LMFDB - Embedded newform 6015.2.a.b.1.15

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:	$23$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.15
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)

$f(q)$	$=$	$q+0.592282 q^{2} +1.00000 q^{3} -1.64920 q^{4} +1.00000 q^{5} +0.592282 q^{6} -0.542800 q^{7} -2.16136 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+0.592282 q^{2} +1.00000 q^{3} -1.64920 q^{4} +1.00000 q^{5} +0.592282 q^{6} -0.542800 q^{7} -2.16136 q^{8} +1.00000 q^{9} +0.592282 q^{10} -2.37004 q^{11} -1.64920 q^{12} +4.21601 q^{13} -0.321491 q^{14} +1.00000 q^{15} +2.01827 q^{16} -4.91094 q^{17} +0.592282 q^{18} +0.967989 q^{19} -1.64920 q^{20} -0.542800 q^{21} -1.40373 q^{22} -8.66636 q^{23} -2.16136 q^{24} +1.00000 q^{25} +2.49707 q^{26} +1.00000 q^{27} +0.895186 q^{28} +9.93906 q^{29} +0.592282 q^{30} +2.19174 q^{31} +5.51810 q^{32} -2.37004 q^{33} -2.90866 q^{34} -0.542800 q^{35} -1.64920 q^{36} -10.1057 q^{37} +0.573323 q^{38} +4.21601 q^{39} -2.16136 q^{40} -0.524144 q^{41} -0.321491 q^{42} +3.25148 q^{43} +3.90867 q^{44} +1.00000 q^{45} -5.13293 q^{46} -0.431405 q^{47} +2.01827 q^{48} -6.70537 q^{49} +0.592282 q^{50} -4.91094 q^{51} -6.95305 q^{52} +11.4152 q^{53} +0.592282 q^{54} -2.37004 q^{55} +1.17318 q^{56} +0.967989 q^{57} +5.88673 q^{58} -4.15492 q^{59} -1.64920 q^{60} -12.6077 q^{61} +1.29813 q^{62} -0.542800 q^{63} -0.768263 q^{64} +4.21601 q^{65} -1.40373 q^{66} +3.38889 q^{67} +8.09913 q^{68} -8.66636 q^{69} -0.321491 q^{70} -8.00721 q^{71} -2.16136 q^{72} -4.47373 q^{73} -5.98541 q^{74} +1.00000 q^{75} -1.59641 q^{76} +1.28646 q^{77} +2.49707 q^{78} -14.5928 q^{79} +2.01827 q^{80} +1.00000 q^{81} -0.310442 q^{82} +5.64687 q^{83} +0.895186 q^{84} -4.91094 q^{85} +1.92580 q^{86} +9.93906 q^{87} +5.12251 q^{88} -6.69079 q^{89} +0.592282 q^{90} -2.28845 q^{91} +14.2926 q^{92} +2.19174 q^{93} -0.255514 q^{94} +0.967989 q^{95} +5.51810 q^{96} -14.4940 q^{97} -3.97147 q^{98} -2.37004 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) $ 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * 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 $

$2$	0.592282	0.418807	0.209403	−	0.977829i	$-0.432848\pi$
$2$	0.592282	0.418807	0.209403	+	0.977829i	$0.432848\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−1.64920	−0.824601
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	0.592282	0.241798
$7$	−0.542800	−0.205159	−0.102580	−	0.994725i	$-0.532710\pi$
$7$	−0.542800	−0.205159	−0.102580	+	0.994725i	$0.532710\pi$
$8$	−2.16136	−0.764155
$9$	1.00000	0.333333
$10$	0.592282	0.187296
$11$	−2.37004	−0.714594	−0.357297	−	0.933991i	$-0.616302\pi$
$11$	−2.37004	−0.714594	−0.357297	+	0.933991i	$0.616302\pi$
$12$	−1.64920	−0.476083
$13$	4.21601	1.16931	0.584655	−	0.811282i	$-0.301230\pi$
$13$	4.21601	1.16931	0.584655	+	0.811282i	$0.301230\pi$
$14$	−0.321491	−0.0859220
$15$	1.00000	0.258199
$16$	2.01827	0.504567
$17$	−4.91094	−1.19108	−0.595539	−	0.803326i	$-0.703061\pi$
$17$	−4.91094	−1.19108	−0.595539	+	0.803326i	$0.703061\pi$
$18$	0.592282	0.139602
$19$	0.967989	0.222072	0.111036	−	0.993816i	$-0.464583\pi$
$19$	0.967989	0.222072	0.111036	+	0.993816i	$0.464583\pi$
$20$	−1.64920	−0.368773
$21$	−0.542800	−0.118449
$22$	−1.40373	−0.299277
$23$	−8.66636	−1.80706	−0.903531	−	0.428524i	$-0.859034\pi$
$23$	−8.66636	−1.80706	−0.903531	+	0.428524i	$0.859034\pi$
$24$	−2.16136	−0.441185
$25$	1.00000	0.200000
$26$	2.49707	0.489715
$27$	1.00000	0.192450
$28$	0.895186	0.169174
$29$	9.93906	1.84564	0.922818	−	0.385235i	$-0.125880\pi$
$29$	9.93906	1.84564	0.922818	+	0.385235i	$0.125880\pi$
$30$	0.592282	0.108135
$31$	2.19174	0.393647	0.196824	−	0.980439i	$-0.436937\pi$
$31$	2.19174	0.393647	0.196824	+	0.980439i	$0.436937\pi$
$32$	5.51810	0.975472
$33$	−2.37004	−0.412571
$34$	−2.90866	−0.498832
$35$	−0.542800	−0.0917499
$36$	−1.64920	−0.274867
$37$	−10.1057	−1.66136	−0.830681	−	0.556748i	$-0.812049\pi$
$37$	−10.1057	−1.66136	−0.830681	+	0.556748i	$0.812049\pi$
$38$	0.573323	0.0930053
$39$	4.21601	0.675102
$40$	−2.16136	−0.341741
$41$	−0.524144	−0.0818576	−0.0409288	−	0.999162i	$-0.513032\pi$
$41$	−0.524144	−0.0818576	−0.0409288	+	0.999162i	$0.513032\pi$
$42$	−0.321491	−0.0496071
$43$	3.25148	0.495846	0.247923	−	0.968780i	$-0.420252\pi$
$43$	3.25148	0.495846	0.247923	+	0.968780i	$0.420252\pi$
$44$	3.90867	0.589255
$45$	1.00000	0.149071
$46$	−5.13293	−0.756810
$47$	−0.431405	−0.0629269	−0.0314634	−	0.999505i	$-0.510017\pi$
$47$	−0.431405	−0.0629269	−0.0314634	+	0.999505i	$0.510017\pi$
$48$	2.01827	0.291312
$49$	−6.70537	−0.957910
$50$	0.592282	0.0837614
$51$	−4.91094	−0.687669
$52$	−6.95305	−0.964215
$53$	11.4152	1.56800	0.783998	−	0.620764i	$-0.213177\pi$
$53$	11.4152	1.56800	0.783998	+	0.620764i	$0.213177\pi$
$54$	0.592282	0.0805994
$55$	−2.37004	−0.319576
$56$	1.17318	0.156773
$57$	0.967989	0.128213
$58$	5.88673	0.772965
$59$	−4.15492	−0.540925	−0.270463	−	0.962731i	$-0.587177\pi$
$59$	−4.15492	−0.540925	−0.270463	+	0.962731i	$0.587177\pi$
$60$	−1.64920	−0.212911
$61$	−12.6077	−1.61425	−0.807126	−	0.590379i	$-0.798978\pi$
$61$	−12.6077	−1.61425	−0.807126	+	0.590379i	$0.798978\pi$
$62$	1.29813	0.164862
$63$	−0.542800	−0.0683863
$64$	−0.768263	−0.0960329
$65$	4.21601	0.522932
$66$	−1.40373	−0.172788
$67$	3.38889	0.414019	0.207009	−	0.978339i	$-0.433627\pi$
$67$	3.38889	0.414019	0.207009	+	0.978339i	$0.433627\pi$
$68$	8.09913	0.982164
$69$	−8.66636	−1.04331
$70$	−0.321491	−0.0384255
$71$	−8.00721	−0.950281	−0.475141	−	0.879910i	$-0.657603\pi$
$71$	−8.00721	−0.950281	−0.475141	+	0.879910i	$0.657603\pi$
$72$	−2.16136	−0.254718
$73$	−4.47373	−0.523610	−0.261805	−	0.965121i	$-0.584318\pi$
$73$	−4.47373	−0.523610	−0.261805	+	0.965121i	$0.584318\pi$
$74$	−5.98541	−0.695790
$75$	1.00000	0.115470
$76$	−1.59641	−0.183121
$77$	1.28646	0.146605
$78$	2.49707	0.282737
$79$	−14.5928	−1.64182	−0.820912	−	0.571055i	$-0.806534\pi$
