.01308	0.409449	0.204725	−	0.978820i	$-0.434370\pi$
$383$	8.01308	0.409449	0.204725	+	0.978820i	$0.434370\pi$
$384$	−0.791592	−0.0403957
$385$	12.6372	0.644052
$386$	0.172073	0.00875830
$387$	−0.379223	−0.0192770
$388$	−15.2912	−0.776295
$389$	16.0321	0.812860	0.406430	−	0.913682i	$-0.366773\pi$
$389$	16.0321	0.812860	0.406430	+	0.913682i	$0.366773\pi$
$390$	−0.0896550	−0.00453986
$391$	−37.6428	−1.90368
$392$	1.20986	0.0611073
$393$	3.27105	0.165003
$394$	−0.573016	−0.0288681
$395$	−3.47101	−0.174646
$396$	5.76335	0.289619
$397$	36.1553	1.81458	0.907291	−	0.420503i	$-0.138146\pi$
$397$	36.1553	1.81458	0.907291	+	0.420503i	$0.138146\pi$
$398$	−0.531115	−0.0266224
$399$	10.5325	0.527284
$400$	3.99632	0.199816
$401$	1.00000	0.0499376
$401$	1.00000	0.0499376
$402$	−0.0753069	−0.00375597
$403$	−16.0384	−0.798930
$404$	12.1108	0.602537
$405$	1.00000	0.0496904
$406$	0.578503	0.0287106
$407$	−15.7545	−0.780920
$408$	0.463153	0.0229295
$409$	18.3042	0.905085	0.452543	−	0.891743i	$-0.350517\pi$
$409$	18.3042	0.905085	0.452543	+	0.891743i	$0.350517\pi$
$410$	0.100658	0.00497114
$411$	−12.2860	−0.606026
$412$	0.178309	0.00878463
$413$	17.7877	0.875277
$414$	−0.199213	−0.00979081
$415$	12.7553	0.626133
$416$	1.07542	0.0527268
$417$	−8.96658	−0.439095
$418$	0.171443	0.00838557
$419$	13.8404	0.676148	0.338074	−	0.941120i	$-0.390225\pi$
$419$	13.8404	0.676148	0.338074	+	0.941120i	$0.390225\pi$
$420$	−8.76536	−0.427706
$421$	7.34625	0.358034	0.179017	−	0.983846i	$-0.442708\pi$
$421$	7.34625	0.358034	0.179017	+	0.983846i	$0.442708\pi$
$422$	0.487587	0.0237353
$423$	9.24879	0.449691
$424$	1.23406	0.0599314
$425$	−4.67786	−0.226909
$426$	−0.381223	−0.0184703
$427$	37.4252	1.81113
$428$	−19.4858	−0.941884
$429$	−10.4392	−0.504011
$430$	0.00938811	0.000452735 0
$431$	−17.0647	−0.821976	−0.410988	−	0.911641i	$-0.634816\pi$
$431$	−17.0647	−0.821976	−0.410988	+	0.911641i	$0.634816\pi$
$432$	−3.99632	−0.192273
$433$	−16.7697	−0.805900	−0.402950	−	0.915222i	$-0.632015\pi$
$433$	−16.7697	−0.805900	−0.402950	+	0.915222i	$0.632015\pi$
$434$	0.480648	0.0230719
$435$	−5.33027	−0.255567
$436$	34.0681	1.63156
$437$	19.3327	0.924810
$438$	−0.0663239	−0.00316908
$439$	−18.2911	−0.872988	−0.436494	−	0.899707i	$-0.643780\pi$
$439$	−18.2911	−0.872988	−0.436494	+	0.899707i	$0.643780\pi$
$440$	−0.285401	−0.0136060
$441$	12.2196	0.581888
$442$	−0.419393	−0.0199485
$443$	−23.0367	−1.09451	−0.547254	−	0.836967i	$-0.684327\pi$
$443$	−23.0367	−1.09451	−0.547254	+	0.836967i	$0.684327\pi$
$444$	10.9275	0.518598
$445$	−9.48144	−0.449464
$446$	0.196974	0.00932700
$447$	−8.07373	−0.381875
$448$	35.0077	1.65396
$449$	4.06504	0.191841	0.0959206	−	0.995389i	$-0.469421\pi$
$449$	4.06504	0.191841	0.0959206	+	0.995389i	$0.469421\pi$
$450$	−0.0247562	−0.00116702
$451$	11.7204	0.551892
$452$	−0.214180	−0.0100742
$453$	20.3162	0.954536
$454$	0.167458	0.00785917
$455$	15.8768	0.744316
$456$	−0.237868	−0.0111392
$457$	9.16788	0.428855	0.214428	−	0.976740i	$-0.431211\pi$
$457$	9.16788	0.428855	0.214428	+	0.976740i	$0.431211\pi$
$458$	0.229064	0.0107034
$459$	4.67786	0.218344
$460$	−16.0891	−0.750158
$461$	−33.4555	−1.55818	−0.779090	−	0.626912i	$-0.784319\pi$
$461$	−33.4555	−1.55818	−0.779090	+	0.626912i	$0.784319\pi$
$462$	0.312849	0.0145551
$463$	−37.8792	−1.76040	−0.880198	−	0.474606i	$-0.842590\pi$
$463$	−37.8792	−1.76040	−0.880198	+	0.474606i	$0.842590\pi$
$464$	21.3015	0.988897
$465$	−4.42864	−0.205373
$466$	−0.0645651	−0.00299092
$467$	−24.4045	−1.12931	−0.564653	−	0.825329i	$-0.690990\pi$
$467$	−24.4045	−1.12931	−0.564653	+	0.825329i	$0.690990\pi$
$468$	7.24081	0.334707