$79$	−14.5928	−1.64182	−0.820912	+	0.571055i	$0.806534\pi$
$80$	2.01827	0.225649
$81$	1.00000	0.111111
$82$	−0.310442	−0.0342825
$83$	5.64687	0.619824	0.309912	−	0.950765i	$-0.399700\pi$
$83$	5.64687	0.619824	0.309912	+	0.950765i	$0.399700\pi$
$84$	0.895186	0.0976728
$85$	−4.91094	−0.532666
$86$	1.92580	0.207664
$87$	9.93906	1.06558
$88$	5.12251	0.546061
$89$	−6.69079	−0.709223	−0.354611	−	0.935014i	$-0.615387\pi$
$89$	−6.69079	−0.709223	−0.354611	+	0.935014i	$0.615387\pi$
$90$	0.592282	0.0624321
$91$	−2.28845	−0.239895
$92$	14.2926	1.49010
$93$	2.19174	0.227272
$94$	−0.255514	−0.0263542
$95$	0.967989	0.0993136
$96$	5.51810	0.563189
$97$	−14.4940	−1.47164	−0.735821	−	0.677176i	$-0.763204\pi$
$97$	−14.4940	−1.47164	−0.735821	+	0.677176i	$0.763204\pi$
$98$	−3.97147	−0.401179
$99$	−2.37004	−0.238198
$100$	−1.64920	−0.164920
$101$	−7.27619	−0.724008	−0.362004	−	0.932177i	$-0.617907\pi$
$101$	−7.27619	−0.724008	−0.362004	+	0.932177i	$0.617907\pi$
$102$	−2.90866	−0.288001
$103$	−13.7914	−1.35891	−0.679453	−	0.733719i	$-0.737783\pi$
$103$	−13.7914	−1.35891	−0.679453	+	0.733719i	$0.737783\pi$
$104$	−9.11231	−0.893535
$105$	−0.542800	−0.0529718
$106$	6.76101	0.656687
$107$	12.7287	1.23053	0.615264	−	0.788321i	$-0.289050\pi$
$107$	12.7287	1.23053	0.615264	+	0.788321i	$0.289050\pi$
$108$	−1.64920	−0.158694
$109$	3.10871	0.297760	0.148880	−	0.988855i	$-0.452433\pi$
$109$	3.10871	0.297760	0.148880	+	0.988855i	$0.452433\pi$
$110$	−1.40373	−0.133841
$111$	−10.1057	−0.959188
$112$	−1.09552	−0.103517
$113$	−7.75433	−0.729466	−0.364733	−	0.931112i	$-0.618840\pi$
$113$	−7.75433	−0.729466	−0.364733	+	0.931112i	$0.618840\pi$
$114$	0.573323	0.0536966
$115$	−8.66636	−0.808142
$116$	−16.3915	−1.52191
$117$	4.21601	0.389770
$118$	−2.46089	−0.226543
$119$	2.66566	0.244360
$120$	−2.16136	−0.197304
$121$	−5.38291	−0.489355
$122$	−7.46733	−0.676060
$123$	−0.524144	−0.0472605
$124$	−3.61461	−0.324602
$125$	1.00000	0.0894427
$126$	−0.321491	−0.0286407
$127$	15.8134	1.40321	0.701606	−	0.712565i	$-0.252467\pi$
$127$	15.8134	1.40321	0.701606	+	0.712565i	$0.252467\pi$
$128$	−11.4912	−1.01569
$129$	3.25148	0.286277
$130$	2.49707	0.219007
$131$	−9.20333	−0.804099	−0.402049	−	0.915618i	$-0.631702\pi$
$131$	−9.20333	−0.804099	−0.402049	+	0.915618i	$0.631702\pi$
$132$	3.90867	0.340206
$133$	−0.525424	−0.0455601
$134$	2.00718	0.173394
$135$	1.00000	0.0860663
$136$	10.6143	0.910169
$137$	11.2443	0.960668	0.480334	−	0.877086i	$-0.340515\pi$
$137$	11.2443	0.960668	0.480334	+	0.877086i	$0.340515\pi$
$138$	−5.13293	−0.436944
$139$	2.50909	0.212818	0.106409	−	0.994322i	$-0.466065\pi$
$139$	2.50909	0.212818	0.106409	+	0.994322i	$0.466065\pi$
$140$	0.895186	0.0756570
$141$	−0.431405	−0.0363309
$142$	−4.74253	−0.397984
$143$	−9.99211	−0.835583
$144$	2.01827	0.168189
$145$	9.93906	0.825394
$146$	−2.64971	−0.219292
$147$	−6.70537	−0.553049
$148$	16.6663	1.36996
$149$	1.44944	0.118743	0.0593714	−	0.998236i	$-0.481090\pi$
$149$	1.44944	0.118743	0.0593714	+	0.998236i	$0.481090\pi$
$150$	0.592282	0.0483597
$151$	19.2032	1.56273	0.781367	−	0.624071i	$-0.214523\pi$
$151$	19.2032	1.56273	0.781367	+	0.624071i	$0.214523\pi$
$152$	−2.09217	−0.169697
$153$	−4.91094	−0.397026
$154$	0.761946	0.0613994
$155$	2.19174	0.176044
$156$	−6.95305	−0.556690
$157$	−23.4784	−1.87378	−0.936890	−	0.349625i	$-0.886309\pi$
$157$	−23.4784	−1.87378	−0.936890	+	0.349625i	$0.886309\pi$
$158$	−8.64309	−0.687607
$159$	11.4152	0.905282
$160$	5.51810	0.436244
$161$	4.70410	0.370735
$162$	0.592282	0.0465341
$163$	−10.8958	−0.853423	−0.426711	−	0.904388i	$-0.640328\pi$
$163$	−10.8958	−0.853423	−0.426711	+	0.904388i	$0.640328\pi$
$164$	0.864420	0.0674998
$165$	−2.37004	−0.184507
$166$	3.34454	0.259587
$167$	5.68642	0.440028	0.220014	−	0.975497i	$-0.429390\pi$
$167$	5.68642	0.440028	0.220014	+	0.975497i	$0.429390\pi$
$168$	1.17318	0.0905132
$169$	4.77474	0.367288
$170$	−2.90866	−0.223084
$171$	0.967989	0.0740240
$172$	−5.36235	−0.408875
$173$	0.107826	0.00819782	0.00409891	−	0.999992i	$-0.498695\pi$
$173$	0.107826	0.00819782	0.00409891	+	0.999992i	$0.498695\pi$
$174$	5.88673	0.446272
$175$	−0.542800	−0.0410318
$176$	−4.78338	−0.360561
$177$	−4.15492	−0.312303
$178$	−3.96284	−0.297027
$179$	1.82960	0.136751	0.0683755	−	0.997660i	$-0.478218\pi$
$179$	1.82960	0.136751	0.0683755	+	0.997660i	$0.478218\pi$
$180$	−1.64920	−0.122924
$181$	−24.5447	−1.82440	−0.912198	−	0.409749i	$-0.865616\pi$
$181$	−24.5447	−1.82440	−0.912198	+	0.409749i	$0.865616\pi$
$182$	−1.35541	−0.100470
$183$	−12.6077	−0.931989
$184$	18.7311	1.38088
$185$	−10.1057	−0.742984
$186$	1.29813	0.0951833
$187$	11.6391	0.851137
$188$	0.711474	0.0518896
$189$	−0.542800	−0.0394829
$190$	0.573323	0.0415932
$191$	1.35585	0.0981059	0.0490529	−	0.998796i	$-0.484380\pi$
$191$	1.35585	0.0981059	0.0490529	+	0.998796i	$0.484380\pi$
$192$	−0.768263	−0.0554446
$193$	−10.5994	−0.762962	−0.381481	−	0.924377i	$-0.624586\pi$
$193$	−10.5994	−0.762962	−0.381481	+	0.924377i	$0.624586\pi$
$194$	−8.58454	−0.616334
$195$	4.21601	0.301915
$196$	11.0585	0.789893
$197$	3.29465	0.234734	0.117367	−	0.993089i	$-0.462555\pi$
$197$	3.29465	0.234734	0.117367	+	0.993089i	$0.462555\pi$
$198$	−1.40373	−0.0997590
$199$	4.49450	0.318606	0.159303	−	0.987230i	$-0.449075\pi$
$199$	4.49450	0.318606	0.159303	+	0.987230i	$0.449075\pi$
$200$	−2.16136	−0.152831
$201$	3.38889	0.239034
$202$	−4.30956	−0.303220
$203$	−5.39492	−0.378649
$204$	8.09913	0.567053
$205$	−0.524144	−0.0366078
$206$	−8.16839	−0.569119
$207$	−8.66636	−0.602354
$208$	8.50904	0.589996
$209$	−2.29417	−0.158691
$210$	−0.321491	−0.0221850
$211$	16.5769	1.14120	0.570602	−	0.821227i	$-0.306710\pi$
$211$	16.5769	1.14120	0.570602	+	0.821227i	$0.306710\pi$
$212$	−18.8259	−1.29297
$213$	−8.00721	−0.548645
$214$	7.53897	0.515353
$215$	3.25148	0.221749
$216$	−2.16136	−0.147062
$217$	−1.18967	−0.0807603