$469$	13.3359	0.615796
$470$	−0.228965	−0.0105614
$471$	9.43218	0.434612
$472$	−0.401722	−0.0184907
$473$	1.09313	0.0502623
$474$	−0.0859291	−0.00394685
$475$	2.40247	0.110233
$476$	−41.0031	−1.87937
$477$	12.4641	0.570691
$478$	0.364823	0.0166866
$479$	−7.63439	−0.348824	−0.174412	−	0.984673i	$-0.555803\pi$
$479$	−7.63439	−0.348824	−0.174412	+	0.984673i	$0.555803\pi$
$480$	0.296953	0.0135540
$481$	−19.7932	−0.902492
$482$	−0.551297	−0.0251109
$483$	35.2783	1.60522
$484$	5.38004	0.244547
$485$	7.64797	0.347276
$486$	0.0247562	0.00112296
$487$	27.2502	1.23483	0.617413	−	0.786639i	$-0.288181\pi$
$487$	27.2502	1.23483	0.617413	+	0.786639i	$0.288181\pi$
$488$	−0.845219	−0.0382613
$489$	−1.66345	−0.0752240
$490$	−0.302512	−0.0136661
$491$	11.5061	0.519264	0.259632	−	0.965708i	$-0.416399\pi$
$491$	11.5061	0.519264	0.259632	+	0.965708i	$0.416399\pi$
$492$	−8.12945	−0.366504
$493$	−24.9342	−1.12298
$494$	0.215394	0.00969102
$495$	−2.88256	−0.129561
$496$	17.6983	0.794677
$497$	67.5099	3.02823
$498$	0.315773	0.0141501
$499$	38.2609	1.71279	0.856397	−	0.516318i	$-0.172698\pi$
$499$	38.2609	1.71279	0.856397	+	0.516318i	$0.172698\pi$
$500$	−1.99939	−0.0894153
$501$	−3.01971	−0.134911
$502$	0.163052	0.00727735
$503$	−3.23655	−0.144311	−0.0721553	−	0.997393i	$-0.522988\pi$
$503$	−3.23655	−0.144311	−0.0721553	+	0.997393i	$0.522988\pi$
$504$	−0.434060	−0.0193346
$505$	−6.05728	−0.269545
$506$	0.574245	0.0255283
$507$	−0.115386	−0.00512446
$508$	−8.19610	−0.363643
$509$	−12.0688	−0.534938	−0.267469	−	0.963566i	$-0.586187\pi$
$509$	−12.0688	−0.534938	−0.267469	+	0.963566i	$0.586187\pi$
$510$	−0.115806	−0.00512797
$511$	11.7451	0.519575
$512$	−1.97807	−0.0874191
$513$	−2.40247	−0.106072
$514$	0.235755	0.0103987
$515$	−0.0891816	−0.00392981
$516$	−0.758213	−0.0333785
$517$	−26.6602	−1.17251
$518$	0.593174	0.0260626
$519$	14.8911	0.653645
$520$	−0.358565	−0.0157241
$521$	7.79595	0.341547	0.170773	−	0.985310i	$-0.445373\pi$
$521$	7.79595	0.341547	0.170773	+	0.985310i	$0.445373\pi$
$522$	−0.131957	−0.00577561
$523$	16.9300	0.740299	0.370149	−	0.928972i	$-0.379307\pi$
$523$	16.9300	0.740299	0.370149	+	0.928972i	$0.379307\pi$
$524$	6.54009	0.285705
$525$	4.38402	0.191334
$526$	−0.769298	−0.0335430
$527$	−20.7166	−0.902427
$528$	11.5196	0.501328
$529$	41.7544	1.81541
$530$	−0.308563	−0.0134031
$531$	−4.05740	−0.176076
$532$	21.0585	0.913003
$533$	14.7250	0.637809
$534$	−0.234724	−0.0101575
$535$	9.74591	0.421352
$536$	−0.301182	−0.0130091
$537$	−4.88371	−0.210748
$538$	0.333404	0.0143741
$539$	−35.2239	−1.51720
$540$	1.99939	0.0860399
$541$	18.9956	0.816686	0.408343	−	0.912829i	$-0.366107\pi$
$541$	18.9956	0.816686	0.408343	+	0.912829i	$0.366107\pi$
$542$	−0.465775	−0.0200067
$543$	12.8046	0.549497
$544$	1.38910	0.0595573
$545$	−17.0393	−0.729881
$546$	0.393049	0.0168210
$547$	−3.27910	−0.140204	−0.0701022	−	0.997540i	$-0.522333\pi$
$547$	−3.27910	−0.140204	−0.0701022	+	0.997540i	$0.522333\pi$
$548$	−24.5646	−1.04935
$549$	−8.53674	−0.364339
$550$	0.0713612	0.00304285
$551$	12.8058	0.545547
$552$	−0.796732	−0.0339111
$553$	15.2170	0.647093
$554$	−0.671215	−0.0285172
$555$	−5.46544	−0.231995
$556$	−17.9277	−0.760302
$557$	−5.79019	−0.245338	−0.122669	−	0.992448i	$-0.539145\pi$
$557$	−5.79019	−0.245338	−0.122669	+	0.992448i	$0.539145\pi$
$558$	−0.109636	−0.00464128
$559$	1.37336	0.0580870
$560$	−17.5200	−0.740354
$561$	−13.4842	−0.569303
$562$	−0.332483	−0.0140250
$563$	−46.2350	−1.94857	−0.974286	−	0.225313i	$-0.927659\pi$
$563$	−46.2350	−1.94857	−0.974286	+	0.225313i	$0.927659\pi$
$564$	18.4919	0.778650
$565$	0.107123	0.00450669