$218$	1.84123	0.124704
$219$	−4.47373	−0.302306
$220$	3.90867	0.263523
$221$	−20.7046	−1.39274
$222$	−5.98541	−0.401715
$223$	−0.198493	−0.0132921	−0.00664605	−	0.999978i	$-0.502116\pi$
$223$	−0.198493	−0.0132921	−0.00664605	+	0.999978i	$0.502116\pi$
$224$	−2.99522	−0.200127
$225$	1.00000	0.0666667
$226$	−4.59275	−0.305505
$227$	−22.1343	−1.46911	−0.734553	−	0.678551i	$-0.762608\pi$
$227$	−22.1343	−1.46911	−0.734553	+	0.678551i	$0.762608\pi$
$228$	−1.59641	−0.105725
$229$	−10.7984	−0.713580	−0.356790	−	0.934185i	$-0.616129\pi$
$229$	−10.7984	−0.713580	−0.356790	+	0.934185i	$0.616129\pi$
$230$	−5.13293	−0.338456
$231$	1.28646	0.0846427
$232$	−21.4819	−1.41035
$233$	4.88452	0.319996	0.159998	−	0.987117i	$-0.448851\pi$
$233$	4.88452	0.319996	0.159998	+	0.987117i	$0.448851\pi$
$234$	2.49707	0.163238
$235$	−0.431405	−0.0281418
$236$	6.85231	0.446047
$237$	−14.5928	−0.947907
$238$	1.57882	0.102340
$239$	21.6243	1.39876	0.699379	−	0.714751i	$-0.253460\pi$
$239$	21.6243	1.39876	0.699379	+	0.714751i	$0.253460\pi$
$240$	2.01827	0.130279
$241$	−16.5855	−1.06836	−0.534182	−	0.845369i	$-0.679380\pi$
$241$	−16.5855	−1.06836	−0.534182	+	0.845369i	$0.679380\pi$
$242$	−3.18820	−0.204945
$243$	1.00000	0.0641500
$244$	20.7927	1.33111
$245$	−6.70537	−0.428390
$246$	−0.310442	−0.0197930
$247$	4.08105	0.259671
$248$	−4.73713	−0.300808
$249$	5.64687	0.357856
$250$	0.592282	0.0374592
$251$	−16.4694	−1.03954	−0.519768	−	0.854307i	$-0.673982\pi$
$251$	−16.4694	−1.03954	−0.519768	+	0.854307i	$0.673982\pi$
$252$	0.895186	0.0563914
$253$	20.5396	1.29132
$254$	9.36600	0.587675
$255$	−4.91094	−0.307535
$256$	−5.26953	−0.329346
$257$	28.1824	1.75797	0.878985	−	0.476849i	$-0.158221\pi$
$257$	28.1824	1.75797	0.878985	+	0.476849i	$0.158221\pi$
$258$	1.92580	0.119895
$259$	5.48536	0.340844
$260$	−6.95305	−0.431210
$261$	9.93906	0.615212
$262$	−5.45097	−0.336762
$263$	−20.4784	−1.26275	−0.631376	−	0.775477i	$-0.717509\pi$
$263$	−20.4784	−1.26275	−0.631376	+	0.775477i	$0.717509\pi$
$264$	5.12251	0.315268
$265$	11.4152	0.701229
$266$	−0.311200	−0.0190809
$267$	−6.69079	−0.409470
$268$	−5.58896	−0.341400
$269$	−7.09807	−0.432777	−0.216388	−	0.976307i	$-0.569428\pi$
$269$	−7.09807	−0.432777	−0.216388	+	0.976307i	$0.569428\pi$
$270$	0.592282	0.0360452
$271$	20.1865	1.22624	0.613121	−	0.789989i	$-0.289914\pi$
$271$	20.1865	1.22624	0.613121	+	0.789989i	$0.289914\pi$
$272$	−9.91160	−0.600979
$273$	−2.28845	−0.138503
$274$	6.65982	0.402334
$275$	−2.37004	−0.142919
$276$	14.2926	0.860312
$277$	−7.17189	−0.430917	−0.215458	−	0.976513i	$-0.569125\pi$
$277$	−7.17189	−0.430917	−0.215458	+	0.976513i	$0.569125\pi$
$278$	1.48609	0.0891296
$279$	2.19174	0.131216
$280$	1.17318	0.0701112
$281$	−29.6661	−1.76973	−0.884867	−	0.465845i	$-0.845751\pi$
$281$	−29.6661	−1.76973	−0.884867	+	0.465845i	$0.845751\pi$
$282$	−0.255514	−0.0152156
$283$	−2.41029	−0.143277	−0.0716383	−	0.997431i	$-0.522823\pi$
$283$	−2.41029	−0.143277	−0.0716383	+	0.997431i	$0.522823\pi$
$284$	13.2055	0.783602
$285$	0.967989	0.0573387
$286$	−5.91815	−0.349948
$287$	0.284505	0.0167938
$288$	5.51810	0.325157
$289$	7.11734	0.418667
$290$	5.88673	0.345681
$291$	−14.4940	−0.849653
$292$	7.37808	0.431769
$293$	−23.2144	−1.35620	−0.678101	−	0.734969i	$-0.737197\pi$
$293$	−23.2144	−1.35620	−0.678101	+	0.734969i	$0.737197\pi$
$294$	−3.97147	−0.231621
$295$	−4.15492	−0.241909
$296$	21.8420	1.26954
$297$	−2.37004	−0.137524
$298$	0.858479	0.0497303
$299$	−36.5375	−2.11302
$300$	−1.64920	−0.0952167
$301$	−1.76490	−0.101727
$302$	11.3737	0.654484
$303$	−7.27619	−0.418006
$304$	1.95366	0.112050
$305$	−12.6077	−0.721915
$306$	−2.90866	−0.166277
$307$	−9.75997	−0.557031	−0.278515	−	0.960432i	$-0.589842\pi$
$307$	−9.75997	−0.557031	−0.278515	+	0.960432i	$0.589842\pi$
$308$	−2.12163	−0.120891
$309$	−13.7914	−0.784564
$310$	1.29813	0.0737286
$311$	−12.7567	−0.723364	−0.361682	−	0.932302i	$-0.617797\pi$
$311$	−12.7567	−0.723364	−0.361682	+	0.932302i	$0.617797\pi$
$312$	−9.11231	−0.515883
$313$	−6.45106	−0.364636	−0.182318	−	0.983240i	$-0.558360\pi$
$313$	−6.45106	−0.364636	−0.182318	+	0.983240i	$0.558360\pi$
$314$	−13.9058	−0.784752
$315$	−0.542800	−0.0305833
$316$	24.0665	1.35385
$317$	−14.8231	−0.832548	−0.416274	−	0.909239i	$-0.636664\pi$
$317$	−14.8231	−0.832548	−0.416274	+	0.909239i	$0.636664\pi$
$318$	6.76101	0.379139
$319$	−23.5560	−1.31888
$320$	−0.768263	−0.0429472
$321$	12.7287	0.710445
$322$	2.78616	0.155266
$323$	−4.75374	−0.264505
$324$	−1.64920	−0.0916223
$325$	4.21601	0.233862
$326$	−6.45338	−0.357419
$327$	3.10871	0.171912
$328$	1.13286	0.0625519
$329$	0.234167	0.0129100
$330$	−1.40373	−0.0772730
$331$	−21.6263	−1.18869	−0.594345	−	0.804210i	$-0.702588\pi$
$331$	−21.6263	−1.18869	−0.594345	+	0.804210i	$0.702588\pi$
$332$	−9.31283	−0.511108
$333$	−10.1057	−0.553787
$334$	3.36797	0.184287
$335$	3.38889	0.185155
$336$	−1.09552	−0.0597653
$337$	−17.9985	−0.980441	−0.490221	−	0.871598i	$-0.663084\pi$
$337$	−17.9985	−0.980441	−0.490221	+	0.871598i	$0.663084\pi$
$338$	2.82800	0.153823
$339$	−7.75433	−0.421157
$340$	8.09913	0.439237
$341$	−5.19450	−0.281298
$342$	0.573323	0.0310018
$343$	7.43927	0.401683
$344$	−7.02762	−0.378904
$345$	−8.66636	−0.466581
$346$	0.0638632	0.00343331
$347$	25.2467	1.35532	0.677658	−	0.735377i	$-0.262995\pi$
$347$	25.2467	1.35532	0.677658	+	0.735377i	$0.262995\pi$
$348$	−16.3915	−0.878677
$349$	26.1193	1.39813	0.699067	−	0.715056i	$-0.253599\pi$
$349$	26.1193	1.39813	0.699067	+	0.715056i	$0.253599\pi$
$350$	−0.321491	−0.0171844
$351$	4.21601	0.225034
$352$	−13.0781	−0.697066
$353$	32.9367	1.75305	0.876523	−	0.481360i	$-0.159857\pi$
$353$	32.9367	1.75305	0.876523	+	0.481360i	$0.159857\pi$
$354$	−2.46089	−0.130795
$355$	−8.00721	−0.424979
$356$	11.0345	0.584825
$357$	2.66566	0.141082
$358$	1.08364	0.0572723
$359$	34.1089	1.80020	0.900099	−	0.435684i	$-0.143494\pi$