$566$	−0.0992191	−0.00417049
$567$	−4.38402	−0.184112
$568$	−1.52466	−0.0639732
$569$	−15.4026	−0.645711	−0.322855	−	0.946448i	$-0.604643\pi$
$569$	−15.4026	−0.645711	−0.322855	+	0.946448i	$0.604643\pi$
$570$	0.0594761	0.00249118
$571$	13.1186	0.548996	0.274498	−	0.961588i	$-0.411488\pi$
$571$	13.1186	0.548996	0.274498	+	0.961588i	$0.411488\pi$
$572$	−20.8721	−0.872706
$573$	−26.3753	−1.10185
$574$	−0.441287	−0.0184189
$575$	8.04701	0.335584
$576$	−7.98529	−0.332721
$577$	−24.7477	−1.03026	−0.515130	−	0.857112i	$-0.672256\pi$
$577$	−24.7477	−1.03026	−0.515130	+	0.857112i	$0.672256\pi$
$578$	−0.120868	−0.00502744
$579$	6.95072	0.288862
$580$	−10.6573	−0.442519
$581$	−55.9195	−2.31993
$582$	0.189335	0.00784817
$583$	−35.9284	−1.48800
$584$	−0.265255	−0.0109763
$585$	−3.62152	−0.149731
$586$	0.810056	0.0334631
$587$	−7.10402	−0.293214	−0.146607	−	0.989195i	$-0.546835\pi$
$587$	−7.10402	−0.293214	−0.146607	+	0.989195i	$0.546835\pi$
$588$	24.4318	1.00755
$589$	10.6397	0.438401
$590$	0.100446	0.00413529
$591$	−23.1464	−0.952115
$592$	21.8417	0.897687
$593$	−4.41263	−0.181205	−0.0906024	−	0.995887i	$-0.528879\pi$
$593$	−4.41263	−0.181205	−0.0906024	+	0.995887i	$0.528879\pi$
$594$	−0.0713612	−0.00292799
$595$	20.5078	0.840738
$596$	−16.1425	−0.661223
$597$	−21.4538	−0.878046
$598$	0.721455	0.0295025
$599$	−4.14312	−0.169283	−0.0846416	−	0.996411i	$-0.526975\pi$
$599$	−4.14312	−0.169283	−0.0846416	+	0.996411i	$0.526975\pi$
$600$	−0.0990096	−0.00404205
$601$	−41.0848	−1.67589	−0.837943	−	0.545758i	$-0.816242\pi$
$601$	−41.0848	−1.67589	−0.837943	+	0.545758i	$0.816242\pi$
$602$	−0.0411577	−0.00167746
$603$	−3.04194	−0.123877
$604$	40.6199	1.65280
$605$	−2.69084	−0.109398
$606$	−0.149955	−0.00609151
$607$	2.10550	0.0854595	0.0427297	−	0.999087i	$-0.486395\pi$
$607$	2.10550	0.0854595	0.0427297	+	0.999087i	$0.486395\pi$
$608$	−0.713422	−0.0289331
$609$	23.3680	0.946920
$610$	0.211337	0.00855679
$611$	−33.4946	−1.35505
$612$	9.35284	0.378066
$613$	9.37083	0.378484	0.189242	−	0.981930i	$-0.439397\pi$
$613$	9.37083	0.378484	0.189242	+	0.981930i	$0.439397\pi$
$614$	−0.242809	−0.00979898
$615$	4.06597	0.163956
$616$	1.25121	0.0504125
$617$	−47.6217	−1.91718	−0.958589	−	0.284793i	$-0.908075\pi$
$617$	−47.6217	−1.91718	−0.958589	+	0.284793i	$0.908075\pi$
$618$	−0.00220780	−8.88106e−5 0
$619$	37.1314	1.49244	0.746218	−	0.665702i	$-0.231868\pi$
$619$	37.1314	1.49244	0.746218	+	0.665702i	$0.231868\pi$
$620$	−8.85457	−0.355608
$621$	−8.04701	−0.322915
$622$	0.708687	0.0284157
$623$	41.5668	1.66534
$624$	14.4728	0.579374
$625$	1.00000	0.0400000
$626$	0.374843	0.0149817
$627$	6.92527	0.276569
$628$	18.8586	0.752539
$629$	−25.5666	−1.01941
$630$	0.108532	0.00432401
$631$	17.4217	0.693545	0.346773	−	0.937949i	$-0.387278\pi$
$631$	17.4217	0.693545	0.346773	+	0.937949i	$0.387278\pi$
$632$	−0.343664	−0.0136702
$633$	19.6955	0.782827
$634$	0.833357	0.0330968
$635$	4.09930	0.162676
$636$	24.9205	0.988162
$637$	−44.2536	−1.75339
$638$	0.380375	0.0150592
$639$	−15.3991	−0.609178
$640$	0.791592	0.0312904
$641$	2.84745	0.112467	0.0562337	−	0.998418i	$-0.482091\pi$
$641$	2.84745	0.112467	0.0562337	+	0.998418i	$0.482091\pi$
$642$	0.241272	0.00952223
$643$	33.0206	1.30220	0.651102	−	0.758990i	$-0.274307\pi$
$643$	33.0206	1.30220	0.651102	+	0.758990i	$0.274307\pi$
$644$	70.5349	2.77947
$645$	0.379223	0.0149319
$646$	0.278221	0.0109464
$647$	−25.6225	−1.00732	−0.503662	−	0.863901i	$-0.668014\pi$
$647$	−25.6225	−1.00732	−0.503662	+	0.863901i	$0.668014\pi$
$648$	0.0990096	0.00388947
$649$	11.6957	0.459096
$650$	0.0896550	0.00351656
$651$	19.4153	0.760944