$359$	34.1089	1.80020	0.900099	+	0.435684i	$0.143494\pi$
$360$	−2.16136	−0.113914
$361$	−18.0630	−0.950684
$362$	−14.5374	−0.764070
$363$	−5.38291	−0.282529
$364$	3.77411	0.197817
$365$	−4.47373	−0.234166
$366$	−7.46733	−0.390323
$367$	10.7228	0.559723	0.279862	−	0.960040i	$-0.409711\pi$
$367$	10.7228	0.559723	0.279862	+	0.960040i	$0.409711\pi$
$368$	−17.4910	−0.911784
$369$	−0.524144	−0.0272859
$370$	−5.98541	−0.311167
$371$	−6.19616	−0.321688
$372$	−3.61461	−0.187409
$373$	34.6096	1.79201	0.896007	−	0.444039i	$-0.146455\pi$
$373$	34.6096	1.79201	0.896007	+	0.444039i	$0.146455\pi$
$374$	6.89365	0.356462
$375$	1.00000	0.0516398
$376$	0.932421	0.0480859
$377$	41.9032	2.15812
$378$	−0.321491	−0.0165357
$379$	−11.0460	−0.567393	−0.283697	−	0.958914i	$-0.591561\pi$
$379$	−11.0460	−0.567393	−0.283697	+	0.958914i	$0.591561\pi$
$380$	−1.59641	−0.0818941
$381$	15.8134	0.810145
$382$	0.803046	0.0410874
$383$	−18.3558	−0.937935	−0.468968	−	0.883215i	$-0.655374\pi$
$383$	−18.3558	−0.937935	−0.468968	+	0.883215i	$0.655374\pi$
$384$	−11.4912	−0.586409
$385$	1.28646	0.0655639
$386$	−6.27784	−0.319534
$387$	3.25148	0.165282
$388$	23.9035	1.21352
$389$	21.7791	1.10425	0.552123	−	0.833763i	$-0.313818\pi$
$389$	21.7791	1.10425	0.552123	+	0.833763i	$0.313818\pi$
$390$	2.49707	0.126444
$391$	42.5600	2.15235
$392$	14.4927	0.731992
$393$	−9.20333	−0.464247
$394$	1.95136	0.0983081
$395$	−14.5928	−0.734246
$396$	3.90867	0.196418
$397$	−32.4968	−1.63097	−0.815484	−	0.578780i	$-0.803529\pi$
$397$	−32.4968	−1.63097	−0.815484	+	0.578780i	$0.803529\pi$
$398$	2.66201	0.133435
$399$	−0.525424	−0.0263041
$400$	2.01827	0.100913
$401$	−1.00000	−0.0499376
$401$	−1.00000	−0.0499376
$402$	2.00718	0.100109
$403$	9.24038	0.460296
$404$	11.9999	0.597017
$405$	1.00000	0.0496904
$406$	−3.19532	−0.158581
$407$	23.9509	1.18720
$408$	10.6143	0.525486
$409$	−30.0707	−1.48690	−0.743450	−	0.668792i	$-0.766812\pi$
$409$	−30.0707	−1.48690	−0.743450	+	0.668792i	$0.766812\pi$
$410$	−0.310442	−0.0153316
$411$	11.2443	0.554642
$412$	22.7448	1.12055
$413$	2.25529	0.110976
$414$	−5.13293	−0.252270
$415$	5.64687	0.277194
$416$	23.2644	1.14063
$417$	2.50909	0.122870
$418$	−1.35880	−0.0664610
$419$	20.9503	1.02349	0.511745	−	0.859137i	$-0.328999\pi$
$419$	20.9503	1.02349	0.511745	+	0.859137i	$0.328999\pi$
$420$	0.895186	0.0436806
$421$	−24.9159	−1.21432	−0.607162	−	0.794578i	$-0.707692\pi$
$421$	−24.9159	−1.21432	−0.607162	+	0.794578i	$0.707692\pi$
$422$	9.81823	0.477944
$423$	−0.431405	−0.0209756
$424$	−24.6723	−1.19819
$425$	−4.91094	−0.238216
$426$	−4.74253	−0.229776
$427$	6.84346	0.331178
$428$	−20.9921	−1.01469
$429$	−9.99211	−0.482424
$430$	1.92580	0.0928701
$431$	20.5969	0.992118	0.496059	−	0.868289i	$-0.334780\pi$
$431$	20.5969	0.992118	0.496059	+	0.868289i	$0.334780\pi$
$432$	2.01827	0.0971040
$433$	−29.4242	−1.41403	−0.707017	−	0.707196i	$-0.749960\pi$
$433$	−29.4242	−1.41403	−0.707017	+	0.707196i	$0.749960\pi$
$434$	−0.704623	−0.0338230
$435$	9.93906	0.476541
$436$	−5.12688	−0.245533
$437$	−8.38894	−0.401298
$438$	−2.64971	−0.126608
$439$	5.26979	0.251513	0.125757	−	0.992061i	$-0.459864\pi$
$439$	5.26979	0.251513	0.125757	+	0.992061i	$0.459864\pi$
$440$	5.12251	0.244206
$441$	−6.70537	−0.319303
$442$	−12.2630	−0.583289
$443$	29.3860	1.39617	0.698085	−	0.716015i	$-0.254036\pi$
$443$	29.3860	1.39617	0.698085	+	0.716015i	$0.254036\pi$
$444$	16.6663	0.790947
$445$	−6.69079	−0.317174
$446$	−0.117564	−0.00556682
$447$	1.44944	0.0685562
$448$	0.417013	0.0197020
$449$	8.40709	0.396755	0.198378	−	0.980126i	$-0.436433\pi$
$449$	8.40709	0.396755	0.198378	+	0.980126i	$0.436433\pi$
$450$	0.592282	0.0279205
$451$	1.24224	0.0584950
$452$	12.7884	0.601518
$453$	19.2032	0.902245
$454$	−13.1098	−0.615272
$455$	−2.28845	−0.107284
$456$	−2.09217	−0.0979749
$457$	32.6437	1.52701	0.763504	−	0.645803i	$-0.223477\pi$
$457$	32.6437	1.52701	0.763504	+	0.645803i	$0.223477\pi$
$458$	−6.39572	−0.298852
$459$	−4.91094	−0.229223
$460$	14.2926	0.666395
$461$	10.6904	0.497903	0.248951	−	0.968516i	$-0.419914\pi$
$461$	10.6904	0.497903	0.248951	+	0.968516i	$0.419914\pi$
$462$	0.761946	0.0354489
$463$	−4.69483	−0.218187	−0.109094	−	0.994031i	$-0.534795\pi$
$463$	−4.69483	−0.218187	−0.109094	+	0.994031i	$0.534795\pi$
$464$	20.0597	0.931248
$465$	2.19174	0.101639
$466$	2.89302	0.134016
$467$	28.6502	1.32577	0.662887	−	0.748719i	$-0.269331\pi$
$467$	28.6502	1.32577	0.662887	+	0.748719i	$0.269331\pi$
$468$	−6.95305	−0.321405
$469$	−1.83949	−0.0849397
$470$	−0.255514	−0.0117860
$471$	−23.4784	−1.08183
$472$	8.98028	0.413351
$473$	−7.70614	−0.354329
$474$	−8.64309	−0.396990
$475$	0.967989	0.0444144
$476$	−4.39621	−0.201500
$477$	11.4152	0.522665
$478$	12.8077	0.585809
$479$	11.0755	0.506055	0.253027	−	0.967459i	$-0.418574\pi$
$479$	11.0755	0.506055	0.253027	+	0.967459i	$0.418574\pi$
$480$	5.51810	0.251866
$481$	−42.6056	−1.94265
$482$	−9.82329	−0.447439
$483$	4.70410	0.214044
$484$	8.87750	0.403523
$485$	−14.4940	−0.658139
$486$	0.592282	0.0268665
$487$	25.2040	1.14210	0.571050	−	0.820915i	$-0.306536\pi$
$487$	25.2040	1.14210	0.571050	+	0.820915i	$0.306536\pi$
$488$	27.2498	1.23354
$489$	−10.8958	−0.492724
$490$	−3.97147	−0.179413
$491$	0.135118	0.00609780	0.00304890	−	0.999995i	$-0.499030\pi$
$491$	0.135118	0.00609780	0.00304890	+	0.999995i	$0.499030\pi$
$492$	0.864420	0.0389710
$493$	−48.8101	−2.19830
$494$	2.41714	0.108752
$495$	−2.37004	−0.106525
$496$	4.42351	0.198622
$497$	4.34631	0.194959
$498$	3.34454	0.149872
$499$	20.6730	0.925449	0.462724	−	0.886502i	$-0.346872\pi$
$499$	20.6730	0.925449	0.462724	+	0.886502i	$0.346872\pi$
$500$	−1.64920	−0.0737545
$501$	5.68642	0.254050
$502$	−9.75451	−0.435365
$503$	−41.2674	−1.84002	−0.920010	−	0.391894i	$-0.871820\pi$
$503$	−41.2674	−1.84002	−0.920010	+	0.391894i	$0.871820\pi$
$504$	1.17318	0.0522578
$505$	−7.27619	−0.323786
$506$	12.1653	0.540812
$507$	4.77474	0.212054