$652$	−3.32589	−0.130252
$653$	−16.6385	−0.651115	−0.325557	−	0.945522i	$-0.605552\pi$
$653$	−16.6385	−0.651115	−0.325557	+	0.945522i	$0.605552\pi$
$654$	−0.421827	−0.0164947
$655$	−3.27105	−0.127810
$656$	−16.2489	−0.634414
$657$	−2.67908	−0.104521
$658$	1.00379	0.0391317
$659$	28.7932	1.12163	0.560813	−	0.827943i	$-0.310489\pi$
$659$	28.7932	1.12163	0.560813	+	0.827943i	$0.310489\pi$
$660$	−5.76335	−0.224338
$661$	−40.8922	−1.59052	−0.795261	−	0.606267i	$-0.792666\pi$
$661$	−40.8922	−1.59052	−0.795261	+	0.606267i	$0.792666\pi$
$662$	0.361033	0.0140319
$663$	−16.9409	−0.657931
$664$	1.26290	0.0490099
$665$	−10.5325	−0.408433
$666$	−0.135304	−0.00524291
$667$	42.8927	1.66081
$668$	−6.03758	−0.233601
$669$	7.95656	0.307618
$670$	0.0753069	0.00290936
$671$	24.6077	0.949968
$672$	−1.30185	−0.0502199
$673$	−23.2558	−0.896445	−0.448223	−	0.893922i	$-0.647943\pi$
$673$	−23.2558	−0.896445	−0.448223	+	0.893922i	$0.647943\pi$
$674$	0.234170	0.00901991
$675$	−1.00000	−0.0384900
$676$	−0.230701	−0.00887311
$677$	−2.22072	−0.0853494	−0.0426747	−	0.999089i	$-0.513588\pi$
$677$	−2.22072	−0.0853494	−0.0426747	+	0.999089i	$0.513588\pi$
$678$	0.00265195	0.000101848 0
$679$	−33.5288	−1.28672
$680$	−0.463153	−0.0177611
$681$	6.76427	0.259207
$682$	0.316034	0.0121016
$683$	−10.7140	−0.409959	−0.204980	−	0.978766i	$-0.565713\pi$
$683$	−10.7140	−0.409959	−0.204980	+	0.978766i	$0.565713\pi$
$684$	−4.80347	−0.183665
$685$	12.2860	0.469426
$686$	0.566497	0.0216289
$687$	9.25278	0.353016
$688$	−1.51550	−0.0577778
$689$	−45.1388	−1.71965
$690$	0.199213	0.00758393
$691$	31.5018	1.19838	0.599192	−	0.800605i	$-0.295489\pi$
$691$	31.5018	1.19838	0.599192	+	0.800605i	$0.295489\pi$
$692$	29.7730	1.13180
$693$	12.6372	0.480048
$694$	−0.657174	−0.0249460
$695$	8.96658	0.340122
$696$	−0.527748	−0.0200042
$697$	19.0200	0.720434
$698$	0.597928	0.0226319
$699$	−2.60804	−0.0986450
$700$	8.76536	0.331299
$701$	−25.5757	−0.965980	−0.482990	−	0.875626i	$-0.660449\pi$
$701$	−25.5757	−0.965980	−0.482990	+	0.875626i	$0.660449\pi$
$702$	−0.0896550	−0.00338381
$703$	13.1306	0.495229
$704$	23.0181	0.867527
$705$	−9.24879	−0.348329
$706$	−0.743202	−0.0279708
$707$	26.5552	0.998712
$708$	−8.11231	−0.304879
$709$	−34.2664	−1.28690	−0.643451	−	0.765487i	$-0.722498\pi$
$709$	−34.2664	−1.28690	−0.643451	+	0.765487i	$0.722498\pi$
$710$	0.381223	0.0143070
$711$	−3.47101	−0.130173
$712$	−0.938754	−0.0351813
$713$	35.6374	1.33463
$714$	0.507696	0.0190000
$715$	10.4392	0.390406
$716$	−9.76443	−0.364914
$717$	14.7366	0.550350
$718$	0.306386	0.0114342
$719$	36.2848	1.35320	0.676598	−	0.736353i	$-0.263454\pi$
$719$	36.2848	1.35320	0.676598	+	0.736353i	$0.263454\pi$
$720$	3.99632	0.148934
$721$	0.390974	0.0145606
$722$	0.327478	0.0121875
$723$	−22.2690	−0.828194
$724$	25.6013	0.951466
$725$	5.33027	0.197961
$726$	−0.0666151	−0.00247232
$727$	−36.4441	−1.35164	−0.675818	−	0.737069i	$-0.736209\pi$
$727$	−36.4441	−1.35164	−0.675818	+	0.737069i	$0.736209\pi$
$728$	1.57196	0.0582606
$729$	1.00000	0.0370370
$730$	0.0663239	0.00245476
$731$	1.77395	0.0656119
$732$	−17.0682	−0.630860
$733$	7.33853	0.271055	0.135527	−	0.990774i	$-0.456727\pi$
$733$	7.33853	0.271055	0.135527	+	0.990774i	$0.456727\pi$
$734$	0.684167	0.0252531
$735$	−12.2196	−0.450728
$736$	−2.38958	−0.0880813
$737$	8.76858	0.322995
$738$	0.100658	0.00370527
$739$	40.8822	1.50388	0.751939	−	0.659233i	$-0.229119\pi$
$739$	40.8822	1.50388	0.751939	+	0.659233i	$0.229119\pi$
$740$	−10.9275	−0.401704
$741$	8.70060	0.319624
$742$	1.35275	0.0496609
$743$	−12.9712	−0.475865	−0.237933	−	0.971282i	$-0.576470\pi$
$743$	−12.9712	−0.475865	−0.237933	+	0.971282i	$0.576470\pi$
$744$	−0.438478	−0.0160754
$745$	8.07373	0.295799
$746$	0.737961	0.0270187
$747$	12.7553	0.466692
$748$	−26.9601	−0.985760
$749$	−42.7263	−1.56118
$750$	0.0247562	0.000903969 0
$751$	−5.20598	−0.189969	−0.0949844	−	0.995479i	$-0.530280\pi$
$751$	−5.20598	−0.189969	−0.0949844	+	0.995479i	$0.530280\pi$
$752$	36.9611	1.34783
$753$	6.58630	0.240018
$754$	0.477885	0.0174036
$755$	−20.3162	−0.739381
$756$	−8.76536	−0.318793
$757$	35.6695	1.29643	0.648216	−	0.761457i	$-0.275516\pi$
$757$	35.6695	1.29643	0.648216	+	0.761457i	$0.275516\pi$
$758$	−0.565864	−0.0205531
$759$	23.1960	0.841961
$760$	0.237868	0.00862838
$761$	8.73141	0.316513	0.158257	−	0.987398i	$-0.449413\pi$
$761$	8.73141	0.316513	0.158257	+	0.987398i	$0.449413\pi$
$762$	0.101483	0.00367635
$763$	74.7005	2.70434
$764$	−52.7345	−1.90787
$765$	−4.67786	−0.169128
$766$	−0.198373	−0.00716752
$767$	14.6939	0.530567
$768$	−15.9510	−0.575582
$769$	29.5708	1.06635	0.533175	−	0.846005i	$-0.320999\pi$
$769$	29.5708	1.06635	0.533175	+	0.846005i	$0.320999\pi$
$770$	−0.312849	−0.0112743
$771$	9.52308	0.342965
$772$	13.8972	0.500170
$773$	2.56332	0.0921961	0.0460980	−	0.998937i	$-0.485321\pi$
$773$	2.56332	0.0921961	0.0460980	+	0.998937i	$0.485321\pi$
$774$	0.00938811	0.000337449 0
$775$	4.42864	0.159082
$776$	0.757222	0.0271827
$777$	23.9606	0.859582
$778$	−0.396894	−0.0142293
$779$	−9.76838	−0.349989
$780$	−7.24081	−0.259263
$781$	44.3888	1.58836
$782$	0.931892	0.0333244
$783$	−5.33027	−0.190488
$784$	48.8336	1.74406
$785$	−9.43218	−0.336649
$786$	−0.0809787	−0.00288841
$787$	−0.207048	−0.00738045	−0.00369022	−	0.999993i	$-0.501175\pi$
$787$	−0.207048	−0.00738045	−0.00369022	+	0.999993i	$0.501175\pi$
$788$	−46.2786	−1.64861
$789$	−31.0750	−1.10630
$790$	0.0859291	0.00305722
$791$	−0.469629	−0.0166981
$792$	−0.285401	−0.0101413
$793$	30.9159	1.09786
$794$	−0.895068	−0.0317648
$795$	−12.4641	−0.442055
$796$	−42.8945	−1.52035
$797$	4.80753	0.170292	0.0851458	−	0.996369i	$-0.472864\pi$
$797$	4.80753	0.170292	0.0851458	+	0.996369i	$0.472864\pi$
$798$	−0.260744	−0.00923025
$799$	−43.2645	−1.53059
$800$	−0.296953	−0.0104989
$801$	−9.48144	−0.335010
$802$	−0.0247562	−0.000874172 0
$803$	7.72261	0.272525
$804$	−6.08202	−0.214496
$805$	−35.2783	−1.24340
$806$	0.397050	0.0139855
$807$	13.4675	0.474079
$808$	−0.599729	−0.0210984
$809$	−17.0225	−0.598478	−0.299239	−	0.954178i	$-0.596733\pi$
$809$	−17.0225	−0.598478	−0.299239	+	0.954178i	$0.596733\pi$
$810$	−0.0247562	−0.000869844 0
$811$	−24.5367	−0.861601	−0.430801	−	0.902447i	$-0.641769\pi$
$811$	−24.5367	−0.861601	−0.430801	+	0.902447i	$0.641769\pi$
$812$	46.7217	1.63961
$813$	−18.8145	−0.659852
$814$	0.390021	0.0136702
$815$	1.66345	0.0582683
$816$	18.6942	0.654429
$817$	−0.911072	−0.0318744
$818$	−0.453143	−0.0158438
$819$	15.8768	0.554781
$820$	8.12945	0.283893
$821$	−17.8926	−0.624455	−0.312227	−	0.950007i	$-0.601075\pi$
$821$	−17.8926	−0.624455	−0.312227	+	0.950007i	$0.601075\pi$
$822$	0.304156	0.0106087
$823$	−7.16004	−0.249583	−0.124792	−	0.992183i	$-0.539826\pi$
$823$	−7.16004	−0.249583	−0.124792	+	0.992183i	$0.539826\pi$
$824$	−0.00882984	−0.000307602 0
$825$	2.88256	0.100358
$826$	−0.440356	−0.0153220
$827$	−4.58558	−0.159456	−0.0797281	−	0.996817i	$-0.525405\pi$
$827$	−4.58558	−0.159456	−0.0797281	+	0.996817i	$0.525405\pi$
$828$	−16.0891	−0.559135
$829$	10.7326	0.372758	0.186379	−	0.982478i	$-0.440325\pi$
$829$	10.7326	0.372758	0.186379	+	0.982478i	$0.440325\pi$
$830$	−0.315773	−0.0109606
$831$	−27.1130	−0.940539
$832$	28.9189	1.00258
$833$	−57.1617	−1.98054