$508$	−26.0795	−1.15709
$509$	−42.8614	−1.89980	−0.949900	−	0.312554i	$-0.898815\pi$
$509$	−42.8614	−1.89980	−0.949900	+	0.312554i	$0.898815\pi$
$510$	−2.90866	−0.128798
$511$	2.42834	0.107423
$512$	19.8614	0.877759
$513$	0.967989	0.0427378
$514$	16.6919	0.736250
$515$	−13.7914	−0.607721
$516$	−5.36235	−0.236064
$517$	1.02245	0.0449672
$518$	3.24888	0.142748
$519$	0.107826	0.00473302
$520$	−9.11231	−0.399601
$521$	−0.148025	−0.00648508	−0.00324254	−	0.999995i	$-0.501032\pi$
$521$	−0.148025	−0.00648508	−0.00324254	+	0.999995i	$0.501032\pi$
$522$	5.88673	0.257655
$523$	−11.9400	−0.522098	−0.261049	−	0.965326i	$-0.584068\pi$
$523$	−11.9400	−0.522098	−0.261049	+	0.965326i	$0.584068\pi$
$524$	15.1781	0.663060
$525$	−0.542800	−0.0236897
$526$	−12.1290	−0.528849
$527$	−10.7635	−0.468865
$528$	−4.78338	−0.208170
$529$	52.1058	2.26547
$530$	6.76101	0.293679
$531$	−4.15492	−0.180308
$532$	0.866530	0.0375689
$533$	−2.20980	−0.0957170
$534$	−3.96284	−0.171489
$535$	12.7287	0.550308
$536$	−7.32460	−0.316375
$537$	1.82960	0.0789533
$538$	−4.20406	−0.181250
$539$	15.8920	0.684517
$540$	−1.64920	−0.0709703
$541$	−44.4693	−1.91189	−0.955943	−	0.293551i	$-0.905163\pi$
$541$	−44.4693	−1.91189	−0.955943	+	0.293551i	$0.905163\pi$
$542$	11.9561	0.513559
$543$	−24.5447	−1.05332
$544$	−27.0991	−1.16186
$545$	3.10871	0.133162
$546$	−1.35541	−0.0580061
$547$	42.9040	1.83444	0.917222	−	0.398377i	$-0.130426\pi$
$547$	42.9040	1.83444	0.917222	+	0.398377i	$0.130426\pi$
$548$	−18.5442	−0.792168
$549$	−12.6077	−0.538084
$550$	−1.40373	−0.0598554
$551$	9.62090	0.409864
$552$	18.7311	0.797249
$553$	7.92099	0.336835
$554$	−4.24778	−0.180471
$555$	−10.1057	−0.428962
$556$	−4.13799	−0.175490
$557$	−18.7048	−0.792546	−0.396273	−	0.918133i	$-0.629697\pi$
$557$	−18.7048	−0.792546	−0.396273	+	0.918133i	$0.629697\pi$
$558$	1.29813	0.0549541
$559$	13.7083	0.579799
$560$	−1.09552	−0.0462940
$561$	11.6391	0.491404
$562$	−17.5707	−0.741176
$563$	14.1732	0.597331	0.298665	−	0.954358i	$-0.403459\pi$
$563$	14.1732	0.597331	0.298665	+	0.954358i	$0.403459\pi$
$564$	0.711474	0.0299584
$565$	−7.75433	−0.326227
$566$	−1.42757	−0.0600053
$567$	−0.542800	−0.0227954
$568$	17.3064	0.726162
$569$	−9.77991	−0.409995	−0.204998	−	0.978762i	$-0.565719\pi$
$569$	−9.77991	−0.409995	−0.204998	+	0.978762i	$0.565719\pi$
$570$	0.573323	0.0240139
$571$	−19.1389	−0.800940	−0.400470	−	0.916310i	$-0.631153\pi$
$571$	−19.1389	−0.800940	−0.400470	+	0.916310i	$0.631153\pi$
$572$	16.4790	0.689022
$573$	1.35585	0.0566415
$574$	0.168508	0.00703337
$575$	−8.66636	−0.361412
$576$	−0.768263	−0.0320110
$577$	36.5026	1.51962	0.759812	−	0.650143i	$-0.225291\pi$
$577$	36.5026	1.51962	0.759812	+	0.650143i	$0.225291\pi$
$578$	4.21547	0.175341
$579$	−10.5994	−0.440496
$580$	−16.3915	−0.680620
$581$	−3.06512	−0.127163
$582$	−8.58454	−0.355841
$583$	−27.0544	−1.12048
$584$	9.66932	0.400119
$585$	4.21601	0.174311
$586$	−13.7495	−0.567987
$587$	−29.5354	−1.21906	−0.609528	−	0.792765i	$-0.708641\pi$
$587$	−29.5354	−1.21906	−0.609528	+	0.792765i	$0.708641\pi$
$588$	11.0585	0.456045
$589$	2.12158	0.0874180
$590$	−2.46089	−0.101313
$591$	3.29465	0.135524
$592$	−20.3960	−0.838269
$593$	30.9102	1.26933	0.634665	−	0.772787i	$-0.281138\pi$
$593$	30.9102	1.26933	0.634665	+	0.772787i	$0.281138\pi$
$594$	−1.40373	−0.0575959
$595$	2.66566	0.109281
$596$	−2.39042	−0.0979155
$597$	4.49450	0.183948
$598$	−21.6405	−0.884946
$599$	−19.4794	−0.795907	−0.397954	−	0.917406i	$-0.630280\pi$
$599$	−19.4794	−0.795907	−0.397954	+	0.917406i	$0.630280\pi$
$600$	−2.16136	−0.0882371
$601$	36.6056	1.49317	0.746587	−	0.665288i	$-0.231691\pi$
$601$	36.6056	1.49317	0.746587	+	0.665288i	$0.231691\pi$
$602$	−1.04532	−0.0426041
$603$	3.38889	0.138006
$604$	−31.6700	−1.28863
$605$	−5.38291	−0.218846
$606$	−4.30956	−0.175064
$607$	21.4120	0.869086	0.434543	−	0.900651i	$-0.356910\pi$
$607$	21.4120	0.869086	0.434543	+	0.900651i	$0.356910\pi$
$608$	5.34146	0.216625
$609$	−5.39492	−0.218613
$610$	−7.46733	−0.302343
$611$	−1.81881	−0.0735811
$612$	8.09913	0.327388
$613$	12.3953	0.500641	0.250320	−	0.968163i	$-0.419464\pi$
$613$	12.3953	0.500641	0.250320	+	0.968163i	$0.419464\pi$
$614$	−5.78066	−0.233288
$615$	−0.524144	−0.0211355
$616$	−2.78050	−0.112029
$617$	3.82557	0.154012	0.0770058	−	0.997031i	$-0.475464\pi$
$617$	3.82557	0.154012	0.0770058	+	0.997031i	$0.475464\pi$
$618$	−8.16839	−0.328581
$619$	−15.5165	−0.623662	−0.311831	−	0.950138i	$-0.600942\pi$
$619$	−15.5165	−0.623662	−0.311831	+	0.950138i	$0.600942\pi$
$620$	−3.61461	−0.145166
$621$	−8.66636	−0.347769
$622$	−7.55554	−0.302950
$623$	3.63176	0.145503
$624$	8.50904	0.340634
$625$	1.00000	0.0400000
$626$	−3.82085	−0.152712
$627$	−2.29417	−0.0916204
$628$	38.7206	1.54512
$629$	49.6284	1.97881
$630$	−0.321491	−0.0128085
$631$	−8.40118	−0.334446	−0.167223	−	0.985919i	$-0.553480\pi$
$631$	−8.40118	−0.334446	−0.167223	+	0.985919i	$0.553480\pi$
$632$	31.5404	1.25461
$633$	16.5769	0.658874
$634$	−8.77946	−0.348677
$635$	15.8134	0.627536
$636$	−18.8259	−0.746497
$637$	−28.2699	−1.12009
$638$	−13.9518	−0.552357
$639$	−8.00721	−0.316760
$640$	−11.4912	−0.454231
$641$	5.96392	0.235561	0.117780	−	0.993040i	$-0.462422\pi$
$641$	5.96392	0.235561	0.117780	+	0.993040i	$0.462422\pi$
$642$	7.53897	0.297539
$643$	−46.0685	−1.81676	−0.908382	−	0.418141i	$-0.862682\pi$
$643$	−46.0685	−1.81676	−0.908382	+	0.418141i	$0.862682\pi$
$644$	−7.75801	−0.305708
$645$	3.25148	0.128027
$646$	−2.81555	−0.110777
$647$	13.3042	0.523041	0.261521	−	0.965198i	$-0.415776\pi$
$647$	13.3042	0.523041	0.261521	+	0.965198i	$0.415776\pi$
$648$	−2.16136	−0.0849062
$649$	9.84734	0.386542
$650$	2.49707	0.0979431
$651$	−1.18967	−0.0466270
$652$	17.9693	0.703733
$653$	−37.2132	−1.45626	−0.728132	−	0.685437i	$-0.759611\pi$
$653$	−37.2132	−1.45626	−0.728132	+	0.685437i	$0.759611\pi$
$654$	1.84123	0.0719979
$655$	−9.20333	−0.359604
$656$	−1.05786	−0.0413027
$657$	−4.47373	−0.174537
$658$	0.138693	0.00540680
$659$	26.5854	1.03562	0.517810	−	0.855496i	$-0.326748\pi$
$659$	26.5854	1.03562	0.517810	+	0.855496i	$0.326748\pi$
$660$	3.90867	0.152145
$661$	−28.2702	−1.09958	−0.549791	−	0.835302i	$-0.685293\pi$
$661$	−28.2702	−1.09958	−0.549791	+	0.835302i	$0.685293\pi$
$662$	−12.8089	−0.497831
$663$	−20.7046	−0.804099
$664$	−12.2049	−0.473642
$665$	−0.525424	−0.0203751
$666$	−5.98541	−0.231930
$667$	−86.1355	−3.33518
$668$	−9.37805	−0.362848
$669$	−0.198493	−0.00767419
$670$	2.00718	0.0775441
$671$	29.8808	1.15353
$672$	−2.99522	−0.115543
$673$	−25.4726	−0.981895	−0.490948	−	0.871189i	$-0.663349\pi$
$673$	−25.4726	−0.981895	−0.490948	+	0.871189i	$0.663349\pi$
$674$	−10.6602	−0.410616
$675$	1.00000	0.0384900
$676$	−7.87451	−0.302866
$677$	−1.29568	−0.0497969	−0.0248985	−	0.999690i	$-0.507926\pi$
$677$	−1.29568	−0.0497969	−0.0248985	+	0.999690i	$0.507926\pi$
$678$	−4.59275	−0.176384
$679$	7.86734	0.301921
$680$	10.6143	0.407040
$681$	−22.1343	−0.848189
$682$	−3.07661	−0.117810
$683$	28.8079	1.10230	0.551152	−	0.834405i	$-0.314189\pi$
$683$	28.8079	1.10230	0.551152	+	0.834405i	$0.314189\pi$
$684$	−1.59641	−0.0610402
$685$	11.2443	0.429624
$686$	4.40615	0.168228
$687$	−10.7984	−0.411986
$688$	6.56236	0.250188
$689$	48.1265	1.83347
$690$	−5.13293	−0.195407
$691$	−1.92259	−0.0731387	−0.0365693	−	0.999331i	$-0.511643\pi$
$691$	−1.92259	−0.0731387	−0.0365693	+	0.999331i	$0.511643\pi$
$692$	−0.177826	−0.00675993
$693$	1.28646	0.0488685
$694$	14.9532	0.567616
$695$	2.50909	0.0951751
$696$	−21.4819	−0.814268
$697$	2.57404	0.0974988
$698$	15.4700	0.585549
$699$	4.88452	0.184750
$700$	0.895186	0.0338349
$701$	26.6945	1.00824	0.504118	−	0.863635i	$-0.331818\pi$
$701$	26.6945	1.00824	0.504118	+	0.863635i	$0.331818\pi$
$702$	2.49707	0.0942458
$703$	−9.78218	−0.368942
$704$	1.82081	0.0686245
$705$	−0.431405	−0.0162477
$706$	19.5079	0.734188
$707$	3.94951	0.148537
$708$	6.85231	0.257525
$709$	−20.1975	−0.758534	−0.379267	−	0.925287i	$-0.623824\pi$
$709$	−20.1975	−0.758534	−0.379267	+	0.925287i	$0.623824\pi$
$710$	−4.74253	−0.177984
$711$	−14.5928	−0.547274
$712$	14.4612	0.541956
$713$	−18.9944	−0.711345
$714$	1.57882	0.0590859
$715$	−9.99211	−0.373684
$716$	−3.01739	−0.112765
$717$	21.6243	0.807573
$718$	20.2021	0.753936
$719$	−23.9859	−0.894525	−0.447262	−	0.894403i	$-0.647601\pi$
$719$	−23.9859	−0.894525	−0.447262	+	0.894403i	$0.647601\pi$
$720$	2.01827	0.0752164
$721$	7.48596	0.278792
$722$	−10.6984	−0.398153
$723$	−16.5855	−0.616821
$724$	40.4792	1.50440
$725$	9.93906	0.369127
$726$	−3.18820	−0.118325
$727$	41.2645	1.53042	0.765208	−	0.643783i	$-0.222636\pi$
$727$	41.2645	1.53042	0.765208	+	0.643783i	$0.222636\pi$
$728$	4.94616	0.183317
$729$	1.00000	0.0370370
$730$	−2.64971	−0.0980701
$731$	−15.9678	−0.590592
$732$	20.7927	0.768519
$733$	−0.231926	−0.00856637	−0.00428319	−	0.999991i	$-0.501363\pi$
$733$	−0.231926	−0.00856637	−0.00428319	+	0.999991i	$0.501363\pi$
$734$	6.35090	0.234416
$735$	−6.70537	−0.247331
$736$	−47.8219	−1.76274
$737$	−8.03181	−0.295855
$738$	−0.310442	−0.0114275
$739$	23.2202	0.854170	0.427085	−	0.904212i	$-0.359541\pi$
$739$	23.2202	0.854170	0.427085	+	0.904212i	$0.359541\pi$
$740$	16.6663	0.612665
$741$	4.08105	0.149921
$742$	−3.66987	−0.134725
$743$	−19.0164	−0.697644	−0.348822	−	0.937189i	$-0.613418\pi$
$743$	−19.0164	−0.697644	−0.348822	+	0.937189i	$0.613418\pi$
$744$	−4.73713	−0.173671
$745$	1.44944	0.0531034
$746$	20.4986	0.750508
$747$	5.64687	0.206608
$748$	−19.1953	−0.701848
$749$	−6.90912	−0.252454
$750$	0.592282	0.0216271
$751$	54.3696	1.98397	0.991987	−	0.126342i	$-0.0403236\pi$
$751$	54.3696	1.98397	0.991987	+	0.126342i	$0.0403236\pi$
$752$	−0.870691	−0.0317508
$753$	−16.4694	−0.600177
$754$	24.8185	0.903837
$755$	19.2032	0.698876
$756$	0.895186	0.0325576
$757$	−24.7225	−0.898553	−0.449277	−	0.893393i	$-0.648318\pi$
$757$	−24.7225	−0.898553	−0.449277	+	0.893393i	$0.648318\pi$
$758$	−6.54233	−0.237628
$759$	20.5396	0.745541
$760$	−2.09217	−0.0758910
$761$	−13.2202	−0.479232	−0.239616	−	0.970868i	$-0.577022\pi$
$761$	−13.2202	−0.479232	−0.239616	+	0.970868i	$0.577022\pi$
$762$	9.36600	0.339294
$763$	−1.68741	−0.0610882
$764$	−2.23607	−0.0808982
$765$	−4.91094	−0.177555
$766$	−10.8718	−0.392814
$767$	−17.5172	−0.632510
$768$	−5.26953	−0.190148
$769$	16.5394	0.596425	0.298213	−	0.954499i	$-0.403610\pi$
$769$	16.5394	0.596425	0.298213	+	0.954499i	$0.403610\pi$
$770$	0.761946	0.0274586
$771$	28.1824	1.01496
$772$	17.4806	0.629139
$773$	49.1307	1.76711	0.883553	−	0.468330i	$-0.155144\pi$
$773$	49.1307	1.76711	0.883553	+	0.468330i	$0.155144\pi$
$774$	1.92580	0.0692213
$775$	2.19174	0.0787295
$776$	31.3267	1.12456
$777$	5.48536	0.196786
$778$	12.8994	0.462466
$779$	−0.507366	−0.0181783
$780$	−6.95305	−0.248959
$781$	18.9774	0.679065
$782$	25.2075	0.901419
$783$	9.93906	0.355193
$784$	−13.5332	−0.483330
$785$	−23.4784	−0.837980
$786$	−5.45097	−0.194430
$787$	20.2503	0.721847	0.360923	−	0.932595i	$-0.382462\pi$
$787$	20.2503	0.721847	0.360923	+	0.932595i	$0.382462\pi$
$788$	−5.43354	−0.193562
$789$	−20.4784	−0.729050
$790$	−8.64309	−0.307507
$791$	4.20905	0.149656
$792$	5.12251	0.182020
$793$	−53.1542	−1.88756
$794$	−19.2473	−0.683060
$795$	11.4152	0.404855
$796$	−7.41233	−0.262723
$797$	13.5924	0.481468	0.240734	−	0.970591i	$-0.422612\pi$
$797$	13.5924	0.481468	0.240734	+	0.970591i	$0.422612\pi$
$798$	−0.311200	−0.0110163
$799$	2.11860	0.0749508
$800$	5.51810	0.195094
$801$	−6.69079	−0.236408
$802$	−0.592282	−0.0209142
$803$	10.6029	0.374169
$804$	−5.58896	−0.197108
$805$	4.70410	0.165798
$806$	5.47291	0.192775
$807$	−7.09807	−0.249864
$808$	15.7264	0.553255
$809$	25.0626	0.881153	0.440576	−	0.897715i	$-0.354774\pi$
$809$	25.0626	0.881153	0.440576	+	0.897715i	$0.354774\pi$
$810$	0.592282	0.0208107
$811$	−27.2905	−0.958299	−0.479150	−	0.877733i	$-0.659055\pi$