$834$	0.221978	0.00768648
$835$	3.01971	0.104501
$836$	13.8463	0.478884
$837$	−4.42864	−0.153076
$838$	−0.342636	−0.0118362
$839$	−20.4827	−0.707142	−0.353571	−	0.935408i	$-0.615033\pi$
$839$	−20.4827	−0.707142	−0.353571	+	0.935408i	$0.615033\pi$
$840$	0.434060	0.0149765
$841$	−0.588218	−0.0202834
$842$	−0.181865	−0.00626749
$843$	−13.4303	−0.462564
$844$	39.3790	1.35548
$845$	0.115386	0.00396939
$846$	−0.228965	−0.00787197
$847$	11.7967	0.405340
$848$	49.8105	1.71050
$849$	−4.00785	−0.137549
$850$	0.115806	0.00397211
$851$	43.9805	1.50763
$852$	−30.7887	−1.05480
$853$	−25.4200	−0.870363	−0.435182	−	0.900343i	$-0.643316\pi$
$853$	−25.4200	−0.870363	−0.435182	+	0.900343i	$0.643316\pi$
$854$	−0.926507	−0.0317044
$855$	2.40247	0.0821628
$856$	0.964939	0.0329809
$857$	−28.1965	−0.963174	−0.481587	−	0.876398i	$-0.659939\pi$
$857$	−28.1965	−0.963174	−0.481587	+	0.876398i	$0.659939\pi$
$858$	0.258436	0.00882286
$859$	7.74690	0.264321	0.132160	−	0.991228i	$-0.457809\pi$
$859$	7.74690	0.264321	0.132160	+	0.991228i	$0.457809\pi$
$860$	0.758213	0.0258549
$861$	−17.8253	−0.607484
$862$	0.422456	0.0143889
$863$	23.3729	0.795622	0.397811	−	0.917467i	$-0.369770\pi$
$863$	23.3729	0.795622	0.397811	+	0.917467i	$0.369770\pi$
$864$	0.296953	0.0101025
$865$	−14.8911	−0.506312
$866$	0.415154	0.0141075
$867$	−4.88233	−0.165813
$868$	38.8186	1.31759
$869$	10.0054	0.339410
$870$	0.131957	0.00447377
$871$	11.0164	0.373278
$872$	−1.68705	−0.0571307
$873$	7.64797	0.258844
$874$	−0.478605	−0.0161891
$875$	−4.38402	−0.148207
$876$	−5.35652	−0.180980
$877$	46.2392	1.56139	0.780693	−	0.624915i	$-0.214866\pi$
$877$	46.2392	1.56139	0.780693	+	0.624915i	$0.214866\pi$
$878$	0.452819	0.0152819
$879$	32.7213	1.10366
$880$	−11.5196	−0.388327
$881$	−10.5299	−0.354763	−0.177381	−	0.984142i	$-0.556763\pi$
$881$	−10.5299	−0.354763	−0.177381	+	0.984142i	$0.556763\pi$
$882$	−0.302512	−0.0101861
$883$	−32.6395	−1.09841	−0.549204	−	0.835689i	$-0.685069\pi$
$883$	−32.6395	−1.09841	−0.549204	+	0.835689i	$0.685069\pi$
$884$	−33.8715	−1.13922
$885$	4.05740	0.136388
$886$	0.570301	0.0191596
$887$	−39.0750	−1.31201	−0.656005	−	0.754757i	$-0.727755\pi$
$887$	−39.0750	−1.31201	−0.656005	+	0.754757i	$0.727755\pi$
$888$	−0.541131	−0.0181592
$889$	−17.9714	−0.602743
$890$	0.234724	0.00786798
$891$	−2.88256	−0.0965694
$892$	15.9082	0.532648
$893$	22.2200	0.743563
$894$	0.199875	0.00668482
$895$	4.88371	0.163244
$896$	−3.47035	−0.115936
$897$	29.1424	0.973036
$898$	−0.100635	−0.00335823
$899$	23.6059	0.787300
$900$	−1.99939	−0.0666462
$901$	−58.3051	−1.94243
$902$	−0.290153	−0.00966102
$903$	−1.66252	−0.0553252
$904$	0.0106062	0.000352757 0
$905$	−12.8046	−0.425639
$906$	−0.502951	−0.0167094
$907$	−27.5766	−0.915668	−0.457834	−	0.889038i	$-0.651375\pi$
$907$	−27.5766	−0.915668	−0.457834	+	0.889038i	$0.651375\pi$
$908$	13.5244	0.448823
$909$	−6.05728	−0.200907
$910$	−0.393049	−0.0130295
$911$	−33.4555	−1.10843	−0.554215	−	0.832374i	$-0.686981\pi$
$911$	−33.4555	−1.10843	−0.554215	+	0.832374i	$0.686981\pi$
$912$	−9.60106	−0.317923
$913$	−36.7679	−1.21684
$914$	−0.226962	−0.00750723
$915$	8.53674	0.282216
$916$	18.4999	0.611253
$917$	14.3403	0.473560
$918$	−0.115806	−0.00382216
$919$	28.9980	0.956554	0.478277	−	0.878209i	$-0.341261\pi$
$919$	28.9980	0.956554	0.478277	+	0.878209i	$0.341261\pi$
$920$	0.796732	0.0262675
$921$	−9.80801	−0.323185
$922$	0.828232	0.0272764
$923$	55.7680	1.83563
$924$	25.2667	0.831212
$925$	5.46544	0.179703
$926$	0.937745	0.0308162
$927$	−0.0891816	−0.00292911
$928$	−1.58284	−0.0519593
$929$	7.98077	0.261840	0.130920	−	0.991393i	$-0.458207\pi$