$811$	−27.2905	−0.958299	−0.479150	+	0.877733i	$0.659055\pi$
$812$	8.89731	0.312234
$813$	20.1865	0.707971
$814$	14.1857	0.497207
$815$	−10.8958	−0.381662
$816$	−9.91160	−0.346975
$817$	3.14740	0.110114
$818$	−17.8103	−0.622724
$819$	−2.28845	−0.0799649
$820$	0.864420	0.0301868
$821$	−0.157581	−0.00549961	−0.00274980	−	0.999996i	$-0.500875\pi$
$821$	−0.157581	−0.00549961	−0.00274980	+	0.999996i	$0.500875\pi$
$822$	6.65982	0.232288
$823$	41.6383	1.45142	0.725710	−	0.688001i	$-0.241511\pi$
$823$	41.6383	1.45142	0.725710	+	0.688001i	$0.241511\pi$
$824$	29.8081	1.03841
$825$	−2.37004	−0.0825142
$826$	1.33577	0.0464774
$827$	51.2479	1.78206	0.891032	−	0.453941i	$-0.149982\pi$
$827$	51.2479	1.78206	0.891032	+	0.453941i	$0.149982\pi$
$828$	14.2926	0.496701
$829$	−16.6255	−0.577429	−0.288714	−	0.957415i	$-0.593228\pi$
$829$	−16.6255	−0.577429	−0.288714	+	0.957415i	$0.593228\pi$
$830$	3.34454	0.116091
$831$	−7.17189	−0.248790
$832$	−3.23900	−0.112292
$833$	32.9297	1.14095
$834$	1.48609	0.0514590
$835$	5.68642	0.196787
$836$	3.78355	0.130857
$837$	2.19174	0.0757575
$838$	12.4085	0.428645
$839$	−9.31617	−0.321630	−0.160815	−	0.986985i	$-0.551412\pi$
$839$	−9.31617	−0.321630	−0.160815	+	0.986985i	$0.551412\pi$
$840$	1.17318	0.0404787
$841$	69.7849	2.40637
$842$	−14.7572	−0.508568
$843$	−29.6661	−1.02176
$844$	−27.3387	−0.941037
$845$	4.77474	0.164256
$846$	−0.255514	−0.00878474
$847$	2.92184	0.100396
$848$	23.0389	0.791159
$849$	−2.41029	−0.0827208
$850$	−2.90866	−0.0997663
$851$	87.5794	3.00218
$852$	13.2055	0.452413
$853$	48.3803	1.65651	0.828255	−	0.560352i	$-0.189334\pi$
$853$	48.3803	1.65651	0.828255	+	0.560352i	$0.189334\pi$
$854$	4.05326	0.138700
$855$	0.967989	0.0331045
$856$	−27.5112	−0.940314
$857$	−40.5315	−1.38453	−0.692265	−	0.721643i	$-0.743387\pi$
$857$	−40.5315	−1.38453	−0.692265	+	0.721643i	$0.743387\pi$
$858$	−5.91815	−0.202042
$859$	24.2042	0.825838	0.412919	−	0.910768i	$-0.364509\pi$
$859$	24.2042	0.825838	0.412919	+	0.910768i	$0.364509\pi$
$860$	−5.36235	−0.182855
$861$	0.284505	0.00969592
$862$	12.1992	0.415506
$863$	39.9497	1.35990	0.679951	−	0.733257i	$-0.262001\pi$
$863$	39.9497	1.35990	0.679951	+	0.733257i	$0.262001\pi$
$864$	5.51810	0.187730
$865$	0.107826	0.00366618
$866$	−17.4274	−0.592208
$867$	7.11734	0.241717
$868$	1.96201	0.0665950
$869$	34.5856	1.17324
$870$	5.88673	0.199579
$871$	14.2876	0.484117
$872$	−6.71903	−0.227535
$873$	−14.4940	−0.490547
$874$	−4.96862	−0.168066
$875$	−0.542800	−0.0183500
$876$	7.37808	0.249282
$877$	31.7235	1.07123	0.535613	−	0.844464i	$-0.320081\pi$
$877$	31.7235	1.07123	0.535613	+	0.844464i	$0.320081\pi$
$878$	3.12120	0.105335
$879$	−23.2144	−0.783004
$880$	−4.78338	−0.161248
$881$	23.0126	0.775316	0.387658	−	0.921803i	$-0.373284\pi$
$881$	23.0126	0.775316	0.387658	+	0.921803i	$0.373284\pi$
$882$	−3.97147	−0.133726
$883$	−2.48810	−0.0837313	−0.0418656	−	0.999123i	$-0.513330\pi$
$883$	−2.48810	−0.0837313	−0.0418656	+	0.999123i	$0.513330\pi$
$884$	34.1460	1.14845
$885$	−4.15492	−0.139666
$886$	17.4048	0.584726
$887$	−46.1366	−1.54912	−0.774558	−	0.632503i	$-0.782028\pi$
$887$	−46.1366	−1.54912	−0.774558	+	0.632503i	$0.782028\pi$
$888$	21.8420	0.732969
$889$	−8.58351	−0.287882
$890$	−3.96284	−0.132835
$891$	−2.37004	−0.0793993
$892$	0.327355	0.0109607
$893$	−0.417595	−0.0139743
$894$	0.858479	0.0287118
$895$	1.82960	0.0611569
$896$	6.23744	0.208378
$897$	−36.5375	−1.21995
$898$	4.97937	0.166164
$899$	21.7838	0.726530
$900$	−1.64920	−0.0549734
$901$	−56.0592	−1.86760
$902$	0.735759	0.0244981
$903$	−1.76490	−0.0587323
$904$	16.7599	0.557425
$905$	−24.5447	−0.815895
$906$	11.3737	0.377867
$907$	7.40960	0.246032	0.123016	−	0.992405i	$-0.460743\pi$
$907$	7.40960	0.246032	0.123016	+	0.992405i	$0.460743\pi$
$908$	36.5040	1.21143
$909$	−7.27619	−0.241336
$910$	−1.35541	−0.0449314
$911$	−45.0387	−1.49220	−0.746099	−	0.665835i	$-0.768076\pi$
$911$	−45.0387	−1.49220	−0.746099	+	0.665835i	$0.768076\pi$
$912$	1.95366	0.0646922
$913$	−13.3833	−0.442923
$914$	19.3343	0.639522
$915$	−12.6077	−0.416798
$916$	17.8088	0.588419
$917$	4.99557	0.164968
$918$	−2.90866	−0.0960002
$919$	−23.3011	−0.768632	−0.384316	−	0.923202i	$-0.625563\pi$
$919$	−23.3011	−0.768632	−0.384316	+	0.923202i	$0.625563\pi$
$920$	18.7311	0.617546
$921$	−9.75997	−0.321602
$922$	6.33175	0.208525
$923$	−33.7585	−1.11117
$924$	−2.12163	−0.0697964
$925$	−10.1057	−0.332272
$926$	−2.78066	−0.0913783
$927$	−13.7914	−0.452968
$928$	54.8447	1.80037
$929$	31.2466	1.02517	0.512583	−	0.858637i	$-0.328689\pi$
$929$	31.2466	1.02517	0.512583	+	0.858637i	$0.328689\pi$
$930$	1.29813	0.0425672
$931$	−6.49072	−0.212725
$932$	−8.05556	−0.263869
$933$	−12.7567	−0.417634
$934$	16.9690	0.555244
$935$	11.6391	0.380640
$936$	−9.11231	−0.297845
$937$	−11.0149	−0.359842	−0.179921	−	0.983681i	$-0.557584\pi$
$937$	−11.0149	−0.359842	−0.179921	+	0.983681i	$0.557584\pi$
$938$	−1.08950	−0.0355733
$939$	−6.45106	−0.210522
$940$	0.711474	0.0232057
$941$	10.8470	0.353602	0.176801	−	0.984247i	$-0.443425\pi$
$941$	10.8470	0.353602	0.176801	+	0.984247i	$0.443425\pi$
$942$	−13.9058	−0.453077
$943$	4.54242	0.147922
$944$	−8.38575	−0.272933
$945$	−0.542800	−0.0176573
$946$	−4.56421	−0.148395
$947$	43.6071	1.41704	0.708520	−	0.705690i	$-0.249363\pi$
$947$	43.6071	1.41704	0.708520	+	0.705690i	$0.249363\pi$
$948$	24.0665	0.781645
$949$	−18.8613	−0.612263
$950$	0.573323	0.0186011
$951$	−14.8231	−0.480672
$952$	−5.76144	−0.186729
$953$	36.0566	1.16799	0.583993	−	0.811759i	$-0.301489\pi$
$953$	36.0566	1.16799	0.583993	+	0.811759i	$0.301489\pi$
$954$	6.76101	0.218896
$955$	1.35585	0.0438743
$956$	−35.6628	−1.15342
$957$	−23.5560	−0.761456
$958$	6.55985	0.211939
$959$	−6.10342	−0.197090
$960$	−0.768263	−0.0247956
$961$	−26.1963	−0.845042
$962$	−25.2346	−0.813595
$963$	12.7287	0.410176
$964$	27.3528	0.880974
$965$	−10.5994	−0.341207