$929$	7.98077	0.261840	0.130920	+	0.991393i	$0.458207\pi$
$930$	0.109636	0.00359512
$931$	29.3574	0.962149
$932$	−5.21447	−0.170806
$933$	28.6266	0.937194
$934$	0.604162	0.0197688
$935$	13.4842	0.440981
$936$	−0.358565	−0.0117201
$937$	53.3797	1.74384	0.871920	−	0.489649i	$-0.162875\pi$
$937$	53.3797	1.74384	0.871920	+	0.489649i	$0.162875\pi$
$938$	−0.330147	−0.0107797
$939$	15.1414	0.494120
$940$	−18.4919	−0.603139
$941$	−51.8389	−1.68990	−0.844950	−	0.534846i	$-0.820370\pi$
$941$	−51.8389	−1.68990	−0.844950	+	0.534846i	$0.820370\pi$
$942$	−0.233505	−0.00760800
$943$	−32.7189	−1.06547
$944$	−16.2147	−0.527743
$945$	4.38402	0.142612
$946$	−0.0270618	−0.000879855 0
$947$	12.5815	0.408843	0.204421	−	0.978883i	$-0.434469\pi$
$947$	12.5815	0.408843	0.204421	+	0.978883i	$0.434469\pi$
$948$	−6.93990	−0.225397
$949$	9.70234	0.314951
$950$	−0.0594761	−0.00192966
$951$	33.6626	1.09158
$952$	2.03047	0.0658079
$953$	10.3766	0.336131	0.168066	−	0.985776i	$-0.446248\pi$
$953$	10.3766	0.336131	0.168066	+	0.985776i	$0.446248\pi$
$954$	−0.308563	−0.00999010
$955$	26.3753	0.853486
$956$	29.4643	0.952942
$957$	15.3648	0.496674
$958$	0.188999	0.00610627
$959$	−53.8623	−1.73930
$960$	7.98529	0.257724
$961$	−11.3871	−0.367326
$962$	0.490004	0.0157984
$963$	9.74591	0.314058
$964$	−44.5244	−1.43403
$965$	−6.95072	−0.223752
$966$	−0.873356	−0.0280998
$967$	52.7088	1.69500	0.847501	−	0.530794i	$-0.178106\pi$
$967$	52.7088	1.69500	0.847501	+	0.530794i	$0.178106\pi$
$968$	−0.266419	−0.00856305
$969$	11.2384	0.361030
$970$	−0.189335	−0.00607917
$971$	16.3395	0.524360	0.262180	−	0.965019i	$-0.415559\pi$
$971$	16.3395	0.524360	0.262180	+	0.965019i	$0.415559\pi$
$972$	1.99939	0.0641304
$973$	−39.3097	−1.26021
$974$	−0.674612	−0.0216160
$975$	3.62152	0.115981
$976$	−34.1156	−1.09201
$977$	17.0176	0.544441	0.272220	−	0.962235i	$-0.412242\pi$
$977$	17.0176	0.544441	0.272220	+	0.962235i	$0.412242\pi$
$978$	0.0411808	0.00131682
$979$	27.3308	0.873497
$980$	−24.4318	−0.780445
$981$	−17.0393	−0.544022
$982$	−0.284848	−0.00908986
$983$	−45.3587	−1.44672	−0.723359	−	0.690472i	$-0.757403\pi$
$983$	−45.3587	−1.44672	−0.723359	+	0.690472i	$0.757403\pi$
$984$	0.402570	0.0128335
$985$	23.1464	0.737505
$986$	0.617277	0.0196581
$987$	40.5469	1.29062
$988$	17.3959	0.553436
$989$	−3.05161	−0.0970356
$990$	0.0713612	0.00226801
$991$	33.7573	1.07234	0.536169	−	0.844111i	$-0.319871\pi$
$991$	33.7573	1.07234	0.536169	+	0.844111i	$0.319871\pi$
$992$	−1.31510	−0.0417544
$993$	14.5835	0.462794
$994$	−1.67129	−0.0530100
$995$	21.4538	0.680132
$996$	25.5028	0.808086
$997$	5.98284	0.189478	0.0947392	−	0.995502i	$-0.469798\pi$
$997$	5.98284	0.189478	0.0947392	+	0.995502i	$0.469798\pi$
$998$	−0.947195	−0.0299829
$999$	−5.46544	−0.172919

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.d.1.16	✓	29

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.d.1.16	✓	29	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:	\( N \)	\(=\)	\( 6015 = 3 \cdot 5 \cdot 401 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6015.a (trivial)

\(f(q)\)	\(=\)	\(q-0.0247562 q^{2} -1.00000 q^{3} -1.99939 q^{4} +1.00000 q^{5} +0.0247562 q^{6} -4.38402 q^{7} +0.0990096 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.0247562 q^{2} -1.00000 q^{3} -1.99939 q^{4} +1.00000 q^{5} +0.0247562 q^{6} -4.38402 q^{7} +0.0990096 q^{8} +1.00000 q^{9} -0.0247562 q^{10} -2.88256 q^{11} +1.99939 q^{12} -3.62152 q^{13} +0.108532 q^{14} -1.00000 q^{15} +3.99632 q^{16} -4.67786 q^{17} -0.0247562 q^{18} +2.40247 q^{19} -1.99939 q^{20} +4.38402 q^{21} +0.0713612 q^{22} +8.04701 q^{23} -0.0990096 q^{24} +1.00000 