$966$	2.78616	0.0896431
$967$	−48.1166	−1.54732	−0.773662	−	0.633598i	$-0.781577\pi$
$967$	−48.1166	−1.54732	−0.773662	+	0.633598i	$0.781577\pi$
$968$	11.6344	0.373944
$969$	−4.75374	−0.152712
$970$	−8.58454	−0.275633
$971$	−41.8495	−1.34301	−0.671507	−	0.740998i	$-0.734353\pi$
$971$	−41.8495	−1.34301	−0.671507	+	0.740998i	$0.734353\pi$
$972$	−1.64920	−0.0528982
$973$	−1.36193	−0.0436615
$974$	14.9279	0.478319
$975$	4.21601	0.135020
$976$	−25.4457	−0.814499
$977$	−9.11293	−0.291548	−0.145774	−	0.989318i	$-0.546567\pi$
$977$	−9.11293	−0.291548	−0.145774	+	0.989318i	$0.546567\pi$
$978$	−6.45338	−0.206356
$979$	15.8574	0.506806
$980$	11.0585	0.353251
$981$	3.10871	0.0992534
$982$	0.0800281	0.00255380
$983$	13.1951	0.420857	0.210429	−	0.977609i	$-0.432514\pi$
$983$	13.1951	0.420857	0.210429	+	0.977609i	$0.432514\pi$
$984$	1.13286	0.0361144
$985$	3.29465	0.104976
$986$	−28.9094	−0.920662
$987$	0.234167	0.00745360
$988$	−6.73048	−0.214125
$989$	−28.1785	−0.896025
$990$	−1.40373	−0.0446136
$991$	−52.2860	−1.66092	−0.830459	−	0.557079i	$-0.811922\pi$
$991$	−52.2860	−1.66092	−0.830459	+	0.557079i	$0.811922\pi$
$992$	12.0942	0.383992
$993$	−21.6263	−0.686290
$994$	2.57424	0.0816501
$995$	4.49450	0.142485
$996$	−9.31283	−0.295088
$997$	−1.85206	−0.0586552	−0.0293276	−	0.999570i	$-0.509337\pi$
$997$	−1.85206	−0.0586552	−0.0293276	+	0.999570i	$0.509337\pi$
$998$	12.2442	0.387584
$999$	−10.1057	−0.319729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6015.2.a.b.1.15	✓	23

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6015.2.a.b.1.15	✓	23	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+0.592282 q^{2} +1.00000 q^{3} -1.64920 q^{4} +1.00000 q^{5} +0.592282 q^{6} -0.542800 q^{7} -2.16136 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+0.592282 q^{2} +1.00000 q^{3} -1.64920 q^{4} +1.00000 q^{5} +0.592282 q^{6} -0.542800 q^{7} -2.16136 q^{8} +1.00000 q^{9} +0.592282 q^{10} -2.37004 q^{11} -1.64920 q^{12} +4.21601 q^{13} -0.321491 q^{14} +1.00000 q^{15} +2.01827 q^{16} -4.91094 q^{17} +0.592282 q^{18} +0.967989 q^{19} -1.64920 q^{20} -0.542800 q^{21} -1.40373 q^{22} -8.66636 q^{23} -2.16136 q^{24} +1.00000 q^{25} +2.49707 q^{26} +1.00000 q^{27} +0.895186 q^{28} +9.93906 q^{29} +0.592282 q^{30} +2.19174 q^{31} +5.51810 q^{32} -2.37004 q^{33} -2.90866 q^{34} -0.542800 q^{35} -1.64920 q^{36} -10.1057 q^{37} +0.573323 q^{38} +4.21601 q^{39} -2.16136 q^{40} -0.524144 q^{41} -0.321491 q^{42} +3.25148 q^{43} +3.90867 q^{44} +1.00000 q^{45} -5.13293 q^{46} -0.431405 q^{47} +2.01827 q^{48} -6.70537 q^{49} +0.592282 q^{50} -4.91094 q^{51} -6.95305 q^{52} +11.4152 q^{53} +0.592282 q^{54} -2.37004 q^{55} +1.17318 q^{56} +0.967989 q^{57} +5.88673 q^{58} -4.15492 q^{59} -1.64920 q^{60} -12.6077 q^{61} +1.29813 q^{62} -0.542800 q^{63} -0.768263 q^{64} +4.21601 q^{65} -1.40373 q^{66} +3.38889 q^{67} +8.09913 q^{68} -8.66636 q^{69} -0.321491 q^{70} -8.00721 q^{71} -2.16136 q^{72} -4.47373 q^{73} -5.98541 q^{74} +1.00000 q^{75} -1.59641 q^{76} +1.28646 q^{77} +2.49707 q^{78} -14.5928 q^{79} +2.01827 q^{80} +1.00000 q^{81} -0.310442 q^{82} +5.64687 q^{83} +0.895186 q^{84} -4.91094 q^{85} +1.92580 q^{86} +9.93906 q^{87} +5.12251 q^{88} -6.69079 q^{89} +0.592282 q^{90} -2.28845 q^{91} +14.2926 q^{92} +2.19174 q^{93} -0.255514 q^{94} +0.967989 q^{95} +5.51810 q^{96} -14.4940 q^{97} -3.97147 q^{98} -2.37004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9}+O(q^{10}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9	\( 23 q - 5 q^{2} + 23 q^{3} + 9 q^{4} + 23 q^{5} - 5 q^{6} - 16 q^{7} - 12 q^{8} + 23 q^{9} - 5 q^{10} - 13 q^{11} + 9 q^{12} - 18 q^{13} - 6 q^{14} + 23 q^{15} - 11 q^{16} - 34 q^{17} - 5 q^{18} - 35 q^{19} + 9 q^{20} - 16 q^{21} - 11 q^{22} - 14 q^{23} - 12 q^{24} + 23 q^{25} - 6 q^{26} + 23 q^{27} - 26 q^{28} - 43 q^{29} - 5 q^{30} - 21 q^{31} - 14 q^{32} - 13 q^{33} - 12 q^{34} - 16 q^{35} + 9 q^{36} - 18 q^{37} + 6 q^{38} - 18 q^{39} - 12 q^{40} - 45 q^{41} - 6 q^{42} - 43 q^{43} - 11 q^{44} + 23 q^{45} - 29 q^{46} - 14 q^{47} - 11 q^{48} - 25 q^{49} - 5 q^{50} - 34 q^{51} - 20 q^{52} - 3 q^{53} - 5 q^{54} - 13 q^{55} + 3 q^{56} - 35 q^{57} + 10 q^{58} - 9 q^{59} + 9 q^{60} - 67 q^{61} - 7 q^{62} - 16 q^{63} - 8 q^{64} - 18 q^{65} - 11 q^{66} - 32 q^{67} - 24 q^{68} - 14 q^{69} - 6 q^{70} - 8 q^{71} - 12 q^{72} - 39 q^{73} - 16 q^{74} + 23 q^{75} - 48 q^{76} - 26 q^{77} - 6 q^{78} - 59 q^{79} - 11 q^{80} + 23 q^{81} - q^{82} - 23 q^{83} - 26 q^{84} - 34 q^{85} - 7 q^{86} - 43 q^{87} + 17 q^{88} - 51 q^{89} - 5 q^{90} - 37 q^{91} + 11 q^{92} - 21 q^{93} + 8 q^{94} - 35 q^{95} - 14 q^{96} - 29 q^{97} + 32 q^{98} - 13 q^{99}+O(q^{100}) \) 23 * q - 5 * q^2 + 23 * q^3 + 9 * q^4 + 23 * q^5 - 5 * q^6 - 16 * q^7 - 12 * q^8 + 23 * q^9 - 5 * q^10 - 13 * q^11 + 9 * q^12 - 18 * q^13 - 6 * q^14 + 23 * q^15 - 11 * q^16 - 34 * q^17 - 5 * q^18 - 35 * q^19 + 9 * q^20 - 16 * q^21 - 11 * q^22 - 14 * q^23 - 12 * q^24 + 23 * q^25 - 6 * q^26 + 23 * q^27 - 26 * q^28 - 43 * q^29 - 5 * q^30 - 21 * q^31 - 14 * q^32 - 13 * q^33 - 12 * q^34 - 16 * q^35 + 9 * q^36 - 18 * q^37 + 6 * q^38 - 18 * q^39 - 12 * q^40 - 45 * q^41 - 6 * q^42 - 43 * q^43 - 11 * q^44 + 23 * q^45 - 29 * q^46 - 14 * q^47 - 11 * q^48 - 25 * q^49 - 5 * q^50 - 34 * q^51 - 20 * q^52 - 3 * q^53 - 5 * q^54 - 13 * q^55 + 3 * q^56 - 35 * q^57 + 10 * q^58 - 9 * q^59 + 9 * q^60 - 67 * q^61 - 7 * q^62 - 16 * q^63 - 8 * q^64 - 18 * q^65 - 11 * q^66 - 32 * q^67 - 24 * q^68 - 14 * q^69 - 6 * q^70 - 8 * q^71 - 12 * q^72 - 39 * q^73 - 16 * q^74 + 23 * q^75 - 48 * q^76 - 26 * q^77 - 6 * q^78 - 59 * q^79 - 11 * q^80 + 23 * q^81 - q^82 - 23 * q^83 - 26 * q^84 - 34 * q^85 - 7 * q^86 - 43 * q^87 + 17 * q^88 - 51 * q^89 - 5 * q^90 - 37 * q^91 + 11 * q^92 - 21 * q^93 + 8 * q^94 - 35 * q^95 - 14 * q^96 - 29 * q^97 + 32 * q^98 - 13 * q^99

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