q^{25} +0.0896550 q^{26} -1.00000 q^{27} +8.76536 q^{28} +5.33027 q^{29} +0.0247562 q^{30} +4.42864 q^{31} -0.296953 q^{32} +2.88256 q^{33} +0.115806 q^{34} -4.38402 q^{35} -1.99939 q^{36} +5.46544 q^{37} -0.0594761 q^{38} +3.62152 q^{39} +0.0990096 q^{40} -4.06597 q^{41} -0.108532 q^{42} -0.379223 q^{43} +5.76335 q^{44} +1.00000 q^{45} -0.199213 q^{46} +9.24879 q^{47} -3.99632 q^{48} +12.2196 q^{49} -0.0247562 q^{50} +4.67786 q^{51} +7.24081 q^{52} +12.4641 q^{53} +0.0247562 q^{54} -2.88256 q^{55} -0.434060 q^{56} -2.40247 q^{57} -0.131957 q^{58} -4.05740 q^{59} +1.99939 q^{60} -8.53674 q^{61} -0.109636 q^{62} -4.38402 q^{63} -7.98529 q^{64} -3.62152 q^{65} -0.0713612 q^{66} -3.04194 q^{67} +9.35284 q^{68} -8.04701 q^{69} +0.108532 q^{70} -15.3991 q^{71} +0.0990096 q^{72} -2.67908 q^{73} -0.135304 q^{74} -1.00000 q^{75} -4.80347 q^{76} +12.6372 q^{77} -0.0896550 q^{78} -3.47101 q^{79} +3.99632 q^{80} +1.00000 q^{81} +0.100658 q^{82} +12.7553 q^{83} -8.76536 q^{84} -4.67786 q^{85} +0.00938811 q^{86} -5.33027 q^{87} -0.285401 q^{88} -9.48144 q^{89} -0.0247562 q^{90} +15.8768 q^{91} -16.0891 q^{92} -4.42864 q^{93} -0.228965 q^{94} +2.40247 q^{95} +0.296953 q^{96} +7.64797 q^{97} -0.302512 q^{98} -2.88256 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9}+O(q^{10}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9	\( 29 q - q^{2} - 29 q^{3} + 27 q^{4} + 29 q^{5} + q^{6} + 2 q^{7} - 6 q^{8} + 29 q^{9} - q^{10} - 21 q^{11} - 27 q^{12} - 8 q^{13} - 30 q^{14} - 29 q^{15} + 23 q^{16} - 28 q^{17} - q^{18} - 9 q^{19} + 27 q^{20} - 2 q^{21} - 9 q^{22} + 6 q^{24} + 29 q^{25} - 34 q^{26} - 29 q^{27} + 6 q^{28} - 61 q^{29} + q^{30} - 19 q^{31} - 8 q^{32} + 21 q^{33} - 16 q^{34} + 2 q^{35} + 27 q^{36} - 4 q^{37} + 4 q^{38} + 8 q^{39} - 6 q^{40} - 85 q^{41} + 30 q^{42} + 29 q^{43} - 69 q^{44} + 29 q^{45} - 35 q^{46} - 2 q^{47} - 23 q^{48} + q^{49} - q^{50} + 28 q^{51} - 28 q^{52} - 5 q^{53} + q^{54} - 21 q^{55} - 97 q^{56} + 9 q^{57} + 6 q^{58} - 43 q^{59} - 27 q^{60} - 59 q^{61} - 17 q^{62} + 2 q^{63} - 6 q^{64} - 8 q^{65} + 9 q^{66} + 28 q^{67} - 44 q^{68} - 30 q^{70} - 44 q^{71} - 6 q^{72} - 41 q^{73} - 50 q^{74} - 29 q^{75} - 62 q^{76} - 20 q^{77} + 34 q^{78} - 25 q^{79} + 23 q^{80} + 29 q^{81} - 29 q^{82} - 7 q^{83} - 6 q^{84} - 28 q^{85} - 43 q^{86} + 61 q^{87} - 3 q^{88} - 109 q^{89} - q^{90} - q^{91} - 11 q^{92} + 19 q^{93} - 20 q^{94} - 9 q^{95} + 8 q^{96} - 51 q^{97} - 12 q^{98} - 21 q^{99}+O(q^{100}) \) 29 * q - q^2 - 29 * q^3 + 27 * q^4 + 29 * q^5 + q^6 + 2 * q^7 - 6 * q^8 + 29 * q^9 - q^10 - 21 * q^11 - 27 * q^12 - 8 * q^13 - 30 * q^14 - 29 * q^15 + 23 * q^16 - 28 * q^17 - q^18 - 9 * q^19 + 27 * q^20 - 2 * q^21 - 9 * q^22 + 6 * q^24 + 29 * q^25 - 34 * q^26 - 29 * q^27 + 6 * q^28 - 61 * q^29 + q^30 - 19 * q^31 - 8 * q^32 + 21 * q^33 - 16 * q^34 + 2 * q^35 + 27 * q^36 - 4 * q^37 + 4 * q^38 + 8 * q^39 - 6 * q^40 - 85 * q^41 + 30 * q^42 + 29 * q^43 - 69 * q^44 + 29 * q^45 - 35 * q^46 - 2 * q^47 - 23 * q^48 + q^49 - q^50 + 28 * q^51 - 28 * q^52 - 5 * q^53 + q^54 - 21 * q^55 - 97 * q^56 + 9 * q^57 + 6 * q^58 - 43 * q^59 - 27 * q^60 - 59 * q^61 - 17 * q^62 + 2 * q^63 - 6 * q^64 - 8 * q^65 + 9 * q^66 + 28 * q^67 - 44 * q^68 - 30 * q^70 - 44 * q^71 - 6 * q^72 - 41 * q^73 - 50 * q^74 - 29 * q^75 - 62 * q^76 - 20 * q^77 + 34 * q^78 - 25 * q^79 + 23 * q^80 + 29 * q^81 - 29 * q^82 - 7 * q^83 - 6 * q^84 - 28 * q^85 - 43 * q^86 + 61 * q^87 - 3 * q^88 - 109 * q^89 - q^90 - q^91 - 11 * q^92 + 19 * q^93 - 20 * q^94 - 9 * q^95 + 8 * q^96 - 51 * q^97 - 12 * q^98 - 21 * q^99

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